LMFDB - Embedded newform 435.2.q.c.191.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(41,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 1]))

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

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

chi := DirichletCharacter("435.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.q (of order $4$, 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:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			191.17
Character	$\chi$	$=$	435.191
Dual form			435.2.q.c.41.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82725 + 1.82725i) q^{2} +(1.68768 + 0.389527i) q^{3} +4.67770i q^{4} -1.00000 q^{5} +(2.37206 + 3.79558i) q^{6} +1.47752 q^{7} +(-4.89284 + 4.89284i) q^{8} +(2.69654 + 1.31480i) q^{9} +O(q^{10})$	\(q+(1.82725 + 1.82725i) q^{2} +(1.68768 + 0.389527i) q^{3} +4.67770i q^{4} -1.00000 q^{5} +(2.37206 + 3.79558i) q^{6} +1.47752 q^{7} +(-4.89284 + 4.89284i) q^{8} +(2.69654 + 1.31480i) q^{9} +(-1.82725 - 1.82725i) q^{10} +(-4.06330 - 4.06330i) q^{11} +(-1.82209 + 7.89447i) q^{12} -3.06893i q^{13} +(2.69980 + 2.69980i) q^{14} +(-1.68768 - 0.389527i) q^{15} -8.52551 q^{16} +(-2.44077 - 2.44077i) q^{17} +(2.52479 + 7.32972i) q^{18} +(5.06551 - 5.06551i) q^{19} -4.67770i q^{20} +(2.49358 + 0.575534i) q^{21} -14.8493i q^{22} +4.53932i q^{23} +(-10.1635 + 6.35166i) q^{24} +1.00000 q^{25} +(5.60771 - 5.60771i) q^{26} +(4.03875 + 3.26933i) q^{27} +6.91140i q^{28} +(-3.32624 + 4.23511i) q^{29} +(-2.37206 - 3.79558i) q^{30} +(-6.46434 + 6.46434i) q^{31} +(-5.79257 - 5.79257i) q^{32} +(-5.27479 - 8.44032i) q^{33} -8.91981i q^{34} -1.47752 q^{35} +(-6.15022 + 12.6136i) q^{36} +(2.96880 + 2.96880i) q^{37} +18.5119 q^{38} +(1.19543 - 5.17937i) q^{39} +(4.89284 - 4.89284i) q^{40} +(-1.91239 + 1.91239i) q^{41} +(3.50476 + 5.60805i) q^{42} +(-1.94725 + 1.94725i) q^{43} +(19.0069 - 19.0069i) q^{44} +(-2.69654 - 1.31480i) q^{45} +(-8.29449 + 8.29449i) q^{46} +(5.96413 - 5.96413i) q^{47} +(-14.3883 - 3.32092i) q^{48} -4.81693 q^{49} +(1.82725 + 1.82725i) q^{50} +(-3.16850 - 5.06999i) q^{51} +14.3555 q^{52} -4.16479i q^{53} +(1.40592 + 13.3537i) q^{54} +(4.06330 + 4.06330i) q^{55} +(-7.22927 + 7.22927i) q^{56} +(10.5221 - 6.57581i) q^{57} +(-13.8165 + 1.66073i) q^{58} +4.55159i q^{59} +(1.82209 - 7.89447i) q^{60} +(7.54268 - 7.54268i) q^{61} -23.6240 q^{62} +(3.98419 + 1.94264i) q^{63} -4.11797i q^{64} +3.06893i q^{65} +(5.78422 - 25.0610i) q^{66} -10.9993i q^{67} +(11.4172 - 11.4172i) q^{68} +(-1.76819 + 7.66093i) q^{69} +(-2.69980 - 2.69980i) q^{70} -3.37252 q^{71} +(-19.6268 + 6.76065i) q^{72} +(-1.11203 - 1.11203i) q^{73} +10.8495i q^{74} +(1.68768 + 0.389527i) q^{75} +(23.6950 + 23.6950i) q^{76} +(-6.00361 - 6.00361i) q^{77} +(11.6484 - 7.27967i) q^{78} +(3.77896 - 3.77896i) q^{79} +8.52551 q^{80} +(5.54263 + 7.09079i) q^{81} -6.98885 q^{82} +6.93647i q^{83} +(-2.69218 + 11.6642i) q^{84} +(2.44077 + 2.44077i) q^{85} -7.11625 q^{86} +(-7.26332 + 5.85185i) q^{87} +39.7622 q^{88} +(-3.53060 - 3.53060i) q^{89} +(-2.52479 - 7.32972i) q^{90} -4.53440i q^{91} -21.2336 q^{92} +(-13.4278 + 8.39172i) q^{93} +21.7959 q^{94} +(-5.06551 + 5.06551i) q^{95} +(-7.51965 - 12.0324i) q^{96} +(-2.64311 - 2.64311i) q^{97} +(-8.80176 - 8.80176i) q^{98} +(-5.61443 - 16.2992i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8}+O(q^{10}) $ 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8	$ 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8} + 4 q^{10} - 12 q^{11} + 10 q^{12} + 28 q^{14} - 6 q^{15} - 60 q^{16} - 20 q^{17} - 28 q^{18} + 16 q^{19} + 12 q^{21} + 24 q^{24} + 36 q^{25} + 4 q^{26} + 30 q^{27} - 28 q^{29} - 8 q^{30} - 8 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{35} - 28 q^{36} - 4 q^{37} + 24 q^{38} - 40 q^{39} - 4 q^{40} + 48 q^{41} - 8 q^{42} + 4 q^{43} + 16 q^{44} + 20 q^{46} - 20 q^{47} - 14 q^{48} + 28 q^{49} - 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} - 84 q^{56} + 28 q^{57} - 64 q^{58} - 10 q^{60} + 20 q^{61} + 8 q^{62} + 32 q^{63} + 40 q^{66} + 60 q^{68} + 36 q^{69} - 28 q^{70} - 16 q^{71} - 132 q^{72} + 8 q^{73} + 6 q^{75} + 16 q^{76} + 32 q^{77} + 48 q^{78} + 12 q^{79} + 60 q^{80} - 60 q^{81} + 56 q^{82} + 44 q^{84} + 20 q^{85} + 8 q^{86} + 22 q^{87} - 24 q^{88} + 20 q^{89} + 28 q^{90} - 16 q^{92} + 24 q^{93} + 52 q^{94} - 16 q^{95} - 8 q^{96} + 4 q^{97} - 8 q^{98} - 48 q^{99}+O(q^{100}) $ 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8 + 4 * q^10 - 12 * q^11 + 10 * q^12 + 28 * q^14 - 6 * q^15 - 60 * q^16 - 20 * q^17 - 28 * q^18 + 16 * q^19 + 12 * q^21 + 24 * q^24 + 36 * q^25 + 4 * q^26 + 30 * q^27 - 28 * q^29 - 8 * q^30 - 8 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^35 - 28 * q^36 - 4 * q^37 + 24 * q^38 - 40 * q^39 - 4 * q^40 + 48 * q^41 - 8 * q^42 + 4 * q^43 + 16 * q^44 + 20 * q^46 - 20 * q^47 - 14 * q^48 + 28 * q^49 - 4 * q^50 - 44 * q^52 - 24 * q^54 + 12 * q^55 - 84 * q^56 + 28 * q^57 - 64 * q^58 - 10 * q^60 + 20 * q^61 + 8 * q^62 + 32 * q^63 + 40 * q^66 + 60 * q^68 + 36 * q^69 - 28 * q^70 - 16 * q^71 - 132 * q^72 + 8 * q^73 + 6 * q^75 + 16 * q^76 + 32 * q^77 + 48 * q^78 + 12 * q^79 + 60 * q^80 - 60 * q^81 + 56 * q^82 + 44 * q^84 + 20 * q^85 + 8 * q^86 + 22 * q^87 - 24 * q^88 + 20 * q^89 + 28 * q^90 - 16 * q^92 + 24 * q^93 + 52 * q^94 - 16 * q^95 - 8 * q^96 + 4 * q^97 - 8 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.82725	+	1.82725i	1.29206	+	1.29206i	0.933509	+	0.358554i	$0.116730\pi$
$2$	1.82725	+	1.82725i	1.29206	+	1.29206i	0.358554	+	0.933509i	$0.383270\pi$
$3$	1.68768	+	0.389527i	0.974383	+	0.224894i
$3$	1.68768	+	0.389527i	0.974383	+	0.224894i
$4$			4.67770i			2.33885i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	2.37206	+	3.79558i	0.968388	+	1.54954i
$7$	1.47752			0.558450			0.279225	−	0.960226i	$-0.409922\pi$
$7$	1.47752			0.558450			0.279225	+	0.960226i	$0.409922\pi$
$8$	−4.89284	+	4.89284i	−1.72988	+	1.72988i
$9$	2.69654	+	1.31480i	0.898846	+	0.438265i
$10$	−1.82725	−	1.82725i	−0.577828	−	0.577828i
$11$	−4.06330	−	4.06330i	−1.22513	−	1.22513i	−0.965784	−	0.259347i	$-0.916493\pi$
$11$	−4.06330	−	4.06330i	−1.22513	−	1.22513i	−0.259347	−	0.965784i	$-0.583507\pi$
$12$	−1.82209	+	7.89447i	−0.525993	+	2.27894i
$13$		−	3.06893i		−	0.851167i	−0.904919	−	0.425584i	$-0.860069\pi$
$13$		−	3.06893i		−	0.851167i	0.904919	−	0.425584i	$-0.139931\pi$
$14$	2.69980	+	2.69980i	0.721553	+	0.721553i
$15$	−1.68768	−	0.389527i	−0.435757	−	0.100575i
$16$	−8.52551			−2.13138
$17$	−2.44077	−	2.44077i	−0.591974	−	0.591974i	0.346191	−	0.938164i	$-0.387475\pi$
$17$	−2.44077	−	2.44077i	−0.591974	−	0.591974i	−0.938164	+	0.346191i	$0.887475\pi$
$18$	2.52479	+	7.32972i	0.595099	+	1.72763i
$19$	5.06551	−	5.06551i	1.16211	−	1.16211i	0.178094	−	0.984013i	$-0.443007\pi$
$19$	5.06551	−	5.06551i	1.16211	−	1.16211i	0.984013	−	0.178094i	$-0.0569932\pi$
$20$		−	4.67770i		−	1.04597i
$21$	2.49358	+	0.575534i	0.544144	+	0.125592i
$22$		−	14.8493i		−	3.16589i
$23$			4.53932i			0.946514i	0.880924	+	0.473257i	$0.156922\pi$
$23$			4.53932i			0.946514i	−0.880924	+	0.473257i	$0.843078\pi$
$24$	−10.1635	+	6.35166i	−2.07461	+	1.29653i
$25$	1.00000			0.200000
$26$	5.60771	−	5.60771i	1.09976	−	1.09976i
$27$	4.03875	+	3.26933i	0.777257	+	0.629183i
$28$			6.91140i			1.30613i
$29$	−3.32624	+	4.23511i	−0.617667	+	0.786439i
$29$	−3.32624	+	4.23511i	−0.617667	+	0.786439i
$30$	−2.37206	−	3.79558i	−0.433076	−	0.692976i
$31$	−6.46434	+	6.46434i	−1.16103	+	1.16103i	−0.176780	+	0.984250i	$0.556568\pi$
$31$	−6.46434	+	6.46434i	−1.16103	+	1.16103i	−0.984250	+	0.176780i	$0.943432\pi$
$32$	−5.79257	−	5.79257i	−1.02399	−	1.02399i
$33$	−5.27479	−	8.44032i	−0.918223	−	1.46927i
$34$		−	8.91981i		−	1.52973i
$35$	−1.47752			−0.249746
$36$	−6.15022	+	12.6136i	−1.02504	+	2.10227i
$37$	2.96880	+	2.96880i	0.488067	+	0.488067i	0.907696	−	0.419629i	$-0.137840\pi$
$37$	2.96880	+	2.96880i	0.488067	+	0.488067i	−0.419629	+	0.907696i	$0.637840\pi$
$38$	18.5119			3.00303
$39$	1.19543	−	5.17937i	0.191422	−	0.829363i
$40$	4.89284	−	4.89284i	0.773626	−	0.773626i
$41$	−1.91239	+	1.91239i	−0.298666	+	0.298666i	−0.840491	−	0.541825i	$-0.817733\pi$
$41$	−1.91239	+	1.91239i	−0.298666	+	0.298666i	0.541825	+	0.840491i	$0.317733\pi$
$42$	3.50476	+	5.60805i	0.540796	+	0.865341i
$43$	−1.94725	+	1.94725i	−0.296954	+	0.296954i	−0.839819	−	0.542866i	$-0.817339\pi$
$43$	−1.94725	+	1.94725i	−0.296954	+	0.296954i	0.542866	+	0.839819i	$0.317339\pi$
$44$	19.0069	−	19.0069i	2.86540	−	2.86540i
$45$	−2.69654	−	1.31480i	−0.401976	−	0.195998i
$46$	−8.29449	+	8.29449i	−1.22296	+	1.22296i
$47$	5.96413	−	5.96413i	0.869957	−	0.869957i	−0.122510	−	0.992467i	$-0.539094\pi$
$47$	5.96413	−	5.96413i	0.869957	−	0.869957i	0.992467	+	0.122510i	$0.0390944\pi$
$48$	−14.3883	−	3.32092i	−2.07678	−	0.479333i
$49$	−4.81693			−0.688133
$50$	1.82725	+	1.82725i	0.258413	+	0.258413i
$51$	−3.16850	−	5.06999i	−0.443678	−	0.709940i
$52$	14.3555			1.99075
$53$		−	4.16479i		−	0.572078i	−0.958218	−	0.286039i	$-0.907661\pi$
$53$		−	4.16479i		−	0.572078i	0.958218	−	0.286039i	$-0.0923387\pi$
$54$	1.40592	+	13.3537i	0.191322	+	1.81721i
$55$	4.06330	+	4.06330i	0.547895	+	0.547895i
$56$	−7.22927	+	7.22927i	−0.966052	+	0.966052i
$57$	10.5221	−	6.57581i	1.39369	−	0.870988i
$58$	−13.8165	+	1.66073i	−1.81419	+	0.218064i
$59$			4.55159i			0.592567i	0.955100	+	0.296283i	$0.0957473\pi$
$59$			4.55159i			0.592567i	−0.955100	+	0.296283i	$0.904253\pi$
$60$	1.82209	−	7.89447i	0.235231	−	1.01917i
$61$	7.54268	−	7.54268i	0.965742	−	0.965742i	−0.0336907	−	0.999432i	$-0.510726\pi$
$61$	7.54268	−	7.54268i	0.965742	−	0.965742i	0.999432	+	0.0336907i	$0.0107261\pi$
$62$	−23.6240			−3.00025
$63$	3.98419	+	1.94264i	0.501961	+	0.244749i
$64$		−	4.11797i		−	0.514746i
$65$			3.06893i			0.380654i
$66$	5.78422	−	25.0610i	0.711989	−	3.08479i
$67$		−	10.9993i		−	1.34378i	−0.740653	−	0.671888i	$-0.765484\pi$
$67$		−	10.9993i		−	1.34378i	0.740653	−	0.671888i	$-0.234516\pi$
$68$	11.4172	−	11.4172i	1.38454	−	1.38454i
$69$	−1.76819	+	7.66093i	−0.212865	+	0.922268i
$70$	−2.69980	−	2.69980i	−0.322688	−	0.322688i
$71$	−3.37252			−0.400245			−0.200122	−	0.979771i	$-0.564134\pi$
$71$	−3.37252			−0.400245			−0.200122	+	0.979771i	$0.564134\pi$
$72$	−19.6268	+	6.76065i	−2.31304	+	0.796750i
$73$	−1.11203	−	1.11203i	−0.130153	−	0.130153i	0.639029	−	0.769182i	$-0.279336\pi$
$73$	−1.11203	−	1.11203i	−0.130153	−	0.130153i	−0.769182	+	0.639029i	$0.779336\pi$
$74$			10.8495i			1.26123i
$75$	1.68768	+	0.389527i	0.194877	+	0.0449787i
$76$	23.6950	+	23.6950i	2.71800	+	2.71800i
$77$	−6.00361	−	6.00361i	−0.684175	−	0.684175i
$78$	11.6484	−	7.27967i	1.31892	−	0.824260i
$79$	3.77896	−	3.77896i	0.425166	−	0.425166i	−0.461812	−	0.886978i	$-0.652800\pi$
$79$	3.77896	−	3.77896i	0.425166	−	0.425166i	0.886978	+	0.461812i	$0.152800\pi$
$80$	8.52551			0.953181
$81$	5.54263	+	7.09079i	0.615847	+	0.787865i
$82$	−6.98885			−0.771789
$83$			6.93647i			0.761376i	0.924704	+	0.380688i	$0.124313\pi$
$83$			6.93647i			0.761376i	−0.924704	+	0.380688i	$0.875687\pi$
$84$	−2.69218	+	11.6642i	−0.293741	+	1.27267i
$85$	2.44077	+	2.44077i	0.264739	+	0.264739i
$86$	−7.11625			−0.767365
$87$	−7.26332	+	5.85185i	−0.778710	+	0.627384i
$88$	39.7622			4.23866
$89$	−3.53060	−	3.53060i	−0.374243	−	0.374243i	0.494777	−	0.869020i	$-0.335250\pi$
$89$	−3.53060	−	3.53060i	−0.374243	−	0.374243i	−0.869020	+	0.494777i	$0.835250\pi$
$90$	−2.52479	−	7.32972i	−0.266136	−	0.772620i
$91$		−	4.53440i		−	0.475335i
$92$	−21.2336			−2.21376
$93$	−13.4278	+	8.39172i	−1.39240	+	0.870181i
$94$	21.7959			2.24808
$95$	−5.06551	+	5.06551i	−0.519710	+	0.519710i
$96$	−7.51965	−	12.0324i	−0.767471	−	1.22805i
$97$	−2.64311	−	2.64311i	−0.268367	−	0.268367i	0.560075	−	0.828442i	$-0.310772\pi$
$97$	−2.64311	−	2.64311i	−0.268367	−	0.268367i	−0.828442	+	0.560075i	$0.810772\pi$
$98$	−8.80176	−	8.80176i	−0.889112	−	0.889112i
$99$	−5.61443	−	16.2992i	−0.564272	−	1.63814i
$100$			4.67770i			0.467770i
$101$	0.605366	+	0.605366i	0.0602362	+	0.0602362i	0.736583	−	0.676347i	$-0.236438\pi$
$101$	0.605366	+	0.605366i	0.0602362	+	0.0602362i	−0.676347	+	0.736583i	$0.736438\pi$
$102$	3.47451	−	15.0538i	0.344027	−	1.49055i
$103$	−7.12895			−0.702436			−0.351218	−	0.936294i	$-0.614232\pi$
$103$	−7.12895			−0.702436			−0.351218	+	0.936294i	$0.614232\pi$
$104$	15.0158	+	15.0158i	1.47242	+	1.47242i
$105$	−2.49358	−	0.575534i	−0.243349	−	0.0561664i
$106$	7.61013	−	7.61013i	0.739161	−	0.739161i
$107$			7.72650i			0.746949i	0.927640	+	0.373475i	$0.121834\pi$
$107$			7.72650i			0.746949i	−0.927640	+	0.373475i	$0.878166\pi$
$108$	−15.2930	+	18.8921i	−1.47157	+	1.81789i
$109$			11.4614i			1.09780i	0.835886	+	0.548902i	$0.184954\pi$
$109$			11.4614i			1.09780i	−0.835886	+	0.548902i	$0.815046\pi$
$110$			14.8493i			1.41583i
$111$	3.85396	+	6.16681i	0.365801	+	0.585328i
$112$	−12.5966			−1.19027
$113$	−10.0819	+	10.0819i	−0.948426	+	0.948426i	−0.998734	−	0.0503081i	$-0.983980\pi$
$113$	−10.0819	+	10.0819i	−0.948426	+	0.948426i	0.0503081	+	0.998734i	$0.483980\pi$
$114$	31.2422	+	7.21090i	2.92610	+	0.675363i
$115$		−	4.53932i		−	0.423294i
$116$	−19.8106	−	15.5592i	−1.83937	−	1.44463i
$117$	4.03501	−	8.27548i	0.373037	−	0.765068i
$118$	−8.31691	+	8.31691i	−0.765633	+	0.765633i
$119$	−3.60629	−	3.60629i	−0.330588	−	0.330588i
$120$	10.1635	−	6.35166i	0.927792	−	0.579825i
$121$			22.0208i			2.00189i
$122$	27.5648			2.49560
$123$	−3.97244	+	2.48258i	−0.358183	+	0.223847i
$124$	−30.2383	−	30.2383i	−2.71548	−	2.71548i
$125$	−1.00000			−0.0894427
$126$	3.73043	+	10.8298i	0.332333	+	0.964796i
$127$	0.406447	−	0.406447i	0.0360664	−	0.0360664i	−0.688844	−	0.724910i	$-0.741881\pi$
$127$	0.406447	−	0.406447i	0.0360664	−	0.0360664i	0.724910	+	0.688844i	$0.241881\pi$
$128$	−4.06057	+	4.06057i	−0.358907	+	0.358907i
$129$	−4.04485	+	2.52784i	−0.356130	+	0.222564i
$130$	−5.60771	+	5.60771i	−0.491828	+	0.491828i
$131$	11.2325	−	11.2325i	0.981388	−	0.981388i	−0.0184418	−	0.999830i	$-0.505871\pi$
$131$	11.2325	−	11.2325i	0.981388	−	0.981388i	0.999830	+	0.0184418i	$0.00587054\pi$
$132$	39.4813	−	24.6739i	3.43641	−	2.14759i
$133$	7.48439	−	7.48439i	0.648979	−	0.648979i
$134$	20.0985	−	20.0985i	1.73624	−	1.73624i
$135$	−4.03875	−	3.26933i	−0.347600	−	0.281379i
$136$	23.8846			2.04809
$137$	−10.9680	−	10.9680i	−0.937058	−	0.937058i	0.0610750	−	0.998133i	$-0.480547\pi$
$137$	−10.9680	−	10.9680i	−0.937058	−	0.937058i	−0.998133	+	0.0610750i	$0.980547\pi$
$138$	−17.2294	+	10.7675i	−1.46666	+	0.916593i
$139$	−8.29765			−0.703798			−0.351899	−	0.936038i	$-0.614464\pi$
$139$	−8.29765			−0.703798			−0.351899	+	0.936038i	$0.614464\pi$
$140$		−	6.91140i		−	0.584120i
$141$	12.3887	−	7.74236i	1.04332	−	0.652024i
$142$	−6.16245	−	6.16245i	−0.517141	−	0.517141i
$143$	−12.4700	+	12.4700i	−1.04279	+	1.04279i
$144$	−22.9893	−	11.2093i	−1.91578	−	0.934108i
$145$	3.32624	−	4.23511i	0.276229	−	0.351706i
$146$		−	4.06391i		−	0.336331i
$147$	−8.12945	−	1.87633i	−0.670506	−	0.154757i
$148$	−13.8872	+	13.8872i	−1.14152	+	1.14152i
$149$	17.3893			1.42459			0.712293	−	0.701882i	$-0.247657\pi$
$149$	17.3893			1.42459			0.712293	+	0.701882i	$0.247657\pi$
$150$	2.37206	+	3.79558i	0.193678	+	0.309908i
$151$			1.87504i			0.152589i	0.997085	+	0.0762945i	$0.0243089\pi$
$151$			1.87504i			0.152589i	−0.997085	+	0.0762945i	$0.975691\pi$
$152$			49.5695i			4.02062i
$153$	−3.37251	−	9.79074i	−0.272652	−	0.791534i
$154$		−	21.9402i		−	1.76799i
$155$	6.46434	−	6.46434i	0.519229	−	0.519229i
$156$	24.2276	+	5.59187i	1.93976	+	0.447708i
$157$	8.57158	+	8.57158i	0.684086	+	0.684086i	0.960918	−	0.276832i	$-0.0892845\pi$
$157$	8.57158	+	8.57158i	0.684086	+	0.684086i	−0.276832	+	0.960918i	$0.589285\pi$
$158$	13.8102			1.09868
$159$	1.62230	−	7.02884i	0.128657	−	0.557424i
$160$	5.79257	+	5.79257i	0.457943	+	0.457943i
$161$			6.70694i			0.528581i
$162$	−2.82888	+	23.0844i	−0.222258	+	1.81369i
$163$	−6.42050	−	6.42050i	−0.502892	−	0.502892i	0.409443	−	0.912336i	$-0.365723\pi$
$163$	−6.42050	−	6.42050i	−0.502892	−	0.502892i	−0.912336	+	0.409443i	$0.865723\pi$
$164$	−8.94561	−	8.94561i	−0.698535	−	0.698535i
$165$	5.27479	+	8.44032i	0.410642	+	0.657078i
$166$	−12.6747	+	12.6747i	−0.983746	+	0.983746i
$167$	20.9254			1.61925			0.809627	−	0.586945i	$-0.199670\pi$
$167$	20.9254			1.61925			0.809627	+	0.586945i	$0.199670\pi$
$168$	−15.0167	+	9.38471i	−1.15856	+	0.724046i
$169$	3.58168			0.275514
$170$			8.91981i			0.684118i
$171$	20.3194	−	6.99923i	1.55387	−	0.535244i
$172$	−9.10868	−	9.10868i	−0.694530	−	0.694530i
$173$	−1.39189			−0.105823			−0.0529117	−	0.998599i	$-0.516850\pi$
$173$	−1.39189			−0.105823			−0.0529117	+	0.998599i	$0.516850\pi$
$174$	−23.9647	−	2.57912i	−1.81676	−	0.195522i
$175$	1.47752			0.111690
$176$	34.6417	+	34.6417i	2.61122	+	2.61122i
$177$	−1.77297	+	7.68164i	−0.133264	+	0.577387i
$178$		−	12.9026i		−	0.967092i
$179$	−18.7509			−1.40151			−0.700755	−	0.713402i	$-0.747154\pi$
$179$	−18.7509			−1.40151			−0.700755	+	0.713402i	$0.747154\pi$
$180$	6.15022	−	12.6136i	0.458411	−	0.940163i
$181$	11.4599			0.851808			0.425904	−	0.904768i	$-0.359956\pi$
$181$	11.4599			0.851808			0.425904	+	0.904768i	$0.359956\pi$
$182$	8.28550	−	8.28550i	0.614162	−	0.614162i
$183$	15.6677	−	9.79157i	1.15819	−	0.723813i
$184$	−22.2102	−	22.2102i	−1.63736	−	1.63736i
$185$	−2.96880	−	2.96880i	−0.218270	−	0.218270i
$186$	−39.8698	−	9.20218i	−2.92339	−	0.674737i
$187$			19.8352i			1.45049i
$188$	27.8984	+	27.8984i	2.03470	+	2.03470i
$189$	5.96733	+	4.83050i	0.434059	+	0.351367i
$190$	−18.5119			−1.34300
$191$	−4.62467	−	4.62467i	−0.334630	−	0.334630i	0.519712	−	0.854342i	$-0.326039\pi$
$191$	−4.62467	−	4.62467i	−0.334630	−	0.334630i	−0.854342	+	0.519712i	$0.826039\pi$
$192$	1.60406	−	6.94982i	0.115763	−	0.501560i
$193$	0.323644	−	0.323644i	0.0232964	−	0.0232964i	−0.695363	−	0.718659i	$-0.744756\pi$
$193$	0.323644	−	0.323644i	0.0232964	−	0.0232964i	0.718659	+	0.695363i	$0.244756\pi$
$194$		−	9.65927i		−	0.693495i
$195$	−1.19543	+	5.17937i	−0.0856066	+	0.370903i
$196$		−	22.5322i		−	1.60944i
$197$		−	5.28605i		−	0.376615i	−0.982110	−	0.188308i	$-0.939700\pi$
$197$		−	5.28605i		−	0.376615i	0.982110	−	0.188308i	$-0.0603002\pi$
$198$	19.5239	−	40.0418i	1.38750	−	2.84565i
$199$	−7.15522			−0.507220			−0.253610	−	0.967307i	$-0.581618\pi$
$199$	−7.15522			−0.507220			−0.253610	+	0.967307i	$0.581618\pi$
$200$	−4.89284	+	4.89284i	−0.345976	+	0.345976i
$201$	4.28451	−	18.5633i	0.302206	−	1.30935i
$202$			2.21231i			0.155658i
$203$	−4.91459	+	6.25745i	−0.344936	+	0.439187i
$204$	23.7159	−	14.8213i	1.66045	−	1.03770i
$205$	1.91239	−	1.91239i	0.133567	−	0.133567i
$206$	−13.0264	−	13.0264i	−0.907591	−	0.907591i
$207$	−5.96828	+	12.2405i	−0.414824	+	0.850770i
$208$			26.1642i			1.81416i
$209$	−41.1654			−2.84747
$210$	−3.50476	−	5.60805i	−0.241851	−	0.386992i
$211$	8.48679	+	8.48679i	0.584255	+	0.584255i	0.936070	−	0.351815i	$-0.114435\pi$
$211$	8.48679	+	8.48679i	0.584255	+	0.584255i	−0.351815	+	0.936070i	$0.614435\pi$
$212$	19.4817			1.33801
$213$	−5.69174	−	1.31369i	−0.389992	−	0.0900124i
$214$	−14.1183	+	14.1183i	−0.965105	+	0.965105i
$215$	1.94725	−	1.94725i	0.132802	−	0.132802i
$216$	−35.7573	+	3.76464i	−2.43297	+	0.256151i
$217$	−9.55120	+	9.55120i	−0.648378	+	0.648378i
$218$	−20.9429	+	20.9429i	−1.41843	+	1.41843i
$219$	−1.44358	−	2.30991i	−0.0975482	−	0.156089i
$220$	−19.0069	+	19.0069i	−1.28145	+	1.28145i
$221$	−7.49055	+	7.49055i	−0.503869	+	0.503869i
$222$	−4.22617	+	18.3105i	−0.283642	+	1.22892i
$223$	−27.5792			−1.84684			−0.923418	−	0.383795i	$-0.874617\pi$
$223$	−27.5792			−1.84684			−0.923418	+	0.383795i	$0.874617\pi$
$224$	−8.55864	−	8.55864i	−0.571848	−	0.571848i
$225$	2.69654	+	1.31480i	0.179769	+	0.0876530i
$226$	−36.8444			−2.45085
$227$			7.78472i			0.516690i	0.966053	+	0.258345i	$0.0831771\pi$
$227$			7.78472i			0.516690i	−0.966053	+	0.258345i	$0.916823\pi$
$228$	30.7597	+	49.2194i	2.03711	+	3.25963i
$229$	−1.75411	−	1.75411i	−0.115915	−	0.115915i	0.646770	−	0.762685i	$-0.276119\pi$
$229$	−1.75411	−	1.75411i	−0.115915	−	0.115915i	−0.762685	+	0.646770i	$0.776119\pi$
$230$	8.29449	−	8.29449i	0.546922	−	0.546922i
$231$	−7.79361	−	12.4707i	−0.512782	−	0.820515i
$232$	−4.44694	−	36.9965i	−0.291956	−	2.42894i
$233$		−	17.9630i		−	1.17680i	−0.808571	−	0.588398i	$-0.799759\pi$
$233$		−	17.9630i		−	1.17680i	0.808571	−	0.588398i	$-0.200241\pi$
$234$	22.4944	−	7.74840i	1.47050	−	0.506529i
$235$	−5.96413	+	5.96413i	−0.389057	+	0.389057i
$236$	−21.2910			−1.38593
$237$	7.84969	−	4.90567i	0.509892	−	0.318658i
$238$		−	13.1792i		−	0.854280i
$239$			1.09314i			0.0707092i	0.999375	+	0.0353546i	$0.0112561\pi$
$239$			1.09314i			0.0707092i	−0.999375	+	0.0353546i	$0.988744\pi$
$240$	14.3883	+	3.32092i	0.928763	+	0.214364i
$241$		−	2.19181i		−	0.141187i	−0.997505	−	0.0705935i	$-0.977511\pi$
$241$		−	2.19181i		−	0.141187i	0.997505	−	0.0705935i	$-0.0224893\pi$
$242$	−40.2376	+	40.2376i	−2.58657	+	2.58657i
$243$	6.59214	+	14.1260i	0.422886	+	0.906183i
$244$	35.2824	+	35.2824i	2.25873	+	2.25873i
$245$	4.81693			0.307743
$246$	−11.7950	−	2.72235i	−0.752019	−	0.173570i
$247$	−15.5457	−	15.5457i	−0.989148	−	0.989148i
$248$		−	63.2580i		−	4.01689i
$249$	−2.70194	+	11.7065i	−0.171229	+	0.741872i
$250$	−1.82725	−	1.82725i	−0.115566	−	0.115566i
$251$	18.6438	+	18.6438i	1.17678	+	1.17678i	0.980559	+	0.196226i	$0.0628685\pi$
$251$	18.6438	+	18.6438i	1.17678	+	1.17678i	0.196226	+	0.980559i	$0.437132\pi$
$252$	−9.08708	+	18.6369i	−0.572432	+	1.17401i
$253$	18.4446	−	18.4446i	1.15960	−	1.15960i
$254$	1.48536			0.0932000
$255$	3.16850	+	5.06999i	0.198419	+	0.317495i
$256$	−23.0753			−1.44221
$257$			11.7420i			0.732446i	0.930527	+	0.366223i	$0.119349\pi$
$257$			11.7420i			0.732446i	−0.930527	+	0.366223i	$0.880651\pi$
$258$	−12.0100	−	2.77197i	−0.747708	−	0.172576i
$259$	4.38646	+	4.38646i	0.272561	+	0.272561i
$260$	−14.3555			−0.890293
$261$	−14.5376	+	7.04680i	−0.899857	+	0.436186i
$262$	41.0492			2.53603
$263$	−5.14256	−	5.14256i	−0.317104	−	0.317104i	0.530550	−	0.847654i	$-0.321985\pi$
$263$	−5.14256	−	5.14256i	−0.317104	−	0.317104i	−0.847654	+	0.530550i	$0.821985\pi$
$264$	67.1059	+	15.4884i	4.13008	+	0.953248i
$265$			4.16479i			0.255841i
$266$	27.3518			1.67704
$267$	−4.58327	−	7.33380i	−0.280492	−	0.448821i
$268$	51.4513			3.14289
$269$	16.2344	−	16.2344i	0.989831	−	0.989831i	−0.0101179	−	0.999949i	$-0.503221\pi$
$269$	16.2344	−	16.2344i	0.989831	−	0.989831i	0.999949	+	0.0101179i	$0.00322067\pi$
$270$	−1.40592	−	13.3537i	−0.0855616	−	0.812681i
$271$	8.99063	+	8.99063i	0.546142	+	0.546142i	0.925323	−	0.379181i	$-0.123794\pi$
$271$	8.99063	+	8.99063i	0.546142	+	0.546142i	−0.379181	+	0.925323i	$0.623794\pi$
$272$	20.8088	+	20.8088i	1.26172	+	1.26172i
$273$	1.76627	−	7.65263i	0.106900	−	0.463158i
$274$		−	40.0826i		−	2.42148i
$275$	−4.06330	−	4.06330i	−0.245026	−	0.245026i
$276$	−35.8356	−	8.27106i	−2.15705	−	0.497860i
$277$	−4.51320			−0.271172			−0.135586	−	0.990766i	$-0.543292\pi$
$277$	−4.51320			−0.271172			−0.135586	+	0.990766i	$0.543292\pi$
$278$	−15.1619	−	15.1619i	−0.909351	−	0.909351i
$279$	−25.9306	+	8.93206i	−1.55243	+	0.534748i
$280$	7.22927	−	7.22927i	0.432032	−	0.432032i
$281$		−	20.9716i		−	1.25106i	−0.780200	−	0.625530i	$-0.784883\pi$
$281$		−	20.9716i		−	1.25106i	0.780200	−	0.625530i	$-0.215117\pi$
$282$	36.7846	+	8.49010i	2.19049	+	0.505578i
$283$			30.6922i			1.82446i	0.409675	+	0.912232i	$0.365642\pi$
$283$			30.6922i			1.82446i	−0.409675	+	0.912232i	$0.634358\pi$
$284$		−	15.7757i		−	0.936113i
$285$	−10.5221	+	6.57581i	−0.623277	+	0.389518i
$286$	−45.5716			−2.69470
$287$	−2.82560	+	2.82560i	−0.166790	+	0.166790i
$288$	−8.00384	−	23.2359i	−0.471631	−	1.36919i
$289$		−	5.08529i		−	0.299135i
$290$	13.8165	−	1.66073i	0.811332	−	0.0975213i
$291$	−3.43117	−	5.49030i	−0.201139	−	0.321847i
$292$	5.20173	−	5.20173i	0.304408	−	0.304408i
$293$	−12.3112	−	12.3112i	−0.719227	−	0.719227i	0.249220	−	0.968447i	$-0.419826\pi$
$293$	−12.3112	−	12.3112i	−0.719227	−	0.719227i	−0.968447	+	0.249220i	$0.919826\pi$
$294$	−11.4260	−	18.2831i	−0.666380	−	1.06629i
$295$		−	4.55159i		−	0.265004i
$296$	−29.0517			−1.68860
$297$	−3.12638	−	29.6949i	−0.181411	−	1.72307i
$298$	31.7746	+	31.7746i	1.84065	+	1.84065i
$299$	13.9309			0.805642
$300$	−1.82209	+	7.89447i	−0.105199	+	0.455788i
$301$	−2.87711	+	2.87711i	−0.165834	+	0.165834i
$302$	−3.42618	+	3.42618i	−0.197155	+	0.197155i
$303$	0.785859	+	1.25747i	0.0451464	+	0.0722398i
$304$	−43.1860	+	43.1860i	−2.47689	+	2.47689i
$305$	−7.54268	+	7.54268i	−0.431893	+	0.431893i
$306$	11.7277	−	24.0526i	0.670429	−	1.37499i
$307$	−10.2548	+	10.2548i	−0.585274	+	0.585274i	−0.936348	−	0.351074i	$-0.885817\pi$
$307$	−10.2548	+	10.2548i	−0.585274	+	0.585274i	0.351074	+	0.936348i	$0.385817\pi$
$308$	28.0831	−	28.0831i	1.60018	−	1.60018i
$309$	−12.0314	−	2.77692i	−0.684442	−	0.157973i
$310$	23.6240			1.34175
$311$	15.6365	+	15.6365i	0.886662	+	0.886662i	0.994201	−	0.107539i	$-0.0342969\pi$
$311$	15.6365	+	15.6365i	0.886662	+	0.886662i	−0.107539	+	0.994201i	$0.534297\pi$
$312$	19.4928	+	31.1909i	1.10356	+	1.76584i
$313$	−1.20515			−0.0681192			−0.0340596	−	0.999420i	$-0.510844\pi$
$313$	−1.20515			−0.0681192			−0.0340596	+	0.999420i	$0.510844\pi$
$314$			31.3249i			1.76777i
$315$	−3.98419	−	1.94264i	−0.224484	−	0.109455i
$316$	17.6769	+	17.6769i	0.994401	+	0.994401i
$317$	17.7580	−	17.7580i	0.997387	−	0.997387i	−0.00260910	−	0.999997i	$-0.500831\pi$
$317$	17.7580	−	17.7580i	0.997387	−	0.997387i	0.999997	+	0.00260910i	$0.000830505\pi$
$318$	15.8078	−	9.87912i	0.886459	−	0.553994i
$319$	30.7240	−	3.69299i	1.72021	−	0.206768i
$320$			4.11797i			0.230202i
$321$	−3.00968	+	13.0399i	−0.167984	+	0.727815i
$322$	−12.2553	+	12.2553i	−0.682960	+	0.682960i
$323$	−24.7275			−1.37587
$324$	−33.1686	+	25.9268i	−1.84270	+	1.44038i
$325$		−	3.06893i		−	0.170233i
$326$		−	23.4637i		−	1.29954i
$327$	−4.46453	+	19.3432i	−0.246889	+	1.06968i
$328$		−	18.7141i		−	1.03331i
$329$	8.81212	−	8.81212i	0.485828	−	0.485828i
$330$	−5.78422	+	25.0610i	−0.318411	+	1.37956i
$331$	13.5452	+	13.5452i	0.744512	+	0.744512i	0.973443	−	0.228931i	$-0.0735230\pi$
$331$	13.5452	+	13.5452i	0.744512	+	0.744512i	−0.228931	+	0.973443i	$0.573523\pi$
$332$	−32.4467			−1.78075
$333$	4.10211	+	11.9088i	0.224794	+	0.652600i
$334$	38.2359	+	38.2359i	2.09218	+	2.09218i
$335$			10.9993i			0.600954i
$336$	−21.2591	−	4.90672i	−1.15978	−	0.267684i
$337$	21.8729	+	21.8729i	1.19149	+	1.19149i	0.976649	+	0.214841i	$0.0689234\pi$
$337$	21.8729	+	21.8729i	1.19149	+	1.19149i	0.214841	+	0.976649i	$0.431077\pi$
$338$	6.54464	+	6.54464i	0.355981	+	0.355981i
$339$	−20.9422	+	13.0879i	−1.13742	+	0.710835i
$340$	−11.4172	+	11.4172i	−0.619184	+	0.619184i
$341$	52.5331			2.84483
$342$	49.9181	+	24.3394i	2.69926	+	1.31612i
$343$	−17.4598			−0.942738
$344$		−	19.0552i		−	1.02739i
$345$	1.76819	−	7.66093i	0.0951961	−	0.412451i
$346$	−2.54333	−	2.54333i	−0.136730	−	0.136730i
$347$	−25.5146			−1.36970			−0.684848	−	0.728686i	$-0.740131\pi$
$347$	−25.5146			−1.36970			−0.684848	+	0.728686i	$0.740131\pi$
$348$	−27.3732	−	33.9757i	−1.46736	−	1.82129i
$349$	30.2482			1.61915			0.809574	−	0.587018i	$-0.199698\pi$
$349$	30.2482			1.61915			0.809574	+	0.587018i	$0.199698\pi$
$350$	2.69980	+	2.69980i	0.144311	+	0.144311i
$351$	10.0333	−	12.3946i	0.535540	−	0.661576i
$352$			47.0739i			2.50905i
$353$	11.0474			0.587995			0.293997	−	0.955806i	$-0.405014\pi$
$353$	11.0474			0.587995			0.293997	+	0.955806i	$0.405014\pi$
$354$	−17.2759	+	10.7966i	−0.918206	+	0.573834i
$355$	3.37252			0.178995
$356$	16.5151	−	16.5151i	0.875300	−	0.875300i
$357$	−4.68152	−	7.49101i	−0.247772	−	0.396466i
$358$	−34.2627	−	34.2627i	−1.81084	−	1.81084i
$359$	8.41742	+	8.41742i	0.444255	+	0.444255i	0.893439	−	0.449184i	$-0.148285\pi$
$359$	8.41742	+	8.41742i	0.444255	+	0.444255i	−0.449184	+	0.893439i	$0.648285\pi$
$360$	19.6268	−	6.76065i	1.03442	−	0.356317i
$361$		−	32.3188i		−	1.70099i
$362$	20.9401	+	20.9401i	1.10059	+	1.10059i
$363$	−8.57770	+	37.1641i	−0.450212	+	1.95061i
$364$	21.2106			1.11174
$365$	1.11203	+	1.11203i	0.0582061	+	0.0582061i
$366$	46.5206	+	10.7372i	2.43167	+	0.561244i
$367$	−9.39718	+	9.39718i	−0.490529	+	0.490529i	−0.908473	−	0.417944i	$-0.862751\pi$
$367$	−9.39718	+	9.39718i	−0.490529	+	0.490529i	0.417944	+	0.908473i	$0.362751\pi$
$368$		−	38.7000i		−	2.01738i
$369$	−7.67124	+	2.64243i	−0.399349	+	0.137560i
$370$		−	10.8495i		−	0.564038i
$371$		−	6.15356i		−	0.319477i
$372$	−39.2540	−	62.8112i	−2.03522	−	3.25661i
$373$	−25.9493			−1.34360			−0.671802	−	0.740730i	$-0.734480\pi$
$373$	−25.9493			−1.34360			−0.671802	+	0.740730i	$0.734480\pi$
$374$	−36.2438	+	36.2438i	−1.87412	+	1.87412i
$375$	−1.68768	−	0.389527i	−0.0871515	−	0.0201151i
$376$			58.3631i			3.00984i
$377$	12.9972	+	10.2080i	0.669392	+	0.525738i
$378$	2.07728	+	19.7304i	0.106844	+	1.01482i
$379$	−17.3472	+	17.3472i	−0.891063	+	0.891063i	−0.994623	−	0.103560i	$-0.966977\pi$
$379$	−17.3472	+	17.3472i	−0.891063	+	0.891063i	0.103560	+	0.994623i	$0.466977\pi$
$380$	−23.6950	−	23.6950i	−1.21553	−	1.21553i
$381$	0.844276	−	0.527632i	0.0432536	−	0.0270314i
$382$		−	16.9009i		−	0.864725i
$383$	2.93781			0.150115			0.0750576	−	0.997179i	$-0.476086\pi$
$383$	2.93781			0.150115			0.0750576	+	0.997179i	$0.476086\pi$
$384$	−8.43466	+	5.27125i	−0.430429	+	0.268997i
$385$	6.00361	+	6.00361i	0.305972	+	0.305972i
$386$	1.18276			0.0602008
$387$	−7.81109	+	2.69060i	−0.397060	+	0.136771i
$388$	12.3637	−	12.3637i	0.627672	−	0.627672i
$389$	15.9578	−	15.9578i	0.809092	−	0.809092i	−0.175405	−	0.984496i	$-0.556123\pi$
$389$	15.9578	−	15.9578i	0.809092	−	0.809092i	0.984496	+	0.175405i	$0.0561234\pi$
$390$	−11.6484	+	7.27967i	−0.589838	+	0.368620i
$391$	11.0794	−	11.0794i	0.560311	−	0.560311i
$392$	23.5685	−	23.5685i	1.19039	−	1.19039i
$393$	23.3322	−	14.5815i	1.17696	−	0.735540i
$394$	9.65894	−	9.65894i	0.486610	−	0.486610i
$395$	−3.77896	+	3.77896i	−0.190140	+	0.190140i
$396$	76.2430	−	26.2627i	3.83136	−	1.31975i
$397$	8.79333			0.441325			0.220662	−	0.975350i	$-0.429178\pi$
$397$	8.79333			0.441325			0.220662	+	0.975350i	$0.429178\pi$
$398$	−13.0744	−	13.0744i	−0.655360	−	0.655360i
$399$	15.5466	−	9.71590i	0.778306	−	0.486403i
$400$	−8.52551			−0.426275
$401$		−	1.03350i		−	0.0516103i	−0.999667	−	0.0258051i	$-0.991785\pi$
$401$		−	1.03350i		−	0.0516103i	0.999667	−	0.0258051i	$-0.00821494\pi$
$402$	41.7487	−	26.0909i	2.08223	−	1.30130i
$403$	19.8386	+	19.8386i	0.988231	+	0.988231i
$404$	−2.83172	+	2.83172i	−0.140883	+	0.140883i
$405$	−5.54263	−	7.09079i	−0.275415	−	0.352344i
$406$	−20.4141	+	2.45376i	−1.01314	+	0.121778i
$407$		−	24.1262i		−	1.19589i
$408$	40.3096	+	9.30370i	1.99562	+	0.460602i
$409$	24.6545	−	24.6545i	1.21909	−	1.21909i	0.251135	−	0.967952i	$-0.419196\pi$
$409$	24.6545	−	24.6545i	1.21909	−	1.21909i	0.967952	−	0.251135i	$-0.0808037\pi$
$410$	6.98885			0.345155
$411$	−14.2381	−	22.7828i	−0.702316	−	1.12379i
$412$		−	33.3471i		−	1.64289i
$413$			6.72507i			0.330919i
$414$	−33.2720	+	11.4608i	−1.63523	+	0.563270i
$415$		−	6.93647i		−	0.340498i
$416$	−17.7770	+	17.7770i	−0.871588	+	0.871588i
$417$	−14.0038	−	3.23216i	−0.685769	−	0.158280i
$418$	−75.2195	−	75.2195i	−3.67911	−	3.67911i
$419$	19.6439			0.959669			0.479834	−	0.877359i	$-0.340697\pi$
$419$	19.6439			0.959669			0.479834	+	0.877359i	$0.340697\pi$
$420$	2.69218	−	11.6642i	0.131365	−	0.569157i
$421$	−0.118612	−	0.118612i	−0.00578079	−	0.00578079i	0.704210	−	0.709991i	$-0.251301\pi$
$421$	−0.118612	−	0.118612i	−0.00578079	−	0.00578079i	−0.709991	+	0.704210i	$0.751301\pi$
$422$			31.0150i			1.50979i
$423$	23.9241	−	8.24088i	1.16323	−	0.400686i
$424$	20.3777	+	20.3777i	0.989627	+	0.989627i
$425$	−2.44077	−	2.44077i	−0.118395	−	0.118395i
$426$	−7.99981	−	12.8007i	−0.387592	−	0.620195i
$427$	11.1445	−	11.1445i	0.539319	−	0.539319i
$428$	−36.1423			−1.74700
$429$	−25.9027	+	16.1880i	−1.25060	+	0.781562i
$430$	7.11625			0.343176
$431$			20.3592i			0.980667i	0.871535	+	0.490333i	$0.163125\pi$
$431$			20.3592i			0.980667i	−0.871535	+	0.490333i	$0.836875\pi$
$432$	−34.4324	−	27.8727i	−1.65663	−	1.34103i
$433$	−14.1609	−	14.1609i	−0.680528	−	0.680528i	0.279591	−	0.960119i	$-0.409801\pi$
$433$	−14.1609	−	14.1609i	−0.680528	−	0.680528i	−0.960119	+	0.279591i	$0.909801\pi$
$434$	−34.9049			−1.67549
$435$	7.26332	−	5.85185i	0.348250	−	0.280575i
$436$	−53.6131			−2.56760
$437$	22.9940	+	22.9940i	1.09995	+	1.09995i
$438$	1.58300	−	6.85858i	0.0756387	−	0.327716i
$439$			20.5325i			0.979964i	0.871733	+	0.489982i	$0.162997\pi$
$439$			20.5325i			0.979964i	−0.871733	+	0.489982i	$0.837003\pi$
$440$	−39.7622			−1.89559
$441$	−12.9890	−	6.33328i	−0.618526	−	0.301585i
$442$	−27.3742			−1.30206
$443$	6.39426	−	6.39426i	0.303801	−	0.303801i	−0.538698	−	0.842499i	$-0.681084\pi$
$443$	6.39426	−	6.39426i	0.303801	−	0.303801i	0.842499	+	0.538698i	$0.181084\pi$
$444$	−28.8465	+	18.0277i	−1.36900	+	0.855555i
$445$	3.53060	+	3.53060i	0.167367	+	0.167367i
$446$	−50.3941	−	50.3941i	−2.38623	−	2.38623i
$447$	29.3476	+	6.77360i	1.38809	+	0.320380i
$448$		−	6.08438i		−	0.287460i
$449$	−19.0188	−	19.0188i	−0.897552	−	0.897552i	0.0976673	−	0.995219i	$-0.468862\pi$
$449$	−19.0188	−	19.0188i	−0.897552	−	0.897552i	−0.995219	+	0.0976673i	$0.968862\pi$
$450$	2.52479	+	7.32972i	0.119020	+	0.345526i
$451$	15.5412			0.731809
$452$	−47.1602	−	47.1602i	−2.21823	−	2.21823i
$453$	−0.730381	+	3.16448i	−0.0343163	+	0.148680i
$454$	−14.2247	+	14.2247i	−0.667596	+	0.667596i
$455$			4.53440i			0.212576i
$456$	−19.3087	+	83.6575i	−0.904211	+	3.91762i
$457$		−	39.5954i		−	1.85220i	−0.377282	−	0.926098i	$-0.623141\pi$
$457$		−	39.5954i		−	1.85220i	0.377282	−	0.926098i	$-0.376859\pi$
$458$		−	6.41041i		−	0.299539i
$459$	−1.87797	−	17.8373i	−0.0876562	−	0.832575i
$460$	21.2336			0.990022
$461$	−16.3394	+	16.3394i	−0.761002	+	0.761002i	−0.976504	−	0.215502i	$-0.930861\pi$
$461$	−16.3394	+	16.3394i	−0.761002	+	0.761002i	0.215502	+	0.976504i	$0.430861\pi$
$462$	8.54631	−	37.0281i	0.397610	−	1.72270i
$463$			12.1917i			0.566595i	0.959032	+	0.283298i	$0.0914284\pi$
$463$			12.1917i			0.566595i	−0.959032	+	0.283298i	$0.908572\pi$
$464$	28.3579	−	36.1064i	1.31648	−	1.67620i
$465$	13.4278	−	8.39172i	0.622699	−	0.389157i
$466$	32.8230	−	32.8230i	1.52050	−	1.52050i
$467$	−8.75343	−	8.75343i	−0.405061	−	0.405061i	0.474951	−	0.880012i	$-0.342466\pi$
$467$	−8.75343	−	8.75343i	−0.405061	−	0.405061i	−0.880012	+	0.474951i	$0.842466\pi$
$468$	38.7102	+	18.8746i	1.78938	+	0.872478i
$469$		−	16.2516i		−	0.750431i
$470$	−21.7959			−1.00537
$471$	11.1272	+	17.8050i	0.512716	+	0.820409i
$472$	−22.2702	−	22.2702i	−1.02507	−	1.02507i
$473$	15.8246			0.727614
$474$	23.3073	+	5.37946i	1.07054	+	0.247087i
$475$	5.06551	−	5.06551i	0.232422	−	0.232422i
$476$	16.8691	−	16.8691i	0.773196	−	0.773196i
$477$	5.47585	−	11.2305i	0.250722	−	0.514210i
$478$	−1.99744	+	1.99744i	−0.0913607	+	0.0913607i
$479$	18.7473	−	18.7473i	0.856586	−	0.856586i	−0.134348	−	0.990934i	$-0.542894\pi$
$479$	18.7473	−	18.7473i	0.856586	−	0.856586i	0.990934	+	0.134348i	$0.0428940\pi$
$480$	7.51965	+	12.0324i	0.343224	+	0.549201i
$481$	9.11103	−	9.11103i	0.415427	−	0.415427i
$482$	4.00499	−	4.00499i	0.182422	−	0.182422i
$483$	−2.61253	+	11.3192i	−0.118874	+	0.515040i
$484$	−103.007			−4.68213
$485$	2.64311	+	2.64311i	0.120018	+	0.120018i
$486$	−13.7663	+	37.8573i	−0.624451	+	1.71724i
$487$	21.9386			0.994133			0.497067	−	0.867712i	$-0.334410\pi$
$487$	21.9386			0.994133			0.497067	+	0.867712i	$0.334410\pi$
$488$			73.8103i			3.34124i
$489$	−8.33480	−	13.3367i	−0.376913	−	0.603107i
$490$	8.80176	+	8.80176i	0.397623	+	0.397623i
$491$	1.78185	−	1.78185i	0.0804138	−	0.0804138i	−0.665756	−	0.746170i	$-0.731891\pi$
$491$	1.78185	−	1.78185i	0.0804138	−	0.0804138i	0.746170	+	0.665756i	$0.231891\pi$
$492$	−11.6128	−	18.5819i	−0.523545	−	0.837736i
$493$	18.4555	−	2.21833i	0.831194	−	0.0999086i
$494$		−	56.8118i		−	2.55608i
$495$	5.61443	+	16.2992i	0.252350	+	0.732597i
$496$	55.1118	−	55.1118i	2.47459	−	2.47459i
$497$	−4.98297			−0.223517
$498$	−26.3279	+	16.4537i	−1.17978	+	0.737307i
$499$		−	10.3697i		−	0.464213i	−0.972690	−	0.232106i	$-0.925438\pi$
$499$		−	10.3697i		−	0.464213i	0.972690	−	0.232106i	$-0.0745617\pi$
$500$		−	4.67770i		−	0.209193i
$501$	35.3154	+	8.15100i	1.57777	+	0.364160i
$502$			68.1338i			3.04096i
$503$	9.19562	−	9.19562i	0.410013	−	0.410013i	−0.471730	−	0.881743i	$-0.656370\pi$
$503$	9.19562	−	9.19562i	0.410013	−	0.410013i	0.881743	+	0.471730i	$0.156370\pi$
$504$	−28.9990	+	9.98899i	−1.29172	+	0.444945i
$505$	−0.605366	−	0.605366i	−0.0269384	−	0.0269384i
$506$	67.4060			2.99656
$507$	6.04474	+	1.39516i	0.268456	+	0.0619613i
$508$	1.90124	+	1.90124i	0.0843539	+	0.0843539i
$509$			28.5583i			1.26583i	0.774223	+	0.632913i	$0.218141\pi$
$509$			28.5583i			1.26583i	−0.774223	+	0.632913i	$0.781859\pi$
$510$	−3.47451	+	15.0538i	−0.153854	+	0.666593i
$511$	−1.64304	−	1.64304i	−0.0726839	−	0.0726839i
$512$	−34.0433	−	34.0433i	−1.50452	−	1.50452i
$513$	37.0191	−	3.89749i	1.63443	−	0.172079i
$514$	−21.4556	+	21.4556i	−0.946366	+	0.946366i
$515$	7.12895			0.314139
$516$	−11.8245	−	18.9206i	−0.520544	−	0.832934i
$517$	−48.4681			−2.13162
$518$			16.0303i			0.704332i
$519$	−2.34906	−	0.542178i	−0.103112	−	0.0237990i
$520$	−15.0158	−	15.0158i	−0.658485	−	0.658485i
$521$	8.88814			0.389396			0.194698	−	0.980863i	$-0.437627\pi$
$521$	8.88814			0.389396			0.194698	+	0.980863i	$0.437627\pi$
$522$	−39.4402	−	13.6876i	−1.72625	−	0.599092i
$523$	−37.4041			−1.63557			−0.817783	−	0.575526i	$-0.804797\pi$
$523$	−37.4041			−1.63557			−0.817783	+	0.575526i	$0.804797\pi$
$524$	52.5423	+	52.5423i	2.29532	+	2.29532i
$525$	2.49358	+	0.575534i	0.108829	+	0.0251184i
$526$		−	18.7935i		−	0.819436i
$527$	31.5560			1.37460
$528$	44.9703	+	71.9580i	1.95708	+	3.13157i
$529$	2.39455			0.104111
$530$	−7.61013	+	7.61013i	−0.330563	+	0.330563i
$531$	−5.98441	+	12.2735i	−0.259701	+	0.532626i
$532$	35.0098	+	35.0098i	1.51787	+	1.51787i
$533$	5.86900	+	5.86900i	0.254214	+	0.254214i
$534$	5.02592	−	21.7755i	0.217493	−	0.942318i
$535$		−	7.72650i		−	0.334046i
$536$	53.8177	+	53.8177i	2.32457	+	2.32457i
$537$	−31.6456	−	7.30400i	−1.36561	−	0.315191i
$538$	59.3288			2.55785
$539$	19.5726	+	19.5726i	0.843054	+	0.843054i
$540$	15.2930	−	18.8921i	0.658104	−	0.812985i
$541$	−13.5201	+	13.5201i	−0.581273	+	0.581273i	−0.935253	−	0.353980i	$-0.884828\pi$
$541$	−13.5201	+	13.5201i	−0.581273	+	0.581273i	0.353980	+	0.935253i	$0.384828\pi$
$542$			32.8563i			1.41130i
$543$	19.3407	+	4.46394i	0.829987	+	0.191566i
$544$			28.2767i			1.21235i
$545$		−	11.4614i		−	0.490953i
$546$	17.2107	−	10.7559i	0.736550	−	0.460308i
$547$	−39.2360			−1.67761			−0.838804	−	0.544433i	$-0.816745\pi$
$547$	−39.2360			−1.67761			−0.838804	+	0.544433i	$0.816745\pi$
$548$	51.3050	−	51.3050i	2.19164	−	2.19164i
$549$	30.2562	−	10.4220i	1.29130	−	0.444802i
$550$		−	14.8493i		−	0.633178i
$551$	4.60387	+	38.3021i	0.196131	+	1.63172i
$552$	−28.8323	−	46.1352i	−1.22718	−	1.96364i
$553$	5.58349	−	5.58349i	0.237434	−	0.237434i
$554$	−8.24676	−	8.24676i	−0.350371	−	0.350371i
$555$	−3.85396	−	6.16681i	−0.163591	−	0.261767i
$556$		−	38.8140i		−	1.64608i
$557$	4.76498			0.201899			0.100949	−	0.994892i	$-0.467812\pi$
$557$	4.76498			0.201899			0.100949	+	0.994892i	$0.467812\pi$
$558$	−63.7029	−	31.0607i	−2.69676	−	1.31490i
$559$	5.97598	+	5.97598i	0.252757	+	0.252757i
$560$	12.5966			0.532304
$561$	−7.72633	+	33.4754i	−0.326206	+	1.41333i
$562$	38.3204	−	38.3204i	1.61645	−	1.61645i
$563$	−16.8184	+	16.8184i	−0.708813	+	0.708813i	−0.966286	−	0.257473i	$-0.917110\pi$
$563$	−16.8184	+	16.8184i	−0.708813	+	0.708813i	0.257473	+	0.966286i	$0.417110\pi$
$564$	36.2165	+	57.9508i	1.52499	+	2.44017i
$565$	10.0819	−	10.0819i	0.424149	−	0.424149i
$566$	−56.0824	+	56.0824i	−2.35732	+	2.35732i
$567$	8.18934	+	10.4768i	0.343920	+	0.439984i
$568$	16.5012	−	16.5012i	0.692375	−	0.692375i
$569$	−19.9980	+	19.9980i	−0.838359	+	0.838359i	−0.988643	−	0.150284i	$-0.951981\pi$
$569$	−19.9980	+	19.9980i	−0.838359	+	0.838359i	0.150284	+	0.988643i	$0.451981\pi$
$570$	−31.2422	−	7.21090i	−1.30859	−	0.302031i
$571$	−0.743065			−0.0310963			−0.0155481	−	0.999879i	$-0.504949\pi$
$571$	−0.743065			−0.0310963			−0.0155481	+	0.999879i	$0.504949\pi$
$572$	−58.3308	−	58.3308i	−2.43894	−	2.43894i
$573$	−6.00354	−	9.60641i	−0.250801	−	0.401314i
$574$	−10.3262			−0.431006
$575$			4.53932i			0.189303i
$576$	5.41429	−	11.1043i	0.225595	−	0.462678i
$577$	3.28074	+	3.28074i	0.136579	+	0.136579i	0.772091	−	0.635512i	$-0.219211\pi$
$577$	3.28074	+	3.28074i	0.136579	+	0.136579i	−0.635512	+	0.772091i	$0.719211\pi$
$578$	9.29211	−	9.29211i	0.386501	−	0.386501i
$579$	0.672275	−	0.420139i	0.0279388	−	0.0174604i
$580$	19.8106	+	15.5592i	0.822589	+	0.646059i
$581$			10.2488i			0.425191i
$582$	3.76255	−	16.3018i	0.155963	−	0.675730i
$583$	−16.9228	+	16.9228i	−0.700871	+	0.700871i
$584$	10.8819			0.450298
$585$	−4.03501	+	8.27548i	−0.166827	+	0.342149i
$586$		−	44.9913i		−	1.85857i
$587$		−	36.5193i		−	1.50731i	−0.657269	−	0.753656i	$-0.728289\pi$
$587$		−	36.5193i		−	1.50731i	0.657269	−	0.753656i	$-0.271711\pi$
$588$	8.77690	−	38.0272i	0.361953	−	1.56821i
$589$			65.4904i			2.69849i
$590$	8.31691	−	8.31691i	0.342402	−	0.342402i
$591$	2.05906	−	8.92116i	0.0846983	−	0.366968i
$592$	−25.3105	−	25.3105i	−1.04026	−	1.04026i
$593$	36.2426			1.48830			0.744152	−	0.668010i	$-0.232854\pi$
$593$	36.2426			1.48830			0.744152	+	0.668010i	$0.232854\pi$
$594$	48.5474	−	59.9728i	1.99192	−	2.46071i
$595$	3.60629	+	3.60629i	0.147843	+	0.147843i
$596$			81.3419i			3.33190i
$597$	−12.0757	−	2.78715i	−0.494227	−	0.114071i
$598$	25.4552	+	25.4552i	1.04094	+	1.04094i
$599$	29.9471	+	29.9471i	1.22361	+	1.22361i	0.966341	+	0.257265i	$0.0828215\pi$
$599$	29.9471	+	29.9471i	1.22361	+	1.22361i	0.257265	+	0.966341i	$0.417179\pi$
$600$	−10.1635	+	6.35166i	−0.414921	+	0.259306i
$601$	−13.7025	+	13.7025i	−0.558936	+	0.558936i	−0.929005	−	0.370068i	$-0.879334\pi$
$601$	−13.7025	+	13.7025i	−0.558936	+	0.558936i	0.370068	+	0.929005i	$0.379334\pi$
$602$	−10.5144			−0.428535
$603$	14.4618	−	29.6600i	0.588930	−	1.20785i
$604$	−8.77091			−0.356883
$605$		−	22.0208i		−	0.895273i
$606$	−0.861756	+	3.73368i	−0.0350064	+	0.151670i
$607$	−4.12024	−	4.12024i	−0.167236	−	0.167236i	0.618528	−	0.785763i	$-0.287730\pi$
$607$	−4.12024	−	4.12024i	−0.167236	−	0.167236i	−0.785763	+	0.618528i	$0.787730\pi$
$608$	−58.6847			−2.37998
$609$	−10.7317	+	8.64623i	−0.434871	+	0.350363i
$610$	−27.5648			−1.11607
$611$	−18.3035	−	18.3035i	−0.740479	−	0.740479i
$612$	45.7982	−	15.7756i	1.85128	−	0.637692i
$613$		−	18.8727i		−	0.762260i	−0.924521	−	0.381130i	$-0.875535\pi$
$613$		−	18.8727i		−	0.762260i	0.924521	−	0.381130i	$-0.124465\pi$
$614$	−37.4763			−1.51242
$615$	3.97244	−	2.48258i	0.160184	−	0.100107i
$616$	58.7494			2.36708
$617$	−3.27074	+	3.27074i	−0.131675	+	0.131675i	−0.769873	−	0.638198i	$-0.779680\pi$
$617$	−3.27074	+	3.27074i	−0.131675	+	0.131675i	0.638198	+	0.769873i	$0.279680\pi$
$618$	−16.9103	−	27.0585i	−0.680230	−	1.08845i
$619$	−5.79114	−	5.79114i	−0.232766	−	0.232766i	0.581080	−	0.813846i	$-0.302630\pi$
$619$	−5.79114	−	5.79114i	−0.232766	−	0.232766i	−0.813846	+	0.581080i	$0.802630\pi$
$620$	30.2383	+	30.2383i	1.21440	+	1.21440i
$621$	−14.8405	+	18.3332i	−0.595530	+	0.735685i
$622$			57.1435i			2.29125i
$623$	−5.21654	−	5.21654i	−0.208996	−	0.208996i
$624$	−10.1917	+	44.1568i	−0.407993	+	1.76769i
$625$	1.00000			0.0400000
$626$	−2.20212	−	2.20212i	−0.0880142	−	0.0880142i
$627$	−69.4740	−	16.0350i	−2.77453	−	0.640377i
$628$	−40.0953	+	40.0953i	−1.59998	+	1.59998i
$629$		−	14.4923i		−	0.577846i
$630$	−3.73043	−	10.8298i	−0.148624	−	0.431470i
$631$		−	24.3720i		−	0.970234i	−0.874449	−	0.485117i	$-0.838777\pi$
$631$		−	24.3720i		−	0.970234i	0.874449	−	0.485117i	$-0.161223\pi$
$632$			36.9797i			1.47097i
$633$	11.0172	+	17.6288i	0.437893	+	0.700683i
$634$	64.8966			2.57737
$635$	−0.406447	+	0.406447i	−0.0161294	+	0.0161294i
$636$	32.8788	+	7.58864i	1.30373	+	0.300909i
$637$			14.7828i			0.585717i
$638$	62.8886	+	49.3925i	2.48978	+	1.95547i
$639$	−9.09413	−	4.43417i	−0.359758	−	0.175413i
$640$	4.06057	−	4.06057i	0.160508	−	0.160508i
$641$	7.64137	+	7.64137i	0.301816	+	0.301816i	0.841724	−	0.539908i	$-0.181541\pi$
$641$	7.64137	+	7.64137i	0.301816	+	0.301816i	−0.539908	+	0.841724i	$0.681541\pi$
$642$	−29.3266	+	18.3277i	−1.15743	+	0.723337i
$643$			20.0941i			0.792434i	0.918157	+	0.396217i	$0.129677\pi$
$643$			20.0941i			0.792434i	−0.918157	+	0.396217i	$0.870323\pi$
$644$	−31.3731			−1.23627
$645$	4.04485	−	2.52784i	0.159266	−	0.0995335i
$646$	−45.1834	−	45.1834i	−1.77772	−	1.77772i
$647$	−15.5535			−0.611472			−0.305736	−	0.952116i	$-0.598902\pi$
$647$	−15.5535			−0.611472			−0.305736	+	0.952116i	$0.598902\pi$
$648$	−61.8133	−	7.57491i	−2.42826	−	0.297571i
$649$	18.4945	−	18.4945i	0.725972	−	0.725972i
$650$	5.60771	−	5.60771i	0.219952	−	0.219952i
$651$	−19.8398	+	12.3989i	−0.777584	+	0.485952i
$652$	30.0332	−	30.0332i	1.17619	−	1.17619i
$653$	−0.628039	+	0.628039i	−0.0245771	+	0.0245771i	−0.719289	−	0.694711i	$-0.755532\pi$
$653$	−0.628039	+	0.628039i	−0.0245771	+	0.0245771i	0.694711	+	0.719289i	$0.255532\pi$
$654$	−43.5028	+	27.1871i	−1.70109	+	1.06310i
$655$	−11.2325	+	11.2325i	−0.438890	+	0.438890i
$656$	16.3041	−	16.3041i	0.636569	−	0.636569i
$657$	−1.53653	−	4.46071i	−0.0599459	−	0.174029i
$658$	32.2039			1.25544
$659$	−8.44075	−	8.44075i	−0.328805	−	0.328805i	0.523327	−	0.852132i	$-0.324691\pi$
$659$	−8.44075	−	8.44075i	−0.328805	−	0.328805i	−0.852132	+	0.523327i	$0.824691\pi$
$660$	−39.4813	+	24.6739i	−1.53681	+	0.960431i
$661$	8.03657			0.312587			0.156293	−	0.987711i	$-0.450046\pi$
$661$	8.03657			0.312587			0.156293	+	0.987711i	$0.450046\pi$
$662$			49.5010i			1.92391i
$663$	−15.5594	+	9.72389i	−0.604278	+	0.377644i
$664$	−33.9390	−	33.9390i	−1.31709	−	1.31709i
$665$	−7.48439	+	7.48439i	−0.290232	+	0.290232i
$666$	−14.2649	+	29.2560i	−0.552752	+	1.13365i
$667$	−19.2245	−	15.0989i	−0.744376	−	0.584631i
$668$			97.8827i			3.78719i
$669$	−46.5448	−	10.7428i	−1.79953	−	0.415342i
$670$	−20.0985	+	20.0985i	−0.776471	+	0.776471i
$671$	−61.2964			−2.36632
$672$	−11.1104	−	17.7781i	−0.428594	−	0.685804i
$673$		−	20.2070i		−	0.778923i	−0.921043	−	0.389462i	$-0.872661\pi$
$673$		−	20.2070i		−	0.778923i	0.921043	−	0.389462i	$-0.127339\pi$
$674$			79.9345i			3.07896i
$675$	4.03875	+	3.26933i	0.155451	+	0.125837i
$676$			16.7540i			0.644386i
$677$	19.2200	−	19.2200i	0.738684	−	0.738684i	−0.233640	−	0.972323i	$-0.575064\pi$
$677$	19.2200	−	19.2200i	0.738684	−	0.738684i	0.972323	+	0.233640i	$0.0750636\pi$
$678$	−62.1816	−	14.3519i	−2.38807	−	0.551181i
$679$	−3.90525	−	3.90525i	−0.149870	−	0.149870i
$680$	−23.8846			−0.915933
$681$	−3.03236	+	13.1381i	−0.116200	+	0.503454i
$682$	95.9913	+	95.9913i	3.67570	+	3.67570i
$683$		−	39.1668i		−	1.49868i	−0.662188	−	0.749338i	$-0.730372\pi$
$683$		−	39.1668i		−	1.49868i	0.662188	−	0.749338i	$-0.269628\pi$
$684$	32.7403	+	95.0483i	1.25186	+	3.63426i
$685$	10.9680	+	10.9680i	0.419065	+	0.419065i
$686$	−31.9034	−	31.9034i	−1.21808	−	1.21808i
$687$	−2.27711	−	3.64365i	−0.0868770	−	0.139014i
$688$	16.6013	−	16.6013i	0.632920	−	0.632920i
$689$	−12.7814			−0.486934
$690$	17.2294	−	10.7675i	0.655911	−	0.409913i
$691$	2.49481			0.0949071			0.0474535	−	0.998873i	$-0.484889\pi$
$691$	2.49481			0.0949071			0.0474535	+	0.998873i	$0.484889\pi$
$692$		−	6.51084i		−	0.247505i
$693$	−8.29544	−	24.0825i	−0.315118	−	0.914817i
$694$	−46.6216	−	46.6216i	−1.76973	−	1.76973i
$695$	8.29765			0.314748
$696$	6.90612	−	64.1705i	0.261776	−	2.43238i
$697$	9.33542			0.353604
$698$	55.2710	+	55.2710i	2.09204	+	2.09204i
$699$	6.99708	−	30.3159i	0.264654	−	1.14665i
$700$			6.91140i			0.261226i
$701$	22.8620			0.863487			0.431744	−	0.901996i	$-0.357898\pi$
$701$	22.8620			0.863487			0.431744	+	0.901996i	$0.357898\pi$
$702$	40.9816	−	4.31467i	1.54675	−	0.162847i
$703$	30.0769			1.13437
$704$	−16.7325	+	16.7325i	−0.630632	+	0.630632i
$705$	−12.3887	+	7.74236i	−0.466587	+	0.291594i
$706$	20.1864	+	20.1864i	0.759726	+	0.759726i
$707$	0.894440	+	0.894440i	0.0336389	+	0.0336389i
$708$	−35.9324	−	8.29342i	−1.35042	−	0.311686i
$709$			26.1378i			0.981627i	0.871265	+	0.490814i	$0.163300\pi$
$709$			26.1378i			0.981627i	−0.871265	+	0.490814i	$0.836700\pi$
$710$	6.16245	+	6.16245i	0.231272	+	0.231272i
$711$	15.1587	−	5.22155i	0.568494	−	0.195823i
$712$	34.5494			1.29479
$713$	−29.3437	−	29.3437i	−1.09893	−	1.09893i
$714$	5.13365	−	22.2423i	0.192122	−	0.832396i
$715$	12.4700	−	12.4700i	0.466351	−	0.466351i
$716$		−	87.7113i		−	3.27793i
$717$	−0.425806	+	1.84487i	−0.0159020	+	0.0688978i
$718$			30.7615i			1.14801i
$719$			18.4321i			0.687403i	0.939079	+	0.343702i	$0.111681\pi$
$719$			18.4321i			0.687403i	−0.939079	+	0.343702i	$0.888319\pi$
$720$	22.9893	+	11.2093i	0.856762	+	0.417746i
$721$	−10.5332			−0.392275
$722$	59.0546	−	59.0546i	2.19778	−	2.19778i
$723$	0.853770	−	3.69908i	0.0317520	−	0.137570i
$724$			53.6060i			1.99225i
$725$	−3.32624	+	4.23511i	−0.123533	+	0.157288i
$726$	−83.5818	+	52.2346i	−3.10201	+	1.93861i
$727$	24.8303	−	24.8303i	0.920906	−	0.920906i	−0.0761880	−	0.997093i	$-0.524275\pi$
$727$	24.8303	−	24.8303i	0.920906	−	0.920906i	0.997093	+	0.0761880i	$0.0242749\pi$
$728$	22.1861	+	22.1861i	0.822272	+	0.822272i
$729$	5.62297	+	26.4080i	0.208258	+	0.978074i
$730$			4.06391i			0.150412i
$731$	9.50560			0.351577
$732$	45.8021	+	73.2890i	1.69289	+	2.70884i
$733$	14.9376	+	14.9376i	0.551732	+	0.551732i	0.926940	−	0.375208i	$-0.122429\pi$
$733$	14.9376	+	14.9376i	0.551732	+	0.551732i	−0.375208	+	0.926940i	$0.622429\pi$
$734$	−34.3420			−1.26759
$735$	8.12945	+	1.87633i	0.299859	+	0.0692093i
$736$	26.2944	−	26.2944i	0.969223	−	0.969223i
$737$	−44.6933	+	44.6933i	−1.64630	+	1.64630i
$738$	−18.8457	−	9.18891i	−0.693720	−	0.338248i
$739$	31.9780	−	31.9780i	1.17633	−	1.17633i	0.195658	−	0.980672i	$-0.437316\pi$
$739$	31.9780	−	31.9780i	1.17633	−	1.17633i	0.980672	−	0.195658i	$-0.0626843\pi$
$740$	13.8872	−	13.8872i	0.510502	−	0.510502i
$741$	−20.1807	−	32.2916i	−0.741357	−	1.18626i
$742$	11.2441	−	11.2441i	0.412785	−	0.412785i
$743$	21.9492	−	21.9492i	0.805238	−	0.805238i	−0.178671	−	0.983909i	$-0.557180\pi$
$743$	21.9492	−	21.9492i	0.805238	−	0.805238i	0.983909	+	0.178671i	$0.0571797\pi$
$744$	24.6407	−	106.759i	0.903372	−	3.91399i
$745$	−17.3893			−0.637094
$746$	−47.4160	−	47.4160i	−1.73602	−	1.73602i
$747$	−9.12003	+	18.7044i	−0.333685	+	0.684360i
$748$	−92.7830			−3.39248
$749$			11.4161i			0.417134i
$750$	−2.37206	−	3.79558i	−0.0866152	−	0.138595i
$751$	−31.1220	−	31.1220i	−1.13566	−	1.13566i	−0.989220	−	0.146440i	$-0.953219\pi$
$751$	−31.1220	−	31.1220i	−1.13566	−	1.13566i	−0.146440	−	0.989220i	$-0.546781\pi$
$752$	−50.8472	+	50.8472i	−1.85421	+	1.85421i
$753$	24.2025	+	38.7270i	0.881988	+	1.41129i
$754$	5.09665	+	42.4018i	0.185609	+	1.54418i
$755$		−	1.87504i		−	0.0682399i
$756$	−22.5957	+	27.9134i	−0.821796	+	1.01520i
$757$	−2.55829	+	2.55829i	−0.0929825	+	0.0929825i	−0.752068	−	0.659086i	$-0.770944\pi$
$757$	−2.55829	+	2.55829i	−0.0929825	+	0.0929825i	0.659086	+	0.752068i	$0.270944\pi$
$758$	−63.3953			−2.30262
$759$	38.3133	−	23.9440i	1.39069	−	0.869111i
$760$		−	49.5695i		−	1.79807i
$761$		−	50.2357i		−	1.82104i	−0.413461	−	0.910522i	$-0.635680\pi$
$761$		−	50.2357i		−	1.82104i	0.413461	−	0.910522i	$-0.364320\pi$
$762$	2.50682	+	0.578590i	0.0908126	+	0.0209601i
$763$			16.9345i			0.613069i
$764$	21.6329	−	21.6329i	0.782649	−	0.782649i
$765$	3.37251	+	9.79074i	0.121934	+	0.353985i
$766$	5.36813	+	5.36813i	0.193958	+	0.193958i
$767$	13.9685			0.504373
$768$	−38.9438	−	8.98846i	−1.40526	−	0.324343i
$769$	−4.76282	−	4.76282i	−0.171752	−	0.171752i	0.615997	−	0.787749i	$-0.288753\pi$
$769$	−4.76282	−	4.76282i	−0.171752	−	0.171752i	−0.787749	+	0.615997i	$0.788753\pi$
$770$			21.9402i			0.790670i
$771$	−4.57383	+	19.8168i	−0.164722	+	0.713683i
$772$	1.51391	+	1.51391i	0.0544868	+	0.0544868i
$773$	−1.90572	−	1.90572i	−0.0685440	−	0.0685440i	0.672004	−	0.740548i	$-0.265434\pi$
$773$	−1.90572	−	1.90572i	−0.0685440	−	0.0685440i	−0.740548	+	0.672004i	$0.765434\pi$
$774$	−19.1892	−	9.35642i	−0.689743	−	0.336309i
$775$	−6.46434	+	6.46434i	−0.232206	+	0.232206i
$776$	25.8647			0.928487
$777$	5.69430	+	9.11159i	0.204282	+	0.326876i
$778$	58.3178			2.09079
$779$			19.3745i			0.694163i
$780$	−24.2276	−	5.59187i	−0.867486	−	0.200221i
$781$	13.7036	+	13.7036i	0.490352	+	0.490352i
$782$	40.4899			1.44791
$783$	−27.2798	+	6.22995i	−0.974901	+	0.222640i
$784$	41.0668			1.46667
$785$	−8.57158	−	8.57158i	−0.305933	−	0.305933i
$786$	69.2780	+	15.9898i	2.47107	+	0.570337i
$787$		−	15.5772i		−	0.555268i	−0.960687	−	0.277634i	$-0.910450\pi$
$787$		−	15.5772i		−	0.555268i	0.960687	−	0.277634i	$-0.0895502\pi$
$788$	24.7266			0.880847
$789$	−6.67584	−	10.6822i	−0.237666	−	0.380295i
$790$	−13.8102			−0.491346
$791$	−14.8962	+	14.8962i	−0.529648	+	0.529648i
$792$	107.220	+	52.2791i	3.80990	+	1.85766i
$793$	−23.1480	−	23.1480i	−0.822008	−	0.822008i
$794$	16.0676	+	16.0676i	0.570219	+	0.570219i
$795$	−1.62230	+	7.02884i	−0.0575370	+	0.249287i
$796$		−	33.4700i		−	1.18631i
$797$	−7.78162	−	7.78162i	−0.275639	−	0.275639i	0.555726	−	0.831365i	$-0.312440\pi$
$797$	−7.78162	−	7.78162i	−0.275639	−	0.275639i	−0.831365	+	0.555726i	$0.812440\pi$
$798$	46.1610	+	10.6542i	1.63408	+	0.377156i
$799$	−29.1141			−1.02998
$800$	−5.79257	−	5.79257i	−0.204798	−	0.204798i
$801$	−4.87838	−	14.1624i	−0.172369	−	0.500405i
$802$	1.88846	−	1.88846i	0.0666837	−	0.0666837i
$803$			9.03699i			0.318909i
$804$	86.8335	+	20.0417i	3.06238	+	0.706816i
$805$		−	6.70694i		−	0.236389i
$806$			72.5003i			2.55371i
$807$	33.7223	−	21.0748i	1.18708	−	0.741868i
$808$	−5.92392			−0.208403
$809$	14.1222	−	14.1222i	0.496511	−	0.496511i	−0.413839	−	0.910350i	$-0.635812\pi$
$809$	14.1222	−	14.1222i	0.496511	−	0.496511i	0.910350	+	0.413839i	$0.135812\pi$
$810$	2.82888	−	23.0844i	0.0993968	−	0.811105i
$811$			45.7669i			1.60709i	0.595242	+	0.803547i	$0.297056\pi$
$811$			45.7669i			1.60709i	−0.595242	+	0.803547i	$0.702944\pi$
$812$	−29.2705	−	22.9890i	−1.02719	−	0.806755i
$813$	11.6712	+	18.6754i	0.409328	+	0.654975i
$814$	44.0847	−	44.0847i	1.54517	−	1.54517i
$815$	6.42050	+	6.42050i	0.224900	+	0.224900i
$816$	27.0130	+	43.2242i	0.945645	+	1.51315i
$817$			19.7277i			0.690184i
$818$	90.1000			3.15027
$819$	5.96181	−	12.2272i	0.208323	−	0.427252i
$820$	8.94561	+	8.94561i	0.312394	+	0.312394i
$821$	19.5884			0.683641			0.341821	−	0.939765i	$-0.388957\pi$
$821$	19.5884			0.683641			0.341821	+	0.939765i	$0.388957\pi$
$822$	15.6132	−	67.6466i	0.544574	−	2.35945i
$823$	−33.1934	+	33.1934i	−1.15705	+	1.15705i	−0.171944	+	0.985107i	$0.555005\pi$
$823$	−33.1934	+	33.1934i	−1.15705	+	1.15705i	−0.985107	+	0.171944i	$0.944995\pi$
$824$	34.8808	−	34.8808i	1.21513	−	1.21513i
$825$	−5.27479	−	8.44032i	−0.183645	−	0.293854i
$826$	−12.2884	+	12.2884i	−0.427568	+	0.427568i
$827$	−21.1787	+	21.1787i	−0.736455	+	0.736455i	−0.971890	−	0.235435i	$-0.924348\pi$
$827$	−21.1787	+	21.1787i	−0.736455	+	0.736455i	0.235435	+	0.971890i	$0.424348\pi$
$828$	−57.2572	−	27.9178i	−1.98983	−	0.970212i
$829$	21.2914	−	21.2914i	0.739481	−	0.739481i	−0.232997	−	0.972478i	$-0.574853\pi$
$829$	21.2914	−	21.2914i	0.739481	−	0.739481i	0.972478	+	0.232997i	$0.0748531\pi$
$830$	12.6747	−	12.6747i	0.439944	−	0.439944i
$831$	−7.61685	−	1.75801i	−0.264225	−	0.0609848i
$832$	−12.6378			−0.438135
$833$	11.7570	+	11.7570i	0.407357	+	0.407357i
$834$	−19.6825	−	31.4944i	−0.681549	−	1.09056i
$835$	−20.9254			−0.724152
$836$		−	192.559i		−	6.65981i
$837$	−47.2419	+	4.97378i	−1.63292	+	0.171919i
$838$	35.8944	+	35.8944i	1.23995	+	1.23995i
$839$	−22.1609	+	22.1609i	−0.765080	+	0.765080i	−0.977236	−	0.212156i	$-0.931952\pi$
$839$	−22.1609	+	22.1609i	−0.765080	+	0.765080i	0.212156	+	0.977236i	$0.431952\pi$
$840$	15.0167	−	9.38471i	0.518126	−	0.323803i
$841$	−6.87225	−	28.1740i	−0.236974	−	0.971516i
$842$		−	0.433467i		−	0.0149383i
$843$	8.16900	−	35.3934i	0.281355	−	1.21901i
$844$	−39.6987	+	39.6987i	−1.36649	+	1.36649i
$845$	−3.58168			−0.123214
$846$	58.7735	+	28.6572i	2.02068	+	0.985254i
$847$			32.5362i			1.11796i
$848$			35.5070i			1.21931i
$849$	−11.9555	+	51.7987i	−0.410310	+	1.77773i
$850$		−	8.91981i		−	0.305947i
$851$	−13.4763	+	13.4763i	−0.461963	+	0.461963i
$852$	6.14504	−	26.6243i	0.210526	−	0.912133i
$853$	11.5043	+	11.5043i	0.393899	+	0.393899i	0.876075	−	0.482175i	$-0.160153\pi$
$853$	11.5043	+	11.5043i	0.393899	+	0.393899i	−0.482175	+	0.876075i	$0.660153\pi$
$854$	40.7275			1.39367
$855$	−20.3194	+	6.99923i	−0.694910	+	0.239369i
$856$	−37.8046	−	37.8046i	−1.29213	−	1.29213i
$857$			13.4094i			0.458058i	0.973420	+	0.229029i	$0.0735551\pi$
$857$			13.4094i			0.458058i	−0.973420	+	0.229029i	$0.926445\pi$
$858$	−76.9103	−	17.7514i	−2.62567	−	0.606022i
$859$	−12.2687	−	12.2687i	−0.418604	−	0.418604i	0.466118	−	0.884722i	$-0.345652\pi$
$859$	−12.2687	−	12.2687i	−0.418604	−	0.418604i	−0.884722	+	0.466118i	$0.845652\pi$
$860$	9.10868	+	9.10868i	0.310603	+	0.310603i
$861$	−5.86936	+	3.66806i	−0.200027	+	0.125007i
$862$	−37.2013	+	37.2013i	−1.26708	+	1.26708i
$863$	−32.3492			−1.10118			−0.550589	−	0.834776i	$-0.685597\pi$
$863$	−32.3492			−1.10118			−0.550589	+	0.834776i	$0.685597\pi$
$864$	−4.45691	−	42.3326i	−0.151627	−	1.44018i
$865$	1.39189			0.0473256
$866$		−	51.7510i		−	1.75857i
$867$	1.98086	−	8.58235i	0.0672734	−	0.291472i
$868$	−44.6777	−	44.6777i	−1.51646	−	1.51646i
$869$	−30.7101			−1.04177
$870$	23.9647	+	2.57912i	0.812481	+	0.0874403i
$871$	−33.7560			−1.14378
$872$	−56.0789	−	56.0789i	−1.89907	−	1.89907i
$873$	−3.65210	−	10.6024i	−0.123605	−	0.358837i
$874$			84.0316i			2.84241i
$875$	−1.47752			−0.0499493
$876$	10.8051	−	6.75265i	0.365070	−	0.228151i
$877$	−41.0284			−1.38543			−0.692716	−	0.721210i	$-0.743586\pi$
$877$	−41.0284			−1.38543			−0.692716	+	0.721210i	$0.743586\pi$
$878$	−37.5181	+	37.5181i	−1.26617	+	1.26617i
$879$	−15.9818	−	25.5729i	−0.539054	−	0.862553i
$880$	−34.6417	−	34.6417i	−1.16777	−	1.16777i
$881$	−1.15422	−	1.15422i	−0.0388866	−	0.0388866i	0.687396	−	0.726283i	$-0.258754\pi$
$881$	−1.15422	−	1.15422i	−0.0388866	−	0.0388866i	−0.726283	+	0.687396i	$0.758754\pi$
$882$	−12.1618	−	35.3068i	−0.409508	−	1.18884i
$883$			18.8009i			0.632701i	0.948642	+	0.316351i	$0.102458\pi$
$883$			18.8009i			0.632701i	−0.948642	+	0.316351i	$0.897542\pi$
$884$	−35.0386	−	35.0386i	−1.17847	−	1.17847i
$885$	1.77297	−	7.68164i	0.0595977	−	0.258215i
$886$	23.3679			0.785059
$887$	13.5814	+	13.5814i	0.456018	+	0.456018i	0.897346	−	0.441328i	$-0.145492\pi$
$887$	13.5814	+	13.5814i	0.456018	+	0.456018i	−0.441328	+	0.897346i	$0.645492\pi$
$888$	−49.0300	−	11.3164i	−1.64534	−	0.379754i
$889$	0.600534	−	0.600534i	0.0201413	−	0.0201413i
$890$			12.9026i			0.432496i
$891$	6.29064	−	51.3334i	0.210744	−	1.71973i
$892$		−	129.007i		−	4.31948i
$893$		−	60.4227i		−	2.02197i
$894$	41.2484	+	66.0025i	1.37955	+	2.20745i
$895$	18.7509			0.626775
$896$	−5.99958	+	5.99958i	−0.200432	+	0.200432i
$897$	23.5108	+	5.42644i	0.785004	+	0.181184i
$898$		−	69.5042i		−	2.31939i
$899$	−5.87522	−	48.8792i	−0.195950	−	1.63021i
$900$	−6.15022	+	12.6136i	−0.205007	+	0.420453i
$901$	−10.1653	+	10.1653i	−0.338655	+	0.338655i
$902$	28.3978	+	28.3978i	0.945543	+	0.945543i
$903$	−5.97635	+	3.73493i	−0.198881	+	0.124291i
$904$		−	98.6583i		−	3.28133i
$905$	−11.4599			−0.380940
$906$	−7.11689	+	4.44771i	−0.236443	+	0.147765i
$907$	−15.9667	−	15.9667i	−0.530165	−	0.530165i	0.390457	−	0.920621i	$-0.372317\pi$
$907$	−15.9667	−	15.9667i	−0.530165	−	0.530165i	−0.920621	+	0.390457i	$0.872317\pi$
$908$	−36.4146			−1.20846
$909$	0.836460	+	2.42832i	0.0277436	+	0.0805424i
$910$	−8.28550	+	8.28550i	−0.274662	+	0.274662i
$911$	−3.24011	+	3.24011i	−0.107350	+	0.107350i	−0.758741	−	0.651392i	$-0.774185\pi$
$911$	−3.24011	+	3.24011i	−0.107350	+	0.107350i	0.651392	+	0.758741i	$0.274185\pi$
$912$	−89.7064	+	56.0622i	−2.97048	+	1.85640i
$913$	28.1849	−	28.1849i	0.932785	−	0.932785i
$914$	72.3509	−	72.3509i	2.39315	−	2.39315i
$915$	−15.6677	+	9.79157i	−0.517959	+	0.323699i
$916$	8.20521	−	8.20521i	0.271108	−	0.271108i
$917$	16.5962	−	16.5962i	0.548056	−	0.548056i
$918$	29.1618	−	36.0248i	0.962482	−	1.18900i
$919$	10.0391			0.331158			0.165579	−	0.986197i	$-0.447051\pi$
$919$	10.0391			0.331158			0.165579	+	0.986197i	$0.447051\pi$
$920$	22.2102	+	22.2102i	0.732248	+	0.732248i
$921$	−21.3014	+	13.3124i	−0.701906	+	0.438657i
$922$	−59.7124			−1.96652
$923$			10.3500i			0.340675i
$924$	58.3344	−	36.4562i	1.91906	−	1.19932i
$925$	2.96880	+	2.96880i	0.0976135	+	0.0976135i
$926$	−22.2773	+	22.2773i	−0.732076	+	0.732076i
$927$	−19.2235	−	9.37311i	−0.631382	−	0.307853i
$928$	43.7996	−	5.26467i	1.43779	−	0.172821i
$929$		−	29.0252i		−	0.952285i	−0.879368	−	0.476143i	$-0.842035\pi$
$929$		−	29.0252i		−	0.952285i	0.879368	−	0.476143i	$-0.157965\pi$
$930$	39.8698	+	9.20218i	1.30738	+	0.301751i
$931$	−24.4002	+	24.4002i	−0.799685	+	0.799685i
$932$	84.0257			2.75235
$933$	20.2985	+	32.4802i	0.664544	+	1.06335i
$934$		−	31.9895i		−	1.04673i
$935$		−	19.8352i		−	0.648679i
$936$	20.7479	+	60.2333i	0.678167	+	1.96879i
$937$		−	26.5712i		−	0.868043i	−0.900902	−	0.434022i	$-0.857094\pi$
$937$		−	26.5712i		−	0.868043i	0.900902	−	0.434022i	$-0.142906\pi$
$938$	29.6959	−	29.6959i	0.969604	−	0.969604i
$939$	−2.03391	−	0.469439i	−0.0663742	−	0.0153196i
$940$	−27.8984	−	27.8984i	−0.909946	−	0.909946i
$941$	−33.1000			−1.07903			−0.539514	−	0.841977i	$-0.681392\pi$
$941$	−33.1000			−1.07903			−0.539514	+	0.841977i	$0.681392\pi$
$942$	−12.2019	+	52.8664i	−0.397559	+	1.72248i
$943$	−8.68097	−	8.68097i	−0.282691	−	0.282691i
$944$		−	38.8046i		−	1.26298i
$945$	−5.96733	−	4.83050i	−0.194117	−	0.157136i
$946$	28.9155	+	28.9155i	0.940123	+	0.940123i
$947$	24.6302	+	24.6302i	0.800375	+	0.800375i	0.983154	−	0.182779i	$-0.0585093\pi$
$947$	24.6302	+	24.6302i	0.800375	+	0.800375i	−0.182779	+	0.983154i	$0.558509\pi$
$948$	22.9473	+	36.7185i	0.745293	+	1.19256i
$949$	−3.41273	+	3.41273i	−0.110782	+	0.110782i
$950$	18.5119			0.600606
$951$	36.8870	−	23.0526i	1.19614	−	0.747532i
$952$	35.2900			1.14375
$953$			15.2406i			0.493691i	0.969055	+	0.246845i	$0.0793940\pi$
$953$			15.2406i			0.493691i	−0.969055	+	0.246845i	$0.920606\pi$
$954$	30.5268	−	10.5152i	0.988340	−	0.340443i
$955$	4.62467	+	4.62467i	0.149651	+	0.149651i
$956$	−5.11337			−0.165378
$957$	53.2909	+	5.73524i	1.72265	+	0.185394i
$958$	68.5121			2.21353
$959$	−16.2054	−	16.2054i	−0.523300	−	0.523300i
$960$	−1.60406	+	6.94982i	−0.0517708	+	0.224305i
$961$		−	52.5755i		−	1.69598i
$962$	33.2963			1.07352
$963$	−10.1588	+	20.8348i	−0.327362	+	0.671392i
$964$	10.2526			0.330216
$965$	−0.323644	+	0.323644i	−0.0104185	+	0.0104185i
$966$	−25.4568	+	15.9092i	−0.819058	+	0.511871i
$967$	15.6043	+	15.6043i	0.501799	+	0.501799i	0.911997	−	0.410197i	$-0.134540\pi$
$967$	15.6043	+	15.6043i	0.501799	+	0.501799i	−0.410197	+	0.911997i	$0.634540\pi$
$968$	−107.744	−	107.744i	−3.46303	−	3.46303i
$969$	−41.7321	−	9.63202i	−1.34063	−	0.309425i
$970$			9.65927i			0.310140i
$971$	−18.0177	−	18.0177i	−0.578214	−	0.578214i	0.356197	−	0.934411i	$-0.384073\pi$
$971$	−18.0177	−	18.0177i	−0.578214	−	0.578214i	−0.934411	+	0.356197i	$0.884073\pi$
$972$	−66.0772	+	30.8361i	−2.11943	+	0.989067i
$973$	−12.2599			−0.393036
$974$	40.0874	+	40.0874i	1.28448	+	1.28448i
$975$	1.19543	−	5.17937i	0.0382844	−	0.165873i
$976$	−64.3052	+	64.3052i	−2.05836	+	2.05836i
$977$		−	8.97161i		−	0.287027i	−0.989648	−	0.143514i	$-0.954160\pi$
$977$		−	8.97161i		−	0.287027i	0.989648	−	0.143514i	$-0.0458401\pi$
$978$	9.13976	−	39.5993i	0.292257	−	1.26625i
$979$			28.6918i			0.916994i
$980$			22.5322i			0.719765i
$981$	−15.0694	+	30.9061i	−0.481130	+	0.986757i
$982$	6.51178			0.207799
$983$	19.4126	−	19.4126i	0.619165	−	0.619165i	−0.326152	−	0.945317i	$-0.605752\pi$
$983$	19.4126	−	19.4126i	0.619165	−	0.619165i	0.945317	+	0.326152i	$0.105752\pi$
$984$	7.28964	−	31.5834i	0.232385	−	1.00684i
$985$			5.28605i			0.168427i
$986$	37.7763	+	29.6694i	1.20304	+	0.944867i
$987$	18.3046	−	11.4395i	0.582642	−	0.364123i
$988$	72.7181	−	72.7181i	2.31347	−	2.31347i
$989$	−8.83922	−	8.83922i	−0.281071	−	0.281071i
$990$	−19.5239	+	40.0418i	−0.620509	+	1.27261i
$991$		−	0.880939i		−	0.0279840i	−0.999902	−	0.0139920i	$-0.995546\pi$
$991$		−	0.880939i		−	0.0279840i	0.999902	−	0.0139920i	$-0.00445393\pi$
$992$	74.8904			2.37777
$993$	17.5838	+	28.1362i	0.558004	+	0.892876i
$994$	−9.10514	−	9.10514i	−0.288797	−	0.288797i
$995$	7.15522			0.226836
$996$	−54.7598	−	12.6389i	−1.73513	−	0.400478i
$997$	−2.98903	+	2.98903i	−0.0946635	+	0.0946635i	−0.752853	−	0.658189i	$-0.771323\pi$
$997$	−2.98903	+	2.98903i	−0.0946635	+	0.0946635i	0.658189	+	0.752853i	$0.271323\pi$
$998$	18.9481	−	18.9481i	0.599792	−	0.599792i
$999$	2.28425	+	21.6962i	0.0722704	+	0.686437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.q.c.191.17	yes	36
3.2	odd	2		435.2.q.d.191.2	yes	36
29.12	odd	4		435.2.q.d.41.2	yes	36
87.41	even	4	inner	435.2.q.c.41.17	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.q.c.41.17	✓	36	87.41	even	4	inner
435.2.q.c.191.17	yes	36	1.1	even	1	trivial
435.2.q.d.41.2	yes	36	29.12	odd	4
435.2.q.d.191.2	yes	36	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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.82725 + 1.82725i) q^{2} +(1.68768 + 0.389527i) q^{3} +4.67770i q^{4} -1.00000 q^{5} +(2.37206 + 3.79558i) q^{6} +1.47752 q^{7} +(-4.89284 + 4.89284i) q^{8} +(2.69654 + 1.31480i) q^{9} +O(q^{10})\)	\(q+(1.82725 + 1.82725i) q^{2} +(1.68768 + 0.389527i) q^{3} +4.67770i q^{4} -1.00000 q^{5} +(2.37206 + 3.79558i) q^{6} +1.47752 q^{7} +(-4.89284 + 4.89284i) q^{8} +(2.69654 + 1.31480i) q^{9} +(-1.82725 - 1.82725i) q^{10} +(-4.06330 - 4.06330i) q^{11} +(-1.82209 + 7.89447i) q^{12} -3.06893i q^{13} +(2.69980 + 2.69980i) q^{14} +(-1.68768 - 0.389527i) q^{15} -8.52551 q^{16} +(-2.44077 - 2.44077i) q^{17} +(2.52479 + 7.32972i) q^{18} +(5.06551 - 5.06551i) q^{19} -4.67770i q^{20} +(2.49358 + 0.575534i) q^{21} -14.8493i q^{22} +4.53932i q^{23} +(-10.1635 + 6.35166i) q^{24} +1.00000 q^{25} +(5.60771 - 5.60771i) q^{26} +(4.03875 + 3.26933i) q^{27} +6.91140i q^{28} +(-3.32624 + 4.23511i) q^{29} +(-2.37206 - 3.79558i) q^{30} +(-6.46434 + 6.46434i) q^{31} +(-5.79257 - 5.79257i) q^{32} +(-5.27479 - 8.44032i) q^{33} -8.91981i q^{34} -1.47752 q^{35} +(-6.15022 + 12.6136i) q^{36} +(2.96880 + 2.96880i) q^{37} +18.5119 q^{38} +(1.19543 - 5.17937i) q^{39} +(4.89284 - 4.89284i) q^{40} +(-1.91239 + 1.91239i) q^{41} +(3.50476 + 5.60805i) q^{42} +(-1.94725 + 1.94725i) q^{43} +(19.0069 - 19.0069i) q^{44} +(-2.69654 - 1.31480i) q^{45} +(-8.29449 + 8.29449i) q^{46} +(5.96413 - 5.96413i) q^{47} +(-14.3883 - 3.32092i) q^{48} -4.81693 q^{49} +(1.82725 + 1.82725i) q^{50} +(-3.16850 - 5.06999i) q^{51} +14.3555 q^{52} -4.16479i q^{53} +(1.40592 + 13.3537i) q^{54} +(4.06330 + 4.06330i) q^{55} +(-7.22927 + 7.22927i) q^{56} +(10.5221 - 6.57581i) q^{57} +(-13.8165 + 1.66073i) q^{58} +4.55159i q^{59} +(1.82209 - 7.89447i) q^{60} +(7.54268 - 7.54268i) q^{61} -23.6240 q^{62} +(3.98419 + 1.94264i) q^{63} -4.11797i q^{64} +3.06893i q^{65} +(5.78422 - 25.0610i) q^{66} -10.9993i q^{67} +(11.4172 - 11.4172i) q^{68} +(-1.76819 + 7.66093i) q^{69} +(-2.69980 - 2.69980i) q^{70} -3.37252 q^{71} +(-19.6268 + 6.76065i) q^{72} +(-1.11203 - 1.11203i) q^{73} +10.8495i q^{74} +(1.68768 + 0.389527i) q^{75} +(23.6950 + 23.6950i) q^{76} +(-6.00361 - 6.00361i) q^{77} +(11.6484 - 7.27967i) q^{78} +(3.77896 - 3.77896i) q^{79} +8.52551 q^{80} +(5.54263 + 7.09079i) q^{81} -6.98885 q^{82} +6.93647i q^{83} +(-2.69218 + 11.6642i) q^{84} +(2.44077 + 2.44077i) q^{85} -7.11625 q^{86} +(-7.26332 + 5.85185i) q^{87} +39.7622 q^{88} +(-3.53060 - 3.53060i) q^{89} +(-2.52479 - 7.32972i) q^{90} -4.53440i q^{91} -21.2336 q^{92} +(-13.4278 + 8.39172i) q^{93} +21.7959 q^{94} +(-5.06551 + 5.06551i) q^{95} +(-7.51965 - 12.0324i) q^{96} +(-2.64311 - 2.64311i) q^{97} +(-8.80176 - 8.80176i) q^{98} +(-5.61443 - 16.2992i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8}+O(q^{10}) \) 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8	\( 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8} + 4 q^{10} - 12 q^{11} + 10 q^{12} + 28 q^{14} - 6 q^{15} - 60 q^{16} - 20 q^{17} - 28 q^{18} + 16 q^{19} + 12 q^{21} + 24 q^{24} + 36 q^{25} + 4 q^{26} + 30 q^{27} - 28 q^{29} - 8 q^{30} - 8 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{35} - 28 q^{36} - 4 q^{37} + 24 q^{38} - 40 q^{39} - 4 q^{40} + 48 q^{41} - 8 q^{42} + 4 q^{43} + 16 q^{44} + 20 q^{46} - 20 q^{47} - 14 q^{48} + 28 q^{49} - 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} - 84 q^{56} + 28 q^{57} - 64 q^{58} - 10 q^{60} + 20 q^{61} + 8 q^{62} + 32 q^{63} + 40 q^{66} + 60 q^{68} + 36 q^{69} - 28 q^{70} - 16 q^{71} - 132 q^{72} + 8 q^{73} + 6 q^{75} + 16 q^{76} + 32 q^{77} + 48 q^{78} + 12 q^{79} + 60 q^{80} - 60 q^{81} + 56 q^{82} + 44 q^{84} + 20 q^{85} + 8 q^{86} + 22 q^{87} - 24 q^{88} + 20 q^{89} + 28 q^{90} - 16 q^{92} + 24 q^{93} + 52 q^{94} - 16 q^{95} - 8 q^{96} + 4 q^{97} - 8 q^{98} - 48 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8 + 4 * q^10 - 12 * q^11 + 10 * q^12 + 28 * q^14 - 6 * q^15 - 60 * q^16 - 20 * q^17 - 28 * q^18 + 16 * q^19 + 12 * q^21 + 24 * q^24 + 36 * q^25 + 4 * q^26 + 30 * q^27 - 28 * q^29 - 8 * q^30 - 8 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^35 - 28 * q^36 - 4 * q^37 + 24 * q^38 - 40 * q^39 - 4 * q^40 + 48 * q^41 - 8 * q^42 + 4 * q^43 + 16 * q^44 + 20 * q^46 - 20 * q^47 - 14 * q^48 + 28 * q^49 - 4 * q^50 - 44 * q^52 - 24 * q^54 + 12 * q^55 - 84 * q^56 + 28 * q^57 - 64 * q^58 - 10 * q^60 + 20 * q^61 + 8 * q^62 + 32 * q^63 + 40 * q^66 + 60 * q^68 + 36 * q^69 - 28 * q^70 - 16 * q^71 - 132 * q^72 + 8 * q^73 + 6 * q^75 + 16 * q^76 + 32 * q^77 + 48 * q^78 + 12 * q^79 + 60 * q^80 - 60 * q^81 + 56 * q^82 + 44 * q^84 + 20 * q^85 + 8 * q^86 + 22 * q^87 - 24 * q^88 + 20 * q^89 + 28 * q^90 - 16 * q^92 + 24 * q^93 + 52 * q^94 - 16 * q^95 - 8 * q^96 + 4 * q^97 - 8 * q^98 - 48 * q^99

Introduction

L-functions

Modular forms

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