LMFDB - Embedded newform 770.2.bv.a.103.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			103.21
Character	$\chi$	$=$	770.103
Dual form			770.2.bv.a.157.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.358368 + 0.933580i) q^{2} +(1.40223 - 2.15925i) q^{3} +(-0.743145 - 0.669131i) q^{4} +(-2.15617 + 0.592387i) q^{5} +(1.51332 + 2.08290i) q^{6} +(-1.14925 + 2.38311i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-1.47589 - 3.31491i) q^{9} +O(q^{10})$	\(q+(-0.358368 + 0.933580i) q^{2} +(1.40223 - 2.15925i) q^{3} +(-0.743145 - 0.669131i) q^{4} +(-2.15617 + 0.592387i) q^{5} +(1.51332 + 2.08290i) q^{6} +(-1.14925 + 2.38311i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-1.47589 - 3.31491i) q^{9} +(0.219662 - 2.22525i) q^{10} +(2.94289 + 1.52951i) q^{11} +(-2.48688 + 0.666358i) q^{12} +(-5.30666 + 0.840493i) q^{13} +(-1.81298 - 1.92695i) q^{14} +(-1.74435 + 5.48638i) q^{15} +(0.104528 + 0.994522i) q^{16} +(2.19420 + 5.71608i) q^{17} +(3.62365 - 0.189907i) q^{18} +(3.44028 + 3.82082i) q^{19} +(1.99873 + 1.00253i) q^{20} +(3.53423 + 5.82319i) q^{21} +(-2.48256 + 2.19930i) q^{22} +(0.00828083 - 0.00221884i) q^{23} +(0.269120 - 2.56051i) q^{24} +(4.29816 - 2.55458i) q^{25} +(1.11707 - 5.25540i) q^{26} +(-1.59853 - 0.253183i) q^{27} +(2.44867 - 1.00200i) q^{28} +(-2.01379 + 0.654319i) q^{29} +(-4.49686 - 3.59463i) q^{30} +(6.30853 + 0.663054i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(7.42921 - 4.20971i) q^{33} -6.12275 q^{34} +(1.06625 - 5.81920i) q^{35} +(-1.12131 + 3.45103i) q^{36} +(-5.74217 + 3.72901i) q^{37} +(-4.79993 + 1.84252i) q^{38} +(-5.62635 + 12.6370i) q^{39} +(-1.65223 + 1.50670i) q^{40} +(-8.17581 - 2.65648i) q^{41} +(-6.70297 + 1.21264i) q^{42} +(5.91891 + 5.91891i) q^{43} +(-1.16355 - 3.10582i) q^{44} +(5.14599 + 6.27322i) q^{45} +(-0.000896117 + 0.00852599i) q^{46} +(0.115345 - 2.20090i) q^{47} +(2.29400 + 1.16885i) q^{48} +(-4.35846 - 5.47757i) q^{49} +(0.844580 + 4.92815i) q^{50} +(15.4192 + 3.27746i) q^{51} +(4.50602 + 2.92624i) q^{52} +(2.59023 - 2.09753i) q^{53} +(0.809230 - 1.40163i) q^{54} +(-7.25144 - 1.55456i) q^{55} +(0.0579247 + 2.64512i) q^{56} +(13.0742 - 2.07075i) q^{57} +(0.110817 - 2.11452i) q^{58} +(0.731127 - 0.811999i) q^{59} +(4.96741 - 2.90998i) q^{60} +(1.83632 - 0.193005i) q^{61} +(-2.87979 + 5.65191i) q^{62} +(9.59598 + 0.292428i) q^{63} +(0.587785 - 0.809017i) q^{64} +(10.9442 - 4.95585i) q^{65} +(1.26771 + 8.44439i) q^{66} +(-0.771891 - 0.206828i) q^{67} +(2.19420 - 5.71608i) q^{68} +(0.00682063 - 0.0209917i) q^{69} +(5.05058 + 3.08084i) q^{70} +(-4.54961 + 3.30549i) q^{71} +(-2.81997 - 2.28357i) q^{72} +(0.777884 + 14.8429i) q^{73} +(-1.42352 - 6.69714i) q^{74} +(0.511051 - 12.8629i) q^{75} -5.14142i q^{76} +(-7.02710 + 5.25546i) q^{77} +(-9.78134 - 9.78134i) q^{78} +(2.01939 + 4.53563i) q^{79} +(-0.814523 - 2.08244i) q^{80} +(4.49586 - 4.99316i) q^{81} +(5.40999 - 6.68078i) q^{82} +(-1.85582 + 11.7172i) q^{83} +(1.27003 - 6.69234i) q^{84} +(-8.11720 - 11.0250i) q^{85} +(-7.64692 + 3.40463i) q^{86} +(-1.41096 + 5.26578i) q^{87} +(3.31652 + 0.0267596i) q^{88} +(-4.35615 + 7.54508i) q^{89} +(-7.70071 + 2.55608i) q^{90} +(4.09568 - 13.6123i) q^{91} +(-0.00763855 - 0.00389204i) q^{92} +(10.2777 - 12.6919i) q^{93} +(2.01339 + 0.896417i) q^{94} +(-9.68124 - 6.20037i) q^{95} +(-1.91331 + 1.72275i) q^{96} +(-0.972990 - 6.14321i) q^{97} +(6.67569 - 2.10599i) q^{98} +(0.726799 - 12.0128i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.358368	+	0.933580i	−0.253404	+	0.660141i
$2$	−0.358368	+	0.933580i	−0.253404	+	0.660141i
$3$	1.40223	−	2.15925i	0.809580	−	1.24664i	−0.156314	−	0.987707i	$-0.549961\pi$
$3$	1.40223	−	2.15925i	0.809580	−	1.24664i	0.965894	−	0.258937i	$-0.0833721\pi$
$4$	−0.743145	−	0.669131i	−0.371572	−	0.334565i
$5$	−2.15617	+	0.592387i	−0.964269	+	0.264923i
$5$	−2.15617	+	0.592387i	−0.964269	+	0.264923i
$6$	1.51332	+	2.08290i	0.617810	+	0.850342i
$7$	−1.14925	+	2.38311i	−0.434374	+	0.900732i
$7$	−1.14925	+	2.38311i	−0.434374	+	0.900732i
$8$	0.891007	−	0.453990i	0.315018	−	0.160510i
$9$	−1.47589	−	3.31491i	−0.491965	−	1.10497i
$10$	0.219662	−	2.22525i	0.0694633	−	0.703687i
$11$	2.94289	+	1.52951i	0.887315	+	0.461165i
$11$	2.94289	+	1.52951i	0.887315	+	0.461165i
$12$	−2.48688	+	0.666358i	−0.717901	+	0.192361i
$13$	−5.30666	+	0.840493i	−1.47180	+	0.233111i	−0.840241	−	0.542214i	$-0.817586\pi$
$13$	−5.30666	+	0.840493i	−1.47180	+	0.233111i	−0.631563	+	0.775324i	$0.717586\pi$
$14$	−1.81298	−	1.92695i	−0.484538	−	0.514998i
$15$	−1.74435	+	5.48638i	−0.450388	+	1.41658i
$16$	0.104528	+	0.994522i	0.0261321	+	0.248630i
$17$	2.19420	+	5.71608i	0.532171	+	1.38635i	0.891448	+	0.453123i	$0.149690\pi$
$17$	2.19420	+	5.71608i	0.532171	+	1.38635i	−0.359277	+	0.933231i	$0.616977\pi$
$18$	3.62365	−	0.189907i	0.854102	−	0.0447616i
$19$	3.44028	+	3.82082i	0.789255	+	0.876556i	0.994774	−	0.102097i	$-0.0325551\pi$
$19$	3.44028	+	3.82082i	0.789255	+	0.876556i	−0.205520	+	0.978653i	$0.565888\pi$
$20$	1.99873	+	1.00253i	0.446930	+	0.224173i
$21$	3.53423	+	5.82319i	0.771232	+	1.27073i
$22$	−2.48256	+	2.19930i	−0.529283	+	0.468892i
$23$	0.00828083	−	0.00221884i	0.00172667	−	0.000462661i	−0.257956	−	0.966157i	$-0.583049\pi$
$23$	0.00828083	−	0.00221884i	0.00172667	−	0.000462661i	0.259682	+	0.965694i	$0.416382\pi$
$24$	0.269120	−	2.56051i	0.0549339	−	0.522661i
$25$	4.29816	−	2.55458i	0.859631	−	0.510915i
$26$	1.11707	−	5.25540i	0.219076	−	1.03067i
$27$	−1.59853	−	0.253183i	−0.307638	−	0.0487251i
$28$	2.44867	−	1.00200i	0.462755	−	0.189361i
$29$	−2.01379	+	0.654319i	−0.373951	+	0.121504i	−0.489962	−	0.871744i	$-0.662989\pi$
$29$	−2.01379	+	0.654319i	−0.373951	+	0.121504i	0.116011	+	0.993248i	$0.462989\pi$
$30$	−4.49686	−	3.59463i	−0.821011	−	0.656287i
$31$	6.30853	+	0.663054i	1.13305	+	0.119088i	0.652434	−	0.757845i	$-0.273748\pi$
$31$	6.30853	+	0.663054i	1.13305	+	0.119088i	0.480612	+	0.876933i	$0.340415\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	7.42921	−	4.20971i	1.29326	−	0.732816i
$34$	−6.12275			−1.05004
$35$	1.06625	−	5.81920i	0.180229	−	0.983625i
$36$	−1.12131	+	3.45103i	−0.186884	+	0.575171i
$37$	−5.74217	+	3.72901i	−0.944007	+	0.613045i	−0.922199	−	0.386717i	$-0.873609\pi$
$37$	−5.74217	+	3.72901i	−0.944007	+	0.613045i	−0.0218085	+	0.999762i	$0.506942\pi$
$38$	−4.79993	+	1.84252i	−0.778651	+	0.298896i
$39$	−5.62635	+	12.6370i	−0.900937	+	2.02354i
$40$	−1.65223	+	1.50670i	−0.261240	+	0.238231i
$41$	−8.17581	−	2.65648i	−1.27685	−	0.414873i	−0.409378	−	0.912365i	$-0.634254\pi$
$41$	−8.17581	−	2.65648i	−1.27685	−	0.414873i	−0.867468	+	0.497492i	$0.834254\pi$
$42$	−6.70297	+	1.21264i	−1.03429	+	0.187114i
$43$	5.91891	+	5.91891i	0.902625	+	0.902625i	0.995663	−	0.0930379i	$-0.0296578\pi$
$43$	5.91891	+	5.91891i	0.902625	+	0.902625i	−0.0930379	+	0.995663i	$0.529658\pi$
$44$	−1.16355	−	3.10582i	−0.175412	−	0.468221i
$45$	5.14599	+	6.27322i	0.767119	+	0.935157i
$46$	−0.000896117		0.00852599i	−0.000132125		0.00125709i
$47$	0.115345	−	2.20090i	0.0168247	−	0.321035i	−0.977232	−	0.212173i	$-0.931946\pi$
$47$	0.115345	−	2.20090i	0.0168247	−	0.321035i	0.994057	−	0.108862i	$-0.0347207\pi$
$48$	2.29400	+	1.16885i	0.331110	+	0.168709i
$49$	−4.35846	−	5.47757i	−0.622638	−	0.782510i
$50$	0.844580	+	4.92815i	0.119442	+	0.696946i
$51$	15.4192	+	3.27746i	2.15912	+	0.458936i
$52$	4.50602	+	2.92624i	0.624873	+	0.405797i
$53$	2.59023	−	2.09753i	0.355796	−	0.288118i	−0.434712	−	0.900569i	$-0.643150\pi$
$53$	2.59023	−	2.09753i	0.355796	−	0.288118i	0.790508	+	0.612452i	$0.209817\pi$
$54$	0.809230	−	1.40163i	0.110122	−	0.190737i
$55$	−7.25144	−	1.55456i	−0.977784	−	0.209617i
$56$	0.0579247	+	2.64512i	0.00774052	+	0.353469i
$57$	13.0742	−	2.07075i	1.73172	−	0.274277i
$58$	0.110817	−	2.11452i	0.0145510	−	0.277650i
$59$	0.731127	−	0.811999i	0.0951846	−	0.105713i	−0.693670	−	0.720293i	$-0.744008\pi$
$59$	0.731127	−	0.811999i	0.0951846	−	0.105713i	0.788855	+	0.614579i	$0.210674\pi$
$60$	4.96741	−	2.90998i	0.641289	−	0.375677i
$61$	1.83632	−	0.193005i	0.235117	−	0.0247118i	0.0137630	−	0.999905i	$-0.495619\pi$
$61$	1.83632	−	0.193005i	0.235117	−	0.0247118i	0.221354	+	0.975193i	$0.428952\pi$
$62$	−2.87979	+	5.65191i	−0.365734	+	0.717793i
$63$	9.59598	+	0.292428i	1.20898	+	0.0368425i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	10.9442	−	4.95585i	1.35746	−	0.614697i
$66$	1.26771	+	8.44439i	0.156044	+	1.03943i
$67$	−0.771891	−	0.206828i	−0.0943015	−	0.0252680i	0.211360	−	0.977408i	$-0.432211\pi$
$67$	−0.771891	−	0.206828i	−0.0943015	−	0.0252680i	−0.305661	+	0.952140i	$0.598878\pi$
$68$	2.19420	−	5.71608i	0.266086	−	0.693177i
$69$	0.00682063	−	0.0209917i	0.000821107	−	0.00252711i
$70$	5.05058	+	3.08084i	0.603660	+	0.368231i
$71$	−4.54961	+	3.30549i	−0.539940	+	0.392289i	−0.824063	−	0.566499i	$-0.808298\pi$
$71$	−4.54961	+	3.30549i	−0.539940	+	0.392289i	0.284123	+	0.958788i	$0.408298\pi$
$72$	−2.81997	−	2.28357i	−0.332337	−	0.269121i
$73$	0.777884	+	14.8429i	0.0910444	+	1.73723i	0.538237	+	0.842793i	$0.319090\pi$
$73$	0.777884	+	14.8429i	0.0910444	+	1.73723i	−0.447193	+	0.894437i	$0.647576\pi$
$74$	−1.42352	−	6.69714i	−0.165481	−	0.778526i
$75$	0.511051	−	12.8629i	0.0590110	−	1.48528i
$76$		−	5.14142i		−	0.589761i
$77$	−7.02710	+	5.25546i	−0.800813	+	0.598915i
$78$	−9.78134	−	9.78134i	−1.10752	−	1.10752i
$79$	2.01939	+	4.53563i	0.227199	+	0.510298i	0.990791	−	0.135402i	$-0.0432325\pi$
$79$	2.01939	+	4.53563i	0.227199	+	0.510298i	−0.763592	+	0.645700i	$0.776566\pi$
$80$	−0.814523	−	2.08244i	−0.0910664	−	0.232824i
$81$	4.49586	−	4.99316i	0.499541	−	0.554796i
$82$	5.40999	−	6.68078i	0.597433	−	0.737768i
$83$	−1.85582	+	11.7172i	−0.203702	+	1.28613i	0.647815	+	0.761798i	$0.275683\pi$
$83$	−1.85582	+	11.7172i	−0.203702	+	1.28613i	−0.851517	+	0.524327i	$0.824317\pi$
$84$	1.27003	−	6.69234i	0.138572	−	0.730194i
$85$	−8.11720	−	11.0250i	−0.880434	−	1.19583i
$86$	−7.64692	+	3.40463i	−0.824589	+	0.367131i
$87$	−1.41096	+	5.26578i	−0.151271	+	0.564550i
$88$	3.31652	+	0.0267596i	0.353542	+	0.00285259i
$89$	−4.35615	+	7.54508i	−0.461751	+	0.799777i	−0.999048	−	0.0436164i	$-0.986112\pi$
$89$	−4.35615	+	7.54508i	−0.461751	+	0.799777i	0.537297	+	0.843393i	$0.319445\pi$
$90$	−7.70071	+	2.55608i	−0.811727	+	0.269434i
$91$	4.09568	−	13.6123i	0.429344	−	1.42696i
$92$	−0.00763855	−	0.00389204i	−0.000796374	−	0.000405773i
$93$	10.2777	−	12.6919i	1.06575	−	1.31609i
$94$	2.01339	+	0.896417i	0.207665	+	0.0924584i
$95$	−9.68124	−	6.20037i	−0.993275	−	0.636144i
$96$	−1.91331	+	1.72275i	−0.195276	+	0.175828i
$97$	−0.972990	−	6.14321i	−0.0987921	−	0.623749i	−0.986553	−	0.163443i	$-0.947740\pi$
$97$	−0.972990	−	6.14321i	−0.0987921	−	0.623749i	0.887761	−	0.460306i	$-0.152260\pi$
$98$	6.67569	−	2.10599i	0.674346	−	0.212737i
$99$	0.726799	−	12.0128i	0.0730460	−	1.20733i
$100$	−4.90350	−	0.977608i	−0.490350	−	0.0977608i
$101$	−7.92590	−	0.833046i	−0.788657	−	0.0828912i	−0.298368	−	0.954451i	$-0.596442\pi$
$101$	−7.92590	−	0.833046i	−0.788657	−	0.0828912i	−0.490289	+	0.871560i	$0.663109\pi$
$102$	−8.58553	+	13.2206i	−0.850094	+	1.30903i
$103$	−8.40646	+	5.45922i	−0.828313	+	0.537913i	−0.887754	−	0.460319i	$-0.847735\pi$
$103$	−8.40646	+	5.45922i	−0.828313	+	0.537913i	0.0594404	+	0.998232i	$0.481068\pi$
$104$	−4.34670	+	3.15806i	−0.426229	+	0.309673i
$105$	−11.0700	−	10.4622i	−1.08032	−	1.02100i
$106$	1.02995	+	3.16988i	0.100038	+	0.307886i
$107$	−13.0489	−	0.683866i	−1.26149	−	0.0661118i	−0.590169	−	0.807280i	$-0.700939\pi$
$107$	−13.0489	−	0.683866i	−1.26149	−	0.0661118i	−0.671319	+	0.741168i	$0.734272\pi$
$108$	1.01853	+	1.25778i	0.0980081	+	0.121030i
$109$	12.7831	−	7.38033i	1.22440	−	0.706907i	0.258546	−	0.965999i	$-0.416757\pi$
$109$	12.7831	−	7.38033i	1.22440	−	0.706907i	0.965853	+	0.259092i	$0.0834233\pi$
$110$	4.04999	−	6.21270i	0.386151	−	0.592357i
$111$			17.6277i			1.67315i
$112$	−2.49019	−	0.893848i	−0.235301	−	0.0844607i
$113$	−6.04890	+	3.08207i	−0.569033	+	0.289937i	−0.714739	−	0.699391i	$-0.753455\pi$
$113$	−6.04890	+	3.08207i	−0.569033	+	0.289937i	0.145706	+	0.989328i	$0.453455\pi$
$114$	−2.75216	+	12.9479i	−0.257763	+	1.21268i
$115$	−0.0165405	+	0.00968966i	−0.00154241	+	0.000903566i
$116$	1.93436	+	0.861232i	0.179601	+	0.0799634i
$117$	10.6182	+	16.3506i	0.981656	+	1.51162i
$118$	0.496054	+	0.973560i	0.0456654	+	0.0896235i
$119$	−16.1438	−	1.34016i	−1.47990	−	0.122853i
$120$	0.936541	+	5.68032i	0.0854941	+	0.518540i
$121$	6.32120	+	9.00236i	0.574654	+	0.818396i
$122$	−0.477894	+	1.78352i	−0.0432664	+	0.161473i
$123$	−17.2004	+	13.9286i	−1.55091	+	1.25590i
$124$	−4.24448	−	4.71398i	−0.381166	−	0.423328i
$125$	−7.75427	+	8.05427i	−0.693563	+	0.720396i
$126$	−3.71190	+	8.85382i	−0.330682	+	0.788761i
$127$	3.06499	−	19.3516i	0.271974	−	1.71717i	−0.352231	−	0.935913i	$-0.614577\pi$
$127$	3.06499	−	19.3516i	0.271974	−	1.71717i	0.624205	−	0.781261i	$-0.285423\pi$
$128$	0.544639	+	0.838671i	0.0481397	+	0.0741287i
$129$	21.0801	−	4.48071i	1.85600	−	0.394505i
$130$	0.704635	+	11.9933i	0.0618006	+	1.05188i
$131$	−13.5585	−	7.82802i	−1.18461	−	0.683937i	−0.227536	−	0.973770i	$-0.573067\pi$
$131$	−13.5585	−	7.82802i	−1.18461	−	0.683937i	−0.957077	+	0.289833i	$0.906400\pi$
$132$	−8.33783	−	1.84269i	−0.725715	−	0.160386i
$133$	−13.0592	+	3.80752i	−1.13237	+	0.330154i
$134$	0.469711	−	0.646502i	0.0405769	−	0.0558493i
$135$	3.59670	−	0.401044i	0.309554	−	0.0345164i
$136$	4.55009	+	4.09692i	0.390167	+	0.351308i
$137$	14.2477	−	5.46916i	1.21726	−	0.467262i	0.336887	−	0.941545i	$-0.390626\pi$
$137$	14.2477	−	5.46916i	1.21726	−	0.467262i	0.880372	+	0.474283i	$0.157293\pi$
$138$	0.0171532	+	0.0138904i	0.00146018	+	0.00118243i
$139$	−3.54628	−	10.9143i	−0.300792	−	0.925741i	−0.981214	−	0.192921i	$-0.938204\pi$
$139$	−3.54628	−	10.9143i	−0.300792	−	0.925741i	0.680423	−	0.732820i	$-0.261796\pi$
$140$	−4.68618	+	3.61105i	−0.396055	+	0.305189i
$141$	−4.59057	−	3.33524i	−0.386595	−	0.280878i
$142$	−1.45550	−	5.43201i	−0.122143	−	0.455844i
$143$	−16.9025	−	5.64312i	−1.41346	−	0.471901i
$144$	3.14248	−	1.81431i	0.261873	−	0.151193i
$145$	3.95446	−	2.60376i	0.328400	−	0.216231i
$146$	−14.1358	−	4.59300i	−1.16989	−	0.380120i
$147$	−17.9390	+	1.73018i	−1.47959	+	0.142703i
$148$	6.76246	+	1.07107i	0.555871	+	0.0880413i
$149$	12.7321	−	1.33819i	1.04305	−	0.109629i	0.432523	−	0.901623i	$-0.357624\pi$
$149$	12.7321	−	1.33819i	1.04305	−	0.109629i	0.610529	+	0.791994i	$0.290957\pi$
$150$	11.8254	+	5.08676i	0.965541	+	0.415332i
$151$	12.9659	−	2.75598i	1.05515	−	0.224279i	0.352497	−	0.935813i	$-0.385333\pi$
$151$	12.9659	−	2.75598i	1.05515	−	0.224279i	0.702652	+	0.711534i	$0.251999\pi$
$152$	4.79993	+	1.84252i	0.389326	+	0.149448i
$153$	15.7099	−	15.7099i	1.27007	−	1.27007i
$154$	−2.38810	−	8.44375i	−0.192439	−	0.680417i
$155$	−13.9951	+	2.30743i	−1.12411	+	0.185338i
$156$	12.6370	−	5.62635i	1.01177	−	0.450468i
$157$	−5.21225	−	3.38488i	−0.415983	−	0.270143i	0.319633	−	0.947541i	$-0.396440\pi$
$157$	−5.21225	−	3.38488i	−0.415983	−	0.270143i	−0.735616	+	0.677399i	$0.763107\pi$
$158$	−4.95806	+	0.259841i	−0.394442	+	0.0206718i
$159$	−0.896979	−	8.53418i	−0.0711350	−	0.676805i
$160$	2.23602	−	0.0141433i	0.176773	−	0.00111812i
$161$	−0.00422897	+	0.0222842i	−0.000333289	+	0.00175624i
$162$	3.05035	+	5.98664i	0.239658	+	0.470355i
$163$	5.82049	+	2.23427i	0.455896	+	0.175002i	0.575469	−	0.817823i	$-0.304819\pi$
$163$	5.82049	+	2.23427i	0.455896	+	0.175002i	−0.119574	+	0.992825i	$0.538153\pi$
$164$	4.29828	+	7.44483i	0.335639	+	0.581344i
$165$	−13.5249	+	13.4778i	−1.05291	+	1.04925i
$166$	−10.2738	−	5.93161i	−0.797405	−	0.460382i
$167$	−0.642649	−	4.05753i	−0.0497297	−	0.313981i	−0.999997	−	0.00254474i	$-0.999190\pi$
$167$	−0.642649	−	4.05753i	−0.0497297	−	0.313981i	0.950267	−	0.311436i	$-0.100810\pi$
$168$	5.79269	+	3.58400i	0.446916	+	0.276511i
$169$	15.0905	−	4.90321i	1.16081	−	0.377170i
$170$	13.2017	−	3.62704i	1.01252	−	0.278181i
$171$	7.58819	−	17.0434i	0.580284	−	1.30334i
$172$	−0.438083	−	8.35912i	−0.0334035	−	0.637377i
$173$	−6.83990	−	0.358464i	−0.520028	−	0.0272535i	−0.209483	−	0.977812i	$-0.567178\pi$
$173$	−6.83990	−	0.358464i	−0.520028	−	0.0272535i	−0.310545	+	0.950559i	$0.600511\pi$
$174$	−4.41038	−	3.20433i	−0.334350	−	0.242920i
$175$	1.14820	+	13.1788i	0.0867960	+	0.996226i
$176$	−1.21352	+	3.08665i	−0.0914722	+	0.232665i
$177$	−0.728098	−	2.71730i	−0.0547272	−	0.204245i
$178$	−5.48283	−	6.77073i	−0.410956	−	0.507488i
$179$	−3.59714	−	16.9232i	−0.268863	−	1.26490i	−0.880608	−	0.473845i	$-0.842866\pi$
$179$	−3.59714	−	16.9232i	−0.268863	−	1.26490i	0.611746	−	0.791054i	$-0.290468\pi$
$180$	0.373387	−	8.10525i	0.0278306	−	0.604130i
$181$	6.62999	+	9.12540i	0.492803	+	0.678286i	0.980902	−	0.194503i	$-0.0623094\pi$
$181$	6.62999	+	9.12540i	0.492803	+	0.678286i	−0.488099	+	0.872788i	$0.662309\pi$
$182$	11.2404	+	8.70186i	0.833197	+	0.645025i
$183$	2.15821	−	4.23572i	0.159539	−	0.313114i
$184$	0.00637094	−	0.00573642i	0.000469672	−	0.000422895i
$185$	10.1721	−	11.4420i	0.747867	−	0.841230i
$186$	8.16574	+	14.1435i	0.598741	+	1.03705i
$187$	−2.28552	+	20.1778i	−0.167134	+	1.47555i
$188$	−1.55841	+	1.55841i	−0.113659	+	0.113659i
$189$	2.44047	−	3.51852i	0.177518	−	0.255935i
$190$	9.25799	−	6.81621i	0.671645	−	0.494500i
$191$	20.7511	+	4.41078i	1.50150	+	0.319153i	0.884024	−	0.467441i	$-0.154824\pi$
$191$	20.7511	+	4.41078i	1.50150	+	0.319153i	0.617471	+	0.786594i	$0.288157\pi$
$192$	−0.922658	−	2.40361i	−0.0665871	−	0.173465i
$193$	−3.02246	−	7.87378i	−0.217561	−	0.566767i	0.780751	−	0.624843i	$-0.214837\pi$
$193$	−3.02246	−	7.87378i	−0.217561	−	0.566767i	−0.998312	+	0.0580757i	$0.981504\pi$
$194$	6.08387	+	1.29317i	0.436797	+	0.0928440i
$195$	4.64539	−	30.5805i	0.332664	−	2.18991i
$196$	−0.426241	+	6.98701i	−0.0304458	+	0.499072i
$197$	1.51257	−	1.51257i	0.107766	−	0.107766i	−0.651168	−	0.758934i	$-0.725721\pi$
$197$	1.51257	−	1.51257i	0.107766	−	0.107766i	0.758934	+	0.651168i	$0.225721\pi$
$198$	10.9545	+	4.98353i	0.778500	+	0.354164i
$199$	0.620874	+	1.07538i	0.0440126	+	0.0762320i	0.887192	−	0.461399i	$-0.152653\pi$
$199$	0.620874	+	1.07538i	0.0440126	+	0.0762320i	−0.843180	+	0.537631i	$0.819319\pi$
$200$	2.66993	−	4.22747i	0.188793	−	0.298927i
$201$	−1.52896	+	1.37669i	−0.107845	+	0.0971039i
$202$	3.61810	−	7.10093i	0.254569	−	0.499620i
$203$	0.755021	−	5.55105i	0.0529921	−	0.389608i
$204$	−9.26568	−	12.7531i	−0.648727	−	0.892896i
$205$	19.2021	+	0.884590i	1.34113	+	0.0617824i
$206$	−2.08401	−	9.80452i	−0.145200	−	0.683113i
$207$	−0.0195769	−	0.0241755i	−0.00136069	−	0.00168031i
$208$	−1.39059	−	5.18974i	−0.0964198	−	0.359844i
$209$	4.28039	+	16.5062i	0.296081	+	1.14176i
$210$	13.7344	−	6.58541i	0.947765	−	0.454437i
$211$	15.7840	+	11.4677i	1.08661	+	0.789472i	0.978824	−	0.204702i	$-0.0656226\pi$
$211$	15.7840	+	11.4677i	1.08661	+	0.789472i	0.107790	+	0.994174i	$0.465623\pi$
$212$	−3.32844	−	0.174436i	−0.228598	−	0.0119803i
$213$	0.757755	+	14.4588i	0.0519205	+	0.990702i
$214$	5.31476	−	11.9372i	0.363310	−	0.816007i
$215$	−16.2685	−	9.25590i	−1.10950	−	0.631247i
$216$	−1.53925	+	0.500132i	−0.104732	+	0.0340296i
$217$	−8.83019	+	14.2719i	−0.599433	+	0.968842i
$218$	2.30907	+	14.5789i	0.156390	+	0.987409i
$219$	33.1403	+	19.1336i	2.23942	+	1.29293i
$220$	4.34867	+	6.00742i	0.293187	+	0.405020i
$221$	−16.4482	−	28.4891i	−1.10643	−	1.91639i
$222$	−16.4569	−	6.31721i	−1.10451	−	0.423984i
$223$	10.6677	+	20.9365i	0.714360	+	1.40201i	0.907166	+	0.420773i	$0.138241\pi$
$223$	10.6677	+	20.9365i	0.714360	+	1.40201i	−0.192806	+	0.981237i	$0.561759\pi$
$224$	1.72688	−	2.00446i	0.115382	−	0.133929i
$225$	−14.8118	−	10.4777i	−0.987454	−	0.698515i
$226$	−0.709627	−	6.75165i	−0.0472037	−	0.449113i
$227$	−12.8771	+	0.674862i	−0.854686	+	0.0447922i	−0.474645	−	0.880177i	$-0.657423\pi$
$227$	−12.8771	+	0.674862i	−0.854686	+	0.0447922i	−0.380041	+	0.924970i	$0.624090\pi$
$228$	−11.1016	−	7.20947i	−0.735223	−	0.477459i
$229$	−8.92266	+	3.97262i	−0.589626	+	0.262518i	−0.679788	−	0.733409i	$-0.737928\pi$
$229$	−8.92266	+	3.97262i	−0.589626	+	0.262518i	0.0901621	+	0.995927i	$0.471261\pi$
$230$	−0.00311850	−	0.0189143i	−0.000205628	−	0.00124717i
$231$	1.49421	+	22.5427i	0.0983116	+	1.48320i
$232$	−1.49724	+	1.49724i	−0.0982987	+	0.0982987i
$233$	−10.6680	−	4.09504i	−0.698881	−	0.268275i	−0.0171234	−	0.999853i	$-0.505451\pi$
$233$	−10.6680	−	4.09504i	−0.698881	−	0.268275i	−0.681758	+	0.731578i	$0.738784\pi$
$234$	−19.0699	+	4.05343i	−1.24664	+	0.264981i
$235$	1.05508	+	4.81386i	0.0688261	+	0.314022i
$236$	−1.08667	+	0.114213i	−0.0707359	+	0.00743465i
$237$	12.6252	+	1.99964i	0.820096	+	0.129890i
$238$	7.03655	−	14.5912i	0.456112	−	0.945808i
$239$	4.94922	+	1.60810i	0.320138	+	0.104019i	0.464678	−	0.885480i	$-0.346170\pi$
$239$	4.94922	+	1.60810i	0.320138	+	0.104019i	−0.144540	+	0.989499i	$0.546170\pi$
$240$	−5.63866	−	1.16131i	−0.363974	−	0.0749621i
$241$	20.7090	−	11.9563i	1.33398	−	0.770175i	0.348075	−	0.937467i	$-0.386835\pi$
$241$	20.7090	−	11.9563i	1.33398	−	0.770175i	0.985907	+	0.167292i	$0.0535021\pi$
$242$	−10.6697	+	2.67519i	−0.685877	+	0.171968i
$243$	−5.73390	−	21.3992i	−0.367830	−	1.37276i
$244$	−1.49380	−	1.08531i	−0.0956308	−	0.0694798i
$245$	12.6424	+	9.22869i	0.807696	+	0.589599i
$246$	−6.83941	−	21.0495i	−0.436065	−	1.34207i
$247$	−21.4678	−	17.3843i	−1.36596	−	1.10614i
$248$	5.92196	−	2.27323i	0.376045	−	0.144350i
$249$	22.6980	+	20.4374i	1.43843	+	1.29517i
$250$	−4.74043	−	10.1256i	−0.299811	−	0.640401i
$251$	14.8251	−	20.4051i	0.935754	−	1.28796i	−0.0218179	−	0.999762i	$-0.506945\pi$
$251$	14.8251	−	20.4051i	0.935754	−	1.28796i	0.957572	−	0.288193i	$-0.0930546\pi$
$252$	−6.93553	−	6.63828i	−0.436897	−	0.418172i
$253$	0.0277633	+	0.00613581i	0.00174547	+	0.000385755i
$254$	16.9678	+	9.79639i	1.06466	+	0.614680i
$255$	−35.1880	+	2.06738i	−2.20356	+	0.129465i
$256$	−0.978148	+	0.207912i	−0.0611342	+	0.0129945i
$257$	−0.0874347	−	0.134638i	−0.00545403	−	0.00839847i	0.835933	−	0.548831i	$-0.184927\pi$
$257$	−0.0874347	−	0.134638i	−0.00545403	−	0.00839847i	−0.841387	+	0.540433i	$0.818260\pi$
$258$	−3.37132	+	21.2857i	−0.209889	+	1.32519i
$259$	−2.28748	−	17.9698i	−0.142137	−	1.11659i
$260$	−11.4492	−	3.64018i	−0.710051	−	0.225754i
$261$	5.14114	+	5.70982i	0.318229	+	0.353429i
$262$	12.1670	−	9.85266i	0.751681	−	0.608699i
$263$	−2.14053	+	7.98858i	−0.131991	+	0.492597i	−0.999992	−	0.00396533i	$-0.998738\pi$
$263$	−2.14053	+	7.98858i	−0.131991	+	0.492597i	0.868001	+	0.496562i	$0.165404\pi$
$264$	4.70831	−	7.12367i	0.289777	−	0.438431i
$265$	−4.34244	+	6.05705i	−0.266754	+	0.372082i
$266$	1.12537	−	13.5563i	0.0690007	−	0.831189i
$267$	10.1834	+	19.9860i	0.623212	+	1.22312i
$268$	0.435232	+	0.670199i	0.0265860	+	0.0409389i
$269$	−20.6712	−	9.20340i	−1.26034	−	0.561141i	−0.335698	−	0.941970i	$-0.608972\pi$
$269$	−20.6712	−	9.20340i	−1.26034	−	0.561141i	−0.924646	+	0.380828i	$0.875639\pi$
$270$	−0.914533	+	3.50153i	−0.0556567	+	0.213096i
$271$	2.15477	−	10.1374i	0.130893	−	0.615804i	−0.862976	−	0.505244i	$-0.831402\pi$
$271$	2.15477	−	10.1374i	0.130893	−	0.615804i	0.993870	−	0.110559i	$-0.0352643\pi$
$272$	−5.45541	+	2.77967i	−0.330783	+	0.168542i
$273$	−23.6493	−	27.9312i	−1.43132	−	1.69048i
$274$			15.2613i			0.921969i
$275$	16.5562	−	0.943760i	0.998379	−	0.0569109i
$276$	−0.0191149	+	0.0110360i	−0.00115058	+	0.000664290i
$277$	5.65232	+	6.98004i	0.339615	+	0.419390i	0.918128	−	0.396283i	$-0.129700\pi$
$277$	5.65232	+	6.98004i	0.339615	+	0.419390i	−0.578513	+	0.815673i	$0.696367\pi$
$278$	11.4603	+	0.600608i	0.687342	+	0.0360221i
$279$	−7.11276	−	21.8908i	−0.425830	−	1.31057i
$280$	−1.69183	−	5.66901i	−0.101106	−	0.338788i
$281$	13.5166	−	9.82037i	0.806332	−	0.585834i	−0.106433	−	0.994320i	$-0.533943\pi$
$281$	13.5166	−	9.82037i	0.806332	−	0.585834i	0.912765	+	0.408486i	$0.133943\pi$
$282$	4.75883	−	3.09042i	0.283384	−	0.184032i
$283$	15.7978	−	24.3264i	0.939080	−	1.44606i	0.0445718	−	0.999006i	$-0.485808\pi$
$283$	15.7978	−	24.3264i	0.939080	−	1.44606i	0.894509	−	0.447051i	$-0.147526\pi$
$284$	5.59282	+	0.587830i	0.331873	+	0.0348813i
$285$	−26.9635	+	12.2099i	−1.59718	+	0.723250i
$286$	11.3256	−	13.7575i	0.669697	−	0.813498i
$287$	15.7267	−	16.4309i	0.928319	−	0.969887i
$288$	0.567642	+	3.58395i	0.0334486	+	0.211186i
$289$	−15.2256	+	13.7092i	−0.895625	+	0.806424i
$290$	1.01367	+	4.62491i	0.0595248	+	0.271584i
$291$	−14.6291	−	6.51329i	−0.857573	−	0.381816i
$292$	9.35376	−	11.5509i	0.547388	−	0.675967i
$293$	−3.12116	−	1.59031i	−0.182340	−	0.0929070i	0.360438	−	0.932783i	$-0.382627\pi$
$293$	−3.12116	−	1.59031i	−0.182340	−	0.0929070i	−0.542778	+	0.839876i	$0.682627\pi$
$294$	4.81351	−	17.3676i	0.280730	−	1.01290i
$295$	−1.09542	+	2.18392i	−0.0637777	+	0.127153i
$296$	−3.42338	+	5.92946i	−0.198980	+	0.344643i
$297$	−4.31706	−	3.19006i	−0.250501	−	0.185106i
$298$	−3.31345	+	12.3660i	−0.191943	+	0.716342i
$299$	−0.0420787	+	0.0187346i	−0.00243347	+	0.00108345i
$300$	−8.98675	+	9.21704i	−0.518850	+	0.532146i
$301$	−20.9077	+	7.30314i	−1.20510	+	0.420946i
$302$	−2.07363	+	13.0924i	−0.119324	+	0.753380i
$303$	−12.9127	+	15.9459i	−0.741816	+	0.916067i
$304$	−3.44028	+	3.82082i	−0.197314	+	0.219139i
$305$	−3.84510	+	1.50397i	−0.220170	+	0.0861169i
$306$	9.03653	+	20.2964i	0.516584	+	1.16027i
$307$	7.49543	+	7.49543i	0.427787	+	0.427787i	0.887874	−	0.460087i	$-0.152182\pi$
$307$	7.49543	+	7.49543i	0.427787	+	0.427787i	−0.460087	+	0.887874i	$0.652182\pi$
$308$	8.73874	+	0.796484i	0.497936	+	0.0453839i
$309$			25.8068i			1.46810i
$310$	2.86121	−	13.8924i	0.162506	−	0.789037i
$311$	3.70070	+	17.4104i	0.209847	+	0.987254i	0.949379	+	0.314132i	$0.101714\pi$
$311$	3.70070	+	17.4104i	0.209847	+	0.987254i	−0.739532	+	0.673121i	$0.764953\pi$
$312$	0.723958	+	13.8139i	0.0409861	+	0.782061i
$313$	12.5594	+	10.1704i	0.709899	+	0.574865i	0.914795	−	0.403919i	$-0.132352\pi$
$313$	12.5594	+	10.1704i	0.709899	+	0.574865i	−0.204896	+	0.978784i	$0.565686\pi$
$314$	5.02796	−	3.65303i	0.283744	−	0.206152i
$315$	−20.8638	+	5.05400i	−1.17554	+	0.284761i
$316$	1.53423	−	4.72186i	0.0863070	−	0.265626i
$317$	0.202020	−	0.526280i	0.0113466	−	0.0295588i	−0.927790	−	0.373102i	$-0.878294\pi$
$317$	0.202020	−	0.526280i	0.0113466	−	0.0295588i	0.939137	+	0.343544i	$0.111627\pi$
$318$	8.28879	+	2.22098i	0.464812	+	0.124546i
$319$	−6.92714	−	1.15452i	−0.387845	−	0.0646406i
$320$	−0.788115	+	2.09258i	−0.0440570	+	0.116979i
$321$	−19.7743	+	27.2170i	−1.10369	+	1.51910i
$322$	−0.0192885	−	0.0119340i	−0.00107491	−	0.000665057i
$323$	−14.2915	+	28.0486i	−0.795198	+	1.56066i
$324$	−6.68216	+	0.702323i	−0.371231	+	0.0390179i
$325$	−20.6618	+	17.1688i	−1.14611	+	0.952356i
$326$	−4.17175	+	4.63320i	−0.231052	+	0.256609i
$327$	1.98892	−	37.9509i	0.109988	−	2.09869i
$328$	−8.49072	+	1.34480i	−0.468821	+	0.0742540i
$329$	5.11245	+	2.80426i	0.281858	+	0.154604i
$330$	−7.73574	−	17.4566i	−0.425838	−	0.960954i
$331$	4.23700	−	7.33870i	0.232887	−	0.403372i	−0.725770	−	0.687938i	$-0.758516\pi$
$331$	4.23700	−	7.33870i	0.232887	−	0.403372i	0.958656	+	0.284566i	$0.0918495\pi$
$332$	9.21945	−	7.46576i	0.505983	−	0.409737i
$333$	20.8362	+	13.5312i	1.14182	+	0.741503i
$334$	4.01833	+	0.854123i	0.219873	+	0.0467355i
$335$	1.78685	−	0.0113022i	0.0976262	−	0.000617503i
$336$	−5.42187	+	4.12356i	−0.295787	+	0.224958i
$337$	23.1037	+	11.7719i	1.25854	+	0.641256i	0.950679	−	0.310176i	$-0.100388\pi$
$337$	23.1037	+	11.7719i	1.25854	+	0.641256i	0.307857	+	0.951433i	$0.400388\pi$
$338$	−0.830421	+	15.8454i	−0.0451689	+	0.861875i
$339$	−1.82701	+	17.3829i	−0.0992298	+	0.944109i
$340$	−1.34494	+	13.6247i	−0.0729395	+	0.738902i
$341$	17.5512	+	11.6003i	0.950449	+	0.628189i
$342$	13.1920	+	13.1920i	0.713341	+	0.713341i
$343$	18.0626	−	4.09163i	0.975290	−	0.220928i
$344$	7.96091	+	2.58666i	0.429224	+	0.139463i
$345$	−0.00227122	+	0.0493022i	−0.000122278	+	0.00265434i
$346$	2.78586	−	6.25713i	0.149769	−	0.336386i
$347$	−26.9129	+	10.3309i	−1.44476	+	0.554592i	−0.949393	−	0.314091i	$-0.898300\pi$
$347$	−26.9129	+	10.3309i	−1.44476	+	0.554592i	−0.495368	+	0.868683i	$0.664967\pi$
$348$	4.57204	−	2.96912i	0.245087	−	0.159161i
$349$	−0.972163	+	2.99201i	−0.0520387	+	0.160159i	−0.973699	−	0.227840i	$-0.926834\pi$
$349$	−0.972163	+	2.99201i	−0.0520387	+	0.160159i	0.921660	+	0.387999i	$0.126834\pi$
$350$	−12.7150	−	3.65093i	−0.679644	−	0.195151i
$351$	8.69568			0.464141
$352$	−2.44675	−	2.23907i	−0.130412	−	0.119343i
$353$	20.4365	+	5.47594i	1.08773	+	0.291455i	0.757757	−	0.652537i	$-0.226295\pi$
$353$	20.4365	+	5.47594i	1.08773	+	0.291455i	0.329968	+	0.943992i	$0.392962\pi$
$354$	2.79774	+	0.294055i	0.148698	+	0.0156288i
$355$	7.85162	−	9.82233i	0.416721	−	0.521315i
$356$	8.28589	−	2.69225i	0.439152	−	0.142689i
$357$	−25.5311	+	32.9792i	−1.35125	+	1.74544i
$358$	17.0883	+	2.70652i	0.903143	+	0.143044i
$359$	7.52589	−	35.4065i	0.397201	−	1.86869i	−0.0908399	−	0.995866i	$-0.528955\pi$
$359$	7.52589	−	35.4065i	0.397201	−	1.86869i	0.488041	−	0.872820i	$-0.337712\pi$
$360$	7.43309	+	3.25325i	0.391758	+	0.171461i
$361$	−0.777086	+	7.39348i	−0.0408993	+	0.389131i
$362$	−10.8953	+	2.91938i	−0.572643	+	0.153439i
$363$	28.3021	−	1.02564i	1.48548	−	0.0538320i
$364$	−12.1521	+	7.37538i	−0.636943	+	0.386575i
$365$	−10.4700	−	31.5430i	−0.548024	−	1.65104i
$366$	3.18095	+	3.53281i	0.166271	+	0.184663i
$367$	−23.6733	+	1.24067i	−1.23574	+	0.0647623i	−0.658985	−	0.752156i	$-0.729014\pi$
$367$	−23.6733	+	1.24067i	−1.23574	+	0.0647623i	−0.576753	+	0.816918i	$0.695681\pi$
$368$	0.00307227	+	0.00800354i	0.000160153	+	0.000417213i
$369$	3.26062	+	31.0228i	0.169741	+	1.61498i
$370$	7.03665	+	13.5969i	0.365818	+	0.706869i
$371$	2.02183	+	8.58339i	0.104968	+	0.445627i
$372$	−16.1304	+	2.55481i	−0.836323	+	0.132461i
$373$	−17.1930	+	4.60685i	−0.890220	+	0.238534i	−0.674811	−	0.737990i	$-0.735775\pi$
$373$	−17.1930	+	4.60685i	−0.890220	+	0.238534i	−0.215409	+	0.976524i	$0.569108\pi$
$374$	−18.0186	−	9.36481i	−0.931719	−	0.484243i
$375$	6.51790	+	28.0374i	0.336583	+	1.44784i
$376$	−0.896417	−	2.01339i	−0.0462292	−	0.103832i
$377$	10.1365	−	5.16482i	0.522058	−	0.266002i
$378$	2.41023	+	3.53930i	0.123969	+	0.182042i
$379$	20.3955	+	28.0720i	1.04765	+	1.44196i	0.890832	+	0.454333i	$0.150122\pi$
$379$	20.3955	+	28.0720i	1.04765	+	1.44196i	0.156814	+	0.987628i	$0.449878\pi$
$380$	3.04571	+	11.0858i	0.156242	+	0.568689i
$381$	−37.4871	−	33.7535i	−1.92052	−	1.72924i
$382$	−11.5543	+	17.7921i	−0.591171	+	0.910324i
$383$	−1.18350	+	3.08312i	−0.0604741	+	0.157540i	−0.960488	−	0.278320i	$-0.910222\pi$
$383$	−1.18350	+	3.08312i	−0.0604741	+	0.157540i	0.900014	+	0.435860i	$0.143556\pi$
$384$	2.57461			0.131385
$385$	12.0384	−	15.4944i	0.613533	−	0.789669i
$386$	8.43396			0.429277
$387$	10.8850	−	28.3563i	0.553314	−	1.44143i
$388$	−3.38754	+	5.21636i	−0.171976	+	0.264820i
$389$	5.77845	+	5.20294i	0.292979	+	0.263800i	0.802491	−	0.596664i	$-0.203507\pi$
$389$	5.77845	+	5.20294i	0.292979	+	0.263800i	−0.509512	+	0.860464i	$0.670174\pi$
$390$	26.8846	+	15.2959i	1.36135	+	0.774539i
$391$	0.0308529	+	0.0424653i	0.00156030	+	0.00214756i
$392$	−6.37019	−	2.90185i	−0.321743	−	0.146566i
$393$	−35.9149	+	18.2995i	−1.81167	+	0.923090i
$394$	0.870051	+	1.95417i	0.0438325	+	0.0984495i
$395$	−7.04100	−	8.58333i	−0.354271	−	0.431874i
$396$	−8.57826	+	8.44094i	−0.431074	+	0.424173i
$397$	14.0566	−	3.76645i	0.705479	−	0.189033i	0.111796	−	0.993731i	$-0.464340\pi$
$397$	14.0566	−	3.76645i	0.705479	−	0.189033i	0.593684	+	0.804699i	$0.297673\pi$
$398$	−1.22646	+	0.194252i	−0.0614769	+	0.00973698i
$399$	−10.0906	+	33.5371i	−0.505164	+	1.67895i
$400$	2.98986	+	4.00758i	0.149493	+	0.200379i
$401$	−0.379075	−	3.60666i	−0.0189301	−	0.180108i	0.980971	−	0.194153i	$-0.0621958\pi$
$401$	−0.379075	−	3.60666i	−0.0189301	−	0.180108i	−0.999901	+	0.0140451i	$0.995529\pi$
$402$	−0.737315	−	1.92077i	−0.0367739	−	0.0957994i
$403$	−34.0346	+	1.78368i	−1.69538	+	0.0888512i
$404$	5.33268	+	5.92254i	0.265311	+	0.294657i
$405$	−6.73597	+	13.4294i	−0.334713	+	0.667313i
$406$	4.91178	+	2.69419i	0.243768	+	0.133711i
$407$	−22.6021	+	2.19135i	−1.12035	+	0.108621i
$408$	15.2266	−	4.07995i	0.753828	−	0.201988i
$409$	−2.65052	+	25.2180i	−0.131060	+	1.24695i	0.709295	+	0.704912i	$0.249013\pi$
$409$	−2.65052	+	25.2180i	−0.131060	+	1.24695i	−0.840355	+	0.542037i	$0.817653\pi$
$410$	−7.70726	+	17.6097i	−0.380634	+	0.869681i
$411$	8.16925	−	38.4333i	0.402959	−	1.89577i
$412$	9.90015	+	1.56803i	0.487745	+	0.0772513i
$413$	1.09484	+	2.67555i	0.0538736	+	0.131655i
$414$	0.0295855	−	0.00961290i	0.00145405	−	0.000472448i
$415$	−2.93963	−	26.3636i	−0.144301	−	1.29414i
$416$	5.34338	+	0.561612i	0.261981	+	0.0275353i
$417$	−28.5395	−	7.64713i	−1.39758	−	0.374482i
$418$	−16.9438	−	1.91921i	−0.828749	−	0.0938715i
$419$	−32.6569			−1.59540			−0.797698	−	0.603058i	$-0.793949\pi$
$419$	−32.6569			−1.59540			−0.797698	+	0.603058i	$0.793949\pi$
$420$	1.22604	+	15.1822i	0.0598245	+	0.740815i
$421$	−2.86881	+	8.82930i	−0.139817	+	0.430314i	−0.996308	−	0.0858486i	$-0.972640\pi$
$421$	−2.86881	+	8.82930i	−0.139817	+	0.430314i	0.856491	+	0.516162i	$0.172640\pi$
$422$	−16.3625	+	10.6260i	−0.796515	+	0.517263i
$423$	−7.46604	+	2.86595i	−0.363011	+	0.139347i
$424$	1.35565	−	3.04485i	0.0658364	−	0.147871i
$425$	24.0332	+	18.9634i	1.16578	+	0.919858i
$426$	−13.7700	−	4.47415i	−0.667160	−	0.216773i
$427$	−1.65044	+	4.59798i	−0.0798702	+	0.222512i
$428$	9.23965	+	9.23965i	0.446615	+	0.446615i
$429$	−35.8861	+	28.5837i	−1.73260	+	1.38003i
$430$	14.4712	−	11.8709i	0.697864	−	0.572466i
$431$	−2.24721	+	21.3808i	−0.108245	+	1.02988i	0.796708	+	0.604365i	$0.206573\pi$
$431$	−2.24721	+	21.3808i	−0.108245	+	1.02988i	−0.904952	+	0.425513i	$0.860094\pi$
$432$	0.0847036	−	1.61624i	0.00407531	−	0.0777615i
$433$	13.8030	+	7.03299i	0.663331	+	0.337984i	0.753031	−	0.657985i	$-0.228591\pi$
$433$	13.8030	+	7.03299i	0.663331	+	0.337984i	−0.0897003	+	0.995969i	$0.528591\pi$
$434$	−10.1595	−	13.3583i	−0.487674	−	0.641219i
$435$	−0.0771024	−	12.1898i	−0.00369678	−	0.584454i
$436$	−14.4381	−	3.06891i	−0.691459	−	0.146974i
$437$	0.0369662	+	0.0240061i	0.00176833	+	0.00114837i
$438$	−29.7392	+	24.0823i	−1.42099	+	1.15070i
$439$	11.1404	−	19.2958i	0.531703	−	0.920936i	−0.467612	−	0.883934i	$-0.654886\pi$
$439$	11.1404	−	19.2958i	0.531703	−	0.920936i	0.999315	−	0.0370027i	$-0.0117810\pi$
$440$	−7.16683	+	1.90696i	−0.341665	+	0.0909109i
$441$	−11.7250	+	22.5322i	−0.558335	+	1.07296i
$442$	32.4914	−	5.14613i	1.54546	−	0.244777i
$443$	0.366572	−	6.99460i	0.0174163	−	0.332324i	−0.976001	−	0.217768i	$-0.930122\pi$
$443$	0.366572	−	6.99460i	0.0174163	−	0.332324i	0.993417	−	0.114555i	$-0.0365443\pi$
$444$	11.7953	−	13.1000i	0.559778	−	0.621696i
$445$	4.92301	−	18.8490i	0.233373	−	0.893529i
$446$	−23.3688	+	2.45616i	−1.10655	+	0.116303i
$447$	14.9638	−	29.3682i	0.707765	−	1.38907i
$448$	1.25247	+	2.33052i	0.0591736	+	0.110107i
$449$	11.5035	−	15.8332i	0.542883	−	0.747214i	−0.446142	−	0.894962i	$-0.647203\pi$
$449$	11.5035	−	15.8332i	0.542883	−	0.747214i	0.989025	+	0.147748i	$0.0472025\pi$
$450$	15.0899	−	10.0731i	0.711344	−	0.474852i
$451$	−19.9974	−	20.3227i	−0.941640	−	0.956959i
$452$	6.55752	+	1.75708i	0.308440	+	0.0826462i
$453$	12.2303	−	31.8611i	0.574632	−	1.49697i
$454$	3.98472	−	12.2637i	0.187012	−	0.575564i
$455$	−0.767224	+	31.7767i	−0.0359680	+	1.48972i
$456$	10.7091	−	7.78061i	0.501499	−	0.364360i
$457$	10.4340	+	8.44930i	0.488083	+	0.395241i	0.841528	−	0.540214i	$-0.181657\pi$
$457$	10.4340	+	8.44930i	0.488083	+	0.395241i	−0.353445	+	0.935455i	$0.614990\pi$
$458$	−0.511169	−	9.75368i	−0.0238853	−	0.455760i
$459$	−2.06029	−	9.69288i	−0.0961659	−	0.452425i
$460$	0.0187756	+	0.00386693i	0.000875418	+	0.000180296i
$461$			4.99391i			0.232590i	0.993215	+	0.116295i	$0.0371017\pi$
$461$			4.99391i			0.232590i	−0.993215	+	0.116295i	$0.962898\pi$
$462$	−21.5809	−	6.68360i	−1.00403	−	0.310949i
$463$	−11.2233	−	11.2233i	−0.521591	−	0.521591i	0.396461	−	0.918052i	$-0.370238\pi$
$463$	−11.2233	−	11.2233i	−0.521591	−	0.521591i	−0.918052	+	0.396461i	$0.870238\pi$
$464$	−0.861232	−	1.93436i	−0.0399817	−	0.0898004i
$465$	−14.6420	+	33.4544i	−0.679008	+	1.55141i
$466$	7.64611	−	8.49186i	0.354199	−	0.393378i
$467$	9.44237	−	11.6604i	0.436941	−	0.539577i	−0.510344	−	0.859970i	$-0.670482\pi$
$467$	9.44237	−	11.6604i	0.436941	−	0.539577i	0.947284	+	0.320394i	$0.103815\pi$
$468$	3.04983	−	19.2559i	0.140979	−	0.890104i
$469$	1.37999	−	1.60181i	0.0637219	−	0.0739647i
$470$	−4.87223	−	0.740127i	−0.224739	−	0.0341395i
$471$	−14.6176	+	6.50817i	−0.673543	+	0.299881i
$472$	0.282799	−	1.05542i	0.0130169	−	0.0485797i
$473$	8.36566	+	26.4717i	0.384653	+	1.21717i
$474$	−6.39129	+	11.0700i	−0.293562	+	0.508464i
$475$	24.5474	+	7.63402i	1.12631	+	0.350273i
$476$	11.1004	+	11.7982i	0.508786	+	0.540770i
$477$	−10.7760	−	5.49066i	−0.493400	−	0.251400i
$478$	−3.27493	+	4.04420i	−0.149792	+	0.184978i
$479$	19.1261	+	8.51551i	0.873896	+	0.389083i	0.794143	−	0.607731i	$-0.207920\pi$
$479$	19.1261	+	8.51551i	0.873896	+	0.389083i	0.0797530	+	0.996815i	$0.474587\pi$
$480$	3.10489	−	4.84797i	0.141718	−	0.221278i
$481$	27.3376	−	24.6149i	1.24649	−	1.12234i
$482$	3.74077	+	23.6183i	0.170387	+	1.07578i
$483$	0.0421871	+	0.0403790i	0.00191958	+	0.00183731i
$484$	1.32619	−	10.9198i	0.0602813	−	0.496353i
$485$	5.73709	+	12.6694i	0.260508	+	0.575290i
$486$	22.0327	+	2.31573i	0.999425	+	0.105044i
$487$	10.4223	−	16.0489i	0.472278	−	0.727244i	−0.519604	−	0.854407i	$-0.673920\pi$
$487$	10.4223	−	16.0489i	0.472278	−	0.727244i	0.991882	+	0.127163i	$0.0405871\pi$
$488$	1.54855	−	1.00564i	0.0700997	−	0.0455233i
$489$	12.9860	−	9.43491i	0.587249	−	0.426661i
$490$	−13.1464	+	8.49547i	−0.593892	+	0.383786i
$491$	−12.0224	−	37.0011i	−0.542562	−	1.66983i	−0.726717	−	0.686937i	$-0.758955\pi$
$491$	−12.0224	−	37.0011i	−0.542562	−	1.66983i	0.184155	−	0.982897i	$-0.441045\pi$
$492$	22.1024	+	1.15834i	0.996455	+	0.0522220i
$493$	−8.15878	−	10.0753i	−0.367453	−	0.453767i
$494$	23.9230	−	13.8119i	1.07635	−	0.621429i
$495$	5.54913	+	26.3322i	0.249415	+	1.18355i
$496$			6.34328i			0.284822i
$497$	−2.64873	−	14.6411i	−0.118812	−	0.656742i
$498$	−27.2142	+	13.8663i	−1.21950	+	0.621364i
$499$	1.60812	−	7.56559i	0.0719891	−	0.338682i	−0.927383	−	0.374113i	$-0.877947\pi$
$499$	1.60812	−	7.56559i	0.0719891	−	0.338682i	0.999372	+	0.0354311i	$0.0112804\pi$
$500$	11.1519	−	0.796875i	0.498728	−	0.0356373i
$501$	−9.66236	−	4.30196i	−0.431683	−	0.192197i
$502$	13.7369	+	21.1530i	0.613108	+	0.944103i
$503$	18.3045	+	35.9246i	0.816158	+	1.60180i	0.798529	+	0.601956i	$0.205612\pi$
$503$	18.3045	+	35.9246i	0.816158	+	1.60180i	0.0176293	+	0.999845i	$0.494388\pi$
$504$	8.68284	−	4.09593i	0.386764	−	0.182447i
$505$	17.5831	−	2.89901i	0.782437	−	0.129004i
$506$	−0.0156778	+	0.0237204i	−0.000696961	+	0.00105450i
$507$	10.5732	−	39.4597i	0.469572	−	1.75247i
$508$	−15.2265	+	12.3301i	−0.675565	+	0.547061i
$509$	2.82321	+	3.13549i	0.125136	+	0.138978i	0.802457	−	0.596710i	$-0.203526\pi$
$509$	2.82321	+	3.13549i	0.125136	+	0.138978i	−0.677321	+	0.735688i	$0.736859\pi$
$510$	10.6802	−	33.5918i	0.472927	−	1.48747i
$511$	−36.2663	−	15.2044i	−1.60433	−	0.672602i
$512$	0.156434	−	0.987688i	0.00691349	−	0.0436501i
$513$	−4.53204	−	6.97873i	−0.200094	−	0.308118i
$514$	0.157029	−	0.0333775i	0.00692625	−	0.00147222i
$515$	14.8918	−	16.7509i	0.656211	−	0.738132i
$516$	−18.6637	−	10.7755i	−0.821625	−	0.474366i
$517$	3.70575	−	6.30060i	0.162979	−	0.277100i
$518$	17.5960	+	4.30425i	0.773124	+	0.189118i
$519$	−10.3652	+	14.2664i	−0.454980	+	0.626226i
$520$	7.50143	−	9.38425i	0.328960	−	0.411526i
$521$	13.2605	+	11.9398i	0.580951	+	0.523091i	0.906373	−	0.422478i	$-0.138840\pi$
$521$	13.2605	+	11.9398i	0.580951	+	0.523091i	−0.325422	+	0.945569i	$0.605506\pi$
$522$	−7.17299	+	2.75345i	−0.313953	+	0.120515i
$523$	−14.2792	−	11.5631i	−0.624385	−	0.505617i	0.264116	−	0.964491i	$-0.414920\pi$
$523$	−14.2792	−	11.5631i	−0.624385	−	0.505617i	−0.888502	+	0.458874i	$0.848253\pi$
$524$	4.83798	+	14.8898i	0.211348	+	0.650463i
$525$	30.0665	+	16.0005i	1.31221	+	0.698321i
$526$	−6.69088	−	4.86121i	−0.291736	−	0.211959i
$527$	10.0521	+	37.5150i	0.437877	+	1.63418i
$528$	4.96321	+	6.94848i	0.215996	+	0.302394i
$529$	−19.9185	+	11.5000i	−0.866023	+	0.499998i
$530$	−4.09855	−	6.22467i	−0.178030	−	0.270382i
$531$	−3.77077	−	1.22520i	−0.163637	−	0.0531690i
$532$	12.2526	+	5.90876i	0.531217	+	0.256177i
$533$	45.6190	+	7.22534i	1.97598	+	0.312964i
$534$	−22.3079	+	2.34466i	−0.965358	+	0.101463i
$535$	28.5409	−	6.25548i	1.23393	−	0.270448i
$536$	−0.781658	+	0.166147i	−0.0337625	+	0.00717644i
$537$	−41.5855	−	15.9632i	−1.79454	−	0.688861i
$538$	16.0000	−	16.0000i	0.689809	−	0.689809i
$539$	−4.44848	−	22.7862i	−0.191609	−	0.981471i
$540$	−2.94122	−	2.10863i	−0.126570	−	0.0907408i
$541$	18.5367	−	8.25305i	0.796953	−	0.354826i	0.0324720	−	0.999473i	$-0.489662\pi$
$541$	18.5367	−	8.25305i	0.796953	−	0.354826i	0.764481	+	0.644646i	$0.222995\pi$
$542$	8.69188	+	5.64458i	0.373348	+	0.242455i
$543$	29.0008	−	1.51987i	1.24454	−	0.0652238i
$544$	−0.640002	−	6.08921i	−0.0274399	−	0.261073i
$545$	−23.1906	+	23.4858i	−0.993374	+	1.00602i
$546$	34.5512	−	12.0689i	1.47866	−	0.516500i
$547$	5.81016	+	11.4031i	0.248425	+	0.487561i	0.981221	−	0.192887i	$-0.0617852\pi$
$547$	5.81016	+	11.4031i	0.248425	+	0.487561i	−0.732796	+	0.680448i	$0.761785\pi$
$548$	−14.2477	−	5.46916i	−0.608630	−	0.233631i
$549$	−3.35002	−	5.80240i	−0.142975	−	0.247640i
$550$	−5.05215	+	15.7948i	−0.215424	+	0.673493i
$551$	−9.42802	−	5.44327i	−0.401647	−	0.231891i
$552$	−0.00345282	−	0.0218003i	−0.000146962	−	0.000927881i
$553$	−13.1297	−	0.400115i	−0.558331	−	0.0170146i
$554$	−8.54204	+	2.77548i	−0.362916	+	0.117919i
$555$	−10.4424	−	38.0084i	−0.443257	−	1.61337i
$556$	−4.66771	+	10.4839i	−0.197955	+	0.444614i
$557$	−0.777492	−	14.8354i	−0.0329434	−	0.628597i	−0.964352	−	0.264622i	$-0.914753\pi$
$557$	−0.777492	−	14.8354i	−0.0329434	−	0.628597i	0.931409	−	0.363975i	$-0.118581\pi$
$558$	22.9858	+	1.20464i	0.973068	+	0.0509963i
$559$	−36.3844	−	26.4348i	−1.53890	−	1.11807i
$560$	5.89878	+	0.452135i	0.249269	+	0.0191062i
$561$	40.3642	+	33.2291i	1.70418	+	1.40293i
$562$	4.32420	+	16.1381i	0.182405	+	0.680746i
$563$	−5.62704	−	6.94882i	−0.237152	−	0.292858i	0.644651	−	0.764477i	$-0.277003\pi$
$563$	−5.62704	−	6.94882i	−0.237152	−	0.292858i	−0.881802	+	0.471620i	$0.843670\pi$
$564$	1.17974	+	5.55026i	0.0496761	+	0.233708i
$565$	11.2167	−	10.2288i	0.471890	−	0.430327i
$566$	17.0493	+	23.4663i	0.716634	+	0.986363i
$567$	6.73242	+	16.4525i	0.282735	+	0.690942i
$568$	−2.55308	+	5.01069i	−0.107125	+	0.210244i
$569$	−16.4169	+	14.7818i	−0.688231	+	0.619686i	−0.937186	−	0.348829i	$-0.886579\pi$
$569$	−16.4169	+	14.7818i	−0.688231	+	0.619686i	0.248955	+	0.968515i	$0.419913\pi$
$570$	−1.73603	−	29.5482i	−0.0727143	−	1.23764i
$571$	−3.53397	−	6.12102i	−0.147892	−	0.256157i	0.782556	−	0.622580i	$-0.213916\pi$
$571$	−3.53397	−	6.12102i	−0.147892	−	0.256157i	−0.930448	+	0.366423i	$0.880582\pi$
$572$	8.78500	+	15.5036i	0.367319	+	0.648239i
$573$	38.6218	−	38.6218i	1.61345	−	1.61345i
$574$	9.70364	+	20.5705i	0.405022	+	0.858595i
$575$	0.0299241	−	0.0306909i	0.00124792	−	0.00127990i
$576$	−3.54933	−	0.754433i	−0.147889	−	0.0314347i
$577$	5.46309	+	14.2318i	0.227432	+	0.592480i	0.999049	−	0.0436077i	$-0.0138852\pi$
$577$	5.46309	+	14.2318i	0.227432	+	0.592480i	−0.771617	+	0.636087i	$0.780552\pi$
$578$	−7.34228	−	19.1273i	−0.305399	−	0.795590i
$579$	−21.2397	−	4.51463i	−0.882690	−	0.187622i
$580$	−4.68099	−	0.711076i	−0.194368	−	0.0295258i
$581$	−25.7905	−	17.8885i	−1.06997	−	0.742141i
$582$	11.3233	−	11.3233i	0.469365	−	0.469365i
$583$	10.8310	−	2.21101i	0.448572	−	0.0915706i
$584$	7.43164	+	12.8720i	0.307523	+	0.532646i
$585$	−32.5806	−	28.9647i	−1.34704	−	1.19754i
$586$	2.60321	−	2.34394i	0.107538	−	0.0968272i
$587$	−8.98170	+	17.6276i	−0.370714	+	0.727568i	−0.998717	−	0.0506433i	$-0.983873\pi$
$587$	−8.98170	+	17.6276i	−0.370714	+	0.727568i	0.628002	+	0.778211i	$0.283873\pi$
$588$	14.4890	+	10.7178i	0.597517	+	0.441994i
$589$	19.1697	+	26.3849i	0.789875	+	1.08717i
$590$	−1.64630	−	1.80531i	−0.0677771	−	0.0743233i
$591$	−1.14504	−	5.38701i	−0.0471008	−	0.221592i
$592$	−4.30880	−	5.32093i	−0.177091	−	0.218689i
$593$	−6.42151	−	23.9654i	−0.263700	−	0.984142i	−0.963041	−	0.269354i	$-0.913190\pi$
$593$	−6.42151	−	23.9654i	−0.263700	−	0.984142i	0.699341	−	0.714788i	$-0.253477\pi$
$594$	4.52528	−	2.88711i	0.185674	−	0.118459i
$595$	35.6026	−	6.67372i	1.45956	−	0.273596i
$596$	−10.3572	−	7.52494i	−0.424247	−	0.308234i
$597$	3.19264	+	0.167319i	0.130666	+	0.00684791i
$598$	−0.00241064	−	0.0459977i	−9.85784e−5	−	0.00188099i
$599$	1.79775	−	4.03782i	0.0734542	−	0.164981i	−0.873086	−	0.487566i	$-0.837885\pi$
$599$	1.79775	−	4.03782i	0.0734542	−	0.164981i	0.946541	+	0.322585i	$0.104552\pi$
$600$	−5.38429	−	11.6929i	−0.219813	−	0.477363i
$601$	−45.5374	+	14.7960i	−1.85751	+	0.603542i	−0.862229	+	0.506519i	$0.830932\pi$
$601$	−45.5374	+	14.7960i	−1.85751	+	0.603542i	−0.995282	+	0.0970230i	$0.969068\pi$
$602$	0.674581	−	22.1362i	0.0274939	−	0.902206i
$603$	0.453614	+	2.86401i	0.0184726	+	0.116631i
$604$	−11.4796	−	6.62778i	−0.467100	−	0.269680i
$605$	−18.9625	−	15.6660i	−0.770934	−	0.636915i
$606$	−10.2593	−	17.7696i	−0.416754	−	0.721839i
$607$	21.3244	+	8.18566i	0.865530	+	0.332246i	0.750304	−	0.661093i	$-0.229907\pi$
$607$	21.3244	+	8.18566i	0.865530	+	0.332246i	0.115226	+	0.993339i	$0.463241\pi$
$608$	−2.33416	−	4.58104i	−0.0946625	−	0.185786i
$609$	−10.9274	−	9.41415i	−0.442801	−	0.381481i
$610$	−0.0261147	−	4.12868i	−0.00105735	−	0.167165i
$611$	1.23775	+	11.7764i	0.0500740	+	0.476423i
$612$	−22.1867	+	1.16276i	−0.896845	+	0.0470016i
$613$	−9.03167	−	5.86523i	−0.364786	−	0.236895i	0.349210	−	0.937044i	$-0.386450\pi$
$613$	−9.03167	−	5.86523i	−0.364786	−	0.236895i	−0.713996	+	0.700150i	$0.753117\pi$
$614$	−9.68371	+	4.31146i	−0.390803	+	0.173997i
$615$	28.8359	−	40.2218i	1.16278	−	1.62190i
$616$	−3.87527	+	7.87288i	−0.156139	+	0.317208i
$617$	20.3482	−	20.3482i	0.819188	−	0.819188i	−0.166802	−	0.985990i	$-0.553344\pi$
$617$	20.3482	−	20.3482i	0.819188	−	0.819188i	0.985990	+	0.166802i	$0.0533441\pi$
$618$	−24.0927	−	9.24831i	−0.969150	−	0.372022i
$619$	−34.2180	+	7.27327i	−1.37534	+	0.292337i	−0.835528	−	0.549448i	$-0.814838\pi$
$619$	−34.2180	+	7.27327i	−1.37534	+	0.292337i	−0.539812	+	0.841786i	$0.681505\pi$
$620$	11.9443	+	7.64977i	0.479696	+	0.307222i
$621$	−0.0137990	+	0.00145033i	−0.000553733	+	5.81997e-5i
$622$	−17.5802	−	2.78443i	−0.704903	−	0.111646i
$623$	−12.9745	−	19.0524i	−0.519812	−	0.763317i
$624$	−13.1559	−	4.27460i	−0.526656	−	0.171121i
$625$	11.9483	−	21.9599i	0.477932	−	0.878397i
$626$	−13.9958	+	8.08046i	−0.559383	+	0.322960i
$627$	41.6431	+	13.9031i	1.66307	+	0.555237i
$628$	1.60853	+	6.00313i	0.0641875	+	0.239551i
$629$	−33.9148	−	24.6405i	−1.35227	−	0.982482i
$630$	2.75860	−	21.2892i	0.109905	−	0.848184i
$631$	8.34202	+	25.6741i	0.332091	+	1.02207i	0.968137	+	0.250420i	$0.0805686\pi$
$631$	8.34202	+	25.6741i	0.332091	+	1.02207i	−0.636047	+	0.771651i	$0.719431\pi$
$632$	3.85842	+	3.12449i	0.153480	+	0.124285i
$633$	46.8946	−	18.0011i	1.86389	−	0.715481i
$634$	0.418927	+	0.377204i	0.0166377	+	0.0149807i
$635$	4.85497	+	43.5410i	0.192664	+	1.72787i
$636$	−5.04390	+	6.94233i	−0.200004	+	0.275281i
$637$	27.7328	+	25.4044i	1.09881	+	1.00656i
$638$	3.56030	−	6.05330i	0.140954	−	0.239652i
$639$	17.6721	+	10.2030i	0.699099	+	0.403625i
$640$	−1.67115	−	1.48568i	−0.0660581	−	0.0587267i
$641$	4.37689	−	0.930337i	0.172877	−	0.0367461i	−0.120660	−	0.992694i	$-0.538501\pi$
$641$	4.37689	−	0.930337i	0.172877	−	0.0367461i	0.293537	+	0.955948i	$0.405168\pi$
$642$	−18.3228	−	28.2146i	−0.723142	−	1.11354i
$643$	5.14094	−	32.4586i	0.202739	−	1.28004i	−0.650895	−	0.759168i	$-0.725606\pi$
$643$	5.14094	−	32.4586i	0.202739	−	1.28004i	0.853633	−	0.520874i	$-0.174394\pi$
$644$	0.0180538	−	0.0137306i	0.000711418	−	0.000541063i
$645$	−42.7980	+	22.1488i	−1.68517	+	0.872106i
$646$	−21.0640	−	23.3939i	−0.828752	−	0.920422i
$647$	−2.23020	+	1.80598i	−0.0876782	+	0.0710004i	−0.672157	−	0.740408i	$-0.734632\pi$
$647$	−2.23020	+	1.80598i	−0.0876782	+	0.0710004i	0.584479	+	0.811409i	$0.301299\pi$
$648$	1.73900	−	6.49002i	0.0683142	−	0.254952i
$649$	3.39359	−	1.27136i	0.133210	−	0.0499051i
$650$	−8.62398	−	25.4422i	−0.338260	−	0.997925i
$651$	18.4347	+	39.0792i	0.722513	+	1.53163i
$652$	−2.83044	−	5.55505i	−0.110849	−	0.217553i
$653$	5.54473	+	8.53814i	0.216982	+	0.334123i	0.930354	−	0.366662i	$-0.119500\pi$
$653$	5.54473	+	8.53814i	0.216982	+	0.334123i	−0.713372	+	0.700786i	$0.752833\pi$
$654$	34.7174	+	15.4572i	1.35756	+	0.604424i
$655$	33.8717	+	8.84666i	1.32348	+	0.345668i
$656$	1.78732	−	8.40870i	0.0697833	−	0.328304i
$657$	48.0549	−	24.4852i	1.87480	−	0.955257i
$658$	−4.45014	+	3.76792i	−0.173485	+	0.146889i
$659$			14.7245i			0.573584i	0.957993	+	0.286792i	$0.0925889\pi$
$659$			14.7245i			0.573584i	−0.957993	+	0.286792i	$0.907411\pi$
$660$	19.0694	−	0.966051i	0.742274	−	0.0376035i
$661$	23.1240	−	13.3506i	0.899419	−	0.519280i	0.0224074	−	0.999749i	$-0.492867\pi$
$661$	23.1240	−	13.3506i	0.899419	−	0.519280i	0.877012	+	0.480469i	$0.159534\pi$
$662$	5.33286	+	6.58554i	0.207268	+	0.255954i
$663$	−84.5794	−	4.43262i	−3.28479	−	0.172149i
$664$	3.66594	+	11.2826i	0.142266	+	0.437849i
$665$	25.9023	−	15.9458i	1.00445	−	0.618350i
$666$	−20.0995	+	14.6031i	−0.778838	+	0.565859i
$667$	−0.0152240	+	0.00988658i	−0.000589475	+	0.000382810i
$668$	−2.23743	+	3.44535i	−0.0865689	+	0.133304i
$669$	60.1657	+	6.32367i	2.32614	+	0.244487i
$670$	−0.629799	+	1.67222i	−0.0243313	+	0.0646035i
$671$	5.69930	+	2.24068i	0.220019	+	0.0865006i
$672$	−1.90665	−	6.53950i	−0.0735505	−	0.252267i
$673$	−3.56024	−	22.4785i	−0.137237	−	0.866483i	−0.956217	−	0.292660i	$-0.905460\pi$
$673$	−3.56024	−	22.4785i	−0.137237	−	0.866483i	0.818979	−	0.573823i	$-0.194540\pi$
$674$	−19.2696	+	17.3504i	−0.742238	+	0.668314i
$675$	−7.51752	+	2.99536i	−0.289350	+	0.115291i
$676$	−14.4953	−	6.45374i	−0.557513	−	0.248221i
$677$	26.7175	−	32.9933i	1.02684	−	1.26804i	0.0639991	−	0.997950i	$-0.479615\pi$
$677$	26.7175	−	32.9933i	1.02684	−	1.26804i	0.962836	−	0.270086i	$-0.0870521\pi$
$678$	−15.5736	−	7.93513i	−0.598100	−	0.304747i
$679$	15.7582	+	4.74132i	0.604744	+	0.181955i
$680$	−12.2377	−	6.13825i	−0.469296	−	0.235391i
$681$	−16.5996	+	28.7513i	−0.636097	+	1.10175i
$682$	−17.1195	+	12.2283i	−0.655541	+	0.468245i
$683$	−3.57269	+	13.3335i	−0.136705	+	0.510191i	0.863280	+	0.504726i	$0.168406\pi$
$683$	−3.57269	+	13.3335i	−0.136705	+	0.510191i	−0.999985	+	0.00546543i	$0.998260\pi$
$684$	−17.0434	+	7.58819i	−0.651669	+	0.290142i
$685$	−27.4805	+	20.2326i	−1.04998	+	0.773047i
$686$	−2.65320	+	18.3292i	−0.101300	+	0.699813i
$687$	−3.93376	+	24.8368i	−0.150082	+	0.947583i
$688$	−5.26779	+	6.50518i	−0.200832	+	0.248007i
$689$	−11.9825	+	13.3079i	−0.456498	+	0.506992i
$690$	−0.0452137	−	0.0197887i	−0.00172126	−	0.000753343i
$691$	−6.61906	−	14.8666i	−0.251801	−	0.565554i	0.742778	−	0.669538i	$-0.233508\pi$
$691$	−6.61906	−	14.8666i	−0.251801	−	0.565554i	−0.994579	+	0.103984i	$0.966841\pi$
$692$	4.84318	+	4.84318i	0.184110	+	0.184110i
$693$	27.7926	+	15.5377i	1.05575	+	0.590230i
$694$		−	28.8276i		−	1.09428i
$695$	14.1119	+	21.4324i	0.535295	+	0.812977i
$696$	1.13344	+	5.33240i	0.0429628	+	0.202124i
$697$	−2.75468	−	52.5624i	−0.104341	−	1.99094i
$698$	−2.44489	−	1.97983i	−0.0925404	−	0.0749377i
$699$	−23.8012	+	17.2926i	−0.900244	+	0.654065i
$700$	7.96508	−	10.5621i	0.301052	−	0.399209i
$701$	−14.8000	+	45.5498i	−0.558989	+	1.72039i	0.126179	+	0.992007i	$0.459728\pi$
$701$	−14.8000	+	45.5498i	−0.558989	+	1.72039i	−0.685169	+	0.728384i	$0.740272\pi$
$702$	−3.11625	+	8.11812i	−0.117615	+	0.306399i
$703$	−34.0026	−	9.11096i	−1.28243	−	0.343626i
$704$	2.96719	−	1.48182i	0.111830	−	0.0558483i
$705$	11.8738	+	4.47196i	0.447193	+	0.168424i
$706$	−12.4360	+	17.1167i	−0.468036	+	0.644196i
$707$	11.0941	−	17.9310i	0.417235	−	0.674363i
$708$	−1.27715	+	2.50654i	−0.0479981	+	0.0942015i
$709$	−2.20653	+	0.231916i	−0.0828681	+	0.00870979i	−0.145872	−	0.989304i	$-0.546599\pi$
$709$	−2.20653	+	0.231916i	−0.0828681	+	0.00870979i	0.0630037	+	0.998013i	$0.479932\pi$
$710$	6.35617	+	10.8501i	0.238543	+	0.407198i
$711$	12.0548	−	13.3882i	0.452090	−	0.502097i
$712$	−0.455967	+	8.70037i	−0.0170881	+	0.326060i
$713$	0.0537111	−	0.00850701i	0.00201150	−	0.000318590i
$714$	−21.6392	−	35.6540i	−0.809827	−	1.33432i
$715$	39.7875	+	2.15474i	1.48797	+	0.0805826i
$716$	−8.65064	+	14.9833i	−0.323289	+	0.559954i
$717$	10.4123	−	8.43167i	0.388853	−	0.314887i
$718$	30.3578	+	19.7146i	1.13294	+	0.735742i
$719$	24.9908	+	5.31196i	0.932001	+	0.198103i	0.648801	−	0.760958i	$-0.275271\pi$
$719$	24.9908	+	5.31196i	0.932001	+	0.198103i	0.283200	+	0.959061i	$0.408604\pi$
$720$	−5.70095	+	5.77353i	−0.212462	+	0.215167i
$721$	−3.34884	−	26.3075i	−0.124717	−	0.979744i
$722$	−6.62393	−	3.37506i	−0.246517	−	0.125607i
$723$	3.22211	−	61.4814i	0.119831	−	2.28652i
$724$	1.17904	−	11.2178i	0.0438187	−	0.416907i
$725$	−6.98406	+	7.95673i	−0.259381	+	0.295506i
$726$	−9.18507	+	26.7899i	−0.340890	+	0.994266i
$727$	−23.1306	−	23.1306i	−0.857866	−	0.857866i	0.133221	−	0.991086i	$-0.457468\pi$
$727$	−23.1306	−	23.1306i	−0.857866	−	0.857866i	−0.991086	+	0.133221i	$0.957468\pi$
$728$	−2.53059	−	13.9881i	−0.0937899	−	0.518432i
$729$	−35.0762	−	11.3969i	−1.29912	−	0.422109i
$730$	33.2001	+	1.52944i	1.22879	+	0.0566071i
$731$	−20.8457	+	46.8202i	−0.771006	+	1.73171i
$732$	−4.43811	+	1.70363i	−0.164037	+	0.0629680i
$733$	−42.6745	+	27.7131i	−1.57622	+	1.02361i	−0.601860	+	0.798601i	$0.705574\pi$
$733$	−42.6745	+	27.7131i	−1.57622	+	1.02361i	−0.974357	+	0.225006i	$0.927760\pi$
$734$	7.32550	−	22.5456i	0.270389	−	0.832172i
$735$	37.6547	−	14.3574i	1.38891	−	0.529581i
$736$	−0.00857295			−0.000316003
$737$	−1.95525	−	1.78929i	−0.0720224	−	0.0659092i
$738$	−30.1308	−	8.07351i	−1.10913	−	0.297190i
$739$	−13.3519	−	1.40334i	−0.491156	−	0.0516226i	−0.144287	−	0.989536i	$-0.546089\pi$
$739$	−13.3519	−	1.40334i	−0.491156	−	0.0516226i	−0.346870	+	0.937913i	$0.612755\pi$
$740$	−15.2155	+	1.69658i	−0.559333	+	0.0623676i
$741$	−67.6399	+	21.9775i	−2.48481	+	0.807365i
$742$	−8.73785	−	1.18847i	−0.320776	−	0.0436301i
$743$	29.3448	+	4.64775i	1.07656	+	0.170510i	0.669439	−	0.742867i	$-0.266534\pi$
$743$	29.3448	+	4.64775i	1.07656	+	0.170510i	0.407116	+	0.913376i	$0.366534\pi$
$744$	3.39551	−	15.9746i	0.124485	−	0.585657i
$745$	−26.6598	+	10.4277i	−0.976740	+	0.382041i
$746$	1.86055	−	17.7020i	0.0681198	−	0.648116i
$747$	41.5803	−	11.1414i	1.52135	−	0.407643i
$748$	15.2001	−	13.4657i	0.555770	−	0.492357i
$749$	16.6262	−	30.3112i	0.607507	−	1.10755i
$750$	−28.5110	−	3.96271i	−1.04107	−	0.144698i
$751$	21.4748	+	23.8502i	0.783626	+	0.870305i	0.994230	−	0.107266i	$-0.0342097\pi$
$751$	21.4748	+	23.8502i	0.783626	+	0.870305i	−0.210604	+	0.977571i	$0.567543\pi$
$752$	2.20090	−	0.115345i	0.0802587	−	0.00420618i
$753$	−23.2713	−	60.6238i	−0.848054	−	2.20926i
$754$	1.18917	+	11.3142i	0.0433069	+	0.412038i
$755$	−26.3241	+	13.6232i	−0.958031	+	0.495799i
$756$	−4.16797	+	0.981773i	−0.151588	+	0.0357068i
$757$	32.3802	−	5.12852i	1.17688	−	0.186399i	0.462799	−	0.886463i	$-0.346845\pi$
$757$	32.3802	−	5.12852i	1.17688	−	0.186399i	0.714080	+	0.700064i	$0.246845\pi$
$758$	−33.5165	+	8.98073i	−1.21738	+	0.326195i
$759$	0.0521794	−	0.0513441i	0.00189399	−	0.00186367i
$760$	−11.4410	−	1.12938i	−0.415007	−	0.0409668i
$761$	21.0813	+	47.3495i	0.764198	+	1.71642i	0.695218	+	0.718799i	$0.255308\pi$
$761$	21.0813	+	47.3495i	0.764198	+	1.71642i	0.0689797	+	0.997618i	$0.478026\pi$
$762$	44.9458	−	22.9010i	1.62821	−	0.829616i
$763$	2.89722	+	38.9454i	0.104886	+	1.40992i
$764$	−12.4697	−	17.1630i	−0.451137	−	0.620937i
$765$	−24.5669	+	43.1796i	−0.888219	+	1.56116i
$766$	−2.45422	−	2.20979i	−0.0886744	−	0.0798428i
$767$	−3.19737	+	4.92351i	−0.115450	+	0.177778i
$768$	−0.922658	+	2.40361i	−0.0332936	+	0.0867327i
$769$	1.32803			0.0478898			0.0239449	−	0.999713i	$-0.492377\pi$
$769$	1.32803			0.0478898			0.0239449	+	0.999713i	$0.492377\pi$
$770$	10.1511	+	16.7915i	0.365821	+	0.605124i
$771$	−0.413320			−0.0148854
$772$	−3.02246	+	7.87378i	−0.108781	+	0.283383i
$773$	21.3031	−	32.8039i	0.766219	−	1.17987i	−0.212997	−	0.977053i	$-0.568322\pi$
$773$	21.3031	−	32.8039i	0.766219	−	1.17987i	0.979216	−	0.202821i	$-0.0650110\pi$
$774$	22.5721	+	20.3240i	0.811337	+	0.730531i
$775$	28.8089	−	13.2657i	1.03485	−	0.476519i
$776$	−3.65590	−	5.03192i	−0.131239	−	0.180635i
$777$	−42.0089	−	20.2586i	−1.50706	−	0.726774i
$778$	−6.92818	+	3.53008i	−0.248387	+	0.126560i
$779$	−17.9771	−	40.3773i	−0.644098	−	1.44667i
$780$	−23.9145	+	19.6174i	−0.856278	+	0.702414i
$781$	−18.4448	+	2.76901i	−0.660006	+	0.0990828i
$782$	−0.0507015	+	0.0135854i	−0.00181308	+	0.000485814i
$783$	3.38477	−	0.536094i	0.120962	−	0.0191584i
$784$	4.99198	−	4.90715i	0.178285	−	0.175255i
$785$	13.2437	+	4.21071i	0.472687	+	0.150287i
$786$	−4.21335	−	40.0874i	−0.150285	−	1.42987i
$787$	13.2173	+	34.4322i	0.471146	+	1.22738i	0.939106	+	0.343627i	$0.111656\pi$
$787$	13.2173	+	34.4322i	0.471146	+	1.22738i	−0.467960	+	0.883750i	$0.655011\pi$
$788$	−2.13617	+	0.111952i	−0.0760979	+	0.00398812i
$789$	14.2478	+	15.8238i	0.507235	+	0.563342i
$790$	10.5365	−	3.49735i	0.374872	−	0.124430i
$791$	−0.393242	−	17.9573i	−0.0139821	−	0.638488i
$792$	−4.80612	−	11.0335i	−0.170778	−	0.392057i
$793$	−9.58253	+	2.56763i	−0.340286	+	0.0911793i
$794$	−1.52114	+	14.4727i	−0.0539834	+	0.513618i
$795$	6.98958	+	17.8698i	0.247895	+	0.633777i
$796$	0.258174	−	1.21461i	0.00915073	−	0.0430508i
$797$	43.9231	+	6.95673i	1.55584	+	0.246420i	0.874308	−	0.485372i	$-0.161316\pi$
$797$	43.9231	+	6.95673i	1.55584	+	0.246420i	0.681528	+	0.731792i	$0.261316\pi$
$798$	−27.6934	−	21.4390i	−0.980336	−	0.758934i
$799$	12.8336	−	4.16990i	0.454022	−	0.147521i
$800$	−4.81287	+	1.35509i	−0.170161	+	0.0479095i
$801$	31.4405	+	3.30453i	1.11089	+	0.116760i
$802$	3.50295	+	0.938613i	0.123694	+	0.0331436i
$803$	−20.4131	+	44.8708i	−0.720364	+	1.58346i
$804$	2.05742			0.0725598
$805$	−0.00408247	−	0.0505537i	−0.000143888	−	0.00178178i
$806$	10.5317	−	32.4132i	0.370963	−	1.14171i
$807$	−48.8583	+	31.7289i	−1.71989	+	1.11691i
$808$	−7.44022	+	2.85603i	−0.261746	+	0.100475i
$809$	−2.15424	+	4.83850i	−0.0757390	+	0.170113i	−0.947447	−	0.319914i	$-0.896346\pi$
$809$	−2.15424	+	4.83850i	−0.0757390	+	0.170113i	0.871708	+	0.490026i	$0.163013\pi$
$810$	−10.1235	−	11.1012i	−0.355703	−	0.390058i
$811$	2.24950	+	0.730907i	0.0789907	+	0.0256656i	0.348246	−	0.937403i	$-0.386777\pi$
$811$	2.24950	+	0.730907i	0.0789907	+	0.0256656i	−0.269255	+	0.963069i	$0.586777\pi$
$812$	−4.27547	+	3.62003i	−0.150040	+	0.127038i
$813$	−18.8677	−	18.8677i	−0.661719	−	0.661719i
$814$	6.05407	−	21.8862i	0.212195	−	0.767112i
$815$	−13.8735	−	1.36950i	−0.485968	−	0.0479716i
$816$	−1.64776	+	15.6774i	−0.0576830	+	0.548817i
$817$	−2.25237	+	42.9778i	−0.0788004	+	1.50360i
$818$	−22.5932	−	11.5118i	−0.789951	−	0.402500i
$819$	−51.1684	+	6.51353i	−1.78797	+	0.227601i
$820$	−13.6780	−	13.5061i	−0.477658	−	0.471653i
$821$	−3.52166	−	0.748553i	−0.122907	−	0.0261247i	0.146047	−	0.989278i	$-0.453345\pi$
$821$	−3.52166	−	0.748553i	−0.122907	−	0.0261247i	−0.268954	+	0.963153i	$0.586678\pi$
$822$	32.9530	+	21.3999i	1.14937	+	0.746408i
$823$	11.6947	−	9.47015i	0.407650	−	0.330109i	−0.403465	−	0.914995i	$-0.632194\pi$
$823$	11.6947	−	9.47015i	0.407650	−	0.330109i	0.811115	+	0.584886i	$0.198861\pi$
$824$	−5.01178	+	8.68065i	−0.174594	+	0.302405i
$825$	21.1779	−	37.0725i	0.737320	−	1.29070i
$826$	−2.89019	+	0.0632916i	−0.100563	+	0.00220220i
$827$	−41.2296	+	6.53012i	−1.43369	+	0.227075i	−0.824461	−	0.565918i	$-0.808522\pi$
$827$	−41.2296	+	6.53012i	−1.43369	+	0.227075i	−0.609231	+	0.792993i	$0.708522\pi$
$828$	−0.00162807	+	0.0310654i	−5.65792e−5	+	0.00107960i
$829$	26.6299	−	29.5755i	0.924893	−	1.02720i	−0.0746570	−	0.997209i	$-0.523786\pi$
$829$	26.6299	−	29.5755i	0.924893	−	1.02720i	0.999550	−	0.0299887i	$-0.00954714\pi$
$830$	25.6660	+	6.70348i	0.890879	+	0.232681i
$831$	22.9975	−	2.41714i	0.797776	−	0.0838496i
$832$	−2.43921	+	4.78721i	−0.0845643	+	0.165967i
$833$	21.7469	−	36.9322i	0.753486	−	1.27963i
$834$	17.3669	−	23.9034i	0.601365	−	0.827708i
$835$	3.78929	+	8.36803i	0.131134	+	0.289588i
$836$	7.86386	−	15.1306i	0.271977	−	0.523304i
$837$	−9.91653	−	2.65713i	−0.342765	−	0.0918437i
$838$	11.7032	−	30.4879i	0.404280	−	1.05319i
$839$	−5.97591	+	18.3920i	−0.206311	+	0.634961i	0.793346	+	0.608772i	$0.208337\pi$
$839$	−5.97591	+	18.3920i	−0.206311	+	0.634961i	−0.999657	+	0.0261898i	$0.991663\pi$
$840$	−14.6132	−	4.29620i	−0.504202	−	0.148233i
$841$	−19.8343	+	14.4105i	−0.683941	+	0.496912i
$842$	−7.21477	−	5.84241i	−0.248637	−	0.201343i
$843$	−2.25124	−	42.9561i	−0.0775367	−	1.47949i
$844$	−4.05637	−	19.0837i	−0.139626	−	0.656889i
$845$	−29.6332	+	19.5116i	−1.01941	+	0.671219i
$846$		−	7.99721i		−	0.274950i
$847$	−28.7183	+	4.71820i	−0.986771	+	0.162119i
$848$	2.35679	+	2.35679i	0.0809325	+	0.0809325i
$849$	−30.3747	−	68.2227i	−1.04246	−	2.34140i
$850$	−26.3165	+	15.6410i	−0.902650	+	0.536483i
$851$	−0.0392759	+	0.0436203i	−0.00134636	+	0.00149528i
$852$	9.11172	−	11.2520i	0.312162	−	0.385488i
$853$	−2.08516	+	13.1652i	−0.0713946	+	0.450768i	0.925932	+	0.377691i	$0.123282\pi$
$853$	−2.08516	+	13.1652i	−0.0713946	+	0.450768i	−0.997326	+	0.0730768i	$0.976718\pi$
$854$	−3.70112	−	3.18858i	−0.126650	−	0.109111i
$855$	−6.26519	+	41.2436i	−0.214265	+	1.41050i
$856$	−11.9372	+	5.31476i	−0.408004	+	0.181655i
$857$	10.9930	−	41.0264i	0.375513	−	1.40143i	−0.477080	−	0.878860i	$-0.658305\pi$
$857$	10.9930	−	41.0264i	0.375513	−	1.40143i	0.852593	−	0.522575i	$-0.175028\pi$
$858$	−13.8247	−	43.7461i	−0.471969	−	1.49347i
$859$	−1.77085	+	3.06721i	−0.0604208	+	0.104652i	−0.894654	−	0.446761i	$-0.852578\pi$
$859$	−1.77085	+	3.06721i	−0.0604208	+	0.104652i	0.834233	+	0.551412i	$0.185911\pi$
$860$	5.89642	+	17.7642i	0.201066	+	0.605754i
$861$	−13.4260	−	56.9979i	−0.457556	−	1.94248i
$862$	−19.1554	−	9.76015i	−0.652435	−	0.332432i
$863$	−3.15714	+	3.89874i	−0.107470	+	0.132715i	−0.828043	−	0.560665i	$-0.810546\pi$
$863$	−3.15714	+	3.89874i	−0.107470	+	0.132715i	0.720573	+	0.693379i	$0.243879\pi$
$864$	1.47854	+	0.658287i	0.0503008	+	0.0223954i
$865$	14.9603	−	3.27896i	0.508667	−	0.111488i
$866$	−11.5124	+	10.3658i	−0.391208	+	0.352245i
$867$	8.25175	+	52.0995i	0.280244	+	1.76939i
$868$	16.1119	−	4.69757i	0.546874	−	0.159446i
$869$	−0.994442	+	16.4365i	−0.0337341	+	0.557571i
$870$	11.4077	+	4.29644i	0.386759	+	0.145663i
$871$	4.27001	+	0.448796i	0.144684	+	0.0152069i
$872$	8.03923	−	12.3793i	0.272243	−	0.419217i
$873$	−18.9282	+	12.2921i	−0.640622	+	0.416025i
$874$	−0.0356592	+	0.0259079i	−0.00120619	+	0.000876348i
$875$	−10.2827	−	27.7357i	−0.347618	−	0.937636i
$876$	−11.8252	−	36.3942i	−0.399537	−	1.22965i
$877$	−43.9240	−	2.30196i	−1.48321	−	0.0777316i	−0.706554	−	0.707659i	$-0.749751\pi$
$877$	−43.9240	−	2.30196i	−1.48321	−	0.0777316i	−0.776654	+	0.629928i	$0.783085\pi$
$878$	14.0218	+	17.3155i	0.473212	+	0.584368i
$879$	−7.81048	+	4.50938i	−0.263441	+	0.152098i
$880$	0.788061	−	7.37421i	0.0265655	−	0.248585i
$881$		−	14.6923i		−	0.494997i	−0.968888	−	0.247498i	$-0.920391\pi$
$881$		−	14.6923i		−	0.494997i	0.968888	−	0.247498i	$-0.0796085\pi$
$882$	−16.8338	−	19.0211i	−0.566823	−	0.640474i
$883$	−6.60662	+	3.36624i	−0.222330	+	0.113283i	−0.561608	−	0.827403i	$-0.689817\pi$
$883$	−6.60662	+	3.36624i	−0.222330	+	0.113283i	0.339278	+	0.940686i	$0.389817\pi$
$884$	−6.83955	+	32.1775i	−0.230039	+	1.08225i
$885$	3.17960	+	5.42765i	0.106881	+	0.182448i
$886$	6.39866	+	2.84887i	0.214967	+	0.0957095i
$887$	21.9769	+	33.8415i	0.737913	+	1.13629i	0.985869	+	0.167515i	$0.0535743\pi$
$887$	21.9769	+	33.8415i	0.737913	+	1.13629i	−0.247957	+	0.968771i	$0.579759\pi$
$888$	8.00282	+	15.7064i	0.268557	+	0.527073i
$889$	42.5946	+	29.5439i	1.42858	+	0.990872i
$890$	15.8328	+	11.3509i	0.530717	+	0.380483i
$891$	20.8679	−	7.81786i	0.699102	−	0.261908i
$892$	6.08162	−	22.6969i	0.203628	−	0.759948i
$893$	8.80608	−	7.13102i	0.294684	−	0.238631i
$894$	22.0550	+	24.4946i	0.737630	+	0.819221i
$895$	17.7811	+	34.3584i	0.594357	+	1.14848i
$896$	−2.62457	+	0.334097i	−0.0876808	+	0.0111614i
$897$	−0.0185514	+	0.117129i	−0.000619412	+	0.00391082i
$898$	10.6591	+	16.4135i	0.355698	+	0.547726i
$899$	−13.1379	+	2.79254i	−0.438173	+	0.0931365i
$900$	3.99636	+	17.6975i	0.133212	+	0.589917i
$901$	17.6731	+	10.2036i	0.588777	+	0.339931i
$902$	26.1393	−	11.3862i	0.870344	−	0.379118i
$903$	−13.5482	+	55.3857i	−0.450855	+	1.84312i
$904$	−3.99038	+	5.49229i	−0.132718	+	0.182671i
$905$	−19.7012	−	15.7484i	−0.654889	−	0.523495i
$906$	25.3620	+	22.8360i	0.842595	+	0.758676i
$907$	−21.8301	+	8.37979i	−0.724857	+	0.278246i	−0.692689	−	0.721236i	$-0.743574\pi$
$907$	−21.8301	+	8.37979i	−0.724857	+	0.278246i	−0.0321674	+	0.999482i	$0.510241\pi$
$908$	10.0212	+	8.11497i	0.332564	+	0.269305i
$909$	8.93632	+	27.5032i	0.296399	+	0.912222i
$910$	−29.3912	−	12.1040i	−0.974308	−	0.401245i
$911$	−15.5271	−	11.2811i	−0.514435	−	0.373759i	0.300069	−	0.953918i	$-0.402990\pi$
$911$	−15.5271	−	11.2811i	−0.514435	−	0.373759i	−0.814503	+	0.580159i	$0.802990\pi$
$912$	3.42603	+	12.7861i	0.113447	+	0.423391i
$913$	−23.3830	+	31.6438i	−0.773864	+	1.04726i
$914$	−11.6273	+	6.71303i	−0.384597	+	0.222047i
$915$	−2.14428	+	10.4114i	−0.0708878	+	0.344192i
$916$	9.28903	+	3.01819i	0.306918	+	0.0997238i
$917$	34.2371	−	23.3152i	1.13061	−	0.769935i
$918$	9.78743	+	1.55018i	0.323033	+	0.0511634i
$919$	−18.0821	+	1.90050i	−0.596473	+	0.0626919i	−0.397954	−	0.917405i	$-0.630280\pi$
$919$	−18.0821	+	1.90050i	−0.596473	+	0.0626919i	−0.198519	+	0.980097i	$0.563613\pi$
$920$	−0.0103387	+	0.0161428i	−0.000340856	+	0.000532212i
$921$	26.6949	−	5.67417i	0.879625	−	0.186970i
$922$	−4.66222	−	1.78966i	−0.153542	−	0.0589392i
$923$	21.3650	−	21.3650i	0.703239	−	0.703239i
$924$	13.9736	−	17.7523i	0.459697	−	0.584007i
$925$	−15.1547	+	30.6967i	−0.498284	+	1.00930i
$926$	14.4999	−	6.45579i	0.476497	−	0.212150i
$927$	30.5039	+	19.8094i	1.00188	+	0.650628i
$928$	2.11452	−	0.110817i	0.0694124	−	0.00363775i
$929$	−5.48621	−	52.1978i	−0.179997	−	1.71255i	−0.595827	−	0.803113i	$-0.703176\pi$
$929$	−5.48621	−	52.1978i	−0.179997	−	1.71255i	0.415831	−	0.909442i	$-0.363491\pi$
$930$	−25.9852	−	25.6585i	−0.852087	−	0.841375i
$931$	5.93447	−	35.4973i	0.194494	−	1.16338i
$932$	5.18772	+	10.1815i	0.169929	+	0.333505i
$933$	42.7827	+	16.4227i	1.40064	+	0.537656i
$934$	7.50203	+	12.9939i	0.245474	+	0.425174i
$935$	−7.02511	−	44.8608i	−0.229746	−	1.46711i
$936$	16.8840	+	9.74796i	0.551869	+	0.318622i
$937$	1.85443	+	11.7084i	0.0605815	+	0.382497i	0.999286	+	0.0377744i	$0.0120268\pi$
$937$	1.85443	+	11.7084i	0.0605815	+	0.382497i	−0.938705	+	0.344722i	$0.887973\pi$
$938$	1.00087	+	1.86237i	0.0326797	+	0.0608084i
$939$	39.5716	−	12.8576i	1.29137	−	0.419592i
$940$	2.43702	−	4.28338i	0.0794868	−	0.139709i
$941$	13.5968	−	30.5389i	0.443243	−	0.995540i	−0.544401	−	0.838825i	$-0.683243\pi$
$941$	13.5968	−	30.5389i	0.443243	−	0.995540i	0.987644	−	0.156715i	$-0.0500904\pi$
$942$	−0.837425	−	15.9790i	−0.0272848	−	0.520625i
$943$	−0.0735968	−	0.00385705i	−0.00239664	−	0.000125603i
$944$	0.883974	+	0.642245i	0.0287709	+	0.0209033i
$945$	−3.17776	+	9.03223i	−0.103372	+	0.293819i
$946$	−27.7115	−	1.67660i	−0.900977	−	0.0545109i
$947$	−10.7347	−	40.0626i	−0.348832	−	1.30186i	−0.888071	−	0.459706i	$-0.847955\pi$
$947$	−10.7347	−	40.0626i	−0.348832	−	1.30186i	0.539239	−	0.842153i	$-0.318712\pi$
$948$	−8.04434	−	9.93393i	−0.261268	−	0.322639i
$949$	−16.6033	−	78.1125i	−0.538967	−	2.53564i
$950$	−15.9240	+	20.1812i	−0.516642	+	0.654765i
$951$	−0.853091	−	1.17418i	−0.0276634	−	0.0380754i
$952$	−14.9926	+	6.13501i	−0.485913	+	0.198837i
$953$	3.93706	−	7.72692i	0.127534	−	0.250299i	−0.818407	−	0.574640i	$-0.805142\pi$
$953$	3.93706	−	7.72692i	0.127534	−	0.250299i	0.945941	+	0.324340i	$0.105142\pi$
$954$	8.98775	−	8.09261i	0.290989	−	0.262008i
$955$	−47.3558	+	2.78227i	−1.53240	+	0.0900321i
$956$	−2.60196	−	4.50672i	−0.0841534	−	0.145758i
$957$	−12.2064	+	13.3385i	−0.394576	+	0.431173i
$958$	−14.8041	+	14.8041i	−0.478299	+	0.478299i
$959$	−3.34043	+	40.2392i	−0.107868	+	1.29939i
$960$	3.41327	+	4.63602i	0.110163	+	0.149627i
$961$	9.03537	+	1.92053i	0.291464	+	0.0619525i
$962$	13.1830	+	34.3430i	0.425038	+	1.10726i
$963$	16.9919	+	44.2654i	0.547556	+	1.42643i
$964$	−23.3901	−	4.97172i	−0.753345	−	0.160128i
$965$	11.1813	+	15.1868i	0.359938	+	0.488879i
$966$	−0.0528156	+	0.0249145i	−0.00169931	+	0.000801611i
$967$	−15.9266	+	15.9266i	−0.512166	+	0.512166i	−0.915189	−	0.403024i	$-0.867959\pi$
$967$	−15.9266	+	15.9266i	−0.512166	+	0.512166i	0.403024	+	0.915189i	$0.367959\pi$
$968$	9.71921	+	5.15140i	0.312387	+	0.165572i
$969$	40.5239	+	70.1895i	1.30182	+	2.25481i
$970$	−13.8839	+	0.815715i	−0.445786	+	0.0261910i
$971$	−8.58942	+	7.73395i	−0.275648	+	0.248194i	−0.795346	−	0.606155i	$-0.792711\pi$
$971$	−8.58942	+	7.73395i	−0.275648	+	0.248194i	0.519699	+	0.854350i	$0.326044\pi$
$972$	−10.0578	+	19.7394i	−0.322603	+	0.633143i
$973$	30.0856	+	4.09207i	0.964502	+	0.131186i
$974$	11.2479	+	15.4814i	0.360407	+	0.496057i
$975$	8.09921	+	68.6887i	0.259382	+	2.19980i
$976$	0.383896	+	1.80609i	0.0122882	+	0.0578115i
$977$	−19.1612	−	23.6621i	−0.613022	−	0.757019i	0.372228	−	0.928141i	$-0.378594\pi$
$977$	−19.1612	−	23.6621i	−0.613022	−	0.757019i	−0.985250	+	0.171123i	$0.945261\pi$
$978$	4.15447	+	15.5047i	0.132845	+	0.495785i
$979$	−24.3599	+	15.5415i	−0.778547	+	0.496710i
$980$	−3.21996	−	15.3177i	−0.102858	−	0.489306i
$981$	−43.3316	−	31.4823i	−1.38347	−	1.00515i
$982$	38.8519	+	2.03614i	1.23981	+	0.0649759i
$983$	−0.281215	−	5.36590i	−0.00896936	−	0.171146i	−0.999441	−	0.0334294i	$-0.989357\pi$
$983$	−0.281215	−	5.36590i	−0.00896936	−	0.171146i	0.990472	−	0.137716i	$-0.0439762\pi$
$984$	−9.00221	+	20.2193i	−0.286980	+	0.644568i
$985$	−2.36534	+	4.15740i	−0.0753660	+	0.132466i
$986$	12.3299	−	4.00623i	0.392664	−	0.127584i
$987$	13.2240	−	7.10683i	0.420923	−	0.226213i
$988$	4.32133	+	27.2838i	0.137480	+	0.868013i
$989$	0.0621466	+	0.0358804i	0.00197615	+	0.00114093i
$990$	−26.5719	−	4.25607i	−0.844510	−	0.135267i
$991$	−0.126235	−	0.218645i	−0.00400998	−	0.00694548i	0.864013	−	0.503469i	$-0.167943\pi$
$991$	−0.126235	−	0.218645i	−0.00400998	−	0.00694548i	−0.868023	+	0.496523i	$0.834610\pi$
$992$	−5.92196	−	2.27323i	−0.188023	−	0.0721751i
$993$	−9.90483	−	19.4393i	−0.314320	−	0.616888i
$994$	14.6178	+	2.77409i	0.463650	+	0.0879888i
$995$	−1.97575	−	1.95092i	−0.0626356	−	0.0618482i
$996$	−3.19263	−	30.3759i	−0.101162	−	0.962496i
$997$	−42.6690	+	2.23619i	−1.35134	+	0.0708207i	−0.714208	−	0.699934i	$-0.753213\pi$
$997$	−42.6690	+	2.23619i	−1.35134	+	0.0708207i	−0.637132	+	0.770755i	$0.719879\pi$
$998$	6.48679	+	4.21257i	0.205336	+	0.133347i
$999$	10.1232	−	4.50713i	0.320283	−	0.142599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.103.21	yes	768
5.2	odd	4	inner	770.2.bv.a.257.4	yes	768
7.3	odd	6	inner	770.2.bv.a.213.21	yes	768
11.3	even	5	inner	770.2.bv.a.663.45	yes	768
35.17	even	12	inner	770.2.bv.a.367.45	yes	768
55.47	odd	20	inner	770.2.bv.a.47.21	yes	768
77.3	odd	30	inner	770.2.bv.a.3.4	✓	768
385.157	even	60	inner	770.2.bv.a.157.21	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.3.4	✓	768	77.3	odd	30	inner
770.2.bv.a.47.21	yes	768	55.47	odd	20	inner
770.2.bv.a.103.21	yes	768	1.1	even	1	trivial
770.2.bv.a.157.21	yes	768	385.157	even	60	inner
770.2.bv.a.213.21	yes	768	7.3	odd	6	inner
770.2.bv.a.257.4	yes	768	5.2	odd	4	inner
770.2.bv.a.367.45	yes	768	35.17	even	12	inner
770.2.bv.a.663.45	yes	768	11.3	even	5	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.358368 + 0.933580i) q^{2} +(1.40223 - 2.15925i) q^{3} +(-0.743145 - 0.669131i) q^{4} +(-2.15617 + 0.592387i) q^{5} +(1.51332 + 2.08290i) q^{6} +(-1.14925 + 2.38311i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-1.47589 - 3.31491i) q^{9} +O(q^{10})\)	\(q+(-0.358368 + 0.933580i) q^{2} +(1.40223 - 2.15925i) q^{3} +(-0.743145 - 0.669131i) q^{4} +(-2.15617 + 0.592387i) q^{5} +(1.51332 + 2.08290i) q^{6} +(-1.14925 + 2.38311i) q^{7} +(0.891007 - 0.453990i) q^{8} +(-1.47589 - 3.31491i) q^{9} +(0.219662 - 2.22525i) q^{10} +(2.94289 + 1.52951i) q^{11} +(-2.48688 + 0.666358i) q^{12} +(-5.30666 + 0.840493i) q^{13} +(-1.81298 - 1.92695i) q^{14} +(-1.74435 + 5.48638i) q^{15} +(0.104528 + 0.994522i) q^{16} +(2.19420 + 5.71608i) q^{17} +(3.62365 - 0.189907i) q^{18} +(3.44028 + 3.82082i) q^{19} +(1.99873 + 1.00253i) q^{20} +(3.53423 + 5.82319i) q^{21} +(-2.48256 + 2.19930i) q^{22} +(0.00828083 - 0.00221884i) q^{23} +(0.269120 - 2.56051i) q^{24} +(4.29816 - 2.55458i) q^{25} +(1.11707 - 5.25540i) q^{26} +(-1.59853 - 0.253183i) q^{27} +(2.44867 - 1.00200i) q^{28} +(-2.01379 + 0.654319i) q^{29} +(-4.49686 - 3.59463i) q^{30} +(6.30853 + 0.663054i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(7.42921 - 4.20971i) q^{33} -6.12275 q^{34} +(1.06625 - 5.81920i) q^{35} +(-1.12131 + 3.45103i) q^{36} +(-5.74217 + 3.72901i) q^{37} +(-4.79993 + 1.84252i) q^{38} +(-5.62635 + 12.6370i) q^{39} +(-1.65223 + 1.50670i) q^{40} +(-8.17581 - 2.65648i) q^{41} +(-6.70297 + 1.21264i) q^{42} +(5.91891 + 5.91891i) q^{43} +(-1.16355 - 3.10582i) q^{44} +(5.14599 + 6.27322i) q^{45} +(-0.000896117 + 0.00852599i) q^{46} +(0.115345 - 2.20090i) q^{47} +(2.29400 + 1.16885i) q^{48} +(-4.35846 - 5.47757i) q^{49} +(0.844580 + 4.92815i) q^{50} +(15.4192 + 3.27746i) q^{51} +(4.50602 + 2.92624i) q^{52} +(2.59023 - 2.09753i) q^{53} +(0.809230 - 1.40163i) q^{54} +(-7.25144 - 1.55456i) q^{55} +(0.0579247 + 2.64512i) q^{56} +(13.0742 - 2.07075i) q^{57} +(0.110817 - 2.11452i) q^{58} +(0.731127 - 0.811999i) q^{59} +(4.96741 - 2.90998i) q^{60} +(1.83632 - 0.193005i) q^{61} +(-2.87979 + 5.65191i) q^{62} +(9.59598 + 0.292428i) q^{63} +(0.587785 - 0.809017i) q^{64} +(10.9442 - 4.95585i) q^{65} +(1.26771 + 8.44439i) q^{66} +(-0.771891 - 0.206828i) q^{67} +(2.19420 - 5.71608i) q^{68} +(0.00682063 - 0.0209917i) q^{69} +(5.05058 + 3.08084i) q^{70} +(-4.54961 + 3.30549i) q^{71} +(-2.81997 - 2.28357i) q^{72} +(0.777884 + 14.8429i) q^{73} +(-1.42352 - 6.69714i) q^{74} +(0.511051 - 12.8629i) q^{75} -5.14142i q^{76} +(-7.02710 + 5.25546i) q^{77} +(-9.78134 - 9.78134i) q^{78} +(2.01939 + 4.53563i) q^{79} +(-0.814523 - 2.08244i) q^{80} +(4.49586 - 4.99316i) q^{81} +(5.40999 - 6.68078i) q^{82} +(-1.85582 + 11.7172i) q^{83} +(1.27003 - 6.69234i) q^{84} +(-8.11720 - 11.0250i) q^{85} +(-7.64692 + 3.40463i) q^{86} +(-1.41096 + 5.26578i) q^{87} +(3.31652 + 0.0267596i) q^{88} +(-4.35615 + 7.54508i) q^{89} +(-7.70071 + 2.55608i) q^{90} +(4.09568 - 13.6123i) q^{91} +(-0.00763855 - 0.00389204i) q^{92} +(10.2777 - 12.6919i) q^{93} +(2.01339 + 0.896417i) q^{94} +(-9.68124 - 6.20037i) q^{95} +(-1.91331 + 1.72275i) q^{96} +(-0.972990 - 6.14321i) q^{97} +(6.67569 - 2.10599i) q^{98} +(0.726799 - 12.0128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

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