LMFDB - Embedded newform 429.2.be.a.89.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(89,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("429.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.be (of order $12$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			89.12
Character	$\chi$	$=$	429.89
Dual form			429.2.be.a.188.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.52005 - 0.407295i) q^{2} +(1.56613 - 0.739746i) q^{3} +(0.412602 + 0.238216i) q^{4} +(1.90285 - 1.90285i) q^{5} +(-2.68189 + 0.486569i) q^{6} +(-1.32203 - 4.93388i) q^{7} +(1.69535 + 1.69535i) q^{8} +(1.90555 - 2.31708i) q^{9} +O(q^{10})$	\(q+(-1.52005 - 0.407295i) q^{2} +(1.56613 - 0.739746i) q^{3} +(0.412602 + 0.238216i) q^{4} +(1.90285 - 1.90285i) q^{5} +(-2.68189 + 0.486569i) q^{6} +(-1.32203 - 4.93388i) q^{7} +(1.69535 + 1.69535i) q^{8} +(1.90555 - 2.31708i) q^{9} +(-3.66744 + 2.11740i) q^{10} +(0.258819 - 0.965926i) q^{11} +(0.822410 + 0.0678576i) q^{12} +(-1.37272 + 3.33401i) q^{13} +8.03818i q^{14} +(1.57249 - 4.38774i) q^{15} +(-2.36294 - 4.09273i) q^{16} +(-0.464145 + 0.803922i) q^{17} +(-3.84027 + 2.74595i) q^{18} +(-2.87884 + 0.771382i) q^{19} +(1.23841 - 0.331830i) q^{20} +(-5.72029 - 6.74915i) q^{21} +(-0.786834 + 1.36284i) q^{22} +(4.28495 + 7.42175i) q^{23} +(3.90928 + 1.40102i) q^{24} -2.24166i q^{25} +(3.44453 - 4.50875i) q^{26} +(1.27030 - 5.03849i) q^{27} +(0.629857 - 2.35066i) q^{28} +(1.61773 - 0.933998i) q^{29} +(-4.17737 + 6.02910i) q^{30} +(-0.838107 - 0.838107i) q^{31} +(0.683743 + 2.55176i) q^{32} +(-0.309194 - 1.70423i) q^{33} +(1.03296 - 1.03296i) q^{34} +(-11.9040 - 6.87280i) q^{35} +(1.33820 - 0.502100i) q^{36} +(5.42747 + 1.45429i) q^{37} +4.69015 q^{38} +(0.316454 + 6.23697i) q^{39} +6.45200 q^{40} +(5.56664 + 1.49158i) q^{41} +(5.94621 + 12.5889i) q^{42} +(-5.64759 - 3.26064i) q^{43} +(0.336888 - 0.336888i) q^{44} +(-0.783077 - 8.03503i) q^{45} +(-3.49048 - 13.0267i) q^{46} +(-6.11240 - 6.11240i) q^{47} +(-6.72826 - 4.66179i) q^{48} +(-16.5332 + 9.54546i) q^{49} +(-0.913018 + 3.40743i) q^{50} +(-0.132215 + 1.60240i) q^{51} +(-1.36060 + 1.04862i) q^{52} -5.24956i q^{53} +(-3.98307 + 7.14135i) q^{54} +(-1.34552 - 2.33050i) q^{55} +(6.12336 - 10.6060i) q^{56} +(-3.93802 + 3.33770i) q^{57} +(-2.83944 + 0.760826i) q^{58} +(8.53194 - 2.28613i) q^{59} +(1.69404 - 1.43580i) q^{60} +(-3.64778 + 6.31814i) q^{61} +(0.932605 + 1.61532i) q^{62} +(-13.9514 - 6.33852i) q^{63} +5.29447i q^{64} +(3.73204 + 8.95620i) q^{65} +(-0.224136 + 2.71644i) q^{66} +(2.60320 - 9.71527i) q^{67} +(-0.383014 + 0.221133i) q^{68} +(12.2010 + 8.45369i) q^{69} +(15.2954 + 15.2954i) q^{70} +(-0.282569 - 1.05456i) q^{71} +(7.15886 - 0.697686i) q^{72} +(8.87218 - 8.87218i) q^{73} +(-7.65768 - 4.42117i) q^{74} +(-1.65826 - 3.51074i) q^{75} +(-1.37157 - 0.367511i) q^{76} -5.10793 q^{77} +(2.05927 - 9.60938i) q^{78} +4.53164 q^{79} +(-12.2842 - 3.29153i) q^{80} +(-1.73774 - 8.83064i) q^{81} +(-7.85404 - 4.53453i) q^{82} +(-4.39090 + 4.39090i) q^{83} +(-0.752448 - 4.14738i) q^{84} +(0.646545 + 2.41294i) q^{85} +(7.25656 + 7.25656i) q^{86} +(1.84266 - 2.65948i) q^{87} +(2.07637 - 1.19880i) q^{88} +(-2.67759 + 9.99292i) q^{89} +(-2.08232 + 12.5326i) q^{90} +(18.2644 + 2.36518i) q^{91} +4.08298i q^{92} +(-1.93257 - 0.692602i) q^{93} +(6.80158 + 11.7807i) q^{94} +(-4.01017 + 6.94581i) q^{95} +(2.95849 + 3.49061i) q^{96} +(11.9037 - 3.18958i) q^{97} +(29.0191 - 7.77564i) q^{98} +(-1.74494 - 2.44033i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 12 q^{6} + 12 q^{7}+O(q^{10}) $ 184 * q - 12 * q^6 + 12 * q^7	$ 184 q - 12 q^{6} + 12 q^{7} - 48 q^{10} - 16 q^{13} + 16 q^{15} + 80 q^{16} - 8 q^{18} - 4 q^{19} - 24 q^{24} - 48 q^{27} - 40 q^{28} + 48 q^{30} - 20 q^{31} + 16 q^{34} - 36 q^{36} + 44 q^{37} + 48 q^{39} - 80 q^{40} + 20 q^{42} - 84 q^{43} - 4 q^{45} - 64 q^{46} + 44 q^{48} - 60 q^{49} - 200 q^{52} - 4 q^{54} - 64 q^{57} - 48 q^{58} - 148 q^{60} - 48 q^{61} + 40 q^{66} + 48 q^{67} - 12 q^{69} + 24 q^{70} - 128 q^{72} + 108 q^{73} - 60 q^{75} - 24 q^{76} + 148 q^{78} + 32 q^{79} + 16 q^{81} - 48 q^{82} + 116 q^{84} + 104 q^{85} - 24 q^{87} + 72 q^{88} + 60 q^{91} + 36 q^{93} + 16 q^{94} - 72 q^{96} + 4 q^{97}+O(q^{100}) $ 184 * q - 12 * q^6 + 12 * q^7 - 48 * q^10 - 16 * q^13 + 16 * q^15 + 80 * q^16 - 8 * q^18 - 4 * q^19 - 24 * q^24 - 48 * q^27 - 40 * q^28 + 48 * q^30 - 20 * q^31 + 16 * q^34 - 36 * q^36 + 44 * q^37 + 48 * q^39 - 80 * q^40 + 20 * q^42 - 84 * q^43 - 4 * q^45 - 64 * q^46 + 44 * q^48 - 60 * q^49 - 200 * q^52 - 4 * q^54 - 64 * q^57 - 48 * q^58 - 148 * q^60 - 48 * q^61 + 40 * q^66 + 48 * q^67 - 12 * q^69 + 24 * q^70 - 128 * q^72 + 108 * q^73 - 60 * q^75 - 24 * q^76 + 148 * q^78 + 32 * q^79 + 16 * q^81 - 48 * q^82 + 116 * q^84 + 104 * q^85 - 24 * q^87 + 72 * q^88 + 60 * q^91 + 36 * q^93 + 16 * q^94 - 72 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

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 $

$2$	−1.52005	−	0.407295i	−1.07484	−	0.288001i	−0.322357	−	0.946618i	$-0.604475\pi$
$2$	−1.52005	−	0.407295i	−1.07484	−	0.288001i	−0.752478	+	0.658617i	$0.771142\pi$
$3$	1.56613	−	0.739746i	0.904208	−	0.427092i
$3$	1.56613	−	0.739746i	0.904208	−	0.427092i
$4$	0.412602	+	0.238216i	0.206301	+	0.119108i
$5$	1.90285	−	1.90285i	0.850979	−	0.850979i	−0.139274	−	0.990254i	$-0.544477\pi$
$5$	1.90285	−	1.90285i	0.850979	−	0.850979i	0.990254	+	0.139274i	$0.0444770\pi$
$6$	−2.68189	+	0.486569i	−1.09488	+	0.198641i
$7$	−1.32203	−	4.93388i	−0.499680	−	1.86483i	−0.502058	−	0.864834i	$-0.667424\pi$
$7$	−1.32203	−	4.93388i	−0.499680	−	1.86483i	0.00237853	−	0.999997i	$-0.499243\pi$
$8$	1.69535	+	1.69535i	0.599398	+	0.599398i
$9$	1.90555	−	2.31708i	0.635184	−	0.772361i
$10$	−3.66744	+	2.11740i	−1.15975	+	0.669580i
$11$	0.258819	−	0.965926i	0.0780369	−	0.291238i
$11$	0.258819	−	0.965926i	0.0780369	−	0.291238i
$12$	0.822410	+	0.0678576i	0.237409	+	0.0195888i
$13$	−1.37272	+	3.33401i	−0.380725	+	0.924688i
$13$	−1.37272	+	3.33401i	−0.380725	+	0.924688i
$14$			8.03818i			2.14829i
$15$	1.57249	−	4.38774i	0.406016	−	1.13291i
$16$	−2.36294	−	4.09273i	−0.590735	−	1.02318i
$17$	−0.464145	+	0.803922i	−0.112572	+	0.194980i	−0.916806	−	0.399332i	$-0.869242\pi$
$17$	−0.464145	+	0.803922i	−0.112572	+	0.194980i	0.804235	+	0.594312i	$0.202575\pi$
$18$	−3.84027	+	2.74595i	−0.905159	+	0.647227i
$19$	−2.87884	+	0.771382i	−0.660451	+	0.176967i	−0.573449	−	0.819241i	$-0.694395\pi$
$19$	−2.87884	+	0.771382i	−0.660451	+	0.176967i	−0.0870013	+	0.996208i	$0.527728\pi$
$20$	1.23841	−	0.331830i	0.276916	−	0.0741995i
$21$	−5.72029	−	6.74915i	−1.24827	−	1.47279i
$22$	−0.786834	+	1.36284i	−0.167754	+	0.290558i
$23$	4.28495	+	7.42175i	0.893474	+	1.54754i	0.835682	+	0.549214i	$0.185073\pi$
$23$	4.28495	+	7.42175i	0.893474	+	1.54754i	0.0577925	+	0.998329i	$0.481594\pi$
$24$	3.90928	+	1.40102i	0.797978	+	0.285982i
$25$		−	2.24166i		−	0.448332i
$26$	3.44453	−	4.50875i	0.675528	−	0.884239i
$27$	1.27030	−	5.03849i	0.244470	−	0.969657i
$28$	0.629857	−	2.35066i	0.119032	−	0.444233i
$29$	1.61773	−	0.933998i	0.300405	−	0.173439i	−0.342220	−	0.939620i	$-0.611179\pi$
$29$	1.61773	−	0.933998i	0.300405	−	0.173439i	0.642625	+	0.766181i	$0.277845\pi$
$30$	−4.17737	+	6.02910i	−0.762679	+	1.10076i
$31$	−0.838107	−	0.838107i	−0.150529	−	0.150529i	0.627826	−	0.778354i	$-0.283945\pi$
$31$	−0.838107	−	0.838107i	−0.150529	−	0.150529i	−0.778354	+	0.627826i	$0.783945\pi$
$32$	0.683743	+	2.55176i	0.120870	+	0.451092i
$33$	−0.309194	−	1.70423i	−0.0538238	−	0.296668i
$34$	1.03296	−	1.03296i	0.177150	−	0.177150i
$35$	−11.9040	−	6.87280i	−2.01215	−	1.16172i
$36$	1.33820	−	0.502100i	0.223034	−	0.0836833i
$37$	5.42747	+	1.45429i	0.892271	+	0.239083i	0.675694	−	0.737182i	$-0.263844\pi$
$37$	5.42747	+	1.45429i	0.892271	+	0.239083i	0.216577	+	0.976266i	$0.430511\pi$
$38$	4.69015			0.760843
$39$	0.316454	+	6.23697i	0.0506731	+	0.998715i
$40$	6.45200			1.02015
$41$	5.56664	+	1.49158i	0.869363	+	0.232945i	0.665812	−	0.746119i	$-0.268085\pi$
$41$	5.56664	+	1.49158i	0.869363	+	0.232945i	0.203551	+	0.979064i	$0.434752\pi$
$42$	5.94621	+	12.5889i	0.917520	+	1.94251i
$43$	−5.64759	−	3.26064i	−0.861249	−	0.497242i	0.00318134	−	0.999995i	$-0.498987\pi$
$43$	−5.64759	−	3.26064i	−0.861249	−	0.497242i	−0.864430	+	0.502753i	$0.832321\pi$
$44$	0.336888	−	0.336888i	0.0507878	−	0.0507878i
$45$	−0.783077	−	8.03503i	−0.116734	−	1.19779i
$46$	−3.49048	−	13.0267i	−0.514643	−	1.92068i
$47$	−6.11240	−	6.11240i	−0.891585	−	0.891585i	0.103087	−	0.994672i	$-0.467128\pi$
$47$	−6.11240	−	6.11240i	−0.891585	−	0.891585i	−0.994672	+	0.103087i	$0.967128\pi$
$48$	−6.72826	−	4.66179i	−0.971140	−	0.672871i
$49$	−16.5332	+	9.54546i	−2.36189	+	1.36364i
$50$	−0.913018	+	3.40743i	−0.129120	+	0.481883i
$51$	−0.132215	+	1.60240i	−0.0185138	+	0.224381i
$52$	−1.36060	+	1.04862i	−0.188682	+	0.145417i
$53$		−	5.24956i		−	0.721083i	−0.932743	−	0.360541i	$-0.882592\pi$
$53$		−	5.24956i		−	0.721083i	0.932743	−	0.360541i	$-0.117408\pi$
$54$	−3.98307	+	7.14135i	−0.542027	+	0.971814i
$55$	−1.34552	−	2.33050i	−0.181429	−	0.314245i
$56$	6.12336	−	10.6060i	0.818268	−	1.41728i
$57$	−3.93802	+	3.33770i	−0.521603	+	0.442089i
$58$	−2.83944	+	0.760826i	−0.372837	+	0.0999013i
$59$	8.53194	−	2.28613i	1.11076	−	0.297628i	0.343623	−	0.939108i	$-0.388346\pi$
$59$	8.53194	−	2.28613i	1.11076	−	0.297628i	0.767140	+	0.641479i	$0.221679\pi$
$60$	1.69404	−	1.43580i	0.218700	−	0.185361i
$61$	−3.64778	+	6.31814i	−0.467050	+	0.808955i	−0.999291	−	0.0376379i	$-0.988017\pi$
$61$	−3.64778	+	6.31814i	−0.467050	+	0.808955i	0.532241	+	0.846593i	$0.321350\pi$
$62$	0.932605	+	1.61532i	0.118441	+	0.205146i
$63$	−13.9514	−	6.33852i	−1.75771	−	0.798578i
$64$			5.29447i			0.661808i
$65$	3.73204	+	8.95620i	0.462902	+	1.11088i
$66$	−0.224136	+	2.71644i	−0.0275892	+	0.334371i
$67$	2.60320	−	9.71527i	0.318031	−	1.18691i	−0.603103	−	0.797664i	$-0.706069\pi$
$67$	2.60320	−	9.71527i	0.318031	−	1.18691i	0.921134	−	0.389245i	$-0.127264\pi$
$68$	−0.383014	+	0.221133i	−0.0464473	+	0.0268164i
$69$	12.2010	+	8.45369i	1.46883	+	1.01770i
$70$	15.2954	+	15.2954i	1.82815	+	1.82815i
$71$	−0.282569	−	1.05456i	−0.0335348	−	0.125154i	0.947129	−	0.320852i	$-0.103969\pi$
$71$	−0.282569	−	1.05456i	−0.0335348	−	0.125154i	−0.980664	+	0.195699i	$0.937303\pi$
$72$	7.15886	−	0.697686i	0.843679	−	0.0822231i
$73$	8.87218	−	8.87218i	1.03841	−	1.03841i	0.0391783	−	0.999232i	$-0.487526\pi$
$73$	8.87218	−	8.87218i	1.03841	−	1.03841i	0.999232	−	0.0391783i	$-0.0124740\pi$
$74$	−7.65768	−	4.42117i	−0.890188	−	0.513950i
$75$	−1.65826	−	3.51074i	−0.191479	−	0.405386i
$76$	−1.37157	−	0.367511i	−0.157330	−	0.0421564i
$77$	−5.10793			−0.582102
$78$	2.05927	−	9.60938i	0.233166	−	1.08805i
$79$	4.53164			0.509850			0.254925	−	0.966961i	$-0.417949\pi$
$79$	4.53164			0.509850			0.254925	+	0.966961i	$0.417949\pi$
$80$	−12.2842	−	3.29153i	−1.37341	−	0.368004i
$81$	−1.73774	−	8.83064i	−0.193082	−	0.981183i
$82$	−7.85404	−	4.53453i	−0.867334	−	0.500755i
$83$	−4.39090	+	4.39090i	−0.481964	+	0.481964i	−0.905758	−	0.423795i	$-0.860698\pi$
$83$	−4.39090	+	4.39090i	−0.481964	+	0.481964i	0.423795	+	0.905758i	$0.360698\pi$
$84$	−0.752448	−	4.14738i	−0.0820988	−	0.452516i
$85$	0.646545	+	2.41294i	0.0701276	+	0.261720i
$86$	7.25656	+	7.25656i	0.782495	+	0.782495i
$87$	1.84266	−	2.65948i	0.197554	−	0.285126i
$88$	2.07637	−	1.19880i	0.221342	−	0.127792i
$89$	−2.67759	+	9.99292i	−0.283824	+	1.05925i	0.665870	+	0.746068i	$0.268061\pi$
$89$	−2.67759	+	9.99292i	−0.283824	+	1.05925i	−0.949694	+	0.313179i	$0.898606\pi$
$90$	−2.08232	+	12.5326i	−0.219496	+	1.32105i
$91$	18.2644	+	2.36518i	1.91463	+	0.247939i
$92$			4.08298i			0.425680i
$93$	−1.93257	−	0.692602i	−0.200399	−	0.0718195i
$94$	6.80158	+	11.7807i	0.701530	+	1.21509i
$95$	−4.01017	+	6.94581i	−0.411434	+	0.712625i
$96$	2.95849	+	3.49061i	0.301950	+	0.356259i
$97$	11.9037	−	3.18958i	1.20863	−	0.323852i	0.402408	−	0.915461i	$-0.368173\pi$
$97$	11.9037	−	3.18958i	1.20863	−	0.323852i	0.806226	+	0.591608i	$0.201507\pi$
$98$	29.0191	−	7.77564i	2.93137	−	0.785458i
$99$	−1.74494	−	2.44033i	−0.175373	−	0.245262i
$100$	0.533999	−	0.924914i	0.0533999	−	0.0924914i
$101$	7.35894	+	12.7461i	0.732241	+	1.26828i	0.955923	+	0.293617i	$0.0948591\pi$
$101$	7.35894	+	12.7461i	0.732241	+	1.26828i	−0.223682	+	0.974662i	$0.571808\pi$
$102$	0.853623	−	2.38187i	0.0845212	−	0.235840i
$103$			10.4932i			1.03392i	0.856008	+	0.516962i	$0.172937\pi$
$103$			10.4932i			1.03392i	−0.856008	+	0.516962i	$0.827063\pi$
$104$	−7.97957	+	3.32508i	−0.782462	+	0.326051i
$105$	−23.7275	−	1.95777i	−2.31556	−	0.191059i
$106$	−2.13812	+	7.97958i	−0.207673	+	0.775045i
$107$	3.78055	−	2.18270i	0.365479	−	0.211010i	−0.306002	−	0.952031i	$-0.598992\pi$
$107$	3.78055	−	2.18270i	0.365479	−	0.211010i	0.671482	+	0.741021i	$0.265658\pi$
$108$	1.72438	−	1.77628i	0.165928	−	0.170923i
$109$	−1.70608	−	1.70608i	−0.163412	−	0.163412i	0.620664	−	0.784077i	$-0.286863\pi$
$109$	−1.70608	−	1.70608i	−0.163412	−	0.163412i	−0.784077	+	0.620664i	$0.786863\pi$
$110$	1.09605	+	4.09050i	0.104504	+	0.390014i
$111$	9.57595	−	1.73734i	0.908909	−	0.164901i
$112$	−17.0692	+	17.0692i	−1.61288	+	1.61288i
$113$	−0.231646	−	0.133741i	−0.0217914	−	0.0125813i	0.489065	−	0.872247i	$-0.337338\pi$
$113$	−0.231646	−	0.133741i	−0.0217914	−	0.0125813i	−0.510856	+	0.859666i	$0.670672\pi$
$114$	7.34540	−	3.46952i	0.687960	−	0.324950i
$115$	22.2761	+	5.96886i	2.07726	+	0.556599i
$116$	0.889973			0.0826319
$117$	5.10938	+	9.53385i	0.472363	+	0.881404i
$118$	−13.9001			−1.27961
$119$	4.58007	+	1.22723i	0.419854	+	0.112500i
$120$	10.1047	−	4.77284i	0.922428	−	0.435698i
$121$	−0.866025	−	0.500000i	−0.0787296	−	0.0454545i
$122$	8.11815	−	8.11815i	0.734982	−	0.734982i
$123$	9.82149	−	1.78189i	0.885574	−	0.160667i
$124$	−0.146154	−	0.545455i	−0.0131250	−	0.0489833i
$125$	5.24870	+	5.24870i	0.469458	+	0.469458i
$126$	18.6251	+	15.3172i	1.65926	+	1.36456i
$127$	3.75699	−	2.16910i	0.333379	−	0.192476i	−0.323961	−	0.946070i	$-0.605015\pi$
$127$	3.75699	−	2.16910i	0.333379	−	0.192476i	0.657340	+	0.753594i	$0.271681\pi$
$128$	3.52390	−	13.1514i	0.311472	−	1.16243i
$129$	−11.2569	−	0.928816i	−0.991117	−	0.0817777i
$130$	−2.02505	−	15.1339i	−0.177609	−	1.32733i
$131$			10.3221i			0.901842i	0.892564	+	0.450921i	$0.148904\pi$
$131$			10.3221i			0.901842i	−0.892564	+	0.450921i	$0.851096\pi$
$132$	0.278401	−	0.776824i	0.0242317	−	0.0676138i
$133$	7.61181	+	13.1840i	0.660028	+	1.14320i
$134$	−7.91397	+	13.7074i	−0.683663	+	1.18414i
$135$	−7.17028	−	12.0047i	−0.617120	−	1.03320i
$136$	−2.14982	+	0.576043i	−0.184346	+	0.0493953i
$137$	−0.387881	+	0.103932i	−0.0331389	+	0.00887955i	−0.275350	−	0.961344i	$-0.588794\pi$
$137$	−0.387881	+	0.103932i	−0.0331389	+	0.00887955i	0.242211	+	0.970223i	$0.422127\pi$
$138$	−15.1030	−	17.8194i	−1.28565	−	1.51689i
$139$	7.68347	−	13.3082i	0.651703	−	1.12878i	−0.331006	−	0.943629i	$-0.607388\pi$
$139$	7.68347	−	13.3082i	0.651703	−	1.12878i	0.982709	−	0.185155i	$-0.0592786\pi$
$140$	−3.27442	−	5.67147i	−0.276739	−	0.479326i
$141$	−14.0945	−	5.05122i	−1.18697	−	0.425389i
$142$			1.71807i			0.144178i
$143$	2.86512	+	2.18885i	0.239593	+	0.183041i
$144$	−13.9859	−	2.32379i	−1.16549	−	0.193649i
$145$	1.30104	−	4.85555i	0.108046	−	0.403232i
$146$	−17.0997	+	9.87254i	−1.41518	+	0.817057i
$147$	−18.8320	+	27.1798i	−1.55324	+	2.24176i
$148$	1.89295	+	1.89295i	0.155600	+	0.155600i
$149$	0.570509	+	2.12917i	0.0467379	+	0.174428i	0.985349	−	0.170548i	$-0.0545537\pi$
$149$	0.570509	+	2.12917i	0.0467379	+	0.174428i	−0.938611	+	0.344976i	$0.887887\pi$
$150$	1.09072	+	6.01189i	0.0890571	+	0.490869i
$151$	2.83557	−	2.83557i	0.230756	−	0.230756i	−0.582252	−	0.813008i	$-0.697828\pi$
$151$	2.83557	−	2.83557i	0.230756	−	0.230756i	0.813008	+	0.582252i	$0.197828\pi$
$152$	−6.18841	−	3.57288i	−0.501946	−	0.289799i
$153$	0.978301	+	2.60738i	0.0790910	+	0.210794i
$154$	7.76429	+	2.08043i	0.625664	+	0.167646i
$155$	−3.18958			−0.256193
$156$	−1.35518	+	2.64877i	−0.108501	+	0.212072i
$157$	−13.2405			−1.05671			−0.528354	−	0.849024i	$-0.677191\pi$
$157$	−13.2405			−1.05671			−0.528354	+	0.849024i	$0.677191\pi$
$158$	−6.88831	−	1.84572i	−0.548005	−	0.146837i
$159$	−3.88334	−	8.22152i	−0.307969	−	0.652009i
$160$	6.15668	+	3.55456i	0.486728	+	0.281013i
$161$	30.9532	−	30.9532i	2.43945	−	2.43945i
$162$	−0.955241	+	14.1308i	−0.0750508	+	1.11022i
$163$	−1.49978	−	5.59726i	−0.117472	−	0.438411i	0.881988	−	0.471272i	$-0.156205\pi$
$163$	−1.49978	−	5.59726i	−0.117472	−	0.438411i	−0.999460	+	0.0328605i	$0.989538\pi$
$164$	1.94149	+	1.94149i	0.151605	+	0.151605i
$165$	−3.83124	−	2.65454i	−0.298262	−	0.206656i
$166$	8.46276	−	4.88598i	0.656838	−	0.379225i
$167$	−1.80157	+	6.72354i	−0.139409	+	0.520283i	0.860531	+	0.509397i	$0.170132\pi$
$167$	−1.80157	+	6.72354i	−0.139409	+	0.520283i	−0.999941	+	0.0108854i	$0.996535\pi$
$168$	1.74428	−	21.1401i	0.134574	−	1.63099i
$169$	−9.23127	−	9.15334i	−0.710098	−	0.704103i
$170$		−	3.93111i		−	0.301503i
$171$	−3.69842	+	8.14041i	−0.282825	+	0.622513i
$172$	−1.55347	−	2.69069i	−0.118451	−	0.205163i
$173$	6.81108	−	11.7971i	0.517837	−	0.896920i	−0.481948	−	0.876200i	$-0.660071\pi$
$173$	6.81108	−	11.7971i	0.517837	−	0.896920i	0.999785	−	0.0207203i	$-0.00659596\pi$
$174$	−3.88413	+	3.29202i	−0.294455	+	0.249567i
$175$	−11.0601	+	2.96354i	−0.836064	+	0.224023i
$176$	−4.56485	+	1.22315i	−0.344088	+	0.0921982i
$177$	11.6710	−	9.89184i	0.877247	−	0.743516i
$178$	8.14014	−	14.0991i	0.610129	−	1.05677i
$179$	2.13096	+	3.69094i	0.159276	+	0.275874i	0.934608	−	0.355680i	$-0.115751\pi$
$179$	2.13096	+	3.69094i	0.159276	+	0.275874i	−0.775332	+	0.631554i	$0.782417\pi$
$180$	1.59097	−	3.50181i	0.118584	−	0.261010i
$181$			23.4656i			1.74418i	0.489345	+	0.872090i	$0.337236\pi$
$181$			23.4656i			1.74418i	−0.489345	+	0.872090i	$0.662764\pi$
$182$	−26.7994	−	11.0342i	−1.98650	−	0.817909i
$183$	−1.03910	+	12.5935i	−0.0768123	+	0.930937i
$184$	−5.31799	+	19.8470i	−0.392047	+	1.46314i
$185$	13.0949	−	7.56036i	0.962759	−	0.555849i
$186$	2.65551	+	1.83992i	0.194711	+	0.134909i
$187$	0.656400	+	0.656400i	0.0480007	+	0.0480007i
$188$	−1.06592	−	3.97806i	−0.0777401	−	0.290130i
$189$	−26.5387	+	0.393512i	−1.93040	+	0.0286238i
$190$	8.92464	−	8.92464i	0.647461	−	0.647461i
$191$	−4.92573	−	2.84387i	−0.356413	−	0.205775i	0.311093	−	0.950379i	$-0.399305\pi$
$191$	−4.92573	−	2.84387i	−0.356413	−	0.205775i	−0.667506	+	0.744604i	$0.732638\pi$
$192$	3.91656	+	8.29185i	0.282653	+	0.598412i
$193$	−13.1952	−	3.53564i	−0.949812	−	0.254501i	−0.249529	−	0.968367i	$-0.580276\pi$
$193$	−13.1952	−	3.53564i	−0.949812	−	0.254501i	−0.700282	+	0.713866i	$0.746943\pi$
$194$	−19.3932			−1.39235
$195$	12.4702	+	11.2659i	0.893008	+	0.806764i
$196$	−9.09552			−0.649680
$197$	−2.93179	−	0.785571i	−0.208881	−	0.0559696i	0.152861	−	0.988248i	$-0.451151\pi$
$197$	−2.93179	−	0.785571i	−0.208881	−	0.0559696i	−0.361742	+	0.932278i	$0.617818\pi$
$198$	1.65845	+	4.42012i	0.117861	+	0.314124i
$199$	−2.14900	−	1.24072i	−0.152338	−	0.0879525i	0.421893	−	0.906646i	$-0.361366\pi$
$199$	−2.14900	−	1.24072i	−0.152338	−	0.0879525i	−0.574231	+	0.818693i	$0.694699\pi$
$200$	3.80041	−	3.80041i	0.268729	−	0.268729i
$201$	−3.10987	−	17.1411i	−0.219353	−	1.20904i
$202$	−5.99452	−	22.3719i	−0.421773	−	1.57408i
$203$	−6.74692	−	6.74692i	−0.473541	−	0.473541i
$204$	−0.436269	+	0.629658i	−0.0305450	+	0.0440849i
$205$	13.4307	−	7.75423i	0.938042	−	0.541579i
$206$	4.27382	−	15.9501i	0.297771	−	1.11130i
$207$	25.3620	+	4.21396i	1.76278	+	0.292891i
$208$	16.8889	−	2.25989i	1.17103	−	0.156695i
$209$			2.98039i			0.206158i
$210$	35.2694	+	12.6400i	2.43382	+	0.872241i
$211$	−1.46144	−	2.53129i	−0.100610	−	0.174261i	0.811326	−	0.584594i	$-0.198746\pi$
$211$	−1.46144	−	2.53129i	−0.100610	−	0.174261i	−0.911936	+	0.410332i	$0.865413\pi$
$212$	1.25053	−	2.16598i	0.0858867	−	0.148760i
$213$	−1.22265	−	1.44256i	−0.0837745	−	0.0988424i
$214$	−6.63561	+	1.77801i	−0.453601	+	0.121542i
$215$	−16.9510	+	4.54201i	−1.15605	+	0.309762i
$216$	10.6956	−	6.38840i	0.727745	−	0.434676i
$217$	−3.02712	+	5.24312i	−0.205494	+	0.355926i
$218$	1.89844	+	3.28819i	0.128579	+	0.222705i
$219$	7.33187	−	20.4582i	0.495442	−	1.38244i
$220$		−	1.28209i		−	0.0864388i
$221$	−2.04314	−	2.65103i	−0.137437	−	0.178327i
$222$	−15.2635	−	1.25940i	−1.02442	−	0.0845255i
$223$	−1.99133	+	7.43173i	−0.133349	+	0.497665i	−0.999999	−	0.00125095i	$-0.999602\pi$
$223$	−1.99133	+	7.43173i	−0.133349	+	0.497665i	0.866650	+	0.498916i	$0.166268\pi$
$224$	11.6862	−	6.74701i	0.780815	−	0.450804i
$225$	−5.19411	−	4.27160i	−0.346274	−	0.284774i
$226$	0.297641	+	0.297641i	0.0197988	+	0.0197988i
$227$	1.16343	+	4.34196i	0.0772193	+	0.288186i	0.993727	−	0.111830i	$-0.0356712\pi$
$227$	1.16343	+	4.34196i	0.0772193	+	0.288186i	−0.916508	+	0.400016i	$0.869005\pi$
$228$	−2.41993	+	0.439041i	−0.160264	+	0.0290762i
$229$	−13.4730	+	13.4730i	−0.890319	+	0.890319i	−0.994553	−	0.104234i	$-0.966761\pi$
$229$	−13.4730	+	13.4730i	−0.890319	+	0.890319i	0.104234	+	0.994553i	$0.466761\pi$
$230$	−31.4296	−	18.1459i	−2.07241	−	1.19650i
$231$	−7.99970	+	3.77857i	−0.526342	+	0.248611i
$232$	4.32608	+	1.15917i	0.284021	+	0.0761032i
$233$	−4.45754			−0.292023			−0.146011	−	0.989283i	$-0.546644\pi$
$233$	−4.45754			−0.292023			−0.146011	+	0.989283i	$0.546644\pi$
$234$	−3.88341	−	16.5729i	−0.253867	−	1.08341i
$235$	−23.2619			−1.51744
$236$	4.06489	+	1.08918i	0.264602	+	0.0708998i
$237$	7.09716	−	3.35226i	0.461010	−	0.217753i
$238$	−6.46207	−	3.73088i	−0.418874	−	0.241837i
$239$	−8.73097	+	8.73097i	−0.564759	+	0.564759i	−0.930656	−	0.365896i	$-0.880762\pi$
$239$	−8.73097	+	8.73097i	−0.564759	+	0.564759i	0.365896	+	0.930656i	$0.380762\pi$
$240$	−21.6735	+	3.93217i	−1.39902	+	0.253821i
$241$	−0.724606	−	2.70427i	−0.0466760	−	0.174197i	0.938653	−	0.344863i	$-0.112075\pi$
$241$	−0.724606	−	2.70427i	−0.0466760	−	0.174197i	−0.985329	+	0.170666i	$0.945408\pi$
$242$	1.11275	+	1.11275i	0.0715304	+	0.0715304i
$243$	−9.25396	−	12.5445i	−0.593642	−	0.804730i
$244$	−3.01016	+	1.73792i	−0.192706	+	0.111259i
$245$	−13.2966	+	49.6238i	−0.849492	+	3.17035i
$246$	−15.6549	−	1.29170i	−0.998119	−	0.0823555i
$247$	1.38005	−	10.6570i	0.0878102	−	0.678087i
$248$		−	2.84177i		−	0.180453i
$249$	−3.62859	+	10.1249i	−0.229952	+	0.641638i
$250$	−5.84050	−	10.1160i	−0.369386	−	0.639795i
$251$	1.49277	−	2.58556i	0.0942231	−	0.163199i	−0.815061	−	0.579375i	$-0.803297\pi$
$251$	1.49277	−	2.58556i	0.0942231	−	0.163199i	0.909284	+	0.416176i	$0.136630\pi$
$252$	−4.24644	−	5.93873i	−0.267501	−	0.374105i
$253$	8.27789	−	2.21805i	0.520427	−	0.139448i
$254$	−6.59426	+	1.76693i	−0.413761	+	0.110867i
$255$	2.79754	+	3.30071i	0.175189	+	0.206698i
$256$	−5.41851	+	9.38514i	−0.338657	+	0.586571i
$257$	−12.0974	−	20.9533i	−0.754616	−	1.30703i	−0.945565	−	0.325434i	$-0.894490\pi$
$257$	−12.0974	−	20.9533i	−0.754616	−	1.30703i	0.190949	−	0.981600i	$-0.438844\pi$
$258$	16.7327	+	5.99674i	1.04174	+	0.373340i
$259$		−	28.7011i		−	1.78340i
$260$	−0.593663	+	4.58438i	−0.0368174	+	0.284311i
$261$	0.918524	−	5.52820i	0.0568552	−	0.342187i
$262$	4.20413	−	15.6900i	0.259732	−	0.969332i
$263$	13.3034	−	7.68069i	0.820320	−	0.473612i	−0.0302069	−	0.999544i	$-0.509617\pi$
$263$	13.3034	−	7.68069i	0.820320	−	0.473612i	0.850527	+	0.525932i	$0.176283\pi$
$264$	2.36508	−	3.41346i	0.145560	−	0.210084i
$265$	−9.98912	−	9.98912i	−0.613627	−	0.613627i
$266$	−6.20051	−	23.1406i	−0.380178	−	1.41884i
$267$	3.19874	+	17.6310i	0.195760	+	1.07900i
$268$	3.38842	−	3.38842i	0.206981	−	0.206981i
$269$	24.8610	+	14.3535i	1.51580	+	0.875148i	0.999828	+	0.0185429i	$0.00590274\pi$
$269$	24.8610	+	14.3535i	1.51580	+	0.875148i	0.515973	+	0.856605i	$0.327431\pi$
$270$	6.00972	+	21.1681i	0.365740	+	1.28825i
$271$	−13.6024	−	3.64474i	−0.826284	−	0.221402i	−0.179192	−	0.983814i	$-0.557348\pi$
$271$	−13.6024	−	3.64474i	−0.826284	−	0.221402i	−0.647092	+	0.762412i	$0.724015\pi$
$272$	4.38698			0.266000
$273$	30.3541	−	9.80680i	1.83711	−	0.593535i
$274$	0.631929			0.0381762
$275$	−2.16528	−	0.580185i	−0.130571	−	0.0349864i
$276$	3.02036	+	6.39449i	0.181805	+	0.384903i
$277$	−9.59997	−	5.54254i	−0.576806	−	0.333019i	0.183057	−	0.983102i	$-0.441401\pi$
$277$	−9.59997	−	5.54254i	−0.576806	−	0.333019i	−0.759863	+	0.650083i	$0.774734\pi$
$278$	−17.0996	+	17.0996i	−1.02556	+	1.02556i
$279$	−3.53902	+	0.344905i	−0.211876	+	0.0206489i
$280$	−8.52973	−	31.8334i	−0.509749	−	1.90241i
$281$	6.16747	+	6.16747i	0.367920	+	0.367920i	0.866718	−	0.498798i	$-0.166225\pi$
$281$	6.16747	+	6.16747i	0.367920	+	0.367920i	−0.498798	+	0.866718i	$0.666225\pi$
$282$	19.3669	+	13.4187i	1.15328	+	0.799072i
$283$	17.0539	−	9.84607i	1.01375	−	0.585288i	0.101462	−	0.994839i	$-0.467648\pi$
$283$	17.0539	−	9.84607i	1.01375	−	0.585288i	0.912287	+	0.409551i	$0.134315\pi$
$284$	0.134625	−	0.502427i	0.00798852	−	0.0298136i
$285$	−1.14233	+	13.8446i	−0.0676655	+	0.820082i
$286$	−3.46361	−	4.49411i	−0.204808	−	0.265742i
$287$		−	29.4370i		−	1.73761i
$288$	7.21555	+	3.27823i	0.425181	+	0.193172i
$289$	8.06914	+	13.9762i	0.474655	+	0.822127i
$290$	−3.95529	+	6.85076i	−0.232263	+	0.402290i
$291$	16.2833	−	13.8010i	0.954541	−	0.809028i
$292$	5.77418	−	1.54719i	0.337908	−	0.0905422i
$293$	16.7700	−	4.49350i	0.979713	−	0.262513i	0.266789	−	0.963755i	$-0.414037\pi$
$293$	16.7700	−	4.49350i	0.979713	−	0.262513i	0.712924	+	0.701242i	$0.247371\pi$
$294$	39.6958	−	33.6444i	2.31511	−	1.96218i
$295$	11.8848	−	20.5851i	0.691961	−	1.19851i
$296$	6.73595	+	11.6670i	0.391519	+	0.678131i
$297$	−4.53803	−	2.53107i	−0.263323	−	0.146868i
$298$		−	3.46880i		−	0.200942i
$299$	−30.6263	+	4.09808i	−1.77116	+	0.236998i
$300$	0.152114	−	1.84356i	0.00878229	−	0.106438i
$301$	−8.62131	+	32.1752i	−0.496924	+	1.85455i
$302$	−5.46512	+	3.15529i	−0.314482	+	0.181566i
$303$	20.9539	+	14.5183i	1.20377	+	0.834054i
$304$	9.95957	+	9.95957i	0.571221	+	0.571221i
$305$	5.08129	+	18.9636i	0.290954	+	1.08585i
$306$	−0.425091	−	4.36179i	−0.0243008	−	0.249347i
$307$	8.42157	−	8.42157i	0.480644	−	0.480644i	−0.424693	−	0.905337i	$-0.639618\pi$
$307$	8.42157	−	8.42157i	0.480644	−	0.480644i	0.905337	+	0.424693i	$0.139618\pi$
$308$	−2.10754	−	1.21679i	−0.120088	−	0.0693330i
$309$	7.76228	+	16.4337i	0.441581	+	0.934882i
$310$	4.84831	+	1.29910i	0.275366	+	0.0737840i
$311$	11.9937			0.680098			0.340049	−	0.940408i	$-0.389556\pi$
$311$	11.9937			0.680098			0.340049	+	0.940408i	$0.389556\pi$
$312$	−10.0374	+	11.1104i	−0.568254	+	0.629001i
$313$	25.8595			1.46166			0.730832	−	0.682557i	$-0.239132\pi$
$313$	25.8595			1.46166			0.730832	+	0.682557i	$0.239132\pi$
$314$	20.1262	+	5.39280i	1.13579	+	0.304333i
$315$	−38.6086	+	14.4861i	−2.17535	+	0.816202i
$316$	1.86977	+	1.07951i	0.105183	+	0.0607272i
$317$	−19.8356	+	19.8356i	−1.11408	+	1.11408i	−0.121483	+	0.992594i	$0.538765\pi$
$317$	−19.8356	+	19.8356i	−1.11408	+	1.11408i	−0.992594	+	0.121483i	$0.961235\pi$
$318$	2.55427	+	14.0788i	0.143236	+	0.789498i
$319$	−0.483473	−	1.80434i	−0.0270693	−	0.101024i
$320$	10.0746	+	10.0746i	0.563185	+	0.563185i
$321$	4.30620	−	6.21505i	0.240349	−	0.346890i
$322$	−59.6574	+	34.4432i	−3.32458	+	1.91945i
$323$	0.716066	−	2.67239i	0.0398430	−	0.148696i
$324$	1.38661	−	4.05750i	0.0770337	−	0.225417i
$325$	7.47372	+	3.07718i	0.414568	+	0.170691i
$326$			9.11896i			0.505052i
$327$	−3.93401	−	1.40988i	−0.217551	−	0.0779667i
$328$	6.90867	+	11.9662i	0.381468	+	0.660721i
$329$	−22.0771	+	38.2386i	−1.21715	+	2.10816i
$330$	4.74248	+	5.59547i	0.261065	+	0.308021i
$331$	−25.2635	+	6.76934i	−1.38861	+	0.372076i	−0.874240	−	0.485493i	$-0.838640\pi$
$331$	−25.2635	+	6.76934i	−1.38861	+	0.372076i	−0.514368	+	0.857570i	$0.671973\pi$
$332$	−2.85768	+	0.765712i	−0.156835	+	0.0420239i
$333$	13.7120	−	9.80467i	0.751415	−	0.537293i
$334$	5.47693	−	9.48632i	0.299684	−	0.519068i
$335$	−13.5332	−	23.4402i	−0.739397	−	1.28067i
$336$	−14.1058	+	39.3594i	−0.769532	+	2.14723i
$337$			20.9061i			1.13883i	0.822050	+	0.569415i	$0.192830\pi$
$337$			20.9061i			1.13883i	−0.822050	+	0.569415i	$0.807170\pi$
$338$	10.3038	+	17.6734i	0.560455	+	0.961304i
$339$	−0.461723	−	0.0380971i	−0.0250773	−	0.00206915i
$340$	−0.308035	+	1.14960i	−0.0167055	+	0.0623459i
$341$	−1.02647	+	0.592631i	−0.0555863	+	0.0320928i
$342$	8.93733	−	10.8675i	0.483275	−	0.587645i
$343$	43.6706	+	43.6706i	2.35799	+	2.35799i
$344$	−4.04672	−	15.1026i	−0.218185	−	0.814277i
$345$	39.3028	−	7.13060i	2.11599	−	0.383899i
$346$	−15.1581	+	15.1581i	−0.814904	+	0.814904i
$347$	27.3753	+	15.8051i	1.46958	+	0.848463i	0.999418	−	0.0341164i	$-0.0108617\pi$
$347$	27.3753	+	15.8051i	1.46958	+	0.848463i	0.470163	+	0.882579i	$0.344195\pi$
$348$	1.39382	−	0.658353i	0.0747164	−	0.0352914i
$349$	−15.9211	−	4.26604i	−0.852235	−	0.228356i	−0.193845	−	0.981032i	$-0.562096\pi$
$349$	−15.9211	−	4.26604i	−0.852235	−	0.228356i	−0.658391	+	0.752676i	$0.728762\pi$
$350$	18.0189			0.963150
$351$	15.0546	+	11.1516i	0.803555	+	0.595230i
$352$	2.64178			0.140807
$353$	2.76388	+	0.740578i	0.147106	+	0.0394170i	0.331621	−	0.943413i	$-0.392405\pi$
$353$	2.76388	+	0.740578i	0.147106	+	0.0394170i	−0.184514	+	0.982830i	$0.559071\pi$
$354$	−21.7694	+	10.2825i	−1.15703	+	0.546510i
$355$	−2.54436	−	1.46899i	−0.135041	−	0.0779657i
$356$	−3.48525	+	3.48525i	−0.184718	+	0.184718i
$357$	8.08083	−	1.46608i	0.427683	−	0.0775934i
$358$	−1.73586	−	6.47833i	−0.0917432	−	0.342390i
$359$	2.74988	+	2.74988i	0.145133	+	0.145133i	0.775940	−	0.630807i	$-0.217276\pi$
$359$	2.74988	+	2.74988i	0.145133	+	0.145133i	−0.630807	+	0.775940i	$0.717276\pi$
$360$	12.2946	−	14.9498i	0.647983	−	0.787924i
$361$	−8.76181	+	5.05863i	−0.461148	+	0.266244i
$362$	9.55741	−	35.6687i	0.502326	−	1.87471i
$363$	−1.72618	−	0.142429i	−0.0906012	−	0.00747557i
$364$	6.97250	+	5.32675i	0.365458	+	0.279198i
$365$		−	33.7648i		−	1.76733i
$366$	6.70874	−	18.7195i	0.350672	−	0.978482i
$367$	−3.78378	−	6.55369i	−0.197511	−	0.342100i	0.750209	−	0.661200i	$-0.229953\pi$
$367$	−3.78378	−	6.55369i	−0.197511	−	0.342100i	−0.947721	+	0.319100i	$0.896619\pi$
$368$	20.2502	−	35.0743i	1.05561	−	1.82837i
$369$	14.0636	−	10.0561i	0.732124	−	0.523499i
$370$	−22.9842	+	6.15860i	−1.19489	+	0.320170i
$371$	−25.9007	+	6.94007i	−1.34470	+	0.360311i
$372$	−0.632396	−	0.746139i	−0.0327882	−	0.0386855i
$373$	−14.8994	+	25.8065i	−0.771461	+	1.33621i	0.165302	+	0.986243i	$0.447140\pi$
$373$	−14.8994	+	25.8065i	−0.771461	+	1.33621i	−0.936762	+	0.349966i	$0.886193\pi$
$374$	−0.730410	−	1.26511i	−0.0377686	−	0.0654171i
$375$	12.1029	+	4.33747i	0.624990	+	0.223986i
$376$		−	20.7253i		−	1.06883i
$377$	0.893264	+	6.67565i	0.0460054	+	0.343814i
$378$	40.5003	+	10.2109i	2.08311	+	0.525193i
$379$	0.192485	−	0.718364i	0.00988730	−	0.0368999i	−0.960806	−	0.277222i	$-0.910586\pi$
$379$	0.192485	−	0.718364i	0.00988730	−	0.0368999i	0.970693	+	0.240322i	$0.0772530\pi$
$380$	−3.30921	+	1.91057i	−0.169759	+	0.0980103i
$381$	4.27937	−	6.17632i	0.219239	−	0.316422i
$382$	6.32904	+	6.32904i	0.323822	+	0.323822i
$383$	−4.33151	−	16.1654i	−0.221330	−	0.826013i	−0.983842	−	0.179040i	$-0.942701\pi$
$383$	−4.33151	−	16.1654i	−0.221330	−	0.826013i	0.762512	−	0.646974i	$-0.223966\pi$
$384$	−4.20977	−	23.2036i	−0.214829	−	1.18410i
$385$	−9.71961	+	9.71961i	−0.495357	+	0.495357i
$386$	18.6173	+	10.7487i	0.947595	+	0.547094i
$387$	−18.3169	+	6.87261i	−0.931102	+	0.349354i
$388$	5.67128	+	1.51962i	0.287916	+	0.0771468i
$389$	1.25192			0.0634750			0.0317375	−	0.999496i	$-0.489896\pi$
$389$	1.25192			0.0634750			0.0317375	+	0.999496i	$0.489896\pi$
$390$	−14.3667	−	22.2037i	−0.727487	−	1.12433i
$391$	−7.95535			−0.402319
$392$	−44.2126	−	11.8467i	−2.23307	−	0.598350i
$393$	7.63570	+	16.1657i	0.385170	+	0.815453i
$394$	4.13650	+	2.38821i	0.208394	+	0.120316i
$395$	8.62303	−	8.62303i	0.433872	−	0.433872i
$396$	−0.138639	−	1.42256i	−0.00696688	−	0.0714861i
$397$	−2.15512	−	8.04300i	−0.108162	−	0.403667i	0.890523	−	0.454939i	$-0.150339\pi$
$397$	−2.15512	−	8.04300i	−0.108162	−	0.403667i	−0.998685	+	0.0512725i	$0.983672\pi$
$398$	2.76123	+	2.76123i	0.138408	+	0.138408i
$399$	21.6740	+	15.0172i	1.08506	+	0.751799i
$400$	−9.17451	+	5.29691i	−0.458726	+	0.264845i
$401$	−4.75986	+	17.7641i	−0.237696	+	0.887094i	0.739219	+	0.673465i	$0.235195\pi$
$401$	−4.75986	+	17.7641i	−0.237696	+	0.887094i	−0.976915	+	0.213629i	$0.931472\pi$
$402$	−2.25435	+	27.3219i	−0.112437	+	1.36269i
$403$	3.94475	−	1.64377i	0.196502	−	0.0818821i
$404$			7.01206i			0.348863i
$405$	−20.1100	−	13.4967i	−0.999275	−	0.670658i
$406$	7.50764	+	13.0036i	0.372598	+	0.645359i
$407$	2.80947	−	4.86614i	0.139260	−	0.241205i
$408$	−2.94078	+	2.49248i	−0.145590	+	0.123396i
$409$	27.7035	−	7.42312i	1.36985	−	0.367050i	0.502425	−	0.864621i	$-0.332441\pi$
$409$	27.7035	−	7.42312i	1.36985	−	0.367050i	0.867423	+	0.497571i	$0.165775\pi$
$410$	−23.5736	+	6.31652i	−1.16422	+	0.311951i
$411$	−0.530591	+	0.449706i	−0.0261721	+	0.0221823i
$412$	−2.49964	+	4.32951i	−0.123149	+	0.213300i
$413$	−22.5589	−	39.0732i	−1.11005	−	1.92267i
$414$	−36.8351	−	16.7353i	−1.81035	−	0.822493i
$415$			16.7104i			0.820282i
$416$	−9.44620	−	1.22325i	−0.463138	−	0.0599750i
$417$	2.18869	−	26.5262i	0.107181	−	1.29899i
$418$	1.21390	−	4.53034i	0.0593738	−	0.221586i
$419$	17.0918	−	9.86793i	0.834987	−	0.482080i	−0.0205701	−	0.999788i	$-0.506548\pi$
$419$	17.0918	−	9.86793i	0.834987	−	0.482080i	0.855557	+	0.517708i	$0.173215\pi$
$420$	−9.32363	−	6.46004i	−0.454946	−	0.315218i
$421$	−6.09642	−	6.09642i	−0.297121	−	0.297121i	0.542764	−	0.839885i	$-0.317378\pi$
$421$	−6.09642	−	6.09642i	−0.297121	−	0.297121i	−0.839885	+	0.542764i	$0.817378\pi$
$422$	1.19048	+	4.44292i	0.0579515	+	0.216278i
$423$	−25.8104	+	2.51543i	−1.25495	+	0.122304i
$424$	8.89986	−	8.89986i	0.432215	−	0.432215i
$425$	1.80212	+	1.04046i	0.0874157	+	0.0504695i
$426$	1.27094	+	2.69073i	0.0615771	+	0.130366i
$427$	35.9954	+	9.64494i	1.74194	+	0.466751i
$428$	2.07982			0.100532
$429$	6.10636	+	1.30858i	0.294818	+	0.0631787i
$430$	27.6162			1.33177
$431$	−0.272176	−	0.0729292i	−0.0131102	−	0.00351288i	0.252258	−	0.967660i	$-0.418827\pi$
$431$	−0.272176	−	0.0729292i	−0.0131102	−	0.00351288i	−0.265368	+	0.964147i	$0.585494\pi$
$432$	−23.6228	+	6.70663i	−1.13655	+	0.322673i
$433$	−33.4516	−	19.3133i	−1.60758	−	0.928137i	−0.989909	−	0.141701i	$-0.954743\pi$
$433$	−33.4516	−	19.3133i	−1.60758	−	0.928137i	−0.617672	−	0.786436i	$-0.711924\pi$
$434$	6.73686	−	6.73686i	0.323380	−	0.323380i
$435$	−1.55427	−	8.56689i	−0.0745214	−	0.410751i
$436$	−0.297516	−	1.11035i	−0.0142484	−	0.0531759i
$437$	−18.0607	−	18.0607i	−0.863960	−	0.863960i
$438$	−19.4773	+	28.1112i	−0.930662	+	1.34320i
$439$	7.21981	−	4.16836i	0.344583	−	0.198945i	−0.317714	−	0.948187i	$-0.602915\pi$
$439$	7.21981	−	4.16836i	0.344583	−	0.198945i	0.662297	+	0.749242i	$0.269582\pi$
$440$	1.66990	−	6.23215i	0.0796093	−	0.297106i
$441$	−9.38732	+	56.4982i	−0.447015	+	2.69039i
$442$	2.02593	+	4.86185i	0.0963634	+	0.231254i
$443$		−	4.51934i		−	0.214720i	−0.994220	−	0.107360i	$-0.965760\pi$
$443$		−	4.51934i		−	0.214720i	0.994220	−	0.107360i	$-0.0342398\pi$
$444$	4.36492	+	1.56431i	0.207150	+	0.0742391i
$445$	13.9199	+	24.1101i	0.659869	+	1.14293i
$446$	6.05382	−	10.4855i	0.286656	−	0.496504i
$447$	2.46854	+	2.91253i	0.116758	+	0.137758i
$448$	26.1223	−	6.99944i	1.23416	−	0.330692i
$449$	−24.4458	+	6.55022i	−1.15367	+	0.309124i	−0.784434	−	0.620213i	$-0.787046\pi$
$449$	−24.4458	+	6.55022i	−1.15367	+	0.309124i	−0.369233	+	0.929337i	$0.620380\pi$
$450$	6.15549	+	8.60858i	0.290173	+	0.405812i
$451$	2.88151	−	4.99091i	0.135685	−	0.235013i
$452$	−0.0637184	−	0.110363i	−0.00299706	−	0.00519106i
$453$	2.34328	−	6.53849i	0.110097	−	0.307205i
$454$		−	7.07385i		−	0.331992i
$455$	39.2549	−	30.2538i	1.84030	−	1.41832i
$456$	−12.3349	−	1.01776i	−0.577635	−	0.0476610i
$457$	7.00327	−	26.1365i	0.327599	−	1.22262i	−0.584074	−	0.811700i	$-0.698542\pi$
$457$	7.00327	−	26.1365i	0.327599	−	1.22262i	0.911673	−	0.410916i	$-0.134791\pi$
$458$	25.9670	−	14.9921i	1.21336	−	0.700533i
$459$	3.46095	+	3.35981i	0.161543	+	0.156822i
$460$	7.76928	+	7.76928i	0.362245	+	0.362245i
$461$	0.251178	+	0.937411i	0.0116985	+	0.0436596i	0.971528	−	0.236923i	$-0.0761390\pi$
$461$	0.251178	+	0.937411i	0.0116985	+	0.0436596i	−0.959830	+	0.280583i	$0.909472\pi$
$462$	13.6989	−	2.48536i	0.637331	−	0.115629i
$463$	−7.26604	+	7.26604i	−0.337681	+	0.337681i	−0.855494	−	0.517813i	$-0.826746\pi$
$463$	−7.26604	+	7.26604i	−0.337681	+	0.337681i	0.517813	+	0.855494i	$0.326746\pi$
$464$	−7.64520	−	4.41396i	−0.354919	−	0.204913i
$465$	−4.99531	+	2.35948i	−0.231652	+	0.109418i
$466$	6.77567	+	1.81553i	0.313877	+	0.0841030i
$467$	22.5178			1.04200			0.520999	−	0.853557i	$-0.325560\pi$
$467$	22.5178			1.04200			0.520999	+	0.853557i	$0.325560\pi$
$468$	−0.162971	+	5.15082i	−0.00753336	+	0.238097i
$469$	−51.3755			−2.37230
$470$	35.3592	+	9.47448i	1.63100	+	0.437025i
$471$	−20.7364	+	9.79461i	−0.955484	+	0.451312i
$472$	18.3404	+	10.5889i	0.844187	+	0.487391i
$473$	−4.61124	+	4.61124i	−0.212025	+	0.212025i
$474$	−12.1534	+	2.20496i	−0.558223	+	0.101277i
$475$	1.72918	+	6.45338i	0.0793401	+	0.296101i
$476$	1.59740	+	1.59740i	0.0732168	+	0.0732168i
$477$	−12.1637	−	10.0033i	−0.556936	−	0.458020i
$478$	16.8276	−	9.71540i	0.769675	−	0.444372i
$479$	−4.89175	+	18.2562i	−0.223510	+	0.834149i	0.759487	+	0.650523i	$0.225450\pi$
$479$	−4.89175	+	18.2562i	−0.223510	+	0.834149i	−0.982996	+	0.183626i	$0.941216\pi$
$480$	12.2717	+	1.01254i	0.560122	+	0.0462160i
$481$	−12.2990	+	16.0989i	−0.560787	+	0.734047i
$482$			4.40574i			0.200676i
$483$	25.5794	−	71.3744i	1.16390	−	3.24765i
$484$	−0.238216	−	0.412602i	−0.0108280	−	0.0187546i
$485$	16.5816	−	28.7201i	0.752931	−	1.30411i
$486$	8.95713	+	22.8373i	0.406304	+	1.03592i
$487$	9.50245	−	2.54617i	0.430597	−	0.115378i	−0.0370093	−	0.999315i	$-0.511783\pi$
$487$	9.50245	−	2.54617i	0.430597	−	0.115378i	0.467606	+	0.883937i	$0.345116\pi$
$488$	−16.8957	+	4.52720i	−0.764835	+	0.204937i
$489$	−6.48941	−	7.65661i	−0.293461	−	0.346244i
$490$	40.4231	−	70.0148i	1.82613	−	3.16295i
$491$	−2.72884	−	4.72649i	−0.123151	−	0.213303i	0.797858	−	0.602846i	$-0.205967\pi$
$491$	−2.72884	−	4.72649i	−0.123151	−	0.213303i	−0.921009	+	0.389542i	$0.872633\pi$
$492$	4.47684	+	1.60443i	0.201832	+	0.0723331i
$493$			1.73404i			0.0780972i
$494$	−6.43827	+	15.6370i	−0.289671	+	0.703542i
$495$	−7.96392	−	1.32323i	−0.357952	−	0.0594746i
$496$	−1.44975	+	5.41054i	−0.0650957	+	0.242940i
$497$	−4.82952	+	2.78832i	−0.216634	+	0.125073i
$498$	9.63944	−	13.9124i	0.431954	−	0.623429i
$499$	−3.81586	−	3.81586i	−0.170821	−	0.170821i	0.616519	−	0.787340i	$-0.288542\pi$
$499$	−3.81586	−	3.81586i	−0.170821	−	0.170821i	−0.787340	+	0.616519i	$0.788542\pi$
$500$	0.915301	+	3.41595i	0.0409335	+	0.152766i
$501$	2.15221	+	11.8627i	0.0961537	+	0.529985i
$502$	−3.32218	+	3.32218i	−0.148276	+	0.148276i
$503$	−32.8520	−	18.9671i	−1.46480	−	0.845701i	−0.465570	−	0.885011i	$-0.654151\pi$
$503$	−32.8520	−	18.9671i	−1.46480	−	0.845701i	−0.999227	+	0.0393105i	$0.987484\pi$
$504$	−12.9065	−	34.3986i	−0.574902	−	1.53223i
$505$	38.2567	+	10.2509i	1.70240	+	0.456157i
$506$	−13.4862			−0.599534
$507$	−21.2286	−	7.50657i	−0.942793	−	0.333379i
$508$	2.06686			0.0917019
$509$	−20.0231	−	5.36517i	−0.887507	−	0.237807i	−0.213864	−	0.976863i	$-0.568605\pi$
$509$	−20.0231	−	5.36517i	−0.887507	−	0.237807i	−0.673643	+	0.739057i	$0.735272\pi$
$510$	−2.90802	−	6.15665i	−0.128769	−	0.272621i
$511$	−55.5036	−	32.0450i	−2.45533	−	1.41759i
$512$	−7.19602	+	7.19602i	−0.318022	+	0.318022i
$513$	0.229608	+	15.4849i	0.0101374	+	0.683674i
$514$	9.85445	+	36.7773i	0.434661	+	1.62218i
$515$	19.9669	+	19.9669i	0.879848	+	0.879848i
$516$	−4.42337	−	3.06481i	−0.194728	−	0.134921i
$517$	−7.48613	+	4.32212i	−0.329240	+	0.190087i
$518$	−11.6898	+	43.6270i	−0.513621	+	1.91686i
$519$	1.94019	−	23.5144i	0.0851648	−	1.03217i
$520$	−8.85680	+	21.5110i	−0.388396	+	0.943321i
$521$			31.8966i			1.39741i	0.715408	+	0.698707i	$0.246241\pi$
$521$			31.8966i			1.39741i	−0.715408	+	0.698707i	$0.753759\pi$
$522$	−3.64781	+	8.02901i	−0.159660	+	0.351420i
$523$	−5.40079	−	9.35445i	−0.236160	−	0.409042i	0.723449	−	0.690378i	$-0.242556\pi$
$523$	−5.40079	−	9.35445i	−0.236160	−	0.409042i	−0.959609	+	0.281336i	$0.909222\pi$
$524$	−2.45888	+	4.25890i	−0.107417	+	0.186051i
$525$	−15.1293	+	12.8230i	−0.660297	+	0.559639i
$526$	−23.3500	+	6.25662i	−1.01811	+	0.272802i
$527$	1.06278	−	0.284770i	0.0462953	−	0.0124048i
$528$	−6.24434	+	5.29244i	−0.271750	+	0.230324i
$529$	−25.2216	+	43.6851i	−1.09659	+	1.89935i
$530$	11.1154	+	19.2524i	0.482822	+	0.836273i
$531$	10.9609	−	24.1255i	0.475663	−	1.04696i
$532$			7.25302i			0.314458i
$533$	−12.6144	+	16.5117i	−0.546390	+	0.715202i
$534$	2.31878	−	28.1028i	0.100343	−	1.21613i
$535$	3.04046	−	11.3472i	0.131451	−	0.490580i
$536$	20.8841	−	12.0575i	0.902058	−	0.520803i
$537$	6.06773	+	4.20413i	0.261842	+	0.181422i
$538$	−31.9437	−	31.9437i	−1.37719	−	1.37719i
$539$	4.94109	+	18.4404i	0.212828	+	0.794285i
$540$	−0.0987719	−	6.66123i	−0.00425047	−	0.286654i
$541$	3.46959	−	3.46959i	0.149170	−	0.149170i	−0.628577	−	0.777747i	$-0.716362\pi$
$541$	3.46959	−	3.46959i	0.149170	−	0.149170i	0.777747	+	0.628577i	$0.216362\pi$
$542$	19.1917	+	11.0804i	0.824355	+	0.475942i
$543$	17.3585	+	36.7502i	0.744926	+	1.57710i
$544$	−2.36878	−	0.634712i	−0.101560	−	0.0272130i
$545$	−6.49281			−0.278121
$546$	−50.1339	+	2.54371i	−2.14553	+	0.108861i
$547$	24.9998			1.06891			0.534456	−	0.845196i	$-0.320516\pi$
$547$	24.9998			1.06891			0.534456	+	0.845196i	$0.320516\pi$
$548$	−0.184799	−	0.0495167i	−0.00789422	−	0.00211525i
$549$	7.68861	+	20.4918i	0.328142	+	0.874567i
$550$	3.05502	+	1.76382i	0.130266	+	0.0752093i
$551$	−3.93672	+	3.93672i	−0.167710	+	0.167710i
$552$	6.35305	+	35.0170i	0.270404	+	1.49042i
$553$	−5.99097	−	22.3586i	−0.254762	−	0.950784i
$554$	12.3349	+	12.3349i	0.524062	+	0.524062i
$555$	14.9157	−	21.5275i	0.633135	−	0.913790i
$556$	6.34043	−	3.66065i	0.268894	−	0.155246i
$557$	−0.849703	+	3.17113i	−0.0360031	+	0.134365i	−0.981588	−	0.191010i	$-0.938824\pi$
$557$	−0.849703	+	3.17113i	−0.0360031	+	0.134365i	0.945585	+	0.325375i	$0.105490\pi$
$558$	5.51996	+	0.917155i	0.233678	+	0.0388262i
$559$	18.6236	−	14.3532i	0.787693	−	0.607075i
$560$			64.9600i			2.74506i
$561$	1.51358	+	0.542441i	0.0639033	+	0.0229019i
$562$	−6.86286	−	11.8868i	−0.289492	−	0.501415i
$563$	8.18627	−	14.1790i	0.345010	−	0.597575i	−0.640345	−	0.768087i	$-0.721209\pi$
$563$	8.18627	−	14.1790i	0.345010	−	0.597575i	0.985356	+	0.170512i	$0.0545421\pi$
$564$	−4.61212	−	5.44167i	−0.194205	−	0.229136i
$565$	−0.695275	+	0.186298i	−0.0292505	+	0.00783763i
$566$	−29.9330	+	8.02052i	−1.25818	+	0.337127i
$567$	−41.2720	+	20.2481i	−1.73326	+	0.850342i
$568$	1.30880	−	2.26691i	0.0549161	−	0.0951174i
$569$	−3.86178	−	6.68879i	−0.161894	−	0.280409i	0.773654	−	0.633608i	$-0.218427\pi$
$569$	−3.86178	−	6.68879i	−0.161894	−	0.280409i	−0.935548	+	0.353200i	$0.885094\pi$
$570$	7.37522	−	20.5791i	0.308914	−	0.861966i
$571$		−	10.7431i		−	0.449586i	−0.974407	−	0.224793i	$-0.927829\pi$
$571$		−	10.7431i		−	0.449586i	0.974407	−	0.224793i	$-0.0721705\pi$
$572$	0.660736	+	1.58564i	0.0276267	+	0.0662991i
$573$	−9.81809	−	0.810097i	−0.410157	−	0.0338423i
$574$	−11.9896	+	44.7457i	−0.500435	+	1.86765i
$575$	16.6371	−	9.60541i	0.693813	−	0.400573i
$576$	12.2677	+	10.0889i	0.511155	+	0.420370i
$577$	13.5048	+	13.5048i	0.562211	+	0.562211i	0.929935	−	0.367724i	$-0.119863\pi$
$577$	13.5048	+	13.5048i	0.562211	+	0.562211i	−0.367724	+	0.929935i	$0.619863\pi$
$578$	−6.57305	−	24.5309i	−0.273403	−	1.02035i
$579$	−23.2809	+	4.22380i	−0.967523	+	0.175535i
$580$	1.69348	−	1.69348i	0.0703180	−	0.0703180i
$581$	27.4690	+	15.8593i	1.13961	+	0.657953i
$582$	−30.3724	+	14.3460i	−1.25898	+	0.594663i
$583$	−5.07069	−	1.35869i	−0.210006	−	0.0562710i
$584$	30.0830			1.24484
$585$	27.8638	+	8.41908i	1.15203	+	0.348086i
$586$	−27.3213			−1.12863
$587$	−4.47868	−	1.20006i	−0.184855	−	0.0495318i	0.165204	−	0.986259i	$-0.447172\pi$
$587$	−4.47868	−	1.20006i	−0.184855	−	0.0495318i	−0.350059	+	0.936728i	$0.613838\pi$
$588$	−14.2448	+	6.72837i	−0.587446	+	0.277473i
$589$	3.05928	+	1.76627i	0.126055	+	0.0727780i
$590$	−26.4497	+	26.4497i	−1.08892	+	1.08892i
$591$	−5.17270	+	0.938469i	−0.212776	+	0.0386035i
$592$	−6.87278	−	25.6496i	−0.282469	−	1.05419i
$593$	−16.2154	−	16.2154i	−0.665886	−	0.665886i	0.290875	−	0.956761i	$-0.406054\pi$
$593$	−16.2154	−	16.2154i	−0.665886	−	0.665886i	−0.956761	+	0.290875i	$0.906054\pi$
$594$	5.86712	+	5.69567i	0.240731	+	0.233696i
$595$	11.0504	−	6.37995i	0.453022	−	0.261552i
$596$	−0.271809	+	1.01440i	−0.0111337	+	0.0415516i
$597$	−4.28344	−	0.353429i	−0.175309	−	0.0144649i
$598$	48.2225	+	6.24467i	1.97196	+	0.255363i
$599$			12.0663i			0.493017i	0.969141	+	0.246509i	$0.0792833\pi$
$599$			12.0663i			0.493017i	−0.969141	+	0.246509i	$0.920717\pi$
$600$	3.14061	−	8.76328i	0.128215	−	0.357759i
$601$	15.7133	+	27.2162i	0.640957	+	1.11017i	0.985219	+	0.171297i	$0.0547957\pi$
$601$	15.7133	+	27.2162i	0.640957	+	1.11017i	−0.344262	+	0.938873i	$0.611871\pi$
$602$	26.2096	−	45.3963i	1.06822	−	1.85022i
$603$	−17.5505	−	24.5448i	−0.714713	−	0.999541i
$604$	1.84544	−	0.494485i	0.0750900	−	0.0201203i
$605$	−2.59934	+	0.696491i	−0.105678	+	0.0283164i
$606$	−25.9377	−	30.6029i	−1.05365	−	1.24316i
$607$	−23.7733	+	41.1765i	−0.964927	+	1.67130i	−0.255116	+	0.966910i	$0.582114\pi$
$607$	−23.7733	+	41.1765i	−0.964927	+	1.67130i	−0.709811	+	0.704392i	$0.751220\pi$
$608$	−3.93677	−	6.81869i	−0.159657	−	0.276534i
$609$	−15.5576	−	5.57558i	−0.630425	−	0.225934i
$610$		−	30.8952i		−	1.25091i
$611$	28.7694	−	11.9882i	1.16389	−	0.484990i
$612$	−0.217470	+	1.30886i	−0.00879070	+	0.0529074i
$613$	6.96635	−	25.9988i	0.281368	−	1.05008i	−0.670085	−	0.742285i	$-0.733742\pi$
$613$	6.96635	−	25.9988i	0.281368	−	1.05008i	0.951453	−	0.307795i	$-0.0995912\pi$
$614$	−16.2312	+	9.37111i	−0.655040	+	0.378187i
$615$	15.2981	−	22.0795i	0.616881	−	0.890330i
$616$	−8.65974	−	8.65974i	−0.348911	−	0.348911i
$617$	8.24865	+	30.7844i	0.332078	+	1.23933i	0.907002	+	0.421125i	$0.138365\pi$
$617$	8.24865	+	30.7844i	0.332078	+	1.23933i	−0.574924	+	0.818206i	$0.694969\pi$
$618$	−5.10565	−	28.1416i	−0.205380	−	1.13202i
$619$	−17.8757	+	17.8757i	−0.718486	+	0.718486i	−0.968295	−	0.249809i	$-0.919632\pi$
$619$	−17.8757	+	17.8757i	−0.718486	+	0.718486i	0.249809	+	0.968295i	$0.419632\pi$
$620$	−1.31603	−	0.759809i	−0.0528530	−	0.0305147i
$621$	42.8376	−	12.1618i	1.71901	−	0.488036i
$622$	−18.2309	−	4.88496i	−0.730993	−	0.195869i
$623$	52.8437			2.11714
$624$	24.7785	−	16.0327i	0.991933	−	0.641824i
$625$	31.1833			1.24733
$626$	−39.3076	−	10.5324i	−1.57105	−	0.420961i
$627$	2.20473	+	4.66769i	0.0880485	+	0.186410i
$628$	−5.46307	−	3.15410i	−0.218000	−	0.125862i
$629$	−3.68826	+	3.68826i	−0.147061	+	0.147061i
$630$	64.5871	−	6.29451i	2.57321	−	0.250779i
$631$	−1.14909	−	4.28845i	−0.0457444	−	0.170720i	0.939275	−	0.343167i	$-0.111500\pi$
$631$	−1.14909	−	4.28845i	−0.0457444	−	0.170720i	−0.985019	+	0.172446i	$0.944833\pi$
$632$	7.68274	+	7.68274i	0.305603	+	0.305603i
$633$	−4.16132	−	2.88324i	−0.165398	−	0.114599i
$634$	38.2299	−	22.0721i	1.51830	−	0.876593i
$635$	3.02151	−	11.2764i	0.119905	−	0.447492i
$636$	0.356223	−	4.31729i	0.0141251	−	0.171192i
$637$	−9.12916	−	68.2252i	−0.361711	−	2.70318i
$638$			2.93961i			0.116380i
$639$	−2.98196	−	1.35479i	−0.117964	−	0.0535946i
$640$	−18.3196	−	31.7305i	−0.724146	−	1.25426i
$641$	−4.44179	+	7.69341i	−0.175440	+	0.303871i	−0.940314	−	0.340309i	$-0.889468\pi$
$641$	−4.44179	+	7.69341i	−0.175440	+	0.303871i	0.764873	+	0.644181i	$0.222802\pi$
$642$	−9.07699	+	7.69326i	−0.358240	+	0.303629i
$643$	−38.5098	+	10.3187i	−1.51868	+	0.406929i	−0.919307	−	0.393542i	$-0.871250\pi$
$643$	−38.5098	+	10.3187i	−1.51868	+	0.406929i	−0.599372	+	0.800471i	$0.704583\pi$
$644$	20.1449	−	5.39781i	0.793821	−	0.212704i
$645$	−23.1876	+	19.6528i	−0.913011	+	0.773829i
$646$	−2.17691	+	3.77051i	−0.0856493	+	0.148349i
$647$	15.8987	+	27.5373i	0.625041	+	1.08260i	0.988533	+	0.151006i	$0.0482512\pi$
$647$	15.8987	+	27.5373i	0.625041	+	1.08260i	−0.363492	+	0.931597i	$0.618415\pi$
$648$	12.0250	−	17.9171i	0.472386	−	0.703851i
$649$		−	8.83291i		−	0.346722i
$650$	−10.1071	−	7.72147i	−0.396433	−	0.302861i
$651$	−0.862297	+	10.4507i	−0.0337961	+	0.409596i
$652$	0.714544	−	2.66672i	0.0279837	−	0.104437i
$653$	8.22772	−	4.75028i	0.321976	−	0.185893i	−0.330297	−	0.943877i	$-0.607149\pi$
$653$	8.22772	−	4.75028i	0.321976	−	0.185893i	0.652273	+	0.757984i	$0.273816\pi$
$654$	5.40564	+	3.74539i	0.211377	+	0.146456i
$655$	19.6413	+	19.6413i	0.767449	+	0.767449i
$656$	−7.04901	−	26.3073i	−0.275218	−	1.02713i
$657$	−3.65116	−	37.4640i	−0.142445	−	1.46161i
$658$	49.1326	−	49.1326i	1.91539	−	1.91539i
$659$	4.30263	+	2.48413i	0.167607	+	0.0967678i	0.581457	−	0.813577i	$-0.302483\pi$
$659$	4.30263	+	2.48413i	0.167607	+	0.0967678i	−0.413850	+	0.910345i	$0.635816\pi$
$660$	−0.948424	−	2.00793i	−0.0369173	−	0.0781586i
$661$	−16.2118	−	4.34395i	−0.630568	−	0.168960i	−0.0706403	−	0.997502i	$-0.522504\pi$
$661$	−16.2118	−	4.34395i	−0.630568	−	0.168960i	−0.559927	+	0.828542i	$0.689171\pi$
$662$	41.1588			1.59968
$663$	−5.16092	−	2.64045i	−0.200434	−	0.102547i
$664$	−14.8882			−0.577776
$665$	39.5714	+	10.6031i	1.53451	+	0.411171i
$666$	−24.8363	+	9.31871i	−0.962388	+	0.361093i
$667$	13.8638	+	8.00427i	0.536809	+	0.309927i
$668$	−2.34498	+	2.34498i	−0.0907301	+	0.0907301i
$669$	2.37890	+	13.1122i	0.0919738	+	0.506945i
$670$	11.0240	+	41.1422i	0.425895	+	1.58946i
$671$	5.15874	+	5.15874i	0.199151	+	0.199151i
$672$	13.3110	−	19.2115i	0.513484	−	0.741100i
$673$	29.3856	−	16.9658i	1.13273	−	0.653982i	0.188110	−	0.982148i	$-0.439764\pi$
$673$	29.3856	−	16.9658i	1.13273	−	0.653982i	0.944620	+	0.328166i	$0.106430\pi$
$674$	8.51497	−	31.7783i	0.327984	−	1.22405i
$675$	−11.2946	−	2.84758i	−0.434728	−	0.109604i
$676$	−1.62837	−	5.97572i	−0.0626296	−	0.229836i
$677$			51.6987i			1.98694i	0.114078	+	0.993472i	$0.463609\pi$
$677$			51.6987i			1.98694i	−0.114078	+	0.993472i	$0.536391\pi$
$678$	0.686323	+	0.245967i	0.0263581	+	0.00944630i
$679$	−31.4740	−	54.5145i	−1.20786	−	2.09207i
$680$	−2.99466	+	5.18690i	−0.114840	+	0.198909i
$681$	5.03403	+	5.93946i	0.192904	+	0.227601i
$682$	1.80165	−	0.482752i	0.0689889	−	0.0184855i
$683$	−45.2136	+	12.1150i	−1.73005	+	0.463566i	−0.980195	−	0.198035i	$-0.936544\pi$
$683$	−45.2136	+	12.1150i	−1.73005	+	0.463566i	−0.749856	+	0.661601i	$0.769877\pi$
$684$	−3.46515	+	2.47773i	−0.132493	+	0.0947383i
$685$	−0.540311	+	0.935847i	−0.0206442	+	0.0357569i
$686$	−48.5945	−	84.1682i	−1.85535	−	3.21356i
$687$	−11.1339	+	31.0670i	−0.424785	+	1.18528i
$688$			30.8187i			1.17495i
$689$	17.5021	+	7.20619i	0.666777	+	0.274534i
$690$	−62.6463	−	5.16899i	−2.38490	−	0.196780i
$691$	0.122736	−	0.458056i	0.00466909	−	0.0174253i	−0.963552	−	0.267521i	$-0.913795\pi$
$691$	0.122736	−	0.458056i	0.00466909	−	0.0174253i	0.968221	+	0.250096i	$0.0804621\pi$
$692$	5.62053	−	3.24502i	0.213661	−	0.123357i
$693$	−9.73343	+	11.8355i	−0.369742	+	0.449593i
$694$	−35.1743	−	35.1743i	−1.33520	−	1.33520i
$695$	−10.7029	−	39.9439i	−0.405985	−	1.51516i
$696$	7.63271	−	1.38478i	0.289317	−	0.0524901i
$697$	−3.78284	+	3.78284i	−0.143285	+	0.143285i
$698$	22.4632	+	12.9692i	0.850246	+	0.490890i
$699$	−6.98110	+	3.29744i	−0.264050	+	0.124721i
$700$	−5.26938	−	1.41193i	−0.199164	−	0.0533658i
$701$	−40.7015			−1.53727			−0.768637	−	0.639685i	$-0.779065\pi$
$701$	−40.7015			−1.53727			−0.768637	+	0.639685i	$0.779065\pi$
$702$	−18.3417	−	23.0827i	−0.692262	−	0.871200i
$703$	−16.7466			−0.631611
$704$	5.11406	+	1.37031i	0.192743	+	0.0516455i
$705$	−36.4313	+	17.2079i	−1.37208	+	0.648088i
$706$	−3.89959	−	2.25143i	−0.146763	−	0.0847336i
$707$	53.1587	−	53.1587i	1.99924	−	1.99924i
$708$	7.17188	−	1.30118i	0.269536	−	0.0489012i
$709$	11.0713	+	41.3188i	0.415793	+	1.55176i	0.783243	+	0.621716i	$0.213564\pi$
$709$	11.0713	+	41.3188i	0.415793	+	1.55176i	−0.367450	+	0.930043i	$0.619769\pi$
$710$	3.26923	+	3.26923i	0.122692	+	0.122692i
$711$	8.63529	−	10.5002i	0.323849	−	0.393788i
$712$	−21.4810	+	12.4021i	−0.805034	+	0.464787i
$713$	2.62898	−	9.81148i	0.0984560	−	0.367443i
$714$	−12.8804	−	1.06277i	−0.482036	−	0.0397731i
$715$	9.61695	−	1.28684i	0.359653	−	0.0481249i
$716$			2.03052i			0.0758840i
$717$	−7.21517	+	20.1326i	−0.269456	+	0.751864i
$718$	−3.05993	−	5.29995i	−0.114196	−	0.197793i
$719$	0.365381	−	0.632859i	0.0136264	−	0.0236017i	−0.859132	−	0.511754i	$-0.828996\pi$
$719$	0.365381	−	0.632859i	0.0136264	−	0.0236017i	0.872758	+	0.488153i	$0.162329\pi$
$720$	−31.0348	+	22.1912i	−1.15660	+	0.827017i
$721$	51.7721	−	13.8723i	1.92809	−	0.516631i
$722$	15.3787	−	4.12071i	0.572336	−	0.153357i
$723$	−3.13530	−	3.69922i	−0.116603	−	0.137576i
$724$	−5.58987	+	9.68194i	−0.207746	+	0.359826i
$725$	−2.09371	−	3.62641i	−0.0777583	−	0.134681i
$726$	2.56587	+	0.919565i	0.0952284	+	0.0341283i
$727$			7.21791i			0.267698i	0.991002	+	0.133849i	$0.0427336\pi$
$727$			7.21791i			0.267698i	−0.991002	+	0.133849i	$0.957266\pi$
$728$	26.9548	+	34.9744i	0.999010	+	1.29624i
$729$	−23.7727	−	12.8008i	−0.880469	−	0.474103i
$730$	−13.7523	+	51.3241i	−0.508994	+	1.89959i
$731$	5.24260	−	3.02681i	0.193904	−	0.111951i
$732$	−3.42870	+	4.94857i	−0.126729	+	0.182904i
$733$	21.8107	+	21.8107i	0.805598	+	0.805598i	0.983964	−	0.178367i	$-0.0570813\pi$
$733$	21.8107	+	21.8107i	0.805598	+	0.805598i	−0.178367	+	0.983964i	$0.557081\pi$
$734$	3.08223	+	11.5030i	0.113767	+	0.424585i
$735$	15.8846	+	87.5536i	0.585913	+	3.22946i
$736$	−16.0088	+	16.0088i	−0.590091	+	0.590091i
$737$	−8.71047	−	5.02899i	−0.320854	−	0.185245i
$738$	−25.4732	+	9.55766i	−0.937681	+	0.351823i
$739$	−21.6080	−	5.78985i	−0.794864	−	0.212983i	−0.161536	−	0.986867i	$-0.551645\pi$
$739$	−21.6080	−	5.78985i	−0.794864	−	0.212983i	−0.633328	+	0.773884i	$0.718311\pi$
$740$	7.20400			0.264824
$741$	−5.72211	−	17.7111i	−0.210207	−	0.650635i
$742$	42.1969			1.54910
$743$	−46.9685	−	12.5852i	−1.72311	−	0.461706i	−0.744532	−	0.667587i	$-0.767327\pi$
$743$	−46.9685	−	12.5852i	−1.72311	−	0.461706i	−0.978577	+	0.205881i	$0.933994\pi$
$744$	−2.10219	−	4.45060i	−0.0770700	−	0.163167i
$745$	5.13708	+	2.96589i	0.188208	+	0.108662i
$746$	33.1586	−	33.1586i	1.21402	−	1.21402i
$747$	1.80698	+	18.5412i	0.0661140	+	0.678385i
$748$	0.114467	+	0.427197i	0.00418533	+	0.0156199i
$749$	−15.7672	−	15.7672i	−0.576120	−	0.576120i
$750$	−16.6303	−	11.5226i	−0.607253	−	0.420746i
$751$	−16.0905	+	9.28985i	−0.587150	+	0.338991i	−0.763970	−	0.645252i	$-0.776752\pi$
$751$	−16.0905	+	9.28985i	−0.587150	+	0.338991i	0.176820	+	0.984243i	$0.443419\pi$
$752$	−10.5732	+	39.4596i	−0.385564	+	1.43894i
$753$	0.425228	−	5.15361i	0.0154962	−	0.187808i
$754$	1.36116	−	10.5111i	0.0495705	−	0.382793i
$755$		−	10.7913i		−	0.392737i
$756$	−11.0436	−	6.15957i	−0.401654	−	0.224021i
$757$	5.25388	+	9.09999i	0.190956	+	0.330745i	0.945567	−	0.325427i	$-0.105508\pi$
$757$	5.25388	+	9.09999i	0.190956	+	0.330745i	−0.754612	+	0.656172i	$0.772175\pi$
$758$	−0.585173	+	1.01355i	−0.0212544	+	0.0368138i
$759$	11.3235	−	9.59730i	0.411017	−	0.348360i
$760$	−18.5743	+	4.97696i	−0.673759	+	0.180533i
$761$	24.1179	−	6.46236i	0.874272	−	0.234260i	0.206338	−	0.978481i	$-0.433845\pi$
$761$	24.1179	−	6.46236i	0.874272	−	0.234260i	0.667934	+	0.744220i	$0.267179\pi$
$762$	−9.02042	+	7.64532i	−0.326775	+	0.276961i
$763$	−6.16209	+	10.6731i	−0.223083	+	0.386391i
$764$	−1.35491	−	2.34677i	−0.0490190	−	0.0849033i
$765$	6.82300	+	3.09988i	0.246686	+	0.112077i
$766$			26.3364i			0.951572i
$767$	−4.09001	+	31.5838i	−0.147682	+	1.14042i
$768$	−1.54350	+	18.7067i	−0.0556964	+	0.675020i
$769$	−10.8876	+	40.6332i	−0.392618	+	1.46527i	0.433182	+	0.901307i	$0.357391\pi$
$769$	−10.8876	+	40.6332i	−0.392618	+	1.46527i	−0.825800	+	0.563963i	$0.809276\pi$
$770$	18.7330	−	10.8155i	0.675091	−	0.389764i
$771$	−34.4463	−	23.8667i	−1.24055	−	0.859540i
$772$	−4.60212	−	4.60212i	−0.165634	−	0.165634i
$773$	7.60460	+	28.3808i	0.273518	+	1.02078i	0.956828	+	0.290656i	$0.0938735\pi$
$773$	7.60460	+	28.3808i	0.273518	+	1.02078i	−0.683309	+	0.730129i	$0.739460\pi$
$774$	30.6418	−	2.98628i	1.10140	−	0.107340i
$775$	−1.87875	+	1.87875i	−0.0674868	+	0.0674868i
$776$	25.5884	+	14.7734i	0.918568	+	0.530336i
$777$	−21.2315	−	44.9498i	−0.761676	−	1.61256i
$778$	−1.90298	−	0.509903i	−0.0682252	−	0.0182809i
$779$	−17.1760			−0.615395
$780$	2.46152	+	7.61891i	0.0881364	+	0.272801i
$781$	−1.09176			−0.0390664
$782$	12.0925	+	3.24018i	0.432427	+	0.115868i
$783$	−2.65093	−	9.33737i	−0.0947364	−	0.333691i
$784$	78.1340	+	45.1107i	2.79050	+	1.61110i
$785$	−25.1947	+	25.1947i	−0.899237	+	0.899237i
$786$	−5.02239	−	27.6826i	−0.179143	−	0.987407i
$787$	−3.90994	−	14.5921i	−0.139374	−	0.520152i	−0.999942	−	0.0108151i	$-0.996557\pi$
$787$	−3.90994	−	14.5921i	−0.139374	−	0.520152i	0.860567	−	0.509337i	$-0.170109\pi$
$788$	−1.02253	−	1.02253i	−0.0364260	−	0.0364260i
$789$	15.1531	−	21.8701i	0.539464	−	0.778596i
$790$	−16.6195	+	9.59529i	−0.591296	+	0.341385i
$791$	−0.353618	+	1.31972i	−0.0125732	+	0.0469239i
$792$	1.17893	−	7.09550i	0.0418916	−	0.252128i
$793$	−16.0574	−	20.8348i	−0.570214	−	0.739865i
$794$			13.1035i			0.465026i
$795$	−23.0337	−	8.25489i	−0.816921	−	0.292771i
$796$	−0.591120	−	1.02385i	−0.0209517	−	0.0362894i
$797$	−9.71765	+	16.8315i	−0.344217	+	0.596201i	−0.985211	−	0.171345i	$-0.945189\pi$
$797$	−9.71765	+	16.8315i	−0.344217	+	0.596201i	0.640994	+	0.767545i	$0.278522\pi$
$798$	−26.8290	−	31.6545i	−0.949737	−	1.12056i
$799$	7.75093	−	2.07686i	0.274208	−	0.0734739i
$800$	5.72019	−	1.53272i	0.202239	−	0.0541898i
$801$	18.0521	+	25.2462i	0.637840	+	0.892032i
$802$	14.4704	−	25.0635i	0.510969	−	0.885024i
$803$	−6.27358	−	10.8662i	−0.221390	−	0.383458i
$804$	2.80015	−	7.81328i	0.0987537	−	0.275553i
$805$		−	117.798i		−	4.15185i
$806$	−6.66570	+	0.891932i	−0.234789	+	0.0314170i
$807$	49.5536	+	4.08870i	1.74437	+	0.143929i
$808$	−9.13306	+	34.0850i	−0.321300	+	1.19911i
$809$	35.8403	−	20.6924i	1.26008	−	0.727506i	0.286988	−	0.957934i	$-0.407346\pi$
$809$	35.8403	−	20.6924i	1.26008	−	0.727506i	0.973089	+	0.230428i	$0.0740127\pi$
$810$	25.0710	+	28.7064i	0.880906	+	1.00864i
$811$	−26.4357	−	26.4357i	−0.928282	−	0.928282i	0.0693126	−	0.997595i	$-0.477919\pi$
$811$	−26.4357	−	26.4357i	−0.928282	−	0.928282i	−0.997595	+	0.0693126i	$0.977919\pi$
$812$	−1.17657	−	4.39102i	−0.0412895	−	0.154095i
$813$	−23.9993	+	4.35413i	−0.841692	+	0.152706i
$814$	−6.25247	+	6.25247i	−0.219149	+	0.219149i
$815$	−13.5046	−	7.79688i	−0.473045	−	0.273113i
$816$	6.87060	−	3.24525i	0.240519	−	0.113606i
$817$	18.7737	+	5.03039i	0.656808	+	0.175991i
$818$	−45.1340			−1.57807
$819$	40.2841	−	37.8131i	1.40764	−	1.32130i
$820$	7.38872			0.258025
$821$	−8.43376	−	2.25982i	−0.294340	−	0.0788682i	0.108627	−	0.994083i	$-0.465355\pi$
$821$	−8.43376	−	2.25982i	−0.294340	−	0.0788682i	−0.402967	+	0.915214i	$0.632021\pi$
$822$	0.989685	−	0.467467i	0.0345192	−	0.0163048i
$823$	−34.5896	−	19.9703i	−1.20572	−	0.696122i	−0.243897	−	0.969801i	$-0.578426\pi$
$823$	−34.5896	−	19.9703i	−1.20572	−	0.696122i	−0.961821	+	0.273680i	$0.911759\pi$
$824$	−17.7896	+	17.7896i	−0.619732	+	0.619732i
$825$	−3.82031	+	0.693108i	−0.133006	+	0.0241309i
$826$	18.3763	+	68.5813i	0.639393	+	2.38625i
$827$	29.7592	+	29.7592i	1.03483	+	1.03483i	0.999371	+	0.0354563i	$0.0112885\pi$
$827$	29.7592	+	29.7592i	1.03483	+	1.03483i	0.0354563	+	0.999371i	$0.488712\pi$
$828$	9.46059	+	7.78033i	0.328778	+	0.270385i
$829$	17.6492	−	10.1898i	0.612983	−	0.353906i	−0.161149	−	0.986930i	$-0.551520\pi$
$829$	17.6492	−	10.1898i	0.612983	−	0.353906i	0.774132	+	0.633024i	$0.218187\pi$
$830$	6.80608	−	25.4006i	0.236242	−	0.881669i
$831$	−19.1349	−	1.57883i	−0.663783	−	0.0547691i
$832$	−17.6518	−	7.26783i	−0.611967	−	0.251967i
$833$		−	17.7219i		−	0.614027i
$834$	−14.1309	+	39.4296i	−0.489313	+	1.36533i
$835$	9.36576	+	16.2220i	0.324115	+	0.561384i
$836$	−0.709977	+	1.22972i	−0.0245551	+	0.0425306i
$837$	−5.28744	+	3.15814i	−0.182761	+	0.109161i
$838$	−29.9994	+	8.03832i	−1.03631	+	0.277679i
$839$	18.3039	−	4.90451i	0.631920	−	0.169323i	0.0713794	−	0.997449i	$-0.477260\pi$
$839$	18.3039	−	4.90451i	0.631920	−	0.169323i	0.560541	+	0.828127i	$0.310593\pi$
$840$	−36.9073	−	43.5455i	−1.27342	−	1.50246i
$841$	−12.7553	+	22.0928i	−0.439838	+	0.761821i
$842$	6.78380	+	11.7499i	0.233785	+	0.404928i
$843$	14.2214	+	5.09672i	0.489812	+	0.175541i
$844$		−	1.39255i		−	0.0479337i
$845$	−34.9831	+	0.148284i	−1.20346	+	0.00510113i
$846$	40.2576	+	6.68890i	1.38408	+	0.229969i
$847$	−1.32203	+	4.93388i	−0.0454254	+	0.169530i
$848$	−21.4850	+	12.4044i	−0.737799	+	0.425968i
$849$	19.4251	−	28.0358i	0.666668	−	0.962187i
$850$	−2.31554	−	2.31554i	−0.0794222	−	0.0794222i
$851$	12.4631	+	46.5129i	0.427229	+	1.59444i
$852$	−0.160828	−	0.886457i	−0.00550986	−	0.0303695i
$853$	23.0068	−	23.0068i	0.787738	−	0.787738i	−0.193385	−	0.981123i	$-0.561947\pi$
$853$	23.0068	−	23.0068i	0.787738	−	0.787738i	0.981123	+	0.193385i	$0.0619465\pi$
$854$	−50.7864	−	29.3215i	−1.73787	−	1.00336i
$855$	8.45243	+	22.5275i	0.289067	+	0.770424i
$856$	10.1098	+	2.70892i	0.345546	+	0.0925888i
$857$	−36.0977			−1.23307			−0.616537	−	0.787326i	$-0.711465\pi$
$857$	−36.0977			−1.23307			−0.616537	+	0.787326i	$0.711465\pi$
$858$	−8.74898	−	4.47619i	−0.298685	−	0.152815i
$859$	26.6962			0.910863			0.455431	−	0.890271i	$-0.349485\pi$
$859$	26.6962			0.910863			0.455431	+	0.890271i	$0.349485\pi$
$860$	−8.07600	−	2.16396i	−0.275389	−	0.0737903i
$861$	−21.7759	−	46.1024i	−0.742121	−	1.57116i
$862$	0.384016	+	0.221712i	0.0130796	+	0.00755153i
$863$	0.0474064	−	0.0474064i	0.00161373	−	0.00161373i	−0.706299	−	0.707913i	$-0.749637\pi$
$863$	0.0474064	−	0.0474064i	0.00161373	−	0.00161373i	0.707913	+	0.706299i	$0.249637\pi$
$864$	13.7256	−	0.203521i	0.466954	−	0.00692394i
$865$	−9.48771	−	35.4086i	−0.322592	−	1.20393i
$866$	42.9818	+	42.9818i	1.46058	+	1.46058i
$867$	22.9762	+	15.9194i	0.780311	+	0.540652i
$868$	−2.49799	+	1.44222i	−0.0847873	+	0.0489520i
$869$	1.17288	−	4.37723i	0.0397871	−	0.148487i
$870$	−1.12669	+	13.6551i	−0.0381985	+	0.462952i
$871$	28.8174	+	22.0155i	0.976439	+	0.745965i
$872$		−	5.78480i		−	0.195898i
$873$	15.2925	−	33.6597i	0.517574	−	1.13921i
$874$	20.0971	+	34.8091i	0.679793	+	1.17744i
$875$	18.9575	−	32.8354i	0.640881	−	1.11004i
$876$	7.89861	−	6.69452i	0.266869	−	0.226187i
$877$	10.7021	−	2.86761i	0.361383	−	0.0968323i	−0.0735587	−	0.997291i	$-0.523436\pi$
$877$	10.7021	−	2.86761i	0.361383	−	0.0968323i	0.434942	+	0.900459i	$0.356769\pi$
$878$	−12.6722	+	3.39550i	−0.427666	+	0.114593i
$879$	22.9400	−	19.4429i	0.773747	−	0.655794i
$880$	−6.35875	+	11.0137i	−0.214353	+	0.371271i
$881$	−20.5668	−	35.6228i	−0.692913	−	1.20016i	−0.970879	−	0.239570i	$-0.922994\pi$
$881$	−20.5668	−	35.6228i	−0.692913	−	1.20016i	0.277966	−	0.960591i	$-0.410340\pi$
$882$	37.2806	−	82.0565i	1.25530	−	2.76299i
$883$		−	16.6946i		−	0.561817i	−0.959735	−	0.280908i	$-0.909364\pi$
$883$		−	16.6946i		−	0.561817i	0.959735	−	0.280908i	$-0.0906357\pi$
$884$	−0.211489	−	1.58053i	−0.00711315	−	0.0531589i
$885$	3.38548	−	41.0308i	0.113802	−	1.37924i
$886$	−1.84071	+	6.86961i	−0.0618398	+	0.230789i
$887$	−12.3820	+	7.14873i	−0.415746	+	0.240031i	−0.693256	−	0.720692i	$-0.743824\pi$
$887$	−12.3820	+	7.14873i	−0.415746	+	0.240031i	0.277510	+	0.960723i	$0.410491\pi$
$888$	19.1800	+	13.2892i	0.643639	+	0.445957i
$889$	−15.6689	−	15.6689i	−0.525519	−	0.525519i
$890$	−11.3391	−	42.3180i	−0.380086	−	1.41850i
$891$	−8.97951	−	0.607015i	−0.300825	−	0.0203358i
$892$	−2.59198	+	2.59198i	−0.0867860	+	0.0867860i
$893$	22.3116	+	12.8816i	0.746629	+	0.431067i
$894$	−2.56603	−	5.43261i	−0.0858209	−	0.181694i
$895$	11.0782	+	2.96839i	0.370303	+	0.0992224i
$896$	−69.5459			−2.32337
$897$	−44.9333	+	29.0738i	−1.50028	+	0.970745i
$898$	39.8266			1.32903
$899$	−2.13862	−	0.573042i	−0.0713271	−	0.0191120i
$900$	−1.12554	−	2.99979i	−0.0375179	−	0.0999931i
$901$	4.22024	+	2.43656i	0.140597	+	0.0811734i
$902$	−6.41280	+	6.41280i	−0.213523	+	0.213523i
$903$	10.2993	+	56.7682i	0.342739	+	1.88913i
$904$	−0.165984	−	0.619459i	−0.00552053	−	0.0206029i
$905$	44.6514	+	44.6514i	1.48426	+	1.48426i
$906$	−6.22500	+	8.98440i	−0.206812	+	0.298487i
$907$	17.8948	−	10.3315i	0.594186	−	0.343053i	−0.172565	−	0.984998i	$-0.555206\pi$
$907$	17.8948	−	10.3315i	0.594186	−	0.343053i	0.766751	+	0.641945i	$0.221872\pi$
$908$	−0.554293	+	2.06865i	−0.0183949	+	0.0686506i
$909$	43.5565	+	7.23702i	1.44468	+	0.240037i
$910$	−71.9916	+	29.9988i	−2.38650	+	0.994450i
$911$		−	20.7542i		−	0.687618i	−0.939040	−	0.343809i	$-0.888283\pi$
$911$		−	20.7542i		−	0.687618i	0.939040	−	0.343809i	$-0.111717\pi$
$912$	22.9656	+	8.23048i	0.760466	+	0.272538i
$913$	3.10483	+	5.37773i	0.102755	+	0.177977i
$914$	−21.2906	+	36.8764i	−0.704230	+	1.21976i
$915$	21.9862	+	25.9407i	0.726843	+	0.857574i
$916$	−8.76845	+	2.34950i	−0.289718	+	0.0776297i
$917$	50.9278	−	13.6461i	1.68178	−	0.450633i
$918$	−3.89237	−	6.51670i	−0.128467	−	0.215083i
$919$	−25.5858	+	44.3159i	−0.843998	+	1.46185i	0.0424902	+	0.999097i	$0.486471\pi$
$919$	−25.5858	+	44.3159i	−0.843998	+	1.46185i	−0.886488	+	0.462751i	$0.846862\pi$
$920$	27.6465	+	47.8851i	0.911478	+	1.57873i
$921$	6.95949	−	19.4191i	0.229323	−	0.639882i
$922$		−	1.52721i		−	0.0502960i
$923$	3.90381	+	0.505532i	0.128496	+	0.0166398i
$924$	−4.20081	−	0.346612i	−0.138196	−	0.0114027i
$925$	3.26002	−	12.1665i	0.107189	−	0.400034i
$926$	14.0041	−	8.08529i	0.460205	−	0.265699i
$927$	24.3136	+	19.9953i	0.798562	+	0.656732i
$928$	3.48945	+	3.48945i	0.114547	+	0.114547i
$929$	−5.55016	−	20.7135i	−0.182095	−	0.679587i	−0.995234	−	0.0975176i	$-0.968910\pi$
$929$	−5.55016	−	20.7135i	−0.182095	−	0.679587i	0.813139	−	0.582070i	$-0.197757\pi$
$930$	8.55411	−	1.55195i	0.280500	−	0.0508905i
$931$	40.2333	−	40.2333i	1.31859	−	1.31859i
$932$	−1.83919	−	1.06186i	−0.0602447	−	0.0347823i
$933$	18.7837	−	8.87226i	0.614950	−	0.290465i
$934$	−34.2280	−	9.17138i	−1.11998	−	0.300097i
$935$	2.49806			0.0816952
$936$	−7.50102	+	24.8254i	−0.245179	+	0.811445i
$937$	−45.2973			−1.47980			−0.739899	−	0.672718i	$-0.765127\pi$
$937$	−45.2973			−1.47980			−0.739899	+	0.672718i	$0.765127\pi$
$938$	78.0931	+	20.9250i	2.54983	+	0.683225i
$939$	40.4994	−	19.1294i	1.32165	−	0.624266i
$940$	−9.59793	−	5.54137i	−0.313050	−	0.180739i
$941$	−18.2766	+	18.2766i	−0.595799	+	0.595799i	−0.939192	−	0.343393i	$-0.888424\pi$
$941$	−18.2766	+	18.2766i	−0.595799	+	0.595799i	0.343393	+	0.939192i	$0.388424\pi$
$942$	35.5096	−	6.44242i	1.15697	−	0.209905i
$943$	12.7827	+	47.7056i	0.416261	+	1.55351i
$944$	−29.5169	−	29.5169i	−0.960694	−	0.960694i
$945$	−49.7502	+	51.2478i	−1.61837	+	1.66709i
$946$	8.88743	−	5.13116i	0.288955	−	0.166828i
$947$	2.46434	−	9.19704i	0.0800803	−	0.298864i	−0.914257	−	0.405135i	$-0.867225\pi$
$947$	2.46434	−	9.19704i	0.0800803	−	0.298864i	0.994337	+	0.106271i	$0.0338912\pi$
$948$	3.72687	+	0.307506i	0.121043	+	0.00998735i
$949$	17.4009	+	41.7590i	0.564858	+	1.35555i
$950$		−	10.5137i		−	0.341110i
$951$	−16.3919	+	45.7384i	−0.531543	+	1.48317i
$952$	5.68425	+	9.84541i	0.184228	+	0.319092i
$953$	−2.67447	+	4.63232i	−0.0866347	+	0.150056i	−0.906087	−	0.423092i	$-0.860945\pi$
$953$	−2.67447	+	4.63232i	−0.0866347	+	0.150056i	0.819452	+	0.573148i	$0.194278\pi$
$954$	14.4150	+	20.1597i	0.466704	+	0.652695i
$955$	−14.7844	+	3.96146i	−0.478411	+	0.128190i
$956$	−5.68227	+	1.52256i	−0.183778	+	0.0492431i
$957$	−2.09194	−	2.46820i	−0.0676228	−	0.0797856i
$958$	14.8714	−	25.7580i	0.480472	−	0.832202i
$959$	1.02558	+	1.77636i	0.0331177	+	0.0573616i
$960$	23.2307	+	8.32551i	0.749769	+	0.268705i
$961$		−	29.5952i		−	0.954682i
$962$	25.2521	−	19.4618i	0.814160	−	0.627473i
$963$	2.14654	−	12.9191i	0.0691713	−	0.416312i
$964$	0.345226	−	1.28840i	0.0111190	−	0.0414966i
$965$	−31.8363	+	18.3807i	−1.02485	+	0.591695i
$966$	−67.9523	+	98.0740i	−2.18633	+	3.15548i
$967$	−34.0197	−	34.0197i	−1.09400	−	1.09400i	−0.995097	−	0.0989010i	$-0.968467\pi$
$967$	−34.0197	−	34.0197i	−1.09400	−	1.09400i	−0.0989010	−	0.995097i	$-0.531533\pi$
$968$	−0.620542	−	2.31589i	−0.0199450	−	0.0744357i
$969$	−0.855437	−	4.71504i	−0.0274806	−	0.151469i
$970$	−36.9023	+	36.9023i	−1.18486	+	1.18486i
$971$	−35.4814	−	20.4852i	−1.13865	−	0.657402i	−0.192557	−	0.981286i	$-0.561678\pi$
$971$	−35.4814	−	20.4852i	−1.13865	−	0.657402i	−0.946097	+	0.323884i	$0.895011\pi$
$972$	−0.829904	−	7.38033i	−0.0266192	−	0.236724i
$973$	−75.8186	−	20.3155i	−2.43063	−	0.651286i
$974$	−15.4812			−0.496050
$975$	13.9812	−	0.709382i	0.447756	−	0.0227184i
$976$	34.4779			1.10361
$977$	−46.6851	−	12.5092i	−1.49359	−	0.400206i	−0.582641	−	0.812730i	$-0.697981\pi$
$977$	−46.6851	−	12.5092i	−1.49359	−	0.400206i	−0.910947	+	0.412524i	$0.864647\pi$
$978$	6.74571	+	14.2815i	0.215704	+	0.456672i
$979$	8.95941	+	5.17272i	0.286344	+	0.165321i
$980$	−17.3074	+	17.3074i	−0.552865	+	0.552865i
$981$	−7.20414	+	0.702099i	−0.230010	+	0.0224163i
$982$	2.22289	+	8.29593i	0.0709352	+	0.264734i
$983$	−15.3072	−	15.3072i	−0.488223	−	0.488223i	0.419522	−	0.907745i	$-0.362198\pi$
$983$	−15.3072	−	15.3072i	−0.488223	−	0.488223i	−0.907745	+	0.419522i	$0.862198\pi$
$984$	19.6718	+	13.6300i	0.627115	+	0.434508i
$985$	−7.07357	+	4.08393i	−0.225383	+	0.130125i
$986$	0.706267	−	2.63582i	0.0224921	−	0.0839417i
$987$	−6.28882	+	76.2182i	−0.200175	+	2.42605i
$988$	3.10807	−	4.06834i	0.0988809	−	0.129431i
$989$		−	55.8867i		−	1.77709i
$990$	11.5666	+	5.25503i	0.367610	+	0.167016i
$991$	3.80128	+	6.58400i	0.120752	+	0.209148i	0.920064	−	0.391767i	$-0.128136\pi$
$991$	3.80128	+	6.58400i	0.120752	+	0.209148i	−0.799313	+	0.600915i	$0.794803\pi$
$992$	1.56560	−	2.71170i	0.0497079	−	0.0860966i
$993$	−34.5585	+	29.2903i	−1.09668	+	0.929498i
$994$	8.47677	−	2.27134i	0.268867	−	0.0720426i
$995$	−6.45012	+	1.72830i	−0.204483	+	0.0547909i
$996$	−3.90907	+	3.31316i	−0.123864	+	0.104982i
$997$	11.4899	−	19.9010i	0.363888	−	0.630272i	−0.624709	−	0.780857i	$-0.714783\pi$
$997$	11.4899	−	19.9010i	0.363888	−	0.630272i	0.988597	+	0.150586i	$0.0481159\pi$
$998$	4.24610	+	7.35446i	0.134408	+	0.232801i
$999$	14.2219	−	25.4988i	0.449962	−	0.806748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.be.a.89.12	✓	184
3.2	odd	2	inner	429.2.be.a.89.35	yes	184
13.6	odd	12	inner	429.2.be.a.188.35	yes	184
39.32	even	12	inner	429.2.be.a.188.12	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.be.a.89.12	✓	184	1.1	even	1	trivial
429.2.be.a.89.35	yes	184	3.2	odd	2	inner
429.2.be.a.188.12	yes	184	39.32	even	12	inner
429.2.be.a.188.35	yes	184	13.6	odd	12	inner

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.52005 - 0.407295i) q^{2} +(1.56613 - 0.739746i) q^{3} +(0.412602 + 0.238216i) q^{4} +(1.90285 - 1.90285i) q^{5} +(-2.68189 + 0.486569i) q^{6} +(-1.32203 - 4.93388i) q^{7} +(1.69535 + 1.69535i) q^{8} +(1.90555 - 2.31708i) q^{9} +O(q^{10})\)	\(q+(-1.52005 - 0.407295i) q^{2} +(1.56613 - 0.739746i) q^{3} +(0.412602 + 0.238216i) q^{4} +(1.90285 - 1.90285i) q^{5} +(-2.68189 + 0.486569i) q^{6} +(-1.32203 - 4.93388i) q^{7} +(1.69535 + 1.69535i) q^{8} +(1.90555 - 2.31708i) q^{9} +(-3.66744 + 2.11740i) q^{10} +(0.258819 - 0.965926i) q^{11} +(0.822410 + 0.0678576i) q^{12} +(-1.37272 + 3.33401i) q^{13} +8.03818i q^{14} +(1.57249 - 4.38774i) q^{15} +(-2.36294 - 4.09273i) q^{16} +(-0.464145 + 0.803922i) q^{17} +(-3.84027 + 2.74595i) q^{18} +(-2.87884 + 0.771382i) q^{19} +(1.23841 - 0.331830i) q^{20} +(-5.72029 - 6.74915i) q^{21} +(-0.786834 + 1.36284i) q^{22} +(4.28495 + 7.42175i) q^{23} +(3.90928 + 1.40102i) q^{24} -2.24166i q^{25} +(3.44453 - 4.50875i) q^{26} +(1.27030 - 5.03849i) q^{27} +(0.629857 - 2.35066i) q^{28} +(1.61773 - 0.933998i) q^{29} +(-4.17737 + 6.02910i) q^{30} +(-0.838107 - 0.838107i) q^{31} +(0.683743 + 2.55176i) q^{32} +(-0.309194 - 1.70423i) q^{33} +(1.03296 - 1.03296i) q^{34} +(-11.9040 - 6.87280i) q^{35} +(1.33820 - 0.502100i) q^{36} +(5.42747 + 1.45429i) q^{37} +4.69015 q^{38} +(0.316454 + 6.23697i) q^{39} +6.45200 q^{40} +(5.56664 + 1.49158i) q^{41} +(5.94621 + 12.5889i) q^{42} +(-5.64759 - 3.26064i) q^{43} +(0.336888 - 0.336888i) q^{44} +(-0.783077 - 8.03503i) q^{45} +(-3.49048 - 13.0267i) q^{46} +(-6.11240 - 6.11240i) q^{47} +(-6.72826 - 4.66179i) q^{48} +(-16.5332 + 9.54546i) q^{49} +(-0.913018 + 3.40743i) q^{50} +(-0.132215 + 1.60240i) q^{51} +(-1.36060 + 1.04862i) q^{52} -5.24956i q^{53} +(-3.98307 + 7.14135i) q^{54} +(-1.34552 - 2.33050i) q^{55} +(6.12336 - 10.6060i) q^{56} +(-3.93802 + 3.33770i) q^{57} +(-2.83944 + 0.760826i) q^{58} +(8.53194 - 2.28613i) q^{59} +(1.69404 - 1.43580i) q^{60} +(-3.64778 + 6.31814i) q^{61} +(0.932605 + 1.61532i) q^{62} +(-13.9514 - 6.33852i) q^{63} +5.29447i q^{64} +(3.73204 + 8.95620i) q^{65} +(-0.224136 + 2.71644i) q^{66} +(2.60320 - 9.71527i) q^{67} +(-0.383014 + 0.221133i) q^{68} +(12.2010 + 8.45369i) q^{69} +(15.2954 + 15.2954i) q^{70} +(-0.282569 - 1.05456i) q^{71} +(7.15886 - 0.697686i) q^{72} +(8.87218 - 8.87218i) q^{73} +(-7.65768 - 4.42117i) q^{74} +(-1.65826 - 3.51074i) q^{75} +(-1.37157 - 0.367511i) q^{76} -5.10793 q^{77} +(2.05927 - 9.60938i) q^{78} +4.53164 q^{79} +(-12.2842 - 3.29153i) q^{80} +(-1.73774 - 8.83064i) q^{81} +(-7.85404 - 4.53453i) q^{82} +(-4.39090 + 4.39090i) q^{83} +(-0.752448 - 4.14738i) q^{84} +(0.646545 + 2.41294i) q^{85} +(7.25656 + 7.25656i) q^{86} +(1.84266 - 2.65948i) q^{87} +(2.07637 - 1.19880i) q^{88} +(-2.67759 + 9.99292i) q^{89} +(-2.08232 + 12.5326i) q^{90} +(18.2644 + 2.36518i) q^{91} +4.08298i q^{92} +(-1.93257 - 0.692602i) q^{93} +(6.80158 + 11.7807i) q^{94} +(-4.01017 + 6.94581i) q^{95} +(2.95849 + 3.49061i) q^{96} +(11.9037 - 3.18958i) q^{97} +(29.0191 - 7.77564i) q^{98} +(-1.74494 - 2.44033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 12 q^{6} + 12 q^{7}+O(q^{10}) \) 184 * q - 12 * q^6 + 12 * q^7	\( 184 q - 12 q^{6} + 12 q^{7} - 48 q^{10} - 16 q^{13} + 16 q^{15} + 80 q^{16} - 8 q^{18} - 4 q^{19} - 24 q^{24} - 48 q^{27} - 40 q^{28} + 48 q^{30} - 20 q^{31} + 16 q^{34} - 36 q^{36} + 44 q^{37} + 48 q^{39} - 80 q^{40} + 20 q^{42} - 84 q^{43} - 4 q^{45} - 64 q^{46} + 44 q^{48} - 60 q^{49} - 200 q^{52} - 4 q^{54} - 64 q^{57} - 48 q^{58} - 148 q^{60} - 48 q^{61} + 40 q^{66} + 48 q^{67} - 12 q^{69} + 24 q^{70} - 128 q^{72} + 108 q^{73} - 60 q^{75} - 24 q^{76} + 148 q^{78} + 32 q^{79} + 16 q^{81} - 48 q^{82} + 116 q^{84} + 104 q^{85} - 24 q^{87} + 72 q^{88} + 60 q^{91} + 36 q^{93} + 16 q^{94} - 72 q^{96} + 4 q^{97}+O(q^{100}) \) 184 * q - 12 * q^6 + 12 * q^7 - 48 * q^10 - 16 * q^13 + 16 * q^15 + 80 * q^16 - 8 * q^18 - 4 * q^19 - 24 * q^24 - 48 * q^27 - 40 * q^28 + 48 * q^30 - 20 * q^31 + 16 * q^34 - 36 * q^36 + 44 * q^37 + 48 * q^39 - 80 * q^40 + 20 * q^42 - 84 * q^43 - 4 * q^45 - 64 * q^46 + 44 * q^48 - 60 * q^49 - 200 * q^52 - 4 * q^54 - 64 * q^57 - 48 * q^58 - 148 * q^60 - 48 * q^61 + 40 * q^66 + 48 * q^67 - 12 * q^69 + 24 * q^70 - 128 * q^72 + 108 * q^73 - 60 * q^75 - 24 * q^76 + 148 * q^78 + 32 * q^79 + 16 * q^81 - 48 * q^82 + 116 * q^84 + 104 * q^85 - 24 * q^87 + 72 * q^88 + 60 * q^91 + 36 * q^93 + 16 * q^94 - 72 * q^96 + 4 * q^97

Introduction

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