LMFDB - Embedded newform 672.2.bs.a.155.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(155,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4, 0]))

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

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

chi := DirichletCharacter("672.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bs (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			155.4
Character	$\chi$	$=$	672.155
Dual form			672.2.bs.a.659.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34893 + 0.424720i) q^{2} +(-1.25748 + 1.19111i) q^{3} +(1.63923 - 1.14583i) q^{4} +(0.367345 - 0.886850i) q^{5} +(1.19037 - 2.14080i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.72454 + 2.24186i) q^{8} +(0.162531 - 2.99559i) q^{9} +O(q^{10})$	\(q+(-1.34893 + 0.424720i) q^{2} +(-1.25748 + 1.19111i) q^{3} +(1.63923 - 1.14583i) q^{4} +(0.367345 - 0.886850i) q^{5} +(1.19037 - 2.14080i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.72454 + 2.24186i) q^{8} +(0.162531 - 2.99559i) q^{9} +(-0.118861 + 1.35232i) q^{10} +(-0.503326 + 1.21514i) q^{11} +(-0.696489 + 3.39336i) q^{12} +(1.94342 - 0.804990i) q^{13} +(0.653516 - 1.25416i) q^{14} +(0.594402 + 1.55275i) q^{15} +(1.37413 - 3.75656i) q^{16} -3.93266 q^{17} +(1.05305 + 4.10988i) q^{18} +(0.282340 + 0.681629i) q^{19} +(-0.414022 - 1.87467i) q^{20} +(0.0469359 - 1.73141i) q^{21} +(0.162859 - 1.85291i) q^{22} +(-4.90159 + 4.90159i) q^{23} +(-0.501712 - 4.87322i) q^{24} +(2.88397 + 2.88397i) q^{25} +(-2.27964 + 1.91128i) q^{26} +(3.36369 + 3.96050i) q^{27} +(-0.348880 + 1.96934i) q^{28} +(-2.94719 + 1.22076i) q^{29} +(-1.46129 - 1.84209i) q^{30} +1.69494i q^{31} +(-0.258112 + 5.65096i) q^{32} +(-0.814432 - 2.12753i) q^{33} +(5.30489 - 1.67028i) q^{34} +(0.367345 + 0.886850i) q^{35} +(-3.16603 - 5.09669i) q^{36} +(-3.49732 - 1.44864i) q^{37} +(-0.670358 - 0.799555i) q^{38} +(-1.48499 + 3.32708i) q^{39} +(1.35469 + 2.35295i) q^{40} +(0.0865589 + 0.0865589i) q^{41} +(0.672053 + 2.35549i) q^{42} +(-4.71747 - 1.95404i) q^{43} +(0.567280 + 2.56861i) q^{44} +(-2.59694 - 1.24456i) q^{45} +(4.53010 - 8.69371i) q^{46} +1.96116i q^{47} +(2.74653 + 6.36055i) q^{48} -1.00000i q^{49} +(-5.11516 - 2.66540i) q^{50} +(4.94526 - 4.68422i) q^{51} +(2.26332 - 3.54640i) q^{52} +(-9.67856 - 4.00899i) q^{53} +(-6.21949 - 3.91382i) q^{54} +(0.892749 + 0.892749i) q^{55} +(-0.365800 - 2.80467i) q^{56} +(-1.16693 - 0.520841i) q^{57} +(3.45707 - 2.89845i) q^{58} +(-6.76379 - 2.80165i) q^{59} +(2.75355 + 1.86422i) q^{60} +(-3.36669 - 8.12790i) q^{61} +(-0.719873 - 2.28635i) q^{62} +(2.00328 + 2.23313i) q^{63} +(-2.05190 - 7.73238i) q^{64} -2.01923i q^{65} +(2.00221 + 2.52398i) q^{66} +(-13.5875 + 5.62812i) q^{67} +(-6.44652 + 4.50618i) q^{68} +(0.325355 - 12.0020i) q^{69} +(-0.872186 - 1.04028i) q^{70} +(-0.898304 - 0.898304i) q^{71} +(6.43542 + 5.53040i) q^{72} +(-11.9662 + 11.9662i) q^{73} +(5.33291 + 0.468731i) q^{74} +(-7.06167 - 0.191431i) q^{75} +(1.24385 + 0.793829i) q^{76} +(-0.503326 - 1.21514i) q^{77} +(0.590069 - 5.11870i) q^{78} -0.676091 q^{79} +(-2.82673 - 2.59860i) q^{80} +(-8.94717 - 0.973754i) q^{81} +(-0.153525 - 0.0799986i) q^{82} +(11.5153 - 4.76979i) q^{83} +(-1.90698 - 2.89196i) q^{84} +(-1.44465 + 3.48768i) q^{85} +(7.19346 + 0.632261i) q^{86} +(2.25198 - 5.04550i) q^{87} +(-1.85616 - 3.22394i) q^{88} +(-2.45196 + 2.45196i) q^{89} +(4.03168 + 0.575852i) q^{90} +(-0.804990 + 1.94342i) q^{91} +(-2.41840 + 13.6512i) q^{92} +(-2.01885 - 2.13135i) q^{93} +(-0.832944 - 2.64547i) q^{94} +0.708220 q^{95} +(-6.40633 - 7.41343i) q^{96} +14.4188 q^{97} +(0.424720 + 1.34893i) q^{98} +(3.55825 + 1.70526i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 16 q^{4}+O(q^{10}) $ 192 * q - 16 * q^4	$ 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) $ 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.34893	+	0.424720i	−0.953838	+	0.300322i
$2$	−1.34893	+	0.424720i	−0.953838	+	0.300322i
$3$	−1.25748	+	1.19111i	−0.726009	+	0.687686i
$3$	−1.25748	+	1.19111i	−0.726009	+	0.687686i
$4$	1.63923	−	1.14583i	0.819613	−	0.572917i
$5$	0.367345	−	0.886850i	0.164282	−	0.396612i	−0.820205	−	0.572070i	$-0.806141\pi$
$5$	0.367345	−	0.886850i	0.164282	−	0.396612i	0.984487	+	0.175458i	$0.0561407\pi$
$6$	1.19037	−	2.14080i	0.485967	−	0.873977i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−1.72454	+	2.24186i	−0.609718	+	0.792618i
$9$	0.162531	−	2.99559i	0.0541770	−	0.998531i
$10$	−0.118861	+	1.35232i	−0.0375870	+	0.427641i
$11$	−0.503326	+	1.21514i	−0.151758	+	0.366377i	−0.981415	−	0.191897i	$-0.938536\pi$
$11$	−0.503326	+	1.21514i	−0.151758	+	0.366377i	0.829657	+	0.558274i	$0.188536\pi$
$12$	−0.696489	+	3.39336i	−0.201059	+	0.979579i
$13$	1.94342	−	0.804990i	0.539007	−	0.223264i	−0.0965359	−	0.995330i	$-0.530776\pi$
$13$	1.94342	−	0.804990i	0.539007	−	0.223264i	0.635543	+	0.772065i	$0.280776\pi$
$14$	0.653516	−	1.25416i	0.174659	−	0.335188i
$15$	0.594402	+	1.55275i	0.153474	+	0.400918i
$16$	1.37413	−	3.75656i	0.343531	−	0.939141i
$17$	−3.93266			−0.953811			−0.476905	−	0.878955i	$-0.658242\pi$
$17$	−3.93266			−0.953811			−0.476905	+	0.878955i	$0.658242\pi$
$18$	1.05305	+	4.10988i	0.248205	+	0.968708i
$19$	0.282340	+	0.681629i	0.0647733	+	0.156376i	0.952952	−	0.303122i	$-0.0980291\pi$
$19$	0.282340	+	0.681629i	0.0647733	+	0.156376i	−0.888178	+	0.459499i	$0.848029\pi$
$20$	−0.414022	−	1.87467i	−0.0925781	−	0.419188i
$21$	0.0469359	−	1.73141i	0.0102423	−	0.377826i
$22$	0.162859	−	1.85291i	0.0347217	−	0.395041i
$23$	−4.90159	+	4.90159i	−1.02205	+	1.02205i	−0.0223015	+	0.999751i	$0.507099\pi$
$23$	−4.90159	+	4.90159i	−1.02205	+	1.02205i	−0.999751	+	0.0223015i	$0.992901\pi$
$24$	−0.501712	−	4.87322i	−0.102412	−	0.994742i
$25$	2.88397	+	2.88397i	0.576795	+	0.576795i
$26$	−2.27964	+	1.91128i	−0.447074	+	0.374834i
$27$	3.36369	+	3.96050i	0.647343	+	0.762199i
$28$	−0.348880	+	1.96934i	−0.0659322	+	0.372169i
$29$	−2.94719	+	1.22076i	−0.547279	+	0.226690i	−0.639152	−	0.769080i	$-0.720715\pi$
$29$	−2.94719	+	1.22076i	−0.547279	+	0.226690i	0.0918732	+	0.995771i	$0.470715\pi$
$30$	−1.46129	−	1.84209i	−0.266794	−	0.336319i
$31$			1.69494i			0.304419i	0.988348	+	0.152210i	$0.0486389\pi$
$31$			1.69494i			0.304419i	−0.988348	+	0.152210i	$0.951361\pi$
$32$	−0.258112	+	5.65096i	−0.0456282	+	0.998958i
$33$	−0.814432	−	2.12753i	−0.141774	−	0.370355i
$34$	5.30489	−	1.67028i	0.909781	−	0.286450i
$35$	0.367345	+	0.886850i	0.0620927	+	0.149905i
$36$	−3.16603	−	5.09669i	−0.527672	−	0.849448i
$37$	−3.49732	−	1.44864i	−0.574957	−	0.238155i	0.0762073	−	0.997092i	$-0.475719\pi$
$37$	−3.49732	−	1.44864i	−0.574957	−	0.238155i	−0.651164	+	0.758937i	$0.725719\pi$
$38$	−0.670358	−	0.799555i	−0.108747	−	0.129705i
$39$	−1.48499	+	3.32708i	−0.237788	+	0.532759i
$40$	1.35469	+	2.35295i	0.214196	+	0.372034i
$41$	0.0865589	+	0.0865589i	0.0135182	+	0.0135182i	0.713834	−	0.700315i	$-0.246957\pi$
$41$	0.0865589	+	0.0865589i	0.0135182	+	0.0135182i	−0.700315	+	0.713834i	$0.746957\pi$
$42$	0.672053	+	2.35549i	0.103700	+	0.363460i
$43$	−4.71747	−	1.95404i	−0.719408	−	0.297988i	−0.00721650	−	0.999974i	$-0.502297\pi$
$43$	−4.71747	−	1.95404i	−0.719408	−	0.297988i	−0.712191	+	0.701986i	$0.752297\pi$
$44$	0.567280	+	2.56861i	0.0855207	+	0.387232i
$45$	−2.59694	−	1.24456i	−0.387129	−	0.185528i
$46$	4.53010	−	8.69371i	0.667927	−	1.28182i
$47$			1.96116i			0.286065i	0.989718	+	0.143032i	$0.0456853\pi$
$47$			1.96116i			0.286065i	−0.989718	+	0.143032i	$0.954315\pi$
$48$	2.74653	+	6.36055i	0.396427	+	0.918066i
$49$		−	1.00000i		−	0.142857i
$50$	−5.11516	−	2.66540i	−0.723393	−	0.376944i
$51$	4.94526	−	4.68422i	0.692475	−	0.655922i
$52$	2.26332	−	3.54640i	0.313865	−	0.491797i
$53$	−9.67856	−	4.00899i	−1.32945	−	0.550677i	−0.398953	−	0.916971i	$-0.630626\pi$
$53$	−9.67856	−	4.00899i	−1.32945	−	0.550677i	−0.930499	+	0.366294i	$0.880626\pi$
$54$	−6.21949	−	3.91382i	−0.846365	−	0.532603i
$55$	0.892749	+	0.892749i	0.120378	+	0.120378i
$56$	−0.365800	−	2.80467i	−0.0488821	−	0.374790i
$57$	−1.16693	−	0.520841i	−0.154564	−	0.0689870i
$58$	3.45707	−	2.89845i	0.453935	−	0.380586i
$59$	−6.76379	−	2.80165i	−0.880571	−	0.364744i	−0.103853	−	0.994593i	$-0.533117\pi$
$59$	−6.76379	−	2.80165i	−0.880571	−	0.364744i	−0.776718	+	0.629848i	$0.783117\pi$
$60$	2.75355	+	1.86422i	0.355482	+	0.240669i
$61$	−3.36669	−	8.12790i	−0.431060	−	1.04067i	−0.978946	−	0.204118i	$-0.934567\pi$
$61$	−3.36669	−	8.12790i	−0.431060	−	1.04067i	0.547886	−	0.836553i	$-0.315433\pi$
$62$	−0.719873	−	2.28635i	−0.0914239	−	0.290367i
$63$	2.00328	+	2.23313i	0.252389	+	0.281348i
$64$	−2.05190	−	7.73238i	−0.256488	−	0.966548i
$65$		−	2.01923i		−	0.250455i
$66$	2.00221	+	2.52398i	0.246456	+	0.310681i
$67$	−13.5875	+	5.62812i	−1.65997	+	0.687584i	−0.998076	−	0.0620097i	$-0.980249\pi$
$67$	−13.5875	+	5.62812i	−1.65997	+	0.687584i	−0.661898	+	0.749593i	$0.730249\pi$
$68$	−6.44652	+	4.50618i	−0.781756	+	0.546455i
$69$	0.325355	−	12.0020i	0.0391681	−	1.44487i
$70$	−0.872186	−	1.04028i	−0.104246	−	0.124337i
$71$	−0.898304	−	0.898304i	−0.106609	−	0.106609i	0.651790	−	0.758399i	$-0.274018\pi$
$71$	−0.898304	−	0.898304i	−0.106609	−	0.106609i	−0.758399	+	0.651790i	$0.774018\pi$
$72$	6.43542	+	5.53040i	0.758422	+	0.651764i
$73$	−11.9662	+	11.9662i	−1.40054	+	1.40054i	−0.602169	+	0.798369i	$0.705697\pi$
$73$	−11.9662	+	11.9662i	−1.40054	+	1.40054i	−0.798369	+	0.602169i	$0.794303\pi$
$74$	5.33291	+	0.468731i	0.619939	+	0.0544888i
$75$	−7.06167	−	0.191431i	−0.815411	−	0.0221045i
$76$	1.24385	+	0.793829i	0.142680	+	0.0910585i
$77$	−0.503326	−	1.21514i	−0.0573593	−	0.138478i
$78$	0.590069	−	5.11870i	0.0668121	−	0.579579i
$79$	−0.676091			−0.0760662			−0.0380331	−	0.999276i	$-0.512109\pi$
$79$	−0.676091			−0.0760662			−0.0380331	+	0.999276i	$0.512109\pi$
$80$	−2.82673	−	2.59860i	−0.316038	−	0.290532i
$81$	−8.94717	−	0.973754i	−0.994130	−	0.108195i
$82$	−0.153525	−	0.0799986i	−0.0169540	−	0.00883437i
$83$	11.5153	−	4.76979i	1.26397	−	0.523552i	0.352842	−	0.935683i	$-0.385215\pi$
$83$	11.5153	−	4.76979i	1.26397	−	0.523552i	0.911125	+	0.412131i	$0.135215\pi$
$84$	−1.90698	−	2.89196i	−0.208068	−	0.315539i
$85$	−1.44465	+	3.48768i	−0.156694	+	0.378292i
$86$	7.19346	+	0.632261i	0.775691	+	0.0681785i
$87$	2.25198	−	5.04550i	0.241437	−	0.540935i
$88$	−1.85616	−	3.22394i	−0.197867	−	0.343673i
$89$	−2.45196	+	2.45196i	−0.259908	+	0.259908i	−0.825016	−	0.565109i	$-0.808834\pi$
$89$	−2.45196	+	2.45196i	−0.259908	+	0.259908i	0.565109	+	0.825016i	$0.308834\pi$
$90$	4.03168	+	0.575852i	0.424976	+	0.0607001i
$91$	−0.804990	+	1.94342i	−0.0843859	+	0.203726i
$92$	−2.41840	+	13.6512i	−0.252136	+	1.42324i
$93$	−2.01885	−	2.13135i	−0.209345	−	0.221011i
$94$	−0.832944	−	2.64547i	−0.0859116	−	0.272859i
$95$	0.708220			0.0726618
$96$	−6.40633	−	7.41343i	−0.653843	−	0.756630i
$97$	14.4188			1.46400			0.732001	−	0.681303i	$-0.238587\pi$
$97$	14.4188			1.46400			0.732001	+	0.681303i	$0.238587\pi$
$98$	0.424720	+	1.34893i	0.0429032	+	0.136263i
$99$	3.55825	+	1.70526i	0.357617	+	0.171385i
$100$	8.03204	+	1.42293i	0.803204	+	0.142293i
$101$	3.29807	−	7.96226i	0.328171	−	0.792274i	−0.670558	−	0.741857i	$-0.733945\pi$
$101$	3.29807	−	7.96226i	0.328171	−	0.792274i	0.998728	−	0.0504166i	$-0.0160549\pi$
$102$	−4.68133	+	8.41903i	−0.463521	+	0.833608i
$103$	−1.70454	+	1.70454i	−0.167953	+	0.167953i	−0.786079	−	0.618126i	$-0.787892\pi$
$103$	−1.70454	+	1.70454i	−0.167953	+	0.167953i	0.618126	+	0.786079i	$0.287892\pi$
$104$	−1.54683	+	5.74512i	−0.151679	+	0.563355i
$105$	−1.51826	−	0.677652i	−0.148167	−	0.0661321i
$106$	14.7584	+	1.29717i	1.43346	+	0.125993i
$107$	−1.30940	+	3.16117i	−0.126584	+	0.305602i	−0.974448	−	0.224612i	$-0.927888\pi$
$107$	−1.30940	+	3.16117i	−0.126584	+	0.305602i	0.847864	+	0.530214i	$0.177888\pi$
$108$	10.0519	+	2.63793i	0.967248	+	0.253835i
$109$	−12.3669	+	5.12255i	−1.18454	+	0.490651i	−0.885972	−	0.463738i	$-0.846508\pi$
$109$	−12.3669	+	5.12255i	−1.18454	+	0.490651i	−0.298565	+	0.954389i	$0.596508\pi$
$110$	−1.58342	−	0.825088i	−0.150974	−	0.0786691i
$111$	6.12331	−	2.34405i	0.581199	−	0.222487i
$112$	1.68464	+	3.62795i	0.159183	+	0.342809i
$113$	0.966234			0.0908957			0.0454478	−	0.998967i	$-0.485529\pi$
$113$	0.966234			0.0908957			0.0454478	+	0.998967i	$0.485529\pi$
$114$	1.79532	+	0.206959i	0.168147	+	0.0193835i
$115$	2.54640	+	6.14756i	0.237453	+	0.573263i
$116$	−3.43231	+	5.37810i	−0.318682	+	0.499344i
$117$	−2.09556	−	5.95253i	−0.193734	−	0.550311i
$118$	10.3138	+	0.906520i	0.949462	+	0.0834520i
$119$	2.78081	−	2.78081i	0.254917	−	0.254917i
$120$	−4.50612	−	1.34521i	−0.411351	−	0.122801i
$121$	6.55496	+	6.55496i	0.595905	+	0.595905i
$122$	7.99350	+	9.53407i	0.723698	+	0.863174i
$123$	−0.211947	−	0.00574555i	−0.0191106	−	0.000518059i
$124$	1.94212	+	2.77838i	0.174407	+	0.249506i
$125$	8.05132	−	3.33497i	0.720132	−	0.298288i
$126$	−3.65074	−	2.16151i	−0.325234	−	0.192562i
$127$			8.53243i			0.757131i	0.925575	+	0.378565i	$0.123582\pi$
$127$			8.53243i			0.757131i	−0.925575	+	0.378565i	$0.876418\pi$
$128$	6.05197	+	9.55896i	0.534923	+	0.844901i
$129$	8.25961	−	3.16184i	0.727219	−	0.278384i
$130$	0.857607	+	2.72380i	0.0752171	+	0.238893i
$131$	4.06563	+	9.81531i	0.355216	+	0.857567i	0.995959	+	0.0898117i	$0.0286265\pi$
$131$	4.06563	+	9.81531i	0.355216	+	0.857567i	−0.640743	+	0.767756i	$0.721373\pi$
$132$	−3.77283	−	2.55429i	−0.328383	−	0.222323i
$133$	−0.681629	−	0.282340i	−0.0591047	−	0.0244820i
$134$	15.9382	−	13.3628i	1.37685	−	1.15437i
$135$	4.74801	−	1.52822i	0.408644	−	0.131528i
$136$	6.78205	−	8.81649i	0.581556	−	0.756008i
$137$	2.00725	+	2.00725i	0.171491	+	0.171491i	0.787634	−	0.616143i	$-0.211306\pi$
$137$	2.00725	+	2.00725i	0.171491	+	0.171491i	−0.616143	+	0.787634i	$0.711306\pi$
$138$	4.65860	+	16.3280i	0.396567	+	1.38993i
$139$	−6.43171	−	2.66410i	−0.545531	−	0.225966i	0.0928592	−	0.995679i	$-0.470399\pi$
$139$	−6.43171	−	2.66410i	−0.545531	−	0.225966i	−0.638390	+	0.769713i	$0.720399\pi$
$140$	1.61835	+	1.03283i	0.136775	+	0.0872902i
$141$	−2.33595	−	2.46613i	−0.196723	−	0.207685i
$142$	1.59328	+	0.830222i	0.133705	+	0.0696707i
$143$			2.76669i			0.231362i
$144$	−11.0298	−	4.72688i	−0.919150	−	0.393907i
$145$			3.06216i			0.254298i
$146$	11.0593	−	21.2238i	0.915273	−	1.75650i
$147$	1.19111	+	1.25748i	0.0982408	+	0.103716i
$148$	−7.39281	+	1.63271i	−0.607685	+	0.134208i
$149$	−2.05528	−	0.851323i	−0.168375	−	0.0697431i	0.296904	−	0.954907i	$-0.404046\pi$
$149$	−2.05528	−	0.851323i	−0.168375	−	0.0697431i	−0.465279	+	0.885164i	$0.654046\pi$
$150$	9.60700	−	2.74100i	0.784408	−	0.223802i
$151$	3.13563	+	3.13563i	0.255174	+	0.255174i	0.823088	−	0.567914i	$-0.192249\pi$
$151$	3.13563	+	3.13563i	0.255174	+	0.255174i	−0.567914	+	0.823088i	$0.692249\pi$
$152$	−2.01503	−	0.542531i	−0.163440	−	0.0440051i
$153$	−0.639179	+	11.7807i	−0.0516746	+	0.952410i
$154$	1.19504	+	1.42536i	0.0962993	+	0.114859i
$155$	1.50315	+	0.622627i	0.120736	+	0.0500106i
$156$	1.37805	+	7.15539i	0.110332	+	0.572889i
$157$	−0.148972	−	0.359650i	−0.0118893	−	0.0287032i	0.917823	−	0.396989i	$-0.129945\pi$
$157$	−0.148972	−	0.359650i	−0.0118893	−	0.0287032i	−0.929713	+	0.368286i	$0.879945\pi$
$158$	0.912000	−	0.287149i	0.0725548	−	0.0228444i
$159$	16.9458	−	6.48695i	1.34389	−	0.514449i
$160$	4.91674	+	2.30476i	0.388703	+	0.182207i
$161$		−	6.93190i		−	0.546310i
$162$	12.4827	−	2.48651i	0.980732	−	0.195359i
$163$	−6.23212	+	2.58143i	−0.488137	+	0.202193i	−0.613157	−	0.789961i	$-0.710101\pi$
$163$	−6.23212	+	2.58143i	−0.488137	+	0.202193i	0.125020	+	0.992154i	$0.460101\pi$
$164$	0.241072	+	0.0427074i	0.0188245	+	0.00333489i
$165$	−2.18598	−	0.0592583i	−0.170178	−	0.00461325i
$166$	−13.5075	+	11.3249i	−1.04838	+	0.878981i
$167$	8.19217	+	8.19217i	0.633929	+	0.633929i	0.949051	−	0.315122i	$-0.102046\pi$
$167$	8.19217	+	8.19217i	0.633929	+	0.633929i	−0.315122	+	0.949051i	$0.602046\pi$
$168$	3.80065	+	3.09112i	0.293227	+	0.238485i
$169$	−6.06352	+	6.06352i	−0.466425	+	0.466425i
$170$	0.467438	−	5.31821i	0.0358509	−	0.407888i
$171$	2.08777	−	0.734990i	0.159656	−	0.0562061i
$172$	−9.97201	+	2.20233i	−0.760359	+	0.167926i
$173$	8.49759	+	20.5150i	0.646060	+	1.55973i	0.818375	+	0.574685i	$0.194875\pi$
$173$	8.49759	+	20.5150i	0.646060	+	1.55973i	−0.172315	+	0.985042i	$0.555125\pi$
$174$	−0.894837	+	7.76249i	−0.0678374	+	0.588473i
$175$	−4.07855			−0.308310
$176$	3.87310	+	3.56052i	0.291946	+	0.268385i
$177$	11.8424	−	4.53336i	0.890131	−	0.340748i
$178$	2.26613	−	4.34893i	0.169854	−	0.325966i
$179$	8.62800	−	3.57383i	0.644887	−	0.267121i	−0.0361766	−	0.999345i	$-0.511518\pi$
$179$	8.62800	−	3.57383i	0.644887	−	0.267121i	0.681063	+	0.732225i	$0.261518\pi$
$180$	−5.68303	+	0.935550i	−0.423588	+	0.0697318i
$181$	6.97586	−	16.8412i	0.518511	−	1.25180i	−0.420306	−	0.907382i	$-0.638077\pi$
$181$	6.97586	−	16.8412i	0.518511	−	1.25180i	0.938818	−	0.344415i	$-0.111923\pi$
$182$	0.260468	−	2.96343i	0.0193071	−	0.219664i
$183$	13.9147	+	6.21062i	1.02861	+	0.459102i
$184$	−2.53569	−	19.4417i	−0.186934	−	1.43326i
$185$	−2.56945	+	2.56945i	−0.188910	+	0.188910i
$186$	3.62851	+	2.01760i	0.266056	+	0.147938i
$187$	1.97941	−	4.77872i	0.144749	−	0.349454i
$188$	2.24717	+	3.21479i	0.163891	+	0.234462i
$189$	−5.17899	−	0.422009i	−0.376716	−	0.0306967i
$190$	−0.955339	+	0.300795i	−0.0693076	+	0.0218220i
$191$	−22.1565			−1.60319			−0.801596	−	0.597866i	$-0.796015\pi$
$191$	−22.1565			−1.60319			−0.801596	+	0.597866i	$0.796015\pi$
$192$	11.7903	+	7.27931i	0.850893	+	0.525339i
$193$	−8.41352			−0.605618			−0.302809	−	0.953051i	$-0.597924\pi$
$193$	−8.41352			−0.605618			−0.302809	+	0.953051i	$0.597924\pi$
$194$	−19.4499	+	6.12393i	−1.39642	+	0.439672i
$195$	2.40512	+	2.53915i	0.172234	+	0.181832i
$196$	−1.14583	−	1.63923i	−0.0818453	−	0.117088i
$197$	6.93604	−	16.7451i	0.494172	−	1.19304i	−0.458406	−	0.888743i	$-0.651579\pi$
$197$	6.93604	−	16.7451i	0.494172	−	1.19304i	0.952578	−	0.304294i	$-0.0984207\pi$
$198$	−5.52408	−	0.789014i	−0.392579	−	0.0560728i
$199$	5.46269	−	5.46269i	0.387240	−	0.387240i	−0.486462	−	0.873702i	$-0.661713\pi$
$199$	5.46269	−	5.46269i	0.387240	−	0.387240i	0.873702	+	0.486462i	$0.161713\pi$
$200$	−11.4390	+	1.49194i	−0.808860	+	0.105496i
$201$	10.3823	−	23.2614i	0.732314	−	1.64073i
$202$	−1.06715	+	12.1413i	−0.0750841	+	0.854258i
$203$	1.22076	−	2.94719i	0.0856809	−	0.206852i
$204$	2.73906	−	13.3449i	0.191772	−	0.934333i
$205$	0.108562	−	0.0449678i	0.00758228	−	0.00314069i
$206$	1.57535	−	3.02326i	0.109760	−	0.210640i
$207$	13.8865	+	15.4798i	0.965180	+	1.07592i
$208$	−0.353497	−	8.40673i	−0.0245106	−	0.582902i
$209$	−0.970381			−0.0671226
$210$	2.33585	+	0.269269i	0.161189	+	0.0185813i
$211$	7.58390	+	18.3092i	0.522097	+	1.26045i	0.936598	+	0.350406i	$0.113956\pi$
$211$	7.58390	+	18.3092i	0.522097	+	1.26045i	−0.414501	+	0.910049i	$0.636044\pi$
$212$	−20.4590	+	4.51839i	−1.40513	+	0.310324i
$213$	2.19958	+	0.0596271i	0.150713	+	0.00408558i
$214$	0.423677	−	4.82033i	0.0289620	−	0.329511i
$215$	−3.46588	+	3.46588i	−0.236371	+	0.236371i
$216$	−14.6797	+	0.710876i	−0.998830	+	0.0483690i
$217$	−1.19850	−	1.19850i	−0.0813595	−	0.0813595i
$218$	14.5065	−	12.1624i	0.982503	−	0.823745i
$219$	0.794285	−	29.3003i	0.0536728	−	1.97993i
$220$	2.48636	+	0.440475i	0.167630	+	0.0296968i
$221$	−7.64280	+	3.16575i	−0.514111	+	0.212952i
$222$	−7.26436	+	5.76265i	−0.487552	+	0.386763i
$223$		−	26.5051i		−	1.77491i	−0.460894	−	0.887455i	$-0.652471\pi$
$223$		−	26.5051i		−	1.77491i	0.460894	−	0.887455i	$-0.347529\pi$
$224$	−3.81332	−	4.17835i	−0.254788	−	0.279178i
$225$	9.10795	−	8.17048i	0.607196	−	0.544698i
$226$	−1.30338	+	0.410379i	−0.0866997	+	0.0272980i
$227$	−4.48143	−	10.8191i	−0.297443	−	0.718091i	−0.999979	−	0.00644297i	$-0.997949\pi$
$227$	−4.48143	−	10.8191i	−0.297443	−	0.718091i	0.702536	−	0.711648i	$-0.252051\pi$
$228$	−2.50966	+	0.483334i	−0.166206	+	0.0320096i
$229$	8.50863	+	3.52439i	0.562266	+	0.232898i	0.645669	−	0.763618i	$-0.276579\pi$
$229$	8.50863	+	3.52439i	0.562266	+	0.232898i	−0.0834026	+	0.996516i	$0.526579\pi$
$230$	−6.04591	−	7.21112i	−0.398655	−	0.475487i
$231$	2.08028	+	0.928499i	0.136872	+	0.0610907i
$232$	2.34576	−	8.71245i	0.154007	−	0.572000i
$233$	14.1416	+	14.1416i	0.926445	+	0.926445i	0.997474	−	0.0710297i	$-0.0226285\pi$
$233$	14.1416	+	14.1416i	0.926445	+	0.926445i	−0.0710297	+	0.997474i	$0.522628\pi$
$234$	5.35492	+	7.13952i	0.350062	+	0.466725i
$235$	1.73926	+	0.720423i	0.113457	+	0.0469952i
$236$	−14.2976	+	3.15764i	−0.930696	+	0.205545i
$237$	0.850174	−	0.805297i	0.0552247	−	0.0523096i
$238$	−2.57006	+	4.93219i	−0.166592	+	0.319706i
$239$			4.13989i			0.267787i	0.990996	+	0.133894i	$0.0427481\pi$
$239$			4.13989i			0.267787i	−0.990996	+	0.133894i	$0.957252\pi$
$240$	6.64978	−	0.0992407i	0.429241	−	0.00640596i
$241$			23.4740i			1.51209i	0.654519	+	0.756046i	$0.272871\pi$
$241$			23.4740i			1.51209i	−0.654519	+	0.756046i	$0.727129\pi$
$242$	−11.6262	−	6.05816i	−0.747361	−	0.389433i
$243$	12.4108	−	9.43255i	0.796151	−	0.605098i
$244$	−14.8320	−	9.46580i	−0.949521	−	0.605986i
$245$	−0.886850	−	0.367345i	−0.0566588	−	0.0234688i
$246$	0.288342	−	0.0822678i	0.0183840	−	0.00524521i
$247$	1.09741	+	1.09741i	0.0698265	+	0.0698265i
$248$	−3.79981	−	2.92299i	−0.241288	−	0.185610i
$249$	−8.79896	+	19.7139i	−0.557611	+	1.24931i
$250$	−9.44424	+	7.91819i	−0.597306	+	0.500790i
$251$	−22.4828	−	9.31269i	−1.41910	−	0.587812i	−0.464468	−	0.885590i	$-0.653754\pi$
$251$	−22.4828	−	9.31269i	−1.41910	−	0.587812i	−0.954635	+	0.297778i	$0.903754\pi$
$252$	5.84263	+	1.36518i	0.368051	+	0.0859984i
$253$	−3.48900	−	8.42319i	−0.219352	−	0.529562i
$254$	−3.62389	−	11.5097i	−0.227383	−	0.722180i
$255$	−2.33758	−	6.10643i	−0.146385	−	0.382400i
$256$	−12.2236	−	10.3240i	−0.763972	−	0.645249i
$257$			8.78630i			0.548074i	0.961719	+	0.274037i	$0.0883591\pi$
$257$			8.78630i			0.548074i	−0.961719	+	0.274037i	$0.911641\pi$
$258$	−9.79875	+	7.77312i	−0.610044	+	0.483933i
$259$	3.49732	−	1.44864i	0.217313	−	0.0900141i
$260$	−2.31370	−	3.30998i	−0.143490	−	0.205276i
$261$	3.17791	+	9.02699i	0.196707	+	0.558756i
$262$	−9.65301	−	11.5134i	−0.596365	−	0.711301i
$263$	10.7405	+	10.7405i	0.662286	+	0.662286i	0.955918	−	0.293633i	$-0.0948642\pi$
$263$	10.7405	+	10.7405i	0.662286	+	0.662286i	−0.293633	+	0.955918i	$0.594864\pi$
$264$	6.17415	+	1.84317i	0.379993	+	0.113439i
$265$	−7.11075	+	7.11075i	−0.436810	+	0.436810i
$266$	1.03939	+	0.0913557i	0.0637288	+	0.00560138i
$267$	0.162755	−	6.00386i	0.00996044	−	0.367430i
$268$	−15.8241	+	24.7948i	−0.966608	+	1.51458i
$269$	6.22175	+	15.0206i	0.379347	+	0.915824i	0.992088	+	0.125541i	$0.0400666\pi$
$269$	6.22175	+	15.0206i	0.379347	+	0.915824i	−0.612742	+	0.790283i	$0.709933\pi$
$270$	−5.75567	+	4.07803i	−0.350279	+	0.248181i
$271$	21.9807			1.33523			0.667616	−	0.744506i	$-0.267315\pi$
$271$	21.9807			1.33523			0.667616	+	0.744506i	$0.267315\pi$
$272$	−5.40397	+	14.7733i	−0.327664	+	0.895763i
$273$	−1.30256	−	3.40265i	−0.0788342	−	0.205937i
$274$	−3.56015	−	1.85512i	−0.215077	−	0.112072i
$275$	−4.95599	+	2.05284i	−0.298858	+	0.123791i
$276$	−13.2190	−	20.0468i	−0.795688	−	1.20667i
$277$	8.98036	−	21.6805i	0.539578	−	1.30266i	−0.385441	−	0.922733i	$-0.625951\pi$
$277$	8.98036	−	21.6805i	0.539578	−	1.30266i	0.925018	−	0.379923i	$-0.124049\pi$
$278$	9.80743	+	0.862014i	0.588211	+	0.0517001i
$279$	5.07734	+	0.275480i	0.303972	+	0.0164925i
$280$	−2.62170	−	0.705874i	−0.156677	−	0.0421840i
$281$	−9.67379	+	9.67379i	−0.577090	+	0.577090i	−0.934100	−	0.357010i	$-0.883796\pi$
$281$	−9.67379	+	9.67379i	−0.577090	+	0.577090i	0.357010	+	0.934100i	$0.383796\pi$
$282$	4.19845	+	2.33451i	0.250014	+	0.139018i
$283$	−5.54807	+	13.3942i	−0.329798	+	0.796204i	0.668808	+	0.743435i	$0.266805\pi$
$283$	−5.54807	+	13.3942i	−0.329798	+	0.796204i	−0.998607	+	0.0527690i	$0.983195\pi$
$284$	−2.50183	−	0.443215i	−0.148456	−	0.0263000i
$285$	−0.890575	+	0.843565i	−0.0527531	+	0.0499685i
$286$	−1.17507	−	3.73207i	−0.0694832	−	0.220682i
$287$	−0.122413			−0.00722580
$288$	16.8860	+	1.69166i	0.995019	+	0.0996818i
$289$	−1.53417			−0.0902455
$290$	−1.30056	−	4.13064i	−0.0763714	−	0.242559i
$291$	−18.1313	+	17.1743i	−1.06288	+	1.00677i
$292$	−5.90402	+	33.3266i	−0.345507	+	1.95029i
$293$	3.98412	−	9.61853i	0.232755	−	0.561920i	−0.763745	−	0.645519i	$-0.776641\pi$
$293$	3.98412	−	9.61853i	0.232755	−	0.561920i	0.996500	+	0.0835983i	$0.0266413\pi$
$294$	−2.14080	−	1.19037i	−0.124854	−	0.0694239i
$295$	−4.96930	+	4.96930i	−0.289324	+	0.289324i
$296$	9.27894	−	5.34228i	0.539327	−	0.310514i
$297$	−6.50558	+	2.09392i	−0.377492	+	0.121501i
$298$	3.13400	+	0.275459i	0.181548	+	0.0159569i
$299$	−5.58011	+	13.4716i	−0.322706	+	0.779081i
$300$	−11.7950	+	7.77771i	−0.680986	+	0.449046i
$301$	4.71747	−	1.95404i	0.271911	−	0.112629i
$302$	−5.56152	−	2.89799i	−0.320029	−	0.166760i
$303$	5.33662	+	13.9408i	0.306581	+	0.800876i
$304$	2.94856	−	0.123985i	0.169111	−	0.00711101i
$305$	−8.44497			−0.483557
$306$	−4.14127	−	16.1628i	−0.236741	−	0.923963i
$307$	1.96832	+	4.75195i	0.112338	+	0.271208i	0.970043	−	0.242935i	$-0.0781101\pi$
$307$	1.96832	+	4.75195i	0.112338	+	0.271208i	−0.857705	+	0.514143i	$0.828110\pi$
$308$	−2.21741	−	1.41515i	−0.126349	−	0.0806359i
$309$	0.113143	−	4.17372i	0.00643647	−	0.237435i
$310$	−2.29209	−	0.201461i	−0.130182	−	0.0114422i
$311$	18.1819	−	18.1819i	1.03100	−	1.03100i	0.0314964	−	0.999504i	$-0.489973\pi$
$311$	18.1819	−	18.1819i	1.03100	−	1.03100i	0.999504	−	0.0314964i	$-0.0100273\pi$
$312$	−4.89793	−	9.06683i	−0.277291	−	0.513308i
$313$	−18.8918	−	18.8918i	−1.06783	−	1.06783i	−0.997526	−	0.0703038i	$-0.977603\pi$
$313$	−18.8918	−	18.8918i	−1.06783	−	1.06783i	−0.0703038	−	0.997526i	$-0.522397\pi$
$314$	0.353703	+	0.421872i	0.0199606	+	0.0238076i
$315$	2.71635	−	0.956277i	0.153049	−	0.0538801i
$316$	−1.10827	+	0.774689i	−0.0623449	+	0.0435797i
$317$	26.7386	−	11.0755i	1.50179	−	0.622060i	0.527943	−	0.849280i	$-0.322963\pi$
$317$	26.7386	−	11.0755i	1.50179	−	0.622060i	0.973844	+	0.227219i	$0.0729634\pi$
$318$	−20.1035	+	15.9476i	−1.12735	+	0.894300i
$319$		−	4.19567i		−	0.234913i
$320$	−7.61122	−	1.02073i	−0.425480	−	0.0570603i
$321$	−2.11874	−	5.53476i	−0.118257	−	0.308920i
$322$	2.94411	+	9.35065i	0.164069	+	0.521091i
$323$	−1.11035	−	2.68062i	−0.0617814	−	0.149154i
$324$	−15.7822	+	8.65577i	−0.876788	+	0.480876i
$325$	7.92633	+	3.28319i	0.439674	+	0.182119i
$326$	7.31031	−	6.12907i	0.404881	−	0.339458i
$327$	9.44971	−	21.1719i	0.522570	−	1.17081i
$328$	−0.343328	+	0.0447786i	−0.0189571	+	0.00247249i
$329$	−1.38675	−	1.38675i	−0.0764540	−	0.0764540i
$330$	2.97390	−	0.848492i	0.163708	−	0.0467079i
$331$	2.25712	+	0.934930i	0.124063	+	0.0513884i	0.443851	−	0.896101i	$-0.353612\pi$
$331$	2.25712	+	0.934930i	0.124063	+	0.0513884i	−0.319789	+	0.947489i	$0.603612\pi$
$332$	13.4108	−	21.0134i	0.736011	−	1.15326i
$333$	−4.90796	+	10.2411i	−0.268954	+	0.561210i
$334$	−14.5300	−	7.57129i	−0.795048	−	0.414282i
$335$			14.1175i			0.771322i
$336$	−6.43968	−	2.55550i	−0.351313	−	0.139414i
$337$			18.6460i			1.01571i	0.861442	+	0.507856i	$0.169562\pi$
$337$			18.6460i			1.01571i	−0.861442	+	0.507856i	$0.830438\pi$
$338$	5.60397	−	10.7546i	0.304816	−	0.584972i
$339$	−1.21502	+	1.15089i	−0.0659910	+	0.0625076i
$340$	1.62821	+	7.37243i	0.0883019	+	0.399826i
$341$	−2.05958	−	0.853104i	−0.111532	−	0.0461982i
$342$	−2.50410	+	1.87817i	−0.135406	+	0.101560i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	12.5162	−	7.20610i	0.674827	−	0.388527i
$345$	−10.5245	−	4.69742i	−0.566618	−	0.252901i
$346$	−20.1758	−	24.0642i	−1.08466	−	1.29370i
$347$	−25.0932	−	10.3939i	−1.34707	−	0.557976i	−0.411598	−	0.911366i	$-0.635029\pi$
$347$	−25.0932	−	10.3939i	−1.34707	−	0.557976i	−0.935476	+	0.353389i	$0.885029\pi$
$348$	−2.08981	−	10.8511i	−0.112026	−	0.581681i
$349$	−12.5057	−	30.1915i	−0.669417	−	1.61612i	−0.782588	−	0.622540i	$-0.786101\pi$
$349$	−12.5057	−	30.1915i	−0.669417	−	1.61612i	0.113171	−	0.993576i	$-0.463899\pi$
$350$	5.50168	−	1.73224i	0.294077	−	0.0925922i
$351$	9.72522	+	4.98917i	0.519094	+	0.266302i
$352$	−6.73677	−	3.15791i	−0.359071	−	0.168317i
$353$		−	13.5206i		−	0.719630i	−0.933024	−	0.359815i	$-0.882840\pi$
$353$		−	13.5206i		−	0.719630i	0.933024	−	0.359815i	$-0.117160\pi$
$354$	−14.0492	+	11.1449i	−0.746707	+	0.592345i
$355$	−1.12665	+	0.466673i	−0.0597963	+	0.0247684i
$356$	−1.20978	+	6.82887i	−0.0641181	+	0.361929i
$357$	−0.184583	+	6.80907i	−0.00976917	+	0.360374i
$358$	−10.1207	+	8.48533i	−0.534895	+	0.448464i
$359$	−18.8502	−	18.8502i	−0.994877	−	0.994877i	0.00510992	−	0.999987i	$-0.498373\pi$
$359$	−18.8502	−	18.8502i	−0.994877	−	0.994877i	−0.999987	+	0.00510992i	$0.998373\pi$
$360$	7.26866	−	3.67569i	0.383092	−	0.193726i
$361$	13.0501	−	13.0501i	0.686849	−	0.686849i
$362$	−2.25715	+	25.6804i	−0.118633	+	1.34973i
$363$	−16.0504	−	0.435101i	−0.842428	−	0.0228369i
$364$	0.907275	+	4.10809i	0.0475541	+	0.215322i
$365$	6.21650	+	15.0080i	0.325386	+	0.785552i
$366$	−21.4078	−	2.46783i	−1.11900	−	0.128995i
$367$	−12.3277			−0.643500			−0.321750	−	0.946825i	$-0.604271\pi$
$367$	−12.3277			−0.643500			−0.321750	+	0.946825i	$0.604271\pi$
$368$	11.6777	+	25.1486i	0.608745	+	1.31096i
$369$	0.273364	−	0.245227i	0.0142307	−	0.0127660i
$370$	2.37472	−	4.55731i	0.123456	−	0.236923i
$371$	9.67856	−	4.00899i	0.502486	−	0.208136i
$372$	−5.75153	−	1.18050i	−0.298203	−	0.0612063i
$373$	−0.920752	+	2.22289i	−0.0476747	+	0.115097i	−0.945923	−	0.324392i	$-0.894840\pi$
$373$	−0.920752	+	2.22289i	−0.0476747	+	0.115097i	0.898248	+	0.439489i	$0.144840\pi$
$374$	−0.640470	+	7.28685i	−0.0331179	+	0.376794i
$375$	−6.15210	+	13.7836i	−0.317693	+	0.711784i
$376$	−4.39665	−	3.38211i	−0.226740	−	0.174419i
$377$	−4.74491	+	4.74491i	−0.244375	+	0.244375i
$378$	7.16533	−	1.63036i	0.368545	−	0.0838565i
$379$	−8.14828	+	19.6717i	−0.418549	+	1.01047i	0.564219	+	0.825625i	$0.309177\pi$
$379$	−8.14828	+	19.6717i	−0.418549	+	1.01047i	−0.982768	+	0.184842i	$0.940823\pi$
$380$	1.16093	−	0.811503i	0.0595546	−	0.0416292i
$381$	−10.1630	−	10.7294i	−0.520668	−	0.549683i
$382$	29.8876	−	9.41032i	1.52918	−	0.481474i
$383$	0.949079			0.0484957			0.0242478	−	0.999706i	$-0.492281\pi$
$383$	0.949079			0.0484957			0.0242478	+	0.999706i	$0.492281\pi$
$384$	−18.9960	−	4.81170i	−0.969385	−	0.245546i
$385$	−1.26254			−0.0643449
$386$	11.3493	−	3.57339i	0.577662	−	0.181881i
$387$	−6.62025	+	13.8140i	−0.336526	+	0.702207i
$388$	23.6356	−	16.5215i	1.19992	−	0.838752i
$389$	−2.94637	+	7.11316i	−0.149387	+	0.360651i	−0.980804	−	0.194998i	$-0.937530\pi$
$389$	−2.94637	+	7.11316i	−0.149387	+	0.360651i	0.831417	+	0.555649i	$0.187530\pi$
$390$	−4.32276	−	2.40363i	−0.218892	−	0.121713i
$391$	19.2763	−	19.2763i	0.974845	−	0.974845i
$392$	2.24186	+	1.72454i	0.113231	+	0.0871026i
$393$	−16.8035	−	7.49999i	−0.847627	−	0.378324i
$394$	−2.24427	+	25.5338i	−0.113065	+	1.28638i
$395$	−0.248359	+	0.599592i	−0.0124963	+	0.0301687i
$396$	7.78671	−	1.28186i	0.391297	−	0.0644160i
$397$	4.32229	−	1.79035i	0.216930	−	0.0898552i	−0.271572	−	0.962418i	$-0.587544\pi$
$397$	4.32229	−	1.79035i	0.216930	−	0.0898552i	0.488502	+	0.872563i	$0.337544\pi$
$398$	−5.04868	+	9.68891i	−0.253067	+	0.485661i
$399$	1.19343	−	0.456855i	0.0597465	−	0.0228714i
$400$	14.7968	−	6.87089i	0.739839	−	0.343545i
$401$	36.4445			1.81995			0.909975	−	0.414663i	$-0.136101\pi$
$401$	36.4445			1.81995			0.909975	+	0.414663i	$0.136101\pi$
$402$	−4.12548	+	35.7876i	−0.205760	+	1.78492i
$403$	1.36441	+	3.29397i	0.0679659	+	0.164084i
$404$	−3.71714	−	16.8310i	−0.184935	−	0.837373i
$405$	−4.15028	+	7.57710i	−0.206229	+	0.376509i
$406$	−0.394998	+	4.49403i	−0.0196034	+	0.223035i
$407$	3.52059	−	3.52059i	0.174509	−	0.174509i
$408$	1.97306	+	19.1647i	0.0976812	+	0.948795i
$409$	10.7660	+	10.7660i	0.532346	+	0.532346i	0.921270	−	0.388924i	$-0.127153\pi$
$409$	10.7660	+	10.7660i	0.532346	+	0.532346i	−0.388924	+	0.921270i	$0.627153\pi$
$410$	−0.127344	+	0.106767i	−0.00628905	+	0.00527283i
$411$	−4.91492	−	0.133236i	−0.242435	−	0.00657203i
$412$	−0.841006	+	4.74725i	−0.0414334	+	0.233880i
$413$	6.76379	−	2.80165i	0.332824	−	0.137860i
$414$	−25.3065	−	14.9834i	−1.24375	−	0.736391i
$415$		−	11.9645i		−	0.587314i
$416$	4.04735	+	11.1900i	0.198438	+	0.548633i
$417$	11.2610	−	4.31079i	0.551454	−	0.211100i
$418$	1.30898	−	0.412140i	0.0640241	−	0.0201584i
$419$	−10.2380	−	24.7167i	−0.500158	−	1.20749i	−0.949397	−	0.314077i	$-0.898305\pi$
$419$	−10.2380	−	24.7167i	−0.500158	−	1.20749i	0.449239	−	0.893412i	$-0.351695\pi$
$420$	−3.26526	+	0.628854i	−0.159328	+	0.0306849i
$421$	25.5449	+	10.5811i	1.24498	+	0.515689i	0.905269	−	0.424839i	$-0.139669\pi$
$421$	25.5449	+	10.5811i	1.24498	+	0.515689i	0.339715	+	0.940528i	$0.389669\pi$
$422$	−18.0064	−	21.4767i	−0.876539	−	1.04547i
$423$	5.87484	+	0.318749i	0.285644	+	0.0154981i
$424$	25.6787	−	14.7843i	1.24707	−	0.717990i
$425$	−11.3417	−	11.3417i	−0.550153	−	0.550153i
$426$	−2.99240	+	0.853772i	−0.144982	+	0.0413654i
$427$	8.12790	+	3.36669i	0.393337	+	0.162925i
$428$	1.47578	+	6.68223i	0.0713344	+	0.322998i
$429$	−3.29542	−	3.47906i	−0.159104	−	0.167971i
$430$	3.20321	−	6.14727i	0.154472	−	0.296447i
$431$			12.4387i			0.599149i	0.954073	+	0.299575i	$0.0968448\pi$
$431$			12.4387i			0.599149i	−0.954073	+	0.299575i	$0.903155\pi$
$432$	19.5000	−	7.19370i	0.938195	−	0.346107i
$433$			15.7318i			0.756024i	0.925801	+	0.378012i	$0.123392\pi$
$433$			15.7318i			0.756024i	−0.925801	+	0.378012i	$0.876608\pi$
$434$	2.12572	+	1.10767i	0.102038	+	0.0531697i
$435$	−3.64735	−	3.85061i	−0.174877	−	0.184623i
$436$	−14.4026	+	22.5675i	−0.689759	+	1.08079i
$437$	−4.72498	−	1.95715i	−0.226027	−	0.0936233i
$438$	11.3730	+	39.8614i	0.543422	+	1.90465i
$439$	−12.3332	−	12.3332i	−0.588629	−	0.588629i	0.348631	−	0.937260i	$-0.386647\pi$
$439$	−12.3332	−	12.3332i	−0.588629	−	0.588629i	−0.937260	+	0.348631i	$0.886647\pi$
$440$	−3.54100	+	0.461837i	−0.168811	+	0.0220172i
$441$	−2.99559	−	0.162531i	−0.142647	−	0.00773957i
$442$	8.96505	−	7.51643i	0.426424	−	0.357520i
$443$	−28.0084	−	11.6015i	−1.33072	−	0.551202i	−0.399859	−	0.916576i	$-0.630941\pi$
$443$	−28.0084	−	11.6015i	−1.33072	−	0.551202i	−0.930861	+	0.365374i	$0.880941\pi$
$444$	7.35161	−	10.8587i	0.348892	−	0.515332i
$445$	1.27381	+	3.07524i	0.0603843	+	0.145781i
$446$	11.2572	+	35.7535i	0.533045	+	1.69298i
$447$	3.59849	−	1.37753i	0.170203	−	0.0651548i
$448$	6.91853	+	4.01671i	0.326870	+	0.189772i
$449$		−	21.5459i		−	1.01682i	−0.861116	−	0.508408i	$-0.830234\pi$
$449$		−	21.5459i		−	1.01682i	0.861116	−	0.508408i	$-0.169766\pi$
$450$	−8.81582	+	14.8897i	−0.415582	+	0.701909i
$451$	−0.148748	+	0.0616135i	−0.00700427	+	0.00290126i
$452$	1.58388	−	1.10714i	0.0744993	−	0.0520757i
$453$	−7.67788	−	0.208135i	−0.360738	−	0.00977904i
$454$	10.6402	+	12.6909i	0.499371	+	0.595614i
$455$	1.42781	+	1.42781i	0.0669368	+	0.0669368i
$456$	3.18008	−	1.71789i	0.148921	−	0.0804474i
$457$	−15.6557	+	15.6557i	−0.732343	+	0.732343i	−0.971083	−	0.238741i	$-0.923265\pi$
$457$	−15.6557	+	15.6557i	−0.732343	+	0.732343i	0.238741	+	0.971083i	$0.423265\pi$
$458$	−12.9744	−	1.14037i	−0.606255	−	0.0532861i
$459$	−13.2283	−	15.5753i	−0.617442	−	0.726994i
$460$	11.2182	+	7.15948i	0.523052	+	0.333813i
$461$	10.8831	+	26.2740i	0.506874	+	1.22370i	0.945674	+	0.325118i	$0.105404\pi$
$461$	10.8831	+	26.2740i	0.506874	+	1.22370i	−0.438799	+	0.898585i	$0.644596\pi$
$462$	−3.20050	−	0.368944i	−0.148901	−	0.0171648i
$463$	−34.8535			−1.61978			−0.809889	−	0.586583i	$-0.800473\pi$
$463$	−34.8535			−1.61978			−0.809889	+	0.586583i	$0.800473\pi$
$464$	0.536078	+	12.7488i	0.0248868	+	0.591847i
$465$	−2.63181	+	1.00747i	−0.122047	+	0.0467205i
$466$	−25.0822	−	13.0698i	−1.16191	−	0.605446i
$467$	14.5891	−	6.04300i	0.675102	−	0.279636i	−0.0186756	−	0.999826i	$-0.505945\pi$
$467$	14.5891	−	6.04300i	0.675102	−	0.279636i	0.693778	+	0.720189i	$0.255945\pi$
$468$	−10.2557	−	7.35637i	−0.474070	−	0.340049i
$469$	5.62812	−	13.5875i	0.259882	−	0.627411i
$470$	−2.65211	−	0.233105i	−0.122333	−	0.0107523i
$471$	0.615712	+	0.274813i	0.0283705	+	0.0126627i
$472$	17.9454	−	10.3319i	0.826003	−	0.475565i
$473$	4.74885	−	4.74885i	0.218352	−	0.218352i
$474$	−0.804800	+	1.44737i	−0.0369657	+	0.0664801i
$475$	−1.15154	+	2.78006i	−0.0528362	+	0.127558i
$476$	1.37203	−	7.74473i	0.0628868	−	0.354979i
$477$	−13.5824	+	28.3414i	−0.621894	+	1.29767i
$478$	−1.75829	−	5.58443i	−0.0804225	−	0.255426i
$479$	−8.38541			−0.383139			−0.191570	−	0.981479i	$-0.561358\pi$
$479$	−8.38541			−0.383139			−0.191570	+	0.981479i	$0.561358\pi$
$480$	−8.92794	+	2.95816i	−0.407503	+	0.135021i
$481$	−7.96290			−0.363077
$482$	−9.96986	−	31.6648i	−0.454115	−	1.44229i
$483$	8.25663	+	8.71675i	0.375690	+	0.396626i
$484$	18.2560	+	3.23416i	0.829816	+	0.147007i
$485$	5.29666	−	12.7873i	0.240509	−	0.580640i
$486$	−12.7351	+	17.9949i	−0.577674	+	0.816267i
$487$	16.3184	−	16.3184i	0.739457	−	0.739457i	−0.233016	−	0.972473i	$-0.574859\pi$
$487$	16.3184	−	16.3184i	0.739457	−	0.739457i	0.972473	+	0.233016i	$0.0748594\pi$
$488$	24.0276	+	6.46927i	1.08768	+	0.292850i
$489$	4.76203	−	10.6692i	0.215347	−	0.482479i
$490$	1.35232	+	0.118861i	0.0610915	+	0.00536957i
$491$	−8.96385	+	21.6406i	−0.404533	+	0.976629i	0.582018	+	0.813176i	$0.302263\pi$
$491$	−8.96385	+	21.6406i	−0.404533	+	0.976629i	−0.986551	+	0.163453i	$0.947737\pi$
$492$	−0.354013	+	0.233438i	−0.0159601	+	0.0105242i
$493$	11.5903	−	4.80085i	0.522000	−	0.216220i
$494$	−1.94642	−	1.01424i	−0.0875736	−	0.0456327i
$495$	2.81941	−	2.52921i	0.126723	−	0.113680i
$496$	6.36714	+	2.32905i	0.285893	+	0.104578i
$497$	1.27039			0.0569849
$498$	3.49632	−	30.3297i	0.156674	−	1.35911i
$499$	−1.22162	−	2.94926i	−0.0546874	−	0.132027i	0.894174	−	0.447719i	$-0.147763\pi$
$499$	−1.22162	−	2.94926i	−0.0546874	−	0.132027i	−0.948862	+	0.315692i	$0.897763\pi$
$500$	9.37661	−	14.6922i	0.419335	−	0.657057i
$501$	−20.0593	−	0.543775i	−0.896182	−	0.0242941i
$502$	34.2830	+	3.01327i	1.53013	+	0.134489i
$503$	7.76279	−	7.76279i	0.346126	−	0.346126i	−0.512538	−	0.858664i	$-0.671295\pi$
$503$	7.76279	−	7.76279i	0.346126	−	0.346126i	0.858664	+	0.512538i	$0.171295\pi$
$504$	−8.46112	+	0.639943i	−0.376888	+	0.0285053i
$505$	−5.84980	−	5.84980i	−0.260313	−	0.260313i
$506$	8.28392	+	9.88046i	0.368265	+	0.439240i
$507$	0.402481	−	14.8471i	0.0178748	−	0.659382i
$508$	9.77676	+	13.9866i	0.433773	+	0.620554i
$509$	−0.446618	+	0.184995i	−0.0197960	+	0.00819976i	−0.392559	−	0.919727i	$-0.628410\pi$
$509$	−0.446618	+	0.184995i	−0.0197960	+	0.00819976i	0.372763	+	0.927926i	$0.378410\pi$
$510$	5.74676	+	7.24433i	0.254471	+	0.320784i
$511$		−	16.9228i		−	0.748619i
$512$	20.8735	+	8.73475i	0.922488	+	0.386025i
$513$	−1.74989	+	3.41100i	−0.0772595	+	0.150599i
$514$	−3.73171	−	11.8521i	−0.164599	−	0.522774i
$515$	0.885517	+	2.13783i	0.0390205	+	0.0942039i
$516$	9.91644	−	14.6471i	0.436547	−	0.644803i
$517$	−2.38307	−	0.987102i	−0.104808	−	0.0434127i
$518$	−4.10238	+	3.43950i	−0.180248	+	0.151123i
$519$	−35.1211	−	15.6757i	−1.54165	−	0.688089i
$520$	4.52684	+	3.48225i	0.198515	+	0.152707i
$521$	11.3163	+	11.3163i	0.495777	+	0.495777i	0.910121	−	0.414343i	$-0.135989\pi$
$521$	11.3163	+	11.3163i	0.495777	+	0.495777i	−0.414343	+	0.910121i	$0.635989\pi$
$522$	−8.12071	−	10.8271i	−0.355434	−	0.473887i
$523$	−9.06106	−	3.75321i	−0.396212	−	0.164117i	0.175676	−	0.984448i	$-0.443789\pi$
$523$	−9.06106	−	3.75321i	−0.396212	−	0.164117i	−0.571888	+	0.820332i	$0.693789\pi$
$524$	17.9112	+	11.4310i	0.782455	+	0.499364i
$525$	5.12872	−	4.85799i	0.223835	−	0.212020i
$526$	−19.0498	−	9.92646i	−0.830612	−	0.432814i
$527$		−	6.66561i		−	0.290358i
$528$	−9.11132	+	0.135977i	−0.396520	+	0.00591762i
$529$		−	25.0512i		−	1.08918i
$530$	6.57183	−	12.6120i	0.285462	−	0.547829i
$531$	−9.49194	+	19.8062i	−0.411915	+	0.859517i
$532$	−1.44086	+	0.318215i	−0.0624692	+	0.0137964i
$533$	0.237899	+	0.0985410i	0.0103046	+	0.00426829i
$534$	2.33041	+	8.16791i	0.100847	+	0.353460i
$535$	2.32248	+	2.32248i	0.100410	+	0.100410i
$536$	10.8147	−	40.1672i	0.467125	−	1.73496i
$537$	−6.59275	+	14.7709i	−0.284498	+	0.637411i
$538$	−14.7723	−	17.6193i	−0.636878	−	0.759621i
$539$	1.21514	+	0.503326i	0.0523396	+	0.0216798i
$540$	6.03198	−	7.94553i	0.259575	−	0.341921i
$541$	16.9071	+	40.8174i	0.726894	+	1.75488i	0.652678	+	0.757635i	$0.273645\pi$
$541$	16.9071	+	40.8174i	0.726894	+	1.75488i	0.0742159	+	0.997242i	$0.476355\pi$
$542$	−29.6504	+	9.33563i	−1.27359	+	0.401000i
$543$	11.2876	+	29.4865i	0.484399	+	1.26539i
$544$	1.01507	−	22.2233i	0.0435207	−	0.952817i
$545$			12.8494i			0.550406i
$546$	3.20223	+	4.03671i	0.137043	+	0.172755i
$547$	15.7491	−	6.52347i	0.673381	−	0.278923i	−0.0196760	−	0.999806i	$-0.506263\pi$
$547$	15.7491	−	6.52347i	0.673381	−	0.278923i	0.693057	+	0.720883i	$0.256263\pi$
$548$	5.59030	+	0.990358i	0.238806	+	0.0423060i
$549$	−24.8951	+	8.76419i	−1.06250	+	0.374046i
$550$	5.81341	−	4.87405i	0.247885	−	0.207830i
$551$	−1.66422	−	1.66422i	−0.0708981	−	0.0708981i
$552$	26.3457	+	21.4274i	1.12135	+	0.912009i
$553$	0.478069	−	0.478069i	0.0203296	−	0.0203296i
$554$	−2.90574	+	33.0596i	−0.123453	+	1.40457i
$555$	0.170554	−	6.29154i	0.00723959	−	0.267061i
$556$	−13.5957	+	3.00261i	−0.576584	+	0.127339i
$557$	−4.79936	−	11.5867i	−0.203355	−	0.490943i	0.788995	−	0.614400i	$-0.210602\pi$
$557$	−4.79936	−	11.5867i	−0.203355	−	0.490943i	−0.992350	+	0.123457i	$0.960602\pi$
$558$	−6.96598	+	1.78484i	−0.294893	+	0.0755585i
$559$	−10.7410			−0.454296
$560$	3.83629	−	0.161313i	0.162113	−	0.00681674i
$561$	3.20288	+	8.36684i	0.135226	+	0.353248i
$562$	8.94062	−	17.1579i	0.377137	−	0.723763i
$563$	14.4187	−	5.97240i	0.607674	−	0.251707i	−0.0575597	−	0.998342i	$-0.518332\pi$
$563$	14.4187	−	5.97240i	0.607674	−	0.251707i	0.665234	+	0.746635i	$0.268332\pi$
$564$	−6.65493	−	1.36593i	−0.280223	−	0.0575159i
$565$	0.354942	−	0.856905i	0.0149325	−	0.0360503i
$566$	1.79517	−	20.4242i	0.0754565	−	0.858495i
$567$	7.01515	−	5.63805i	0.294609	−	0.236776i
$568$	3.56304	−	0.464710i	0.149502	−	0.0194988i
$569$	23.7069	−	23.7069i	0.993844	−	0.993844i	−0.00613683	−	0.999981i	$-0.501953\pi$
$569$	23.7069	−	23.7069i	0.993844	−	0.993844i	0.999981	+	0.00613683i	$0.00195342\pi$
$570$	0.843044	−	1.51615i	0.0353112	−	0.0635047i
$571$	−3.54490	+	8.55816i	−0.148350	+	0.358148i	−0.980533	−	0.196352i	$-0.937090\pi$
$571$	−3.54490	+	8.55816i	−0.148350	+	0.358148i	0.832184	+	0.554500i	$0.187090\pi$
$572$	3.17017	+	4.53523i	0.132551	+	0.189627i
$573$	27.8615	−	26.3908i	1.16393	−	1.10249i
$574$	0.165126	−	0.0519911i	0.00689224	−	0.00217007i
$575$	−28.2721			−1.17903
$576$	−23.4966	+	4.88991i	−0.979024	+	0.203746i
$577$	10.9798			0.457096			0.228548	−	0.973533i	$-0.426602\pi$
$577$	10.9798			0.457096			0.228548	+	0.973533i	$0.426602\pi$
$578$	2.06949	−	0.651594i	0.0860796	−	0.0271027i
$579$	10.5799	−	10.0214i	0.439684	−	0.416475i
$580$	3.50872	+	5.01957i	0.145692	+	0.208426i
$581$	−4.76979	+	11.5153i	−0.197884	+	0.477734i
$582$	17.1637	−	30.8676i	0.711457	−	1.27950i
$583$	9.74293	−	9.74293i	0.403511	−	0.403511i
$584$	−6.19035	−	47.4628i	−0.256159	−	1.96402i
$585$	−6.04879	−	0.328188i	−0.250087	−	0.0135689i
$586$	−1.28913	+	14.6669i	−0.0532534	+	0.605882i
$587$	−8.28183	+	19.9941i	−0.341828	+	0.825245i	0.655703	+	0.755019i	$0.272372\pi$
$587$	−8.28183	+	19.9941i	−0.341828	+	0.825245i	−0.997531	+	0.0702267i	$0.977628\pi$
$588$	3.39336	+	0.696489i	0.139940	+	0.0287227i
$589$	−1.15532	+	0.478548i	−0.0476040	+	0.0197182i
$590$	4.59268	−	8.81379i	0.189077	−	0.362858i
$591$	11.2232	+	29.3182i	0.461661	+	1.20599i
$592$	−10.2477	+	11.1473i	−0.421177	+	0.458152i
$593$	38.7497			1.59126			0.795629	−	0.605784i	$-0.207141\pi$
$593$	38.7497			1.59126			0.795629	+	0.605784i	$0.207141\pi$
$594$	7.88624	−	5.58760i	0.323576	−	0.229262i
$595$	−1.44465	−	3.48768i	−0.0592247	−	0.142981i
$596$	−4.34454	+	0.959496i	−0.177959	+	0.0393025i
$597$	−0.362599	+	13.3759i	−0.0148402	+	0.547439i
$598$	1.80553	−	20.5422i	0.0738338	−	0.840033i
$599$	27.1189	−	27.1189i	1.10805	−	1.10805i	0.114639	−	0.993407i	$-0.463429\pi$
$599$	27.1189	−	27.1189i	1.10805	−	1.10805i	0.993407	−	0.114639i	$-0.0365712\pi$
$600$	12.6073	−	15.5012i	0.514691	−	0.632832i
$601$	11.9206	+	11.9206i	0.486252	+	0.486252i	0.907121	−	0.420870i	$-0.138275\pi$
$601$	11.9206	+	11.9206i	0.486252	+	0.486252i	−0.420870	+	0.907121i	$0.638275\pi$
$602$	−5.53362	+	4.63947i	−0.225534	+	0.189091i
$603$	14.6512	+	41.6173i	0.596642	+	1.69479i
$604$	8.73293	+	1.54709i	0.355338	+	0.0629504i
$605$	8.22120	−	3.40533i	0.334239	−	0.138446i
$606$	−13.1196	−	16.5386i	−0.532949	−	0.671833i
$607$			39.3643i			1.59775i	0.601498	+	0.798874i	$0.294571\pi$
$607$			39.3643i			1.59775i	−0.601498	+	0.798874i	$0.705429\pi$
$608$	−3.92474	+	1.41956i	−0.159169	+	0.0575706i
$609$	1.97532	+	5.16010i	0.0800441	+	0.209098i
$610$	11.3917	−	3.58674i	0.461235	−	0.145223i
$611$	1.57871	+	3.81135i	0.0638679	+	0.154191i
$612$	12.4509	+	20.0436i	0.503299	+	0.810213i
$613$	−29.1071	−	12.0566i	−1.17563	−	0.486960i	−0.292577	−	0.956242i	$-0.594513\pi$
$613$	−29.1071	−	12.0566i	−1.17563	−	0.486960i	−0.883048	+	0.469282i	$0.844513\pi$
$614$	−4.67337	−	5.57406i	−0.188602	−	0.224951i
$615$	−0.0829533	+	0.185855i	−0.00334500	+	0.00749439i
$616$	3.59217	+	0.967167i	0.144733	+	0.0389683i
$617$	18.1496	+	18.1496i	0.730676	+	0.730676i	0.970754	−	0.240078i	$-0.0771729\pi$
$617$	18.1496	+	18.1496i	0.730676	+	0.730676i	−0.240078	+	0.970754i	$0.577173\pi$
$618$	1.62004	+	5.67811i	0.0651676	+	0.228407i
$619$	32.1141	+	13.3021i	1.29078	+	0.534657i	0.919217	−	0.393752i	$-0.128823\pi$
$619$	32.1141	+	13.3021i	1.29078	+	0.534657i	0.371560	+	0.928409i	$0.378823\pi$
$620$	3.17744	−	0.701740i	0.127609	−	0.0281826i
$621$	−35.9002	−	2.92533i	−1.44063	−	0.117389i
$622$	−16.8039	+	32.2483i	−0.673775	+	1.29304i
$623$		−	3.46760i		−	0.138927i
$624$	10.4578	+	10.1503i	0.418648	+	0.406336i
$625$			12.0274i			0.481095i
$626$	33.5075	+	17.4600i	1.33923	+	0.697843i
$627$	1.22024	−	1.15583i	0.0487316	−	0.0461593i
$628$	−0.656299	−	0.418851i	−0.0261892	−	0.0167140i
$629$	13.7538	+	5.69701i	0.548400	+	0.227155i
$630$	−3.25802	+	2.44364i	−0.129802	+	0.0973569i
$631$	1.69754	+	1.69754i	0.0675779	+	0.0675779i	0.740088	−	0.672510i	$-0.234784\pi$
$631$	1.69754	+	1.69754i	0.0675779	+	0.0675779i	−0.672510	+	0.740088i	$0.734784\pi$
$632$	1.16595	−	1.51570i	0.0463790	−	0.0602915i
$633$	−31.3448	−	13.9902i	−1.24584	−	0.556062i
$634$	−31.3645	+	26.2964i	−1.24564	+	1.04436i
$635$	7.56699	+	3.13435i	0.300287	+	0.124383i
$636$	20.3450	−	30.0506i	0.806730	−	1.19158i
$637$	−0.804990	−	1.94342i	−0.0318949	−	0.0770010i
$638$	1.78198	+	5.65967i	0.0705495	+	0.224068i
$639$	−2.83696	+	2.54495i	−0.112228	+	0.100677i
$640$	10.7005	−	1.85575i	0.422976	−	0.0733549i
$641$			11.8928i			0.469738i	0.972027	+	0.234869i	$0.0754661\pi$
$641$			11.8928i			0.469738i	−0.972027	+	0.234869i	$0.924534\pi$
$642$	5.20875	+	6.56613i	0.205573	+	0.259144i
$643$	8.69799	−	3.60282i	0.343015	−	0.142081i	−0.204524	−	0.978862i	$-0.565565\pi$
$643$	8.69799	−	3.60282i	0.343015	−	0.142081i	0.547539	+	0.836780i	$0.315565\pi$
$644$	−7.94281	−	11.3630i	−0.312991	−	0.447763i
$645$	0.230056	−	8.48653i	0.00905846	−	0.334157i
$646$	2.63629	+	3.14438i	0.103724	+	0.123714i
$647$	−4.94634	−	4.94634i	−0.194461	−	0.194461i	0.603160	−	0.797620i	$-0.293908\pi$
$647$	−4.94634	−	4.94634i	−0.194461	−	0.194461i	−0.797620	+	0.603160i	$0.793908\pi$
$648$	17.6128	−	18.3790i	0.691896	−	0.721997i
$649$	6.80878	−	6.80878i	0.267268	−	0.267268i
$650$	−12.0865	−	1.06233i	−0.474072	−	0.0416680i
$651$	2.93464	+	0.0795533i	0.115017	+	0.00311794i
$652$	−7.25796	+	11.3725i	−0.284244	+	0.445382i
$653$	18.3503	+	44.3016i	0.718104	+	1.73366i	0.678680	+	0.734434i	$0.262552\pi$
$653$	18.3503	+	44.3016i	0.718104	+	1.73366i	0.0394239	+	0.999223i	$0.487448\pi$
$654$	−3.75490	+	32.5728i	−0.146828	+	1.27370i
$655$	10.1982			0.398477
$656$	0.444107	−	0.206221i	0.0173395	−	0.00805159i
$657$	33.9010	+	37.7908i	1.32260	+	1.47436i
$658$	2.45961	+	1.28165i	0.0958855	+	0.0499639i
$659$	−29.1523	+	12.0753i	−1.13561	+	0.470386i	−0.869685	−	0.493608i	$-0.835678\pi$
$659$	−29.1523	+	12.0753i	−1.13561	+	0.470386i	−0.265927	+	0.963993i	$0.585678\pi$
$660$	−3.65121	+	2.40763i	−0.142123	+	0.0937169i
$661$	−4.45284	+	10.7501i	−0.173195	+	0.418131i	−0.986512	−	0.163691i	$-0.947660\pi$
$661$	−4.45284	+	10.7501i	−0.173195	+	0.418131i	0.813316	+	0.581822i	$0.197660\pi$
$662$	−3.44178	−	0.302512i	−0.133769	−	0.0117575i
$663$	5.83995	−	13.0843i	0.226805	−	0.508151i
$664$	−9.16540	+	34.0414i	−0.355686	+	1.32106i
$665$	−0.500787	+	0.500787i	−0.0194197	+	0.0194197i
$666$	2.27089	−	15.8991i	0.0879952	−	0.616076i
$667$	8.46222	−	20.4296i	0.327658	−	0.791037i
$668$	22.8157	+	4.04195i	0.882765	+	0.156388i
$669$	31.5703	+	33.3297i	1.22058	+	1.28860i
$670$	−5.99599	−	19.0435i	−0.231645	−	0.735717i
$671$	11.5710			0.446695
$672$	9.77205	+	0.712132i	0.376965	+	0.0274711i
$673$	−36.3995			−1.40310			−0.701549	−	0.712621i	$-0.747508\pi$
$673$	−36.3995			−1.40310			−0.701549	+	0.712621i	$0.747508\pi$
$674$	−7.91932	−	25.1521i	−0.305041	−	0.968824i
$675$	−1.72119	+	21.1228i	−0.0662486	+	0.813016i
$676$	−2.99169	+	16.8873i	−0.115065	+	0.649511i
$677$	1.83397	−	4.42759i	0.0704850	−	0.170166i	−0.884711	−	0.466140i	$-0.845644\pi$
$677$	1.83397	−	4.42759i	0.0704850	−	0.170166i	0.955196	+	0.295974i	$0.0956442\pi$
$678$	1.15018	−	2.06851i	0.0441723	−	0.0794407i
$679$	−10.1956	+	10.1956i	−0.391271	+	0.391271i
$680$	−5.32755	−	9.25336i	−0.204302	−	0.354850i
$681$	18.5221	+	8.26702i	0.709767	+	0.316793i
$682$	3.14056	+	0.276036i	0.120258	+	0.0105700i
$683$	17.8974	−	43.2081i	0.684824	−	1.65331i	−0.0701335	−	0.997538i	$-0.522343\pi$
$683$	17.8974	−	43.2081i	0.684824	−	1.65331i	0.754958	−	0.655774i	$-0.227657\pi$
$684$	2.58016	−	3.59706i	0.0986547	−	0.137537i
$685$	2.51748	−	1.04277i	0.0961880	−	0.0398424i
$686$	−1.25416	−	0.653516i	−0.0478841	−	0.0249513i
$687$	−14.8974	+	5.70282i	−0.568371	+	0.217576i
$688$	−13.8229	+	15.0364i	−0.526992	+	0.573257i
$689$	−22.0367			−0.839531
$690$	16.1918	+	1.86655i	0.616413	+	0.0710582i
$691$	−0.444253	−	1.07252i	−0.0169002	−	0.0408006i	0.915204	−	0.402990i	$-0.132029\pi$
$691$	−0.444253	−	1.07252i	−0.0169002	−	0.0408006i	−0.932104	+	0.362190i	$0.882029\pi$
$692$	37.4363	+	23.8919i	1.42311	+	0.908233i
$693$	−3.72186	+	1.31026i	−0.141382	+	0.0497727i
$694$	38.2635	+	3.36313i	1.45246	+	0.127663i
$695$	−4.72532	+	4.72532i	−0.179242	+	0.179242i
$696$	7.42770	+	13.7498i	0.281546	+	0.521186i
$697$	−0.340407	−	0.340407i	−0.0128938	−	0.0128938i
$698$	29.6923	+	35.4148i	1.12387	+	1.34047i
$699$	−34.6269	−	0.938680i	−1.30971	−	0.0355041i
$700$	−6.68567	+	4.67335i	−0.252695	+	0.176636i
$701$	−12.2317	+	5.06654i	−0.461986	+	0.191361i	−0.601522	−	0.798856i	$-0.705439\pi$
$701$	−12.2317	+	5.06654i	−0.461986	+	0.191361i	0.139536	+	0.990217i	$0.455439\pi$
$702$	−15.2376	−	2.59955i	−0.575108	−	0.0981138i
$703$		−	2.79289i		−	0.105336i
$704$	10.4287	+	1.39857i	0.393045	+	0.0527105i
$705$	−3.04519	+	1.16572i	−0.114688	+	0.0439035i
$706$	5.74247	+	18.2384i	0.216121	+	0.686410i
$707$	3.29807	+	7.96226i	0.124037	+	0.299451i
$708$	14.2179	−	21.0007i	0.534343	−	0.789253i
$709$	−25.8835	−	10.7213i	−0.972076	−	0.402647i	−0.160592	−	0.987021i	$-0.551340\pi$
$709$	−25.8835	−	10.7213i	−0.972076	−	0.402647i	−0.811485	+	0.584374i	$0.801340\pi$
$710$	1.32157	−	1.10802i	0.0495975	−	0.0415832i
$711$	−0.109886	+	2.02530i	−0.00412104	+	0.0759545i
$712$	−1.26845	−	9.72549i	−0.0475372	−	0.364478i
$713$	−8.30788	−	8.30788i	−0.311133	−	0.311133i
$714$	−2.64296	−	9.26335i	−0.0989101	−	0.346672i
$715$	2.45364	+	1.01633i	0.0917609	+	0.0380086i
$716$	10.0482	−	15.7446i	0.375519	−	0.588402i
$717$	−4.93105	−	5.20585i	−0.184154	−	0.194416i
$718$	33.4337	+	17.4216i	1.24773	+	0.650168i
$719$		−	25.8040i		−	0.962326i	−0.876631	−	0.481163i	$-0.840215\pi$
$719$		−	25.8040i		−	0.962326i	0.876631	−	0.481163i	$-0.159785\pi$
$720$	−8.24378	+	8.04539i	−0.307228	+	0.299834i
$721$		−	2.41058i		−	0.0897748i
$722$	−12.0611	+	23.1464i	−0.448866	+	0.861418i
$723$	−27.9600	−	29.5181i	−1.03984	−	1.09779i
$724$	−7.86223	−	35.5997i	−0.292198	−	1.32305i
$725$	−12.0203	−	4.97895i	−0.446421	−	0.184914i
$726$	21.8357	−	6.23000i	0.810398	−	0.231217i
$727$	−29.0279	−	29.0279i	−1.07658	−	1.07658i	−0.996813	−	0.0797710i	$-0.974581\pi$
$727$	−29.0279	−	29.0279i	−1.07658	−	1.07658i	−0.0797710	−	0.996813i	$-0.525419\pi$
$728$	−2.96864	−	5.15619i	−0.110025	−	0.191101i
$729$	−4.37116	+	26.6438i	−0.161895	+	0.986808i
$730$	−14.7598	−	17.6044i	−0.546285	−	0.651569i
$731$	18.5522	+	7.68458i	0.686179	+	0.284224i
$732$	29.9258	−	5.76339i	1.10609	−	0.213021i
$733$	7.41080	+	17.8913i	0.273724	+	0.660829i	0.999637	−	0.0269585i	$-0.00858220\pi$
$733$	7.41080	+	17.8913i	0.273724	+	0.660829i	−0.725912	+	0.687787i	$0.758582\pi$
$734$	16.6292	−	5.23581i	0.613795	−	0.193257i
$735$	1.55275	−	0.594402i	0.0572740	−	0.0219249i
$736$	−26.4336	−	28.9639i	−0.974354	−	1.06762i
$737$		−	19.3434i		−	0.712523i
$738$	−0.264596	+	0.446897i	−0.00973991	+	0.0164505i
$739$	0.937525	−	0.388336i	0.0344874	−	0.0142852i	−0.365373	−	0.930861i	$-0.619059\pi$
$739$	0.937525	−	0.388336i	0.0344874	−	0.0142852i	0.399860	+	0.916576i	$0.369059\pi$
$740$	−1.26775	+	7.15608i	−0.0466033	+	0.263063i
$741$	−2.68711	−	0.0728432i	−0.0987133	−	0.00267596i
$742$	−11.3530	+	9.51852i	−0.416782	+	0.349436i
$743$	−34.8095	−	34.8095i	−1.27704	−	1.27704i	−0.942319	−	0.334717i	$-0.891359\pi$
$743$	−34.8095	−	34.8095i	−1.27704	−	1.27704i	−0.334717	−	0.942319i	$-0.608641\pi$
$744$	8.25980	−	0.850370i	0.302819	−	0.0311761i
$745$	−1.50999	+	1.50999i	−0.0553219	+	0.0553219i
$746$	0.297924	−	3.38959i	0.0109078	−	0.124102i
$747$	−12.4168	−	35.2703i	−0.454305	−	1.29047i
$748$	−2.23092	−	10.1015i	−0.0815705	−	0.369346i
$749$	−1.30940	−	3.16117i	−0.0478444	−	0.115507i
$750$	2.44457	−	21.2061i	0.0892633	−	0.774337i
$751$	−17.2476			−0.629372			−0.314686	−	0.949196i	$-0.601899\pi$
$751$	−17.2476			−0.629372			−0.314686	+	0.949196i	$0.601899\pi$
$752$	7.36723	+	2.69488i	0.268655	+	0.0982722i
$753$	39.3642	−	15.0689i	1.43451	−	0.549140i
$754$	4.38530	−	8.41581i	0.159703	−	0.306486i
$755$	3.93270	−	1.62898i	0.143126	−	0.0592846i
$756$	−8.97308	+	5.24249i	−0.326348	+	0.190668i
$757$	−1.32261	+	3.19307i	−0.0480712	+	0.116054i	−0.946091	−	0.323901i	$-0.895006\pi$
$757$	−1.32261	+	3.19307i	−0.0480712	+	0.116054i	0.898020	+	0.439955i	$0.145006\pi$
$758$	2.63651	−	29.9965i	0.0957623	−	1.08952i
$759$	14.4203	+	6.43626i	0.523423	+	0.233621i
$760$	−1.22136	+	1.58773i	−0.0443032	+	0.0575931i
$761$	−11.6933	+	11.6933i	−0.423881	+	0.423881i	−0.886538	−	0.462657i	$-0.846896\pi$
$761$	−11.6933	+	11.6933i	−0.423881	+	0.423881i	0.462657	+	0.886538i	$0.346896\pi$
$762$	18.2662	+	10.1568i	0.661715	+	0.367941i
$763$	5.12255	−	12.3669i	0.185449	−	0.447713i
$764$	−36.3196	+	25.3877i	−1.31400	+	0.918496i
$765$	10.2129	+	4.89443i	0.369247	+	0.176958i
$766$	−1.28024	+	0.403093i	−0.0462570	+	0.0145643i
$767$	−15.4002			−0.556068
$768$	27.6679	−	1.57732i	0.998379	−	0.0569166i
$769$	−26.6376			−0.960577			−0.480289	−	0.877111i	$-0.659468\pi$
$769$	−26.6376			−0.960577			−0.480289	+	0.877111i	$0.659468\pi$
$770$	1.70308	−	0.536225i	0.0613746	−	0.0193242i
$771$	−10.4654	−	11.0486i	−0.376903	−	0.397907i
$772$	−13.7917	+	9.64050i	−0.496373	+	0.346969i
$773$	4.35134	−	10.5051i	0.156507	−	0.377841i	−0.826104	−	0.563518i	$-0.809448\pi$
$773$	4.35134	−	10.5051i	0.156507	−	0.377841i	0.982611	+	0.185677i	$0.0594477\pi$
$774$	3.06316	−	21.4459i	0.110103	−	0.770858i
$775$	−4.88815	+	4.88815i	−0.175587	+	0.175587i
$776$	−24.8658	+	32.3249i	−0.892629	+	1.16040i
$777$	−2.67235	+	5.98733i	−0.0958699	+	0.214794i
$778$	0.953344	−	10.8465i	0.0341790	−	0.388867i
$779$	−0.0345620	+	0.0834401i	−0.00123831	+	0.00298955i
$780$	6.85198	+	1.40637i	0.245340	+	0.0503562i
$781$	1.54370	−	0.639421i	0.0552379	−	0.0228803i
$782$	−17.8154	+	34.1894i	−0.637076	+	1.22261i
$783$	−14.7483	−	7.56607i	−0.527060	−	0.270389i
$784$	−3.75656	−	1.37413i	−0.134163	−	0.0490759i
$785$	−0.373680			−0.0133372
$786$	25.8522	+	2.98016i	0.922117	+	0.106299i
$787$	8.54540	+	20.6304i	0.304611	+	0.735395i	0.999862	+	0.0166284i	$0.00529322\pi$
$787$	8.54540	+	20.6304i	0.304611	+	0.735395i	−0.695251	+	0.718767i	$0.744707\pi$
$788$	−7.81736	−	35.3965i	−0.278482	−	1.26095i
$789$	−26.2990	−	0.712924i	−0.936270	−	0.0253808i
$790$	0.0803606	−	0.914291i	0.00285910	−	0.0325290i
$791$	−0.683231	+	0.683231i	−0.0242929	+	0.0242929i
$792$	−9.95930	+	5.03631i	−0.353888	+	0.178958i
$793$	−13.0858	−	13.0858i	−0.464689	−	0.464689i
$794$	−5.07007	+	4.25082i	−0.179930	+	0.150856i
$795$	0.471993	−	17.4113i	0.0167399	−	0.617516i
$796$	2.69525	−	15.2139i	0.0955305	−	0.539244i
$797$	12.7091	−	5.26427i	0.450179	−	0.186470i	−0.146063	−	0.989275i	$-0.546660\pi$
$797$	12.7091	−	5.26427i	0.450179	−	0.186470i	0.596241	+	0.802805i	$0.296660\pi$
$798$	−1.41583	+	1.12314i	−0.0501197	+	0.0397588i
$799$		−	7.71258i		−	0.272851i
$800$	−17.0416	+	15.5528i	−0.602512	+	0.549876i
$801$	6.94657	+	7.74361i	0.245445	+	0.273607i
$802$	−49.1611	+	15.4787i	−1.73594	+	0.546571i
$803$	−8.51766	−	20.5634i	−0.300582	−	0.725668i
$804$	−9.63470	−	50.0271i	−0.339790	−	1.76432i
$805$	−6.14756	−	2.54640i	−0.216673	−	0.0897489i
$806$	−3.23950	−	3.86384i	−0.114107	−	0.136098i
$807$	−25.7149	−	11.4774i	−0.905208	−	0.404025i
$808$	12.1626	+	21.1251i	0.427879	+	0.743178i
$809$	21.0096	+	21.0096i	0.738658	+	0.738658i	0.972318	−	0.233660i	$-0.0750703\pi$
$809$	21.0096	+	21.0096i	0.738658	+	0.738658i	−0.233660	+	0.972318i	$0.575070\pi$
$810$	2.38029	−	11.9837i	0.0836349	−	0.421064i
$811$	33.3075	+	13.7964i	1.16958	+	0.484457i	0.881055	−	0.473014i	$-0.156834\pi$
$811$	33.3075	+	13.7964i	1.16958	+	0.484457i	0.288529	+	0.957471i	$0.406834\pi$
$812$	−1.37588	−	6.22990i	−0.0482839	−	0.218627i
$813$	−27.6403	+	26.1813i	−0.969389	+	0.918219i
$814$	−3.25376	+	6.24429i	−0.114044	+	0.218862i
$815$			6.47523i			0.226818i
$816$	−10.8012	−	25.0139i	−0.378116	−	0.875661i
$817$		−	3.76727i		−	0.131800i
$818$	−19.0952	−	9.95009i	−0.667647	−	0.347897i
$819$	5.69085	+	2.72729i	0.198855	+	0.0952992i
$820$	0.126432	−	0.198106i	0.00441519	−	0.00691817i
$821$	5.04434	+	2.08944i	0.176049	+	0.0729218i	0.468967	−	0.883216i	$-0.344626\pi$
$821$	5.04434	+	2.08944i	0.176049	+	0.0729218i	−0.292918	+	0.956138i	$0.594626\pi$
$822$	6.68648	−	1.90774i	0.233218	−	0.0665400i
$823$	29.9176	+	29.9176i	1.04286	+	1.04286i	0.999039	+	0.0438240i	$0.0139541\pi$
$823$	29.9176	+	29.9176i	1.04286	+	1.04286i	0.0438240	+	0.999039i	$0.486046\pi$
$824$	−0.881792	−	6.76090i	−0.0307187	−	0.235527i
$825$	3.78693	−	8.48453i	0.131844	−	0.295393i
$826$	−7.93397	+	6.65195i	−0.276058	+	0.231451i
$827$	−20.0019	−	8.28507i	−0.695535	−	0.288100i	0.00676894	−	0.999977i	$-0.497845\pi$
$827$	−20.0019	−	8.28507i	−0.695535	−	0.288100i	−0.702304	+	0.711877i	$0.747845\pi$
$828$	40.5005	+	9.46331i	1.40749	+	0.328873i
$829$	−9.39784	−	22.6884i	−0.326400	−	0.788000i	−0.998854	−	0.0478609i	$-0.984760\pi$
$829$	−9.39784	−	22.6884i	−0.326400	−	0.788000i	0.672454	−	0.740139i	$-0.265240\pi$
$830$	5.08156	+	16.1393i	0.176383	+	0.560202i
$831$	14.5311	+	37.9595i	0.504080	+	1.31680i
$832$	−10.2122	−	13.3755i	−0.354044	−	0.463712i
$833$			3.93266i			0.136259i
$834$	−13.3594	+	10.5977i	−0.462599	+	0.366969i
$835$	10.2746	−	4.25587i	0.355567	−	0.147280i
$836$	−1.59067	+	1.11190i	−0.0550146	+	0.0384557i
$837$	−6.71280	+	5.70124i	−0.232028	+	0.197064i
$838$	24.3080	+	28.9928i	0.839706	+	1.00154i
$839$	−23.6596	−	23.6596i	−0.816819	−	0.816819i	0.168826	−	0.985646i	$-0.446002\pi$
$839$	−23.6596	−	23.6596i	−0.816819	−	0.816819i	−0.985646	+	0.168826i	$0.946002\pi$
$840$	4.13752	−	2.23510i	0.142758	−	0.0771183i
$841$	−13.3105	+	13.3105i	−0.458981	+	0.458981i
$842$	−38.9523	−	3.42367i	−1.34239	−	0.117988i
$843$	0.642121	−	23.6872i	0.0221158	−	0.815829i
$844$	33.4110	+	21.3230i	1.15005	+	0.733966i
$845$	3.15003	+	7.60485i	0.108364	+	0.261615i
$846$	−8.06013	+	2.06519i	−0.277113	+	0.0710027i
$847$	−9.27011			−0.318525
$848$	−28.3596	+	30.8493i	−0.973872	+	1.05937i
$849$	−8.97734	−	23.4514i	−0.308101	−	0.804849i
$850$	20.1162	+	10.4821i	0.689980	+	0.359533i
$851$	24.2431	−	10.0418i	0.831043	−	0.344229i
$852$	3.67393	−	2.42261i	0.125867	−	0.0829973i
$853$	11.7563	−	28.3823i	0.402529	−	0.971791i	−0.584521	−	0.811379i	$-0.698718\pi$
$853$	11.7563	−	28.3823i	0.402529	−	0.971791i	0.987050	−	0.160413i	$-0.0512825\pi$
$854$	−12.3939	−	1.08935i	−0.424109	−	0.0372766i
$855$	0.115108	−	2.12154i	0.00393660	−	0.0725551i
$856$	−4.82880	−	8.38707i	−0.165045	−	0.286664i
$857$	−29.7025	+	29.7025i	−1.01462	+	1.01462i	−0.0147266	+	0.999892i	$0.504688\pi$
$857$	−29.7025	+	29.7025i	−1.01462	+	1.01462i	−0.999892	+	0.0147266i	$0.995312\pi$
$858$	5.92292	+	3.29339i	0.202205	+	0.112434i
$859$	14.5723	−	35.1806i	0.497199	−	1.20035i	−0.453786	−	0.891111i	$-0.649927\pi$
$859$	14.5723	−	35.1806i	0.497199	−	1.20035i	0.950986	−	0.309235i	$-0.100073\pi$
$860$	−1.71004	+	9.65270i	−0.0583118	+	0.329154i
$861$	0.153932	−	0.145807i	0.00524599	−	0.00496908i
$862$	−5.28295	−	16.7789i	−0.179938	−	0.571491i
$863$	−46.3071			−1.57631			−0.788156	−	0.615475i	$-0.788964\pi$
$863$	−46.3071			−1.57631			−0.788156	+	0.615475i	$0.788964\pi$
$864$	−23.2489	+	17.9858i	−0.790942	+	0.611891i
$865$	21.3153			0.724741
$866$	−6.68163	−	21.2212i	−0.227051	−	0.721125i
$867$	1.92920	−	1.82736i	0.0655190	−	0.0620605i
$868$	−3.33790	−	0.591330i	−0.113296	−	0.0200710i
$869$	0.340294	−	0.821542i	0.0115437	−	0.0278689i
$870$	6.55546	+	3.64510i	0.222251	+	0.123581i
$871$	−21.8756	+	21.8756i	−0.741225	+	0.741225i
$872$	9.84325	−	36.5590i	0.333335	−	1.23804i
$873$	2.34349	−	43.1927i	0.0793152	−	1.46185i
$874$	7.20492	+	0.633268i	0.243710	+	0.0214206i
$875$	−3.33497	+	8.05132i	−0.112742	+	0.272184i
$876$	−32.2713	−	48.9400i	−1.09035	−	1.65353i
$877$	13.4821	−	5.58446i	0.455257	−	0.188574i	−0.143258	−	0.989685i	$-0.545758\pi$
$877$	13.4821	−	5.58446i	0.455257	−	0.188574i	0.598515	+	0.801112i	$0.295758\pi$
$878$	21.8747	+	11.3984i	0.738235	+	0.384678i
$879$	6.44672	+	16.8407i	0.217442	+	0.568021i
$880$	4.58042	−	2.12692i	0.154406	−	0.0716985i
$881$	−11.5510			−0.389162			−0.194581	−	0.980886i	$-0.562335\pi$
$881$	−11.5510			−0.389162			−0.194581	+	0.980886i	$0.562335\pi$
$882$	4.10988	−	1.05305i	0.138387	−	0.0354579i
$883$	−9.21323	−	22.2427i	−0.310050	−	0.748526i	−0.999703	−	0.0243862i	$-0.992237\pi$
$883$	−9.21323	−	22.2427i	−0.310050	−	0.748526i	0.689653	−	0.724140i	$-0.257763\pi$
$884$	−8.90086	+	13.9468i	−0.299368	+	0.469081i
$885$	0.329849	−	12.1678i	0.0110877	−	0.409015i
$886$	42.7088	+	3.75384i	1.43483	+	0.126113i
$887$	−30.3315	+	30.3315i	−1.01843	+	1.01843i	−0.0186052	+	0.999827i	$0.505923\pi$
$887$	−30.3315	+	30.3315i	−1.01843	+	1.01843i	−0.999827	+	0.0186052i	$0.994077\pi$
$888$	−5.30489	+	17.7700i	−0.178020	+	0.596323i
$889$	−6.03334	−	6.03334i	−0.202352	−	0.202352i
$890$	−3.02439	−	3.60728i	−0.101378	−	0.120916i
$891$	5.68658	−	10.3819i	0.190508	−	0.347807i
$892$	−30.3704	−	43.4478i	−1.01688	−	1.45474i
$893$	−1.33678	+	0.553714i	−0.0447338	+	0.0185293i
$894$	−4.26905	+	3.38654i	−0.142779	+	0.113263i
$895$		−	8.96457i		−	0.299653i
$896$	−11.0386	−	2.47982i	−0.368773	−	0.0828450i
$897$	−9.02918	−	23.5868i	−0.301476	−	0.787540i
$898$	9.15099	+	29.0640i	0.305372	+	0.969878i
$899$	−2.06912	−	4.99529i	−0.0690089	−	0.166602i
$900$	5.56797	−	23.8295i	0.185599	−	0.794315i
$901$	38.0625	+	15.7660i	1.26805	+	0.525242i
$902$	0.174482	−	0.146288i	0.00580963	−	0.00487087i
$903$	−3.60467	+	8.07619i	−0.119956	+	0.268759i
$904$	−1.66631	+	2.16616i	−0.0554207	+	0.0720456i
$905$	−12.3731	−	12.3731i	−0.411295	−	0.411295i
$906$	10.4453	−	2.98019i	0.347023	−	0.0990101i
$907$	−27.5210	−	11.3996i	−0.913821	−	0.378517i	−0.124303	−	0.992244i	$-0.539669\pi$
$907$	−27.5210	−	11.3996i	−0.913821	−	0.378517i	−0.789518	+	0.613727i	$0.789669\pi$
$908$	−19.7430	−	12.6000i	−0.655195	−	0.418146i
$909$	−23.3156	−	11.1738i	−0.773331	−	0.370612i
$910$	−2.53244	−	1.31960i	−0.0839495	−	0.0437443i
$911$			41.5508i			1.37664i	0.725407	+	0.688320i	$0.241652\pi$
$911$			41.5508i			1.37664i	−0.725407	+	0.688320i	$0.758348\pi$
$912$	−3.56008	+	3.66795i	−0.117886	+	0.121458i
$913$			16.3934i			0.542542i
$914$	14.4692	−	27.7677i	0.478597	−	0.918475i
$915$	10.6194	−	10.0589i	0.351067	−	0.332535i
$916$	17.9859	−	3.97221i	0.594272	−	0.131246i
$917$	−9.81531	−	4.06563i	−0.324130	−	0.134259i
$918$	24.4591	+	15.3917i	0.807272	+	0.508002i
$919$	−12.1662	−	12.1662i	−0.401326	−	0.401326i	0.477374	−	0.878700i	$-0.341589\pi$
$919$	−12.1662	−	12.1662i	−0.401326	−	0.401326i	−0.878700	+	0.477374i	$0.841589\pi$
$920$	−18.1734	−	4.89305i	−0.599158	−	0.161319i
$921$	−8.13521	−	3.63102i	−0.268064	−	0.119646i
$922$	−25.8396	−	30.8196i	−0.850981	−	1.01499i
$923$	−2.46891	−	1.02265i	−0.0812650	−	0.0336611i
$924$	4.47395	−	0.861637i	0.147182	−	0.0283458i
$925$	−5.90835	−	14.2640i	−0.194265	−	0.468998i
$926$	47.0149	−	14.8030i	1.54501	−	0.486455i
$927$	4.82907	+	5.38315i	0.158607	+	0.176806i
$928$	−6.13779	−	16.9695i	−0.201483	−	0.557052i
$929$			49.5491i			1.62565i	0.582506	+	0.812826i	$0.302072\pi$
$929$			49.5491i			1.62565i	−0.582506	+	0.812826i	$0.697928\pi$
$930$	3.12223	−	2.47679i	0.102382	−	0.0812172i
$931$	0.681629	−	0.282340i	0.0223395	−	0.00925332i
$932$	39.3851	+	6.97733i	1.29010	+	0.228550i
$933$	−1.20687	+	44.5200i	−0.0395110	+	1.45752i
$934$	−17.1131	+	14.3479i	−0.559957	+	0.469476i
$935$	−3.51088	−	3.51088i	−0.114818	−	0.114818i
$936$	16.9586	+	5.56744i	0.554310	+	0.181977i
$937$	−4.33198	+	4.33198i	−0.141520	+	0.141520i	−0.774317	−	0.632798i	$-0.781906\pi$
$937$	−4.33198	+	4.33198i	−0.141520	+	0.141520i	0.632798	+	0.774317i	$0.281906\pi$
$938$	−1.82107	+	20.7189i	−0.0594600	+	0.676497i
$939$	46.2584	+	1.25399i	1.50958	+	0.0409224i
$940$	3.67652	−	0.811963i	0.119915	−	0.0264833i
$941$	−2.85641	−	6.89598i	−0.0931163	−	0.224803i	0.870458	−	0.492242i	$-0.163823\pi$
$941$	−2.85641	−	6.89598i	−0.0931163	−	0.224803i	−0.963575	+	0.267439i	$0.913823\pi$
$942$	−0.947271	−	0.109199i	−0.0308637	−	0.00355788i
$943$	−0.848553			−0.0276327
$944$	−19.8189	+	21.5588i	−0.645050	+	0.701679i
$945$	−2.27674	+	4.43796i	−0.0740623	+	0.144367i
$946$	−4.38894	+	8.42279i	−0.142697	+	0.273849i
$947$	−9.76096	+	4.04312i	−0.317189	+	0.131384i	−0.535597	−	0.844474i	$-0.679913\pi$
$947$	−9.76096	+	4.04312i	−0.317189	+	0.131384i	0.218409	+	0.975857i	$0.429913\pi$
$948$	0.470890	−	2.29422i	0.0152938	−	0.0745129i
$949$	−13.6227	+	32.8880i	−0.442210	+	1.06759i
$950$	0.372599	−	4.23919i	0.0120887	−	0.137538i
$951$	−20.4312	+	45.7757i	−0.662528	+	1.48438i
$952$	1.43857	+	11.0298i	0.0466243	+	0.357479i
$953$	27.2994	−	27.2994i	0.884316	−	0.884316i	−0.109654	−	0.993970i	$-0.534974\pi$
$953$	27.2994	−	27.2994i	0.884316	−	0.884316i	0.993970	+	0.109654i	$0.0349744\pi$
$954$	6.28450	−	43.9993i	0.203468	−	1.42453i
$955$	−8.13911	+	19.6495i	−0.263375	+	0.635844i
$956$	4.74363	+	6.78622i	0.153420	+	0.219482i
$957$	4.99749	+	5.27599i	0.161546	+	0.170549i
$958$	11.3113	−	3.56145i	0.365453	−	0.115065i
$959$	−2.83867			−0.0916656
$960$	10.7868	−	7.78223i	0.348142	−	0.251170i
$961$	28.1272			0.907329
$962$	10.7414	−	3.38200i	0.346317	−	0.109040i
$963$	9.25677	+	4.43622i	0.298295	+	0.142955i
$964$	26.8973	+	38.4791i	0.866303	+	1.23933i
$965$	−3.09067	+	7.46153i	−0.0994921	+	0.240195i
$966$	−14.8398	−	8.25154i	−0.477463	−	0.265489i
$967$	13.4880	−	13.4880i	0.433744	−	0.433744i	−0.456156	−	0.889900i	$-0.650774\pi$
$967$	13.4880	−	13.4880i	0.433744	−	0.433744i	0.889900	+	0.456156i	$0.150774\pi$
$968$	−25.9996	+	3.39101i	−0.835660	+	0.108991i
$969$	4.58914	+	2.04829i	0.147425	+	0.0658006i
$970$	−1.71382	+	19.4987i	−0.0550275	+	0.626067i
$971$	−15.8260	+	38.2075i	−0.507882	+	1.22614i	0.437218	+	0.899355i	$0.355964\pi$
$971$	−15.8260	+	38.2075i	−0.507882	+	1.22614i	−0.945100	+	0.326780i	$0.894036\pi$
$972$	9.53590	−	29.6828i	0.305864	−	0.952075i
$973$	6.43171	−	2.66410i	0.206191	−	0.0854072i
$974$	−15.0816	+	28.9431i	−0.483247	+	0.927397i
$975$	−13.8779	+	5.31254i	−0.444448	+	0.170138i
$976$	−35.1592	+	1.47842i	−1.12542	+	0.0473231i
$977$	−23.8105			−0.761765			−0.380882	−	0.924623i	$-0.624380\pi$
$977$	−23.8105			−0.761765			−0.380882	+	0.924623i	$0.624380\pi$
$978$	−1.89222	+	16.4146i	−0.0605066	+	0.524880i
$979$	−1.74533	−	4.21360i	−0.0557811	−	0.134667i
$980$	−1.87467	+	0.414022i	−0.0598840	+	0.0132254i
$981$	13.3351	+	37.8789i	0.425756	+	1.20938i
$982$	2.90040	−	32.9989i	0.0925554	−	1.05304i
$983$	19.7593	−	19.7593i	0.630225	−	0.630225i	−0.317899	−	0.948124i	$-0.602977\pi$
$983$	19.7593	−	19.7593i	0.630225	−	0.630225i	0.948124	+	0.317899i	$0.102977\pi$
$984$	0.378393	−	0.465248i	0.0120627	−	0.0148316i
$985$	−12.3025	−	12.3025i	−0.391989	−	0.391989i
$986$	−13.5955	+	11.3986i	−0.432968	+	0.363007i
$987$	3.39558	+	0.0920488i	0.108083	+	0.00292995i
$988$	3.05635	+	0.541452i	0.0972355	+	0.0172259i
$989$	32.7010	−	13.5452i	1.03983	−	0.430713i
$990$	−2.72898	+	4.60919i	−0.0867328	+	0.146490i
$991$		−	21.8133i		−	0.692922i	−0.938064	−	0.346461i	$-0.887383\pi$
$991$		−	21.8133i		−	0.692922i	0.938064	−	0.346461i	$-0.112617\pi$
$992$	−9.57802	−	0.437483i	−0.304102	−	0.0138901i
$993$	−3.95189	+	1.51281i	−0.125410	+	0.0480076i
$994$	−1.71367	+	0.539561i	−0.0543544	+	0.0171138i
$995$	−2.83790	−	6.85129i	−0.0899674	−	0.217200i
$996$	8.16534	+	42.3976i	0.258729	+	1.34342i
$997$	−3.61805	−	1.49864i	−0.114585	−	0.0474625i	0.324655	−	0.945833i	$-0.394752\pi$
$997$	−3.61805	−	1.49864i	−0.114585	−	0.0474625i	−0.439239	+	0.898370i	$0.644752\pi$
$998$	2.90050	+	3.45950i	0.0918136	+	0.109509i
$999$	−6.02658	−	18.7239i	−0.190673	−	0.592399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bs.a.155.4	✓	192
3.2	odd	2	inner	672.2.bs.a.155.45	yes	192
32.19	odd	8	inner	672.2.bs.a.659.45	yes	192
96.83	even	8	inner	672.2.bs.a.659.4	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bs.a.155.4	✓	192	1.1	even	1	trivial
672.2.bs.a.155.45	yes	192	3.2	odd	2	inner
672.2.bs.a.659.4	yes	192	96.83	even	8	inner
672.2.bs.a.659.45	yes	192	32.19	odd	8	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bs (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34893 + 0.424720i) q^{2} +(-1.25748 + 1.19111i) q^{3} +(1.63923 - 1.14583i) q^{4} +(0.367345 - 0.886850i) q^{5} +(1.19037 - 2.14080i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.72454 + 2.24186i) q^{8} +(0.162531 - 2.99559i) q^{9} +O(q^{10})\)	\(q+(-1.34893 + 0.424720i) q^{2} +(-1.25748 + 1.19111i) q^{3} +(1.63923 - 1.14583i) q^{4} +(0.367345 - 0.886850i) q^{5} +(1.19037 - 2.14080i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.72454 + 2.24186i) q^{8} +(0.162531 - 2.99559i) q^{9} +(-0.118861 + 1.35232i) q^{10} +(-0.503326 + 1.21514i) q^{11} +(-0.696489 + 3.39336i) q^{12} +(1.94342 - 0.804990i) q^{13} +(0.653516 - 1.25416i) q^{14} +(0.594402 + 1.55275i) q^{15} +(1.37413 - 3.75656i) q^{16} -3.93266 q^{17} +(1.05305 + 4.10988i) q^{18} +(0.282340 + 0.681629i) q^{19} +(-0.414022 - 1.87467i) q^{20} +(0.0469359 - 1.73141i) q^{21} +(0.162859 - 1.85291i) q^{22} +(-4.90159 + 4.90159i) q^{23} +(-0.501712 - 4.87322i) q^{24} +(2.88397 + 2.88397i) q^{25} +(-2.27964 + 1.91128i) q^{26} +(3.36369 + 3.96050i) q^{27} +(-0.348880 + 1.96934i) q^{28} +(-2.94719 + 1.22076i) q^{29} +(-1.46129 - 1.84209i) q^{30} +1.69494i q^{31} +(-0.258112 + 5.65096i) q^{32} +(-0.814432 - 2.12753i) q^{33} +(5.30489 - 1.67028i) q^{34} +(0.367345 + 0.886850i) q^{35} +(-3.16603 - 5.09669i) q^{36} +(-3.49732 - 1.44864i) q^{37} +(-0.670358 - 0.799555i) q^{38} +(-1.48499 + 3.32708i) q^{39} +(1.35469 + 2.35295i) q^{40} +(0.0865589 + 0.0865589i) q^{41} +(0.672053 + 2.35549i) q^{42} +(-4.71747 - 1.95404i) q^{43} +(0.567280 + 2.56861i) q^{44} +(-2.59694 - 1.24456i) q^{45} +(4.53010 - 8.69371i) q^{46} +1.96116i q^{47} +(2.74653 + 6.36055i) q^{48} -1.00000i q^{49} +(-5.11516 - 2.66540i) q^{50} +(4.94526 - 4.68422i) q^{51} +(2.26332 - 3.54640i) q^{52} +(-9.67856 - 4.00899i) q^{53} +(-6.21949 - 3.91382i) q^{54} +(0.892749 + 0.892749i) q^{55} +(-0.365800 - 2.80467i) q^{56} +(-1.16693 - 0.520841i) q^{57} +(3.45707 - 2.89845i) q^{58} +(-6.76379 - 2.80165i) q^{59} +(2.75355 + 1.86422i) q^{60} +(-3.36669 - 8.12790i) q^{61} +(-0.719873 - 2.28635i) q^{62} +(2.00328 + 2.23313i) q^{63} +(-2.05190 - 7.73238i) q^{64} -2.01923i q^{65} +(2.00221 + 2.52398i) q^{66} +(-13.5875 + 5.62812i) q^{67} +(-6.44652 + 4.50618i) q^{68} +(0.325355 - 12.0020i) q^{69} +(-0.872186 - 1.04028i) q^{70} +(-0.898304 - 0.898304i) q^{71} +(6.43542 + 5.53040i) q^{72} +(-11.9662 + 11.9662i) q^{73} +(5.33291 + 0.468731i) q^{74} +(-7.06167 - 0.191431i) q^{75} +(1.24385 + 0.793829i) q^{76} +(-0.503326 - 1.21514i) q^{77} +(0.590069 - 5.11870i) q^{78} -0.676091 q^{79} +(-2.82673 - 2.59860i) q^{80} +(-8.94717 - 0.973754i) q^{81} +(-0.153525 - 0.0799986i) q^{82} +(11.5153 - 4.76979i) q^{83} +(-1.90698 - 2.89196i) q^{84} +(-1.44465 + 3.48768i) q^{85} +(7.19346 + 0.632261i) q^{86} +(2.25198 - 5.04550i) q^{87} +(-1.85616 - 3.22394i) q^{88} +(-2.45196 + 2.45196i) q^{89} +(4.03168 + 0.575852i) q^{90} +(-0.804990 + 1.94342i) q^{91} +(-2.41840 + 13.6512i) q^{92} +(-2.01885 - 2.13135i) q^{93} +(-0.832944 - 2.64547i) q^{94} +0.708220 q^{95} +(-6.40633 - 7.41343i) q^{96} +14.4188 q^{97} +(0.424720 + 1.34893i) q^{98} +(3.55825 + 1.70526i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 16 q^{4}+O(q^{10}) \) 192 * q - 16 * q^4	\( 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) \) 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more