LMFDB - Embedded newform 21.7.b.a.8.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(8,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("21.8");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.b (of order $2$, degree $1$, 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:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 642x^{10} + 155265x^{8} + 17813036x^{6} + 1003321428x^{4} + 26369892864x^{2} + 256461520896 $ x^12 + 642x^10 + 155265x^8 + 17813036x^6 + 1003321428x^4 + 26369892864*x^2 + 256461520896
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{8}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			8.6
Root			$-5.05795i$ of defining polynomial
Character	$\chi$	$=$	21.8
Dual form			21.7.b.a.8.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.05795i q^{2} +(10.0378 - 25.0648i) q^{3} +38.4172 q^{4} -24.8176i q^{5} +(-126.776 - 50.7707i) q^{6} -129.642 q^{7} -518.021i q^{8} +(-527.485 - 503.190i) q^{9} +O(q^{10})$	\(q-5.05795i q^{2} +(10.0378 - 25.0648i) q^{3} +38.4172 q^{4} -24.8176i q^{5} +(-126.776 - 50.7707i) q^{6} -129.642 q^{7} -518.021i q^{8} +(-527.485 - 503.190i) q^{9} -125.526 q^{10} +230.584i q^{11} +(385.624 - 962.917i) q^{12} +690.732 q^{13} +655.722i q^{14} +(-622.046 - 249.114i) q^{15} -161.424 q^{16} +4808.07i q^{17} +(-2545.11 + 2667.99i) q^{18} +11105.9 q^{19} -953.420i q^{20} +(-1301.32 + 3249.44i) q^{21} +1166.28 q^{22} +8678.68i q^{23} +(-12984.1 - 5199.79i) q^{24} +15009.1 q^{25} -3493.69i q^{26} +(-17907.1 + 8170.36i) q^{27} -4980.47 q^{28} -24282.0i q^{29} +(-1260.00 + 3146.28i) q^{30} -7150.68 q^{31} -32336.9i q^{32} +(5779.54 + 2314.56i) q^{33} +24319.0 q^{34} +3217.39i q^{35} +(-20264.5 - 19331.1i) q^{36} +29502.1 q^{37} -56173.1i q^{38} +(6933.44 - 17313.0i) q^{39} -12856.0 q^{40} +102478. i q^{41} +(16435.5 + 6582.01i) q^{42} -108429. q^{43} +8858.39i q^{44} +(-12488.0 + 13090.9i) q^{45} +43896.3 q^{46} +203296. i q^{47} +(-1620.34 + 4046.05i) q^{48} +16807.0 q^{49} -75915.2i q^{50} +(120513. + 48262.4i) q^{51} +26536.0 q^{52} -35192.0i q^{53} +(41325.3 + 90573.4i) q^{54} +5722.54 q^{55} +67157.1i q^{56} +(111479. - 278367. i) q^{57} -122817. q^{58} -224755. i q^{59} +(-23897.2 - 9570.24i) q^{60} -35470.3 q^{61} +36167.8i q^{62} +(68384.1 + 65234.5i) q^{63} -173889. q^{64} -17142.3i q^{65} +(11706.9 - 29232.6i) q^{66} -523102. q^{67} +184712. i q^{68} +(217529. + 87114.9i) q^{69} +16273.4 q^{70} -622802. i q^{71} +(-260663. + 273248. i) q^{72} -99977.5 q^{73} -149220. i q^{74} +(150658. - 376199. i) q^{75} +426658. q^{76} -29893.4i q^{77} +(-87568.5 - 35069.0i) q^{78} +275833. q^{79} +4006.14i q^{80} +(25039.8 + 530851. i) q^{81} +518330. q^{82} +375630. i q^{83} +(-49993.0 + 124834. i) q^{84} +119324. q^{85} +548431. i q^{86} +(-608622. - 243738. i) q^{87} +119447. q^{88} +617008. i q^{89} +(66213.0 + 63163.4i) q^{90} -89547.8 q^{91} +333410. i q^{92} +(-71777.1 + 179230. i) q^{93} +1.02826e6 q^{94} -275622. i q^{95} +(-810516. - 324591. i) q^{96} -1.14802e6 q^{97} -85008.9i q^{98} +(116028. - 121630. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9}+O(q^{10}) $ 12 * q + 52 * q^3 - 516 * q^4 + 350 * q^6 - 644 * q^9	$ 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9} - 1092 q^{10} - 1726 q^{12} + 384 q^{13} - 632 q^{15} + 5892 q^{16} - 40 q^{18} + 11304 q^{19} - 5488 q^{21} + 15312 q^{22} + 12138 q^{24} - 77292 q^{25} + 114796 q^{27} + 41160 q^{28} - 101908 q^{30} - 9360 q^{31} - 65744 q^{33} - 169008 q^{34} - 195652 q^{36} + 212016 q^{37} + 159544 q^{39} + 196644 q^{40} - 37730 q^{42} + 28080 q^{43} - 4760 q^{45} - 418512 q^{46} + 865742 q^{48} + 201684 q^{49} - 371880 q^{51} - 138300 q^{52} - 254170 q^{54} - 732144 q^{55} - 440624 q^{57} + 1164240 q^{58} + 677660 q^{60} + 926736 q^{61} + 2744 q^{63} - 1380108 q^{64} - 1414588 q^{66} - 223104 q^{67} + 153048 q^{69} - 382788 q^{70} - 540192 q^{72} + 600984 q^{73} + 594716 q^{75} + 604596 q^{76} + 1866140 q^{78} - 276864 q^{79} + 617596 q^{81} + 1138200 q^{82} + 1398754 q^{84} - 3002472 q^{85} - 3372824 q^{87} - 1599048 q^{88} - 788032 q^{90} - 1243032 q^{91} + 408168 q^{93} + 8059296 q^{94} - 1141658 q^{96} + 1621416 q^{97} + 5211904 q^{99}+O(q^{100}) $ 12 * q + 52 * q^3 - 516 * q^4 + 350 * q^6 - 644 * q^9 - 1092 * q^10 - 1726 * q^12 + 384 * q^13 - 632 * q^15 + 5892 * q^16 - 40 * q^18 + 11304 * q^19 - 5488 * q^21 + 15312 * q^22 + 12138 * q^24 - 77292 * q^25 + 114796 * q^27 + 41160 * q^28 - 101908 * q^30 - 9360 * q^31 - 65744 * q^33 - 169008 * q^34 - 195652 * q^36 + 212016 * q^37 + 159544 * q^39 + 196644 * q^40 - 37730 * q^42 + 28080 * q^43 - 4760 * q^45 - 418512 * q^46 + 865742 * q^48 + 201684 * q^49 - 371880 * q^51 - 138300 * q^52 - 254170 * q^54 - 732144 * q^55 - 440624 * q^57 + 1164240 * q^58 + 677660 * q^60 + 926736 * q^61 + 2744 * q^63 - 1380108 * q^64 - 1414588 * q^66 - 223104 * q^67 + 153048 * q^69 - 382788 * q^70 - 540192 * q^72 + 600984 * q^73 + 594716 * q^75 + 604596 * q^76 + 1866140 * q^78 - 276864 * q^79 + 617596 * q^81 + 1138200 * q^82 + 1398754 * q^84 - 3002472 * q^85 - 3372824 * q^87 - 1599048 * q^88 - 788032 * q^90 - 1243032 * q^91 + 408168 * q^93 + 8059296 * q^94 - 1141658 * q^96 + 1621416 * q^97 + 5211904 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$8$	$10$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	5.05795i		−	0.632244i	−0.948719	−	0.316122i	$-0.897619\pi$
$2$		−	5.05795i		−	0.632244i	0.948719	−	0.316122i	$-0.102381\pi$
$3$	10.0378	−	25.0648i	0.371771	−	0.928325i
$3$	10.0378	−	25.0648i	0.371771	−	0.928325i
$4$	38.4172			0.600268
$5$		−	24.8176i		−	0.198540i	−0.995061	−	0.0992702i	$-0.968349\pi$
$5$		−	24.8176i		−	0.198540i	0.995061	−	0.0992702i	$-0.0316508\pi$
$6$	−126.776	−	50.7707i	−0.586927	−	0.235050i
$7$	−129.642			−0.377964
$7$	−129.642			−0.377964
$8$		−	518.021i		−	1.01176i
$9$	−527.485	−	503.190i	−0.723573	−	0.690248i
$10$	−125.526			−0.125526
$11$			230.584i			0.173241i	0.996241	+	0.0866207i	$0.0276068\pi$
$11$			230.584i			0.173241i	−0.996241	+	0.0866207i	$0.972393\pi$
$12$	385.624	−	962.917i	0.223162	−	0.557244i
$13$	690.732			0.314398			0.157199	−	0.987567i	$-0.449754\pi$
$13$	690.732			0.314398			0.157199	+	0.987567i	$0.449754\pi$
$14$			655.722i			0.238966i
$15$	−622.046	−	249.114i	−0.184310	−	0.0738115i
$16$	−161.424			−0.0394101
$17$			4808.07i			0.978642i	0.872104	+	0.489321i	$0.162755\pi$
$17$			4808.07i			0.978642i	−0.872104	+	0.489321i	$0.837245\pi$
$18$	−2545.11	+	2667.99i	−0.436405	+	0.457475i
$19$	11105.9			1.61917			0.809587	−	0.587000i	$-0.199691\pi$
$19$	11105.9			1.61917			0.809587	+	0.587000i	$0.199691\pi$
$20$		−	953.420i		−	0.119177i
$21$	−1301.32	+	3249.44i	−0.140516	+	0.350874i
$22$	1166.28			0.109531
$23$			8678.68i			0.713297i	0.934239	+	0.356648i	$0.116081\pi$
$23$			8678.68i			0.713297i	−0.934239	+	0.356648i	$0.883919\pi$
$24$	−12984.1	−	5199.79i	−0.939241	−	0.376142i
$25$	15009.1			0.960582
$26$		−	3493.69i		−	0.198776i
$27$	−17907.1	+	8170.36i	−0.909777	+	0.415097i
$28$	−4980.47			−0.226880
$29$		−	24282.0i		−	0.995612i	−0.867288	−	0.497806i	$-0.834139\pi$
$29$		−	24282.0i		−	0.995612i	0.867288	−	0.497806i	$-0.165861\pi$
$30$	−1260.00	+	3146.28i	−0.0466668	+	0.116529i
$31$	−7150.68			−0.240028			−0.120014	−	0.992772i	$-0.538294\pi$
$31$	−7150.68			−0.240028			−0.120014	+	0.992772i	$0.538294\pi$
$32$		−	32336.9i		−	0.986842i
$33$	5779.54	+	2314.56i	0.160824	+	0.0644061i
$34$	24319.0			0.618740
$35$			3217.39i			0.0750412i
$36$	−20264.5	−	19331.1i	−0.434338	−	0.414334i
$37$	29502.1			0.582435			0.291218	−	0.956657i	$-0.405940\pi$
$37$	29502.1			0.582435			0.291218	+	0.956657i	$0.405940\pi$
$38$		−	56173.1i		−	1.02371i
$39$	6933.44	−	17313.0i	0.116884	−	0.291863i
$40$	−12856.0			−0.200875
$41$			102478.i			1.48690i	0.668794	+	0.743448i	$0.266811\pi$
$41$			102478.i			1.48690i	−0.668794	+	0.743448i	$0.733189\pi$
$42$	16435.5	+	6582.01i	0.221838	+	0.0888404i
$43$	−108429.			−1.36377			−0.681886	−	0.731458i	$-0.738840\pi$
$43$	−108429.			−1.36377			−0.681886	+	0.731458i	$0.738840\pi$
$44$			8858.39i			0.103991i
$45$	−12488.0	+	13090.9i	−0.137042	+	0.143659i
$46$	43896.3			0.450977
$47$			203296.i			1.95810i	0.203613	+	0.979051i	$0.434732\pi$
$47$			203296.i			1.95810i	−0.203613	+	0.979051i	$0.565268\pi$
$48$	−1620.34	+	4046.05i	−0.0146515	+	0.0365854i
$49$	16807.0			0.142857
$50$		−	75915.2i		−	0.607322i
$51$	120513.	+	48262.4i	0.908497	+	0.363830i
$52$	26536.0			0.188723
$53$		−	35192.0i		−	0.236383i	−0.992991	−	0.118192i	$-0.962290\pi$
$53$		−	35192.0i		−	0.236383i	0.992991	−	0.118192i	$-0.0377097\pi$
$54$	41325.3	+	90573.4i	0.262443	+	0.575201i
$55$	5722.54			0.0343954
$56$			67157.1i			0.382409i
$57$	111479.	−	278367.i	0.601961	−	1.50312i
$58$	−122817.			−0.629469
$59$		−	224755.i		−	1.09434i	−0.837021	−	0.547170i	$-0.815705\pi$
$59$		−	224755.i		−	1.09434i	0.837021	−	0.547170i	$-0.184295\pi$
$60$	−23897.2	−	9570.24i	−0.110635	−	0.0443067i
$61$	−35470.3			−0.156270			−0.0781350	−	0.996943i	$-0.524897\pi$
$61$	−35470.3			−0.156270			−0.0781350	+	0.996943i	$0.524897\pi$
$62$			36167.8i			0.151756i
$63$	68384.1	+	65234.5i	0.273485	+	0.260889i
$64$	−173889.			−0.663335
$65$		−	17142.3i		−	0.0624207i
$66$	11706.9	−	29232.6i	0.0407203	−	0.101680i
$67$	−523102.			−1.73925			−0.869624	−	0.493714i	$-0.835639\pi$
$67$	−523102.			−1.73925			−0.869624	+	0.493714i	$0.835639\pi$
$68$			184712.i			0.587447i
$69$	217529.	+	87114.9i	0.662171	+	0.265183i
$70$	16273.4			0.0474443
$71$		−	622802.i		−	1.74010i	−0.492961	−	0.870052i	$-0.664085\pi$
$71$		−	622802.i		−	1.74010i	0.492961	−	0.870052i	$-0.335915\pi$
$72$	−260663.	+	273248.i	−0.698364	+	0.732082i
$73$	−99977.5			−0.257000			−0.128500	−	0.991709i	$-0.541016\pi$
$73$	−99977.5			−0.257000			−0.128500	+	0.991709i	$0.541016\pi$
$74$		−	149220.i		−	0.368241i
$75$	150658.	−	376199.i	0.357116	−	0.891732i
$76$	426658.			0.971938
$77$		−	29893.4i		−	0.0654791i
$78$	−87568.5	−	35069.0i	−0.184529	−	0.0738991i
$79$	275833.			0.559454			0.279727	−	0.960080i	$-0.409756\pi$
$79$	275833.			0.559454			0.279727	+	0.960080i	$0.409756\pi$
$80$			4006.14i			0.00782450i
$81$	25039.8	+	530851.i	0.0471167	+	0.998889i
$82$	518330.			0.940080
$83$			375630.i			0.656940i	0.944514	+	0.328470i	$0.106533\pi$
$83$			375630.i			0.656940i	−0.944514	+	0.328470i	$0.893467\pi$
$84$	−49993.0	+	124834.i	−0.0843473	+	0.210618i
$85$	119324.			0.194300
$86$			548431.i			0.862237i
$87$	−608622.	−	243738.i	−0.924251	−	0.370139i
$88$	119447.			0.175279
$89$			617008.i			0.875227i	0.899163	+	0.437614i	$0.144176\pi$
$89$			617008.i			0.875227i	−0.899163	+	0.437614i	$0.855824\pi$
$90$	66213.0	+	63163.4i	0.0908272	+	0.0866439i
$91$	−89547.8			−0.118831
$92$			333410.i			0.428169i
$93$	−71777.1	+	179230.i	−0.0892354	+	0.222824i
$94$	1.02826e6			1.23800
$95$		−	275622.i		−	0.321471i
$96$	−810516.	−	324591.i	−0.916110	−	0.366879i
$97$	−1.14802e6			−1.25787			−0.628933	−	0.777460i	$-0.716508\pi$
$97$	−1.14802e6			−1.25787			−0.628933	+	0.777460i	$0.716508\pi$
$98$		−	85008.9i		−	0.0903205i
$99$	116028.	−	121630.i	0.119579	−	0.125353i
$100$	576607.			0.576607
$101$			106534.i			0.103401i	0.998663	+	0.0517004i	$0.0164641\pi$
$101$			106534.i			0.103401i	−0.998663	+	0.0517004i	$0.983536\pi$
$102$	244109.	−	609549.i	0.230029	−	0.574391i
$103$	21323.9			0.0195144			0.00975719	−	0.999952i	$-0.496894\pi$
$103$	21323.9			0.0195144			0.00975719	+	0.999952i	$0.496894\pi$
$104$		−	357814.i		−	0.318095i
$105$	80643.2	+	32295.6i	0.0696626	+	0.0278981i
$106$	−178000.			−0.149452
$107$		−	1.89640e6i		−	1.54803i	−0.633168	−	0.774014i	$-0.718246\pi$
$107$		−	1.89640e6i		−	1.54803i	0.633168	−	0.774014i	$-0.281754\pi$
$108$	−687941.	+	313882.i	−0.546110	+	0.249170i
$109$	551935.			0.426195			0.213097	−	0.977031i	$-0.431645\pi$
$109$	551935.			0.426195			0.213097	+	0.977031i	$0.431645\pi$
$110$		−	28944.3i		−	0.0217463i
$111$	296136.	−	739463.i	0.216532	−	0.540689i
$112$	20927.3			0.0148956
$113$			2.03418e6i			1.40979i	0.709314	+	0.704893i	$0.249005\pi$
$113$			2.03418e6i			1.40979i	−0.709314	+	0.704893i	$0.750995\pi$
$114$	−1.40797e6	−	563855.i	−0.950337	−	0.380586i
$115$	215384.			0.141618
$116$		−	932845.i		−	0.597634i
$117$	−364351.	−	347570.i	−0.227490	−	0.217012i
$118$	−1.13680e6			−0.691890
$119$		−	623326.i		−	0.369892i
$120$	−129046.	+	322233.i	−0.0746794	+	0.186477i
$121$	1.71839e6			0.969987
$122$			179407.i			0.0988006i
$123$	2.56859e6	+	1.02866e6i	1.38032	+	0.552784i
$124$	−274709.			−0.144081
$125$		−	760263.i		−	0.389255i
$126$	329953.	−	345883.i	0.164945	−	0.172909i
$127$	−1.27146e6			−0.620715			−0.310357	−	0.950620i	$-0.600449\pi$
$127$	−1.27146e6			−0.620715			−0.310357	+	0.950620i	$0.600449\pi$
$128$		−	1.19004e6i		−	0.567453i
$129$	−1.08839e6	+	2.71776e6i	−0.507011	+	1.26602i
$130$	−86704.8			−0.0394651
$131$		−	719484.i		−	0.320042i	−0.987114	−	0.160021i	$-0.948844\pi$
$131$		−	719484.i		−	0.320042i	0.987114	−	0.160021i	$-0.0511562\pi$
$132$	222034.	+	88918.8i	0.0965377	+	0.0386609i
$133$	−1.43979e6			−0.611990
$134$			2.64582e6i			1.09963i
$135$	202768.	+	444411.i	0.0824136	+	0.180628i
$136$	2.49068e6			0.990150
$137$			2.85051e6i			1.10856i	0.832329	+	0.554282i	$0.187007\pi$
$137$			2.85051e6i			1.10856i	−0.832329	+	0.554282i	$0.812993\pi$
$138$	440623.	−	1.10025e6i	0.167660	−	0.418653i
$139$	−973777.			−0.362589			−0.181295	−	0.983429i	$-0.558029\pi$
$139$	−973777.			−0.362589			−0.181295	+	0.983429i	$0.558029\pi$
$140$			123603.i			0.0450449i
$141$	5.09557e6	+	2.04065e6i	1.81776	+	0.727965i
$142$	−3.15010e6			−1.10017
$143$			159272.i			0.0544668i
$144$	85148.6	+	81226.9i	0.0285161	+	0.0272027i
$145$	−602620.			−0.197669
$146$			505681.i			0.162487i
$147$	168705.	−	421264.i	0.0531101	−	0.132618i
$148$	1.13339e6			0.349617
$149$			2.91215e6i			0.880350i	0.897912	+	0.440175i	$0.145084\pi$
$149$			2.91215e6i			0.880350i	−0.897912	+	0.440175i	$0.854916\pi$
$150$	−1.90280e6	−	762022.i	−0.563792	−	0.225784i
$151$	−5.49247e6			−1.59528			−0.797640	−	0.603133i	$-0.793919\pi$
$151$	−5.49247e6			−1.59528			−0.797640	+	0.603133i	$0.793919\pi$
$152$		−	5.75309e6i		−	1.63821i
$153$	2.41937e6	−	2.53618e6i	0.675505	−	0.708119i
$154$	−151199.			−0.0413987
$155$			177462.i			0.0476553i
$156$	266363.	−	665118.i	0.0701617	−	0.175196i
$157$	4.14432e6			1.07091			0.535457	−	0.844562i	$-0.320139\pi$
$157$	4.14432e6			1.07091			0.535457	+	0.844562i	$0.320139\pi$
$158$		−	1.39515e6i		−	0.353711i
$159$	−882080.	−	353251.i	−0.219441	−	0.0878804i
$160$	−802521.			−0.195928
$161$		−	1.12512e6i		−	0.269601i
$162$	2.68502e6	−	126650.i	0.631541	−	0.0297893i
$163$	1.41248e6			0.326151			0.163076	−	0.986614i	$-0.447859\pi$
$163$	1.41248e6			0.326151			0.163076	+	0.986614i	$0.447859\pi$
$164$			3.93692e6i			0.892536i
$165$	57441.7	−	143434.i	0.0127872	−	0.0319301i
$166$	1.89992e6			0.415346
$167$		−	7.57450e6i		−	1.62631i	−0.582045	−	0.813157i	$-0.697747\pi$
$167$		−	7.57450e6i		−	1.62631i	0.582045	−	0.813157i	$-0.302253\pi$
$168$	1.68328e6	+	674110.i	0.355000	+	0.142168i
$169$	−4.34970e6			−0.901154
$170$		−	603537.i		−	0.122845i
$171$	−5.85820e6	−	5.58839e6i	−1.17159	−	1.11763i
$172$	−4.16555e6			−0.818629
$173$			955257.i			0.184494i	0.995736	+	0.0922469i	$0.0294049\pi$
$173$			955257.i			0.184494i	−0.995736	+	0.0922469i	$0.970595\pi$
$174$	−1.23281e6	+	3.07838e6i	−0.234018	+	0.584352i
$175$	−1.94581e6			−0.363066
$176$		−	37221.8i		−	0.00682746i
$177$	−5.63342e6	−	2.25604e6i	−1.01590	−	0.406844i
$178$	3.12080e6			0.553357
$179$			6.09170e6i			1.06214i	0.847329	+	0.531068i	$0.178209\pi$
$179$			6.09170e6i			1.06214i	−0.847329	+	0.531068i	$0.821791\pi$
$180$	−479752.	+	502915.i	−0.0822620	+	0.0862336i
$181$	3.91245e6			0.659802			0.329901	−	0.944016i	$-0.392985\pi$
$181$	3.91245e6			0.659802			0.329901	+	0.944016i	$0.392985\pi$
$182$			452928.i			0.0751303i
$183$	−356044.	+	889055.i	−0.0580966	+	0.145069i
$184$	4.49574e6			0.721684
$185$		−	732169.i		−	0.115637i
$186$	906536.	+	363045.i	0.140879	+	0.0564185i
$187$	−1.10866e6			−0.169541
$188$			7.81006e6i			1.17539i
$189$	2.32151e6	−	1.05922e6i	0.343863	−	0.156892i
$190$	−1.39408e6			−0.203248
$191$			1.02097e6i			0.146525i	0.997313	+	0.0732627i	$0.0233411\pi$
$191$			1.02097e6i			0.146525i	−0.997313	+	0.0732627i	$0.976659\pi$
$192$	−1.74547e6	+	4.35849e6i	−0.246608	+	0.615790i
$193$	8.60150e6			1.19647			0.598236	−	0.801320i	$-0.295869\pi$
$193$	8.60150e6			1.19647			0.598236	+	0.801320i	$0.295869\pi$
$194$			5.80663e6i			0.795278i
$195$	−429667.	−	172071.i	−0.0579467	−	0.0232062i
$196$	645677.			0.0857526
$197$		−	1.15308e7i		−	1.50821i	−0.656753	−	0.754106i	$-0.728071\pi$
$197$		−	1.15308e7i		−	1.50821i	0.656753	−	0.754106i	$-0.271929\pi$
$198$	−615197.	−	586863.i	−0.0792535	−	0.0756033i
$199$	1.31963e7			1.67452			0.837262	−	0.546802i	$-0.184155\pi$
$199$	1.31963e7			1.67452			0.837262	+	0.546802i	$0.184155\pi$
$200$		−	7.77502e6i		−	0.971877i
$201$	−5.25079e6	+	1.31114e7i	−0.646601	+	1.61459i
$202$	538844.			0.0653745
$203$			3.14796e6i			0.376306i
$204$	4.62977e6	+	1.85411e6i	0.545342	+	0.218396i
$205$	2.54326e6			0.295209
$206$		−	107855.i		−	0.0123378i
$207$	4.36703e6	−	4.57787e6i	0.492351	−	0.516122i
$208$	−111501.			−0.0123905
$209$			2.56085e6i			0.280508i
$210$	163349.	−	407889.i	0.0176384	−	0.0440437i
$211$	−7.77953e6			−0.828144			−0.414072	−	0.910244i	$-0.635894\pi$
$211$	−7.77953e6			−0.828144			−0.414072	+	0.910244i	$0.635894\pi$
$212$		−	1.35198e6i		−	0.141893i
$213$	−1.56104e7	−	6.25156e6i	−1.61538	−	0.646919i
$214$	−9.59190e6			−0.978731
$215$			2.69095e6i			0.270764i
$216$	4.23242e6	+	9.27627e6i	0.419978	+	0.920475i
$217$	927027.			0.0907221
$218$		−	2.79166e6i		−	0.269459i
$219$	−1.00355e6	+	2.50591e6i	−0.0955452	+	0.238580i
$220$	219844.			0.0206465
$221$			3.32109e6i			0.307683i
$222$	−3.74016e6	−	1.49784e6i	−0.341847	−	0.136901i
$223$	−1.23203e7			−1.11098			−0.555492	−	0.831522i	$-0.687470\pi$
$223$	−1.23203e7			−1.11098			−0.555492	+	0.831522i	$0.687470\pi$
$224$			4.19221e6i			0.372991i
$225$	−7.91707e6	−	7.55243e6i	−0.695051	−	0.663039i
$226$	1.02888e7			0.891328
$227$		−	1.68616e7i		−	1.44152i	−0.693182	−	0.720762i	$-0.743792\pi$
$227$		−	1.68616e7i		−	1.44152i	0.693182	−	0.720762i	$-0.256208\pi$
$228$	4.28271e6	−	1.06941e7i	0.361338	−	0.902274i
$229$	1.88076e7			1.56613			0.783064	−	0.621941i	$-0.213656\pi$
$229$	1.88076e7			1.56613			0.783064	+	0.621941i	$0.213656\pi$
$230$		−	1.08940e6i		−	0.0895372i
$231$	−749270.	−	300064.i	−0.0607859	−	0.0243432i
$232$	−1.25786e7			−1.00732
$233$			1.08234e7i			0.855647i	0.903862	+	0.427824i	$0.140720\pi$
$233$			1.08234e7i			0.855647i	−0.903862	+	0.427824i	$0.859280\pi$
$234$	−1.75799e6	+	1.84287e6i	−0.137205	+	0.143829i
$235$	5.04531e6			0.388763
$236$		−	8.63443e6i		−	0.656898i
$237$	2.76876e6	−	6.91369e6i	0.207989	−	0.519355i
$238$	−3.15275e6			−0.233862
$239$		−	9.41829e6i		−	0.689888i	−0.938623	−	0.344944i	$-0.887898\pi$
$239$		−	9.41829e6i		−	0.689888i	0.938623	−	0.344944i	$-0.112102\pi$
$240$	100413.	+	40212.9i	0.00726368	+	0.00290892i
$241$	−1.15621e7			−0.826010			−0.413005	−	0.910729i	$-0.635521\pi$
$241$	−1.15621e7			−0.826010			−0.413005	+	0.910729i	$0.635521\pi$
$242$		−	8.69154e6i		−	0.613268i
$243$	1.35570e7	+	4.70096e6i	0.944810	+	0.327618i
$244$	−1.36267e6			−0.0938038
$245$		−	417109.i		−	0.0283629i
$246$	5.20289e6	−	1.29918e7i	0.349494	−	0.872699i
$247$	7.67121e6			0.509065
$248$			3.70420e6i			0.242851i
$249$	9.41507e6	+	3.77050e6i	0.609853	+	0.244231i
$250$	−3.84537e6			−0.246104
$251$			1.73215e7i			1.09538i	0.836682	+	0.547689i	$0.184492\pi$
$251$			1.73215e7i			1.09538i	−0.836682	+	0.547689i	$0.815508\pi$
$252$	2.62712e6	+	2.50612e6i	0.164164	+	0.156603i
$253$	−2.00117e6			−0.123573
$254$			6.43099e6i			0.392443i
$255$	1.19776e6	−	2.99084e6i	0.0722350	−	0.180373i
$256$	−1.71481e7			−1.02210
$257$			1.19973e6i			0.0706779i	0.999375	+	0.0353390i	$0.0112511\pi$
$257$			1.19973e6i			0.0706779i	−0.999375	+	0.0353390i	$0.988749\pi$
$258$	1.37463e7	+	5.50504e6i	0.800435	+	0.320554i
$259$	−3.82470e6			−0.220140
$260$		−	658558.i		−	0.0374692i
$261$	−1.22185e7	+	1.28084e7i	−0.687219	+	0.720399i
$262$	−3.63911e6			−0.202345
$263$			2.34931e7i			1.29144i	0.763575	+	0.645719i	$0.223442\pi$
$263$			2.34931e7i			1.29144i	−0.763575	+	0.645719i	$0.776558\pi$
$264$	1.19899e6	−	2.99392e6i	0.0651634	−	0.162715i
$265$	−873381.			−0.0469317
$266$			7.28239e6i			0.386927i
$267$	1.54652e7	+	6.19341e6i	0.812495	+	0.325384i
$268$	−2.00961e7			−1.04402
$269$			1.36239e7i			0.699912i	0.936766	+	0.349956i	$0.113804\pi$
$269$			1.36239e7i			0.699912i	−0.936766	+	0.349956i	$0.886196\pi$
$270$	2.24781e6	−	1.02559e6i	0.114201	−	0.0521055i
$271$	1.38490e6			0.0695843			0.0347922	−	0.999395i	$-0.488923\pi$
$271$	1.38490e6			0.0695843			0.0347922	+	0.999395i	$0.488923\pi$
$272$		−	776137.i		−	0.0385684i
$273$	−898863.	+	2.24449e6i	−0.0441780	+	0.110314i
$274$	1.44177e7			0.700883
$275$			3.46086e6i			0.166413i
$276$	8.35685e6	+	3.34671e6i	0.397480	+	0.159181i
$277$	−9.21086e6			−0.433372			−0.216686	−	0.976241i	$-0.569525\pi$
$277$	−9.21086e6			−0.433372			−0.216686	+	0.976241i	$0.569525\pi$
$278$			4.92531e6i			0.229245i
$279$	3.77188e6	+	3.59815e6i	0.173678	+	0.165679i
$280$	1.66668e6			0.0759236
$281$		−	1.91243e7i		−	0.861921i	−0.902371	−	0.430961i	$-0.858175\pi$
$281$		−	1.91243e7i		−	0.861921i	0.902371	−	0.430961i	$-0.141825\pi$
$282$	1.03215e7	−	2.57731e7i	0.460251	−	1.14926i
$283$	1.59127e7			0.702076			0.351038	−	0.936361i	$-0.385829\pi$
$283$	1.59127e7			0.702076			0.351038	+	0.936361i	$0.385829\pi$
$284$		−	2.39263e7i		−	1.04453i
$285$	−6.90839e6	−	2.76664e6i	−0.298430	−	0.119514i
$286$	805590.			0.0344363
$287$		−	1.32855e7i		−	0.561994i
$288$	−1.62716e7	+	1.70572e7i	−0.681166	+	0.714053i
$289$	1.02007e6			0.0422605
$290$			3.04802e6i			0.124975i
$291$	−1.15236e7	+	2.87749e7i	−0.467638	+	1.16771i
$292$	−3.84085e6			−0.154269
$293$		−	2.62096e7i		−	1.04198i	−0.853564	−	0.520988i	$-0.825564\pi$
$293$		−	2.62096e7i		−	1.04198i	0.853564	−	0.520988i	$-0.174436\pi$
$294$	−2.13073e6	−	853303.i	−0.0838468	−	0.0335785i
$295$	−5.57786e6			−0.217271
$296$		−	1.52827e7i		−	0.589284i
$297$	−1.88396e6	−	4.12911e6i	−0.0719120	−	0.157611i
$298$	1.47295e7			0.556596
$299$			5.99465e6i			0.224259i
$300$	5.78786e6	−	1.44525e7i	0.214365	−	0.535278i
$301$	1.40570e7			0.515458
$302$			2.77806e7i			1.00861i
$303$	2.67025e6	+	1.06937e6i	0.0959896	+	0.0384414i
$304$	−1.79276e6			−0.0638118
$305$			880286.i			0.0310259i
$306$	−1.28279e7	−	1.22371e7i	−0.447704	−	0.427084i
$307$	−1.56647e7			−0.541384			−0.270692	−	0.962666i	$-0.587253\pi$
$307$	−1.56647e7			−0.541384			−0.270692	+	0.962666i	$0.587253\pi$
$308$		−	1.14842e6i		−	0.0393050i
$309$	214045.	−	534478.i	0.00725487	−	0.0181157i
$310$	897595.			0.0301297
$311$		−	1.54014e7i		−	0.512011i	−0.966675	−	0.256006i	$-0.917593\pi$
$311$		−	1.54014e7i		−	0.512011i	0.966675	−	0.256006i	$-0.0824065\pi$
$312$	−8.96852e6	−	3.59166e6i	−0.295296	−	0.118258i
$313$	−1.75634e7			−0.572763			−0.286382	−	0.958116i	$-0.592453\pi$
$313$	−1.75634e7			−0.572763			−0.286382	+	0.958116i	$0.592453\pi$
$314$		−	2.09618e7i		−	0.677079i
$315$	1.61896e6	−	1.69713e6i	0.0517970	−	0.0542978i
$316$	1.05967e7			0.335823
$317$		−	3.77721e7i		−	1.18575i	−0.805294	−	0.592876i	$-0.797992\pi$
$317$		−	3.77721e7i		−	1.18575i	0.805294	−	0.592876i	$-0.202008\pi$
$318$	−1.78672e6	+	4.46152e6i	−0.0555618	+	0.138740i
$319$	5.59905e6			0.172481
$320$			4.31551e6i			0.131699i
$321$	−4.75329e7	−	1.90357e7i	−1.43707	−	0.575511i
$322$	−5.69080e6			−0.170453
$323$			5.33980e7i			1.58459i
$324$	961957.	+	2.03938e7i	0.0282827	+	0.599601i
$325$	1.03673e7			0.302005
$326$		−	7.14424e6i		−	0.206207i
$327$	5.54021e6	−	1.38341e7i	0.158447	−	0.395647i
$328$	5.30859e7			1.50438
$329$		−	2.63557e7i		−	0.740093i
$330$	−725482.	−	290537.i	−0.0201876	−	0.00808463i
$331$	−3.53421e6			−0.0974559			−0.0487279	−	0.998812i	$-0.515517\pi$
$331$	−3.53421e6			−0.0974559			−0.0487279	+	0.998812i	$0.515517\pi$
$332$			1.44306e7i			0.394340i
$333$	−1.55619e7	−	1.48452e7i	−0.421434	−	0.402024i
$334$	−3.83114e7			−1.02823
$335$			1.29821e7i			0.345311i
$336$	210064.	−	524537.i	0.00553775	−	0.0138280i
$337$	4.61131e7			1.20485			0.602427	−	0.798174i	$-0.294201\pi$
$337$	4.61131e7			1.20485			0.602427	+	0.798174i	$0.294201\pi$
$338$			2.20005e7i			0.569749i
$339$	5.09862e7	+	2.04187e7i	1.30874	+	0.524117i
$340$	4.58411e6			0.116632
$341$		−	1.64883e6i		−	0.0415828i
$342$	−2.82658e7	+	2.96305e7i	−0.706615	+	0.740731i
$343$	−2.17889e6			−0.0539949
$344$			5.61687e7i			1.37981i
$345$	2.16198e6	−	5.39854e6i	0.0526495	−	0.131468i
$346$	4.83164e6			0.116645
$347$			2.66807e7i			0.638571i	0.947659	+	0.319285i	$0.103443\pi$
$347$			2.66807e7i			0.638571i	−0.947659	+	0.319285i	$0.896557\pi$
$348$	−2.33815e7	−	9.36372e6i	−0.554799	−	0.222183i
$349$	1.06810e7			0.251268			0.125634	−	0.992077i	$-0.459904\pi$
$349$	1.06810e7			0.251268			0.125634	+	0.992077i	$0.459904\pi$
$350$			9.84178e6i			0.229546i
$351$	−1.23690e7	+	5.64353e6i	−0.286032	+	0.130506i
$352$	7.45637e6			0.170962
$353$			6.31242e6i			0.143506i	0.997422	+	0.0717532i	$0.0228594\pi$
$353$			6.31242e6i			0.143506i	−0.997422	+	0.0717532i	$0.977141\pi$
$354$	−1.14109e7	+	2.84936e7i	−0.257224	+	0.642298i
$355$	−1.54564e7			−0.345481
$356$			2.37037e7i			0.525371i
$357$	−1.56235e7	−	6.25683e6i	−0.343380	−	0.137515i
$358$	3.08115e7			0.671528
$359$		−	2.70408e7i		−	0.584436i	−0.956352	−	0.292218i	$-0.905607\pi$
$359$		−	2.70408e7i		−	0.584436i	0.956352	−	0.292218i	$-0.0943933\pi$
$360$	6.78135e6	+	6.46902e6i	0.145348	+	0.138654i
$361$	7.62954e7			1.62172
$362$		−	1.97890e7i		−	0.417155i
$363$	1.72489e7	−	4.30711e7i	0.360613	−	0.900463i
$364$	−3.44017e6			−0.0713306
$365$			2.48120e6i			0.0510250i
$366$	4.49679e6	+	1.80085e6i	0.0917191	+	0.0367312i
$367$	−7.63777e7			−1.54514			−0.772571	−	0.634928i	$-0.781030\pi$
$367$	−7.63777e7			−1.54514			−0.772571	+	0.634928i	$0.781030\pi$
$368$		−	1.40095e6i		−	0.0281111i
$369$	5.15661e7	−	5.40558e7i	1.02633	−	1.07588i
$370$	−3.70328e6			−0.0731107
$371$			4.56236e6i			0.0893445i
$372$	−2.75747e6	+	6.88551e6i	−0.0535652	+	0.133754i
$373$	−5.76666e7			−1.11121			−0.555607	−	0.831445i	$-0.687514\pi$
$373$	−5.76666e7			−1.11121			−0.555607	+	0.831445i	$0.687514\pi$
$374$			5.60757e6i			0.107191i
$375$	−1.90558e7	−	7.63137e6i	−0.361355	−	0.144713i
$376$	1.05312e8			1.98113
$377$		−	1.67724e7i		−	0.313019i
$378$	−5.35748e6	−	1.17421e7i	−0.0991940	−	0.217405i
$379$	−3.28161e7			−0.602795			−0.301397	−	0.953499i	$-0.597453\pi$
$379$	−3.28161e7			−0.602795			−0.301397	+	0.953499i	$0.597453\pi$
$380$		−	1.05886e7i		−	0.192969i
$381$	−1.27627e7	+	3.18689e7i	−0.230764	+	0.576225i
$382$	5.16401e6			0.0926397
$383$		−	3.06896e7i		−	0.546254i	−0.961978	−	0.273127i	$-0.911942\pi$
$383$		−	3.06896e7i		−	0.546254i	0.961978	−	0.273127i	$-0.0880579\pi$
$384$	−2.98280e7	−	1.19453e7i	−0.526781	−	0.210962i
$385$	−741880.			−0.0130002
$386$		−	4.35060e7i		−	0.756461i
$387$	5.71949e7	+	5.45607e7i	0.986790	+	0.941341i
$388$	−4.41037e7			−0.755057
$389$		−	8.48450e6i		−	0.144138i	−0.997400	−	0.0720688i	$-0.977040\pi$
$389$		−	8.48450e6i		−	0.144138i	0.997400	−	0.0720688i	$-0.0229601\pi$
$390$	−870326.	+	2.17324e6i	−0.0146720	+	0.0366364i
$391$	−4.17277e7			−0.698062
$392$		−	8.70637e6i		−	0.144537i
$393$	−1.80337e7	−	7.22204e6i	−0.297103	−	0.118982i
$394$	−5.83224e7			−0.953557
$395$		−	6.84550e6i		−	0.111074i
$396$	4.45746e6	−	4.67267e6i	0.0717797	−	0.0752453i
$397$	−7.06433e7			−1.12902			−0.564508	−	0.825428i	$-0.690934\pi$
$397$	−7.06433e7			−1.12902			−0.564508	+	0.825428i	$0.690934\pi$
$398$		−	6.67460e7i		−	1.05871i
$399$	−1.44523e7	+	3.60880e7i	−0.227520	+	0.568125i
$400$	−2.42282e6			−0.0378566
$401$		−	3.52542e7i		−	0.546736i	−0.961910	−	0.273368i	$-0.911862\pi$
$401$		−	3.52542e7i		−	0.546736i	0.961910	−	0.273368i	$-0.0881376\pi$
$402$	6.63169e7	+	2.65582e7i	1.02081	+	0.408809i
$403$	−4.93921e6			−0.0754644
$404$			4.09273e6i			0.0620682i
$405$	1.31744e7	−	621426.i	0.198320	−	0.00935458i
$406$	1.59222e7			0.237917
$407$			6.80272e6i			0.100902i
$408$	2.50009e7	−	6.24283e7i	0.368108	−	0.919180i
$409$	−8.93055e7			−1.30529			−0.652647	−	0.757662i	$-0.726341\pi$
$409$	−8.93055e7			−1.30529			−0.652647	+	0.757662i	$0.726341\pi$
$410$		−	1.28637e7i		−	0.186644i
$411$	7.14474e7	+	2.86129e7i	1.02911	+	0.412132i
$412$	819204.			0.0117139
$413$			2.91376e7i			0.413622i
$414$	−2.31546e7	−	2.20882e7i	−0.326315	−	0.311286i
$415$	9.32221e6			0.130429
$416$		−	2.23361e7i		−	0.310261i
$417$	−9.77458e6	+	2.44075e7i	−0.134800	+	0.336601i
$418$	1.29526e7			0.177349
$419$			8.05066e7i			1.09443i	0.836991	+	0.547217i	$0.184313\pi$
$419$			8.05066e7i			1.09443i	−0.836991	+	0.547217i	$0.815687\pi$
$420$	3.09808e6	+	1.24070e6i	0.0418162	+	0.0167463i
$421$	6.22934e7			0.834825			0.417413	−	0.908717i	$-0.362937\pi$
$421$	6.22934e7			0.834825			0.417413	+	0.908717i	$0.362937\pi$
$422$			3.93484e7i			0.523589i
$423$	1.02297e8	−	1.07236e8i	1.35158	−	1.41683i
$424$	−1.82302e7			−0.239163
$425$			7.21647e7i			0.940065i
$426$	−3.16201e7	+	7.89565e7i	−0.409010	+	1.02131i
$427$	4.59843e6			0.0590645
$428$		−	7.28544e7i		−	0.929232i
$429$	3.99212e6	+	1.59874e6i	0.0505628	+	0.0202491i
$430$	1.36107e7			0.171189
$431$		−	6.89532e7i		−	0.861237i	−0.902534	−	0.430619i	$-0.858295\pi$
$431$		−	6.89532e7i		−	0.861237i	0.902534	−	0.430619i	$-0.141705\pi$
$432$	2.89064e6	−	1.31889e6i	0.0358544	−	0.0163590i
$433$	7.87562e7			0.970110			0.485055	−	0.874484i	$-0.338800\pi$
$433$	7.87562e7			0.970110			0.485055	+	0.874484i	$0.338800\pi$
$434$		−	4.68885e6i		−	0.0573585i
$435$	−6.04898e6	+	1.51045e7i	−0.0734876	+	0.183501i
$436$	2.12038e7			0.255831
$437$			9.63846e7i			1.15495i
$438$	1.26748e7	+	5.07593e6i	0.150841	+	0.0604078i
$439$	−7.00109e7			−0.827508			−0.413754	−	0.910389i	$-0.635783\pi$
$439$	−7.00109e7			−0.827508			−0.413754	+	0.910389i	$0.635783\pi$
$440$		−	2.96439e6i		−	0.0347999i
$441$	−8.86544e6	−	8.45712e6i	−0.103368	−	0.0986068i
$442$	1.67979e7			0.194531
$443$			1.12349e8i			1.29229i	0.763216	+	0.646143i	$0.223619\pi$
$443$			1.12349e8i			1.29229i	−0.763216	+	0.646143i	$0.776381\pi$
$444$	1.13767e7	−	2.84081e7i	0.129977	−	0.324558i
$445$	1.53126e7			0.173768
$446$			6.23156e7i			0.702413i
$447$	7.29924e7	+	2.92316e7i	0.817251	+	0.327288i
$448$	2.25433e7			0.250717
$449$		−	5.57815e7i		−	0.616242i	−0.951347	−	0.308121i	$-0.900300\pi$
$449$		−	5.57815e7i		−	0.616242i	0.951347	−	0.308121i	$-0.0997002\pi$
$450$	−3.81998e7	+	4.00441e7i	−0.419202	+	0.439442i
$451$	−2.36299e7			−0.257592
$452$			7.81473e7i			0.846250i
$453$	−5.51324e7	+	1.37668e8i	−0.593078	+	1.48094i
$454$	−8.52853e7			−0.911395
$455$			2.22236e6i			0.0235928i
$456$	−1.44200e8	−	5.77484e7i	−1.52079	−	0.609040i
$457$	7.88955e7			0.826616			0.413308	−	0.910591i	$-0.364373\pi$
$457$	7.88955e7			0.826616			0.413308	+	0.910591i	$0.364373\pi$
$458$		−	9.51280e7i		−	0.990175i
$459$	−3.92836e7	−	8.60987e7i	−0.406231	−	0.890346i
$460$	8.27443e6			0.0850089
$461$			8.57691e7i			0.875444i	0.899110	+	0.437722i	$0.144215\pi$
$461$			8.57691e7i			0.875444i	−0.899110	+	0.437722i	$0.855785\pi$
$462$	−1.51771e6	+	3.78977e6i	−0.0153908	+	0.0384315i
$463$	−8.76401e7			−0.882998			−0.441499	−	0.897262i	$-0.645553\pi$
$463$	−8.76401e7			−0.882998			−0.441499	+	0.897262i	$0.645553\pi$
$464$			3.91969e6i			0.0392372i
$465$	4.44805e6	+	1.78133e6i	0.0442396	+	0.0177168i
$466$	5.47441e7			0.540978
$467$		−	6.79717e6i		−	0.0667387i	−0.999443	−	0.0333694i	$-0.989376\pi$
$467$		−	6.79717e6i		−	0.0667387i	0.999443	−	0.0333694i	$-0.0106238\pi$
$468$	−1.39973e7	−	1.33526e7i	−0.136555	−	0.130266i
$469$	6.78158e7			0.657374
$470$		−	2.55189e7i		−	0.245793i
$471$	4.15999e7	−	1.03877e8i	0.398134	−	0.994156i
$472$	−1.16428e8			−1.10721
$473$		−	2.50021e7i		−	0.236262i
$474$	−3.49691e7	−	1.40042e7i	−0.328359	−	0.131499i
$475$	1.66690e8			1.55535
$476$		−	2.39464e7i		−	0.222034i
$477$	−1.77083e7	+	1.85633e7i	−0.163163	+	0.171041i
$478$	−4.76372e7			−0.436177
$479$		−	1.44663e8i		−	1.31629i	−0.752891	−	0.658145i	$-0.771341\pi$
$479$		−	1.44663e8i		−	1.31629i	0.752891	−	0.658145i	$-0.228659\pi$
$480$	−8.05555e6	+	2.01150e7i	−0.0728403	+	0.181885i
$481$	2.03780e7			0.183116
$482$			5.84804e7i			0.522239i
$483$	−2.82009e7	−	1.12937e7i	−0.250277	−	0.100230i
$484$	6.60157e7			0.582252
$485$			2.84911e7i			0.249737i
$486$	2.37772e7	−	6.85706e7i	0.207134	−	0.597350i
$487$	−6.06863e7			−0.525416			−0.262708	−	0.964875i	$-0.584616\pi$
$487$	−6.06863e7			−0.525416			−0.262708	+	0.964875i	$0.584616\pi$
$488$			1.83744e7i			0.158108i
$489$	1.41782e7	−	3.54034e7i	0.121253	−	0.302774i
$490$	−2.10971e6			−0.0179323
$491$		−	1.76370e8i		−	1.48998i	−0.667074	−	0.744991i	$-0.732454\pi$
$491$		−	1.76370e8i		−	1.48998i	0.667074	−	0.744991i	$-0.267546\pi$
$492$	9.86781e7	+	3.95181e7i	0.828563	+	0.331818i
$493$	1.16749e8			0.974348
$494$		−	3.88006e7i		−	0.321853i
$495$	−3.01855e6	−	2.87953e6i	−0.0248876	−	0.0237414i
$496$	1.15429e6			0.00945954
$497$			8.07412e7i			0.657697i
$498$	1.90710e7	−	4.76209e7i	0.154413	−	0.385576i
$499$	−2.02073e7			−0.162632			−0.0813161	−	0.996688i	$-0.525912\pi$
$499$	−2.02073e7			−0.162632			−0.0813161	+	0.996688i	$0.525912\pi$
$500$		−	2.92071e7i		−	0.233657i
$501$	−1.89853e8	−	7.60313e7i	−1.50975	−	0.604615i
$502$	8.76112e7			0.692546
$503$		−	8.81635e7i		−	0.692763i	−0.938094	−	0.346382i	$-0.887410\pi$
$503$		−	8.81635e7i		−	0.692763i	0.938094	−	0.346382i	$-0.112590\pi$
$504$	3.37928e7	−	3.54244e7i	0.263957	−	0.276701i
$505$	2.64391e6			0.0205293
$506$			1.01218e7i			0.0781279i
$507$	−4.36614e7	+	1.09024e8i	−0.335022	+	0.836563i
$508$	−4.88460e7			−0.372595
$509$		−	8.14242e7i		−	0.617448i	−0.951152	−	0.308724i	$-0.900098\pi$
$509$		−	8.14242e7i		−	0.617448i	0.951152	−	0.308724i	$-0.0999019\pi$
$510$	−1.51275e7	−	6.05819e6i	−0.114040	−	0.0456701i
$511$	1.29613e7			0.0971370
$512$			1.05717e7i			0.0787651i
$513$	−1.98875e8	+	9.07393e7i	−1.47309	+	0.672115i
$514$	6.06817e6			0.0446857
$515$		−	529207.i		−	0.00387439i
$516$	−4.18130e7	+	1.04409e8i	−0.304342	+	0.759954i
$517$	−4.68769e7			−0.339225
$518$			1.93452e7i			0.139182i
$519$	2.39433e7	+	9.58868e6i	0.171270	+	0.0685894i
$520$	−8.88006e6			−0.0631547
$521$			1.28904e8i			0.911491i	0.890110	+	0.455745i	$0.150627\pi$
$521$			1.28904e8i			0.911491i	−0.890110	+	0.455745i	$0.849373\pi$
$522$	6.47841e7	+	6.18004e7i	0.455467	+	0.434490i
$523$	−9.04202e7			−0.632063			−0.316032	−	0.948749i	$-0.602351\pi$
$523$	−9.04202e7			−0.632063			−0.316032	+	0.948749i	$0.602351\pi$
$524$		−	2.76405e7i		−	0.192111i
$525$	−1.95316e7	+	4.87712e7i	−0.134977	+	0.337043i
$526$	1.18827e8			0.816503
$527$		−	3.43809e7i		−	0.234902i
$528$	−932956.	−	373625.i	−0.00633810	−	0.00253825i
$529$	7.27164e7			0.491208
$530$			4.41751e6i			0.0296722i
$531$	−1.13094e8	+	1.18555e8i	−0.755366	+	0.791836i
$532$	−5.53127e7			−0.367358
$533$			7.07851e7i			0.467477i
$534$	3.13259e7	−	7.82220e7i	0.205722	−	0.513695i
$535$	−4.70640e7			−0.307346
$536$			2.70977e8i			1.75970i
$537$	1.52687e8	+	6.11473e7i	0.986006	+	0.394871i
$538$	6.89088e7			0.442515
$539$			3.87543e6i			0.0247488i
$540$	7.78978e6	+	1.70730e7i	0.0494702	+	0.108425i
$541$	6.32413e7			0.399401			0.199700	−	0.979857i	$-0.436003\pi$
$541$	6.32413e7			0.399401			0.199700	+	0.979857i	$0.436003\pi$
$542$		−	7.00477e6i		−	0.0439943i
$543$	3.92724e7	−	9.80647e7i	0.245295	−	0.612510i
$544$	1.55478e8			0.965765
$545$		−	1.36977e7i		−	0.0846169i
$546$	1.13525e7	+	4.54640e6i	0.0697453	+	0.0279312i
$547$	5.93163e7			0.362420			0.181210	−	0.983444i	$-0.441999\pi$
$547$	5.93163e7			0.362420			0.181210	+	0.983444i	$0.441999\pi$
$548$			1.09509e8i			0.665436i
$549$	1.87101e7	+	1.78483e7i	0.113073	+	0.107865i
$550$	1.75049e7			0.105213
$551$		−	2.69674e8i		−	1.61207i
$552$	4.51273e7	−	1.12685e8i	0.268301	−	0.669957i
$553$	−3.57595e7			−0.211454
$554$			4.65880e7i			0.273997i
$555$	−1.83517e7	−	7.34937e6i	−0.107349	−	0.0429904i
$556$	−3.74097e7			−0.217651
$557$			1.44815e7i			0.0838005i	0.999122	+	0.0419003i	$0.0133412\pi$
$557$			1.44815e7i			0.0838005i	−0.999122	+	0.0419003i	$0.986659\pi$
$558$	1.81993e7	−	1.90779e7i	0.104749	−	0.109807i
$559$	−7.48958e7			−0.428767
$560$		−	519364.i		−	0.00295738i
$561$	−1.11286e7	+	2.77884e7i	−0.0630304	+	0.157389i
$562$	−9.67300e7			−0.544944
$563$			1.93149e8i			1.08235i	0.840910	+	0.541175i	$0.182020\pi$
$563$			1.93149e8i			1.08235i	−0.840910	+	0.541175i	$0.817980\pi$
$564$	1.95757e8	+	7.83958e7i	1.09114	+	0.436974i
$565$	5.04833e7			0.279900
$566$		−	8.04855e7i		−	0.443883i
$567$	−3.24620e6	−	6.88205e7i	−0.0178085	−	0.377545i
$568$	−3.22624e8			−1.76057
$569$		−	2.61758e8i		−	1.42090i	−0.703749	−	0.710449i	$-0.748492\pi$
$569$		−	2.61758e8i		−	1.42090i	0.703749	−	0.710449i	$-0.251508\pi$
$570$	−1.39935e7	+	3.49423e7i	−0.0755617	+	0.188680i
$571$	−3.71956e7			−0.199794			−0.0998971	−	0.994998i	$-0.531851\pi$
$571$	−3.71956e7			−0.199794			−0.0998971	+	0.994998i	$0.531851\pi$
$572$			6.11878e6i			0.0326947i
$573$	2.55904e7	+	1.02483e7i	0.136023	+	0.0544738i
$574$	−6.71972e7			−0.355317
$575$			1.30259e8i			0.685180i
$576$	9.17240e7	+	8.74994e7i	0.479971	+	0.457865i
$577$	1.22705e8			0.638754			0.319377	−	0.947628i	$-0.396526\pi$
$577$	1.22705e8			0.638754			0.319377	+	0.947628i	$0.396526\pi$
$578$		−	5.15944e6i		−	0.0267189i
$579$	8.63402e7	−	2.15595e8i	0.444813	−	1.11071i
$580$	−2.31509e7			−0.118655
$581$		−	4.86973e7i		−	0.248300i
$582$	1.45542e8	+	5.82858e7i	0.738276	+	0.295661i
$583$	8.11474e6			0.0409514
$584$			5.17904e7i			0.260022i
$585$	−8.62584e6	+	9.04230e6i	−0.0430857	+	0.0451660i
$586$	−1.32567e8			−0.658783
$587$			1.30022e8i			0.642840i	0.946937	+	0.321420i	$0.104160\pi$
$587$			1.30022e8i			0.642840i	−0.946937	+	0.321420i	$0.895840\pi$
$588$	6.48118e6	−	1.61837e7i	0.0318803	−	0.0796062i
$589$	−7.94148e7			−0.388647
$590$			2.82125e7i			0.137368i
$591$	−2.89018e8	−	1.15744e8i	−1.40011	−	0.560709i
$592$	−4.76234e6			−0.0229538
$593$			499581.i			0.00239575i	0.999999	+	0.00119788i	$0.000381296\pi$
$593$			499581.i			0.00239575i	−0.999999	+	0.00119788i	$0.999619\pi$
$594$	−2.08848e7	+	9.52896e6i	−0.0996486	+	0.0454659i
$595$	−1.54694e7			−0.0734385
$596$			1.11877e8i			0.528446i
$597$	1.32461e8	−	3.30761e8i	0.622539	−	1.55450i
$598$	3.03206e7			0.141786
$599$		−	3.74144e8i		−	1.74084i	−0.492312	−	0.870419i	$-0.663848\pi$
$599$		−	3.74144e8i		−	1.74084i	0.492312	−	0.870419i	$-0.336152\pi$
$600$	−1.94879e8	−	7.80441e7i	−0.902218	−	0.361315i
$601$	−1.80986e8			−0.833722			−0.416861	−	0.908970i	$-0.636870\pi$
$601$	−1.80986e8			−0.833722			−0.416861	+	0.908970i	$0.636870\pi$
$602$		−	7.10996e7i		−	0.325895i
$603$	2.75928e8	+	2.63220e8i	1.25847	+	1.20051i
$604$	−2.11005e8			−0.957596
$605$		−	4.26463e7i		−	0.192582i
$606$	5.40881e6	−	1.35060e7i	0.0243043	−	0.0606888i
$607$	−3.74919e8			−1.67637			−0.838187	−	0.545383i	$-0.816384\pi$
$607$	−3.74919e8			−1.67637			−0.838187	+	0.545383i	$0.816384\pi$
$608$		−	3.59130e8i		−	1.59787i
$609$	7.89029e7	+	3.15986e7i	0.349334	+	0.139900i
$610$	4.45244e6			0.0196159
$611$			1.40423e8i			0.615624i
$612$	9.29454e7	−	9.74329e7i	0.405484	−	0.425061i
$613$	1.88911e8			0.820118			0.410059	−	0.912059i	$-0.365508\pi$
$613$	1.88911e8			0.820118			0.410059	+	0.912059i	$0.365508\pi$
$614$			7.92310e7i			0.342287i
$615$	2.55288e7	−	6.37462e7i	0.109750	−	0.274050i
$616$	−1.54854e7			−0.0662491
$617$			1.92575e8i			0.819867i	0.912115	+	0.409933i	$0.134448\pi$
$617$			1.92575e8i			0.819867i	−0.912115	+	0.409933i	$0.865552\pi$
$618$	−2.70336e6	−	1.08263e6i	−0.0114535	−	0.00458685i
$619$	2.47431e8			1.04324			0.521618	−	0.853179i	$-0.325328\pi$
$619$	2.47431e8			1.04324			0.521618	+	0.853179i	$0.325328\pi$
$620$			6.81760e6i			0.0286059i
$621$	−7.09079e7	−	1.55410e8i	−0.296087	−	0.648941i
$622$	−7.78996e7			−0.323716
$623$		−	7.99900e7i		−	0.330805i
$624$	−1.11922e6	+	2.79474e6i	−0.00460641	+	0.0115024i
$625$	2.15649e8			0.883299
$626$			8.88347e7i			0.362126i
$627$	6.41871e7	+	2.57053e7i	0.260402	+	0.104285i
$628$	1.59213e8			0.642836
$629$			1.41848e8i			0.569995i
$630$	−8.58398e6	−	8.18862e6i	−0.0343295	−	0.0327483i
$631$	1.43118e8			0.569649			0.284825	−	0.958580i	$-0.408065\pi$
$631$	1.43118e8			0.569649			0.284825	+	0.958580i	$0.408065\pi$
$632$		−	1.42887e8i		−	0.566033i
$633$	−7.80894e7	+	1.94992e8i	−0.307879	+	0.768786i
$634$	−1.91050e8			−0.749684
$635$			3.15546e7i			0.123237i
$636$	−3.38870e7	−	1.35709e7i	−0.131723	−	0.0527518i
$637$	1.16091e7			0.0449140
$638$		−	2.83197e7i		−	0.109050i
$639$	−3.13388e8	+	3.28519e8i	−1.20110	+	1.25909i
$640$	−2.95338e7			−0.112662
$641$			1.77654e8i			0.674530i	0.941410	+	0.337265i	$0.109502\pi$
$641$			1.77654e8i			0.674530i	−0.941410	+	0.337265i	$0.890498\pi$
$642$	−9.62816e7	+	2.40419e8i	−0.363863	+	0.908580i
$643$	−1.61496e8			−0.607477			−0.303739	−	0.952755i	$-0.598235\pi$
$643$	−1.61496e8			−0.607477			−0.303739	+	0.952755i	$0.598235\pi$
$644$		−	4.32239e7i		−	0.161833i
$645$	6.74481e7	+	2.70113e7i	0.251357	+	0.100662i
$646$	2.70084e8			1.00185
$647$			1.19839e8i			0.442472i	0.975220	+	0.221236i	$0.0710092\pi$
$647$			1.19839e8i			0.442472i	−0.975220	+	0.221236i	$0.928991\pi$
$648$	2.74992e8	−	1.29711e7i	1.01064	−	0.0476708i
$649$	5.18249e7			0.189585
$650$		−	5.24371e7i		−	0.190941i
$651$	9.30531e6	−	2.32357e7i	0.0337278	−	0.0842196i
$652$	5.42634e7			0.195778
$653$		−	1.07660e8i		−	0.386647i	−0.981135	−	0.193324i	$-0.938073\pi$
$653$		−	1.07660e8i		−	0.386647i	0.981135	−	0.193324i	$-0.0619268\pi$
$654$	−6.99722e7	−	2.80221e7i	−0.250145	−	0.100177i
$655$	−1.78558e7			−0.0635413
$656$		−	1.65424e7i		−	0.0585987i
$657$	5.27366e7	+	5.03077e7i	0.185959	+	0.177394i
$658$	−1.33306e8			−0.467919
$659$			4.17916e8i			1.46027i	0.683303	+	0.730135i	$0.260543\pi$
$659$			4.17916e8i			1.46027i	−0.683303	+	0.730135i	$0.739457\pi$
$660$	2.20675e6	−	5.51033e6i	0.00767575	−	0.0191666i
$661$	4.82007e8			1.66897			0.834486	−	0.551028i	$-0.185764\pi$
$661$	4.82007e8			1.66897			0.834486	+	0.551028i	$0.185764\pi$
$662$			1.78758e7i			0.0616159i
$663$	8.32423e7	+	3.33364e7i	0.285630	+	0.114387i
$664$	1.94584e8			0.664665
$665$			3.57321e7i			0.121505i
$666$	−7.50861e7	+	7.87113e7i	−0.254177	+	0.266449i
$667$	2.10736e8			0.710167
$668$		−	2.90991e8i		−	0.976224i
$669$	−1.23669e8	+	3.08806e8i	−0.413031	+	1.03135i
$670$	6.56628e7			0.218321
$671$		−	8.17890e6i		−	0.0270724i
$672$	1.05077e8	+	4.20806e7i	0.346257	+	0.138667i
$673$	−3.60190e8			−1.18164			−0.590822	−	0.806802i	$-0.701196\pi$
$673$	−3.60190e8			−1.18164			−0.590822	+	0.806802i	$0.701196\pi$
$674$		−	2.33238e8i		−	0.761761i
$675$	−2.68770e8	+	1.22630e8i	−0.873915	+	0.398735i
$676$	−1.67103e8			−0.540934
$677$			6.06843e7i			0.195574i	0.995207	+	0.0977869i	$0.0311763\pi$
$677$			6.06843e7i			0.195574i	−0.995207	+	0.0977869i	$0.968824\pi$
$678$	1.03277e8	−	2.57885e8i	0.331370	−	0.827442i
$679$	1.48831e8			0.475429
$680$		−	6.18125e7i		−	0.196585i
$681$	−4.22633e8	−	1.69254e8i	−1.33820	−	0.535916i
$682$	−8.33972e6			−0.0262905
$683$			1.72870e8i			0.542573i	0.962499	+	0.271287i	$0.0874492\pi$
$683$			1.72870e8i			0.542573i	−0.962499	+	0.271287i	$0.912551\pi$
$684$	−2.25055e8	−	2.14690e8i	−0.703269	−	0.670878i
$685$	7.07427e7			0.220095
$686$			1.10207e7i			0.0341379i
$687$	1.88787e8	−	4.71409e8i	0.582240	−	1.45388i
$688$	1.75031e7			0.0537464
$689$		−	2.43083e7i		−	0.0743185i
$690$	−2.73055e7	−	1.09352e7i	−0.0831196	−	0.0332873i
$691$	1.06853e8			0.323856			0.161928	−	0.986803i	$-0.448229\pi$
$691$	1.06853e8			0.323856			0.161928	+	0.986803i	$0.448229\pi$
$692$			3.66983e7i			0.110746i
$693$	−1.50421e7	+	1.57683e7i	−0.0451968	+	0.0473789i
$694$	1.34950e8			0.403732
$695$			2.41668e7i			0.0719886i
$696$	−1.26261e8	+	3.15279e8i	−0.374492	+	0.935120i
$697$	−4.92722e8			−1.45514
$698$		−	5.40241e7i		−	0.158862i
$699$	2.71285e8	+	1.08643e8i	0.794319	+	0.318104i
$700$	−7.47523e7			−0.217937
$701$		−	2.10475e8i		−	0.611007i	−0.952191	−	0.305503i	$-0.901175\pi$
$701$		−	2.10475e8i		−	0.611007i	0.952191	−	0.305503i	$-0.0988247\pi$
$702$	2.85447e7	+	6.25620e7i	0.0825114	+	0.180842i
$703$	3.27647e8			0.943063
$704$		−	4.00961e7i		−	0.114917i
$705$	5.06439e7	−	1.26460e8i	0.144530	−	0.360898i
$706$	3.19279e7			0.0907310
$707$		−	1.38113e7i		−	0.0390819i
$708$	−2.16420e8	−	8.66707e7i	−0.609814	−	0.244215i
$709$	−4.24747e8			−1.19177			−0.595884	−	0.803070i	$-0.703198\pi$
$709$	−4.24747e8			−1.19177			−0.595884	+	0.803070i	$0.703198\pi$
$710$			7.81778e7i			0.218428i
$711$	−1.45498e8	−	1.38796e8i	−0.404806	−	0.386162i
$712$	3.19623e8			0.885519
$713$		−	6.20584e7i		−	0.171211i
$714$	−3.16467e7	+	7.90230e7i	−0.0869429	+	0.217100i
$715$	3.95274e6			0.0108139
$716$			2.34026e8i			0.637566i
$717$	−2.36067e8	−	9.45389e7i	−0.640440	−	0.256480i
$718$	−1.36771e8			−0.369506
$719$			2.09831e8i			0.564526i	0.959337	+	0.282263i	$0.0910851\pi$
$719$			2.09831e8i			0.564526i	−0.959337	+	0.282263i	$0.908915\pi$
$720$	2.01585e6	−	2.11318e6i	0.00540084	−	0.00566160i
$721$	−2.76447e6			−0.00737574
$722$		−	3.85898e8i		−	1.02532i
$723$	−1.16058e8	+	2.89801e8i	−0.307086	+	0.766805i
$724$	1.50305e8			0.396058
$725$		−	3.64451e8i		−	0.956367i
$726$	−2.17851e8	−	8.72440e7i	−0.569312	−	0.227995i
$727$	−6.02308e7			−0.156753			−0.0783765	−	0.996924i	$-0.524974\pi$
$727$	−6.02308e7			−0.156753			−0.0783765	+	0.996924i	$0.524974\pi$
$728$			4.63876e7i			0.120229i
$729$	2.53911e8	−	2.92616e8i	0.655388	−	0.755292i
$730$	1.25498e7			0.0322602
$731$		−	5.21336e8i		−	1.33464i
$732$	−1.36782e7	+	3.41550e7i	−0.0348735	+	0.0870804i
$733$	2.24031e8			0.568847			0.284423	−	0.958699i	$-0.408198\pi$
$733$	2.24031e8			0.568847			0.284423	+	0.958699i	$0.408198\pi$
$734$			3.86314e8i			0.976906i
$735$	−1.04547e7	−	4.18685e6i	−0.0263300	−	0.0105445i
$736$	2.80641e8			0.703911
$737$		−	1.20619e8i		−	0.301310i
$738$	−2.73411e8	−	2.60819e8i	−0.680217	−	0.648888i
$739$	1.32642e8			0.328660			0.164330	−	0.986405i	$-0.447454\pi$
$739$	1.32642e8			0.328660			0.164330	+	0.986405i	$0.447454\pi$
$740$		−	2.81279e7i		−	0.0694131i
$741$	7.70021e7	−	1.92277e8i	0.189255	−	0.472578i
$742$	2.30762e7			0.0564875
$743$		−	3.18777e8i		−	0.777178i	−0.921411	−	0.388589i	$-0.872963\pi$
$743$		−	3.18777e8i		−	0.777178i	0.921411	−	0.388589i	$-0.127037\pi$
$744$	9.28449e7	+	3.71820e7i	0.225444	+	0.0902847i
$745$	7.22725e7			0.174785
$746$			2.91675e8i			0.702558i
$747$	1.89013e8	−	1.98139e8i	0.453451	−	0.475344i
$748$	−4.25918e7			−0.101770
$749$			2.45853e8i			0.585100i
$750$	−3.85991e7	+	9.63833e7i	−0.0914941	+	0.228464i
$751$	5.79013e8			1.36700			0.683500	−	0.729951i	$-0.260457\pi$
$751$	5.79013e8			1.36700			0.683500	+	0.729951i	$0.260457\pi$
$752$		−	3.28168e7i		−	0.0771691i
$753$	4.34159e8	+	1.73870e8i	1.01687	+	0.407229i
$754$	−8.48337e7			−0.197904
$755$			1.36310e8i			0.316728i
$756$	8.91860e7	−	4.06922e7i	0.206410	−	0.0941773i
$757$	−5.93337e8			−1.36777			−0.683886	−	0.729589i	$-0.739712\pi$
$757$	−5.93337e8			−1.36777			−0.683886	+	0.729589i	$0.739712\pi$
$758$			1.65982e8i			0.381113i
$759$	−2.00873e7	+	5.01588e7i	−0.0459406	+	0.114715i
$760$	−1.42778e8			−0.325252
$761$			5.95666e8i			1.35160i	0.737084	+	0.675801i	$0.236202\pi$
$761$			5.95666e8i			1.35160i	−0.737084	+	0.675801i	$0.763798\pi$
$762$	1.61191e8	+	6.45530e7i	0.364315	+	0.145899i
$763$	−7.15538e7			−0.161086
$764$			3.92227e7i			0.0879545i
$765$	−6.29418e7	−	6.00429e7i	−0.140590	−	0.134115i
$766$	−1.55226e8			−0.345365
$767$		−	1.55245e8i		−	0.344059i
$768$	−1.72129e8	+	4.29812e8i	−0.379988	+	0.948844i
$769$	−6.24679e8			−1.37366			−0.686828	−	0.726820i	$-0.740997\pi$
$769$	−6.24679e8			−1.37366			−0.686828	+	0.726820i	$0.740997\pi$
$770$			3.75239e6i			0.00821932i
$771$	3.00709e7	+	1.20426e7i	0.0656121	+	0.0262760i
$772$	3.30445e8			0.718204
$773$		−	1.23150e8i		−	0.266623i	−0.991074	−	0.133311i	$-0.957439\pi$
$773$		−	1.23150e8i		−	0.266623i	0.991074	−	0.133311i	$-0.0425610\pi$
$774$	2.75965e8	−	2.89289e8i	0.595157	−	0.623891i
$775$	−1.07325e8			−0.230567
$776$			5.94698e8i			1.27266i
$777$	−3.83916e7	+	9.58653e7i	−0.0818415	+	0.204361i
$778$	−4.29142e7			−0.0911301
$779$			1.13811e9i			2.40754i
$780$	−1.65066e7	−	6.61048e6i	−0.0347835	−	0.0139299i
$781$	1.43608e8			0.301458
$782$			2.11056e8i			0.441345i
$783$	1.98393e8	+	4.34821e8i	0.413276	+	0.905785i
$784$	−2.71305e6			−0.00563002
$785$		−	1.02852e8i		−	0.212620i
$786$	−3.65287e7	+	9.12136e7i	−0.0752258	+	0.187842i
$787$	−7.93771e8			−1.62844			−0.814219	−	0.580558i	$-0.802834\pi$
$787$	−7.93771e8			−1.62844			−0.814219	+	0.580558i	$0.802834\pi$
$788$		−	4.42982e8i		−	0.905331i
$789$	5.88849e8	+	2.35819e8i	1.19887	+	0.480118i
$790$	−3.46242e7			−0.0702260
$791$		−	2.63714e8i		−	0.532849i
$792$	−6.30067e7	−	6.01048e7i	−0.126827	−	0.120986i
$793$	−2.45005e7			−0.0491310
$794$			3.57310e8i			0.713813i
$795$	−8.76682e6	+	2.18911e7i	−0.0174478	+	0.0435678i
$796$	5.06963e8			1.00516
$797$		−	8.56808e8i		−	1.69242i	−0.532848	−	0.846211i	$-0.678878\pi$
$797$		−	8.56808e8i		−	1.69242i	0.532848	−	0.846211i	$-0.321122\pi$
$798$	1.82531e8	+	7.30992e7i	0.359194	+	0.143848i
$799$	−9.77461e8			−1.91628
$800$		−	4.85347e8i		−	0.947943i
$801$	3.10473e8	−	3.25462e8i	0.604123	−	0.633291i
$802$	−1.78314e8			−0.345670
$803$		−	2.30532e7i		−	0.0445231i
$804$	−2.01720e8	+	5.03703e8i	−0.388134	+	0.969185i
$805$	−2.79227e7			−0.0535267
$806$			2.49822e7i			0.0477119i
$807$	3.41479e8	+	1.36754e8i	0.649746	+	0.260207i
$808$	5.51868e7			0.104617
$809$		−	3.69671e8i		−	0.698184i	−0.937088	−	0.349092i	$-0.886490\pi$
$809$		−	3.69671e8i		−	0.698184i	0.937088	−	0.349092i	$-0.113510\pi$
$810$	−3.14314e6	−	6.66355e7i	−0.00591437	−	0.125386i
$811$	7.57101e8			1.41936			0.709678	−	0.704526i	$-0.248840\pi$
$811$	7.57101e8			1.41936			0.709678	+	0.704526i	$0.248840\pi$
$812$			1.20936e8i			0.225885i
$813$	1.39014e7	−	3.47123e7i	0.0258694	−	0.0645969i
$814$	3.44078e7			0.0637946
$815$		−	3.50543e7i		−	0.0647542i
$816$	−1.94537e7	−	7.79071e6i	−0.0358040	−	0.0143386i
$817$	−1.20421e9			−2.20818
$818$			4.51702e8i			0.825263i
$819$	4.72351e7	+	4.50596e7i	0.0859831	+	0.0820230i
$820$	9.77048e7			0.177204
$821$		−	9.58875e8i		−	1.73274i	−0.499406	−	0.866368i	$-0.666448\pi$
$821$		−	9.58875e8i		−	1.73274i	0.499406	−	0.866368i	$-0.333552\pi$
$822$	1.44722e8	−	3.61377e8i	0.260568	−	0.650647i
$823$	8.30255e8			1.48940			0.744701	−	0.667398i	$-0.232592\pi$
$823$	8.30255e8			1.48940			0.744701	+	0.667398i	$0.232592\pi$
$824$		−	1.10462e7i		−	0.0197439i
$825$	8.67457e7	+	3.47394e7i	0.154485	+	0.0618673i
$826$	1.47376e8			0.261510
$827$		−	7.38927e8i		−	1.30643i	−0.757174	−	0.653213i	$-0.773420\pi$
$827$		−	7.38927e8i		−	1.30643i	0.757174	−	0.653213i	$-0.226580\pi$
$828$	1.67769e8	−	1.75869e8i	0.295543	−	0.309812i
$829$	4.57605e8			0.803207			0.401603	−	0.915814i	$-0.368453\pi$
$829$	4.57605e8			0.803207			0.401603	+	0.915814i	$0.368453\pi$
$830$		−	4.71512e7i		−	0.0824630i
$831$	−9.24568e7	+	2.30868e8i	−0.161115	+	0.402310i
$832$	−1.20111e8			−0.208551
$833$			8.08092e7i			0.139806i
$834$	1.23452e8	+	4.94393e7i	0.212814	+	0.0852264i
$835$	−1.87980e8			−0.322889
$836$			9.83805e7i			0.168380i
$837$	1.28048e8	−	5.84236e7i	0.218372	−	0.0996350i
$838$	4.07198e8			0.691949
$839$			2.73528e8i			0.463143i	0.972818	+	0.231572i	$0.0743867\pi$
$839$			2.73528e8i			0.463143i	−0.972818	+	0.231572i	$0.925613\pi$
$840$	1.67298e7	−	4.17748e7i	0.0282262	−	0.0704818i
$841$	5.20830e6			0.00875605
$842$		−	3.15077e8i		−	0.527813i
$843$	−4.79347e8	−	1.91966e8i	−0.800143	−	0.320437i
$844$	−2.98867e8			−0.497108
$845$			1.07949e8i			0.178915i
$846$	−5.42392e8	−	5.17411e8i	−0.895782	−	0.854525i
$847$	−2.22775e8			−0.366621
$848$			5.68084e6i			0.00931590i
$849$	1.59728e8	−	3.98848e8i	0.261011	−	0.651754i
$850$	3.65005e8			0.594350
$851$			2.56039e8i			0.415449i
$852$	−5.99707e8	−	2.40167e8i	−0.969661	−	0.388325i
$853$	−6.33977e8			−1.02147			−0.510736	−	0.859738i	$-0.670627\pi$
$853$	−6.33977e8			−1.02147			−0.510736	+	0.859738i	$0.670627\pi$
$854$		−	2.32586e7i		−	0.0373431i
$855$	−1.38690e8	+	1.45386e8i	−0.221895	+	0.232608i
$856$	−9.82375e8			−1.56623
$857$		−	3.02812e8i		−	0.481095i	−0.970637	−	0.240548i	$-0.922673\pi$
$857$		−	3.02812e8i		−	0.481095i	0.970637	−	0.240548i	$-0.0773270\pi$
$858$	8.08635e6	−	2.01919e7i	0.0128024	−	0.0319680i
$859$	9.67375e7			0.152621			0.0763107	−	0.997084i	$-0.475686\pi$
$859$	9.67375e7			0.152621			0.0763107	+	0.997084i	$0.475686\pi$
$860$			1.03379e8i			0.162531i
$861$	−3.32997e8	−	1.33357e8i	−0.521712	−	0.208933i
$862$	−3.48762e8			−0.544512
$863$			8.09109e8i			1.25885i	0.777061	+	0.629426i	$0.216710\pi$
$863$			8.09109e8i			1.25885i	−0.777061	+	0.629426i	$0.783290\pi$
$864$	2.64204e8	+	5.79061e8i	0.409636	+	0.897807i
$865$	2.37071e7			0.0366295
$866$		−	3.98345e8i		−	0.613346i
$867$	1.02392e7	−	2.55677e7i	0.0157112	−	0.0392315i
$868$	3.56137e7			0.0544576
$869$			6.36027e7i			0.0969207i
$870$	7.63979e7	+	3.05954e7i	0.116017	+	0.0464621i
$871$	−3.61323e8			−0.546816
$872$		−	2.85914e8i		−	0.431206i
$873$	6.05563e8	+	5.77673e8i	0.910158	+	0.868239i
$874$	4.87509e8			0.730210
$875$			9.85619e7i			0.147124i
$876$	−3.85537e7	+	9.62700e7i	−0.0573527	+	0.143212i
$877$	3.70800e8			0.549719			0.274860	−	0.961484i	$-0.411369\pi$
$877$	3.70800e8			0.549719			0.274860	+	0.961484i	$0.411369\pi$
$878$			3.54112e8i			0.523187i
$879$	−6.56938e8	−	2.63087e8i	−0.967292	−	0.387376i
$880$	−923754.			−0.00135553
$881$		−	1.00505e9i		−	1.46980i	−0.678175	−	0.734900i	$-0.737229\pi$
$881$		−	1.00505e9i		−	1.46980i	0.678175	−	0.734900i	$-0.262771\pi$
$882$	−4.27757e7	+	4.48409e7i	−0.0623435	+	0.0653535i
$883$	9.82183e8			1.42663			0.713313	−	0.700846i	$-0.247194\pi$
$883$	9.82183e8			1.42663			0.713313	+	0.700846i	$0.247194\pi$
$884$			1.27587e8i			0.184692i
$885$	−5.59895e7	+	1.39808e8i	−0.0807749	+	0.201698i
$886$	5.68256e8			0.817039
$887$		−	1.55330e8i		−	0.222579i	−0.993788	−	0.111290i	$-0.964502\pi$
$887$		−	1.55330e8i		−	0.222579i	0.993788	−	0.111290i	$-0.0354981\pi$
$888$	−3.83057e8	−	1.53405e8i	−0.547047	−	0.219078i
$889$	1.64835e8			0.234608
$890$		−	7.74505e7i		−	0.109864i
$891$	−1.22406e8	+	5.77378e6i	−0.173049	+	0.00816257i
$892$	−4.73312e8			−0.666889
$893$			2.25779e9i			3.17051i
$894$	1.47852e8	−	3.69192e8i	0.206926	−	0.516702i
$895$	1.51181e8			0.210877
$896$			1.54278e8i			0.214477i
$897$	1.50254e8	+	6.01731e7i	0.208185	+	0.0833729i
$898$	−2.82140e8			−0.389615
$899$			1.73633e8i			0.238975i
$900$	−3.04151e8	−	2.90143e8i	−0.417217	−	0.398001i
$901$	1.69206e8			0.231335
$902$			1.19519e8i			0.162861i
$903$	1.41101e8	−	3.52335e8i	0.191632	−	0.478512i
$904$	1.05375e9			1.42636
$905$		−	9.70975e7i		−	0.130997i
$906$	6.96315e8	+	2.78857e8i	0.936314	+	0.374970i
$907$	−2.18956e7			−0.0293451			−0.0146725	−	0.999892i	$-0.504671\pi$
$907$	−2.18956e7			−0.0293451			−0.0146725	+	0.999892i	$0.504671\pi$
$908$		−	6.47776e8i		−	0.865301i
$909$	5.36069e7	−	5.61951e7i	0.0713722	−	0.0748181i
$910$	1.12406e7			0.0149164
$911$			1.45755e9i			1.92783i	0.266207	+	0.963916i	$0.414229\pi$
$911$			1.45755e9i			1.92783i	−0.266207	+	0.963916i	$0.585771\pi$
$912$	−1.79954e7	+	4.49351e7i	−0.0237234	+	0.0592381i
$913$	−8.66143e7			−0.113809
$914$		−	3.99049e8i		−	0.522622i
$915$	2.20642e7	+	8.83614e6i	0.0288021	+	0.0115345i
$916$	7.22535e8			0.940097
$917$			9.32752e7i			0.120965i
$918$	−4.35483e8	+	1.98695e8i	−0.562915	+	0.256837i
$919$	2.19853e8			0.283260			0.141630	−	0.989920i	$-0.454766\pi$
$919$	2.19853e8			0.283260			0.141630	+	0.989920i	$0.454766\pi$
$920$		−	1.11573e8i		−	0.143284i
$921$	−1.57239e8	+	3.92631e8i	−0.201271	+	0.502580i
$922$	4.33816e8			0.553494
$923$		−	4.30190e8i		−	0.547085i
$924$	−2.87848e7	−	1.15276e7i	−0.0364878	−	0.0146124i
$925$	4.42799e8			0.559476
$926$			4.43279e8i			0.558270i
$927$	−1.12480e7	−	1.07300e7i	−0.0141201	−	0.0134698i
$928$	−7.85203e8			−0.982512
$929$		−	7.14835e8i		−	0.891576i	−0.895138	−	0.445788i	$-0.852923\pi$
$929$		−	7.14835e8i		−	0.891576i	0.895138	−	0.445788i	$-0.147077\pi$
$930$	9.00989e6	−	2.24980e7i	0.0112014	−	0.0279702i
$931$	1.86657e8			0.231311
$932$			4.15803e8i			0.513618i
$933$	−3.86033e8	−	1.54596e8i	−0.475313	−	0.190351i
$934$	−3.43798e7			−0.0421951
$935$			2.75143e7i			0.0336608i
$936$	−1.80048e8	+	1.88741e8i	−0.219564	+	0.230165i
$937$	1.23168e9			1.49719			0.748597	−	0.663025i	$-0.230728\pi$
$937$	1.23168e9			1.49719			0.748597	+	0.663025i	$0.230728\pi$
$938$		−	3.43009e8i		−	0.415621i
$939$	−1.76298e8	+	4.40222e8i	−0.212937	+	0.531710i
$940$	1.93827e8			0.233362
$941$			1.03258e9i			1.23924i	0.784904	+	0.619618i	$0.212712\pi$
$941$			1.03258e9i			1.23924i	−0.784904	+	0.619618i	$0.787288\pi$
$942$	−5.25402e8	−	2.10410e8i	−0.628549	−	0.251718i
$943$	−8.89376e8			−1.06060
$944$			3.62807e7i			0.0431281i
$945$	−2.62873e7	−	5.76143e7i	−0.0311494	−	0.0682708i
$946$	−1.26460e8			−0.149375
$947$			5.32292e8i			0.626758i	0.949628	+	0.313379i	$0.101461\pi$
$947$			5.32292e8i			0.626758i	−0.949628	+	0.313379i	$0.898539\pi$
$948$	1.06368e8	−	2.65604e8i	0.124849	−	0.311752i
$949$	−6.90577e7			−0.0808004
$950$		−	8.43107e8i		−	0.983359i
$951$	−9.46750e8	−	3.79149e8i	−1.10076	−	0.440828i
$952$	−3.22896e8			−0.374241
$953$			5.77302e7i			0.0666998i	0.999444	+	0.0333499i	$0.0106176\pi$
$953$			5.77302e7i			0.0666998i	−0.999444	+	0.0333499i	$0.989382\pi$
$954$	9.38921e7	+	8.95677e7i	0.108139	+	0.103159i
$955$	2.53380e7			0.0290912
$956$		−	3.61824e8i		−	0.414117i
$957$	5.62021e7	−	1.40339e8i	0.0641235	−	0.160119i
$958$	−7.31699e8			−0.832216
$959$		−	3.69545e8i		−	0.418998i
$960$	1.08167e8	+	4.33182e7i	0.122259	+	0.0489617i
$961$	−8.36371e8			−0.942386
$962$		−	1.03071e8i		−	0.115774i
$963$	−9.54251e8	+	1.00032e9i	−1.06852	+	1.12011i
$964$	−4.44182e8			−0.495827
$965$		−	2.13468e8i		−	0.237548i
$966$	−5.71231e7	+	1.42639e8i	−0.0633695	+	0.158236i
$967$	1.16749e9			1.29114			0.645572	−	0.763699i	$-0.276619\pi$
$967$	1.16749e9			1.29114			0.645572	+	0.763699i	$0.276619\pi$
$968$		−	8.90163e8i		−	0.981394i
$969$	1.33841e9	+	5.35998e8i	1.47101	+	0.589104i
$970$	1.44106e8			0.157895
$971$		−	1.00383e9i		−	1.09648i	−0.836320	−	0.548242i	$-0.815297\pi$
$971$		−	1.00383e9i		−	1.09648i	0.836320	−	0.548242i	$-0.184703\pi$
$972$	5.20821e8	+	1.80598e8i	0.567139	+	0.196659i
$973$	1.26242e8			0.137046
$974$			3.06948e8i			0.332191i
$975$	1.04065e8	−	2.59853e8i	0.112277	−	0.280359i
$976$	5.72575e6			0.00615862
$977$			7.81614e8i			0.838125i	0.907957	+	0.419062i	$0.137641\pi$
$977$			7.81614e8i			0.838125i	−0.907957	+	0.419062i	$0.862359\pi$
$978$	−1.79069e8	−	7.17125e7i	−0.191427	−	0.0766617i
$979$	−1.42272e8			−0.151626
$980$		−	1.60241e7i		−	0.0170254i
$981$	−2.91137e8	−	2.77728e8i	−0.308383	−	0.294180i
$982$	−8.92073e8			−0.942032
$983$		−	1.54179e9i		−	1.62317i	−0.584235	−	0.811585i	$-0.698605\pi$
$983$		−	1.54179e9i		−	1.62317i	0.584235	−	0.811585i	$-0.301395\pi$
$984$	5.32866e8	−	1.33059e9i	0.559284	−	1.39655i
$985$	−2.86167e8			−0.299441
$986$		−	5.90513e8i		−	0.616025i
$987$	−6.60599e8	−	2.64553e8i	−0.687047	−	0.275145i
$988$	2.94706e8			0.305575
$989$		−	9.41025e8i		−	0.972774i
$990$	−1.45645e7	+	1.52677e7i	−0.0150103	+	0.0157350i
$991$	1.59156e9			1.63532			0.817661	−	0.575701i	$-0.195271\pi$
$991$	1.59156e9			1.63532			0.817661	+	0.575701i	$0.195271\pi$
$992$			2.31230e8i			0.236870i
$993$	−3.54757e7	+	8.85841e7i	−0.0362312	+	0.0904707i
$994$	4.08385e8			0.415825
$995$		−	3.27499e8i		−	0.332461i
$996$	3.61700e8	+	1.44852e8i	0.366076	+	0.146604i
$997$	−1.16332e9			−1.17385			−0.586927	−	0.809640i	$-0.699662\pi$
$997$	−1.16332e9			−1.17385			−0.586927	+	0.809640i	$0.699662\pi$
$998$			1.02208e8i			0.102823i
$999$	−5.28298e8	+	2.41043e8i	−0.529886	+	0.241767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.b.a.8.6	✓	12
3.2	odd	2	inner	21.7.b.a.8.7	yes	12
4.3	odd	2		336.7.d.a.113.6		12
7.6	odd	2		147.7.b.b.50.6		12
12.11	even	2		336.7.d.a.113.5		12
21.20	even	2		147.7.b.b.50.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.b.a.8.6	✓	12	1.1	even	1	trivial
21.7.b.a.8.7	yes	12	3.2	odd	2	inner
147.7.b.b.50.6		12	7.6	odd	2
147.7.b.b.50.7		12	21.20	even	2
336.7.d.a.113.5		12	12.11	even	2
336.7.d.a.113.6		12	4.3	odd	2

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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.05795i q^{2} +(10.0378 - 25.0648i) q^{3} +38.4172 q^{4} -24.8176i q^{5} +(-126.776 - 50.7707i) q^{6} -129.642 q^{7} -518.021i q^{8} +(-527.485 - 503.190i) q^{9} +O(q^{10})\)	\(q-5.05795i q^{2} +(10.0378 - 25.0648i) q^{3} +38.4172 q^{4} -24.8176i q^{5} +(-126.776 - 50.7707i) q^{6} -129.642 q^{7} -518.021i q^{8} +(-527.485 - 503.190i) q^{9} -125.526 q^{10} +230.584i q^{11} +(385.624 - 962.917i) q^{12} +690.732 q^{13} +655.722i q^{14} +(-622.046 - 249.114i) q^{15} -161.424 q^{16} +4808.07i q^{17} +(-2545.11 + 2667.99i) q^{18} +11105.9 q^{19} -953.420i q^{20} +(-1301.32 + 3249.44i) q^{21} +1166.28 q^{22} +8678.68i q^{23} +(-12984.1 - 5199.79i) q^{24} +15009.1 q^{25} -3493.69i q^{26} +(-17907.1 + 8170.36i) q^{27} -4980.47 q^{28} -24282.0i q^{29} +(-1260.00 + 3146.28i) q^{30} -7150.68 q^{31} -32336.9i q^{32} +(5779.54 + 2314.56i) q^{33} +24319.0 q^{34} +3217.39i q^{35} +(-20264.5 - 19331.1i) q^{36} +29502.1 q^{37} -56173.1i q^{38} +(6933.44 - 17313.0i) q^{39} -12856.0 q^{40} +102478. i q^{41} +(16435.5 + 6582.01i) q^{42} -108429. q^{43} +8858.39i q^{44} +(-12488.0 + 13090.9i) q^{45} +43896.3 q^{46} +203296. i q^{47} +(-1620.34 + 4046.05i) q^{48} +16807.0 q^{49} -75915.2i q^{50} +(120513. + 48262.4i) q^{51} +26536.0 q^{52} -35192.0i q^{53} +(41325.3 + 90573.4i) q^{54} +5722.54 q^{55} +67157.1i q^{56} +(111479. - 278367. i) q^{57} -122817. q^{58} -224755. i q^{59} +(-23897.2 - 9570.24i) q^{60} -35470.3 q^{61} +36167.8i q^{62} +(68384.1 + 65234.5i) q^{63} -173889. q^{64} -17142.3i q^{65} +(11706.9 - 29232.6i) q^{66} -523102. q^{67} +184712. i q^{68} +(217529. + 87114.9i) q^{69} +16273.4 q^{70} -622802. i q^{71} +(-260663. + 273248. i) q^{72} -99977.5 q^{73} -149220. i q^{74} +(150658. - 376199. i) q^{75} +426658. q^{76} -29893.4i q^{77} +(-87568.5 - 35069.0i) q^{78} +275833. q^{79} +4006.14i q^{80} +(25039.8 + 530851. i) q^{81} +518330. q^{82} +375630. i q^{83} +(-49993.0 + 124834. i) q^{84} +119324. q^{85} +548431. i q^{86} +(-608622. - 243738. i) q^{87} +119447. q^{88} +617008. i q^{89} +(66213.0 + 63163.4i) q^{90} -89547.8 q^{91} +333410. i q^{92} +(-71777.1 + 179230. i) q^{93} +1.02826e6 q^{94} -275622. i q^{95} +(-810516. - 324591. i) q^{96} -1.14802e6 q^{97} -85008.9i q^{98} +(116028. - 121630. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9}+O(q^{10}) \) 12 * q + 52 * q^3 - 516 * q^4 + 350 * q^6 - 644 * q^9	\( 12 q + 52 q^{3} - 516 q^{4} + 350 q^{6} - 644 q^{9} - 1092 q^{10} - 1726 q^{12} + 384 q^{13} - 632 q^{15} + 5892 q^{16} - 40 q^{18} + 11304 q^{19} - 5488 q^{21} + 15312 q^{22} + 12138 q^{24} - 77292 q^{25} + 114796 q^{27} + 41160 q^{28} - 101908 q^{30} - 9360 q^{31} - 65744 q^{33} - 169008 q^{34} - 195652 q^{36} + 212016 q^{37} + 159544 q^{39} + 196644 q^{40} - 37730 q^{42} + 28080 q^{43} - 4760 q^{45} - 418512 q^{46} + 865742 q^{48} + 201684 q^{49} - 371880 q^{51} - 138300 q^{52} - 254170 q^{54} - 732144 q^{55} - 440624 q^{57} + 1164240 q^{58} + 677660 q^{60} + 926736 q^{61} + 2744 q^{63} - 1380108 q^{64} - 1414588 q^{66} - 223104 q^{67} + 153048 q^{69} - 382788 q^{70} - 540192 q^{72} + 600984 q^{73} + 594716 q^{75} + 604596 q^{76} + 1866140 q^{78} - 276864 q^{79} + 617596 q^{81} + 1138200 q^{82} + 1398754 q^{84} - 3002472 q^{85} - 3372824 q^{87} - 1599048 q^{88} - 788032 q^{90} - 1243032 q^{91} + 408168 q^{93} + 8059296 q^{94} - 1141658 q^{96} + 1621416 q^{97} + 5211904 q^{99}+O(q^{100}) \) 12 * q + 52 * q^3 - 516 * q^4 + 350 * q^6 - 644 * q^9 - 1092 * q^10 - 1726 * q^12 + 384 * q^13 - 632 * q^15 + 5892 * q^16 - 40 * q^18 + 11304 * q^19 - 5488 * q^21 + 15312 * q^22 + 12138 * q^24 - 77292 * q^25 + 114796 * q^27 + 41160 * q^28 - 101908 * q^30 - 9360 * q^31 - 65744 * q^33 - 169008 * q^34 - 195652 * q^36 + 212016 * q^37 + 159544 * q^39 + 196644 * q^40 - 37730 * q^42 + 28080 * q^43 - 4760 * q^45 - 418512 * q^46 + 865742 * q^48 + 201684 * q^49 - 371880 * q^51 - 138300 * q^52 - 254170 * q^54 - 732144 * q^55 - 440624 * q^57 + 1164240 * q^58 + 677660 * q^60 + 926736 * q^61 + 2744 * q^63 - 1380108 * q^64 - 1414588 * q^66 - 223104 * q^67 + 153048 * q^69 - 382788 * q^70 - 540192 * q^72 + 600984 * q^73 + 594716 * q^75 + 604596 * q^76 + 1866140 * q^78 - 276864 * q^79 + 617596 * q^81 + 1138200 * q^82 + 1398754 * q^84 - 3002472 * q^85 - 3372824 * q^87 - 1599048 * q^88 - 788032 * q^90 - 1243032 * q^91 + 408168 * q^93 + 8059296 * q^94 - 1141658 * q^96 + 1621416 * q^97 + 5211904 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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