LMFDB - Embedded newform 322.2.e.c.277.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(93,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("322.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1767277521.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 $ x^8 - 2x^7 + x^6 - 10x^5 + 38x^4 - 40x^3 + 64x^2 - 38x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.3
Root			$0.0512865 - 1.21608i$ of defining polynomial
Character	$\chi$	$=$	322.277
Dual form			322.2.e.c.93.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.319548 - 0.553474i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.268262 + 0.464643i) q^{5} +0.639096 q^{6} +(0.716975 + 2.54675i) q^{7} -1.00000 q^{8} +(1.29578 + 2.24435i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.319548 - 0.553474i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.268262 + 0.464643i) q^{5} +0.639096 q^{6} +(0.716975 + 2.54675i) q^{7} -1.00000 q^{8} +(1.29578 + 2.24435i) q^{9} +(-0.268262 + 0.464643i) q^{10} +(2.07880 - 3.60059i) q^{11} +(0.319548 + 0.553474i) q^{12} -2.41594 q^{13} +(-1.84706 + 1.89429i) q^{14} +0.342890 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.23174 + 2.13343i) q^{17} +(-1.29578 + 2.24435i) q^{18} +(3.42587 + 5.93378i) q^{19} -0.536523 q^{20} +(1.63867 + 0.416983i) q^{21} +4.15761 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.319548 + 0.553474i) q^{24} +(2.35607 - 4.08084i) q^{25} +(-1.20797 - 2.09226i) q^{26} +3.57354 q^{27} +(-2.56404 - 0.652457i) q^{28} +1.01801 q^{29} +(0.171445 + 0.296951i) q^{30} +(-0.560293 + 0.970457i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.32856 - 2.30112i) q^{33} -2.46348 q^{34} +(-0.990993 + 1.01633i) q^{35} -2.59156 q^{36} +(-5.62483 - 9.74249i) q^{37} +(-3.42587 + 5.93378i) q^{38} +(-0.772008 + 1.33716i) q^{39} +(-0.268262 - 0.464643i) q^{40} +2.65711 q^{41} +(0.458216 + 1.62762i) q^{42} -3.50884 q^{43} +(2.07880 + 3.60059i) q^{44} +(-0.695215 + 1.20415i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-4.86557 - 8.42742i) q^{47} -0.639096 q^{48} +(-5.97189 + 3.65192i) q^{49} +4.71214 q^{50} +(0.787199 + 1.36347i) q^{51} +(1.20797 - 2.09226i) q^{52} +(6.44763 - 11.1676i) q^{53} +(1.78677 + 3.09478i) q^{54} +2.23065 q^{55} +(-0.716975 - 2.54675i) q^{56} +4.37892 q^{57} +(0.509007 + 0.881626i) q^{58} +(-1.45772 + 2.52485i) q^{59} +(-0.171445 + 0.296951i) q^{60} +(-7.23923 - 12.5387i) q^{61} -1.12059 q^{62} +(-4.78677 + 4.90917i) q^{63} +1.00000 q^{64} +(-0.648103 - 1.12255i) q^{65} +(1.32856 - 2.30112i) q^{66} +(1.45864 - 2.52645i) q^{67} +(-1.23174 - 2.13343i) q^{68} -0.639096 q^{69} +(-1.37567 - 0.350059i) q^{70} +2.21079 q^{71} +(-1.29578 - 2.24435i) q^{72} +(-2.59731 + 4.49868i) q^{73} +(5.62483 - 9.74249i) q^{74} +(-1.50576 - 2.60805i) q^{75} -6.85173 q^{76} +(10.6603 + 2.71266i) q^{77} -1.54402 q^{78} +(5.32379 + 9.22107i) q^{79} +(0.268262 - 0.464643i) q^{80} +(-2.74542 + 4.75520i) q^{81} +(1.32856 + 2.30112i) q^{82} +10.4063 q^{83} +(-1.18045 + 1.21064i) q^{84} -1.32171 q^{85} +(-1.75442 - 3.03875i) q^{86} +(0.325304 - 0.563444i) q^{87} +(-2.07880 + 3.60059i) q^{88} +(-1.85233 - 3.20832i) q^{89} -1.39043 q^{90} +(-1.73217 - 6.15279i) q^{91} +1.00000 q^{92} +(0.358081 + 0.620215i) q^{93} +(4.86557 - 8.42742i) q^{94} +(-1.83806 + 3.18361i) q^{95} +(-0.319548 - 0.553474i) q^{96} -14.7945 q^{97} +(-6.14860 - 3.34585i) q^{98} +10.7747 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - q^{12} - 2 q^{13} + q^{14} + 6 q^{15} - 4 q^{16} - 15 q^{17} + 7 q^{18} + q^{19} + 6 q^{20} - q^{21} + 12 q^{22} - 4 q^{23} + q^{24} + 5 q^{25} - q^{26} - 10 q^{27} + 2 q^{28} + 12 q^{29} + 3 q^{30} - 8 q^{31} + 4 q^{32} - 9 q^{33} - 30 q^{34} - 6 q^{35} + 14 q^{36} - 8 q^{37} - q^{38} + 25 q^{39} + 3 q^{40} + 18 q^{41} - 14 q^{42} + 28 q^{43} + 6 q^{44} - 21 q^{45} + 4 q^{46} - 9 q^{47} + 2 q^{48} + 5 q^{49} + 10 q^{50} - 6 q^{51} + q^{52} + 3 q^{53} - 5 q^{54} - 24 q^{55} + q^{56} + 46 q^{57} + 6 q^{58} - 12 q^{59} - 3 q^{60} - 11 q^{61} - 16 q^{62} - 19 q^{63} + 8 q^{64} + 9 q^{66} + q^{67} - 15 q^{68} + 2 q^{69} - 30 q^{70} - 6 q^{71} + 7 q^{72} + 4 q^{73} + 8 q^{74} - 22 q^{75} - 2 q^{76} - 9 q^{77} + 50 q^{78} - 5 q^{79} - 3 q^{80} + 8 q^{81} + 9 q^{82} + 24 q^{83} - 13 q^{84} + 48 q^{85} + 14 q^{86} + 9 q^{87} - 6 q^{88} - 27 q^{89} - 42 q^{90} - 26 q^{91} + 8 q^{92} + 25 q^{93} + 9 q^{94} + 3 q^{95} + q^{96} + 4 q^{97} - 26 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - q^12 - 2 * q^13 + q^14 + 6 * q^15 - 4 * q^16 - 15 * q^17 + 7 * q^18 + q^19 + 6 * q^20 - q^21 + 12 * q^22 - 4 * q^23 + q^24 + 5 * q^25 - q^26 - 10 * q^27 + 2 * q^28 + 12 * q^29 + 3 * q^30 - 8 * q^31 + 4 * q^32 - 9 * q^33 - 30 * q^34 - 6 * q^35 + 14 * q^36 - 8 * q^37 - q^38 + 25 * q^39 + 3 * q^40 + 18 * q^41 - 14 * q^42 + 28 * q^43 + 6 * q^44 - 21 * q^45 + 4 * q^46 - 9 * q^47 + 2 * q^48 + 5 * q^49 + 10 * q^50 - 6 * q^51 + q^52 + 3 * q^53 - 5 * q^54 - 24 * q^55 + q^56 + 46 * q^57 + 6 * q^58 - 12 * q^59 - 3 * q^60 - 11 * q^61 - 16 * q^62 - 19 * q^63 + 8 * q^64 + 9 * q^66 + q^67 - 15 * q^68 + 2 * q^69 - 30 * q^70 - 6 * q^71 + 7 * q^72 + 4 * q^73 + 8 * q^74 - 22 * q^75 - 2 * q^76 - 9 * q^77 + 50 * q^78 - 5 * q^79 - 3 * q^80 + 8 * q^81 + 9 * q^82 + 24 * q^83 - 13 * q^84 + 48 * q^85 + 14 * q^86 + 9 * q^87 - 6 * q^88 - 27 * q^89 - 42 * q^90 - 26 * q^91 + 8 * q^92 + 25 * q^93 + 9 * q^94 + 3 * q^95 + q^96 + 4 * q^97 - 26 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.319548	−	0.553474i	0.184491	−	0.319548i	−0.758914	−	0.651191i	$-0.774270\pi$
$3$	0.319548	−	0.553474i	0.184491	−	0.319548i	0.943405	+	0.331643i	$0.107603\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.268262	+	0.464643i	0.119970	+	0.207795i	0.919756	−	0.392491i	$-0.128387\pi$
$5$	0.268262	+	0.464643i	0.119970	+	0.207795i	−0.799785	+	0.600286i	$0.795053\pi$
$6$	0.639096			0.260910
$7$	0.716975	+	2.54675i	0.270991	+	0.962582i
$7$	0.716975	+	2.54675i	0.270991	+	0.962582i
$8$	−1.00000			−0.353553
$9$	1.29578	+	2.24435i	0.431926	+	0.748118i
$10$	−0.268262	+	0.464643i	−0.0848318	+	0.146933i
$11$	2.07880	−	3.60059i	0.626783	−	1.08562i	−0.361411	−	0.932407i	$-0.617705\pi$
$11$	2.07880	−	3.60059i	0.626783	−	1.08562i	0.988193	−	0.153213i	$-0.0489619\pi$
$12$	0.319548	+	0.553474i	0.0922456	+	0.159774i
$13$	−2.41594			−0.670060			−0.335030	−	0.942207i	$-0.608746\pi$
$13$	−2.41594			−0.670060			−0.335030	+	0.942207i	$0.608746\pi$
$14$	−1.84706	+	1.89429i	−0.493649	+	0.506272i
$15$	0.342890			0.0885338
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.23174	+	2.13343i	−0.298740	+	0.517434i	−0.975848	−	0.218450i	$-0.929900\pi$
$17$	−1.23174	+	2.13343i	−0.298740	+	0.517434i	0.677108	+	0.735884i	$0.263233\pi$
$18$	−1.29578	+	2.24435i	−0.305418	+	0.528999i
$19$	3.42587	+	5.93378i	0.785948	+	1.36130i	0.928431	+	0.371504i	$0.121158\pi$
$19$	3.42587	+	5.93378i	0.785948	+	1.36130i	−0.142483	+	0.989797i	$0.545509\pi$
$20$	−0.536523			−0.119970
$21$	1.63867	+	0.416983i	0.357587	+	0.0909932i
$22$	4.15761			0.886405
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	−0.319548	+	0.553474i	−0.0652275	+	0.112977i
$25$	2.35607	−	4.08084i	0.471214	−	0.816167i
$26$	−1.20797	−	2.09226i	−0.236902	−	0.410326i
$27$	3.57354			0.687729
$28$	−2.56404	−	0.652457i	−0.484558	−	0.123303i
$29$	1.01801			0.189040			0.0945202	−	0.995523i	$-0.469868\pi$
$29$	1.01801			0.189040			0.0945202	+	0.995523i	$0.469868\pi$
$30$	0.171445	+	0.296951i	0.0313014	+	0.0542157i
$31$	−0.560293	+	0.970457i	−0.100632	+	0.174299i	−0.911945	−	0.410312i	$-0.865420\pi$
$31$	−0.560293	+	0.970457i	−0.100632	+	0.174299i	0.811313	+	0.584611i	$0.198753\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.32856	−	2.30112i	−0.231272	−	0.400574i
$34$	−2.46348			−0.422483
$35$	−0.990993	+	1.01633i	−0.167508	+	0.171792i
$36$	−2.59156			−0.431926
$37$	−5.62483	−	9.74249i	−0.924716	−	1.60166i	−0.792017	−	0.610499i	$-0.790969\pi$
$37$	−5.62483	−	9.74249i	−0.924716	−	1.60166i	−0.132699	−	0.991156i	$-0.542364\pi$
$38$	−3.42587	+	5.93378i	−0.555749	+	0.962586i
$39$	−0.772008	+	1.33716i	−0.123620	+	0.214116i
$40$	−0.268262	−	0.464643i	−0.0424159	−	0.0734665i
$41$	2.65711			0.414971			0.207485	−	0.978238i	$-0.433472\pi$
$41$	2.65711			0.414971			0.207485	+	0.978238i	$0.433472\pi$
$42$	0.458216	+	1.62762i	0.0707043	+	0.251147i
$43$	−3.50884			−0.535094			−0.267547	−	0.963545i	$-0.586213\pi$
$43$	−3.50884			−0.535094			−0.267547	+	0.963545i	$0.586213\pi$
$44$	2.07880	+	3.60059i	0.313391	+	0.542810i
$45$	−0.695215	+	1.20415i	−0.103637	+	0.179504i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	−4.86557	−	8.42742i	−0.709717	−	1.22927i	−0.964962	−	0.262389i	$-0.915490\pi$
$47$	−4.86557	−	8.42742i	−0.709717	−	1.22927i	0.255245	−	0.966876i	$-0.417844\pi$
$48$	−0.639096			−0.0922456
$49$	−5.97189	+	3.65192i	−0.853128	+	0.521702i
$50$	4.71214			0.666398
$51$	0.787199	+	1.36347i	0.110230	+	0.190924i
$52$	1.20797	−	2.09226i	0.167515	−	0.290145i
$53$	6.44763	−	11.1676i	0.885650	−	1.53399i	0.0406826	−	0.999172i	$-0.487047\pi$
$53$	6.44763	−	11.1676i	0.885650	−	1.53399i	0.844967	−	0.534818i	$-0.179620\pi$
$54$	1.78677	+	3.09478i	0.243149	+	0.421146i
$55$	2.23065			0.300781
$56$	−0.716975	−	2.54675i	−0.0958098	−	0.340324i
$57$	4.37892			0.580002
$58$	0.509007	+	0.881626i	0.0668359	+	0.115763i
$59$	−1.45772	+	2.52485i	−0.189779	+	0.328707i	−0.945176	−	0.326560i	$-0.894110\pi$
$59$	−1.45772	+	2.52485i	−0.189779	+	0.328707i	0.755397	+	0.655267i	$0.227444\pi$
$60$	−0.171445	+	0.296951i	−0.0221335	+	0.0383363i
$61$	−7.23923	−	12.5387i	−0.926889	−	1.60542i	−0.788495	−	0.615041i	$-0.789140\pi$
$61$	−7.23923	−	12.5387i	−0.926889	−	1.60542i	−0.138393	−	0.990377i	$-0.544194\pi$
$62$	−1.12059			−0.142315
$63$	−4.78677	+	4.90917i	−0.603076	+	0.618497i
$64$	1.00000			0.125000
$65$	−0.648103	−	1.12255i	−0.0803873	−	0.139235i
$66$	1.32856	−	2.30112i	0.163534	−	0.283249i
$67$	1.45864	−	2.52645i	0.178202	−	0.308655i	−0.763063	−	0.646324i	$-0.776305\pi$
$67$	1.45864	−	2.52645i	0.178202	−	0.308655i	0.941265	+	0.337670i	$0.109639\pi$
$68$	−1.23174	−	2.13343i	−0.149370	−	0.258717i
$69$	−0.639096			−0.0769381
$70$	−1.37567	−	0.350059i	−0.164424	−	0.0418400i
$71$	2.21079			0.262373			0.131186	−	0.991358i	$-0.458121\pi$
$71$	2.21079			0.262373			0.131186	+	0.991358i	$0.458121\pi$
$72$	−1.29578	−	2.24435i	−0.152709	−	0.264500i
$73$	−2.59731	+	4.49868i	−0.303992	+	0.526530i	−0.977036	−	0.213072i	$-0.931653\pi$
$73$	−2.59731	+	4.49868i	−0.303992	+	0.526530i	0.673044	+	0.739602i	$0.264986\pi$
$74$	5.62483	−	9.74249i	0.653873	−	1.13254i
$75$	−1.50576	−	2.60805i	−0.173870	−	0.301151i
$76$	−6.85173			−0.785948
$77$	10.6603	+	2.71266i	1.21485	+	0.309136i
$78$	−1.54402			−0.174825
$79$	5.32379	+	9.22107i	0.598973	+	1.03745i	0.992973	+	0.118341i	$0.0377577\pi$
$79$	5.32379	+	9.22107i	0.598973	+	1.03745i	−0.394000	+	0.919111i	$0.628909\pi$
$80$	0.268262	−	0.464643i	0.0299926	−	0.0519486i
$81$	−2.74542	+	4.75520i	−0.305046	+	0.528355i
$82$	1.32856	+	2.30112i	0.146714	+	0.254117i
$83$	10.4063			1.14224			0.571118	−	0.820868i	$-0.306510\pi$
$83$	10.4063			1.14224			0.571118	+	0.820868i	$0.306510\pi$
$84$	−1.18045	+	1.21064i	−0.128798	+	0.132091i
$85$	−1.32171			−0.143360
$86$	−1.75442	−	3.03875i	−0.189184	−	0.327677i
$87$	0.325304	−	0.563444i	0.0348763	−	0.0604075i
$88$	−2.07880	+	3.60059i	−0.221601	+	0.383824i
$89$	−1.85233	−	3.20832i	−0.196346	−	0.340081i	0.750995	−	0.660308i	$-0.229574\pi$
$89$	−1.85233	−	3.20832i	−0.196346	−	0.340081i	−0.947341	+	0.320227i	$0.896241\pi$
$90$	−1.39043			−0.146564
$91$	−1.73217	−	6.15279i	−0.181580	−	0.644988i
$92$	1.00000			0.104257
$93$	0.358081	+	0.620215i	0.0371313	+	0.0643133i
$94$	4.86557	−	8.42742i	0.501846	−	0.869222i
$95$	−1.83806	+	3.18361i	−0.188581	+	0.326631i
$96$	−0.319548	−	0.553474i	−0.0326137	−	0.0564887i
$97$	−14.7945			−1.50216			−0.751078	−	0.660213i	$-0.770466\pi$
$97$	−14.7945			−1.50216			−0.751078	+	0.660213i	$0.770466\pi$
$98$	−6.14860	−	3.34585i	−0.621102	−	0.337982i
$99$	10.7747			1.08289
$100$	2.35607	+	4.08084i	0.235607	+	0.408084i
$101$	−3.33756	+	5.78083i	−0.332100	+	0.575214i	−0.982923	−	0.184015i	$-0.941090\pi$
$101$	−3.33756	+	5.78083i	−0.332100	+	0.575214i	0.650824	+	0.759229i	$0.274424\pi$
$102$	−0.787199	+	1.36347i	−0.0779443	+	0.135004i
$103$	−1.54928	−	2.68343i	−0.152655	−	0.264406i	0.779548	−	0.626343i	$-0.215449\pi$
$103$	−1.54928	−	2.68343i	−0.152655	−	0.264406i	−0.932203	+	0.361937i	$0.882116\pi$
$104$	2.41594			0.236902
$105$	0.245844	+	0.873256i	0.0239919	+	0.0852210i
$106$	12.8953			1.25250
$107$	1.66661	+	2.88666i	0.161118	+	0.279064i	0.935270	−	0.353936i	$-0.115157\pi$
$107$	1.66661	+	2.88666i	0.161118	+	0.279064i	−0.774152	+	0.632999i	$0.781824\pi$
$108$	−1.78677	+	3.09478i	−0.171932	+	0.297795i
$109$	7.43445	−	12.8768i	0.712091	−	1.23338i	−0.251980	−	0.967732i	$-0.581082\pi$
$109$	7.43445	−	12.8768i	0.712091	−	1.23338i	0.964071	−	0.265645i	$-0.0855849\pi$
$110$	1.11533	+	1.93180i	0.106342	+	0.184190i
$111$	−7.18961			−0.682408
$112$	1.84706	−	1.89429i	0.174531	−	0.178994i
$113$	10.1536			0.955169			0.477584	−	0.878586i	$-0.341512\pi$
$113$	10.1536			0.955169			0.477584	+	0.878586i	$0.341512\pi$
$114$	2.18946	+	3.79225i	0.205062	+	0.355177i
$115$	0.268262	−	0.464643i	0.0250155	−	0.0433282i
$116$	−0.509007	+	0.881626i	−0.0472601	+	0.0818569i
$117$	−3.13052	−	5.42222i	−0.289416	−	0.501284i
$118$	−2.91544			−0.268388
$119$	−6.31645	−	1.60731i	−0.579028	−	0.147342i
$120$	−0.342890			−0.0313014
$121$	−3.14284	−	5.44356i	−0.285713	−	0.494869i
$122$	7.23923	−	12.5387i	0.655409	−	1.13520i
$123$	0.849074	−	1.47064i	0.0765585	−	0.132603i
$124$	−0.560293	−	0.970457i	−0.0503158	−	0.0871496i
$125$	5.21079			0.466067
$126$	−6.64485	−	1.69088i	−0.591971	−	0.150636i
$127$	3.85259			0.341862			0.170931	−	0.985283i	$-0.445322\pi$
$127$	3.85259			0.341862			0.170931	+	0.985283i	$0.445322\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.12124	+	1.94205i	−0.0987201	+	0.170988i
$130$	0.648103	−	1.12255i	0.0568424	−	0.0984539i
$131$	9.64225	+	16.7009i	0.842447	+	1.45916i	0.887820	+	0.460192i	$0.152219\pi$
$131$	9.64225	+	16.7009i	0.842447	+	1.45916i	−0.0453721	+	0.998970i	$0.514447\pi$
$132$	2.65711			0.231272
$133$	−12.6556	+	12.9792i	−1.09738	+	1.12544i
$134$	2.91729			0.252015
$135$	0.958644	+	1.66042i	0.0825070	+	0.142906i
$136$	1.23174	−	2.13343i	0.105621	−	0.182940i
$137$	−2.50092	+	4.33173i	−0.213668	+	0.370084i	−0.952860	−	0.303411i	$-0.901875\pi$
$137$	−2.50092	+	4.33173i	−0.213668	+	0.370084i	0.739191	+	0.673495i	$0.235208\pi$
$138$	−0.319548	−	0.553474i	−0.0272017	−	0.0471148i
$139$	−10.1651			−0.862192			−0.431096	−	0.902306i	$-0.641873\pi$
$139$	−10.1651			−0.862192			−0.431096	+	0.902306i	$0.641873\pi$
$140$	−0.384674	−	1.36639i	−0.0325109	−	0.115481i
$141$	−6.21914			−0.523746
$142$	1.10540	+	1.91460i	0.0927627	+	0.160670i
$143$	−5.02226	+	8.69880i	−0.419982	+	0.727430i
$144$	1.29578	−	2.24435i	0.107982	−	0.187029i
$145$	0.273094	+	0.473013i	0.0226792	+	0.0392816i
$146$	−5.19462			−0.429910
$147$	0.112932	+	4.47225i	0.00931446	+	0.368865i
$148$	11.2497			0.924716
$149$	0.451964	+	0.782825i	0.0370263	+	0.0641315i	0.883945	−	0.467591i	$-0.154878\pi$
$149$	0.451964	+	0.782825i	0.0370263	+	0.0641315i	−0.846918	+	0.531723i	$0.821545\pi$
$150$	1.50576	−	2.60805i	0.122944	−	0.212946i
$151$	−8.83323	+	15.2996i	−0.718838	+	1.24506i	0.242623	+	0.970121i	$0.421992\pi$
$151$	−8.83323	+	15.2996i	−0.718838	+	1.24506i	−0.961461	+	0.274943i	$0.911341\pi$
$152$	−3.42587	−	5.93378i	−0.277875	−	0.481293i
$153$	−6.38424			−0.516135
$154$	2.98090	+	10.5884i	0.240208	+	0.853237i
$155$	−0.601221			−0.0482912
$156$	−0.772008	−	1.33716i	−0.0618101	−	0.107058i
$157$	−5.46614	+	9.46763i	−0.436245	+	0.755599i	−0.997396	−	0.0721145i	$-0.977025\pi$
$157$	−5.46614	+	9.46763i	−0.436245	+	0.755599i	0.561151	+	0.827713i	$0.310359\pi$
$158$	−5.32379	+	9.22107i	−0.423538	+	0.733589i
$159$	−4.12065	−	7.13718i	−0.326789	−	0.566015i
$160$	0.536523			0.0424159
$161$	1.84706	−	1.89429i	0.145569	−	0.149291i
$162$	−5.49083			−0.431400
$163$	6.98991	+	12.1069i	0.547492	+	0.948284i	0.998446	+	0.0557362i	$0.0177506\pi$
$163$	6.98991	+	12.1069i	0.547492	+	0.948284i	−0.450954	+	0.892547i	$0.648916\pi$
$164$	−1.32856	+	2.30112i	−0.103743	+	0.179688i
$165$	0.712801	−	1.23461i	0.0554915	−	0.0961140i
$166$	5.20314	+	9.01210i	0.403842	+	0.699474i
$167$	21.3292			1.65050			0.825252	−	0.564765i	$-0.191033\pi$
$167$	21.3292			1.65050			0.825252	+	0.564765i	$0.191033\pi$
$168$	−1.63867	−	0.416983i	−0.126426	−	0.0321709i
$169$	−7.16325			−0.551019
$170$	−0.660856	−	1.14464i	−0.0506854	−	0.0877896i
$171$	−8.87833	+	15.3777i	−0.678943	+	1.17596i
$172$	1.75442	−	3.03875i	0.133773	−	0.231702i
$173$	−11.1290	−	19.2760i	−0.846122	−	1.46553i	−0.884643	−	0.466269i	$-0.845598\pi$
$173$	−11.1290	−	19.2760i	−0.846122	−	1.46553i	0.0385204	−	0.999258i	$-0.487736\pi$
$174$	0.650609			0.0493225
$175$	12.0821	+	3.07447i	0.913322	+	0.232408i
$176$	−4.15761			−0.313391
$177$	0.931624	+	1.61362i	0.0700251	+	0.121287i
$178$	1.85233	−	3.20832i	0.138838	−	0.240474i
$179$	−4.76625	+	8.25539i	−0.356246	+	0.617037i	−0.987330	−	0.158678i	$-0.949277\pi$
$179$	−4.76625	+	8.25539i	−0.356246	+	0.617037i	0.631084	+	0.775714i	$0.282610\pi$
$180$	−0.695215	−	1.20415i	−0.0518183	−	0.0897519i
$181$	21.5372			1.60085			0.800423	−	0.599435i	$-0.204608\pi$
$181$	21.5372			1.60085			0.800423	+	0.599435i	$0.204608\pi$
$182$	4.46239	−	4.57650i	0.330774	−	0.339232i
$183$	−9.25313			−0.684011
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	3.01785	−	5.22707i	0.221877	−	0.384302i
$186$	−0.358081	+	0.620215i	−0.0262558	+	0.0454764i
$187$	5.12108	+	8.86997i	0.374491	+	0.648637i
$188$	9.73115			0.709717
$189$	2.56214	+	9.10093i	0.186368	+	0.661995i
$190$	−3.67612			−0.266693
$191$	−11.7453	−	20.3434i	−0.849857	−	1.47199i	−0.881336	−	0.472491i	$-0.843355\pi$
$191$	−11.7453	−	20.3434i	−0.849857	−	1.47199i	0.0314790	−	0.999504i	$-0.489978\pi$
$192$	0.319548	−	0.553474i	0.0230614	−	0.0399435i
$193$	−2.76343	+	4.78640i	−0.198916	+	0.344533i	−0.948177	−	0.317742i	$-0.897075\pi$
$193$	−2.76343	+	4.78640i	−0.198916	+	0.344533i	0.749261	+	0.662275i	$0.230409\pi$
$194$	−7.39726	−	12.8124i	−0.531093	−	0.919879i
$195$	−0.828400			−0.0593230
$196$	−0.176706	−	6.99777i	−0.0126218	−	0.499841i
$197$	3.35309			0.238898			0.119449	−	0.992840i	$-0.461887\pi$
$197$	3.35309			0.238898			0.119449	+	0.992840i	$0.461887\pi$
$198$	5.38733	+	9.33114i	0.382861	+	0.663135i
$199$	−8.78611	+	15.2180i	−0.622831	+	1.07878i	0.366125	+	0.930566i	$0.380684\pi$
$199$	−8.78611	+	15.2180i	−0.622831	+	1.07878i	−0.988956	+	0.148209i	$0.952649\pi$
$200$	−2.35607	+	4.08084i	−0.166599	+	0.288559i
$201$	−0.932214	−	1.61464i	−0.0657533	−	0.113888i
$202$	−6.67512			−0.469660
$203$	0.729891	+	2.59263i	0.0512283	+	0.181967i
$204$	−1.57440			−0.110230
$205$	0.712801	+	1.23461i	0.0497842	+	0.0862287i
$206$	1.54928	−	2.68343i	0.107943	−	0.186963i
$207$	1.29578	−	2.24435i	0.0900628	−	0.155993i
$208$	1.20797	+	2.09226i	0.0837575	+	0.145072i
$209$	28.4868			1.97047
$210$	−0.633340	+	0.649535i	−0.0437046	+	0.0448222i
$211$	−17.4159			−1.19896			−0.599481	−	0.800389i	$-0.704626\pi$
$211$	−17.4159			−1.19896			−0.599481	+	0.800389i	$0.704626\pi$
$212$	6.44763	+	11.1676i	0.442825	+	0.766995i
$213$	0.706454	−	1.22361i	0.0484054	−	0.0838407i
$214$	−1.66661	+	2.88666i	−0.113927	+	0.197328i
$215$	−0.941288	−	1.63036i	−0.0641953	−	0.111190i
$216$	−3.57354			−0.243149
$217$	−2.87323	−	0.731135i	−0.195047	−	0.0496327i
$218$	14.8689			1.00705
$219$	1.65993	+	2.87509i	0.112168	+	0.194280i
$220$	−1.11533	+	1.93180i	−0.0751953	+	0.130242i
$221$	2.97580	−	5.15424i	0.200174	−	0.346712i
$222$	−3.59481	−	6.22639i	−0.241268	−	0.417888i
$223$	−20.0308			−1.34136			−0.670682	−	0.741745i	$-0.733998\pi$
$223$	−20.0308			−1.34136			−0.670682	+	0.741745i	$0.733998\pi$
$224$	2.56404	+	0.652457i	0.171317	+	0.0435941i
$225$	12.2118			0.814119
$226$	5.07679	+	8.79326i	0.337703	+	0.584919i
$227$	−0.874085	+	1.51396i	−0.0580151	+	0.100485i	−0.893574	−	0.448915i	$-0.851810\pi$
$227$	−0.874085	+	1.51396i	−0.0580151	+	0.100485i	0.835559	+	0.549400i	$0.185144\pi$
$228$	−2.18946	+	3.79225i	−0.145000	+	0.251148i
$229$	1.65277	+	2.86269i	0.109218	+	0.189172i	0.915454	−	0.402423i	$-0.131832\pi$
$229$	1.65277	+	2.86269i	0.109218	+	0.189172i	−0.806235	+	0.591595i	$0.798499\pi$
$230$	0.536523			0.0353773
$231$	4.90785	−	5.03335i	0.322913	−	0.331170i
$232$	−1.01801			−0.0668359
$233$	−5.26452	−	9.11841i	−0.344890	−	0.597367i	0.640444	−	0.768005i	$-0.278750\pi$
$233$	−5.26452	−	9.11841i	−0.344890	−	0.597367i	−0.985334	+	0.170638i	$0.945417\pi$
$234$	3.13052	−	5.42222i	0.204648	−	0.354461i
$235$	2.61049	−	4.52151i	0.170290	−	0.294951i
$236$	−1.45772	−	2.52485i	−0.0948895	−	0.164353i
$237$	6.80483			0.442021
$238$	−1.76625	−	6.27386i	−0.114489	−	0.406674i
$239$	12.6379			0.817479			0.408739	−	0.912651i	$-0.365969\pi$
$239$	12.6379			0.817479			0.408739	+	0.912651i	$0.365969\pi$
$240$	−0.171445	−	0.296951i	−0.0110667	−	0.0191681i
$241$	9.22539	−	15.9788i	0.594260	−	1.02929i	−0.399391	−	0.916781i	$-0.630778\pi$
$241$	9.22539	−	15.9788i	0.594260	−	1.02929i	0.993651	−	0.112507i	$-0.0358882\pi$
$242$	3.14284	−	5.44356i	0.202030	−	0.349925i
$243$	7.11490	+	12.3234i	0.456421	+	0.790544i
$244$	14.4785			0.926889
$245$	−3.29887	−	1.79513i	−0.210757	−	0.114687i
$246$	1.69815			0.108270
$247$	−8.27668	−	14.3356i	−0.526632	−	0.912154i
$248$	0.560293	−	0.970457i	0.0355787	−	0.0616241i
$249$	3.32530	−	5.75960i	0.210733	−	0.365000i
$250$	2.60540	+	4.51268i	0.164780	+	0.285407i
$251$	11.9353			0.753350			0.376675	−	0.926346i	$-0.377067\pi$
$251$	11.9353			0.753350			0.376675	+	0.926346i	$0.377067\pi$
$252$	−1.85808	−	6.60005i	−0.117048	−	0.415764i
$253$	−4.15761			−0.261386
$254$	1.92630	+	3.33644i	0.120867	+	0.209347i
$255$	−0.422351	+	0.731533i	−0.0264486	+	0.0458104i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.83079	−	11.8313i	−0.426093	−	0.738014i	0.570429	−	0.821347i	$-0.306777\pi$
$257$	−6.83079	−	11.8313i	−0.426093	−	0.738014i	−0.996522	+	0.0833326i	$0.973444\pi$
$258$	−2.24249			−0.139611
$259$	20.7788	−	21.3102i	1.29113	−	1.32415i
$260$	1.29621			0.0803873
$261$	1.31912	+	2.28478i	0.0816515	+	0.141424i
$262$	−9.64225	+	16.7009i	−0.595700	+	1.03178i
$263$	5.23499	−	9.06727i	0.322803	−	0.559112i	−0.658262	−	0.752789i	$-0.728708\pi$
$263$	5.23499	−	9.06727i	0.322803	−	0.559112i	0.981065	+	0.193677i	$0.0620415\pi$
$264$	1.32856	+	2.30112i	0.0817669	+	0.141624i
$265$	6.91860			0.425006
$266$	−17.5681	−	4.47046i	−1.07717	−	0.274102i
$267$	−2.36763			−0.144896
$268$	1.45864	+	2.52645i	0.0891009	+	0.154327i
$269$	−5.45072	+	9.44093i	−0.332336	+	0.575624i	−0.982970	−	0.183769i	$-0.941170\pi$
$269$	−5.45072	+	9.44093i	−0.332336	+	0.575624i	0.650633	+	0.759392i	$0.274504\pi$
$270$	−0.958644	+	1.66042i	−0.0583412	+	0.101050i
$271$	0.667108	+	1.15547i	0.0405239	+	0.0701895i	0.885576	−	0.464495i	$-0.153764\pi$
$271$	0.667108	+	1.15547i	0.0405239	+	0.0701895i	−0.845052	+	0.534684i	$0.820431\pi$
$272$	2.46348			0.149370
$273$	−3.95892	−	1.00740i	−0.239605	−	0.0609709i
$274$	−5.00185			−0.302173
$275$	−9.79562	−	16.9665i	−0.590698	−	1.02312i
$276$	0.319548	−	0.553474i	0.0192345	−	0.0333152i
$277$	−13.6945	+	23.7195i	−0.822820	+	1.42517i	0.0807532	+	0.996734i	$0.474267\pi$
$277$	−13.6945	+	23.7195i	−0.822820	+	1.42517i	−0.903574	+	0.428433i	$0.859066\pi$
$278$	−5.08255	−	8.80323i	−0.304831	−	0.527983i
$279$	−2.90406			−0.173862
$280$	0.990993	−	1.01633i	0.0592232	−	0.0607375i
$281$	−7.99783			−0.477110			−0.238555	−	0.971129i	$-0.576674\pi$
$281$	−7.99783			−0.477110			−0.238555	+	0.971129i	$0.576674\pi$
$282$	−3.10957	−	5.38593i	−0.185172	−	0.320728i
$283$	9.92494	−	17.1905i	0.589977	−	1.02187i	−0.404258	−	0.914645i	$-0.632470\pi$
$283$	9.92494	−	17.1905i	0.589977	−	1.02187i	0.994235	−	0.107225i	$-0.0341964\pi$
$284$	−1.10540	+	1.91460i	−0.0655931	+	0.113611i
$285$	1.17470	+	2.03463i	0.0695830	+	0.120521i
$286$	−10.0445			−0.593944
$287$	1.90508	+	6.76700i	0.112453	+	0.399443i
$288$	2.59156			0.152709
$289$	5.46564	+	9.46677i	0.321508	+	0.556869i
$290$	−0.273094	+	0.473013i	−0.0160366	+	0.0277763i
$291$	−4.72756	+	8.18838i	−0.277135	+	0.480011i
$292$	−2.59731	−	4.49868i	−0.151996	−	0.263265i
$293$	−24.2303			−1.41555			−0.707775	−	0.706437i	$-0.750301\pi$
$293$	−24.2303			−1.41555			−0.707775	+	0.706437i	$0.750301\pi$
$294$	−3.81661	+	2.33393i	−0.222589	+	0.136117i
$295$	−1.56420			−0.0910714
$296$	5.62483	+	9.74249i	0.326937	+	0.566271i
$297$	7.42869	−	12.8669i	0.431056	−	0.746611i
$298$	−0.451964	+	0.782825i	−0.0261816	+	0.0453478i
$299$	1.20797	+	2.09226i	0.0698586	+	0.120999i
$300$	3.01151			0.173870
$301$	−2.51575	−	8.93616i	−0.145006	−	0.515072i
$302$	−17.6665			−1.01659
$303$	2.13302	+	3.69450i	0.122539	+	0.212244i
$304$	3.42587	−	5.93378i	0.196487	−	0.340325i
$305$	3.88402	−	6.72731i	0.222398	−	0.385205i
$306$	−3.19212	−	5.52891i	−0.182481	−	0.316067i
$307$	11.8204			0.674624			0.337312	−	0.941393i	$-0.390482\pi$
$307$	11.8204			0.674624			0.337312	+	0.941393i	$0.390482\pi$
$308$	−7.67937	+	7.87573i	−0.437572	+	0.448761i
$309$	−1.98027			−0.112654
$310$	−0.300610	−	0.520673i	−0.0170735	−	0.0295722i
$311$	1.07587	−	1.86346i	0.0610069	−	0.105667i	−0.833909	−	0.551902i	$-0.813902\pi$
$311$	1.07587	−	1.86346i	0.0610069	−	0.105667i	0.894916	+	0.446235i	$0.147235\pi$
$312$	0.772008	−	1.33716i	0.0437063	−	0.0757016i
$313$	−12.3682	−	21.4224i	−0.699094	−	1.21087i	−0.968781	−	0.247918i	$-0.920254\pi$
$313$	−12.3682	−	21.4224i	−0.699094	−	1.21087i	0.269687	−	0.962948i	$-0.413080\pi$
$314$	−10.9323			−0.616944
$315$	−3.56512	−	0.907196i	−0.200872	−	0.0511147i
$316$	−10.6476			−0.598973
$317$	9.12201	+	15.7998i	0.512343	+	0.887404i	0.999898	+	0.0143115i	$0.00455565\pi$
$317$	9.12201	+	15.7998i	0.512343	+	0.887404i	−0.487555	+	0.873092i	$0.662111\pi$
$318$	4.12065	−	7.13718i	0.231075	−	0.400233i
$319$	2.11625	−	3.66545i	0.118487	−	0.205226i
$320$	0.268262	+	0.464643i	0.0149963	+	0.0259743i
$321$	2.13025			0.118899
$322$	2.56404	+	0.652457i	0.142888	+	0.0363600i
$323$	−16.8791			−0.939178
$324$	−2.74542	−	4.75520i	−0.152523	−	0.264178i
$325$	−5.69212	+	9.85904i	−0.315742	+	0.546881i
$326$	−6.98991	+	12.1069i	−0.387135	+	0.670538i
$327$	−4.75133	−	8.22954i	−0.262749	−	0.455095i
$328$	−2.65711			−0.146714
$329$	17.9741	−	18.4337i	0.990942	−	1.01628i
$330$	1.42560			0.0784768
$331$	0.299524	+	0.518791i	0.0164633	+	0.0285154i	0.874140	−	0.485675i	$-0.161426\pi$
$331$	0.299524	+	0.518791i	0.0164633	+	0.0285154i	−0.857676	+	0.514190i	$0.828093\pi$
$332$	−5.20314	+	9.01210i	−0.285559	+	0.494603i
$333$	14.5771	−	25.2482i	0.798818	−	1.38359i
$334$	10.6646	+	18.4716i	0.583541	+	1.01072i
$335$	1.56519			0.0855156
$336$	−0.458216	−	1.62762i	−0.0249977	−	0.0887939i
$337$	−7.80452			−0.425139			−0.212570	−	0.977146i	$-0.568183\pi$
$337$	−7.80452			−0.425139			−0.212570	+	0.977146i	$0.568183\pi$
$338$	−3.58163	−	6.20356i	−0.194815	−	0.337429i
$339$	3.24456	−	5.61974i	0.176220	−	0.305222i
$340$	0.660856	−	1.14464i	0.0358400	−	0.0620766i
$341$	2.32948	+	4.03478i	0.126148	+	0.218495i
$342$	−17.7567			−0.960170
$343$	−13.5822	−	12.5906i	−0.733371	−	0.679828i
$344$	3.50884			0.189184
$345$	−0.171445	−	0.296951i	−0.00923029	−	0.0159873i
$346$	11.1290	−	19.2760i	0.598299	−	1.03628i
$347$	14.0908	−	24.4060i	0.756434	−	1.31018i	−0.188224	−	0.982126i	$-0.560273\pi$
$347$	14.0908	−	24.4060i	0.756434	−	1.31018i	0.944658	−	0.328056i	$-0.106393\pi$
$348$	0.325304	+	0.563444i	0.0174381	+	0.0302038i
$349$	2.33887			0.125197			0.0625984	−	0.998039i	$-0.480061\pi$
$349$	2.33887			0.125197			0.0625984	+	0.998039i	$0.480061\pi$
$350$	3.37849	+	12.0007i	0.180588	+	0.641462i
$351$	−8.63345			−0.460820
$352$	−2.07880	−	3.60059i	−0.110801	−	0.191912i
$353$	−8.26501	+	14.3154i	−0.439902	+	0.761933i	−0.997681	−	0.0680564i	$-0.978320\pi$
$353$	−8.26501	+	14.3154i	−0.439902	+	0.761933i	0.557779	+	0.829989i	$0.311654\pi$
$354$	−0.931624	+	1.61362i	−0.0495152	+	0.0857629i
$355$	0.593070	+	1.02723i	0.0314769	+	0.0545196i
$356$	3.70465			0.196346
$357$	−2.90802	+	2.98238i	−0.153909	+	0.157844i
$358$	−9.53250			−0.503808
$359$	−10.4577	−	18.1133i	−0.551937	−	0.955984i	−0.998135	−	0.0610490i	$-0.980555\pi$
$359$	−10.4577	−	18.1133i	−0.551937	−	0.955984i	0.446197	−	0.894935i	$-0.352778\pi$
$360$	0.695215	−	1.20415i	0.0366411	−	0.0634642i
$361$	−13.9731	+	24.2022i	−0.735428	+	1.27380i
$362$	10.7686	+	18.6518i	0.565985	+	0.980314i
$363$	−4.01716			−0.210846
$364$	6.19456	+	1.57630i	0.324683	+	0.0826203i
$365$	−2.78704			−0.145880
$366$	−4.62657	−	8.01345i	−0.241834	−	0.418870i
$367$	6.36856	−	11.0307i	0.332436	−	0.575796i	−0.650553	−	0.759461i	$-0.725463\pi$
$367$	6.36856	−	11.0307i	0.332436	−	0.575796i	0.982989	+	0.183665i	$0.0587961\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$	3.44302	+	5.96349i	0.179237	+	0.310447i
$370$	6.03570			0.313781
$371$	33.0639	+	8.41360i	1.71659	+	0.436813i
$372$	−0.716163			−0.0371313
$373$	−9.14892	−	15.8464i	−0.473713	−	0.820495i	0.525834	−	0.850587i	$-0.323753\pi$
$373$	−9.14892	−	15.8464i	−0.473713	−	0.820495i	−0.999547	+	0.0300923i	$0.990420\pi$
$374$	−5.12108	+	8.86997i	−0.264805	+	0.458655i
$375$	1.66510	−	2.88403i	0.0859853	−	0.148931i
$376$	4.86557	+	8.42742i	0.250923	+	0.434611i
$377$	−2.45946			−0.126668
$378$	−6.60056	+	6.76934i	−0.339496	+	0.348177i
$379$	16.1232			0.828193			0.414097	−	0.910233i	$-0.364098\pi$
$379$	16.1232			0.828193			0.414097	+	0.910233i	$0.364098\pi$
$380$	−1.83806	−	3.18361i	−0.0942904	−	0.163316i
$381$	1.23109	−	2.13231i	0.0630706	−	0.109241i
$382$	11.7453	−	20.3434i	0.600939	−	1.04086i
$383$	8.51927	+	14.7558i	0.435314	+	0.753987i	0.997321	−	0.0731459i	$-0.0233039\pi$
$383$	8.51927	+	14.7558i	0.435314	+	0.753987i	−0.562007	+	0.827133i	$0.689971\pi$
$384$	0.639096			0.0326137
$385$	1.59932	+	5.68092i	0.0815090	+	0.289526i
$386$	−5.52686			−0.281310
$387$	−4.54668	−	7.87509i	−0.231121	−	0.400313i
$388$	7.39726	−	12.8124i	0.375539	−	0.650453i
$389$	−6.49474	+	11.2492i	−0.329296	+	0.570358i	−0.982372	−	0.186934i	$-0.940145\pi$
$389$	−6.49474	+	11.2492i	−0.329296	+	0.570358i	0.653076	+	0.757292i	$0.273478\pi$
$390$	−0.414200	−	0.717416i	−0.0209738	−	0.0363278i
$391$	2.46348			0.124583
$392$	5.97189	−	3.65192i	0.301626	−	0.184450i
$393$	12.3247			0.621697
$394$	1.67654	+	2.90386i	0.0844630	+	0.146294i
$395$	−2.85634	+	4.94732i	−0.143718	+	0.248927i
$396$	−5.38733	+	9.33114i	−0.270724	+	0.468907i
$397$	7.38532	+	12.7918i	0.370659	+	0.642000i	0.989667	−	0.143385i	$-0.0457986\pi$
$397$	7.38532	+	12.7918i	0.370659	+	0.642000i	−0.619008	+	0.785384i	$0.712465\pi$
$398$	−17.5722			−0.880816
$399$	3.13958	+	11.1520i	0.157175	+	0.558299i
$400$	−4.71214			−0.235607
$401$	−10.0791	−	17.4576i	−0.503328	−	0.871790i	−0.999993	−	0.00384717i	$-0.998775\pi$
$401$	−10.0791	−	17.4576i	−0.503328	−	0.871790i	0.496665	−	0.867943i	$-0.334558\pi$
$402$	0.932214	−	1.61464i	0.0464946	−	0.0805310i
$403$	1.35363	−	2.34456i	0.0674293	−	0.116791i
$404$	−3.33756	−	5.78083i	−0.166050	−	0.287607i
$405$	−2.94596			−0.146386
$406$	−1.88034	+	1.92842i	−0.0933196	+	0.0957058i
$407$	−46.7716			−2.31838
$408$	−0.787199	−	1.36347i	−0.0389722	−	0.0675018i
$409$	−11.8641	+	20.5492i	−0.586640	+	1.01609i	0.408029	+	0.912969i	$0.366216\pi$
$409$	−11.8641	+	20.5492i	−0.586640	+	1.01609i	−0.994669	+	0.103121i	$0.967117\pi$
$410$	−0.712801	+	1.23461i	−0.0352027	+	0.0609729i
$411$	1.59833	+	2.76839i	0.0788399	+	0.136555i
$412$	3.09855			0.152655
$413$	−7.47531	−	1.90220i	−0.367836	−	0.0936012i
$414$	2.59156			0.127368
$415$	2.79160	+	4.83520i	0.137034	+	0.237351i
$416$	−1.20797	+	2.09226i	−0.0592255	+	0.102582i
$417$	−3.24824	+	5.62611i	−0.159067	+	0.275512i
$418$	14.2434	+	24.6703i	0.696668	+	1.20666i
$419$	6.59255			0.322067			0.161034	−	0.986949i	$-0.448517\pi$
$419$	6.59255			0.322067			0.161034	+	0.986949i	$0.448517\pi$
$420$	−0.879184	−	0.223721i	−0.0428998	−	0.0109165i
$421$	10.6291			0.518031			0.259015	−	0.965873i	$-0.416602\pi$
$421$	10.6291			0.518031			0.259015	+	0.965873i	$0.416602\pi$
$422$	−8.70797	−	15.0826i	−0.423897	−	0.734212i
$423$	12.6094	−	21.8401i	0.613090	−	1.06190i
$424$	−6.44763	+	11.1676i	−0.313124	+	0.542347i
$425$	5.80413	+	10.0530i	0.281542	+	0.487644i
$426$	1.41291			0.0684556
$427$	26.7427	−	27.4265i	1.29417	−	1.32726i
$428$	−3.33323			−0.161118
$429$	3.20970	+	5.55937i	0.154966	+	0.268409i
$430$	0.941288	−	1.63036i	0.0453930	−	0.0786229i
$431$	−0.666184	+	1.15387i	−0.0320890	+	0.0555797i	−0.881624	−	0.471953i	$-0.843549\pi$
$431$	−0.666184	+	1.15387i	−0.0320890	+	0.0555797i	0.849535	+	0.527532i	$0.176883\pi$
$432$	−1.78677	−	3.09478i	−0.0859661	−	0.148898i
$433$	−6.24032			−0.299891			−0.149945	−	0.988694i	$-0.547910\pi$
$433$	−6.24032			−0.299891			−0.149945	+	0.988694i	$0.547910\pi$
$434$	−0.803433	−	2.85386i	−0.0385660	−	0.136990i
$435$	0.349067			0.0167365
$436$	7.43445	+	12.8768i	0.356045	+	0.616689i
$437$	3.42587	−	5.93378i	0.163881	−	0.283851i
$438$	−1.65993	+	2.87509i	−0.0793146	+	0.137377i
$439$	1.09540	+	1.89728i	0.0522805	+	0.0905524i	0.890981	−	0.454040i	$-0.150018\pi$
$439$	1.09540	+	1.89728i	0.0522805	+	0.0905524i	−0.838701	+	0.544592i	$0.816684\pi$
$440$	−2.23065			−0.106342
$441$	−15.9344	−	8.67097i	−0.758783	−	0.412903i
$442$	5.95160			0.283089
$443$	−0.990497	−	1.71559i	−0.0470600	−	0.0815102i	0.841536	−	0.540201i	$-0.181652\pi$
$443$	−0.990497	−	1.71559i	−0.0470600	−	0.0815102i	−0.888596	+	0.458691i	$0.848319\pi$
$444$	3.59481	−	6.22639i	0.170602	−	0.295491i
$445$	0.993816	−	1.72134i	0.0471114	−	0.0815993i
$446$	−10.0154	−	17.3472i	−0.474244	−	0.821414i
$447$	0.577697			0.0273241
$448$	0.716975	+	2.54675i	0.0338739	+	0.120323i
$449$	23.3519			1.10204			0.551022	−	0.834491i	$-0.314238\pi$
$449$	23.3519			1.10204			0.551022	+	0.834491i	$0.314238\pi$
$450$	6.10589	+	10.5757i	0.287834	+	0.498544i
$451$	5.52361	−	9.56717i	0.260097	−	0.450500i
$452$	−5.07679	+	8.79326i	−0.238792	+	0.413600i
$453$	5.64528	+	9.77791i	0.265238	+	0.459406i
$454$	−1.74817			−0.0820457
$455$	2.39418	−	2.45540i	0.112241	−	0.115111i
$456$	−4.37892			−0.205062
$457$	10.4238	+	18.0545i	0.487604	+	0.844555i	0.999898	−	0.0142546i	$-0.00453754\pi$
$457$	10.4238	+	18.0545i	0.487604	+	0.844555i	−0.512294	+	0.858810i	$0.671204\pi$
$458$	−1.65277	+	2.86269i	−0.0772290	+	0.133765i
$459$	−4.40167	+	7.62391i	−0.205452	+	0.355854i
$460$	0.268262	+	0.464643i	0.0125078	+	0.0216641i
$461$	2.13177			0.0992867			0.0496433	−	0.998767i	$-0.484192\pi$
$461$	2.13177			0.0992867			0.0496433	+	0.998767i	$0.484192\pi$
$462$	6.81294	+	1.73365i	0.316966	+	0.0806567i
$463$	−30.2113			−1.40404			−0.702020	−	0.712158i	$-0.747718\pi$
$463$	−30.2113			−1.40404			−0.702020	+	0.712158i	$0.747718\pi$
$464$	−0.509007	−	0.881626i	−0.0236301	−	0.0409285i
$465$	−0.192119	+	0.332760i	−0.00890930	+	0.0154314i
$466$	5.26452	−	9.11841i	0.243874	−	0.422402i
$467$	19.0339	+	32.9676i	0.880782	+	1.52556i	0.850473	+	0.526018i	$0.176316\pi$
$467$	19.0339	+	32.9676i	0.880782	+	1.52556i	0.0303085	+	0.999541i	$0.490351\pi$
$468$	6.26103			0.289416
$469$	7.48004	+	1.90341i	0.345396	+	0.0878911i
$470$	5.22099			0.240826
$471$	3.49339	+	6.05072i	0.160967	+	0.278803i
$472$	1.45772	−	2.52485i	0.0670970	−	0.116215i
$473$	−7.29420	+	12.6339i	−0.335388	+	0.580908i
$474$	3.40241	+	5.89315i	0.156278	+	0.270682i
$475$	32.2864			1.48140
$476$	4.55020	−	4.66655i	0.208558	−	0.213891i
$477$	33.4188			1.53014
$478$	6.31896	+	10.9448i	0.289022	+	0.500601i
$479$	−11.5364	+	19.9816i	−0.527110	+	0.912981i	0.472391	+	0.881389i	$0.343391\pi$
$479$	−11.5364	+	19.9816i	−0.527110	+	0.912981i	−0.999501	+	0.0315919i	$0.989942\pi$
$480$	0.171445	−	0.296951i	0.00782536	−	0.0135539i
$481$	13.5892	+	23.5372i	0.619616	+	1.07321i
$482$	18.4508			0.840410
$483$	−0.458216	−	1.62762i	−0.0208496	−	0.0740593i
$484$	6.28569			0.285713
$485$	−3.96880	−	6.87417i	−0.180214	−	0.312140i
$486$	−7.11490	+	12.3234i	−0.322738	+	0.558999i
$487$	−5.26842	+	9.12518i	−0.238735	+	0.413501i	−0.960352	−	0.278792i	$-0.910066\pi$
$487$	−5.26842	+	9.12518i	−0.238735	+	0.413501i	0.721617	+	0.692293i	$0.243399\pi$
$488$	7.23923	+	12.5387i	0.327705	+	0.567601i
$489$	8.93445			0.404030
$490$	−0.0948067	−	3.75447i	−0.00428293	−	0.169609i
$491$	6.74134			0.304233			0.152116	−	0.988363i	$-0.451391\pi$
$491$	6.74134			0.304233			0.152116	+	0.988363i	$0.451391\pi$
$492$	0.849074	+	1.47064i	0.0382792	+	0.0663016i
$493$	−1.25393	+	2.17186i	−0.0564740	+	0.0978159i
$494$	8.27668	−	14.3356i	0.372385	−	0.644990i
$495$	2.89043	+	5.00637i	0.129915	+	0.225020i
$496$	1.12059			0.0503158
$497$	1.58508	+	5.63034i	0.0711006	+	0.252555i
$498$	6.65061			0.298021
$499$	−4.65142	−	8.05650i	−0.208226	−	0.360658i	0.742930	−	0.669370i	$-0.233436\pi$
$499$	−4.65142	−	8.05650i	−0.208226	−	0.360658i	−0.951156	+	0.308711i	$0.900102\pi$
$500$	−2.60540	+	4.51268i	−0.116517	+	0.201813i
$501$	6.81571	−	11.8052i	0.304503	−	0.527415i
$502$	5.96765	+	10.3363i	0.266349	+	0.461331i
$503$	−43.0965			−1.92158			−0.960789	−	0.277279i	$-0.910567\pi$
$503$	−43.0965			−1.92158			−0.960789	+	0.277279i	$0.910567\pi$
$504$	4.78677	−	4.90917i	0.213220	−	0.218672i
$505$	−3.58136			−0.159368
$506$	−2.07880	−	3.60059i	−0.0924141	−	0.160066i
$507$	−2.28900	+	3.96467i	−0.101658	+	0.176077i
$508$	−1.92630	+	3.33644i	−0.0854655	+	0.148031i
$509$	4.75833	+	8.24167i	0.210909	+	0.365306i	0.951999	−	0.306100i	$-0.0990242\pi$
$509$	4.75833	+	8.24167i	0.210909	+	0.365306i	−0.741090	+	0.671406i	$0.765691\pi$
$510$	−0.844702			−0.0374040
$511$	−13.3192	−	3.38927i	−0.589208	−	0.149933i
$512$	−1.00000			−0.0441942
$513$	12.2425	+	21.2046i	0.540519	+	0.936206i
$514$	6.83079	−	11.8313i	0.301293	−	0.521855i
$515$	0.831223	−	1.43972i	0.0366281	−	0.0634417i
$516$	−1.12124	−	1.94205i	−0.0493600	−	0.0854941i
$517$	−40.4583			−1.77935
$518$	28.8446	+	7.33992i	1.26736	+	0.322498i
$519$	−14.2250			−0.624409
$520$	0.648103	+	1.12255i	0.0284212	+	0.0492270i
$521$	−15.9821	+	27.6819i	−0.700190	+	1.21277i	0.268209	+	0.963361i	$0.413568\pi$
$521$	−15.9821	+	27.6819i	−0.700190	+	1.21277i	−0.968399	+	0.249404i	$0.919765\pi$
$522$	−1.31912	+	2.28478i	−0.0577363	+	0.100002i
$523$	−2.09672	−	3.63163i	−0.0916832	−	0.158800i	0.816536	−	0.577294i	$-0.195891\pi$
$523$	−2.09672	−	3.63163i	−0.0916832	−	0.158800i	−0.908220	+	0.418494i	$0.862558\pi$
$524$	−19.2845			−0.842447
$525$	5.56246	−	5.70469i	0.242766	−	0.248973i
$526$	10.4700			0.456513
$527$	−1.38027	−	2.39070i	−0.0601255	−	0.104140i
$528$	−1.32856	+	2.30112i	−0.0578179	+	0.100144i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	3.45930	+	5.99169i	0.150262	+	0.260262i
$531$	−7.55553			−0.327882
$532$	−4.91252	−	17.4497i	−0.212985	−	0.756539i
$533$	−6.41941			−0.278055
$534$	−1.18381	−	2.05043i	−0.0512286	−	0.0887306i
$535$	−0.894176	+	1.54876i	−0.0386586	+	0.0669587i
$536$	−1.45864	+	2.52645i	−0.0630038	+	0.109126i
$537$	3.04609	+	5.27599i	0.131449	+	0.227676i
$538$	−10.9014			−0.469995
$539$	0.734672	+	29.0940i	0.0316446	+	1.25317i
$540$	−1.91729			−0.0825070
$541$	8.53041	+	14.7751i	0.366751	+	0.635231i	0.989055	−	0.147544i	$-0.0471368\pi$
$541$	8.53041	+	14.7751i	0.366751	+	0.635231i	−0.622305	+	0.782775i	$0.713803\pi$
$542$	−0.667108	+	1.15547i	−0.0286548	+	0.0496315i
$543$	6.88217	−	11.9203i	0.295342	−	0.511548i
$544$	1.23174	+	2.13343i	0.0528103	+	0.0914702i
$545$	7.97751			0.341719
$546$	−1.10702	−	3.93223i	−0.0473761	−	0.168284i
$547$	−31.2833			−1.33758			−0.668789	−	0.743452i	$-0.733187\pi$
$547$	−31.2833			−1.33758			−0.668789	+	0.743452i	$0.733187\pi$
$548$	−2.50092	−	4.33173i	−0.106834	−	0.185042i
$549$	18.7609	−	32.4948i	0.800695	−	1.38684i
$550$	9.79562	−	16.9665i	0.417686	−	0.723454i
$551$	3.48758	+	6.04067i	0.148576	+	0.257341i
$552$	0.639096			0.0272017
$553$	−19.6668	+	20.1697i	−0.836316	+	0.857701i
$554$	−27.3889			−1.16364
$555$	−1.92870	−	3.34060i	−0.0818686	−	0.141801i
$556$	5.08255	−	8.80323i	0.215548	−	0.373340i
$557$	−9.17351	+	15.8890i	−0.388694	+	0.673238i	−0.992274	−	0.124064i	$-0.960407\pi$
$557$	−9.17351	+	15.8890i	−0.388694	+	0.673238i	0.603580	+	0.797303i	$0.293740\pi$
$558$	−1.45203	−	2.51499i	−0.0614694	−	0.106468i
$559$	8.47715			0.358545
$560$	1.37567	+	0.350059i	0.0581325	+	0.0147927i
$561$	6.54573			0.276361
$562$	−3.99891	−	6.92632i	−0.168684	−	0.292169i
$563$	18.4158	−	31.8971i	0.776132	−	1.34430i	−0.158023	−	0.987435i	$-0.550512\pi$
$563$	18.4158	−	31.8971i	0.776132	−	1.34430i	0.934156	−	0.356865i	$-0.116154\pi$
$564$	3.10957	−	5.38593i	0.130937	−	0.226789i
$565$	2.72382	+	4.71779i	0.114592	+	0.198479i
$566$	19.8499			0.834353
$567$	−14.0787	−	3.58253i	−0.591250	−	0.150452i
$568$	−2.21079			−0.0927627
$569$	19.7436	+	34.1969i	0.827694	+	1.43361i	0.899843	+	0.436214i	$0.143681\pi$
$569$	19.7436	+	34.1969i	0.827694	+	1.43361i	−0.0721492	+	0.997394i	$0.522986\pi$
$570$	−1.17470	+	2.03463i	−0.0492026	+	0.0852214i
$571$	−15.0554	+	26.0767i	−0.630047	+	1.09127i	0.357494	+	0.933915i	$0.383631\pi$
$571$	−15.0554	+	26.0767i	−0.630047	+	1.09127i	−0.987541	+	0.157359i	$0.949702\pi$
$572$	−5.02226	−	8.69880i	−0.209991	−	0.363715i
$573$	−15.0127			−0.627164
$574$	−4.90785	+	5.03335i	−0.204850	+	0.210088i
$575$	−4.71214			−0.196510
$576$	1.29578	+	2.24435i	0.0539908	+	0.0935147i
$577$	16.4485	−	28.4896i	0.684758	−	1.18604i	−0.288755	−	0.957403i	$-0.593241\pi$
$577$	16.4485	−	28.4896i	0.684758	−	1.18604i	0.973513	−	0.228633i	$-0.0734255\pi$
$578$	−5.46564	+	9.46677i	−0.227341	+	0.393766i
$579$	1.76610	+	3.05897i	0.0733965	+	0.127126i
$580$	−0.546188			−0.0226792
$581$	7.46104	+	26.5022i	0.309536	+	1.09950i
$582$	−9.45513			−0.391928
$583$	−26.8067	−	46.4306i	−1.11022	−	1.92296i
$584$	2.59731	−	4.49868i	0.107478	−	0.186157i
$585$	1.67960	−	2.90914i	0.0694427	−	0.120278i
$586$	−12.1152	−	20.9841i	−0.500473	−	0.866844i
$587$	−29.5909			−1.22135			−0.610674	−	0.791882i	$-0.709101\pi$
$587$	−29.5909			−1.22135			−0.610674	+	0.791882i	$0.709101\pi$
$588$	−3.92955	−	2.13832i	−0.162052	−	0.0881829i
$589$	−7.67796			−0.316365
$590$	−0.782101	−	1.35464i	−0.0321986	−	0.0557696i
$591$	1.07147	−	1.85584i	0.0440745	−	0.0763393i
$592$	−5.62483	+	9.74249i	−0.231179	+	0.400414i
$593$	−19.8663	−	34.4095i	−0.815813	−	1.41303i	−0.908743	−	0.417356i	$-0.862957\pi$
$593$	−19.8663	−	34.4095i	−0.815813	−	1.41303i	0.0929303	−	0.995673i	$-0.470377\pi$
$594$	14.8574			0.609606
$595$	−0.947635	−	3.36607i	−0.0388493	−	0.137996i
$596$	−0.903928			−0.0370263
$597$	5.61517	+	9.72576i	0.229814	+	0.398049i
$598$	−1.20797	+	2.09226i	−0.0493975	+	0.0855590i
$599$	7.54510	−	13.0685i	0.308285	−	0.533964i	−0.669703	−	0.742629i	$-0.733578\pi$
$599$	7.54510	−	13.0685i	0.308285	−	0.533964i	0.977987	+	0.208665i	$0.0669118\pi$
$600$	1.50576	+	2.60805i	0.0614722	+	0.106473i
$601$	11.3933			0.464741			0.232371	−	0.972627i	$-0.425352\pi$
$601$	11.3933			0.464741			0.232371	+	0.972627i	$0.425352\pi$
$602$	6.48106	−	6.64679i	0.264148	−	0.270903i
$603$	7.56032			0.307880
$604$	−8.83323	−	15.2996i	−0.359419	−	0.622532i
$605$	1.68621	−	2.92060i	0.0685541	−	0.118739i
$606$	−2.13302	+	3.69450i	−0.0866481	+	0.150079i
$607$	13.9017	+	24.0784i	0.564251	+	0.977312i	0.997119	+	0.0758545i	$0.0241684\pi$
$607$	13.9017	+	24.0784i	0.564251	+	0.977312i	−0.432868	+	0.901458i	$0.642498\pi$
$608$	6.85173			0.277875
$609$	1.66819	+	0.424494i	0.0675983	+	0.0172014i
$610$	7.76803			0.314518
$611$	11.7549	+	20.3601i	0.475553	+	0.823682i
$612$	3.19212	−	5.52891i	0.129034	−	0.223493i
$613$	−2.58456	+	4.47659i	−0.104389	+	0.180808i	−0.913489	−	0.406864i	$-0.866622\pi$
$613$	−2.58456	+	4.47659i	−0.104389	+	0.180808i	0.809099	+	0.587672i	$0.199955\pi$
$614$	5.91018	+	10.2367i	0.238515	+	0.413121i
$615$	0.911096			0.0367390
$616$	−10.6603	−	2.71266i	−0.429514	−	0.109296i
$617$	−19.5515			−0.787114			−0.393557	−	0.919300i	$-0.628756\pi$
$617$	−19.5515			−0.787114			−0.393557	+	0.919300i	$0.628756\pi$
$618$	−0.990137	−	1.71497i	−0.0398291	−	0.0689861i
$619$	22.6635	−	39.2544i	0.910924	−	1.57777i	0.0981614	−	0.995171i	$-0.468704\pi$
$619$	22.6635	−	39.2544i	0.910924	−	1.57777i	0.812762	−	0.582596i	$-0.197963\pi$
$620$	0.300610	−	0.520673i	0.0120728	−	0.0209107i
$621$	−1.78677	−	3.09478i	−0.0717007	−	0.124189i
$622$	2.15174			0.0862768
$623$	6.84273	−	7.01770i	0.274148	−	0.281158i
$624$	1.54402			0.0618101
$625$	−10.3825	−	17.9830i	−0.415300	−	0.719321i
$626$	12.3682	−	21.4224i	0.494334	−	0.856212i
$627$	9.10291	−	15.7667i	0.363535	−	0.629661i
$628$	−5.46614	−	9.46763i	−0.218123	−	0.377799i
$629$	27.7133			1.10500
$630$	−0.996904	−	3.54108i	−0.0397176	−	0.141080i
$631$	15.9892			0.636518			0.318259	−	0.948004i	$-0.396902\pi$
$631$	15.9892			0.636518			0.318259	+	0.948004i	$0.396902\pi$
$632$	−5.32379	−	9.22107i	−0.211769	−	0.366795i
$633$	−5.56523	+	9.63926i	−0.221198	+	0.383126i
$634$	−9.12201	+	15.7998i	−0.362281	+	0.627489i
$635$	1.03350	+	1.79008i	0.0410133	+	0.0710371i
$636$	8.24131			0.326789
$637$	14.4277	−	8.82280i	0.571647	−	0.349572i
$638$	4.23250			0.167566
$639$	2.86469	+	4.96180i	0.113326	+	0.196286i
$640$	−0.268262	+	0.464643i	−0.0106040	+	0.0183666i
$641$	5.24623	−	9.08673i	0.207214	−	0.358904i	−0.743622	−	0.668600i	$-0.766894\pi$
$641$	5.24623	−	9.08673i	0.207214	−	0.358904i	0.950836	+	0.309696i	$0.100227\pi$
$642$	1.06513	+	1.84485i	0.0420372	+	0.0728105i
$643$	−34.2502			−1.35070			−0.675348	−	0.737499i	$-0.736006\pi$
$643$	−34.2502			−1.35070			−0.675348	+	0.737499i	$0.736006\pi$
$644$	0.716975	+	2.54675i	0.0282528	+	0.100356i
$645$	−1.20315			−0.0473739
$646$	−8.43954	−	14.6177i	−0.332049	−	0.575126i
$647$	−8.78167	+	15.2103i	−0.345243	+	0.597979i	−0.985398	−	0.170267i	$-0.945537\pi$
$647$	−8.78167	+	15.2103i	−0.345243	+	0.597979i	0.640155	+	0.768246i	$0.278870\pi$
$648$	2.74542	−	4.75520i	0.107850	−	0.186802i
$649$	6.06063	+	10.4973i	0.237900	+	0.412056i
$650$	−11.3842			−0.446527
$651$	−1.32280	+	1.35662i	−0.0518446	+	0.0531703i
$652$	−13.9798			−0.547492
$653$	−6.14442	−	10.6425i	−0.240450	−	0.416471i	0.720393	−	0.693566i	$-0.243962\pi$
$653$	−6.14442	−	10.6425i	−0.240450	−	0.416471i	−0.960843	+	0.277095i	$0.910628\pi$
$654$	4.75133	−	8.22954i	0.185792	−	0.321800i
$655$	−5.17329	+	8.96041i	−0.202137	+	0.350112i
$656$	−1.32856	−	2.30112i	−0.0518714	−	0.0898438i
$657$	−13.4622			−0.525209
$658$	24.9510	+	6.34916i	0.972693	+	0.247516i
$659$	−12.0108			−0.467876			−0.233938	−	0.972252i	$-0.575161\pi$
$659$	−12.0108			−0.467876			−0.233938	+	0.972252i	$0.575161\pi$
$660$	0.712801	+	1.23461i	0.0277457	+	0.0480570i
$661$	−8.21363	+	14.2264i	−0.319473	+	0.553344i	−0.980378	−	0.197126i	$-0.936839\pi$
$661$	−8.21363	+	14.2264i	−0.319473	+	0.553344i	0.660905	+	0.750470i	$0.270173\pi$
$662$	−0.299524	+	0.518791i	−0.0116413	+	0.0201634i
$663$	−1.90182	−	3.29406i	−0.0738607	−	0.127930i
$664$	−10.4063			−0.403842
$665$	−9.42571	−	2.39851i	−0.365513	−	0.0930102i
$666$	29.1541			1.12970
$667$	−0.509007	−	0.881626i	−0.0197088	−	0.0341367i
$668$	−10.6646	+	18.4716i	−0.412626	+	0.714689i
$669$	−6.40081	+	11.0865i	−0.247470	+	0.428630i
$670$	0.782597	+	1.35550i	0.0302343	+	0.0523674i
$671$	−60.1957			−2.32383
$672$	1.18045	−	1.21064i	0.0455369	−	0.0467013i
$673$	30.5627			1.17811			0.589053	−	0.808095i	$-0.299501\pi$
$673$	30.5627			1.17811			0.589053	+	0.808095i	$0.299501\pi$
$674$	−3.90226	−	6.75891i	−0.150309	−	0.260344i
$675$	8.41952	−	14.5830i	0.324067	−	0.561301i
$676$	3.58163	−	6.20356i	0.137755	−	0.238598i
$677$	−3.13118	−	5.42335i	−0.120341	−	0.208436i	0.799561	−	0.600585i	$-0.205065\pi$
$677$	−3.13118	−	5.42335i	−0.120341	−	0.208436i	−0.919902	+	0.392148i	$0.871732\pi$
$678$	6.48912			0.249213
$679$	−10.6073	−	37.6780i	−0.407071	−	1.44595i
$680$	1.32171			0.0506854
$681$	0.558625	+	0.967566i	0.0214065	+	0.0370772i
$682$	−2.32948	+	4.03478i	−0.0892004	+	0.154500i
$683$	−0.555889	+	0.962828i	−0.0212705	+	0.0368416i	−0.876465	−	0.481466i	$-0.840104\pi$
$683$	−0.555889	+	0.962828i	−0.0212705	+	0.0368416i	0.855194	+	0.518308i	$0.173438\pi$
$684$	−8.87833	−	15.3777i	−0.339471	−	0.587982i
$685$	−2.68361			−0.102535
$686$	4.11267	−	18.0579i	0.157022	−	0.689452i
$687$	2.11256			0.0805993
$688$	1.75442	+	3.03875i	0.0668867	+	0.115851i
$689$	−15.5771	+	26.9803i	−0.593439	+	1.02787i
$690$	0.171445	−	0.296951i	0.00652680	−	0.0113047i
$691$	−3.54088	−	6.13298i	−0.134701	−	0.233309i	0.790782	−	0.612098i	$-0.209674\pi$
$691$	−3.54088	−	6.13298i	−0.134701	−	0.233309i	−0.925483	+	0.378788i	$0.876341\pi$
$692$	22.2580			0.846122
$693$	7.72517	+	27.4404i	0.293455	+	1.04237i
$694$	28.1816			1.06976
$695$	−2.72691	−	4.72314i	−0.103437	−	0.179159i
$696$	−0.325304	+	0.563444i	−0.0123306	+	0.0213573i
$697$	−3.27286	+	5.66877i	−0.123969	+	0.214720i
$698$	1.16944	+	2.02552i	0.0442638	+	0.0766671i
$699$	−6.72906			−0.254517
$700$	−8.70363	+	8.92619i	−0.328966	+	0.337378i
$701$	−9.33422			−0.352548			−0.176274	−	0.984341i	$-0.556405\pi$
$701$	−9.33422			−0.352548			−0.176274	+	0.984341i	$0.556405\pi$
$702$	−4.31673	−	7.47679i	−0.162924	−	0.282193i
$703$	38.5398	−	66.7530i	1.45356	−	2.51764i
$704$	2.07880	−	3.60059i	0.0783478	−	0.135702i
$705$	−1.66836	−	2.88968i	−0.0628339	−	0.108832i
$706$	−16.5300			−0.622116
$707$	−17.1153	−	4.35523i	−0.643686	−	0.163795i
$708$	−1.86325			−0.0700251
$709$	−20.0267	−	34.6873i	−0.752118	−	1.30271i	−0.946794	−	0.321840i	$-0.895699\pi$
$709$	−20.0267	−	34.6873i	−0.752118	−	1.30271i	0.194676	−	0.980868i	$-0.437635\pi$
$710$	−0.593070	+	1.02723i	−0.0222575	+	0.0385512i
$711$	−13.7969	+	23.8969i	−0.517424	+	0.896205i
$712$	1.85233	+	3.20832i	0.0694188	+	0.120237i
$713$	1.12059			0.0419663
$714$	−4.03682	−	1.02723i	−0.151074	−	0.0384430i
$715$	−5.38911			−0.201541
$716$	−4.76625	−	8.25539i	−0.178123	−	0.308518i
$717$	4.03842	−	6.99475i	0.150818	−	0.261224i
$718$	10.4577	−	18.1133i	0.390279	−	0.675982i
$719$	−7.04553	−	12.2032i	−0.262754	−	0.455103i	0.704219	−	0.709983i	$-0.251297\pi$
$719$	−7.04553	−	12.2032i	−0.262754	−	0.455103i	−0.966973	+	0.254880i	$0.917964\pi$
$720$	1.39043			0.0518183
$721$	5.72323	−	5.86957i	0.213144	−	0.218594i
$722$	−27.9463			−1.04005
$723$	−5.89591	−	10.2120i	−0.219271	−	0.379789i
$724$	−10.7686	+	18.6518i	−0.400212	+	0.693187i
$725$	2.39851	−	4.15435i	0.0890785	−	0.154289i
$726$	−2.00858	−	3.47896i	−0.0745453	−	0.129116i
$727$	−6.76916			−0.251054			−0.125527	−	0.992090i	$-0.540062\pi$
$727$	−6.76916			−0.251054			−0.125527	+	0.992090i	$0.540062\pi$
$728$	1.73217	+	6.15279i	0.0641984	+	0.228038i
$729$	−7.37828			−0.273270
$730$	−1.39352	−	2.41364i	−0.0515764	−	0.0893330i
$731$	4.32198	−	7.48589i	0.159854	−	0.276876i
$732$	4.62657	−	8.01345i	0.171003	−	0.296185i
$733$	6.87122	+	11.9013i	0.253794	+	0.439585i	0.964567	−	0.263837i	$-0.0849880\pi$
$733$	6.87122	+	11.9013i	0.253794	+	0.439585i	−0.710773	+	0.703421i	$0.751655\pi$
$734$	12.7371			0.470136
$735$	−2.04770	+	1.25221i	−0.0755306	+	0.0461883i
$736$	−1.00000			−0.0368605
$737$	−6.06447	−	10.5040i	−0.223388	−	0.386919i
$738$	−3.44302	+	5.96349i	−0.126739	+	0.219519i
$739$	12.5961	−	21.8170i	0.463354	−	0.802552i	−0.535772	−	0.844363i	$-0.679979\pi$
$739$	12.5961	−	21.8170i	0.463354	−	0.802552i	0.999126	+	0.0418106i	$0.0133126\pi$
$740$	3.01785	+	5.22707i	0.110938	+	0.192151i
$741$	−10.5792			−0.388636
$742$	9.24558	+	32.8410i	0.339416	+	1.20563i
$743$	−2.40488			−0.0882266			−0.0441133	−	0.999027i	$-0.514046\pi$
$743$	−2.40488			−0.0882266			−0.0441133	+	0.999027i	$0.514046\pi$
$744$	−0.358081	−	0.620215i	−0.0131279	−	0.0227382i
$745$	−0.242489	+	0.420004i	−0.00888412	+	0.0153877i
$746$	9.14892	−	15.8464i	0.334966	−	0.580177i
$747$	13.4842	+	23.3554i	0.493362	+	0.854528i
$748$	−10.2422			−0.374491
$749$	−6.15668	+	6.31411i	−0.224960	+	0.230713i
$750$	3.33020			0.121602
$751$	3.65901	+	6.33759i	0.133519	+	0.231262i	0.925031	−	0.379892i	$-0.124039\pi$
$751$	3.65901	+	6.33759i	0.133519	+	0.231262i	−0.791512	+	0.611154i	$0.790706\pi$
$752$	−4.86557	+	8.42742i	−0.177429	+	0.307316i
$753$	3.81390	−	6.60587i	0.138986	−	0.240731i
$754$	−1.22973	−	2.12995i	−0.0447841	−	0.0775683i
$755$	−9.47846			−0.344957
$756$	−9.16270	−	2.33158i	−0.333244	−	0.0847989i
$757$	8.95332			0.325414			0.162707	−	0.986674i	$-0.447978\pi$
$757$	8.95332			0.325414			0.162707	+	0.986674i	$0.447978\pi$
$758$	8.06160	+	13.9631i	0.292811	+	0.507163i
$759$	−1.32856	+	2.30112i	−0.0482235	+	0.0835255i
$760$	1.83806	−	3.18361i	0.0666734	−	0.115482i
$761$	−17.2342	−	29.8506i	−0.624741	−	1.08208i	−0.988591	−	0.150625i	$-0.951871\pi$
$761$	−17.2342	−	29.8506i	−0.624741	−	1.08208i	0.363850	−	0.931457i	$-0.381462\pi$
$762$	2.46218			0.0891952
$763$	38.1244	+	9.70132i	1.38020	+	0.351211i
$764$	23.4905			0.849857
$765$	−1.71265	−	2.96639i	−0.0619209	−	0.107250i
$766$	−8.51927	+	14.7558i	−0.307814	+	0.533149i
$767$	3.52176	−	6.09987i	0.127163	−	0.220253i
$768$	0.319548	+	0.553474i	0.0115307	+	0.0199718i
$769$	9.26470			0.334094			0.167047	−	0.985949i	$-0.446577\pi$
$769$	9.26470			0.334094			0.167047	+	0.985949i	$0.446577\pi$
$770$	−4.12016	+	4.22551i	−0.148480

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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.319548 - 0.553474i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.268262 + 0.464643i) q^{5} +0.639096 q^{6} +(0.716975 + 2.54675i) q^{7} -1.00000 q^{8} +(1.29578 + 2.24435i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.319548 - 0.553474i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.268262 + 0.464643i) q^{5} +0.639096 q^{6} +(0.716975 + 2.54675i) q^{7} -1.00000 q^{8} +(1.29578 + 2.24435i) q^{9} +(-0.268262 + 0.464643i) q^{10} +(2.07880 - 3.60059i) q^{11} +(0.319548 + 0.553474i) q^{12} -2.41594 q^{13} +(-1.84706 + 1.89429i) q^{14} +0.342890 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.23174 + 2.13343i) q^{17} +(-1.29578 + 2.24435i) q^{18} +(3.42587 + 5.93378i) q^{19} -0.536523 q^{20} +(1.63867 + 0.416983i) q^{21} +4.15761 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.319548 + 0.553474i) q^{24} +(2.35607 - 4.08084i) q^{25} +(-1.20797 - 2.09226i) q^{26} +3.57354 q^{27} +(-2.56404 - 0.652457i) q^{28} +1.01801 q^{29} +(0.171445 + 0.296951i) q^{30} +(-0.560293 + 0.970457i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.32856 - 2.30112i) q^{33} -2.46348 q^{34} +(-0.990993 + 1.01633i) q^{35} -2.59156 q^{36} +(-5.62483 - 9.74249i) q^{37} +(-3.42587 + 5.93378i) q^{38} +(-0.772008 + 1.33716i) q^{39} +(-0.268262 - 0.464643i) q^{40} +2.65711 q^{41} +(0.458216 + 1.62762i) q^{42} -3.50884 q^{43} +(2.07880 + 3.60059i) q^{44} +(-0.695215 + 1.20415i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-4.86557 - 8.42742i) q^{47} -0.639096 q^{48} +(-5.97189 + 3.65192i) q^{49} +4.71214 q^{50} +(0.787199 + 1.36347i) q^{51} +(1.20797 - 2.09226i) q^{52} +(6.44763 - 11.1676i) q^{53} +(1.78677 + 3.09478i) q^{54} +2.23065 q^{55} +(-0.716975 - 2.54675i) q^{56} +4.37892 q^{57} +(0.509007 + 0.881626i) q^{58} +(-1.45772 + 2.52485i) q^{59} +(-0.171445 + 0.296951i) q^{60} +(-7.23923 - 12.5387i) q^{61} -1.12059 q^{62} +(-4.78677 + 4.90917i) q^{63} +1.00000 q^{64} +(-0.648103 - 1.12255i) q^{65} +(1.32856 - 2.30112i) q^{66} +(1.45864 - 2.52645i) q^{67} +(-1.23174 - 2.13343i) q^{68} -0.639096 q^{69} +(-1.37567 - 0.350059i) q^{70} +2.21079 q^{71} +(-1.29578 - 2.24435i) q^{72} +(-2.59731 + 4.49868i) q^{73} +(5.62483 - 9.74249i) q^{74} +(-1.50576 - 2.60805i) q^{75} -6.85173 q^{76} +(10.6603 + 2.71266i) q^{77} -1.54402 q^{78} +(5.32379 + 9.22107i) q^{79} +(0.268262 - 0.464643i) q^{80} +(-2.74542 + 4.75520i) q^{81} +(1.32856 + 2.30112i) q^{82} +10.4063 q^{83} +(-1.18045 + 1.21064i) q^{84} -1.32171 q^{85} +(-1.75442 - 3.03875i) q^{86} +(0.325304 - 0.563444i) q^{87} +(-2.07880 + 3.60059i) q^{88} +(-1.85233 - 3.20832i) q^{89} -1.39043 q^{90} +(-1.73217 - 6.15279i) q^{91} +1.00000 q^{92} +(0.358081 + 0.620215i) q^{93} +(4.86557 - 8.42742i) q^{94} +(-1.83806 + 3.18361i) q^{95} +(-0.319548 - 0.553474i) q^{96} -14.7945 q^{97} +(-6.14860 - 3.34585i) q^{98} +10.7747 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} - 3 q^{5} - 2 q^{6} - q^{7} - 8 q^{8} - 7 q^{9} + 3 q^{10} + 6 q^{11} - q^{12} - 2 q^{13} + q^{14} + 6 q^{15} - 4 q^{16} - 15 q^{17} + 7 q^{18} + q^{19} + 6 q^{20} - q^{21} + 12 q^{22} - 4 q^{23} + q^{24} + 5 q^{25} - q^{26} - 10 q^{27} + 2 q^{28} + 12 q^{29} + 3 q^{30} - 8 q^{31} + 4 q^{32} - 9 q^{33} - 30 q^{34} - 6 q^{35} + 14 q^{36} - 8 q^{37} - q^{38} + 25 q^{39} + 3 q^{40} + 18 q^{41} - 14 q^{42} + 28 q^{43} + 6 q^{44} - 21 q^{45} + 4 q^{46} - 9 q^{47} + 2 q^{48} + 5 q^{49} + 10 q^{50} - 6 q^{51} + q^{52} + 3 q^{53} - 5 q^{54} - 24 q^{55} + q^{56} + 46 q^{57} + 6 q^{58} - 12 q^{59} - 3 q^{60} - 11 q^{61} - 16 q^{62} - 19 q^{63} + 8 q^{64} + 9 q^{66} + q^{67} - 15 q^{68} + 2 q^{69} - 30 q^{70} - 6 q^{71} + 7 q^{72} + 4 q^{73} + 8 q^{74} - 22 q^{75} - 2 q^{76} - 9 q^{77} + 50 q^{78} - 5 q^{79} - 3 q^{80} + 8 q^{81} + 9 q^{82} + 24 q^{83} - 13 q^{84} + 48 q^{85} + 14 q^{86} + 9 q^{87} - 6 q^{88} - 27 q^{89} - 42 q^{90} - 26 q^{91} + 8 q^{92} + 25 q^{93} + 9 q^{94} + 3 q^{95} + q^{96} + 4 q^{97} - 26 q^{98} - 18 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 - 3 * q^5 - 2 * q^6 - q^7 - 8 * q^8 - 7 * q^9 + 3 * q^10 + 6 * q^11 - q^12 - 2 * q^13 + q^14 + 6 * q^15 - 4 * q^16 - 15 * q^17 + 7 * q^18 + q^19 + 6 * q^20 - q^21 + 12 * q^22 - 4 * q^23 + q^24 + 5 * q^25 - q^26 - 10 * q^27 + 2 * q^28 + 12 * q^29 + 3 * q^30 - 8 * q^31 + 4 * q^32 - 9 * q^33 - 30 * q^34 - 6 * q^35 + 14 * q^36 - 8 * q^37 - q^38 + 25 * q^39 + 3 * q^40 + 18 * q^41 - 14 * q^42 + 28 * q^43 + 6 * q^44 - 21 * q^45 + 4 * q^46 - 9 * q^47 + 2 * q^48 + 5 * q^49 + 10 * q^50 - 6 * q^51 + q^52 + 3 * q^53 - 5 * q^54 - 24 * q^55 + q^56 + 46 * q^57 + 6 * q^58 - 12 * q^59 - 3 * q^60 - 11 * q^61 - 16 * q^62 - 19 * q^63 + 8 * q^64 + 9 * q^66 + q^67 - 15 * q^68 + 2 * q^69 - 30 * q^70 - 6 * q^71 + 7 * q^72 + 4 * q^73 + 8 * q^74 - 22 * q^75 - 2 * q^76 - 9 * q^77 + 50 * q^78 - 5 * q^79 - 3 * q^80 + 8 * q^81 + 9 * q^82 + 24 * q^83 - 13 * q^84 + 48 * q^85 + 14 * q^86 + 9 * q^87 - 6 * q^88 - 27 * q^89 - 42 * q^90 - 26 * q^91 + 8 * q^92 + 25 * q^93 + 9 * q^94 + 3 * q^95 + q^96 + 4 * q^97 - 26 * q^98 - 18 * q^99

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