LMFDB - Embedded newform 640.2.bm.a.341.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

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

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

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			341.42
Character	$\chi$	$=$	640.341
Dual form			640.2.bm.a.381.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.612916 - 1.27449i) q^{2} +(1.79383 - 2.18578i) q^{3} +(-1.24867 - 1.56232i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(-1.68630 - 3.62592i) q^{6} +(1.60460 + 0.319174i) q^{7} +(-2.75649 + 0.633850i) q^{8} +(-0.974564 - 4.89947i) q^{9} +O(q^{10})$	\(q+(0.612916 - 1.27449i) q^{2} +(1.79383 - 2.18578i) q^{3} +(-1.24867 - 1.56232i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(-1.68630 - 3.62592i) q^{6} +(1.60460 + 0.319174i) q^{7} +(-2.75649 + 0.633850i) q^{8} +(-0.974564 - 4.89947i) q^{9} +(-0.216558 + 1.39753i) q^{10} +(-0.980004 - 0.0965219i) q^{11} +(-5.65477 - 0.0732053i) q^{12} +(1.29174 - 4.25831i) q^{13} +(1.39027 - 1.84942i) q^{14} +(-1.08208 + 2.61238i) q^{15} +(-0.881659 + 3.90163i) q^{16} +(0.223479 + 0.539526i) q^{17} +(-6.84166 - 1.76089i) q^{18} +(-5.83147 + 3.11698i) q^{19} +(1.64842 + 1.13257i) q^{20} +(3.57601 - 2.93476i) q^{21} +(-0.723677 + 1.18985i) q^{22} +(4.46593 - 6.68374i) q^{23} +(-3.55920 + 7.16210i) q^{24} +(0.831470 - 0.555570i) q^{25} +(-4.63546 - 4.25630i) q^{26} +(-4.97614 - 2.65980i) q^{27} +(-1.50496 - 2.90543i) q^{28} +(1.00560 + 10.2100i) q^{29} +(2.66624 + 2.98028i) q^{30} +(-1.44186 - 1.44186i) q^{31} +(4.43221 + 3.51504i) q^{32} +(-1.96893 + 1.96893i) q^{33} +(0.824596 + 0.0458617i) q^{34} +(-1.62815 + 0.160359i) q^{35} +(-6.43760 + 7.64038i) q^{36} +(4.43553 - 8.29830i) q^{37} +(0.398376 + 9.34262i) q^{38} +(-6.99057 - 10.4621i) q^{39} +(2.45380 - 1.40672i) q^{40} +(5.53878 + 3.70090i) q^{41} +(-1.54853 - 6.35636i) q^{42} +(1.92505 + 2.34568i) q^{43} +(1.07290 + 1.65160i) q^{44} +(2.35484 + 4.40560i) q^{45} +(-5.78114 - 9.78838i) q^{46} +(6.80879 - 2.82029i) q^{47} +(6.94656 + 8.92595i) q^{48} +(-3.99430 - 1.65449i) q^{49} +(-0.198449 - 1.40022i) q^{50} +(1.58017 + 0.479339i) q^{51} +(-8.26578 + 3.29910i) q^{52} +(-0.396480 + 4.02553i) q^{53} +(-6.43986 + 4.71182i) q^{54} +(0.965824 - 0.192114i) q^{55} +(-4.62536 + 0.137274i) q^{56} +(-3.64758 + 18.3376i) q^{57} +(13.6289 + 4.97624i) q^{58} +(1.35638 + 4.47138i) q^{59} +(5.43253 - 1.57144i) q^{60} +(10.7479 + 8.82056i) q^{61} +(-2.72139 + 0.953905i) q^{62} -8.17272i q^{63} +(7.19647 - 3.49440i) q^{64} +4.44992i q^{65} +(1.30260 + 3.71618i) q^{66} +(-2.54890 - 2.09183i) q^{67} +(0.563859 - 1.02283i) q^{68} +(-6.59810 - 21.7510i) q^{69} +(-0.793546 + 2.17336i) q^{70} +(2.34733 - 11.8008i) q^{71} +(5.79190 + 12.8876i) q^{72} +(-0.560737 + 0.111538i) q^{73} +(-7.85752 - 10.7392i) q^{74} +(0.277156 - 2.81401i) q^{75} +(12.1513 + 5.21851i) q^{76} +(-1.54170 - 0.467671i) q^{77} +(-17.6186 + 2.49703i) q^{78} +(-1.16475 - 0.482455i) q^{79} +(-0.288887 - 3.98955i) q^{80} +(-0.894487 + 0.370508i) q^{81} +(8.11158 - 4.79081i) q^{82} +(5.34180 + 9.99380i) q^{83} +(-9.05027 - 1.92232i) q^{84} +(-0.370472 - 0.451422i) q^{85} +(4.16946 - 1.01576i) q^{86} +(24.1207 + 16.1169i) q^{87} +(2.76255 - 0.355114i) q^{88} +(-1.08856 - 1.62914i) q^{89} +(7.05822 - 0.300967i) q^{90} +(3.43187 - 6.42058i) q^{91} +(-16.0186 + 1.36858i) q^{92} +(-5.73806 + 0.565149i) q^{93} +(0.578772 - 10.4064i) q^{94} +(4.67555 - 4.67555i) q^{95} +(15.6337 - 3.38249i) q^{96} +(-10.6153 - 10.6153i) q^{97} +(-4.55681 + 4.07664i) q^{98} +(0.482171 + 4.89556i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{29}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	0.612916	−	1.27449i	0.433397	−	0.901203i
$2$	0.612916	−	1.27449i	0.433397	−	0.901203i
$3$	1.79383	−	2.18578i	1.03567	−	1.26196i	0.0712813	−	0.997456i	$-0.477291\pi$
$3$	1.79383	−	2.18578i	1.03567	−	1.26196i	0.964384	−	0.264506i	$-0.0852088\pi$
$4$	−1.24867	−	1.56232i	−0.624334	−	0.781158i
$5$	−0.956940	+	0.290285i	−0.427957	+	0.129819i
$5$	−0.956940	+	0.290285i	−0.427957	+	0.129819i
$6$	−1.68630	−	3.62592i	−0.688429	−	1.48028i
$7$	1.60460	+	0.319174i	0.606481	+	0.120637i	0.488772	−	0.872412i	$-0.337445\pi$
$7$	1.60460	+	0.319174i	0.606481	+	0.120637i	0.117709	+	0.993048i	$0.462445\pi$
$8$	−2.75649	+	0.633850i	−0.974566	+	0.224100i
$9$	−0.974564	−	4.89947i	−0.324855	−	1.63316i
$10$	−0.216558	+	1.39753i	−0.0684817	+	0.441939i
$11$	−0.980004	−	0.0965219i	−0.295482	−	0.0291025i	−0.0508101	−	0.998708i	$-0.516180\pi$
$11$	−0.980004	−	0.0965219i	−0.295482	−	0.0291025i	−0.244672	+	0.969606i	$0.578680\pi$
$12$	−5.65477	−	0.0732053i	−1.63239	−	0.0211326i
$13$	1.29174	−	4.25831i	0.358265	−	1.18104i	−0.573874	−	0.818943i	$-0.694560\pi$
$13$	1.29174	−	4.25831i	0.358265	−	1.18104i	0.932140	−	0.362099i	$-0.117940\pi$
$14$	1.39027	−	1.84942i	0.371565	−	0.494279i
$15$	−1.08208	+	2.61238i	−0.279393	+	0.674514i
$16$	−0.881659	+	3.90163i	−0.220415	+	0.975406i
$17$	0.223479	+	0.539526i	0.0542016	+	0.130854i	0.948661	−	0.316295i	$-0.102439\pi$
$17$	0.223479	+	0.539526i	0.0542016	+	0.130854i	−0.894459	+	0.447150i	$0.852439\pi$
$18$	−6.84166	−	1.76089i	−1.61260	−	0.415045i
$19$	−5.83147	+	3.11698i	−1.33783	+	0.715085i	−0.976125	−	0.217207i	$-0.930305\pi$
$19$	−5.83147	+	3.11698i	−1.33783	+	0.715085i	−0.361705	+	0.932293i	$0.617805\pi$
$20$	1.64842	+	1.13257i	0.368597	+	0.253251i
$21$	3.57601	−	2.93476i	0.780350	−	0.640416i
$22$	−0.723677	+	1.18985i	−0.154288	+	0.253677i
$23$	4.46593	−	6.68374i	0.931212	−	1.39366i	0.0119851	−	0.999928i	$-0.496185\pi$
$23$	4.46593	−	6.68374i	0.931212	−	1.39366i	0.919227	−	0.393729i	$-0.128815\pi$
$24$	−3.55920	+	7.16210i	−0.726519	+	1.46196i
$25$	0.831470	−	0.555570i	0.166294	−	0.111114i
$26$	−4.63546	−	4.25630i	−0.909088	−	0.834730i
$27$	−4.97614	−	2.65980i	−0.957659	−	0.511879i
$28$	−1.50496	−	2.90543i	−0.284410	−	0.549074i
$29$	1.00560	+	10.2100i	0.186735	+	1.89595i	0.396250	+	0.918142i	$0.370311\pi$
$29$	1.00560	+	10.2100i	0.186735	+	1.89595i	−0.209516	+	0.977805i	$0.567189\pi$
$30$	2.66624	+	2.98028i	0.486786	+	0.544122i
$31$	−1.44186	−	1.44186i	−0.258967	−	0.258967i	0.565667	−	0.824634i	$-0.308619\pi$
$31$	−1.44186	−	1.44186i	−0.258967	−	0.258967i	−0.824634	+	0.565667i	$0.808619\pi$
$32$	4.43221	+	3.51504i	0.783512	+	0.621377i
$33$	−1.96893	+	1.96893i	−0.342747	+	0.342747i
$34$	0.824596	+	0.0458617i	0.141417	+	0.00786522i
$35$	−1.62815	+	0.160359i	−0.275208	+	0.0271057i
$36$	−6.43760	+	7.64038i	−1.07293	+	1.27340i
$37$	4.43553	−	8.29830i	0.729197	−	1.36423i	−0.194421	−	0.980918i	$-0.562283\pi$
$37$	4.43553	−	8.29830i	0.729197	−	1.36423i	0.923618	−	0.383314i	$-0.125217\pi$
$38$	0.398376	+	9.34262i	0.0646251	+	1.51557i
$39$	−6.99057	−	10.4621i	−1.11939	−	1.67528i
$40$	2.45380	−	1.40672i	0.387980	−	0.222423i
$41$	5.53878	+	3.70090i	0.865013	+	0.577983i	0.906998	−	0.421135i	$-0.138368\pi$
$41$	5.53878	+	3.70090i	0.865013	+	0.577983i	−0.0419851	+	0.999118i	$0.513368\pi$
$42$	−1.54853	−	6.35636i	−0.238944	−	0.980808i
$43$	1.92505	+	2.34568i	0.293568	+	0.357714i	0.898818	−	0.438322i	$-0.144427\pi$
$43$	1.92505	+	2.34568i	0.293568	+	0.357714i	−0.605250	+	0.796035i	$0.706927\pi$
$44$	1.07290	+	1.65160i	0.161746	+	0.248988i
$45$	2.35484	+	4.40560i	0.351039	+	0.656747i
$46$	−5.78114	−	9.78838i	−0.852383	−	1.44322i
$47$	6.80879	−	2.82029i	0.993165	−	0.411382i	0.173879	−	0.984767i	$-0.444370\pi$
$47$	6.80879	−	2.82029i	0.993165	−	0.411382i	0.819286	+	0.573385i	$0.194370\pi$
$48$	6.94656	+	8.92595i	1.00265	+	1.28835i
$49$	−3.99430	−	1.65449i	−0.570614	−	0.236356i
$50$	−0.198449	−	1.40022i	−0.0280650	−	0.198021i
$51$	1.58017	+	0.479339i	0.221268	+	0.0671209i
$52$	−8.26578	+	3.29910i	−1.14626	+	0.457503i
$53$	−0.396480	+	4.02553i	−0.0544607	+	0.552948i	0.928779	+	0.370633i	$0.120859\pi$
$53$	−0.396480	+	4.02553i	−0.0544607	+	0.552948i	−0.983240	+	0.182315i	$0.941641\pi$
$54$	−6.43986	+	4.71182i	−0.876354	+	0.641198i
$55$	0.965824	−	0.192114i	0.130232	−	0.0259047i
$56$	−4.62536	+	0.137274i	−0.618090	+	0.0183440i
$57$	−3.64758	+	18.3376i	−0.483134	+	2.42888i
$58$	13.6289	+	4.97624i	1.78956	+	0.653413i
$59$	1.35638	+	4.47138i	0.176585	+	0.582124i	0.999894	+	0.0145306i	$0.00462540\pi$
$59$	1.35638	+	4.47138i	0.176585	+	0.582124i	−0.823309	+	0.567593i	$0.807875\pi$
$60$	5.43253	−	1.57144i	0.701337	−	0.202872i
$61$	10.7479	+	8.82056i	1.37612	+	1.12936i	0.977188	+	0.212378i	$0.0681209\pi$
$61$	10.7479	+	8.82056i	1.37612	+	1.12936i	0.398937	+	0.916978i	$0.369379\pi$
$62$	−2.72139	+	0.953905i	−0.345617	+	0.121146i
$63$		−	8.17272i		−	1.02967i
$64$	7.19647	−	3.49440i	0.899558	−	0.436800i
$65$			4.44992i			0.551945i
$66$	1.30260	+	3.71618i	0.160339	+	0.457430i
$67$	−2.54890	−	2.09183i	−0.311398	−	0.255558i	0.465693	−	0.884947i	$-0.345805\pi$
$67$	−2.54890	−	2.09183i	−0.311398	−	0.255558i	−0.777090	+	0.629389i	$0.783305\pi$
$68$	0.563859	−	1.02283i	0.0683779	−	0.124037i
$69$	−6.59810	−	21.7510i	−0.794318	−	2.61852i
$70$	−0.793546	+	2.17336i	−0.0948468	+	0.259766i
$71$	2.34733	−	11.8008i	0.278577	−	1.40050i	−0.547436	−	0.836848i	$-0.684396\pi$
$71$	2.34733	−	11.8008i	0.278577	−	1.40050i	0.826012	−	0.563652i	$-0.190604\pi$
$72$	5.79190	+	12.8876i	0.682582	+	1.51882i
$73$	−0.560737	+	0.111538i	−0.0656294	+	0.0130545i	−0.227796	−	0.973709i	$-0.573152\pi$
$73$	−0.560737	+	0.111538i	−0.0656294	+	0.0130545i	0.162166	+	0.986763i	$0.448152\pi$
$74$	−7.85752	−	10.7392i	−0.913418	−	1.24841i
$75$	0.277156	−	2.81401i	0.0320032	−	0.324934i
$76$	12.1513	+	5.21851i	1.39385	+	0.598605i
$77$	−1.54170	−	0.467671i	−0.175693	−	0.0532960i
$78$	−17.6186	+	2.49703i	−1.99491	+	0.282733i
$79$	−1.16475	−	0.482455i	−0.131045	−	0.0542804i	0.316198	−	0.948693i	$-0.397594\pi$
$79$	−1.16475	−	0.482455i	−0.131045	−	0.0542804i	−0.447242	+	0.894413i	$0.647594\pi$
$80$	−0.288887	−	3.98955i	−0.0322986	−	0.446046i
$81$	−0.894487	+	0.370508i	−0.0993874	+	0.0411676i
$82$	8.11158	−	4.79081i	0.895774	−	0.529056i
$83$	5.34180	+	9.99380i	0.586339	+	1.09696i	0.983787	+	0.179338i	$0.0573956\pi$
$83$	5.34180	+	9.99380i	0.586339	+	1.09696i	−0.397449	+	0.917624i	$0.630104\pi$
$84$	−9.05027	−	1.92232i	−0.987465	−	0.209743i
$85$	−0.370472	−	0.451422i	−0.0401834	−	0.0489636i
$86$	4.16946	−	1.01576i	0.449604	−	0.109532i
$87$	24.1207	+	16.1169i	2.58601	+	1.72792i
$88$	2.76255	−	0.355114i	0.294489	−	0.0378553i
$89$	−1.08856	−	1.62914i	−0.115387	−	0.172689i	0.769281	−	0.638911i	$-0.220615\pi$
$89$	−1.08856	−	1.62914i	−0.115387	−	0.172689i	−0.884668	+	0.466222i	$0.845615\pi$
$90$	7.05822	−	0.300967i	0.744002	−	0.0317247i
$91$	3.43187	−	6.42058i	0.359758	−	0.673059i
$92$	−16.0186	+	1.36858i	−1.67005	+	0.142684i
$93$	−5.73806	+	0.565149i	−0.595009	+	0.0586032i
$94$	0.578772	−	10.4064i	0.0596958	−	1.07333i
$95$	4.67555	−	4.67555i	0.479702	−	0.479702i
$96$	15.6337	−	3.38249i	1.59561	−	0.345224i
$97$	−10.6153	−	10.6153i	−1.07782	−	1.07782i	−0.996705	−	0.0811118i	$-0.974153\pi$
$97$	−10.6153	−	10.6153i	−1.07782	−	1.07782i	−0.0811118	−	0.996705i	$-0.525847\pi$
$98$	−4.55681	+	4.07664i	−0.460307	+	0.411803i
$99$	0.482171	+	4.89556i	0.0484600	+	0.492022i
$100$	−1.90621	−	0.605295i	−0.190621	−	0.0605295i
$101$	−0.932446	−	0.498403i	−0.0927818	−	0.0495929i	0.424353	−	0.905497i	$-0.360502\pi$
$101$	−0.932446	−	0.498403i	−0.0927818	−	0.0495929i	−0.517135	+	0.855904i	$0.673002\pi$
$102$	1.57943	−	1.72012i	0.156386	−	0.170317i
$103$	3.49854	−	2.33765i	0.344721	−	0.230335i	−0.371142	−	0.928576i	$-0.621034\pi$
$103$	3.49854	−	2.33765i	0.344721	−	0.230335i	0.715863	+	0.698241i	$0.246034\pi$
$104$	−0.861548	+	12.5568i	−0.0844817	+	1.23129i
$105$	−2.57011	+	3.84645i	−0.250818	+	0.375375i
$106$	4.88750	+	2.97262i	0.474716	+	0.288726i
$107$	−5.85723	+	4.80690i	−0.566240	+	0.464701i	−0.873432	−	0.486947i	$-0.838111\pi$
$107$	−5.85723	+	4.80690i	−0.566240	+	0.464701i	0.307192	+	0.951648i	$0.400611\pi$
$108$	2.05809	+	11.0955i	0.198040	+	1.06767i
$109$	−9.69450	+	5.18182i	−0.928565	+	0.496328i	−0.865069	−	0.501654i	$-0.832725\pi$
$109$	−9.69450	+	5.18182i	−0.928565	+	0.496328i	−0.0634965	+	0.997982i	$0.520225\pi$
$110$	0.347121	−	1.34869i	0.0330967	−	0.128592i
$111$	−10.1817	−	24.5808i	−0.966405	−	2.33311i
$112$	−2.66001	+	5.97913i	−0.251347	+	0.564975i
$113$	1.09565	−	2.64513i	0.103070	−	0.248833i	−0.863929	−	0.503614i	$-0.832003\pi$
$113$	1.09565	−	2.64513i	0.103070	−	0.248833i	0.966999	+	0.254781i	$0.0820033\pi$
$114$	21.1355	+	15.8883i	1.97953	+	1.48807i
$115$	−2.33344	+	7.69234i	−0.217595	+	0.717314i
$116$	14.6956	−	14.3199i	1.36445	−	1.32957i
$117$	−22.1223	−	2.17886i	−2.04521	−	0.201436i
$118$	6.53009	+	1.01189i	0.601143	+	0.0931516i
$119$	0.186391	+	0.937051i	0.0170864	+	0.0858993i
$120$	1.32689	−	7.88689i	0.121128	−	0.719971i
$121$	−9.83755	−	1.95681i	−0.894322	−	0.177892i
$122$	17.8293	−	8.29184i	1.61419	−	0.750708i
$123$	18.0250	−	5.46781i	1.62526	−	0.493016i
$124$	−0.452238	+	4.05306i	−0.0406122	+	0.363975i
$125$	−0.634393	+	0.773010i	−0.0567419	+	0.0691402i
$126$	−10.4161	−	5.00919i	−0.927939	−	0.446255i
$127$	−12.8367			−1.13907			−0.569537	−	0.821965i	$-0.692878\pi$
$127$	−12.8367			−1.13907			−0.569537	+	0.821965i	$0.692878\pi$
$128$	−0.0427629	−	11.3136i	−0.00377974	−	0.999993i
$129$	8.58036			0.755459
$130$	5.67139	+	2.72743i	0.497414	+	0.239211i
$131$	4.31837	−	5.26195i	0.377298	−	0.459738i	−0.549393	−	0.835564i	$-0.685141\pi$
$131$	4.31837	−	5.26195i	0.377298	−	0.459738i	0.926690	+	0.375826i	$0.122641\pi$
$132$	5.53463	+	0.617551i	0.481728	+	0.0537509i
$133$	−10.3520	+	3.14025i	−0.897634	+	0.272294i
$134$	−4.22828	+	1.96644i	−0.365268	+	0.169875i
$135$	5.53397	+	1.10077i	0.476288	+	0.0947396i
$136$	−0.957996	−	1.34555i	−0.0821475	−	0.115380i
$137$	2.11600	+	10.6378i	0.180782	+	0.908852i	0.959550	+	0.281540i	$0.0908452\pi$
$137$	2.11600	+	10.6378i	0.180782	+	0.908852i	−0.778768	+	0.627313i	$0.784155\pi$
$138$	−31.7656	−	4.92232i	−2.70407	−	0.419016i
$139$	−13.0333	−	1.28367i	−1.10547	−	0.108880i	−0.471228	−	0.882012i	$-0.656189\pi$
$139$	−13.0333	−	1.28367i	−1.10547	−	0.108880i	−0.634245	+	0.773132i	$0.718689\pi$
$140$	2.28356	+	2.34346i	0.192996	+	0.198058i
$141$	6.04924	−	19.9417i	0.509438	−	1.67939i
$142$	−13.6014	−	10.2246i	−1.14140	−	0.858027i
$143$	−1.67693	+	4.04848i	−0.140232	+	0.338551i
$144$	19.9751	+	0.517273i	1.66459	+	0.0431061i
$145$	−3.92610	−	9.47844i	−0.326045	−	0.787142i
$146$	−0.201531	+	0.783019i	−0.0166788	+	0.0648032i
$147$	−10.7814	+	5.76279i	−0.889237	+	0.475307i
$148$	−18.5031	+	3.43212i	−1.52094	+	0.282118i
$149$	5.34659	−	4.38784i	0.438010	−	0.359466i	−0.389395	−	0.921071i	$-0.627316\pi$
$149$	5.34659	−	4.38784i	0.438010	−	0.359466i	0.827405	+	0.561605i	$0.189816\pi$
$150$	−3.41656	−	2.07798i	−0.278961	−	0.169667i
$151$	4.62511	−	6.92197i	0.376386	−	0.563302i	−0.594120	−	0.804376i	$-0.702500\pi$
$151$	4.62511	−	6.92197i	0.376386	−	0.563302i	0.970507	+	0.241074i	$0.0774997\pi$
$152$	14.0987	−	12.2882i	1.14355	−	0.996706i
$153$	2.42559	−	1.62073i	0.196098	−	0.131028i
$154$	−1.54098	+	1.67825i	−0.124176	+	0.135237i
$155$	1.79833	+	0.961227i	0.144445	+	0.0772076i
$156$	−7.61625	+	23.9852i	−0.609788	+	1.92035i
$157$	1.63551	+	16.6056i	0.130528	+	1.32527i	0.807764	+	0.589506i	$0.200678\pi$
$157$	1.63551	+	16.6056i	0.130528	+	1.32527i	−0.677236	+	0.735766i	$0.736822\pi$
$158$	−1.32878	+	1.18876i	−0.105712	+	0.0945728i
$159$	8.08771	+	8.08771i	0.641397	+	0.641397i
$160$	−5.26172	−	2.07708i	−0.415976	−	0.164207i
$161$	9.29930	−	9.29930i	0.732888	−	0.732888i
$162$	−0.0760346	+	1.36711i	−0.00597385	+	0.107410i
$163$	13.0594	−	1.28623i	1.02289	−	0.100746i	0.427361	−	0.904081i	$-0.359443\pi$
$163$	13.0594	−	1.28623i	1.02289	−	0.100746i	0.595527	+	0.803336i	$0.296943\pi$
$164$	−1.13413	−	13.2745i	−0.0885608	−	1.03657i
$165$	1.31260	−	2.45570i	0.102186	−	0.191176i
$166$	16.0111	−	0.682725i	1.24270	−	0.0529897i
$167$	−3.20849	−	4.80184i	−0.248280	−	0.371578i	0.686307	−	0.727312i	$-0.259231\pi$
$167$	−3.20849	−	4.80184i	−0.248280	−	0.371578i	−0.934587	+	0.355735i	$0.884231\pi$
$168$	−7.99704	+	10.3563i	−0.616985	+	0.799005i
$169$	−5.65548	−	3.77887i	−0.435037	−	0.290682i
$170$	−0.802403	+	0.195481i	−0.0615415	+	0.0149927i
$171$	20.9547	+	25.5334i	1.60245	+	1.95259i
$172$	1.26095	−	5.93652i	0.0961463	−	0.452655i
$173$	0.792896	+	1.48340i	0.0602828	+	0.112781i	0.910258	−	0.414042i	$-0.135883\pi$
$173$	0.792896	+	1.48340i	0.0602828	+	0.112781i	−0.849975	+	0.526823i	$0.823383\pi$
$174$	35.3249	−	20.8633i	2.67797	−	1.58164i
$175$	1.51150	−	0.626083i	0.114258	−	0.0473274i
$176$	1.24062	−	3.73851i	0.0935154	−	0.281801i
$177$	12.2066	+	5.05612i	0.917502	+	0.380042i
$178$	−2.74353	+	0.388833i	−0.205636	+	0.0291442i
$179$	8.18182	+	2.48193i	0.611538	+	0.185508i	0.580836	−	0.814021i	$-0.302726\pi$
$179$	8.18182	+	2.48193i	0.611538	+	0.185508i	0.0307018	+	0.999529i	$0.490226\pi$
$180$	3.94252	−	9.18013i	0.293858	−	0.684246i
$181$	−1.44994	+	14.7215i	−0.107773	+	1.09424i	0.777409	+	0.628995i	$0.216533\pi$
$181$	−1.44994	+	14.7215i	−0.107773	+	1.09424i	−0.885183	+	0.465244i	$0.845967\pi$
$182$	−6.07954	−	8.30917i	−0.450645	−	0.615917i
$183$	38.5596	−	7.66999i	2.85041	−	0.566982i
$184$	−8.07381	+	21.2544i	−0.595209	+	1.56690i
$185$	−1.83567	+	9.22855i	−0.134961	+	0.678496i
$186$	−2.79667	+	7.65950i	−0.205062	+	0.561622i
$187$	−0.166934	−	0.550308i	−0.0122074	−	0.0402425i
$188$	−12.9081	−	7.11587i	−0.941421	−	0.518978i
$189$	−7.13576	−	5.85617i	−0.519050	−	0.425973i
$190$	−3.09324	−	8.82469i	−0.224407	−	0.640210i
$191$			13.9867i			1.01204i	0.862521	+	0.506021i	$0.168884\pi$
$191$			13.9867i			1.01204i	−0.862521	+	0.506021i	$0.831116\pi$
$192$	5.27120	−	21.9983i	0.380416	−	1.58759i
$193$			14.3715i			1.03448i	0.855840	+	0.517240i	$0.173041\pi$
$193$			14.3715i			1.03448i	−0.855840	+	0.517240i	$0.826959\pi$
$194$	−20.0354	+	7.02282i	−1.43845	+	0.504209i
$195$	9.72656	+	7.98238i	0.696533	+	0.571630i
$196$	2.40271	+	8.30626i	0.171622	+	0.593304i
$197$	3.17896	+	10.4796i	0.226491	+	0.746641i	0.994362	+	0.106037i	$0.0338162\pi$
$197$	3.17896	+	10.4796i	0.226491	+	0.746641i	−0.767871	+	0.640604i	$0.778684\pi$
$198$	6.53489	+	2.38605i	0.464415	+	0.169569i
$199$	1.34703	−	6.77199i	0.0954886	−	0.480054i	−0.903217	−	0.429185i	$-0.858801\pi$
$199$	1.34703	−	6.77199i	0.0954886	−	0.480054i	0.998705	−	0.0508690i	$-0.0161991\pi$
$200$	−1.93979	+	2.05845i	−0.137164	+	0.145554i
$201$	−9.14456	+	1.81897i	−0.645008	+	0.128300i
$202$	−1.20672	+	0.882917i	−0.0849047	+	0.0621218i
$203$	−1.64519	+	16.7039i	−0.115470	+	1.17238i
$204$	−1.22423	−	3.06726i	−0.0857130	−	0.214751i
$205$	−6.37460	−	1.93371i	−0.445221	−	0.135056i
$206$	−0.835007	−	5.89165i	−0.0581777	−	0.410490i
$207$	−37.0991	−	15.3670i	−2.57857	−	1.06808i
$208$	15.4754	+	8.79427i	1.07303	+	0.609773i
$209$	6.01572	−	2.49179i	0.416116	−	0.172361i
$210$	3.32701	+	5.63315i	0.229585	+	0.388724i
$211$	8.19156	+	15.3253i	0.563930	+	1.05504i	0.988724	+	0.149749i	$0.0478465\pi$
$211$	8.19156	+	15.3253i	0.563930	+	1.05504i	−0.424794	+	0.905290i	$0.639653\pi$
$212$	6.78421	−	4.40712i	0.465942	−	0.302682i
$213$	−21.5833	−	26.2994i	−1.47887	−	1.80200i
$214$	2.53638	+	10.4112i	0.173383	+	0.711697i
$215$	−2.52308	−	1.68587i	−0.172072	−	0.114975i
$216$	15.4026	+	4.17759i	1.04801	+	0.284249i
$217$	−1.85341	−	2.77382i	−0.125817	−	0.188299i
$218$	0.662278	+	15.5316i	0.0448551	+	1.05193i
$219$	−0.762068	+	1.42573i	−0.0514958	+	0.0963418i
$220$	−1.50614	−	1.26903i	−0.101544	−	0.0855583i
$221$	2.58615	−	0.254713i	0.173963	−	0.0171339i
$222$	−37.5686	−	2.08946i	−2.52144	−	0.140235i
$223$	10.3472	−	10.3472i	0.692902	−	0.692902i	−0.269967	−	0.962869i	$-0.587013\pi$
$223$	10.3472	−	10.3472i	0.692902	−	0.692902i	0.962869	+	0.269967i	$0.0870129\pi$
$224$	5.99001	+	7.05487i	0.400224	+	0.471373i
$225$	−3.53232	−	3.53232i	−0.235488	−	0.235488i
$226$	−2.69967	−	3.01765i	−0.179579	−	0.200731i
$227$	−1.81173	−	18.3948i	−0.120249	−	1.22091i	−0.846088	−	0.533044i	$-0.821048\pi$
$227$	−1.81173	−	18.3948i	−0.120249	−	1.22091i	0.725839	−	0.687865i	$-0.241452\pi$
$228$	33.2038	−	17.1989i	2.19898	−	1.13903i
$229$	2.37946	+	1.27185i	0.157239	+	0.0840461i	0.548140	−	0.836387i	$-0.315336\pi$
$229$	2.37946	+	1.27185i	0.157239	+	0.0840461i	−0.390900	+	0.920433i	$0.627836\pi$
$230$	8.37363	+	7.68872i	0.552141	+	0.506979i
$231$	−3.78777	+	2.53091i	−0.249217	+	0.166522i
$232$	−9.24352	−	27.5063i	−0.606867	−	1.80588i
$233$	−7.15909	+	10.7143i	−0.469007	+	0.701919i	−0.988274	−	0.152693i	$-0.951205\pi$
$233$	−7.15909	+	10.7143i	−0.469007	+	0.701919i	0.519266	+	0.854612i	$0.326205\pi$
$234$	−16.3361	+	26.8593i	−1.06792	+	1.75585i
$235$	−5.69692	+	4.67534i	−0.371626	+	0.304986i
$236$	5.29204	−	7.70236i	0.344482	−	0.501381i
$237$	−3.14390	+	1.68045i	−0.204218	+	0.109157i
$238$	1.30851	+	0.336779i	0.0848179	+	0.0218302i
$239$	5.71084	+	13.7872i	0.369404	+	0.891820i	0.993848	+	0.110750i	$0.0353254\pi$
$239$	5.71084	+	13.7872i	0.369404	+	0.891820i	−0.624445	+	0.781069i	$0.714675\pi$
$240$	−9.23851	−	6.52512i	−0.596343	−	0.421195i
$241$	−6.06633	+	14.6454i	−0.390767	+	0.943395i	0.599006	+	0.800744i	$0.295562\pi$
$241$	−6.06633	+	14.6454i	−0.390767	+	0.943395i	−0.989773	+	0.142650i	$0.954438\pi$
$242$	−8.52353	+	11.3385i	−0.547913	+	0.728868i
$243$	4.11899	−	13.5785i	0.264234	−	0.871061i
$244$	0.359964	−	27.8055i	0.0230443	−	1.78007i
$245$	4.30258	+	0.423767i	0.274882	+	0.0270735i
$246$	4.07910	−	26.3240i	0.260074	−	1.67836i
$247$	5.74032	+	28.8585i	0.365248	+	1.83622i
$248$	4.88841	+	3.06056i	0.310414	+	0.194346i
$249$	31.4265	+	6.25113i	1.99158	+	0.396149i
$250$	0.596367	+	1.28232i	0.0377176	+	0.0811011i
$251$	−6.74982	+	2.04754i	−0.426045	+	0.129239i	−0.496023	−	0.868309i	$-0.665207\pi$
$251$	−6.74982	+	2.04754i	−0.426045	+	0.129239i	0.0699785	+	0.997549i	$0.477707\pi$
$252$	−12.7684	+	10.2050i	−0.804332	+	0.642856i
$253$	−5.02176	+	6.11903i	−0.315715	+	0.384700i
$254$	−7.86783	+	16.3603i	−0.493672	+	1.02654i
$255$	−1.65127			−0.103407
$256$	−14.4454	−	6.87980i	−0.902835	−	0.429988i
$257$	12.2647			0.765051			0.382525	−	0.923945i	$-0.375054\pi$
$257$	12.2647			0.765051			0.382525	+	0.923945i	$0.375054\pi$
$258$	5.25904	−	10.9356i	0.327414	−	0.680822i
$259$	9.76585	−	11.8997i	0.606820	−	0.739413i
$260$	6.95218	−	5.55647i	0.431156	−	0.344598i
$261$	49.0435	−	14.8772i	3.03572	−	0.920874i
$262$	−4.05952	−	8.72887i	−0.250798	−	0.539271i
$263$	28.7667	+	5.72205i	1.77383	+	0.352837i	0.970202	−	0.242296i	$-0.0779004\pi$
$263$	28.7667	+	5.72205i	1.77383	+	0.352837i	0.803628	+	0.595132i	$0.202900\pi$
$264$	4.17933	−	6.67535i	0.257220	−	0.410839i
$265$	−0.789141	−	3.96728i	−0.0484765	−	0.243708i
$266$	−2.34269	+	15.1183i	−0.143640	+	0.926962i
$267$	−5.51363	−	0.543046i	−0.337429	−	0.0332339i
$268$	−0.0853668	+	6.59419i	−0.00521461	+	0.402804i
$269$	−7.68081	+	25.3202i	−0.468307	+	1.54380i	0.331446	+	0.943474i	$0.392463\pi$
$269$	−7.68081	+	25.3202i	−0.468307	+	1.54380i	−0.799754	+	0.600328i	$0.795037\pi$
$270$	4.79479	−	6.37833i	0.291802	−	0.388173i
$271$	4.56237	−	11.0145i	0.277144	−	0.669085i	−0.722610	−	0.691256i	$-0.757058\pi$
$271$	4.56237	−	11.0145i	0.277144	−	0.669085i	0.999754	+	0.0221707i	$0.00705773\pi$
$272$	−2.30206	+	0.396253i	−0.139583	+	0.0240264i
$273$	−7.87781	−	19.0187i	−0.476787	−	1.15106i
$274$	14.8548	+	3.82328i	0.897411	+	0.230973i
$275$	−0.868468	+	0.464206i	−0.0523706	+	0.0279927i
$276$	−25.7431	+	37.4681i	−1.54955	+	2.25532i
$277$	−5.93398	+	4.86989i	−0.356538	+	0.292603i	−0.795562	−	0.605872i	$-0.792824\pi$
$277$	−5.93398	+	4.86989i	−0.356538	+	0.292603i	0.439024	+	0.898475i	$0.355324\pi$
$278$	−9.62437	+	15.8241i	−0.577231	+	0.949067i
$279$	−5.65918	+	8.46956i	−0.338806	+	0.507059i
$280$	4.38635	−	1.47404i	0.262134	−	0.0880904i
$281$	−21.1381	+	14.1241i	−1.26100	+	0.842570i	−0.992682	−	0.120761i	$-0.961467\pi$
$281$	−21.1381	+	14.1241i	−1.26100	+	0.842570i	−0.268314	+	0.963331i	$0.586467\pi$
$282$	−21.7078	−	19.9323i	−1.29268	−	1.18695i
$283$	−14.0567	−	7.51348i	−0.835586	−	0.446630i	−0.00264782	−	0.999996i	$-0.500843\pi$
$283$	−14.0567	−	7.51348i	−0.835586	−	0.446630i	−0.832938	+	0.553367i	$0.813343\pi$
$284$	−21.3676	+	11.0680i	−1.26794	+	0.656767i
$285$	−1.83262	−	18.6069i	−0.108555	−	1.10218i
$286$	4.13194	+	4.61862i	0.244327	+	0.273105i
$287$	7.70629	+	7.70629i	0.454888	+	0.454888i
$288$	12.9023	−	25.1411i	0.760277	−	1.48145i
$289$	11.7797	−	11.7797i	0.692922	−	0.692922i
$290$	−14.4866	−	0.805702i	−0.850682	−	0.0473125i
$291$	−42.2446	+	4.16073i	−2.47642	+	0.243906i
$292$	0.874432	+	0.736775i	0.0511722	+	0.0431165i
$293$	−9.62499	+	18.0071i	−0.562298	+	1.05199i	0.426747	+	0.904371i	$0.359660\pi$
$293$	−9.62499	+	18.0071i	−0.562298	+	1.05199i	−0.989045	+	0.147615i	$0.952840\pi$
$294$	0.736531	+	17.2730i	0.0429554	+	1.00738i
$295$	−2.59595	−	3.88511i	−0.151142	−	0.226200i
$296$	−6.96662	+	25.6856i	−0.404927	+	1.49295i
$297$	4.61991	+	3.08692i	0.268074	+	0.179121i
$298$	−2.31526	−	9.50358i	−0.134119	−	0.550527i
$299$	−22.6926	−	27.6510i	−1.31235	−	1.59910i
$300$	−4.74244	+	3.08076i	−0.273805	+	0.177867i
$301$	2.34025	+	4.37831i	0.134890	+	0.252361i
$302$	−5.98720	−	10.1373i	−0.344525	−	0.583334i
$303$	−2.76204	+	1.14408i	−0.158675	+	0.0657255i
$304$	−7.01994	−	25.5003i	−0.402621	−	1.46254i
$305$	−12.8455	−	5.32080i	−0.735534	−	0.304668i
$306$	−0.578924	−	4.08478i	−0.0330949	−	0.233511i
$307$	−23.4172	−	7.10352i	−1.33649	−	0.405420i	−0.460461	−	0.887680i	$-0.652316\pi$
$307$	−23.4172	−	7.10352i	−1.33649	−	0.405420i	−0.876028	+	0.482260i	$0.839816\pi$
$308$	1.19443	+	2.99259i	0.0680588	+	0.170519i
$309$	1.16618	−	11.8404i	0.0663414	−	0.673575i
$310$	2.32730	−	1.70281i	0.132182	−	0.0967130i
$311$	2.13133	−	0.423949i	0.120857	−	0.0240399i	−0.134291	−	0.990942i	$-0.542876\pi$
$311$	2.13133	−	0.423949i	0.120857	−	0.0240399i	0.255148	+	0.966902i	$0.417876\pi$
$312$	25.9009	+	24.4078i	1.46635	+	1.38182i
$313$	−5.63930	+	28.3507i	−0.318752	+	1.60247i	0.406273	+	0.913752i	$0.366828\pi$
$313$	−5.63930	+	28.3507i	−0.318752	+	1.60247i	−0.725025	+	0.688722i	$0.758172\pi$
$314$	22.1662	+	8.09340i	1.25091	+	0.456737i
$315$	2.37242	+	7.82081i	0.133671	+	0.440653i
$316$	0.700638	+	2.42213i	0.0394140	+	0.136256i
$317$	−26.6673	−	21.8853i	−1.49778	−	1.22920i	−0.906126	−	0.423009i	$-0.860974\pi$
$317$	−26.6673	−	21.8853i	−1.49778	−	1.22920i	−0.591657	−	0.806190i	$-0.701526\pi$
$318$	15.2648	−	5.35064i	0.856008	−	0.300049i
$319$		−	10.1029i		−	0.565653i
$320$	−5.87222	+	5.43296i	−0.328267	+	0.303712i
$321$			21.4254i			1.19585i
$322$	−6.15221	−	17.5516i	−0.342849	−	0.978112i
$323$	−2.98491	−	2.44965i	−0.166085	−	0.136302i
$324$	1.69577	+	0.934828i	0.0942093	+	0.0519349i
$325$	−1.29174	−	4.25831i	−0.0716530	−	0.236208i
$326$	6.36499	−	17.4324i	0.352524	−	0.965492i
$327$	−6.06391	+	30.4854i	−0.335335	+	1.68584i
$328$	−17.6134	−	6.69072i	−0.972538	−	0.369433i
$329$	11.8255	−	2.35225i	0.651963	−	0.129683i
$330$	−2.32526	−	3.17804i	−0.128001	−	0.174945i
$331$	2.65645	−	26.9714i	0.146011	−	1.48248i	−0.591040	−	0.806643i	$-0.701282\pi$
$331$	2.65645	−	26.9714i	0.146011	−	1.48248i	0.737051	−	0.675837i	$-0.236218\pi$
$332$	8.94334	−	20.8245i	0.490830	−	1.14289i
$333$	−44.9800	−	13.6445i	−2.46489	−	0.747715i
$334$	−8.08645	+	1.14607i	−0.442471	+	0.0627102i
$335$	3.04637	+	1.26185i	0.166441	+	0.0689422i
$336$	8.29750	+	16.5397i	0.452666	+	0.902315i
$337$	−15.7899	+	6.54038i	−0.860129	+	0.356277i	−0.768758	−	0.639540i	$-0.779125\pi$
$337$	−15.7899	+	6.54038i	−0.860129	+	0.356277i	−0.0913710	+	0.995817i	$0.529125\pi$
$338$	−8.28249	+	4.89174i	−0.450508	+	0.266076i
$339$	−3.81628	−	7.13976i	−0.207272	−	0.387779i
$340$	−0.242666	+	1.14247i	−0.0131604	+	0.0619591i
$341$	1.27386	+	1.55220i	0.0689835	+	0.0840566i
$342$	45.3856	−	11.0568i	2.45417	−	0.597884i
$343$	−15.4033	−	10.2922i	−0.831703	−	0.555726i
$344$	−6.79320	−	5.24566i	−0.366265	−	0.282827i
$345$	12.6280	+	18.8991i	0.679868	+	1.01749i
$346$	2.37657	−	0.101339i	0.127765	−	0.00544799i
$347$	10.2821	−	19.2364i	0.551971	−	1.03267i	−0.438987	−	0.898493i	$-0.644663\pi$
$347$	10.2821	−	19.2364i	0.551971	−	1.03267i	0.990958	−	0.134172i	$-0.0428374\pi$
$348$	−4.93899	−	57.8088i	−0.264758	−	3.09888i
$349$	−7.89758	+	0.777844i	−0.422748	+	0.0416370i	−0.307155	−	0.951660i	$-0.599377\pi$
$349$	−7.89758	+	0.777844i	−0.422748	+	0.0416370i	−0.115593	+	0.993297i	$0.536877\pi$
$350$	0.128483	−	2.31013i	0.00686770	−	0.123482i
$351$	−17.7542	+	17.7542i	−0.947647	+	0.947647i
$352$	−4.00431	−	3.87256i	−0.213430	−	0.206408i
$353$	9.64552	+	9.64552i	0.513379	+	0.513379i	0.915560	−	0.402181i	$-0.131748\pi$
$353$	9.64552	+	9.64552i	0.513379	+	0.513379i	−0.402181	+	0.915560i	$0.631748\pi$
$354$	13.9256	−	12.4582i	0.740137	−	0.662146i
$355$	1.17934	+	11.9741i	0.0625931	+	0.635518i
$356$	−1.18599	+	3.73493i	−0.0628572	+	0.197951i
$357$	2.38254	+	1.27349i	0.126097	+	0.0674005i
$358$	8.17797	−	8.90646i	0.432219	−	0.470721i
$359$	−15.3654	+	10.2668i	−0.810954	+	0.541862i	−0.890508	−	0.454968i	$-0.849651\pi$
$359$	−15.3654	+	10.2668i	−0.810954	+	0.541862i	0.0795534	+	0.996831i	$0.474651\pi$
$360$	−9.28358	−	10.6514i	−0.489288	−	0.561376i
$361$	13.7346	−	20.5553i	0.722873	−	1.08186i
$362$	17.8737	+	10.8710i	0.939423	+	0.571365i
$363$	−21.9240	+	17.9926i	−1.15071	+	0.944365i
$364$	−14.3162	+	2.65550i	−0.750374	+	0.139186i
$365$	0.504215	−	0.269508i	0.0263918	−	0.0141067i
$366$	13.8585	−	53.8451i	0.724394	−	2.81453i
$367$	7.81967	+	18.8783i	0.408183	+	0.985442i	0.985616	+	0.169003i	$0.0540548\pi$
$367$	7.81967	+	18.8783i	0.408183	+	0.985442i	−0.577432	+	0.816439i	$0.695945\pi$
$368$	22.1400	+	23.3172i	1.15413	+	1.21549i
$369$	12.7345	−	30.7438i	0.662933	−	1.60046i
$370$	10.6366	+	7.99588i	0.552971	+	0.415686i
$371$	−1.92103	+	6.33280i	−0.0997351	+	0.328783i
$372$	8.04787	+	8.25897i	0.417262	+	0.428208i
$373$	−34.4185	−	3.38992i	−1.78212	−	0.175524i	−0.847411	−	0.530937i	$-0.821840\pi$
$373$	−34.4185	−	3.38992i	−1.78212	−	0.175524i	−0.934709	+	0.355414i	$0.884340\pi$
$374$	−0.803681	−	0.124536i	−0.0415574	−	0.00643962i
$375$	0.551642	+	2.77329i	0.0284867	+	0.143212i
$376$	−16.9807	+	12.0899i	−0.875714	+	0.623487i
$377$	44.7763	+	8.90655i	2.30609	+	0.458711i
$378$	−11.8373	+	5.50514i	−0.608843	+	0.283154i
$379$	−21.9582	+	6.66093i	−1.12791	+	0.342149i	−0.798475	−	0.602028i	$-0.794360\pi$
$379$	−21.9582	+	6.66093i	−1.12791	+	0.342149i	−0.329439	+	0.944177i	$0.606860\pi$
$380$	−13.1429	−	1.46648i	−0.674217	−	0.0752287i
$381$	−23.0268	+	28.0583i	−1.17970	+	1.43747i
$382$	17.8259	+	8.57267i	0.912055	+	0.438616i
$383$	−12.5193			−0.639708			−0.319854	−	0.947467i	$-0.603634\pi$
$383$	−12.5193			−0.639708			−0.319854	+	0.947467i	$0.603634\pi$
$384$	−24.8058	−	20.2012i	−1.26587	−	1.03089i
$385$	1.61108			0.0821080
$386$	18.3163	+	8.80850i	0.932277	+	0.448341i
$387$	9.61651	−	11.7178i	0.488835	−	0.595647i
$388$	−3.32946	+	29.8393i	−0.169027	+	1.51486i
$389$	12.7010	−	3.85280i	0.643966	−	0.195345i	0.0486235	−	0.998817i	$-0.484517\pi$
$389$	12.7010	−	3.85280i	0.643966	−	0.195345i	0.595342	+	0.803472i	$0.297017\pi$
$390$	16.1351	−	7.50390i	0.817030	−	0.379975i
$391$	4.60410	+	0.915812i	0.232839	+	0.0463146i
$392$	12.0589	+	2.02880i	0.609068	+	0.102470i
$393$	−3.75507	−	18.8780i	−0.189418	−	0.952270i
$394$	15.3046	+	2.37157i	0.771036	+	0.119478i
$395$	1.25465	+	0.123572i	0.0631281	+	0.00621757i
$396$	7.04634	−	6.86623i	0.354092	−	0.345041i
$397$	1.40276	−	4.62428i	0.0704025	−	0.232086i	−0.914677	−	0.404185i	$-0.867555\pi$
$397$	1.40276	−	4.62428i	0.0704025	−	0.232086i	0.985080	+	0.172100i	$0.0550551\pi$
$398$	−7.80524	−	5.86745i	−0.391241	−	0.294109i
$399$	−11.7058	+	28.2603i	−0.586023	+	1.41479i
$400$	1.43455	+	3.73391i	0.0717277	+	0.186695i
$401$	−3.66195	−	8.84073i	−0.182869	−	0.441485i	0.805686	−	0.592342i	$-0.201797\pi$
$401$	−3.66195	−	8.84073i	−0.182869	−	0.441485i	−0.988556	+	0.150857i	$0.951797\pi$
$402$	−3.28659	+	12.7696i	−0.163920	+	0.636888i
$403$	−8.00242	+	4.27739i	−0.398629	+	0.213072i
$404$	0.385653	+	2.07911i	0.0191869	+	0.103440i
$405$	0.748417	−	0.614210i	0.0371892	−	0.0305204i
$406$	20.2806	+	12.3349i	1.00651	+	0.612169i
$407$	−5.14781	+	7.70424i	−0.255167	+	0.381885i
$408$	−4.65955	−	0.319702i	−0.230682	−	0.0158276i
$409$	5.99994	−	4.00903i	0.296678	−	0.198234i	−0.398318	−	0.917247i	$-0.630406\pi$
$409$	5.99994	−	4.00903i	0.296678	−	0.198234i	0.694996	+	0.719014i	$0.255406\pi$
$410$	−6.37160	+	6.93918i	−0.314671	+	0.342702i
$411$	27.0477	+	14.4573i	1.33417	+	0.713127i
$412$	−8.02065	−	2.54687i	−0.395149	−	0.125475i
$413$	0.749291	+	7.60768i	0.0368702	+	0.374350i
$414$	−42.3237	+	37.8639i	−2.08010	+	1.86091i
$415$	−8.01283	−	8.01283i	−0.393334	−	0.393334i
$416$	20.6934	−	14.3332i	1.01458	−	0.702743i
$417$	−26.1853	+	26.1853i	−1.28230	+	1.28230i
$418$	0.511358	−	9.19425i	0.0250113	−	0.449706i
$419$	−9.33278	+	0.919199i	−0.455936	+	0.0449058i	−0.323379	−	0.946270i	$-0.604819\pi$
$419$	−9.33278	+	0.919199i	−0.455936	+	0.0449058i	−0.132557	+	0.991175i	$0.542319\pi$
$420$	9.21858	−	0.787606i	0.449821	−	0.0384312i
$421$	16.1479	−	30.2106i	0.787001	−	1.47237i	−0.0921060	−	0.995749i	$-0.529360\pi$
$421$	16.1479	−	30.2106i	0.787001	−	1.47237i	0.879107	−	0.476625i	$-0.158140\pi$
$422$	24.5528	−	1.04695i	1.19521	−	0.0509646i
$423$	−20.4535	−	30.6109i	−0.994485	−	1.48835i
$424$	−1.45869	−	11.3476i	−0.0708402	−	0.551089i
$425$	0.485561	+	0.324441i	0.0235532	+	0.0157377i
$426$	−46.7471	+	11.3885i	−2.26491	+	0.551775i
$427$	14.4307	+	17.5839i	0.698351	+	0.850944i
$428$	14.8236	+	3.14861i	0.716527	+	0.152194i
$429$	5.84096	+	10.9277i	0.282004	+	0.527593i
$430$	−3.69506	+	2.18235i	−0.178192	+	0.105242i
$431$	−21.1118	+	8.74480i	−1.01692	+	0.421222i	−0.827975	−	0.560766i	$-0.810507\pi$
$431$	−21.1118	+	8.74480i	−1.01692	+	0.421222i	−0.188945	+	0.981988i	$0.560507\pi$
$432$	14.7648	−	17.0700i	0.710372	−	0.821281i
$433$	25.5343	+	10.5766i	1.22710	+	0.508281i	0.899660	−	0.436591i	$-0.143814\pi$
$433$	25.5343	+	10.5766i	1.22710	+	0.508281i	0.327439	+	0.944872i	$0.393814\pi$
$434$	−4.67120	+	0.662036i	−0.224225	+	0.0317787i
$435$	−27.7605	−	8.42107i	−1.33102	−	0.403759i
$436$	20.2008	+	8.67550i	0.967445	+	0.415481i
$437$	−5.20983	+	52.8963i	−0.249220	+	2.53037i
$438$	1.35000	+	1.84510i	0.0645054	+	0.0881624i
$439$	28.4083	−	5.65076i	1.35585	−	0.269696i	0.536944	−	0.843618i	$-0.319579\pi$
$439$	28.4083	−	5.65076i	1.35585	−	0.269696i	0.818910	+	0.573921i	$0.194579\pi$
$440$	−2.54051	+	1.14175i	−0.121114	+	0.0544307i
$441$	−4.21343	+	21.1823i	−0.200639	+	1.00868i
$442$	1.26046	−	3.45214i	0.0599540	−	0.164202i
$443$	−0.826007	−	2.72298i	−0.0392448	−	0.129373i	0.935129	−	0.354307i	$-0.115283\pi$
$443$	−0.826007	−	2.72298i	−0.0392448	−	0.129373i	−0.974374	+	0.224934i	$0.927783\pi$
$444$	−25.6894	+	46.6003i	−1.21917	+	2.21155i
$445$	1.51460	+	1.24300i	0.0717990	+	0.0589239i
$446$	−6.84550	−	19.5295i	−0.324144	−	0.924747i
$447$		−	19.5575i		−	0.925038i
$448$	12.6628	−	3.31018i	0.598259	−	0.156391i
$449$			24.0774i			1.13629i	0.822930	+	0.568143i	$0.192338\pi$
$449$			24.0774i			1.13629i	−0.822930	+	0.568143i	$0.807662\pi$
$450$	−6.66693	+	2.33690i	−0.314282	+	0.110163i
$451$	−5.07081	−	4.16151i	−0.238775	−	0.195958i
$452$	−5.50064	+	1.59114i	−0.258728	+	0.0748410i
$453$	−6.83328	−	22.5263i	−0.321055	−	1.05838i
$454$	−24.5546	−	8.96546i	−1.15240	−	0.420770i
$455$	−1.42030	+	7.14033i	−0.0665847	+	0.334744i
$456$	−1.56879	−	52.8595i	−0.0734655	−	2.47537i
$457$	27.3261	−	5.43550i	1.27826	−	0.254262i	0.491151	−	0.871075i	$-0.336576\pi$
$457$	27.3261	−	5.43550i	1.27826	−	0.254262i	0.787110	+	0.616813i	$0.211576\pi$
$458$	3.07937	−	2.25307i	0.143890	−	0.105279i
$459$	0.322970	−	3.27917i	0.0150749	−	0.153058i
$460$	14.9316	−	5.95959i	0.696187	−	0.277868i
$461$	18.0257	+	5.46802i	0.839538	+	0.254671i	0.680635	−	0.732623i	$-0.261704\pi$
$461$	18.0257	+	5.46802i	0.839538	+	0.254671i	0.158904	+	0.987294i	$0.449204\pi$
$462$	0.904040	+	6.37873i	0.0420597	+	0.296765i
$463$	−30.0489	−	12.4467i	−1.39649	−	0.578445i	−0.447652	−	0.894208i	$-0.647740\pi$
$463$	−30.0489	−	12.4467i	−1.39649	−	0.578445i	−0.948838	+	0.315762i	$0.897740\pi$
$464$	−40.7221	−	5.07827i	−1.89048	−	0.235753i
$465$	5.32692	−	2.20648i	0.247030	−	0.102323i
$466$	9.26742	+	15.6912i	0.429305	+	0.726880i
$467$	6.32681	+	11.8366i	0.292770	+	0.547734i	0.984706	−	0.174225i	$-0.0557420\pi$
$467$	6.32681	+	11.8366i	0.292770	+	0.547734i	−0.691936	+	0.721959i	$0.743242\pi$
$468$	24.2194	+	37.2827i	1.11954	+	1.72339i
$469$	−3.42230	−	4.17009i	−0.158027	−	0.192557i
$470$	2.46696	+	10.1263i	0.113792	+	0.467091i
$471$	39.2301	+	26.2127i	1.80763	+	1.20782i
$472$	−6.57303	−	11.4656i	−0.302548	−	0.527746i
$473$	−1.66015	−	2.48459i	−0.0763338	−	0.114242i
$474$	0.214775	+	5.03685i	0.00986494	+	0.231350i
$475$	−3.11698	+	5.83147i	−0.143017	+	0.267566i
$476$	1.23123	−	1.46127i	0.0564333	−	0.0669770i
$477$	20.1093	−	1.98060i	0.920742	−	0.0906852i
$478$	21.0720	+	1.17196i	0.963809	+	0.0536043i
$479$	8.94432	−	8.94432i	0.408677	−	0.408677i	−0.472600	−	0.881277i	$-0.656685\pi$
$479$	8.94432	−	8.94432i	0.408677	−	0.408677i	0.881277	+	0.472600i	$0.156685\pi$
$480$	−13.9787	+	7.77507i	−0.638035	+	0.354882i
$481$	−29.6072	−	29.6072i	−1.34997	−	1.34997i
$482$	14.9473	+	16.7079i	0.680833	+	0.761025i
$483$	−3.64493	−	37.0076i	−0.165850	−	1.68390i
$484$	9.22667	+	17.8128i	0.419394	+	0.809671i
$485$	13.2396	+	7.07673i	0.601180	+	0.321338i
$486$	−14.7811	−	13.5721i	−0.670485	−	0.615644i
$487$	−9.51946	+	6.36070i	−0.431368	+	0.288231i	−0.752237	−	0.658893i	$-0.771025\pi$
$487$	−9.51946	+	6.36070i	−0.431368	+	0.288231i	0.320869	+	0.947124i	$0.396025\pi$
$488$	−35.2173	−	17.5012i	−1.59421	−	0.792243i
$489$	20.6148	−	30.8522i	0.932232	−	1.39518i
$490$	3.17721	−	5.22387i	0.143532	−	0.235991i
$491$	−24.4366	+	20.0546i	−1.10281	+	0.905051i	−0.996011	−	0.0892295i	$-0.971560\pi$
$491$	−24.4366	+	20.0546i	−1.10281	+	0.905051i	−0.106797	+	0.994281i	$0.534060\pi$
$492$	−31.0496	−	21.3332i	−1.39983	−	0.961775i
$493$	−5.28383	+	2.82426i	−0.237972	+	0.127198i
$494$	40.2983	+	10.3719i	1.81311	+	0.466652i
$495$	−1.88252	−	4.54479i	−0.0846128	−	0.204273i
$496$	6.89685	−	4.35438i	0.309678	−	0.195518i
$497$	7.53303	−	18.1864i	0.337903	−	0.815770i
$498$	27.2288	−	36.2215i	1.22015	−	1.62312i
$499$	0.111640	−	0.368029i	0.00499771	−	0.0164752i	−0.954406	−	0.298512i	$-0.903510\pi$
$499$	0.111640	−	0.368029i	0.00499771	−	0.0164752i	0.959404	+	0.282036i	$0.0910099\pi$
$500$	1.99983	+	0.0258894i	0.0894352	+	0.00115781i
$501$	−16.2512	−	1.60061i	−0.726052	−	0.0715099i
$502$	−1.52750	+	9.85757i	−0.0681758	+	0.439965i
$503$	−5.80002	−	29.1587i	−0.258610	−	1.30012i	−0.863717	−	0.503977i	$-0.831870\pi$
$503$	−5.80002	−	29.1587i	−0.258610	−	1.30012i	0.605107	−	0.796144i	$-0.293130\pi$
$504$	5.18028	+	22.5280i	0.230748	+	1.00348i
$505$	1.03697	+	0.206267i	0.0461447	+	0.00917876i
$506$	4.72075	+	10.1507i	0.209863	+	0.451252i
$507$	−18.4047	+	5.58302i	−0.817383	+	0.247950i
$508$	16.0288	+	20.0550i	0.711163	+	0.889797i
$509$	19.0493	−	23.2117i	0.844346	−	1.02884i	−0.154817	−	0.987943i	$-0.549479\pi$
$509$	19.0493	−	23.2117i	0.844346	−	1.02884i	0.999163	−	0.0408957i	$-0.0130211\pi$
$510$	−1.01209	+	2.10454i	−0.0448162	+	0.0931904i
$511$	−0.935358			−0.0413778
$512$	−17.6221	+	14.1938i	−0.778792	+	0.627282i
$513$	37.3088			1.64722
$514$	7.51723	−	15.6313i	0.331571	−	0.689466i
$515$	−2.66931	+	3.25256i	−0.117624	+	0.143325i
$516$	−10.7140	−	13.4052i	−0.471659	−	0.590133i
$517$	−6.94486	+	2.10670i	−0.305435	+	0.0926526i
$518$	−9.18047	−	19.7400i	−0.403367	−	0.867328i
$519$	4.66472	+	0.927870i	0.204758	+	0.0407290i
$520$	−2.82058	−	12.2662i	−0.123691	−	0.537907i
$521$	5.29614	+	26.6255i	0.232028	+	1.16648i	0.904537	+	0.426395i	$0.140217\pi$
$521$	5.29614	+	26.6255i	0.232028	+	1.16648i	−0.672509	+	0.740089i	$0.734783\pi$
$522$	11.0987	−	71.6241i	0.485776	−	3.13490i
$523$	0.164009	+	0.0161534i	0.00717160	+	0.000706341i	0.101602	−	0.994825i	$-0.467603\pi$
$523$	0.164009	+	0.0161534i	0.00717160	+	0.000706341i	−0.0944307	+	0.995531i	$0.530103\pi$
$524$	−13.6130	−	0.176231i	−0.594688	−	0.00769869i
$525$	1.34288	−	4.42689i	0.0586081	−	0.193205i
$526$	24.9243	−	33.1558i	1.08675	−	1.44566i
$527$	0.455697	−	1.10015i	0.0198505	−	0.0479233i
$528$	−5.94611	−	9.41796i	−0.258771	−	0.409864i
$529$	−15.9261	−	38.4491i	−0.692441	−	1.67170i
$530$	−5.53995	−	1.42585i	−0.240640	−	0.0619352i
$531$	20.5855	−	11.0032i	0.893334	−	0.477497i
$532$	17.8323	+	12.2520i	0.773128	+	0.531191i
$533$	22.9143	−	18.8052i	0.992526	−	0.814545i
$534$	−4.07150	+	6.69425i	−0.176191	+	0.289689i
$535$	4.20965	−	6.30018i	0.181999	−	0.272381i
$536$	8.35192	+	4.15048i	0.360748	+	0.179274i
$537$	20.1017	−	13.4315i	0.867452	−	0.579613i
$538$	27.5628	+	25.3083i	1.18832	+	1.09112i
$539$	3.75473	+	2.00695i	0.161728	+	0.0864453i
$540$	−5.19033	−	10.0203i	−0.223356	−	0.431205i
$541$	−3.82371	−	38.8228i	−0.164394	−	1.66912i	−0.624324	−	0.781166i	$-0.714625\pi$
$541$	−3.82371	−	38.8228i	−0.164394	−	1.66912i	0.459930	−	0.887955i	$-0.347875\pi$
$542$	−11.2416	−	12.5657i	−0.482868	−	0.539743i
$543$	29.5770	+	29.5770i	1.26927	+	1.26927i
$544$	−0.905948	+	3.17683i	−0.0388422	+	0.136206i
$545$	7.77286	−	7.77286i	0.332953	−	0.332953i
$546$	−29.0677	−	1.61666i	−1.24398	−	0.0691867i
$547$	−12.9330	+	1.27379i	−0.552975	+	0.0544632i	−0.370646	−	0.928774i	$-0.620864\pi$
$547$	−12.9330	+	1.27379i	−0.552975	+	0.0544632i	−0.182329	+	0.983238i	$0.558364\pi$
$548$	13.9775	−	16.5890i	0.597089	−	0.708647i
$549$	32.7415	−	61.2551i	1.39737	−	2.61430i
$550$	0.0593292	+	1.39138i	0.00252981	+	0.0593285i
$551$	−37.6885	−	56.4048i	−1.60558	−	2.40293i
$552$	31.9745	+	55.7743i	1.36092	+	2.37391i
$553$	−1.71497	−	1.14590i	−0.0729278	−	0.0487288i
$554$	2.56961	+	10.5477i	0.109172	+	0.448127i
$555$	16.8787	+	20.5668i	0.716462	+	0.873011i
$556$	14.2688	+	21.9651i	0.605132	+	0.931526i
$557$	10.3608	+	19.3836i	0.439000	+	0.821311i	0.999979	−	0.00651918i	$-0.00207513\pi$
$557$	10.3608	+	19.3836i	0.439000	+	0.821311i	−0.560979	+	0.827830i	$0.689575\pi$
$558$	7.32580	+	12.4037i	0.310126	+	0.525091i
$559$	12.4753	−	5.16745i	0.527650	−	0.218560i
$560$	0.809816	−	6.49383i	0.0342210	−	0.274415i
$561$	−1.50230	−	0.622275i	−0.0634274	−	0.0262725i
$562$	5.04511	+	35.5973i	0.212815	+	1.50158i
$563$	−20.6968	−	6.27832i	−0.872268	−	0.264600i	−0.177751	−	0.984076i	$-0.556882\pi$
$563$	−20.6968	−	6.27832i	−0.872268	−	0.264600i	−0.694517	+	0.719476i	$0.744382\pi$
$564$	−38.7086	+	15.4497i	−1.62993	+	0.650549i
$565$	−0.280630	+	2.84929i	−0.0118062	+	0.119870i
$566$	−18.1915	+	13.3101i	−0.764645	+	0.559464i
$567$	−1.55355	+	0.309020i	−0.0652428	+	0.0129776i
$568$	1.00957	+	34.0167i	0.0423604	+	1.42731i
$569$	−6.01974	+	30.2633i	−0.252361	+	1.26870i	0.621842	+	0.783142i	$0.286384\pi$
$569$	−6.01974	+	30.2633i	−0.252361	+	1.26870i	−0.874203	+	0.485560i	$0.838616\pi$
$570$	−24.8376	−	9.06879i	−1.04033	−	0.379850i
$571$	−1.44026	−	4.74790i	−0.0602729	−	0.198693i	0.921633	−	0.388063i	$-0.126856\pi$
$571$	−1.44026	−	4.74790i	−0.0602729	−	0.198693i	−0.981906	+	0.189369i	$0.939356\pi$
$572$	8.41893	−	2.43530i	0.352013	−	0.101825i
$573$	30.5719	+	25.0897i	1.27716	+	1.04814i
$574$	14.5449	−	5.09830i	0.607093	−	0.212799i
$575$		−	8.03847i		−	0.335227i
$576$	−24.1341	−	31.8533i	−1.00559	−	1.32722i
$577$		−	41.4429i		−	1.72529i	−0.505808	−	0.862646i	$-0.668806\pi$
$577$		−	41.4429i		−	1.72529i	0.505808	−	0.862646i	$-0.331194\pi$
$578$	−7.79316	−	22.2331i	−0.324153	−	0.924774i
$579$	31.4129	+	25.7799i	1.30548	+	1.07138i
$580$	−9.90592	+	17.9692i	−0.411321	+	0.746132i
$581$	5.38167	+	17.7410i	0.223269	+	0.736020i
$582$	−20.5896	+	56.3906i	−0.853465	+	2.33747i
$583$	0.777103	−	3.90676i	0.0321843	−	0.161802i
$584$	1.47497	−	0.662876i	0.0610346	−	0.0274300i
$585$	21.8022	−	4.33673i	0.901411	−	0.179302i
$586$	17.0506	+	23.3038i	0.704354	+	0.962672i
$587$	−2.08265	+	21.1455i	−0.0859600	+	0.872766i	0.851426	+	0.524474i	$0.175738\pi$
$587$	−2.08265	+	21.1455i	−0.0859600	+	0.872766i	−0.937386	+	0.348292i	$0.886762\pi$
$588$	22.4657	+	9.64818i	0.926471	+	0.397884i
$589$	12.9025	+	3.91392i	0.531637	+	0.161270i
$590$	−6.54264	+	0.927271i	−0.269356	+	0.0381751i
$591$	28.6086	+	11.8501i	1.17680	+	0.487447i
$592$	28.4662	+	24.6221i	1.16996	+	1.01196i
$593$	−19.6178	+	8.12596i	−0.805606	+	0.333693i	−0.747200	−	0.664600i	$-0.768602\pi$
$593$	−19.6178	+	8.12596i	−0.805606	+	0.333693i	−0.0584068	+	0.998293i	$0.518602\pi$
$594$	6.76588	−	3.99602i	0.277607	−	0.163959i
$595$	−0.450376	−	0.842595i	−0.0184636	−	0.0345430i
$596$	−13.5313	−	2.87412i	−0.554264	−	0.117728i
$597$	−12.3858	−	15.0921i	−0.506915	−	0.617678i
$598$	−49.1497	+	11.9738i	−2.00988	+	0.489646i
$599$	11.4779	+	7.66930i	0.468975	+	0.313359i	0.767507	−	0.641041i	$-0.221497\pi$
$599$	11.4779	+	7.66930i	0.468975	+	0.313359i	−0.298532	+	0.954400i	$0.596497\pi$
$600$	1.01968	+	7.93246i	0.0416284	+	0.323841i
$601$	2.75125	+	4.11754i	0.112226	+	0.167958i	0.883331	−	0.468750i	$-0.155296\pi$
$601$	2.75125	+	4.11754i	0.112226	+	0.167958i	−0.771105	+	0.636708i	$0.780296\pi$
$602$	7.01450	−	0.299103i	0.285890	−	0.0121905i
$603$	−7.76478	+	14.5269i	−0.316206	+	0.591580i
$604$	−16.5895	+	1.41736i	−0.675019	+	0.0576714i
$605$	9.98198	−	0.983139i	0.405825	−	0.0399703i
$606$	−0.234784	+	4.22143i	−0.00953745	+	0.171484i
$607$	6.55180	−	6.55180i	0.265929	−	0.265929i	−0.561528	−	0.827458i	$-0.689786\pi$
$607$	6.55180	−	6.55180i	0.265929	−	0.265929i	0.827458	+	0.561528i	$0.189786\pi$
$608$	−36.8026	−	6.68269i	−1.49254	−	0.271019i
$609$	33.5599	+	33.5599i	1.35991	+	1.35991i
$610$	−14.6546	+	13.1104i	−0.593346	+	0.530823i
$611$	−3.21447	−	32.6370i	−0.130043	−	1.32035i
$612$	−5.56085	−	1.76579i	−0.224784	−	0.0713779i
$613$	26.1566	+	13.9810i	1.05645	+	0.564687i	0.905715	−	0.423887i	$-0.139335\pi$
$613$	26.1566	+	13.9810i	1.05645	+	0.564687i	0.150739	+	0.988574i	$0.451835\pi$
$614$	−23.4062	+	25.4912i	−0.944596	+	1.02874i
$615$	−15.6616	+	10.4647i	−0.631536	+	0.421979i
$616$	4.54612	+	0.311920i	0.183169	+	0.0125676i
$617$	19.3447	−	28.9514i	0.778789	−	1.16554i	−0.203666	−	0.979041i	$-0.565286\pi$
$617$	19.3447	−	28.9514i	0.778789	−	1.16554i	0.982455	−	0.186500i	$-0.0597145\pi$
$618$	−14.3757	−	8.74344i	−0.578276	−	0.351713i
$619$	10.6111	−	8.70834i	0.426498	−	0.350018i	−0.396527	−	0.918023i	$-0.629785\pi$
$619$	10.6111	−	8.70834i	0.426498	−	0.350018i	0.823025	+	0.568005i	$0.192285\pi$
$620$	−0.743776	−	4.00981i	−0.0298708	−	0.161038i
$621$	−40.0006	+	21.3807i	−1.60517	+	0.857980i
$622$	0.766009	−	2.97622i	0.0307142	−	0.119335i
$623$	−1.22672	−	2.96156i	−0.0491474	−	0.118652i
$624$	46.9826	−	18.0506i	1.88081	−	0.722601i
$625$	0.382683	−	0.923880i	0.0153073	−	0.0369552i
$626$	32.6763	+	24.5638i	1.30601	+	0.981768i
$627$	5.34463	−	17.6189i	0.213444	−	0.703631i
$628$	23.9010	−	23.2901i	0.953754	−	0.929375i
$629$	5.46840	+	0.538590i	0.218039	+	0.0214750i
$630$	11.4217	+	1.76987i	0.455050	+	0.0705133i
$631$	−5.04013	−	25.3384i	−0.200644	−	1.00871i	−0.941492	−	0.337034i	$-0.890576\pi$
$631$	−5.04013	−	25.3384i	−0.200644	−	1.00871i	0.740848	−	0.671672i	$-0.234424\pi$
$632$	3.51642	+	0.591606i	0.139876	+	0.0235328i
$633$	48.1920	+	9.58599i	1.91546	+	0.381009i
$634$	−44.2374	+	20.5734i	−1.75689	+	0.817075i
$635$	12.2840	−	3.72630i	0.487475	−	0.147874i
$636$	2.53669	−	22.7344i	0.100586	−	0.901478i
$637$	−12.2049	+	14.8718i	−0.483578	+	0.589241i
$638$	−12.8761	−	6.19223i	−0.509769	−	0.245153i
$639$	−60.1053			−2.37773
$640$	3.32509	+	10.8141i	0.131436	+	0.427463i
$641$	−43.8245			−1.73097			−0.865483	−	0.500939i	$-0.832988\pi$
$641$	−43.8245			−1.73097			−0.865483	+	0.500939i	$0.832988\pi$
$642$	27.3065	+	13.1320i	1.07770	+	0.518277i
$643$	21.9693	−	26.7697i	0.866384	−	1.05569i	−0.131541	−	0.991311i	$-0.541993\pi$
$643$	21.9693	−	26.7697i	0.866384	−	1.05569i	0.997925	−	0.0643816i	$-0.0205075\pi$
$644$	−26.1402	−	2.91671i	−1.03007	−	0.114934i
$645$	−8.21090	+	2.49075i	−0.323304	+	0.0980731i
$646$	−4.95156	+	2.30281i	−0.194816	+	0.0906030i
$647$	−4.20132	−	0.835694i	−0.165171	−	0.0328545i	0.111812	−	0.993729i	$-0.464335\pi$
$647$	−4.20132	−	0.835694i	−0.165171	−	0.0328545i	−0.276983	+	0.960875i	$0.589335\pi$
$648$	2.23080	−	1.58827i	0.0876339	−	0.0623933i
$649$	−0.897669	−	4.51289i	−0.0352366	−	0.177146i
$650$	−6.21892	−	0.963667i	−0.243926	−	0.0377981i
$651$	−9.38765	−	0.924603i	−0.367931	−	0.0362380i
$652$	−18.3163	−	18.7967i	−0.717321	−	0.736137i
$653$	−1.39440	+	4.59673i	−0.0545671	+	0.179884i	−0.979988	−	0.199058i	$-0.936212\pi$
$653$	−1.39440	+	4.59673i	−0.0545671	+	0.179884i	0.925421	+	0.378942i	$0.123712\pi$
$654$	35.1367	+	26.4134i	1.37395	+	1.03285i
$655$	−2.60496	+	6.28893i	−0.101784	+	0.245729i
$656$	−19.3228	+	18.3473i	−0.754430	+	0.716343i
$657$	1.09295	+	2.63861i	0.0426400	+	0.102942i
$658$	4.25014	−	16.5133i	0.165688	−	0.643755i
$659$	14.3536	−	7.67213i	0.559135	−	0.298864i	−0.167518	−	0.985869i	$-0.553575\pi$
$659$	14.3536	−	7.67213i	0.559135	−	0.298864i	0.726652	+	0.687005i	$0.241075\pi$
$660$	−5.47558	+	1.01566i	−0.213137	+	0.0395345i
$661$	−9.50741	+	7.80253i	−0.369795	+	0.303483i	−0.800876	−	0.598830i	$-0.795632\pi$
$661$	−9.50741	+	7.80253i	−0.369795	+	0.303483i	0.431081	+	0.902313i	$0.358132\pi$
$662$	−32.7466	−	19.9168i	−1.27273	−	0.774088i
$663$	4.08235	−	6.10966i	0.158545	−	0.237280i
$664$	−21.0592	−	24.1619i	−0.817255	−	0.937664i
$665$	8.99470	−	6.01006i	0.348799	−	0.233060i
$666$	−44.9588	+	48.9637i	−1.74212	+	1.89731i
$667$	72.7319	+	38.8760i	2.81619	+	1.50528i
$668$	−3.49566	+	11.0086i	−0.135251	+	0.425934i
$669$	−4.05567	−	41.1779i	−0.156801	−	1.59203i
$670$	3.47539	−	3.10917i	0.134266	−	0.120118i
$671$	−9.68158	−	9.68158i	−0.373753	−	0.373753i
$672$	26.1654	−	0.437652i	1.00935	−	0.0168828i
$673$	−20.8237	+	20.8237i	−0.802694	+	0.802694i	−0.983516	−	0.180822i	$-0.942124\pi$
$673$	−20.8237	+	20.8237i	−0.802694	+	0.802694i	0.180822	+	0.983516i	$0.442124\pi$
$674$	−1.34220	+	24.1328i	−0.0516995	+	0.929560i
$675$	−5.61522	+	0.553051i	−0.216130	+	0.0212869i
$676$	1.15803	+	13.5542i	0.0445395	+	0.521315i
$677$	−2.96328	+	5.54391i	−0.113888	+	0.213070i	−0.932407	−	0.361410i	$-0.882296\pi$
$677$	−2.96328	+	5.54391i	−0.113888	+	0.213070i	0.818519	+	0.574480i	$0.194796\pi$
$678$	−11.4386	+	0.487752i	−0.439298	+	0.0187320i
$679$	−13.6451	−	20.4213i	−0.523651	−	0.783699i
$680$	1.30734	+	1.00952i	0.0501341	+	0.0387131i
$681$	−43.4571	−	29.0371i	−1.66528	−	1.11270i
$682$	2.75905	−	0.672157i	0.105649	−	0.0257382i
$683$	9.38839	+	11.4398i	0.359237	+	0.437731i	0.920998	−	0.389568i	$-0.127376\pi$
$683$	9.38839	+	11.4398i	0.359237	+	0.437731i	−0.561761	+	0.827300i	$0.689876\pi$
$684$	13.7257	−	64.6205i	0.524816	−	2.47083i
$685$	−5.11289	−	9.56554i	−0.195353	−	0.365481i
$686$	−22.5583	+	13.3232i	−0.861279	+	0.508683i
$687$	7.04832	−	2.91951i	0.268910	−	0.111386i
$688$	−10.8492	+	5.44274i	−0.413623	+	0.207503i
$689$	16.6298	+	6.88828i	0.633544	+	0.262423i
$690$	31.8267	−	4.51071i	1.21162	−	0.171720i
$691$	2.09990	+	0.636996i	0.0798838	+	0.0242325i	0.329974	−	0.943990i	$-0.392960\pi$
$691$	2.09990	+	0.636996i	0.0798838	+	0.0242325i	−0.250090	+	0.968223i	$0.580460\pi$
$692$	1.32748	−	3.09103i	0.0504633	−	0.117503i
$693$	−0.788847	+	8.00930i	−0.0299658	+	0.304248i
$694$	−18.2146	−	24.8948i	−0.691418	−	0.944992i
$695$	12.8448	−	2.55498i	0.487229	−	0.0969159i
$696$	−76.7041	−	29.1372i	−2.90746	−	1.10444i
$697$	−0.758929	+	3.81539i	−0.0287465	+	0.144518i
$698$	−3.84920	+	10.5422i	−0.145694	+	0.399027i
$699$	10.5770	+	34.8678i	0.400060	+	1.31882i
$700$	−2.86550	−	1.57967i	−0.108306	−	0.0597058i
$701$	−18.0194	−	14.7882i	−0.680584	−	0.558541i	0.229324	−	0.973350i	$-0.426348\pi$
$701$	−18.0194	−	14.7882i	−0.680584	−	0.558541i	−0.909908	+	0.414809i	$0.863848\pi$
$702$	11.7457	+	33.5094i	0.443315	+	1.26473i
$703$			62.2168i			2.34655i
$704$	−7.38985	+	2.72991i	−0.278516	+	0.102887i
$705$			20.8390i			0.784841i
$706$	18.2051	−	6.38126i	0.685156	−	0.240162i
$707$	−1.33712	−	1.09735i	−0.0502877	−	0.0412700i
$708$	−7.34268	−	25.3839i	−0.275955	−	0.953986i
$709$	6.58781	+	21.7171i	0.247410	+	0.815603i	0.989403	+	0.145195i	$0.0463809\pi$
$709$	6.58781	+	21.7171i	0.247410	+	0.815603i	−0.741993	+	0.670408i	$0.766119\pi$
$710$	15.9837	+	5.83604i	0.599858	+	0.219023i
$711$	−1.22865	+	6.17684i	−0.0460779	+	0.231649i
$712$	4.03323	+	3.80073i	0.151152	+	0.142438i
$713$	−16.0763	+	3.19778i	−0.602063	+	0.119758i
$714$	3.08336	−	2.25599i	0.115392	−	0.0844282i
$715$	0.429515	−	4.36094i	0.0160629	−	0.163090i
$716$	−6.33882	−	15.8817i	−0.236893	−	0.593526i
$717$	40.3801	+	12.2492i	1.50802	+	0.457453i
$718$	3.66731	+	25.8758i	0.136863	+	0.965676i
$719$	−3.42561	−	1.41893i	−0.127754	−	0.0529173i	0.317891	−	0.948127i	$-0.397025\pi$
$719$	−3.42561	−	1.41893i	−0.127754	−	0.0529173i	−0.445645	+	0.895210i	$0.647025\pi$
$720$	−19.2651	+	5.30347i	−0.717970	+	0.197649i
$721$	6.35986	−	2.63434i	0.236854	−	0.0981080i
$722$	−17.7794	−	30.1033i	−0.661681	−	1.12033i
$723$	21.1298	+	39.5310i	0.785824	+	1.47017i
$724$	24.8101	−	16.1170i	0.922059	−	0.598982i
$725$	6.50849	+	7.93062i	0.241719	+	0.294536i
$726$	9.49383	+	38.9699i	0.352349	+	1.44631i
$727$	−6.62303	−	4.42537i	−0.245635	−	0.164128i	0.426659	−	0.904413i	$-0.359691\pi$
$727$	−6.62303	−	4.42537i	−0.245635	−	0.164128i	−0.672293	+	0.740285i	$0.734691\pi$
$728$	−5.39023	+	19.8735i	−0.199775	+	0.736563i
$729$	−23.9046	−	35.7757i	−0.885355	−	1.32503i
$730$	−0.0344453	−	0.807804i	−0.00127488	−	0.0298982i
$731$	−0.835349	+	1.56283i	−0.0308965	+	0.0578033i
$732$	−60.1311	−	50.6650i	−2.22251	−	1.87263i
$733$	6.90078	−	0.679668i	0.254886	−	0.0251041i	0.0302330	−	0.999543i	$-0.490375\pi$
$733$	6.90078	−	0.679668i	0.254886	−	0.0251041i	0.224653	+	0.974439i	$0.427875\pi$
$734$	28.8531	+	1.60473i	1.06499	+	0.0592316i
$735$	8.64433	−	8.64433i	0.318851	−	0.318851i
$736$	43.2876	−	13.9258i	1.59560	−	0.513314i
$737$	2.29603	+	2.29603i	0.0845752	+	0.0845752i
$738$	−31.3776	−	35.0735i	−1.15503	−	1.29107i
$739$	−4.37719	−	44.4424i	−0.161018	−	1.63484i	−0.648151	−	0.761512i	$-0.724457\pi$
$739$	−4.37719	−	44.4424i	−0.161018	−	1.63484i	0.487133	−	0.873328i	$-0.338043\pi$
$740$	16.7100	−	8.65549i	0.614274	−	0.318182i
$741$	73.3756	+	39.2201i	2.69552	+	1.44079i
$742$	6.89368	+	6.32982i	0.253075	+	0.232375i
$743$	20.7410	−	13.8587i	0.760912	−	0.508425i	−0.113542	−	0.993533i	$-0.536220\pi$
$743$	20.7410	−	13.8587i	0.760912	−	0.508425i	0.874454	+	0.485108i	$0.161220\pi$
$744$	15.4587	−	5.19490i	0.566742	−	0.190454i
$745$	−3.84265	+	5.75093i	−0.140784	+	0.210698i
$746$	−25.4161	+	41.7884i	−0.930548	+	1.52998i
$747$	43.7584	−	35.9116i	1.60104	−	1.31394i
$748$	−0.651310	+	0.947956i	−0.0238142	+	0.0346607i
$749$	−10.9327	+	5.84367i	−0.399473	+	0.213523i
$750$	3.87265	+	0.996731i	0.141409	+	0.0363955i
$751$	13.3360	+	32.1959i	0.486637	+	1.17484i	0.956402	+	0.292053i	$0.0943385\pi$
$751$	13.3360	+	32.1959i	0.486637	+	1.17484i	−0.469765	+	0.882791i	$0.655662\pi$
$752$	5.00070	+	29.0519i	0.182357	+	1.05941i
$753$	−7.63253	+	18.4266i	−0.278145	+	0.671501i
$754$	38.7954	−	51.6081i	1.41285	−	1.87946i
$755$	−2.41662	+	7.96652i	−0.0879497	+	0.289931i
$756$	−0.238988	+	18.4607i	−0.00869191	+	0.671410i
$757$	−15.9682	−	1.57273i	−0.580373	−	0.0571618i	−0.196429	−	0.980518i	$-0.562935\pi$
$757$	−15.9682	−	1.57273i	−0.580373	−	0.0571618i	−0.383944	+	0.923356i	$0.625435\pi$
$758$	−4.96919	+	32.0681i	−0.180489	+	1.16477i
$759$	4.36671	+	21.9530i	0.158502	+	0.796842i
$760$	−9.92451	+	15.8517i	−0.360000	+	0.575002i
$761$	25.5833	+	5.08884i	0.927396	+	0.184470i	0.635607	−	0.772013i	$-0.280750\pi$
$761$	25.5833	+	5.08884i	0.927396	+	0.184470i	0.291788	+	0.956483i	$0.405750\pi$
$762$	21.6466	+	46.5449i	0.784172	+	1.68614i
$763$	−17.2097	+	5.22050i	−0.623032	+	0.188995i
$764$	21.8516	−	17.4647i	0.790564	−	0.631852i
$765$	−1.85068	+	2.25506i	−0.0669113	+	0.0815317i
$766$	−7.67330	+	15.9558i	−0.277248	+	0.576507i
$767$	20.7926			0.750777
$768$	−40.9502	+	19.2332i	−1.47766	+	0.694020i
$769$	−1.67651			−0.0604563			−0.0302282	−	0.999543i	$-0.509623\pi$
$769$	−1.67651			−0.0604563			−0.0302282	+	0.999543i	$0.509623\pi$
$770$	0.987455	−	2.05331i	0.0355854	−	0.0739960i
$771$	22.0007	−	26.8080i	0.792337	−	0.965465i
$772$	22.4528	−	17.9452i	0.808093	−	0.645861i
$773$	20.9739	−	6.36235i	0.754377	−	0.228838i	0.110405	−	0.993887i	$-0.464785\pi$
$773$	20.9739	−	6.36235i	0.754377	−	0.228838i	0.643972	+	0.765049i	$0.277285\pi$
$774$	−9.04009	−	19.4382i	−0.324939	−	0.698691i
$775$	−1.99992	−	0.397810i	−0.0718394	−	0.0142897i
$776$	35.9894	+	22.5324i	1.29194	+	0.808865i
$777$	−8.49198	−	42.6920i	−0.304648	−	1.53157i
$778$	2.87427	−	18.5488i	0.103048	−	0.665006i
$779$	−43.8349	−	4.31736i	−1.57055	−	0.154685i
$780$	0.325758	−	25.1633i	0.0116640	−	0.900990i
$781$	−3.43943	+	11.3383i	−0.123072	+	0.405716i
$782$	3.98912	−	5.30658i	0.142651	−	0.189763i
$783$	22.1526	−	53.4810i	0.791668	−	1.91126i
$784$	9.97682	−	14.1256i	0.356315	−	0.504484i
$785$	−6.38544	−	15.4158i	−0.227906	−	0.550214i
$786$	−26.3615	−	6.78483i	−0.940282	−	0.242007i
$787$	−15.0102	+	8.02314i	−0.535058	+	0.285994i	−0.716713	−	0.697368i	$-0.754354\pi$
$787$	−15.0102	+	8.02314i	−0.535058	+	0.285994i	0.181656	+	0.983362i	$0.441854\pi$
$788$	12.4030	−	18.0521i	0.441839	−	0.643079i
$789$	64.1096	−	52.6134i	2.28236	−	1.87309i
$790$	0.926484	−	1.52330i	0.0329628	−	0.0541965i
$791$	2.60234	−	3.89467i	0.0925284	−	0.138479i
$792$	−4.43215	−	13.1889i	−0.157490	−	0.468649i
$793$	51.4441	−	34.3739i	1.82684	−	1.22065i
$794$	−5.03384	−	4.62210i	−0.178644	−	0.164032i
$795$	−10.0872	−	5.39172i	−0.357756	−	0.191224i
$796$	−12.2620	+	6.35148i	−0.434614	+	0.225122i
$797$	−3.29004	−	33.4043i	−0.116539	−	1.18324i	−0.858506	−	0.512804i	$-0.828607\pi$
$797$	−3.29004	−	33.4043i	−0.116539	−	1.18324i	0.741967	−	0.670437i	$-0.233893\pi$
$798$	28.8429	+	32.2402i	1.02103	+	1.14129i
$799$	3.04325	+	3.04325i	0.107662	+	0.107662i
$800$	5.63810	+	0.460241i	0.199337	+	0.0162720i
$801$	−6.92106	+	6.92106i	−0.244544	+	0.244544i
$802$	−13.5119	−	0.751495i	−0.477123	−	0.0265362i
$803$	0.560291	−	0.0551838i	0.0197722	−	0.00194739i
$804$	14.2603	+	12.0154i	0.502923	+	0.423751i
$805$	−6.19943	+	11.5983i	−0.218501	+	0.408787i
$806$	0.546684	+	12.8207i	0.0192561	+	0.451591i
$807$	41.5665	+	62.2087i	1.46321	+	2.18985i
$808$	2.88619	+	0.782811i	0.101536	+	0.0275392i
$809$	−19.3824	−	12.9509i	−0.681451	−	0.455331i	0.166055	−	0.986116i	$-0.446897\pi$
$809$	−19.3824	−	12.9509i	−0.681451	−	0.455331i	−0.847506	+	0.530786i	$0.821897\pi$
$810$	−0.324090	−	1.33031i	−0.0113874	−	0.0467424i
$811$	33.3545	+	40.6426i	1.17123	+	1.42715i	0.882860	+	0.469636i	$0.155615\pi$
$811$	33.3545	+	40.6426i	1.17123	+	1.42715i	0.288375	+	0.957518i	$0.406885\pi$
$812$	28.1510	−	18.2873i	0.987907	−	0.641758i
$813$	−15.8913	−	29.7305i	−0.557331	−	1.04269i
$814$	6.66383	+	11.2829i	0.233567	+	0.395466i
$815$	−12.1236	+	5.02178i	−0.424673	+	0.175905i
$816$	−3.26337	+	5.74261i	−0.114241	+	0.201032i
$817$	−18.5373	−	7.67842i	−0.648540	−	0.268634i
$818$	−1.43202	−	10.1041i	−0.0500695	−	0.353281i
$819$	−34.8020	−	10.5571i	−1.21608	−	0.368894i
$820$	4.93869	+	12.3737i	0.172466	+	0.432108i
$821$	3.00701	−	30.5307i	0.104946	−	1.06553i	−0.788095	−	0.615554i	$-0.788932\pi$
$821$	3.00701	−	30.5307i	0.104946	−	1.06553i	0.893041	−	0.449976i	$-0.148568\pi$
$822$	35.0038	−	25.6111i	1.22090	−	0.893288i
$823$	−41.2270	+	8.20056i	−1.43708	+	0.285853i	−0.851327	−	0.524635i	$-0.824202\pi$
$823$	−41.2270	+	8.20056i	−1.43708	+	0.285853i	−0.585755	+	0.810488i	$0.699202\pi$
$824$	−8.16196	+	8.66125i	−0.284335	+	0.301729i
$825$	−0.543227	+	2.73099i	−0.0189127	+	0.0950807i
$826$	10.1552	+	3.70790i	0.353344	+	0.129015i
$827$	−11.2044	−	36.9360i	−0.389615	−	1.28439i	−0.904259	−	0.426985i	$-0.859576\pi$
$827$	−11.2044	−	36.9360i	−0.389615	−	1.28439i	0.514644	−	0.857404i	$-0.327924\pi$
$828$	22.3164	+	77.1487i	0.775549	+	2.68110i
$829$	−13.3627	−	10.9665i	−0.464106	−	0.380882i	0.373081	−	0.927799i	$-0.378301\pi$
$829$	−13.3627	−	10.9665i	−0.464106	−	0.380882i	−0.837187	+	0.546917i	$0.815801\pi$
$830$	−15.1235	+	5.30111i	−0.524944	+	0.184004i
$831$			21.7061i			0.752977i
$832$	−5.58425	−	35.1587i	−0.193599	−	1.21891i
$833$		−	2.52477i		−	0.0874782i
$834$	17.3236	+	49.4225i	0.599868	+	1.71136i
$835$	4.46423	+	3.66370i	0.154491	+	0.126788i
$836$	−11.4046	−	6.28703i	−0.394436	−	0.217441i
$837$	3.33985	+	11.0100i	0.115442	+	0.380561i
$838$	−4.54870	+	12.4580i	−0.157132	+	0.430353i
$839$	−3.84499	+	19.3301i	−0.132744	+	0.667348i	0.855909	+	0.517127i	$0.172999\pi$
$839$	−3.84499	+	19.3301i	−0.132744	+	0.667348i	−0.988652	+	0.150221i	$0.952001\pi$
$840$	4.64642	−	12.2318i	0.160317	−	0.422036i
$841$	−74.7899	+	14.8766i	−2.57896	+	0.512988i
$842$	−28.6059	−	39.0970i	−0.985825	−	1.34737i
$843$	−7.04602	+	71.5395i	−0.242678	+	2.46395i
$844$	13.7145	−	31.9340i	0.472071	−	1.09921i
$845$	6.50891	+	1.97446i	0.223913	+	0.0679233i
$846$	−51.5497	+	7.30600i	−1.77232	+	0.251185i
$847$	−15.1607	−	6.27978i	−0.520929	−	0.215776i
$848$	−15.3565	−	5.09606i	−0.527345	−	0.174999i
$849$	−41.6381	+	17.2471i	−1.42902	+	0.591918i
$850$	0.711106	−	0.419989i	0.0243907	−	0.0144055i
$851$	−35.6549	−	66.7057i	−1.22223	−	2.28664i
$852$	−14.1375	+	66.5591i	−0.484343	+	2.28028i
$853$	9.28983	+	11.3197i	0.318078	+	0.387579i	0.907364	−	0.420345i	$-0.138091\pi$
$853$	9.28983	+	11.3197i	0.318078	+	0.387579i	−0.589287	+	0.807924i	$0.700591\pi$
$854$	31.2554	−	7.61441i	1.06954	−	0.260560i
$855$	−27.4643	−	18.3511i	−0.939261	−	0.627594i
$856$	13.0985	−	16.9628i	0.447698	−	0.579776i
$857$	−13.7196	−	20.5329i	−0.468654	−	0.701390i	0.519566	−	0.854430i	$-0.326094\pi$
$857$	−13.7196	−	20.5329i	−0.468654	−	0.701390i	−0.988220	+	0.153040i	$0.951094\pi$
$858$	17.5073	−	0.746522i	0.597688	−	0.0254858i
$859$	−15.8572	+	29.6668i	−0.541041	+	1.01222i	0.451725	+	0.892157i	$0.350809\pi$
$859$	−15.8572	+	29.6668i	−0.541041	+	1.01222i	−0.992767	+	0.120060i	$0.961691\pi$
$860$	0.516630	+	6.04693i	0.0176169	+	0.206199i
$861$	30.6680	−	3.02053i	1.04516	−	0.102940i
$862$	−1.79458	+	32.2667i	−0.0611237	+	1.09901i
$863$	25.8069	−	25.8069i	0.878476	−	0.878476i	−0.114901	−	0.993377i	$-0.536655\pi$
$863$	25.8069	−	25.8069i	0.878476	−	0.878476i	0.993377	+	0.114901i	$0.0366550\pi$
$864$	−12.7060	−	29.2801i	−0.432267	−	0.996130i
$865$	−1.18936	−	1.18936i	−0.0404396	−	0.0404396i
$866$	29.1302	−	26.0607i	0.989886	−	0.885578i
$867$	−4.61713	−	46.8785i	−0.156806	−	1.59208i
$868$	−2.01929	+	6.35918i	−0.0685392	+	0.215845i
$869$	1.09489	+	0.585232i	0.0371417	+	0.0198526i
$870$	−27.7475	+	30.2192i	−0.940728	+	1.02453i
$871$	−12.2002	+	8.15190i	−0.413387	+	0.276217i
$872$	23.4383	−	20.4285i	0.793721	−	0.691796i
$873$	−41.6639	+	62.3544i	−1.41011	+	2.11038i
$874$	64.2228	+	39.0609i	2.17237	+	1.32125i
$875$	−1.26467	+	1.03789i	−0.0427537	+	0.0350870i
$876$	3.17901	−	0.589671i	0.107409	−	0.0199231i
$877$	20.3737	−	10.8900i	0.687972	−	0.367729i	−0.0900747	−	0.995935i	$-0.528711\pi$
$877$	20.3737	−	10.8900i	0.687972	−	0.367729i	0.778047	+	0.628206i	$0.216211\pi$
$878$	10.2101	−	39.6697i	0.344573	−	1.33879i
$879$	22.0940	+	53.3397i	0.745213	+	1.79910i
$880$	−0.101969	+	3.93766i	−0.00343738	+	0.132739i
$881$	4.43326	−	10.7028i	0.149360	−	0.360587i	−0.831437	−	0.555620i	$-0.812481\pi$
$881$	4.43326	−	10.7028i	0.149360	−	0.360587i	0.980797	+	0.195032i	$0.0624811\pi$
$882$	24.4143	+	18.3530i	0.822071	+	0.617977i
$883$	−3.86816	+	12.7516i	−0.130174	+	0.429126i	−0.997663	−	0.0683306i	$-0.978233\pi$
$883$	−3.86816	+	12.7516i	−0.130174	+	0.429126i	0.867489	+	0.497457i	$0.165733\pi$
$884$	−3.62718	−	3.72232i	−0.121995	−	0.125195i
$885$	−13.1487	−	1.29503i	−0.441988	−	0.0435320i
$886$	−3.97669	−	0.616218i	−0.133600	−	0.0207022i
$887$	4.20369	+	21.1334i	0.141146	+	0.709589i	0.984937	+	0.172916i	$0.0553191\pi$
$887$	4.20369	+	21.1334i	0.141146	+	0.709589i	−0.843790	+	0.536673i	$0.819681\pi$
$888$	43.6463	+	61.3031i	1.46467	+	2.05720i
$889$	−20.5978	−	4.09715i	−0.690827	−	0.137414i
$890$	2.51252	−	1.16849i	0.0842198	−	0.0391680i
$891$	0.912362	−	0.276762i	0.0305653	−	0.00927188i
$892$	−29.0859	−	3.24539i	−0.973868	−	0.108664i
$893$	−30.9144	+	37.6694i	−1.03451	+	1.26056i
$894$	−24.9259	−	11.9871i	−0.833647	−	0.400909i
$895$	−8.54998			−0.285794
$896$	3.54240	−	18.1675i	0.118343	−	0.606932i
$897$	−101.146			−3.37715
$898$	30.6866	+	14.7575i	1.02402	+	0.492463i
$899$	13.2715	−	16.1714i	0.442629	−	0.539345i
$900$	−1.10790	+	9.92929i	−0.0369301	+	0.330976i
$901$	−2.26048	+	0.685709i	−0.0753075	+	0.0228443i
$902$	−8.41180	+	3.91206i	−0.280082	+	0.130257i
$903$	13.7680	+	2.73863i	0.458171	+	0.0911359i
$904$	−1.34353	+	7.98577i	−0.0446851	+	0.265603i
$905$	−2.88591	−	14.5085i	−0.0959310	−	0.482278i
$906$	−32.8979	−	5.09776i	−1.09296	−	0.169362i
$907$	−25.4815	−	2.50970i	−0.846098	−	0.0833334i	−0.334329	−	0.942456i	$-0.608510\pi$
$907$	−25.4815	−	2.50970i	−0.846098	−	0.0833334i	−0.511769	+	0.859123i	$0.671010\pi$
$908$	−26.4763	+	25.7995i	−0.878647	+	0.856188i
$909$	−1.53318	+	5.05421i	−0.0508523	+	0.167638i
$910$	8.22978	+	6.18659i	0.272814	+	0.205083i
$911$	19.1137	−	46.1445i	0.633265	−	1.52884i	−0.202231	−	0.979338i	$-0.564819\pi$
$911$	19.1137	−	46.1445i	0.633265	−	1.52884i	0.835495	−	0.549498i	$-0.185181\pi$
$912$	−68.3307	−	30.3990i	−2.26265	−	1.00661i
$913$	−4.27036	−	10.3096i	−0.141328	−	0.341197i
$914$	9.82110	−	38.1584i	0.324853	−	1.26217i
$915$	−34.6728	+	18.5330i	−1.14625	+	0.612682i
$916$	−0.984127	−	5.30558i	−0.0325165	−	0.175301i
$917$	8.60872	−	7.06499i	0.284285	−	0.233307i
$918$	−3.98132	−	2.42148i	−0.131403	−	0.0799207i
$919$	12.2954	−	18.4013i	0.405587	−	0.607004i	−0.571305	−	0.820738i	$-0.693563\pi$
$919$	12.2954	−	18.4013i	0.405587	−	0.607004i	0.976892	+	0.213734i	$0.0685626\pi$
$920$	1.55633	−	22.6829i	0.0513106	−	0.747833i
$921$	−57.5331	+	38.4424i	−1.89578	+	1.26672i
$922$	18.0172	−	19.6221i	0.593364	−	0.646221i
$923$	−47.2194	−	25.2393i	−1.55424	−	0.830761i
$924$	8.68375	+	2.75743i	0.285674	+	0.0907129i
$925$	−0.922277	−	9.36404i	−0.0303243	−	0.307888i
$926$	−34.2806	+	30.6684i	−1.12653	+	1.00782i
$927$	−14.8628	−	14.8628i	−0.488158	−	0.488158i
$928$	−31.4315	+	48.7876i	−1.03179	+	1.60153i
$929$	−28.5069	+	28.5069i	−0.935283	+	0.935283i	−0.998029	−	0.0627469i	$-0.980014\pi$
$929$	−28.5069	+	28.5069i	−0.935283	+	0.935283i	0.0627469	+	0.998029i	$0.480014\pi$
$930$	0.452808	−	8.14152i	0.0148482	−	0.266971i
$931$	28.4496	−	2.80205i	0.932399	−	0.0918333i
$932$	25.6785	−	2.19388i	0.841126	−	0.0718631i
$933$	2.89658	−	5.41912i	0.0948298	−	0.177414i
$934$	18.9635	−	0.808617i	0.620505	−	0.0264588i
$935$	0.319492	+	0.478154i	0.0104485	+	0.0156373i
$936$	62.3610	−	8.01624i	2.03833	−	0.262019i
$937$	35.6345	+	23.8102i	1.16413	+	0.777846i	0.978798	−	0.204830i	$-0.0656642\pi$
$937$	35.6345	+	23.8102i	1.16413	+	0.777846i	0.185331	+	0.982676i	$0.440664\pi$
$938$	−7.41233	+	1.80579i	−0.242021	+	0.0589610i
$939$	51.8524	+	63.1824i	1.69214	+	2.06188i
$940$	14.4179	+	3.06244i	0.470261	+	0.0998858i
$941$	−6.75376	−	12.6354i	−0.220166	−	0.411902i	0.747453	−	0.664314i	$-0.231276\pi$
$941$	−6.75376	−	12.6354i	−0.220166	−	0.411902i	−0.967620	+	0.252412i	$0.918776\pi$
$942$	57.4527	−	33.9323i	1.87191	−	1.10557i
$943$	49.4717	−	20.4919i	1.61102	−	0.667306i
$944$	−18.6415	+	1.34985i	−0.606729	+	0.0439338i
$945$	8.52845	+	3.53260i	0.277431	+	0.114915i
$946$	−4.18413	+	0.593005i	−0.136038	+	0.0192803i
$947$	46.2059	+	14.0164i	1.50149	+	0.455472i	0.930749	−	0.365657i	$-0.119156\pi$
$947$	46.2059	+	14.0164i	1.50149	+	0.455472i	0.570742	+	0.821130i	$0.306656\pi$
$948$	6.55108	+	2.81344i	0.212769	+	0.0913763i
$949$	−0.249368	+	2.53187i	−0.00809481	+	0.0821880i
$950$	5.52172	+	7.54678i	0.179148	+	0.244850i
$951$	−95.6728	+	19.0305i	−3.10240	+	0.617106i
$952$	−1.10773	−	2.46483i	−0.0359019	−	0.0798855i
$953$	8.15982	−	41.0222i	0.264322	−	1.32884i	−0.589287	−	0.807924i	$-0.700591\pi$
$953$	8.15982	−	41.0222i	0.264322	−	1.32884i	0.853609	−	0.520914i	$-0.174409\pi$
$954$	9.80107	−	26.8431i	0.317321	−	0.869079i
$955$	−4.06012	−	13.3844i	−0.131382	−	0.433110i
$956$	14.4090	−	26.1378i	0.466020	−	0.845356i
$957$	−22.0827	−	18.1228i	−0.713833	−	0.585828i
$958$	−5.91736	−	16.8816i	−0.191181	−	0.545420i
$959$			17.7448i			0.573010i
$960$	1.34153	+	22.5812i	0.0432978	+	0.728804i
$961$		−	26.8421i		−	0.865873i
$962$	−55.8808	+	19.5874i	−1.80167	+	0.631524i
$963$	29.2595	+	24.0126i	0.942874	+	0.773797i
$964$	30.4556	−	8.80974i	0.980909	−	0.283743i
$965$	−4.17182	−	13.7526i	−0.134296	−	0.442713i
$966$	−49.4000	−	18.0371i	−1.58942	−	0.580334i
$967$	10.0255	−	50.4018i	0.322399	−	1.62081i	−0.391233	−	0.920292i	$-0.627951\pi$
$967$	10.0255	−	50.4018i	0.322399	−	1.62081i	0.713633	−	0.700520i	$-0.247049\pi$
$968$	28.3574	−	0.841607i	0.911442	−	0.0270503i
$969$	−10.7088	+	2.13011i	−0.344016	+	0.0684290i
$970$	17.1340	−	12.5364i	0.550140	−	0.402519i
$971$	2.00253	−	20.3320i	0.0642641	−	0.652485i	−0.908059	−	0.418843i	$-0.862436\pi$
$971$	2.00253	−	20.3320i	0.0642641	−	0.652485i	0.972323	−	0.233642i	$-0.0750643\pi$
$972$	−26.3572	+	10.5199i	−0.845406	+	0.337425i
$973$	−20.5035	−	6.21968i	−0.657313	−	0.199394i
$974$	2.27204	+	16.0311i	0.0728008	+	0.513668i
$975$	−11.6249	−	4.81519i	−0.372295	−	0.154209i
$976$	−43.8905	+	34.1575i	−1.40490	+	1.09335i
$977$	−13.5978	+	5.63238i	−0.435031	+	0.180196i	−0.589442	−	0.807811i	$-0.700652\pi$
$977$	−13.5978	+	5.63238i	−0.435031	+	0.180196i	0.154410	+	0.988007i	$0.450652\pi$
$978$	−26.6858	−	45.1832i	−0.853317	−	1.44480i
$979$	0.909543	+	1.70164i	0.0290691	+	0.0543845i
$980$	−4.71043	−	7.25113i	−0.150469	−	0.231629i
$981$	34.8361	+	42.4479i	1.11223	+	1.35526i
$982$	10.5819	+	43.4361i	0.337681	+	1.38610i
$983$	10.8975	+	7.28147i	0.347576	+	0.232243i	0.717087	−	0.696983i	$-0.245475\pi$
$983$	10.8975	+	7.28147i	0.347576	+	0.232243i	−0.369511	+	0.929226i	$0.620475\pi$
$984$	−46.2199	+	26.4971i	−1.47344	+	0.844697i
$985$	−6.08414	−	9.10556i	−0.193857	−	0.290127i
$986$	0.360964	+	8.46524i	0.0114954	+	0.269588i
$987$	16.0714	−	30.0676i	0.511560	−	0.957061i
$988$	37.9184	−	45.0029i	1.20634	−	1.43173i
$989$	24.2751	−	2.39089i	0.771904	−	0.0760259i
$990$	−6.94613	−	0.386324i	−0.220763	−	0.0122782i
$991$	−17.0846	+	17.0846i	−0.542709	+	0.542709i	−0.924322	−	0.381613i	$-0.875369\pi$
$991$	−17.0846	+	17.0846i	−0.542709	+	0.542709i	0.381613	+	0.924322i	$0.375369\pi$
$992$	−1.32244	−	11.4589i	−0.0419876	−	0.363819i
$993$	−54.1883	−	54.1883i	−1.71961	−	1.71961i
$994$	−18.5613	−	20.7475i	−0.588728	−	0.658071i
$995$	0.676775	+	6.87142i	0.0214552	+	0.217839i
$996$	−29.4751	−	56.9037i	−0.933953	−	1.80306i
$997$	−39.9793	−	21.3694i	−1.26616	−	0.676776i	−0.304889	−	0.952388i	$-0.598619\pi$
$997$	−39.9793	−	21.3694i	−1.26616	−	0.676776i	−0.961269	+	0.275612i	$0.911119\pi$
$998$	−0.400624	−	0.367856i	−0.0126815	−	0.0116443i
$999$	−44.1437	+	29.4959i	−1.39664	+	0.933208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.341.42	✓	1024
128.125	even	32	inner	640.2.bm.a.381.42	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.341.42	✓	1024	1.1	even	1	trivial
640.2.bm.a.381.42	yes	1024	128.125	even	32	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.612916 - 1.27449i) q^{2} +(1.79383 - 2.18578i) q^{3} +(-1.24867 - 1.56232i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(-1.68630 - 3.62592i) q^{6} +(1.60460 + 0.319174i) q^{7} +(-2.75649 + 0.633850i) q^{8} +(-0.974564 - 4.89947i) q^{9} +O(q^{10})\)	\(q+(0.612916 - 1.27449i) q^{2} +(1.79383 - 2.18578i) q^{3} +(-1.24867 - 1.56232i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(-1.68630 - 3.62592i) q^{6} +(1.60460 + 0.319174i) q^{7} +(-2.75649 + 0.633850i) q^{8} +(-0.974564 - 4.89947i) q^{9} +(-0.216558 + 1.39753i) q^{10} +(-0.980004 - 0.0965219i) q^{11} +(-5.65477 - 0.0732053i) q^{12} +(1.29174 - 4.25831i) q^{13} +(1.39027 - 1.84942i) q^{14} +(-1.08208 + 2.61238i) q^{15} +(-0.881659 + 3.90163i) q^{16} +(0.223479 + 0.539526i) q^{17} +(-6.84166 - 1.76089i) q^{18} +(-5.83147 + 3.11698i) q^{19} +(1.64842 + 1.13257i) q^{20} +(3.57601 - 2.93476i) q^{21} +(-0.723677 + 1.18985i) q^{22} +(4.46593 - 6.68374i) q^{23} +(-3.55920 + 7.16210i) q^{24} +(0.831470 - 0.555570i) q^{25} +(-4.63546 - 4.25630i) q^{26} +(-4.97614 - 2.65980i) q^{27} +(-1.50496 - 2.90543i) q^{28} +(1.00560 + 10.2100i) q^{29} +(2.66624 + 2.98028i) q^{30} +(-1.44186 - 1.44186i) q^{31} +(4.43221 + 3.51504i) q^{32} +(-1.96893 + 1.96893i) q^{33} +(0.824596 + 0.0458617i) q^{34} +(-1.62815 + 0.160359i) q^{35} +(-6.43760 + 7.64038i) q^{36} +(4.43553 - 8.29830i) q^{37} +(0.398376 + 9.34262i) q^{38} +(-6.99057 - 10.4621i) q^{39} +(2.45380 - 1.40672i) q^{40} +(5.53878 + 3.70090i) q^{41} +(-1.54853 - 6.35636i) q^{42} +(1.92505 + 2.34568i) q^{43} +(1.07290 + 1.65160i) q^{44} +(2.35484 + 4.40560i) q^{45} +(-5.78114 - 9.78838i) q^{46} +(6.80879 - 2.82029i) q^{47} +(6.94656 + 8.92595i) q^{48} +(-3.99430 - 1.65449i) q^{49} +(-0.198449 - 1.40022i) q^{50} +(1.58017 + 0.479339i) q^{51} +(-8.26578 + 3.29910i) q^{52} +(-0.396480 + 4.02553i) q^{53} +(-6.43986 + 4.71182i) q^{54} +(0.965824 - 0.192114i) q^{55} +(-4.62536 + 0.137274i) q^{56} +(-3.64758 + 18.3376i) q^{57} +(13.6289 + 4.97624i) q^{58} +(1.35638 + 4.47138i) q^{59} +(5.43253 - 1.57144i) q^{60} +(10.7479 + 8.82056i) q^{61} +(-2.72139 + 0.953905i) q^{62} -8.17272i q^{63} +(7.19647 - 3.49440i) q^{64} +4.44992i q^{65} +(1.30260 + 3.71618i) q^{66} +(-2.54890 - 2.09183i) q^{67} +(0.563859 - 1.02283i) q^{68} +(-6.59810 - 21.7510i) q^{69} +(-0.793546 + 2.17336i) q^{70} +(2.34733 - 11.8008i) q^{71} +(5.79190 + 12.8876i) q^{72} +(-0.560737 + 0.111538i) q^{73} +(-7.85752 - 10.7392i) q^{74} +(0.277156 - 2.81401i) q^{75} +(12.1513 + 5.21851i) q^{76} +(-1.54170 - 0.467671i) q^{77} +(-17.6186 + 2.49703i) q^{78} +(-1.16475 - 0.482455i) q^{79} +(-0.288887 - 3.98955i) q^{80} +(-0.894487 + 0.370508i) q^{81} +(8.11158 - 4.79081i) q^{82} +(5.34180 + 9.99380i) q^{83} +(-9.05027 - 1.92232i) q^{84} +(-0.370472 - 0.451422i) q^{85} +(4.16946 - 1.01576i) q^{86} +(24.1207 + 16.1169i) q^{87} +(2.76255 - 0.355114i) q^{88} +(-1.08856 - 1.62914i) q^{89} +(7.05822 - 0.300967i) q^{90} +(3.43187 - 6.42058i) q^{91} +(-16.0186 + 1.36858i) q^{92} +(-5.73806 + 0.565149i) q^{93} +(0.578772 - 10.4064i) q^{94} +(4.67555 - 4.67555i) q^{95} +(15.6337 - 3.38249i) q^{96} +(-10.6153 - 10.6153i) q^{97} +(-4.55681 + 4.07664i) q^{98} +(0.482171 + 4.89556i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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