LMFDB - Embedded newform 799.2.g.d.189.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,2,Mod(189,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("799.189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 799 = 17 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	799.g (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:	$6.38004712150$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			189.6
Character	$\chi$	$=$	799.189
Dual form			799.2.g.d.706.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59647 - 1.59647i) q^{2} +(2.24761 - 0.930990i) q^{3} +3.09745i q^{4} +(1.25186 + 3.02225i) q^{5} +(-5.07455 - 2.10195i) q^{6} +(1.82436 - 4.40439i) q^{7} +(1.75205 - 1.75205i) q^{8} +(2.06368 - 2.06368i) q^{9} +O(q^{10})$	\(q+(-1.59647 - 1.59647i) q^{2} +(2.24761 - 0.930990i) q^{3} +3.09745i q^{4} +(1.25186 + 3.02225i) q^{5} +(-5.07455 - 2.10195i) q^{6} +(1.82436 - 4.40439i) q^{7} +(1.75205 - 1.75205i) q^{8} +(2.06368 - 2.06368i) q^{9} +(2.82638 - 6.82349i) q^{10} +(-4.06508 - 1.68381i) q^{11} +(2.88369 + 6.96185i) q^{12} -3.45210i q^{13} +(-9.94402 + 4.11895i) q^{14} +(5.62736 + 5.62736i) q^{15} +0.600710 q^{16} +(-0.782056 - 4.04826i) q^{17} -6.58923 q^{18} +(5.64950 + 5.64950i) q^{19} +(-9.36125 + 3.87756i) q^{20} -11.5978i q^{21} +(3.80163 + 9.17795i) q^{22} +(0.254588 + 0.105454i) q^{23} +(2.30678 - 5.56905i) q^{24} +(-4.03130 + 4.03130i) q^{25} +(-5.51118 + 5.51118i) q^{26} +(-0.0758846 + 0.183202i) q^{27} +(13.6424 + 5.65085i) q^{28} +(-0.744138 - 1.79651i) q^{29} -17.9679i q^{30} +(0.894815 - 0.370644i) q^{31} +(-4.46311 - 4.46311i) q^{32} -10.7043 q^{33} +(-5.21440 + 7.71146i) q^{34} +15.5950 q^{35} +(6.39216 + 6.39216i) q^{36} +(1.49641 - 0.619835i) q^{37} -18.0385i q^{38} +(-3.21387 - 7.75897i) q^{39} +(7.48842 + 3.10181i) q^{40} +(2.38282 - 5.75263i) q^{41} +(-18.5156 + 18.5156i) q^{42} +(9.03213 - 9.03213i) q^{43} +(5.21552 - 12.5914i) q^{44} +(8.82040 + 3.65353i) q^{45} +(-0.238088 - 0.574796i) q^{46} +1.00000i q^{47} +(1.35016 - 0.559255i) q^{48} +(-11.1206 - 11.1206i) q^{49} +12.8717 q^{50} +(-5.52665 - 8.37081i) q^{51} +10.6927 q^{52} +(0.602447 + 0.602447i) q^{53} +(0.413624 - 0.171329i) q^{54} -14.3936i q^{55} +(-4.52033 - 10.9130i) q^{56} +(17.9575 + 7.43824i) q^{57} +(-1.68008 + 4.05607i) q^{58} +(-10.2426 + 10.2426i) q^{59} +(-17.4305 + 17.4305i) q^{60} +(-2.55318 + 6.16392i) q^{61} +(-2.02027 - 0.836823i) q^{62} +(-5.32437 - 12.8542i) q^{63} +13.0490i q^{64} +(10.4331 - 4.32153i) q^{65} +(17.0892 + 17.0892i) q^{66} -0.794089 q^{67} +(12.5393 - 2.42238i) q^{68} +0.670390 q^{69} +(-24.8969 - 24.8969i) q^{70} +(8.04436 - 3.33208i) q^{71} -7.23134i q^{72} +(-0.248595 - 0.600162i) q^{73} +(-3.37853 - 1.39943i) q^{74} +(-5.30768 + 12.8139i) q^{75} +(-17.4990 + 17.4990i) q^{76} +(-14.8323 + 14.8323i) q^{77} +(-7.25612 + 17.5178i) q^{78} +(2.89649 + 1.19977i) q^{79} +(0.752002 + 1.81549i) q^{80} +9.23788i q^{81} +(-12.9880 + 5.37981i) q^{82} +(8.03657 + 8.03657i) q^{83} +35.9236 q^{84} +(11.2558 - 7.43140i) q^{85} -28.8391 q^{86} +(-3.34506 - 3.34506i) q^{87} +(-10.0723 + 4.17210i) q^{88} -11.4100i q^{89} +(-8.24876 - 19.9143i) q^{90} +(-15.2044 - 6.29786i) q^{91} +(-0.326637 + 0.788573i) q^{92} +(1.66613 - 1.66613i) q^{93} +(1.59647 - 1.59647i) q^{94} +(-10.0018 + 24.1465i) q^{95} +(-14.1864 - 5.87621i) q^{96} +(5.32468 + 12.8549i) q^{97} +35.5074i q^{98} +(-11.8639 + 4.91419i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 4 q^{2} + 4 q^{6} + 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) $ 152 * q - 4 * q^2 + 4 * q^6 + 4 * q^7 + 4 * q^8 - 8 * q^9	$ 152 q - 4 q^{2} + 4 q^{6} + 4 q^{7} + 4 q^{8} - 8 q^{9} - 8 q^{11} + 8 q^{12} - 12 q^{14} + 20 q^{15} - 160 q^{16} - 12 q^{17} + 96 q^{18} + 16 q^{19} + 96 q^{20} - 4 q^{22} - 16 q^{23} - 76 q^{24} - 12 q^{25} - 8 q^{26} + 8 q^{28} - 4 q^{29} - 4 q^{31} - 16 q^{32} - 72 q^{33} - 20 q^{34} + 48 q^{35} - 16 q^{36} + 16 q^{37} + 64 q^{40} - 68 q^{41} - 144 q^{42} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 12 q^{48} - 4 q^{49} + 96 q^{50} - 52 q^{51} + 168 q^{52} - 16 q^{53} + 168 q^{54} + 108 q^{56} - 104 q^{58} - 84 q^{59} - 4 q^{60} + 4 q^{61} - 28 q^{62} + 60 q^{63} + 60 q^{65} - 44 q^{66} - 160 q^{67} - 96 q^{68} + 160 q^{69} + 36 q^{70} + 40 q^{71} + 4 q^{73} + 76 q^{74} - 116 q^{75} - 148 q^{76} - 4 q^{77} + 68 q^{78} - 76 q^{80} + 64 q^{82} - 124 q^{83} + 208 q^{84} - 68 q^{85} + 80 q^{86} - 72 q^{87} + 188 q^{88} + 236 q^{90} - 32 q^{91} - 196 q^{92} - 152 q^{93} + 4 q^{94} - 48 q^{95} - 56 q^{96} - 20 q^{97} + 244 q^{99}+O(q^{100}) $ 152 * q - 4 * q^2 + 4 * q^6 + 4 * q^7 + 4 * q^8 - 8 * q^9 - 8 * q^11 + 8 * q^12 - 12 * q^14 + 20 * q^15 - 160 * q^16 - 12 * q^17 + 96 * q^18 + 16 * q^19 + 96 * q^20 - 4 * q^22 - 16 * q^23 - 76 * q^24 - 12 * q^25 - 8 * q^26 + 8 * q^28 - 4 * q^29 - 4 * q^31 - 16 * q^32 - 72 * q^33 - 20 * q^34 + 48 * q^35 - 16 * q^36 + 16 * q^37 + 64 * q^40 - 68 * q^41 - 144 * q^42 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 12 * q^48 - 4 * q^49 + 96 * q^50 - 52 * q^51 + 168 * q^52 - 16 * q^53 + 168 * q^54 + 108 * q^56 - 104 * q^58 - 84 * q^59 - 4 * q^60 + 4 * q^61 - 28 * q^62 + 60 * q^63 + 60 * q^65 - 44 * q^66 - 160 * q^67 - 96 * q^68 + 160 * q^69 + 36 * q^70 + 40 * q^71 + 4 * q^73 + 76 * q^74 - 116 * q^75 - 148 * q^76 - 4 * q^77 + 68 * q^78 - 76 * q^80 + 64 * q^82 - 124 * q^83 + 208 * q^84 - 68 * q^85 + 80 * q^86 - 72 * q^87 + 188 * q^88 + 236 * q^90 - 32 * q^91 - 196 * q^92 - 152 * q^93 + 4 * q^94 - 48 * q^95 - 56 * q^96 - 20 * q^97 + 244 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/799\mathbb{Z}\right)^\times$.

$n$	$52$	$377$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−1.59647	−	1.59647i	−1.12888	−	1.12888i	−0.990360	−	0.138516i	$-0.955767\pi$
$2$	−1.59647	−	1.59647i	−1.12888	−	1.12888i	−0.138516	−	0.990360i	$-0.544233\pi$
$3$	2.24761	−	0.930990i	1.29766	−	0.537507i	0.376399	−	0.926458i	$-0.377162\pi$
$3$	2.24761	−	0.930990i	1.29766	−	0.537507i	0.921259	+	0.388950i	$0.127162\pi$
$4$			3.09745i			1.54872i
$5$	1.25186	+	3.02225i	0.559847	+	1.35159i	0.909887	+	0.414855i	$0.136168\pi$
$5$	1.25186	+	3.02225i	0.559847	+	1.35159i	−0.350041	+	0.936735i	$0.613832\pi$
$6$	−5.07455	−	2.10195i	−2.07167	−	0.858116i
$7$	1.82436	−	4.40439i	0.689542	−	1.66470i	−0.0561599	−	0.998422i	$-0.517886\pi$
$7$	1.82436	−	4.40439i	0.689542	−	1.66470i	0.745702	−	0.666280i	$-0.232114\pi$
$8$	1.75205	−	1.75205i	0.619442	−	0.619442i
$9$	2.06368	−	2.06368i	0.687895	−	0.687895i
$10$	2.82638	−	6.82349i	0.893780	−	2.15778i
$11$	−4.06508	−	1.68381i	−1.22567	−	0.507689i	−0.326461	−	0.945211i	$-0.605856\pi$
$11$	−4.06508	−	1.68381i	−1.22567	−	0.507689i	−0.899208	+	0.437522i	$0.855856\pi$
$12$	2.88369	+	6.96185i	0.832451	+	2.00971i
$13$		−	3.45210i		−	0.957440i	−0.877968	−	0.478720i	$-0.841101\pi$
$13$		−	3.45210i		−	0.957440i	0.877968	−	0.478720i	$-0.158899\pi$
$14$	−9.94402	+	4.11895i	−2.65765	+	1.10083i
$15$	5.62736	+	5.62736i	1.45298	+	1.45298i
$16$	0.600710			0.150177
$17$	−0.782056	−	4.04826i	−0.189677	−	0.981847i
$17$	−0.782056	−	4.04826i	−0.189677	−	0.981847i
$18$	−6.58923			−1.55310
$19$	5.64950	+	5.64950i	1.29608	+	1.29608i	0.930958	+	0.365125i	$0.118974\pi$
$19$	5.64950	+	5.64950i	1.29608	+	1.29608i	0.365125	+	0.930958i	$0.381026\pi$
$20$	−9.36125	+	3.87756i	−2.09324	+	0.867048i
$21$		−	11.5978i		−	2.53085i
$22$	3.80163	+	9.17795i	0.810511	+	1.95675i
$23$	0.254588	+	0.105454i	0.0530852	+	0.0219886i	0.409068	−	0.912504i	$-0.365854\pi$
$23$	0.254588	+	0.105454i	0.0530852	+	0.0219886i	−0.355983	+	0.934492i	$0.615854\pi$
$24$	2.30678	−	5.56905i	0.470869	−	1.13678i
$25$	−4.03130	+	4.03130i	−0.806260	+	0.806260i
$26$	−5.51118	+	5.51118i	−1.08083	+	1.08083i
$27$	−0.0758846	+	0.183202i	−0.0146040	+	0.0352572i
$28$	13.6424	+	5.65085i	2.57816	+	1.06791i
$29$	−0.744138	−	1.79651i	−0.138183	−	0.333603i	0.839606	−	0.543196i	$-0.182786\pi$
$29$	−0.744138	−	1.79651i	−0.138183	−	0.333603i	−0.977789	+	0.209593i	$0.932786\pi$
$30$		−	17.9679i		−	3.28047i
$31$	0.894815	−	0.370644i	0.160713	−	0.0665697i	−0.300876	−	0.953663i	$-0.597279\pi$
$31$	0.894815	−	0.370644i	0.160713	−	0.0665697i	0.461590	+	0.887093i	$0.347279\pi$
$32$	−4.46311	−	4.46311i	−0.788974	−	0.788974i
$33$	−10.7043			−1.86339
$34$	−5.21440	+	7.71146i	−0.894262	+	1.32250i
$35$	15.5950			2.63603
$36$	6.39216	+	6.39216i	1.06536	+	1.06536i
$37$	1.49641	−	0.619835i	0.246009	−	0.101900i	−0.256272	−	0.966605i	$-0.582494\pi$
$37$	1.49641	−	0.619835i	0.246009	−	0.101900i	0.502281	+	0.864704i	$0.332494\pi$
$38$		−	18.0385i		−	2.92624i
$39$	−3.21387	−	7.75897i	−0.514631	−	1.24243i
$40$	7.48842	+	3.10181i	1.18402	+	0.490439i
$41$	2.38282	−	5.75263i	0.372133	−	0.898409i	−0.621255	−	0.783608i	$-0.713377\pi$
$41$	2.38282	−	5.75263i	0.372133	−	0.898409i	0.993389	−	0.114801i	$-0.0366230\pi$
$42$	−18.5156	+	18.5156i	−2.85701	+	2.85701i
$43$	9.03213	−	9.03213i	1.37739	−	1.37739i	0.528377	−	0.849010i	$-0.322801\pi$
$43$	9.03213	−	9.03213i	1.37739	−	1.37739i	0.849010	−	0.528377i	$-0.177199\pi$
$44$	5.21552	−	12.5914i	0.786270	−	1.89822i
$45$	8.82040	+	3.65353i	1.31487	+	0.544636i
$46$	−0.238088	−	0.574796i	−0.0351042	−	0.0847491i
$47$			1.00000i			0.145865i
$47$			1.00000i			0.145865i
$48$	1.35016	−	0.559255i	0.194879	−	0.0807215i
$49$	−11.1206	−	11.1206i	−1.58866	−	1.58866i
$50$	12.8717			1.82034
$51$	−5.52665	−	8.37081i	−0.773885	−	1.17215i
$52$	10.6927			1.48281
$53$	0.602447	+	0.602447i	0.0827525	+	0.0827525i	0.747271	−	0.664519i	$-0.231364\pi$
$53$	0.602447	+	0.602447i	0.0827525	+	0.0827525i	−0.664519	+	0.747271i	$0.731364\pi$
$54$	0.413624	−	0.171329i	0.0562871	−	0.0233149i
$55$		−	14.3936i		−	1.94083i
$56$	−4.52033	−	10.9130i	−0.604055	−	1.45832i
$57$	17.9575	+	7.43824i	2.37853	+	0.985218i
$58$	−1.68008	+	4.05607i	−0.220605	+	0.532588i
$59$	−10.2426	+	10.2426i	−1.33347	+	1.33347i	−0.431220	+	0.902247i	$0.641917\pi$
$59$	−10.2426	+	10.2426i	−1.33347	+	1.33347i	−0.902247	+	0.431220i	$0.858083\pi$
$60$	−17.4305	+	17.4305i	−2.25026	+	2.25026i
$61$	−2.55318	+	6.16392i	−0.326901	+	0.789209i	0.671918	+	0.740626i	$0.265471\pi$
$61$	−2.55318	+	6.16392i	−0.326901	+	0.789209i	−0.998819	+	0.0485836i	$0.984529\pi$
$62$	−2.02027	−	0.836823i	−0.256575	−	0.106277i
$63$	−5.32437	−	12.8542i	−0.670807	−	1.61947i
$64$			13.0490i			1.63113i
$65$	10.4331	−	4.32153i	1.29407	−	0.536020i
$66$	17.0892	+	17.0892i	2.10353	+	2.10353i
$67$	−0.794089			−0.0970135			−0.0485067	−	0.998823i	$-0.515446\pi$
$67$	−0.794089			−0.0970135			−0.0485067	+	0.998823i	$0.515446\pi$
$68$	12.5393	−	2.42238i	1.52061	−	0.293757i
$69$	0.670390			0.0807055
$70$	−24.8969	−	24.8969i	−2.97575	−	2.97575i
$71$	8.04436	−	3.33208i	0.954690	−	0.395446i	0.149699	−	0.988732i	$-0.452170\pi$
$71$	8.04436	−	3.33208i	0.954690	−	0.395446i	0.804992	+	0.593286i	$0.202170\pi$
$72$		−	7.23134i		−	0.852222i
$73$	−0.248595	−	0.600162i	−0.0290959	−	0.0702437i	0.908664	−	0.417529i	$-0.137104\pi$
$73$	−0.248595	−	0.600162i	−0.0290959	−	0.0702437i	−0.937760	+	0.347285i	$0.887104\pi$
$74$	−3.37853	−	1.39943i	−0.392746	−	0.162681i
$75$	−5.30768	+	12.8139i	−0.612879	+	1.47962i
$76$	−17.4990	+	17.4990i	−2.00728	+	2.00728i
$77$	−14.8323	+	14.8323i	−1.69030	+	1.69030i
$78$	−7.25612	+	17.5178i	−0.821594	+	1.98350i
$79$	2.89649	+	1.19977i	0.325881	+	0.134984i	0.539625	−	0.841905i	$-0.318566\pi$
$79$	2.89649	+	1.19977i	0.325881	+	0.134984i	−0.213744	+	0.976890i	$0.568566\pi$
$80$	0.752002	+	1.81549i	0.0840764	+	0.202978i
$81$			9.23788i			1.02643i
$82$	−12.9880	+	5.37981i	−1.43429	+	0.594101i
$83$	8.03657	+	8.03657i	0.882128	+	0.882128i	0.993751	−	0.111623i	$-0.0356049\pi$
$83$	8.03657	+	8.03657i	0.882128	+	0.882128i	−0.111623	+	0.993751i	$0.535605\pi$
$84$	35.9236			3.91958
$85$	11.2558	−	7.43140i	1.22086	−	0.806049i
$86$	−28.8391			−3.10980
$87$	−3.34506	−	3.34506i	−0.358628	−	0.358628i
$88$	−10.0723	+	4.17210i	−1.07371	+	0.444747i
$89$		−	11.4100i		−	1.20946i	−0.796430	−	0.604731i	$-0.793281\pi$
$89$		−	11.4100i		−	1.20946i	0.796430	−	0.604731i	$-0.206719\pi$
$90$	−8.24876	−	19.9143i	−0.869496	−	2.09915i
$91$	−15.2044	−	6.29786i	−1.59385	−	0.660195i
$92$	−0.326637	+	0.788573i	−0.0340543	+	0.0822144i
$93$	1.66613	−	1.66613i	0.172769	−	0.172769i
$94$	1.59647	−	1.59647i	0.164664	−	0.164664i
$95$	−10.0018	+	24.1465i	−1.02617	+	2.47738i
$96$	−14.1864	−	5.87621i	−1.44790	−	0.599739i
$97$	5.32468	+	12.8549i	0.540640	+	1.30522i	0.924272	+	0.381734i	$0.124673\pi$
$97$	5.32468	+	12.8549i	0.540640	+	1.30522i	−0.383633	+	0.923486i	$0.625327\pi$
$98$			35.5074i			3.58679i
$99$	−11.8639	+	4.91419i	−1.19237	+	0.493895i
$100$	−12.4867	−	12.4867i	−1.24867	−	1.24867i
$101$	−16.2260			−1.61454			−0.807272	−	0.590179i	$-0.799057\pi$
$101$	−16.2260			−1.61454			−0.807272	+	0.590179i	$0.799057\pi$
$102$	−4.54064	+	22.1869i	−0.449590	+	2.19683i
$103$	−4.69864			−0.462971			−0.231486	−	0.972838i	$-0.574359\pi$
$103$	−4.69864			−0.462971			−0.231486	+	0.972838i	$0.574359\pi$
$104$	−6.04824	−	6.04824i	−0.593078	−	0.593078i
$105$	35.0514	−	14.5188i	3.42067	−	1.41689i
$106$		−	1.92358i		−	0.186835i
$107$	0.506896	+	1.22375i	0.0490035	+	0.118305i	0.946486	−	0.322746i	$-0.104606\pi$
$107$	0.506896	+	1.22375i	0.0490035	+	0.118305i	−0.897482	+	0.441051i	$0.854606\pi$
$108$	−0.567458	−	0.235049i	−0.0546036	−	0.0226176i
$109$	2.64150	−	6.37715i	0.253010	−	0.610821i	−0.745434	−	0.666579i	$-0.767758\pi$
$109$	2.64150	−	6.37715i	0.253010	−	0.610821i	0.998444	+	0.0557587i	$0.0177578\pi$
$110$	−22.9789	+	22.9789i	−2.19096	+	2.19096i
$111$	2.78629	−	2.78629i	0.264463	−	0.264463i
$112$	1.09591	−	2.64576i	0.103554	−	0.250001i
$113$	6.13569	+	2.54149i	0.577197	+	0.239083i	0.652132	−	0.758106i	$-0.273875\pi$
$113$	6.13569	+	2.54149i	0.577197	+	0.239083i	−0.0749347	+	0.997188i	$0.523875\pi$
$114$	−16.7937	−	40.5436i	−1.57287	−	3.79725i
$115$			0.901440i			0.0840597i
$116$	5.56459	−	2.30493i	0.516659	−	0.214007i
$117$	−7.12404	−	7.12404i	−0.658618	−	0.658618i
$118$	32.7039			3.01064
$119$	−19.2568	−	3.94099i	−1.76527	−	0.361270i
$120$	19.7188			1.80007
$121$	5.91150	+	5.91150i	0.537410	+	0.537410i
$122$	13.9166	−	5.76445i	1.25995	−	0.521889i
$123$		−	15.1480i		−	1.36585i
$124$	1.14805	+	2.77164i	0.103098	+	0.248901i
$125$	−2.11895	−	0.877698i	−0.189525	−	0.0785037i
$126$	−12.0211	+	29.0215i	−1.07093	+	2.58544i
$127$	−6.45009	+	6.45009i	−0.572353	+	0.572353i	−0.932785	−	0.360433i	$-0.882629\pi$
$127$	−6.45009	+	6.45009i	−0.572353	+	0.572353i	0.360433	+	0.932785i	$0.382629\pi$
$128$	11.9062	−	11.9062i	1.05237	−	1.05237i
$129$	11.8919	−	28.7095i	1.04702	−	2.52773i
$130$	−23.5553	−	9.75694i	−2.06594	−	0.855741i
$131$	−0.257006	−	0.620467i	−0.0224547	−	0.0542105i	0.912254	−	0.409624i	$-0.134340\pi$
$131$	−0.257006	−	0.620467i	−0.0224547	−	0.0542105i	−0.934709	+	0.355413i	$0.884340\pi$
$132$		−	33.1561i		−	2.88587i
$133$	35.1893	−	14.5759i	3.05130	−	1.26389i
$134$	1.26774	+	1.26774i	0.109516	+	0.109516i
$135$	−0.648677			−0.0558292
$136$	−8.46293	−	5.72254i	−0.725691	−	0.490703i
$137$	14.0268			1.19839			0.599195	−	0.800603i	$-0.295487\pi$
$137$	14.0268			1.19839			0.599195	+	0.800603i	$0.295487\pi$
$138$	−1.07026	−	1.07026i	−0.0911065	−	0.0911065i
$139$	−14.4211	+	5.97342i	−1.22318	+	0.506659i	−0.898420	−	0.439137i	$-0.855284\pi$
$139$	−14.4211	+	5.97342i	−1.22318	+	0.506659i	−0.324762	+	0.945796i	$0.605284\pi$
$140$			48.3046i			4.08249i
$141$	0.930990	+	2.24761i	0.0784035	+	0.189283i
$142$	−18.1622	−	7.52302i	−1.52414	−	0.631318i
$143$	−5.81269	+	14.0331i	−0.486081	+	1.17350i
$144$	1.23968	−	1.23968i	0.103306	−	0.103306i
$145$	4.49794	−	4.49794i	0.373533	−	0.373533i
$146$	−0.561267	+	1.35502i	−0.0464508	+	0.112142i
$147$	−35.3479	−	14.6416i	−2.91545	−	1.20762i
$148$	1.91991	+	4.63506i	0.157815	+	0.381000i
$149$			22.7590i			1.86449i	0.361833	+	0.932243i	$0.382151\pi$
$149$			22.7590i			1.86449i	−0.361833	+	0.932243i	$0.617849\pi$
$150$	28.9306	−	11.9834i	2.36217	−	0.978444i
$151$	−7.83566	−	7.83566i	−0.637657	−	0.637657i	0.312320	−	0.949977i	$-0.398894\pi$
$151$	−7.83566	−	7.83566i	−0.637657	−	0.637657i	−0.949977	+	0.312320i	$0.898894\pi$
$152$	19.7964			1.60570
$153$	−9.96824	−	6.74041i	−0.805885	−	0.544930i
$154$	47.3588			3.81628
$155$	2.24036	+	2.24036i	0.179950	+	0.179950i
$156$	24.0330	−	9.95480i	1.92418	−	0.797022i
$157$			8.60989i			0.687144i	0.939126	+	0.343572i	$0.111637\pi$
$157$			8.60989i			0.687144i	−0.939126	+	0.343572i	$0.888363\pi$
$158$	−2.70878	−	6.53957i	−0.215499	−	0.520260i
$159$	1.91494	+	0.793193i	0.151864	+	0.0629043i
$160$	7.90145	−	19.0758i	0.624664	−	1.50807i
$161$	0.928918	−	0.928918i	0.0732090	−	0.0732090i
$162$	14.7480	−	14.7480i	1.15871	−	1.15871i
$163$	0.514953	−	1.24321i	0.0403343	−	0.0973755i	−0.902429	−	0.430839i	$-0.858218\pi$
$163$	0.514953	−	1.24321i	0.0403343	−	0.0973755i	0.942763	+	0.333464i	$0.108218\pi$
$164$	17.8185	+	7.38065i	1.39139	+	0.576332i
$165$	−13.4003	−	32.3511i	−1.04321	−	2.51853i
$166$		−	25.6603i		−	1.99163i
$167$	−8.69674	+	3.60231i	−0.672974	+	0.278755i	−0.692886	−	0.721047i	$-0.743661\pi$
$167$	−8.69674	+	3.60231i	−0.672974	+	0.278755i	0.0199123	+	0.999802i	$0.493661\pi$
$168$	−20.3199	−	20.3199i	−1.56771	−	1.56771i
$169$	1.08302			0.0833090
$170$	−29.8336	−	6.10557i	−2.28813	−	0.468276i
$171$	23.3176			1.78314
$172$	27.9766	+	27.9766i	2.13319	+	2.13319i
$173$	−2.79871	+	1.15926i	−0.212782	+	0.0881373i	−0.486529	−	0.873665i	$-0.661737\pi$
$173$	−2.79871	+	1.15926i	−0.212782	+	0.0881373i	0.273746	+	0.961802i	$0.411737\pi$
$174$			10.6806i			0.809694i
$175$	10.4009	+	25.1099i	0.786232	+	1.89813i
$176$	−2.44194	−	1.01148i	−0.184068	−	0.0762434i
$177$	−13.4855	+	32.5570i	−1.01364	+	2.44713i
$178$	−18.2158	+	18.2158i	−1.36533	+	1.36533i
$179$	−3.98506	+	3.98506i	−0.297857	+	0.297857i	−0.840174	−	0.542317i	$-0.817547\pi$
$179$	−3.98506	+	3.98506i	−0.297857	+	0.297857i	0.542317	+	0.840174i	$0.317547\pi$
$180$	−11.3166	+	27.3207i	−0.843491	+	2.03637i
$181$	12.7333	+	5.27430i	0.946458	+	0.392036i	0.801898	−	0.597460i	$-0.203823\pi$
$181$	12.7333	+	5.27430i	0.946458	+	0.392036i	0.144560	+	0.989496i	$0.453823\pi$
$182$	14.2190	+	34.3277i	1.05398	+	2.54454i
$183$			16.2311i			1.19984i
$184$	0.630809	−	0.261290i	0.0465039	−	0.0192625i
$185$	3.74659	+	3.74659i	0.275455	+	0.275455i
$186$	−5.31985			−0.390071
$187$	−3.63738	+	17.7733i	−0.265992	+	1.29972i
$188$	−3.09745			−0.225905
$189$	0.668450	+	0.668450i	0.0486226	+	0.0486226i
$190$	54.5169	−	22.5816i	3.95507	−	1.63824i
$191$			2.77605i			0.200868i	0.994944	+	0.100434i	$0.0320231\pi$
$191$			2.77605i			0.200868i	−0.994944	+	0.100434i	$0.967977\pi$
$192$	12.1485	+	29.3291i	0.876745	+	2.11665i
$193$	−5.11759	−	2.11977i	−0.368372	−	0.152585i	0.190815	−	0.981626i	$-0.438887\pi$
$193$	−5.11759	−	2.11977i	−0.368372	−	0.152585i	−0.559187	+	0.829041i	$0.688887\pi$
$194$	12.0218	−	29.0232i	0.863116	−	2.08375i
$195$	19.4262	−	19.4262i	1.39114	−	1.39114i
$196$	34.4455	−	34.4455i	2.46039	−	2.46039i
$197$	−3.14598	+	7.59508i	−0.224142	+	0.541127i	−0.995445	−	0.0953419i	$-0.969606\pi$
$197$	−3.14598	+	7.59508i	−0.224142	+	0.541127i	0.771302	+	0.636469i	$0.219606\pi$
$198$	26.7858	+	11.0950i	1.90358	+	0.788489i
$199$	2.86605	+	6.91925i	0.203169	+	0.490492i	0.992319	−	0.123708i	$-0.0394786\pi$
$199$	2.86605	+	6.91925i	0.203169	+	0.490492i	−0.789150	+	0.614200i	$0.789479\pi$
$200$			14.1260i			0.998862i
$201$	−1.78480	+	0.739290i	−0.125890	+	0.0521455i
$202$	25.9043	+	25.9043i	1.82262	+	1.82262i
$203$	−9.27009			−0.650633
$204$	25.9282	−	17.1185i	1.81533	−	1.19853i
$205$	20.3688			1.42262
$206$	7.50126	+	7.50126i	0.522637	+	0.522637i
$207$	0.743012	−	0.307766i	0.0516429	−	0.0213912i
$208$		−	2.07371i		−	0.143786i
$209$	−13.4530	−	32.4784i	−0.930562	−	2.24658i
$210$	−79.1374	−	32.7798i	−5.46100	−	2.26202i
$211$	−6.15312	+	14.8550i	−0.423598	+	1.02266i	0.557679	+	0.830057i	$0.311692\pi$
$211$	−6.15312	+	14.8550i	−0.423598	+	1.02266i	−0.981277	+	0.192600i	$0.938308\pi$
$212$	−1.86605	+	1.86605i	−0.128161	+	0.128161i
$213$	14.9784	−	14.9784i	1.02631	−	1.02631i
$214$	1.14445	−	2.76294i	0.0782327	−	0.188870i
$215$	38.6042	+	15.9904i	2.63279	+	1.09054i
$216$	0.188024	+	0.453931i	0.0127934	+	0.0308861i
$217$		−	4.61730i		−	0.313443i
$218$	−14.3980	+	5.96386i	−0.975158	+	0.403924i
$219$	−1.11749	−	1.11749i	−0.0755130	−	0.0755130i
$220$	44.5834			3.00581
$221$	−13.9750	+	2.69974i	−0.940059	+	0.181604i
$222$	−8.89648			−0.597093
$223$	−7.15240	−	7.15240i	−0.478960	−	0.478960i	0.425839	−	0.904799i	$-0.359979\pi$
$223$	−7.15240	−	7.15240i	−0.478960	−	0.478960i	−0.904799	+	0.425839i	$0.859979\pi$
$224$	−27.7996	+	11.5150i	−1.85744	+	0.769375i
$225$			16.6387i			1.10924i
$226$	−5.73805	−	13.8529i	−0.381689	−	0.921479i
$227$	23.3344	+	9.66542i	1.54876	+	0.641516i	0.983091	−	0.183118i	$-0.0586189\pi$
$227$	23.3344	+	9.66542i	1.54876	+	0.641516i	0.565667	+	0.824634i	$0.308619\pi$
$228$	−23.0396	+	55.6224i	−1.52583	+	3.68368i
$229$	3.75589	−	3.75589i	0.248196	−	0.248196i	−0.572034	−	0.820230i	$-0.693845\pi$
$229$	3.75589	−	3.75589i	0.248196	−	0.248196i	0.820230	+	0.572034i	$0.193845\pi$
$230$	1.43912	−	1.43912i	0.0948930	−	0.0948930i
$231$	−19.5285	+	47.1460i	−1.28488	+	3.10198i
$232$	−4.45133	−	1.84380i	−0.292244	−	0.121051i
$233$	0.437309	+	1.05576i	0.0286491	+	0.0691650i	0.937557	−	0.347833i	$-0.113082\pi$
$233$	0.437309	+	1.05576i	0.0286491	+	0.0691650i	−0.908908	+	0.416998i	$0.863082\pi$
$234$			22.7467i			1.48700i
$235$	−3.02225	+	1.25186i	−0.197150	+	0.0816621i
$236$	−31.7258	−	31.7258i	−2.06517	−	2.06517i
$237$	7.62716			0.495437
$238$	24.4513	+	37.0347i	1.58494	+	2.40060i
$239$	6.62451			0.428504			0.214252	−	0.976778i	$-0.431269\pi$
$239$	6.62451			0.428504			0.214252	+	0.976778i	$0.431269\pi$
$240$	3.38041	+	3.38041i	0.218205	+	0.218205i
$241$	−14.0696	+	5.82781i	−0.906301	+	0.375402i	−0.786639	−	0.617413i	$-0.788181\pi$
$241$	−14.0696	+	5.82781i	−0.906301	+	0.375402i	−0.119661	+	0.992815i	$0.538181\pi$
$242$		−	18.8751i		−	1.21334i
$243$	8.37273	+	20.2136i	0.537111	+	1.29670i
$244$	−19.0924	−	7.90834i	−1.22227	−	0.506280i
$245$	19.6878	−	47.5306i	1.25781	−	3.03662i
$246$	−24.1834	+	24.1834i	−1.54188	+	1.54188i
$247$	19.5026	−	19.5026i	1.24092	−	1.24092i
$248$	0.918371	−	2.21714i	0.0583166	−	0.140789i
$249$	25.5450	+	10.5811i	1.61885	+	0.670550i
$250$	1.98163	+	4.78407i	0.125329	+	0.302571i
$251$			2.17596i			0.137345i	0.997639	+	0.0686726i	$0.0218764\pi$
$251$			2.17596i			0.137345i	−0.997639	+	0.0686726i	$0.978124\pi$
$252$	39.8151	−	16.4920i	2.50812	−	1.03890i
$253$	−0.857356	−	0.857356i	−0.0539015	−	0.0539015i
$254$	20.5948			1.29223
$255$	18.3801	−	27.1819i	1.15101	−	1.70220i
$256$	−11.9178			−0.744863
$257$	−6.43395	−	6.43395i	−0.401339	−	0.401339i	0.477366	−	0.878705i	$-0.341592\pi$
$257$	−6.43395	−	6.43395i	−0.401339	−	0.401339i	−0.878705	+	0.477366i	$0.841592\pi$
$258$	−64.8190	+	26.8489i	−4.03546	+	1.67154i
$259$		−	7.72158i		−	0.479796i
$260$	13.3857	+	32.3160i	0.830147	+	2.00415i
$261$	−5.24309	−	2.17176i	−0.324539	−	0.134429i
$262$	−0.580256	+	1.40086i	−0.0358483	+	0.0865455i
$263$	3.04170	−	3.04170i	0.187559	−	0.187559i	−0.607081	−	0.794640i	$-0.707660\pi$
$263$	3.04170	−	3.04170i	0.187559	−	0.187559i	0.794640	+	0.607081i	$0.207660\pi$
$264$	−18.7545	+	18.7545i	−1.15426	+	1.15426i
$265$	−1.06657	+	2.57492i	−0.0655187	+	0.158176i
$266$	−79.4487	−	32.9087i	−4.87131	−	2.01776i
$267$	−10.6226	−	25.6453i	−0.650095	−	1.56947i
$268$		−	2.45965i		−	0.150247i
$269$	22.4713	−	9.30792i	1.37010	−	0.567514i	0.428284	−	0.903644i	$-0.359118\pi$
$269$	22.4713	−	9.30792i	1.37010	−	0.567514i	0.941815	+	0.336130i	$0.109118\pi$
$270$	1.03560	+	1.03560i	0.0630243	+	0.0630243i
$271$	19.3279			1.17409			0.587043	−	0.809556i	$-0.300292\pi$
$271$	19.3279			1.17409			0.587043	+	0.809556i	$0.300292\pi$
$272$	−0.469789	−	2.43183i	−0.0284851	−	0.147451i
$273$	−40.0367			−2.42313
$274$	−22.3934	−	22.3934i	−1.35283	−	1.35283i
$275$	23.1755	−	9.59961i	1.39754	−	0.578879i
$276$			2.07650i			0.124991i
$277$	−0.304341	−	0.734745i	−0.0182861	−	0.0441466i	0.914473	−	0.404647i	$-0.132606\pi$
$277$	−0.304341	−	0.734745i	−0.0182861	−	0.0441466i	−0.932759	+	0.360501i	$0.882606\pi$
$278$	32.5593	+	13.4865i	1.95278	+	0.808866i
$279$	1.08172	−	2.61151i	0.0647610	−	0.156347i
$280$	27.3231	−	27.3231i	1.63287	−	1.63287i
$281$	−12.4462	+	12.4462i	−0.742480	+	0.742480i	−0.973055	−	0.230575i	$-0.925939\pi$
$281$	−12.4462	+	12.4462i	−0.742480	+	0.742480i	0.230575	+	0.973055i	$0.425939\pi$
$282$	2.10195	−	5.07455i	0.125169	−	0.302185i
$283$	−21.6099	−	8.95113i	−1.28458	−	0.532090i	−0.367213	−	0.930137i	$-0.619688\pi$
$283$	−21.6099	−	8.95113i	−1.28458	−	0.532090i	−0.917365	+	0.398047i	$0.869688\pi$
$284$	10.3210	+	24.9170i	0.612436	+	1.47855i
$285$			63.5836i			3.76637i
$286$	31.6832	−	13.1236i	1.87347	−	0.776015i
$287$	−20.9897	−	20.9897i	−1.23898	−	1.23898i
$288$	−18.4209			−1.08546
$289$	−15.7768	+	6.33193i	−0.928046	+	0.372466i
$290$	−14.3617			−0.843346
$291$	23.9356	+	23.9356i	1.40313	+	1.40313i
$292$	1.85897	−	0.770011i	0.108788	−	0.0450615i
$293$			10.1894i			0.595274i	0.954679	+	0.297637i	$0.0961985\pi$
$293$			10.1894i			0.595274i	−0.954679	+	0.297637i	$0.903802\pi$
$294$	33.0571	+	79.8069i	1.92793	+	4.65443i
$295$	−43.7777	−	18.1333i	−2.54884	−	1.05576i
$296$	1.53581	−	3.70777i	0.0892669	−	0.215509i
$297$	0.616954	−	0.616954i	0.0357993	−	0.0357993i
$298$	36.3340	−	36.3340i	2.10477	−	2.10477i
$299$	0.364037	−	0.878862i	0.0210528	−	0.0508259i
$300$	−39.6903	−	16.4403i	−2.29152	−	0.949180i
$301$	−23.3032	−	56.2588i	−1.34317	−	3.24270i
$302$			25.0188i			1.43967i
$303$	−36.4697	+	15.1062i	−2.09513	+	0.867830i
$304$	3.39371	+	3.39371i	0.194643	+	0.194643i
$305$	−21.8251			−1.24970
$306$	5.15315	+	26.6749i	0.294586	+	1.52490i
$307$	−6.57398			−0.375197			−0.187599	−	0.982246i	$-0.560070\pi$
$307$	−6.57398			−0.375197			−0.187599	+	0.982246i	$0.560070\pi$
$308$	−45.9424	−	45.9424i	−2.61781	−	2.61781i
$309$	−10.5607	+	4.37439i	−0.600778	+	0.248850i
$310$		−	7.15334i		−	0.406282i
$311$	−2.82222	−	6.81345i	−0.160034	−	0.386355i	0.823441	−	0.567402i	$-0.192051\pi$
$311$	−2.82222	−	6.81345i	−0.160034	−	0.386355i	−0.983475	+	0.181047i	$0.942051\pi$
$312$	−19.2249	−	7.96322i	−1.08840	−	0.450829i
$313$	−0.754304	+	1.82105i	−0.0426358	+	0.102932i	−0.943763	−	0.330623i	$-0.892741\pi$
$313$	−0.754304	+	1.82105i	−0.0426358	+	0.102932i	0.901127	+	0.433555i	$0.142741\pi$
$314$	13.7455	−	13.7455i	0.775701	−	0.775701i
$315$	32.1831	−	32.1831i	1.81331	−	1.81331i
$316$	−3.71622	+	8.97174i	−0.209053	+	0.504700i
$317$	26.6029	+	11.0193i	1.49417	+	0.618905i	0.972219	−	0.234071i	$-0.0752049\pi$
$317$	26.6029	+	11.0193i	1.49417	+	0.618905i	0.521950	+	0.852976i	$0.325205\pi$
$318$	−1.79083	−	4.32346i	−0.100425	−	0.242447i
$319$			8.55594i			0.479041i
$320$	−39.4374	+	16.3355i	−2.20462	+	0.913183i
$321$	2.27861	+	2.27861i	0.127179	+	0.127179i
$322$	−2.96598			−0.165288
$323$	18.4524	−	27.2888i	1.02672	−	1.51839i
$324$	−28.6139			−1.58966
$325$	13.9164	+	13.9164i	0.771945	+	0.771945i
$326$	−2.80686	+	1.16264i	−0.155457	+	0.0643925i
$327$		−	16.7926i		−	0.928631i
$328$	−5.90406	−	14.2537i	−0.325997	−	0.787027i
$329$	4.40439	+	1.82436i	0.242822	+	0.100580i
$330$	−30.2545	+	73.0409i	−1.66546	+	4.02077i
$331$	−11.6085	+	11.6085i	−0.638063	+	0.638063i	−0.950077	−	0.312014i	$-0.898996\pi$
$331$	−11.6085	+	11.6085i	−0.638063	+	0.638063i	0.312014	+	0.950077i	$0.398996\pi$
$332$	−24.8928	+	24.8928i	−1.36617	+	1.36617i
$333$	1.80898	−	4.36727i	0.0991316	−	0.239325i
$334$	19.6351	+	8.13312i	1.07438	+	0.445025i
$335$	−0.994085	−	2.39993i	−0.0543127	−	0.131122i
$336$		−	6.96691i		−	0.380076i
$337$	−4.23460	+	1.75403i	−0.230673	+	0.0955480i	−0.495026	−	0.868878i	$-0.664842\pi$
$337$	−4.23460	+	1.75403i	−0.230673	+	0.0955480i	0.264353	+	0.964426i	$0.414842\pi$
$338$	−1.72901	−	1.72901i	−0.0940455	−	0.0940455i
$339$	16.1567			0.877513
$340$	23.0184	+	34.8643i	1.24835	+	1.89078i
$341$	−4.26159			−0.230778
$342$	−37.2258	−	37.2258i	−2.01294	−	2.01294i
$343$	−38.4366	+	15.9210i	−2.07538	+	0.859651i
$344$		−	31.6494i		−	1.70642i
$345$	0.839232	+	2.02608i	0.0451827	+	0.109081i
$346$	6.31880	+	2.61733i	0.339701	+	0.140709i
$347$	2.23436	−	5.39422i	0.119947	−	0.289577i	−0.852490	−	0.522743i	$-0.824909\pi$
$347$	2.23436	−	5.39422i	0.119947	−	0.289577i	0.972437	+	0.233166i	$0.0749087\pi$
$348$	10.3612	−	10.3612i	0.555416	−	0.555416i
$349$	5.57588	−	5.57588i	0.298470	−	0.298470i	−0.541944	−	0.840414i	$-0.682312\pi$
$349$	5.57588	−	5.57588i	0.298470	−	0.298470i	0.840414	+	0.541944i	$0.182312\pi$
$350$	23.4826	−	56.6920i	1.25520	−	3.03032i
$351$	0.632430	+	0.261961i	0.0337566	+	0.0139824i
$352$	10.6279	+	25.6580i	0.566467	+	1.36757i
$353$		−	15.0706i		−	0.802129i	−0.916050	−	0.401064i	$-0.868640\pi$
$353$		−	15.0706i		−	0.802129i	0.916050	−	0.401064i	$-0.131360\pi$
$354$	73.5056	−	30.4470i	3.90678	−	1.61824i
$355$	20.1408	+	20.1408i	1.06896	+	1.06896i
$356$	35.3420			1.87312
$357$	−46.9509	+	9.07013i	−2.48490	+	0.480042i
$358$	12.7241			0.672488
$359$	−1.36444	−	1.36444i	−0.0720124	−	0.0720124i	0.670183	−	0.742196i	$-0.266216\pi$
$359$	−1.36444	−	1.36444i	−0.0720124	−	0.0720124i	−0.742196	+	0.670183i	$0.766216\pi$
$360$	21.8549	−	9.05259i	1.15185	−	0.477114i
$361$			44.8336i			2.35967i
$362$	−11.9081	−	28.7486i	−0.625874	−	1.51099i
$363$	18.7903	+	7.78320i	0.986235	+	0.408512i
$364$	19.5073	−	47.0948i	1.02246	−	2.46844i
$365$	1.50263	−	1.50263i	0.0786514	−	0.0786514i
$366$	25.9125	−	25.9125i	1.35447	−	1.35447i
$367$	0.158524	−	0.382711i	0.00827490	−	0.0199774i	−0.919688	−	0.392650i	$-0.871558\pi$
$367$	0.158524	−	0.382711i	0.00827490	−	0.0199774i	0.927963	+	0.372672i	$0.121558\pi$
$368$	0.152933	+	0.0633471i	0.00797221	+	0.00330220i
$369$	−6.95423	−	16.7890i	−0.362023	−	0.874000i
$370$		−	11.9626i		−	0.621908i
$371$	3.75249	−	1.55433i	0.194819	−	0.0806969i
$372$	5.16074	+	5.16074i	0.267572	+	0.267572i
$373$	23.4719			1.21533			0.607664	−	0.794194i	$-0.292107\pi$
$373$	23.4719			1.21533			0.607664	+	0.794194i	$0.292107\pi$
$374$	34.1816	−	22.5677i	1.76749	−	1.16695i
$375$	−5.57970			−0.288135
$376$	1.75205	+	1.75205i	0.0903549	+	0.0903549i
$377$	−6.20172	+	2.56884i	−0.319405	+	0.132302i
$378$		−	2.13432i		−	0.109778i
$379$	−5.96791	−	14.4078i	−0.306551	−	0.740080i	−0.999812	−	0.0193931i	$-0.993827\pi$
$379$	−5.96791	−	14.4078i	−0.306551	−	0.740080i	0.693261	−	0.720687i	$-0.256173\pi$
$380$	−74.7926	−	30.9801i	−3.83678	−	1.58925i
$381$	−8.49231	+	20.5022i	−0.435074	+	1.05036i
$382$	4.43189	−	4.43189i	0.226755	−	0.226755i
$383$	−0.632762	+	0.632762i	−0.0323326	+	0.0323326i	−0.723088	−	0.690756i	$-0.757278\pi$
$383$	−0.632762	+	0.632762i	−0.0323326	+	0.0323326i	0.690756	+	0.723088i	$0.257278\pi$
$384$	15.6760	−	37.8451i	0.799960	−	1.93127i
$385$	−63.3949	−	26.2590i	−3.23090	−	1.33828i
$386$	4.78593	+	11.5542i	0.243597	+	0.588096i
$387$		−	37.2789i		−	1.89499i
$388$	−39.8175	+	16.4929i	−2.02143	+	0.837302i
$389$	18.2657	+	18.2657i	0.926109	+	0.926109i	0.997452	−	0.0713426i	$-0.0227284\pi$
$389$	18.2657	+	18.2657i	0.926109	+	0.926109i	−0.0713426	+	0.997452i	$0.522728\pi$
$390$	−62.0268			−3.14085
$391$	0.227802	−	1.11311i	0.0115204	−	0.0562923i
$392$	−38.9676			−1.96816
$393$	−1.15530	−	1.15530i	−0.0582770	−	0.0582770i
$394$	17.1478	−	7.10286i	0.863894	−	0.357837i
$395$			10.2559i			0.516028i
$396$	−15.2215	−	36.7478i	−0.764907	−	1.84665i
$397$	13.4420	+	5.56785i	0.674634	+	0.279442i	0.693582	−	0.720378i	$-0.256032\pi$
$397$	13.4420	+	5.56785i	0.674634	+	0.279442i	−0.0189479	+	0.999820i	$0.506032\pi$
$398$	6.47082	−	15.6219i	0.324353	−	0.783058i
$399$	65.5217	−	65.5217i	3.28019	−	3.28019i
$400$	−2.42164	+	2.42164i	−0.121082	+	0.121082i
$401$	3.38106	−	8.16259i	0.168842	−	0.407620i	−0.816698	−	0.577066i	$-0.804198\pi$
$401$	3.38106	−	8.16259i	0.168842	−	0.407620i	0.985540	+	0.169445i	$0.0541976\pi$
$402$	4.02964	+	1.66913i	0.200980	+	0.0832488i
$403$	−1.27950	−	3.08899i	−0.0637365	−	0.153873i
$404$		−	50.2591i		−	2.50048i
$405$	−27.9192	+	11.5645i	−1.38731	+	0.574645i
$406$	14.7994	+	14.7994i	0.734484	+	0.734484i
$407$	−7.12673			−0.353259
$408$	−24.3490	−	4.98312i	−1.20545	−	0.246701i
$409$	27.1331			1.34165			0.670823	−	0.741618i	$-0.265941\pi$
$409$	27.1331			1.34165			0.670823	+	0.741618i	$0.265941\pi$
$410$	−32.5182	−	32.5182i	−1.60596	−	1.60596i
$411$	31.5268	−	13.0588i	1.55510	−	0.644144i
$412$		−	14.5538i		−	0.717015i
$413$	26.4261	+	63.7982i	1.30034	+	3.13931i
$414$	−1.67754	−	0.694859i	−0.0824465	−	0.0341504i
$415$	−14.2279	+	34.3491i	−0.698418	+	1.68613i
$416$	−15.4071	+	15.4071i	−0.755395	+	0.755395i
$417$	−26.8518	+	26.8518i	−1.31494	+	1.31494i
$418$	−30.3735	+	73.3281i	−1.48562	+	3.58660i
$419$	−12.4781	−	5.16861i	−0.609597	−	0.252503i	0.0564592	−	0.998405i	$-0.482019\pi$
$419$	−12.4781	−	5.16861i	−0.609597	−	0.252503i	−0.666056	+	0.745902i	$0.732019\pi$
$420$	44.9711	+	108.570i	2.19437	+	5.29767i
$421$		−	15.4472i		−	0.752849i	−0.926447	−	0.376424i	$-0.877153\pi$
$421$		−	15.4472i		−	0.752849i	0.926447	−	0.376424i	$-0.122847\pi$
$422$	33.5388	−	13.8922i	1.63264	−	0.676263i
$423$	2.06368	+	2.06368i	0.100340	+	0.100340i
$424$	2.11103			0.102521
$425$	19.4724	+	13.1670i	0.944552	+	0.638695i
$426$	−47.8254			−2.31715
$427$	22.4904	+	22.4904i	1.08839	+	1.08839i
$428$	−3.79052	+	1.57008i	−0.183222	+	0.0758928i
$429$			36.9524i			1.78408i
$430$	−36.1024	−	87.1589i	−1.74101	−	4.20317i
$431$	10.5250	+	4.35960i	0.506972	+	0.209995i	0.621484	−	0.783427i	$-0.286530\pi$
$431$	10.5250	+	4.35960i	0.506972	+	0.209995i	−0.114511	+	0.993422i	$0.536530\pi$
$432$	−0.0455846	+	0.110051i	−0.00219319	+	0.00529483i
$433$	−22.2142	+	22.2142i	−1.06755	+	1.06755i	−0.0700010	+	0.997547i	$0.522300\pi$
$433$	−22.2142	+	22.2142i	−1.06755	+	1.06755i	−0.997547	+	0.0700010i	$0.977700\pi$
$434$	−7.37139	+	7.37139i	−0.353838	+	0.353838i
$435$	5.92207	−	14.2971i	0.283941	−	0.685495i
$436$	19.7529	+	8.18192i	0.945993	+	0.391843i
$437$	0.842533	+	2.03405i	0.0403038	+	0.0973020i
$438$			3.56809i			0.170490i
$439$	−16.7419	+	6.93471i	−0.799046	+	0.330976i	−0.744574	−	0.667539i	$-0.767348\pi$
$439$	−16.7419	+	6.93471i	−0.799046	+	0.330976i	−0.0544719	+	0.998515i	$0.517348\pi$
$440$	−25.2182	−	25.2182i	−1.20223	−	1.20223i
$441$	−45.8988			−2.18566
$442$	26.6207	+	18.0006i	1.26622	+	0.856202i
$443$	−37.6522			−1.78891			−0.894456	−	0.447157i	$-0.852437\pi$
$443$	−37.6522			−1.78891			−0.894456	+	0.447157i	$0.852437\pi$
$444$	8.63040	+	8.63040i	0.409581	+	0.409581i
$445$	34.4840	−	14.2837i	1.63470	−	0.677113i
$446$			22.8372i			1.08137i
$447$	21.1884	+	51.1532i	1.00218	+	2.41946i
$448$	57.4730	+	23.8061i	2.71535	+	1.12473i
$449$	2.11715	−	5.11124i	0.0999143	−	0.241214i	−0.866016	−	0.500016i	$-0.833328\pi$
$449$	2.11715	−	5.11124i	0.0999143	−	0.241214i	0.965931	+	0.258801i	$0.0833275\pi$
$450$	26.5632	−	26.5632i	1.25220	−	1.25220i
$451$	−19.3727	+	19.3727i	−0.912224	+	0.912224i
$452$	−7.87212	+	19.0050i	−0.370274	+	0.893919i
$453$	−24.9064	−	10.3166i	−1.17021	−	0.484715i
$454$	−21.8221	−	52.6833i	−1.02416	−	2.47255i
$455$		−	53.8354i		−	2.52384i
$456$	44.4945	−	18.4302i	2.08365	−	0.863074i
$457$	−16.3818	−	16.3818i	−0.766309	−	0.766309i	0.211146	−	0.977455i	$-0.432280\pi$
$457$	−16.3818	−	16.3818i	−0.766309	−	0.766309i	−0.977455	+	0.211146i	$0.932280\pi$
$458$	−11.9924			−0.560366
$459$	0.800993	+	0.163926i	0.0373872	+	0.00765143i
$460$	−2.79216			−0.130185
$461$	−8.78559	−	8.78559i	−0.409186	−	0.409186i	0.472269	−	0.881455i	$-0.343435\pi$
$461$	−8.78559	−	8.78559i	−0.409186	−	0.409186i	−0.881455	+	0.472269i	$0.843435\pi$
$462$	106.444	−	44.0906i	4.95223	−	2.05128i
$463$		−	18.6620i		−	0.867296i	−0.901082	−	0.433648i	$-0.857226\pi$
$463$		−	18.6620i		−	0.867296i	0.901082	−	0.433648i	$-0.142774\pi$
$464$	−0.447011	−	1.07918i	−0.0207520	−	0.0500997i
$465$	7.12120	+	2.94970i	0.330238	+	0.136789i
$466$	0.987336	−	2.38364i	0.0457375	−	0.110420i
$467$	−20.9367	+	20.9367i	−0.968836	+	0.968836i	−0.999529	−	0.0306930i	$-0.990229\pi$
$467$	−20.9367	+	20.9367i	−0.968836	+	0.968836i	0.0306930	+	0.999529i	$0.490229\pi$
$468$	22.0664	−	22.0664i	1.02002	−	1.02002i
$469$	−1.44870	+	3.49748i	−0.0668949	+	0.161498i
$470$	6.82349	+	2.82638i	0.314744	+	0.130371i
$471$	8.01573	+	19.3517i	0.369345	+	0.891678i
$472$			35.8909i			1.65201i
$473$	−51.9248	+	21.5079i	−2.38750	+	0.988936i
$474$	−12.1765	−	12.1765i	−0.559287	−	0.559287i
$475$	−45.5496			−2.08996
$476$	12.2070	−	59.6471i	0.559507	−	2.73392i
$477$	2.48652			0.113850
$478$	−10.5758	−	10.5758i	−0.483728	−	0.483728i
$479$	16.6920	−	6.91405i	0.762677	−	0.315911i	0.0327747	−	0.999463i	$-0.489566\pi$
$479$	16.6920	−	6.91405i	0.762677	−	0.315911i	0.729902	+	0.683552i	$0.239566\pi$
$480$		−	50.2311i		−	2.29272i
$481$	−2.13973	−	5.16577i	−0.0975633	−	0.235539i
$482$	31.7656	+	13.1577i	1.44688	+	0.599319i
$483$	1.22303	−	2.95266i	0.0556498	−	0.134351i
$484$	−18.3106	+	18.3106i	−0.832299	+	0.832299i
$485$	−32.1850	+	32.1850i	−1.46145	+	1.46145i
$486$	18.9035	−	45.6372i	0.857482	−	2.07015i
$487$	−17.6253	−	7.30062i	−0.798677	−	0.330823i	−0.0542504	−	0.998527i	$-0.517277\pi$
$487$	−17.6253	−	7.30062i	−0.798677	−	0.330823i	−0.744426	+	0.667705i	$0.767277\pi$
$488$	6.32619	+	15.2728i	0.286373	+	0.691366i
$489$		−	3.27366i		−	0.148040i
$490$	−107.312	+	44.4502i	−4.84787	+	2.00805i
$491$	13.8843	+	13.8843i	0.626589	+	0.626589i	0.947208	−	0.320619i	$-0.103891\pi$
$491$	13.8843	+	13.8843i	0.626589	+	0.626589i	−0.320619	+	0.947208i	$0.603891\pi$
$492$	46.9203			2.11533
$493$	−6.69077	+	4.41743i	−0.301337	+	0.198951i
$494$	−62.2708			−2.80170
$495$	−29.7038	−	29.7038i	−1.33509	−	1.33509i
$496$	0.537524	−	0.222650i	0.0241355	−	0.00999727i
$497$		−	41.5094i		−	1.86195i
$498$	−23.8895	−	57.6744i	−1.07051	−	2.58445i
$499$	25.8062	+	10.6893i	1.15524	+	0.478517i	0.876288	−	0.481787i	$-0.160012\pi$
$499$	25.8062	+	10.6893i	1.15524	+	0.478517i	0.278955	+	0.960304i	$0.410012\pi$
$500$	2.71862	−	6.56334i	0.121581	−	0.293521i
$501$	−16.1932	+	16.1932i	−0.723457	+	0.723457i
$502$	3.47386	−	3.47386i	0.155046	−	0.155046i
$503$	12.3379	−	29.7864i	0.550121	−	1.32811i	−0.367267	−	0.930116i	$-0.619706\pi$
$503$	12.3379	−	29.7864i	0.550121	−	1.32811i	0.917388	−	0.397994i	$-0.130294\pi$
$504$	−31.8496	−	13.1925i	−1.41869	−	0.587643i
$505$	−20.3126	−	49.0389i	−0.903898	−	2.18220i
$506$			2.73749i			0.121696i
$507$	2.43420	−	1.00828i	0.108107	−	0.0447792i
$508$	−19.9788	−	19.9788i	−0.886416	−	0.886416i
$509$	10.9617			0.485870			0.242935	−	0.970043i	$-0.421890\pi$
$509$	10.9617			0.485870			0.242935	+	0.970043i	$0.421890\pi$
$510$	−72.7385	+	14.0519i	−3.22092	+	0.622228i
$511$	−3.09687			−0.136998
$512$	−4.78598	−	4.78598i	−0.211512	−	0.211512i
$513$	−1.46371	+	0.606287i	−0.0646242	+	0.0267682i
$514$			20.5433i			0.906124i
$515$	−5.88202	−	14.2005i	−0.259193	−	0.625747i
$516$	88.9263	+	36.8345i	3.91476	+	1.62155i
$517$	1.68381	−	4.06508i	0.0740540	−	0.178782i
$518$	−12.3273	+	12.3273i	−0.541630	+	0.541630i
$519$	−5.21115	+	5.21115i	−0.228744	+	0.228744i
$520$	10.7077	−	25.8508i	0.469566	−	1.13363i
$521$	3.30254	+	1.36796i	0.144687	+	0.0599313i	0.453852	−	0.891077i	$-0.350050\pi$
$521$	3.30254	+	1.36796i	0.144687	+	0.0599313i	−0.309165	+	0.951008i	$0.600050\pi$
$522$	4.90330	+	11.8376i	0.214611	+	0.518118i
$523$		−	16.4820i		−	0.720706i	−0.932816	−	0.360353i	$-0.882656\pi$
$523$		−	16.4820i		−	0.720706i	0.932816	−	0.360353i	$-0.117344\pi$
$524$	1.92186	−	0.796062i	0.0839570	−	0.0347761i
$525$	46.7542	+	46.7542i	2.04052	+	2.04052i
$526$	−9.71197			−0.423462
$527$	−2.20026	−	3.33258i	−0.0958448	−	0.145169i
$528$	−6.43020			−0.279838
$529$	−16.2098	−	16.2098i	−0.704772	−	0.704772i
$530$	5.81354	−	2.40805i	0.252524	−	0.104599i
$531$			42.2748i			1.83457i
$532$	45.1480	+	108.997i	1.95741	+	4.72562i
$533$	−19.8586	−	8.22572i	−0.860173	−	0.356295i
$534$	−23.9833	+	57.9008i	−1.03786	+	2.50561i
$535$	−3.06393	+	3.06393i	−0.132465	+	0.132465i
$536$	−1.39128	+	1.39128i	−0.0600942	+	0.0600942i
$537$	−5.24680	+	12.6669i	−0.226416	+	0.546617i
$538$	−50.7346	−	21.0150i	−2.18733	−	0.906020i
$539$	26.4811	+	63.9311i	1.14062	+	2.75371i
$540$		−	2.00924i		−	0.0864641i
$541$	−15.6769	+	6.49360i	−0.674005	+	0.279182i	−0.693318	−	0.720632i	$-0.743852\pi$
$541$	−15.6769	+	6.49360i	−0.674005	+	0.279182i	0.0193136	+	0.999813i	$0.493852\pi$
$542$	−30.8564	−	30.8564i	−1.32540	−	1.32540i
$543$	33.5298			1.43890
$544$	−14.5774	+	21.5582i	−0.625001	+	0.924301i
$545$	22.5801			0.967226
$546$	63.9176	+	63.9176i	2.73542	+	2.73542i
$547$	−14.2996	+	5.92311i	−0.611409	+	0.253254i	−0.666831	−	0.745209i	$-0.732350\pi$
$547$	−14.2996	+	5.92311i	−0.611409	+	0.253254i	0.0554219	+	0.998463i	$0.482350\pi$
$548$			43.4473i			1.85598i
$549$	7.45143	+	17.9893i	0.318019	+	0.767767i
$550$	−52.3246	−	21.6736i	−2.23113	−	0.924164i
$551$	5.94536	−	14.3534i	0.253281	−	0.611474i
$552$	1.17455	−	1.17455i	0.0499924	−	0.0499924i
$553$	10.5685	−	10.5685i	0.449417	−	0.449417i
$554$	−0.687128	+	1.65887i	−0.0291933	+	0.0704788i
$555$	11.9089	+	4.93283i	0.505505	+	0.209387i
$556$	−18.5023	−	44.6686i	−0.784674	−	1.89437i
$557$		−	31.2752i		−	1.32517i	−0.748985	−	0.662587i	$-0.769459\pi$
$557$		−	31.2752i		−	1.32517i	0.748985	−	0.662587i	$-0.230541\pi$
$558$	−5.89614	+	2.44226i	−0.249603	+	0.103389i
$559$	−31.1798	−	31.1798i	−1.31877	−	1.31877i
$560$	9.36805			0.395873
$561$	8.37139	+	43.3339i	0.353440	+	1.82956i
$562$	39.7401			1.67634
$563$	−4.45770	−	4.45770i	−0.187870	−	0.187870i	0.606905	−	0.794774i	$-0.292411\pi$
$563$	−4.45770	−	4.45770i	−0.187870	−	0.187870i	−0.794774	+	0.606905i	$0.792411\pi$
$564$	−6.96185	+	2.88369i	−0.293147	+	0.121425i
$565$			21.7251i			0.913984i
$566$	20.2094	+	48.7899i	0.849467	+	2.05079i
$567$	40.6872	+	16.8532i	1.70870	+	0.707768i
$568$	8.25613	−	19.9321i	0.346420	−	0.836331i
$569$	22.8014	−	22.8014i	0.955883	−	0.955883i	−0.0431837	−	0.999067i	$-0.513750\pi$
$569$	22.8014	−	22.8014i	0.955883	−	0.955883i	0.999067	+	0.0431837i	$0.0137501\pi$
$570$	101.509	−	101.509i	4.25176	−	4.25176i
$571$	5.85804	−	14.1426i	0.245151	−	0.591848i	−0.752628	−	0.658445i	$-0.771214\pi$
$571$	5.85804	−	14.1426i	0.245151	−	0.591848i	0.997780	+	0.0665975i	$0.0212143\pi$
$572$	−43.4667	−	18.0045i	−1.81743	−	0.752806i
$573$	2.58447	+	6.23947i	0.107968	+	0.260658i
$574$			67.0189i			2.79731i
$575$	−1.45143	+	0.601204i	−0.0605290	+	0.0250719i
$576$	26.9291	+	26.9291i	1.12205	+	1.12205i
$577$	7.48328			0.311533			0.155767	−	0.987794i	$-0.450215\pi$
$577$	7.48328			0.311533			0.155767	+	0.987794i	$0.450215\pi$
$578$	35.2959	+	15.0784i	1.46812	+	0.627180i
$579$	−13.4758			−0.560036
$580$	13.9321	+	13.9321i	0.578500	+	0.578500i
$581$	50.0577	−	20.7346i	2.07674	−	0.860215i
$582$		−	76.4251i		−	3.16792i
$583$	−1.43459	−	3.46341i	−0.0594146	−	0.143440i
$584$	−1.48706	−	0.615961i	−0.0615351	−	0.0254887i
$585$	12.6123	−	30.4489i	0.521456	−	1.25891i
$586$	16.2672	−	16.2672i	0.671991	−	0.671991i
$587$	18.2079	−	18.2079i	0.751522	−	0.751522i	−0.223242	−	0.974763i	$-0.571664\pi$
$587$	18.2079	−	18.2079i	0.751522	−	0.751522i	0.974763	+	0.223242i	$0.0716639\pi$
$588$	45.3516	−	109.488i	1.87027	−	4.51522i
$589$	7.14921	+	2.96130i	0.294578	+	0.122018i
$590$	40.9406	+	98.8393i	1.68550	+	4.06915i
$591$			19.9996i			0.822676i
$592$	0.898910	−	0.372341i	0.0369450	−	0.0153031i
$593$	7.30577	+	7.30577i	0.300012	+	0.300012i	0.841018	−	0.541006i	$-0.181957\pi$
$593$	7.30577	+	7.30577i	0.300012	+	0.300012i	−0.541006	+	0.841018i	$0.681957\pi$
$594$	−1.96990			−0.0808260
$595$	−12.1961	−	63.1325i	−0.499993	−	2.58818i
$596$	−70.4947			−2.88757
$597$	12.8835	+	12.8835i	0.527287	+	0.527287i
$598$	−1.98425	+	0.821905i	−0.0811422	+	0.0336102i
$599$			30.7842i			1.25781i	0.777482	+	0.628905i	$0.216496\pi$
$599$			30.7842i			1.25781i	−0.777482	+	0.628905i	$0.783504\pi$
$600$	13.1512	+	31.7498i	0.536896	+	1.29618i
$601$	−25.8153	−	10.6930i	−1.05303	−	0.436178i	−0.212055	−	0.977258i	$-0.568016\pi$
$601$	−25.8153	−	10.6930i	−1.05303	−	0.436178i	−0.840971	+	0.541080i	$0.818016\pi$
$602$	−52.6128	+	127.019i	−2.14434	+	5.17689i
$603$	−1.63875	+	1.63875i	−0.0667351	+	0.0667351i
$604$	24.2706	−	24.2706i	0.987555	−	0.987555i
$605$	−10.4657	+	25.2664i	−0.425490	+	1.02722i
$606$	82.3395	+	34.1061i	3.34481	+	1.38547i
$607$	9.86157	+	23.8079i	0.400269	+	0.966335i	0.987600	+	0.156988i	$0.0501785\pi$
$607$	9.86157	+	23.8079i	0.400269	+	0.966335i	−0.587332	+	0.809346i	$0.699822\pi$
$608$		−	50.4286i		−	2.04515i
$609$	−20.8355	+	8.63036i	−0.844298	+	0.349720i
$610$	34.8432	+	34.8432i	1.41076	+	1.41076i
$611$	3.45210			0.139657
$612$	20.8781	−	30.8761i	0.843946	−	1.24809i
$613$	46.7463			1.88806			0.944032	−	0.329854i	$-0.106999\pi$
$613$	46.7463			1.88806			0.944032	+	0.329854i	$0.106999\pi$
$614$	10.4952	+	10.4952i	0.423551	+	0.423551i
$615$	45.7811	−	18.9632i	1.84607	−	0.764668i
$616$			51.9738i			2.09409i
$617$	1.66399	+	4.01722i	0.0669896	+	0.161727i	0.953829	−	0.300351i	$-0.0971039\pi$
$617$	1.66399	+	4.01722i	0.0669896	+	0.161727i	−0.886839	+	0.462078i	$0.847104\pi$
$618$	23.8435	+	9.87630i	0.959126	+	0.397283i
$619$	−11.2457	+	27.1496i	−0.452004	+	1.09123i	0.519555	+	0.854437i	$0.326098\pi$
$619$	−11.2457	+	27.1496i	−0.452004	+	1.09123i	−0.971559	+	0.236797i	$0.923902\pi$
$620$	−6.93939	+	6.93939i	−0.278693	+	0.278693i
$621$	−0.0386386	+	0.0386386i	−0.00155051	+	0.00155051i
$622$	−6.37189	+	15.3831i	−0.255489	+	0.616806i
$623$	−50.2542	−	20.8160i	−2.01339	−	0.833975i
$624$	−1.93060	−	4.66089i	−0.0772860	−	0.186585i
$625$			21.0028i			0.840114i
$626$	4.11148	−	1.70303i	0.164328	−	0.0680668i
$627$	−60.4741	−	60.4741i	−2.41510	−	2.41510i
$628$	−26.6687			−1.06420
$629$	−3.67953	−	5.57312i	−0.146712	−	0.222215i
$630$	−102.759			−4.09401
$631$	14.4566	+	14.4566i	0.575509	+	0.575509i	0.933663	−	0.358153i	$-0.116594\pi$
$631$	14.4566	+	14.4566i	0.575509	+	0.575509i	−0.358153	+	0.933663i	$0.616594\pi$
$632$	7.17684	−	2.97274i	0.285479	−	0.118249i
$633$			39.1166i			1.55475i
$634$	−24.8788	−	60.0628i	−0.988065	−	2.38540i
$635$	−27.5683	−	11.4192i	−1.09402	−	0.453156i
$636$	−2.45688	+	5.93142i	−0.0974215	+	0.235196i
$637$	−38.3894	+	38.3894i	−1.52104	+	1.52104i
$638$	13.6593	−	13.6593i	0.540778	−	0.540778i
$639$	9.72466	−	23.4774i	0.384701	−	0.928752i
$640$	50.8884	+	21.0787i	2.01154	+	0.833207i
$641$	−12.3538	−	29.8248i	−0.487947	−	1.17801i	−0.955751	−	0.294175i	$-0.904955\pi$
$641$	−12.3538	−	29.8248i	−0.487947	−	1.17801i	0.467805	−	0.883832i	$-0.345045\pi$
$642$		−	7.27547i		−	0.287140i
$643$	7.08933	−	2.93650i	0.279576	−	0.115804i	−0.238490	−	0.971145i	$-0.576652\pi$
$643$	7.08933	−	2.93650i	0.279576	−	0.115804i	0.518066	+	0.855341i	$0.326652\pi$
$644$	2.87728	+	2.87728i	0.113381	+	0.113381i
$645$	101.654			4.00263
$646$	−73.0246	+	14.1071i	−2.87312	+	0.555038i
$647$	0.876657			0.0344649			0.0172325	−	0.999852i	$-0.494514\pi$
$647$	0.876657			0.0344649			0.0172325	+	0.999852i	$0.494514\pi$
$648$	16.1852	+	16.1852i	0.635815	+	0.635815i
$649$	58.8834	−	24.3903i	2.31137	−	0.957403i
$650$		−	44.4344i		−	1.74286i
$651$	−4.29866	−	10.3779i	−0.168478	−	0.406741i
$652$	3.85077	+	1.59504i	0.150808	+	0.0624666i
$653$	−9.12492	+	22.0295i	−0.357086	+	0.862081i	0.638622	+	0.769521i	$0.279505\pi$
$653$	−9.12492	+	22.0295i	−0.357086	+	0.862081i	−0.995707	+	0.0925599i	$0.970495\pi$
$654$	−26.8089	+	26.8089i	−1.04831	+	1.04831i
$655$	1.55347	−	1.55347i	0.0606991	−	0.0606991i
$656$	1.43138	−	3.45566i	0.0558860	−	0.134921i
$657$	−1.75157	−	0.725523i	−0.0683352	−	0.0283054i
$658$	−4.11895	−	9.94402i	−0.160573	−	0.387658i
$659$			30.9151i			1.20428i	0.798390	+	0.602141i	$0.205686\pi$
$659$			30.9151i			1.20428i	−0.798390	+	0.602141i	$0.794314\pi$
$660$	100.206	−	41.5067i	3.90051	−	1.61565i
$661$	0.348703	+	0.348703i	0.0135630	+	0.0135630i	0.713856	−	0.700293i	$-0.246947\pi$
$661$	0.348703	+	0.348703i	0.0135630	+	0.0135630i	−0.700293	+	0.713856i	$0.746947\pi$
$662$	37.0654			1.44059
$663$	−28.8969	+	19.0785i	−1.12226	+	0.740948i
$664$	28.1609			1.09285
$665$	88.1038	+	88.1038i	3.41652	+	3.41652i
$666$	−9.86021	+	4.08423i	−0.382076	+	0.158261i
$667$		−	0.535841i		−	0.0207478i
$668$	−11.1580	−	26.9377i	−0.431715	−	1.04225i
$669$	−22.7346	−	9.41698i	−0.878970	−	0.364081i
$670$	−2.24440	+	5.41846i	−0.0867087	+	0.209333i
$671$	20.7578	−	20.7578i	0.801345	−	0.801345i
$672$	−51.7622	+	51.7622i	−1.99677	+	1.99677i
$673$	4.34446	−	10.4885i	0.167467	−	0.404301i	−0.817759	−	0.575561i	$-0.804784\pi$
$673$	4.34446	−	10.4885i	0.167467	−	0.404301i	0.985226	+	0.171260i	$0.0547838\pi$
$674$	9.56068	+	3.96016i	0.368263	+	0.152540i
$675$	−0.432627	−	1.04445i	−0.0166518	−	0.0402011i
$676$			3.35459i			0.129023i
$677$	11.8616	−	4.91323i	0.455878	−	0.188831i	−0.142915	−	0.989735i	$-0.545647\pi$
$677$	11.8616	−	4.91323i	0.455878	−	0.188831i	0.598792	+	0.800904i	$0.295647\pi$
$678$	−25.7938	−	25.7938i	−0.990604	−	0.990604i
$679$	66.3322			2.54560
$680$	6.70054	−	32.7409i	0.256954	−	1.25555i
$681$	61.4450			2.35458
$682$	6.80351	+	6.80351i	0.260520	+	0.260520i
$683$	−12.8934	+	5.34062i	−0.493353	+	0.204353i	−0.615467	−	0.788163i	$-0.711033\pi$
$683$	−12.8934	+	5.34062i	−0.493353	+	0.204353i	0.122114	+	0.992516i	$0.461033\pi$
$684$			72.2249i			2.76159i
$685$	17.5595	+	42.3924i	0.670915	+	1.61973i
$686$	86.7804	+	35.9456i	3.31329	+	1.37241i
$687$	4.94508	−	11.9385i	0.188667	−	0.455481i
$688$	5.42569	−	5.42569i	0.206852	−	0.206852i
$689$	2.07971	−	2.07971i	0.0792305	−	0.0792305i
$690$	1.89478	−	4.57440i	0.0721330	−	0.174144i
$691$	−4.05457	−	1.67946i	−0.154243	−	0.0638895i	0.304226	−	0.952600i	$-0.401602\pi$
$691$	−4.05457	−	1.67946i	−0.154243	−	0.0638895i	−0.458469	+	0.888710i	$0.651602\pi$
$692$	−3.59076	−	8.66887i	−0.136500	−	0.329541i
$693$			61.2185i			2.32550i
$694$	−12.1788	+	5.04463i	−0.462301	+	0.191492i
$695$	−36.1063	−	36.1063i	−1.36959	−	1.36959i
$696$	−11.7214			−0.444299
$697$	−25.1516	−	5.14737i	−0.952685	−	0.194971i
$698$	−17.8035			−0.673871
$699$	1.96580	+	1.96580i	0.0743534	+	0.0743534i
$700$	−77.7767	+	32.2162i	−2.93968	+	1.21766i
$701$		−	26.4310i		−	0.998286i	−0.866520	−	0.499143i	$-0.833648\pi$
$701$		−	26.4310i		−	0.998286i	0.866520	−	0.499143i	$-0.166352\pi$
$702$	−0.591443	−	1.42787i	−0.0223226	−	0.0538915i
$703$	11.9557	+	4.95223i	0.450919	+	0.186777i
$704$	21.9721	−	53.0454i	0.828106	−	1.99923i
$705$	−5.62736	+	5.62736i	−0.211939	+	0.211939i
$706$	−24.0598	+	24.0598i	−0.905504	+	0.905504i
$707$	−29.6020	+	71.4655i	−1.11330	+	2.68774i
$708$	−100.844	−	41.7708i	−3.78993	−	1.56984i
$709$	17.7967	+	42.9651i	0.668370	+	1.61359i	0.784337	+	0.620335i	$0.213003\pi$
$709$	17.7967	+	42.9651i	0.668370	+	1.61359i	−0.115966	+	0.993253i	$0.536997\pi$
$710$		−	64.3083i		−	2.41345i
$711$	8.45339	−	3.50151i	0.317027	−	0.131317i
$712$	−19.9909	−	19.9909i	−0.749191	−	0.749191i
$713$	0.266895			0.00999529
$714$	89.4360	+	60.4756i	3.34706	+	2.26324i
$715$	−49.6880			−1.85823
$716$	−12.3435	−	12.3435i	−0.461299	−	0.461299i
$717$	14.8893	−	6.16735i	0.556051	−	0.230324i
$718$			4.35658i			0.162586i
$719$	−11.8550	−	28.6205i	−0.442116	−	1.06736i	−0.975205	−	0.221304i	$-0.928969\pi$
$719$	−11.8550	−	28.6205i	−0.442116	−	1.06736i	0.533089	−	0.846059i	$-0.321031\pi$
$720$	5.29850	+	2.19471i	0.197463	+	0.0817920i
$721$	−8.57200	+	20.6946i	−0.319238	+	0.770709i
$722$	71.5757	−	71.5757i	2.66377	−	2.66377i
$723$	−26.1973	+	26.1973i	−0.974287	+	0.974287i
$724$	−16.3369	+	39.4407i	−0.607155	+	1.46580i
$725$	10.2421	+	4.24242i	0.380382	+	0.157559i
$726$	−17.5725	−	42.4239i	−0.652178	−	1.57450i
$727$			13.3081i			0.493570i	0.969070	+	0.246785i	$0.0793741\pi$
$727$			13.3081i			0.493570i	−0.969070	+	0.246785i	$0.920626\pi$
$728$	−37.6729	+	15.6046i	−1.39625	+	0.578346i
$729$	18.0407	+	18.0407i	0.668175	+	0.668175i
$730$	−4.79782			−0.177575
$731$	−43.6280	−	29.5008i	−1.61364	−	1.09112i
$732$	−50.2749			−1.85821
$733$	6.97875	+	6.97875i	0.257766	+	0.257766i	0.824145	−	0.566379i	$-0.191656\pi$
$733$	6.97875	+	6.97875i	0.257766	+	0.257766i	−0.566379	+	0.824145i	$0.691656\pi$
$734$	−0.864068	+	0.357909i	−0.0318933	+	0.0132106i
$735$		−	125.159i		−	4.61657i
$736$	−0.665602	−	1.60690i	−0.0245344	−	0.0592313i
$737$	3.22804	+	1.33710i	0.118906	+	0.0492526i
$738$	−15.7009	+	37.9054i	−0.577959	+	1.39532i
$739$	−29.7219	+	29.7219i	−1.09334	+	1.09334i	−0.0981686	+	0.995170i	$0.531298\pi$
$739$	−29.7219	+	29.7219i	−1.09334	+	1.09334i	−0.995170	+	0.0981686i	$0.968702\pi$
$740$	−11.6049	+	11.6049i	−0.426603	+	0.426603i
$741$	25.6775	−	61.9910i	0.943287	−	2.27730i
$742$	−8.47219	−	3.50930i	−0.311024	−	0.128830i
$743$	15.9901	+	38.6035i	0.586620	+	1.41623i	0.886715	+	0.462316i	$0.152982\pi$
$743$	15.9901	+	38.6035i	0.586620	+	1.41623i	−0.300095	+	0.953909i	$0.597018\pi$
$744$		−	5.83826i		−	0.214041i
$745$	−68.7832	+	28.4909i	−2.52002	+	1.04383i
$746$	−37.4722	−	37.4722i	−1.37196	−	1.37196i
$747$	33.1699			1.21362
$748$	−55.0520	−	11.2666i	−2.01290	−	0.411948i
$749$	6.31465			0.230732
$750$	8.90784	+	8.90784i	0.325268	+	0.325268i
$751$	33.6580	−	13.9416i	1.22820	−	0.508736i	0.328191	−	0.944611i	$-0.393561\pi$
$751$	33.6580	−	13.9416i	1.22820	−	0.508736i	0.900007	+	0.435875i	$0.143561\pi$
$752$			0.600710i			0.0219056i
$753$	2.02580	+	4.89070i	0.0738241	+	0.178227i
$754$	14.0020	+	5.79980i	0.509921	+	0.211216i
$755$	13.8722	−	33.4904i	0.504860	−	1.21884i
$756$	−2.07049	+	2.07049i	−0.0753030	+	0.0753030i
$757$	−9.31536	+	9.31536i	−0.338573	+	0.338573i	−0.855830	−	0.517257i	$-0.826953\pi$
$757$	−9.31536	+	9.31536i	−0.338573	+	0.338573i	0.517257	+	0.855830i	$0.326953\pi$
$758$	−13.4741	+	32.5293i	−0.489400	+	1.18152i
$759$	−2.72519	−	1.12881i	−0.0989182	−	0.0409733i
$760$	24.7822	+	59.8295i	0.898944	+	2.17024i
$761$		−	53.2574i		−	1.93058i	−0.261180	−	0.965290i	$-0.584112\pi$
$761$		−	53.2574i		−	1.93058i	0.261180	−	0.965290i	$-0.415888\pi$
$762$	46.2890	−	19.1735i	1.67687	−	0.694584i
$763$	−23.2684	−	23.2684i	−0.842373	−	0.842373i
$764$	−8.59867			−0.311089
$765$	7.89238	−	38.5645i	0.285349	−	1.39430i
$766$	2.02037			0.0729991
$767$	35.3583	+	35.3583i	1.27671	+	1.27671i
$768$	−26.7866	+	11.0954i	−0.966578	+	0.400370i
$769$		−	29.4416i		−	1.06169i	−0.847469	−	0.530845i	$-0.821875\pi$
$769$		−	29.4416i		−	1.06169i	0.847469	−	0.530845i	$-0.178125\pi$
$770$	59.2864	+	143.130i	2.13653	+	5.15805i
$771$	−20.4510	−	8.47106i	−0.736523	−	0.305078i
$772$	6.56589	−	15.8515i	0.236312	−	0.570507i
$773$	−19.0854	+	19.0854i	−0.686455	+	0.686455i	−0.961447	−	0.274992i	$-0.911325\pi$
$773$	−19.0854	+	19.0854i	−0.686455	+	0.686455i	0.274992	+	0.961447i	$0.411325\pi$
$774$	−59.5148	+	59.5148i	−2.13921	+	2.13921i
$775$	−2.11309	+	5.10144i	−0.0759043	+	0.183249i
$776$	31.8515	+	13.1933i	1.14340	+	0.473613i
$777$	−7.18872	−	17.3551i	−0.257894	−	0.622611i
$778$		−	58.3215i		−	2.09093i
$779$	45.9612	−	19.0377i	1.64673	−	0.682098i
$780$	60.1717	+	60.1717i	2.15449	+	2.15449i
$781$	−38.3116			−1.37090
$782$	−2.14073	+	1.41337i	−0.0765522	+	0.0505419i
$783$	0.385592			0.0137799
$784$	−6.68025	−	6.68025i	−0.238580	−	0.238580i
$785$	−26.0212	+	10.7783i	−0.928737	+	0.384695i
$786$			3.68880i			0.131575i
$787$	−15.9324	−	38.4642i	−0.567928	−	1.37110i	−0.903298	−	0.429014i	$-0.858861\pi$
$787$	−15.9324	−	38.4642i	−0.567928	−	1.37110i	0.335370	−	0.942087i	$-0.391139\pi$
$788$	−23.5254	−	9.74452i	−0.838056	−	0.347134i
$789$	4.00476	−	9.66834i	0.142573	−	0.344202i
$790$	16.3732	−	16.3732i	0.582532	−	0.582532i
$791$	22.3874	−	22.3874i	0.796003	−	0.796003i
$792$	−12.1762	+	29.3960i	−0.432663	+	1.04454i
$793$	21.2785	+	8.81383i	0.755620	+	0.312988i
$794$	−12.5708	−	30.3487i	−0.446122	−	1.07703i
$795$			6.78038i			0.240475i
$796$	−21.4320	+	8.87743i	−0.759637	+	0.314652i
$797$	−25.8657	−	25.8657i	−0.916209	−	0.916209i	0.0805425	−	0.996751i	$-0.474335\pi$
$797$	−25.8657	−	25.8657i	−0.916209	−	0.916209i	−0.996751	+	0.0805425i	$0.974335\pi$
$798$	−209.207			−7.40586
$799$	4.04826	−	0.782056i	0.143217	−	0.0276672i
$800$	35.9843			1.27224
$801$	−23.5467	−	23.5467i	−0.831982	−	0.831982i
$802$	−18.4291	+	7.63359i	−0.650755	+	0.269551i
$803$			2.85830i			0.100867i
$804$	−2.28991	−	5.52833i	−0.0807589	−	0.194969i
$805$	3.97029	+	1.64455i	0.139934	+	0.0579627i
$806$	−2.88880	+	6.97417i	−0.101754	+	0.245655i
$807$	41.8411	−	41.8411i	1.47288	−	1.47288i
$808$	−28.4287	+	28.4287i	−1.00012	+	1.00012i
$809$	−9.16213	+	22.1193i	−0.322123	+	0.777674i	0.677007	+	0.735976i	$0.263277\pi$
$809$	−9.16213	+	22.1193i	−0.322123	+	0.777674i	−0.999130	+	0.0416976i	$0.986723\pi$
$810$	63.0346	+	26.1098i	2.21481	+	0.917404i
$811$	13.1163	+	31.6656i	0.460577	+	1.11193i	0.968161	+	0.250328i	$0.0805386\pi$
$811$	13.1163	+	31.6656i	0.460577	+	1.11193i	−0.507584	+	0.861602i	$0.669461\pi$
$812$		−	28.7136i		−	1.00765i
$813$	43.4415	−	17.9941i	1.52356	−	0.631080i
$814$	11.3776	+	11.3776i	0.398786	+	0.398786i
$815$	4.40193			0.154193
$816$	−3.31991	−	5.02843i	−0.116220	−	0.176030i
$817$	102.054			3.57042
$818$	−43.3172	−	43.3172i	−1.51455	−	1.51455i
$819$	−44.3738	+	18.3802i	−1.55055	+	0.642258i
$820$			63.0913i			2.20324i
$821$	−6.83291	−	16.4961i	−0.238470	−	0.575718i	0.758655	−	0.651493i	$-0.225857\pi$
$821$	−6.83291	−	16.4961i	−0.238470	−	0.575718i	−0.997125	+	0.0757749i	$0.975857\pi$
$822$	−71.1796	−	29.4836i	−2.48268	−	1.02836i
$823$	0.994573	−	2.40111i	0.0346686	−	0.0836975i	−0.905597	−	0.424139i	$-0.860577\pi$
$823$	0.994573	−	2.40111i	0.0346686	−	0.0836975i	0.940266	+	0.340442i	$0.110577\pi$
$824$	−8.23224	+	8.23224i	−0.286784	+	0.286784i
$825$	43.1524	−	43.1524i	1.50237	−	1.50237i
$826$	59.6636	−	144.041i	2.07596	−	5.01181i
$827$	−34.2373	−	14.1815i	−1.19055	−	0.493141i	−0.302614	−	0.953113i	$-0.597859\pi$
$827$	−34.2373	−	14.1815i	−1.19055	−	0.493141i	−0.887933	+	0.459973i	$0.847859\pi$
$828$	0.953288	+	2.30144i	0.0331291	+	0.0799806i
$829$		−	17.1075i		−	0.594168i	−0.954851	−	0.297084i	$-0.903986\pi$
$829$		−	17.1075i		−	0.594168i	0.954851	−	0.297084i	$-0.0960142\pi$
$830$	77.5518	−	32.1230i	2.69186	−	1.11501i
$831$	−1.36808	−	1.36808i	−0.0474582	−	0.0474582i
$832$	45.0466			1.56171
$833$	−36.3221	+	53.7160i	−1.25849	+	1.86115i
$834$	85.7364			2.96881
$835$	−21.7741	−	21.7741i	−0.753525	−	0.753525i
$836$	100.600	−	41.6699i	3.47933	−	1.44118i
$837$			0.192058i			0.00663848i
$838$	11.6695	+	28.1726i	0.403115	+	0.973205i
$839$	−39.6710	−	16.4323i	−1.36960	−	0.567305i	−0.427917	−	0.903818i	$-0.640753\pi$
$839$	−39.6710	−	16.4323i	−1.36960	−	0.567305i	−0.941679	+	0.336512i	$0.890753\pi$
$840$	35.9741	−	86.8492i	1.24123	−	2.99658i
$841$	17.8324	−	17.8324i	0.614910	−	0.614910i
$842$	−24.6610	+	24.6610i	−0.849873	+	0.849873i
$843$	−16.3869	+	39.5616i	−0.564396	+	1.36257i
$844$	−46.0124	−	19.0590i	−1.58381	−	0.656037i
$845$	1.35578	+	3.27314i	0.0466403	+	0.112600i
$846$		−	6.58923i		−	0.226542i
$847$	36.8212	−	15.2519i	1.26519	−	0.524060i
$848$	0.361896	+	0.361896i	0.0124276	+	0.0124276i
$849$	−56.9041			−1.95295
$850$	−10.0664	−	52.1080i	−0.345275	−	1.78729i
$851$	0.446333			0.0153001
$852$	46.3950	+	46.3950i	1.58947	+	1.58947i
$853$	23.1077	−	9.57153i	0.791194	−	0.327723i	0.0497702	−	0.998761i	$-0.484151\pi$
$853$	23.1077	−	9.57153i	0.791194	−	0.327723i	0.741423	+	0.671038i	$0.234151\pi$
$854$		−	71.8105i		−	2.45731i
$855$	29.1902	+	70.4714i	0.998284	+	2.41007i
$856$	3.03218	+	1.25597i	0.103638	+	0.0429282i
$857$	18.6432	−	45.0087i	0.636840	−	1.53747i	−0.194027	−	0.980996i	$-0.562155\pi$
$857$	18.6432	−	45.0087i	0.636840	−	1.53747i	0.830867	−	0.556471i	$-0.187845\pi$
$858$	58.9935	−	58.9935i	2.01401	−	2.01401i
$859$	−19.0827	+	19.0827i	−0.651094	+	0.651094i	−0.953257	−	0.302162i	$-0.902292\pi$
$859$	−19.0827	+	19.0827i	−0.651094	+	0.651094i	0.302162	+	0.953257i	$0.402292\pi$
$860$	−49.5294	+	119.575i	−1.68894	+	4.07746i
$861$	−66.7178	−	27.6354i	−2.27374	−	0.941812i
$862$	−9.84291	−	23.7629i	−0.335251	−	0.809367i
$863$		−	4.35692i		−	0.148311i	−0.997247	−	0.0741556i	$-0.976374\pi$
$863$		−	4.35692i		−	0.148311i	0.997247	−	0.0741556i	$-0.0236262\pi$
$864$	1.15633	−	0.478968i	0.0393392	−	0.0162948i
$865$	−7.00717	−	7.00717i	−0.238251	−	0.238251i
$866$	70.9288			2.41026
$867$	−29.5651	+	28.9197i	−1.00408	+	0.982166i
$868$	14.3018			0.485436
$869$	−9.75430	−	9.75430i	−0.330892	−	0.330892i
$870$	−32.2794	+	13.3706i	−1.09437	+	0.453305i
$871$			2.74127i			0.0928846i
$872$	−6.54503	−	15.8011i	−0.221643	−	0.535093i
$873$	37.5170	+	15.5400i	1.26976	+	0.525951i
$874$	1.90223	−	4.59239i	0.0643439	−	0.155340i
$875$	−7.73144	+	7.73144i	−0.261370	+	0.261370i
$876$	3.46137	−	3.46137i	0.116949	−	0.116949i
$877$	4.32148	−	10.4330i	0.145926	−	0.352296i	−0.833969	−	0.551812i	$-0.813937\pi$
$877$	4.32148	−	10.4330i	0.145926	−	0.352296i	0.979895	+	0.199515i	$0.0639367\pi$
$878$	37.7990	+	15.6569i	1.27566	+	0.528394i
$879$	9.48627	+	22.9019i	0.319964	+	0.772462i
$880$		−	8.64636i		−	0.291469i
$881$	−18.3273	+	7.59143i	−0.617464	+	0.255762i	−0.669416	−	0.742888i	$-0.733456\pi$
$881$	−18.3273	+	7.59143i	−0.617464	+	0.255762i	0.0519522	+	0.998650i	$0.483456\pi$
$882$	73.2762	+	73.2762i	2.46734	+	2.46734i
$883$	−48.7950			−1.64208			−0.821042	−	0.570868i	$-0.806607\pi$
$883$	−48.7950			−1.64208			−0.821042	+	0.570868i	$0.806607\pi$
$884$	−8.36229	−	43.2868i	−0.281254	−	1.45589i
$885$	−115.277			−3.87500
$886$	60.1107	+	60.1107i	2.01946	+	2.01946i
$887$	−13.0007	+	5.38506i	−0.436521	+	0.180813i	−0.590111	−	0.807322i	$-0.700916\pi$
$887$	−13.0007	+	5.38506i	−0.436521	+	0.180813i	0.153591	+	0.988135i	$0.450916\pi$
$888$		−	9.76343i		−	0.327639i
$889$	16.6414	+	40.1759i	0.558135	+	1.34746i
$890$	−77.8563	−	32.2491i	−2.60975	−	1.08099i
$891$	15.5549	−	37.5528i	0.521108	−	1.25807i
$892$	22.1542	−	22.1542i	0.741777	−	0.741777i
$893$	−5.64950	+	5.64950i	−0.189053	+	0.189053i
$894$	47.8381	−	115.491i	1.59994	−	3.86261i
$895$	−17.0325	−	7.05511i	−0.569335	−	0.235826i
$896$	−30.7184	−	74.1608i	−1.02623	−	2.47754i
$897$		−	2.31425i		−	0.0772707i
$898$	−11.5399	+	4.77999i	−0.385092	+	0.159510i
$899$	−1.33173	−	1.33173i	−0.0444157	−	0.0444157i
$900$	−51.5374			−1.71791
$901$	1.96771	−	2.91001i	0.0655540	−	0.0969464i
$902$	61.8559			2.05958
$903$	−104.753	−	104.753i	−3.48596	−	3.48596i
$904$	15.2028	−	6.29721i	0.505638	−	0.209442i
$905$			45.0858i			1.49870i
$906$	23.2923	+	56.2326i	0.773834	+	1.86820i
$907$	−3.64172	−	1.50845i	−0.120921	−	0.0500873i	0.321402	−	0.946943i	$-0.395846\pi$
$907$	−3.64172	−	1.50845i	−0.120921	−	0.0500873i	−0.442324	+	0.896855i	$0.645846\pi$
$908$	−29.9381	+	72.2771i	−0.993532	+	2.39860i
$909$	−33.4853	+	33.4853i	−1.11064	+	1.11064i
$910$	−85.9467	+	85.9467i	−2.84911	+	2.84911i
$911$	−6.25062	+	15.0903i	−0.207092	+	0.499965i	−0.992963	−	0.118426i	$-0.962215\pi$
$911$	−6.25062	+	15.0903i	−0.207092	+	0.499965i	0.785871	+	0.618391i	$0.212215\pi$
$912$	10.7872	+	4.46822i	0.357201	+	0.147958i
$913$	−19.1372	−	46.2014i	−0.633350	−	1.52904i
$914$			52.3062i			1.73014i
$915$	−49.0543	+	20.3190i	−1.62169	+	0.671724i
$916$	11.6337	+	11.6337i	0.384388	+	0.384388i
$917$	−3.20165			−0.105728
$918$	−1.01706	−	1.54047i	−0.0335680	−	0.0508430i
$919$	−55.5702			−1.83309			−0.916546	−	0.399928i	$-0.869035\pi$
$919$	−55.5702			−1.83309			−0.916546	+	0.399928i	$0.869035\pi$
$920$	1.57936	+	1.57936i	0.0520701	+	0.0520701i
$921$	−14.7757	+	6.12032i	−0.486877	+	0.201671i
$922$			28.0519i			0.923840i
$923$	−11.5027	−	27.7699i	−0.378615	−	0.914059i
$924$	−146.032	−	60.4886i	−4.80411	−	1.98993i
$925$	−3.53375	+	8.53123i	−0.116189	+	0.280505i
$926$	−29.7934	+	29.7934i	−0.979070	+	0.979070i
$927$	−9.69652	+	9.69652i	−0.318475	+	0.318475i
$928$	−4.69684	+	11.3392i	−0.154181	+	0.372227i
$929$	14.9399	+	6.18833i	0.490164	+	0.203032i	0.614055	−	0.789263i	$-0.289537\pi$
$929$	14.9399	+	6.18833i	0.490164	+	0.203032i	−0.123891	+	0.992296i	$0.539537\pi$
$930$	−6.65969	−	16.0779i	−0.218380	−	0.527215i
$931$		−	125.652i		−	4.11806i
$932$	−3.27016	+	1.35454i	−0.107118	+	0.0443695i
$933$	−12.6865	−	12.6865i	−0.415338	−	0.415338i
$934$	66.8498			2.18739
$935$	−58.2689	+	11.2566i	−1.90560	+	0.368130i
$936$	−24.9633			−0.815951
$937$	−1.71013	−	1.71013i	−0.0558677	−	0.0558677i	0.678621	−	0.734489i	$-0.262578\pi$
$937$	−1.71013	−	1.71013i	−0.0558677	−	0.0558677i	−0.734489	+	0.678621i	$0.762578\pi$
$938$	7.89644	−	3.27081i	0.257828	−	0.106796i
$939$			4.79526i			0.156487i
$940$	−3.87756	−	9.36125i	−0.126472	−	0.305330i
$941$	17.9932	+	7.45302i	0.586561	+	0.242962i	0.656170	−	0.754613i	$-0.272175\pi$
$941$	17.9932	+	7.45302i	0.586561	+	0.242962i	−0.0696092	+	0.997574i	$0.522175\pi$
$942$	18.0975	−	43.6913i	0.589649	−	1.42354i
$943$	1.21327	−	1.21327i	0.0395096	−	0.0395096i
$944$	−6.15280	+	6.15280i	−0.200257	+	0.200257i
$945$	−1.18342	+	2.85702i	−0.0384966	+	0.0929390i
$946$	117.233	+	48.5596i	3.81158	+	1.57881i
$947$	0.398134	+	0.961180i	0.0129376	+	0.0312341i	0.930216	−	0.367012i	$-0.119619\pi$
$947$	0.398134	+	0.961180i	0.0129376	+	0.0312341i	−0.917279	+	0.398246i	$0.869619\pi$
$948$			23.6247i			0.767295i
$949$	−2.07182	+	0.858176i	−0.0672541	+	0.0278576i
$950$	72.7187	+	72.7187i	2.35931	+	2.35931i
$951$	70.0518			2.27159
$952$	−40.6437	+	26.8341i	−1.31727	+	0.869698i
$953$	−41.1606			−1.33332			−0.666661	−	0.745361i	$-0.732277\pi$
$953$	−41.1606			−1.33332			−0.666661	+	0.745361i	$0.732277\pi$
$954$	−3.96966	−	3.96966i	−0.128523	−	0.128523i
$955$	−8.38990	+	3.47521i	−0.271491	+	0.112455i
$956$			20.5191i			0.663634i
$957$	7.96550	+	19.2304i	0.257488	+	0.621631i
$958$	−37.6864	−	15.6102i	−1.21759	−	0.504343i
$959$	25.5899	−	61.7794i	0.826340	−	1.99496i
$960$	−73.4317	+	73.4317i	−2.37000	+	2.37000i
$961$	−21.2570	+	21.2570i	−0.685709	+	0.685709i
$962$	−4.83098	+	11.6630i	−0.155757	+	0.376031i
$963$	3.57152	+	1.47937i	0.115090	+	0.0476720i
$964$	−18.0513	−	43.5798i	−0.581394	−	1.40361i
$965$		−	18.1203i		−	0.583312i
$966$	−6.66637	+	2.76130i	−0.214487	+	0.0888434i
$967$	−13.6301	−	13.6301i	−0.438316	−	0.438316i	0.453129	−	0.891445i	$-0.350308\pi$
$967$	−13.6301	−	13.6301i	−0.438316	−	0.438316i	−0.891445	+	0.453129i	$0.850308\pi$
$968$	20.7145			0.665788
$969$	16.0681	−	78.5137i	0.516183	−	2.52222i
$970$	102.765			3.29958
$971$	−8.69954	−	8.69954i	−0.279181	−	0.279181i	0.553601	−	0.832782i	$-0.313253\pi$
$971$	−8.69954	−	8.69954i	−0.279181	−	0.279181i	−0.832782	+	0.553601i	$0.813253\pi$
$972$	−62.6104	+	25.9341i	−2.00823	+	0.831836i
$973$			74.4137i			2.38560i
$974$	16.4830	+	39.7935i	0.528149	+	1.27507i
$975$	44.2348	+	18.3227i	1.41665	+	0.586794i
$976$	−1.53372	+	3.70273i	−0.0490932	+	0.118521i
$977$	−14.9899	+	14.9899i	−0.479569	+	0.479569i	−0.904994	−	0.425425i	$-0.860125\pi$
$977$	−14.9899	+	14.9899i	−0.479569	+	0.479569i	0.425425	+	0.904994i	$0.360125\pi$
$978$	−5.22631	+	5.22631i	−0.167119	+	0.167119i
$979$	−19.2124	+	46.3828i	−0.614030	+	1.48240i
$980$	147.223	+	60.9820i	4.70288	+	1.94800i
$981$	−7.70920	−	18.6117i	−0.246136	−	0.594225i
$982$		−	44.3318i		−	1.41468i
$983$	10.3431	−	4.28425i	0.329894	−	0.136646i	−0.211588	−	0.977359i	$-0.567864\pi$
$983$	10.3431	−	4.28425i	0.329894	−	0.136646i	0.541482	+	0.840712i	$0.317864\pi$
$984$	−26.5401	−	26.5401i	−0.846066	−	0.846066i
$985$	−26.8925			−0.856867
$986$	17.7339	+	3.62932i	0.564764	+	0.115581i
$987$	11.5978			0.369162
$988$	60.4084	+	60.4084i	1.92185	+	1.92185i
$989$	3.25194	−	1.34700i	0.103406	−	0.0428321i
$990$			94.8426i			3.01430i
$991$	−17.8788	−	43.1633i	−0.567940	−	1.37113i	−0.903288	−	0.429034i	$-0.858854\pi$
$991$	−17.8788	−	43.1633i	−0.567940	−	1.37113i	0.335348	−	0.942094i	$-0.391146\pi$
$992$	−5.64788	−	2.33943i	−0.179320	−	0.0742769i
$993$	−15.2840	+	36.8989i	−0.485024	+	1.17095i
$994$	−66.2686	+	66.2686i	−2.10191	+	2.10191i
$995$	−17.3238	+	17.3238i	−0.549201	+	0.549201i
$996$	−32.7744	+	79.1244i	−1.03850	+	2.50715i
$997$	5.72014	+	2.36936i	0.181159	+	0.0750383i	0.471419	−	0.881909i	$-0.343742\pi$
$997$	5.72014	+	2.36936i	0.181159	+	0.0750383i	−0.290261	+	0.956948i	$0.593742\pi$
$998$	−24.1337	−	58.2640i	−0.763940	−	1.84431i
$999$			0.321181i			0.0101617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.g.d.189.6	✓	152
17.9	even	8	inner	799.2.g.d.706.6	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.g.d.189.6	✓	152	1.1	even	1	trivial
799.2.g.d.706.6	yes	152	17.9	even	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:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	799.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59647 - 1.59647i) q^{2} +(2.24761 - 0.930990i) q^{3} +3.09745i q^{4} +(1.25186 + 3.02225i) q^{5} +(-5.07455 - 2.10195i) q^{6} +(1.82436 - 4.40439i) q^{7} +(1.75205 - 1.75205i) q^{8} +(2.06368 - 2.06368i) q^{9} +O(q^{10})\)	\(q+(-1.59647 - 1.59647i) q^{2} +(2.24761 - 0.930990i) q^{3} +3.09745i q^{4} +(1.25186 + 3.02225i) q^{5} +(-5.07455 - 2.10195i) q^{6} +(1.82436 - 4.40439i) q^{7} +(1.75205 - 1.75205i) q^{8} +(2.06368 - 2.06368i) q^{9} +(2.82638 - 6.82349i) q^{10} +(-4.06508 - 1.68381i) q^{11} +(2.88369 + 6.96185i) q^{12} -3.45210i q^{13} +(-9.94402 + 4.11895i) q^{14} +(5.62736 + 5.62736i) q^{15} +0.600710 q^{16} +(-0.782056 - 4.04826i) q^{17} -6.58923 q^{18} +(5.64950 + 5.64950i) q^{19} +(-9.36125 + 3.87756i) q^{20} -11.5978i q^{21} +(3.80163 + 9.17795i) q^{22} +(0.254588 + 0.105454i) q^{23} +(2.30678 - 5.56905i) q^{24} +(-4.03130 + 4.03130i) q^{25} +(-5.51118 + 5.51118i) q^{26} +(-0.0758846 + 0.183202i) q^{27} +(13.6424 + 5.65085i) q^{28} +(-0.744138 - 1.79651i) q^{29} -17.9679i q^{30} +(0.894815 - 0.370644i) q^{31} +(-4.46311 - 4.46311i) q^{32} -10.7043 q^{33} +(-5.21440 + 7.71146i) q^{34} +15.5950 q^{35} +(6.39216 + 6.39216i) q^{36} +(1.49641 - 0.619835i) q^{37} -18.0385i q^{38} +(-3.21387 - 7.75897i) q^{39} +(7.48842 + 3.10181i) q^{40} +(2.38282 - 5.75263i) q^{41} +(-18.5156 + 18.5156i) q^{42} +(9.03213 - 9.03213i) q^{43} +(5.21552 - 12.5914i) q^{44} +(8.82040 + 3.65353i) q^{45} +(-0.238088 - 0.574796i) q^{46} +1.00000i q^{47} +(1.35016 - 0.559255i) q^{48} +(-11.1206 - 11.1206i) q^{49} +12.8717 q^{50} +(-5.52665 - 8.37081i) q^{51} +10.6927 q^{52} +(0.602447 + 0.602447i) q^{53} +(0.413624 - 0.171329i) q^{54} -14.3936i q^{55} +(-4.52033 - 10.9130i) q^{56} +(17.9575 + 7.43824i) q^{57} +(-1.68008 + 4.05607i) q^{58} +(-10.2426 + 10.2426i) q^{59} +(-17.4305 + 17.4305i) q^{60} +(-2.55318 + 6.16392i) q^{61} +(-2.02027 - 0.836823i) q^{62} +(-5.32437 - 12.8542i) q^{63} +13.0490i q^{64} +(10.4331 - 4.32153i) q^{65} +(17.0892 + 17.0892i) q^{66} -0.794089 q^{67} +(12.5393 - 2.42238i) q^{68} +0.670390 q^{69} +(-24.8969 - 24.8969i) q^{70} +(8.04436 - 3.33208i) q^{71} -7.23134i q^{72} +(-0.248595 - 0.600162i) q^{73} +(-3.37853 - 1.39943i) q^{74} +(-5.30768 + 12.8139i) q^{75} +(-17.4990 + 17.4990i) q^{76} +(-14.8323 + 14.8323i) q^{77} +(-7.25612 + 17.5178i) q^{78} +(2.89649 + 1.19977i) q^{79} +(0.752002 + 1.81549i) q^{80} +9.23788i q^{81} +(-12.9880 + 5.37981i) q^{82} +(8.03657 + 8.03657i) q^{83} +35.9236 q^{84} +(11.2558 - 7.43140i) q^{85} -28.8391 q^{86} +(-3.34506 - 3.34506i) q^{87} +(-10.0723 + 4.17210i) q^{88} -11.4100i q^{89} +(-8.24876 - 19.9143i) q^{90} +(-15.2044 - 6.29786i) q^{91} +(-0.326637 + 0.788573i) q^{92} +(1.66613 - 1.66613i) q^{93} +(1.59647 - 1.59647i) q^{94} +(-10.0018 + 24.1465i) q^{95} +(-14.1864 - 5.87621i) q^{96} +(5.32468 + 12.8549i) q^{97} +35.5074i q^{98} +(-11.8639 + 4.91419i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 4 q^{2} + 4 q^{6} + 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) \) 152 * q - 4 * q^2 + 4 * q^6 + 4 * q^7 + 4 * q^8 - 8 * q^9	\( 152 q - 4 q^{2} + 4 q^{6} + 4 q^{7} + 4 q^{8} - 8 q^{9} - 8 q^{11} + 8 q^{12} - 12 q^{14} + 20 q^{15} - 160 q^{16} - 12 q^{17} + 96 q^{18} + 16 q^{19} + 96 q^{20} - 4 q^{22} - 16 q^{23} - 76 q^{24} - 12 q^{25} - 8 q^{26} + 8 q^{28} - 4 q^{29} - 4 q^{31} - 16 q^{32} - 72 q^{33} - 20 q^{34} + 48 q^{35} - 16 q^{36} + 16 q^{37} + 64 q^{40} - 68 q^{41} - 144 q^{42} + 4 q^{43} + 12 q^{44} - 4 q^{46} - 12 q^{48} - 4 q^{49} + 96 q^{50} - 52 q^{51} + 168 q^{52} - 16 q^{53} + 168 q^{54} + 108 q^{56} - 104 q^{58} - 84 q^{59} - 4 q^{60} + 4 q^{61} - 28 q^{62} + 60 q^{63} + 60 q^{65} - 44 q^{66} - 160 q^{67} - 96 q^{68} + 160 q^{69} + 36 q^{70} + 40 q^{71} + 4 q^{73} + 76 q^{74} - 116 q^{75} - 148 q^{76} - 4 q^{77} + 68 q^{78} - 76 q^{80} + 64 q^{82} - 124 q^{83} + 208 q^{84} - 68 q^{85} + 80 q^{86} - 72 q^{87} + 188 q^{88} + 236 q^{90} - 32 q^{91} - 196 q^{92} - 152 q^{93} + 4 q^{94} - 48 q^{95} - 56 q^{96} - 20 q^{97} + 244 q^{99}+O(q^{100}) \) 152 * q - 4 * q^2 + 4 * q^6 + 4 * q^7 + 4 * q^8 - 8 * q^9 - 8 * q^11 + 8 * q^12 - 12 * q^14 + 20 * q^15 - 160 * q^16 - 12 * q^17 + 96 * q^18 + 16 * q^19 + 96 * q^20 - 4 * q^22 - 16 * q^23 - 76 * q^24 - 12 * q^25 - 8 * q^26 + 8 * q^28 - 4 * q^29 - 4 * q^31 - 16 * q^32 - 72 * q^33 - 20 * q^34 + 48 * q^35 - 16 * q^36 + 16 * q^37 + 64 * q^40 - 68 * q^41 - 144 * q^42 + 4 * q^43 + 12 * q^44 - 4 * q^46 - 12 * q^48 - 4 * q^49 + 96 * q^50 - 52 * q^51 + 168 * q^52 - 16 * q^53 + 168 * q^54 + 108 * q^56 - 104 * q^58 - 84 * q^59 - 4 * q^60 + 4 * q^61 - 28 * q^62 + 60 * q^63 + 60 * q^65 - 44 * q^66 - 160 * q^67 - 96 * q^68 + 160 * q^69 + 36 * q^70 + 40 * q^71 + 4 * q^73 + 76 * q^74 - 116 * q^75 - 148 * q^76 - 4 * q^77 + 68 * q^78 - 76 * q^80 + 64 * q^82 - 124 * q^83 + 208 * q^84 - 68 * q^85 + 80 * q^86 - 72 * q^87 + 188 * q^88 + 236 * q^90 - 32 * q^91 - 196 * q^92 - 152 * q^93 + 4 * q^94 - 48 * q^95 - 56 * q^96 - 20 * q^97 + 244 * q^99

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