LMFDB - Embedded newform 18.7.d.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,7,Mod(5,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("18.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	18.d (of order $6$, 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:	$4.14097350516$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600 $ x^12 + 370x^10 + 51793x^8 + 3491832x^6 + 117603792x^4 + 1832032512*x^2 + 10453017600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.3
Root			$11.8022i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.7.d.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 - 2.82843i) q^{2} +(25.6924 - 8.30052i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-9.39126 + 5.42205i) q^{5} +(-149.344 - 32.0051i) q^{6} +(322.041 - 557.792i) q^{7} -181.019i q^{8} +(591.203 - 426.521i) q^{9} +O(q^{10})$	\(q+(-4.89898 - 2.82843i) q^{2} +(25.6924 - 8.30052i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-9.39126 + 5.42205i) q^{5} +(-149.344 - 32.0051i) q^{6} +(322.041 - 557.792i) q^{7} -181.019i q^{8} +(591.203 - 426.521i) q^{9} +61.3435 q^{10} +(-1058.59 - 611.175i) q^{11} +(641.110 + 579.201i) q^{12} +(1163.39 + 2015.05i) q^{13} +(-3155.35 + 1821.74i) q^{14} +(-196.279 + 217.258i) q^{15} +(-512.000 + 886.810i) q^{16} +3382.18i q^{17} +(-4102.67 + 417.346i) q^{18} +6234.31 q^{19} +(-300.520 - 173.506i) q^{20} +(3644.06 - 17004.1i) q^{21} +(3457.33 + 5988.27i) q^{22} +(-12444.3 + 7184.71i) q^{23} +(-1502.56 - 4650.83i) q^{24} +(-7753.70 + 13429.8i) q^{25} -13162.2i q^{26} +(11649.1 - 15865.7i) q^{27} +20610.6 q^{28} +(11757.8 + 6788.37i) q^{29} +(1576.06 - 509.183i) q^{30} +(-4393.16 - 7609.18i) q^{31} +(5016.55 - 2896.31i) q^{32} +(-32270.7 - 6915.75i) q^{33} +(9566.26 - 16569.2i) q^{34} +6984.49i q^{35} +(21279.3 + 9559.54i) q^{36} -27898.6 q^{37} +(-30541.8 - 17633.3i) q^{38} +(46616.2 + 42114.7i) q^{39} +(981.495 + 1700.00i) q^{40} +(-47968.4 + 27694.6i) q^{41} +(-65947.1 + 72996.0i) q^{42} +(-26959.0 + 46694.4i) q^{43} -39115.2i q^{44} +(-3239.52 + 7211.10i) q^{45} +81285.7 q^{46} +(152425. + 88002.4i) q^{47} +(-5793.54 + 27034.2i) q^{48} +(-148597. - 257377. i) q^{49} +(75970.5 - 43861.6i) q^{50} +(28073.9 + 86896.5i) q^{51} +(-37228.4 + 64481.5i) q^{52} -83918.6i q^{53} +(-101943. + 44777.0i) q^{54} +13255.3 q^{55} +(-100971. - 58295.7i) q^{56} +(160175. - 51748.1i) q^{57} +(-38400.8 - 66512.2i) q^{58} +(305843. - 176579. i) q^{59} +(-9161.29 - 1963.30i) q^{60} +(-83314.3 + 144305. i) q^{61} +49702.9i q^{62} +(-47518.5 - 467125. i) q^{63} -32768.0 q^{64} +(-21851.4 - 12615.9i) q^{65} +(138533. + 125156. i) q^{66} +(45249.4 + 78374.3i) q^{67} +(-93729.8 + 54114.9i) q^{68} +(-260087. + 287887. i) q^{69} +(19755.1 - 34216.9i) q^{70} +429740. i q^{71} +(-77208.6 - 107019. i) q^{72} +274010. q^{73} +(136675. + 78909.1i) q^{74} +(-87737.1 + 409404. i) q^{75} +(99749.0 + 172770. i) q^{76} +(-681817. + 393647. i) q^{77} +(-109253. - 338170. i) q^{78} +(-163147. + 282579. i) q^{79} -11104.4i q^{80} +(167600. - 504321. i) q^{81} +313328. q^{82} +(-858836. - 495849. i) q^{83} +(529538. - 171079. i) q^{84} +(-18338.4 - 31763.0i) q^{85} +(264143. - 152503. i) q^{86} +(358434. + 76813.9i) q^{87} +(-110635. + 191625. i) q^{88} -538101. i q^{89} +(36266.4 - 26164.3i) q^{90} +1.49863e6 q^{91} +(-398217. - 229911. i) q^{92} +(-176031. - 159033. i) q^{93} +(-497817. - 862244. i) q^{94} +(-58548.1 + 33802.7i) q^{95} +(104847. - 116053. i) q^{96} +(42974.7 - 74434.4i) q^{97} +1.68118e6i q^{98} +(-886518. + 90181.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9}+O(q^{10}) $ 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9	\( 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9} + 378 q^{11} + 384 q^{12} + 1680 q^{13} - 4752 q^{14} - 10872 q^{15} - 6144 q^{16} - 2976 q^{18} - 2820 q^{19} + 13824 q^{20} + 24876 q^{21} - 3600 q^{22} - 76248 q^{23} - 6144 q^{24} + 8094 q^{25} + 127008 q^{27} + 15360 q^{28} + 97092 q^{29} + 34272 q^{30} + 21480 q^{31} - 246258 q^{33} - 27360 q^{34} + 38208 q^{36} - 25536 q^{37} + 97632 q^{38} + 42204 q^{39} - 410562 q^{41} - 222144 q^{42} + 71430 q^{43} + 13716 q^{45} - 135072 q^{46} + 347652 q^{47} + 55296 q^{48} - 135954 q^{49} + 311040 q^{50} + 336402 q^{51} - 53760 q^{52} - 173520 q^{54} + 580392 q^{55} - 152064 q^{56} - 522282 q^{57} + 159264 q^{58} + 369738 q^{59} - 170496 q^{60} + 135744 q^{61} - 103800 q^{63} - 393216 q^{64} - 753840 q^{65} + 909216 q^{66} - 289938 q^{67} + 744768 q^{68} + 2059272 q^{69} + 155952 q^{70} - 374784 q^{72} - 977700 q^{73} - 2197152 q^{74} - 2115342 q^{75} - 45120 q^{76} - 159192 q^{77} - 631488 q^{78} - 764796 q^{79} - 1428282 q^{81} + 1073088 q^{82} + 396900 q^{83} + 1441536 q^{84} + 1619568 q^{85} + 3264624 q^{86} + 3072636 q^{87} + 115200 q^{88} - 1987200 q^{90} + 355584 q^{91} - 2439936 q^{92} - 2526576 q^{93} - 736848 q^{94} - 2089260 q^{95} - 49152 q^{96} - 38874 q^{97} + 4398804 q^{99}+O(q^{100}) \) 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9 + 378 * q^11 + 384 * q^12 + 1680 * q^13 - 4752 * q^14 - 10872 * q^15 - 6144 * q^16 - 2976 * q^18 - 2820 * q^19 + 13824 * q^20 + 24876 * q^21 - 3600 * q^22 - 76248 * q^23 - 6144 * q^24 + 8094 * q^25 + 127008 * q^27 + 15360 * q^28 + 97092 * q^29 + 34272 * q^30 + 21480 * q^31 - 246258 * q^33 - 27360 * q^34 + 38208 * q^36 - 25536 * q^37 + 97632 * q^38 + 42204 * q^39 - 410562 * q^41 - 222144 * q^42 + 71430 * q^43 + 13716 * q^45 - 135072 * q^46 + 347652 * q^47 + 55296 * q^48 - 135954 * q^49 + 311040 * q^50 + 336402 * q^51 - 53760 * q^52 - 173520 * q^54 + 580392 * q^55 - 152064 * q^56 - 522282 * q^57 + 159264 * q^58 + 369738 * q^59 - 170496 * q^60 + 135744 * q^61 - 103800 * q^63 - 393216 * q^64 - 753840 * q^65 + 909216 * q^66 - 289938 * q^67 + 744768 * q^68 + 2059272 * q^69 + 155952 * q^70 - 374784 * q^72 - 977700 * q^73 - 2197152 * q^74 - 2115342 * q^75 - 45120 * q^76 - 159192 * q^77 - 631488 * q^78 - 764796 * q^79 - 1428282 * q^81 + 1073088 * q^82 + 396900 * q^83 + 1441536 * q^84 + 1619568 * q^85 + 3264624 * q^86 + 3072636 * q^87 + 115200 * q^88 - 1987200 * q^90 + 355584 * q^91 - 2439936 * q^92 - 2526576 * q^93 - 736848 * q^94 - 2089260 * q^95 - 49152 * q^96 - 38874 * q^97 + 4398804 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−4.89898	−	2.82843i	−0.612372	−	0.353553i
$2$	−4.89898	−	2.82843i	−0.612372	−	0.353553i
$3$	25.6924	−	8.30052i	0.951572	−	0.307427i
$3$	25.6924	−	8.30052i	0.951572	−	0.307427i
$4$	16.0000	+	27.7128i	0.250000	+	0.433013i
$5$	−9.39126	+	5.42205i	−0.0751301	+	0.0433764i	−0.537094	−	0.843522i	$-0.680478\pi$
$5$	−9.39126	+	5.42205i	−0.0751301	+	0.0433764i	0.461964	+	0.886898i	$0.347145\pi$
$6$	−149.344	−	32.0051i	−0.691408	−	0.148172i
$7$	322.041	−	557.792i	0.938896	−	1.62622i	0.171360	−	0.985208i	$-0.445184\pi$
$7$	322.041	−	557.792i	0.938896	−	1.62622i	0.767535	−	0.641007i	$-0.221483\pi$
$8$		−	181.019i		−	0.353553i
$9$	591.203	−	426.521i	0.810977	−	0.585077i
$10$	61.3435			0.0613435
$11$	−1058.59	−	611.175i	−0.795332	−	0.459185i	0.0465046	−	0.998918i	$-0.485192\pi$
$11$	−1058.59	−	611.175i	−0.795332	−	0.459185i	−0.841836	+	0.539733i	$0.818525\pi$
$12$	641.110	+	579.201i	0.371013	+	0.335186i
$13$	1163.39	+	2015.05i	0.529535	+	0.917181i	0.999407	+	0.0344462i	$0.0109667\pi$
$13$	1163.39	+	2015.05i	0.529535	+	0.917181i	−0.469872	+	0.882735i	$0.655700\pi$
$14$	−3155.35	+	1821.74i	−1.14991	+	0.663900i
$15$	−196.279	+	217.258i	−0.0581566	+	0.0643727i
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$			3382.18i			0.688415i	0.938894	+	0.344207i	$0.111852\pi$
$17$			3382.18i			0.688415i	−0.938894	+	0.344207i	$0.888148\pi$
$18$	−4102.67	+	417.346i	−0.703476	+	0.0715614i
$19$	6234.31			0.908924			0.454462	−	0.890766i	$-0.349831\pi$
$19$	6234.31			0.908924			0.454462	+	0.890766i	$0.349831\pi$
$20$	−300.520	−	173.506i	−0.0375650	−	0.0216882i
$21$	3644.06	−	17004.1i	0.393484	−	1.83610i
$22$	3457.33	+	5988.27i	0.324693	+	0.562384i
$23$	−12444.3	+	7184.71i	−1.02279	+	0.590508i	−0.914911	−	0.403656i	$-0.867739\pi$
$23$	−12444.3	+	7184.71i	−1.02279	+	0.590508i	−0.107879	+	0.994164i	$0.534406\pi$
$24$	−1502.56	−	4650.83i	−0.108692	−	0.336431i
$25$	−7753.70	+	13429.8i	−0.496237	+	0.859508i
$26$		−	13162.2i		−	0.748875i
$27$	11649.1	−	15865.7i	0.591835	−	0.806059i
$28$	20610.6			0.938896
$29$	11757.8	+	6788.37i	0.482095	+	0.278338i	0.721289	−	0.692634i	$-0.243550\pi$
$29$	11757.8	+	6788.37i	0.482095	+	0.278338i	−0.239194	+	0.970972i	$0.576883\pi$
$30$	1576.06	−	509.183i	0.0583727	−	0.0188586i
$31$	−4393.16	−	7609.18i	−0.147466	−	0.255419i	0.782824	−	0.622243i	$-0.213778\pi$
$31$	−4393.16	−	7609.18i	−0.147466	−	0.255419i	−0.930290	+	0.366824i	$0.880445\pi$
$32$	5016.55	−	2896.31i	0.153093	−	0.0883883i
$33$	−32270.7	−	6915.75i	−0.897981	−	0.192441i
$34$	9566.26	−	16569.2i	0.243391	−	0.421566i
$35$			6984.49i			0.162904i
$36$	21279.3	+	9559.54i	0.456090	+	0.204894i
$37$	−27898.6			−0.550779			−0.275389	−	0.961333i	$-0.588807\pi$
$37$	−27898.6			−0.550779			−0.275389	+	0.961333i	$0.588807\pi$
$38$	−30541.8	−	17633.3i	−0.556600	−	0.321353i
$39$	46616.2	+	42114.7i	0.785856	+	0.709970i
$40$	981.495	+	1700.00i	0.0153359	+	0.0265625i
$41$	−47968.4	+	27694.6i	−0.695991	+	0.401831i	−0.805852	−	0.592116i	$-0.798293\pi$
$41$	−47968.4	+	27694.6i	−0.695991	+	0.401831i	0.109862	+	0.993947i	$0.464959\pi$
$42$	−65947.1	+	72996.0i	−0.890119	+	0.985261i
$43$	−26959.0	+	46694.4i	−0.339077	+	0.587299i	−0.984259	−	0.176730i	$-0.943448\pi$
$43$	−26959.0	+	46694.4i	−0.339077	+	0.587299i	0.645182	+	0.764029i	$0.276781\pi$
$44$		−	39115.2i		−	0.459185i
$45$	−3239.52	+	7211.10i	−0.0355503	+	0.0791342i
$46$	81285.7			0.835104
$47$	152425.	+	88002.4i	1.46812	+	0.847620i	0.999362	−	0.0357064i	$-0.0113681\pi$
$47$	152425.	+	88002.4i	1.46812	+	0.847620i	0.468758	+	0.883326i	$0.344701\pi$
$48$	−5793.54	+	27034.2i	−0.0523866	+	0.244450i
$49$	−148597.	−	257377.i	−1.26305	−	2.18767i
$50$	75970.5	−	43861.6i	0.607764	−	0.350893i
$51$	28073.9	+	86896.5i	0.211637	+	0.655076i
$52$	−37228.4	+	64481.5i	−0.264767	+	0.458590i
$53$		−	83918.6i		−	0.563678i	−0.959462	−	0.281839i	$-0.909056\pi$
$53$		−	83918.6i		−	0.563678i	0.959462	−	0.281839i	$-0.0909443\pi$
$54$	−101943.	+	44777.0i	−0.647408	+	0.284363i
$55$	13255.3			0.0796711
$56$	−100971.	−	58295.7i	−0.574954	−	0.331950i
$57$	160175.	−	51748.1i	0.864907	−	0.279428i
$58$	−38400.8	−	66512.2i	−0.196814	−	0.340892i
$59$	305843.	−	176579.i	1.48917	−	0.859770i	0.489243	−	0.872148i	$-0.337273\pi$
$59$	305843.	−	176579.i	1.48917	−	0.859770i	0.999923	+	0.0123773i	$0.00393991\pi$
$60$	−9161.29	−	1963.30i	−0.0424134	−	0.00908936i
$61$	−83314.3	+	144305.i	−0.367054	+	0.635756i	−0.989104	−	0.147222i	$-0.952967\pi$
$61$	−83314.3	+	144305.i	−0.367054	+	0.635756i	0.622050	+	0.782978i	$0.286300\pi$
$62$			49702.9i			0.208548i
$63$	−47518.5	−	467125.i	−0.190038	−	1.86815i
$64$	−32768.0			−0.125000
$65$	−21851.4	−	12615.9i	−0.0795680	−	0.0459386i
$66$	138533.	+	125156.i	0.481860	+	0.435330i
$67$	45249.4	+	78374.3i	0.150449	+	0.260585i	0.931393	−	0.364016i	$-0.118595\pi$
$67$	45249.4	+	78374.3i	0.150449	+	0.260585i	−0.780944	+	0.624601i	$0.785261\pi$
$68$	−93729.8	+	54114.9i	−0.298092	+	0.172104i
$69$	−260087.	+	287887.i	−0.791719	+	0.876343i
$70$	19755.1	−	34216.9i	0.0575951	−	0.0997577i
$71$			429740.i			1.20069i	0.799741	+	0.600345i	$0.204970\pi$
$71$			429740.i			1.20069i	−0.799741	+	0.600345i	$0.795030\pi$
$72$	−77208.6	−	107019.i	−0.206856	−	0.286724i
$73$	274010.			0.704366			0.352183	−	0.935931i	$-0.385440\pi$
$73$	274010.			0.704366			0.352183	+	0.935931i	$0.385440\pi$
$74$	136675.	+	78909.1i	0.337282	+	0.194730i
$75$	−87737.1	+	409404.i	−0.207969	+	0.970440i
$76$	99749.0	+	172770.i	0.227231	+	0.393576i
$77$	−681817.	+	393647.i	−1.49347	+	0.862253i
$78$	−109253.	−	338170.i	−0.230224	−	0.712608i
$79$	−163147.	+	282579.i	−0.330901	+	0.573137i	−0.982689	−	0.185264i	$-0.940686\pi$
$79$	−163147.	+	282579.i	−0.330901	+	0.573137i	0.651788	+	0.758401i	$0.274019\pi$
$80$		−	11104.4i		−	0.0216882i
$81$	167600.	−	504321.i	0.315369	−	0.948969i
$82$	313328.			0.568274
$83$	−858836.	−	495849.i	−1.50202	−	0.867192i	−0.999997	−	0.00233889i	$-0.999256\pi$
$83$	−858836.	−	495849.i	−1.50202	−	0.867192i	−0.502024	−	0.864854i	$-0.667411\pi$
$84$	529538.	−	171079.i	0.893427	−	0.288642i
$85$	−18338.4	−	31763.0i	−0.0298609	−	0.0517207i
$86$	264143.	−	152503.i	0.415283	−	0.239764i
$87$	358434.	+	76813.9i	0.544316	+	0.116649i
$88$	−110635.	+	191625.i	−0.162346	+	0.281192i
$89$		−	538101.i		−	0.763298i	−0.924307	−	0.381649i	$-0.875356\pi$
$89$		−	538101.i		−	0.763298i	0.924307	−	0.381649i	$-0.124644\pi$
$90$	36266.4	−	26164.3i	0.0497482	−	0.0358907i
$91$	1.49863e6			1.98871
$92$	−398217.	−	229911.i	−0.511395	−	0.295254i
$93$	−176031.	−	159033.i	−0.218847	−	0.197714i
$94$	−497817.	−	862244.i	−0.599358	−	1.03812i
$95$	−58548.1	+	33802.7i	−0.0682876	+	0.0394259i
$96$	104847.	−	116053.i	0.118506	−	0.131173i
$97$	42974.7	−	74434.4i	0.0470867	−	0.0815565i	−0.841521	−	0.540224i	$-0.818340\pi$
$97$	42974.7	−	74434.4i	0.0470867	−	0.0815565i	0.888608	+	0.458667i	$0.151673\pi$
$98$			1.68118e6i			1.78622i
$99$	−886518.	+	90181.4i	−0.913655	+	0.0929419i
$100$	−496237.			−0.496237
$101$	1.04085e6	+	600935.i	1.01024	+	0.583262i	0.911262	−	0.411828i	$-0.135109\pi$
$101$	1.04085e6	+	600935.i	1.01024	+	0.583262i	0.0989776	+	0.995090i	$0.468443\pi$
$102$	108247.	−	505109.i	0.102004	−	0.475976i
$103$	166737.	+	288797.i	0.152588	+	0.264290i	0.932178	−	0.362000i	$-0.117906\pi$
$103$	166737.	+	288797.i	0.152588	+	0.264290i	−0.779590	+	0.626290i	$0.784573\pi$
$104$	364762.	−	210596.i	0.324272	−	0.187219i
$105$	57974.9	+	179449.i	0.0500809	+	0.155014i
$106$	−237358.	+	411116.i	−0.199290	+	0.345181i
$107$		−	2.15926e6i		−	1.76260i	−0.472558	−	0.881299i	$-0.656669\pi$
$107$		−	2.15926e6i		−	1.76260i	0.472558	−	0.881299i	$-0.343331\pi$
$108$	626068.	+	68978.2i	0.496993	+	0.0547571i
$109$	−651642.			−0.503187			−0.251594	−	0.967833i	$-0.580955\pi$
$109$	−651642.			−0.503187			−0.251594	+	0.967833i	$0.580955\pi$
$110$	−64937.4	−	37491.6i	−0.0487884	−	0.0281680i
$111$	−716783.	+	231573.i	−0.524105	+	0.169324i
$112$	329770.	+	571179.i	0.234724	+	0.406554i
$113$	−385869.	+	222782.i	−0.267427	+	0.154399i	−0.627718	−	0.778441i	$-0.716011\pi$
$113$	−385869.	+	222782.i	−0.267427	+	0.154399i	0.360291	+	0.932840i	$0.382677\pi$
$114$	−931058.	−	199530.i	−0.628438	−	0.134677i
$115$	77911.6	−	134947.i	0.0512282	−	0.0887298i
$116$			434456.i			0.278338i
$117$	1.54726e6	+	695091.i	0.966062	+	0.433994i
$118$	−1.99776e6			−1.21590
$119$	1.88655e6	+	1.08920e6i	1.11951	+	0.646350i
$120$	39327.9	+	35530.2i	0.0227592	+	0.0205615i
$121$	−138711.	−	240254.i	−0.0782985	−	0.135617i
$122$	816310.	−	471297.i	0.449547	−	0.259546i
$123$	−1.00255e6	+	1.10970e6i	−0.538752	+	0.596337i
$124$	140581.	−	243494.i	0.0737330	−	0.127709i
$125$		−	337603.i		−	0.172853i
$126$	−1.08844e6	+	2.42284e6i	−0.544117	+	1.21119i
$127$	−3.14533e6			−1.53552			−0.767760	−	0.640737i	$-0.778629\pi$
$127$	−3.14533e6			−1.53552			−0.767760	+	0.640737i	$0.778629\pi$
$128$	160530.	+	92681.9i	0.0765466	+	0.0441942i
$129$	−305055.	+	1.42347e6i	−0.142105	+	0.663098i
$130$	71366.2	+	123610.i	0.0324835	+	0.0562631i
$131$	906108.	−	523142.i	0.403057	−	0.232705i	−0.284745	−	0.958603i	$-0.591909\pi$
$131$	906108.	−	523142.i	0.403057	−	0.232705i	0.687802	+	0.725898i	$0.258576\pi$
$132$	−324677.	−	1.00496e6i	−0.141166	−	0.436947i
$133$	2.00771e6	−	3.47745e6i	0.853385	−	1.47811i
$134$		−	511939.i		−	0.212767i
$135$	−23375.2	+	212161.i	−0.00950066	+	0.0862310i
$136$	612240.			0.243391
$137$	−40404.2	−	23327.4i	−0.0157132	−	0.00907203i	0.492123	−	0.870526i	$-0.336221\pi$
$137$	−40404.2	−	23327.4i	−0.0157132	−	0.00907203i	−0.507836	+	0.861454i	$0.669554\pi$
$138$	2.08843e6	−	674714.i	0.794661	−	0.256733i
$139$	694301.	+	1.20257e6i	0.258526	+	0.447780i	0.965847	−	0.259112i	$-0.0834300\pi$
$139$	694301.	+	1.20257e6i	0.258526	+	0.447780i	−0.707322	+	0.706892i	$0.750097\pi$
$140$	−193560.	+	111752.i	−0.0705393	+	0.0407259i
$141$	4.64663e6	+	995792.i	1.65760	+	0.355231i
$142$	1.21549e6	−	2.10529e6i	0.424508	−	0.735270i
$143$		−	2.84413e6i		−	0.972617i
$144$	75547.7	+	742663.i	0.0253008	+	0.248716i
$145$	−147228.			−0.0482931
$146$	−1.34237e6	−	775018.i	−0.431334	−	0.249031i
$147$	−5.95417e6	−	5.37921e6i	−1.87443	−	1.69343i
$148$	−446377.	−	773148.i	−0.137695	−	0.238494i
$149$	−3.27251e6	+	1.88939e6i	−0.989287	+	0.571165i	−0.905061	−	0.425281i	$-0.860175\pi$
$149$	−3.27251e6	+	1.88939e6i	−0.989287	+	0.571165i	−0.0842261	+	0.996447i	$0.526842\pi$
$150$	1.58779e6	−	1.75751e6i	0.470457	−	0.520742i
$151$	−1.27032e6	+	2.20027e6i	−0.368964	+	0.639064i	−0.989404	−	0.145190i	$-0.953621\pi$
$151$	−1.27032e6	+	2.20027e6i	−0.368964	+	0.639064i	0.620440	+	0.784254i	$0.286954\pi$
$152$		−	1.12853e6i		−	0.321353i
$153$	1.44257e6	+	1.99955e6i	0.402776	+	0.558289i
$154$	4.45361e6			1.21941
$155$	82514.6	+	47639.9i	0.0221583	+	0.0127931i
$156$	−421258.	+	1.96570e6i	−0.110962	+	0.517778i
$157$	−312032.	−	540456.i	−0.0806307	−	0.139656i	0.822890	−	0.568200i	$-0.192360\pi$
$157$	−312032.	−	540456.i	−0.0806307	−	0.139656i	−0.903521	+	0.428544i	$0.859027\pi$
$158$	1.59851e6	−	922899.i	0.405269	−	0.233982i
$159$	−696569.	−	2.15607e6i	−0.173290	−	0.536380i
$160$	−31407.9	+	54400.0i	−0.00766793	+	0.0132812i
$161$			9.25509e6i			2.21770i
$162$	−2.24750e6	+	1.99661e6i	−0.528634	+	0.469623i
$163$	−2.16727e6			−0.500438			−0.250219	−	0.968189i	$-0.580503\pi$
$163$	−2.16727e6			−0.500438			−0.250219	+	0.968189i	$0.580503\pi$
$164$	−1.53499e6	−	886226.i	−0.347995	−	0.200915i
$165$	340560.	−	110026.i	0.0758128	−	0.0244930i
$166$	2.80495e6	+	4.85831e6i	0.613198	+	1.06209i
$167$	−2.87525e6	+	1.66003e6i	−0.617343	+	0.356423i	−0.775834	−	0.630937i	$-0.782671\pi$
$167$	−2.87525e6	+	1.66003e6i	−0.617343	+	0.356423i	0.158491	+	0.987360i	$0.449337\pi$
$168$	−3.07808e6	−	659645.i	−0.649160	−	0.139118i
$169$	−293536.	+	508420.i	−0.0608138	+	0.105333i
$170$			207475.i			0.0422298i
$171$	3.68574e6	−	2.65907e6i	0.737117	−	0.531791i
$172$	−1.72538e6			−0.339077
$173$	791912.	+	457211.i	0.152946	+	0.0883035i	0.574520	−	0.818491i	$-0.305189\pi$
$173$	791912.	+	457211.i	0.152946	+	0.0883035i	−0.421574	+	0.906794i	$0.638522\pi$
$174$	−1.53870e6	−	1.39011e6i	−0.292082	−	0.263878i
$175$	4.99402e6	+	8.64990e6i	0.931830	+	1.61398i
$176$	1.08399e6	−	625843.i	0.198833	−	0.114796i
$177$	6.39217e6	−	7.07540e6i	1.15273	−	1.27594i
$178$	−1.52198e6	+	2.63615e6i	−0.269867	+	0.467423i
$179$		−	3.42647e6i		−	0.597431i	−0.954342	−	0.298716i	$-0.903442\pi$
$179$		−	3.42647e6i		−	0.597431i	0.954342	−	0.298716i	$-0.0965582\pi$
$180$	−251672.	+	25601.5i	−0.0431537	+	0.00438983i
$181$	−5.16532e6			−0.871087			−0.435543	−	0.900168i	$-0.643444\pi$
$181$	−5.16532e6			−0.871087			−0.435543	+	0.900168i	$0.643444\pi$
$182$	−7.34178e6	−	4.23878e6i	−1.21783	−	0.703116i
$183$	−942743.	+	4.39909e6i	−0.153830	+	0.717810i
$184$	1.30057e6	+	2.25265e6i	0.208776	+	0.361611i
$185$	262003.	−	151267.i	0.0413801	−	0.0238908i
$186$	412560.	+	1.27699e6i	0.0641134	+	0.198449i
$187$	2.06711e6	−	3.58033e6i	0.316110	−	0.547518i
$188$			5.63216e6i			0.847620i
$189$	−5.09825e6	−	1.16072e7i	−0.755155	−	1.71926i
$190$	382434.			0.0557566
$191$	4.66116e6	+	2.69112e6i	0.668950	+	0.386218i	0.795679	−	0.605719i	$-0.207114\pi$
$191$	4.66116e6	+	2.69112e6i	0.668950	+	0.386218i	−0.126729	+	0.991937i	$0.540448\pi$
$192$	−841890.	+	271992.i	−0.118946	+	0.0384284i
$193$	−3.73195e6	−	6.46392e6i	−0.519115	−	0.899133i	−0.999753	−	0.0222145i	$-0.992928\pi$
$193$	−3.73195e6	−	6.46392e6i	−0.519115	−	0.899133i	0.480638	−	0.876919i	$-0.340405\pi$
$194$	−421065.	+	243102.i	−0.0576691	+	0.0332953i
$195$	−666133.	−	142755.i	−0.0898374	−	0.0192525i
$196$	4.75509e6	−	8.23606e6i	0.631525	−	1.09383i
$197$		−	2.66109e6i		−	0.348066i	−0.984740	−	0.174033i	$-0.944320\pi$
$197$		−	2.66109e6i		−	0.348066i	0.984740	−	0.174033i	$-0.0556799\pi$
$198$	4.59811e6	+	2.06566e6i	0.592357	+	0.266111i
$199$	1.13134e7			1.43560			0.717801	−	0.696248i	$-0.245149\pi$
$199$	1.13134e7			1.43560			0.717801	+	0.696248i	$0.245149\pi$
$200$	2.43105e6	+	1.40357e6i	0.303882	+	0.175446i
$201$	1.81312e6	+	1.63803e6i	0.223274	+	0.201713i
$202$	−3.39940e6	−	5.88794e6i	−0.412429	−	0.714347i
$203$	7.57300e6	−	4.37227e6i	0.905273	−	0.522660i
$204$	−1.95896e6	+	2.16835e6i	−0.230747	+	0.255411i
$205$	300322.	−	520174.i	0.0348599	−	0.0603791i
$206$		−	1.88641e6i		−	0.215792i
$207$	−4.29266e6	+	9.55537e6i	−0.483966	+	1.07730i
$208$	−2.38262e6			−0.264767
$209$	−6.59956e6	−	3.81026e6i	−0.722896	−	0.417364i
$210$	223539.	−	1.04309e6i	0.0241377	−	0.112633i
$211$	−2.61834e6	−	4.53511e6i	−0.278727	−	0.482770i	0.692341	−	0.721570i	$-0.256579\pi$
$211$	−2.61834e6	−	4.53511e6i	−0.278727	−	0.482770i	−0.971069	+	0.238800i	$0.923246\pi$
$212$	2.32562e6	−	1.34270e6i	0.244080	−	0.140919i
$213$	3.56707e6	+	1.10411e7i	0.369125	+	1.14254i
$214$	−6.10731e6	+	1.05782e7i	−0.623173	+	1.07937i
$215$		−	584692.i		−	0.0588318i
$216$	−2.87199e6	−	2.10871e6i	−0.284985	−	0.209245i
$217$	−5.65912e6			−0.553821
$218$	3.19238e6	+	1.84312e6i	0.308138	+	0.177904i
$219$	7.03999e6	−	2.27443e6i	0.670254	−	0.216541i
$220$	212085.	+	367341.i	0.0199178	+	0.0344986i
$221$	−6.81525e6	+	3.93479e6i	−0.631401	+	0.364539i
$222$	4.16649e6	+	892897.i	0.380813	+	0.0816098i
$223$	−4.46185e6	+	7.72815e6i	−0.402347	+	0.696885i	−0.994009	−	0.109301i	$-0.965139\pi$
$223$	−4.46185e6	+	7.72815e6i	−0.402347	+	0.696885i	0.591662	+	0.806186i	$0.298472\pi$
$224$		−	3.73092e6i		−	0.331950i
$225$	1.14409e6	+	1.12469e7i	0.100441	+	0.987378i
$226$	2.52049e6			0.218353
$227$	1.09112e6	+	629961.i	0.0932817	+	0.0538562i	0.545915	−	0.837840i	$-0.316182\pi$
$227$	1.09112e6	+	629961.i	0.0932817	+	0.0538562i	−0.452633	+	0.891697i	$0.649515\pi$
$228$	3.99688e6	+	3.61092e6i	0.337222	+	0.304659i
$229$	−7.62554e6	−	1.32078e7i	−0.634986	−	1.09983i	−0.986518	−	0.163652i	$-0.947672\pi$
$229$	−7.62554e6	−	1.32078e7i	−0.634986	−	1.09983i	0.351532	−	0.936176i	$-0.385661\pi$
$230$	−763375.	+	440735.i	−0.0627414	+	0.0362238i
$231$	−1.42501e7	+	1.57732e7i	−1.15606	+	1.27963i
$232$	1.22883e6	−	2.12839e6i	0.0984072	−	0.170446i
$233$		−	988329.i		−	0.0781329i	−0.999237	−	0.0390664i	$-0.987562\pi$
$233$		−	988329.i		−	0.0781329i	0.999237	−	0.0390664i	$-0.0124384\pi$
$234$	−5.61397e6	−	7.78154e6i	−0.438150	−	0.607321i
$235$	−1.90861e6			−0.147067
$236$	9.78699e6	+	5.65052e6i	0.744583	+	0.429885i
$237$	−1.84609e6	+	8.61435e6i	−0.138678	+	0.647109i
$238$	−6.16146e6	−	1.06720e7i	−0.457038	−	0.791614i
$239$	1.58228e7	−	9.13533e6i	1.15902	−	0.669161i	0.207951	−	0.978139i	$-0.433320\pi$
$239$	1.58228e7	−	9.13533e6i	1.15902	−	0.669161i	0.951069	+	0.308979i	$0.0999871\pi$
$240$	−92172.0	−	285298.i	−0.00666753	−	0.0206379i
$241$	323303.	−	559977.i	0.0230972	−	0.0400055i	−0.854246	−	0.519869i	$-0.825981\pi$
$241$	323303.	−	559977.i	0.0230972	−	0.0400055i	0.877343	+	0.479864i	$0.159314\pi$
$242$			1.56933e6i			0.110731i
$243$	119921.	−	1.43484e7i	0.00835753	−	0.999965i
$244$	−5.33211e6			−0.367054
$245$	2.79102e6	+	1.61140e6i	0.189786	+	0.109573i
$246$	8.05016e6	−	2.60079e6i	0.540754	−	0.174703i
$247$	7.25292e6	+	1.25624e7i	0.481307	+	0.833648i
$248$	−1.37741e6	+	795247.i	−0.0903041	+	0.0521371i
$249$	−2.61814e7	−	5.61079e6i	−1.69588	−	0.363434i
$250$	−954885.	+	1.65391e6i	−0.0611126	+	0.105850i
$251$		−	1.02408e6i		−	0.0647606i	−0.999476	−	0.0323803i	$-0.989691\pi$
$251$		−	1.02408e6i		−	0.0647606i	0.999476	−	0.0323803i	$-0.0103088\pi$
$252$	1.21851e7	−	8.79088e6i	0.761423	−	0.549327i
$253$	1.75645e7			1.08461
$254$	1.54089e7	+	8.89635e6i	0.940310	+	0.542888i
$255$	−734806.	−	663850.i	−0.0443152	−	0.0400359i
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	−8.77587e6	+	5.06675e6i	−0.517000	+	0.298490i	−0.735707	−	0.677300i	$-0.763150\pi$
$257$	−8.77587e6	+	5.06675e6i	−0.517000	+	0.298490i	0.218706	+	0.975791i	$0.429816\pi$
$258$	5.52063e6	−	6.11071e6i	0.321462	−	0.355822i
$259$	−8.98450e6	+	1.55616e7i	−0.517124	+	0.895685i
$260$		−	807417.i		−	0.0459386i
$261$	9.84663e6	−	1.00165e6i	0.553817	−	0.0563373i
$262$	−5.91868e6			−0.329095
$263$	−1.91632e7	−	1.10639e7i	−1.05342	−	0.608192i	−0.129814	−	0.991538i	$-0.541438\pi$
$263$	−1.91632e7	−	1.10639e7i	−1.05342	−	0.608192i	−0.923605	+	0.383347i	$0.874771\pi$
$264$	−1.25189e6	+	5.84163e6i	−0.0680382	+	0.317484i
$265$	455011.	+	788102.i	0.0244503	+	0.0423492i
$266$	−1.96714e7	+	1.13573e7i	−1.04518	+	0.603435i
$267$	−4.46652e6	−	1.38251e7i	−0.234658	−	0.726333i
$268$	−1.44798e6	+	2.50798e6i	−0.0752244	+	0.130292i
$269$		−	1.79826e7i		−	0.923840i	−0.886922	−	0.461920i	$-0.847161\pi$
$269$		−	1.79826e7i		−	0.923840i	0.886922	−	0.461920i	$-0.152839\pi$
$270$	714595.	−	973255.i	0.0363052	−	0.0494465i
$271$	3.08379e7			1.54945			0.774724	−	0.632299i	$-0.217889\pi$
$271$	3.08379e7			1.54945			0.774724	+	0.632299i	$0.217889\pi$
$272$	−2.99935e6	−	1.73168e6i	−0.149046	−	0.0860519i
$273$	3.85036e7	−	1.24395e7i	1.89240	−	0.611383i
$274$	131960.	+	228561.i	0.00641489	+	0.0111109i
$275$	1.64159e7	−	9.47774e6i	0.789346	−	0.455729i
$276$	−1.21395e7	−	2.60155e6i	−0.577398	−	0.123739i
$277$	5.92606e6	−	1.02642e7i	0.278822	−	0.482934i	−0.692270	−	0.721638i	$-0.743389\pi$
$277$	5.92606e6	−	1.02642e7i	0.278822	−	0.482934i	0.971092	+	0.238705i	$0.0767227\pi$
$278$		−	7.85512e6i		−	0.365610i
$279$	−5.84273e6	−	2.62479e6i	−0.269031	−	0.120860i
$280$	1.26433e6			0.0575951
$281$	4.89692e6	+	2.82724e6i	0.220701	+	0.127422i	0.606275	−	0.795255i	$-0.292663\pi$
$281$	4.89692e6	+	2.82724e6i	0.220701	+	0.127422i	−0.385574	+	0.922677i	$0.625996\pi$
$282$	−1.99472e7	−	1.80210e7i	−0.889477	−	0.803585i
$283$	−1.10442e7	−	1.91291e7i	−0.487277	−	0.843988i	0.512616	−	0.858618i	$-0.328676\pi$
$283$	−1.10442e7	−	1.91291e7i	−0.487277	−	0.843988i	−0.999893	+	0.0146299i	$0.995343\pi$
$284$	−1.19093e7	+	6.87585e6i	−0.519914	+	0.300173i
$285$	−1.22366e6	+	1.35445e6i	−0.0528600	+	0.0585100i
$286$	−8.04443e6	+	1.39334e7i	−0.343872	+	0.595604i
$287$			3.56752e7i			1.50911i
$288$	1.73046e6	−	3.85197e6i	0.0724410	−	0.161252i
$289$	1.26984e7			0.526085
$290$	721265.	+	416422.i	0.0295734	+	0.0170742i
$291$	486281.	−	2.26911e6i	0.0197337	−	0.0920826i
$292$	4.38416e6	+	7.59359e6i	0.176091	+	0.304999i
$293$	−3.73151e7	+	2.15439e7i	−1.48348	+	0.856488i	−0.999824	−	0.0187695i	$-0.994025\pi$
$293$	−3.73151e7	+	2.15439e7i	−1.48348	+	0.856488i	−0.483657	+	0.875258i	$0.660692\pi$
$294$	1.39547e7	+	4.31936e7i	0.549133	+	1.69972i
$295$	−1.91484e6	+	3.31660e6i	−0.0745875	+	0.129189i
$296$			5.05018e6i			0.194730i
$297$	−2.20283e7	+	9.67555e6i	−0.840835	+	0.369323i
$298$	2.13760e7			0.807750
$299$	−2.89550e7	−	1.67172e7i	−1.08320	−	0.625388i
$300$	−1.27495e7	+	4.11903e6i	−0.472205	+	0.152557i
$301$	1.73638e7	+	3.00750e7i	0.636716	+	1.10282i
$302$	1.24466e7	−	7.18604e6i	0.451886	−	0.260897i
$303$	3.17301e7	+	6.79989e6i	1.14063	+	0.244441i
$304$	−3.19197e6	+	5.52865e6i	−0.113616	+	0.196788i
$305$		−	1.80694e6i		−	0.0636859i
$306$	−1.41154e6	−	1.38760e7i	−0.0492640	−	0.484284i
$307$	−7.12229e6			−0.246153			−0.123076	−	0.992397i	$-0.539276\pi$
$307$	−7.12229e6			−0.246153			−0.123076	+	0.992397i	$0.539276\pi$
$308$	−2.18181e7	−	1.25967e7i	−0.746733	−	0.431127i
$309$	6.68104e6	+	6.03589e6i	0.226448	+	0.204581i
$310$	−269492.	−	466773.i	−0.00904608	−	0.0156683i
$311$	−1.93371e7	+	1.11643e7i	−0.642850	+	0.371150i	−0.785712	−	0.618593i	$-0.787703\pi$
$311$	−1.93371e7	+	1.11643e7i	−0.642850	+	0.371150i	0.142861	+	0.989743i	$0.454370\pi$
$312$	7.62358e6	−	8.43843e6i	0.251012	−	0.277842i
$313$	−1.34033e7	+	2.32152e7i	−0.437097	+	0.757075i	−0.997464	−	0.0711697i	$-0.977327\pi$
$313$	−1.34033e7	+	2.32152e7i	−0.437097	+	0.757075i	0.560367	+	0.828245i	$0.310660\pi$
$314$			3.53024e6i			0.114029i
$315$	2.97904e6	+	4.12925e6i	0.0953112	+	0.132111i
$316$	−1.04414e7			−0.330901
$317$	2.46337e7	+	1.42223e7i	0.773307	+	0.446469i	0.834053	−	0.551684i	$-0.186015\pi$
$317$	2.46337e7	+	1.42223e7i	0.773307	+	0.446469i	−0.0607461	+	0.998153i	$0.519348\pi$
$318$	−2.68582e6	+	1.25328e7i	−0.0835211	+	0.389731i
$319$	−8.29777e6	−	1.43722e7i	−0.255617	−	0.442741i
$320$	307733.	−	177670.i	0.00939126	−	0.00542205i
$321$	−1.79230e7	−	5.54766e7i	−0.541870	−	1.67724i
$322$	2.61773e7	−	4.53405e7i	0.784075	−	1.35806i
$323$			2.10856e7i			0.625717i
$324$	1.66578e7	−	3.42447e6i	0.489758	−	0.100684i
$325$	−3.60822e7			−1.05110
$326$	1.06174e7	+	6.12997e6i	0.306454	+	0.176932i
$327$	−1.67423e7	+	5.40897e6i	−0.478819	+	0.154693i
$328$	5.01325e6	+	8.68321e6i	0.142069	+	0.246070i
$329$	9.81741e7	−	5.66808e7i	2.75682	−	1.59165i
$330$	−1.97960e6	−	424236.i	−0.0550853	−	0.0118050i
$331$	3.27727e7	−	5.67639e7i	0.903707	−	1.56527i	0.0810645	−	0.996709i	$-0.474168\pi$
$331$	3.27727e7	−	5.67639e7i	0.903707	−	1.56527i	0.822643	−	0.568558i	$-0.192499\pi$
$332$		−	3.17344e7i		−	0.867192i
$333$	−1.64937e7	+	1.18993e7i	−0.446669	+	0.322248i
$334$	1.87811e7			0.504059
$335$	−849898.	−	490689.i	−0.0226065	−	0.0130518i
$336$	1.32137e7	+	1.19377e7i	0.348342	+	0.314705i
$337$	1.54983e6	+	2.68438e6i	0.0404943	+	0.0701381i	0.885562	−	0.464521i	$-0.153773\pi$
$337$	1.54983e6	+	2.68438e6i	0.0404943	+	0.0701381i	−0.845068	+	0.534659i	$0.820440\pi$
$338$	2.87606e6	−	1.66049e6i	0.0744814	−	0.0430018i
$339$	−8.06472e6	+	8.92672e6i	−0.207009	+	0.229136i
$340$	586827.	−	1.01641e6i	0.0149305	−	0.0258603i
$341$			1.07400e7i			0.270857i
$342$	−2.55774e7	+	2.60187e6i	−0.639407	+	0.0650439i
$343$	−1.15641e8			−2.86570
$344$	8.45258e6	+	4.88010e6i	0.207641	+	0.119882i
$345$	881610.	−	4.11382e6i	0.0214694	−	0.100182i
$346$	−2.58637e6	−	4.47973e6i	−0.0624400	−	0.108149i
$347$	4.25859e6	−	2.45870e6i	0.101924	−	0.0588459i	−0.448171	−	0.893948i	$-0.647925\pi$
$347$	4.25859e6	−	2.45870e6i	0.101924	−	0.0588459i	0.550096	+	0.835102i	$0.314591\pi$
$348$	3.60621e6	+	1.11622e7i	0.0855684	+	0.264858i
$349$	−8.99392e6	+	1.55779e7i	−0.211579	+	0.366466i	−0.952209	−	0.305448i	$-0.901194\pi$
$349$	−8.99392e6	+	1.55779e7i	−0.211579	+	0.366466i	0.740630	+	0.671913i	$0.234527\pi$
$350$		−	5.65009e7i		−	1.31781i
$351$	4.55224e7	+	5.01552e6i	1.05270	+	0.115983i
$352$	−7.08061e6			−0.162346
$353$	1.98330e7	+	1.14506e7i	0.450884	+	0.260318i	0.708203	−	0.706008i	$-0.249506\pi$
$353$	1.98330e7	+	1.14506e7i	0.450884	+	0.260318i	−0.257320	+	0.966326i	$0.582839\pi$
$354$	−5.13273e7	+	1.65825e7i	−1.15702	+	0.373800i
$355$	−2.33007e6	−	4.03581e6i	−0.0520816	−	0.0902080i
$356$	1.49123e7	−	8.60962e6i	0.330518	−	0.190825i
$357$	5.75111e7	+	1.23249e7i	1.26400	+	0.270881i
$358$	−9.69153e6	+	1.67862e7i	−0.211224	+	0.365851i
$359$			4.37616e7i			0.945823i	0.881110	+	0.472911i	$0.156797\pi$
$359$			4.37616e7i			0.945823i	−0.881110	+	0.472911i	$0.843203\pi$
$360$	1.30535e6	+	586416.i	0.0279782	+	0.0125689i
$361$	−8.17922e6			−0.173856
$362$	2.53048e7	+	1.46097e7i	0.533430	+	0.307976i
$363$	−5.55804e6	−	5.02133e6i	−0.116199	−	0.104978i
$364$	2.39782e7	+	4.15314e7i	0.497178	+	0.861137i
$365$	−2.57330e6	+	1.48570e6i	−0.0529191	+	0.0305528i
$366$	1.70610e7	−	1.88846e7i	0.347985	−	0.385180i
$367$	−769845.	+	1.33341e6i	−0.0155742	+	0.0269753i	−0.873707	−	0.486452i	$-0.838291\pi$
$367$	−769845.	+	1.33341e6i	−0.0155742	+	0.0269753i	0.858133	+	0.513427i	$0.171624\pi$
$368$		−	1.47143e7i		−	0.295254i
$369$	−1.65467e7	+	3.68326e7i	−0.329331	+	0.733084i
$370$	−1.71140e6			−0.0337867
$371$	−4.68091e7	−	2.70253e7i	−0.916661	−	0.529235i
$372$	1.59075e6	−	7.42284e6i	0.0309010	−	0.144192i
$373$	−3.28366e6	−	5.68746e6i	−0.0632749	−	0.109595i	0.832653	−	0.553796i	$-0.186821\pi$
$373$	−3.28366e6	−	5.68746e6i	−0.0632749	−	0.109595i	−0.895927	+	0.444200i	$0.853488\pi$
$374$	−2.02534e7	+	1.16933e7i	−0.387154	+	0.223523i
$375$	−2.80228e6	−	8.67384e6i	−0.0531395	−	0.164482i
$376$	1.59301e7	−	2.75918e7i	0.299679	−	0.519059i
$377$			3.15900e7i			0.589557i
$378$	−7.85377e6	+	7.12833e7i	−0.145413	+	1.31981i
$379$	1.40337e7			0.257783			0.128892	−	0.991659i	$-0.458858\pi$
$379$	1.40337e7			0.257783			0.128892	+	0.991659i	$0.458858\pi$
$380$	−1.87354e6	−	1.08169e6i	−0.0341438	−	0.0197129i
$381$	−8.08113e7	+	2.61079e7i	−1.46116	+	0.472060i
$382$	−1.52233e7	−	2.63675e7i	−0.273098	−	0.473019i
$383$	3.36645e7	−	1.94362e7i	0.599205	−	0.345951i	−0.169524	−	0.985526i	$-0.554223\pi$
$383$	3.36645e7	−	1.94362e7i	0.599205	−	0.345951i	0.768729	+	0.639575i	$0.220890\pi$
$384$	4.89371e6	+	1.04874e6i	0.0864260	+	0.0185215i
$385$	4.26875e6	−	7.39369e6i	0.0748029	−	0.129562i
$386$			4.22222e7i			0.734139i
$387$	3.97791e6	+	3.91044e7i	0.0686313	+	0.674672i
$388$	2.75038e6			0.0470867
$389$	1.35216e7	+	7.80670e6i	0.229710	+	0.132623i	0.610438	−	0.792064i	$-0.290993\pi$
$389$	1.35216e7	+	7.80670e6i	0.229710	+	0.132623i	−0.380728	+	0.924687i	$0.624327\pi$
$390$	2.85960e6	+	2.58346e6i	0.0482071	+	0.0435520i
$391$	−2.43000e7	−	4.20888e7i	−0.406514	−	0.704103i
$392$	−4.65902e7	+	2.68989e7i	−0.773457	+	0.446556i
$393$	1.89378e7	−	2.09620e7i	0.311998	−	0.345346i
$394$	−7.52671e6	+	1.30366e7i	−0.123060	+	0.213146i
$395$		−	3.53836e6i		−	0.0574131i
$396$	−1.66835e7	−	2.31250e7i	−0.268659	−	0.372389i
$397$	1.02776e8			1.64255			0.821277	−	0.570530i	$-0.193262\pi$
$397$	1.02776e8			1.64255			0.821277	+	0.570530i	$0.193262\pi$
$398$	−5.54241e7	−	3.19991e7i	−0.879123	−	0.507562i
$399$	2.27182e7	−	1.06009e8i	0.357648	−	1.66888i
$400$	−7.93979e6	−	1.37521e7i	−0.124059	−	0.214877i
$401$	−4.28395e7	+	2.47334e7i	−0.664373	+	0.383576i	−0.793941	−	0.607995i	$-0.791974\pi$
$401$	−4.28395e7	+	2.47334e7i	−0.664373	+	0.383576i	0.129568	+	0.991570i	$0.458641\pi$
$402$	−4.24936e6	−	1.31530e7i	−0.0654102	−	0.202463i
$403$	1.02219e7	−	1.77048e7i	0.156177	−	0.270506i
$404$			3.84599e7i			0.583262i
$405$	1.16048e6	+	5.64495e6i	0.0174692	+	0.0849757i
$406$	−4.94666e7			−0.739153
$407$	2.95331e7	+	1.70509e7i	0.438052	+	0.252909i
$408$	1.57299e7	−	5.08192e6i	0.231604	−	0.0748251i
$409$	6.63201e7	+	1.14870e8i	0.969338	+	1.67894i	0.697478	+	0.716606i	$0.254306\pi$
$409$	6.63201e7	+	1.14870e8i	0.969338	+	1.67894i	0.271860	+	0.962337i	$0.412361\pi$
$410$	−2.94255e6	+	1.69888e6i	−0.0426945	+	0.0246497i
$411$	−1.23171e6	−	263961.i	−0.0177412	−	0.00380202i
$412$	−5.33558e6	+	9.24149e6i	−0.0762939	+	0.132145i
$413$		−	2.27463e8i		−	3.22894i
$414$	4.80563e7	−	3.46701e7i	0.677250	−	0.488600i
$415$	1.07541e7			0.150463
$416$	1.16724e7	+	6.73906e6i	0.162136	+	0.0936094i
$417$	2.78202e7	+	2.51338e7i	0.383665	+	0.346617i
$418$	2.15541e7	+	3.73327e7i	0.295121	+	0.511165i
$419$	−9.60118e7	+	5.54324e7i	−1.30522	+	0.753567i	−0.981294	−	0.192517i	$-0.938335\pi$
$419$	−9.60118e7	+	5.54324e7i	−1.30522	+	0.753567i	−0.323923	+	0.946084i	$0.605002\pi$
$420$	−4.04543e6	+	4.47783e6i	−0.0546030	+	0.0604393i
$421$	4.61752e7	−	7.99777e7i	0.618817	−	1.07182i	−0.370885	−	0.928679i	$-0.620946\pi$
$421$	4.61752e7	−	7.99777e7i	0.618817	−	1.07182i	0.989702	−	0.143143i	$-0.0457210\pi$
$422$			2.96232e7i			0.394180i
$423$	1.27649e8	−	1.29851e7i	1.68654	−	0.171564i
$424$	−1.51909e7			−0.199290
$425$	−4.54221e7	−	2.62244e7i	−0.591698	−	0.341617i
$426$	1.37539e7	−	6.41792e7i	0.177908	−	0.830167i
$427$	5.36613e7	+	9.29440e7i	0.689251	+	1.19382i
$428$	5.98392e7	−	3.45482e7i	0.763228	−	0.440650i
$429$	−2.36078e7	−	7.30727e7i	−0.299009	−	0.925515i
$430$	−1.65376e6	+	2.86439e6i	−0.0208002	+	0.0360269i
$431$			7.54869e7i			0.942844i	0.881908	+	0.471422i	$0.156259\pi$
$431$			7.54869e7i			0.942844i	−0.881908	+	0.471422i	$0.843741\pi$
$432$	8.10550e6	+	1.84537e7i	0.100538	+	0.228893i
$433$	−1.02871e8			−1.26716			−0.633578	−	0.773679i	$-0.718414\pi$
$433$	−1.02871e8			−1.26716			−0.633578	+	0.773679i	$0.718414\pi$
$434$	2.77239e7	+	1.60064e7i	0.339145	+	0.195805i
$435$	−3.78263e6	+	1.22207e6i	−0.0459543	+	0.0148466i
$436$	−1.04263e7	−	1.80588e7i	−0.125797	−	0.217887i
$437$	−7.75815e7	+	4.47917e7i	−0.929638	+	0.536727i
$438$	−4.09218e7	−	8.76972e6i	−0.487004	−	0.104367i
$439$	2.26859e7	−	3.92932e7i	0.268141	−	0.464434i	−0.700241	−	0.713907i	$-0.746924\pi$
$439$	2.26859e7	−	3.92932e7i	0.268141	−	0.464434i	0.968382	+	0.249473i	$0.0802574\pi$
$440$		−	2.39946e6i		−	0.0281680i
$441$	−1.97627e8	−	8.87822e7i	−2.30426	−	1.03517i
$442$	4.45171e7			0.515537
$443$	9.04082e7	+	5.21972e7i	1.03991	+	0.600393i	0.919808	−	0.392368i	$-0.128344\pi$
$443$	9.04082e7	+	5.21972e7i	1.03991	+	0.600393i	0.120103	+	0.992761i	$0.461677\pi$
$444$	−1.78861e7	−	1.61589e7i	−0.204346	−	0.184613i
$445$	2.91761e6	+	5.05345e6i	0.0331091	+	0.0573467i
$446$	4.37170e7	−	2.52400e7i	0.492772	−	0.284502i
$447$	−6.83959e7	+	7.57065e7i	−0.765786	+	0.847638i
$448$	−1.05526e7	+	1.82777e7i	−0.117362	+	0.203277i
$449$		−	1.66601e7i		−	0.184051i	−0.995757	−	0.0920257i	$-0.970666\pi$
$449$		−	1.66601e7i		−	0.184051i	0.995757	−	0.0920257i	$-0.0293342\pi$
$450$	2.62060e7	−	5.83341e7i	0.287583	−	0.640155i
$451$	6.77049e7			0.738058
$452$	−1.23478e7	−	7.12902e6i	−0.133713	−	0.0771995i
$453$	−1.43744e7	+	6.70745e7i	−0.154630	+	0.721544i
$454$	−3.56360e6	−	6.17233e6i	−0.0380821	−	0.0659601i
$455$	−1.40741e7	+	8.12567e6i	−0.149412	+	0.0862631i
$456$	−9.36740e6	−	2.89947e7i	−0.0987926	−	0.305791i
$457$	−8.85805e7	+	1.53426e8i	−0.928088	+	1.60750i	−0.141571	+	0.989928i	$0.545215\pi$
$457$	−8.85805e7	+	1.53426e8i	−0.928088	+	1.60750i	−0.786517	+	0.617568i	$0.788118\pi$
$458$			8.62732e7i			0.898006i
$459$	5.36606e7	+	3.93993e7i	0.554903	+	0.407428i
$460$	4.98634e6			0.0512282
$461$	−1.56103e7	−	9.01261e6i	−0.159334	−	0.0919915i	0.418213	−	0.908349i	$-0.362657\pi$
$461$	−1.56103e7	−	9.01261e6i	−0.159334	−	0.0919915i	−0.577547	+	0.816358i	$0.695990\pi$
$462$	1.14424e8	−	3.69673e7i	1.16036	−	0.374880i
$463$	−2.37373e7	−	4.11143e7i	−0.239160	−	0.414238i	0.721313	−	0.692609i	$-0.243539\pi$
$463$	−2.37373e7	−	4.11143e7i	−0.239160	−	0.414238i	−0.960474	+	0.278371i	$0.910205\pi$
$464$	−1.20400e7	+	6.95129e6i	−0.120524	+	0.0695844i
$465$	2.51544e6	+	539069.i	0.0250181	+	0.00536149i
$466$	−2.79542e6	+	4.84180e6i	−0.0276241	+	0.0478464i
$467$		−	1.97335e7i		−	0.193755i	−0.995296	−	0.0968776i	$-0.969114\pi$
$467$		−	1.97335e7i		−	0.193755i	0.995296	−	0.0968776i	$-0.0308855\pi$
$468$	5.49321e6	+	5.40003e7i	0.0535906	+	0.526816i
$469$	5.82887e7			0.565023
$470$	9.35026e6	+	5.39837e6i	0.0900596	+	0.0519959i
$471$	−1.25029e7	−	1.12956e7i	−0.119660	−	0.108105i
$472$	−3.19642e7	−	5.53636e7i	−0.303975	−	0.526500i
$473$	5.70769e7	−	3.29533e7i	0.539357	−	0.311398i
$474$	3.34090e7	−	3.69800e7i	0.313710	−	0.347242i
$475$	−4.83390e7	+	8.37256e7i	−0.451042	+	0.781228i
$476$			6.97089e7i			0.646350i
$477$	−3.57931e7	−	4.96129e7i	−0.329795	−	0.457130i
$478$	−1.03354e8			−0.946336
$479$	−1.65374e8	−	9.54790e7i	−1.50474	−	0.868763i	−0.999985	−	0.00550079i	$-0.998249\pi$
$479$	−1.65374e8	−	9.54790e7i	−1.50474	−	0.868763i	−0.504756	−	0.863262i	$-0.668418\pi$
$480$	−355396.	+	1.65837e6i	−0.00321358	+	0.0149954i
$481$	−3.24569e7	−	5.62169e7i	−0.291656	−	0.505164i
$482$	−3.16771e6	+	1.82888e6i	−0.0282881	+	0.0163322i
$483$	7.68221e7	+	2.37786e8i	0.681781	+	2.11030i
$484$	4.43874e6	−	7.68812e6i	0.0391492	−	0.0678085i
$485$			932044.i			0.00816980i
$486$	−4.11709e7	+	6.99534e7i	−0.358659	+	0.609396i
$487$	1.45899e8			1.26318			0.631592	−	0.775301i	$-0.282402\pi$
$487$	1.45899e8			1.26318			0.631592	+	0.775301i	$0.282402\pi$
$488$	2.61219e7	+	1.50815e7i	0.224774	+	0.129773i
$489$	−5.56825e7	+	1.79895e7i	−0.476203	+	0.153848i
$490$	−9.11543e6	−	1.57884e7i	−0.0774799	−	0.134199i
$491$	8.25152e7	−	4.76402e7i	0.697091	−	0.402466i	−0.109172	−	0.994023i	$-0.534820\pi$
$491$	8.25152e7	−	4.76402e7i	0.697091	−	0.402466i	0.806263	+	0.591557i	$0.201487\pi$
$492$	−4.67937e7	−	1.00281e7i	−0.392909	−	0.0842021i
$493$	−2.29595e7	+	3.97670e7i	−0.191612	+	0.331881i
$494$		−	8.20574e7i		−	0.680671i
$495$	7.83656e6	−	5.65366e6i	0.0646115	−	0.0466138i
$496$	8.99719e6			0.0737330
$497$	2.39706e8	+	1.38394e8i	1.95258	+	1.12732i
$498$	1.12392e8	+	1.01539e8i	0.910016	+	0.822141i
$499$	−1.09268e8	−	1.89258e8i	−0.879410	−	1.52318i	−0.851990	−	0.523558i	$-0.824604\pi$
$499$	−1.09268e8	−	1.89258e8i	−0.879410	−	1.52318i	−0.0274196	−	0.999624i	$-0.508729\pi$
$500$	9.35592e6	−	5.40164e6i	0.0748474	−	0.0432132i
$501$	−6.00932e7	+	6.65163e7i	−0.477872	+	0.528950i
$502$	−2.89652e6	+	5.01692e6i	−0.0228963	+	0.0396576i
$503$		−	1.09519e8i		−	0.860569i	−0.902693	−	0.430285i	$-0.858413\pi$
$503$		−	1.09519e8i		−	0.860569i	0.902693	−	0.430285i	$-0.141587\pi$
$504$	−8.45587e7	+	8.60177e6i	−0.660491	+	0.0671887i
$505$	−1.30332e7			−0.101199
$506$	−8.60479e7	−	4.96798e7i	−0.664184	−	0.383467i
$507$	−3.32151e6	+	1.54991e7i	−0.0254866	+	0.118927i
$508$	−5.03253e7	−	8.71661e7i	−0.383880	−	0.664900i
$509$	2.82418e7	−	1.63054e7i	0.214161	−	0.123646i	−0.389083	−	0.921203i	$-0.627208\pi$
$509$	2.82418e7	−	1.63054e7i	0.214161	−	0.123646i	0.603243	+	0.797557i	$0.293875\pi$
$510$	1.72215e6	+	5.33053e6i	0.0129826	+	0.0401846i
$511$	8.82426e7	−	1.52841e8i	0.661326	−	1.14545i
$512$			5.93164e6i			0.0441942i
$513$	7.26240e7	−	9.89115e7i	0.537933	−	0.732647i
$514$	5.73238e7			0.422129
$515$	−3.13174e6	−	1.80811e6i	−0.0229279	−	0.0132374i
$516$	−4.43291e7	+	1.43215e7i	−0.322656	+	0.104241i
$517$	−1.07570e8	−	1.86316e8i	−0.778429	−	1.34828i
$518$	8.80297e7	−	5.08240e7i	0.633345	−	0.365662i
$519$	2.41412e7	+	5.17357e6i	0.172686	+	0.0370074i
$520$	−2.28372e6	+	3.95552e6i	−0.0162417	+	0.0281315i
$521$		−	1.60218e8i		−	1.13292i	−0.824090	−	0.566459i	$-0.808313\pi$
$521$		−	1.60218e8i		−	1.13292i	0.824090	−	0.566459i	$-0.191687\pi$
$522$	−5.10716e7	−	2.29434e7i	−0.359060	−	0.161304i
$523$	−1.05186e8			−0.735277			−0.367638	−	0.929969i	$-0.619834\pi$
$523$	−1.05186e8			−0.735277			−0.367638	+	0.929969i	$0.619834\pi$
$524$	2.89955e7	+	1.67405e7i	0.201528	+	0.116352i
$525$	2.00107e8	+	1.80784e8i	1.38288	+	1.24934i
$526$	6.25868e7	+	1.08403e8i	0.430056	+	0.744880i
$527$	2.57356e7	−	1.48585e7i	0.175834	−	0.101518i
$528$	2.26556e7	−	2.50771e7i	0.153912	−	0.170363i
$529$	2.92221e7	−	5.06141e7i	0.197398	−	0.341904i
$530$		−	5.14786e6i		−	0.0345779i
$531$	1.05501e8	−	2.34843e8i	0.704648	−	1.56853i
$532$	1.28493e8			0.853385
$533$	−1.11612e8	−	6.44390e7i	−0.737103	−	0.425566i
$534$	−1.72220e7	+	8.03623e7i	−0.113099	+	0.527750i
$535$	1.17076e7	+	2.02782e7i	0.0764552	+	0.132424i
$536$	1.41873e7	−	8.19102e6i	0.0921307	−	0.0531917i
$537$	−2.84415e7	−	8.80344e7i	−0.183666	−	0.568499i
$538$	−5.08626e7	+	8.80966e7i	−0.326627	+	0.565734i
$539$			3.63274e8i			2.31989i
$540$	−6.25357e6	+	2.74678e6i	−0.0397143	+	0.0174438i
$541$	5.75829e7			0.363665			0.181833	−	0.983329i	$-0.441797\pi$
$541$	5.75829e7			0.363665			0.181833	+	0.983329i	$0.441797\pi$
$542$	−1.51074e8	−	8.72228e7i	−0.948840	−	0.547813i
$543$	−1.32710e8	+	4.28749e7i	−0.828902	+	0.267795i
$544$	9.79585e6	+	1.69669e7i	0.0608479	+	0.105392i
$545$	6.11974e6	−	3.53324e6i	0.0378045	−	0.0218265i
$546$	−2.23812e8	−	4.79639e7i	−1.37501	−	0.294671i
$547$	−1.48740e8	+	2.57625e8i	−0.908793	+	1.57408i	−0.0930497	+	0.995661i	$0.529662\pi$
$547$	−1.48740e8	+	2.57625e8i	−0.908793	+	1.57408i	−0.815743	+	0.578414i	$0.803672\pi$
$548$		−	1.49295e6i		−	0.00907203i
$549$	1.22934e7	+	1.20849e8i	0.0742940	+	0.730339i
$550$	−1.07228e8			−0.644498
$551$	7.33019e7	+	4.23208e7i	0.438188	+	0.252988i
$552$	5.21130e7	+	4.70808e7i	0.309834	+	0.279915i
$553$	1.05080e8	+	1.82004e8i	0.621363	+	1.07623i
$554$	−5.80633e7	+	3.35229e7i	−0.341486	+	0.197157i
$555$	5.47590e6	−	6.06119e6i	0.0320314	−	0.0354551i
$556$	−2.22176e7	+	3.84821e7i	−0.129263	+	0.223890i
$557$			1.72089e8i			0.995837i	0.867224	+	0.497919i	$0.165902\pi$
$557$			1.72089e8i			0.995837i	−0.867224	+	0.497919i	$0.834098\pi$
$558$	2.11994e7	+	2.93845e7i	0.122017	+	0.169128i
$559$	−1.25455e8			−0.718212
$560$	−6.19392e6	−	3.57606e6i	−0.0352697	−	0.0203629i
$561$	2.33903e7	−	1.09146e8i	0.132479	−	0.618183i
$562$	−1.59933e7	−	2.77012e7i	−0.0901008	−	0.156059i
$563$	9.58319e7	−	5.53286e7i	0.537013	−	0.310045i	−0.206855	−	0.978372i	$-0.566323\pi$
$563$	9.58319e7	−	5.53286e7i	0.537013	−	0.310045i	0.743867	+	0.668327i	$0.232989\pi$
$564$	4.67499e7	+	1.44704e8i	0.260581	+	0.806571i
$565$	2.41587e6	−	4.18440e6i	0.0133945	−	0.0232000i
$566$			1.24951e8i			0.689113i
$567$	−2.27332e8	−	2.55898e8i	−1.24713	−	1.40384i
$568$	7.77913e7			0.424508
$569$	2.68592e8	+	1.55071e8i	1.45799	+	0.841773i	0.998913	−	0.0466219i	$-0.0148456\pi$
$569$	2.68592e8	+	1.55071e8i	1.45799	+	0.841773i	0.459081	+	0.888395i	$0.348179\pi$
$570$	9.82567e6	−	3.17441e6i	0.0530564	−	0.0171411i
$571$	4.43183e7	+	7.67616e7i	0.238054	+	0.412321i	0.960156	−	0.279465i	$-0.0901573\pi$
$571$	4.43183e7	+	7.67616e7i	0.238054	+	0.412321i	−0.722102	+	0.691787i	$0.756824\pi$
$572$	7.88189e7	−	4.55061e7i	0.421156	−	0.243154i
$573$	1.42094e8	+	3.04514e7i	0.755287	+	0.161861i
$574$	1.00905e8	−	1.74772e8i	0.533550	−	0.924136i
$575$		−	2.22832e8i		−	1.17213i
$576$	−1.93725e7	+	1.39763e7i	−0.101372	+	0.0731347i
$577$	2.56524e7			0.133537			0.0667683	−	0.997769i	$-0.478731\pi$
$577$	2.56524e7			0.133537			0.0667683	+	0.997769i	$0.478731\pi$
$578$	−6.22093e7	−	3.59165e7i	−0.322160	−	0.185999i
$579$	−1.49537e8	−	1.35097e8i	−0.770393	−	0.696000i
$580$	−2.35564e6	−	4.08009e6i	−0.0120733	−	0.0209115i
$581$	−5.53161e8	+	3.19368e8i	−2.82048	+	1.62841i
$582$	−8.80030e6	+	9.74093e6i	−0.0446405	+	0.0494119i
$583$	−5.12890e7	+	8.88351e7i	−0.258832	+	0.448311i
$584$		−	4.96011e7i		−	0.249031i
$585$	−1.82995e7	+	1.86153e6i	−0.0914055	+	0.00929826i
$586$	2.43741e8			1.21126
$587$	−1.28875e8	−	7.44061e7i	−0.637169	−	0.367870i	0.146354	−	0.989232i	$-0.453246\pi$
$587$	−1.28875e8	−	7.44061e7i	−0.637169	−	0.367870i	−0.783523	+	0.621363i	$0.786579\pi$
$588$	5.38063e7	−	2.51074e8i	0.264668	−	1.23501i
$589$	−2.73883e7	−	4.74380e7i	−0.134035	−	0.232156i
$590$	1.87615e7	−	1.08320e7i	0.0913506	−	0.0527413i
$591$	−2.20885e7	−	6.83700e7i	−0.107005	−	0.331210i
$592$	1.42841e7	−	2.47407e7i	0.0688473	−	0.119247i
$593$		−	2.06413e8i		−	0.989858i	−0.868933	−	0.494929i	$-0.835194\pi$
$593$		−	2.06413e8i		−	0.989858i	0.868933	−	0.494929i	$-0.164806\pi$
$594$	1.35283e8	+	1.49050e7i	0.645480	+	0.0711170i
$595$	−2.36228e7			−0.112145
$596$	−1.04720e8	−	6.04603e7i	−0.494644	−	0.285583i
$597$	2.90669e8	−	9.39072e7i	1.36608	−	0.441343i
$598$	9.45667e7	+	1.63794e8i	0.442216	+	0.765941i
$599$	1.91678e8	−	1.10665e8i	0.891850	−	0.514910i	0.0173027	−	0.999850i	$-0.494492\pi$
$599$	1.91678e8	−	1.10665e8i	0.891850	−	0.514910i	0.874547	+	0.484941i	$0.161159\pi$
$600$	7.41101e7	+	1.58821e7i	0.343102	+	0.0735283i
$601$	−4.57176e7	+	7.91852e7i	−0.210601	+	0.364771i	−0.951903	−	0.306400i	$-0.900875\pi$
$601$	−4.57176e7	+	7.91852e7i	−0.210601	+	0.364771i	0.741302	+	0.671172i	$0.234209\pi$
$602$		−	1.96449e8i		−	0.900453i
$603$	6.01799e7	+	2.70352e7i	0.274473	+	0.123304i
$604$	−8.13007e7			−0.368964
$605$	2.60533e6	+	1.50419e6i	0.0117651	+	0.00679261i
$606$	−1.36212e8	−	1.23059e8i	−0.612065	−	0.552961i
$607$	2.51216e7	+	4.35118e7i	0.112326	+	0.194554i	0.916708	−	0.399558i	$-0.130837\pi$
$607$	2.51216e7	+	4.35118e7i	0.112326	+	0.194554i	−0.804382	+	0.594113i	$0.797503\pi$
$608$	3.12748e7	−	1.80565e7i	0.139150	−	0.0803383i
$609$	1.58277e8	−	1.75194e8i	0.700753	−	0.775654i
$610$	−5.11079e6	+	8.85214e6i	−0.0225164	+	0.0389995i
$611$			4.09524e8i			1.79538i
$612$	−3.23321e7	+	7.19706e7i	−0.141052	+	0.313979i
$613$	7.04589e7			0.305883			0.152941	−	0.988235i	$-0.451125\pi$
$613$	7.04589e7			0.305883			0.152941	+	0.988235i	$0.451125\pi$
$614$	3.48920e7	+	2.01449e7i	0.150737	+	0.0870282i
$615$	3.39830e6	−	1.58574e7i	0.0146095	−	0.0681719i
$616$	7.12577e7	+	1.23422e8i	0.304853	+	0.528020i
$617$	−3.49705e8	+	2.01902e8i	−1.48883	+	0.859578i	−0.999919	−	0.0127536i	$-0.995940\pi$
$617$	−3.49705e8	+	2.01902e8i	−1.48883	+	0.859578i	−0.488914	+	0.872332i	$0.662607\pi$
$618$	−1.56582e7	−	4.84665e7i	−0.0663402	−	0.205341i
$619$	5.01217e7	−	8.68133e7i	0.211326	−	0.366028i	−0.740803	−	0.671722i	$-0.765555\pi$
$619$	5.01217e7	−	8.68133e7i	0.211326	−	0.366028i	0.952130	+	0.305694i	$0.0988883\pi$
$620$			3.04895e6i			0.0127931i
$621$	−3.09743e7	+	2.81132e8i	−0.129338	+	1.17391i
$622$	1.26309e8			0.524885
$623$	−3.00149e8	−	1.73291e8i	−1.24129	−	0.716657i
$624$	−6.12153e7	+	1.97770e7i	−0.251945	+	0.0813966i
$625$	−1.19321e8	−	2.06670e8i	−0.488739	−	0.846521i
$626$	1.31325e8	−	7.58204e7i	0.535333	−	0.309075i
$627$	−2.01186e8	−	4.31150e7i	−0.816197	−	0.174914i
$628$	9.98503e6	−	1.72946e7i	0.0403154	−	0.0698282i
$629$		−	9.43581e7i		−	0.379164i
$630$	−2.91495e6	−	2.86551e7i	−0.0116576	−	0.114599i
$631$	1.87082e8			0.744635			0.372318	−	0.928105i	$-0.378563\pi$
$631$	1.87082e8			0.744635			0.372318	+	0.928105i	$0.378563\pi$
$632$	5.11523e7	+	2.95328e7i	0.202635	+	0.116991i
$633$	−1.04915e8	−	9.47843e7i	−0.413645	−	0.373702i
$634$	−8.04533e7	−	1.39349e8i	−0.315701	−	0.546811i
$635$	2.95387e7	−	1.70542e7i	0.115364	−	0.0666053i
$636$	4.86058e7	−	5.38011e7i	0.188937	−	0.209132i
$637$	3.45751e8	−	5.98858e8i	1.33766	−	2.31689i
$638$			9.38785e7i			0.361497i
$639$	1.83294e8	+	2.54064e8i	0.702497	+	0.973733i
$640$	−2.01010e6			−0.00766793
$641$	3.75881e8	+	2.17015e8i	1.42717	+	0.823977i	0.996897	−	0.0787213i	$-0.0250837\pi$
$641$	3.75881e8	+	2.17015e8i	1.42717	+	0.823977i	0.430274	+	0.902699i	$0.358417\pi$
$642$	−6.91073e7	+	3.22473e8i	−0.261167	+	1.21868i
$643$	2.06418e8	+	3.57527e8i	0.776453	+	1.34486i	0.933974	+	0.357341i	$0.116317\pi$
$643$	2.06418e8	+	3.57527e8i	0.776453	+	1.34486i	−0.157521	+	0.987516i	$0.550350\pi$
$644$	−2.56484e8	+	1.48081e8i	−0.960292	+	0.554425i
$645$	−4.85325e6	−	1.50222e7i	−0.0180865	−	0.0559826i
$646$	5.96390e7	−	1.03298e8i	0.221224	−	0.383172i
$647$		−	2.07934e8i		−	0.767736i	−0.923388	−	0.383868i	$-0.874592\pi$
$647$		−	2.07934e8i		−	0.767736i	0.923388	−	0.383868i	$-0.125408\pi$
$648$	−9.12919e7	−	3.03388e7i	−0.335511	−	0.111500i
$649$	−4.31682e8			−1.57917
$650$	1.76766e8	+	1.02056e8i	0.643664	+	0.371619i
$651$	−1.45396e8	+	4.69736e7i	−0.527000	+	0.170259i
$652$	−3.46763e7	−	6.00612e7i	−0.125109	−	0.216696i
$653$	3.53999e8	−	2.04381e8i	1.27134	−	0.734010i	0.296102	−	0.955156i	$-0.404313\pi$
$653$	3.53999e8	−	2.04381e8i	1.27134	−	0.734010i	0.975241	+	0.221147i	$0.0709799\pi$
$654$	9.73190e7	+	2.08559e7i	0.347908	+	0.0745581i
$655$	−5.67300e6	+	9.82593e6i	−0.0201878	+	0.0349663i
$656$		−	5.67185e7i		−	0.200915i
$657$	1.61996e8	−	1.16871e8i	0.571225	−	0.412108i
$658$	−6.41270e8			−2.25094
$659$	−8.10352e7	−	4.67857e7i	−0.283150	−	0.163477i	0.351698	−	0.936113i	$-0.385604\pi$
$659$	−8.10352e7	−	4.67857e7i	−0.283150	−	0.163477i	−0.634849	+	0.772636i	$0.718938\pi$
$660$	8.49809e6	+	7.67748e6i	0.0295590	+	0.0267046i
$661$	1.45940e8	+	2.52776e8i	0.505326	+	0.875249i	0.999981	+	0.00616033i	$0.00196090\pi$
$661$	1.45940e8	+	2.52776e8i	0.505326	+	0.875249i	−0.494656	+	0.869089i	$0.664706\pi$
$662$	−3.21105e8	+	1.85390e8i	−1.10681	+	0.639018i
$663$	−1.42440e8	+	1.57664e8i	−0.488754	+	0.540995i
$664$	−8.97583e7	+	1.55466e8i	−0.306599	+	0.531045i
$665$			4.35435e7i			0.148067i
$666$	1.14459e8	−	1.16434e7i	0.387460	−	0.0394145i
$667$	−1.95090e8			−0.657442
$668$	−9.20081e7	−	5.31209e7i	−0.308672	−	0.178212i
$669$	−5.04881e7	+	2.35591e8i	−0.168621	+	0.786828i
$670$	2.77576e6	+	4.80775e6i	0.00922905	+	0.0159852i
$671$	1.76391e8	−	1.01839e8i	0.583859	−	0.337091i
$672$	−3.09686e7	−	9.58565e7i	−0.102050	−	0.315874i
$673$	−2.13652e8	+	3.70056e8i	−0.700908	+	1.21401i	0.267240	+	0.963630i	$0.413888\pi$
$673$	−2.13652e8	+	3.70056e8i	−0.700908	+	1.21401i	−0.968148	+	0.250378i	$0.919445\pi$
$674$		−	1.75343e7i		−	0.0572675i
$675$	1.22749e8	+	2.79463e8i	0.399124	+	0.908683i
$676$	−1.87863e7			−0.0608138
$677$	−1.64600e8	−	9.50320e7i	−0.530475	−	0.306270i	0.210735	−	0.977543i	$-0.432414\pi$
$677$	−1.64600e8	−	9.50320e7i	−0.530475	−	0.306270i	−0.741210	+	0.671274i	$0.765748\pi$
$678$	6.47575e7	−	2.09214e7i	0.207779	−	0.0671276i
$679$	−2.76793e7	−	4.79419e7i	−0.0884189	−	0.153146i
$680$	−5.74971e6	+	3.31960e6i	−0.0182860	+	0.0105574i
$681$	3.32626e7	+	7.12832e6i	0.105321	+	0.0225708i
$682$	3.03772e7	−	5.26148e7i	0.0957623	−	0.165865i
$683$		−	4.43458e8i		−	1.39184i	−0.718118	−	0.695921i	$-0.754996\pi$
$683$		−	4.43458e8i		−	1.39184i	0.718118	−	0.695921i	$-0.245004\pi$
$684$	1.32662e8	+	5.95972e7i	0.414552	+	0.186233i
$685$	505929.			0.00157405
$686$	5.66524e8	+	3.27083e8i	1.75487	+	1.01318i
$687$	−3.05551e8	−	2.76045e8i	−0.942352	−	0.851354i
$688$	−2.76060e7	−	4.78150e7i	−0.0847693	−	0.146825i
$689$	1.69100e8	−	9.76299e7i	0.516994	−	0.298487i
$690$	−1.59546e7	+	1.76600e7i	−0.0485668	+	0.0537579i
$691$	2.11824e8	−	3.66889e8i	0.642008	−	1.11199i	−0.342976	−	0.939344i	$-0.611435\pi$
$691$	2.11824e8	−	3.66889e8i	0.642008	−	1.11199i	0.984984	−	0.172646i	$-0.0552315\pi$
$692$			2.92615e7i			0.0883035i
$693$	−2.35193e8	+	5.23535e8i	−0.706683	+	1.57306i
$694$	−2.78170e7			−0.0832207
$695$	−1.30407e7	−	7.52907e6i	−0.0388461	−	0.0224278i
$696$	1.39048e7	−	6.48834e7i	0.0412417	−	0.192445i
$697$	−9.36681e7	−	1.62238e8i	−0.276626	−	0.479130i
$698$	8.81220e7	−	5.08773e7i	0.259130	−	0.149609i
$699$	−8.20365e6	−	2.53926e7i	−0.0240201	−	0.0743490i
$700$	−1.59809e8	+	2.76797e8i	−0.465915	+	0.806988i
$701$			3.61142e8i			1.04839i	0.851598	+	0.524196i	$0.175634\pi$
$701$			3.61142e8i			1.04839i	−0.851598	+	0.524196i	$0.824366\pi$
$702$	−2.08827e8	−	1.53328e8i	−0.603638	−	0.443210i
$703$	−1.73929e8			−0.500616
$704$	3.46878e7	+	2.00270e7i	0.0994164	+	0.0573981i
$705$	−4.90369e7	+	1.58425e7i	−0.139945	+	0.0452123i
$706$	−6.47744e7	−	1.12192e8i	−0.184073	−	0.318823i
$707$	6.70394e8	−	3.87052e8i	1.89702	−	1.09524i
$708$	2.98354e8	+	6.39385e7i	0.840682	+	0.180162i
$709$	8.93551e7	−	1.54768e8i	0.250715	−	0.434252i	−0.713008	−	0.701156i	$-0.752668\pi$
$709$	8.93551e7	−	1.54768e8i	0.250715	−	0.434252i	0.963723	+	0.266905i	$0.0860009\pi$
$710$			2.63618e7i			0.0736545i
$711$	2.40730e7	+	2.36647e8i	0.0669764	+	0.658404i
$712$	−9.74068e7			−0.269867
$713$	1.09339e8	+	6.31271e7i	0.301653	+	0.174160i
$714$	−2.46886e8	−	2.23045e8i	−0.678268	−	0.612771i
$715$	1.54210e7	+	2.67100e7i	0.0421886	+	0.0730728i
$716$	9.49572e7	−	5.48235e7i	0.258695	−	0.149358i
$717$	3.30700e8	−	3.66047e8i	0.897173	−	0.993068i
$718$	1.23776e8	−	2.14387e8i	0.334399	−	0.579196i
$719$			3.00407e8i			0.808209i	0.914713	+	0.404105i	$0.132417\pi$
$719$			3.00407e8i			0.808209i	−0.914713	+	0.404105i	$0.867583\pi$
$720$	−4.73624e6	−	6.56492e6i	−0.0126893	−	0.0175886i
$721$	2.14785e8			0.573056
$722$	4.00698e7	+	2.31343e7i	0.106465	+	0.0614675i
$723$	3.65834e6	−	1.70708e7i	0.00967986	−	0.0451688i
$724$	−8.26451e7	−	1.43146e8i	−0.217772	−	0.377192i
$725$	−1.82333e8	+	1.05270e8i	−0.478466	+	0.276243i
$726$	1.30263e7	+	4.03199e7i	0.0340416	+	0.105368i
$727$	−2.94693e7	+	5.10424e7i	−0.0766950	+	0.132840i	−0.901822	−	0.432107i	$-0.857770\pi$
$727$	−2.94693e7	+	5.10424e7i	−0.0766950	+	0.132840i	0.825127	+	0.564947i	$0.191103\pi$
$728$		−	2.71282e8i		−	0.703116i
$729$	−1.16018e8	−	3.69641e8i	−0.299463	−	0.954108i
$730$	1.68087e7			0.0432082
$731$	−1.57929e8	−	9.11803e7i	−0.404305	−	0.233426i
$732$	−1.36995e8	+	4.42593e7i	−0.349278	+	0.112842i
$733$	−2.24838e8	−	3.89431e8i	−0.570898	−	0.988824i	−0.996474	−	0.0839011i	$-0.973262\pi$
$733$	−2.24838e8	−	3.89431e8i	−0.570898	−	0.988824i	0.425577	−	0.904922i	$-0.360071\pi$
$734$	7.54291e6	−	4.35490e6i	0.0190744	−	0.0110126i
$735$	8.50835e7	+	1.82338e7i	0.214281	+	0.0459213i
$736$	−4.16183e7	+	7.20849e7i	−0.104388	+	0.180805i
$737$		−	1.10621e8i		−	0.276335i
$738$	1.85240e8	−	1.33641e8i	0.460858	−	0.332484i
$739$	5.27583e8			1.30725			0.653623	−	0.756820i	$-0.273248\pi$
$739$	5.27583e8			1.30725			0.653623	+	0.756820i	$0.273248\pi$
$740$	8.38409e6	+	4.84056e6i	0.0206900	+	0.0119454i
$741$	2.90620e8	+	2.62556e8i	0.714284	+	0.645309i
$742$	1.52878e8	+	2.64792e8i	0.374225	+	0.648177i
$743$	−2.13537e8	+	1.23286e8i	−0.520603	+	0.300570i	−0.737181	−	0.675695i	$-0.763844\pi$
$743$	−2.13537e8	+	1.23286e8i	−0.520603	+	0.300570i	0.216578	+	0.976265i	$0.430510\pi$
$744$	−2.87880e7	+	3.18650e7i	−0.0699025	+	0.0773741i
$745$	2.04887e7	−	3.54874e7i	0.0495502	−	0.0858234i
$746$			3.71504e7i			0.0894842i
$747$	−7.19237e8	+	7.31647e7i	−1.72548	+	0.175525i
$748$	1.32295e8			0.316110
$749$	−1.20442e9	−	6.95371e8i	−2.86636	−	1.65490i
$750$	−1.08050e7	+	5.04190e7i	−0.0256119	+	0.119512i
$751$	3.07706e8	+	5.32963e8i	0.726468	+	1.25828i	0.958367	+	0.285539i	$0.0921727\pi$
$751$	3.07706e8	+	5.32963e8i	0.726468	+	1.25828i	−0.231899	+	0.972740i	$0.574494\pi$
$752$	−1.56083e8	+	9.01145e7i	−0.367030	+	0.211905i
$753$	−8.50036e6	−	2.63110e7i	−0.0199091	−	0.0616243i
$754$	8.93501e7	−	1.54759e8i	0.208440	−	0.361029i
$755$		−	2.75510e7i		−	0.0640172i
$756$	2.40095e8	−	3.27002e8i	0.555671	−	0.756806i
$757$	−3.11945e8			−0.719102			−0.359551	−	0.933125i	$-0.617070\pi$
$757$	−3.11945e8			−0.719102			−0.359551	+	0.933125i	$0.617070\pi$
$758$	−6.87509e7	−	3.96933e7i	−0.157859	−	0.0911402i
$759$	4.51274e8	−	1.45794e8i	1.03208	−	0.333438i
$760$	6.11895e6	+	1.05983e7i	0.0139391	+	0.0241433i
$761$	−1.99844e8	+	1.15380e8i	−0.453457	+	0.261804i	−0.709289	−	0.704918i	$-0.750984\pi$
$761$	−1.99844e8	+	1.15380e8i	−0.453457	+	0.261804i	0.255832	+	0.966721i	$0.417651\pi$
$762$	4.69737e8	+	1.00667e8i	1.06167	+	0.227521i
$763$	−2.09856e8	+	3.63481e8i	−0.472441	+	0.818291i
$764$			1.72232e8i			0.386218i
$765$	−2.43893e7	−	1.09566e7i	−0.0544772	−	0.0244733i
$766$	−2.19895e8			−0.489249
$767$	7.11629e8	+	4.10859e8i	1.57713	+	0.910556i
$768$	−2.10079e7	−	1.89793e7i	−0.0463766	−	0.0418982i
$769$	1.57753e8	+	2.73236e8i	0.346895	+	0.600840i	0.985696	−	0.168532i	$-0.0539026\pi$
$769$	1.57753e8	+	2.73236e8i	0.346895	+	0.600840i	−0.638801	+	0.769372i	$0.720569\pi$
$770$	−4.18250e7	+	2.41477e7i	−0.0916144	+	0.0528936i
$771$	−1.83417e8	+	2.03022e8i	−0.400199	+	0.442975i
$772$	1.19422e8	−	2.06845e8i	0.259557	−	0.449567i
$773$			1.28960e8i			0.279200i	0.990208	+	0.139600i	$0.0445817\pi$
$773$			1.28960e8i			0.279200i	−0.990208	+	0.139600i	$0.955418\pi$
$774$	9.11163e7	−	2.02823e8i	0.196505	−	0.437416i
$775$	1.36253e8			0.292712
$776$	−1.34741e7	−	7.77926e6i	−0.0288346	−	0.0166476i
$777$	−1.01664e8	+	4.74392e8i	−0.216723	+	1.01129i
$778$	−4.41614e7	−	7.64897e7i	−0.0937786	−	0.162429i
$779$	−2.99050e8	+	1.72657e8i	−0.632603	+	0.365234i
$780$	−6.70198e6	−	2.07445e7i	−0.0141228	−	0.0437139i
$781$	2.62647e8	−	4.54917e8i	0.551339	−	0.954947i
$782$			2.74923e8i			0.574898i
$783$	2.44670e8	−	1.07467e8i	0.509677	−	0.223867i
$784$	3.04326e8			0.631525
$785$	5.86075e6	+	3.38371e6i	0.0121156	+	0.00699494i
$786$	−1.52065e8	+	4.91281e7i	−0.313157	+	0.101172i
$787$	2.10796e8	+	3.65109e8i	0.432452	+	0.749029i	0.997084	−	0.0763138i	$-0.0243151\pi$
$787$	2.10796e8	+	3.65109e8i	0.432452	+	0.749029i	−0.564632	+	0.825343i	$0.690982\pi$
$788$	7.37464e7	−	4.25775e7i	0.150717	−	0.0870165i
$789$	−5.84186e8	−	1.25193e8i	−1.18938	−	0.254889i
$790$	−1.00080e7	+	1.73344e7i	−0.0202986	+	0.0351582i
$791$			2.86980e8i			0.579858i
$792$	1.63246e7	+	1.60477e8i	0.0328599	+	0.323026i
$793$	−3.87707e8			−0.777471
$794$	−5.03497e8	−	2.90694e8i	−1.00585	−	0.580730i
$795$	1.82320e7	+	1.64714e7i	0.0362855	+	0.0327816i
$796$	1.81014e8	+	3.13526e8i	0.358900	+	0.621634i
$797$	−3.25352e8	+	1.87842e8i	−0.642657	+	0.371038i	−0.785637	−	0.618687i	$-0.787665\pi$
$797$	−3.25352e8	+	1.87842e8i	−0.642657	+	0.371038i	0.142980	+	0.989726i	$0.454331\pi$
$798$	−4.11135e8	+	4.55080e8i	−0.809051	+	0.895527i
$799$	−2.97640e8	+	5.15528e8i	−0.583514	+	1.01068i
$800$			8.98285e7i			0.175446i
$801$	−2.29512e8	−	3.18127e8i	−0.446588	−	0.619017i
$802$	2.79827e8			0.542458
$803$	−2.90063e8	−	1.67468e8i	−0.560204	−	0.323434i
$804$	−1.63846e7	+	7.64550e7i	−0.0315260	+	0.147109i
$805$	−5.01815e7	−	8.69169e7i	−0.0961958	−	0.166616i
$806$	−1.00154e8	+	5.78238e7i	−0.191277	+	0.110434i
$807$	−1.49265e8	−	4.62018e8i	−0.284013	−	0.879100i
$808$	1.08781e8	−	1.88414e8i	0.206214	−	0.357174i
$809$			8.24005e8i			1.55627i	0.628099	+	0.778134i	$0.283833\pi$
$809$			8.24005e8i			1.55627i	−0.628099	+	0.778134i	$0.716167\pi$
$810$	1.02812e7	−	3.09368e7i	0.0193458	−	0.0582131i
$811$	4.93886e8			0.925900			0.462950	−	0.886385i	$-0.346791\pi$
$811$	4.93886e8			0.925900			0.462950	+	0.886385i	$0.346791\pi$
$812$	2.42336e8	+	1.39913e8i	0.452637	+	0.261330i
$813$	7.92301e8	−	2.55971e8i	1.47441	−	0.476342i
$814$	−9.64546e7	−	1.67064e8i	−0.178834	−	0.309749i
$815$	2.03534e7	−	1.17510e7i	0.0375980	−	0.0217072i
$816$	−9.14345e7	−	1.95948e7i	−0.168283	−	0.0360637i
$817$	−1.68071e8	+	2.91107e8i	−0.308196	+	0.533810i
$818$		−	7.50326e8i		−	1.37085i
$819$	8.85997e8	−	6.39200e8i	1.61280	−	1.16355i
$820$	1.92206e7			0.0348599
$821$	−2.45056e8	−	1.41483e8i	−0.442829	−	0.255668i	0.261968	−	0.965077i	$-0.415629\pi$
$821$	−2.45056e8	−	1.41483e8i	−0.442829	−	0.255668i	−0.704797	+	0.709409i	$0.748962\pi$
$822$	5.28754e6	+	4.77695e6i	0.00952003	+	0.00860073i
$823$	−4.51629e8	−	7.82244e8i	−0.810181	−	1.40327i	−0.912737	−	0.408547i	$-0.866036\pi$
$823$	−4.51629e8	−	7.82244e8i	−0.810181	−	1.40327i	0.102556	−	0.994727i	$-0.467298\pi$
$824$	5.22778e7	−	3.01826e7i	0.0934406	−	0.0539479i
$825$	3.43095e8	−	3.79767e8i	0.611016	−	0.676325i
$826$	−6.43361e8	+	1.11433e9i	−1.14160	+	1.97731i
$827$		−	6.02362e8i		−	1.06498i	−0.846437	−	0.532489i	$-0.821257\pi$
$827$		−	6.02362e8i		−	1.06498i	0.846437	−	0.532489i	$-0.178743\pi$
$828$	−3.33489e8	+	3.39243e7i	−0.587476	+	0.0597612i
$829$	7.35623e8			1.29120			0.645598	−	0.763678i	$-0.276608\pi$
$829$	7.35623e8			1.29120			0.645598	+	0.763678i	$0.276608\pi$
$830$	−5.26840e7	−	3.04171e7i	−0.0921392	−	0.0531966i
$831$	6.70564e7	−	3.12903e8i	0.116852	−	0.545263i
$832$	−3.81219e7	−	6.60290e7i	−0.0661918	−	0.114648i
$833$	8.70496e8	−	5.02581e8i	1.50602	−	0.869503i
$834$	−6.52016e7	−	2.01817e8i	−0.112398	−	0.347905i
$835$	1.80015e7	−	3.11795e7i	0.0309207	−	0.0535562i
$836$		−	2.43856e8i		−	0.417364i
$837$	−1.71901e8	−	1.89395e7i	−0.293158	−	0.0322993i
$838$	6.27146e8			1.06570
$839$	5.93671e8	+	3.42756e8i	1.00522	+	0.580362i	0.909788	−	0.415074i	$-0.136244\pi$
$839$	5.93671e8	+	3.42756e8i	1.00522	+	0.580362i	0.0954292	+	0.995436i	$0.469578\pi$
$840$	3.24837e7	−	1.04946e7i	0.0548059	−	0.0177063i
$841$	−2.05248e8	−	3.55499e8i	−0.345056	−	0.597655i
$842$	−4.52422e8	+	2.61206e8i	−0.757893	+	0.437570i
$843$	1.49281e8	+	3.19916e7i	0.249186	+	0.0534015i
$844$	8.37870e7	−	1.45123e8i	0.139364	−	0.241385i
$845$		−	6.36628e6i		−	0.0105515i
$846$	−6.62076e8	−	2.97431e8i	−1.09345	−	0.491220i
$847$	−1.78682e8			−0.294056
$848$	7.44199e7	+	4.29663e7i	0.122040	+	0.0704597i
$849$	−4.42535e8	−	3.99801e8i	−0.723143	−	0.653313i
$850$	1.48348e8	+	2.56946e8i	0.241560	+	0.418394i
$851$	3.47178e8	−	2.00443e8i	0.563330	−	0.325239i
$852$	−2.48906e8	+	2.75511e8i	−0.402455	+	0.445472i
$853$	−5.33205e6	+	9.23538e6i	−0.00859107	+	0.0148802i	−0.870289	−	0.492541i	$-0.836068\pi$
$853$	−5.33205e6	+	9.23538e6i	−0.00859107	+	0.0148802i	0.861698	+	0.507422i	$0.169401\pi$
$854$		−	6.07108e8i		−	0.974748i
$855$	−2.01962e7	+	4.49563e7i	−0.0323125	+	0.0719270i
$856$	−3.90868e8			−0.623173
$857$	5.54611e8	+	3.20205e8i	0.881142	+	0.508727i	0.871035	−	0.491221i	$-0.163449\pi$
$857$	5.54611e8	+	3.20205e8i	0.881142	+	0.508727i	0.0101071	+	0.999949i	$0.496783\pi$
$858$	−9.10267e7	+	4.24755e8i	−0.144114	+	0.672475i
$859$	−4.67240e8	−	8.09283e8i	−0.737157	−	1.27679i	−0.953770	−	0.300537i	$-0.902834\pi$
$859$	−4.67240e8	−	8.09283e8i	−0.737157	−	1.27679i	0.216613	−	0.976258i	$-0.430499\pi$
$860$	1.62035e7	−	9.35507e6i	0.0254749	−	0.0147079i
$861$	2.96123e8	+	9.16582e8i	0.463940	+	1.43602i
$862$	2.13509e8	−	3.69809e8i	0.333346	−	0.577372i
$863$			9.15183e8i			1.42389i	0.702236	+	0.711944i	$0.252185\pi$
$863$			9.15183e8i			1.42389i	−0.702236	+	0.711944i	$0.747815\pi$
$864$	1.24864e7	−	1.13330e8i	0.0193596	−	0.175713i
$865$	−9.91607e6			−0.0153211
$866$	5.03964e8	+	2.90963e8i	0.775971	+	0.448007i
$867$	3.26253e8	−	1.05403e8i	0.500608	−	0.161733i
$868$	−9.05458e7	−	1.56830e8i	−0.138455	−	0.239811i
$869$	3.45411e8	−	1.99423e8i	0.526352	−	0.303889i
$870$	2.19876e7	+	4.71203e6i	0.0333902	+	0.00715567i
$871$	−1.05285e8	+	1.82359e8i	−0.159336	+	0.275977i
$872$			1.17960e8i			0.177904i
$873$	−6.34110e6	−	6.23355e7i	−0.00953064	−	0.0936898i
$874$	5.06760e8			0.759046
$875$	−1.88312e8	−	1.08722e8i	−0.281096	−	0.162291i
$876$	1.75671e8	+	1.58707e8i	0.261329	+	0.236093i
$877$	−2.65852e8	−	4.60469e8i	−0.394131	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$877$	−2.65852e8	−	4.60469e8i	−0.394131	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$878$	−2.22276e8	+	1.28331e8i	−0.328404	+	0.189604i
$879$	−7.79891e8	+	8.63250e8i	−1.14833	+	1.27107i
$880$	−6.78670e6	+	1.17549e7i	−0.00995889	+	0.0172493i
$881$		−	8.42150e8i		−	1.23158i	−0.787911	−	0.615789i	$-0.788838\pi$
$881$		−	8.42150e8i		−	1.23158i	0.787911	−	0.615789i	$-0.211162\pi$
$882$	7.17059e8	+	9.93917e8i	1.04508	+	1.44859i
$883$	−8.92713e8			−1.29667			−0.648335	−	0.761355i	$-0.724534\pi$
$883$	−8.92713e8			−1.29667			−0.648335	+	0.761355i	$0.724534\pi$
$884$	−2.18088e8	−	1.25913e8i	−0.315700	−	0.182270i
$885$	−2.16674e7	+	1.01106e8i	−0.0312591	+	0.145863i
$886$	−2.95272e8	−	5.11426e8i	−0.424542	−	0.735329i
$887$	−5.06990e8	+	2.92711e8i	−0.726488	+	0.419438i	−0.817136	−	0.576445i	$-0.804440\pi$
$887$	−5.06990e8	+	2.92711e8i	−0.726488	+	0.419438i	0.0906478	+	0.995883i	$0.471106\pi$
$888$	4.19192e7	+	1.29752e8i	0.0598651	+	0.185299i
$889$	−1.01293e9	+	1.75444e9i	−1.44169	+	2.49709i
$890$		−	3.30090e7i		−	0.0468233i
$891$	−4.85648e8	+	4.31434e8i	−0.686575	+	0.609932i
$892$	−2.85558e8			−0.402347
$893$	9.50263e8	+	5.48635e8i	1.33441	+	0.770423i
$894$	5.49200e8	−	1.77432e8i	0.768632	−	0.248324i
$895$	1.85785e7	+	3.21789e7i	0.0259144	+	0.0448851i
$896$	1.03394e8	−	5.96948e7i	0.143738	−	0.0829874i
$897$	−8.82687e8	−	1.89164e8i	−1.22301	−	0.262096i
$898$	−4.71219e7	+	8.16176e7i	−0.0650720	+	0.112708i
$899$		−	1.19290e8i		−	0.164181i
$900$	−2.93377e8	+	2.11656e8i	−0.402437	+	0.290337i
$901$	2.83828e8			0.388044
$902$	−3.31685e8	−	1.91498e8i	−0.451966	−	0.260943i
$903$	6.95757e8	+	6.28572e8i	0.944919	+	0.853673i
$904$	4.03278e7	+	6.98498e7i	0.0545883	+	0.0945496i
$905$	4.85089e7	−	2.80066e7i	0.0654448	−	0.0377846i
$906$	2.60135e8	−	2.87940e8i	0.349796	−	0.387184i
$907$	6.00272e8	−	1.03970e9i	0.804500	−	1.39343i	−0.112128	−	0.993694i	$-0.535767\pi$
$907$	6.00272e8	−	1.03970e9i	0.804500	−	1.39343i	0.916628	−	0.399741i	$-0.130900\pi$
$908$			4.03175e7i			0.0538562i
$909$	8.71665e8	−	8.86705e7i	1.16053	−	0.118056i
$910$	9.19315e7			0.121994
$911$	−1.03915e9	−	5.99956e8i	−1.37444	−	0.793532i	−0.382954	−	0.923767i	$-0.625093\pi$
$911$	−1.03915e9	−	5.99956e8i	−1.37444	−	0.793532i	−0.991483	+	0.130236i	$0.958427\pi$
$912$	−3.61187e7	+	1.68540e8i	−0.0476155	+	0.222186i
$913$	6.06102e8	+	1.04980e9i	0.796403	+	1.37941i
$914$	8.67908e8	−	5.01087e8i	1.13667	−	0.656258i
$915$	−1.49985e7	−	4.64246e7i	−0.0195788	−	0.0606017i
$916$	2.44017e8	−	4.22650e8i	0.317493	−	0.549914i
$917$		−	6.73893e8i		−	0.873943i
$918$	−1.51444e8	−	3.44791e8i	−0.195760	−	0.445685i
$919$	−2.76379e8			−0.356089			−0.178045	−	0.984022i	$-0.556977\pi$
$919$	−2.76379e8			−0.356089			−0.178045	+	0.984022i	$0.556977\pi$
$920$	−2.44280e7	−	1.41035e7i	−0.0313707	−	0.0181119i
$921$	−1.82989e8	+	5.91188e7i	−0.234232	+	0.0756740i
$922$	5.09830e7	+	8.83051e7i	0.0650478	+	0.112666i
$923$	−8.65947e8	+	4.99955e8i	−1.10125	+	0.635807i
$924$	−6.65120e8	−	1.42538e8i	−0.843110	−	0.180682i
$925$	2.16317e8	−	3.74673e8i	0.273317	−	0.473398i
$926$			2.68557e8i			0.338224i
$927$	2.21753e8	+	9.96205e7i	0.278375	+	0.125057i
$928$	7.86449e7			0.0984072
$929$	9.94607e8	+	5.74237e8i	1.24052	+	0.716216i	0.969201	−	0.246273i	$-0.0792059\pi$
$929$	9.94607e8	+	5.74237e8i	1.24052	+	0.716216i	0.271322	+	0.962489i	$0.412539\pi$
$930$	−1.07984e7	−	9.75562e6i	−0.0134248	−	0.0121285i
$931$	−9.26398e8	−	1.60457e9i	−1.14802	−	1.98842i
$932$	2.73894e7	−	1.58133e7i	0.0338325	−	0.0195332i
$933$	−4.04148e8	+	4.47345e8i	−0.497617	+	0.550805i
$934$	−5.58148e7	+	9.66740e7i	−0.0685028	+	0.118650i
$935$			4.48318e7i			0.0548468i
$936$	1.25825e8	−	2.80084e8i	0.153440	−	0.341555i
$937$	−3.65044e8			−0.443738			−0.221869	−	0.975077i	$-0.571216\pi$
$937$	−3.65044e8			−0.443738			−0.221869	+	0.975077i	$0.571216\pi$
$938$	−2.85555e8	−	1.64865e8i	−0.346004	−	0.199766i
$939$	−1.51665e8	+	7.07709e8i	−0.183184	+	0.854787i
$940$	−3.05378e7	−	5.28931e7i	−0.0367667	−	0.0636818i
$941$	−5.74855e8	+	3.31893e8i	−0.689906	+	0.398317i	−0.803577	−	0.595201i	$-0.797072\pi$
$941$	−5.74855e8	+	3.31893e8i	−0.689906	+	0.398317i	0.113671	+	0.993518i	$0.463739\pi$
$942$	2.93029e7	+	9.07005e7i	0.0350556	+	0.108507i
$943$	3.97955e8	−	6.89278e8i	0.474568	−	0.821976i
$944$			3.61633e8i			0.429885i
$945$	1.10814e8	+	8.13629e7i	0.131310	+	0.0964120i
$946$	−3.72825e8			−0.440384
$947$	−5.06553e7	−	2.92458e7i	−0.0596451	−	0.0344361i	0.469881	−	0.882730i	$-0.344297\pi$
$947$	−5.06553e7	−	2.92458e7i	−0.0596451	−	0.0344361i	−0.529526	+	0.848294i	$0.677630\pi$
$948$	−2.68265e8	+	8.66692e7i	−0.314876	+	0.101728i
$949$	3.18780e8	+	5.52143e8i	0.372986	+	0.646031i
$950$	4.73624e8	−	2.73447e8i	0.552411	−	0.318935i
$951$	7.50952e8	+	1.60932e8i	0.873114	+	0.187112i
$952$	1.97167e8	−	3.41503e8i	0.228519	−	0.395807i
$953$			1.97385e8i			0.228053i	0.993478	+	0.114026i	$0.0363748\pi$
$953$			1.97385e8i			0.228053i	−0.993478	+	0.114026i	$0.963625\pi$
$954$	3.50231e7	+	3.44291e8i	0.0403376	+	0.396534i
$955$	−5.83655e7			−0.0670110
$956$	5.06331e8	+	2.92330e8i	0.579510	+	0.334580i
$957$	−3.32486e8	−	3.00380e8i	−0.379348	−	0.342717i
$958$	5.40111e8	+	9.35499e8i	0.614308	+	1.06401i
$959$	−2.60237e7	+	1.50248e7i	−0.0295061	+	0.0170354i
$960$	6.43166e6	−	7.11911e6i	0.00726958	−	0.00804659i
$961$	4.05152e8	−	7.01744e8i	0.456508	−	0.790694i
$962$			3.67208e8i			0.412464i
$963$	−9.20970e8	−	1.27656e9i	−1.03126	−	1.42943i
$964$	2.06914e7			0.0230972
$965$	7.00954e7	+	4.04696e7i	0.0780023	+	0.0450347i
$966$	2.96210e8	−	1.38219e9i	0.328600	−	1.53334i
$967$	6.98352e8	+	1.20958e9i	0.772316	+	1.33769i	0.936291	+	0.351226i	$0.114235\pi$
$967$	6.98352e8	+	1.20958e9i	0.772316	+	1.33769i	−0.163975	+	0.986464i	$0.552432\pi$
$968$	−4.34906e7	+	2.51093e7i	−0.0479478	+	0.0276827i
$969$	1.75021e8	+	5.41740e8i	0.192362	+	0.595415i
$970$	2.63622e6	−	4.56606e6i	0.00288846	−	0.00500296i
$971$		−	3.57183e8i		−	0.390152i	−0.980788	−	0.195076i	$-0.937505\pi$
$971$		−	3.57183e8i		−	0.390152i	0.980788	−	0.195076i	$-0.0624953\pi$
$972$	3.99553e8	−	2.26251e8i	0.435087	−	0.246372i
$973$	8.94375e8			0.970914
$974$	−7.14758e8	−	4.12666e8i	−0.773539	−	0.446603i
$975$	−9.27041e8	+	2.99502e8i	−1.00020	+	0.323136i
$976$	−8.53138e7	−	1.47768e8i	−0.0917635	−	0.158939i
$977$	6.67050e8	−	3.85122e8i	0.715278	−	0.412966i	−0.0977344	−	0.995213i	$-0.531160\pi$
$977$	6.67050e8	−	3.85122e8i	0.715278	−	0.412966i	0.813012	+	0.582247i	$0.197826\pi$
$978$	3.23669e8	+	6.93637e7i	0.346007	+	0.0741507i
$979$	−3.28874e8	+	5.69627e8i	−0.350495	+	0.607075i
$980$			1.03129e8i			0.109573i
$981$	−3.85253e8	+	2.77939e8i	−0.408074	+	0.294404i
$982$	−5.38987e8			−0.569172
$983$	−3.98642e8	−	2.30156e8i	−0.419684	−	0.242305i	0.275258	−	0.961370i	$-0.411237\pi$
$983$	−3.98642e8	−	2.30156e8i	−0.419684	−	0.242305i	−0.694942	+	0.719066i	$0.744570\pi$
$984$	2.00878e8	+	1.81480e8i	0.210837	+	0.190478i
$985$	1.44286e7	+	2.49910e7i	0.0150978	+	0.0261502i
$986$	2.24956e8	−	1.29879e8i	0.234675	−	0.135490i
$987$	2.05185e9	−	2.27117e9i	2.13400	−	2.36209i
$988$	−2.32093e8	+	4.01998e8i	−0.240653	+	0.416824i
$989$		−	7.74770e8i		−	0.800911i
$990$	−5.43821e7	+	5.53204e6i	−0.0560467	+	0.00570138i
$991$	1.55561e8			0.159837			0.0799187	−	0.996801i	$-0.474534\pi$
$991$	1.55561e8			0.159837			0.0799187	+	0.996801i	$0.474534\pi$
$992$	−4.40771e7	−	2.54479e7i	−0.0451521	−	0.0260686i
$993$	3.70839e8	−	1.73043e9i	0.378737	−	1.76729i
$994$	−7.82876e8	−	1.35598e9i	−0.797138	−	1.38068i
$995$	−1.06247e8	+	6.13418e7i	−0.107857	+	0.0622712i
$996$	−2.63412e8	−	8.15333e8i	−0.266598	−	0.825196i
$997$	−6.47513e8	+	1.12153e9i	−0.653376	+	1.13168i	0.328922	+	0.944357i	$0.393315\pi$
$997$	−6.47513e8	+	1.12153e9i	−0.653376	+	1.13168i	−0.982298	+	0.187323i	$0.940019\pi$
$998$			1.23623e9i			1.24367i
$999$	−3.24993e8	+	4.42630e8i	−0.325970	+	0.443960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.7.d.a.11.3	yes	12
3.2	odd	2		54.7.d.a.35.5		12
4.3	odd	2		144.7.q.c.65.1		12
9.2	odd	6		162.7.b.c.161.4		12
9.4	even	3		54.7.d.a.17.5		12
9.5	odd	6	inner	18.7.d.a.5.3	✓	12
9.7	even	3		162.7.b.c.161.9		12
12.11	even	2		432.7.q.b.305.4		12
36.23	even	6		144.7.q.c.113.1		12
36.31	odd	6		432.7.q.b.17.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.7.d.a.5.3	✓	12	9.5	odd	6	inner
18.7.d.a.11.3	yes	12	1.1	even	1	trivial
54.7.d.a.17.5		12	9.4	even	3
54.7.d.a.35.5		12	3.2	odd	2
144.7.q.c.65.1		12	4.3	odd	2
144.7.q.c.113.1		12	36.23	even	6
162.7.b.c.161.4		12	9.2	odd	6
162.7.b.c.161.9		12	9.7	even	3
432.7.q.b.17.4		12	36.31	odd	6
432.7.q.b.305.4		12	12.11	even	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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	18.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.89898 - 2.82843i) q^{2} +(25.6924 - 8.30052i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-9.39126 + 5.42205i) q^{5} +(-149.344 - 32.0051i) q^{6} +(322.041 - 557.792i) q^{7} -181.019i q^{8} +(591.203 - 426.521i) q^{9} +O(q^{10})\)	\(q+(-4.89898 - 2.82843i) q^{2} +(25.6924 - 8.30052i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-9.39126 + 5.42205i) q^{5} +(-149.344 - 32.0051i) q^{6} +(322.041 - 557.792i) q^{7} -181.019i q^{8} +(591.203 - 426.521i) q^{9} +61.3435 q^{10} +(-1058.59 - 611.175i) q^{11} +(641.110 + 579.201i) q^{12} +(1163.39 + 2015.05i) q^{13} +(-3155.35 + 1821.74i) q^{14} +(-196.279 + 217.258i) q^{15} +(-512.000 + 886.810i) q^{16} +3382.18i q^{17} +(-4102.67 + 417.346i) q^{18} +6234.31 q^{19} +(-300.520 - 173.506i) q^{20} +(3644.06 - 17004.1i) q^{21} +(3457.33 + 5988.27i) q^{22} +(-12444.3 + 7184.71i) q^{23} +(-1502.56 - 4650.83i) q^{24} +(-7753.70 + 13429.8i) q^{25} -13162.2i q^{26} +(11649.1 - 15865.7i) q^{27} +20610.6 q^{28} +(11757.8 + 6788.37i) q^{29} +(1576.06 - 509.183i) q^{30} +(-4393.16 - 7609.18i) q^{31} +(5016.55 - 2896.31i) q^{32} +(-32270.7 - 6915.75i) q^{33} +(9566.26 - 16569.2i) q^{34} +6984.49i q^{35} +(21279.3 + 9559.54i) q^{36} -27898.6 q^{37} +(-30541.8 - 17633.3i) q^{38} +(46616.2 + 42114.7i) q^{39} +(981.495 + 1700.00i) q^{40} +(-47968.4 + 27694.6i) q^{41} +(-65947.1 + 72996.0i) q^{42} +(-26959.0 + 46694.4i) q^{43} -39115.2i q^{44} +(-3239.52 + 7211.10i) q^{45} +81285.7 q^{46} +(152425. + 88002.4i) q^{47} +(-5793.54 + 27034.2i) q^{48} +(-148597. - 257377. i) q^{49} +(75970.5 - 43861.6i) q^{50} +(28073.9 + 86896.5i) q^{51} +(-37228.4 + 64481.5i) q^{52} -83918.6i q^{53} +(-101943. + 44777.0i) q^{54} +13255.3 q^{55} +(-100971. - 58295.7i) q^{56} +(160175. - 51748.1i) q^{57} +(-38400.8 - 66512.2i) q^{58} +(305843. - 176579. i) q^{59} +(-9161.29 - 1963.30i) q^{60} +(-83314.3 + 144305. i) q^{61} +49702.9i q^{62} +(-47518.5 - 467125. i) q^{63} -32768.0 q^{64} +(-21851.4 - 12615.9i) q^{65} +(138533. + 125156. i) q^{66} +(45249.4 + 78374.3i) q^{67} +(-93729.8 + 54114.9i) q^{68} +(-260087. + 287887. i) q^{69} +(19755.1 - 34216.9i) q^{70} +429740. i q^{71} +(-77208.6 - 107019. i) q^{72} +274010. q^{73} +(136675. + 78909.1i) q^{74} +(-87737.1 + 409404. i) q^{75} +(99749.0 + 172770. i) q^{76} +(-681817. + 393647. i) q^{77} +(-109253. - 338170. i) q^{78} +(-163147. + 282579. i) q^{79} -11104.4i q^{80} +(167600. - 504321. i) q^{81} +313328. q^{82} +(-858836. - 495849. i) q^{83} +(529538. - 171079. i) q^{84} +(-18338.4 - 31763.0i) q^{85} +(264143. - 152503. i) q^{86} +(358434. + 76813.9i) q^{87} +(-110635. + 191625. i) q^{88} -538101. i q^{89} +(36266.4 - 26164.3i) q^{90} +1.49863e6 q^{91} +(-398217. - 229911. i) q^{92} +(-176031. - 159033. i) q^{93} +(-497817. - 862244. i) q^{94} +(-58548.1 + 33802.7i) q^{95} +(104847. - 116053. i) q^{96} +(42974.7 - 74434.4i) q^{97} +1.68118e6i q^{98} +(-886518. + 90181.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9}+O(q^{10}) \) 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9	\( 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9} + 378 q^{11} + 384 q^{12} + 1680 q^{13} - 4752 q^{14} - 10872 q^{15} - 6144 q^{16} - 2976 q^{18} - 2820 q^{19} + 13824 q^{20} + 24876 q^{21} - 3600 q^{22} - 76248 q^{23} - 6144 q^{24} + 8094 q^{25} + 127008 q^{27} + 15360 q^{28} + 97092 q^{29} + 34272 q^{30} + 21480 q^{31} - 246258 q^{33} - 27360 q^{34} + 38208 q^{36} - 25536 q^{37} + 97632 q^{38} + 42204 q^{39} - 410562 q^{41} - 222144 q^{42} + 71430 q^{43} + 13716 q^{45} - 135072 q^{46} + 347652 q^{47} + 55296 q^{48} - 135954 q^{49} + 311040 q^{50} + 336402 q^{51} - 53760 q^{52} - 173520 q^{54} + 580392 q^{55} - 152064 q^{56} - 522282 q^{57} + 159264 q^{58} + 369738 q^{59} - 170496 q^{60} + 135744 q^{61} - 103800 q^{63} - 393216 q^{64} - 753840 q^{65} + 909216 q^{66} - 289938 q^{67} + 744768 q^{68} + 2059272 q^{69} + 155952 q^{70} - 374784 q^{72} - 977700 q^{73} - 2197152 q^{74} - 2115342 q^{75} - 45120 q^{76} - 159192 q^{77} - 631488 q^{78} - 764796 q^{79} - 1428282 q^{81} + 1073088 q^{82} + 396900 q^{83} + 1441536 q^{84} + 1619568 q^{85} + 3264624 q^{86} + 3072636 q^{87} + 115200 q^{88} - 1987200 q^{90} + 355584 q^{91} - 2439936 q^{92} - 2526576 q^{93} - 736848 q^{94} - 2089260 q^{95} - 49152 q^{96} - 38874 q^{97} + 4398804 q^{99}+O(q^{100}) \) 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9 + 378 * q^11 + 384 * q^12 + 1680 * q^13 - 4752 * q^14 - 10872 * q^15 - 6144 * q^16 - 2976 * q^18 - 2820 * q^19 + 13824 * q^20 + 24876 * q^21 - 3600 * q^22 - 76248 * q^23 - 6144 * q^24 + 8094 * q^25 + 127008 * q^27 + 15360 * q^28 + 97092 * q^29 + 34272 * q^30 + 21480 * q^31 - 246258 * q^33 - 27360 * q^34 + 38208 * q^36 - 25536 * q^37 + 97632 * q^38 + 42204 * q^39 - 410562 * q^41 - 222144 * q^42 + 71430 * q^43 + 13716 * q^45 - 135072 * q^46 + 347652 * q^47 + 55296 * q^48 - 135954 * q^49 + 311040 * q^50 + 336402 * q^51 - 53760 * q^52 - 173520 * q^54 + 580392 * q^55 - 152064 * q^56 - 522282 * q^57 + 159264 * q^58 + 369738 * q^59 - 170496 * q^60 + 135744 * q^61 - 103800 * q^63 - 393216 * q^64 - 753840 * q^65 + 909216 * q^66 - 289938 * q^67 + 744768 * q^68 + 2059272 * q^69 + 155952 * q^70 - 374784 * q^72 - 977700 * q^73 - 2197152 * q^74 - 2115342 * q^75 - 45120 * q^76 - 159192 * q^77 - 631488 * q^78 - 764796 * q^79 - 1428282 * q^81 + 1073088 * q^82 + 396900 * q^83 + 1441536 * q^84 + 1619568 * q^85 + 3264624 * q^86 + 3072636 * q^87 + 115200 * q^88 - 1987200 * q^90 + 355584 * q^91 - 2439936 * q^92 - 2526576 * q^93 - 736848 * q^94 - 2089260 * q^95 - 49152 * q^96 - 38874 * q^97 + 4398804 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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