LMFDB - Embedded newform 230.2.l.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	230.17
Dual form			230.2.l.a.203.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.936950 + 0.349464i) q^{2} +(1.26604 - 0.691312i) q^{3} +(0.755750 - 0.654861i) q^{4} +(-0.584903 + 2.15821i) q^{5} +(-0.944630 + 1.09016i) q^{6} +(1.35459 + 1.80952i) q^{7} +(-0.479249 + 0.877679i) q^{8} +(-0.496969 + 0.773299i) q^{9} +(-0.206194 - 2.22654i) q^{10} +(-0.475362 + 0.217091i) q^{11} +(0.504099 - 1.35154i) q^{12} +(3.11241 + 2.32992i) q^{13} +(-1.90155 - 1.22205i) q^{14} +(0.751486 + 3.13674i) q^{15} +(0.142315 - 0.989821i) q^{16} +(-0.578458 - 8.08789i) q^{17} +(0.195395 - 0.898216i) q^{18} +(4.90659 + 5.66250i) q^{19} +(0.971289 + 2.01410i) q^{20} +(2.96592 + 1.35449i) q^{21} +(0.369525 - 0.369525i) q^{22} +(-0.430826 - 4.77644i) q^{23} +1.44249i q^{24} +(-4.31578 - 2.52469i) q^{25} +(-3.73039 - 1.09534i) q^{26} +(-0.403312 + 5.63904i) q^{27} +(2.20872 + 0.480478i) q^{28} +(1.93734 + 1.67872i) q^{29} +(-1.80028 - 2.67635i) q^{30} +(-0.910979 + 0.267488i) q^{31} +(0.212565 + 0.977147i) q^{32} +(-0.451751 + 0.603469i) q^{33} +(3.36841 + 7.37580i) q^{34} +(-4.69765 + 1.86511i) q^{35} +(0.130819 + 0.909866i) q^{36} +(2.51303 - 0.546675i) q^{37} +(-6.57607 - 3.59081i) q^{38} +(5.55114 + 0.798134i) q^{39} +(-1.61390 - 1.54768i) q^{40} +(-5.19777 + 3.34040i) q^{41} +(-3.25226 - 0.232606i) q^{42} +(-4.84144 - 8.86643i) q^{43} +(-0.217091 + 0.475362i) q^{44} +(-1.37827 - 1.52487i) q^{45} +(2.07286 + 4.32473i) q^{46} +(-0.388392 - 0.388392i) q^{47} +(-0.504099 - 1.35154i) q^{48} +(0.532671 - 1.81411i) q^{49} +(4.92596 + 0.857301i) q^{50} +(-6.32361 - 9.83973i) q^{51} +(3.87797 - 0.277358i) q^{52} +(7.32556 - 5.48385i) q^{53} +(-1.59276 - 5.42444i) q^{54} +(-0.190487 - 1.15291i) q^{55} +(-2.23737 + 0.321685i) q^{56} +(10.1265 + 3.77699i) q^{57} +(-2.40185 - 0.895842i) q^{58} +(-7.55765 + 1.08663i) q^{59} +(2.62206 + 1.87847i) q^{60} +(-3.43203 - 11.6884i) q^{61} +(0.760064 - 0.568977i) q^{62} +(-2.07250 + 0.148228i) q^{63} +(-0.540641 - 0.841254i) q^{64} +(-6.84892 + 5.35447i) q^{65} +(0.212378 - 0.723291i) q^{66} +(-3.30790 - 8.86882i) q^{67} +(-5.73361 - 5.73361i) q^{68} +(-3.84745 - 5.74935i) q^{69} +(3.74967 - 3.38917i) q^{70} +(-2.35355 + 5.15355i) q^{71} +(-0.440537 - 0.806783i) q^{72} +(0.283343 + 0.0202651i) q^{73} +(-2.16354 + 1.39042i) q^{74} +(-7.20931 - 0.212823i) q^{75} +(7.41630 + 1.06630i) q^{76} +(-1.03675 - 0.566110i) q^{77} +(-5.48006 + 1.19211i) q^{78} +(0.529838 + 3.68510i) q^{79} +(2.05301 + 0.886096i) q^{80} +(2.24214 + 4.90961i) q^{81} +(3.70270 - 4.94623i) q^{82} +(-1.46663 - 6.74199i) q^{83} +(3.12849 - 0.918609i) q^{84} +(17.7937 + 3.48220i) q^{85} +(7.63468 + 6.61549i) q^{86} +(3.61328 + 0.786020i) q^{87} +(0.0372809 - 0.521256i) q^{88} +(9.07615 + 2.66500i) q^{89} +(1.82425 + 0.947073i) q^{90} +8.78807i q^{91} +(-3.45350 - 3.32766i) q^{92} +(-0.968421 + 0.968421i) q^{93} +(0.499632 + 0.228174i) q^{94} +(-15.0908 + 7.27745i) q^{95} +(0.944630 + 1.09016i) q^{96} +(-1.22057 + 5.61087i) q^{97} +(0.134881 + 1.88588i) q^{98} +(0.0683643 - 0.475484i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{22}\right)$

Coefficient data

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

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

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

$2$	−0.936950	+	0.349464i	−0.662524	+	0.247108i
$2$	−0.936950	+	0.349464i	−0.662524	+	0.247108i
$3$	1.26604	−	0.691312i	0.730950	−	0.399129i	−0.0702468	−	0.997530i	$-0.522379\pi$
$3$	1.26604	−	0.691312i	0.730950	−	0.399129i	0.801197	+	0.598401i	$0.204197\pi$
$4$	0.755750	−	0.654861i	0.377875	−	0.327430i
$5$	−0.584903	+	2.15821i	−0.261577	+	0.965183i
$5$	−0.584903	+	2.15821i	−0.261577	+	0.965183i
$6$	−0.944630	+	1.09016i	−0.385644	+	0.445056i
$7$	1.35459	+	1.80952i	0.511988	+	0.683936i	0.979820	−	0.199881i	$-0.0640557\pi$
$7$	1.35459	+	1.80952i	0.511988	+	0.683936i	−0.467832	+	0.883817i	$0.654965\pi$
$8$	−0.479249	+	0.877679i	−0.169440	+	0.310306i
$9$	−0.496969	+	0.773299i	−0.165656	+	0.257766i
$10$	−0.206194	−	2.22654i	−0.0652041	−	0.704094i
$11$	−0.475362	+	0.217091i	−0.143327	+	0.0654553i	−0.485787	−	0.874077i	$-0.661467\pi$
$11$	−0.475362	+	0.217091i	−0.143327	+	0.0654553i	0.342460	+	0.939532i	$0.388740\pi$
$12$	0.504099	−	1.35154i	0.145521	−	0.390156i
$13$	3.11241	+	2.32992i	0.863227	+	0.646204i	0.936330	−	0.351121i	$-0.114199\pi$
$13$	3.11241	+	2.32992i	0.863227	+	0.646204i	−0.0731033	+	0.997324i	$0.523290\pi$
$14$	−1.90155	−	1.22205i	−0.508211	−	0.326607i
$15$	0.751486	+	3.13674i	0.194033	+	0.809903i
$16$	0.142315	−	0.989821i	0.0355787	−	0.247455i
$17$	−0.578458	−	8.08789i	−0.140297	−	1.96160i	−0.251641	−	0.967821i	$-0.580970\pi$
$17$	−0.578458	−	8.08789i	−0.140297	−	1.96160i	0.111345	−	0.993782i	$-0.464484\pi$
$18$	0.195395	−	0.898216i	0.0460550	−	0.211711i
$19$	4.90659	+	5.66250i	1.12565	+	1.29907i	0.949170	+	0.314763i	$0.101925\pi$
$19$	4.90659	+	5.66250i	1.12565	+	1.29907i	0.176478	+	0.984305i	$0.443529\pi$
$20$	0.971289	+	2.01410i	0.217187	+	0.450366i
$21$	2.96592	+	1.35449i	0.647217	+	0.295574i
$22$	0.369525	−	0.369525i	0.0787830	−	0.0787830i
$23$	−0.430826	−	4.77644i	−0.0898333	−	0.995957i
$23$	−0.430826	−	4.77644i	−0.0898333	−	0.995957i
$24$			1.44249i			0.294447i
$25$	−4.31578	−	2.52469i	−0.863155	−	0.504939i
$26$	−3.73039	−	1.09534i	−0.731590	−	0.214814i
$27$	−0.403312	+	5.63904i	−0.0776174	+	1.08523i
$28$	2.20872	+	0.480478i	0.417409	+	0.0908017i
$29$	1.93734	+	1.67872i	0.359756	+	0.311730i	0.815919	−	0.578166i	$-0.196231\pi$
$29$	1.93734	+	1.67872i	0.359756	+	0.311730i	−0.456164	+	0.889896i	$0.650777\pi$
$30$	−1.80028	−	2.67635i	−0.328685	−	0.488633i
$31$	−0.910979	+	0.267488i	−0.163617	+	0.0480422i	−0.362515	−	0.931978i	$-0.618082\pi$
$31$	−0.910979	+	0.267488i	−0.163617	+	0.0480422i	0.198898	+	0.980020i	$0.436264\pi$
$32$	0.212565	+	0.977147i	0.0375766	+	0.172737i
$33$	−0.451751	+	0.603469i	−0.0786398	+	0.105051i
$34$	3.36841	+	7.37580i	0.577678	+	1.26494i
$35$	−4.69765	+	1.86511i	−0.794047	+	0.315260i
$36$	0.130819	+	0.909866i	0.0218032	+	0.151644i
$37$	2.51303	−	0.546675i	0.413139	−	0.0898729i	−0.00119179	−	0.999999i	$-0.500379\pi$
$37$	2.51303	−	0.546675i	0.413139	−	0.0898729i	0.414331	+	0.910126i	$0.364016\pi$
$38$	−6.57607	−	3.59081i	−1.06678	−	0.582506i
$39$	5.55114	+	0.798134i	0.888895	+	0.127804i
$40$	−1.61390	−	1.54768i	−0.255181	−	0.244710i
$41$	−5.19777	+	3.34040i	−0.811755	+	0.521683i	−0.879432	−	0.476024i	$-0.842078\pi$
$41$	−5.19777	+	3.34040i	−0.811755	+	0.521683i	0.0676770	+	0.997707i	$0.478441\pi$
$42$	−3.25226	−	0.232606i	−0.501835	−	0.0358919i
$43$	−4.84144	−	8.86643i	−0.738312	−	1.35212i	−0.928857	−	0.370439i	$-0.879207\pi$
$43$	−4.84144	−	8.86643i	−0.738312	−	1.35212i	0.190544	−	0.981679i	$-0.438975\pi$
$44$	−0.217091	+	0.475362i	−0.0327276	+	0.0716635i
$45$	−1.37827	−	1.52487i	−0.205460	−	0.227314i
$46$	2.07286	+	4.32473i	0.305626	+	0.637646i
$47$	−0.388392	−	0.388392i	−0.0566527	−	0.0566527i	0.678213	−	0.734866i	$-0.262755\pi$
$47$	−0.388392	−	0.388392i	−0.0566527	−	0.0566527i	−0.734866	+	0.678213i	$0.762755\pi$
$48$	−0.504099	−	1.35154i	−0.0727604	−	0.195078i
$49$	0.532671	−	1.81411i	0.0760959	−	0.259159i
$50$	4.92596	+	0.857301i	0.696635	+	0.121241i
$51$	−6.32361	−	9.83973i	−0.885482	−	1.37784i
$52$	3.87797	−	0.277358i	0.537778	−	0.0384627i
$53$	7.32556	−	5.48385i	1.00624	−	0.753264i	0.0369865	−	0.999316i	$-0.488224\pi$
$53$	7.32556	−	5.48385i	1.00624	−	0.753264i	0.969257	+	0.246051i	$0.0791332\pi$
$54$	−1.59276	−	5.42444i	−0.216747	−	0.738172i
$55$	−0.190487	−	1.15291i	−0.0256853	−	0.155458i
$56$	−2.23737	+	0.321685i	−0.298981	+	0.0429870i
$57$	10.1265	+	3.77699i	1.34129	+	0.500275i
$58$	−2.40185	−	0.895842i	−0.315378	−	0.117630i
$59$	−7.55765	+	1.08663i	−0.983922	+	0.141467i	−0.615453	−	0.788174i	$-0.711027\pi$
$59$	−7.55765	+	1.08663i	−0.983922	+	0.141467i	−0.368469	+	0.929640i	$0.620118\pi$
$60$	2.62206	+	1.87847i	0.338507	+	0.242510i
$61$	−3.43203	−	11.6884i	−0.439426	−	1.49655i	−0.820306	−	0.571924i	$-0.806197\pi$
$61$	−3.43203	−	11.6884i	−0.439426	−	1.49655i	0.380880	−	0.924624i	$-0.375621\pi$
$62$	0.760064	−	0.568977i	0.0965282	−	0.0722601i
$63$	−2.07250	+	0.148228i	−0.261110	+	0.0186749i
$64$	−0.540641	−	0.841254i	−0.0675801	−	0.105157i
$65$	−6.84892	+	5.35447i	−0.849504	+	0.664140i
$66$	0.212378	−	0.723291i	0.0261419	−	0.0890310i
$67$	−3.30790	−	8.86882i	−0.404124	−	1.08350i	−0.966511	−	0.256624i	$-0.917390\pi$
$67$	−3.30790	−	8.86882i	−0.404124	−	1.08350i	0.562387	−	0.826874i	$-0.309883\pi$
$68$	−5.73361	−	5.73361i	−0.695303	−	0.695303i
$69$	−3.84745	−	5.74935i	−0.463179	−	0.692140i
$70$	3.74967	−	3.38917i	0.448172	−	0.405083i
$71$	−2.35355	+	5.15355i	−0.279315	+	0.611614i	−0.996344	−	0.0854288i	$-0.972774\pi$
$71$	−2.35355	+	5.15355i	−0.279315	+	0.611614i	0.717030	+	0.697043i	$0.245501\pi$
$72$	−0.440537	−	0.806783i	−0.0519177	−	0.0950802i
$73$	0.283343	+	0.0202651i	0.0331628	+	0.00237185i	0.0879107	−	0.996128i	$-0.471981\pi$
$73$	0.283343	+	0.0202651i	0.0331628	+	0.00237185i	−0.0547479	+	0.998500i	$0.517436\pi$
$74$	−2.16354	+	1.39042i	−0.251506	+	0.161633i
$75$	−7.20931	−	0.212823i	−0.832459	−	0.0245747i
$76$	7.41630	+	1.06630i	0.850708	+	0.122313i
$77$	−1.03675	−	0.566110i	−0.118149	−	0.0645142i
$78$	−5.48006	+	1.19211i	−0.620495	+	0.134980i
$79$	0.529838	+	3.68510i	0.0596114	+	0.414607i	0.997675	+	0.0681447i	$0.0217080\pi$
$79$	0.529838	+	3.68510i	0.0596114	+	0.414607i	−0.938064	+	0.346462i	$0.887383\pi$
$80$	2.05301	+	0.886096i	0.229533	+	0.0990685i
$81$	2.24214	+	4.90961i	0.249127	+	0.545512i
$82$	3.70270	−	4.94623i	0.408895	−	0.546219i
$83$	−1.46663	−	6.74199i	−0.160983	−	0.740029i	−0.984873	−	0.173278i	$-0.944564\pi$
$83$	−1.46663	−	6.74199i	−0.160983	−	0.740029i	0.823889	−	0.566751i	$-0.191800\pi$
$84$	3.12849	−	0.918609i	0.341347	−	0.100228i
$85$	17.7937	+	3.48220i	1.93000	+	0.377698i
$86$	7.63468	+	6.61549i	0.823269	+	0.713367i
$87$	3.61328	+	0.786020i	0.387384	+	0.0842702i
$88$	0.0372809	−	0.521256i	0.00397416	−	0.0555660i
$89$	9.07615	+	2.66500i	0.962069	+	0.282489i	0.724804	−	0.688956i	$-0.241931\pi$
$89$	9.07615	+	2.66500i	0.962069	+	0.282489i	0.237266	+	0.971445i	$0.423749\pi$
$90$	1.82425	+	0.947073i	0.192293	+	0.0998303i
$91$			8.78807i			0.921240i
$92$	−3.45350	−	3.32766i	−0.360052	−	0.346933i
$93$	−0.968421	+	0.968421i	−0.100421	+	0.100421i
$94$	0.499632	+	0.228174i	0.0515331	+	0.0235344i
$95$	−15.0908	+	7.27745i	−1.54828	+	0.746651i
$96$	0.944630	+	1.09016i	0.0964109	+	0.111264i
$97$	−1.22057	+	5.61087i	−0.123930	+	0.569698i	0.872742	+	0.488182i	$0.162340\pi$
$97$	−1.22057	+	5.61087i	−0.123930	+	0.569698i	−0.996672	+	0.0815157i	$0.974024\pi$
$98$	0.134881	+	1.88588i	0.0136250	+	0.190503i
$99$	0.0683643	−	0.475484i	0.00687088	−	0.0477880i
$100$	−4.91497	+	0.918197i	−0.491497	+	0.0918197i
$101$	1.86099	+	1.19599i	0.185175	+	0.119005i	0.629944	−	0.776640i	$-0.283078\pi$
$101$	1.86099	+	1.19599i	0.185175	+	0.119005i	−0.444769	+	0.895645i	$0.646714\pi$
$102$	9.36354	+	7.00946i	0.927128	+	0.694040i
$103$	−4.12274	+	11.0535i	−0.406226	+	1.08913i	0.559332	+	0.828944i	$0.311058\pi$
$103$	−4.12274	+	11.0535i	−0.406226	+	1.08913i	−0.965558	+	0.260189i	$0.916215\pi$
$104$	−3.53654	+	1.61508i	−0.346786	+	0.158372i
$105$	−4.65805	+	5.60884i	−0.454580	+	0.547367i
$106$	−4.94727	+	7.69811i	−0.480522	+	0.747707i
$107$	−6.56126	+	12.0161i	−0.634301	+	1.16164i	0.340855	+	0.940116i	$0.389284\pi$
$107$	−6.56126	+	12.0161i	−0.634301	+	1.16164i	−0.975156	+	0.221520i	$0.928898\pi$
$108$	3.38798	+	4.52581i	0.326009	+	0.435496i
$109$	5.71726	−	6.59807i	0.547614	−	0.631981i	−0.412711	−	0.910862i	$-0.635418\pi$
$109$	5.71726	−	6.59807i	0.547614	−	0.631981i	0.960326	+	0.278881i	$0.0899636\pi$
$110$	0.581377	+	1.01365i	0.0554322	+	0.0966477i
$111$	2.80368	−	2.42940i	0.266113	−	0.230588i
$112$	1.98388	−	1.08328i	0.187459	−	0.102361i
$113$	17.3633	−	6.47618i	1.63340	−	0.609228i	0.645425	−	0.763823i	$-0.276680\pi$
$113$	17.3633	−	6.47618i	1.63340	−	0.609228i	0.987978	+	0.154596i	$0.0494075\pi$
$114$	−10.8080			−1.01226
$115$	10.5606	+	1.86394i	0.984779	+	0.173814i
$116$	2.56347			0.238012
$117$	−3.34850	+	1.24893i	−0.309569	+	0.115463i
$118$	6.70140	−	3.65924i	0.616914	−	0.336860i
$119$	13.8517	−	12.0025i	1.26978	−	1.10027i
$120$	−3.11320	−	0.843717i	−0.284195	−	0.0770205i
$121$	−7.02463	+	8.10685i	−0.638602	+	0.736987i
$122$	7.30032	+	9.75209i	0.660940	+	0.882913i
$123$	−4.27134	+	7.82238i	−0.385134	+	0.705320i
$124$	−0.513305	+	0.798718i	−0.0460961	+	0.0717270i
$125$	7.97314	−	7.83767i	0.713139	−	0.701022i
$126$	1.89002	−	0.863145i	0.168377	−	0.0768951i
$127$	4.21302	−	11.2955i	0.373845	−	1.00232i	−0.604731	−	0.796430i	$-0.706719\pi$
$127$	4.21302	−	11.2955i	0.373845	−	1.00232i	0.978576	−	0.205887i	$-0.0660081\pi$
$128$	0.800541	+	0.599278i	0.0707585	+	0.0529692i
$129$	−12.2589	−	7.87834i	−1.07934	−	0.693649i
$130$	4.54590	−	7.41032i	0.398702	−	0.649928i
$131$	0.282560	−	1.96525i	0.0246874	−	0.171705i	−0.973747	−	0.227631i	$-0.926902\pi$
$131$	0.282560	−	1.96525i	0.0246874	−	0.171705i	0.998435	+	0.0559261i	$0.0178111\pi$
$132$	0.0537774	+	0.751906i	0.00468072	+	0.0654450i
$133$	−3.60001	+	16.5490i	−0.312160	+	1.43498i
$134$	6.19867	+	7.15364i	0.535483	+	0.617981i
$135$	−11.9343	−	4.16872i	−1.02715	−	0.358787i
$136$	7.37580	+	3.36841i	0.632470	+	0.288839i
$137$	−6.57055	+	6.57055i	−0.561360	+	0.561360i	−0.929694	−	0.368334i	$-0.879928\pi$
$137$	−6.57055	+	6.57055i	−0.561360	+	0.561360i	0.368334	+	0.929694i	$0.379928\pi$
$138$	5.61406	+	4.04230i	0.477901	+	0.344103i
$139$			2.42143i			0.205383i	0.994713	+	0.102692i	$0.0327455\pi$
$139$			2.42143i			0.205383i	−0.994713	+	0.102692i	$0.967254\pi$
$140$	−2.32886	+	4.48586i	−0.196825	+	0.379124i
$141$	−0.760220	−	0.223221i	−0.0640221	−	0.0187986i
$142$	0.404175	−	5.65110i	0.0339176	−	0.474230i
$143$	−1.98532	−	0.431881i	−0.166021	−	0.0361157i
$144$	0.694702	+	0.601963i	0.0578919	+	0.0501636i
$145$	−4.75619	+	3.19931i	−0.394980	+	0.265689i
$146$	−0.272560	+	0.0800309i	−0.0225573	+	0.00662341i
$147$	−0.579732	−	2.66499i	−0.0478155	−	0.219804i
$148$	1.54122	−	2.05883i	0.126688	−	0.169235i
$149$	−4.65417	−	10.1912i	−0.381285	−	0.834897i	−0.998830	−	0.0483615i	$-0.984600\pi$
$149$	−4.65417	−	10.1912i	−0.381285	−	0.834897i	0.617545	−	0.786535i	$-0.288127\pi$
$150$	6.82913	−	2.31999i	0.557596	−	0.189426i
$151$	−0.892666	−	6.20863i	−0.0726441	−	0.505251i	−0.993363	−	0.115024i	$-0.963306\pi$
$151$	−0.892666	−	6.20863i	−0.0726441	−	0.505251i	0.920719	−	0.390227i	$-0.127604\pi$
$152$	−7.32134	+	1.59266i	−0.593839	+	0.129182i
$153$	6.54184	+	3.57211i	0.528876	+	0.288788i
$154$	1.16922	+	0.168108i	0.0942184	+	0.0135466i
$155$	−0.0444608	−	2.12254i	−0.00357118	−	0.170487i
$156$	4.71794	−	3.03204i	0.377738	−	0.242757i
$157$	14.7729	+	1.05658i	1.17900	+	0.0843241i	0.647049	−	0.762448i	$-0.276003\pi$
$157$	14.7729	+	1.05658i	1.17900	+	0.0843241i	0.531955	+	0.846772i	$0.321457\pi$
$158$	−1.78424	−	3.26760i	−0.141947	−	0.259956i
$159$	5.48343	−	12.0070i	0.434864	−	0.952220i
$160$	−2.23322	−	0.112775i	−0.176552	−	0.00891565i
$161$	8.05949	−	7.24972i	0.635177	−	0.571358i
$162$	−3.81651	−	3.81651i	−0.299853	−	0.299853i
$163$	−3.39174	−	9.09361i	−0.265662	−	0.712266i	−0.999459	−	0.0328977i	$-0.989526\pi$
$163$	−3.39174	−	9.09361i	−0.265662	−	0.712266i	0.733797	−	0.679369i	$-0.237746\pi$
$164$	−1.74071	+	5.92832i	−0.135927	+	0.462924i
$165$	−1.03819	−	1.32795i	−0.0808226	−	0.103381i
$166$	3.73024	+	5.80437i	0.289523	+	0.450506i
$167$	−7.22125	+	0.516474i	−0.558797	+	0.0399660i	−0.347882	−	0.937538i	$-0.613099\pi$
$167$	−7.22125	+	0.516474i	−0.558797	+	0.0399660i	−0.210915	+	0.977504i	$0.567644\pi$
$168$	−2.61022	+	1.95399i	−0.201383	+	0.150753i
$169$	0.596038	+	2.02992i	0.0458490	+	0.156147i
$170$	−17.8888	+	2.95563i	−1.37200	+	0.226687i
$171$	−6.81724	+	0.980170i	−0.521327	+	0.0749555i
$172$	−9.46519	−	3.53033i	−0.721714	−	0.269185i
$173$	12.7219	+	4.74501i	0.967226	+	0.360757i	0.782927	−	0.622114i	$-0.213726\pi$
$173$	12.7219	+	4.74501i	0.967226	+	0.360757i	0.184299	+	0.982870i	$0.440999\pi$
$174$	−3.66015	+	0.526250i	−0.277475	+	0.0398949i
$175$	−1.27763	−	11.2294i	−0.0965795	−	0.848865i
$176$	0.147230	+	0.501419i	0.0110979	+	0.0377959i
$177$	−8.81711	+	6.60040i	−0.662734	+	0.496117i
$178$	−9.43521	+	0.674820i	−0.707199	+	0.0505799i
$179$	11.1520	+	17.3528i	0.833537	+	1.29701i	0.952632	+	0.304126i	$0.0983644\pi$
$179$	11.1520	+	17.3528i	0.833537	+	1.29701i	−0.119095	+	0.992883i	$0.537999\pi$
$180$	−2.04020	−	0.249848i	−0.152068	−	0.0186226i
$181$	5.23949	−	17.8441i	0.389448	−	1.32634i	−0.498697	−	0.866777i	$-0.666188\pi$
$181$	5.23949	−	17.8441i	0.389448	−	1.32634i	0.888145	−	0.459563i	$-0.151994\pi$
$182$	−3.07112	−	8.23398i	−0.227646	−	0.610343i
$183$	−12.4254	−	12.4254i	−0.918515	−	0.918515i
$184$	4.39865	+	1.91098i	0.324273	+	0.140879i
$185$	−0.290035	+	5.74340i	−0.0213238	+	0.422263i
$186$	0.568933	−	1.24579i	0.0417162	−	0.0913458i
$187$	2.03078	+	3.71910i	0.148505	+	0.271967i
$188$	−0.547869	−	0.0391844i	−0.0399575	−	0.00285781i
$189$	−10.7503	+	6.90880i	−0.781969	+	0.502541i
$190$	11.5961	−	12.0923i	0.841269	−	0.877267i
$191$	−0.895316	−	0.128727i	−0.0647828	−	0.00931436i	0.109847	−	0.993948i	$-0.464964\pi$
$191$	−0.895316	−	0.128727i	−0.0647828	−	0.00931436i	−0.174630	+	0.984634i	$0.555873\pi$
$192$	−1.26604	−	0.691312i	−0.0913688	−	0.0498911i
$193$	−4.52148	+	0.983588i	−0.325463	+	0.0708002i	−0.372328	−	0.928101i	$-0.621441\pi$
$193$	−4.52148	+	0.983588i	−0.325463	+	0.0708002i	0.0468652	+	0.998901i	$0.485077\pi$
$194$	−0.817185	−	5.68365i	−0.0586705	−	0.408062i
$195$	−4.96943	+	11.5137i	−0.355868	+	0.824515i
$196$	−0.785425	−	1.71984i	−0.0561018	−	0.122846i
$197$	−1.29603	+	1.73130i	−0.0923385	+	0.123350i	−0.844331	−	0.535822i	$-0.820002\pi$
$197$	−1.29603	+	1.73130i	−0.0923385	+	0.123350i	0.751993	+	0.659171i	$0.229093\pi$
$198$	0.102111	+	0.469396i	0.00725670	+	0.0333585i
$199$	−5.47200	+	1.60673i	−0.387900	+	0.113898i	−0.469867	−	0.882737i	$-0.655698\pi$
$199$	−5.47200	+	1.60673i	−0.387900	+	0.113898i	0.0819667	+	0.996635i	$0.473880\pi$
$200$	4.28420	−	2.57791i	0.302939	−	0.182286i
$201$	−10.3191	−	8.94151i	−0.727850	−	0.630686i
$202$	−2.16161	−	0.470229i	−0.152090	−	0.0330852i
$203$	−0.413369	+	5.77965i	−0.0290128	+	0.405652i
$204$	−11.2227	−	3.29529i	−0.785747	−	0.230716i
$205$	−4.16911	−	13.1717i	−0.291184	−	0.919952i
$206$		−	11.7973i		−	0.821958i
$207$	3.90773	+	2.04059i	0.271606	+	0.141831i
$208$	2.74915	−	2.74915i	0.190619	−	0.190619i
$209$	−3.56168	−	1.62657i	−0.246367	−	0.112512i
$210$	2.40427	−	6.88303i	0.165911	−	0.474974i
$211$	5.81511	+	6.71099i	0.400328	+	0.462004i	0.919744	−	0.392518i	$-0.128396\pi$
$211$	5.81511	+	6.71099i	0.400328	+	0.462004i	−0.519416	+	0.854522i	$0.673850\pi$
$212$	1.94513	−	8.94164i	0.133592	−	0.614114i
$213$	0.583018	+	8.15165i	0.0399477	+	0.558542i
$214$	1.94839	−	13.5514i	0.133189	−	0.926352i
$215$	21.9674	−	5.26285i	1.49817	−	0.358924i
$216$	−4.75598	−	3.05648i	−0.323603	−	0.207967i
$217$	−1.71803	−	1.28610i	−0.116628	−	0.0873063i
$218$	−3.05100	+	8.18004i	−0.206640	+	0.554022i
$219$	0.372734	−	0.170222i	0.0251871	−	0.0115025i
$220$	−0.898956	−	0.746569i	−0.0606076	−	0.0503336i
$221$	17.0437	−	26.5206i	1.14649	−	1.78397i
$222$	−1.77792	+	3.25601i	−0.119326	+	0.218529i
$223$	14.8999	+	19.9039i	0.997770	+	1.33287i	0.942432	+	0.334397i	$0.108533\pi$
$223$	14.8999	+	19.9039i	0.997770	+	1.33287i	0.0553382	+	0.998468i	$0.482376\pi$
$224$	−1.48023	+	1.70828i	−0.0989021	+	0.114139i
$225$	4.09715	−	2.08269i	0.273143	−	0.138846i
$226$	−14.0054	+	12.1357i	−0.931623	+	0.807256i
$227$	−9.21069	+	5.02942i	−0.611335	+	0.333814i	−0.754913	−	0.655825i	$-0.772321\pi$
$227$	−9.21069	+	5.02942i	−0.611335	+	0.333814i	0.143578	+	0.989639i	$0.454139\pi$
$228$	10.1265	−	3.77699i	0.670644	−	0.250137i
$229$	−5.11159			−0.337783			−0.168892	−	0.985635i	$-0.554019\pi$
$229$	−5.11159			−0.337783			−0.168892	+	0.985635i	$0.554019\pi$
$230$	−10.5461	+	1.94412i	−0.695390	+	0.128192i
$231$	−1.70393			−0.112110
$232$	−2.40185	+	0.895842i	−0.157689	+	0.0588149i
$233$	−1.19301	+	0.651431i	−0.0781564	+	0.0426766i	−0.517852	−	0.855470i	$-0.673268\pi$
$233$	−1.19301	+	0.651431i	−0.0781564	+	0.0426766i	0.439695	+	0.898147i	$0.355086\pi$
$234$	2.70092	−	2.34036i	0.176565	−	0.152994i
$235$	1.06540	−	0.611061i	0.0694993	−	0.0398612i
$236$	−5.00010	+	5.77042i	−0.325479	+	0.375623i
$237$	3.21835	+	4.29922i	0.209055	+	0.279264i
$238$	−8.78386	+	16.0864i	−0.569373	+	1.04273i
$239$	−4.25289	+	6.61762i	−0.275096	+	0.428058i	−0.951120	−	0.308822i	$-0.900065\pi$
$239$	−4.25289	+	6.61762i	−0.275096	+	0.428058i	0.676024	+	0.736880i	$0.263702\pi$
$240$	3.21176	−	0.297432i	0.207318	−	0.0191992i
$241$	−2.02792	+	0.926121i	−0.130630	+	0.0596567i	−0.479658	−	0.877456i	$-0.659239\pi$
$241$	−2.02792	+	0.926121i	−0.130630	+	0.0596567i	0.349028	+	0.937112i	$0.386512\pi$
$242$	3.74867	−	10.0506i	0.240974	−	0.646075i
$243$	−7.34471	−	5.49818i	−0.471163	−	0.352708i
$244$	−10.2480	−	6.58602i	−0.656064	−	0.421626i
$245$	3.60368	+	2.21070i	0.230231	+	0.141236i
$246$	1.26839	−	8.82185i	0.0808697	−	0.562461i
$247$	2.07813	+	29.0560i	0.132228	+	1.84879i
$248$	0.201817	−	0.927740i	0.0128154	−	0.0589116i
$249$	−6.51763	−	7.52175i	−0.413038	−	0.476671i
$250$	−4.73145	+	10.1298i	−0.299243	+	0.640667i
$251$	−4.16585	−	1.90248i	−0.262946	−	0.120083i	0.279580	−	0.960122i	$-0.409805\pi$
$251$	−4.16585	−	1.90248i	−0.262946	−	0.120083i	−0.542526	+	0.840039i	$0.682532\pi$
$252$	−1.46922	+	1.46922i	−0.0925521	+	0.0925521i
$253$	1.24172	+	2.17701i	0.0780662	+	0.136867i
$254$			12.0557i			0.756439i
$255$	24.9349	−	7.89241i	1.56149	−	0.494242i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	1.54866	−	21.6531i	0.0966028	−	1.35068i	−0.685745	−	0.727842i	$-0.740524\pi$
$257$	1.54866	−	21.6531i	0.0966028	−	1.35068i	0.782348	−	0.622842i	$-0.214022\pi$
$258$	14.2392	+	3.09755i	0.886494	+	0.192845i
$259$	4.39335	+	3.80686i	0.272989	+	0.236547i
$260$	−1.66964	+	8.53173i	−0.103547	+	0.529115i
$261$	−2.26095	+	0.663875i	−0.139949	+	0.0410929i
$262$	0.422040	+	1.94009i	0.0260737	+	0.119859i
$263$	−8.53121	+	11.3964i	−0.526057	+	0.702730i	−0.982340	−	0.187105i	$-0.940090\pi$
$263$	−8.53121	+	11.3964i	−0.526057	+	0.702730i	0.456283	+	0.889835i	$0.349180\pi$
$264$	−0.313151	−	0.685705i	−0.0192731	−	0.0422022i
$265$	7.55057	+	19.0177i	0.463828	+	1.16824i
$266$	−2.41025	−	16.7636i	−0.147782	−	1.02784i
$267$	13.3331	−	2.90045i	0.815975	−	0.177504i
$268$	−8.30778	−	4.53639i	−0.507478	−	0.277104i
$269$	19.9935	+	2.87463i	1.21902	+	0.175269i	0.721644	−	0.692264i	$-0.243387\pi$
$269$	19.9935	+	2.87463i	1.21902	+	0.175269i	0.497379	+	0.867533i	$0.334296\pi$
$270$	12.6387	−	0.264742i	0.769167	−	0.0161117i
$271$	4.56689	−	2.93496i	0.277419	−	0.178286i	−0.394532	−	0.918882i	$-0.629093\pi$
$271$	4.56689	−	2.93496i	0.277419	−	0.178286i	0.671950	+	0.740596i	$0.265457\pi$
$272$	−8.08789	−	0.578458i	−0.490401	−	0.0350741i
$273$	6.07530	+	11.1261i	0.367694	+	0.673381i
$274$	3.86010	−	8.45244i	0.233197	−	0.510631i
$275$	2.59964	+	0.263229i	0.156764	+	0.0158733i
$276$	−6.67273	−	1.82552i	−0.401651	−	0.109883i
$277$	−10.9975	−	10.9975i	−0.660775	−	0.660775i	0.294788	−	0.955563i	$-0.404751\pi$
$277$	−10.9975	−	10.9975i	−0.660775	−	0.660775i	−0.955563	+	0.294788i	$0.904751\pi$
$278$	−0.846205	−	2.26876i	−0.0507520	−	0.136071i
$279$	0.245881	−	0.837392i	0.0147205	−	0.0501334i
$280$	0.614379	−	5.01688i	0.0367162	−	0.299816i
$281$	−1.76092	−	2.74005i	−0.105048	−	0.163458i	0.784750	−	0.619812i	$-0.212791\pi$
$281$	−1.76092	−	2.74005i	−0.105048	−	0.163458i	−0.889798	+	0.456355i	$0.849155\pi$
$282$	0.790296	−	0.0565231i	0.0470614	−	0.00336590i
$283$	2.26620	−	1.69645i	0.134711	−	0.100844i	−0.529797	−	0.848124i	$-0.677732\pi$
$283$	2.26620	−	1.69645i	0.134711	−	0.100844i	0.664508	+	0.747281i	$0.268641\pi$
$284$	1.59617	+	5.43604i	0.0947150	+	0.322570i
$285$	−14.0746	+	19.6460i	−0.833707	+	1.16373i
$286$	2.01108	−	0.289149i	0.118917	−	0.0170977i
$287$	−13.0854	−	4.88060i	−0.772407	−	0.288093i
$288$	−0.861266	−	0.321235i	−0.0507506	−	0.0189290i
$289$	−48.2525	+	6.93766i	−2.83838	+	0.408097i
$290$	3.33827	−	4.65972i	0.196030	−	0.273628i
$291$	2.33357	+	7.94740i	0.136796	+	0.465885i
$292$	0.227407	−	0.170235i	0.0133080	−	0.00996225i
$293$	−24.8220	+	1.77530i	−1.45012	+	0.103714i	−0.774049	−	0.633125i	$-0.781772\pi$
$293$	−24.8220	+	1.77530i	−1.45012	+	0.103714i	−0.676068	+	0.736840i	$0.736317\pi$
$294$	1.47450	+	2.29436i	0.0859944	+	0.133810i
$295$	2.07532	−	16.9466i	0.120830	−	0.986669i
$296$	−0.724560	+	2.46762i	−0.0421142	+	0.143428i
$297$	−1.03246	−	2.76814i	−0.0599095	−	0.160624i
$298$	7.92219	+	7.92219i	0.458920	+	0.458920i
$299$	9.78782	−	15.8700i	0.566044	−	0.917787i
$300$	−5.58780	+	4.56025i	−0.322612	+	0.263286i
$301$	9.48585	−	20.7711i	0.546755	−	1.19723i
$302$	3.00608	+	5.50522i	0.172980	+	0.316790i
$303$	3.18289	+	0.227645i	0.182852	+	0.0130779i
$304$	6.30315	−	4.05079i	0.361510	−	0.232329i
$305$	27.2335	−	0.570460i	1.55939	−	0.0326644i
$306$	−7.37770	−	1.06075i	−0.421755	−	0.0606392i
$307$	−15.7114	−	8.57906i	−0.896695	−	0.489633i	−0.0363469	−	0.999339i	$-0.511572\pi$
$307$	−15.7114	−	8.57906i	−0.896695	−	0.489633i	−0.860348	+	0.509707i	$0.829754\pi$
$308$	−1.15425	+	0.251091i	−0.0657694	+	0.0143073i
$309$	2.42184	+	16.8443i	0.137774	+	0.958239i
$310$	0.783410	+	1.97318i	0.0444947	+	0.112069i
$311$	8.86296	+	19.4072i	0.502572	+	1.10048i	0.975625	+	0.219446i	$0.0704249\pi$
$311$	8.86296	+	19.4072i	0.502572	+	1.10048i	−0.473052	+	0.881034i	$0.656848\pi$
$312$	−3.36089	+	4.48962i	−0.190273	+	0.254175i
$313$	3.20777	+	14.7459i	0.181314	+	0.833486i	0.974479	+	0.224479i	$0.0720681\pi$
$313$	3.20777	+	14.7459i	0.181314	+	0.833486i	−0.793165	+	0.609007i	$0.791568\pi$
$314$	−14.2107	+	4.17263i	−0.801955	+	0.235475i
$315$	0.892302	−	4.55959i	0.0502755	−	0.256904i
$316$	2.81366	+	2.43805i	0.158280	+	0.137151i
$317$	−3.89002	−	0.846221i	−0.218485	−	0.0475285i	0.101990	−	0.994785i	$-0.467479\pi$
$317$	−3.89002	−	0.846221i	−0.218485	−	0.0475285i	−0.320475	+	0.947257i	$0.603843\pi$
$318$	−0.941669	+	13.1662i	−0.0528062	+	0.738327i
$319$	−1.28537	−	0.377420i	−0.0719671	−	0.0211314i
$320$	2.13183	−	0.674767i	0.119173	−	0.0377206i
$321$			19.7487i			1.10227i
$322$	−5.01782	+	9.60913i	−0.279632	+	0.535496i
$323$	42.9595	−	42.9595i	2.39033	−	2.39033i
$324$	4.90961	+	2.24214i	0.272756	+	0.124564i
$325$	−7.55013	−	17.9133i	−0.418806	−	0.993651i
$326$	6.35578	+	7.33496i	0.352014	+	0.406246i
$327$	2.67697	−	12.3059i	0.148037	−	0.680515i
$328$	−0.440776	−	6.16286i	−0.0243378	−	0.340287i
$329$	0.176692	−	1.22892i	0.00974132	−	0.0677524i
$330$	1.43680	+	0.881412i	0.0790931	+	0.0485201i
$331$	10.9997	+	7.06911i	0.604601	+	0.388553i	0.806829	−	0.590785i	$-0.201182\pi$
$331$	10.9997	+	7.06911i	0.604601	+	0.388553i	−0.202228	+	0.979338i	$0.564818\pi$
$332$	−5.52347	−	4.13482i	−0.303140	−	0.226927i
$333$	−0.826153	+	2.21500i	−0.0452729	+	0.121381i
$334$	6.58546	−	3.00748i	0.360340	−	0.164562i
$335$	21.0756	−	1.95175i	1.15148	−	0.106636i
$336$	1.76280	−	2.74297i	0.0961685	−	0.149641i
$337$	−13.9478	+	25.5435i	−0.759784	+	1.39144i	0.155172	+	0.987887i	$0.450407\pi$
$337$	−13.9478	+	25.5435i	−0.759784	+	1.39144i	−0.914956	+	0.403553i	$0.867775\pi$
$338$	−1.26784	−	1.69364i	−0.0689614	−	0.0921217i
$339$	17.5056	−	20.2026i	0.950776	−	1.09725i
$340$	15.7280	−	9.02076i	0.852969	−	0.489219i
$341$	0.374976	−	0.324918i	0.0203061	−	0.0175953i
$342$	6.04487	−	3.30075i	0.326869	−	0.178484i
$343$	18.8292	−	7.02295i	1.01668	−	0.379203i
$344$	10.1021			0.544671
$345$	14.6587	−	4.94082i	0.789198	−	0.266005i
$346$	−13.5780			−0.729956
$347$	−23.9421	+	8.92993i	−1.28528	+	0.479384i	−0.896948	−	0.442137i	$-0.854221\pi$
$347$	−23.9421	+	8.92993i	−1.28528	+	0.479384i	−0.388330	+	0.921521i	$0.626948\pi$
$348$	3.24547	−	1.77216i	0.173975	−	0.0949977i
$349$	−14.5948	+	12.6465i	−0.781241	+	0.676949i	−0.951225	−	0.308497i	$-0.900174\pi$
$349$	−14.5948	+	12.6465i	−0.781241	+	0.676949i	0.169984	+	0.985447i	$0.445628\pi$
$350$	5.12136	+	10.0749i	0.273748	+	0.538528i
$351$	−14.3938	+	16.6113i	−0.768283	+	0.886645i
$352$	−0.313175	−	0.418353i	−0.0166923	−	0.0222983i
$353$	−3.69979	+	6.77565i	−0.196920	+	0.360632i	−0.957417	−	0.288710i	$-0.906774\pi$
$353$	−3.69979	+	6.77565i	−0.196920	+	0.360632i	0.760497	+	0.649342i	$0.224955\pi$
$354$	5.95458	−	9.26551i	0.316482	−	0.492456i
$355$	−9.74587	−	8.09379i	−0.517257	−	0.429574i
$356$	8.60449	−	3.92954i	0.456037	−	0.208265i
$357$	9.23931	−	24.7716i	0.488996	−	1.31105i
$358$	−16.5130	−	12.3615i	−0.872740	−	0.653325i
$359$	−23.5302	−	15.1219i	−1.24187	−	0.798104i	−0.256177	−	0.966630i	$-0.582463\pi$
$359$	−23.5302	−	15.1219i	−1.24187	−	0.798104i	−0.985697	+	0.168525i	$0.946099\pi$
$360$	1.99888	−	0.478883i	0.105350	−	0.0252393i
$361$	−5.28537	+	36.7605i	−0.278177	+	1.93477i
$362$	1.32672	+	18.5500i	0.0697310	+	0.974967i
$363$	−3.28912	+	15.1198i	−0.172634	+	0.793585i
$364$	5.75496	+	6.64158i	0.301642	+	0.348114i
$365$	−0.209465	+	0.599662i	−0.0109639	+	0.0313878i
$366$	15.9843	+	7.29977i	0.835511	+	0.381565i
$367$	3.64981	−	3.64981i	0.190519	−	0.190519i	−0.605401	−	0.795920i	$-0.706987\pi$
$367$	3.64981	−	3.64981i	0.190519	−	0.190519i	0.795920	+	0.605401i	$0.206987\pi$
$368$	−4.78914	−	0.253318i	−0.249651	−	0.0132051i
$369$		−	5.67951i		−	0.295664i
$370$	−1.73536	−	5.48263i	−0.0902173	−	0.285029i
$371$	19.8463	+	5.82740i	1.03037	+	0.302544i
$372$	−0.0977029	+	1.36606i	−0.00506566	+	0.0708272i
$373$	−27.1858	−	5.91391i	−1.40763	−	0.306211i	−0.556359	−	0.830942i	$-0.687802\pi$
$373$	−27.1858	−	5.91391i	−1.40763	−	0.306211i	−0.851268	+	0.524731i	$0.824166\pi$
$374$	−3.20243	−	2.77492i	−0.165594	−	0.143488i
$375$	4.67607	−	15.4348i	0.241471	−	0.797047i
$376$	0.527019	−	0.154747i	0.0271790	−	0.00798046i
$377$	2.11853	+	9.73871i	0.109110	+	0.501569i
$378$	7.65811	−	10.2300i	0.393891	−	0.526176i
$379$	7.65304	+	16.7578i	0.393110	+	0.860792i	0.997923	+	0.0644236i	$0.0205209\pi$
$379$	7.65304	+	16.7578i	0.393110	+	0.860792i	−0.604812	+	0.796368i	$0.706752\pi$
$380$	−6.63913	+	15.3823i	−0.340580	+	0.789095i
$381$	−2.47488	−	17.2132i	−0.126792	−	0.881857i
$382$	0.883852	−	0.192270i	0.0452218	−	0.00983740i
$383$	17.5897	+	9.60472i	0.898793	+	0.490778i	0.861056	−	0.508509i	$-0.169803\pi$
$383$	17.5897	+	9.60472i	0.898793	+	0.490778i	0.0377368	+	0.999288i	$0.487985\pi$
$384$	1.42781	+	0.205288i	0.0728625	+	0.0104760i
$385$	1.82819	−	1.90641i	0.0931730	−	0.0971599i
$386$	3.89267	−	2.50167i	0.198132	−	0.127332i
$387$	9.26245	+	0.662464i	0.470837	+	0.0336749i
$388$	2.75189	+	5.03972i	0.139706	+	0.255853i
$389$	−11.1667	+	24.4516i	−0.566172	+	1.23974i	0.382639	+	0.923898i	$0.375015\pi$
$389$	−11.1667	+	24.4516i	−0.566172	+	1.23974i	−0.948811	+	0.315845i	$0.897712\pi$
$390$	0.632468	−	12.5244i	0.0320263	−	0.634199i
$391$	−38.3821	+	6.24744i	−1.94107	+	0.315947i
$392$	1.33693	+	1.33693i	0.0675249	+	0.0675249i
$393$	−1.00087	−	2.68343i	−0.0504871	−	0.135361i
$394$	0.609291	−	2.07505i	0.0306956	−	0.104540i
$395$	−8.26315	−	1.01193i	−0.415764	−	0.0509155i
$396$	−0.259710	−	0.404116i	−0.0130509	−	0.0203076i
$397$	24.0320	−	1.71881i	1.20613	−	0.0862644i	0.546243	−	0.837627i	$-0.316057\pi$
$397$	24.0320	−	1.71881i	1.20613	−	0.0862644i	0.659890	+	0.751362i	$0.270603\pi$
$398$	4.56550	−	3.41769i	0.228848	−	0.171313i
$399$	6.88274	+	23.4405i	0.344568	+	1.17349i
$400$	−3.11319	+	3.91255i	−0.155660	+	0.195627i
$401$	0.812413	−	0.116807i	0.0405700	−	0.00583308i	−0.122000	−	0.992530i	$-0.538931\pi$
$401$	0.812413	−	0.116807i	0.0405700	−	0.00583308i	0.162570	+	0.986697i	$0.448022\pi$
$402$	12.7932	+	4.77161i	0.638066	+	0.237986i
$403$	−3.45856	−	1.28998i	−0.172283	−	0.0642583i
$404$	2.18965	−	0.314824i	0.108939	−	0.0156631i
$405$	−11.9074	+	1.96738i	−0.591685	+	0.0977599i
$406$	−1.63247	−	5.55970i	−0.0810184	−	0.275923i
$407$	−1.07592	+	0.805423i	−0.0533313	+	0.0399233i
$408$	11.6667	−	0.834419i	0.577588	−	0.0413099i
$409$	−12.1007	−	18.8290i	−0.598339	−	0.931034i	−0.999885	−	0.0151945i	$-0.995163\pi$
$409$	−12.1007	−	18.8290i	−0.598339	−	0.931034i	0.401546	−	0.915839i	$-0.368473\pi$
$410$	8.50929	+	10.8843i	0.420244	+	0.537536i
$411$	−3.77630	+	12.8609i	−0.186271	+	0.634381i
$412$	4.12274	+	11.0535i	0.203113	+	0.544567i
$413$	−12.2038	−	12.2038i	−0.600510	−	0.600510i
$414$	−4.37446	−	0.546318i	−0.214993	−	0.0268501i
$415$	15.4085	+	0.778110i	0.756373	+	0.0381959i
$416$	−1.61508	+	3.53654i	−0.0791860	+	0.173393i
$417$	1.67397	+	3.06564i	0.0819745	+	0.150125i
$418$	3.90554	+	0.279330i	0.191026	+	0.0136625i
$419$	−10.6108	+	6.81916i	−0.518373	+	0.333138i	−0.773528	−	0.633762i	$-0.781510\pi$
$419$	−10.6108	+	6.81916i	−0.518373	+	0.333138i	0.255155	+	0.966900i	$0.417873\pi$
$420$	0.152688	+	7.28926i	0.00745040	+	0.355679i
$421$	−5.90050	−	0.848364i	−0.287573	−	0.0413467i	−0.00298117	−	0.999996i	$-0.500949\pi$
$421$	−5.90050	−	0.848364i	−0.287573	−	0.0413467i	−0.284592	+	0.958649i	$0.591858\pi$
$422$	−7.79371	−	4.25569i	−0.379392	−	0.207164i
$423$	0.493362	−	0.107324i	0.0239881	−	0.00521828i
$424$	1.30229	+	9.05762i	0.0632447	+	0.439877i
$425$	−17.9230	+	36.3660i	−0.869391	+	1.76401i
$426$	−3.39497	−	7.43395i	−0.164487	−	0.360176i
$427$	16.5015	−	22.0434i	0.798562	−	1.06675i
$428$	2.91017	+	13.3778i	0.140668	+	0.646642i
$429$	−2.81207	+	0.825698i	−0.135768	+	0.0398651i
$430$	−18.7432	+	12.6079i	−0.903877	+	0.608005i
$431$	3.38073	+	2.92942i	0.162844	+	0.141105i	0.732471	−	0.680798i	$-0.238367\pi$
$431$	3.38073	+	2.92942i	0.162844	+	0.141105i	−0.569627	+	0.821903i	$0.692912\pi$
$432$	5.52424	+	1.20172i	0.265785	+	0.0578180i
$433$	2.88581	−	40.3488i	0.138683	−	1.93904i	−0.165052	−	0.986285i	$-0.552779\pi$
$433$	2.88581	−	40.3488i	0.138683	−	1.93904i	0.303735	−	0.952757i	$-0.401766\pi$
$434$	2.05915	+	0.604622i	0.0988426	+	0.0290228i
$435$	−3.80982	+	7.33848i	−0.182667	+	0.351853i
$436$		−	8.73050i		−	0.418115i
$437$	24.9327	−	25.8756i	1.19269	−	1.23780i
$438$	−0.289747	+	0.289747i	−0.0138446	+	0.0138446i
$439$	−25.1179	−	11.4710i	−1.19881	−	0.547480i	−0.286939	−	0.957949i	$-0.592638\pi$
$439$	−25.1179	−	11.4710i	−1.19881	−	0.547480i	−0.911875	+	0.410469i	$0.865365\pi$
$440$	1.10318	+	0.385344i	0.0525918	+	0.0183706i
$441$	1.13813	+	1.31347i	0.0541967	+	0.0625463i
$442$	−6.70114	+	30.8046i	−0.318741	+	1.46523i
$443$	1.87487	+	26.2141i	0.0890778	+	1.24547i	0.823713	+	0.567008i	$0.191899\pi$
$443$	1.87487	+	26.2141i	0.0890778	+	1.24547i	−0.734635	+	0.678463i	$0.762646\pi$
$444$	0.527959	−	3.67203i	0.0250558	−	0.174267i
$445$	−11.0603	+	18.0295i	−0.524309	+	0.854680i
$446$	−20.9162	−	13.4420i	−0.990409	−	0.636497i
$447$	−12.9377	−	9.68503i	−0.611932	−	0.458086i
$448$	0.789921	−	2.11786i	0.0373202	−	0.100059i
$449$	9.85810	−	4.50204i	0.465232	−	0.212465i	−0.168986	−	0.985618i	$-0.554049\pi$
$449$	9.85810	−	4.50204i	0.465232	−	0.212465i	0.634218	+	0.773154i	$0.281322\pi$
$450$	−3.11100	+	3.38319i	−0.146654	+	0.159485i
$451$	1.74565	−	2.71629i	0.0821995	−	0.127905i
$452$	8.88132	−	16.2649i	0.417742	−	0.765038i
$453$	−5.42225	−	7.24328i	−0.254760	−	0.340319i
$454$	6.87236	−	7.93112i	0.322536	−	0.372226i
$455$	−18.9665	−	5.14017i	−0.889165	−	0.240975i
$456$	−8.16811	+	7.07770i	−0.382507	+	0.331444i
$457$	−0.666602	+	0.363992i	−0.0311823	+	0.0170269i	−0.494765	−	0.869027i	$-0.664746\pi$
$457$	−0.666602	+	0.363992i	−0.0311823	+	0.0170269i	0.463582	+	0.886054i	$0.346564\pi$
$458$	4.78930	−	1.78632i	0.223789	−	0.0834691i
$459$	45.8412			2.13968
$460$	9.20177	−	5.50703i	0.429035	−	0.256767i
$461$	−9.91988			−0.462015			−0.231007	−	0.972952i	$-0.574202\pi$
$461$	−9.91988			−0.462015			−0.231007	+	0.972952i	$0.574202\pi$
$462$	1.59650	−	0.595463i	0.0742758	−	0.0277035i
$463$	−31.0508	+	16.9550i	−1.44305	+	0.787967i	−0.994394	−	0.105736i	$-0.966280\pi$
$463$	−31.0508	+	16.9550i	−1.44305	+	0.787967i	−0.448659	+	0.893703i	$0.648098\pi$
$464$	1.93734	−	1.67872i	0.0899389	−	0.0779325i
$465$	−1.52363	−	2.65649i	−0.0706565	−	0.123192i
$466$	0.890135	−	1.02727i	0.0412347	−	0.0475874i
$467$	−10.2706	−	13.7199i	−0.475265	−	0.634880i	0.497281	−	0.867589i	$-0.334332\pi$
$467$	−10.2706	−	13.7199i	−0.475265	−	0.634880i	−0.972546	+	0.232710i	$0.925241\pi$
$468$	−1.71275	+	3.13667i	−0.0791721	+	0.144993i
$469$	11.5675	−	17.9994i	0.534137	−	0.831133i
$470$	−0.784686	+	0.944854i	−0.0361949	+	0.0435828i
$471$	19.4335	−	8.87500i	0.895450	−	0.408938i
$472$	2.66829	−	7.15395i	0.122818	−	0.329287i
$473$	4.22625	+	3.16373i	0.194323	+	0.145469i
$474$	−4.51786	−	2.90345i	−0.207512	−	0.133360i
$475$	−6.87965	−	36.8257i	−0.315660	−	1.68968i
$476$	2.60840	−	18.1418i	0.119556	−	0.831529i
$477$	0.600076	+	8.39016i	0.0274756	+	0.384159i
$478$	1.67212	−	7.68661i	0.0764810	−	0.351577i
$479$	25.0071	+	28.8598i	1.14260	+	1.31864i	0.940703	+	0.339230i	$0.110166\pi$
$479$	25.0071	+	28.8598i	1.14260	+	1.31864i	0.201901	+	0.979406i	$0.435288\pi$
$480$	−2.90532	+	1.40107i	−0.132609	+	0.0639500i
$481$	9.09527	+	4.15367i	0.414709	+	0.189391i
$482$	1.57642	−	1.57642i	0.0718038	−	0.0718038i
$483$	5.19185	−	14.7501i	0.236237	−	0.671152i
$484$			10.7269i			0.487586i
$485$	−11.3955	−	5.91607i	−0.517445	−	0.268635i
$486$	8.80304	+	2.58481i	0.399314	+	0.117249i
$487$	1.15010	−	16.0805i	0.0521160	−	0.728676i	−0.902472	−	0.430748i	$-0.858250\pi$
$487$	1.15010	−	16.0805i	0.0521160	−	0.728676i	0.954588	−	0.297928i	$-0.0962957\pi$
$488$	11.9035	+	2.58944i	0.538845	+	0.117219i
$489$	−10.5806	−	9.16815i	−0.478472	−	0.414598i
$490$	−4.14903	−	0.811956i	−0.187434	−	0.0366804i
$491$	21.8346	−	6.41123i	0.985383	−	0.289335i	0.250938	−	0.968003i	$-0.419261\pi$
$491$	21.8346	−	6.41123i	0.985383	−	0.289335i	0.734445	+	0.678668i	$0.237443\pi$
$492$	1.89450	+	8.70889i	0.0854108	+	0.392627i
$493$	12.4566	−	16.6401i	0.561018	−	0.749432i
$494$	−12.1011	−	26.4978i	−0.544455	−	1.19219i
$495$	0.986211	+	0.425657i	0.0443269	+	0.0191319i
$496$	0.135119	+	0.939774i	0.00606703	+	0.0421971i
$497$	−12.5136	+	2.72216i	−0.561311	+	0.122106i
$498$	8.73527	+	4.76982i	0.391437	+	0.213741i
$499$	−12.8975	−	1.85438i	−0.577373	−	0.0830137i	−0.152559	−	0.988294i	$-0.548751\pi$
$499$	−12.8975	−	1.85438i	−0.577373	−	0.0830137i	−0.424814	+	0.905281i	$0.639660\pi$
$500$	0.893116	−	11.1446i	0.0399414	−	0.498402i
$501$	−8.78537	+	5.64602i	−0.392501	+	0.252245i
$502$	4.56804	+	0.326713i	0.203882	+	0.0145819i
$503$	−8.09089	−	14.8174i	−0.360755	−	0.660673i	0.632763	−	0.774345i	$-0.281921\pi$
$503$	−8.09089	−	14.8174i	−0.360755	−	0.660673i	−0.993518	+	0.113672i	$0.963739\pi$
$504$	0.863145	−	1.89002i	0.0384475	−	0.0841884i
$505$	−3.66969	+	3.31688i	−0.163299	+	0.147599i
$506$	−1.92421	−	1.60581i	−0.0855418	−	0.0713871i
$507$	2.15792	+	2.15792i	0.0958364	+	0.0958364i
$508$	−4.21302	−	11.2955i	−0.186923	−	0.501159i
$509$	1.88345	−	6.41444i	0.0834825	−	0.284315i	−0.907162	−	0.420781i	$-0.861756\pi$
$509$	1.88345	−	6.41444i	0.0834825	−	0.284315i	0.990645	+	0.136466i	$0.0435743\pi$
$510$	−20.6047	+	16.1087i	−0.912390	+	0.713304i
$511$	0.347145	+	0.540168i	0.0153568	+	0.0238956i
$512$	0.997452	−	0.0713392i	0.0440816	−	0.00315278i
$513$	−33.9099	+	25.3847i	−1.49716	+	1.12076i
$514$	6.11597	+	20.8291i	0.269764	+	0.918731i
$515$	−21.4444	−	15.3630i	−0.944953	−	0.676974i
$516$	−14.4239	+	2.07384i	−0.634977	+	0.0912959i
$517$	0.268943	+	0.100310i	0.0118281	+	0.00441165i
$518$	−5.44671	−	2.03152i	−0.239315	−	0.0892597i
$519$	19.3867	−	2.78739i	0.850983	−	0.122353i
$520$	−1.41716	−	8.57728i	−0.0621467	−	0.376139i
$521$	−7.22430	−	24.6037i	−0.316502	−	1.07791i	−0.952074	−	0.305866i	$-0.901054\pi$
$521$	−7.22430	−	24.6037i	−0.316502	−	1.07791i	0.635572	−	0.772042i	$-0.280764\pi$
$522$	1.88640	−	1.41214i	0.0825654	−	0.0618077i
$523$	−24.8642	+	1.77832i	−1.08724	+	0.0777607i	−0.603431	−	0.797415i	$-0.706200\pi$
$523$	−24.8642	+	1.77832i	−1.08724	+	0.0777607i	−0.483805	+	0.875176i	$0.660746\pi$
$524$	−1.07342	−	1.67028i	−0.0468926	−	0.0729663i
$525$	−9.38057	−	13.3337i	−0.409402	−	0.581931i
$526$	4.01069	−	13.6592i	0.174875	−	0.595568i
$527$	2.69037	+	7.21317i	0.117194	+	0.314211i
$528$	0.533036	+	0.533036i	0.0231974	+	0.0231974i
$529$	−22.6288	+	4.11563i	−0.983860	+	0.178940i
$530$	−13.7205	−	15.1799i	−0.595980	−	0.659374i
$531$	2.91563	−	6.38434i	0.126528	−	0.277057i
$532$	8.11657	+	14.8644i	0.351898	+	0.644453i
$533$	−23.9605	−	1.71369i	−1.03784	−	0.0742280i
$534$	−11.4789	+	7.37703i	−0.496740	+	0.319235i
$535$	−22.0955	−	21.1888i	−0.955272	−	0.916073i
$536$	9.36928	+	1.34710i	0.404691	+	0.0581858i
$537$	26.1151	+	14.2599i	1.12695	+	0.615360i
$538$	−19.7375	+	4.29362i	−0.850942	+	0.185111i
$539$	0.140615	+	0.977998i	0.00605671	+	0.0421253i
$540$	−11.7493	+	4.66482i	−0.505610	+	0.200742i
$541$	13.6799	+	29.9547i	0.588143	+	1.28785i	0.936558	+	0.350514i	$0.113993\pi$
$541$	13.6799	+	29.9547i	0.588143	+	1.28785i	−0.348414	+	0.937341i	$0.613280\pi$
$542$	−3.25328	+	4.34587i	−0.139740	+	0.186671i
$543$	−5.70240	−	26.2135i	−0.244713	−	1.12493i
$544$	7.78010	−	2.28444i	0.333569	−	0.0979447i
$545$	10.8960	+	16.1983i	0.466734	+	0.693859i
$546$	−9.58042	−	8.30148i	−0.410004	−	0.355270i
$547$	−2.39151	−	0.520241i	−0.102254	−	0.0222439i	0.161147	−	0.986930i	$-0.448481\pi$
$547$	−2.39151	−	0.520241i	−0.102254	−	0.0222439i	−0.263401	+	0.964686i	$0.584844\pi$
$548$	−0.662895	+	9.26848i	−0.0283175	+	0.395930i
$549$	10.7443	+	3.15480i	0.458554	+	0.134644i
$550$	−2.52772	+	0.661850i	−0.107782	+	0.0282214i
$551$			19.2070i			0.818245i
$552$	6.88997	−	0.621462i	0.293257	−	0.0264512i
$553$	−5.95057	+	5.95057i	−0.253044	+	0.253044i
$554$	14.1473	+	6.46086i	0.601062	+	0.274496i
$555$	3.60328	+	7.47190i	0.152951	+	0.317164i
$556$	1.58570	+	1.83000i	0.0672488	+	0.0776092i
$557$	9.63947	−	44.3119i	0.408437	−	1.87756i	−0.0669113	−	0.997759i	$-0.521314\pi$
$557$	9.63947	−	44.3119i	0.408437	−	1.87756i	0.475349	−	0.879797i	$-0.342322\pi$
$558$	0.0622609	+	0.870521i	0.00263571	+	0.0368521i
$559$	5.58954	−	38.8761i	0.236412	−	1.64428i
$560$	1.17758	+	4.91526i	0.0497617	+	0.207708i
$561$	5.14211	+	3.30464i	0.217100	+	0.139522i
$562$	2.60744	+	1.95191i	0.109988	+	0.0823363i
$563$	0.197231	−	0.528796i	0.00831228	−	0.0222861i	−0.932727	−	0.360583i	$-0.882578\pi$
$563$	0.197231	−	0.528796i	0.00831228	−	0.0222861i	0.941040	+	0.338296i	$0.109851\pi$
$564$	−0.720715	+	0.329139i	−0.0303476	+	0.0138593i
$565$	3.82113	+	41.2617i	0.160756	+	1.73589i
$566$	−1.53046	+	2.38144i	−0.0643301	+	0.100100i
$567$	−5.84687	+	10.7077i	−0.245545	+	0.449683i
$568$	−3.39523	−	4.53549i	−0.142461	−	0.190305i
$569$	−3.05389	+	3.52438i	−0.128026	+	0.147750i	−0.816143	−	0.577850i	$-0.803892\pi$
$569$	−3.05389	+	3.52438i	−0.128026	+	0.147750i	0.688117	+	0.725599i	$0.258437\pi$
$570$	6.32161	−	23.3259i	0.264783	−	0.977013i
$571$	11.4212	−	9.89653i	0.477963	−	0.414157i	−0.382276	−	0.924048i	$-0.624860\pi$
$571$	11.4212	−	9.89653i	0.477963	−	0.414157i	0.860239	+	0.509891i	$0.170314\pi$
$572$	−1.78323	+	0.973717i	−0.0745606	+	0.0407132i
$573$	−1.22250	+	0.455969i	−0.0510707	+	0.0190484i
$574$	13.9660			0.582928
$575$	−10.1997	+	21.7018i	−0.425357	+	0.905026i
$576$	0.919223			0.0383010
$577$	24.9217	−	9.29531i	1.03750	−	0.386969i	0.227738	−	0.973722i	$-0.426867\pi$
$577$	24.9217	−	9.29531i	1.03750	−	0.386969i	0.809765	+	0.586754i	$0.199594\pi$
$578$	42.7857	−	23.3627i	1.77965	−	0.971762i
$579$	−5.04442	+	4.37102i	−0.209639	+	0.181653i
$580$	−1.49938	+	5.53252i	−0.0622585	+	0.229726i
$581$	10.2131	−	11.7865i	0.423711	−	0.488988i
$582$	−4.96377	−	6.63081i	−0.205755	−	0.274856i
$583$	−2.29180	+	4.19712i	−0.0949167	+	0.173827i
$584$	−0.153578	+	0.238972i	−0.00635511	+	0.00988875i
$585$	−0.736900	−	7.95728i	−0.0304671	−	0.328993i
$586$	22.6366	−	10.3378i	0.935108	−	0.427049i
$587$	−10.1057	+	27.0946i	−0.417109	+	1.11831i	0.543256	+	0.839567i	$0.317191\pi$
$587$	−10.1057	+	27.0946i	−0.417109	+	1.11831i	−0.960365	+	0.278745i	$0.910082\pi$
$588$	−2.18333	−	1.63442i	−0.0900389	−	0.0674023i
$589$	−5.98445	−	3.84597i	−0.246585	−	0.158470i
$590$	3.97775	+	16.6034i	0.163762	+	0.683549i
$591$	−0.443967	+	3.08786i	−0.0182624	+	0.127018i
$592$	−0.183470	−	2.56525i	−0.00754057	−	0.105431i
$593$	6.69629	−	30.7824i	0.274984	−	1.26408i	−0.607721	−	0.794151i	$-0.707916\pi$
$593$	6.69629	−	30.7824i	0.274984	−	1.26408i	0.882704	−	0.469929i	$-0.155720\pi$
$594$	1.93473	+	2.23280i	0.0793829	+	0.0916128i
$595$	17.8022	+	36.9152i	0.729817	+	1.51338i
$596$	−10.1912	−	4.65417i	−0.417448	−	0.190642i
$597$	−5.81704	+	5.81704i	−0.238076	+	0.238076i
$598$	−3.62469	+	18.2899i	−0.148225	+	0.747930i
$599$			36.6177i			1.49616i	0.663609	+	0.748080i	$0.269024\pi$
$599$			36.6177i			1.49616i	−0.663609	+	0.748080i	$0.730976\pi$
$600$	3.64184	−	6.22546i	0.148678	−	0.254153i
$601$	−30.9945	−	9.10080i	−1.26429	−	0.371230i	−0.420201	−	0.907431i	$-0.638041\pi$
$601$	−30.9945	−	9.10080i	−1.26429	−	0.371230i	−0.844090	+	0.536201i	$0.819859\pi$
$602$	−1.62900	+	22.7764i	−0.0663932	+	0.928299i
$603$	8.50217	+	1.84953i	0.346235	+	0.0753189i
$604$	−4.74042	−	4.10760i	−0.192885	−	0.167136i
$605$	−13.3876	−	19.9024i	−0.544283	−	0.809147i
$606$	−3.06176	+	0.899015i	−0.124376	+	0.0365200i
$607$	7.84370	+	36.0569i	0.318366	+	1.46350i	0.806759	+	0.590881i	$0.201220\pi$
$607$	7.84370	+	36.0569i	0.318366	+	1.46350i	−0.488393	+	0.872624i	$0.662417\pi$
$608$	−4.49013	+	5.99811i	−0.182099	+	0.243255i
$609$	3.47220	+	7.60305i	0.140701	+	0.308091i
$610$	−25.3171	+	10.0516i	−1.02506	+	0.406979i
$611$	−0.303912	−	2.11375i	−0.0122950	−	0.0855134i
$612$	7.28323	−	1.58437i	0.294407	−	0.0640444i
$613$	18.2159	+	9.94661i	0.735732	+	0.401740i	0.802988	−	0.595996i	$-0.203243\pi$
$613$	18.2159	+	9.94661i	0.735732	+	0.401740i	−0.0672558	+	0.997736i	$0.521424\pi$
$614$	17.7188	+	2.54758i	0.715074	+	0.102812i
$615$	−14.3840	−	13.7938i	−0.580021	−	0.556220i
$616$	0.993725	−	0.638628i	0.0400383	−	0.0257311i
$617$	−34.8084	−	2.48955i	−1.40133	−	0.100225i	−0.649893	−	0.760026i	$-0.725186\pi$
$617$	−34.8084	−	2.48955i	−1.40133	−	0.100225i	−0.751441	+	0.659800i	$0.770641\pi$
$618$	−8.15563	−	14.9359i	−0.328067	−	0.600811i
$619$	−3.59032	+	7.86170i	−0.144307	+	0.315988i	−0.967959	−	0.251107i	$-0.919205\pi$
$619$	−3.59032	+	7.86170i	−0.144307	+	0.315988i	0.823652	+	0.567095i	$0.191933\pi$
$620$	−1.42357	−	1.57499i	−0.0571720	−	0.0632533i
$621$	27.1083	−	0.503046i	1.08782	−	0.0201865i
$622$	−15.0863	−	15.0863i	−0.604904	−	0.604904i
$623$	7.47211	+	20.0335i	0.299364	+	0.802625i
$624$	1.58002	−	5.38106i	0.0632514	−	0.215415i
$625$	12.2518	+	21.7920i	0.490074	+	0.871681i
$626$	−8.15867	−	12.6951i	−0.326086	−	0.507400i
$627$	−5.63371	+	0.402931i	−0.224989	+	0.0160915i
$628$	11.8565	−	8.87567i	0.473126	−	0.354178i
$629$	−5.87513	−	20.0089i	−0.234257	−	0.797805i
$630$	0.757370	+	4.58393i	0.0301744	+	0.182628i
$631$	−15.1967	+	2.18495i	−0.604969	+	0.0869815i	−0.437991	−	0.898979i	$-0.644310\pi$
$631$	−15.1967	+	2.18495i	−0.604969	+	0.0869815i	−0.166978	+	0.985961i	$0.553401\pi$
$632$	−3.48826	−	1.30106i	−0.138756	−	0.0517532i
$633$	12.0016	+	4.47635i	0.477019	+	0.177919i
$634$	3.94047	−	0.566555i	0.156496	−	0.0225008i
$635$	21.9140	+	15.6994i	0.869630	+	0.623012i
$636$	−3.71884	−	12.6652i	−0.147461	−	0.502208i
$637$	5.88463	−	4.40518i	0.233157	−	0.174539i
$638$	1.33622	−	0.0955687i	0.0529016	−	0.00378360i
$639$	−2.81560	−	4.38115i	−0.111383	−	0.173316i
$640$	−1.76161	+	1.37722i	−0.0696337	+	0.0544394i
$641$	5.85175	−	19.9292i	0.231130	−	0.787158i	−0.759490	−	0.650518i	$-0.774552\pi$
$641$	5.85175	−	19.9292i	0.231130	−	0.787158i	0.990621	−	0.136639i	$-0.0436302\pi$
$642$	−6.90147	−	18.5036i	−0.272379	−	0.730277i
$643$	−8.76434	−	8.76434i	−0.345632	−	0.345632i	0.512848	−	0.858480i	$-0.328591\pi$
$643$	−8.76434	−	8.76434i	−0.345632	−	0.345632i	−0.858480	+	0.512848i	$0.828591\pi$
$644$	1.34340	−	10.7568i	0.0529374	−	0.423878i
$645$	24.1734	−	21.8493i	0.951828	−	0.860317i
$646$	−25.2381	+	55.2637i	−0.992979	+	2.17432i
$647$	12.7092	+	23.2751i	0.499649	+	0.915040i	0.998821	+	0.0485367i	$0.0154558\pi$
$647$	12.7092	+	23.2751i	0.499649	+	0.915040i	−0.499172	+	0.866503i	$0.666362\pi$
$648$	−5.38361	−	0.385043i	−0.211488	−	0.0151259i
$649$	3.35672	−	2.15723i	0.131763	−	0.0846788i
$650$	13.3341	+	14.1454i	0.523008	+	0.554826i
$651$	−3.06420	−	0.440565i	−0.120095	−	0.0172671i
$652$	−8.51835	−	4.65137i	−0.333604	−	0.182162i
$653$	11.7687	−	2.56012i	0.460543	−	0.100185i	0.0236930	−	0.999719i	$-0.492458\pi$
$653$	11.7687	−	2.56012i	0.460543	−	0.100185i	0.436850	+	0.899534i	$0.356094\pi$
$654$	1.79226	+	12.4655i	0.0700831	+	0.487439i
$655$	4.07616	+	1.75931i	0.159269	+	0.0687419i
$656$	2.56668	+	5.62025i	0.100212	+	0.219434i
$657$	−0.156484	+	0.209038i	−0.00610502	+	0.00815535i
$658$	0.263911	+	1.21318i	0.0102883	+	0.0472947i
$659$	38.6637	−	11.3527i	1.50612	−	0.442238i	0.578477	−	0.815699i	$-0.303647\pi$
$659$	38.6637	−	11.3527i	1.50612	−	0.442238i	0.927646	+	0.373461i	$0.121829\pi$
$660$	−1.65423	−	0.323729i	−0.0643908	−	0.0126011i
$661$	34.6228	+	30.0008i	1.34667	+	1.16690i	0.970708	+	0.240264i	$0.0772339\pi$
$661$	34.6228	+	30.0008i	1.34667	+	1.16690i	0.375964	+	0.926634i	$0.377312\pi$
$662$	−12.7766	−	2.77938i	−0.496577	−	0.108024i
$663$	3.24412	−	45.3588i	0.125991	−	1.76159i
$664$	6.62018	+	1.94386i	0.256913	+	0.0754364i
$665$	−33.6106	−	17.4491i	−1.30336	−	0.676649i
$666$		−	2.36406i		−	0.0916053i
$667$	7.18364	−	9.97684i	0.278152	−	0.386305i
$668$	−5.11924	+	5.11924i	−0.198069	+	0.198069i
$669$	32.6237	+	14.8988i	1.26131	+	0.576019i
$670$	−19.0647	+	9.19386i	−0.736534	+	0.355190i
$671$	4.16890	+	4.81117i	0.160939	+	0.185733i
$672$	−0.693084	+	3.18606i	−0.0267363	+	0.122905i
$673$	−0.765988	−	10.7099i	−0.0295267	−	0.412837i	−0.990623	−	0.136624i	$-0.956375\pi$
$673$	−0.765988	−	10.7099i	−0.0295267	−	0.412837i	0.961096	−	0.276213i	$-0.0890796\pi$
$674$	4.14185	−	28.8072i	0.159538	−	1.10961i
$675$	15.9774	−	23.3186i	0.614972	−	0.897532i
$676$	1.77977	+	1.14379i	0.0684526	+	0.0439918i
$677$	11.1316	+	8.33303i	0.427823	+	0.320264i	0.791399	−	0.611300i	$-0.209353\pi$
$677$	11.1316	+	8.33303i	0.427823	+	0.320264i	−0.363576	+	0.931565i	$0.618444\pi$
$678$	−9.34183	+	25.0464i	−0.358771	+	0.961901i
$679$	−11.8064	+	5.39179i	−0.453087	+	0.206918i
$680$	−11.5839	+	13.9484i	−0.444222	+	0.534895i
$681$	−8.18424	+	12.7349i	−0.313621	+	0.488003i
$682$	−0.237786	+	0.435473i	−0.00910530	+	0.0166751i
$683$	−21.1912	−	28.3081i	−0.810859	−	1.08318i	−0.994960	−	0.100274i	$-0.968028\pi$
$683$	−21.1912	−	28.3081i	−0.810859	−	1.08318i	0.184101	−	0.982907i	$-0.441063\pi$
$684$	−4.51025	+	5.20510i	−0.172454	+	0.199022i
$685$	−10.3375	−	18.0238i	−0.394976	−	0.688653i
$686$	−15.1878	+	13.1603i	−0.579872	+	0.502462i
$687$	−6.47149	+	3.53370i	−0.246903	+	0.134819i
$688$	−9.46519	+	3.53033i	−0.360857	+	0.134593i
$689$	35.5771			1.35538
$690$	−12.0078	+	9.75199i	−0.457130	+	0.371252i
$691$	−5.16115			−0.196339			−0.0981696	−	0.995170i	$-0.531299\pi$
$691$	−5.16115			−0.196339			−0.0981696	+	0.995170i	$0.531299\pi$
$692$	12.7219	−	4.74501i	0.483613	−	0.180378i
$693$	0.953007	−	0.520381i	0.0362017	−	0.0197676i
$694$	19.3118	−	16.7338i	0.733067	−	0.635206i
$695$	−5.22597	−	1.41631i	−0.198233	−	0.0537235i
$696$	−2.42153	+	2.79460i	−0.0917880	+	0.105929i
$697$	30.0235	+	40.1067i	1.13722	+	1.51915i
$698$	9.25510	−	16.9495i	0.350311	−	0.641546i
$699$	−1.06006	+	1.64948i	−0.0400950	+	0.0623890i
$700$	−8.31928	−	7.64997i	−0.314439	−	0.289142i
$701$	17.8148	−	8.13573i	0.672855	−	0.307282i	−0.0495313	−	0.998773i	$-0.515773\pi$
$701$	17.8148	−	8.13573i	0.672855	−	0.307282i	0.722386	+	0.691490i	$0.243045\pi$
$702$	7.68119	−	20.5941i	0.289908	−	0.777273i
$703$	15.4259	+	11.5477i	0.581800	+	0.435530i
$704$	0.439628	+	0.282532i	0.0165691	+	0.0106483i
$705$	0.926414	−	1.51016i	0.0348908	−	0.0568757i
$706$	1.09867	−	7.64139i	0.0413488	−	0.287588i
$707$	0.356719	+	4.98758i	0.0134158	+	0.187577i
$708$	−2.34118	+	10.7622i	−0.0879869	+	0.404469i
$709$	27.4645	+	31.6957i	1.03145	+	1.19036i	0.981472	+	0.191608i	$0.0613701\pi$
$709$	27.4645	+	31.6957i	1.03145	+	1.19036i	0.0499794	+	0.998750i	$0.484084\pi$
$710$	11.9599	+	4.17764i	0.448846	+	0.156784i
$711$	−3.11300	−	1.42166i	−0.116747	−	0.0533164i
$712$	−6.68875	+	6.68875i	−0.250671	+	0.250671i
$713$	1.67011	+	4.23600i	0.0625462	+	0.158639i
$714$			26.4385i			0.989436i
$715$	2.09331	−	4.03215i	0.0782855	−	0.150794i
$716$	19.7918	+	5.81139i	0.739653	+	0.217182i
$717$	−0.809498	+	11.3183i	−0.0302313	+	0.422688i
$718$	27.3312	+	5.94553i	1.01999	+	0.221885i
$719$	23.2740	+	20.1671i	0.867975	+	0.752105i	0.970110	−	0.242666i	$-0.0780218\pi$
$719$	23.2740	+	20.1671i	0.867975	+	0.752105i	−0.102135	+	0.994771i	$0.532567\pi$
$720$	−1.70550	+	1.14723i	−0.0635602	+	0.0427546i
$721$	−25.5862	+	7.51279i	−0.952880	+	0.279791i
$722$	−7.89437	−	36.2898i	−0.293798	−	1.35057i
$723$	−1.92720	+	2.57444i	−0.0716733	+	0.0957443i
$724$	−7.72564	−	16.9168i	−0.287121	−	0.628707i
$725$	−4.12289	−	12.1362i	−0.153120	−	0.450726i
$726$	−2.20210	−	15.3160i	−0.0817276	−	0.568428i
$727$	18.2603	−	3.97229i	0.677238	−	0.147324i	0.139225	−	0.990261i	$-0.455539\pi$
$727$	18.2603	−	3.97229i	0.677238	−	0.147324i	0.538013	+	0.842937i	$0.319175\pi$
$728$	−7.71311	−	4.21168i	−0.285867	−	0.156095i
$729$	−29.1269	−	4.18782i	−1.07878	−	0.155105i
$730$	−0.0133025	−	0.635054i	−0.000492346	−	0.0235044i
$731$	−68.9102	+	44.2859i	−2.54874	+	1.63797i
$732$	−17.5275	−	1.25359i	−0.647833	−	0.0463340i
$733$	11.0483	+	20.2334i	0.408078	+	0.747338i	0.998200	−	0.0599755i	$-0.0191023\pi$
$733$	11.0483	+	20.2334i	0.408078	+	0.747338i	−0.590122	+	0.807314i	$0.700920\pi$
$734$	−2.14421	+	4.69517i	−0.0791443	+	0.173302i
$735$	6.09070	+	0.307573i	0.224659	+	0.0113450i
$736$	4.57571	−	1.43629i	0.168663	−	0.0529422i
$737$	3.49778	+	3.49778i	0.128843	+	0.128843i
$738$	1.98479	+	5.32142i	0.0730610	+	0.195884i
$739$	−3.41208	+	11.6205i	−0.125515	+	0.427466i	−0.998143	−	0.0609209i	$-0.980596\pi$
$739$	−3.41208	+	11.6205i	−0.125515	+	0.427466i	0.872627	+	0.488387i	$0.162414\pi$
$740$	3.54193	+	4.53050i	0.130204	+	0.166545i
$741$	22.7177	+	35.3495i	0.834557	+	1.29860i
$742$	−20.6315	+	1.47559i	−0.757405	+	0.0541707i
$743$	1.44895	−	1.08467i	0.0531567	−	0.0397926i	−0.572369	−	0.819996i	$-0.693975\pi$
$743$	1.44895	−	1.08467i	0.0531567	−	0.0397926i	0.625526	+	0.780204i	$0.284885\pi$
$744$	−0.385848	−	1.31408i	−0.0141459	−	0.0481764i
$745$	24.7171	−	4.08382i	0.905563	−	0.149620i
$746$	27.5384	−	3.95943i	1.00825	−	0.144965i
$747$	5.94244	+	2.21642i	0.217423	+	0.0810945i
$748$	3.97025	+	1.48083i	0.145167	+	0.0541444i
$749$	−30.6312	+	4.40410i	−1.11924	+	0.160922i
$750$	1.01265	+	16.0957i	0.0369769	+	0.587732i
$751$	0.696354	+	2.37156i	0.0254103	+	0.0865396i	0.971222	−	0.238176i	$-0.0765496\pi$
$751$	0.696354	+	2.37156i	0.0254103	+	0.0865396i	−0.945812	+	0.324716i	$0.894731\pi$
$752$	−0.439712	+	0.329164i	−0.0160347	+	0.0120034i
$753$	−6.58935	+	0.471280i	−0.240129	+	0.0171744i
$754$	−5.38828	−	8.38433i	−0.196230	−	0.305339i
$755$	13.9217	+	1.70488i	0.506661	+	0.0620470i
$756$	−3.60023	+	12.2613i	−0.130939	+	0.445938i
$757$	11.9034	+	31.9142i	0.432635	+	1.15994i	0.952191	+	0.305504i	$0.0988248\pi$
$757$	11.9034	+	31.9142i	0.432635	+	1.15994i	−0.519555	+	0.854437i	$0.673902\pi$
$758$	−13.0268	−	13.0268i	−0.473154	−	0.473154i
$759$	3.07706	+	1.89777i	0.111690	+	0.0688848i
$760$	0.844974	−	16.7326i	0.0306504	−	0.606954i
$761$	−7.29879	+	15.9821i	−0.264581	+	0.579352i	−0.994566	−	0.104112i	$-0.966800\pi$
$761$	−7.29879	+	15.9821i	−0.264581	+	0.579352i	0.729984	+	0.683464i	$0.239527\pi$
$762$	8.33422	+	15.2630i	0.301917	+	0.552920i
$763$	19.6839	+	1.40782i	0.712606	+	0.0509666i
$764$	−0.760933	+	0.489022i	−0.0275296	+	0.0176922i
$765$	−11.5357	+	12.0293i	−0.417075	+	0.434922i
$766$	−19.8372	−	2.85216i	−0.716747	−	0.103053i
$767$	−26.0542	−	14.2267i	−0.940764	−	0.513696i
$768$	−1.40952	+	0.306623i	−0.0508618	+	0.0110643i
$769$	−0.390929	−	2.71897i	−0.0140972	−	0.0980485i	0.981558	−	0.191164i	$-0.0612264\pi$
$769$	−0.390929	−	2.71897i	−0.0140972	−	0.0980485i	−0.995655	+	0.0931159i	$0.970317\pi$
$770$	−1.04669	+	2.42510i	−0.0377203	+	0.0873945i
$771$	−13.0084	−	28.4844i	−0.468485	−	1.02584i
$772$	−2.77299	+	3.70429i	−0.0998022	+	0.133320i
$773$	3.17616	+	14.6005i	0.114238	+	0.525145i	0.998327	+	0.0578255i	$0.0184167\pi$
$773$	3.17616	+	14.6005i	0.114238	+	0.525145i	−0.884088	+	0.467320i	$0.845220\pi$
$774$	−8.90996	+	2.61620i	−0.320262	+	0.0940374i
$775$	4.60690	+	1.14553i	0.165485	+	0.0411485i
$776$	−4.33959	−	3.76027i	−0.155782	−	0.134986i
$777$	8.19390	+	1.78247i	0.293954	+	0.0639459i
$778$	1.91765	−	26.8122i	0.0687510	−	0.961265i
$779$	−44.4184	−	13.0424i	−1.59145	−	0.467293i
$780$	3.78425	+	11.9558i	0.135498	+	0.428086i
$781$		−	2.96073i		−	0.105943i
$782$	33.7789	−	19.2667i	1.20793	−	0.688976i
$783$	−10.2477	+	10.2477i	−0.366223	+	0.366223i
$784$	−1.71984	−	0.785425i	−0.0614229	−	0.0280509i
$785$	−10.9210	+	31.2650i	−0.389788	+	1.11590i
$786$	1.87553	+	2.16447i	0.0668978	+	0.0772042i
$787$	3.87437	−	17.8102i	0.138106	−	0.634864i	−0.855097	−	0.518468i	$-0.826502\pi$
$787$	3.87437	−	17.8102i	0.138106	−	0.634864i	0.993203	−	0.116396i	$-0.0371340\pi$
$788$	0.154282	+	2.15715i	0.00549608	+	0.0768452i
$789$	−2.92244	+	20.3260i	−0.104042	+	0.723625i
$790$	8.09579	−	1.93955i	0.288035	−	0.0690061i
$791$	35.2390	+	22.6467i	1.25296	+	0.805226i
$792$	0.384559	+	0.287877i	0.0136647	+	0.0102293i
$793$	16.5512	−	44.3755i	0.587750	−	1.57582i
$794$	−21.9162	+	10.0088i	−0.777775	+	0.355198i
$795$	22.7065	+	18.8574i	0.805316	+	0.668802i
$796$	−3.08328	+	4.79768i	−0.109284	+	0.170049i
$797$	10.1028	−	18.5019i	0.357860	−	0.655372i	−0.635282	−	0.772280i	$-0.719116\pi$
$797$	10.1028	−	18.5019i	0.357860	−	0.655372i	0.993143	+	0.116907i	$0.0372981\pi$
$798$	−14.6404	−	19.5573i	−0.518264	−	0.692319i
$799$	−2.91660	+	3.36594i	−0.103182	+	0.119078i
$800$	1.54961	−	4.75381i	0.0547870	−	0.168073i
$801$	−6.57141	+	5.69416i	−0.232189	+	0.201193i
$802$	−0.720370	+	0.393352i	−0.0254372	+	0.0138897i
$803$	−0.139090	+	0.0518779i	−0.00490838	+	0.00183073i
$804$	−13.6541			−0.481542
$805$	10.9324	+	21.6345i	0.385318	+	0.762516i
$806$	3.69130			0.130021
$807$	27.2999	−	10.1823i	0.961001	−	0.358435i
$808$	−1.94157	+	1.06018i	−0.0683042	+	0.0372969i
$809$	−31.9096	+	27.6498i	−1.12188	+	0.972115i	−0.999792	−	0.0204040i	$-0.993505\pi$
$809$	−31.9096	+	27.6498i	−1.12188	+	0.972115i	−0.122089	+	0.992519i	$0.538959\pi$
$810$	10.4691	−	6.00456i	0.367848	−	0.210979i
$811$	33.6421	−	38.8251i	1.18134	−	1.36333i	0.264343	−	0.964429i	$-0.414845\pi$
$811$	33.6421	−	38.8251i	1.18134	−	1.36333i	0.916992	−	0.398905i	$-0.130610\pi$
$812$	3.47246	+	4.63867i	0.121860	+	0.162785i
$813$	3.75290	−	6.87293i	0.131620	−	0.241044i
$814$	0.726615	−	1.13064i	0.0254679	−	0.0396288i
$815$	21.6098	−	2.00122i	0.756958	−	0.0700997i
$816$	−10.6395	+	4.85890i	−0.372458	+	0.170096i
$817$	26.4513	−	70.9186i	0.925413	−	2.48113i
$818$	17.9178	+	13.4131i	0.626480	+	0.468977i
$819$	−6.79581	−	4.36740i	−0.237465	−	0.152609i
$820$	−11.7764	−	7.22433i	−0.411251	−	0.252284i
$821$	1.53157	−	10.6523i	0.0534520	−	0.371767i	−0.945485	−	0.325666i	$-0.894411\pi$
$821$	1.53157	−	10.6523i	0.0534520	−	0.371767i	0.998937	−	0.0461007i	$-0.0146795\pi$
$822$	−0.956219	−	13.3697i	−0.0333520	−	0.466321i
$823$	−6.07293	+	27.9168i	−0.211689	+	0.973119i	0.741549	+	0.670899i	$0.234091\pi$
$823$	−6.07293	+	27.9168i	−0.211689	+	0.973119i	−0.953238	+	0.302220i	$0.902272\pi$
$824$	−7.72560	−	8.91582i	−0.269134	−	0.310597i
$825$	3.47323	−	1.46390i	0.120922	−	0.0509666i
$826$	15.6992	+	7.16956i	0.546243	+	0.249461i
$827$	−24.2348	+	24.2348i	−0.842727	+	0.842727i	−0.989213	−	0.146486i	$-0.953204\pi$
$827$	−24.2348	+	24.2348i	−0.842727	+	0.842727i	0.146486	+	0.989213i	$0.453204\pi$
$828$	4.28956	−	1.01684i	0.149073	−	0.0353377i
$829$			2.71732i			0.0943763i	0.998886	+	0.0471882i	$0.0150260\pi$
$829$			2.71732i			0.0943763i	−0.998886	+	0.0471882i	$0.984974\pi$
$830$	−14.7089	+	4.65566i	−0.510553	+	0.161600i
$831$	−21.5260	−	6.32060i	−0.746728	−	0.219259i
$832$	0.277358	−	3.87797i	0.00961567	−	0.134445i
$833$	−14.9805	−	3.25880i	−0.519043	−	0.112911i
$834$	−2.63975	−	2.28736i	−0.0914072	−	0.0792048i
$835$	3.10907	−	15.8871i	0.107594	−	0.549796i
$836$	−3.75691	+	1.10313i	−0.129936	+	0.0381525i
$837$	−1.14096	−	5.24492i	−0.0394374	−	0.181291i
$838$	7.55875	−	10.0973i	0.261113	−	0.348806i
$839$	−20.0126	−	43.8216i	−0.690913	−	1.51289i	−0.850652	−	0.525730i	$-0.823792\pi$
$839$	−20.0126	−	43.8216i	−0.690913	−	1.51289i	0.159738	−	0.987159i	$-0.448935\pi$
$840$	−2.69040	−	6.77631i	−0.0928275	−	0.233805i
$841$	−3.19192	−	22.2003i	−0.110066	−	0.765528i
$842$	5.82495	−	1.26714i	0.200741	−	0.0436685i
$843$	−4.12363	−	2.25167i	−0.142025	−	0.0775517i
$844$	8.78953	+	1.26374i	0.302548	+	0.0434998i
$845$	−4.72962	+	0.0990712i	−0.162704	+	0.00340815i
$846$	−0.424749	+	0.272970i	−0.0146032	+	0.00938489i
$847$	−24.1851	−	1.72975i	−0.831008	−	0.0594349i
$848$	−4.38549	−	8.03143i	−0.150598	−	0.275800i
$849$	1.69632	−	3.71443i	0.0582177	−	0.127479i
$850$	4.08431	−	40.3365i	0.140091	−	1.38353i
$851$	−3.69384	−	11.7678i	−0.126623	−	0.403395i
$852$	5.77881	+	5.77881i	0.197979	+	0.197979i
$853$	7.80325	+	20.9213i	0.267178	+	0.716332i	0.999379	+	0.0352432i	$0.0112206\pi$
$853$	7.80325	+	20.9213i	0.267178	+	0.716332i	−0.732201	+	0.681089i	$0.761507\pi$
$854$	−7.75768	+	26.4202i	−0.265462	+	0.904082i
$855$	1.87201	−	15.2864i	0.0640212	−	0.522782i
$856$	−7.40176	−	11.5174i	−0.252987	−	0.393655i
$857$	−13.1402	+	0.939805i	−0.448860	+	0.0321031i	−0.293940	−	0.955824i	$-0.594967\pi$
$857$	−13.1402	+	0.939805i	−0.448860	+	0.0321031i	−0.154920	+	0.987927i	$0.549512\pi$
$858$	2.34622	−	1.75636i	0.0800985	−	0.0599610i
$859$	−7.27326	−	24.7704i	−0.248160	−	0.845156i	−0.985506	−	0.169641i	$-0.945739\pi$
$859$	−7.27326	−	24.7704i	−0.248160	−	0.845156i	0.737346	−	0.675516i	$-0.236079\pi$
$860$	13.1554	−	18.3630i	0.448597	−	0.626173i
$861$	−19.9407	+	2.86704i	−0.679578	+	0.0977085i
$862$	−4.19130	−	1.56327i	−0.142756	−	0.0532453i
$863$	−41.0889	−	15.3254i	−1.39868	−	0.521682i	−0.466776	−	0.884376i	$-0.654584\pi$
$863$	−41.0889	−	15.3254i	−1.39868	−	0.521682i	−0.931908	+	0.362694i	$0.881857\pi$
$864$	−5.59590	+	0.804568i	−0.190376	+	0.0273720i
$865$	−17.6818	+	24.6812i	−0.601200	+	0.839184i
$866$	11.3966	+	38.8133i	0.387273	+	1.31893i
$867$	−56.2936	+	42.1409i	−1.91183	+	1.43118i
$868$	−2.14062	+	0.153100i	−0.0726573	+	0.00519655i
$869$	−1.05187	−	1.63674i	−0.0356821	−	0.0555225i
$870$	1.00507	−	8.20718i	0.0340751	−	0.278250i
$871$	10.3681	−	35.3105i	0.351310	−	1.19645i
$872$	3.05100	+	8.18004i	0.103320	+	0.277011i
$873$	−3.73230	−	3.73230i	−0.126319	−	0.126319i
$874$	−14.3181	+	32.9572i	−0.484318	+	1.11479i
$875$	24.9828	+	3.81074i	0.844573	+	0.128827i
$876$	0.170222	−	0.372734i	0.00575127	−	0.0125935i
$877$	−22.7676	−	41.6958i	−0.768809	−	1.40797i	−0.908548	−	0.417780i	$-0.862808\pi$
$877$	−22.7676	−	41.6958i	−0.768809	−	1.40797i	0.139740	−	0.990188i	$-0.455373\pi$
$878$	27.5429	+	1.96991i	0.929529	+	0.0664812i
$879$	−30.1984	+	19.4074i	−1.01857	+	0.654594i
$880$	−1.16828	+	0.0244720i	−0.0393828	+	0.000824951i
$881$	41.6370	+	5.98650i	1.40279	+	0.201690i	0.801812	−	0.597577i	$-0.203870\pi$
$881$	41.6370	+	5.98650i	1.40279	+	0.201690i	0.600976	+	0.799267i	$0.294779\pi$
$882$	−1.52538	−	0.832922i	−0.0513623	−	0.0280459i
$883$	−2.52304	+	0.548854i	−0.0849071	+	0.0184704i	−0.254818	−	0.966989i	$-0.582016\pi$
$883$	−2.52304	+	0.548854i	−0.0849071	+	0.0184704i	0.169911	+	0.985459i	$0.445652\pi$
$884$	−4.48649	−	31.2042i	−0.150897	−	1.04951i
$885$	−9.08793	−	22.8898i	−0.305487	−	0.769432i
$886$	−10.9176	−	23.9061i	−0.366782	−	0.803141i
$887$	10.5886	−	14.1447i	0.355529	−	0.474931i	−0.586746	−	0.809771i	$-0.699591\pi$
$887$	10.5886	−	14.1447i	0.355529	−	0.474931i	0.942275	+	0.334840i	$0.108682\pi$
$888$	0.788573	+	3.62501i	0.0264628	+	0.121647i
$889$	26.1465	−	7.67730i	0.876925	−	0.257489i
$890$	4.06228	−	20.7579i	0.136168	−	0.695807i
$891$	−2.13166	−	1.84709i	−0.0714133	−	0.0618800i
$892$	24.2949	+	5.28503i	0.813453	+	0.176956i
$893$	0.293592	−	4.10495i	0.00982467	−	0.137367i
$894$	15.5065	+	4.55313i	0.518616	+	0.152279i
$895$	−43.9739	+	13.9186i	−1.46988	+	0.465248i
$896$			2.26038i			0.0755139i
$897$	1.42067	−	26.8586i	0.0474346	−	0.896782i
$898$	−7.66324	+	7.66324i	−0.255726	+	0.255726i
$899$	−2.21391	−	1.01106i	−0.0738382	−	0.0337208i
$900$	1.73255	−	4.25706i	0.0577516	−	0.141902i
$901$	−48.5903	−	56.0762i	−1.61878	−	1.86817i
$902$	−0.686343	+	3.15507i	−0.0228527	+	0.105052i
$903$	−2.34982	−	32.8548i	−0.0781971	−	1.09334i
$904$	−2.63734	+	18.3431i	−0.0877167	+	0.610083i
$905$	35.4467	+	21.7450i	1.17829	+	0.722828i
$906$	7.61164	+	4.89171i	0.252880	+	0.162516i
$907$	−9.14271	−	6.84415i	−0.303579	−	0.227256i	0.436617	−	0.899647i	$-0.356176\pi$
$907$	−9.14271	−	6.84415i	−0.303579	−	0.227256i	−0.740196	+	0.672391i	$0.765267\pi$
$908$	−3.66741	+	9.83270i	−0.121707	+	0.326310i
$909$	−1.84971	+	0.844734i	−0.0613510	+	0.0280181i
$910$	19.5670	−	1.81204i	0.648640	−	0.0600687i
$911$	−15.2646	+	23.7522i	−0.505739	+	0.786945i	−0.996433	−	0.0843867i	$-0.973107\pi$
$911$	−15.2646	+	23.7522i	−0.505739	+	0.786945i	0.490694	+	0.871332i	$0.336743\pi$
$912$	5.17970	−	9.48591i	0.171517	−	0.314110i
$913$	2.16080	+	2.88649i	0.0715121	+	0.0955290i
$914$	0.497371	−	0.573996i	0.0164516	−	0.0189861i
$915$	34.0844	−	19.5491i	1.12680	−	0.646273i
$916$	−3.86308	+	3.34738i	−0.127640	+	0.110600i
$917$	3.93893	−	2.15082i	0.130075	−	0.0710262i
$918$	−42.9509	+	16.0199i	−1.41759	+	0.528734i
$919$	26.5030			0.874252			0.437126	−	0.899400i	$-0.355996\pi$
$919$	26.5030			0.874252			0.437126	+	0.899400i	$0.355996\pi$
$920$	−6.69709	+	8.37550i	−0.220796	+	0.276132i
$921$	−25.8221			−0.850866
$922$	9.29443	−	3.46664i	0.306096	−	0.114168i
$923$	−19.3326	+	10.5564i	−0.636339	+	0.347467i
$924$	−1.28775	+	1.11584i	−0.0423637	+	0.0367084i
$925$	−12.2258	−	3.98529i	−0.401983	−	0.131036i
$926$	23.1679	−	26.7372i	0.761344	−	0.878637i
$927$	−6.49879	−	8.68136i	−0.213448	−	0.285133i
$928$	−1.22854	+	2.24991i	−0.0403289	+	0.0738568i
$929$	21.6060	−	33.6195i	0.708868	−	1.10302i	−0.280817	−	0.959761i	$-0.590605\pi$
$929$	21.6060	−	33.6195i	0.708868	−	1.10302i	0.989685	−	0.143259i	$-0.0457583\pi$
$930$	2.35591	+	1.95655i	0.0772534	+	0.0641577i
$931$	12.8860	−	5.88485i	0.422322	−	0.192868i
$932$	−0.475018	+	1.27357i	−0.0155597	+	0.0417172i
$933$	24.6373	+	18.4433i	0.806589	+	0.603805i
$934$	14.4176	+	9.26563i	0.471758	+	0.303181i
$935$	−9.21442	+	2.20755i	−0.301344	+	0.0721946i
$936$	0.508609	−	3.53745i	0.0166244	−	0.115625i
$937$	−0.0327120	−	0.457374i	−0.00106866	−	0.0149418i	0.996890	−	0.0788081i	$-0.0251114\pi$
$937$	−0.0327120	−	0.457374i	−0.00106866	−	0.0149418i	−0.997958	+	0.0638663i	$0.979657\pi$
$938$	−4.54802	+	20.9069i	−0.148498	+	0.682635i
$939$	14.2552	+	16.4513i	0.465200	+	0.536869i
$940$	0.405019	−	1.15950i	0.0132103	−	0.0378187i
$941$	−7.85482	−	3.58718i	−0.256060	−	0.116939i	0.283250	−	0.959046i	$-0.408587\pi$
$941$	−7.85482	−	3.58718i	−0.256060	−	0.116939i	−0.539310	+	0.842108i	$0.681315\pi$
$942$	−15.1067	+	15.1067i	−0.492204	+	0.492204i
$943$	18.1946	+	23.3877i	0.592497	+	0.761609i
$944$			7.63536i			0.248510i
$945$	−8.62278	−	27.2424i	−0.280499	−	0.886196i
$946$	−5.06540	−	1.48733i	−0.164690	−	0.0483574i
$947$	−0.363486	+	5.08220i	−0.0118117	+	0.165149i	0.988122	+	0.153669i	$0.0491090\pi$
$947$	−0.363486	+	5.08220i	−0.0118117	+	0.165149i	−0.999934	+	0.0114804i	$0.996346\pi$
$948$	5.24766	+	1.14156i	0.170436	+	0.0370761i
$949$	0.834664	+	0.723241i	0.0270943	+	0.0234774i
$950$	19.3152	+	32.0997i	0.626667	+	1.04145i
$951$	−5.50993	+	1.61786i	−0.178672	+	0.0524628i
$952$	3.89598	+	17.9095i	0.126269	+	0.580451i
$953$	1.54865	−	2.06876i	0.0501658	−	0.0670137i	−0.774757	−	0.632259i	$-0.782128\pi$
$953$	1.54865	−	2.06876i	0.0501658	−	0.0670137i	0.824923	+	0.565246i	$0.191219\pi$
$954$	−3.49430	−	7.65145i	−0.113132	−	0.247725i
$955$	0.801494	−	1.85699i	0.0259357	−	0.0600908i
$956$	1.11950	+	7.78631i	0.0362073	+	0.251827i
$957$	−1.88825	+	0.410764i	−0.0610385	+	0.0132781i
$958$	−33.5159	−	18.3010i	−1.08285	−	0.591280i
$959$	−20.7900	−	2.98915i	−0.671343	−	0.0965246i
$960$	2.23251	−	2.32804i	0.0720540	−	0.0751372i
$961$	−25.3205	+	16.2725i	−0.816791	+	0.524920i
$962$	−9.97337	−	0.713310i	−0.321554	−	0.0229980i
$963$	−6.03126	−	11.0454i	−0.194355	−	0.355934i
$964$	−0.926121	+	2.02792i	−0.0298284	+	0.0653150i
$965$	0.521836	−	10.3336i	0.0167985	−	0.332651i
$966$	0.290127	+	15.6345i	0.00933469	+	0.503030i
$967$	−19.8270	−	19.8270i	−0.637595	−	0.637595i	0.312367	−	0.949962i	$-0.398878\pi$
$967$	−19.8270	−	19.8270i	−0.637595	−	0.637595i	−0.949962	+	0.312367i	$0.898878\pi$
$968$	−3.74867	−	10.0506i	−0.120487	−	0.323038i
$969$	24.6902	−	84.0870i	0.793162	−	2.70126i
$970$	12.7445	+	1.56072i	0.409201	+	0.0501118i
$971$	−23.7328	−	36.9290i	−0.761622	−	1.18511i	−0.977961	−	0.208789i	$-0.933048\pi$
$971$	−23.7328	−	36.9290i	−0.761622	−	1.18511i	0.216339	−	0.976318i	$-0.430589\pi$
$972$	−9.15130	+	0.654514i	−0.293528	+	0.0209936i
$973$	−4.38165	+	3.28006i	−0.140469	+	0.105154i
$974$	4.54197	+	15.4685i	0.145534	+	0.495644i
$975$	−21.9425	−	17.4595i	−0.702721	−	0.559152i
$976$	−12.0579	+	1.73366i	−0.385963	+	0.0554931i
$977$	−12.1720	−	4.53992i	−0.389417	−	0.145245i	0.147127	−	0.989118i	$-0.452998\pi$
$977$	−12.1720	−	4.53992i	−0.389417	−	0.145245i	−0.536543	+	0.843873i	$0.680270\pi$
$978$	13.1174	+	4.89255i	0.419449	+	0.156447i
$979$	−4.89300	+	0.703507i	−0.156381	+	0.0224842i
$980$	4.17118	−	0.689174i	0.133243	−	0.0220149i
$981$	2.26098	+	7.70019i	0.0721876	+	0.245848i
$982$	−18.2175	+	13.6374i	−0.581343	+	0.435188i
$983$	−18.2018	+	1.30181i	−0.580546	+	0.0415214i	−0.358524	−	0.933520i	$-0.616720\pi$
$983$	−18.2018	+	1.30181i	−0.580546	+	0.0415214i	−0.222021	+	0.975042i	$0.571265\pi$
$984$	−4.81850	−	7.49773i	−0.153608	−	0.239019i
$985$	−2.97846	−	3.80976i	−0.0949015	−	0.121389i
$986$	−5.85611	+	19.9441i	−0.186497	+	0.635149i
$987$	−0.625866	−	1.67801i	−0.0199215	−	0.0534117i
$988$	20.5982	+	20.5982i	0.655315	+	0.655315i
$989$	−40.2642	+	26.9447i	−1.28033	+	0.856792i
$990$	−1.07278	−	0.0541742i	−0.0340952	−	0.00172177i
$991$	11.4755	−	25.1279i	0.364532	−	0.798213i	−0.635135	−	0.772401i	$-0.719056\pi$
$991$	11.4755	−	25.1279i	0.364532	−	0.798213i	0.999667	−	0.0258118i	$-0.00821708\pi$
$992$	−0.455017	−	0.833301i	−0.0144468	−	0.0264573i
$993$	18.8131	+	1.34554i	0.597016	+	0.0426994i
$994$	10.7733	−	6.92358i	0.341708	−	0.219602i
$995$	−0.267064	−	12.7495i	−0.00846650	−	0.404187i
$996$	−9.85139	−	1.41642i	−0.312153	−	0.0448809i
$997$	−3.43772	−	1.87714i	−0.108874	−	0.0594495i	0.423889	−	0.905714i	$-0.360665\pi$
$997$	−3.43772	−	1.87714i	−0.108874	−	0.0594495i	−0.532763	+	0.846264i	$0.678846\pi$
$998$	12.7324	−	2.76976i	0.403036	−	0.0876752i
$999$	2.06919	+	14.3915i	0.0654662	+	0.455328i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.17.4	✓	240
5.3	odd	4	inner	230.2.l.a.63.10	yes	240
23.19	odd	22	inner	230.2.l.a.157.10	yes	240
115.88	even	44	inner	230.2.l.a.203.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.17.4	✓	240	1.1	even	1	trivial
230.2.l.a.63.10	yes	240	5.3	odd	4	inner
230.2.l.a.157.10	yes	240	23.19	odd	22	inner
230.2.l.a.203.4	yes	240	115.88	even	44	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.936950 + 0.349464i) q^{2} +(1.26604 - 0.691312i) q^{3} +(0.755750 - 0.654861i) q^{4} +(-0.584903 + 2.15821i) q^{5} +(-0.944630 + 1.09016i) q^{6} +(1.35459 + 1.80952i) q^{7} +(-0.479249 + 0.877679i) q^{8} +(-0.496969 + 0.773299i) q^{9} +(-0.206194 - 2.22654i) q^{10} +(-0.475362 + 0.217091i) q^{11} +(0.504099 - 1.35154i) q^{12} +(3.11241 + 2.32992i) q^{13} +(-1.90155 - 1.22205i) q^{14} +(0.751486 + 3.13674i) q^{15} +(0.142315 - 0.989821i) q^{16} +(-0.578458 - 8.08789i) q^{17} +(0.195395 - 0.898216i) q^{18} +(4.90659 + 5.66250i) q^{19} +(0.971289 + 2.01410i) q^{20} +(2.96592 + 1.35449i) q^{21} +(0.369525 - 0.369525i) q^{22} +(-0.430826 - 4.77644i) q^{23} +1.44249i q^{24} +(-4.31578 - 2.52469i) q^{25} +(-3.73039 - 1.09534i) q^{26} +(-0.403312 + 5.63904i) q^{27} +(2.20872 + 0.480478i) q^{28} +(1.93734 + 1.67872i) q^{29} +(-1.80028 - 2.67635i) q^{30} +(-0.910979 + 0.267488i) q^{31} +(0.212565 + 0.977147i) q^{32} +(-0.451751 + 0.603469i) q^{33} +(3.36841 + 7.37580i) q^{34} +(-4.69765 + 1.86511i) q^{35} +(0.130819 + 0.909866i) q^{36} +(2.51303 - 0.546675i) q^{37} +(-6.57607 - 3.59081i) q^{38} +(5.55114 + 0.798134i) q^{39} +(-1.61390 - 1.54768i) q^{40} +(-5.19777 + 3.34040i) q^{41} +(-3.25226 - 0.232606i) q^{42} +(-4.84144 - 8.86643i) q^{43} +(-0.217091 + 0.475362i) q^{44} +(-1.37827 - 1.52487i) q^{45} +(2.07286 + 4.32473i) q^{46} +(-0.388392 - 0.388392i) q^{47} +(-0.504099 - 1.35154i) q^{48} +(0.532671 - 1.81411i) q^{49} +(4.92596 + 0.857301i) q^{50} +(-6.32361 - 9.83973i) q^{51} +(3.87797 - 0.277358i) q^{52} +(7.32556 - 5.48385i) q^{53} +(-1.59276 - 5.42444i) q^{54} +(-0.190487 - 1.15291i) q^{55} +(-2.23737 + 0.321685i) q^{56} +(10.1265 + 3.77699i) q^{57} +(-2.40185 - 0.895842i) q^{58} +(-7.55765 + 1.08663i) q^{59} +(2.62206 + 1.87847i) q^{60} +(-3.43203 - 11.6884i) q^{61} +(0.760064 - 0.568977i) q^{62} +(-2.07250 + 0.148228i) q^{63} +(-0.540641 - 0.841254i) q^{64} +(-6.84892 + 5.35447i) q^{65} +(0.212378 - 0.723291i) q^{66} +(-3.30790 - 8.86882i) q^{67} +(-5.73361 - 5.73361i) q^{68} +(-3.84745 - 5.74935i) q^{69} +(3.74967 - 3.38917i) q^{70} +(-2.35355 + 5.15355i) q^{71} +(-0.440537 - 0.806783i) q^{72} +(0.283343 + 0.0202651i) q^{73} +(-2.16354 + 1.39042i) q^{74} +(-7.20931 - 0.212823i) q^{75} +(7.41630 + 1.06630i) q^{76} +(-1.03675 - 0.566110i) q^{77} +(-5.48006 + 1.19211i) q^{78} +(0.529838 + 3.68510i) q^{79} +(2.05301 + 0.886096i) q^{80} +(2.24214 + 4.90961i) q^{81} +(3.70270 - 4.94623i) q^{82} +(-1.46663 - 6.74199i) q^{83} +(3.12849 - 0.918609i) q^{84} +(17.7937 + 3.48220i) q^{85} +(7.63468 + 6.61549i) q^{86} +(3.61328 + 0.786020i) q^{87} +(0.0372809 - 0.521256i) q^{88} +(9.07615 + 2.66500i) q^{89} +(1.82425 + 0.947073i) q^{90} +8.78807i q^{91} +(-3.45350 - 3.32766i) q^{92} +(-0.968421 + 0.968421i) q^{93} +(0.499632 + 0.228174i) q^{94} +(-15.0908 + 7.27745i) q^{95} +(0.944630 + 1.09016i) q^{96} +(-1.22057 + 5.61087i) q^{97} +(0.134881 + 1.88588i) q^{98} +(0.0683643 - 0.475484i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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