LMFDB - Embedded newform 21.30.e.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,30,Mod(4,21)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 30, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("21.4");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	21.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$111.883889004$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Character	$\chi$	$=$	21.16
Dual form			21.30.e.a.4.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-21682.7 + 37555.5i) q^{2} +(2.39148e6 + 4.14217e6i) q^{3} +(-6.71844e8 - 1.16367e9i) q^{4} +(-3.79032e9 + 6.56503e9i) q^{5} -2.07415e11 q^{6} +(-1.42775e12 - 1.08693e12i) q^{7} +3.49879e13 q^{8} +(-1.14384e13 + 1.98119e13i) q^{9} +O(q^{10})$	\(q+(-21682.7 + 37555.5i) q^{2} +(2.39148e6 + 4.14217e6i) q^{3} +(-6.71844e8 - 1.16367e9i) q^{4} +(-3.79032e9 + 6.56503e9i) q^{5} -2.07415e11 q^{6} +(-1.42775e12 - 1.08693e12i) q^{7} +3.49879e13 q^{8} +(-1.14384e13 + 1.98119e13i) q^{9} +(-1.64369e14 - 2.84695e14i) q^{10} +(-4.44909e14 - 7.70604e14i) q^{11} +(3.21341e15 - 5.56579e15i) q^{12} -2.64915e16 q^{13} +(7.17779e16 - 3.00525e16i) q^{14} -3.62580e16 q^{15} +(-3.97940e17 + 6.89252e17i) q^{16} +(-5.35059e17 - 9.26750e17i) q^{17} +(-4.96031e17 - 8.59150e17i) q^{18} +(-4.79881e17 + 8.31178e17i) q^{19} +1.01860e19 q^{20} +(1.08781e18 - 8.51339e18i) q^{21} +3.85873e19 q^{22} +(3.62121e19 - 6.27211e19i) q^{23} +(8.36731e19 + 1.44926e20i) q^{24} +(6.43991e19 + 1.11543e20i) q^{25} +(5.74407e20 - 9.94902e20i) q^{26} -1.09419e20 q^{27} +(-3.05599e20 + 2.39168e21i) q^{28} -1.66339e21 q^{29} +(7.86172e20 - 1.36169e21i) q^{30} +(-3.77230e21 - 6.53381e21i) q^{31} +(-7.86482e21 - 1.36223e22i) q^{32} +(2.12798e21 - 3.68578e21i) q^{33} +4.64061e22 q^{34} +(1.25474e22 - 5.25344e21i) q^{35} +3.07393e22 q^{36} +(4.65042e22 - 8.05477e22i) q^{37} +(-2.08102e22 - 3.60444e22i) q^{38} +(-6.33540e22 - 1.09732e23i) q^{39} +(-1.32616e23 + 2.29697e23i) q^{40} -8.09583e22 q^{41} +(2.96138e23 + 2.25446e23i) q^{42} -4.67966e23 q^{43} +(-5.97818e23 + 1.03545e24i) q^{44} +(-8.67105e22 - 1.50187e23i) q^{45} +(1.57035e24 + 2.71993e24i) q^{46} +(9.90629e22 - 1.71582e23i) q^{47} -3.80667e24 q^{48} +(8.57063e23 + 3.10375e24i) q^{49} -5.58539e24 q^{50} +(2.55917e24 - 4.43262e24i) q^{51} +(1.77981e25 + 3.08273e25i) q^{52} +(3.53508e24 + 6.12294e24i) q^{53} +(2.37250e24 - 4.10929e24i) q^{54} +6.74539e24 q^{55} +(-4.99542e25 - 3.80295e25i) q^{56} -4.59051e24 q^{57} +(3.60668e25 - 6.24694e25i) q^{58} +(2.00132e25 + 3.46639e25i) q^{59} +(2.43597e25 + 4.21923e25i) q^{60} +(-3.93882e25 + 6.82223e25i) q^{61} +3.27175e26 q^{62} +(3.78654e25 - 1.58538e25i) q^{63} +2.54837e26 q^{64} +(1.00411e26 - 1.73918e26i) q^{65} +(9.22809e25 + 1.59835e26i) q^{66} +(-7.64134e25 - 1.32352e26i) q^{67} +(-7.18953e26 + 1.24526e27i) q^{68} +3.46402e26 q^{69} +(-7.47660e25 + 5.85133e26i) q^{70} -7.05299e26 q^{71} +(-4.00206e26 + 6.93177e26i) q^{72} +(1.21511e26 + 2.10463e26i) q^{73} +(2.01668e27 + 3.49298e27i) q^{74} +(-3.08019e26 + 5.33505e26i) q^{75} +1.28962e27 q^{76} +(-2.02374e26 + 1.58382e27i) q^{77} +5.49474e27 q^{78} +(1.18640e25 - 2.05490e25i) q^{79} +(-3.01664e27 - 5.22498e27i) q^{80} +(-2.61674e26 - 4.53232e26i) q^{81} +(1.75539e27 - 3.04043e27i) q^{82} -8.78152e27 q^{83} +(-1.06376e28 + 4.45382e27i) q^{84} +8.11219e27 q^{85} +(1.01468e28 - 1.75747e28i) q^{86} +(-3.97797e27 - 6.89004e27i) q^{87} +(-1.55664e28 - 2.69619e28i) q^{88} +(-5.33170e27 + 9.23477e27i) q^{89} +7.52047e27 q^{90} +(3.78234e28 + 2.87945e28i) q^{91} -9.73154e28 q^{92} +(1.80428e28 - 3.12510e28i) q^{93} +(4.29590e27 + 7.44072e27i) q^{94} +(-3.63781e27 - 6.30087e27i) q^{95} +(3.76172e28 - 6.51549e28i) q^{96} -1.41306e28 q^{97} +(-1.35146e29 - 3.51101e28i) q^{98} +2.03562e28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 25025 q^{2} + 90876411 q^{3} - 5448583733 q^{4} - 2101591778 q^{5} + 239387598450 q^{6} - 1147384421099 q^{7} - 53840580588510 q^{8} - 434659056644259 q^{9}+O(q^{10}) $ 38 * q + 25025 * q^2 + 90876411 * q^3 - 5448583733 * q^4 - 2101591778 * q^5 + 239387598450 * q^6 - 1147384421099 * q^7 - 53840580588510 * q^8 - 434659056644259 * q^9	$ 38 q + 25025 q^{2} + 90876411 q^{3} - 5448583733 q^{4} - 2101591778 q^{5} + 239387598450 q^{6} - 1147384421099 q^{7} - 53840580588510 q^{8} - 434659056644259 q^{9} - 226333527764279 q^{10} + 968182184010316 q^{11} + 26\!\cdots\!77 q^{12}+ \cdots - 44\!\cdots\!52 q^{99}+O(q^{100}) $ 38 * q + 25025 * q^2 + 90876411 * q^3 - 5448583733 * q^4 - 2101591778 * q^5 + 239387598450 * q^6 - 1147384421099 * q^7 - 53840580588510 * q^8 - 434659056644259 * q^9 - 226333527764279 * q^10 + 968182184010316 * q^11 + 26060407088843277 * q^12 + 30248752986495458 * q^13 + 188292059868669736 * q^14 - 20103696649657764 * q^15 - 1414287713687569841 * q^16 + 102438111755912556 * q^17 + 572491731185399025 * q^18 - 6872193027481150651 * q^19 + 16866263496288505610 * q^20 - 5139459612060640272 * q^21 + 84243517982597870158 * q^22 + 182508386582843064516 * q^23 - 128758913948422543095 * q^24 - 382162743635168213111 * q^25 + 273922968110752759988 * q^26 - 4157921586997469649942 * q^27 + 446171481016036543439 * q^28 + 281390518253865391744 * q^29 + 1082546246957185764351 * q^30 - 4929614086953636263583 * q^31 + 8866445878410226322935 * q^32 - 4630785372473637108204 * q^33 + 50361339344572132704984 * q^34 - 81794408570709523734766 * q^35 + 249292238466635279498826 * q^36 + 89823590712918979606269 * q^37 - 71913737995612310138956 * q^38 + 72339423911532597127401 * q^39 + 239411588777146294644135 * q^40 - 87942011922863277796324 * q^41 + 42507596433452096284317 * q^42 - 998334377830130582257058 * q^43 - 273085832669135222196817 * q^44 - 48077678930358472910658 * q^45 + 1477208812031594497944852 * q^46 + 663752760815551395364602 * q^47 - 13528988583297044469675858 * q^48 + 12702719376591835722353537 * q^49 - 18072517907683707274881248 * q^50 - 489958312947065322058764 * q^51 + 31739881554208954447778464 * q^52 - 7756933906079396951027112 * q^53 - 2738210203016096789205225 * q^54 + 104982116314469285161107056 * q^55 + 43372930131234039576619953 * q^56 - 65738972424916983296125638 * q^57 + 102453432804996437331910603 * q^58 + 114603050264779854082124610 * q^59 + 40335407724289768694478045 * q^60 - 139825411428909464532671986 * q^61 + 1134093332259905081074973442 * q^62 + 1666599266299329474494571 * q^63 - 148837669255394086765278622 * q^64 + 640556086591054006830698254 * q^65 + 201467067480854076215869551 * q^66 - 56315776880006609951132917 * q^67 - 697317633686048315259709452 * q^68 + 1745863910531508618890056008 * q^69 + 433002366057136467231968657 * q^70 - 1824065145665995608812965764 * q^71 + 615849893888972622524549055 * q^72 + 1789614217588580556564713367 * q^73 - 4257059926604086801593103848 * q^74 + 1827872555761956873095306559 * q^75 + 15166984931487860090924899312 * q^76 + 6892418991139201958931374756 * q^77 + 2620330129723438035374088744 * q^78 + 3126227451212705816416145239 * q^79 + 469705326396281168184173015 * q^80 - 9943605027519850207056718899 * q^81 - 15954412288094954111486068024 * q^82 + 12686840070702737045002032792 * q^83 - 10284086370388485211004655396 * q^84 + 280144859318398185224279400 * q^85 + 14385045580944496750492040974 * q^86 + 672941062851086149442203968 * q^87 - 20844393366380736578332102317 * q^88 - 26279447891842894095818723312 * q^89 + 10355570280525127676264276238 * q^90 - 22701798036712589137512005879 * q^91 - 374697938227250791106256400776 * q^92 + 23578191359862546685993317927 * q^93 + 73717519436348854656628916898 * q^94 - 56410666407609081482857118294 * q^95 - 42407935776613881785582094015 * q^96 + 235542920591717835435096218928 * q^97 - 293433749500426066164790446415 * q^98 - 44297805764389719211578755352 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−21682.7	+	37555.5i	−0.935790	+	1.62084i	−0.162572	+	0.986697i	$0.551979\pi$
$2$	−21682.7	+	37555.5i	−0.935790	+	1.62084i	−0.773219	+	0.634139i	$0.781354\pi$
$3$	2.39148e6	+	4.14217e6i	0.288675	+	0.500000i
$3$	2.39148e6	+	4.14217e6i	0.288675	+	0.500000i
$4$	−6.71844e8	−	1.16367e9i	−1.25141	−	2.16750i
$5$	−3.79032e9	+	6.56503e9i	−0.277723	+	0.481030i	−0.970818	−	0.239816i	$-0.922913\pi$
$5$	−3.79032e9	+	6.56503e9i	−0.277723	+	0.481030i	0.693096	+	0.720846i	$0.256246\pi$
$6$	−2.07415e11			−1.08056
$7$	−1.42775e12	−	1.08693e12i	−0.795668	−	0.605732i
$7$	−1.42775e12	−	1.08693e12i	−0.795668	−	0.605732i
$8$	3.49879e13			2.81264
$9$	−1.14384e13	+	1.98119e13i	−0.166667	+	0.288675i
$10$	−1.64369e14	−	2.84695e14i	−0.519780	−	0.900286i
$11$	−4.44909e14	−	7.70604e14i	−0.353246	−	0.611839i	0.633570	−	0.773685i	$-0.281589\pi$
$11$	−4.44909e14	−	7.70604e14i	−0.353246	−	0.611839i	−0.986816	+	0.161846i	$0.948255\pi$
$12$	3.21341e15	−	5.56579e15i	0.722500	−	1.25141i
$13$	−2.64915e16			−1.86607			−0.933035	−	0.359786i	$-0.882850\pi$
$13$	−2.64915e16			−1.86607			−0.933035	+	0.359786i	$0.882850\pi$
$14$	7.17779e16	−	3.00525e16i	1.72637	−	0.722810i
$15$	−3.62580e16			−0.320687
$16$	−3.97940e17	+	6.89252e17i	−1.38063	+	2.39132i
$17$	−5.35059e17	−	9.26750e17i	−0.770713	−	1.33491i	−0.937173	−	0.348866i	$-0.886567\pi$
$17$	−5.35059e17	−	9.26750e17i	−0.770713	−	1.33491i	0.166460	−	0.986048i	$-0.446766\pi$
$18$	−4.96031e17	−	8.59150e17i	−0.311930	−	0.540279i
$19$	−4.79881e17	+	8.31178e17i	−0.137786	+	0.238653i	−0.926658	−	0.375904i	$-0.877332\pi$
$19$	−4.79881e17	+	8.31178e17i	−0.137786	+	0.238653i	0.788872	+	0.614557i	$0.210665\pi$
$20$	1.01860e19			1.39018
$21$	1.08781e18	−	8.51339e18i	0.0731766	−	0.572694i
$22$	3.85873e19			1.32226
$23$	3.62121e19	−	6.27211e19i	0.651328	−	1.12813i	−0.331473	−	0.943465i	$-0.607546\pi$
$23$	3.62121e19	−	6.27211e19i	0.651328	−	1.12813i	0.982801	−	0.184668i	$-0.0591211\pi$
$24$	8.36731e19	+	1.44926e20i	0.811938	+	1.40632i
$25$	6.43991e19	+	1.11543e20i	0.345740	+	0.598840i
$26$	5.74407e20	−	9.94902e20i	1.74625	−	3.02459i
$27$	−1.09419e20			−0.192450
$28$	−3.05599e20	+	2.39168e21i	−0.317220	+	2.48263i
$29$	−1.66339e21			−1.03806			−0.519030	−	0.854756i	$-0.673707\pi$
$29$	−1.66339e21			−1.03806			−0.519030	+	0.854756i	$0.673707\pi$
$30$	7.86172e20	−	1.36169e21i	0.300095	−	0.519780i
$31$	−3.77230e21	−	6.53381e21i	−0.895079	−	1.55032i	−0.833706	−	0.552208i	$-0.813785\pi$
$31$	−3.77230e21	−	6.53381e21i	−0.895079	−	1.55032i	−0.0613733	−	0.998115i	$-0.519548\pi$
$32$	−7.86482e21	−	1.36223e22i	−1.17764	−	2.03974i
$33$	2.12798e21	−	3.68578e21i	0.203946	−	0.353246i
$34$	4.64061e22			2.88490
$35$	1.25474e22	−	5.25344e21i	0.512351	−	0.214515i
$36$	3.07393e22			0.834271
$37$	4.65042e22	−	8.05477e22i	0.848335	−	1.46936i	−0.0343577	−	0.999410i	$-0.510939\pi$
$37$	4.65042e22	−	8.05477e22i	0.848335	−	1.46936i	0.882693	−	0.469950i	$-0.155728\pi$
$38$	−2.08102e22	−	3.60444e22i	−0.257878	−	0.446658i
$39$	−6.33540e22	−	1.09732e23i	−0.538688	−	0.933035i
$40$	−1.32616e23	+	2.29697e23i	−0.781133	+	1.35296i
$41$	−8.09583e22			−0.333346			−0.166673	−	0.986012i	$-0.553302\pi$
$41$	−8.09583e22			−0.333346			−0.166673	+	0.986012i	$0.553302\pi$
$42$	2.96138e23	+	2.25446e23i	0.859765	+	0.654529i
$43$	−4.67966e23			−0.965876			−0.482938	−	0.875655i	$-0.660430\pi$
$43$	−4.67966e23			−0.965876			−0.482938	+	0.875655i	$0.660430\pi$
$44$	−5.97818e23	+	1.03545e24i	−0.884108	+	1.53132i
$45$	−8.67105e22	−	1.50187e23i	−0.0925742	−	0.160343i
$46$	1.57035e24	+	2.71993e24i	1.21901	+	2.11139i
$47$	9.90629e22	−	1.71582e23i	0.0562979	−	0.0975108i	−0.836503	−	0.547962i	$-0.815404\pi$
$47$	9.90629e22	−	1.71582e23i	0.0562979	−	0.0975108i	0.892801	+	0.450452i	$0.148737\pi$
$48$	−3.80667e24			−1.59422
$49$	8.57063e23	+	3.10375e24i	0.266176	+	0.963924i
$50$	−5.58539e24			−1.29416
$51$	2.55917e24	−	4.43262e24i	0.444971	−	0.770713i
$52$	1.77981e25	+	3.08273e25i	2.33521	+	4.04471i
$53$	3.53508e24	+	6.12294e24i	0.351884	+	0.609481i	0.986580	−	0.163281i	$-0.0522079\pi$
$53$	3.53508e24	+	6.12294e24i	0.351884	+	0.609481i	−0.634696	+	0.772762i	$0.718875\pi$
$54$	2.37250e24	−	4.10929e24i	0.180093	−	0.311930i
$55$	6.74539e24			0.392417
$56$	−4.99542e25	−	3.80295e25i	−2.23793	−	1.70371i
$57$	−4.59051e24			−0.159102
$58$	3.60668e25	−	6.24694e25i	0.971407	−	1.68253i
$59$	2.00132e25	+	3.46639e25i	0.420690	+	0.728657i	0.996007	−	0.0892737i	$-0.0284546\pi$
$59$	2.00132e25	+	3.46639e25i	0.420690	+	0.728657i	−0.575317	+	0.817931i	$0.695121\pi$
$60$	2.43597e25	+	4.21923e25i	0.401309	+	0.695088i
$61$	−3.93882e25	+	6.82223e25i	−0.510603	+	0.884390i	0.489321	+	0.872103i	$0.337244\pi$
$61$	−3.93882e25	+	6.82223e25i	−0.510603	+	0.884390i	−0.999925	+	0.0122869i	$0.996089\pi$
$62$	3.27175e26			3.35043
$63$	3.78654e25	−	1.58538e25i	0.307471	−	0.128734i
$64$	2.54837e26			1.64685
$65$	1.00411e26	−	1.73918e26i	0.518250	−	0.897635i
$66$	9.22809e25	+	1.59835e26i	0.381702	+	0.661128i
$67$	−7.64134e25	−	1.32352e26i	−0.254147	−	0.440196i	0.710516	−	0.703681i	$-0.248461\pi$
$67$	−7.64134e25	−	1.32352e26i	−0.254147	−	0.440196i	−0.964663	+	0.263485i	$0.915128\pi$
$68$	−7.18953e26	+	1.24526e27i	−1.92895	+	3.34104i
$69$	3.46402e26			0.752089
$70$	−7.47660e25	+	5.85133e26i	−0.131760	+	1.03118i
$71$	−7.05299e26			−1.01188			−0.505938	−	0.862570i	$-0.668853\pi$
$71$	−7.05299e26			−1.01188			−0.505938	+	0.862570i	$0.668853\pi$
$72$	−4.00206e26	+	6.93177e26i	−0.468773	+	0.811938i
$73$	1.21511e26	+	2.10463e26i	0.116529	+	0.201834i	0.918390	−	0.395677i	$-0.129490\pi$
$73$	1.21511e26	+	2.10463e26i	0.116529	+	0.201834i	−0.801861	+	0.597511i	$0.796157\pi$
$74$	2.01668e27	+	3.49298e27i	1.58773	+	2.75003i
$75$	−3.08019e26	+	5.33505e26i	−0.199613	+	0.345740i
$76$	1.28962e27			0.689707
$77$	−2.02374e26	+	1.58382e27i	−0.0895446	+	0.700794i
$78$	5.49474e27			2.01640
$79$	1.18640e25	−	2.05490e25i	0.00361941	−	0.00626900i	−0.864210	−	0.503131i	$-0.832181\pi$
$79$	1.18640e25	−	2.05490e25i	0.00361941	−	0.00626900i	0.867829	+	0.496862i	$0.165515\pi$
$80$	−3.01664e27	−	5.22498e27i	−0.766865	−	1.32825i
$81$	−2.61674e26	−	4.53232e26i	−0.0555556	−	0.0962250i
$82$	1.75539e27	−	3.04043e27i	0.311942	−	0.540299i
$83$	−8.78152e27			−1.30899			−0.654496	−	0.756065i	$-0.727119\pi$
$83$	−8.78152e27			−1.30899			−0.654496	+	0.756065i	$0.727119\pi$
$84$	−1.06376e28	+	4.45382e27i	−1.33289	+	0.558063i
$85$	8.11219e27			0.856178
$86$	1.01468e28	−	1.75747e28i	0.903857	−	1.56553i
$87$	−3.97797e27	−	6.89004e27i	−0.299662	−	0.519030i
$88$	−1.55664e28	−	2.69619e28i	−0.993552	−	1.72088i
$89$	−5.33170e27	+	9.23477e27i	−0.288875	+	0.500347i	−0.973542	−	0.228510i	$-0.926615\pi$
$89$	−5.33170e27	+	9.23477e27i	−0.288875	+	0.500347i	0.684666	+	0.728857i	$0.259948\pi$
$90$	7.52047e27			0.346520
$91$	3.78234e28	+	2.87945e28i	1.48477	+	1.13034i
$92$	−9.73154e28			−3.26030
$93$	1.80428e28	−	3.12510e28i	0.516774	−	0.895079i
$94$	4.29590e27	+	7.44072e27i	0.105366	+	0.182499i
$95$	−3.63781e27	−	6.30087e27i	−0.0765328	−	0.132559i
$96$	3.76172e28	−	6.51549e28i	0.679913	−	1.17764i
$97$	−1.41306e28			−0.219771			−0.109886	−	0.993944i	$-0.535048\pi$
$97$	−1.41306e28			−0.219771			−0.109886	+	0.993944i	$0.535048\pi$
$98$	−1.35146e29	−	3.51101e28i	−1.81145	−	0.470603i
$99$	2.03562e28			0.235497
$100$	8.65323e28	−	1.49878e29i	0.865323	−	1.49878i
$101$	−1.56305e28	−	2.70728e28i	−0.135305	−	0.234354i	0.790409	−	0.612579i	$-0.209868\pi$
$101$	−1.56305e28	−	2.70728e28i	−0.135305	−	0.234354i	−0.925714	+	0.378225i	$0.876535\pi$
$102$	1.10980e29	+	1.92222e29i	0.832800	+	1.44245i
$103$	−5.56865e28	+	9.64519e28i	−0.362752	+	0.628306i	−0.988413	−	0.151790i	$-0.951496\pi$
$103$	−5.56865e28	+	9.64519e28i	−0.362752	+	0.628306i	0.625660	+	0.780096i	$0.284830\pi$
$104$	−9.26883e29			−5.24857
$105$	5.17676e28	+	3.94100e28i	0.255160	+	0.194250i
$106$	−3.06601e29			−1.31716
$107$	1.77706e29	−	3.07796e29i	0.666251	−	1.15398i	−0.312694	−	0.949854i	$-0.601231\pi$
$107$	1.77706e29	−	3.07796e29i	0.666251	−	1.15398i	0.978945	−	0.204126i	$-0.0654352\pi$
$108$	7.35125e28	+	1.27327e29i	0.240833	+	0.417136i
$109$	−1.18214e29	−	2.04752e29i	−0.338831	−	0.586873i	0.645382	−	0.763860i	$-0.276698\pi$
$109$	−1.18214e29	−	2.04752e29i	−0.338831	−	0.586873i	−0.984213	+	0.176987i	$0.943365\pi$
$110$	−1.46258e29	+	2.53327e29i	−0.367220	+	0.636044i
$111$	4.44857e29			0.979573
$112$	1.31733e30	−	5.51549e29i	2.54703	−	1.06641i
$113$	1.64374e28			0.0279381			0.0139690	−	0.999902i	$-0.495553\pi$
$113$	1.64374e28			0.0279381			0.0139690	+	0.999902i	$0.495553\pi$
$114$	9.95347e28	−	1.72399e29i	0.148886	−	0.257878i
$115$	2.74511e29	+	4.75467e29i	0.361777	+	0.626616i
$116$	1.11754e30	+	1.93563e30i	1.29904	+	2.25000i
$117$	3.03020e29	−	5.24846e29i	0.311012	−	0.538688i
$118$	−1.73576e30			−1.57471
$119$	−2.43381e29	+	1.90475e30i	−0.195369	+	1.52899i
$120$	−1.26859e30			−0.901975
$121$	3.97267e29	−	6.88087e29i	0.250435	−	0.433766i
$122$	−1.70808e30	−	2.95849e30i	−0.955635	−	1.65521i
$123$	−1.93610e29	−	3.35343e29i	−0.0962287	−	0.166673i
$124$	−5.06879e30	+	8.77941e30i	−2.24022	+	3.88017i
$125$	−2.38838e30			−0.939525
$126$	−2.25628e29	+	1.76581e30i	−0.0790715	+	0.618829i
$127$	1.60534e30			0.501666			0.250833	−	0.968030i	$-0.419296\pi$
$127$	1.60534e30			0.501666			0.250833	+	0.968030i	$0.419296\pi$
$128$	−1.30317e30	+	2.25716e30i	−0.363461	+	0.629533i
$129$	−1.11913e30	−	1.93839e30i	−0.278824	−	0.482938i
$130$	4.35438e30	+	7.54201e30i	0.969946	+	1.68000i
$131$	1.53396e30	−	2.65689e30i	0.305759	−	0.529590i	−0.671671	−	0.740850i	$-0.734423\pi$
$131$	1.53396e30	−	2.65689e30i	0.305759	−	0.529590i	0.977430	+	0.211259i	$0.0677564\pi$
$132$	−5.71869e30			−1.02088
$133$	1.58859e30	−	6.65121e29i	0.254192	−	0.106427i
$134$	6.62740e30			0.951313
$135$	4.14733e29	−	7.18339e29i	0.0534478	−	0.0925742i
$136$	−1.87206e31	−	3.24251e31i	−2.16774	−	3.75463i
$137$	−2.53069e30	−	4.38329e30i	−0.263506	−	0.456407i	0.703665	−	0.710532i	$-0.251546\pi$
$137$	−2.53069e30	−	4.38329e30i	−0.263506	−	0.456407i	−0.967171	+	0.254126i	$0.918212\pi$
$138$	−7.51094e30	+	1.30093e31i	−0.703797	+	1.21901i
$139$	−8.33427e30			−0.703320			−0.351660	−	0.936128i	$-0.614383\pi$
$139$	−8.33427e30			−0.703320			−0.351660	+	0.936128i	$0.614383\pi$
$140$	−1.45431e31	−	1.10715e31i	−1.10612	−	0.842075i
$141$	9.47630e29			0.0650072
$142$	1.52928e31	−	2.64879e31i	0.946903	−	1.64008i
$143$	1.17863e31	+	2.04145e31i	0.659181	+	1.14173i
$144$	−9.10359e30	−	1.57679e31i	−0.460210	−	0.797108i
$145$	6.30478e30	−	1.09202e31i	0.288293	−	0.499338i
$146$	−1.05387e31			−0.436186
$147$	−1.08066e31	+	1.09727e31i	−0.405124	+	0.411349i
$148$	−1.24974e32			−4.24645
$149$	1.55915e31	−	2.70053e31i	0.480493	−	0.832238i	−0.519257	−	0.854618i	$-0.673791\pi$
$149$	1.55915e31	−	2.70053e31i	0.480493	−	0.832238i	0.999750	+	0.0223804i	$0.00712450\pi$
$150$	−1.33574e31	−	2.31356e31i	−0.373592	−	0.647081i
$151$	−6.15973e30	−	1.06690e31i	−0.156457	−	0.270992i	0.777131	−	0.629338i	$-0.216674\pi$
$151$	−6.15973e30	−	1.06690e31i	−0.156457	−	0.270992i	−0.933589	+	0.358346i	$0.883341\pi$
$152$	−1.67900e31	+	2.90812e31i	−0.387543	+	0.671244i
$153$	2.44809e31			0.513809
$154$	−5.50932e31	−	4.19418e31i	−1.05208	−	0.800933i
$155$	5.71930e31			0.994335
$156$	−8.51280e31	+	1.47446e32i	−1.34824	+	2.33521i
$157$	3.04222e31	+	5.26928e31i	0.439183	+	0.760688i	0.997627	−	0.0688549i	$-0.0219345\pi$
$157$	3.04222e31	+	5.26928e31i	0.439183	+	0.760688i	−0.558443	+	0.829543i	$0.688601\pi$
$158$	5.14486e29	+	8.91116e29i	0.00677401	+	0.0117329i
$159$	−1.69082e31	+	2.92858e31i	−0.203160	+	0.351884i
$160$	1.19241e32			1.30823
$161$	−1.19876e32	+	5.01904e31i	−1.20159	+	0.503089i
$162$	2.26952e31			0.207953
$163$	−7.54388e31	+	1.30664e32i	−0.632229	+	1.09505i	0.354866	+	0.934917i	$0.384527\pi$
$163$	−7.54388e31	+	1.30664e32i	−0.632229	+	1.09505i	−0.987095	+	0.160136i	$0.948807\pi$
$164$	5.43913e31	+	9.42086e31i	0.417152	+	0.722528i
$165$	1.61315e31	+	2.79406e31i	0.113281	+	0.196209i
$166$	1.90407e32	−	3.29795e32i	1.22494	−	2.12166i
$167$	−1.49437e32			−0.881190			−0.440595	−	0.897706i	$-0.645233\pi$
$167$	−1.49437e32			−0.881190			−0.440595	+	0.897706i	$0.645233\pi$
$168$	3.80601e31	−	2.97866e32i	0.205819	−	1.61078i
$169$	5.00261e32			2.48221
$170$	−1.75894e32	+	3.04658e32i	−0.801203	+	1.38772i
$171$	−1.09781e31	−	1.90147e31i	−0.0459288	−	0.0795510i
$172$	3.14400e32	+	5.44556e32i	1.20870	+	2.09354i
$173$	1.47917e32	−	2.56201e32i	0.522818	−	0.905548i	−0.476829	−	0.878996i	$-0.658214\pi$
$173$	1.47917e32	−	2.56201e32i	0.522818	−	0.905548i	0.999647	−	0.0265520i	$-0.00845275\pi$
$174$	3.45012e32			1.12168
$175$	2.92930e31	−	2.29253e32i	0.0876420	−	0.685904i
$176$	7.08187e32			1.95081
$177$	−9.57225e31	+	1.65796e32i	−0.242886	+	0.420690i
$178$	−2.31211e32	−	4.00470e32i	−0.540654	−	0.936439i
$179$	−7.85912e31	−	1.36124e32i	−0.169436	−	0.293471i	0.768786	−	0.639506i	$-0.220861\pi$
$179$	−7.85912e31	−	1.36124e32i	−0.169436	−	0.293471i	−0.938222	+	0.346035i	$0.887528\pi$
$180$	−1.16512e32	+	2.01804e32i	−0.231696	+	0.401309i
$181$	5.19745e32			0.953786			0.476893	−	0.878961i	$-0.341763\pi$
$181$	5.19745e32			0.953786			0.476893	+	0.878961i	$0.341763\pi$
$182$	−1.90150e33	+	7.96135e32i	−3.22153	+	1.34881i
$183$	−3.76785e32			−0.589594
$184$	1.26699e33	−	2.19448e33i	1.83195	−	3.17303i
$185$	3.52532e32	+	6.10604e32i	0.471204	+	0.816149i
$186$	7.82433e32	+	1.35521e33i	0.967185	+	1.67521i
$187$	−4.76105e32	+	8.24638e32i	−0.544502	+	0.943105i
$188$	−2.66219e32			−0.281806
$189$	1.56224e32	+	1.18931e32i	0.153126	+	0.116573i
$190$	3.15510e32			0.286475
$191$	−3.58850e31	+	6.21547e31i	−0.0301946	+	0.0522986i	−0.880728	−	0.473623i	$-0.842946\pi$
$191$	−3.58850e31	+	6.21547e31i	−0.0301946	+	0.0522986i	0.850533	+	0.525921i	$0.176279\pi$
$192$	6.09440e32	+	1.05558e33i	0.475404	+	0.823424i
$193$	−8.51461e32	−	1.47477e33i	−0.616004	−	1.06695i	−0.990207	−	0.139604i	$-0.955417\pi$
$193$	−8.51461e32	−	1.47477e33i	−0.616004	−	1.06695i	0.374203	−	0.927347i	$-0.377916\pi$
$194$	3.06390e32	−	5.30683e32i	0.205660	−	0.356213i
$195$	9.60529e32			0.598423
$196$	3.03592e33	−	3.08257e33i	1.75621	−	1.78320i
$197$	−3.22202e33			−1.73128			−0.865640	−	0.500667i	$-0.833088\pi$
$197$	−3.22202e33			−1.73128			−0.865640	+	0.500667i	$0.833088\pi$
$198$	−4.41377e32	+	7.64487e32i	−0.220376	+	0.381702i
$199$	−1.63892e33	−	2.83869e33i	−0.760654	−	1.31749i	−0.942514	−	0.334167i	$-0.891545\pi$
$199$	−1.63892e33	−	2.83869e33i	−0.760654	−	1.31749i	0.181860	−	0.983324i	$-0.441788\pi$
$200$	2.25319e33	+	3.90265e33i	0.972442	+	1.68432i
$201$	3.65483e32	−	6.33035e32i	0.146732	−	0.254147i
$202$	1.35564e33			0.506467
$203$	2.37491e33	+	1.80799e33i	0.825952	+	0.628787i
$204$	−6.87746e33			−2.22736
$205$	3.06858e32	−	5.31494e32i	0.0925778	−	0.160349i
$206$	−2.41487e33	−	4.18268e33i	−0.678920	−	1.17592i
$207$	8.28416e32	+	1.43486e33i	0.217109	+	0.376044i
$208$	1.05420e34	−	1.82593e34i	2.57635	−	4.46237i
$209$	8.54012e32			0.194690
$210$	−2.60252e33	+	1.08964e33i	−0.553624	+	0.231795i
$211$	−5.85327e33			−1.16226			−0.581129	−	0.813811i	$-0.697389\pi$
$211$	−5.85327e33			−1.16226			−0.581129	+	0.813811i	$0.697389\pi$
$212$	4.75005e33	−	8.22732e33i	0.880700	−	1.52542i
$213$	−1.68671e33	−	2.92147e33i	−0.292103	−	0.505938i
$214$	7.70630e33	+	1.33477e34i	1.24694	+	2.15977i
$215$	1.77374e33	−	3.07221e33i	0.268246	−	0.464615i
$216$	−3.82835e33			−0.541292
$217$	−1.71589e33	+	1.34289e34i	−0.226895	+	1.77572i
$218$	1.02528e34			1.26830
$219$	−5.81182e32	+	1.00664e33i	−0.0672780	+	0.116529i
$220$	−4.53185e33	−	7.84939e33i	−0.491074	−	0.850564i
$221$	1.41745e34	+	2.45510e34i	1.43820	+	2.49104i
$222$	−9.64569e33	+	1.67068e34i	−0.916675	+	1.58773i
$223$	1.48257e33			0.132007			0.0660033	−	0.997819i	$-0.478975\pi$
$223$	1.48257e33			0.132007			0.0660033	+	0.997819i	$0.478975\pi$
$224$	−3.57744e33	+	2.79978e34i	−0.298522	+	2.33629i
$225$	−2.94649e33			−0.230493
$226$	−3.56408e32	+	6.17316e32i	−0.0261442	+	0.0452830i
$227$	4.81341e33	+	8.33707e33i	0.331191	+	0.573639i	0.982746	−	0.184962i	$-0.0592164\pi$
$227$	4.81341e33	+	8.33707e33i	0.331191	+	0.573639i	−0.651555	+	0.758601i	$0.725883\pi$
$228$	3.08411e33	+	5.34183e33i	0.199101	+	0.344854i
$229$	1.26173e34	−	2.18538e34i	0.764455	−	1.32407i	−0.176080	−	0.984376i	$-0.556342\pi$
$229$	1.26173e34	−	2.18538e34i	0.764455	−	1.32407i	0.940534	−	0.339698i	$-0.110325\pi$
$230$	−2.38086e34			−1.35419
$231$	−7.04443e33	+	2.94941e33i	−0.376246	+	0.157529i
$232$	−5.81985e34			−2.91969
$233$	−2.09373e34	+	3.62645e34i	−0.986871	+	1.70931i	−0.353565	+	0.935410i	$0.615031\pi$
$233$	−2.09373e34	+	3.62645e34i	−0.986871	+	1.70931i	−0.633307	+	0.773901i	$0.718303\pi$
$234$	1.31406e34	+	2.27602e34i	0.582083	+	1.00820i
$235$	7.50961e32	+	1.30070e33i	0.0312704	+	0.0541619i
$236$	2.68915e34	−	4.65774e34i	1.05291	−	1.82369i
$237$	1.13490e32			0.00417933
$238$	−6.62566e34	−	5.04403e34i	−2.29543	−	1.74748i
$239$	−2.88639e34			−0.940990			−0.470495	−	0.882403i	$-0.655925\pi$
$239$	−2.88639e34			−0.940990			−0.470495	+	0.882403i	$0.655925\pi$
$240$	1.44285e34	−	2.49909e34i	0.442750	−	0.766865i
$241$	2.44988e34	+	4.24332e34i	0.707780	+	1.22591i	0.965679	+	0.259738i	$0.0836364\pi$
$241$	2.44988e34	+	4.24332e34i	0.707780	+	1.22591i	−0.257899	+	0.966172i	$0.583030\pi$
$242$	1.72277e34	+	2.98392e34i	0.468709	+	0.811828i
$243$	1.25158e33	−	2.16780e33i	0.0320750	−	0.0555556i
$244$	1.05851e35			2.55589
$245$	−2.36247e34	−	6.13756e33i	−0.537600	−	0.139665i
$246$	1.67920e34			0.360200
$247$	1.27128e34	−	2.20191e34i	0.257119	−	0.445343i
$248$	−1.31985e35	−	2.28605e35i	−2.51753	−	4.36050i
$249$	−2.10009e34	−	3.63746e34i	−0.377874	−	0.654496i
$250$	5.17865e34	−	8.96969e34i	0.879198	−	1.52282i
$251$	1.28196e34			0.205403			0.102702	−	0.994712i	$-0.467251\pi$
$251$	1.28196e34			0.205403			0.102702	+	0.994712i	$0.467251\pi$
$252$	−4.38881e34	−	3.34115e34i	−0.663803	−	0.505345i
$253$	−6.44442e34			−0.920315
$254$	−3.48082e34	+	6.02896e34i	−0.469454	+	0.813118i
$255$	1.94002e34	+	3.36021e34i	0.247157	+	0.428089i
$256$	1.18948e34	+	2.06023e34i	0.143178	+	0.247991i
$257$	−7.50140e34	+	1.29928e35i	−0.853320	+	1.47799i	0.0248748	+	0.999691i	$0.492081\pi$
$257$	−7.50140e34	+	1.29928e35i	−0.853320	+	1.47799i	−0.878195	+	0.478303i	$0.841252\pi$
$258$	9.70633e34			1.04368
$259$	−1.53947e35	+	6.44554e34i	−1.56503	+	0.655259i
$260$	−2.69843e35			−2.59417
$261$	1.90265e34	−	3.29549e34i	0.173010	−	0.299662i
$262$	6.65207e34	+	1.15217e35i	0.572253	+	0.991171i
$263$	−2.61896e34	−	4.53617e34i	−0.213192	−	0.369259i	0.739520	−	0.673135i	$-0.235053\pi$
$263$	−2.61896e34	−	4.53617e34i	−0.213192	−	0.369259i	−0.952712	+	0.303876i	$0.901719\pi$
$264$	7.44538e34	−	1.28958e35i	0.573627	−	0.993552i
$265$	−5.35964e34			−0.390905
$266$	−9.46588e33	+	7.40818e34i	−0.0653698	+	0.511597i
$267$	−5.10027e34			−0.333565
$268$	−1.02676e35	+	1.77840e35i	−0.636083	+	1.10173i
$269$	−3.89021e34	−	6.73805e34i	−0.228331	−	0.395481i	0.728982	−	0.684532i	$-0.239994\pi$
$269$	−3.89021e34	−	6.73805e34i	−0.228331	−	0.395481i	−0.957314	+	0.289051i	$0.906660\pi$
$270$	1.79851e34	+	3.11511e34i	0.100032	+	0.173260i
$271$	−9.27252e34	+	1.60605e35i	−0.488813	+	0.846649i	−0.999917	−	0.0128696i	$-0.995903\pi$
$271$	−9.27252e34	+	1.60605e35i	−0.488813	+	0.846649i	0.511104	+	0.859519i	$0.329237\pi$
$272$	8.51686e35			4.25628
$273$	−2.88176e34	+	2.25532e35i	−0.136553	+	1.06869i
$274$	2.19489e35			0.986347
$275$	5.73034e34	−	9.92525e34i	0.244262	−	0.423075i
$276$	−2.32728e35	−	4.03097e35i	−0.941169	−	1.63015i
$277$	1.68265e35	+	2.91443e35i	0.645709	+	1.11840i	0.984137	+	0.177409i	$0.0567716\pi$
$277$	1.68265e35	+	2.91443e35i	0.645709	+	1.11840i	−0.338428	+	0.940992i	$0.609895\pi$
$278$	1.80710e35	−	3.12998e35i	0.658160	−	1.13997i
$279$	1.72596e35			0.596720
$280$	4.39008e35	−	1.83807e35i	1.44106	−	0.603351i
$281$	2.05051e35			0.639175			0.319588	−	0.947557i	$-0.396456\pi$
$281$	2.05051e35			0.639175			0.319588	+	0.947557i	$0.396456\pi$
$282$	−2.05472e34	+	3.55887e34i	−0.0608331	+	0.105366i
$283$	−5.09103e34	−	8.81792e34i	−0.143187	−	0.248006i	0.785508	−	0.618851i	$-0.212402\pi$
$283$	−5.09103e34	−	8.81792e34i	−0.143187	−	0.248006i	−0.928695	+	0.370845i	$0.879068\pi$
$284$	4.73851e35	+	8.20734e35i	1.26627	+	2.19324i
$285$	1.73995e34	−	3.01369e34i	0.0441862	−	0.0765328i
$286$	−1.02223e36			−2.46742
$287$	1.15589e35	+	8.79962e34i	0.265233	+	0.201919i
$288$	3.59844e35			0.785096
$289$	−3.31593e35	+	5.74335e35i	−0.687997	+	1.19165i
$290$	2.73409e35	+	4.73559e35i	0.539563	+	0.934551i
$291$	−3.37932e34	−	5.85315e34i	−0.0634425	−	0.109886i
$292$	1.63273e35	−	2.82796e35i	0.291650	−	0.505153i
$293$	1.10458e35			0.187766			0.0938831	−	0.995583i	$-0.470072\pi$
$293$	1.10458e35			0.187766			0.0938831	+	0.995583i	$0.470072\pi$
$294$	−1.77768e35	−	6.43765e35i	−0.287619	−	1.04158i
$295$	−3.03426e35			−0.467341
$296$	1.62709e36	−	2.81820e36i	2.38606	−	4.13277i
$297$	4.86814e34	+	8.43187e34i	0.0679822	+	0.117749i
$298$	6.76132e35	+	1.17109e36i	0.899281	+	1.55760i
$299$	−9.59312e35	+	1.66158e36i	−1.21542	+	2.10517i
$300$	8.27763e35			0.999189
$301$	6.68140e35	+	5.08647e35i	0.768517	+	0.585062i
$302$	5.34238e35			0.585645
$303$	7.47601e34	−	1.29488e35i	0.0781181	−	0.135305i
$304$	−3.81927e35	−	6.61518e35i	−0.380464	−	0.658983i
$305$	−2.98588e35	−	5.17170e35i	−0.283612	−	0.491231i
$306$	−5.30812e35	+	9.19393e35i	−0.480817	+	0.832800i
$307$	−1.09624e36			−0.947105			−0.473553	−	0.880765i	$-0.657029\pi$
$307$	−1.09624e36			−0.947105			−0.473553	+	0.880765i	$0.657029\pi$
$308$	1.97900e36	−	8.28583e35i	1.63103	−	0.682890i
$309$	−5.32694e35			−0.418870
$310$	−1.24010e36	+	2.14791e36i	−0.930489	+	1.61165i
$311$	−5.96131e34	−	1.03253e35i	−0.0426890	−	0.0739396i	0.843891	−	0.536514i	$-0.180259\pi$
$311$	−5.96131e34	−	1.03253e35i	−0.0426890	−	0.0739396i	−0.886580	+	0.462574i	$0.846926\pi$
$312$	−2.21663e36	−	3.83931e36i	−1.51513	−	2.62429i
$313$	−6.58463e35	+	1.14049e36i	−0.429673	+	0.744216i	−0.996844	−	0.0793843i	$-0.974705\pi$
$313$	−6.58463e35	+	1.14049e36i	−0.429673	+	0.744216i	0.567171	+	0.823600i	$0.308038\pi$
$314$	−2.63854e36			−1.64393
$315$	−3.94417e34	+	3.08679e35i	−0.0234667	+	0.183655i
$316$	−3.18830e34			−0.0181174
$317$	8.80122e35	−	1.52442e36i	0.477731	−	0.827455i	−0.521943	−	0.852981i	$-0.674793\pi$
$317$	8.80122e35	−	1.52442e36i	0.477731	−	0.827455i	0.999674	+	0.0255254i	$0.00812587\pi$
$318$	−7.33230e35	−	1.26999e36i	−0.380231	−	0.658579i
$319$	7.40056e35	+	1.28181e36i	0.366690	+	0.635126i
$320$	−9.65917e35	+	1.67302e36i	−0.457367	+	0.792183i
$321$	1.69993e36			0.769320
$322$	7.14300e35	−	5.59025e36i	0.309009	−	2.41836i
$323$	1.02706e36			0.424775
$324$	−3.51608e35	+	6.09003e35i	−0.139045	+	0.240833i
$325$	−1.70603e36	−	2.95493e36i	−0.645175	−	1.11748i
$326$	−3.27143e36	−	5.66629e36i	−1.18327	−	2.04948i
$327$	5.65412e35	−	9.79323e35i	0.195624	−	0.338831i
$328$	−2.83256e36			−0.937581
$329$	−3.27935e35	+	1.37302e35i	−0.103860	+	0.0434848i
$330$	−1.39910e36			−0.424029
$331$	1.33681e35	−	2.31543e35i	0.0387762	−	0.0671624i	−0.845986	−	0.533205i	$-0.820987\pi$
$331$	1.33681e35	−	2.31543e35i	0.0387762	−	0.0671624i	0.884762	+	0.466043i	$0.154321\pi$
$332$	5.89981e36	+	1.02188e37i	1.63808	+	2.83724i
$333$	1.06387e36	+	1.84267e36i	0.282778	+	0.489787i
$334$	3.24020e36	−	5.61219e36i	0.824609	−	1.42827i
$335$	1.15853e36			0.282330
$336$	5.43499e36	+	4.13759e36i	1.26847	+	0.965668i
$337$	6.04154e36			1.35056			0.675281	−	0.737561i	$-0.264022\pi$
$337$	6.04154e36			1.35056			0.675281	+	0.737561i	$0.264022\pi$
$338$	−1.08470e37	+	1.87876e37i	−2.32283	+	4.02326i
$339$	3.93098e34	+	6.80866e34i	0.00806502	+	0.0139690i
$340$	−5.45013e36	−	9.43990e36i	−1.07143	−	1.85577i
$341$	−3.35666e36	+	5.81390e36i	−0.632366	+	1.09529i
$342$	9.52143e35			0.171919
$343$	2.14989e36	−	5.36296e36i	0.372092	−	0.928196i
$344$	−1.63732e37			−2.71666
$345$	−1.31298e36	+	2.27414e36i	−0.208872	+	0.361777i
$346$	6.41450e36	+	1.11102e37i	0.978497	+	1.69481i
$347$	−6.08625e36	−	1.05417e37i	−0.890374	−	1.54217i	−0.839427	−	0.543472i	$-0.817109\pi$
$347$	−6.08625e36	−	1.05417e37i	−0.890374	−	1.54217i	−0.0509468	−	0.998701i	$-0.516224\pi$
$348$	−5.34515e36	+	9.25806e36i	−0.749999	+	1.29904i
$349$	−4.48410e36			−0.603541			−0.301771	−	0.953381i	$-0.597578\pi$
$349$	−4.48410e36			−0.603541			−0.301771	+	0.953381i	$0.597578\pi$
$350$	7.97457e36	+	6.07094e36i	1.02972	+	0.783916i
$351$	2.89867e36			0.359125
$352$	−6.99825e36	+	1.21213e37i	−0.831995	+	1.44106i
$353$	4.18305e36	+	7.24525e36i	0.477265	+	0.826647i	0.999660	−	0.0260559i	$-0.00829480\pi$
$353$	4.18305e36	+	7.24525e36i	0.477265	+	0.826647i	−0.522395	+	0.852703i	$0.674961\pi$
$354$	−4.15105e36	−	7.18982e36i	−0.454580	−	0.787356i
$355$	2.67331e36	−	4.63031e36i	0.281021	−	0.486742i
$356$	1.43283e37			1.44600
$357$	−8.47182e36	+	3.54704e36i	−0.820895	+	0.343698i
$358$	6.81628e36			0.634225
$359$	9.56664e36	−	1.65699e37i	0.854850	−	1.48064i	−0.0219341	−	0.999759i	$-0.506982\pi$
$359$	9.56664e36	−	1.65699e37i	0.854850	−	1.48064i	0.876784	−	0.480884i	$-0.159684\pi$
$360$	−3.03382e36	−	5.25473e36i	−0.260378	−	0.450987i
$361$	5.60434e36	+	9.70700e36i	0.462030	+	0.800259i
$362$	−1.12695e37	+	1.95193e37i	−0.892544	+	1.54593i
$363$	3.80024e36			0.289177
$364$	8.09578e36	−	6.33592e37i	0.591955	−	4.63276i
$365$	−1.84226e36			−0.129451
$366$	8.16972e36	−	1.41504e37i	0.551736	−	0.955635i
$367$	2.32765e36	+	4.03161e36i	0.151098	+	0.261710i	0.931632	−	0.363404i	$-0.118386\pi$
$367$	2.32765e36	+	4.03161e36i	0.151098	+	0.261710i	−0.780533	+	0.625114i	$0.785052\pi$
$368$	2.88204e37	+	4.99185e37i	1.79849	+	3.11507i
$369$	9.26033e35	−	1.60394e36i	0.0555577	−	0.0962287i
$370$	−3.05754e37			−1.76379
$371$	1.60799e36	−	1.25845e37i	0.0891994	−	0.698092i
$372$	−4.84878e37			−2.58678
$373$	1.21373e37	−	2.10225e37i	0.622795	−	1.07871i	−0.366168	−	0.930549i	$-0.619330\pi$
$373$	1.21373e37	−	2.10225e37i	0.622795	−	1.07871i	0.988963	−	0.148164i	$-0.0473363\pi$
$374$	−2.06465e37	−	3.57608e37i	−1.01908	−	1.76510i
$375$	−5.71177e36	−	9.89308e36i	−0.271217	−	0.469762i
$376$	3.46601e36	−	6.00330e36i	0.158345	−	0.274262i
$377$	4.40656e37			1.93709
$378$	−7.85387e36	+	3.28831e36i	−0.332240	+	0.139105i
$379$	−1.28329e37			−0.522465			−0.261232	−	0.965276i	$-0.584129\pi$
$379$	−1.28329e37			−0.522465			−0.261232	+	0.965276i	$0.584129\pi$
$380$	−4.88808e36	+	8.46640e36i	−0.191547	+	0.331770i
$381$	3.83916e36	+	6.64962e36i	0.144818	+	0.250833i
$382$	−1.55617e36	−	2.69536e36i	−0.0565117	−	0.0978811i
$383$	−2.86397e36	+	4.96054e36i	−0.100135	+	0.173439i	−0.911740	−	0.410767i	$-0.865261\pi$
$383$	−2.86397e36	+	4.96054e36i	−0.100135	+	0.173439i	0.811605	+	0.584206i	$0.198594\pi$
$384$	−1.24661e37			−0.419688
$385$	−9.63077e36	−	7.33178e36i	−0.312234	−	0.237700i
$386$	7.38479e37			2.30580
$387$	5.35278e36	−	9.27128e36i	0.160979	−	0.278824i
$388$	9.49357e36	+	1.64433e37i	0.275023	+	0.476354i
$389$	−1.35691e37	−	2.35024e37i	−0.378689	−	0.655908i	0.612183	−	0.790716i	$-0.290292\pi$
$389$	−1.35691e37	−	2.35024e37i	−0.378689	−	0.655908i	−0.990872	+	0.134808i	$0.956958\pi$
$390$	−2.08269e37	+	3.60732e37i	−0.559999	+	0.969946i
$391$	−7.75024e37			−2.00795
$392$	2.99869e37	+	1.08594e38i	0.748657	+	2.71117i
$393$	1.46737e37			0.353060
$394$	6.98620e37	−	1.21005e38i	1.62012	−	2.80612i
$395$	8.99366e34	+	1.55775e35i	0.00201038	+	0.00348209i
$396$	−1.36762e37	−	2.36878e37i	−0.294703	−	0.510440i
$397$	2.73526e37	−	4.73762e37i	0.568247	−	0.984232i	−0.428493	−	0.903545i	$-0.640955\pi$
$397$	2.73526e37	−	4.73762e37i	0.568247	−	0.984232i	0.996739	−	0.0806871i	$-0.0257115\pi$
$398$	1.42145e38			2.84725
$399$	6.55412e36	+	4.98957e36i	0.126592	+	0.0963732i
$400$	−1.02508e38			−1.90936
$401$	−2.08324e37	+	3.60827e37i	−0.374236	+	0.648195i	−0.990212	−	0.139569i	$-0.955428\pi$
$401$	−2.08324e37	+	3.60827e37i	−0.374236	+	0.648195i	0.615977	+	0.787764i	$0.288762\pi$
$402$	1.58493e37	+	2.74518e37i	0.274620	+	0.475657i
$403$	9.99338e37	+	1.73090e38i	1.67028	+	2.89301i
$404$	−2.10025e37	+	3.63774e37i	−0.338642	+	0.586545i
$405$	3.96731e36			0.0617161
$406$	−1.19395e38	+	4.99890e37i	−1.79208	+	0.750320i
$407$	−8.27605e37			−1.19868
$408$	8.95402e37	−	1.55088e38i	1.25154	−	2.16774i
$409$	−4.78608e37	−	8.28974e37i	−0.645643	−	1.11829i	−0.984153	−	0.177323i	$-0.943256\pi$
$409$	−4.78608e37	−	8.28974e37i	−0.645643	−	1.11829i	0.338510	−	0.940963i	$-0.390077\pi$
$410$	1.33070e37	+	2.30485e37i	0.173267	+	0.300107i
$411$	1.21042e37	−	2.09651e37i	0.152136	−	0.263506i
$412$	1.49651e38			1.81580
$413$	9.10334e36	−	7.12445e37i	0.106641	−	0.834595i
$414$	−7.18492e37			−0.812675
$415$	3.32848e37	−	5.76510e37i	0.363537	−	0.629664i
$416$	2.08351e38	+	3.60874e38i	2.19757	+	3.80629i
$417$	−1.99313e37	−	3.45220e37i	−0.203031	−	0.351660i
$418$	−1.85173e37	+	3.20729e37i	−0.182189	+	0.315560i
$419$	−8.51756e37			−0.809491			−0.404745	−	0.914429i	$-0.632640\pi$
$419$	−8.51756e37			−0.809491			−0.404745	+	0.914429i	$0.632640\pi$
$420$	1.10804e37	−	8.67176e37i	0.101728	−	0.796146i
$421$	5.88310e37			0.521814			0.260907	−	0.965364i	$-0.415978\pi$
$421$	5.88310e37			0.521814			0.260907	+	0.965364i	$0.415978\pi$
$422$	1.26915e38	−	2.19823e38i	1.08763	−	1.88383i
$423$	2.26624e36	+	3.92525e36i	0.0187660	+	0.0325036i
$424$	1.23685e38	+	2.14229e38i	0.989721	+	1.71425i
$425$	6.89147e37	−	1.19364e38i	0.532933	−	0.923067i
$426$	1.46290e38			1.09339
$427$	1.30390e38	−	5.45925e37i	0.941975	−	0.394393i
$428$	−4.77563e38			−3.33500
$429$	−5.63735e37	+	9.76417e37i	−0.380578	+	0.659181i
$430$	7.69190e37	+	1.33228e38i	0.502043	+	0.869564i
$431$	1.18021e38	+	2.04419e38i	0.744801	+	1.29003i	0.950288	+	0.311373i	$0.100789\pi$
$431$	1.18021e38	+	2.04419e38i	0.744801	+	1.29003i	−0.205487	+	0.978660i	$0.565878\pi$
$432$	4.35422e37	−	7.54173e37i	0.265703	−	0.460210i
$433$	1.36145e38			0.803392			0.401696	−	0.915773i	$-0.368421\pi$
$433$	1.36145e38			0.803392			0.401696	+	0.915773i	$0.368421\pi$
$434$	−4.67125e38	−	3.55617e38i	−2.66583	−	2.02946i
$435$	6.03111e37			0.332892
$436$	−1.58842e38	+	2.75123e38i	−0.848031	+	1.46883i
$437$	3.47550e37	+	6.01973e37i	0.179488	+	0.310883i
$438$	−2.52032e37	−	4.36533e37i	−0.125916	−	0.218093i
$439$	−1.46404e38	+	2.53580e38i	−0.707650	+	1.22569i	0.258076	+	0.966125i	$0.416911\pi$
$439$	−1.46404e38	+	2.53580e38i	−0.707650	+	1.22569i	−0.965727	+	0.259562i	$0.916422\pi$
$440$	2.36007e38			1.10373
$441$	−7.12945e37	−	1.85218e37i	−0.322624	−	0.0838156i
$442$	−1.22937e39			−5.38343
$443$	−1.44319e38	+	2.49967e38i	−0.611602	+	1.05932i	0.379369	+	0.925245i	$0.376141\pi$
$443$	−1.44319e38	+	2.49967e38i	−0.611602	+	1.05932i	−0.990971	+	0.134079i	$0.957192\pi$
$444$	−2.98874e38	−	5.17665e38i	−1.22584	−	2.12322i
$445$	−4.04177e37	−	7.00056e37i	−0.160454	−	0.277915i
$446$	−3.21462e37	+	5.56789e37i	−0.123531	+	0.213961i
$447$	1.49147e38			0.554825
$448$	−3.63845e38	−	2.76991e38i	−1.31035	−	0.997550i
$449$	1.65925e38			0.578548			0.289274	−	0.957246i	$-0.406586\pi$
$449$	1.65925e38			0.578548			0.289274	+	0.957246i	$0.406586\pi$
$450$	6.38879e37	−	1.10657e38i	0.215694	−	0.373592i
$451$	3.60190e37	+	6.23868e37i	0.117753	+	0.203954i
$452$	−1.10434e37	−	1.91277e37i	−0.0349619	−	0.0605557i
$453$	2.94618e37	−	5.10293e37i	0.0903306	−	0.156457i
$454$	−4.17471e38			−1.23970
$455$	−3.32399e38	+	1.39171e38i	−0.956082	+	0.400299i
$456$	−1.60613e38			−0.447496
$457$	8.21942e37	−	1.42365e38i	0.221848	−	0.384253i	−0.733521	−	0.679667i	$-0.762124\pi$
$457$	8.21942e37	−	1.42365e38i	0.221848	−	0.384253i	0.955369	+	0.295414i	$0.0954576\pi$
$458$	5.47154e38	+	9.47699e38i	1.43074	+	2.47811i
$459$	5.85457e37	+	1.01404e38i	0.148324	+	0.256904i
$460$	3.68857e38	−	6.38879e38i	0.905460	−	1.56830i
$461$	4.67204e38			1.11133			0.555665	−	0.831406i	$-0.312464\pi$
$461$	4.67204e38			1.11133			0.555665	+	0.831406i	$0.312464\pi$
$462$	4.19755e37	−	3.28509e38i	0.0967581	−	0.757248i
$463$	1.36053e38			0.303937			0.151968	−	0.988385i	$-0.451439\pi$
$463$	1.36053e38			0.303937			0.151968	+	0.988385i	$0.451439\pi$
$464$	6.61928e38	−	1.14649e39i	1.43318	−	2.48234i
$465$	1.36776e38	+	2.36903e38i	0.287040	+	0.497168i
$466$	−9.07956e38	−	1.57263e39i	−1.84701	−	3.19911i
$467$	2.79497e38	−	4.84103e38i	0.551166	−	0.954648i	−0.447024	−	0.894522i	$-0.647516\pi$
$467$	2.79497e38	−	4.84103e38i	0.551166	−	0.954648i	0.998191	−	0.0601263i	$-0.0191504\pi$
$468$	−8.14329e38			−1.55681
$469$	−3.47579e37	+	2.72022e38i	−0.0644240	+	0.504195i
$470$	−6.51315e37			−0.117050
$471$	−1.45508e38	+	2.52028e38i	−0.253563	+	0.439183i
$472$	7.00221e38	+	1.21282e39i	1.18325	+	2.04945i
$473$	2.08202e38	+	3.60616e38i	0.341191	+	0.590961i
$474$	−2.46077e36	+	4.26218e36i	−0.00391098	+	0.00677401i
$475$	−1.23616e38			−0.190553
$476$	2.38000e39	−	9.96477e38i	3.55858	−	1.48993i
$477$	−1.61743e38			−0.234589
$478$	6.25847e38	−	1.08400e39i	0.880569	−	1.52519i
$479$	1.99514e38	+	3.45568e38i	0.272338	+	0.471702i	0.969460	−	0.245250i	$-0.0788699\pi$
$479$	1.99514e38	+	3.45568e38i	0.272338	+	0.471702i	−0.697122	+	0.716952i	$0.745537\pi$
$480$	2.85163e38	+	4.93916e38i	0.377655	+	0.654117i
$481$	−1.23197e39	+	2.13383e39i	−1.58305	+	2.74193i
$482$	−2.12480e39			−2.64933
$483$	−4.94578e38	−	3.76516e38i	−0.598413	−	0.455564i
$484$	−1.06761e39			−1.25358
$485$	5.35596e37	−	9.27680e37i	0.0610355	−	0.105717i
$486$	5.42752e37	+	9.40074e37i	0.0600310	+	0.103977i
$487$	5.94748e38	+	1.03013e39i	0.638503	+	1.10592i	0.985761	+	0.168150i	$0.0537792\pi$
$487$	5.94748e38	+	1.03013e39i	0.638503	+	1.10592i	−0.347259	+	0.937769i	$0.612887\pi$
$488$	−1.37811e39	+	2.38696e39i	−1.43614	+	2.48747i
$489$	−7.21643e38			−0.730035
$490$	7.42748e38	−	7.54161e38i	0.729454	−	0.740664i
$491$	−1.97818e39			−1.88618			−0.943092	−	0.332532i	$-0.892097\pi$
$491$	−1.97818e39			−1.88618			−0.943092	+	0.332532i	$0.892097\pi$
$492$	−2.60152e38	+	4.50597e38i	−0.240843	+	0.417152i
$493$	8.90011e38	+	1.54154e39i	0.800046	+	1.38572i
$494$	5.51294e38	+	9.54869e38i	0.481219	+	0.833495i
$495$	−7.71565e37	+	1.33639e38i	−0.0654029	+	0.113281i
$496$	6.00459e39			4.94310
$497$	1.00699e39	+	7.66612e38i	0.805117	+	0.612926i
$498$	1.82142e39			1.41444
$499$	9.12792e38	−	1.58100e39i	0.688516	−	1.19254i	−0.283802	−	0.958883i	$-0.591596\pi$
$499$	9.12792e38	−	1.58100e39i	0.688516	−	1.19254i	0.972318	−	0.233662i	$-0.0750708\pi$
$500$	1.60462e39	+	2.77928e39i	1.17573	+	2.03642i
$501$	−3.57377e38	−	6.18994e38i	−0.254378	−	0.440595i
$502$	−2.77965e38	+	4.81449e38i	−0.192214	+	0.332925i
$503$	1.52641e38			0.102550			0.0512749	−	0.998685i	$-0.483672\pi$
$503$	1.52641e38			0.102550			0.0512749	+	0.998685i	$0.483672\pi$
$504$	1.32483e39	−	5.54690e38i	0.864805	−	0.362083i
$505$	2.36978e38			0.150309
$506$	1.39732e39	−	2.42024e39i	0.861222	−	1.49168i
$507$	1.19637e39	+	2.07217e39i	0.716554	+	1.24111i
$508$	−1.07854e39	−	1.86809e39i	−0.627788	−	1.08736i
$509$	−8.94740e38	+	1.54973e39i	−0.506161	+	0.876697i	0.493813	+	0.869568i	$0.335603\pi$
$509$	−8.94740e38	+	1.54973e39i	−0.506161	+	0.876697i	−0.999975	+	0.00712892i	$0.997731\pi$
$510$	−1.68259e39			−0.925149
$511$	5.52712e37	−	4.32563e38i	0.0295390	−	0.231178i
$512$	−2.43091e39			−1.26286
$513$	5.25081e37	−	9.09467e37i	0.0265170	−	0.0459288i
$514$	−3.25301e39	−	5.63438e39i	−1.59706	−	2.76618i
$515$	−4.22140e38	−	7.31168e38i	−0.201489	−	0.348989i
$516$	−1.50376e39	+	2.60460e39i	−0.697845	+	1.20870i
$517$	−1.76296e38			−0.0795479
$518$	9.17318e38	−	7.17911e39i	0.402475	−	3.14985i
$519$	1.41497e39			0.603699
$520$	3.51319e39	−	6.08502e39i	1.45765	−	2.52472i
$521$	−2.42165e38	−	4.19442e38i	−0.0977156	−	0.169248i	0.813023	−	0.582231i	$-0.197820\pi$
$521$	−2.42165e38	−	4.19442e38i	−0.0977156	−	0.169248i	−0.910739	+	0.412983i	$0.864487\pi$
$522$	8.25092e38	+	1.42910e39i	0.323802	+	0.560842i
$523$	1.27044e39	−	2.20046e39i	0.484930	−	0.839924i	−0.514920	−	0.857238i	$-0.672178\pi$
$523$	1.27044e39	−	2.20046e39i	0.484930	−	0.839924i	0.999850	+	0.0173144i	$0.00551164\pi$
$524$	−4.12232e39			−1.53052
$525$	1.01966e39	−	4.26918e38i	0.368252	−	0.154182i
$526$	2.27145e39			0.798011
$527$	−4.03681e39	+	6.99196e39i	−1.37970	+	2.38971i
$528$	1.69362e39	+	2.93343e39i	0.563150	+	0.975404i
$529$	−1.07710e39	−	1.86559e39i	−0.348456	−	0.603543i
$530$	1.16212e39	−	2.01284e39i	0.365805	−	0.633592i
$531$	−9.15676e38			−0.280460
$532$	−1.84126e39	−	1.40173e39i	−0.548778	−	0.417778i
$533$	2.14471e39			0.622047
$534$	1.10588e39	−	1.91543e39i	0.312146	−	0.540654i
$535$	1.34713e39	+	2.33329e39i	0.370066	+	0.640973i
$536$	−2.67355e39	−	4.63072e39i	−0.714823	−	1.23811i
$537$	3.75899e38	−	6.51076e38i	0.0978237	−	0.169436i
$538$	3.37401e39			0.854681
$539$	2.01044e39	−	2.04134e39i	0.495741	−	0.503359i
$540$	−1.11454e39			−0.267540
$541$	−9.55108e38	+	1.65430e39i	−0.223199	+	0.386592i	−0.955778	−	0.294091i	$-0.904983\pi$
$541$	−9.55108e38	+	1.65430e39i	−0.223199	+	0.386592i	0.732579	+	0.680682i	$0.238317\pi$
$542$	−4.02106e39	−	6.96469e39i	−0.914853	−	1.58457i
$543$	1.24296e39	+	2.15287e39i	0.275334	+	0.476893i
$544$	−8.41629e39	+	1.45774e40i	−1.81525	+	3.14411i
$545$	1.79227e39			0.376404
$546$	−7.84515e39	−	5.97241e39i	−1.60438	−	1.22140i
$547$	−1.26434e39			−0.251796			−0.125898	−	0.992043i	$-0.540181\pi$
$547$	−1.26434e39			−0.251796			−0.125898	+	0.992043i	$0.540181\pi$
$548$	−3.40046e39	+	5.88977e39i	−0.659507	+	1.14230i
$549$	−9.01075e38	−	1.56071e39i	−0.170201	−	0.294797i
$550$	2.48499e39	+	4.30412e39i	0.457157	+	0.791819i
$551$	7.98228e38	−	1.38257e39i	0.143031	−	0.247736i
$552$	1.21199e40			2.11535
$553$	−3.92742e37	+	1.64436e37i	−0.00667718	+	0.00279565i
$554$	−1.45938e40			−2.41699
$555$	−1.68615e39	+	2.92050e39i	−0.272050	+	0.471204i
$556$	5.59933e39	+	9.69832e39i	0.880140	+	1.52445i
$557$	5.55099e38	+	9.61459e38i	0.0850100	+	0.147242i	0.905395	−	0.424569i	$-0.139574\pi$
$557$	5.55099e38	+	9.61459e38i	0.0850100	+	0.147242i	−0.820385	+	0.571811i	$0.806241\pi$
$558$	−3.74235e39	+	6.48195e39i	−0.558404	+	0.967185i
$559$	1.23971e40			1.80239
$560$	−1.37217e39	+	1.07389e40i	−0.194393	+	1.52136i
$561$	−4.55439e39			−0.628737
$562$	−4.44606e39	+	7.70080e39i	−0.598134	+	1.03600i
$563$	2.54665e39	+	4.41092e39i	0.333885	+	0.578306i	0.983270	−	0.182154i	$-0.0583069\pi$
$563$	2.54665e39	+	4.41092e39i	0.333885	+	0.578306i	−0.649385	+	0.760460i	$0.724974\pi$
$564$	−6.36659e38	−	1.10273e39i	−0.0813504	−	0.140903i
$565$	−6.23031e37	+	1.07912e38i	−0.00775903	+	0.0134390i
$566$	4.41549e39			0.535970
$567$	−1.19027e38	+	9.31526e38i	−0.0140828	+	0.110215i
$568$	−2.46770e40			−2.84604
$569$	6.79842e39	−	1.17752e40i	0.764328	−	1.32386i	−0.176273	−	0.984341i	$-0.556404\pi$
$569$	6.79842e39	−	1.17752e40i	0.764328	−	1.32386i	0.940601	−	0.339514i	$-0.110263\pi$
$570$	7.54538e38	+	1.30690e39i	0.0826981	+	0.143237i
$571$	−3.08762e38	−	5.34792e38i	−0.0329914	−	0.0571428i	0.849058	−	0.528299i	$-0.177170\pi$
$571$	−3.08762e38	−	5.34792e38i	−0.0329914	−	0.0571428i	−0.882050	+	0.471156i	$0.843837\pi$
$572$	1.58371e40	−	2.74307e40i	1.64981	−	2.85755i
$573$	−3.43274e38			−0.0348658
$574$	−5.81102e39	+	2.43300e39i	−0.575479	+	0.240946i
$575$	9.32810e39			0.900761
$576$	−2.91493e39	+	5.04881e39i	−0.274475	+	0.475404i
$577$	3.57615e39	+	6.19408e39i	0.328373	+	0.568758i	0.982189	−	0.187895i	$-0.0601665\pi$
$577$	3.57615e39	+	6.19408e39i	0.328373	+	0.568758i	−0.653817	+	0.756653i	$0.726833\pi$
$578$	−1.43797e40	−	2.49063e40i	−1.28764	−	2.23026i
$579$	4.07251e39	−	7.05379e39i	0.355650	−	0.616004i
$580$	−1.69433e40			−1.44309
$581$	1.25379e40	+	9.54491e39i	1.04152	+	0.792899i
$582$	2.93091e39			0.237476
$583$	3.14558e39	−	5.44830e39i	0.248603	−	0.430593i
$584$	4.25141e39	+	7.36366e39i	0.327753	+	0.567685i
$585$	2.29709e39	+	3.97868e39i	0.172750	+	0.299212i
$586$	−2.39503e39	+	4.14832e39i	−0.175710	+	0.304338i
$587$	−7.71554e39			−0.552222			−0.276111	−	0.961126i	$-0.589046\pi$
$587$	−7.71554e39			−0.552222			−0.276111	+	0.961126i	$0.589046\pi$
$588$	2.00289e40	+	5.20337e39i	1.39857	+	0.363340i
$589$	7.24102e39			0.493319
$590$	6.57910e39	−	1.13953e40i	0.437333	−	0.757483i
$591$	−7.70540e39	−	1.33461e40i	−0.499778	−	0.865640i
$592$	3.70118e40	+	6.41063e40i	2.34248	+	4.05729i
$593$	9.33912e39	−	1.61758e40i	0.576784	−	0.999019i	−0.419062	−	0.907958i	$-0.637641\pi$
$593$	9.33912e39	−	1.61758e40i	0.576784	−	0.999019i	0.995845	−	0.0910610i	$-0.0290258\pi$
$594$	−4.22218e39			−0.254468
$595$	−1.15822e40	−	8.81740e39i	−0.681234	−	0.518615i
$596$	−4.19002e40			−2.40517
$597$	7.83888e39	−	1.35773e40i	0.439164	−	0.760654i
$598$	−4.16009e40	−	7.20549e40i	−2.27476	−	3.94000i
$599$	8.76351e39	+	1.51788e40i	0.467723	+	0.810120i	0.999320	−	0.0368772i	$-0.0117411\pi$
$599$	8.76351e39	+	1.51788e40i	0.467723	+	0.810120i	−0.531597	+	0.846998i	$0.678408\pi$
$600$	−1.07770e40	+	1.86662e40i	−0.561439	+	0.972442i
$601$	−2.95428e40			−1.50235			−0.751177	−	0.660101i	$-0.770514\pi$
$601$	−2.95428e40			−1.50235			−0.751177	+	0.660101i	$0.770514\pi$
$602$	−3.35896e40	+	1.40635e40i	−1.66746	+	0.698144i
$603$	3.49619e39			0.169431
$604$	−8.27675e39	+	1.43357e40i	−0.391583	+	0.678242i
$605$	3.01155e39	+	5.21615e39i	0.139103	+	0.240933i
$606$	3.24200e39	+	5.61531e39i	0.146204	+	0.253233i
$607$	1.14498e40	−	1.98317e40i	0.504155	−	0.873221i	−0.495834	−	0.868417i	$-0.665138\pi$
$607$	1.14498e40	−	1.98317e40i	0.504155	−	0.873221i	0.999988	−	0.00480392i	$-0.00152914\pi$
$608$	1.50967e40			0.649053
$609$	−1.80944e39	+	1.41611e40i	−0.0759617	+	0.594491i
$610$	2.58968e40			1.06161
$611$	−2.62432e39	+	4.54546e39i	−0.105056	+	0.181962i
$612$	−1.64473e40	−	2.84876e40i	−0.642984	−	1.11368i
$613$	2.51075e40	+	4.34874e40i	0.958576	+	1.66030i	0.725965	+	0.687732i	$0.241394\pi$
$613$	2.51075e40	+	4.34874e40i	0.958576	+	1.66030i	0.232611	+	0.972570i	$0.425273\pi$
$614$	2.37694e40	−	4.11698e40i	0.886292	−	1.53510i
$615$	2.93539e39			0.106900
$616$	−7.08065e39	+	5.54146e40i	−0.251856	+	1.97108i
$617$	−1.55808e39			−0.0541322			−0.0270661	−	0.999634i	$-0.508616\pi$
$617$	−1.55808e39			−0.0541322			−0.0270661	+	0.999634i	$0.508616\pi$
$618$	1.15502e40	−	2.00056e40i	0.391975	−	0.678920i
$619$	1.96149e40	+	3.39740e40i	0.650236	+	1.12624i	0.983065	+	0.183255i	$0.0586635\pi$
$619$	1.96149e40	+	3.39740e40i	0.650236	+	1.12624i	−0.332829	+	0.942987i	$0.608003\pi$
$620$	−3.84247e40	−	6.65536e40i	−1.24432	−	2.15522i
$621$	−3.96229e39	+	6.86288e39i	−0.125348	+	0.217109i
$622$	5.17029e39			0.159792
$623$	1.76499e40	−	7.38980e39i	0.532925	−	0.223129i
$624$	1.00844e41			2.97492
$625$	−2.94254e39	+	5.09662e39i	−0.0848128	+	0.146900i
$626$	−2.85545e40	−	4.94579e40i	−0.804168	−	1.39286i
$627$	2.04236e39	+	3.53747e39i	0.0562021	+	0.0973449i
$628$	4.08779e40	−	7.08027e40i	1.09919	−	1.90386i
$629$	−9.95301e40			−2.61529
$630$	−1.07374e40	−	8.17424e39i	−0.275715	−	0.209899i
$631$	4.34204e40			1.08960			0.544801	−	0.838565i	$-0.316605\pi$
$631$	4.34204e40			1.08960			0.544801	+	0.838565i	$0.316605\pi$
$632$	4.15096e38	−	7.18968e38i	0.0101801	−	0.0176324i
$633$	−1.39980e40	−	2.42452e40i	−0.335515	−	0.581129i
$634$	3.81669e40	+	6.61070e40i	0.894113	+	1.54865i
$635$	−6.08478e39	+	1.05391e40i	−0.139324	+	0.241316i
$636$	4.54386e40			1.01694
$637$	−2.27049e40	−	8.22228e40i	−0.496704	−	1.79875i
$638$	−6.41856e40			−1.37258
$639$	8.06749e39	−	1.39733e40i	0.168646	−	0.292103i
$640$	−9.87890e39	−	1.71108e40i	−0.201883	−	0.349671i
$641$	2.86437e39	+	4.96124e39i	0.0572253	+	0.0991171i	0.893219	−	0.449622i	$-0.148441\pi$
$641$	2.86437e39	+	4.96124e39i	0.0572253	+	0.0991171i	−0.835994	+	0.548739i	$0.815108\pi$
$642$	−3.68590e40	+	6.38416e40i	−0.719922	+	1.24694i
$643$	4.34543e40			0.829801			0.414900	−	0.909867i	$-0.363816\pi$
$643$	4.34543e40			0.829801			0.414900	+	0.909867i	$0.363816\pi$
$644$	1.38943e41	+	1.05775e41i	2.59412	+	1.97487i
$645$	1.69675e40			0.309743
$646$	−2.22694e40	+	3.85718e40i	−0.397500	+	0.688491i
$647$	2.62375e40	+	4.54447e40i	0.457942	+	0.793179i	0.998852	−	0.0479017i	$-0.0152534\pi$
$647$	2.62375e40	+	4.54447e40i	0.457942	+	0.793179i	−0.540910	+	0.841080i	$0.681920\pi$
$648$	−9.15543e39	−	1.58577e40i	−0.156258	−	0.270646i
$649$	1.78081e40	−	3.08445e40i	0.297214	−	0.514790i
$650$	1.47965e41			2.41499
$651$	−5.97284e40	+	2.50075e40i	−0.953360	+	0.399159i
$652$	2.02732e41			3.16470
$653$	−5.01687e40	+	8.68947e40i	−0.765934	+	1.32664i	0.173817	+	0.984778i	$0.444390\pi$
$653$	−5.01687e40	+	8.68947e40i	−0.765934	+	1.32664i	−0.939751	+	0.341859i	$0.888943\pi$
$654$	2.45193e40	+	4.24687e40i	0.366127	+	0.634150i
$655$	1.16284e40	+	2.01410e40i	0.169832	+	0.294158i
$656$	3.22165e40	−	5.58007e40i	0.460228	−	0.797138i
$657$	−5.55956e39			−0.0776859
$658$	1.95406e39	−	1.52929e40i	0.0267093	−	0.209033i
$659$	−3.33498e40			−0.445917			−0.222959	−	0.974828i	$-0.571571\pi$
$659$	−3.33498e40			−0.445917			−0.222959	+	0.974828i	$0.571571\pi$
$660$	2.16757e40	−	3.75434e40i	0.283521	−	0.491074i
$661$	−2.02679e40	−	3.51051e40i	−0.259351	−	0.449209i	0.706717	−	0.707496i	$-0.250175\pi$
$661$	−2.02679e40	−	3.51051e40i	−0.259351	−	0.449209i	−0.966068	+	0.258287i	$0.916842\pi$
$662$	5.79715e39	+	1.00410e40i	0.0725728	+	0.125700i
$663$	−6.77963e40	+	1.17427e41i	−0.830347	+	1.43820i
$664$	−3.07247e41			−3.68172
$665$	−1.65472e39	+	1.29501e40i	−0.0194004	+	0.151831i
$666$	−9.22701e40			−1.05849
$667$	−6.02347e40	+	1.04330e41i	−0.676118	+	1.17107i
$668$	1.00398e41	+	1.73895e41i	1.10273	+	1.90998i
$669$	3.54555e39	+	6.14108e39i	0.0381070	+	0.0660033i
$670$	−2.51200e40	+	4.35091e40i	−0.264201	+	0.457610i
$671$	7.00966e40			0.721473
$672$	−1.24527e41	+	5.21379e40i	−1.25432	+	0.525169i
$673$	1.30182e41			1.28332			0.641658	−	0.766991i	$-0.278247\pi$
$673$	1.30182e41			1.28332			0.641658	+	0.766991i	$0.278247\pi$
$674$	−1.30997e41	+	2.26894e41i	−1.26384	+	2.18904i
$675$	−7.04649e39	−	1.22049e40i	−0.0665377	−	0.115247i
$676$	−3.36097e41	−	5.82138e41i	−3.10626	−	5.38020i
$677$	1.21412e40	−	2.10292e40i	0.109831	−	0.190233i	−0.805871	−	0.592092i	$-0.798302\pi$
$677$	1.21412e40	−	2.10292e40i	0.109831	−	0.190233i	0.915702	+	0.401859i	$0.131636\pi$
$678$	−3.40937e39			−0.0301887
$679$	2.01751e40	+	1.53590e40i	0.174865	+	0.133123i
$680$	2.83829e41			2.40812
$681$	−2.30224e40	+	3.98760e40i	−0.191213	+	0.331191i
$682$	−1.45563e41	−	2.52122e41i	−1.18352	−	2.04992i
$683$	−7.69469e40	−	1.33276e41i	−0.612478	−	1.06084i	−0.990821	−	0.135178i	$-0.956839\pi$
$683$	−7.69469e40	−	1.33276e41i	−0.612478	−	1.06084i	0.378343	−	0.925665i	$-0.376494\pi$
$684$	−1.47512e40	+	2.55498e40i	−0.114951	+	0.199101i
$685$	3.83686e40			0.292727
$686$	1.54793e41	+	1.97024e41i	1.15625	+	1.47170i
$687$	1.20696e41			0.882716
$688$	1.86222e41	−	3.22546e41i	1.33352	−	2.30972i
$689$	−9.36496e40	−	1.62206e41i	−0.656640	−	1.13733i
$690$	−5.69378e40	−	9.86192e40i	−0.390921	−	0.677095i
$691$	−1.04511e41	+	1.81019e41i	−0.702639	+	1.21701i	0.264898	+	0.964276i	$0.414662\pi$
$691$	−1.04511e41	+	1.81019e41i	−0.702639	+	1.21701i	−0.967537	+	0.252729i	$0.918672\pi$
$692$	−3.97510e41			−2.61703
$693$	−2.90636e40	−	2.21258e40i	−0.187378	−	0.142648i
$694$	5.27866e41			3.33281
$695$	3.15896e40	−	5.47148e40i	0.195328	−	0.338318i
$696$	−1.39181e41	−	2.41068e41i	−0.842841	−	1.45984i
$697$	4.33175e40	+	7.50281e40i	0.256914	+	0.444988i
$698$	9.72275e40	−	1.68403e41i	0.564788	−	0.978242i
$699$	−2.00285e41			−1.13954
$700$	−2.86455e41	+	1.19935e41i	−1.59637	+	0.668381i
$701$	−5.72807e40			−0.312678			−0.156339	−	0.987703i	$-0.549969\pi$
$701$	−5.72807e40			−0.312678			−0.156339	+	0.987703i	$0.549969\pi$
$702$	−6.28511e40	+	1.08861e41i	−0.336066	+	0.582083i
$703$	4.46330e40	+	7.73066e40i	0.233778	+	0.404915i
$704$	−1.13379e41	−	1.96379e41i	−0.581742	−	1.00761i
$705$	−3.59182e39	+	6.22122e39i	−0.0180540	+	0.0312704i
$706$	−3.62799e41			−1.78648
$707$	−7.10978e39	+	5.56426e40i	−0.0342985	+	0.268427i
$708$	2.57242e41			1.21580
$709$	9.29914e40	−	1.61066e41i	0.430598	−	0.745818i	−0.566327	−	0.824181i	$-0.691636\pi$
$709$	9.29914e40	−	1.61066e41i	0.430598	−	0.745818i	0.996925	+	0.0783628i	$0.0249692\pi$
$710$	1.15929e41	+	2.00795e41i	0.525953	+	0.910977i
$711$	2.71410e38	+	4.70095e38i	0.00120647	+	0.00208967i
$712$	−1.86545e41	+	3.23106e41i	−0.812501	+	1.40729i
$713$	−5.46411e41			−2.33196
$714$	5.04809e40	−	3.95073e41i	0.211107	−	1.65217i
$715$	−1.78695e41			−0.732278
$716$	−1.05602e41	+	1.82908e41i	−0.424066	+	0.734504i
$717$	−6.90275e40	−	1.19559e41i	−0.271640	−	0.470495i
$718$	4.14861e41	+	7.18561e41i	1.59992	+	2.77114i
$719$	3.94463e40	−	6.83230e40i	0.149086	−	0.258225i	−0.781804	−	0.623525i	$-0.785700\pi$
$719$	3.94463e40	−	6.83230e40i	0.149086	−	0.258225i	0.930890	+	0.365300i	$0.119033\pi$
$720$	1.38022e41			0.511243
$721$	1.84343e41	−	7.71822e40i	0.669216	−	0.280192i
$722$	−4.86069e41			−1.72945
$723$	−1.17177e41	+	2.02957e41i	−0.408637	+	0.707780i
$724$	−3.49188e41	−	6.04811e41i	−1.19357	−	2.06733i
$725$	−1.07121e41	−	1.85539e41i	−0.358899	−	0.621632i
$726$	−8.23994e40	+	1.42720e41i	−0.270609	+	0.468709i
$727$	3.31527e41			1.06726			0.533630	−	0.845718i	$-0.320827\pi$
$727$	3.31527e41			1.06726			0.533630	+	0.845718i	$0.320827\pi$
$728$	1.32336e42	+	1.00746e42i	4.17613	+	3.17923i
$729$	1.19725e40			0.0370370
$730$	3.99452e40	−	6.91871e40i	0.121139	−	0.209819i
$731$	2.50389e41	+	4.33687e41i	0.744413	+	1.28936i
$732$	2.53141e41	+	4.38452e41i	0.737821	+	1.27794i
$733$	1.18153e41	−	2.04647e41i	0.337626	−	0.584786i	−0.646359	−	0.763033i	$-0.723709\pi$
$733$	1.18153e41	−	2.04647e41i	0.337626	−	0.584786i	0.983986	+	0.178247i	$0.0570426\pi$
$734$	−2.01879e41			−0.565586
$735$	−3.10754e40	−	1.12536e41i	−0.0853592	−	0.309118i
$736$	−1.13921e42			−3.06813
$737$	−6.79940e40	+	1.17769e41i	−0.179553	+	0.310994i
$738$	4.01578e40	+	6.95554e40i	0.103981	+	0.180100i
$739$	−1.34150e41	−	2.32354e41i	−0.340600	−	0.589937i	0.643944	−	0.765073i	$-0.277297\pi$
$739$	−1.34150e41	−	2.32354e41i	−0.340600	−	0.589937i	−0.984544	+	0.175136i	$0.943964\pi$
$740$	4.73693e41	−	8.20461e41i	1.17934	−	2.04267i
$741$	1.21609e41			0.296895
$742$	4.37750e41	+	3.33254e41i	1.04802	+	0.797845i
$743$	6.95838e40			0.163369			0.0816846	−	0.996658i	$-0.473970\pi$
$743$	6.95838e40			0.163369			0.0816846	+	0.996658i	$0.473970\pi$
$744$	6.31280e41	−	1.09341e42i	1.45350	−	2.51753i
$745$	1.18194e41	+	2.04717e41i	0.266887	+	0.462263i
$746$	5.26340e41	+	9.11648e41i	1.16561	+	2.01890i
$747$	1.00446e41	−	1.73978e41i	0.218165	−	0.377874i
$748$	1.27947e42			2.72557
$749$	−5.88274e41	+	2.46303e41i	−1.22912	+	0.514616i
$750$	4.95387e41			1.01521
$751$	3.79023e41	−	6.56487e41i	0.761880	−	1.31961i	−0.180001	−	0.983666i	$-0.557610\pi$
$751$	3.79023e41	−	6.56487e41i	0.761880	−	1.31961i	0.941881	−	0.335948i	$-0.109057\pi$
$752$	7.88421e40	+	1.36559e41i	0.155453	+	0.269253i
$753$	3.06580e40	+	5.31012e40i	0.0592948	+	0.102702i
$754$	−9.55462e41	+	1.65491e42i	−1.81271	+	3.13971i
$755$	9.33894e40			0.173807
$756$	3.34384e40	−	2.61695e41i	0.0610491	−	0.477782i
$757$	1.72894e41			0.309663			0.154831	−	0.987941i	$-0.450517\pi$
$757$	1.72894e41			0.309663			0.154831	+	0.987941i	$0.450517\pi$
$758$	2.78252e41	−	4.81947e41i	0.488917	−	0.846830i
$759$	−1.54117e41	−	2.66939e41i	−0.265672	−	0.460157i
$760$	−1.27279e41	−	2.20454e41i	−0.215259	−	0.372839i
$761$	4.18420e41	−	7.24724e41i	0.694280	−	1.20253i	−0.276143	−	0.961117i	$-0.589056\pi$
$761$	4.18420e41	−	7.24724e41i	0.694280	−	1.20253i	0.970423	−	0.241412i	$-0.0776104\pi$
$762$	−3.32973e41			−0.542079
$763$	−5.37715e40	+	4.20826e41i	−0.0858907	+	0.672197i
$764$	9.64366e40			0.151143
$765$	−9.27905e40	+	1.60718e41i	−0.142696	+	0.247157i
$766$	−1.24197e41	−	2.15116e41i	−0.187411	−	0.324605i
$767$	−5.30180e41	−	9.18298e41i	−0.785037	−	1.35972i
$768$	−5.68923e40	+	9.85403e40i	−0.0826638	+	0.143178i
$769$	1.93458e41			0.275839			0.137920	−	0.990443i	$-0.455958\pi$
$769$	1.93458e41			0.275839			0.137920	+	0.990443i	$0.455958\pi$
$770$	4.84170e41	−	2.02716e41i	0.677458	−	0.283643i
$771$	−7.17579e41			−0.985329
$772$	−1.14410e42	+	1.98163e42i	−1.54174	+	2.67038i
$773$	6.15141e40	+	1.06546e41i	0.0813528	+	0.140907i	0.903831	−	0.427889i	$-0.140743\pi$
$773$	6.15141e40	+	1.06546e41i	0.0813528	+	0.140907i	−0.822478	+	0.568796i	$0.807409\pi$
$774$	2.32125e41	+	4.02053e41i	0.301286	+	0.521842i
$775$	4.85866e41	−	8.41544e41i	0.618930	−	1.07202i
$776$	−4.94401e41			−0.618137
$777$	−6.35146e41	−	4.83529e41i	−0.779415	−	0.593359i
$778$	1.17686e42			1.41749
$779$	3.88503e40	−	6.72908e40i	0.0459305	−	0.0795540i
$780$	−6.45325e41	−	1.11774e42i	−0.748871	−	1.29708i
$781$	3.13793e41	+	5.43506e41i	0.357441	+	0.619105i
$782$	1.68046e42	−	2.91065e42i	1.87902	−	3.25455i
$783$	1.82006e41			0.199775
$784$	−2.48032e42	−	6.44372e41i	−2.67255	−	0.694310i
$785$	−4.61240e41			−0.487885
$786$	−3.18166e41	+	5.51080e41i	−0.330390	+	0.572253i
$787$	−2.99958e41	−	5.19543e41i	−0.305793	−	0.529648i	0.671645	−	0.740873i	$-0.265588\pi$
$787$	−2.99958e41	−	5.19543e41i	−0.305793	−	0.529648i	−0.977437	+	0.211225i	$0.932255\pi$
$788$	2.16469e42	+	3.74936e42i	2.16654	+	3.75255i
$789$	1.25264e41	−	2.16964e41i	0.123086	−	0.213192i
$790$	−7.80028e39			−0.00752519
$791$	−2.34686e40	−	1.78664e40i	−0.0222294	−	0.0169230i
$792$	7.12220e41			0.662368
$793$	1.04345e42	−	1.80731e42i	0.952821	−	1.65033i
$794$	1.18616e42	+	2.05449e42i	1.06352	+	1.84207i
$795$	−1.28175e41	−	2.22006e41i	−0.112844	−	0.195452i
$796$	−2.20219e42	+	3.81431e42i	−1.90377	+	3.29743i
$797$	3.01613e41			0.256038			0.128019	−	0.991772i	$-0.459138\pi$
$797$	3.01613e41			0.256038			0.128019	+	0.991772i	$0.459138\pi$
$798$	−3.29497e41	+	1.37956e41i	−0.274669	+	0.115000i
$799$	−2.12018e41			−0.173558
$800$	1.01297e42	−	1.75452e42i	0.814318	−	1.41044i
$801$	−1.21972e41	−	2.11262e41i	−0.0962918	−	0.166782i
$802$	−9.03404e41	−	1.56474e42i	−0.700412	−	1.21315i
$803$	1.08122e41	−	1.87273e41i	0.0823266	−	0.142594i
$804$	−9.82190e41			−0.734485
$805$	1.24866e41	−	9.77225e41i	0.0917072	−	0.717719i
$806$	−8.66734e42			−6.25213
$807$	1.86068e41	−	3.22279e41i	0.131827	−	0.228331i
$808$	−5.46878e41	−	9.47221e41i	−0.380562	−	0.659154i
$809$	−5.21117e41	−	9.02602e41i	−0.356190	−	0.616940i	0.631131	−	0.775677i	$-0.282591\pi$
$809$	−5.21117e41	−	9.02602e41i	−0.356190	−	0.616940i	−0.987321	+	0.158737i	$0.949258\pi$
$810$	−8.60221e40	+	1.48995e41i	−0.0577534	+	0.100032i
$811$	1.54853e42			1.02122			0.510608	−	0.859813i	$-0.329420\pi$
$811$	1.54853e42			1.02122			0.510608	+	0.859813i	$0.329420\pi$
$812$	5.08330e41	−	3.97829e42i	0.329294	−	2.57712i
$813$	−8.87003e41			−0.564433
$814$	1.79447e42	−	3.10812e42i	1.12172	−	1.94287i
$815$	−5.71875e41	−	9.90517e41i	−0.351169	−	0.608242i
$816$	2.03679e42	+	3.52783e42i	1.22868	+	2.12814i
$817$	2.24568e41	−	3.88963e41i	0.133085	−	0.230509i
$818$	4.15101e42			2.41674
$819$	−1.00311e42	+	4.19990e41i	−0.573763	+	0.240227i
$820$	−8.24643e41			−0.463410
$821$	−8.53556e41	+	1.47840e42i	−0.471255	+	0.816238i	−0.999459	−	0.0328792i	$-0.989532\pi$
$821$	−8.53556e41	+	1.47840e42i	−0.471255	+	0.816238i	0.528204	+	0.849118i	$0.322866\pi$
$822$	5.24905e41	+	9.09162e41i	0.284734	+	0.493173i
$823$	1.03426e42	+	1.79139e42i	0.551229	+	0.954757i	0.998186	+	0.0602017i	$0.0191744\pi$
$823$	1.03426e42	+	1.79139e42i	0.551229	+	0.954757i	−0.446957	+	0.894555i	$0.647492\pi$
$824$	−1.94836e42	+	3.37465e42i	−1.02029	+	1.76720i
$825$	5.48161e41			0.282050
$826$	2.47824e42	+	1.88666e42i	1.25295	+	0.953854i
$827$	1.04931e42			0.521282			0.260641	−	0.965436i	$-0.416066\pi$
$827$	1.04931e42			0.521282			0.260641	+	0.965436i	$0.416066\pi$
$828$	1.11313e42	−	1.92800e42i	0.543384	−	0.941169i
$829$	−1.64530e41	−	2.84974e41i	−0.0789231	−	0.136699i	0.823862	−	0.566790i	$-0.191815\pi$
$829$	−1.64530e41	−	2.84974e41i	−0.0789231	−	0.136699i	−0.902786	+	0.430091i	$0.858481\pi$
$830$	1.44341e42	+	2.50006e42i	0.680389	+	1.17847i
$831$	−8.04806e41	+	1.39397e42i	−0.372800	+	0.645709i
$832$	−6.75102e42			−3.07313
$833$	2.41782e42	−	2.45497e42i	1.08161	−	1.09823i
$834$	1.72866e42			0.759978
$835$	5.66415e41	−	9.81060e41i	0.244727	−	0.423879i
$836$	−5.73763e41	−	9.93787e41i	−0.243636	−	0.421990i
$837$	4.12761e41	+	7.14923e41i	0.172258	+	0.298360i
$838$	1.84684e42	−	3.19882e42i	0.757514	−	1.31205i
$839$	−3.15290e42			−1.27105			−0.635523	−	0.772082i	$-0.719216\pi$
$839$	−3.15290e42			−1.27105			−0.635523	+	0.772082i	$0.719216\pi$
$840$	1.81124e42	+	1.37887e42i	0.717673	+	0.546355i
$841$	1.99174e41			0.0775694
$842$	−1.27562e42	+	2.20943e42i	−0.488309	+	0.845776i
$843$	4.90376e41	+	8.49356e41i	0.184514	+	0.319588i
$844$	3.93248e42	+	6.81126e42i	1.45446	+	2.51920i
$845$	−1.89615e42	+	3.28423e42i	−0.689367	+	1.19402i
$846$	−1.96553e41			−0.0702440
$847$	−1.31510e42	+	5.50617e41i	−0.462010	+	0.193437i
$848$	−5.62700e42			−1.94329
$849$	2.43502e41	−	4.21758e41i	0.0826688	−	0.143187i
$850$	2.98852e42	+	5.17626e42i	0.997427	+	1.72759i
$851$	−3.36803e42	−	5.83360e42i	−1.10509	−	1.91407i
$852$	−2.26641e42	+	3.92554e42i	−0.731080	+	1.26627i
$853$	−6.40452e41			−0.203107			−0.101554	−	0.994830i	$-0.532381\pi$
$853$	−6.40452e41			−0.203107			−0.101554	+	0.994830i	$0.532381\pi$
$854$	−7.76951e41	+	6.08057e42i	−0.242245	+	1.89586i
$855$	1.66443e41			0.0510219
$856$	6.21757e42	−	1.07691e43i	1.87392	−	3.24573i
$857$	5.70627e41	+	9.88355e41i	0.169095	+	0.292881i	0.938102	−	0.346359i	$-0.112582\pi$
$857$	5.70627e41	+	9.88355e41i	0.169095	+	0.292881i	−0.769007	+	0.639240i	$0.779249\pi$
$858$	−2.44466e42	−	4.23427e42i	−0.712283	−	1.23371i
$859$	−3.45136e41	+	5.97793e41i	−0.0988757	+	0.171258i	−0.911220	−	0.411921i	$-0.864858\pi$
$859$	−3.45136e41	+	5.97793e41i	−0.0988757	+	0.171258i	0.812344	+	0.583179i	$0.198191\pi$
$860$	−4.76671e42			−1.34274
$861$	−8.80670e40	+	6.89229e41i	−0.0243931	+	0.190905i
$862$	−1.02361e43			−2.78791
$863$	−1.26223e42	+	2.18625e42i	−0.338051	+	0.585521i	−0.984066	−	0.177803i	$-0.943101\pi$
$863$	−1.26223e42	+	2.18625e42i	−0.338051	+	0.585521i	0.646015	+	0.763324i	$0.276434\pi$
$864$	8.60560e41	+	1.49053e42i	0.226638	+	0.392548i
$865$	1.12131e42	+	1.94217e42i	0.290397	+	0.502982i
$866$	−2.95199e42	+	5.11301e42i	−0.751807	+	1.30217i
$867$	−3.17200e42			−0.794430
$868$	1.67796e43	−	7.02541e42i	4.13281	−	1.73036i
$869$	−2.11135e40			−0.00511416
$870$	−1.30771e42	+	2.26502e42i	−0.311517	+	0.539563i
$871$	2.02431e42	+	3.50620e42i	0.474256	+	0.821435i
$872$	−4.13605e42	−	7.16385e42i	−0.953009	−	1.65066i
$873$	1.61632e41	−	2.79954e41i	0.0366286	−	0.0634425i
$874$	−3.01433e42			−0.671853
$875$	3.41002e42	+	2.59601e42i	0.747550	+	0.569101i
$876$	1.56186e42			0.336768
$877$	−1.94871e40	+	3.37526e40i	−0.00413287	+	0.00715835i	−0.868084	−	0.496417i	$-0.834649\pi$
$877$	−1.94871e40	+	3.37526e40i	−0.00413287	+	0.00715835i	0.863952	+	0.503575i	$0.167982\pi$
$878$	−6.34889e42	−	1.09966e43i	−1.32442	−	2.29397i
$879$	2.64159e41	+	4.57537e41i	0.0542034	+	0.0938831i
$880$	−2.68426e42	+	4.64927e42i	−0.541783	+	0.938396i
$881$	−3.65711e42			−0.726085			−0.363043	−	0.931773i	$-0.618262\pi$
$881$	−3.65711e42			−0.726085			−0.363043	+	0.931773i	$0.618262\pi$
$882$	2.24145e42	−	2.27590e42i	0.437759	−	0.444486i
$883$	9.03539e42			1.73587			0.867934	−	0.496679i	$-0.165448\pi$
$883$	9.03539e42			1.73587			0.867934	+	0.496679i	$0.165448\pi$
$884$	1.90461e43	−	3.29889e43i	3.59956	−	6.23461i
$885$	−7.25639e41	−	1.25684e42i	−0.134910	−	0.233670i
$886$	−6.25844e42	−	1.08399e43i	−1.14466	−	1.98261i
$887$	−2.46406e42	+	4.26788e42i	−0.443363	+	0.767927i	−0.997937	−	0.0642078i	$-0.979548\pi$
$887$	−2.46406e42	+	4.26788e42i	−0.443363	+	0.767927i	0.554574	+	0.832135i	$0.312881\pi$
$888$	1.55646e43			2.75518
$889$	−2.29204e42	−	1.74490e42i	−0.399160	−	0.303875i
$890$	3.50546e42			0.600607
$891$	−2.32842e41	+	4.03294e41i	−0.0392495	+	0.0679822i
$892$	−9.96058e41	−	1.72522e42i	−0.165194	−	0.286124i
$893$	9.50768e40	+	1.64678e41i	0.0155142	+	0.0268713i
$894$	−3.23392e42	+	5.60131e42i	−0.519200	+	0.899281i
$895$	1.19154e42			0.188224
$896$	4.31400e42	−	1.80621e42i	0.670523	−	0.280739i
$897$	−9.17671e42			−1.40345
$898$	−3.59770e42	+	6.23140e42i	−0.541400	+	0.937732i
$899$	6.27480e42	+	1.08683e43i	0.929147	+	1.60933i
$900$	1.97958e42	+	3.42874e42i	0.288441	+	0.499595i
$901$	3.78296e42	−	6.55227e42i	0.542403	−	0.939469i
$902$	−3.12396e42			−0.440769
$903$	−5.09056e41	+	3.98397e42i	−0.0706795	+	0.553151i
$904$	5.75111e41			0.0785796
$905$	−1.97000e42	+	3.41214e42i	−0.264888	+	0.458800i
$906$	1.27762e42	+	2.21291e42i	0.169061	+	0.292822i
$907$	1.60921e42	+	2.78723e42i	0.209559	+	0.362967i	0.951576	−	0.307415i	$-0.0994639\pi$
$907$	1.60921e42	+	2.78723e42i	0.209559	+	0.362967i	−0.742017	+	0.670381i	$0.766131\pi$
$908$	6.46772e42	−	1.12024e43i	0.828908	−	1.43571i
$909$	7.15150e41			0.0902030
$910$	1.98066e42	−	1.55011e43i	0.245873	−	1.92425i
$911$	−7.56639e42			−0.924426			−0.462213	−	0.886769i	$-0.652944\pi$
$911$	−7.56639e42			−0.924426			−0.462213	+	0.886769i	$0.652944\pi$
$912$	1.82675e42	−	3.16402e42i	0.219661	−	0.380464i
$913$	3.90697e42	+	6.76707e42i	0.462396	+	0.800893i
$914$	3.56439e42	+	6.17370e42i	0.415207	+	0.719160i
$915$	1.42814e42	−	2.47361e42i	0.163744	−	0.283612i
$916$	−3.39074e43			−3.82657
$917$	−5.07798e42	+	2.12608e42i	−0.564073	+	0.236170i
$918$	−5.07771e42			−0.555200
$919$	−3.41818e42	+	5.92046e42i	−0.367891	+	0.637206i	−0.989236	−	0.146331i	$-0.953253\pi$
$919$	−3.41818e42	+	5.92046e42i	−0.367891	+	0.637206i	0.621344	+	0.783538i	$0.286587\pi$
$920$	9.60457e42	+	1.66356e43i	1.01755	+	1.76244i
$921$	−2.62164e42	−	4.54081e42i	−0.273406	−	0.473553i
$922$	−1.01302e43	+	1.75461e43i	−1.03997	+	1.80128i
$923$	1.86844e43			1.88823
$924$	8.16489e42	+	6.21583e42i	0.812282	+	0.618380i
$925$	1.19793e43			1.17321
$926$	−2.94999e42	+	5.10953e42i	−0.284421	+	0.492631i
$927$	−1.27393e42	−	2.20651e42i	−0.120917	−	0.209435i
$928$	1.30822e43	+	2.26591e43i	1.22247	+	2.11737i
$929$	−9.90516e42	+	1.71562e43i	−0.911242	+	1.57832i	−0.0989293	+	0.995094i	$0.531542\pi$
$929$	−9.90516e42	+	1.71562e43i	−0.911242	+	1.57832i	−0.812312	+	0.583223i	$0.801792\pi$
$930$	−1.18627e43			−1.07444
$931$	−2.99105e42	−	7.77056e41i	−0.266719	−	0.0692918i
$932$	5.62665e43			4.93991
$933$	2.85128e41	−	4.93856e41i	0.0246465	−	0.0426890i
$934$	1.21205e43	+	2.09933e43i	1.03155	+	1.78670i
$935$	−3.60918e42	−	6.25129e42i	−0.302441	−	0.523843i
$936$	1.06021e43	−	1.83633e43i	0.874762	−	1.51513i
$937$	1.44338e43			1.17262			0.586308	−	0.810089i	$-0.300581\pi$
$937$	1.44338e43			1.17262			0.586308	+	0.810089i	$0.300581\pi$
$938$	−9.46230e42	−	7.20353e42i	−0.756930	−	0.576241i
$939$	−6.29881e42			−0.496144
$940$	1.00906e42	−	1.74774e42i	0.0782640	−	0.135557i
$941$	−9.28042e42	−	1.60742e43i	−0.708791	−	1.22766i	−0.965306	−	0.261122i	$-0.915908\pi$
$941$	−9.28042e42	−	1.60742e43i	−0.708791	−	1.22766i	0.256515	−	0.966540i	$-0.417426\pi$
$942$	−6.31003e42	−	1.09293e43i	−0.474563	−	0.821967i
$943$	−2.93167e42	+	5.07780e42i	−0.217118	+	0.376059i
$944$	−3.18562e43			−2.32327
$945$	−1.37292e42	+	5.74826e41i	−0.0986019	+	0.0412833i
$946$	−1.80575e43			−1.27713
$947$	1.18463e43	−	2.05184e43i	0.825103	−	1.42912i	−0.0767383	−	0.997051i	$-0.524451\pi$
$947$	1.18463e43	−	2.05184e43i	0.825103	−	1.42912i	0.901841	−	0.432068i	$-0.142216\pi$
$948$	−7.62476e40	−	1.32065e41i	−0.00523004	−	0.00905870i
$949$	−3.21900e42	−	5.57548e42i	−0.217451	−	0.376636i
$950$	2.68032e42	−	4.64245e42i	0.178318	−	0.308855i
$951$	8.41920e42			0.551637
$952$	−8.51539e42	+	6.66431e43i	−0.549501	+	4.30051i
$953$	7.08449e42			0.450258			0.225129	−	0.974329i	$-0.427720\pi$
$953$	7.08449e42			0.450258			0.225129	+	0.974329i	$0.427720\pi$
$954$	3.50702e42	−	6.07433e42i	0.219526	−	0.380231i
$955$	−2.72032e41	−	4.71173e41i	−0.0167715	−	0.0290490i
$956$	1.93920e43	+	3.35880e43i	1.17756	+	2.03960i
$957$	−3.53966e42	+	6.13088e42i	−0.211709	+	0.366690i
$958$	−1.73040e43			−1.01940
$959$	−1.15113e42	+	9.00895e42i	−0.0667965	+	0.522763i
$960$	−9.23990e42			−0.528122
$961$	−1.95795e43	+	3.39128e43i	−1.10233	+	1.90930i
$962$	−5.34247e43	−	9.25344e43i	−2.96281	−	5.13174i
$963$	4.06535e42	+	7.04139e42i	0.222084	+	0.384660i
$964$	3.29188e43	−	5.70170e43i	1.77144	−	3.06822i
$965$	1.29092e43			0.684313
$966$	2.48640e43	−	1.04103e43i	1.29838	−	0.543617i
$967$	−3.40884e42			−0.175357			−0.0876784	−	0.996149i	$-0.527945\pi$
$967$	−3.40884e42			−0.175357			−0.0876784	+	0.996149i	$0.527945\pi$
$968$	1.38996e43	−	2.40748e43i	0.704383	−	1.22003i
$969$	2.45620e42	+	4.25426e42i	0.122622	+	0.212387i
$970$	2.32264e42	+	4.02292e42i	0.114233	+	0.197857i
$971$	−6.86986e42	+	1.18990e43i	−0.332866	+	0.576541i	−0.983073	−	0.183217i	$-0.941349\pi$
$971$	−6.86986e42	+	1.18990e43i	−0.332866	+	0.576541i	0.650207	+	0.759757i	$0.274682\pi$
$972$	−3.36346e42			−0.160556
$973$	1.18993e43	+	9.05879e42i	0.559610	+	0.426024i
$974$	−5.15829e43			−2.39002
$975$	8.15988e42	−	1.41333e43i	0.372492	−	0.645175i
$976$	−3.13483e43	−	5.42968e43i	−1.40991	−	2.44203i
$977$	1.93430e43	+	3.35031e43i	0.857142	+	1.48461i	0.874644	+	0.484767i	$0.161095\pi$
$977$	1.93430e43	+	3.35031e43i	0.857142	+	1.48461i	−0.0175016	+	0.999847i	$0.505571\pi$
$978$	1.56472e43	−	2.71017e43i	0.683160	−	1.18327i
$979$	9.48847e42			0.408176
$980$	8.73006e42	+	3.16148e43i	0.370032	+	1.34002i
$981$	5.40870e42			0.225887
$982$	4.28923e43	−	7.42916e43i	1.76507	−	3.05719i
$983$	−1.59448e43	−	2.76172e43i	−0.646537	−	1.11983i	−0.983944	−	0.178476i	$-0.942883\pi$
$983$	−1.59448e43	−	2.76172e43i	−0.646537	−	1.11983i	0.337407	−	0.941359i	$-0.390450\pi$
$984$	−6.77403e42	−	1.17330e43i	−0.270656	−	0.468791i
$985$	1.22125e43	−	2.11526e43i	0.480816	−	0.832797i
$986$	−7.71914e43			−2.99470
$987$	−1.35298e42	−	1.03001e42i	−0.0517242	−	0.0393770i
$988$	−3.41640e43			−1.28704
$989$	−1.69460e43	+	2.93513e43i	−0.629102	+	1.08964i
$990$	−3.34592e42	−	5.79531e42i	−0.122407	−	0.212015i
$991$	−4.39219e42	−	7.60750e42i	−0.158348	−	0.274267i	0.775925	−	0.630825i	$-0.217284\pi$
$991$	−4.39219e42	−	7.60750e42i	−0.158348	−	0.274267i	−0.934273	+	0.356558i	$0.883950\pi$
$992$	−5.93369e43	+	1.02775e44i	−2.10817	+	3.65146i
$993$	1.27879e42			0.0447749
$994$	−5.06249e43	+	2.11960e43i	−1.74687	+	0.731393i
$995$	2.48481e43			0.845003
$996$	−2.82186e43	+	4.88761e43i	−0.945747	+	1.63808i
$997$	−3.19189e42	−	5.52852e42i	−0.105431	−	0.182612i	0.808483	−	0.588519i	$-0.200289\pi$
$997$	−3.19189e42	−	5.52852e42i	−0.105431	−	0.182612i	−0.913914	+	0.405907i	$0.866956\pi$
$998$	3.95836e43	+	6.85608e43i	1.28861	+	2.23194i
$999$	−5.08845e42	+	8.81345e42i	−0.163262	+	0.282778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.e.a.16.1	yes	38
7.4	even	3	inner	21.30.e.a.4.1	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.e.a.4.1	✓	38	7.4	even	3	inner
21.30.e.a.16.1	yes	38	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-21682.7 + 37555.5i) q^{2} +(2.39148e6 + 4.14217e6i) q^{3} +(-6.71844e8 - 1.16367e9i) q^{4} +(-3.79032e9 + 6.56503e9i) q^{5} -2.07415e11 q^{6} +(-1.42775e12 - 1.08693e12i) q^{7} +3.49879e13 q^{8} +(-1.14384e13 + 1.98119e13i) q^{9} +O(q^{10})\)	\(q+(-21682.7 + 37555.5i) q^{2} +(2.39148e6 + 4.14217e6i) q^{3} +(-6.71844e8 - 1.16367e9i) q^{4} +(-3.79032e9 + 6.56503e9i) q^{5} -2.07415e11 q^{6} +(-1.42775e12 - 1.08693e12i) q^{7} +3.49879e13 q^{8} +(-1.14384e13 + 1.98119e13i) q^{9} +(-1.64369e14 - 2.84695e14i) q^{10} +(-4.44909e14 - 7.70604e14i) q^{11} +(3.21341e15 - 5.56579e15i) q^{12} -2.64915e16 q^{13} +(7.17779e16 - 3.00525e16i) q^{14} -3.62580e16 q^{15} +(-3.97940e17 + 6.89252e17i) q^{16} +(-5.35059e17 - 9.26750e17i) q^{17} +(-4.96031e17 - 8.59150e17i) q^{18} +(-4.79881e17 + 8.31178e17i) q^{19} +1.01860e19 q^{20} +(1.08781e18 - 8.51339e18i) q^{21} +3.85873e19 q^{22} +(3.62121e19 - 6.27211e19i) q^{23} +(8.36731e19 + 1.44926e20i) q^{24} +(6.43991e19 + 1.11543e20i) q^{25} +(5.74407e20 - 9.94902e20i) q^{26} -1.09419e20 q^{27} +(-3.05599e20 + 2.39168e21i) q^{28} -1.66339e21 q^{29} +(7.86172e20 - 1.36169e21i) q^{30} +(-3.77230e21 - 6.53381e21i) q^{31} +(-7.86482e21 - 1.36223e22i) q^{32} +(2.12798e21 - 3.68578e21i) q^{33} +4.64061e22 q^{34} +(1.25474e22 - 5.25344e21i) q^{35} +3.07393e22 q^{36} +(4.65042e22 - 8.05477e22i) q^{37} +(-2.08102e22 - 3.60444e22i) q^{38} +(-6.33540e22 - 1.09732e23i) q^{39} +(-1.32616e23 + 2.29697e23i) q^{40} -8.09583e22 q^{41} +(2.96138e23 + 2.25446e23i) q^{42} -4.67966e23 q^{43} +(-5.97818e23 + 1.03545e24i) q^{44} +(-8.67105e22 - 1.50187e23i) q^{45} +(1.57035e24 + 2.71993e24i) q^{46} +(9.90629e22 - 1.71582e23i) q^{47} -3.80667e24 q^{48} +(8.57063e23 + 3.10375e24i) q^{49} -5.58539e24 q^{50} +(2.55917e24 - 4.43262e24i) q^{51} +(1.77981e25 + 3.08273e25i) q^{52} +(3.53508e24 + 6.12294e24i) q^{53} +(2.37250e24 - 4.10929e24i) q^{54} +6.74539e24 q^{55} +(-4.99542e25 - 3.80295e25i) q^{56} -4.59051e24 q^{57} +(3.60668e25 - 6.24694e25i) q^{58} +(2.00132e25 + 3.46639e25i) q^{59} +(2.43597e25 + 4.21923e25i) q^{60} +(-3.93882e25 + 6.82223e25i) q^{61} +3.27175e26 q^{62} +(3.78654e25 - 1.58538e25i) q^{63} +2.54837e26 q^{64} +(1.00411e26 - 1.73918e26i) q^{65} +(9.22809e25 + 1.59835e26i) q^{66} +(-7.64134e25 - 1.32352e26i) q^{67} +(-7.18953e26 + 1.24526e27i) q^{68} +3.46402e26 q^{69} +(-7.47660e25 + 5.85133e26i) q^{70} -7.05299e26 q^{71} +(-4.00206e26 + 6.93177e26i) q^{72} +(1.21511e26 + 2.10463e26i) q^{73} +(2.01668e27 + 3.49298e27i) q^{74} +(-3.08019e26 + 5.33505e26i) q^{75} +1.28962e27 q^{76} +(-2.02374e26 + 1.58382e27i) q^{77} +5.49474e27 q^{78} +(1.18640e25 - 2.05490e25i) q^{79} +(-3.01664e27 - 5.22498e27i) q^{80} +(-2.61674e26 - 4.53232e26i) q^{81} +(1.75539e27 - 3.04043e27i) q^{82} -8.78152e27 q^{83} +(-1.06376e28 + 4.45382e27i) q^{84} +8.11219e27 q^{85} +(1.01468e28 - 1.75747e28i) q^{86} +(-3.97797e27 - 6.89004e27i) q^{87} +(-1.55664e28 - 2.69619e28i) q^{88} +(-5.33170e27 + 9.23477e27i) q^{89} +7.52047e27 q^{90} +(3.78234e28 + 2.87945e28i) q^{91} -9.73154e28 q^{92} +(1.80428e28 - 3.12510e28i) q^{93} +(4.29590e27 + 7.44072e27i) q^{94} +(-3.63781e27 - 6.30087e27i) q^{95} +(3.76172e28 - 6.51549e28i) q^{96} -1.41306e28 q^{97} +(-1.35146e29 - 3.51101e28i) q^{98} +2.03562e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 25025 q^{2} + 90876411 q^{3} - 5448583733 q^{4} - 2101591778 q^{5} + 239387598450 q^{6} - 1147384421099 q^{7} - 53840580588510 q^{8} - 434659056644259 q^{9}+O(q^{10}) \) 38 * q + 25025 * q^2 + 90876411 * q^3 - 5448583733 * q^4 - 2101591778 * q^5 + 239387598450 * q^6 - 1147384421099 * q^7 - 53840580588510 * q^8 - 434659056644259 * q^9	\( 38 q + 25025 q^{2} + 90876411 q^{3} - 5448583733 q^{4} - 2101591778 q^{5} + 239387598450 q^{6} - 1147384421099 q^{7} - 53840580588510 q^{8} - 434659056644259 q^{9} - 226333527764279 q^{10} + 968182184010316 q^{11} + 26\!\cdots\!77 q^{12}+ \cdots - 44\!\cdots\!52 q^{99}+O(q^{100}) \) 38 * q + 25025 * q^2 + 90876411 * q^3 - 5448583733 * q^4 - 2101591778 * q^5 + 239387598450 * q^6 - 1147384421099 * q^7 - 53840580588510 * q^8 - 434659056644259 * q^9 - 226333527764279 * q^10 + 968182184010316 * q^11 + 26060407088843277 * q^12 + 30248752986495458 * q^13 + 188292059868669736 * q^14 - 20103696649657764 * q^15 - 1414287713687569841 * q^16 + 102438111755912556 * q^17 + 572491731185399025 * q^18 - 6872193027481150651 * q^19 + 16866263496288505610 * q^20 - 5139459612060640272 * q^21 + 84243517982597870158 * q^22 + 182508386582843064516 * q^23 - 128758913948422543095 * q^24 - 382162743635168213111 * q^25 + 273922968110752759988 * q^26 - 4157921586997469649942 * q^27 + 446171481016036543439 * q^28 + 281390518253865391744 * q^29 + 1082546246957185764351 * q^30 - 4929614086953636263583 * q^31 + 8866445878410226322935 * q^32 - 4630785372473637108204 * q^33 + 50361339344572132704984 * q^34 - 81794408570709523734766 * q^35 + 249292238466635279498826 * q^36 + 89823590712918979606269 * q^37 - 71913737995612310138956 * q^38 + 72339423911532597127401 * q^39 + 239411588777146294644135 * q^40 - 87942011922863277796324 * q^41 + 42507596433452096284317 * q^42 - 998334377830130582257058 * q^43 - 273085832669135222196817 * q^44 - 48077678930358472910658 * q^45 + 1477208812031594497944852 * q^46 + 663752760815551395364602 * q^47 - 13528988583297044469675858 * q^48 + 12702719376591835722353537 * q^49 - 18072517907683707274881248 * q^50 - 489958312947065322058764 * q^51 + 31739881554208954447778464 * q^52 - 7756933906079396951027112 * q^53 - 2738210203016096789205225 * q^54 + 104982116314469285161107056 * q^55 + 43372930131234039576619953 * q^56 - 65738972424916983296125638 * q^57 + 102453432804996437331910603 * q^58 + 114603050264779854082124610 * q^59 + 40335407724289768694478045 * q^60 - 139825411428909464532671986 * q^61 + 1134093332259905081074973442 * q^62 + 1666599266299329474494571 * q^63 - 148837669255394086765278622 * q^64 + 640556086591054006830698254 * q^65 + 201467067480854076215869551 * q^66 - 56315776880006609951132917 * q^67 - 697317633686048315259709452 * q^68 + 1745863910531508618890056008 * q^69 + 433002366057136467231968657 * q^70 - 1824065145665995608812965764 * q^71 + 615849893888972622524549055 * q^72 + 1789614217588580556564713367 * q^73 - 4257059926604086801593103848 * q^74 + 1827872555761956873095306559 * q^75 + 15166984931487860090924899312 * q^76 + 6892418991139201958931374756 * q^77 + 2620330129723438035374088744 * q^78 + 3126227451212705816416145239 * q^79 + 469705326396281168184173015 * q^80 - 9943605027519850207056718899 * q^81 - 15954412288094954111486068024 * q^82 + 12686840070702737045002032792 * q^83 - 10284086370388485211004655396 * q^84 + 280144859318398185224279400 * q^85 + 14385045580944496750492040974 * q^86 + 672941062851086149442203968 * q^87 - 20844393366380736578332102317 * q^88 - 26279447891842894095818723312 * q^89 + 10355570280525127676264276238 * q^90 - 22701798036712589137512005879 * q^91 - 374697938227250791106256400776 * q^92 + 23578191359862546685993317927 * q^93 + 73717519436348854656628916898 * q^94 - 56410666407609081482857118294 * q^95 - 42407935776613881785582094015 * q^96 + 235542920591717835435096218928 * q^97 - 293433749500426066164790446415 * q^98 - 44297805764389719211578755352 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more