LMFDB - Embedded newform 315.2.l.b.121.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.8
Character	$\chi$	$=$	315.121
Dual form			315.2.l.b.151.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.518491 q^{2} +(1.09609 - 1.34112i) q^{3} -1.73117 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.568312 - 0.695356i) q^{6} +(-0.619045 - 2.57231i) q^{7} -1.93458 q^{8} +(-0.597182 - 2.93996i) q^{9} +O(q^{10})$	\(q+0.518491 q^{2} +(1.09609 - 1.34112i) q^{3} -1.73117 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.568312 - 0.695356i) q^{6} +(-0.619045 - 2.57231i) q^{7} -1.93458 q^{8} +(-0.597182 - 2.93996i) q^{9} +(0.259245 + 0.449026i) q^{10} +(2.08370 - 3.60907i) q^{11} +(-1.89751 + 2.32170i) q^{12} +(2.27115 - 3.93375i) q^{13} +(-0.320969 - 1.33372i) q^{14} +(1.70948 + 0.278682i) q^{15} +2.45927 q^{16} +(1.39573 + 2.41747i) q^{17} +(-0.309633 - 1.52434i) q^{18} +(-2.22814 + 3.85926i) q^{19} +(-0.865584 - 1.49923i) q^{20} +(-4.12829 - 1.98927i) q^{21} +(1.08038 - 1.87127i) q^{22} +(2.72751 + 4.72418i) q^{23} +(-2.12047 + 2.59449i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.17757 - 2.03961i) q^{26} +(-4.59739 - 2.42157i) q^{27} +(1.07167 + 4.45310i) q^{28} +(-2.18145 - 3.77837i) q^{29} +(0.886352 + 0.144494i) q^{30} -1.71938 q^{31} +5.14426 q^{32} +(-2.55626 - 6.75033i) q^{33} +(0.723673 + 1.25344i) q^{34} +(1.91816 - 1.82226i) q^{35} +(1.03382 + 5.08956i) q^{36} +(-4.66225 + 8.07525i) q^{37} +(-1.15527 + 2.00099i) q^{38} +(-2.78623 - 7.35761i) q^{39} +(-0.967288 - 1.67539i) q^{40} +(0.217468 - 0.376665i) q^{41} +(-2.14048 - 1.03142i) q^{42} +(5.19296 + 8.99448i) q^{43} +(-3.60723 + 6.24790i) q^{44} +(2.24749 - 1.98716i) q^{45} +(1.41419 + 2.44944i) q^{46} +7.50186 q^{47} +(2.69558 - 3.29817i) q^{48} +(-6.23357 + 3.18475i) q^{49} +(-0.259245 + 0.449026i) q^{50} +(4.77195 + 0.777930i) q^{51} +(-3.93174 + 6.80997i) q^{52} +(-4.17271 - 7.22734i) q^{53} +(-2.38371 - 1.25556i) q^{54} +4.16739 q^{55} +(1.19759 + 4.97633i) q^{56} +(2.73347 + 7.21828i) q^{57} +(-1.13106 - 1.95905i) q^{58} +10.7415 q^{59} +(-2.95940 - 0.482446i) q^{60} +4.11034 q^{61} -0.891481 q^{62} +(-7.19281 + 3.35610i) q^{63} -2.25129 q^{64} +4.54230 q^{65} +(-1.32540 - 3.49999i) q^{66} -7.55841 q^{67} +(-2.41624 - 4.18505i) q^{68} +(9.32525 + 1.52022i) q^{69} +(0.994551 - 0.944827i) q^{70} +15.1001 q^{71} +(1.15529 + 5.68758i) q^{72} +(-1.11154 - 1.92524i) q^{73} +(-2.41733 + 4.18695i) q^{74} +(0.613396 + 1.61980i) q^{75} +(3.85729 - 6.68102i) q^{76} +(-10.5735 - 3.12574i) q^{77} +(-1.44463 - 3.81485i) q^{78} +0.991866 q^{79} +(1.22964 + 2.12979i) q^{80} +(-8.28675 + 3.51138i) q^{81} +(0.112755 - 0.195298i) q^{82} +(0.763861 + 1.32305i) q^{83} +(7.14677 + 3.44376i) q^{84} +(-1.39573 + 2.41747i) q^{85} +(2.69251 + 4.66356i) q^{86} +(-7.45829 - 1.21586i) q^{87} +(-4.03107 + 6.98202i) q^{88} +(1.04124 - 1.80348i) q^{89} +(1.16530 - 1.03032i) q^{90} +(-11.5248 - 3.40694i) q^{91} +(-4.72177 - 8.17834i) q^{92} +(-1.88459 + 2.30588i) q^{93} +3.88965 q^{94} -4.45629 q^{95} +(5.63857 - 6.89905i) q^{96} +(-8.43928 - 14.6173i) q^{97} +(-3.23205 + 1.65126i) q^{98} +(-11.8549 - 3.97072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) $ 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.518491			0.366628			0.183314	−	0.983054i	$-0.441317\pi$
$2$	0.518491			0.366628			0.183314	+	0.983054i	$0.441317\pi$
$3$	1.09609	−	1.34112i	0.632827	−	0.774293i
$3$	1.09609	−	1.34112i	0.632827	−	0.774293i
$4$	−1.73117			−0.865584
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.568312	−	0.695356i	0.232012	−	0.283878i
$7$	−0.619045	−	2.57231i	−0.233977	−	0.972242i
$7$	−0.619045	−	2.57231i	−0.233977	−	0.972242i
$8$	−1.93458			−0.683976
$9$	−0.597182	−	2.93996i	−0.199061	−	0.979987i
$10$	0.259245	+	0.449026i	0.0819806	+	0.141995i
$11$	2.08370	−	3.60907i	0.628258	−	1.08817i	−0.359643	−	0.933090i	$-0.617102\pi$
$11$	2.08370	−	3.60907i	0.628258	−	1.08817i	0.987901	−	0.155085i	$-0.0495651\pi$
$12$	−1.89751	+	2.32170i	−0.547764	+	0.670216i
$13$	2.27115	−	3.93375i	0.629904	−	1.09103i	−0.357667	−	0.933849i	$-0.616428\pi$
$13$	2.27115	−	3.93375i	0.629904	−	1.09103i	0.987571	−	0.157176i	$-0.0502390\pi$
$14$	−0.320969	−	1.33372i	−0.0857826	−	0.356452i
$15$	1.70948	+	0.278682i	0.441387	+	0.0719555i
$16$	2.45927			0.614818
$17$	1.39573	+	2.41747i	0.338514	+	0.586323i	0.984153	−	0.177319i	$-0.0567425\pi$
$17$	1.39573	+	2.41747i	0.338514	+	0.586323i	−0.645640	+	0.763642i	$0.723409\pi$
$18$	−0.309633	−	1.52434i	−0.0729813	−	0.359291i
$19$	−2.22814	+	3.85926i	−0.511171	+	0.885374i	0.488745	+	0.872427i	$0.337455\pi$
$19$	−2.22814	+	3.85926i	−0.511171	+	0.885374i	−0.999916	+	0.0129475i	$0.995879\pi$
$20$	−0.865584	−	1.49923i	−0.193550	−	0.335239i
$21$	−4.12829	−	1.98927i	−0.900868	−	0.434094i
$22$	1.08038	−	1.87127i	0.230337	−	0.398956i
$23$	2.72751	+	4.72418i	0.568724	+	0.985059i	0.996692	+	0.0812654i	$0.0258961\pi$
$23$	2.72751	+	4.72418i	0.568724	+	0.985059i	−0.427968	+	0.903794i	$0.640771\pi$
$24$	−2.12047	+	2.59449i	−0.432838	+	0.529598i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.17757	−	2.03961i	0.230941	−	0.400001i
$27$	−4.59739	−	2.42157i	−0.884768	−	0.466031i
$28$	1.07167	+	4.45310i	0.202527	+	0.841557i
$29$	−2.18145	−	3.77837i	−0.405084	−	0.701627i	0.589247	−	0.807953i	$-0.299424\pi$
$29$	−2.18145	−	3.77837i	−0.405084	−	0.701627i	−0.994331	+	0.106326i	$0.966091\pi$
$30$	0.886352	+	0.144494i	0.161825	+	0.0263809i
$31$	−1.71938			−0.308809			−0.154405	−	0.988008i	$-0.549346\pi$
$31$	−1.71938			−0.308809			−0.154405	+	0.988008i	$0.549346\pi$
$32$	5.14426			0.909386
$33$	−2.55626	−	6.75033i	−0.444988	−	1.17508i
$34$	0.723673	+	1.25344i	0.124109	+	0.214963i
$35$	1.91816	−	1.82226i	0.324229	−	0.308019i
$36$	1.03382	+	5.08956i	0.172304	+	0.848261i
$37$	−4.66225	+	8.07525i	−0.766469	+	1.32756i	0.172998	+	0.984922i	$0.444655\pi$
$37$	−4.66225	+	8.07525i	−0.766469	+	1.32756i	−0.939466	+	0.342641i	$0.888679\pi$
$38$	−1.15527	+	2.00099i	−0.187410	+	0.324603i
$39$	−2.78623	−	7.35761i	−0.446154	−	1.17816i
$40$	−0.967288	−	1.67539i	−0.152942	−	0.264903i
$41$	0.217468	−	0.376665i	0.0339628	−	0.0588253i	−0.848544	−	0.529124i	$-0.822521\pi$
$41$	0.217468	−	0.376665i	0.0339628	−	0.0588253i	0.882507	+	0.470299i	$0.155854\pi$
$42$	−2.14048	−	1.03142i	−0.330284	−	0.159151i
$43$	5.19296	+	8.99448i	0.791920	+	1.37165i	0.924777	+	0.380510i	$0.124252\pi$
$43$	5.19296	+	8.99448i	0.791920	+	1.37165i	−0.132857	+	0.991135i	$0.542415\pi$
$44$	−3.60723	+	6.24790i	−0.543810	+	0.941906i
$45$	2.24749	−	1.98716i	0.335036	−	0.296228i
$46$	1.41419	+	2.44944i	0.208510	+	0.361151i
$47$	7.50186			1.09426			0.547130	−	0.837048i	$-0.315720\pi$
$47$	7.50186			1.09426			0.547130	+	0.837048i	$0.315720\pi$
$48$	2.69558	−	3.29817i	0.389074	−	0.476050i
$49$	−6.23357	+	3.18475i	−0.890510	+	0.454964i
$50$	−0.259245	+	0.449026i	−0.0366628	+	0.0635019i
$51$	4.77195	+	0.777930i	0.668207	+	0.108932i
$52$	−3.93174	+	6.80997i	−0.545234	+	0.944373i
$53$	−4.17271	−	7.22734i	−0.573165	−	0.992751i	−0.996238	−	0.0866556i	$-0.972382\pi$
$53$	−4.17271	−	7.22734i	−0.573165	−	0.992751i	0.423073	−	0.906096i	$-0.360951\pi$
$54$	−2.38371	−	1.25556i	−0.324381	−	0.170860i
$55$	4.16739			0.561931
$56$	1.19759	+	4.97633i	0.160035	+	0.664990i
$57$	2.73347	+	7.21828i	0.362057	+	0.956085i
$58$	−1.13106	−	1.95905i	−0.148515	−	0.257236i
$59$	10.7415			1.39843			0.699214	−	0.714913i	$-0.253534\pi$
$59$	10.7415			1.39843			0.699214	+	0.714913i	$0.253534\pi$
$60$	−2.95940	−	0.482446i	−0.382057	−	0.0622835i
$61$	4.11034			0.526275			0.263137	−	0.964758i	$-0.415243\pi$
$61$	4.11034			0.526275			0.263137	+	0.964758i	$0.415243\pi$
$62$	−0.891481			−0.113218
$63$	−7.19281	+	3.35610i	−0.906209	+	0.422829i
$64$	−2.25129			−0.281412
$65$	4.54230			0.563403
$66$	−1.32540	−	3.49999i	−0.163145	−	0.430819i
$67$	−7.55841			−0.923407			−0.461703	−	0.887034i	$-0.652762\pi$
$67$	−7.55841			−0.923407			−0.461703	+	0.887034i	$0.652762\pi$
$68$	−2.41624	−	4.18505i	−0.293012	−	0.507512i
$69$	9.32525	+	1.52022i	1.12263	+	0.183012i
$70$	0.994551	−	0.944827i	0.118872	−	0.112928i
$71$	15.1001			1.79205			0.896026	−	0.444003i	$-0.146442\pi$
$71$	15.1001			1.79205			0.896026	+	0.444003i	$0.146442\pi$
$72$	1.15529	+	5.68758i	0.136153	+	0.670288i
$73$	−1.11154	−	1.92524i	−0.130096	−	0.225332i	0.793618	−	0.608417i	$-0.208195\pi$
$73$	−1.11154	−	1.92524i	−0.130096	−	0.225332i	−0.923713	+	0.383085i	$0.874862\pi$
$74$	−2.41733	+	4.18695i	−0.281009	+	0.486722i
$75$	0.613396	+	1.61980i	0.0708289	+	0.187038i
$76$	3.85729	−	6.68102i	0.442461	−	0.766365i
$77$	−10.5735	−	3.12574i	−1.20497	−	0.356211i
$78$	−1.44463	−	3.81485i	−0.163573	−	0.431947i
$79$	0.991866			0.111594			0.0557968	−	0.998442i	$-0.482230\pi$
$79$	0.991866			0.111594			0.0557968	+	0.998442i	$0.482230\pi$
$80$	1.22964	+	2.12979i	0.137478	+	0.238118i
$81$	−8.28675	+	3.51138i	−0.920750	+	0.390154i
$82$	0.112755	−	0.195298i	0.0124517	−	0.0215670i
$83$	0.763861	+	1.32305i	0.0838446	+	0.145223i	0.904898	−	0.425628i	$-0.139947\pi$
$83$	0.763861	+	1.32305i	0.0838446	+	0.145223i	−0.821054	+	0.570851i	$0.806613\pi$
$84$	7.14677	+	3.44376i	0.779776	+	0.375745i
$85$	−1.39573	+	2.41747i	−0.151388	+	0.262212i
$86$	2.69251	+	4.66356i	0.290340	+	0.502884i
$87$	−7.45829	−	1.21586i	−0.799613	−	0.130354i
$88$	−4.03107	+	6.98202i	−0.429713	+	0.744285i
$89$	1.04124	−	1.80348i	0.110371	−	0.191168i	−0.805549	−	0.592529i	$-0.798129\pi$
$89$	1.04124	−	1.80348i	0.110371	−	0.191168i	0.915920	+	0.401361i	$0.131463\pi$
$90$	1.16530	−	1.03032i	0.122834	−	0.108605i
$91$	−11.5248	−	3.40694i	−1.20812	−	0.357144i
$92$	−4.72177	−	8.17834i	−0.492278	−	0.852651i
$93$	−1.88459	+	2.30588i	−0.195423	+	0.239109i
$94$	3.88965			0.401187
$95$	−4.45629			−0.457205
$96$	5.63857	−	6.89905i	0.575484	−	0.704132i
$97$	−8.43928	−	14.6173i	−0.856879	−	1.48416i	−0.874891	−	0.484320i	$-0.839067\pi$
$97$	−8.43928	−	14.6173i	−0.856879	−	1.48416i	0.0180116	−	0.999838i	$-0.494266\pi$
$98$	−3.23205	+	1.65126i	−0.326486	+	0.166803i
$99$	−11.8549	−	3.97072i	−1.19146	−	0.399072i
$100$	0.865584	−	1.49923i	0.0865584	−	0.149923i
$101$	3.93478	−	6.81524i	0.391525	−	0.678142i	−0.601126	−	0.799154i	$-0.705281\pi$
$101$	3.93478	−	6.81524i	0.391525	−	0.678142i	0.992651	+	0.121013i	$0.0386142\pi$
$102$	2.47421	+	0.403350i	0.244984	+	0.0399376i
$103$	8.22726	+	14.2500i	0.810656	+	1.40410i	0.912406	+	0.409287i	$0.134222\pi$
$103$	8.22726	+	14.2500i	0.810656	+	1.40410i	−0.101750	+	0.994810i	$0.532444\pi$
$104$	−4.39371	+	7.61013i	−0.430839	+	0.746235i
$105$	−0.341389	−	4.56984i	−0.0333162	−	0.445971i
$106$	−2.16351	−	3.74731i	−0.210139	−	0.363971i
$107$	−4.53367	+	7.85255i	−0.438286	+	0.759134i	−0.997557	−	0.0698504i	$-0.977748\pi$
$107$	−4.53367	+	7.85255i	−0.438286	+	0.759134i	0.559271	+	0.828985i	$0.311081\pi$
$108$	7.95885	+	4.19214i	0.765841	+	0.403389i
$109$	5.37447	+	9.30885i	0.514780	+	0.891626i	0.999853	+	0.0171519i	$0.00545990\pi$
$109$	5.37447	+	9.30885i	0.514780	+	0.891626i	−0.485072	+	0.874474i	$0.661207\pi$
$110$	2.16075			0.206020
$111$	5.71961	+	15.1038i	0.542881	+	1.43359i
$112$	−1.52240	−	6.32602i	−0.143853	−	0.597752i
$113$	−4.68431	+	8.11346i	−0.440663	+	0.763250i	−0.997739	−	0.0672113i	$-0.978590\pi$
$113$	−4.68431	+	8.11346i	−0.440663	+	0.763250i	0.557076	+	0.830461i	$0.311923\pi$
$114$	1.41728	+	3.74261i	0.132740	+	0.350528i
$115$	−2.72751	+	4.72418i	−0.254341	+	0.440532i
$116$	3.77645	+	6.54100i	0.350634	+	0.607316i
$117$	−12.9214	−	4.32793i	−1.19458	−	0.400117i
$118$	5.56938			0.512703
$119$	5.35447	−	5.08677i	0.490844	−	0.466303i
$120$	−3.30713	−	0.539132i	−0.301898	−	0.0492158i
$121$	−3.18358	−	5.51411i	−0.289416	−	0.501283i
$122$	2.13117			0.192947
$123$	−0.266788	−	0.704508i	−0.0240555	−	0.0635234i
$124$	2.97653			0.267300
$125$	−1.00000			−0.0894427
$126$	−3.72941	+	1.74011i	−0.332242	+	0.155021i
$127$	−4.33358			−0.384543			−0.192271	−	0.981342i	$-0.561585\pi$
$127$	−4.33358			−0.384543			−0.192271	+	0.981342i	$0.561585\pi$
$128$	−11.4558			−1.01256
$129$	17.7546	+	2.89438i	1.56320	+	0.254836i
$130$	2.35514			0.206560
$131$	−4.96448	−	8.59873i	−0.433749	−	0.751275i	0.563444	−	0.826154i	$-0.309476\pi$
$131$	−4.96448	−	8.59873i	−0.433749	−	0.751275i	−0.997193	+	0.0748795i	$0.976143\pi$
$132$	4.42532	+	11.6860i	0.385174	+	1.01713i
$133$	11.3065	+	3.34242i	0.980400	+	0.289825i
$134$	−3.91897			−0.338547
$135$	−0.201557	−	5.19224i	−0.0173473	−	0.446877i
$136$	−2.70014	−	4.67679i	−0.231535	−	0.401031i
$137$	−3.60261	+	6.23990i	−0.307792	+	0.533111i	−0.977879	−	0.209171i	$-0.932923\pi$
$137$	−3.60261	+	6.23990i	−0.307792	+	0.533111i	0.670087	+	0.742282i	$0.266257\pi$
$138$	4.83506	+	0.788218i	0.411588	+	0.0670976i
$139$	7.04875	−	12.2088i	0.597868	−	1.03554i	−0.395268	−	0.918566i	$-0.629348\pi$
$139$	7.04875	−	12.2088i	0.597868	−	1.03554i	0.993135	−	0.116971i	$-0.0373185\pi$
$140$	−3.32066	+	3.15464i	−0.280647	+	0.266616i
$141$	8.22270	−	10.0609i	0.692477	−	0.847278i
$142$	7.82926			0.657017
$143$	−9.46477	−	16.3935i	−0.791484	−	1.37089i
$144$	−1.46863	−	7.23017i	−0.122386	−	0.602514i
$145$	2.18145	−	3.77837i	0.181159	−	0.313777i
$146$	−0.576322	−	0.998219i	−0.0476967	−	0.0826132i
$147$	−2.56142	+	11.8507i	−0.211262	+	0.977429i
$148$	8.07113	−	13.9796i	0.663443	−	1.14912i
$149$	−3.59477	−	6.22632i	−0.294495	−	0.510080i	0.680372	−	0.732867i	$-0.261818\pi$
$149$	−3.59477	−	6.22632i	−0.294495	−	0.510080i	−0.974867	+	0.222787i	$0.928485\pi$
$150$	0.318040	+	0.839851i	0.0259679	+	0.0685735i
$151$	4.91890	−	8.51978i	0.400294	−	0.693330i	−0.593467	−	0.804858i	$-0.702241\pi$
$151$	4.91890	−	8.51978i	0.400294	−	0.693330i	0.993761	+	0.111529i	$0.0355746\pi$
$152$	4.31051	−	7.46603i	0.349629	−	0.605575i
$153$	6.27377	−	5.54706i	0.507204	−	0.448453i
$154$	−5.48229	−	1.62067i	−0.441775	−	0.130597i
$155$	−0.859688	−	1.48902i	−0.0690518	−	0.119601i
$156$	4.82343	+	12.7372i	0.386183	+	1.01980i
$157$	10.2432			0.817499			0.408750	−	0.912647i	$-0.365965\pi$
$157$	10.2432			0.817499			0.408750	+	0.912647i	$0.365965\pi$
$158$	0.514274			0.0409134
$159$	−14.2663	−	2.32572i	−1.13139	−	0.184441i
$160$	2.57213	+	4.45506i	0.203345	+	0.352204i
$161$	10.4636	−	9.94047i	0.824648	−	0.783419i
$162$	−4.29660	+	1.82062i	−0.337573	+	0.143041i
$163$	−6.15718	+	10.6645i	−0.482268	+	0.835312i	−0.999793	−	0.0203561i	$-0.993520\pi$
$163$	−6.15718	+	10.6645i	−0.482268	+	0.835312i	0.517525	+	0.855668i	$0.326853\pi$
$164$	−0.376473	+	0.652071i	−0.0293976	+	0.0509182i
$165$	4.56783	−	5.58895i	0.355605	−	0.435099i
$166$	0.396055	+	0.685987i	0.0307398	+	0.0532429i
$167$	7.25996	−	12.5746i	0.561793	−	0.973054i	−0.435547	−	0.900166i	$-0.643445\pi$
$167$	7.25996	−	12.5746i	0.561793	−	0.973054i	0.997340	−	0.0728879i	$-0.0232215\pi$
$168$	7.98650	+	3.84839i	0.616172	+	0.296910i
$169$	−3.81624	−	6.60993i	−0.293557	−	0.508456i
$170$	−0.723673	+	1.25344i	−0.0555031	+	0.0961343i
$171$	12.6767	+	4.24598i	0.969409	+	0.324698i
$172$	−8.98989	−	15.5709i	−0.685473	−	1.18727i
$173$	−3.79127			−0.288245			−0.144123	−	0.989560i	$-0.546036\pi$
$173$	−3.79127			−0.288245			−0.144123	+	0.989560i	$0.546036\pi$
$174$	−3.86706	−	0.630413i	−0.293161	−	0.0477915i
$175$	2.53721	+	0.750047i	0.191795	+	0.0566982i
$176$	5.12438	−	8.87568i	0.386265	−	0.669030i
$177$	11.7737	−	14.4056i	0.884962	−	1.08279i
$178$	0.539873	−	0.935088i	0.0404652	−	0.0700878i
$179$	10.8720	+	18.8309i	0.812614	+	1.40749i	0.911029	+	0.412343i	$0.135289\pi$
$179$	10.8720	+	18.8309i	0.812614	+	1.40749i	−0.0984148	+	0.995145i	$0.531377\pi$
$180$	−3.89078	+	3.44010i	−0.290002	+	0.256410i
$181$	−13.4199			−0.997494			−0.498747	−	0.866748i	$-0.666206\pi$
$181$	−13.4199			−0.997494			−0.498747	+	0.866748i	$0.666206\pi$
$182$	−5.97549	−	1.76647i	−0.442932	−	0.130939i
$183$	4.50529	−	5.51244i	0.333041	−	0.407491i
$184$	−5.27657	−	9.13928i	−0.388994	−	0.673757i
$185$	−9.32450			−0.685551
$186$	−0.977142	+	1.19558i	−0.0716475	+	0.0876641i
$187$	11.6331			0.850696
$188$	−12.9870			−0.947173
$189$	−3.38303	+	13.3250i	−0.246079	+	0.969250i
$190$	−2.31054			−0.167624
$191$	−10.6094			−0.767668			−0.383834	−	0.923402i	$-0.625396\pi$
$191$	−10.6094			−0.767668			−0.383834	+	0.923402i	$0.625396\pi$
$192$	−2.46762	+	3.01924i	−0.178085	+	0.217895i
$193$	−22.1321			−1.59310			−0.796552	−	0.604570i	$-0.793345\pi$
$193$	−22.1321			−1.59310			−0.796552	+	0.604570i	$0.793345\pi$
$194$	−4.37569	−	7.57892i	−0.314156	−	0.544135i
$195$	4.97876	−	6.09175i	0.356536	−	0.436239i
$196$	10.7913	−	5.51334i	0.770810	−	0.393810i
$197$	7.40378			0.527497			0.263749	−	0.964591i	$-0.415041\pi$
$197$	7.40378			0.527497			0.263749	+	0.964591i	$0.415041\pi$
$198$	−6.14664	−	2.05878i	−0.436823	−	0.146311i
$199$	−5.47597	−	9.48465i	−0.388181	−	0.672349i	0.604024	−	0.796966i	$-0.293563\pi$
$199$	−5.47597	−	9.48465i	−0.388181	−	0.672349i	−0.992205	+	0.124617i	$0.960230\pi$
$200$	0.967288	−	1.67539i	0.0683976	−	0.118468i
$201$	−8.28468	+	10.1367i	−0.584357	+	0.714988i
$202$	2.04015	−	3.53364i	0.143544	−	0.248626i
$203$	−8.36874	+	7.95034i	−0.587371	+	0.558004i
$204$	−8.26104	−	1.34673i	−0.578389	−	0.0942897i
$205$	0.434936			0.0303772
$206$	4.26576	+	7.38851i	0.297209	+	0.514782i
$207$	12.2601	−	10.8400i	0.852135	−	0.753429i
$208$	5.58538	−	9.67416i	0.387276	−	0.670782i
$209$	9.28554	+	16.0830i	0.642294	+	1.11249i
$210$	−0.177007	−	2.36942i	−0.0122147	−	0.163506i
$211$	−8.02408	+	13.8981i	−0.552401	+	0.956786i	0.445700	+	0.895182i	$0.352955\pi$
$211$	−8.02408	+	13.8981i	−0.552401	+	0.956786i	−0.998101	+	0.0616037i	$0.980379\pi$
$212$	7.22365	+	12.5117i	0.496122	+	0.859309i
$213$	16.5510	−	20.2510i	1.13406	−	1.38757i
$214$	−2.35067	+	4.07148i	−0.160688	+	0.278320i
$215$	−5.19296	+	8.99448i	−0.354157	+	0.613418i
$216$	8.89401	+	4.68471i	0.605160	+	0.318754i
$217$	1.06437	+	4.42277i	0.0722542	+	0.300237i
$218$	2.78661	+	4.82655i	0.188733	+	0.326895i
$219$	−3.80031	−	0.619532i	−0.256801	−	0.0418641i
$220$	−7.21445			−0.486398
$221$	12.6796			0.852924
$222$	2.96557	+	7.83118i	0.199036	+	0.525595i
$223$	0.311357	+	0.539286i	0.0208500	+	0.0361133i	0.876262	−	0.481835i	$-0.160029\pi$
$223$	0.311357	+	0.539286i	0.0208500	+	0.0361133i	−0.855412	+	0.517948i	$0.826696\pi$
$224$	−3.18453	−	13.2326i	−0.212775	−	0.884143i
$225$	2.84467	+	0.952806i	0.189645	+	0.0635204i
$226$	−2.42877	+	4.20676i	−0.161559	+	0.279829i
$227$	−8.75679	+	15.1672i	−0.581208	+	1.00668i	0.414128	+	0.910219i	$0.364087\pi$
$227$	−8.75679	+	15.1672i	−0.581208	+	1.00668i	−0.995336	+	0.0964638i	$0.969247\pi$
$228$	−4.73209	−	12.4961i	−0.313390	−	0.827571i
$229$	−4.75430	−	8.23469i	−0.314173	−	0.544163i	0.665088	−	0.746765i	$-0.268394\pi$
$229$	−4.75430	−	8.23469i	−0.314173	−	0.544163i	−0.979261	+	0.202601i	$0.935061\pi$
$230$	−1.41419	+	2.44944i	−0.0932487	+	0.161512i
$231$	−15.7815	+	10.7543i	−1.03835	+	0.707578i
$232$	4.22017	+	7.30955i	0.277068	+	0.479896i
$233$	−0.129981	+	0.225134i	−0.00851534	+	0.0147490i	−0.870252	−	0.492607i	$-0.836044\pi$
$233$	−0.129981	+	0.225134i	−0.00851534	+	0.0147490i	0.861736	+	0.507356i	$0.169377\pi$
$234$	−6.69961	−	2.24399i	−0.437967	−	0.146694i
$235$	3.75093	+	6.49681i	0.244684	+	0.423805i
$236$	−18.5954			−1.21046
$237$	1.08717	−	1.33021i	0.0706195	−	0.0864062i
$238$	2.77625	−	2.63744i	0.179957	−	0.170960i
$239$	1.90947	−	3.30730i	0.123514	−	0.213932i	−0.797637	−	0.603137i	$-0.793917\pi$
$239$	1.90947	−	3.30730i	0.123514	−	0.213932i	0.921151	+	0.389206i	$0.127250\pi$
$240$	4.20409	+	0.685356i	0.271373	+	0.0442396i
$241$	4.01796	−	6.95932i	0.258820	−	0.448289i	−0.707106	−	0.707107i	$-0.750000\pi$
$241$	4.01796	−	6.95932i	0.258820	−	0.448289i	0.965926	+	0.258818i	$0.0833331\pi$
$242$	−1.65066	−	2.85902i	−0.106108	−	0.183785i
$243$	−4.37384	+	14.9623i	−0.280582	+	0.959830i
$244$	−7.11568			−0.455535
$245$	−5.87486	−	3.80605i	−0.375331	−	0.243160i
$246$	−0.138327	−	0.365281i	−0.00881942	−	0.0232895i
$247$	10.1209	+	17.5299i	0.643977	+	1.11540i
$248$	3.32627			0.211218
$249$	2.61162	+	0.425749i	0.165504	+	0.0269808i
$250$	−0.518491			−0.0327922
$251$	−16.7391			−1.05656			−0.528280	−	0.849070i	$-0.677163\pi$
$251$	−16.7391			−1.05656			−0.528280	+	0.849070i	$0.677163\pi$
$252$	12.4520	−	5.80998i	0.784400	−	0.365994i
$253$	22.7332			1.42922
$254$	−2.24692			−0.140984
$255$	1.71227	+	4.52160i	0.107226	+	0.283153i
$256$	−1.43715			−0.0898216
$257$	−4.99373	−	8.64940i	−0.311501	−	0.539535i	0.667187	−	0.744890i	$-0.267498\pi$
$257$	−4.99373	−	8.64940i	−0.311501	−	0.539535i	−0.978687	+	0.205356i	$0.934165\pi$
$258$	9.20559	+	1.50071i	0.573115	+	0.0934300i
$259$	23.6582	+	6.99381i	1.47005	+	0.434574i
$260$	−7.86348			−0.487672
$261$	−9.80556	+	8.66974i	−0.606949	+	0.536644i
$262$	−2.57404	−	4.45837i	−0.159025	−	0.275439i
$263$	−1.15998	+	2.00914i	−0.0715274	+	0.123889i	−0.899571	−	0.436775i	$-0.856121\pi$
$263$	−1.15998	+	2.00914i	−0.0715274	+	0.123889i	0.828044	+	0.560664i	$0.189454\pi$
$264$	4.94528	+	13.0590i	0.304361	+	0.803728i
$265$	4.17271	−	7.22734i	0.256327	−	0.443972i
$266$	5.86233	+	1.73302i	0.359443	+	0.106258i
$267$	−1.27738	−	3.37320i	−0.0781747	−	0.206436i
$268$	13.0849			0.799286
$269$	3.50368	+	6.06855i	0.213623	+	0.370006i	0.952846	−	0.303455i	$-0.0981402\pi$
$269$	3.50368	+	6.06855i	0.213623	+	0.370006i	−0.739223	+	0.673461i	$0.764807\pi$
$270$	−0.104506	−	2.69213i	−0.00636001	−	0.163838i
$271$	−1.38943	+	2.40656i	−0.0844016	+	0.146188i	−0.905136	−	0.425122i	$-0.860231\pi$
$271$	−1.38943	+	2.40656i	−0.0844016	+	0.146188i	0.820734	+	0.571310i	$0.193565\pi$
$272$	3.43248	+	5.94523i	0.208125	+	0.360482i
$273$	−17.2013	+	11.7217i	−1.04107	+	0.709432i
$274$	−1.86792	+	3.23533i	−0.112845	+	0.195454i
$275$	2.08370	+	3.60907i	0.125652	+	0.217635i
$276$	−16.1436	−	2.63175i	−0.971729	−	0.158413i
$277$	3.61669	−	6.26428i	0.217306	−	0.376384i	−0.736678	−	0.676244i	$-0.763607\pi$
$277$	3.61669	−	6.26428i	0.217306	−	0.376384i	0.953983	+	0.299860i	$0.0969398\pi$
$278$	3.65472	−	6.33015i	0.219195	−	0.379657i
$279$	1.02678	+	5.05490i	0.0614717	+	0.302629i
$280$	−3.71084	+	3.52531i	−0.221765	+	0.210678i
$281$	7.13246	+	12.3538i	0.425487	+	0.736965i	0.996466	−	0.0839998i	$-0.0267695\pi$
$281$	7.13246	+	12.3538i	0.425487	+	0.736965i	−0.570979	+	0.820965i	$0.693436\pi$
$282$	4.26340	−	5.21647i	0.253882	−	0.310636i
$283$	−9.35159			−0.555894			−0.277947	−	0.960596i	$-0.589654\pi$
$283$	−9.35159			−0.555894			−0.277947	+	0.960596i	$0.589654\pi$
$284$	−26.1408			−1.55117
$285$	−4.88448	+	5.97639i	−0.289332	+	0.354011i
$286$	−4.90740	−	8.49986i	−0.290181	−	0.502607i
$287$	−1.10352	−	0.326222i	−0.0651389	−	0.0192563i
$288$	−3.07206	−	15.1239i	−0.181023	−	0.891187i
$289$	4.60389	−	7.97416i	0.270817	−	0.469068i
$290$	1.13106	−	1.95905i	0.0664181	−	0.115040i
$291$	−28.8536	−	4.70376i	−1.69143	−	0.275739i
$292$	1.92426	+	3.33291i	0.112609	+	0.195044i
$293$	−13.6282	+	23.6047i	−0.796166	+	1.37900i	0.125931	+	0.992039i	$0.459808\pi$
$293$	−13.6282	+	23.6047i	−0.796166	+	1.37900i	−0.922096	+	0.386960i	$0.873525\pi$
$294$	−1.32807	+	6.14448i	−0.0774548	+	0.358353i
$295$	5.37076	+	9.30243i	0.312698	+	0.541609i
$296$	9.01948	−	15.6222i	0.524246	−	0.908021i
$297$	−18.3192	+	11.5465i	−1.06299	+	0.669995i
$298$	−1.86385	−	3.22829i	−0.107970	−	0.187010i
$299$	24.7783			1.43297
$300$	−1.06189	−	2.80414i	−0.0613083	−	0.161897i
$301$	19.9219	−	18.9259i	1.14828	−	1.09087i
$302$	2.55040	−	4.41743i	0.146759	−	0.254194i
$303$	−4.82716	−	12.7471i	−0.277313	−	0.732302i
$304$	−5.47961	+	9.49097i	−0.314277	+	0.544344i
$305$	2.05517	+	3.55966i	0.117679	+	0.203825i
$306$	3.25289	−	2.87610i	0.185956	−	0.164416i
$307$	11.6773			0.666457			0.333228	−	0.942846i	$-0.391862\pi$
$307$	11.6773			0.666457			0.333228	+	0.942846i	$0.391862\pi$
$308$	18.3046	+	5.41118i	1.04300	+	0.308330i
$309$	28.1287	+	4.58558i	1.60019	+	0.260865i
$310$	−0.445741	−	0.772045i	−0.0253164	−	0.0438492i
$311$	1.02374			0.0580510			0.0290255	−	0.999579i	$-0.490760\pi$
$311$	1.02374			0.0580510			0.0290255	+	0.999579i	$0.490760\pi$
$312$	5.39017	+	14.2339i	0.305158	+	0.805833i
$313$	−11.0583			−0.625055			−0.312527	−	0.949909i	$-0.601176\pi$
$313$	−11.0583			−0.625055			−0.312527	+	0.949909i	$0.601176\pi$
$314$	5.31103			0.299719
$315$	−6.50288	−	4.55111i	−0.366396	−	0.256426i
$316$	−1.71709			−0.0965936
$317$	9.48679			0.532831			0.266416	−	0.963858i	$-0.414161\pi$
$317$	9.48679			0.532831			0.266416	+	0.963858i	$0.414161\pi$
$318$	−7.39697	−	1.20586i	−0.414802	−	0.0676215i
$319$	−18.1819			−1.01799
$320$	−1.12565	−	1.94968i	−0.0629255	−	0.108990i
$321$	5.56187	+	14.6873i	0.310433	+	0.819763i
$322$	5.42529	−	5.15404i	0.302339	−	0.287224i
$323$	−12.4395			−0.692154
$324$	14.3457	−	6.07879i	0.796986	−	0.337711i
$325$	2.27115	+	3.93375i	0.125981	+	0.218205i
$326$	−3.19244	+	5.52947i	−0.176813	+	0.306249i
$327$	18.3751	+	2.99554i	1.01615	+	0.165654i
$328$	−0.420708	+	0.728688i	−0.0232297	+	0.0402351i
$329$	−4.64399	−	19.2971i	−0.256031	−	1.06389i
$330$	2.36838	−	2.89782i	0.130375	−	0.159520i
$331$	−35.4324			−1.94754			−0.973770	−	0.227534i	$-0.926934\pi$
$331$	−35.4324			−1.94754			−0.973770	+	0.227534i	$0.926934\pi$
$332$	−1.32237	−	2.29041i	−0.0725745	−	0.125703i
$333$	26.5251	+	8.88444i	1.45357	+	0.486864i
$334$	3.76423	−	6.51983i	0.205969	−	0.356749i
$335$	−3.77921	−	6.54578i	−0.206480	−	0.357634i
$336$	−10.1526	−	4.89216i	−0.553870	−	0.266889i
$337$	−12.5415	+	21.7225i	−0.683179	+	1.18330i	0.290827	+	0.956776i	$0.406070\pi$
$337$	−12.5415	+	21.7225i	−0.683179	+	1.18330i	−0.974005	+	0.226525i	$0.927264\pi$
$338$	−1.97869	−	3.42719i	−0.107626	−	0.186414i
$339$	5.74667	+	15.1753i	0.312116	+	0.824207i
$340$	2.41624	−	4.18505i	0.131039	−	0.226966i
$341$	−3.58266	+	6.20535i	−0.194012	+	0.336038i
$342$	6.57274	+	2.20150i	0.355413	+	0.119044i
$343$	12.0510	+	14.0632i	0.650694	+	0.759340i
$344$	−10.0462	−	17.4005i	−0.541654	−	0.938173i
$345$	3.34608	+	8.83601i	0.180147	+	0.475715i
$346$	−1.96574			−0.105679
$347$	29.7689			1.59808			0.799038	−	0.601281i	$-0.205343\pi$
$347$	29.7689			1.59808			0.799038	+	0.601281i	$0.205343\pi$
$348$	12.9116	+	2.10486i	0.692132	+	0.112832i
$349$	−8.66268	−	15.0042i	−0.463703	−	0.803157i	0.535439	−	0.844574i	$-0.320146\pi$
$349$	−8.66268	−	15.0042i	−0.463703	−	0.803157i	−0.999142	+	0.0414169i	$0.986813\pi$
$350$	1.31552	+	0.388893i	0.0703175	+	0.0207872i
$351$	−19.9672	+	12.5852i	−1.06577	+	0.671750i
$352$	10.7191	−	18.5660i	0.571329	−	0.989571i
$353$	−8.68181	+	15.0373i	−0.462086	+	0.800357i	−0.999065	−	0.0432391i	$-0.986232\pi$
$353$	−8.68181	+	15.0373i	−0.462086	+	0.800357i	0.536979	+	0.843596i	$0.319566\pi$
$354$	6.10453	−	7.46919i	0.324452	−	0.396983i
$355$	7.55005	+	13.0771i	0.400715	+	0.694058i
$356$	−1.80256	+	3.12212i	−0.0955355	+	0.165472i
$357$	−0.952974	−	12.7565i	−0.0504367	−	0.675146i
$358$	5.63705	+	9.76366i	0.297927	+	0.516025i
$359$	−0.480637	+	0.832488i	−0.0253671	+	0.0439371i	−0.878430	−	0.477871i	$-0.841409\pi$
$359$	−0.480637	+	0.832488i	−0.0253671	+	0.0439371i	0.853063	+	0.521808i	$0.174742\pi$
$360$	−4.34794	+	3.84430i	−0.229157	+	0.202613i
$361$	−0.429240	−	0.743465i	−0.0225916	−	0.0391297i
$362$	−6.95810			−0.365710
$363$	−10.8845	−	1.77441i	−0.571290	−	0.0931325i
$364$	19.9513	+	5.89798i	1.04573	+	0.309138i
$365$	1.11154	−	1.92524i	0.0581805	−	0.100772i
$366$	2.33595	−	2.85815i	0.122102	−	0.149398i
$367$	−10.3464	+	17.9205i	−0.540078	+	0.935442i	0.458821	+	0.888529i	$0.348272\pi$
$367$	−10.3464	+	17.9205i	−0.540078	+	0.935442i	−0.998899	+	0.0469137i	$0.985061\pi$
$368$	6.70768	+	11.6180i	0.349662	+	0.605633i
$369$	−1.23725	−	0.414410i	−0.0644087	−	0.0215733i
$370$	−4.83467			−0.251342
$371$	−16.0079	+	15.2075i	−0.831087	+	0.789536i
$372$	3.26254	−	3.99187i	0.169155	−	0.206969i
$373$	−6.92705	−	11.9980i	−0.358669	−	0.621233i	0.629070	−	0.777349i	$-0.283436\pi$
$373$	−6.92705	−	11.9980i	−0.358669	−	0.621233i	−0.987739	+	0.156116i	$0.950103\pi$
$374$	6.03165			0.311889
$375$	−1.09609	+	1.34112i	−0.0566017	+	0.0692549i
$376$	−14.5129			−0.748447
$377$	−19.8176			−1.02066
$378$	−1.75407	+	6.90888i	−0.0902197	+	0.355355i
$379$	−32.8112			−1.68540			−0.842700	−	0.538383i	$-0.819035\pi$
$379$	−32.8112			−1.68540			−0.842700	+	0.538383i	$0.819035\pi$
$380$	7.71457			0.395749
$381$	−4.74998	+	5.81183i	−0.243349	+	0.297749i
$382$	−5.50087			−0.281449
$383$	−3.08456	−	5.34262i	−0.157614	−	0.272995i	0.776394	−	0.630248i	$-0.217047\pi$
$383$	−3.08456	−	5.34262i	−0.157614	−	0.272995i	−0.934008	+	0.357253i	$0.883713\pi$
$384$	−12.5566	+	15.3636i	−0.640775	+	0.784018i
$385$	−2.57980	−	10.7198i	−0.131479	−	0.546333i
$386$	−11.4753			−0.584078
$387$	23.3423	−	20.6385i	1.18655	−	1.04911i
$388$	14.6098	+	25.3049i	0.741700	+	1.28466i
$389$	17.3799	−	30.1028i	0.881194	−	1.52627i	0.0311798	−	0.999514i	$-0.490074\pi$
$389$	17.3799	−	30.1028i	0.881194	−	1.52627i	0.850014	−	0.526759i	$-0.176593\pi$
$390$	2.58144	−	3.15852i	0.130716	−	0.159938i
$391$	−7.61371	+	13.1873i	−0.385042	+	0.666912i
$392$	12.0593	−	6.16114i	0.609087	−	0.311185i
$393$	−16.9734	−	2.76703i	−0.856195	−	0.139578i
$394$	3.83879			0.193396
$395$	0.495933	+	0.858981i	0.0249531	+	0.0432200i
$396$	20.5227	+	6.87397i	1.03131	+	0.345430i
$397$	2.98728	−	5.17412i	0.149927	−	0.259682i	−0.781273	−	0.624189i	$-0.785429\pi$
$397$	2.98728	−	5.17412i	0.149927	−	0.259682i	0.931200	+	0.364508i	$0.118763\pi$
$398$	−2.83924	−	4.91771i	−0.142318	−	0.246502i
$399$	16.8755	−	11.4998i	0.844833	−	0.575709i
$400$	−1.22964	+	2.12979i	−0.0614818	+	0.106490i
$401$	9.81882	+	17.0067i	0.490328	+	0.849274i	0.999938	−	0.0111320i	$-0.00354350\pi$
$401$	9.81882	+	17.0067i	0.490328	+	0.849274i	−0.509610	+	0.860406i	$0.670210\pi$
$402$	−4.29553	+	5.25579i	−0.214242	+	0.262135i
$403$	−3.90496	+	6.76359i	−0.194520	+	0.336919i
$404$	−6.81176	+	11.7983i	−0.338898	+	0.586988i
$405$	−7.18432	−	5.42084i	−0.356992	−	0.269364i
$406$	−4.33912	+	4.12218i	−0.215347	+	0.204580i
$407$	19.4294	+	33.6527i	0.963080	+	1.66810i
$408$	−9.23170	−	1.50496i	−0.457037	−	0.0745068i
$409$	23.5646			1.16519			0.582596	−	0.812762i	$-0.302037\pi$
$409$	23.5646			1.16519			0.582596	+	0.812762i	$0.302037\pi$
$410$	0.225510			0.0111372
$411$	4.41965	+	11.6710i	0.218005	+	0.575688i
$412$	−14.2428	−	24.6692i	−0.701690	−	1.21536i
$413$	−6.64948	−	27.6305i	−0.327200	−	1.35961i
$414$	6.35674	−	5.62042i	0.312417	−	0.276228i
$415$	−0.763861	+	1.32305i	−0.0374965	+	0.0649458i
$416$	11.6834	−	20.2362i	0.572826	−	0.992163i
$417$	−8.64736	−	22.8351i	−0.423463	−	1.11824i
$418$	4.81447	+	8.33891i	0.235483	+	0.407869i
$419$	−8.48897	+	14.7033i	−0.414713	+	0.718304i	−0.995398	−	0.0958239i	$-0.969451\pi$
$419$	−8.48897	+	14.7033i	−0.414713	+	0.718304i	0.580685	+	0.814128i	$0.302785\pi$
$420$	0.591002	+	7.91116i	0.0288380	+	0.386025i
$421$	−4.80555	−	8.32346i	−0.234208	−	0.405660i	0.724834	−	0.688923i	$-0.241916\pi$
$421$	−4.80555	−	8.32346i	−0.234208	−	0.405660i	−0.959042	+	0.283263i	$0.908583\pi$
$422$	−4.16042	+	7.20605i	−0.202526	+	0.350785i
$423$	−4.47998	−	22.0552i	−0.217824	−	1.07236i
$424$	8.07242	+	13.9818i	0.392031	+	0.679018i
$425$	−2.79146			−0.135406
$426$	8.58156	−	10.4999i	0.415778	−	0.508724i
$427$	−2.54448	−	10.5731i	−0.123136	−	0.511666i
$428$	7.84854	−	13.5941i	0.379374	−	0.657094i
$429$	−32.3598	−	5.27533i	−1.56234	−	0.254695i
$430$	−2.69251	+	4.66356i	−0.129844	+	0.224897i
$431$	17.4758	+	30.2689i	0.841778	+	1.45800i	0.888390	+	0.459090i	$0.151824\pi$
$431$	17.4758	+	30.2689i	0.841778	+	1.45800i	−0.0466114	+	0.998913i	$0.514842\pi$
$432$	−11.3062	−	5.95530i	−0.543972	−	0.286524i
$433$	−8.29330			−0.398551			−0.199275	−	0.979944i	$-0.563859\pi$
$433$	−8.29330			−0.398551			−0.199275	+	0.979944i	$0.563859\pi$
$434$	0.551867	+	2.29317i	0.0264905	+	0.110076i
$435$	−2.67618	−	7.06700i	−0.128313	−	0.338837i
$436$	−9.30410	−	16.1152i	−0.445585	−	0.771777i
$437$	−24.3091			−1.16286
$438$	−1.97043	−	0.321222i	−0.0941506	−	0.0153486i
$439$	−3.02507			−0.144379			−0.0721893	−	0.997391i	$-0.522999\pi$
$439$	−3.02507			−0.144379			−0.0721893	+	0.997391i	$0.522999\pi$
$440$	−8.06214			−0.384347
$441$	13.0856	+	16.4246i	0.623125	+	0.782123i
$442$	6.57428			0.312706
$443$	−9.45391			−0.449169			−0.224584	−	0.974455i	$-0.572102\pi$
$443$	−9.45391			−0.449169			−0.224584	+	0.974455i	$0.572102\pi$
$444$	−9.90160	−	26.1472i	−0.469909	−	1.24089i
$445$	2.08248			0.0987190
$446$	0.161436	+	0.279615i	0.00764421	+	0.0132402i
$447$	−12.2904	−	2.00360i	−0.581316	−	0.0947669i
$448$	1.39365	+	5.79102i	0.0658438	+	0.273600i
$449$	27.0744			1.27772			0.638860	−	0.769323i	$-0.279406\pi$
$449$	27.0744			1.27772			0.638860	+	0.769323i	$0.279406\pi$
$450$	1.47494	+	0.494021i	0.0695292	+	0.0232884i
$451$	−0.906274	−	1.56971i	−0.0426748	−	0.0739149i
$452$	8.10932	−	14.0458i	0.381430	−	0.660657i
$453$	−6.03446	−	15.9352i	−0.283524	−	0.748703i
$454$	−4.54032	+	7.86406i	−0.213088	+	0.369078i
$455$	−2.81189	−	11.6842i	−0.131823	−	0.547764i
$456$	−5.28810	−	13.9643i	−0.247638	−	0.653939i
$457$	−5.04062			−0.235790			−0.117895	−	0.993026i	$-0.537615\pi$
$457$	−5.04062			−0.235790			−0.117895	+	0.993026i	$0.537615\pi$
$458$	−2.46506	−	4.26961i	−0.115185	−	0.199506i
$459$	−0.562639	−	14.4939i	−0.0262617	−	0.676518i
$460$	4.72177	−	8.17834i	0.220154	−	0.381317i
$461$	−16.0088	−	27.7281i	−0.745605	−	1.29143i	−0.949911	−	0.312519i	$-0.898827\pi$
$461$	−16.0088	−	27.7281i	−0.745605	−	1.29143i	0.204306	−	0.978907i	$-0.434506\pi$
$462$	−8.18257	+	5.57599i	−0.380688	+	0.259418i
$463$	0.486386	−	0.842445i	0.0226043	−	0.0391517i	−0.854502	−	0.519448i	$-0.826138\pi$
$463$	0.486386	−	0.842445i	0.0226043	−	0.0391517i	0.877106	+	0.480296i	$0.159471\pi$
$464$	−5.36477	−	9.29206i	−0.249053	−	0.431373i
$465$	−2.93925	−	0.479160i	−0.136304	−	0.0222205i
$466$	−0.0673940	+	0.116730i	−0.00312197	+	0.00540740i
$467$	18.1325	−	31.4064i	0.839070	−	1.45331i	−0.0516023	−	0.998668i	$-0.516433\pi$
$467$	18.1325	−	31.4064i	0.839070	−	1.45331i	0.890673	−	0.454645i	$-0.150234\pi$
$468$	22.3690	+	7.49237i	1.03401	+	0.346335i
$469$	4.67899	+	19.4426i	0.216056	+	0.897775i
$470$	1.94482	+	3.36853i	0.0897081	+	0.155379i
$471$	11.2275	−	13.7374i	0.517335	−	0.632984i
$472$	−20.7803			−0.956491
$473$	43.2822			1.99012
$474$	0.563689	−	0.689700i	0.0258911	−	0.0316790i
$475$	−2.22814	−	3.85926i	−0.102234	−	0.177075i
$476$	−9.26949	+	8.80605i	−0.424866	+	0.403625i
$477$	−18.7562	+	16.5836i	−0.858789	+	0.759312i
$478$	0.990044	−	1.71481i	0.0452836	−	0.0784334i
$479$	19.4385	−	33.6684i	0.888167	−	1.53835i	0.0461258	−	0.998936i	$-0.485312\pi$
$479$	19.4385	−	33.6684i	0.888167	−	1.53835i	0.842041	−	0.539414i	$-0.181354\pi$
$480$	8.79404	+	1.43362i	0.401391	+	0.0654353i
$481$	21.1773	+	36.6802i	0.965603	+	1.67247i
$482$	2.08328	−	3.60834i	0.0948907	−	0.164355i
$483$	−1.86228	−	24.9285i	−0.0847368	−	1.13429i
$484$	5.51130	+	9.54585i	0.250514	+	0.433902i
$485$	8.43928	−	14.6173i	0.383208	−	0.663736i
$486$	−2.26779	+	7.75780i	−0.102869	+	0.351901i
$487$	18.1746	+	31.4793i	0.823570	+	1.42647i	0.903007	+	0.429625i	$0.141354\pi$
$487$	18.1746	+	31.4793i	0.823570	+	1.42647i	−0.0794371	+	0.996840i	$0.525312\pi$
$488$	−7.95176			−0.359959
$489$	7.55358	+	19.9468i	0.341585	+	0.902024i
$490$	−3.04606	−	1.97340i	−0.137607	−	0.0891493i
$491$	3.11985	−	5.40374i	0.140797	−	0.243867i	−0.787000	−	0.616953i	$-0.788367\pi$
$491$	3.11985	−	5.40374i	0.140797	−	0.243867i	0.927797	+	0.373086i	$0.121700\pi$
$492$	0.461854	+	1.21962i	0.0208220	+	0.0549848i
$493$	6.08941	−	10.5472i	0.274253	−	0.475021i
$494$	5.24759	+	9.08909i	0.236100	+	0.408938i
$495$	−2.48869	−	12.2520i	−0.111858	−	0.550685i
$496$	−4.22842			−0.189862
$497$	−9.34763	−	38.8421i	−0.419299	−	1.74231i
$498$	1.35410	+	0.220747i	0.0606786	+	0.00989191i
$499$	−2.77747	−	4.81072i	−0.124337	−	0.215358i	0.797137	−	0.603799i	$-0.206347\pi$
$499$	−2.77747	−	4.81072i	−0.124337	−	0.215358i	−0.921473	+	0.388441i	$0.873014\pi$
$500$	1.73117			0.0774201
$501$	−8.90647	−	23.5193i	−0.397912	−	1.05077i
$502$	−8.67906			−0.387365
$503$	13.0787			0.583151			0.291576	−	0.956548i	$-0.405820\pi$
$503$	13.0787			0.583151			0.291576	+	0.956548i	$0.405820\pi$
$504$	13.9150	−	6.49264i	0.619825	−	0.289205i
$505$	7.86956			0.350191
$506$	11.7869			0.523993
$507$	−13.0476	−	2.12704i	−0.579465	−	0.0944651i
$508$	7.50215			0.332854
$509$	2.67657	+	4.63596i	0.118637	+	0.205485i	0.919228	−	0.393726i	$-0.128814\pi$
$509$	2.67657	+	4.63596i	0.118637	+	0.205485i	−0.800591	+	0.599212i	$0.795481\pi$
$510$	0.887796	+	2.34441i	0.0393123	+	0.103812i
$511$	−4.26422	+	4.05103i	−0.188638	+	0.179207i
$512$	22.1665			0.979628
$513$	19.5891	−	12.3469i	0.864880	−	0.545130i
$514$	−2.58921	−	4.48464i	−0.114205	−	0.197809i
$515$	−8.22726	+	14.2500i	−0.362536	+	0.627931i
$516$	−30.7361	−	5.01065i	−1.35308	−	0.220581i
$517$	15.6316	−	27.0747i	0.687477	−	1.19075i
$518$	12.2666	+	3.62623i	0.538962	+	0.159327i
$519$	−4.15557	+	5.08453i	−0.182409	+	0.223186i
$520$	−8.78743			−0.385354
$521$	−10.9063	−	18.8903i	−0.477815	−	0.827600i	0.521861	−	0.853030i	$-0.325238\pi$
$521$	−10.9063	−	18.8903i	−0.477815	−	0.827600i	−0.999677	+	0.0254300i	$0.991905\pi$
$522$	−5.08409	+	4.49518i	−0.222525	+	0.196749i
$523$	8.20565	−	14.2126i	0.358808	−	0.621473i	−0.628954	−	0.777442i	$-0.716517\pi$
$523$	8.20565	−	14.2126i	0.358808	−	0.621473i	0.987762	+	0.155969i	$0.0498500\pi$
$524$	8.59435	+	14.8858i	0.375446	+	0.650291i
$525$	3.78690	−	2.58057i	0.165274	−	0.112625i
$526$	−0.601439	+	1.04172i	−0.0262240	+	0.0454212i
$527$	−2.39978	−	4.15655i	−0.104536	−	0.181062i
$528$	−6.28655	−	16.6009i	−0.273587	−	0.722462i
$529$	−3.37857	+	5.85186i	−0.146894	+	0.254429i
$530$	2.16351	−	3.74731i	0.0939769	−	0.162773i
$531$	−6.41464	−	31.5797i	−0.278372	−	1.37044i
$532$	−19.5735	−	5.78629i	−0.848618	−	0.250868i
$533$	−0.987804	−	1.71093i	−0.0427866	−	0.0741085i
$534$	−0.662312	−	1.74897i	−0.0286611	−	0.0756854i
$535$	−9.06734			−0.392015
$536$	14.6223			0.631588
$537$	37.1711	+	6.05969i	1.60405	+	0.261495i
$538$	1.81663	+	3.14649i	0.0783203	+	0.135655i
$539$	−1.49488	+	29.1334i	−0.0643890	+	1.25486i
$540$	0.348930	+	8.98864i	0.0150155	+	0.386809i
$541$	8.77183	−	15.1933i	0.377130	−	0.653209i	−0.613513	−	0.789685i	$-0.710244\pi$
$541$	8.77183	−	15.1933i	0.377130	−	0.653209i	0.990643	+	0.136476i	$0.0435775\pi$
$542$	−0.720405	+	1.24778i	−0.0309440	+	0.0535967i
$543$	−14.7094	+	17.9976i	−0.631241	+	0.772353i
$544$	7.18000	+	12.4361i	0.307840	+	0.533194i
$545$	−5.37447	+	9.30885i	−0.230217	+	0.398747i
$546$	−8.91870	+	6.07761i	−0.381685	+	0.260098i
$547$	−8.72588	−	15.1137i	−0.373092	−	0.646214i	0.616948	−	0.787004i	$-0.288369\pi$
$547$	−8.72588	−	15.1137i	−0.373092	−	0.646214i	−0.990039	+	0.140790i	$0.955036\pi$
$548$	6.23672	−	10.8023i	0.266419	−	0.461452i
$549$	−2.45462	−	12.0842i	−0.104761	−	0.515742i
$550$	1.08038	+	1.87127i	0.0460674	+	0.0797912i
$551$	19.4423			0.828269
$552$	−18.0404	−	2.94097i	−0.767851	−	0.125176i
$553$	−0.614010	−	2.55139i	−0.0261103	−	0.108496i
$554$	1.87522	−	3.24797i	0.0796704	−	0.137993i
$555$	−10.2205	+	12.5052i	−0.433835	+	0.530817i
$556$	−12.2026	+	21.1355i	−0.517504	+	0.896344i
$557$	−6.58901	−	11.4125i	−0.279186	−	0.483564i	0.691997	−	0.721900i	$-0.256731\pi$
$557$	−6.58901	−	11.4125i	−0.279186	−	0.483564i	−0.971183	+	0.238337i	$0.923398\pi$
$558$	0.532376	+	2.62092i	0.0225373	+	0.110952i
$559$	47.1760			1.99533
$560$	4.71729	−	4.48145i	0.199342	−	0.189376i
$561$	12.7509	−	15.6013i	0.538343	−	0.658688i
$562$	3.69812	+	6.40533i	0.155996	+	0.270192i
$563$	45.5663			1.92039			0.960195	−	0.279330i	$-0.0901124\pi$
$563$	45.5663			1.92039			0.960195	+	0.279330i	$0.0901124\pi$
$564$	−14.2349	+	17.4170i	−0.599396	+	0.733390i
$565$	−9.36862			−0.394141
$566$	−4.84872			−0.203807
$567$	14.1622	+	19.1424i	0.594758	+	0.803905i
$568$	−29.2123			−1.22572
$569$	−21.2459			−0.890676			−0.445338	−	0.895363i	$-0.646916\pi$
$569$	−21.2459			−0.890676			−0.445338	+	0.895363i	$0.646916\pi$
$570$	−2.53256	+	3.09871i	−0.106077	+	0.129791i
$571$	−33.6275			−1.40727			−0.703634	−	0.710562i	$-0.748441\pi$
$571$	−33.6275			−1.40727			−0.703634	+	0.710562i	$0.748441\pi$
$572$	16.3851	+	28.3798i	0.685095	+	1.18662i
$573$	−11.6288	+	14.2284i	−0.485801	+	0.594400i
$574$	−0.572167	−	0.169143i	−0.0238818	−	0.00705991i
$575$	−5.45501			−0.227490
$576$	1.34443	+	6.61871i	0.0560180	+	0.275780i
$577$	−2.15113	−	3.72587i	−0.0895527	−	0.155110i	0.817769	−	0.575546i	$-0.195210\pi$
$577$	−2.15113	−	3.72587i	−0.0895527	−	0.155110i	−0.907322	+	0.420436i	$0.861877\pi$
$578$	2.38707	−	4.13453i	0.0992891	−	0.171974i
$579$	−24.2587	+	29.6817i	−1.00816	+	1.23353i
$580$	−3.77645	+	6.54100i	−0.156808	+	0.271600i
$581$	2.93042	−	2.78391i	0.121574	−	0.115496i
$582$	−14.9603	−	2.43886i	−0.620126	−	0.101094i
$583$	−34.7786			−1.44038
$584$	2.15035	+	3.72452i	0.0889823	+	0.154122i
$585$	−2.71258	−	13.3542i	−0.112151	−	0.552128i
$586$	−7.06608	+	12.2388i	−0.291897	+	0.505580i
$587$	6.02889	+	10.4424i	0.248839	+	0.431002i	0.963204	−	0.268771i	$-0.0866176\pi$
$587$	6.02889	+	10.4424i	0.248839	+	0.431002i	−0.714365	+	0.699773i	$0.753284\pi$
$588$	4.43425	−	20.5155i	0.182865	−	0.846047i
$589$	3.83102	−	6.63551i	0.157854	−	0.273412i
$590$	2.78469	+	4.82323i	0.114644	+	0.198569i
$591$	8.11519	−	9.92932i	0.333814	−	0.408438i
$592$	−11.4657	+	19.8593i	−0.471239	+	0.816210i
$593$	−10.6009	+	18.3612i	−0.435325	+	0.754005i	−0.997322	−	0.0731342i	$-0.976700\pi$
$593$	−10.6009	+	18.3612i	−0.435325	+	0.754005i	0.561997	+	0.827139i	$0.310033\pi$
$594$	−9.49832	+	5.98675i	−0.389721	+	0.245639i
$595$	7.08251	+	2.09372i	0.290355	+	0.0858343i
$596$	6.22314	+	10.7788i	0.254910	+	0.441517i
$597$	−18.7222	−	3.05211i	−0.766247	−	0.124915i
$598$	12.8473			0.525366
$599$	−25.8314			−1.05544			−0.527722	−	0.849417i	$-0.676954\pi$
$599$	−25.8314			−1.05544			−0.527722	+	0.849417i	$0.676954\pi$
$600$	−1.18666	−	3.13362i	−0.0484453	−	0.127930i
$601$	19.5434	+	33.8501i	0.797190	+	1.38077i	0.921439	+	0.388523i	$0.127014\pi$
$601$	19.5434	+	33.8501i	0.797190	+	1.38077i	−0.124249	+	0.992251i	$0.539652\pi$
$602$	10.3293	−	9.81291i	0.420992	−	0.399944i
$603$	4.51375	+	22.2214i	0.183814	+	0.904927i
$604$	−8.51543	+	14.7492i	−0.346488	+	0.600135i
$605$	3.18358	−	5.51411i	0.129431	−	0.224181i
$606$	−2.50284	−	6.60926i	−0.101671	−	0.268483i
$607$	11.6034	+	20.0977i	0.470968	+	0.815740i	0.999449	−	0.0332052i	$-0.0105715\pi$
$607$	11.6034	+	20.0977i	0.470968	+	0.815740i	−0.528481	+	0.848945i	$0.677238\pi$
$608$	−11.4622	+	19.8530i	−0.464852	+	0.805147i
$609$	1.48944	+	19.9377i	0.0603554	+	0.807917i
$610$	1.06559	+	1.84565i	0.0431443	+	0.0747282i
$611$	17.0379	−	29.5104i	0.689278	−	1.19386i
$612$	−10.8609	+	9.60288i	−0.439028	+	0.388174i
$613$	1.42443	+	2.46719i	0.0575324	+	0.0996490i	0.893357	−	0.449347i	$-0.148343\pi$
$613$	1.42443	+	2.46719i	0.0575324	+	0.0996490i	−0.835825	+	0.548996i	$0.815010\pi$
$614$	6.05456			0.244342
$615$	0.476728	−	0.583299i	0.0192235	−	0.0235209i
$616$	20.4553	+	6.04698i	0.824169	+	0.243640i
$617$	−14.3988	+	24.9394i	−0.579673	+	1.00402i	0.415844	+	0.909436i	$0.363486\pi$
$617$	−14.3988	+	24.9394i	−0.579673	+	1.00402i	−0.995517	+	0.0945869i	$0.969847\pi$
$618$	14.5845	+	2.37758i	0.586674	+	0.0956404i
$619$	18.2320	−	31.5787i	0.732805	−	1.26926i	−0.222875	−	0.974847i	$-0.571544\pi$
$619$	18.2320	−	31.5787i	0.732805	−	1.26926i	0.955680	−	0.294409i	$-0.0951226\pi$
$620$	1.48826	+	2.57775i	0.0597701	+	0.103525i
$621$	−1.09950	−	28.3237i	−0.0441213	−	1.13659i
$622$	0.530800			0.0212831
$623$	−5.28368	−	1.56196i	−0.211686	−	0.0625785i
$624$	−6.85210	−	18.0944i	−0.274304	−	0.724355i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−5.73365			−0.229163
$627$	31.7470	+	5.17543i	1.26785	+	0.206687i
$628$	−17.7328			−0.707614
$629$	−26.0289			−1.03784
$630$	−3.37168	−	2.35971i	−0.134331	−	0.0940130i
$631$	2.09147			0.0832602			0.0416301	−	0.999133i	$-0.486745\pi$
$631$	2.09147			0.0832602			0.0416301	+	0.999133i	$0.486745\pi$
$632$	−1.91884			−0.0763274
$633$	9.84388	+	25.9948i	0.391259	+	1.03320i
$634$	4.91882			0.195351
$635$	−2.16679	−	3.75299i	−0.0859864	−	0.148933i
$636$	24.6974	+	4.02621i	0.979317	+	0.159650i
$637$	−1.62936	+	31.7543i	−0.0645577	+	1.25815i
$638$	−9.42714			−0.373224
$639$	−9.01750	−	44.3937i	−0.356727	−	1.75619i
$640$	−5.72790	−	9.92102i	−0.226415	−	0.392163i
$641$	−10.4251	+	18.0569i	−0.411769	+	0.713204i	−0.995083	−	0.0990422i	$-0.968422\pi$
$641$	−10.4251	+	18.0569i	−0.411769	+	0.713204i	0.583315	+	0.812246i	$0.301755\pi$
$642$	2.88378	+	7.61521i	0.113814	+	0.300548i
$643$	−19.8691	+	34.4143i	−0.783560	+	1.35717i	0.146295	+	0.989241i	$0.453265\pi$
$643$	−19.8691	+	34.4143i	−0.783560	+	1.35717i	−0.929855	+	0.367925i	$0.880068\pi$
$644$	−18.1143	+	17.2086i	−0.713802	+	0.678114i
$645$	6.37069	+	16.8231i	0.250846	+	0.662409i
$646$	−6.44978			−0.253763
$647$	12.4989	+	21.6487i	0.491381	+	0.851097i	0.999951	−	0.00992365i	$-0.00315885\pi$
$647$	12.4989	+	21.6487i	0.491381	+	0.851097i	−0.508570	+	0.861021i	$0.669826\pi$
$648$	16.0313	−	6.79304i	0.629771	−	0.266856i
$649$	22.3821	−	38.7669i	0.878573	−	1.52173i
$650$	1.17757	+	2.03961i	0.0461881	+	0.0800002i
$651$	7.09809	+	3.42030i	0.278196	+	0.134052i
$652$	10.6591	−	18.4621i	0.417443	−	0.723032i
$653$	9.01252	+	15.6101i	0.352687	+	0.610872i	0.986719	−	0.162434i	$-0.0519346\pi$
$653$	9.01252	+	15.6101i	0.352687	+	0.610872i	−0.634032	+	0.773307i	$0.718601\pi$
$654$	9.52734	+	1.55316i	0.372548	+	0.0607333i
$655$	4.96448	−	8.59873i	0.193978	−	0.335980i
$656$	0.534813	−	0.926323i	0.0208809	−	0.0361669i
$657$	−4.99634	+	4.41759i	−0.194926	+	0.172347i
$658$	−2.40787	−	10.0054i	−0.0938684	−	0.390051i
$659$	−10.2791	−	17.8039i	−0.400417	−	0.693543i	0.593359	−	0.804938i	$-0.297801\pi$
$659$	−10.2791	−	17.8039i	−0.400417	−	0.693543i	−0.993776	+	0.111395i	$0.964468\pi$
$660$	−7.90767	+	9.67541i	−0.307806	+	0.376615i
$661$	19.7603			0.768586			0.384293	−	0.923211i	$-0.374445\pi$
$661$	19.7603			0.768586			0.384293	+	0.923211i	$0.374445\pi$
$662$	−18.3714			−0.714024
$663$	13.8980	−	17.0049i	0.539753	−	0.660414i
$664$	−1.47775	−	2.55953i	−0.0573477	−	0.0993292i
$665$	2.75864	+	11.4630i	0.106975	+	0.444514i
$666$	13.7530	+	4.60650i	0.532920	+	0.178498i
$667$	11.8998	−	20.6111i	0.460762	−	0.798064i
$668$	−12.5682	+	21.7688i	−0.486279	+	0.842259i
$669$	1.06452	+	0.173539i	0.0411567	+	0.00670942i
$670$	−1.95948	−	3.39393i	−0.0757015	−	0.131119i
$671$	8.56469	−	14.8345i	0.330636	−	0.572679i
$672$	−21.2370	−	10.2333i	−0.819236	−	0.394759i
$673$	−4.01350	−	6.95159i	−0.154709	−	0.267964i	0.778244	−	0.627962i	$-0.216111\pi$
$673$	−4.01350	−	6.95159i	−0.154709	−	0.267964i	−0.932953	+	0.359998i	$0.882777\pi$
$674$	−6.50265	+	11.2629i	−0.250473	+	0.433832i
$675$	4.39583	−	2.77067i	0.169196	−	0.106643i
$676$	6.60655	+	11.4429i	0.254098	+	0.440111i
$677$	−32.0276			−1.23092			−0.615460	−	0.788168i	$-0.711030\pi$
$677$	−32.0276			−1.23092			−0.615460	+	0.788168i	$0.711030\pi$
$678$	2.97960	+	7.86824i	0.114431	+	0.302178i
$679$	−32.3759	+	30.7572i	−1.24247	+	1.18035i
$680$	2.70014	−	4.67679i	0.103546	−	0.179347i
$681$	10.7428	+	28.3684i	0.411663	+	1.08708i
$682$	−1.85758	+	3.21742i	−0.0711302	+	0.123201i
$683$	−11.3678	−	19.6895i	−0.434975	−	0.753399i	0.562318	−	0.826921i	$-0.309910\pi$
$683$	−11.3678	−	19.6895i	−0.434975	−	0.753399i	−0.997294	+	0.0735216i	$0.976576\pi$
$684$	−21.9454	−	7.35049i	−0.839105	−	0.281053i
$685$	−7.20522			−0.275297
$686$	6.24835	+	7.29163i	0.238563	+	0.278396i
$687$	−16.2548	−	2.64988i	−0.620159	−	0.101099i
$688$	12.7709	+	22.1199i	0.486887	+	0.843313i
$689$	−37.9074			−1.44416
$690$	1.73491	+	4.58139i	0.0660470	+	0.174411i
$691$	24.6785			0.938815			0.469408	−	0.882982i	$-0.344468\pi$
$691$	24.6785			0.938815			0.469408	+	0.882982i	$0.344468\pi$
$692$	6.56332			0.249500
$693$	−2.87523	+	32.9524i	−0.109221	+	1.25176i
$694$	15.4349			0.585900
$695$	14.0975			0.534749
$696$	14.4286	+	2.35218i	0.546916	+	0.0891590i
$697$	1.21410			0.0459875
$698$	−4.49152	−	7.77955i	−0.170007	−	0.294460i
$699$	0.159460	+	0.421086i	0.00603132	+	0.0159269i
$700$	−4.39233	−	1.29846i	−0.166015	−	0.0490771i
$701$	−32.8193			−1.23957			−0.619785	−	0.784772i	$-0.712780\pi$
$701$	−32.8193			−1.23957			−0.619785	+	0.784772i	$0.712780\pi$
$702$	−10.3528	+	6.52533i	−0.390742	+	0.246283i
$703$	−20.7763	−	35.9856i	−0.783593	−	1.35722i
$704$	−4.69101	+	8.12507i	−0.176799	+	0.306225i
$705$	12.8243	+	2.09064i	0.482992	+	0.0787380i
$706$	−4.50144	+	7.79673i	−0.169414	+	0.293434i
$707$	−19.9667	−	5.90254i	−0.750926	−	0.221988i
$708$	−20.3822	+	24.9385i	−0.766009	+	0.937248i
$709$	−42.2571			−1.58700			−0.793499	−	0.608572i	$-0.791743\pi$
$709$	−42.2571			−1.58700			−0.793499	+	0.608572i	$0.791743\pi$
$710$	3.91463	+	6.78034i	0.146913	+	0.254462i
$711$	−0.592324	−	2.91605i	−0.0222139	−	0.109360i
$712$	−2.01436	+	3.48897i	−0.0754912	+	0.130755i
$713$	−4.68961	−	8.12264i	−0.175627	−	0.304195i
$714$	−0.494108	−	6.61414i	−0.0184915	−	0.247528i
$715$	9.46477	−	16.3935i	0.353962	−	0.613081i
$716$	−18.8213	−	32.5995i	−0.703385	−	1.21830i
$717$	−2.34253	−	6.18592i	−0.0874832	−	0.231017i
$718$	−0.249206	+	0.431638i	−0.00930029	+	0.0161086i
$719$	−4.51490	+	7.82003i	−0.168377	+	0.291638i	−0.937849	−	0.347042i	$-0.887186\pi$
$719$	−4.51490	+	7.82003i	−0.168377	+	0.291638i	0.769472	+	0.638680i	$0.220519\pi$
$720$	5.52719	−	4.88696i	0.205986	−	0.182126i
$721$	31.5625	−	29.9845i	1.17545	−	1.11668i
$722$	−0.222557	−	0.385480i	−0.00828271	−	0.0143461i
$723$	−4.92920	−	13.0166i	−0.183319	−	0.484092i
$724$	23.2321			0.863414
$725$	4.36289			0.162034
$726$	−5.64354	−	0.920017i	−0.209451	−	0.0341450i
$727$	−15.3705	−	26.6225i	−0.570061	−	0.987375i	−0.996559	−	0.0828866i	$-0.973586\pi$
$727$	−15.3705	−	26.6225i	−0.570061	−	0.987375i	0.426498	−	0.904489i	$-0.359747\pi$
$728$	22.2955	+	6.59098i	0.826328	+	0.244278i
$729$	15.2720	+	22.2658i	0.565631	+	0.824659i
$730$	0.576322	−	0.998219i	0.0213306	−	0.0369457i
$731$	−14.4959	+	25.1077i	−0.536152	+	0.928642i
$732$	−7.79941	+	9.54295i	−0.288275	+	0.352717i
$733$	−4.94218	−	8.56010i	−0.182543	−	0.316174i	0.760203	−	0.649686i	$-0.225100\pi$
$733$	−4.94218	−	8.56010i	−0.182543	−	0.316174i	−0.942746	+	0.333512i	$0.891766\pi$
$734$	−5.36452	+	9.29162i	−0.198008	+	0.342960i
$735$	−11.5437	+	3.70710i	−0.425796	+	0.136738i
$736$	14.0310	+	24.3024i	0.517190	+	0.895799i
$737$	−15.7494	+	27.2788i	−0.580138	+	1.00483i
$738$	−0.641503	−	0.214868i	−0.0236140	−	0.00790939i
$739$	4.97735	+	8.62102i	0.183095	+	0.317129i	0.942933	−	0.332983i	$-0.108055\pi$
$739$	4.97735	+	8.62102i	0.183095	+	0.317129i	−0.759838	+	0.650112i	$0.774722\pi$
$740$	16.1423			0.593401
$741$	34.6030	+	5.64103i	1.27117	+	0.207228i
$742$	−8.29994	+	7.88497i	−0.304700	+	0.289466i
$743$	3.72404	−	6.45022i	0.136622	−	0.236636i	−0.789594	−	0.613629i	$-0.789709\pi$
$743$	3.72404	−	6.45022i	0.136622	−	0.236636i	0.926216	+	0.376994i	$0.123042\pi$
$744$	3.64588	−	4.46091i	0.133664	−	0.163545i
$745$	3.59477	−	6.22632i	0.131702	−	0.228115i
$746$	−3.59161	−	6.22085i	−0.131498	−	0.227762i
$747$	3.43354	−	3.03582i	0.125627	−	0.111075i
$748$	−20.1388			−0.736348
$749$	23.0057	+	6.80093i	0.840611	+	0.248501i
$750$	−0.568312	+	0.695356i	−0.0207518	+	0.0253908i
$751$	−18.1334	−	31.4080i	−0.661697	−	1.14609i	−0.980169	−	0.198161i	$-0.936503\pi$
$751$	−18.1334	−	31.4080i	−0.661697	−	1.14609i	0.318472	−	0.947932i	$-0.396830\pi$
$752$	18.4491			0.672771
$753$	−18.3475	+	22.4490i	−0.668620	+	0.818088i
$754$	−10.2752			−0.374202
$755$	9.83779			0.358034
$756$	5.85659	−	23.0678i	0.213002	−	0.838967i
$757$	−9.90893			−0.360146			−0.180073	−	0.983653i	$-0.557633\pi$
$757$	−9.90893			−0.360146			−0.180073	+	0.983653i	$0.557633\pi$
$758$	−17.0123			−0.617916
$759$	24.9176	−	30.4878i	0.904450	−	1.10664i
$760$	8.62102			0.312717
$761$	14.0329	+	24.3058i	0.508694	+	0.881084i	0.999949	+	0.0100683i	$0.00320489\pi$
$761$	14.0329	+	24.3058i	0.508694	+	0.881084i	−0.491255	+	0.871016i	$0.663462\pi$
$762$	−2.46282	+	3.01338i	−0.0892187	+	0.109163i
$763$	20.6182	−	19.5874i	0.746430	−	0.709111i
$764$	18.3666			0.664481
$765$	7.94078	+	2.65972i	0.287099	+	0.0961623i
$766$	−1.59932	−	2.77010i	−0.0577857	−	0.100088i
$767$	24.3956	−	42.2544i	0.880874	−	1.52572i
$768$	−1.57524	+	1.92738i	−0.0568415	+	0.0695483i
$769$	−15.0181	+	26.0121i	−0.541565	+	0.938019i	0.457249	+	0.889339i	$0.348835\pi$
$769$	−15.0181	+	26.0121i	−0.541565	+	0.938019i	−0.998814	+	0.0486801i	$0.984499\pi$
$770$	−1.33760	−	5.55813i	−0.0482039	−	0.200301i
$771$	−17.0734	−	2.78333i	−0.614884	−	0.100239i
$772$	38.3144			1.37897
$773$	12.5815	+	21.7918i	0.452524	+	0.783795i	0.998542	−	0.0539783i	$-0.0171902\pi$
$773$	12.5815	+	21.7918i	0.452524	+	0.783795i	−0.546018	+	0.837774i	$0.683857\pi$
$774$	12.1028	−	10.7009i	0.435025	−	0.384634i
$775$	0.859688	−	1.48902i	0.0308809	−	0.0534873i
$776$	16.3264	+	28.2782i	0.586085	+	1.01513i
$777$	35.3110	−	24.0625i	1.26677	−	0.863239i
$778$	9.01130	−	15.6080i	0.323071	−	0.559575i
$779$	0.969099	+	1.67853i	0.0347216	+	0.0601395i
$780$	−8.61907	+	10.5458i	−0.308612	+	0.377601i
$781$	31.4640	−	54.4972i	1.12587	−	1.95006i
$782$	−3.94764	+	6.83752i	−0.141167	+	0.244509i
$783$	0.879373	+	22.6532i	0.0314262	+	0.809559i
$784$	−15.3300	+	7.83217i	−0.547502	+	0.279721i
$785$	5.12162	+	8.87090i	0.182798	+	0.316616i
$786$	−8.80056	−	1.43468i	−0.313906	−	0.0511733i
$787$	5.16710			0.184187			0.0920935	−	0.995750i	$-0.470644\pi$
$787$	5.16710			0.184187			0.0920935	+	0.995750i	$0.470644\pi$
$788$	−12.8172			−0.456593
$789$	1.42305	+	3.75786i	0.0506620	+	0.133783i
$790$	0.257137	+	0.445374i	0.00914852	+	0.0158457i
$791$	23.7701	+	7.02690i	0.845169	+	0.249848i
$792$	22.9341	+	7.68165i	0.814929	+	0.272956i
$793$	9.33519	−	16.1690i	0.331502	−	0.574179i
$794$	1.54888	−	2.68273i	0.0549676	−	0.0952067i
$795$	−5.11904	−	13.5179i	−0.181554	−	0.479430i
$796$	9.47981	+	16.4195i	0.336003	+	0.581974i
$797$	3.35427	−	5.80977i	0.118814	−	0.205793i	−0.800484	−	0.599355i	$-0.795424\pi$
$797$	3.35427	−	5.80977i	0.118814	−	0.205793i	0.919298	+	0.393562i	$0.128757\pi$
$798$	8.74981	−	5.96253i	0.309740	−	0.211071i
$799$	10.4706	+	18.1355i	0.370422	+	0.641590i
$800$	−2.57213	+	4.45506i	−0.0909386	+	0.157510i
$801$	−5.92397	−	1.98420i	−0.209313	−	0.0701082i
$802$	5.09097	+	8.81782i	0.179768	+	0.311368i
$803$	−9.26442			−0.326934
$804$	14.3422	−	17.5483i	0.505809	−	0.618882i
$805$	13.8405	+	4.09151i	0.487814	+	0.144207i
$806$	−2.02469	+	3.50686i	−0.0713166	+	0.123524i
$807$	11.9790	+	1.95283i	0.421680	+	0.0687428i
$808$	−7.61213	+	13.1846i	−0.267794	+	0.463833i
$809$	−3.33325	−	5.77336i	−0.117191	−	0.202981i	0.801462	−	0.598045i	$-0.204056\pi$
$809$	−3.33325	−	5.77336i	−0.117191	−	0.202981i	−0.918653	+	0.395064i	$0.870722\pi$
$810$	−3.72501	−	2.81066i	−0.130883	−	0.0987565i
$811$	43.9145			1.54205			0.771024	−	0.636806i	$-0.219745\pi$
$811$	43.9145			1.54205			0.771024	+	0.636806i	$0.219745\pi$
$812$	14.4877	−	13.7634i	0.508418	−	0.482999i
$813$	1.70454	+	4.50118i	0.0597807	+	0.157863i
$814$	10.0740	+	17.4486i	0.353093	+	0.611574i
$815$	−12.3144			−0.431353
$816$	11.7355	+	1.91314i	0.410826	+	0.0669734i
$817$	−46.2827			−1.61923
$818$	12.2180			0.427193
$819$	−3.13389	+	35.9169i	−0.109507	+	1.25504i
$820$	−0.752947			−0.0262940
$821$	28.7790			1.00439			0.502196	−	0.864754i	$-0.332525\pi$
$821$	28.7790			1.00439			0.502196	+	0.864754i	$0.332525\pi$
$822$	2.29155	+	6.05131i	0.0799270	+	0.211064i
$823$	−12.5712			−0.438204			−0.219102	−	0.975702i	$-0.570313\pi$
$823$	−12.5712			−0.438204			−0.219102	+	0.975702i	$0.570313\pi$
$824$	−15.9163	−	27.5678i	−0.554469	−	0.960369i
$825$	7.12409	+	1.16138i	0.248029	+	0.0404340i
$826$	−3.44770	−	14.3262i	−0.119961	−	0.498472i
$827$	−30.9917			−1.07769			−0.538844	−	0.842405i	$-0.681139\pi$
$827$	−30.9917			−1.07769			−0.538844	+	0.842405i	$0.681139\pi$
$828$	−21.2243	+	18.7658i	−0.737594	+	0.652156i
$829$	−13.8314	−	23.9566i	−0.480383	−	0.832048i	0.519364	−	0.854553i	$-0.326169\pi$
$829$	−13.8314	−	23.9566i	−0.480383	−	0.832048i	−0.999747	+	0.0225055i	$0.992836\pi$
$830$	−0.396055	+	0.685987i	−0.0137473	+	0.0238110i
$831$	−4.43692	−	11.7166i	−0.153915	−	0.406444i
$832$	−5.11302	+	8.85602i	−0.177262	+	0.307027i
$833$	−16.3994	−	10.6244i	−0.568206	−	0.368115i
$834$	−4.48358	−	11.8398i	−0.155254	−	0.409979i
$835$	14.5199			0.502483
$836$	−16.0748	−	27.8424i	−0.555959	−	0.962950i
$837$	7.90465	+	4.16359i	0.273225	+	0.143915i
$838$	−4.40145	+	7.62354i	−0.152046	+	0.263351i
$839$	−17.3283	−	30.0134i	−0.598238	−	1.03618i	−0.993081	−	0.117430i	$-0.962534\pi$
$839$	−17.3283	−	30.0134i	−0.598238	−	1.03618i	0.394843	−	0.918748i	$-0.370799\pi$
$840$	0.660444	+	8.84071i	0.0227875	+	0.305033i
$841$	4.98259	−	8.63010i	0.171813	−	0.297590i
$842$	−2.49163	−	4.31564i	−0.0858674	−	0.148727i
$843$	24.3857	+	3.97538i	0.839887	+	0.136919i
$844$	13.8910	−	24.0600i	0.478149	−	0.828178i
$845$	3.81624	−	6.60993i	0.131283	−	0.227388i
$846$	−2.32283	−	11.4354i	−0.0798605	−	0.393158i
$847$	−12.2132	+	11.6026i	−0.419652	+	0.398671i
$848$	−10.2618	−	17.7740i	−0.352392	−	0.610362i
$849$	−10.2502	+	12.5416i	−0.351785	+	0.430425i
$850$	−1.44735			−0.0496435
$851$	−50.8652			−1.74364
$852$	−28.6526	+	35.0578i	−0.981622	+	1.20106i
$853$	−14.8192	−	25.6676i	−0.507400	−	0.878842i	−0.999963	−	0.00856569i	$-0.997273\pi$
$853$	−14.8192	−	25.6676i	−0.507400	−	0.878842i	0.492564	−	0.870276i	$-0.336060\pi$
$854$	−1.31929	−	5.48204i	−0.0451452	−	0.187591i
$855$	2.66121	+	13.1013i	0.0910115	+	0.448055i
$856$	8.77073	−	15.1914i	0.299777	−	0.519230i
$857$	−24.9165	+	43.1567i	−0.851133	+	1.47421i	0.0290542	+	0.999578i	$0.490750\pi$
$857$	−24.9165	+	43.1567i	−0.851133	+	1.47421i	−0.880187	+	0.474627i	$0.842583\pi$
$858$	−16.7782	−	2.73521i	−0.572800	−	0.0933786i
$859$	−13.1505	−	22.7773i	−0.448689	−	0.777151i	0.549612	−	0.835420i	$-0.314775\pi$
$859$	−13.1505	−	22.7773i	−0.448689	−	0.777151i	−0.998301	+	0.0582683i	$0.981442\pi$
$860$	8.98989	−	15.5709i	0.306553	−	0.530965i
$861$	−1.64706	+	1.12238i	−0.0561317	+	0.0382507i
$862$	9.06103	+	15.6942i	0.308620	+	0.534545i
$863$	14.6857	−	25.4363i	0.499906	−	0.865862i	−0.500094	−	0.865971i	$-0.666701\pi$
$863$	14.6857	−	25.4363i	0.499906	−	0.865862i	1.00000		0.000108680i	$3.45940e-5\pi$
$864$	−23.6502	−	12.4572i	−0.804596	−	0.423802i
$865$	−1.89564	−	3.28334i	−0.0644535	−	0.111637i
$866$	−4.30000			−0.146120
$867$	−5.64801	−	14.9147i	−0.191816	−	0.506531i
$868$	−1.84260	−	7.65656i	−0.0625421	−	0.259880i
$869$	2.06675	−	3.57971i	0.0701096	−	0.121433i
$870$	−1.38758	−	3.66418i	−0.0470432	−	0.124227i
$871$	−17.1663	+	29.7329i	−0.581657	+	1.00746i
$872$	−10.3973	−	18.0087i	−0.352098	−	0.609851i
$873$	−37.9344	+	33.5403i	−1.28389	+	1.13517i
$874$	−12.6040			−0.426338
$875$	0.619045	+	2.57231i	0.0209275	+	0.0869600i
$876$	6.57897	+	1.07251i	0.222283	+	0.0362368i
$877$	25.4099	+	44.0113i	0.858032	+	1.48615i	0.873803	+	0.486279i	$0.161646\pi$
$877$	25.4099	+	44.0113i	0.858032	+	1.48615i	−0.0157714	+	0.999876i	$0.505020\pi$
$878$	−1.56847			−0.0529333
$879$	16.7189	+	44.1497i	0.563915	+	1.48913i
$880$	10.2488			0.345485
$881$	−57.2561			−1.92901			−0.964504	−	0.264068i	$-0.914936\pi$
$881$	−57.2561			−1.92901			−0.964504	+	0.264068i	$0.914936\pi$
$882$	6.78478	+	8.51599i	0.228455	+	0.286748i
$883$	−13.4051			−0.451118			−0.225559	−	0.974230i	$-0.572421\pi$
$883$	−13.4051			−0.451118			−0.225559	+	0.974230i	$0.572421\pi$
$884$	−21.9506			−0.738277
$885$	18.3625	+	2.99347i	0.617247	+	0.100624i
$886$	−4.90177			−0.164678
$887$	13.6122	+	23.5770i	0.457052	+	0.791637i	0.998804	−	0.0489017i	$-0.0155721\pi$
$887$	13.6122	+	23.5770i	0.457052	+	0.791637i	−0.541752	+	0.840538i	$0.682239\pi$
$888$	−11.0650	−	29.2195i	−0.371318	−	0.980541i
$889$	2.68268	+	11.1473i	0.0899741	+	0.373869i
$890$	1.07975			0.0361932
$891$	−4.59424	+	37.2241i	−0.153913	+	1.24705i
$892$	−0.539011	−	0.933595i	−0.0180474	−	0.0312591i
$893$	−16.7152	+	28.9516i	−0.559354	+	0.968829i
$894$	−6.37246	−	1.03885i	−0.213127	−	0.0347442i
$895$	−10.8720	+	18.8309i	−0.363412	+	0.629448i
$896$	7.09165	+	29.4679i	0.236916	+	0.984453i
$897$	27.1592	−	33.2306i	0.906819	−	1.10954i
$898$	14.0378			0.468448
$899$	3.75073	+	6.49645i	0.125094	+	0.216669i
$900$	−4.92460	−	1.64947i	−0.164153	−	0.0549822i
$901$	11.6479	−	20.1748i	0.388049	−	0.672120i
$902$	−0.469895	−	0.813882i	−0.0156458	−	0.0270993i
$903$	−3.54565	−	47.4621i	−0.117992	−	1.57944i
$904$	9.06215	−	15.6961i	0.301403	−	0.522045i
$905$	−6.70995	−	11.6220i	−0.223046	−	0.386328i
$906$	−3.12881	−	8.26228i	−0.103948	−	0.274496i
$907$	2.71750	−	4.70686i	0.0902333	−	0.156289i	−0.817376	−	0.576105i	$-0.804572\pi$
$907$	2.71750	−	4.70686i	0.0902333	−	0.156289i	0.907609	+	0.419816i	$0.137905\pi$
$908$	15.1595	−	26.2570i	0.503084	−	0.871368i
$909$	−22.3863	−	7.49817i	−0.742507	−	0.248698i
$910$	−1.45794	−	6.05816i	−0.0483302	−	0.200826i
$911$	−19.9220	−	34.5060i	−0.660047	−	1.14323i	−0.980603	−	0.196005i	$-0.937203\pi$
$911$	−19.9220	−	34.5060i	−0.660047	−	1.14323i	0.320556	−	0.947230i	$-0.396130\pi$
$912$	6.72235	+	17.7517i	0.222599	+	0.587819i
$913$	6.36661			0.210704
$914$	−2.61352			−0.0864475
$915$	7.02655	+	1.14548i	0.232291	+	0.0378683i
$916$	8.23049	+	14.2556i	0.271943	+	0.471019i
$917$	−19.0454	+	18.0932i	−0.628934	+	0.597490i
$918$	−0.291723	−	7.51497i	−0.00962830	−	0.248031i
$919$	2.17725	−	3.77110i	0.0718207	−	0.124397i	−0.827879	−	0.560907i	$-0.810452\pi$
$919$	2.17725	−	3.77110i	0.0718207	−	0.124397i	0.899699	+	0.436510i	$0.143786\pi$
$920$	5.27657	−	9.13928i	0.173963	−	0.301313i
$921$	12.7993	−	15.6606i	0.421752	−	0.516033i
$922$	−8.30043	−	14.3768i	−0.273360	−	0.473474i
$923$	34.2946	−	59.3999i	1.12882	−	1.95517i
$924$	27.3204	−	18.6174i	0.898776	−	0.612468i
$925$	−4.66225	−	8.07525i	−0.153294	−	0.265513i
$926$	0.252187	−	0.436800i	0.00828737	−	0.0143541i
$927$	36.9814	−	32.6977i	1.21463	−	1.07393i
$928$	−11.2219	−	19.4370i	−0.368378	−	0.638049i
$929$	34.2963			1.12523			0.562613	−	0.826720i	$-0.309796\pi$
$929$	34.2963			1.12523			0.562613	+	0.826720i	$0.309796\pi$
$930$	−1.52397	−	0.248440i	−0.0499730	−	0.00814667i
$931$	1.59851	−	31.1530i	0.0523890	−	1.02100i
$932$	0.225019	−	0.389744i	0.00737074	−	0.0127665i
$933$	1.12211	−	1.37295i	0.0367362	−	0.0449485i
$934$	9.40152	−	16.2839i	0.307627	−	0.532826i
$935$	5.81655	+	10.0746i	0.190221	+	0.329473i
$936$	24.9973	+	8.37271i	0.817064	+	0.273671i
$937$	12.8590			0.420084			0.210042	−	0.977692i	$-0.432640\pi$
$937$	12.8590			0.420084			0.210042	+	0.977692i	$0.432640\pi$
$938$	2.42602	+	10.0808i	0.0792122	+	0.329150i
$939$	−12.1209	+	14.8305i	−0.395551	+	0.483976i
$940$	−6.49349	−	11.2471i	−0.211794	−	0.366838i
$941$	30.2626			0.986534			0.493267	−	0.869878i	$-0.335803\pi$
$941$	30.2626			0.986534			0.493267	+	0.869878i	$0.335803\pi$
$942$	5.82135	−	7.12270i	0.189670	−	0.232070i
$943$	2.37258			0.0772618
$944$	26.4163			0.859779
$945$	−13.2313	+	3.73270i	−0.430414	+	0.121425i
$946$	22.4414			0.729634
$947$	−49.2208			−1.59946			−0.799730	−	0.600360i	$-0.795024\pi$
$947$	−49.2208			−1.59946			−0.799730	+	0.600360i	$0.795024\pi$
$948$	−1.88208	+	2.30281i	−0.0611270	+	0.0747918i
$949$	−10.0979			−0.327791
$950$	−1.15527	−	2.00099i	−0.0374820	−	0.0649207i
$951$	10.3984	−	12.7229i	0.337190	−	0.412568i
$952$	−10.3586	+	9.84075i	−0.335725	+	0.318940i
$953$	23.7257			0.768552			0.384276	−	0.923218i	$-0.374451\pi$
$953$	23.7257			0.768552			0.384276	+	0.923218i	$0.374451\pi$
$954$	−9.72494	+	8.59846i	−0.314856	+	0.278385i
$955$	−5.30469	−	9.18799i	−0.171656	−	0.297316i
$956$	−3.30562	+	5.72549i	−0.106911	+	0.185176i
$957$	−19.9289	+	24.3840i	−0.644211	+	0.788223i
$958$	10.0787	−	17.4568i	0.325627	−	0.564003i
$959$	18.2811	+	5.40425i	0.590329	+	0.174512i
$960$	−3.84855	−	0.627396i	−0.124211	−	0.0202491i
$961$	−28.0437			−0.904637
$962$	10.9803	+	19.0184i	0.354018	+	0.613177i
$963$	25.7936	+	8.63942i	0.831188	+	0.278401i
$964$	−6.95576	+	12.0477i	−0.224030	+	0.388031i
$965$	−11.0661	−	19.1670i	−0.356229	−	0.617007i
$966$	−0.965577	−	12.9252i	−0.0310669	−	0.415862i
$967$	8.60234	−	14.8997i	0.276632	−	0.479141i	−0.693913	−	0.720059i	$-0.744115\pi$
$967$	8.60234	−	14.8997i	0.276632	−	0.479141i	0.970546	+	0.240917i	$0.0774482\pi$
$968$	6.15887	+	10.6675i	0.197954	+	0.342866i
$969$	−13.6348	+	16.6828i	−0.438013	+	0.535930i
$970$	4.37569	−	7.57892i	0.140495	−	0.243344i
$971$	17.7098	−	30.6742i	0.568333	−	0.984382i	−0.428398	−	0.903590i	$-0.640922\pi$
$971$	17.7098	−	30.6742i	0.568333	−	0.984382i	0.996731	−	0.0807916i	$-0.0257448\pi$
$972$	7.57184	−	25.9022i	0.242867	−	0.830813i
$973$	−35.7683	−	10.5738i	−1.14668	−	0.338980i
$974$	9.42337	+	16.3218i	0.301944	+	0.522983i
$975$	7.76499	+	1.26586i	0.248679	+	0.0405399i
$976$	10.1084			0.323563
$977$	−37.6967			−1.20602			−0.603012	−	0.797732i	$-0.706033\pi$
$977$	−37.6967			−1.20602			−0.603012	+	0.797732i	$0.706033\pi$
$978$	3.91646	+	10.3422i	0.125235	+	0.330708i
$979$	−4.33925	−	7.51581i	−0.138683	−	0.240206i
$980$	10.1704	+	6.58891i	0.324880	+	0.210475i
$981$	24.1581	−	21.3598i	0.771309	−	0.681966i
$982$	1.61761	−	2.80179i	0.0516201	−	0.0894087i
$983$	−12.9760	+	22.4751i	−0.413871	+	0.716845i	−0.995309	−	0.0967450i	$-0.969157\pi$
$983$	−12.9760	+	22.4751i	−0.413871	+	0.716845i	0.581438	+	0.813591i	$0.302490\pi$
$984$	0.516122	+	1.36292i	0.0164534	+	0.0434485i
$985$	3.70189	+	6.41186i	0.117952	+	0.204299i
$986$	3.15730	−	5.46861i	0.100549	−	0.174156i
$987$	−30.9699	−	14.9232i	−0.985783	−	0.475012i
$988$	−17.5210	−	30.3472i	−0.557416	−	0.965473i
$989$	−28.3277	+	49.0650i	−0.900768	+	1.56018i
$990$	−1.29036	−	6.35254i	−0.0410104	−	0.201897i
$991$	19.7117	+	34.1418i	0.626164	+	1.08455i	0.988314	+	0.152429i	$0.0487094\pi$
$991$	19.7117	+	34.1418i	0.626164	+	1.08455i	−0.362150	+	0.932120i	$0.617957\pi$
$992$	−8.84493			−0.280827
$993$	−38.8370	+	47.5189i	−1.23246	+	1.50797i
$994$	−4.84666	−	20.1393i	−0.153727	−	0.638780i
$995$	5.47597	−	9.48465i	0.173600	−	0.300684i
$996$	−4.52114	−	0.737043i	−0.143258	−	0.0233541i
$997$	18.6909	−	32.3736i	0.591947	−	1.02528i	−0.402023	−	0.915630i	$-0.631693\pi$
$997$	18.6909	−	32.3736i	0.591947	−	1.02528i	0.993970	−	0.109653i	$-0.0349739\pi$
$998$	−1.44009	−	2.49432i	−0.0455854	−	0.0789562i
$999$	40.9889	−	25.8351i	1.29683	−	0.817388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.b.121.8	yes	24
3.2	odd	2		945.2.l.b.226.5		24
7.4	even	3		315.2.k.b.256.5	yes	24
9.2	odd	6		945.2.k.b.856.8		24
9.7	even	3		315.2.k.b.16.5	✓	24
21.11	odd	6		945.2.k.b.361.8		24
63.11	odd	6		945.2.l.b.46.5		24
63.25	even	3	inner	315.2.l.b.151.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.5	✓	24	9.7	even	3
315.2.k.b.256.5	yes	24	7.4	even	3
315.2.l.b.121.8	yes	24	1.1	even	1	trivial
315.2.l.b.151.8	yes	24	63.25	even	3	inner
945.2.k.b.361.8		24	21.11	odd	6
945.2.k.b.856.8		24	9.2	odd	6
945.2.l.b.46.5		24	63.11	odd	6
945.2.l.b.226.5		24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.518491 q^{2} +(1.09609 - 1.34112i) q^{3} -1.73117 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.568312 - 0.695356i) q^{6} +(-0.619045 - 2.57231i) q^{7} -1.93458 q^{8} +(-0.597182 - 2.93996i) q^{9} +O(q^{10})\)	\(q+0.518491 q^{2} +(1.09609 - 1.34112i) q^{3} -1.73117 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.568312 - 0.695356i) q^{6} +(-0.619045 - 2.57231i) q^{7} -1.93458 q^{8} +(-0.597182 - 2.93996i) q^{9} +(0.259245 + 0.449026i) q^{10} +(2.08370 - 3.60907i) q^{11} +(-1.89751 + 2.32170i) q^{12} +(2.27115 - 3.93375i) q^{13} +(-0.320969 - 1.33372i) q^{14} +(1.70948 + 0.278682i) q^{15} +2.45927 q^{16} +(1.39573 + 2.41747i) q^{17} +(-0.309633 - 1.52434i) q^{18} +(-2.22814 + 3.85926i) q^{19} +(-0.865584 - 1.49923i) q^{20} +(-4.12829 - 1.98927i) q^{21} +(1.08038 - 1.87127i) q^{22} +(2.72751 + 4.72418i) q^{23} +(-2.12047 + 2.59449i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.17757 - 2.03961i) q^{26} +(-4.59739 - 2.42157i) q^{27} +(1.07167 + 4.45310i) q^{28} +(-2.18145 - 3.77837i) q^{29} +(0.886352 + 0.144494i) q^{30} -1.71938 q^{31} +5.14426 q^{32} +(-2.55626 - 6.75033i) q^{33} +(0.723673 + 1.25344i) q^{34} +(1.91816 - 1.82226i) q^{35} +(1.03382 + 5.08956i) q^{36} +(-4.66225 + 8.07525i) q^{37} +(-1.15527 + 2.00099i) q^{38} +(-2.78623 - 7.35761i) q^{39} +(-0.967288 - 1.67539i) q^{40} +(0.217468 - 0.376665i) q^{41} +(-2.14048 - 1.03142i) q^{42} +(5.19296 + 8.99448i) q^{43} +(-3.60723 + 6.24790i) q^{44} +(2.24749 - 1.98716i) q^{45} +(1.41419 + 2.44944i) q^{46} +7.50186 q^{47} +(2.69558 - 3.29817i) q^{48} +(-6.23357 + 3.18475i) q^{49} +(-0.259245 + 0.449026i) q^{50} +(4.77195 + 0.777930i) q^{51} +(-3.93174 + 6.80997i) q^{52} +(-4.17271 - 7.22734i) q^{53} +(-2.38371 - 1.25556i) q^{54} +4.16739 q^{55} +(1.19759 + 4.97633i) q^{56} +(2.73347 + 7.21828i) q^{57} +(-1.13106 - 1.95905i) q^{58} +10.7415 q^{59} +(-2.95940 - 0.482446i) q^{60} +4.11034 q^{61} -0.891481 q^{62} +(-7.19281 + 3.35610i) q^{63} -2.25129 q^{64} +4.54230 q^{65} +(-1.32540 - 3.49999i) q^{66} -7.55841 q^{67} +(-2.41624 - 4.18505i) q^{68} +(9.32525 + 1.52022i) q^{69} +(0.994551 - 0.944827i) q^{70} +15.1001 q^{71} +(1.15529 + 5.68758i) q^{72} +(-1.11154 - 1.92524i) q^{73} +(-2.41733 + 4.18695i) q^{74} +(0.613396 + 1.61980i) q^{75} +(3.85729 - 6.68102i) q^{76} +(-10.5735 - 3.12574i) q^{77} +(-1.44463 - 3.81485i) q^{78} +0.991866 q^{79} +(1.22964 + 2.12979i) q^{80} +(-8.28675 + 3.51138i) q^{81} +(0.112755 - 0.195298i) q^{82} +(0.763861 + 1.32305i) q^{83} +(7.14677 + 3.44376i) q^{84} +(-1.39573 + 2.41747i) q^{85} +(2.69251 + 4.66356i) q^{86} +(-7.45829 - 1.21586i) q^{87} +(-4.03107 + 6.98202i) q^{88} +(1.04124 - 1.80348i) q^{89} +(1.16530 - 1.03032i) q^{90} +(-11.5248 - 3.40694i) q^{91} +(-4.72177 - 8.17834i) q^{92} +(-1.88459 + 2.30588i) q^{93} +3.88965 q^{94} -4.45629 q^{95} +(5.63857 - 6.89905i) q^{96} +(-8.43928 - 14.6173i) q^{97} +(-3.23205 + 1.65126i) q^{98} +(-11.8549 - 3.97072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9}+O(q^{10}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9	\( 24 q + 2 q^{2} - 5 q^{3} + 14 q^{4} + 12 q^{5} + 3 q^{6} - 11 q^{7} + 12 q^{8} - 3 q^{9} + q^{10} + q^{11} - 7 q^{12} - 4 q^{13} + 8 q^{14} - q^{15} + 10 q^{16} - 7 q^{17} + 18 q^{18} - 2 q^{19} + 7 q^{20} - 17 q^{21} + 19 q^{22} + q^{23} + 18 q^{24} - 12 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 16 q^{31} - 34 q^{32} + 7 q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} - 35 q^{38} - 17 q^{39} + 6 q^{40} + 20 q^{41} - 36 q^{42} + 31 q^{43} - 7 q^{44} + 6 q^{45} - 10 q^{46} + 62 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} + 14 q^{51} - 4 q^{52} + 8 q^{53} - 51 q^{54} + 2 q^{55} + 5 q^{57} + 45 q^{58} + 42 q^{59} - 23 q^{60} - 10 q^{61} + 14 q^{62} + 18 q^{63} - 56 q^{64} - 8 q^{65} + 4 q^{66} - 86 q^{67} - 48 q^{68} + 26 q^{69} - 5 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{73} + 9 q^{74} + 4 q^{75} - 13 q^{76} + 35 q^{77} + 19 q^{78} - 80 q^{79} + 5 q^{80} + 21 q^{81} + 5 q^{82} - 60 q^{83} + 35 q^{84} + 7 q^{85} + 12 q^{86} + 68 q^{87} + 50 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} + 7 q^{93} + 22 q^{94} - 4 q^{95} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 2 * q^2 - 5 * q^3 + 14 * q^4 + 12 * q^5 + 3 * q^6 - 11 * q^7 + 12 * q^8 - 3 * q^9 + q^10 + q^11 - 7 * q^12 - 4 * q^13 + 8 * q^14 - q^15 + 10 * q^16 - 7 * q^17 + 18 * q^18 - 2 * q^19 + 7 * q^20 - 17 * q^21 + 19 * q^22 + q^23 + 18 * q^24 - 12 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 16 * q^31 - 34 * q^32 + 7 * q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 - 35 * q^38 - 17 * q^39 + 6 * q^40 + 20 * q^41 - 36 * q^42 + 31 * q^43 - 7 * q^44 + 6 * q^45 - 10 * q^46 + 62 * q^47 - 36 * q^48 - 11 * q^49 - q^50 + 14 * q^51 - 4 * q^52 + 8 * q^53 - 51 * q^54 + 2 * q^55 + 5 * q^57 + 45 * q^58 + 42 * q^59 - 23 * q^60 - 10 * q^61 + 14 * q^62 + 18 * q^63 - 56 * q^64 - 8 * q^65 + 4 * q^66 - 86 * q^67 - 48 * q^68 + 26 * q^69 - 5 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^73 + 9 * q^74 + 4 * q^75 - 13 * q^76 + 35 * q^77 + 19 * q^78 - 80 * q^79 + 5 * q^80 + 21 * q^81 + 5 * q^82 - 60 * q^83 + 35 * q^84 + 7 * q^85 + 12 * q^86 + 68 * q^87 + 50 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 + 7 * q^93 + 22 * q^94 - 4 * q^95 + 6 * q^97 - 15 * q^98 - q^99

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