LMFDB - Embedded newform 684.2.bi.a.239.97

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(83,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 2]))

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

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

chi := DirichletCharacter("684.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$232$
Relative dimension:	$116$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			239.97
Character	$\chi$	$=$	684.239
Dual form			684.2.bi.a.83.97

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.21158 + 0.729433i) q^{2} +(1.72277 - 0.179033i) q^{3} +(0.935855 + 1.76753i) q^{4} +(2.62026 - 1.51281i) q^{5} +(2.21787 + 1.03974i) q^{6} +(-3.37115 + 1.94633i) q^{7} +(-0.155435 + 2.82415i) q^{8} +(2.93589 - 0.616865i) q^{9} +(4.27815 + 0.0784162i) q^{10} +(-1.50566 - 2.60787i) q^{11} +(1.92871 + 2.87751i) q^{12} +4.01575 q^{13} +(-5.50413 - 0.100888i) q^{14} +(4.24328 - 3.07534i) q^{15} +(-2.24835 + 3.30831i) q^{16} +(-4.32629 - 2.49779i) q^{17} +(4.00703 + 1.39416i) q^{18} +(2.72273 + 3.40393i) q^{19} +(5.12613 + 3.21563i) q^{20} +(-5.45926 + 3.95663i) q^{21} +(0.0780453 - 4.25792i) q^{22} -4.78008 q^{23} +(0.237837 + 4.89320i) q^{24} +(2.07719 - 3.59779i) q^{25} +(4.86540 + 2.92922i) q^{26} +(4.94744 - 1.58834i) q^{27} +(-6.59511 - 4.13713i) q^{28} +(0.376168 + 0.217181i) q^{29} +(7.38433 - 0.630836i) q^{30} +(-2.21690 - 1.27993i) q^{31} +(-5.13725 + 2.36826i) q^{32} +(-3.06080 - 4.22321i) q^{33} +(-3.41968 - 6.18201i) q^{34} +(-5.88886 + 10.1998i) q^{35} +(3.83790 + 4.61200i) q^{36} -3.09614 q^{37} +(0.815870 + 6.11018i) q^{38} +(6.91822 - 0.718950i) q^{39} +(3.86513 + 7.63517i) q^{40} +(0.358473 - 0.206965i) q^{41} +(-9.50043 + 0.811613i) q^{42} -1.88599i q^{43} +(3.20043 - 5.10189i) q^{44} +(6.75962 - 6.05780i) q^{45} +(-5.79146 - 3.48675i) q^{46} +(6.18138 - 10.7065i) q^{47} +(-3.28111 + 6.10200i) q^{48} +(4.07641 - 7.06056i) q^{49} +(5.14103 - 2.84385i) q^{50} +(-7.90041 - 3.52857i) q^{51} +(3.75815 + 7.09797i) q^{52} +(-9.32144 + 5.38174i) q^{53} +(7.15281 + 1.68443i) q^{54} +(-7.89043 - 4.55554i) q^{55} +(-4.97275 - 9.82316i) q^{56} +(5.30006 + 5.37674i) q^{57} +(0.297339 + 0.537522i) q^{58} +(-5.29597 - 9.17289i) q^{59} +(9.40686 + 4.62207i) q^{60} +(3.21206 - 5.56345i) q^{61} +(-1.75233 - 3.16782i) q^{62} +(-8.69670 + 7.79377i) q^{63} +(-7.95168 - 0.877943i) q^{64} +(10.5223 - 6.07506i) q^{65} +(-0.627853 - 7.34941i) q^{66} +12.8978i q^{67} +(0.366141 - 9.98443i) q^{68} +(-8.23500 + 0.855791i) q^{69} +(-14.5749 + 8.06235i) q^{70} +(-4.86918 + 8.43367i) q^{71} +(1.28578 + 8.38730i) q^{72} +(0.298078 - 0.516286i) q^{73} +(-3.75122 - 2.25842i) q^{74} +(2.93440 - 6.57007i) q^{75} +(-3.46848 + 7.99810i) q^{76} +(10.1516 + 5.86101i) q^{77} +(8.90641 + 4.17531i) q^{78} +13.4730i q^{79} +(-0.886433 + 12.0700i) q^{80} +(8.23895 - 3.62210i) q^{81} +(0.585286 + 0.0107280i) q^{82} +(-1.87399 - 3.24584i) q^{83} +(-12.1026 - 5.94660i) q^{84} -15.1147 q^{85} +(1.37570 - 2.28503i) q^{86} +(0.686935 + 0.306807i) q^{87} +(7.59906 - 3.84685i) q^{88} +(12.3615 - 7.13690i) q^{89} +(12.6086 - 2.40882i) q^{90} +(-13.5377 + 7.81597i) q^{91} +(-4.47346 - 8.44896i) q^{92} +(-4.04837 - 1.80813i) q^{93} +(15.2989 - 8.46284i) q^{94} +(12.2838 + 4.80022i) q^{95} +(-8.42632 + 4.99971i) q^{96} +2.86992 q^{97} +(10.0891 - 5.58096i) q^{98} +(-6.02915 - 6.72765i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 232 q - 2 q^{4} - 6 q^{5} - 9 q^{6} - 6 q^{9} + 2 q^{10} - q^{12} - 4 q^{13} - 3 q^{14} - 2 q^{16} + 12 q^{17} - 16 q^{18} - 27 q^{20} + 4 q^{21} - 3 q^{22} - 13 q^{24} + 102 q^{25} - 6 q^{28} - 6 q^{29}+ \cdots + 162 q^{98}+O(q^{100}) $ 232 * q - 2 * q^4 - 6 * q^5 - 9 * q^6 - 6 * q^9 + 2 * q^10 - q^12 - 4 * q^13 - 3 * q^14 - 2 * q^16 + 12 * q^17 - 16 * q^18 - 27 * q^20 + 4 * q^21 - 3 * q^22 - 13 * q^24 + 102 * q^25 - 6 * q^28 - 6 * q^29 - 9 * q^30 - 24 * q^33 - q^34 - 35 * q^36 - 16 * q^37 + 21 * q^38 + 8 * q^40 + 24 * q^41 + 32 * q^42 - 21 * q^44 + 2 * q^45 - 24 * q^46 - 5 * q^48 + 88 * q^49 + 9 * q^50 - 34 * q^52 - 22 * q^54 - 48 * q^56 - 6 * q^57 + 2 * q^58 - 5 * q^60 + 2 * q^61 - 6 * q^62 + 16 * q^64 + 12 * q^65 + 15 * q^66 - 18 * q^68 - 14 * q^69 - 30 * q^70 - 51 * q^72 + 2 * q^73 - 3 * q^76 - 12 * q^77 + 8 * q^78 - 54 * q^80 + 34 * q^81 + 2 * q^82 - 10 * q^84 - 44 * q^85 - 18 * q^88 + 59 * q^90 - 14 * q^93 - 6 * q^94 - 17 * q^96 + 8 * q^97 + 162 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.21158	+	0.729433i	0.856717	+	0.515787i
$2$	1.21158	+	0.729433i	0.856717	+	0.515787i
$3$	1.72277	−	0.179033i	0.994644	−	0.103365i
$3$	1.72277	−	0.179033i	0.994644	−	0.103365i
$4$	0.935855	+	1.76753i	0.467927	+	0.883767i
$5$	2.62026	−	1.51281i	1.17182	−	0.676549i	0.217710	−	0.976013i	$-0.430141\pi$
$5$	2.62026	−	1.51281i	1.17182	−	0.676549i	0.954108	+	0.299464i	$0.0968080\pi$
$6$	2.21787	+	1.03974i	0.905442	+	0.424470i
$7$	−3.37115	+	1.94633i	−1.27417	+	0.735644i	−0.975771	−	0.218796i	$-0.929787\pi$
$7$	−3.37115	+	1.94633i	−1.27417	+	0.735644i	−0.298403	+	0.954440i	$0.596454\pi$
$8$	−0.155435	+	2.82415i	−0.0549545	+	0.998489i
$9$	2.93589	−	0.616865i	0.978632	−	0.205622i
$10$	4.27815	+	0.0784162i	1.35287	+	0.0247974i
$11$	−1.50566	−	2.60787i	−0.453972	−	0.786303i	0.544656	−	0.838660i	$-0.316660\pi$
$11$	−1.50566	−	2.60787i	−0.453972	−	0.786303i	−0.998628	+	0.0523562i	$0.983327\pi$
$12$	1.92871	+	2.87751i	0.556771	+	0.830666i
$13$	4.01575			1.11377			0.556884	−	0.830590i	$-0.311997\pi$
$13$	4.01575			1.11377			0.556884	+	0.830590i	$0.311997\pi$
$14$	−5.50413	−	0.100888i	−1.47104	−	0.0269634i
$15$	4.24328	−	3.07534i	1.09561	−	0.794050i
$16$	−2.24835	+	3.30831i	−0.562088	+	0.827077i
$17$	−4.32629	−	2.49779i	−1.04928	−	0.605802i	−0.126832	−	0.991924i	$-0.540481\pi$
$17$	−4.32629	−	2.49779i	−1.04928	−	0.605802i	−0.922448	+	0.386122i	$0.873814\pi$
$18$	4.00703	+	1.39416i	0.944467	+	0.328606i
$19$	2.72273	+	3.40393i	0.624637	+	0.780915i
$19$	2.72273	+	3.40393i	0.624637	+	0.780915i
$20$	5.12613	+	3.21563i	1.14624	+	0.719038i
$21$	−5.45926	+	3.95663i	−1.19131	+	0.863408i
$22$	0.0780453	−	4.25792i	0.0166393	−	0.907792i
$23$	−4.78008			−0.996716			−0.498358	−	0.866971i	$-0.666064\pi$
$23$	−4.78008			−0.996716			−0.498358	+	0.866971i	$0.666064\pi$
$24$	0.237837	+	4.89320i	0.0485482	+	0.998821i
$25$	2.07719	−	3.59779i	0.415438	−	0.719559i
$26$	4.86540	+	2.92922i	0.954183	+	0.574467i
$27$	4.94744	−	1.58834i	0.952136	−	0.305676i
$28$	−6.59511	−	4.13713i	−1.24636	−	0.781844i
$29$	0.376168	+	0.217181i	0.0698527	+	0.0403295i	0.534520	−	0.845156i	$-0.320493\pi$
$29$	0.376168	+	0.217181i	0.0698527	+	0.0403295i	−0.464667	+	0.885486i	$0.653826\pi$
$30$	7.38433	−	0.630836i	1.34819	−	0.115174i
$31$	−2.21690	−	1.27993i	−0.398167	−	0.229882i	0.287525	−	0.957773i	$-0.407167\pi$
$31$	−2.21690	−	1.27993i	−0.398167	−	0.229882i	−0.685693	+	0.727891i	$0.740501\pi$
$32$	−5.13725	+	2.36826i	−0.908146	+	0.418653i
$33$	−3.06080	−	4.22321i	−0.532817	−	0.735167i
$34$	−3.41968	−	6.18201i	−0.586471	−	1.06021i
$35$	−5.88886	+	10.1998i	−0.995399	+	1.72408i
$36$	3.83790	+	4.61200i	0.639650	+	0.768666i
$37$	−3.09614			−0.509002			−0.254501	−	0.967073i	$-0.581911\pi$
$37$	−3.09614			−0.509002			−0.254501	+	0.967073i	$0.581911\pi$
$38$	0.815870	+	6.11018i	0.132352	+	0.991203i
$39$	6.91822	−	0.718950i	1.10780	−	0.115124i
$40$	3.86513	+	7.63517i	0.611130	+	1.20723i
$41$	0.358473	−	0.206965i	0.0559841	−	0.0323224i	−0.471747	−	0.881734i	$-0.656376\pi$
$41$	0.358473	−	0.206965i	0.0559841	−	0.0323224i	0.527731	+	0.849412i	$0.323043\pi$
$42$	−9.50043	+	0.811613i	−1.46595	+	0.125235i
$43$		−	1.88599i		−	0.287611i	−0.989606	−	0.143805i	$-0.954066\pi$
$43$		−	1.88599i		−	0.287611i	0.989606	−	0.143805i	$-0.0459339\pi$
$44$	3.20043	−	5.10189i	0.482483	−	0.769139i
$45$	6.75962	−	6.05780i	1.00766	−	0.903044i
$46$	−5.79146	−	3.48675i	−0.853904	−	0.514093i
$47$	6.18138	−	10.7065i	0.901647	−	1.56170i	0.0762901	−	0.997086i	$-0.475692\pi$
$47$	6.18138	−	10.7065i	0.901647	−	1.56170i	0.825356	−	0.564612i	$-0.190974\pi$
$48$	−3.28111	+	6.10200i	−0.473587	+	0.880747i
$49$	4.07641	−	7.06056i	0.582345	−	1.00865i
$50$	5.14103	−	2.84385i	0.727052	−	0.402181i
$51$	−7.90041	−	3.52857i	−1.10628	−	0.494099i
$52$	3.75815	+	7.09797i	0.521162	+	0.984311i
$53$	−9.32144	+	5.38174i	−1.28040	+	0.739238i	−0.976921	−	0.213600i	$-0.931481\pi$
$53$	−9.32144	+	5.38174i	−1.28040	+	0.739238i	−0.303477	+	0.952839i	$0.598148\pi$
$54$	7.15281	+	1.68443i	0.973374	+	0.229221i
$55$	−7.89043	−	4.55554i	−1.06395	−	0.614269i
$56$	−4.97275	−	9.82316i	−0.664511	−	1.31267i
$57$	5.30006	+	5.37674i	0.702011	+	0.712167i
$58$	0.297339	+	0.537522i	0.0390426	+	0.0705801i
$59$	−5.29597	−	9.17289i	−0.689477	−	1.19421i	−0.972007	−	0.234951i	$-0.924507\pi$
$59$	−5.29597	−	9.17289i	−0.689477	−	1.19421i	0.282530	−	0.959258i	$-0.408826\pi$
$60$	9.40686	+	4.62207i	1.21442	+	0.596706i
$61$	3.21206	−	5.56345i	0.411262	−	0.712326i	−0.583766	−	0.811922i	$-0.698422\pi$
$61$	3.21206	−	5.56345i	0.411262	−	0.712326i	0.995028	+	0.0995955i	$0.0317549\pi$
$62$	−1.75233	−	3.16782i	−0.222547	−	0.402314i
$63$	−8.69670	+	7.79377i	−1.09568	+	0.981922i
$64$	−7.95168	−	0.877943i	−0.993960	−	0.109743i
$65$	10.5223	−	6.07506i	1.30513	−	0.753519i
$66$	−0.627853	−	7.34941i	−0.0772833	−	0.904650i
$67$			12.8978i			1.57572i	0.615858	+	0.787858i	$0.288810\pi$
$67$			12.8978i			1.57572i	−0.615858	+	0.787858i	$0.711190\pi$
$68$	0.366141	−	9.98443i	0.0444011	−	1.21079i
$69$	−8.23500	+	0.855791i	−0.991377	+	0.103025i
$70$	−14.5749	+	8.06235i	−1.74203	+	0.963636i
$71$	−4.86918	+	8.43367i	−0.577866	+	1.00089i	0.417858	+	0.908512i	$0.362781\pi$
$71$	−4.86918	+	8.43367i	−0.577866	+	1.00089i	−0.995724	+	0.0923804i	$0.970552\pi$
$72$	1.28578	+	8.38730i	0.151531	+	0.988453i
$73$	0.298078	−	0.516286i	0.0348874	−	0.0604267i	−0.848055	−	0.529909i	$-0.822226\pi$
$73$	0.298078	−	0.516286i	0.0348874	−	0.0604267i	0.882942	+	0.469482i	$0.155559\pi$
$74$	−3.75122	−	2.25842i	−0.436070	−	0.262537i
$75$	2.93440	−	6.57007i	0.338835	−	0.758646i
$76$	−3.46848	+	7.99810i	−0.397862	+	0.917445i
$77$	10.1516	+	5.86101i	1.15688	+	0.667924i
$78$	8.90641	+	4.17531i	1.00845	+	0.472761i
$79$			13.4730i			1.51583i	0.652355	+	0.757913i	$0.273781\pi$
$79$			13.4730i			1.51583i	−0.652355	+	0.757913i	$0.726219\pi$
$80$	−0.886433	+	12.0700i	−0.0991062	+	1.34946i
$81$	8.23895	−	3.62210i	0.915439	−	0.402456i
$82$	0.585286	+	0.0107280i	0.0646340	+	0.00118471i
$83$	−1.87399	−	3.24584i	−0.205697	−	0.356277i	0.744658	−	0.667446i	$-0.232613\pi$
$83$	−1.87399	−	3.24584i	−0.205697	−	0.356277i	−0.950354	+	0.311169i	$0.899279\pi$
$84$	−12.1026	−	5.94660i	−1.32050	−	0.648827i
$85$	−15.1147			−1.63942
$86$	1.37570	−	2.28503i	0.148346	−	0.246401i
$87$	0.686935	+	0.306807i	0.0736472	+	0.0328932i
$88$	7.59906	−	3.84685i	0.810063	−	0.410076i
$89$	12.3615	−	7.13690i	1.31031	−	0.756510i	0.328165	−	0.944620i	$-0.393570\pi$
$89$	12.3615	−	7.13690i	1.31031	−	0.756510i	0.982148	+	0.188111i	$0.0602364\pi$
$90$	12.6086	−	2.40882i	1.32906	−	0.253912i
$91$	−13.5377	+	7.81597i	−1.41913	+	0.819337i
$92$	−4.47346	−	8.44896i	−0.466391	−	0.880865i
$93$	−4.04837	−	1.80813i	−0.419796	−	0.187494i
$94$	15.2989	−	8.46284i	1.57796	−	0.872875i
$95$	12.2838	+	4.80022i	1.26029	+	0.492492i
$96$	−8.42632	+	4.99971i	−0.860008	+	0.510281i
$97$	2.86992			0.291396			0.145698	−	0.989329i	$-0.453457\pi$
$97$	2.86992			0.291396			0.145698	+	0.989329i	$0.453457\pi$
$98$	10.0891	−	5.58096i	1.01915	−	0.563762i
$99$	−6.02915	−	6.72765i	−0.605953	−	0.676155i
$100$	8.30317	+	0.304487i	0.830317	+	0.0304487i
$101$	4.65184	+	2.68574i	0.462876	+	0.267241i	0.713253	−	0.700907i	$-0.247221\pi$
$101$	4.65184	+	2.68574i	0.462876	+	0.267241i	−0.250377	+	0.968148i	$0.580555\pi$
$102$	−6.99812	−	10.0380i	−0.692917	−	0.993907i
$103$	−7.02928	−	4.05836i	−0.692615	−	0.399882i	0.111976	−	0.993711i	$-0.464282\pi$
$103$	−7.02928	−	4.05836i	−0.692615	−	0.399882i	−0.804591	+	0.593829i	$0.797615\pi$
$104$	−0.624186	+	11.3411i	−0.0612065	+	1.11208i
$105$	−8.31907	+	18.6262i	−0.811858	+	1.81774i
$106$	−15.2193	−	0.278961i	−1.47823	−	0.0270951i
$107$	6.23445			0.602707			0.301354	−	0.953512i	$-0.402562\pi$
$107$	6.23445			0.602707			0.301354	+	0.953512i	$0.402562\pi$
$108$	7.43753	+	7.25832i	0.715677	+	0.698432i
$109$	−8.83890	+	15.3094i	−0.846613	+	1.46638i	0.0376005	+	0.999293i	$0.488029\pi$
$109$	−8.83890	+	15.3094i	−0.846613	+	1.46638i	−0.884213	+	0.467083i	$0.845305\pi$
$110$	−6.23693	−	11.2750i	−0.594668	−	1.07502i
$111$	−5.33394	+	0.554309i	−0.506275	+	0.0526127i
$112$	1.14046	−	15.5288i	0.107763	−	1.46734i
$113$	−10.0674	−	5.81240i	−0.947058	−	0.546784i	−0.0548923	−	0.998492i	$-0.517482\pi$
$113$	−10.0674	−	5.81240i	−0.947058	−	0.546784i	−0.892166	+	0.451708i	$0.850815\pi$
$114$	2.49948	+	10.3804i	0.234098	+	0.972213i
$115$	−12.5251	+	7.23136i	−1.16797	+	0.674328i
$116$	−0.0318357	+	0.868140i	−0.00295587	+	0.0806048i
$117$	11.7898	−	2.47717i	1.08997	−	0.229015i
$118$	0.274516	−	14.9768i	0.0252712	−	1.37872i
$119$	19.4461			1.78262
$120$	8.02568	+	12.4617i	0.732641	+	1.13759i
$121$	0.965999	−	1.67316i	0.0878181	−	0.152105i
$122$	7.94983	−	4.39758i	0.719744	−	0.398138i
$123$	0.580514	−	0.420731i	0.0523432	−	0.0379361i
$124$	0.187620	−	5.11628i	0.0168488	−	0.459455i
$125$			2.55854i			0.228843i
$126$	−16.2218	+	3.09911i	−1.44515	+	0.276091i
$127$	5.52271	−	3.18854i	0.490062	−	0.282937i	−0.234538	−	0.972107i	$-0.575358\pi$
$127$	5.52271	−	3.18854i	0.490062	−	0.282937i	0.724600	+	0.689170i	$0.242025\pi$
$128$	−8.99370	−	6.86392i	−0.794938	−	0.606690i
$129$	−0.337654	−	3.24913i	−0.0297287	−	0.286070i
$130$	17.1800	+	0.314899i	1.50678	+	0.0276185i
$131$	4.98061	+	8.62667i	0.435158	+	0.753715i	0.997309	−	0.0733194i	$-0.0233592\pi$
$131$	4.98061	+	8.62667i	0.435158	+	0.753715i	−0.562151	+	0.827035i	$0.690026\pi$
$132$	4.60021	−	9.36238i	0.400397	−	0.814890i
$133$	−15.8039	−	6.17580i	−1.37037	−	0.535510i
$134$	−9.40807	+	15.6267i	−0.812734	+	1.34994i
$135$	10.5607	−	11.6464i	0.908924	−	1.00236i
$136$	7.72659	−	11.8299i	0.662549	−	1.01440i
$137$	−15.5165	−	8.95848i	−1.32567	−	0.765375i	−0.341041	−	0.940048i	$-0.610780\pi$
$137$	−15.5165	−	8.95848i	−1.32567	−	0.765375i	−0.984626	+	0.174674i	$0.944113\pi$
$138$	−10.6016	−	4.97002i	−0.902469	−	0.423076i
$139$		−	15.0034i		−	1.27257i	−0.771453	−	0.636286i	$-0.780470\pi$
$139$		−	15.0034i		−	1.27257i	0.771453	−	0.636286i	$-0.219530\pi$
$140$	−23.5396	−	0.863226i	−1.98946	−	0.0729559i
$141$	8.73231	−	19.5515i	0.735393	−	1.64653i
$142$	−12.0512	+	6.66633i	−1.01131	+	0.559426i
$143$	−6.04633	−	10.4726i	−0.505620	−	0.875759i
$144$	−4.56014	+	11.0998i	−0.380012	+	0.924982i
$145$	1.31421			0.109140
$146$	0.737741	−	0.408094i	0.0610559	−	0.0337741i
$147$	5.75867	−	12.8935i	0.474967	−	1.06344i
$148$	−2.89753	−	5.47253i	−0.238176	−	0.449839i
$149$	15.3694	−	8.87351i	1.25911	−	0.726946i	0.286206	−	0.958168i	$-0.407606\pi$
$149$	15.3694	−	8.87351i	1.25911	−	0.726946i	0.972901	+	0.231222i	$0.0742724\pi$
$150$	8.34769	−	5.81972i	0.681586	−	0.475178i
$151$	−2.78743	+	1.60932i	−0.226838	+	0.130965i	−0.609112	−	0.793084i	$-0.708474\pi$
$151$	−2.78743	+	1.60932i	−0.226838	+	0.130965i	0.382275	+	0.924049i	$0.375141\pi$
$152$	−10.0364	+	7.16032i	−0.814061	+	0.580779i
$153$	−14.2423	−	4.66450i	−1.15142	−	0.377102i
$154$	8.02423	+	14.5060i	0.646611	+	1.16893i
$155$	−7.74516			−0.622106
$156$	7.74522	+	11.5554i	0.620114	+	0.925169i
$157$	1.25362	+	2.17133i	0.100050	+	0.173291i	0.911705	−	0.410846i	$-0.134766\pi$
$157$	1.25362	+	2.17133i	0.100050	+	0.173291i	−0.811655	+	0.584137i	$0.801433\pi$
$158$	−9.82763	+	16.3236i	−0.781844	+	1.29863i
$159$	−15.0952	+	10.9404i	−1.19713	+	0.867626i
$160$	−9.87822	+	13.9772i	−0.780942	+	1.10499i
$161$	16.1144	−	9.30363i	1.26999	−	0.733229i
$162$	12.6242	+	1.62130i	0.991854	+	0.127381i
$163$		−	18.7315i		−	1.46717i	−0.679600	−	0.733583i	$-0.737847\pi$
$163$		−	18.7315i		−	1.46717i	0.679600	−	0.733583i	$-0.262153\pi$
$164$	0.701296	+	0.439925i	0.0547620	+	0.0343523i
$165$	−14.4090	−	6.43552i	−1.12174	−	0.501005i
$166$	0.0971376	−	5.29954i	0.00753934	−	0.411324i
$167$	16.3271			1.26343			0.631713	−	0.775202i	$-0.282352\pi$
$167$	16.3271			1.26343			0.631713	+	0.775202i	$0.282352\pi$
$168$	−10.3256	−	16.0328i	−0.796636	−	1.23696i
$169$	3.12622			0.240478
$170$	−18.3127	−	11.0252i	−1.40452	−	0.845592i
$171$	10.0934	+	8.31402i	0.771863	+	0.635789i
$172$	3.33355	−	1.76501i	0.254181	−	0.134581i
$173$			5.24971i			0.399128i	0.979885	+	0.199564i	$0.0639526\pi$
$173$			5.24971i			0.399128i	−0.979885	+	0.199564i	$0.936047\pi$
$174$	0.608482	+	0.872795i	0.0461289	+	0.0661664i
$175$			16.1716i			1.22246i
$176$	12.0129	+	0.882241i	0.905506	+	0.0665014i
$177$	−10.7660	−	14.8547i	−0.809223	−	1.11654i
$178$	20.1828	+	0.369939i	1.51277	+	0.0277281i
$179$	9.00022			0.672708			0.336354	−	0.941736i	$-0.390806\pi$
$179$	9.00022			0.672708			0.336354	+	0.941736i	$0.390806\pi$
$180$	17.0334	+	6.27863i	1.26959	+	0.467982i
$181$	6.89054	+	11.9348i	0.512170	+	0.887104i	0.999900	+	0.0141097i	$0.00449141\pi$
$181$	6.89054	+	11.9348i	0.512170	+	0.887104i	−0.487731	+	0.872994i	$0.662175\pi$
$182$	−22.1032	−	0.405139i	−1.63840	−	0.0300309i
$183$	4.53761	−	10.1596i	0.335430	−	0.751021i
$184$	0.742991	−	13.4997i	0.0547740	−	0.995210i
$185$	−8.11269	+	4.68387i	−0.596457	+	0.344365i
$186$	−3.58602	−	5.14371i	−0.262939	−	0.377155i
$187$			15.0432i			1.10007i
$188$	24.7089	+	0.906105i	1.80208	+	0.0660845i
$189$	−13.5871	+	14.9839i	−0.988317	+	1.08992i
$190$	11.3813	+	14.7760i	0.825689	+	1.07197i
$191$	7.15070	+	12.3854i	0.517406	+	0.896174i	0.999796	+	0.0202169i	$0.00643569\pi$
$191$	7.15070	+	12.3854i	0.517406	+	0.896174i	−0.482389	+	0.875957i	$0.660231\pi$
$192$	−13.8561	−	0.0888857i	−0.999979	−	0.00641478i
$193$	2.27233	+	3.93580i	0.163566	+	0.283305i	0.936145	−	0.351614i	$-0.114367\pi$
$193$	2.27233	+	3.93580i	0.163566	+	0.283305i	−0.772579	+	0.634919i	$0.781034\pi$
$194$	3.47714	+	2.09342i	0.249644	+	0.150298i
$195$	17.0399	−	12.3498i	1.22025	−	0.884387i
$196$	16.2947	+	0.597546i	1.16391	+	0.0426819i
$197$			19.3601i			1.37935i	0.724121	+	0.689673i	$0.242246\pi$
$197$			19.3601i			1.37935i	−0.724121	+	0.689673i	$0.757754\pi$
$198$	−2.39743	−	12.5490i	−0.170378	−	0.891816i
$199$	−5.50195	+	3.17655i	−0.390023	+	0.225180i	−0.682170	−	0.731194i	$-0.738964\pi$
$199$	−5.50195	+	3.17655i	−0.390023	+	0.225180i	0.292147	+	0.956373i	$0.405630\pi$
$200$	9.83786	+	6.42552i	0.695641	+	0.454353i
$201$	2.30912	+	22.2200i	0.162873	+	1.56727i
$202$	3.67701	+	6.64720i	0.258714	+	0.467695i
$203$	−1.69082			−0.118673
$204$	−1.15676	−	17.2665i	−0.0809895	−	1.20889i
$205$	0.626196	−	1.08460i	0.0437354	−	0.0757520i
$206$	−5.55624	−	10.0444i	−0.387121	−	0.699827i
$207$	−14.0338	+	2.94867i	−0.975418	+	0.204947i
$208$	−9.02881	+	13.2853i	−0.626036	+	0.921172i
$209$	4.77752	−	12.2257i	0.330468	−	0.845668i
$210$	−23.6658	+	16.4990i	−1.63310	+	1.13854i
$211$	−3.20871	+	1.85255i	−0.220897	+	0.127535i	−0.606366	−	0.795186i	$-0.707373\pi$
$211$	−3.20871	+	1.85255i	−0.220897	+	0.127535i	0.385469	+	0.922721i	$0.374040\pi$
$212$	−18.2359	−	11.4394i	−1.25245	−	0.785664i
$213$	−6.87859	+	15.4010i	−0.471314	+	1.05526i
$214$	7.55354	+	4.54762i	0.516350	+	0.310869i
$215$	−2.85314	−	4.94179i	−0.194583	−	0.337027i
$216$	3.71671	+	14.2192i	0.252890	+	0.967495i
$217$	9.96467			0.676446
$218$	−21.8762	+	12.1012i	−1.48165	+	0.819597i
$219$	0.421088	−	0.942809i	0.0284545	−	0.0637091i
$220$	0.667780	−	18.2099i	0.0450217	−	1.22771i
$221$	−17.3733	−	10.0305i	−1.16865	−	0.674723i
$222$	−6.86683	−	3.21916i	−0.460871	−	0.216056i
$223$		−	11.6308i		−	0.778858i	−0.921057	−	0.389429i	$-0.872672\pi$
$223$		−	11.6308i		−	0.778858i	0.921057	−	0.389429i	$-0.127328\pi$
$224$	12.7090	−	17.9825i	0.849156	−	1.20151i
$225$	3.87905	−	11.8441i	0.258603	−	0.789606i
$226$	−7.95767	−	14.3857i	−0.529336	−	0.956920i
$227$	1.26292	+	2.18744i	0.0838227	+	0.145185i	0.904889	−	0.425648i	$-0.139954\pi$
$227$	1.26292	+	2.18744i	0.0838227	+	0.145185i	−0.821066	+	0.570833i	$0.806620\pi$
$228$	−4.54348	+	14.3999i	−0.300899	+	0.953656i
$229$	−13.4497	+	23.2956i	−0.888782	+	1.53942i	−0.0474665	+	0.998873i	$0.515115\pi$
$229$	−13.4497	+	23.2956i	−0.888782	+	1.53942i	−0.841316	+	0.540544i	$0.818219\pi$
$230$	−20.4499	−	0.374836i	−1.34843	−	0.0247159i
$231$	18.5382	+	8.27973i	1.21972	+	0.544766i
$232$	−0.671822	+	1.02860i	−0.0441073	+	0.0675309i
$233$	−4.82101	−	2.78341i	−0.315835	−	0.182347i	0.333700	−	0.942679i	$-0.391703\pi$
$233$	−4.82101	−	2.78341i	−0.315835	−	0.182347i	−0.649534	+	0.760332i	$0.725036\pi$
$234$	16.0912	+	5.59858i	1.05192	+	0.365991i
$235$		−	37.4050i		−	2.44003i
$236$	11.2571	−	17.9453i	0.732778	−	1.16814i
$237$	2.41210	+	23.2109i	0.156683	+	1.50771i
$238$	23.5605	+	14.1846i	1.52720	+	0.919452i
$239$	−0.139802	+	0.242144i	−0.00904302	+	0.0156630i	−0.870512	−	0.492148i	$-0.836212\pi$
$239$	−0.139802	+	0.242144i	−0.00904302	+	0.0156630i	0.861468	+	0.507811i	$0.169545\pi$
$240$	0.633797	+	20.9525i	0.0409114	+	1.35248i
$241$	7.39004	−	12.7999i	0.476034	−	0.824516i	−0.523589	−	0.851971i	$-0.675407\pi$
$241$	7.39004	−	12.7999i	0.476034	−	0.824516i	0.999623	+	0.0274555i	$0.00874046\pi$
$242$	2.39084	−	1.32254i	0.153689	−	0.0850158i
$243$	13.5454	−	7.71510i	0.868936	−	0.494924i
$244$	12.8396	+	0.470843i	0.821971	+	0.0301427i
$245$		−	24.6674i		−	1.57594i
$246$	1.01024	−	0.0863034i	0.0644103	−	0.00550251i
$247$	10.9338	+	13.6693i	0.695701	+	0.869758i
$248$	3.95930	−	6.06193i	0.251416	−	0.384933i
$249$	−3.80956	−	5.25634i	−0.241421	−	0.333107i
$250$	−1.86628	+	3.09987i	−0.118034	+	0.196053i
$251$	3.57806	+	6.19739i	0.225845	+	0.391176i	0.956573	−	0.291494i	$-0.0941522\pi$
$251$	3.57806	+	6.19739i	0.225845	+	0.391176i	−0.730727	+	0.682669i	$0.760819\pi$
$252$	−21.9146	−	8.07789i	−1.38049	−	0.508859i
$253$	7.19716	+	12.4658i	0.452482	+	0.783721i
$254$	9.01704	+	0.165277i	0.565779	+	0.0103704i
$255$	−26.0392	+	2.70602i	−1.63064	+	0.169458i
$256$	−5.88982	−	14.8765i	−0.368114	−	0.929781i
$257$		−	20.7987i		−	1.29739i	−0.761050	−	0.648693i	$-0.775316\pi$
$257$		−	20.7987i		−	1.29739i	0.761050	−	0.648693i	$-0.224684\pi$
$258$	1.96093	−	4.18288i	0.122082	−	0.260415i
$259$	10.4375	−	6.02611i	0.648556	−	0.374444i
$260$	20.5852	+	12.9132i	1.27664	+	0.800841i
$261$	1.23836	+	0.405575i	0.0766527	+	0.0251045i
$262$	−0.258169	+	14.0849i	−0.0159497	+	0.870169i
$263$	8.99537			0.554678			0.277339	−	0.960772i	$-0.410547\pi$
$263$	8.99537			0.554678			0.277339	+	0.960772i	$0.410547\pi$
$264$	12.4028	−	7.98773i	0.763337	−	0.491611i
$265$	−16.2831	+	28.2031i	−1.00026	+	1.73251i
$266$	−14.6429	−	19.0104i	−0.897811	−	1.16560i
$267$	20.0183	−	14.5084i	1.22510	−	0.887897i
$268$	−22.7973	+	12.0704i	−1.39256	+	0.737320i
$269$	9.99790	+	5.77229i	0.609583	+	0.351943i	0.772802	−	0.634647i	$-0.218854\pi$
$269$	9.99790	+	5.77229i	0.609583	+	0.351943i	−0.163219	+	0.986590i	$0.552188\pi$
$270$	21.2905	−	6.40720i	1.29570	−	0.389930i
$271$	0.0117891	+	0.00680646i	0.000716139	+	0.000413463i	0.500358	−	0.865819i	$-0.333202\pi$
$271$	0.0117891	+	0.00680646i	0.000716139	+	0.000413463i	−0.499642	+	0.866232i	$0.666535\pi$
$272$	17.9905	−	8.69681i	1.09083	−	0.527322i
$273$	−21.9230	+	15.8888i	−1.32684	+	0.961636i
$274$	−12.2649	−	22.1722i	−0.740951	−	1.33947i
$275$	−12.5101			−0.754389
$276$	−9.21940	−	13.7547i	−0.554943	−	0.827938i
$277$	4.86773	+	8.43115i	0.292473	+	0.506579i	0.974394	−	0.224847i	$-0.0721883\pi$
$277$	4.86773	+	8.43115i	0.292473	+	0.506579i	−0.681921	+	0.731426i	$0.738855\pi$
$278$	10.9440	−	18.1778i	0.656376	−	1.09023i
$279$	−7.29814	−	2.39021i	−0.436928	−	0.143098i
$280$	−27.8905	−	18.2164i	−1.66677	−	1.08864i
$281$	10.0049	+	5.77633i	0.596843	+	0.344587i	0.767798	−	0.640691i	$-0.221352\pi$
$281$	10.0049	+	5.77633i	0.596843	+	0.344587i	−0.170956	+	0.985279i	$0.554686\pi$
$282$	24.8414	−	17.3185i	1.47928	−	1.03130i
$283$	−19.5080	+	11.2629i	−1.15963	+	0.669511i	−0.951215	−	0.308529i	$-0.900163\pi$
$283$	−19.5080	+	11.2629i	−1.15963	+	0.669511i	−0.208413	+	0.978041i	$0.566830\pi$
$284$	−19.4636	−	0.713755i	−1.15495	−	0.0423536i
$285$	22.0215	+	6.07049i	1.30444	+	0.359585i
$286$	0.313410	−	17.0987i	0.0185323	−	1.01107i
$287$	−0.805643	+	1.39542i	−0.0475556	+	0.0823688i
$288$	−13.6215	+	10.1220i	−0.802656	+	0.596442i
$289$	3.97787	+	6.88987i	0.233992	+	0.405287i
$290$	1.59228	+	0.958631i	0.0935017	+	0.0562928i
$291$	4.94422	−	0.513810i	0.289836	−	0.0301201i
$292$	1.19151	+	0.0436941i	0.0697279	+	0.00255700i
$293$	16.3725	+	9.45267i	0.956492	+	0.552231i	0.895092	−	0.445882i	$-0.147110\pi$
$293$	16.3725	+	9.45267i	0.956492	+	0.552231i	0.0614006	+	0.998113i	$0.480443\pi$
$294$	16.3821	−	11.4210i	0.955422	−	0.666087i
$295$	−27.7537	−	16.0236i	−1.61588	−	0.932930i
$296$	0.481247	−	8.74396i	0.0279719	−	0.508232i
$297$	−11.5913	−	10.5108i	−0.672597	−	0.609899i
$298$	25.0938	+	0.459956i	1.45365	+	0.0266445i
$299$	−19.1956			−1.11011
$300$	14.3590	−	0.961976i	0.829017	−	0.0555397i
$301$	3.67076	+	6.35794i	0.211579	+	0.366466i
$302$	−4.55108	−	0.0834188i	−0.261885	−	0.00480021i
$303$	8.49491	+	3.79409i	0.488020	+	0.217965i
$304$	−17.3829	+	1.35441i	−0.996978	+	0.0776805i
$305$		−	19.4369i		−	1.11296i
$306$	−13.8533	−	16.0402i	−0.791940	−	0.916960i
$307$	24.8145	+	14.3266i	1.41624	+	0.817664i	0.995966	−	0.0897351i	$-0.0286020\pi$
$307$	24.8145	+	14.3266i	1.41624	+	0.817664i	0.420270	+	0.907399i	$0.361935\pi$
$308$	−0.859144	+	23.4283i	−0.0489543	+	1.33495i
$309$	−12.8364	−	5.73316i	−0.730239	−	0.326148i
$310$	−9.38388	−	5.64958i	−0.532969	−	0.320874i
$311$	−0.926512	+	1.60477i	−0.0525377	+	0.0909979i	−0.891098	−	0.453811i	$-0.850064\pi$
$311$	−0.926512	+	1.60477i	−0.0525377	+	0.0909979i	0.838561	+	0.544808i	$0.183398\pi$
$312$	0.955092	+	19.6499i	0.0540715	+	1.11245i
$313$	2.23796	−	3.87626i	0.126497	−	0.219099i	−0.795820	−	0.605533i	$-0.792960\pi$
$313$	2.23796	−	3.87626i	0.126497	−	0.219099i	0.922317	+	0.386434i	$0.126293\pi$
$314$	−0.0649811	+	3.54518i	−0.00366710	+	0.200066i
$315$	−10.9972	+	33.5782i	−0.619620	+	1.89192i
$316$	−23.8139	+	12.6087i	−1.33964	+	0.709297i
$317$	−23.3120	−	13.4592i	−1.30933	−	0.755943i	−0.327347	−	0.944904i	$-0.606154\pi$
$317$	−23.3120	−	13.4592i	−1.30933	−	0.755943i	−0.981984	+	0.188962i	$0.939488\pi$
$318$	−26.2693	+	2.24416i	−1.47311	+	0.125846i
$319$		−	1.30800i		−	0.0732339i
$320$	−22.1637	+	9.72894i	−1.23899	+	0.543864i
$321$	10.7405	−	1.11617i	0.599479	−	0.0622986i
$322$	26.3102	+	0.482251i	1.46621	+	0.0268748i
$323$	−3.27705	−	21.5272i	−0.182340	−	1.19781i
$324$	14.1127	+	11.1729i	0.784036	+	0.620715i
$325$	8.34146	−	14.4478i	0.462701	−	0.801421i
$326$	13.6634	−	22.6947i	0.756745	−	1.25695i
$327$	−12.4865	+	27.9571i	−0.690507	+	1.54603i
$328$	0.528780	+	1.04455i	0.0291970	+	0.0576758i
$329$			48.1240i			2.65316i
$330$	−12.7634	−	18.3076i	−0.702602	−	1.00780i
$331$	24.8192	−	14.3294i	1.36419	−	0.787613i	0.374007	−	0.927426i	$-0.377983\pi$
$331$	24.8192	−	14.3294i	1.36419	−	0.787613i	0.990178	+	0.139813i	$0.0446501\pi$
$332$	3.98335	−	6.34997i	0.218615	−	0.348500i
$333$	−9.08993	+	1.90990i	−0.498125	+	0.104662i
$334$	19.7816	+	11.9095i	1.08240	+	0.651659i
$335$	19.5119	+	33.7956i	1.06605	+	1.84645i
$336$	−0.815422	−	26.9568i	−0.0444849	−	1.47062i
$337$	14.2390	+	24.6626i	0.775647	+	1.34346i	0.934430	+	0.356147i	$0.115910\pi$
$337$	14.2390	+	24.6626i	0.775647	+	1.34346i	−0.158783	+	0.987313i	$0.550757\pi$
$338$	3.78766	+	2.28037i	0.206022	+	0.124036i
$339$	−18.3844	−	8.21105i	−0.998503	−	0.445963i
$340$	−14.1452	−	26.7157i	−0.767129	−	1.44886i
$341$			7.70853i			0.417441i
$342$	6.16447	+	17.4356i	0.333336	+	0.942808i
$343$			4.48757i			0.242306i
$344$	5.32632	+	0.293148i	0.287176	+	0.0158055i
$345$	−20.2832	+	14.7004i	−1.09201	+	0.791442i
$346$	−3.82931	+	6.36044i	−0.205865	+	0.341940i
$347$	2.89889	+	5.02102i	0.155621	+	0.269543i	0.933285	−	0.359137i	$-0.116929\pi$
$347$	2.89889	+	5.02102i	0.155621	+	0.269543i	−0.777664	+	0.628680i	$0.783596\pi$
$348$	0.100580	+	1.50131i	0.00539164	+	0.0804786i
$349$	0.0557583	+	0.0965762i	0.00298467	+	0.00516961i	0.867514	−	0.497413i	$-0.165717\pi$
$349$	0.0557583	+	0.0965762i	0.00298467	+	0.00516961i	−0.864529	+	0.502583i	$0.832383\pi$
$350$	−11.7961	+	19.5932i	−0.630528	+	1.04730i
$351$	19.8677	−	6.37837i	1.06046	−	0.340452i
$352$	13.9111	+	9.83151i	0.741462	+	0.524021i
$353$	−31.2249	+	18.0277i	−1.66194	+	0.959519i	−0.690146	+	0.723670i	$0.742454\pi$
$353$	−31.2249	+	18.0277i	−1.66194	+	0.959519i	−0.971790	+	0.235849i	$0.924213\pi$
$354$	−2.20840	−	25.8507i	−0.117375	−	1.37395i
$355$			29.4646i			1.56382i
$356$	24.1832	+	15.1702i	1.28171	+	0.804020i
$357$	33.5012	−	3.48148i	1.77307	−	0.184260i
$358$	10.9045	+	6.56506i	0.576320	+	0.346974i
$359$	−12.7970	+	22.1650i	−0.675399	+	1.16983i	0.300953	+	0.953639i	$0.402695\pi$
$359$	−12.7970	+	22.1650i	−0.675399	+	1.16983i	−0.976352	+	0.216186i	$0.930638\pi$
$360$	16.0575	+	20.0318i	0.846303	+	1.05577i
$361$	−4.17347	+	18.5360i	−0.219656	+	0.975577i
$362$	−0.357169	+	19.4861i	−0.0187724	+	1.02417i
$363$	1.36465	−	3.05542i	0.0716254	−	0.160368i
$364$	−26.4843	−	16.6137i	−1.38815	−	0.870793i
$365$		−	1.80374i		−	0.0944121i
$366$	12.9084	−	8.99932i	0.674735	−	0.470402i
$367$	−10.1171	−	5.84109i	−0.528106	−	0.304902i	0.212139	−	0.977240i	$-0.431957\pi$
$367$	−10.1171	−	5.84109i	−0.528106	−	0.304902i	−0.740245	+	0.672337i	$0.765290\pi$
$368$	10.7473	−	15.8140i	0.560242	−	0.824361i
$369$	0.924770	−	0.828756i	0.0481416	−	0.0431433i
$370$	−13.2457	−	0.242787i	−0.688614	−	0.0126219i
$371$	20.9493	−	36.2852i	1.08763	−	1.88384i
$372$	−0.592754	−	8.84778i	−0.0307329	−	0.458736i
$373$	13.7257	−	23.7736i	0.710691	−	1.23095i	−0.253908	−	0.967228i	$-0.581716\pi$
$373$	13.7257	−	23.7736i	0.710691	−	1.23095i	0.964598	−	0.263724i	$-0.0849508\pi$
$374$	−10.9730	+	18.2261i	−0.567402	+	0.942448i
$375$	0.458062	+	4.40778i	0.0236542	+	0.227617i
$376$	29.2759	+	19.1213i	1.50979	+	0.986106i
$377$	1.51060	+	0.872144i	0.0777997	+	0.0449177i
$378$	−27.3916	+	8.24330i	−1.40887	+	0.423989i
$379$			8.84686i			0.454433i	0.973844	+	0.227216i	$0.0729624\pi$
$379$			8.84686i			0.454433i	−0.973844	+	0.227216i	$0.927038\pi$
$380$	3.01128	+	26.2043i	0.154475	+	1.34425i
$381$	8.94353	−	6.48188i	0.458191	−	0.332077i
$382$	−0.370655	+	20.2218i	−0.0189643	+	1.03464i
$383$	−0.686490	−	1.18904i	−0.0350780	−	0.0607569i	0.847953	−	0.530071i	$-0.177835\pi$
$383$	−0.686490	−	1.18904i	−0.0350780	−	0.0607569i	−0.883031	+	0.469314i	$0.844501\pi$
$384$	−16.7230	−	10.2148i	−0.853390	−	0.521272i
$385$	35.4664			1.80753
$386$	−0.117786	+	6.42605i	−0.00599515	+	0.327078i
$387$	−1.16340	−	5.53706i	−0.0591390	−	0.281465i
$388$	2.68583	+	5.07268i	0.136352	+	0.257526i
$389$	28.1824	+	16.2711i	1.42890	+	0.824977i	0.997034	−	0.0769596i	$-0.0245212\pi$
$389$	28.1824	+	16.2711i	1.42890	+	0.824977i	0.431868	+	0.901937i	$0.357855\pi$
$390$	29.6536	−	2.53328i	1.50157	−	0.128277i
$391$	20.6800	+	11.9396i	1.04583	+	0.603813i
$392$	19.3065	+	12.6099i	0.975124	+	0.636895i
$393$	10.1249	+	13.9701i	0.510734	+	0.704698i
$394$	−14.1219	+	23.4563i	−0.711449	+	1.18171i
$395$	20.3820	+	35.3027i	1.02553	+	1.77627i
$396$	6.24894	−	16.9528i	0.314021	−	0.851912i
$397$	8.64308	−	14.9703i	0.433784	−	0.751335i	−0.563412	−	0.826176i	$-0.690512\pi$
$397$	8.64308	−	14.9703i	0.433784	−	0.751335i	0.997195	+	0.0748408i	$0.0238449\pi$
$398$	−8.98313	−	0.164656i	−0.450284	−	0.00825345i
$399$	−28.3322	−	7.81009i	−1.41838	−	0.390994i
$400$	7.23237	+	14.9611i	0.361618	+	0.748055i
$401$	−12.8684	+	7.42958i	−0.642618	+	0.371015i	−0.785622	−	0.618707i	$-0.787657\pi$
$401$	−12.8684	+	7.42958i	−0.642618	+	0.371015i	0.143005	+	0.989722i	$0.454324\pi$
$402$	−13.4103	+	28.6056i	−0.668844	+	1.42672i
$403$	−8.90252	−	5.13987i	−0.443466	−	0.256035i
$404$	−0.393693	+	10.7358i	−0.0195870	+	0.534124i
$405$	16.1087	−	21.9548i	0.800447	−	1.09094i
$406$	−2.04857	−	1.23334i	−0.101669	−	0.0612098i
$407$	4.66172	+	8.07433i	0.231073	+	0.400230i
$408$	11.1932	−	21.7635i	0.554147	−	1.07745i
$409$	−0.0903771			−0.00446886			−0.00223443	−	0.999998i	$-0.500711\pi$
$409$	−0.0903771			−0.00446886			−0.00223443	+	0.999998i	$0.500711\pi$
$410$	1.54983	−	0.857316i	0.0765408	−	0.0423398i
$411$	−28.3353	−	12.6555i	−1.39768	−	0.624248i
$412$	0.594899	−	16.2225i	0.0293086	−	0.799226i
$413$	35.7070	+	20.6154i	1.75703	+	1.01442i
$414$	−19.1540	−	6.66419i	−0.941366	−	0.327527i
$415$	−9.82067	−	5.66997i	−0.482078	−	0.278328i
$416$	−20.6299	+	9.51033i	−1.01146	+	0.466282i
$417$	−2.68610	−	25.8475i	−0.131539	−	1.26576i
$418$	14.7062	−	11.3275i	0.719302	−	0.554047i
$419$	6.82563	−	11.8223i	0.333454	−	0.577559i	−0.649733	−	0.760163i	$-0.725119\pi$
$419$	6.82563	−	11.8223i	0.333454	−	0.577559i	0.983187	+	0.182604i	$0.0584525\pi$
$420$	−40.7080	+	2.72722i	−1.98635	+	0.133075i
$421$	−18.1106			−0.882657			−0.441328	−	0.897346i	$-0.645493\pi$
$421$	−18.1106			−0.882657			−0.441328	+	0.897346i	$0.645493\pi$
$422$	−5.23893	−	0.0960266i	−0.255027	−	0.00467450i
$423$	11.5434	−	35.2461i	0.561261	−	1.71372i
$424$	−13.7500	−	27.1617i	−0.667758	−	1.31909i
$425$	−17.9730	+	10.3767i	−0.871821	+	0.503346i
$426$	−19.5680	+	13.6421i	−0.948073	+	0.660963i
$427$			25.0069i			1.21017i
$428$	5.83454	+	11.0196i	0.282023	+	0.532653i
$429$	−12.2914	−	16.9593i	−0.593434	−	0.818805i
$430$	0.147892	−	8.06855i	0.00713199	−	0.389100i
$431$	6.32209	+	10.9502i	0.304525	+	0.527452i	0.977155	−	0.212526i	$-0.0681691\pi$
$431$	6.32209	+	10.9502i	0.304525	+	0.527452i	−0.672631	+	0.739978i	$0.734836\pi$
$432$	−5.86887	+	19.9388i	−0.282366	+	0.959307i
$433$	10.3116	+	17.8602i	0.495544	+	0.858307i	0.999987	−	0.00513780i	$-0.00163542\pi$
$433$	10.3116	+	17.8602i	0.495544	+	0.858307i	−0.504443	+	0.863445i	$0.668302\pi$
$434$	12.0730	+	7.26856i	0.579522	+	0.348902i
$435$	2.26409	−	0.235287i	0.108555	−	0.0112812i
$436$	−35.3318	−	1.29566i	−1.69209	−	0.0620509i
$437$	−13.0149	−	16.2711i	−0.622586	−	0.778351i
$438$	1.19790	−	0.835133i	0.0572378	−	0.0399042i
$439$		−	12.3295i		−	0.588457i	−0.955735	−	0.294228i	$-0.904937\pi$
$439$		−	12.3295i		−	0.588457i	0.955735	−	0.294228i	$-0.0950626\pi$
$440$	14.0920	−	21.5757i	0.671810	−	1.02858i
$441$	7.61251	−	23.2436i	0.362501	−	1.10684i
$442$	−13.7326	−	24.8254i	−0.653192	−	1.18082i
$443$	1.62914	−	2.82175i	0.0774026	−	0.134065i	−0.824726	−	0.565533i	$-0.808671\pi$
$443$	1.62914	−	2.82175i	0.0774026	−	0.134065i	0.902129	+	0.431467i	$0.142004\pi$
$444$	−5.97155	−	8.90917i	−0.283397	−	0.422810i
$445$	21.5935	−	37.4011i	1.02363	−	1.77298i
$446$	8.48391	−	14.0917i	0.401725	−	0.667261i
$447$	24.8893	−	18.0387i	1.17722	−	0.853199i
$448$	28.5150	−	12.5169i	1.34721	−	0.591370i
$449$			19.0008i			0.896701i	0.893858	+	0.448351i	$0.147988\pi$
$449$			19.0008i			0.896701i	−0.893858	+	0.448351i	$0.852012\pi$
$450$	13.3393	−	11.5206i	0.628818	−	0.543085i
$451$	−1.07947	−	0.623235i	−0.0508305	−	0.0293470i
$452$	0.852017	−	23.2340i	0.0400755	−	1.09283i
$453$	−4.51398	+	3.27154i	−0.212085	+	0.153710i
$454$	−0.0654630	+	3.57147i	−0.00307233	+	0.167617i
$455$	−23.6482	+	40.9598i	−1.10864	+	1.92023i
$456$	−16.0085	+	14.1325i	−0.749669	+	0.661813i
$457$	7.55453	+	13.0848i	0.353386	+	0.612083i	0.986840	−	0.161697i	$-0.0516968\pi$
$457$	7.55453	+	13.0848i	0.353386	+	0.612083i	−0.633454	+	0.773780i	$0.718363\pi$
$458$	−33.2880	+	18.4138i	−1.55545	+	0.860421i
$459$	−25.3714	−	5.48603i	−1.18424	−	0.256066i
$460$	−24.5033	−	15.3710i	−1.14247	−	0.716677i
$461$			8.52976i			0.397271i	0.980073	+	0.198635i	$0.0636509\pi$
$461$			8.52976i			0.397271i	−0.980073	+	0.198635i	$0.936349\pi$
$462$	16.4210	+	23.5539i	0.763973	+	1.09583i
$463$	−8.79687	−	5.07887i	−0.408825	−	0.236035i	0.281460	−	0.959573i	$-0.409181\pi$
$463$	−8.79687	−	5.07887i	−0.408825	−	0.236035i	−0.690285	+	0.723538i	$0.742515\pi$
$464$	−1.56426	+	0.756182i	−0.0726190	+	0.0351049i
$465$	−13.3432	+	1.38664i	−0.618774	+	0.0643037i
$466$	−3.81073	−	6.88893i	−0.176529	−	0.319123i
$467$	6.04500			0.279729			0.139865	−	0.990171i	$-0.455333\pi$
$467$	6.04500			0.279729			0.139865	+	0.990171i	$0.455333\pi$
$468$	15.4120	+	18.5206i	0.712422	+	0.856116i
$469$	−25.1034	−	43.4803i	−1.15917	−	2.00773i
$470$	27.2844	−	45.3192i	1.25854	−	2.09042i
$471$	2.54844	+	3.51628i	0.117426	+	0.162022i
$472$	26.7288	−	13.5309i	1.23029	−	0.622808i
$473$	−4.91842	+	2.83965i	−0.226149	+	0.130567i
$474$	−14.0083	+	29.8813i	−0.643423	+	1.37249i
$475$	17.9023	−	2.72523i	0.821412	−	0.125042i
$476$	18.1987	+	34.3716i	0.834136	+	1.57542i
$477$	−24.0470	+	21.5503i	−1.10103	+	0.986720i
$478$	−0.346009	+	0.191401i	−0.0158261	+	0.00875446i
$479$	−5.46715	+	9.46938i	−0.249800	+	0.432667i	−0.963470	−	0.267815i	$-0.913698\pi$
$479$	−5.46715	+	9.46938i	−0.249800	+	0.432667i	0.713670	+	0.700482i	$0.247032\pi$
$480$	−14.5156	+	25.8480i	−0.662542	+	1.17979i
$481$	−12.4333			−0.566910
$482$	18.2903	−	10.1176i	0.833101	−	0.460844i
$483$	26.0957	−	18.9130i	1.18740	−	0.860573i
$484$	3.86140	+	0.141602i	0.175518	+	0.00643646i
$485$	7.51995	−	4.34165i	0.341463	−	0.197144i
$486$	22.0390	+	0.532977i	0.999708	+	0.0241763i
$487$			31.2745i			1.41718i	0.705619	+	0.708592i	$0.250669\pi$
$487$			31.2745i			1.41718i	−0.705619	+	0.708592i	$0.749331\pi$
$488$	15.2128	+	9.93609i	0.688649	+	0.449786i
$489$	−3.35355	−	32.2702i	−0.151653	−	1.45931i
$490$	17.9932	−	29.8865i	0.812849	−	1.35013i
$491$	−3.58026	−	6.20119i	−0.161575	−	0.279856i	0.773859	−	0.633358i	$-0.218324\pi$
$491$	−3.58026	−	6.20119i	−0.161575	−	0.279856i	−0.935434	+	0.353502i	$0.884991\pi$
$492$	1.28693	+	0.632336i	0.0580195	+	0.0285079i
$493$	−1.08494	−	1.87918i	−0.0488634	−	0.0846338i
$494$	3.27633	+	24.5370i	0.147409	+	1.10397i
$495$	−25.9756	−	8.50726i	−1.16752	−	0.382373i
$496$	9.21878	−	4.45647i	0.413935	−	0.200101i
$497$		−	37.9082i		−	1.70041i
$498$	−0.781445	−	9.14730i	−0.0350174	−	0.409900i
$499$	29.4358	−	16.9948i	1.31773	−	0.760791i	0.334366	−	0.942443i	$-0.391478\pi$
$499$	29.4358	−	16.9948i	1.31773	−	0.760791i	0.983363	+	0.181652i	$0.0581444\pi$
$500$	−4.52230	+	2.39442i	−0.202244	+	0.107082i
$501$	28.1278	−	2.92308i	1.25666	−	0.130594i
$502$	−0.185468	+	10.1186i	−0.00827785	+	0.451615i
$503$	−21.1844	−	36.6924i	−0.944565	−	1.63603i	−0.756619	−	0.653855i	$-0.773150\pi$
$503$	−21.1844	−	36.6924i	−0.944565	−	1.63603i	−0.187946	−	0.982179i	$-0.560183\pi$
$504$	−20.6590	−	25.7722i	−0.920226	−	1.14799i
$505$	16.2521			0.723208
$506$	−0.373063	+	20.3532i	−0.0165847	+	0.904811i
$507$	5.38576	−	0.559695i	0.239190	−	0.0248569i
$508$	10.8043	+	6.77758i	0.479364	+	0.300706i
$509$		−	7.43689i		−	0.329634i	−0.986324	−	0.164817i	$-0.947297\pi$
$509$		−	7.43689i		−	0.329634i	0.986324	−	0.164817i	$-0.0527034\pi$
$510$	−33.5225	−	15.7153i	−1.48440	−	0.695885i
$511$			2.32063i			0.102659i
$512$	3.71541	−	22.3203i	0.164200	−	0.986427i
$513$	18.8772	+	12.5161i	0.833447	+	0.552600i
$514$	15.1713	−	25.1993i	0.669175	−	1.11149i
$515$	−24.5581			−1.08216
$516$	5.42695	−	3.63753i	0.238908	−	0.160133i
$517$	−37.2281			−1.63729
$518$	17.0415	+	0.312362i	0.748763	+	0.0137244i
$519$	0.939869	+	9.04406i	0.0412557	+	0.396990i
$520$	15.5214	+	30.6609i	0.680657	+	1.34457i
$521$		−	1.07049i		−	0.0468992i	−0.999725	−	0.0234496i	$-0.992535\pi$
$521$		−	1.07049i		−	0.0468992i	0.999725	−	0.0234496i	$-0.00746492\pi$
$522$	1.20454	+	1.39469i	0.0527211	+	0.0610439i
$523$	7.38254	−	4.26231i	0.322816	−	0.186378i	−0.329831	−	0.944040i	$-0.606992\pi$
$523$	7.38254	−	4.26231i	0.322816	−	0.186378i	0.652647	+	0.757662i	$0.273658\pi$
$524$	−10.5868	+	16.8767i	−0.462487	+	0.737262i
$525$	2.89524	+	27.8600i	0.126359	+	1.21591i
$526$	10.8986	+	6.56152i	0.475202	+	0.286096i
$527$	6.39398	+	11.0747i	0.278526	+	0.482421i
$528$	20.8534	−	0.630799i	0.907530	−	0.0274520i
$529$	−0.150806			−0.00655678
$530$	−40.3006	+	22.2929i	−1.75055	+	0.968344i
$531$	−21.2069	−	23.6638i	−0.920299	−	1.02692i
$532$	−3.87421	−	33.7136i	−0.167968	−	1.46167i
$533$	1.43954	−	0.831117i	0.0623533	−	0.0359997i
$534$	34.8366	−	2.97606i	1.50753	−	0.128787i
$535$	16.3359	−	9.43154i	0.706263	−	0.407761i
$536$	−36.4253	−	2.00476i	−1.57333	−	0.0865926i
$537$	15.5053	−	1.61133i	0.669104	−	0.0695341i
$538$	7.90276	+	14.2864i	0.340712	+	0.615930i
$539$	−24.5507			−1.05747
$540$	30.4687	+	7.76713i	1.31117	+	0.334244i
$541$	0.207415	+	0.359253i	0.00891746	+	0.0154455i	0.870450	−	0.492257i	$-0.163828\pi$
$541$	0.207415	+	0.359253i	0.00891746	+	0.0154455i	−0.861532	+	0.507703i	$0.830495\pi$
$542$	0.00931863	+	0.0168460i	0.000400269	+	0.000723596i
$543$	14.0075	+	19.3273i	0.601121	+	0.829412i
$544$	28.1407	+	2.58597i	1.20652	+	0.110872i
$545$			53.4863i			2.29110i
$546$	−38.1513	+	3.25923i	−1.63273	+	0.139482i
$547$	−24.1684	−	13.9536i	−1.03337	−	0.596614i	−0.115419	−	0.993317i	$-0.536821\pi$
$547$	−24.1684	−	13.9536i	−1.03337	−	0.596614i	−0.917947	+	0.396703i	$0.870154\pi$
$548$	1.31319	−	35.8099i	0.0560967	−	1.52972i
$549$	5.99837	−	18.3151i	0.256004	−	0.781669i
$550$	−15.1570	−	9.12530i	−0.646298	−	0.389104i
$551$	0.284937	+	1.87178i	0.0121387	+	0.0797403i
$552$	−1.13688	−	23.3899i	−0.0483888	−	0.995541i
$553$	−26.2229	−	45.4193i	−1.11511	−	1.93143i
$554$	−0.252318	+	13.7657i	−0.0107199	+	0.584849i
$555$	−13.1378	+	9.52167i	−0.557667	+	0.404173i
$556$	26.5190	−	14.0410i	1.12466	−	0.595471i
$557$	−9.40864	+	5.43208i	−0.398657	+	0.230165i	−0.685904	−	0.727692i	$-0.740593\pi$
$557$	−9.40864	+	5.43208i	−0.398657	+	0.230165i	0.287247	+	0.957856i	$0.407260\pi$
$558$	−7.09878	−	8.21943i	−0.300515	−	0.347956i
$559$		−	7.57365i		−	0.320331i
$560$	−20.5039	−	42.4149i	−0.866447	−	1.79236i
$561$	2.69323	+	25.9161i	0.113708	+	1.09418i
$562$	7.90830	+	14.2964i	0.333591	+	0.603057i
$563$	6.07143	−	10.5160i	0.255880	−	0.443198i	−0.709254	−	0.704953i	$-0.750968\pi$
$563$	6.07143	−	10.5160i	0.255880	−	0.443198i	0.965134	+	0.261755i	$0.0843013\pi$
$564$	42.7301	−	2.86269i	1.79926	−	0.120541i
$565$	−35.1722			−1.47971
$566$	−31.8510	−	0.583811i	−1.33880	−	0.0245394i
$567$	−20.7249	+	28.2464i	−0.870364	+	1.18624i
$568$	−23.0611	−	15.0622i	−0.967624	−	0.631996i
$569$	−10.8712	+	6.27649i	−0.455745	+	0.263124i	−0.710253	−	0.703946i	$-0.751420\pi$
$569$	−10.8712	+	6.27649i	−0.455745	+	0.263124i	0.254509	+	0.967071i	$0.418086\pi$
$570$	22.2529	+	23.4181i	0.932070	+	0.980878i
$571$	−27.6064	−	15.9386i	−1.15529	−	0.667008i	−0.205120	−	0.978737i	$-0.565759\pi$
$571$	−27.6064	−	15.9386i	−1.15529	−	0.667008i	−0.950171	+	0.311729i	$0.899092\pi$
$572$	12.8521	−	20.4879i	0.537374	−	0.856642i
$573$	14.5364	+	20.0570i	0.607267	+	0.837892i
$574$	−1.99396	+	1.10299i	−0.0832264	+	0.0460381i
$575$	−9.92913	+	17.1978i	−0.414073	+	0.717196i
$576$	−23.8869	+	2.32757i	−0.995286	+	0.0969820i
$577$	16.0365			0.667607			0.333803	−	0.942643i	$-0.391668\pi$
$577$	16.0365			0.667607			0.333803	+	0.942643i	$0.391668\pi$
$578$	−0.206192	+	11.2492i	−0.00857646	+	0.467906i
$579$	4.61935	+	6.37367i	0.191974	+	0.264881i
$580$	1.22991	+	2.32292i	0.0510694	+	0.0964539i
$581$	12.6350	+	7.29479i	0.524186	+	0.302639i
$582$	6.36511	+	2.98396i	0.263842	+	0.123689i
$583$	28.0698	+	16.2061i	1.16253	+	0.671188i
$584$	1.41174	+	0.922066i	0.0584182	+	0.0381554i
$585$	27.1449	−	24.3266i	1.12230	−	1.00578i
$586$	12.9415	+	23.3953i	0.534609	+	0.966452i
$587$	37.8894			1.56386			0.781932	−	0.623364i	$-0.214234\pi$
$587$	37.8894			1.56386			0.781932	+	0.623364i	$0.214234\pi$
$588$	28.1791	−	1.88785i	1.16208	−	0.0778535i
$589$	−1.67924	−	11.0311i	−0.0691920	−	0.454528i
$590$	−21.9377	−	39.6583i	−0.903160	−	1.63271i
$591$	3.46608	+	33.3530i	0.142576	+	1.37196i
$592$	6.96121	−	10.2430i	0.286104	−	0.420984i
$593$	0.224349	−	0.129528i	0.00921292	−	0.00531908i	−0.495386	−	0.868673i	$-0.664974\pi$
$593$	0.224349	−	0.129528i	0.00921292	−	0.00531908i	0.504599	+	0.863354i	$0.331640\pi$
$594$	−6.37690	−	21.1898i	−0.261648	−	0.869428i
$595$	50.9539	−	29.4182i	2.08890	−	1.20603i
$596$	30.0677	+	18.8616i	1.23162	+	0.772600i
$597$	−8.90990	+	6.45750i	−0.364658	+	0.264288i
$598$	−23.2570	−	14.0019i	−0.951050	−	0.572581i
$599$	11.9751			0.489289			0.244645	−	0.969613i	$-0.421329\pi$
$599$	11.9751			0.489289			0.244645	+	0.969613i	$0.421329\pi$
$600$	18.0988	+	9.30841i	0.738879	+	0.380014i
$601$	12.1188	+	20.9904i	0.494337	+	0.856216i	0.999979	−	0.00652730i	$-0.00207772\pi$
$601$	12.1188	+	20.9904i	0.494337	+	0.856216i	−0.505642	+	0.862743i	$0.668744\pi$
$602$	−0.190273	+	10.3807i	−0.00775495	+	0.423087i
$603$	7.95619	+	37.8665i	0.324001	+	1.54204i
$604$	−5.45316	−	3.42078i	−0.221886	−	0.139190i
$605$		−	5.84549i		−	0.237653i
$606$	7.52472	+	10.7933i	0.305671	+	0.438448i
$607$	−8.98311	−	5.18640i	−0.364613	−	0.210510i	0.306489	−	0.951874i	$-0.400846\pi$
$607$	−8.98311	−	5.18640i	−0.364613	−	0.210510i	−0.671103	+	0.741365i	$0.734179\pi$
$608$	−22.0487	−	11.0387i	−0.894195	−	0.447678i
$609$	−2.91291	+	0.302713i	−0.118037	+	0.0122665i
$610$	14.1779	−	23.5494i	0.574048	−	0.953488i
$611$	24.8228	−	42.9944i	1.00422	−	1.73937i
$612$	−5.08410	−	29.5391i	−0.205512	−	1.19405i
$613$	−17.3644	+	30.0761i	−0.701343	+	1.21476i	0.266652	+	0.963793i	$0.414083\pi$
$613$	−17.3644	+	30.0761i	−0.701343	+	1.21476i	−0.967995	+	0.250969i	$0.919251\pi$
$614$	19.6144	+	35.4584i	0.791572	+	1.43098i
$615$	0.884614	−	1.98064i	0.0356711	−	0.0798669i
$616$	−18.1303	+	27.7586i	−0.730491	+	1.11843i
$617$		−	26.3702i		−	1.06162i	−0.847490	−	0.530812i	$-0.821887\pi$
$617$		−	26.3702i		−	1.06162i	0.847490	−	0.530812i	$-0.178113\pi$
$618$	−11.3704	−	16.3095i	−0.457385	−	0.656064i
$619$	−13.0555	+	7.53759i	−0.524745	+	0.302961i	−0.738874	−	0.673844i	$-0.764642\pi$
$619$	−13.0555	+	7.53759i	−0.524745	+	0.302961i	0.214129	+	0.976805i	$0.431309\pi$
$620$	−7.24834	−	13.6898i	−0.291100	−	0.549797i
$621$	−23.6492	+	7.59240i	−0.949009	+	0.304672i
$622$	−2.29311	+	1.26847i	−0.0919454	+	0.0508612i
$623$	−27.7815	+	48.1190i	−1.11304	+	1.92785i
$624$	−13.1761	+	24.5041i	−0.527466	+	0.980948i
$625$	14.2565	+	24.6930i	0.570261	+	0.987721i
$626$	5.53895	−	3.06396i	0.221381	−	0.122461i
$627$	6.04178	−	21.9174i	0.241286	−	0.875297i
$628$	−2.66470	+	4.24787i	−0.106333	+	0.169508i
$629$	13.3948	+	7.73349i	0.534085	+	0.308354i
$630$	−37.8170	+	32.6610i	−1.50667	+	1.30124i
$631$	20.8654	−	12.0466i	0.830638	−	0.479569i	−0.0234332	−	0.999725i	$-0.507460\pi$
$631$	20.8654	−	12.0466i	0.830638	−	0.479569i	0.854071	+	0.520156i	$0.174126\pi$
$632$	−38.0497	−	2.09417i	−1.51354	−	0.0833014i
$633$	−5.19622	+	3.76599i	−0.206531	+	0.149685i
$634$	−18.4268	−	33.3114i	−0.731820	−	1.32296i
$635$	9.64731	−	16.7096i	0.382842	−	0.663102i
$636$	−33.4644	−	16.4427i	−1.32695	−	0.651997i
$637$	16.3698	−	28.3534i	0.648597	−	1.12340i
$638$	0.954098	−	1.58475i	0.0377731	−	0.0627407i
$639$	−9.09297	+	27.7640i	−0.359712	+	1.09833i
$640$	−33.9497	−	4.37951i	−1.34198	−	0.173115i
$641$		−	35.9495i		−	1.41992i	−0.704243	−	0.709959i	$-0.748713\pi$
$641$		−	35.9495i		−	1.41992i	0.704243	−	0.709959i	$-0.251287\pi$
$642$	13.8272	+	6.48218i	0.545717	+	0.255831i
$643$	25.5696	−	14.7626i	1.00836	−	0.582180i	0.0976525	−	0.995221i	$-0.468867\pi$
$643$	25.5696	−	14.7626i	1.00836	−	0.582180i	0.910713	+	0.413041i	$0.135533\pi$
$644$	31.5252	+	19.7758i	1.24227	+	0.779277i
$645$	−5.80006	−	8.00277i	−0.228377	−	0.315109i
$646$	11.7322	−	28.4723i	0.461599	−	1.12023i
$647$	−20.2868			−0.797555			−0.398778	−	0.917048i	$-0.630565\pi$
$647$	−20.2868			−0.797555			−0.398778	+	0.917048i	$0.630565\pi$
$648$	8.94875	+	23.8311i	0.351540	+	0.936173i
$649$	−15.9478	+	27.6225i	−0.626007	+	1.08428i
$650$	20.6451	−	11.4202i	0.809767	−	0.447936i
$651$	17.1669	−	1.78400i	0.672822	−	0.0699205i
$652$	33.1086	−	17.5300i	1.29663	−	0.686527i
$653$	−41.8593	−	24.1675i	−1.63808	−	0.945746i	−0.981493	−	0.191496i	$-0.938666\pi$
$653$	−41.8593	−	24.1675i	−1.63808	−	0.945746i	−0.656587	−	0.754250i	$-0.728001\pi$
$654$	−35.5213	+	24.7642i	−1.38899	+	0.968357i
$655$	26.1010	+	15.0694i	1.01985	+	0.588811i
$656$	−0.121271	+	1.65127i	−0.00473484	+	0.0644712i
$657$	0.556646	−	1.69963i	0.0217168	−	0.0663091i
$658$	−35.1033	+	58.3062i	−1.36847	+	2.27301i
$659$	4.89232	−	8.47374i	0.190578	−	0.330090i	−0.754864	−	0.655881i	$-0.772297\pi$
$659$	4.89232	−	8.47374i	0.190578	−	0.330090i	0.945442	+	0.325791i	$0.105631\pi$
$660$	−2.10974	−	31.4911i	−0.0821215	−	1.22579i
$661$	−47.6330			−1.85271			−0.926355	−	0.376652i	$-0.877075\pi$
$661$	−47.6330			−1.85271			−0.926355	+	0.376652i	$0.877075\pi$
$662$	40.5227	+	0.742759i	1.57496	+	0.0288681i
$663$	−31.7260	−	14.1698i	−1.23214	−	0.550311i
$664$	9.45803	−	4.78791i	0.367043	−	0.185807i
$665$	−50.7532	+	7.72607i	−1.96812	+	0.299604i
$666$	−12.4063	−	4.31650i	−0.480735	−	0.167261i
$667$	−1.79812	−	1.03814i	−0.0696233	−	0.0401971i
$668$	15.2798	+	28.8586i	0.591192	+	1.11657i
$669$	−2.08230	−	20.0373i	−0.0805063	−	0.774686i
$670$	−1.01139	+	55.1787i	−0.0390736	+	2.13174i
$671$	−19.3450			−0.746806
$672$	18.6753	−	33.2552i	0.720414	−	1.28285i
$673$	−18.5127	−	32.0650i	−0.713614	−	1.23602i	−0.963492	−	0.267738i	$-0.913724\pi$
$673$	−18.5127	−	32.0650i	−0.713614	−	1.23602i	0.249878	−	0.968277i	$-0.419610\pi$
$674$	−0.738075	+	40.2672i	−0.0284296	+	1.55103i
$675$	4.56224	−	21.0992i	0.175601	−	0.812107i
$676$	2.92569	+	5.52570i	0.112526	+	0.212527i
$677$	11.5974	−	6.69576i	0.445724	−	0.257339i	−0.260298	−	0.965528i	$-0.583821\pi$
$677$	11.5974	−	6.69576i	0.445724	−	0.257339i	0.706023	+	0.708189i	$0.250488\pi$
$678$	−16.2848	−	23.3585i	−0.625412	−	0.897079i
$679$	−9.67492	+	5.58582i	−0.371289	+	0.214364i
$680$	2.34935	−	42.6862i	0.0900934	−	1.63694i
$681$	2.56734	+	3.54235i	0.0983807	+	0.135743i
$682$	−5.62286	+	9.33951i	−0.215310	+	0.357628i
$683$	17.3858			0.665251			0.332625	−	0.943059i	$-0.392066\pi$
$683$	17.3858			0.665251			0.332625	+	0.943059i	$0.392066\pi$
$684$	−5.24934	+	25.6212i	−0.200713	+	0.979650i
$685$	−54.2099			−2.07125
$686$	−3.27338	+	5.43706i	−0.124978	+	0.207588i
$687$	−19.0001	+	42.5410i	−0.724901	+	1.62304i
$688$	6.23943	+	4.24037i	0.237876	+	0.161662i
$689$	−37.4325	+	21.6117i	−1.42607	+	0.823340i
$690$	−35.2977	+	3.01545i	−1.34376	+	0.114796i
$691$	−10.2721	+	5.93061i	−0.390770	+	0.225611i	−0.682494	−	0.730892i	$-0.739105\pi$
$691$	−10.2721	+	5.93061i	−0.390770	+	0.225611i	0.291724	+	0.956503i	$0.405771\pi$
$692$	−9.27904	+	4.91296i	−0.352736	+	0.186763i
$693$	33.4194	+	10.9452i	1.26950	+	0.415772i
$694$	−0.150263	+	8.19792i	−0.00570392	+	0.311189i
$695$	−22.6973	−	39.3129i	−0.860957	−	1.49122i
$696$	−0.973244	+	1.89232i	−0.0368907	+	0.0717283i
$697$	−2.06781			−0.0783240
$698$	−0.00289022	+	0.157682i	−0.000109396	+	0.00596834i
$699$	−8.80383	−	3.93207i	−0.332991	−	0.148724i
$700$	−28.5838	+	15.1343i	−1.08037	+	0.572021i
$701$	−34.5702	−	19.9591i	−1.30570	−	0.753846i	−0.324324	−	0.945946i	$-0.605137\pi$
$701$	−34.5702	−	19.9591i	−1.30570	−	0.753846i	−0.981375	+	0.192101i	$0.938470\pi$
$702$	28.7239	+	6.76423i	1.08411	+	0.255299i
$703$	−8.42995	−	10.5390i	−0.317941	−	0.397487i
$704$	9.68293	+	22.0589i	0.364939	+	0.831374i
$705$	−6.69672	−	64.4403i	−0.252213	−	2.42696i
$706$	−50.9815	−	0.934463i	−1.91872	−	0.0351690i
$707$	−20.9094			−0.786378
$708$	16.1807	−	32.9311i	0.608108	−	1.23763i
$709$	5.85136	−	10.1349i	0.219753	−	0.380623i	−0.734980	−	0.678089i	$-0.762808\pi$
$709$	5.85136	−	10.1349i	0.219753	−	0.380623i	0.954732	+	0.297467i	$0.0961417\pi$
$710$	−21.4924	+	35.6987i	−0.806597	+	1.33975i
$711$	8.31100	+	39.5552i	0.311687	+	1.48344i
$712$	18.2343	+	36.0200i	0.683359	+	1.34991i
$713$	10.5970	+	6.11817i	0.396860	+	0.229127i
$714$	43.1289	+	20.2188i	1.61406	+	0.756669i
$715$	−31.6860	−	18.2939i	−1.18499	−	0.684153i
$716$	8.42289	+	15.9082i	0.314778	+	0.594517i
$717$	−0.197495	+	0.442188i	−0.00737559	+	0.0165138i
$718$	−31.6725	+	17.5202i	−1.18201	+	0.653847i
$719$	19.9654	−	34.5812i	0.744585	−	1.28966i	−0.205803	−	0.978593i	$-0.565981\pi$
$719$	19.9654	−	34.5812i	0.744585	−	1.28966i	0.950388	−	0.311066i	$-0.100686\pi$
$720$	4.84307	+	35.9830i	0.180491	+	1.34101i
$721$	31.5956			1.17668
$722$	−18.5772	+	19.4136i	−0.691373	+	0.722498i
$723$	10.4398	−	23.3744i	0.388259	−	0.869304i
$724$	−14.6466	+	23.3485i	−0.544335	+	0.867739i
$725$	1.56274	−	0.902251i	0.0580389	−	0.0335088i
$726$	3.88210	−	2.70647i	0.144078	−	0.100446i
$727$			2.61343i			0.0969268i	0.998825	+	0.0484634i	$0.0154324\pi$
$727$			2.61343i			0.0969268i	−0.998825	+	0.0484634i	$0.984568\pi$
$728$	−19.9693	−	39.4473i	−0.740111	−	1.46201i
$729$	21.9544	−	15.7164i	0.813124	−	0.582090i
$730$	1.31571	−	2.18538i	0.0486965	−	0.0808844i
$731$	−4.71080	+	8.15934i	−0.174235	+	0.301784i
$732$	22.2040	−	1.48755i	0.820684	−	0.0549815i
$733$	−16.7836	+	29.0701i	−0.619918	+	1.07373i	0.369582	+	0.929198i	$0.379501\pi$
$733$	−16.7836	+	29.0701i	−0.619918	+	1.07373i	−0.989500	+	0.144532i	$0.953832\pi$
$734$	−7.99695	−	14.4567i	−0.295173	−	0.533605i
$735$	−4.41626	−	42.4963i	−0.162896	−	1.56750i
$736$	24.5565	−	11.3205i	0.905164	−	0.417278i
$737$	33.6358	−	19.4196i	1.23899	−	0.715331i
$738$	1.72496	−	0.329546i	0.0634965	−	0.0121308i
$739$	−15.2623	−	8.81167i	−0.561431	−	0.324142i	0.192288	−	0.981338i	$-0.438409\pi$
$739$	−15.2623	−	8.81167i	−0.561431	−	0.324142i	−0.753720	+	0.657196i	$0.771742\pi$
$740$	−15.8712	−	9.95604i	−0.583437	−	0.365991i
$741$	21.2837	+	21.5916i	0.781877	+	0.793188i
$742$	51.8494	−	28.6814i	1.90345	−	1.05293i
$743$	−9.13527	−	15.8228i	−0.335141	−	0.580481i	0.648371	−	0.761324i	$-0.275450\pi$
$743$	−9.13527	−	15.8228i	−0.335141	−	0.580481i	−0.983512	+	0.180844i	$0.942117\pi$
$744$	5.73569	−	11.1522i	0.210281	−	0.408858i
$745$	26.8479	−	46.5018i	0.983629	−	1.70370i
$746$	33.9711	−	18.7917i	1.24377	−	0.688012i
$747$	−7.50407	−	8.37344i	−0.274560	−	0.306368i
$748$	−26.5894	+	14.0783i	−0.972205	+	0.514753i
$749$	−21.0172	+	12.1343i	−0.767954	+	0.443378i
$750$	−2.66020	+	5.67451i	−0.0971369	+	0.207204i
$751$		−	42.5385i		−	1.55225i	−0.630577	−	0.776127i	$-0.717182\pi$
$751$		−	42.5385i		−	1.55225i	0.630577	−	0.776127i	$-0.282818\pi$
$752$	21.5224	+	44.5218i	0.784840	+	1.62354i
$753$	7.27373	+	10.0361i	0.265069	+	0.365736i
$754$	1.19404	+	2.15855i	0.0434843	+	0.0786098i
$755$	−4.86919	+	8.43369i	−0.177208	+	0.306933i
$756$	−39.2001	−	9.99294i	−1.42569	−	0.363440i
$757$	14.5044	−	25.1223i	0.527171	−	0.913087i	−0.472328	−	0.881423i	$-0.656586\pi$
$757$	14.5044	−	25.1223i	0.527171	−	0.913087i	0.999499	−	0.0316637i	$-0.0100805\pi$
$758$	−6.45319	+	10.7187i	−0.234391	+	0.389320i
$759$	14.6309	+	20.1873i	0.531067	+	0.732753i
$760$	−15.4659	+	33.9451i	−0.561006	+	1.23132i
$761$	−8.77550	−	5.06654i	−0.318112	−	0.183662i	0.332439	−	0.943125i	$-0.392128\pi$
$761$	−8.77550	−	5.06654i	−0.318112	−	0.183662i	−0.650551	+	0.759463i	$0.725462\pi$
$762$	15.5639	−	1.32961i	0.563821	−	0.0481667i
$763$		−	68.8137i		−	2.49122i
$764$	−15.1995	+	24.2300i	−0.549900	+	0.876611i
$765$	−44.3752	+	9.32373i	−1.60439	+	0.337100i
$766$	0.0355841	−	1.94136i	0.00128570	−	0.0701443i
$767$	−21.2673	−	36.8360i	−0.767917	−	1.33007i
$768$	−12.8102	−	24.5743i	−0.462248	−	0.886750i
$769$	−14.4248			−0.520171			−0.260086	−	0.965586i	$-0.583751\pi$
$769$	−14.4248			−0.520171			−0.260086	+	0.965586i	$0.583751\pi$
$770$	42.9704	+	25.8704i	1.54855	+	0.932303i
$771$	−3.72365	−	35.8314i	−0.134104	−	1.29044i
$772$	−4.83008	+	7.69976i	−0.173839	+	0.277121i
$773$	20.1732	−	11.6470i	0.725580	−	0.418914i	−0.0912227	−	0.995831i	$-0.529078\pi$
$773$	20.1732	−	11.6470i	0.725580	−	0.418914i	0.816803	+	0.576916i	$0.195744\pi$
$774$	2.62936	−	7.55722i	0.0945105	−	0.271639i
$775$	−9.20985	+	5.31731i	−0.330827	+	0.191003i
$776$	−0.446085	+	8.10510i	−0.0160135	+	0.290956i
$777$	16.9026	−	12.2503i	0.606378	−	0.439476i
$778$	22.2765	+	40.2709i	0.798652	+	1.44378i
$779$	1.68052	+	0.656708i	0.0602108	+	0.0235290i
$780$	37.7756	+	18.5610i	1.35258	+	0.664592i
$781$	29.3253			1.04934
$782$	16.3464	+	29.5505i	0.584545	+	1.05672i
$783$	2.20603	+	0.477007i	0.0788370	+	0.0170468i
$784$	14.1933	+	29.3607i	0.506903	+	1.04859i
$785$	6.56963	+	3.79298i	0.234480	+	0.135377i
$786$	2.07689	+	24.3113i	0.0740804	+	0.867157i
$787$	−41.3050	−	23.8474i	−1.47236	−	0.850069i	−0.472845	−	0.881145i	$-0.656773\pi$
$787$	−41.3050	−	23.8474i	−1.47236	−	0.850069i	−0.999517	+	0.0310765i	$0.990106\pi$
$788$	−34.2196	+	18.1182i	−1.21902	+	0.645434i
$789$	15.4970	−	1.61047i	0.551707	−	0.0573341i
$790$	−1.05650	+	57.6394i	−0.0375885	+	2.05072i
$791$	45.2514			1.60895
$792$	19.9371	−	15.9815i	0.708433	−	0.567879i
$793$	12.8988	−	22.3414i	0.458050	−	0.793366i
$794$	21.3916	−	11.8331i	0.759159	−	0.419942i
$795$	−23.0028	+	51.5028i	−0.815825	+	1.82662i
$796$	−10.7637	−	6.75209i	−0.381509	−	0.239321i
$797$	17.5689	+	10.1434i	0.622323	+	0.359299i	0.777773	−	0.628545i	$-0.216349\pi$
$797$	17.5689	+	10.1434i	0.622323	+	0.359299i	−0.155450	+	0.987844i	$0.549683\pi$
$798$	−28.6298	−	30.1290i	−1.01348	−	1.06656i
$799$	−53.4849	+	30.8795i	−1.89216	+	1.09244i
$800$	−2.15052	+	23.4021i	−0.0760323	+	0.827389i
$801$	31.8895	−	28.5785i	1.12676	−	1.00977i
$802$	−21.0105	−	0.385111i	−0.741906	−	0.0135987i
$803$	−1.79521			−0.0633516
$804$	−37.1135	+	24.8761i	−1.30889	+	0.877312i
$805$	28.1492	−	48.7559i	0.992130	−	1.71842i
$806$	−7.03693	−	12.7212i	−0.247865	−	0.448084i
$807$	18.2575	+	8.15440i	0.642696	+	0.287048i
$808$	−8.30801	+	12.7201i	−0.292275	+	0.447490i
$809$		−	14.0970i		−	0.495624i	−0.968808	−	0.247812i	$-0.920288\pi$
$809$		−	14.0970i		−	0.495624i	0.968808	−	0.247812i	$-0.0797116\pi$
$810$	35.5315	−	14.8498i	1.24845	−	0.521770i
$811$	5.19959	−	3.00199i	0.182582	−	0.105414i	−0.405923	−	0.913907i	$-0.633050\pi$
$811$	5.19959	−	3.00199i	0.182582	−	0.105414i	0.588505	+	0.808493i	$0.299717\pi$
$812$	−1.58237	−	2.98859i	−0.0555302	−	0.104879i
$813$	0.0215286	+	0.00961535i	0.000755041	+	0.000337225i
$814$	−0.241639	+	13.1831i	−0.00846944	+	0.462068i
$815$	−28.3372	−	49.0815i	−0.992610	−	1.71925i
$816$	29.4365	−	18.2035i	1.03048	−	0.637250i
$817$	6.41977	−	5.13504i	0.224599	−	0.179652i
$818$	−0.109499	−	0.0659241i	−0.00382855	−	0.00230498i
$819$	−34.9238	+	31.2978i	−1.22033	+	1.09363i
$820$	2.50310	+	0.0917917i	0.0874121	+	0.00320551i
$821$	22.0605	+	12.7366i	0.769916	+	0.444511i	0.832845	−	0.553507i	$-0.186711\pi$
$821$	22.0605	+	12.7366i	0.769916	+	0.444511i	−0.0629285	+	0.998018i	$0.520044\pi$
$822$	−25.0992	−	36.0018i	−0.875436	−	1.25571i
$823$			18.5404i			0.646277i	0.946352	+	0.323139i	$0.104738\pi$
$823$			18.5404i			0.646277i	−0.946352	+	0.323139i	$0.895262\pi$
$824$	12.5540	−	19.2209i	0.437340	−	0.669593i
$825$	−21.5521	+	2.23972i	−0.750348	+	0.0779771i
$826$	28.2243	+	51.0231i	0.982049	+	1.77532i
$827$	1.50477	+	2.60634i	0.0523261	+	0.0906314i	0.891002	−	0.453999i	$-0.150003\pi$
$827$	1.50477	+	2.60634i	0.0523261	+	0.0906314i	−0.838676	+	0.544631i	$0.816670\pi$
$828$	−18.3455	−	22.0457i	−0.637550	−	0.766142i
$829$	28.3457			0.984487			0.492244	−	0.870457i	$-0.336177\pi$
$829$	28.3457			0.984487			0.492244	+	0.870457i	$0.336177\pi$
$830$	−7.76267	−	14.0331i	−0.269446	−	0.487098i
$831$	9.89544	+	13.6535i	0.343269	+	0.473634i
$832$	−31.9319	−	3.52559i	−1.10704	−	0.122228i
$833$	−35.2715	+	20.3640i	−1.22209	+	0.705572i
$834$	15.5996	−	33.2756i	0.540169	−	1.15224i
$835$	42.7812	−	24.6998i	1.48051	−	0.854770i
$836$	26.0804	−	2.99704i	0.902009	−	0.103655i
$837$	−13.0010	−	2.81118i	−0.449379	−	0.0971686i
$838$	16.8934	−	9.34487i	0.583573	−	0.322813i
$839$	−42.8980			−1.48100			−0.740502	−	0.672054i	$-0.765412\pi$
$839$	−42.8980			−1.48100			−0.740502	+	0.672054i	$0.765412\pi$
$840$	−51.3103	−	26.3895i	−1.77037	−	0.910524i
$841$	−14.4057	−	24.9513i	−0.496747	−	0.860391i
$842$	−21.9425	−	13.2105i	−0.756187	−	0.455263i
$843$	18.2703	+	8.16011i	0.629264	+	0.281049i
$844$	−6.27734	−	3.93779i	−0.216075	−	0.135544i
$845$	8.19152	−	4.72937i	0.281797	−	0.162695i
$846$	39.6955	−	34.2833i	1.36476	−	1.17869i
$847$			7.52062i			0.258411i
$848$	3.15343	−	42.9383i	0.108289	−	1.47451i
$849$	−31.5914	+	22.8960i	−1.08421	+	0.785790i
$850$	−29.3449	−	0.537876i	−1.00652	−	0.0184490i
$851$	14.7998			0.507330
$852$	−33.6592	+	2.25499i	−1.15315	+	0.0772547i
$853$	−25.5352			−0.874309			−0.437155	−	0.899386i	$-0.644014\pi$
$853$	−25.5352			−0.874309			−0.437155	+	0.899386i	$0.644014\pi$
$854$	−18.2409	+	30.2979i	−0.624190	+	1.03677i
$855$	39.0249	+	6.51550i	1.33463	+	0.222825i
$856$	−0.969050	+	17.6071i	−0.0331215	+	0.601797i
$857$			20.6298i			0.704700i	0.935868	+	0.352350i	$0.114617\pi$
$857$			20.6298i			0.704700i	−0.935868	+	0.352350i	$0.885383\pi$
$858$	−2.52130	−	29.5134i	−0.0860757	−	1.00757i
$859$			50.9952i			1.73993i	0.493111	+	0.869967i	$0.335860\pi$
$859$			50.9952i			1.73993i	−0.493111	+	0.869967i	$0.664140\pi$
$860$	6.06465	−	9.66782i	0.206803	−	0.329670i
$861$	−1.13812	+	2.54822i	−0.0387869	+	0.0868431i
$862$	−0.327704	+	17.8786i	−0.0111617	+	0.608947i
$863$	−0.580286			−0.0197532			−0.00987658	−	0.999951i	$-0.503144\pi$
$863$	−0.580286			−0.0197532			−0.00987658	+	0.999951i	$0.503144\pi$
$864$	−21.6546	+	19.8765i	−0.736706	+	0.676213i
$865$	7.94181	+	13.7556i	0.270030	+	0.467705i
$866$	−0.534500	+	29.1607i	−0.0181630	+	0.990921i
$867$	8.08648	+	11.1575i	0.274631	+	0.378929i
$868$	9.32548	+	17.6129i	0.316527	+	0.597820i
$869$	35.1358	−	20.2857i	1.19190	−	0.688144i
$870$	2.91476	+	1.36643i	0.0988195	+	0.0463265i
$871$			51.7942i			1.75498i
$872$	−41.8623	−	27.3420i	−1.41764	−	0.925917i
$873$	8.42579	−	1.77035i	0.285170	−	0.0599174i
$874$	−3.89992	−	29.2072i	−0.131917	−	0.987948i
$875$	−4.97976	−	8.62520i	−0.168347	−	0.291585i
$876$	2.06052	−	0.138044i	0.0696187	−	0.00466408i
$877$	11.6216	+	20.1293i	0.392435	+	0.679717i	0.992770	−	0.120031i	$-0.0382995\pi$
$877$	11.6216	+	20.1293i	0.392435	+	0.679717i	−0.600335	+	0.799748i	$0.704966\pi$
$878$	8.99357	−	14.9382i	0.303518	−	0.504141i
$879$	29.8985	+	13.3536i	1.00845	+	0.450406i
$880$	32.8116	−	15.8615i	1.10608	−	0.534692i
$881$		−	7.48812i		−	0.252281i	−0.992012	−	0.126141i	$-0.959741\pi$
$881$		−	7.48812i		−	0.252281i	0.992012	−	0.126141i	$-0.0402590\pi$
$882$	26.1779	−	22.6087i	0.881454	−	0.761276i
$883$	−24.9720	+	14.4176i	−0.840374	+	0.485190i	−0.857391	−	0.514665i	$-0.827916\pi$
$883$	−24.9720	+	14.4176i	−0.840374	+	0.485190i	0.0170172	+	0.999855i	$0.494583\pi$
$884$	1.47033	−	40.0949i	0.0494525	−	1.34854i
$885$	−50.6821	−	22.6362i	−1.70366	−	0.760908i
$886$	4.03210	−	2.23043i	0.135461	−	0.0749326i
$887$	−29.6580			−0.995818			−0.497909	−	0.867229i	$-0.665899\pi$
$887$	−29.6580			−0.995818			−0.497909	+	0.867229i	$0.665899\pi$
$888$	−0.736375	−	15.1500i	−0.0247111	−	0.508401i
$889$	−12.4119	+	21.4981i	−0.416282	+	0.721022i
$890$	53.4439	−	29.5634i	1.79144	−	0.990968i
$891$	−21.8510	−	16.0325i	−0.732037	−	0.537109i
$892$	20.5579	−	10.8848i	0.688329	−	0.364449i
$893$	53.2743	−	8.10984i	1.78276	−	0.271386i
$894$	43.3134	−	3.70022i	1.44862	−	0.123754i
$895$	23.5829	−	13.6156i	0.788291	−	0.455120i
$896$	43.6785	+	5.63454i	1.45920	+	0.188237i
$897$	−33.0697	+	3.43664i	−1.10416	+	0.114746i
$898$	−13.8598	+	23.0210i	−0.462507	+	0.768219i
$899$	−0.555953	−	0.962938i	−0.0185421	−	0.0321158i
$900$	24.5651	−	4.22799i	0.818835	−	0.140933i
$901$	53.7697			1.79133
$902$	−0.853262	−	1.54250i	−0.0284105	−	0.0513598i
$903$	7.46217	+	10.2961i	0.248325	+	0.342633i
$904$	17.9799	−	27.5283i	0.598003	−	0.915579i
$905$	36.1100	+	20.8481i	1.20034	+	0.693016i
$906$	−7.85542	+	0.671081i	−0.260979	+	0.0222952i
$907$		−	36.8507i		−	1.22361i	−0.791010	−	0.611804i	$-0.790444\pi$
$907$		−	36.8507i		−	1.22361i	0.791010	−	0.611804i	$-0.209556\pi$
$908$	−2.68446	+	4.27937i	−0.0890869	+	0.142016i
$909$	15.3141	+	5.01550i	0.507935	+	0.166354i
$910$	−58.5291	+	32.3764i	−1.94022	+	1.07327i
$911$	−5.88938	−	10.2007i	−0.195124	−	0.337965i	0.751817	−	0.659372i	$-0.229178\pi$
$911$	−5.88938	−	10.2007i	−0.195124	−	0.337965i	−0.946941	+	0.321407i	$0.895844\pi$
$912$	−29.7043	+	5.44544i	−0.983609	+	0.180317i
$913$	−5.64316	+	9.77423i	−0.186761	+	0.323480i
$914$	−0.391588	+	21.3639i	−0.0129526	+	0.706654i
$915$	−3.47984	−	33.4854i	−0.115040	−	1.10699i
$916$	−53.7627	−	1.97154i	−1.77637	−	0.0651416i
$917$	−33.5807	−	19.3878i	−1.10893	−	0.640243i
$918$	−26.7378	−	25.1535i	−0.882479	−	0.830190i
$919$			48.5036i			1.59999i	0.600010	+	0.799993i	$0.295163\pi$
$919$			48.5036i			1.59999i	−0.600010	+	0.799993i	$0.704837\pi$
$920$	−18.4756	−	36.4967i	−0.609123	−	1.20326i
$921$	45.3146	+	20.2389i	1.49317	+	0.666896i
$922$	−6.22189	+	10.3345i	−0.204907	+	0.340348i
$923$	−19.5534	+	33.8675i	−0.643608	+	1.11476i
$924$	2.71432	+	40.5155i	0.0892946	+	1.33286i
$925$	−6.43126	+	11.1393i	−0.211458	+	0.366257i
$926$	−6.95341	−	12.5702i	−0.228503	−	0.413082i
$927$	−23.1407	−	7.57879i	−0.760040	−	0.248920i
$928$	−2.44681	−	0.224848i	−0.0803205	−	0.00738100i
$929$		−	16.0980i		−	0.528159i	−0.964501	−	0.264079i	$-0.914932\pi$
$929$		−	16.0980i		−	0.528159i	0.964501	−	0.264079i	$-0.0850681\pi$
$930$	−17.1778	−	8.05292i	−0.563281	−	0.264066i
$931$	35.1326	−	5.34817i	1.15142	−	0.175279i
$932$	0.408010	−	11.1262i	0.0133648	−	0.364450i
$933$	−1.30886	+	2.93052i	−0.0428503	+	0.0959410i
$934$	7.32400	+	4.40942i	0.239649	+	0.144281i
$935$	22.7575	+	39.4172i	0.744251	+	1.28908i
$936$	5.16337	+	33.6813i	0.168770	+	1.10091i
$937$	−2.32881	−	4.03361i	−0.0760788	−	0.131772i	0.825476	−	0.564437i	$-0.190907\pi$
$937$	−2.32881	−	4.03361i	−0.0760788	−	0.131772i	−0.901555	+	0.432665i	$0.857573\pi$
$938$	1.30123	−	70.9911i	0.0424866	−	2.31794i
$939$	3.16152	−	7.07859i	0.103172	−	0.231001i
$940$	66.1146	−	35.0056i	2.15642	−	1.14176i
$941$		−	46.0236i		−	1.50033i	−0.661253	−	0.750163i	$-0.729975\pi$
$941$		−	46.0236i		−	1.50033i	0.661253	−	0.750163i	$-0.270025\pi$
$942$	0.522755	+	6.11917i	0.0170323	+	0.199373i
$943$	−1.71353	+	0.989308i	−0.0558003	+	0.0322163i
$944$	42.2540	+	3.10318i	1.37525	+	0.101000i
$945$	−12.9340	+	59.8164i	−0.420744	+	1.94583i
$946$	−8.03040	−	0.147193i	−0.261091	−	0.00478565i
$947$	−14.3278			−0.465591			−0.232796	−	0.972526i	$-0.574787\pi$
$947$	−14.3278			−0.465591			−0.232796	+	0.972526i	$0.574787\pi$
$948$	−38.7686	+	25.9855i	−1.25915	+	0.843968i
$949$	1.19700	−	2.07327i	0.0388564	−	0.0673013i
$950$	23.6779	+	9.75667i	0.768213	+	0.316548i
$951$	−42.5709	−	19.0135i	−1.38046	−	0.616555i
$952$	−3.02260	+	54.9187i	−0.0979629	+	1.77993i
$953$	−26.2384	−	15.1488i	−0.849946	−	0.490717i	0.0106866	−	0.999943i	$-0.496598\pi$
$953$	−26.2384	−	15.1488i	−0.849946	−	0.490717i	−0.860633	+	0.509226i	$0.829932\pi$
$954$	−44.8543	+	8.56925i	−1.45221	+	0.277440i
$955$	37.4734	+	21.6353i	1.21261	+	0.700101i
$956$	−0.558831	−	0.0204930i	−0.0180739	−	0.000662791i
$957$	−0.234175	−	2.25339i	−0.00756979	−	0.0728416i
$958$	−13.5312	+	7.48499i	−0.437172	+	0.241829i
$959$	69.7447			2.25217
$960$	−36.4412	+	20.7288i	−1.17613	+	0.669018i
$961$	−12.2236	−	21.1718i	−0.394308	−	0.682962i
$962$	−15.0639	−	9.06926i	−0.485681	−	0.292405i
$963$	18.3037	−	3.84582i	0.589828	−	0.123930i
$964$	29.5403	+	1.08328i	0.951429	+	0.0348900i
$965$	11.9082	+	6.87522i	0.383340	+	0.221321i
$966$	45.4129	−	3.87958i	1.46114	−	0.124823i
$967$	42.7138	−	24.6608i	1.37358	−	0.793038i	0.382206	−	0.924077i	$-0.375165\pi$
$967$	42.7138	−	24.6608i	1.37358	−	0.793038i	0.991377	+	0.131039i	$0.0418313\pi$
$968$	4.57511	+	2.98820i	0.147050	+	0.0960442i
$969$	−9.49968	−	36.4998i	−0.305174	−	1.17254i
$970$	12.2780	+	0.225048i	0.394222	+	0.00722586i
$971$	14.3746	−	24.8975i	0.461303	−	0.798999i	−0.537724	−	0.843121i	$-0.680716\pi$
$971$	14.3746	−	24.8975i	0.461303	−	0.798999i	0.999026	+	0.0441217i	$0.0140489\pi$
$972$	26.3132	+	16.7217i	0.843997	+	0.536349i
$973$	29.2016	+	50.5786i	0.936160	+	1.62148i
$974$	−22.8127	+	37.8916i	−0.730965	+	1.21412i
$975$	11.7838	−	26.3837i	0.377384	−	0.844956i
$976$	11.1838	+	23.1351i	0.357984	+	0.740536i
$977$	−7.76297	−	4.48195i	−0.248359	−	0.143390i	0.370653	−	0.928771i	$-0.379134\pi$
$977$	−7.76297	−	4.48195i	−0.248359	−	0.143390i	−0.619013	+	0.785381i	$0.712467\pi$
$978$	19.4758	−	41.5441i	0.622768	−	1.32843i
$979$	−37.2242	−	21.4914i	−1.18969	−	0.686869i
$980$	43.6004	−	23.0851i	1.39276	−	0.737425i
$981$	−16.5062	+	50.3992i	−0.527003	+	1.60912i
$982$	0.185582	−	10.1248i	0.00592216	−	0.323095i
$983$	−26.2824			−0.838278			−0.419139	−	0.907922i	$-0.637668\pi$
$983$	−26.2824			−0.838278			−0.419139	+	0.907922i	$0.637668\pi$
$984$	1.09798	+	1.70486i	0.0350022	+	0.0543489i
$985$	29.2881	+	50.7284i	0.933196	+	1.61634i
$986$	0.0562378	−	3.06817i	0.00179098	−	0.0977103i
$987$	8.61577	+	82.9068i	0.274243	+	2.63895i
$988$	−13.9285	+	32.1184i	−0.443126	+	1.02182i
$989$			9.01518i			0.286666i
$990$	−25.2661	−	29.2547i	−0.803009	−	0.929776i
$991$	17.2201	+	9.94205i	0.547016	+	0.315820i	0.747918	−	0.663792i	$-0.231054\pi$
$991$	17.2201	+	9.94205i	0.547016	+	0.315820i	−0.200902	+	0.979611i	$0.564387\pi$
$992$	14.4200	+	1.32511i	0.457835	+	0.0420724i
$993$	40.1924	−	29.1297i	1.27547	−	0.924402i
$994$	27.6515	−	45.9288i	0.877052	−	1.45677i
$995$	−9.61103	+	16.6468i	−0.304690	+	0.527739i
$996$	5.72556	−	11.6527i	0.181421	−	0.369230i
$997$	20.1965	−	34.9813i	0.639629	−	1.10787i	−0.345886	−	0.938277i	$-0.612421\pi$
$997$	20.1965	−	34.9813i	0.639629	−	1.10787i	0.985514	−	0.169593i	$-0.0542452\pi$
$998$	48.0605	+	0.880921i	1.52133	+	0.0278851i
$999$	−15.3180	+	4.91772i	−0.484639	+	0.155590i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.bi.a.239.97	yes	232
4.3	odd	2	inner	684.2.bi.a.239.20	yes	232
9.2	odd	6		684.2.o.a.11.59	yes	232
19.7	even	3		684.2.o.a.311.19	yes	232
36.11	even	6		684.2.o.a.11.19	✓	232
76.7	odd	6		684.2.o.a.311.59	yes	232
171.83	odd	6	inner	684.2.bi.a.83.20	yes	232
684.83	even	6	inner	684.2.bi.a.83.97	yes	232

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.o.a.11.19	✓	232	36.11	even	6
684.2.o.a.11.59	yes	232	9.2	odd	6
684.2.o.a.311.19	yes	232	19.7	even	3
684.2.o.a.311.59	yes	232	76.7	odd	6
684.2.bi.a.83.20	yes	232	171.83	odd	6	inner
684.2.bi.a.83.97	yes	232	684.83	even	6	inner
684.2.bi.a.239.20	yes	232	4.3	odd	2	inner
684.2.bi.a.239.97	yes	232	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21158 + 0.729433i) q^{2} +(1.72277 - 0.179033i) q^{3} +(0.935855 + 1.76753i) q^{4} +(2.62026 - 1.51281i) q^{5} +(2.21787 + 1.03974i) q^{6} +(-3.37115 + 1.94633i) q^{7} +(-0.155435 + 2.82415i) q^{8} +(2.93589 - 0.616865i) q^{9} +(4.27815 + 0.0784162i) q^{10} +(-1.50566 - 2.60787i) q^{11} +(1.92871 + 2.87751i) q^{12} +4.01575 q^{13} +(-5.50413 - 0.100888i) q^{14} +(4.24328 - 3.07534i) q^{15} +(-2.24835 + 3.30831i) q^{16} +(-4.32629 - 2.49779i) q^{17} +(4.00703 + 1.39416i) q^{18} +(2.72273 + 3.40393i) q^{19} +(5.12613 + 3.21563i) q^{20} +(-5.45926 + 3.95663i) q^{21} +(0.0780453 - 4.25792i) q^{22} -4.78008 q^{23} +(0.237837 + 4.89320i) q^{24} +(2.07719 - 3.59779i) q^{25} +(4.86540 + 2.92922i) q^{26} +(4.94744 - 1.58834i) q^{27} +(-6.59511 - 4.13713i) q^{28} +(0.376168 + 0.217181i) q^{29} +(7.38433 - 0.630836i) q^{30} +(-2.21690 - 1.27993i) q^{31} +(-5.13725 + 2.36826i) q^{32} +(-3.06080 - 4.22321i) q^{33} +(-3.41968 - 6.18201i) q^{34} +(-5.88886 + 10.1998i) q^{35} +(3.83790 + 4.61200i) q^{36} -3.09614 q^{37} +(0.815870 + 6.11018i) q^{38} +(6.91822 - 0.718950i) q^{39} +(3.86513 + 7.63517i) q^{40} +(0.358473 - 0.206965i) q^{41} +(-9.50043 + 0.811613i) q^{42} -1.88599i q^{43} +(3.20043 - 5.10189i) q^{44} +(6.75962 - 6.05780i) q^{45} +(-5.79146 - 3.48675i) q^{46} +(6.18138 - 10.7065i) q^{47} +(-3.28111 + 6.10200i) q^{48} +(4.07641 - 7.06056i) q^{49} +(5.14103 - 2.84385i) q^{50} +(-7.90041 - 3.52857i) q^{51} +(3.75815 + 7.09797i) q^{52} +(-9.32144 + 5.38174i) q^{53} +(7.15281 + 1.68443i) q^{54} +(-7.89043 - 4.55554i) q^{55} +(-4.97275 - 9.82316i) q^{56} +(5.30006 + 5.37674i) q^{57} +(0.297339 + 0.537522i) q^{58} +(-5.29597 - 9.17289i) q^{59} +(9.40686 + 4.62207i) q^{60} +(3.21206 - 5.56345i) q^{61} +(-1.75233 - 3.16782i) q^{62} +(-8.69670 + 7.79377i) q^{63} +(-7.95168 - 0.877943i) q^{64} +(10.5223 - 6.07506i) q^{65} +(-0.627853 - 7.34941i) q^{66} +12.8978i q^{67} +(0.366141 - 9.98443i) q^{68} +(-8.23500 + 0.855791i) q^{69} +(-14.5749 + 8.06235i) q^{70} +(-4.86918 + 8.43367i) q^{71} +(1.28578 + 8.38730i) q^{72} +(0.298078 - 0.516286i) q^{73} +(-3.75122 - 2.25842i) q^{74} +(2.93440 - 6.57007i) q^{75} +(-3.46848 + 7.99810i) q^{76} +(10.1516 + 5.86101i) q^{77} +(8.90641 + 4.17531i) q^{78} +13.4730i q^{79} +(-0.886433 + 12.0700i) q^{80} +(8.23895 - 3.62210i) q^{81} +(0.585286 + 0.0107280i) q^{82} +(-1.87399 - 3.24584i) q^{83} +(-12.1026 - 5.94660i) q^{84} -15.1147 q^{85} +(1.37570 - 2.28503i) q^{86} +(0.686935 + 0.306807i) q^{87} +(7.59906 - 3.84685i) q^{88} +(12.3615 - 7.13690i) q^{89} +(12.6086 - 2.40882i) q^{90} +(-13.5377 + 7.81597i) q^{91} +(-4.47346 - 8.44896i) q^{92} +(-4.04837 - 1.80813i) q^{93} +(15.2989 - 8.46284i) q^{94} +(12.2838 + 4.80022i) q^{95} +(-8.42632 + 4.99971i) q^{96} +2.86992 q^{97} +(10.0891 - 5.58096i) q^{98} +(-6.02915 - 6.72765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 232 q - 2 q^{4} - 6 q^{5} - 9 q^{6} - 6 q^{9} + 2 q^{10} - q^{12} - 4 q^{13} - 3 q^{14} - 2 q^{16} + 12 q^{17} - 16 q^{18} - 27 q^{20} + 4 q^{21} - 3 q^{22} - 13 q^{24} + 102 q^{25} - 6 q^{28} - 6 q^{29}+ \cdots + 162 q^{98}+O(q^{100}) \) 232 * q - 2 * q^4 - 6 * q^5 - 9 * q^6 - 6 * q^9 + 2 * q^10 - q^12 - 4 * q^13 - 3 * q^14 - 2 * q^16 + 12 * q^17 - 16 * q^18 - 27 * q^20 + 4 * q^21 - 3 * q^22 - 13 * q^24 + 102 * q^25 - 6 * q^28 - 6 * q^29 - 9 * q^30 - 24 * q^33 - q^34 - 35 * q^36 - 16 * q^37 + 21 * q^38 + 8 * q^40 + 24 * q^41 + 32 * q^42 - 21 * q^44 + 2 * q^45 - 24 * q^46 - 5 * q^48 + 88 * q^49 + 9 * q^50 - 34 * q^52 - 22 * q^54 - 48 * q^56 - 6 * q^57 + 2 * q^58 - 5 * q^60 + 2 * q^61 - 6 * q^62 + 16 * q^64 + 12 * q^65 + 15 * q^66 - 18 * q^68 - 14 * q^69 - 30 * q^70 - 51 * q^72 + 2 * q^73 - 3 * q^76 - 12 * q^77 + 8 * q^78 - 54 * q^80 + 34 * q^81 + 2 * q^82 - 10 * q^84 - 44 * q^85 - 18 * q^88 + 59 * q^90 - 14 * q^93 - 6 * q^94 - 17 * q^96 + 8 * q^97 + 162 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more