LMFDB - Embedded newform 370.2.g.e.327.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(43,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("370.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 $ x^20 - 4x^19 + 8x^18 + 4x^17 + 103x^16 - 394x^15 + 760x^14 + 278x^13 + 2009x^12 - 7362x^11 + 13826x^10 + 4848x^9 + 13544x^8 - 44248x^7 + 76384x^6 + 24512x^5 + 28432x^4 - 61952x^3 + 61952x^2 - 5632*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			327.10
Root			$-2.09082 - 2.09082i$ of defining polynomial
Character	$\chi$	$=$	370.327
Dual form			370.2.g.e.43.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(2.09082 + 2.09082i) q^{3} -1.00000 q^{4} +(1.30447 + 1.81614i) q^{5} +(2.09082 - 2.09082i) q^{6} +(-0.643605 - 0.643605i) q^{7} +1.00000i q^{8} +5.74304i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(2.09082 + 2.09082i) q^{3} -1.00000 q^{4} +(1.30447 + 1.81614i) q^{5} +(2.09082 - 2.09082i) q^{6} +(-0.643605 - 0.643605i) q^{7} +1.00000i q^{8} +5.74304i q^{9} +(1.81614 - 1.30447i) q^{10} -1.88405i q^{11} +(-2.09082 - 2.09082i) q^{12} +0.536082i q^{13} +(-0.643605 + 0.643605i) q^{14} +(-1.06980 + 6.52462i) q^{15} +1.00000 q^{16} +0.334703 q^{17} +5.74304 q^{18} +(-1.08518 - 1.08518i) q^{19} +(-1.30447 - 1.81614i) q^{20} -2.69132i q^{21} -1.88405 q^{22} -4.65098i q^{23} +(-2.09082 + 2.09082i) q^{24} +(-1.59670 + 4.73820i) q^{25} +0.536082 q^{26} +(-5.73519 + 5.73519i) q^{27} +(0.643605 + 0.643605i) q^{28} +(-3.33033 + 3.33033i) q^{29} +(6.52462 + 1.06980i) q^{30} +(4.90948 + 4.90948i) q^{31} -1.00000i q^{32} +(3.93919 - 3.93919i) q^{33} -0.334703i q^{34} +(0.329310 - 2.00844i) q^{35} -5.74304i q^{36} +(6.02729 - 0.819646i) q^{37} +(-1.08518 + 1.08518i) q^{38} +(-1.12085 + 1.12085i) q^{39} +(-1.81614 + 1.30447i) q^{40} -8.26486i q^{41} -2.69132 q^{42} -11.9117i q^{43} +1.88405i q^{44} +(-10.4301 + 7.49163i) q^{45} -4.65098 q^{46} +(-0.141535 - 0.141535i) q^{47} +(2.09082 + 2.09082i) q^{48} -6.17154i q^{49} +(4.73820 + 1.59670i) q^{50} +(0.699803 + 0.699803i) q^{51} -0.536082i q^{52} +(-5.03296 + 5.03296i) q^{53} +(5.73519 + 5.73519i) q^{54} +(3.42168 - 2.45768i) q^{55} +(0.643605 - 0.643605i) q^{56} -4.53784i q^{57} +(3.33033 + 3.33033i) q^{58} +(4.10789 + 4.10789i) q^{59} +(1.06980 - 6.52462i) q^{60} +(-8.90180 - 8.90180i) q^{61} +(4.90948 - 4.90948i) q^{62} +(3.69625 - 3.69625i) q^{63} -1.00000 q^{64} +(-0.973599 + 0.699305i) q^{65} +(-3.93919 - 3.93919i) q^{66} +(3.61956 - 3.61956i) q^{67} -0.334703 q^{68} +(9.72436 - 9.72436i) q^{69} +(-2.00844 - 0.329310i) q^{70} +15.5121 q^{71} -5.74304 q^{72} +(-6.82739 - 6.82739i) q^{73} +(-0.819646 - 6.02729i) q^{74} +(-13.2451 + 6.56829i) q^{75} +(1.08518 + 1.08518i) q^{76} +(-1.21258 + 1.21258i) q^{77} +(1.12085 + 1.12085i) q^{78} +(5.73637 + 5.73637i) q^{79} +(1.30447 + 1.81614i) q^{80} -6.75336 q^{81} -8.26486 q^{82} +(-7.90475 + 7.90475i) q^{83} +2.69132i q^{84} +(0.436611 + 0.607866i) q^{85} -11.9117 q^{86} -13.9262 q^{87} +1.88405 q^{88} +(-1.21521 + 1.21521i) q^{89} +(7.49163 + 10.4301i) q^{90} +(0.345025 - 0.345025i) q^{91} +4.65098i q^{92} +20.5297i q^{93} +(-0.141535 + 0.141535i) q^{94} +(0.555249 - 3.38643i) q^{95} +(2.09082 - 2.09082i) q^{96} -17.1767 q^{97} -6.17154 q^{98} +10.8201 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} - 20 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7}+O(q^{10}) $ 20 * q - 4 * q^3 - 20 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7	$ 20 q - 4 q^{3} - 20 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{10} + 4 q^{12} - 2 q^{14} + 20 q^{16} + 20 q^{17} + 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{22} + 4 q^{24} - 10 q^{25} + 20 q^{27} + 2 q^{28} - 18 q^{29} - 4 q^{30} + 12 q^{31} + 4 q^{33} + 12 q^{35} - 6 q^{38} - 6 q^{39} - 4 q^{40} - 12 q^{42} - 18 q^{45} + 4 q^{46} - 22 q^{47} - 4 q^{48} + 4 q^{50} + 8 q^{51} - 4 q^{53} - 20 q^{54} - 34 q^{55} + 2 q^{56} + 18 q^{58} + 10 q^{59} + 10 q^{61} + 12 q^{62} - 2 q^{63} - 20 q^{64} - 20 q^{65} - 4 q^{66} - 8 q^{67} - 20 q^{68} + 34 q^{69} + 12 q^{70} + 16 q^{71} - 24 q^{72} + 6 q^{73} - 32 q^{74} - 26 q^{75} + 6 q^{76} + 4 q^{77} + 6 q^{78} - 12 q^{79} + 2 q^{80} - 28 q^{81} + 20 q^{82} + 6 q^{83} - 10 q^{85} - 16 q^{86} + 44 q^{87} + 8 q^{88} + 44 q^{89} - 22 q^{90} - 40 q^{91} - 22 q^{94} - 50 q^{95} - 4 q^{96} - 72 q^{97} + 52 q^{98} + 20 q^{99}+O(q^{100}) $ 20 * q - 4 * q^3 - 20 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^10 + 4 * q^12 - 2 * q^14 + 20 * q^16 + 20 * q^17 + 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^22 + 4 * q^24 - 10 * q^25 + 20 * q^27 + 2 * q^28 - 18 * q^29 - 4 * q^30 + 12 * q^31 + 4 * q^33 + 12 * q^35 - 6 * q^38 - 6 * q^39 - 4 * q^40 - 12 * q^42 - 18 * q^45 + 4 * q^46 - 22 * q^47 - 4 * q^48 + 4 * q^50 + 8 * q^51 - 4 * q^53 - 20 * q^54 - 34 * q^55 + 2 * q^56 + 18 * q^58 + 10 * q^59 + 10 * q^61 + 12 * q^62 - 2 * q^63 - 20 * q^64 - 20 * q^65 - 4 * q^66 - 8 * q^67 - 20 * q^68 + 34 * q^69 + 12 * q^70 + 16 * q^71 - 24 * q^72 + 6 * q^73 - 32 * q^74 - 26 * q^75 + 6 * q^76 + 4 * q^77 + 6 * q^78 - 12 * q^79 + 2 * q^80 - 28 * q^81 + 20 * q^82 + 6 * q^83 - 10 * q^85 - 16 * q^86 + 44 * q^87 + 8 * q^88 + 44 * q^89 - 22 * q^90 - 40 * q^91 - 22 * q^94 - 50 * q^95 - 4 * q^96 - 72 * q^97 + 52 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	2.09082	+	2.09082i	1.20713	+	1.20713i	0.971951	+	0.235183i	$0.0755689\pi$
$3$	2.09082	+	2.09082i	1.20713	+	1.20713i	0.235183	+	0.971951i	$0.424431\pi$
$4$	−1.00000			−0.500000
$5$	1.30447	+	1.81614i	0.583378	+	0.812201i
$5$	1.30447	+	1.81614i	0.583378	+	0.812201i
$6$	2.09082	−	2.09082i	0.853573	−	0.853573i
$7$	−0.643605	−	0.643605i	−0.243260	−	0.243260i	0.574937	−	0.818197i	$-0.305026\pi$
$7$	−0.643605	−	0.643605i	−0.243260	−	0.243260i	−0.818197	+	0.574937i	$0.805026\pi$
$8$			1.00000i			0.353553i
$9$			5.74304i			1.91435i
$10$	1.81614	−	1.30447i	0.574313	−	0.412510i
$11$		−	1.88405i		−	0.568061i	−0.958815	−	0.284030i	$-0.908328\pi$
$11$		−	1.88405i		−	0.568061i	0.958815	−	0.284030i	$-0.0916717\pi$
$12$	−2.09082	−	2.09082i	−0.603567	−	0.603567i
$13$			0.536082i			0.148683i	0.997233	+	0.0743413i	$0.0236854\pi$
$13$			0.536082i			0.148683i	−0.997233	+	0.0743413i	$0.976315\pi$
$14$	−0.643605	+	0.643605i	−0.172011	+	0.172011i
$15$	−1.06980	+	6.52462i	−0.276220	+	1.68465i
$16$	1.00000			0.250000
$17$	0.334703			0.0811774			0.0405887	−	0.999176i	$-0.487077\pi$
$17$	0.334703			0.0811774			0.0405887	+	0.999176i	$0.487077\pi$
$18$	5.74304			1.35365
$19$	−1.08518	−	1.08518i	−0.248958	−	0.248958i	0.571585	−	0.820543i	$-0.306329\pi$
$19$	−1.08518	−	1.08518i	−0.248958	−	0.248958i	−0.820543	+	0.571585i	$0.806329\pi$
$20$	−1.30447	−	1.81614i	−0.291689	−	0.406101i
$21$		−	2.69132i		−	0.587295i
$22$	−1.88405			−0.401680
$23$		−	4.65098i		−	0.969797i	−0.874570	−	0.484899i	$-0.838856\pi$
$23$		−	4.65098i		−	0.969797i	0.874570	−	0.484899i	$-0.161144\pi$
$24$	−2.09082	+	2.09082i	−0.426786	+	0.426786i
$25$	−1.59670	+	4.73820i	−0.319341	+	0.947640i
$26$	0.536082			0.105134
$27$	−5.73519	+	5.73519i	−1.10374	+	1.10374i
$28$	0.643605	+	0.643605i	0.121630	+	0.121630i
$29$	−3.33033	+	3.33033i	−0.618427	+	0.618427i	−0.945128	−	0.326701i	$-0.894063\pi$
$29$	−3.33033	+	3.33033i	−0.618427	+	0.618427i	0.326701	+	0.945128i	$0.394063\pi$
$30$	6.52462	+	1.06980i	1.19123	+	0.195317i
$31$	4.90948	+	4.90948i	0.881769	+	0.881769i	0.993714	−	0.111945i	$-0.0357081\pi$
$31$	4.90948	+	4.90948i	0.881769	+	0.881769i	−0.111945	+	0.993714i	$0.535708\pi$
$32$		−	1.00000i		−	0.176777i
$33$	3.93919	−	3.93919i	0.685726	−	0.685726i
$34$		−	0.334703i		−	0.0574011i
$35$	0.329310	−	2.00844i	0.0556635	−	0.339488i
$36$		−	5.74304i		−	0.957173i
$37$	6.02729	−	0.819646i	0.990880	−	0.134749i
$37$	6.02729	−	0.819646i	0.990880	−	0.134749i
$38$	−1.08518	+	1.08518i	−0.176040	+	0.176040i
$39$	−1.12085	+	1.12085i	−0.179480	+	0.179480i
$40$	−1.81614	+	1.30447i	−0.287156	+	0.206255i
$41$		−	8.26486i		−	1.29075i	−0.763864	−	0.645377i	$-0.776700\pi$
$41$		−	8.26486i		−	1.29075i	0.763864	−	0.645377i	$-0.223300\pi$
$42$	−2.69132			−0.415280
$43$		−	11.9117i		−	1.81652i	−0.418409	−	0.908259i	$-0.637412\pi$
$43$		−	11.9117i		−	1.81652i	0.418409	−	0.908259i	$-0.362588\pi$
$44$			1.88405i			0.284030i
$45$	−10.4301	+	7.49163i	−1.55483	+	1.11679i
$46$	−4.65098			−0.685750
$47$	−0.141535	−	0.141535i	−0.0206450	−	0.0206450i	0.696709	−	0.717354i	$-0.254647\pi$
$47$	−0.141535	−	0.141535i	−0.0206450	−	0.0206450i	−0.717354	+	0.696709i	$0.754647\pi$
$48$	2.09082	+	2.09082i	0.301784	+	0.301784i
$49$		−	6.17154i		−	0.881649i
$50$	4.73820	+	1.59670i	0.670083	+	0.225808i
$51$	0.699803	+	0.699803i	0.0979920	+	0.0979920i
$52$		−	0.536082i		−	0.0743413i
$53$	−5.03296	+	5.03296i	−0.691330	+	0.691330i	−0.962525	−	0.271194i	$-0.912581\pi$
$53$	−5.03296	+	5.03296i	−0.691330	+	0.691330i	0.271194	+	0.962525i	$0.412581\pi$
$54$	5.73519	+	5.73519i	0.780460	+	0.780460i
$55$	3.42168	−	2.45768i	0.461380	−	0.331394i
$56$	0.643605	−	0.643605i	0.0860054	−	0.0860054i
$57$		−	4.53784i		−	0.601051i
$58$	3.33033	+	3.33033i	0.437294	+	0.437294i
$59$	4.10789	+	4.10789i	0.534802	+	0.534802i	0.921998	−	0.387195i	$-0.126556\pi$
$59$	4.10789	+	4.10789i	0.534802	+	0.534802i	−0.387195	+	0.921998i	$0.626556\pi$
$60$	1.06980	−	6.52462i	0.138110	−	0.842325i
$61$	−8.90180	−	8.90180i	−1.13976	−	1.13976i	−0.988493	−	0.151265i	$-0.951665\pi$
$61$	−8.90180	−	8.90180i	−1.13976	−	1.13976i	−0.151265	−	0.988493i	$-0.548335\pi$
$62$	4.90948	−	4.90948i	0.623505	−	0.623505i
$63$	3.69625	−	3.69625i	0.465683	−	0.465683i
$64$	−1.00000			−0.125000
$65$	−0.973599	+	0.699305i	−0.120760	+	0.0867381i
$66$	−3.93919	−	3.93919i	−0.484881	−	0.484881i
$67$	3.61956	−	3.61956i	0.442199	−	0.442199i	−0.450551	−	0.892751i	$-0.648773\pi$
$67$	3.61956	−	3.61956i	0.442199	−	0.442199i	0.892751	+	0.450551i	$0.148773\pi$
$68$	−0.334703			−0.0405887
$69$	9.72436	−	9.72436i	1.17068	−	1.17068i
$70$	−2.00844	−	0.329310i	−0.240054	−	0.0393601i
$71$	15.5121			1.84095			0.920477	−	0.390798i	$-0.127801\pi$
$71$	15.5121			1.84095			0.920477	+	0.390798i	$0.127801\pi$
$72$	−5.74304			−0.676823
$73$	−6.82739	−	6.82739i	−0.799086	−	0.799086i	0.183866	−	0.982951i	$-0.441139\pi$
$73$	−6.82739	−	6.82739i	−0.799086	−	0.799086i	−0.982951	+	0.183866i	$0.941139\pi$
$74$	−0.819646	−	6.02729i	−0.0952819	−	0.700658i
$75$	−13.2451	+	6.56829i	−1.52942	+	0.758441i
$76$	1.08518	+	1.08518i	0.124479	+	0.124479i
$77$	−1.21258	+	1.21258i	−0.138186	+	0.138186i
$78$	1.12085	+	1.12085i	0.126911	+	0.126911i
$79$	5.73637	+	5.73637i	0.645392	+	0.645392i	0.951876	−	0.306484i	$-0.0991525\pi$
$79$	5.73637	+	5.73637i	0.645392	+	0.645392i	−0.306484	+	0.951876i	$0.599153\pi$
$80$	1.30447	+	1.81614i	0.145844	+	0.203050i
$81$	−6.75336			−0.750373
$82$	−8.26486			−0.912701
$83$	−7.90475	+	7.90475i	−0.867659	+	0.867659i	−0.992213	−	0.124554i	$-0.960250\pi$
$83$	−7.90475	+	7.90475i	−0.867659	+	0.867659i	0.124554	+	0.992213i	$0.460250\pi$
$84$			2.69132i			0.293647i
$85$	0.436611	+	0.607866i	0.0473571	+	0.0659323i
$86$	−11.9117			−1.28447
$87$	−13.9262			−1.49305
$88$	1.88405			0.200840
$89$	−1.21521	+	1.21521i	−0.128812	+	0.128812i	−0.768574	−	0.639761i	$-0.779033\pi$
$89$	−1.21521	+	1.21521i	−0.128812	+	0.128812i	0.639761	+	0.768574i	$0.279033\pi$
$90$	7.49163	+	10.4301i	0.789687	+	1.09943i
$91$	0.345025	−	0.345025i	0.0361685	−	0.0361685i
$92$			4.65098i			0.484899i
$93$			20.5297i			2.12883i
$94$	−0.141535	+	0.141535i	−0.0145982	+	0.0145982i
$95$	0.555249	−	3.38643i	0.0569674	−	0.347440i
$96$	2.09082	−	2.09082i	0.213393	−	0.213393i
$97$	−17.1767			−1.74403			−0.872016	−	0.489477i	$-0.837188\pi$
$97$	−17.1767			−1.74403			−0.872016	+	0.489477i	$0.837188\pi$
$98$	−6.17154			−0.623420
$99$	10.8201			1.08746
$100$	1.59670	−	4.73820i	0.159670	−	0.473820i
$101$			13.4676i			1.34008i	0.742324	+	0.670041i	$0.233723\pi$
$101$			13.4676i			1.34008i	−0.742324	+	0.670041i	$0.766277\pi$
$102$	0.699803	−	0.699803i	0.0692908	−	0.0692908i
$103$	−12.6201			−1.24350			−0.621749	−	0.783216i	$-0.713578\pi$
$103$	−12.6201			−1.24350			−0.621749	+	0.783216i	$0.713578\pi$
$104$	−0.536082			−0.0525672
$105$	4.88781	−	3.51075i	0.477001	−	0.342615i
$106$	5.03296	+	5.03296i	0.488844	+	0.488844i
$107$	−1.64796	−	1.64796i	−0.159314	−	0.159314i	0.622949	−	0.782263i	$-0.285935\pi$
$107$	−1.64796	−	1.64796i	−0.159314	−	0.159314i	−0.782263	+	0.622949i	$0.785935\pi$
$108$	5.73519	−	5.73519i	0.551869	−	0.551869i
$109$	−7.06206	−	7.06206i	−0.676422	−	0.676422i	0.282766	−	0.959189i	$-0.408748\pi$
$109$	−7.06206	−	7.06206i	−0.676422	−	0.676422i	−0.959189	+	0.282766i	$0.908748\pi$
$110$	−2.45768	−	3.42168i	−0.234331	−	0.326245i
$111$	14.3157	+	10.8882i	1.35878	+	1.03346i
$112$	−0.643605	−	0.643605i	−0.0608150	−	0.0608150i
$113$	−15.1701			−1.42709			−0.713543	−	0.700612i	$-0.752911\pi$
$113$	−15.1701			−1.42709			−0.713543	+	0.700612i	$0.752911\pi$
$114$	−4.53784			−0.425007
$115$	8.44682	−	6.06708i	0.787670	−	0.565758i
$116$	3.33033	−	3.33033i	0.309213	−	0.309213i
$117$	−3.07874			−0.284630
$118$	4.10789	−	4.10789i	0.378162	−	0.378162i
$119$	−0.215416	−	0.215416i	−0.0197472	−	0.0197472i
$120$	−6.52462	−	1.06980i	−0.595614	−	0.0976587i
$121$	7.45037			0.677307
$122$	−8.90180	+	8.90180i	−0.805931	+	0.805931i
$123$	17.2803	−	17.2803i	1.55811	−	1.55811i
$124$	−4.90948	−	4.90948i	−0.440885	−	0.440885i
$125$	−10.6881	+	3.28101i	−0.955970	+	0.293463i
$126$	−3.69625	−	3.69625i	−0.329288	−	0.329288i
$127$	−3.59805	−	3.59805i	−0.319275	−	0.319275i	0.529213	−	0.848489i	$-0.322487\pi$
$127$	−3.59805	−	3.59805i	−0.319275	−	0.319275i	−0.848489	+	0.529213i	$0.822487\pi$
$128$			1.00000i			0.0883883i
$129$	24.9052	−	24.9052i	2.19278	−	2.19278i
$130$	0.699305	+	0.973599i	0.0613331	+	0.0853903i
$131$	7.63639	+	7.63639i	0.667194	+	0.667194i	0.957066	−	0.289871i	$-0.0936126\pi$
$131$	7.63639	+	7.63639i	0.667194	+	0.667194i	−0.289871	+	0.957066i	$0.593613\pi$
$132$	−3.93919	+	3.93919i	−0.342863	+	0.342863i
$133$			1.39686i			0.121123i
$134$	−3.61956	−	3.61956i	−0.312682	−	0.312682i
$135$	−17.8973	−	2.93449i	−1.54035	−	0.252561i
$136$			0.334703i			0.0287005i
$137$	5.48037	+	5.48037i	0.468220	+	0.468220i	0.901337	−	0.433118i	$-0.142587\pi$
$137$	5.48037	+	5.48037i	0.468220	+	0.468220i	−0.433118	+	0.901337i	$0.642587\pi$
$138$	−9.72436	−	9.72436i	−0.827793	−	0.827793i
$139$	−4.24414			−0.359983			−0.179991	−	0.983668i	$-0.557607\pi$
$139$	−4.24414			−0.359983			−0.179991	+	0.983668i	$0.557607\pi$
$140$	−0.329310	+	2.00844i	−0.0278318	+	0.169744i
$141$		−	0.591849i		−	0.0498427i
$142$		−	15.5121i		−	1.30175i
$143$	1.01000			0.0844607
$144$			5.74304i			0.478586i
$145$	−10.3927	−	1.70401i	−0.863063	−	0.141510i
$146$	−6.82739	+	6.82739i	−0.565039	+	0.565039i
$147$	12.9036	−	12.9036i	1.06427	−	1.06427i
$148$	−6.02729	+	0.819646i	−0.495440	+	0.0673745i
$149$			20.3080i			1.66370i	0.555002	+	0.831849i	$0.312718\pi$
$149$			20.3080i			1.66370i	−0.555002	+	0.831849i	$0.687282\pi$
$150$	6.56829	+	13.2451i	0.536299	+	1.08146i
$151$		−	13.8362i		−	1.12597i	−0.826466	−	0.562987i	$-0.809652\pi$
$151$		−	13.8362i		−	1.12597i	0.826466	−	0.562987i	$-0.190348\pi$
$152$	1.08518	−	1.08518i	0.0880199	−	0.0880199i
$153$			1.92221i			0.155402i
$154$	1.21258	+	1.21258i	0.0977126	+	0.0977126i
$155$	−2.51201	+	15.3206i	−0.201769	+	1.23058i
$156$	1.12085	−	1.12085i	0.0897399	−	0.0897399i
$157$	13.2682	+	13.2682i	1.05892	+	1.05892i	0.998152	+	0.0607691i	$0.0193553\pi$
$157$	13.2682	+	13.2682i	1.05892	+	1.05892i	0.0607691	+	0.998152i	$0.480645\pi$
$158$	5.73637	−	5.73637i	0.456361	−	0.456361i
$159$	−21.0460			−1.66906
$160$	1.81614	−	1.30447i	0.143578	−	0.103128i
$161$	−2.99340	+	2.99340i	−0.235913	+	0.235913i
$162$			6.75336i			0.530594i
$163$	1.48487			0.116304			0.0581520	−	0.998308i	$-0.481479\pi$
$163$	1.48487			0.116304			0.0581520	+	0.998308i	$0.481479\pi$
$164$			8.26486i			0.645377i
$165$	12.2927	+	2.01555i	0.956984	+	0.156910i
$166$	7.90475	+	7.90475i	0.613527	+	0.613527i
$167$	−4.69210			−0.363086			−0.181543	−	0.983383i	$-0.558109\pi$
$167$	−4.69210			−0.363086			−0.181543	+	0.983383i	$0.558109\pi$
$168$	2.69132			0.207640
$169$	12.7126			0.977894
$170$	0.607866	−	0.436611i	0.0466212	−	0.0334865i
$171$	6.23224	−	6.23224i	0.476591	−	0.476591i
$172$			11.9117i			0.908259i
$173$	1.68127	+	1.68127i	0.127825	+	0.127825i	0.768125	−	0.640300i	$-0.221190\pi$
$173$	1.68127	+	1.68127i	0.127825	+	0.127825i	−0.640300	+	0.768125i	$0.721190\pi$
$174$			13.9262i			1.05574i
$175$	4.07718	−	2.02188i	0.308206	−	0.152840i
$176$		−	1.88405i		−	0.142015i
$177$			17.1777i			1.29116i
$178$	1.21521	+	1.21521i	0.0910840	+	0.0910840i
$179$	13.0168	−	13.0168i	0.972921	−	0.972921i	−0.0267216	−	0.999643i	$-0.508507\pi$
$179$	13.0168	−	13.0168i	0.972921	−	0.972921i	0.999643	+	0.0267216i	$0.00850676\pi$
$180$	10.4301	−	7.49163i	0.777417	−	0.558393i
$181$	5.91911			0.439964			0.219982	−	0.975504i	$-0.429400\pi$
$181$	5.91911			0.439964			0.219982	+	0.975504i	$0.429400\pi$
$182$	−0.345025	−	0.345025i	−0.0255750	−	0.0255750i
$183$		−	37.2241i		−	2.75168i
$184$	4.65098			0.342875
$185$	9.35102	+	9.87717i	0.687500	+	0.726184i
$186$	20.5297			1.50531
$187$		−	0.630595i		−	0.0461137i
$188$	0.141535	+	0.141535i	0.0103225	+	0.0103225i
$189$	7.38239			0.536990
$190$	−3.38643	−	0.555249i	−0.245677	−	0.0402820i
$191$	−8.14150	+	8.14150i	−0.589099	+	0.589099i	−0.937387	−	0.348289i	$-0.886763\pi$
$191$	−8.14150	+	8.14150i	−0.589099	+	0.589099i	0.348289	+	0.937387i	$0.386763\pi$
$192$	−2.09082	−	2.09082i	−0.150892	−	0.150892i
$193$		−	15.8717i		−	1.14247i	−0.820787	−	0.571235i	$-0.806465\pi$
$193$		−	15.8717i		−	1.14247i	0.820787	−	0.571235i	$-0.193535\pi$
$194$			17.1767i			1.23322i
$195$	−3.49774	−	0.573499i	−0.250478	−	0.0410691i
$196$			6.17154i			0.440825i
$197$	3.60225	+	3.60225i	0.256650	+	0.256650i	0.823690	−	0.567040i	$-0.191912\pi$
$197$	3.60225	+	3.60225i	0.256650	+	0.256650i	−0.567040	+	0.823690i	$0.691912\pi$
$198$		−	10.8201i		−	0.768954i
$199$	1.14697	−	1.14697i	0.0813064	−	0.0813064i	−0.665284	−	0.746590i	$-0.731690\pi$
$199$	1.14697	−	1.14697i	0.0813064	−	0.0813064i	0.746590	+	0.665284i	$0.231690\pi$
$200$	−4.73820	−	1.59670i	−0.335041	−	0.112904i
$201$	15.1357			1.06759
$202$	13.4676			0.947581
$203$	4.28683			0.300877
$204$	−0.699803	−	0.699803i	−0.0489960	−	0.0489960i
$205$	15.0101	−	10.7813i	1.04835	−	0.752997i
$206$			12.6201i			0.879286i
$207$	26.7108			1.85653
$208$			0.536082i			0.0371706i
$209$	−2.04453	+	2.04453i	−0.141423	+	0.141423i
$210$	−3.51075	−	4.88781i	−0.242265	−	0.337291i
$211$	3.19579			0.220008			0.110004	−	0.993931i	$-0.464914\pi$
$211$	3.19579			0.220008			0.110004	+	0.993931i	$0.464914\pi$
$212$	5.03296	−	5.03296i	0.345665	−	0.345665i
$213$	32.4331	+	32.4331i	2.22228	+	2.22228i
$214$	−1.64796	+	1.64796i	−0.112652	+	0.112652i
$215$	21.6333	−	15.5385i	1.47538	−	1.05972i
$216$	−5.73519	−	5.73519i	−0.390230	−	0.390230i
$217$		−	6.31954i		−	0.428998i
$218$	−7.06206	+	7.06206i	−0.478303	+	0.478303i
$219$		−	28.5497i		−	1.92921i
$220$	−3.42168	+	2.45768i	−0.230690	+	0.165697i
$221$			0.179428i			0.0120697i
$222$	10.8882	−	14.3157i	0.730770	−	0.960806i
$223$	−7.29909	+	7.29909i	−0.488783	+	0.488783i	−0.907922	−	0.419139i	$-0.862332\pi$
$223$	−7.29909	+	7.29909i	−0.488783	+	0.488783i	0.419139	+	0.907922i	$0.362332\pi$
$224$	−0.643605	+	0.643605i	−0.0430027	+	0.0430027i
$225$	−27.2117	−	9.16993i	−1.81411	−	0.611329i
$226$			15.1701i			1.00910i
$227$	−19.6620			−1.30501			−0.652507	−	0.757783i	$-0.726283\pi$
$227$	−19.6620			−1.30501			−0.652507	+	0.757783i	$0.726283\pi$
$228$			4.53784i			0.300526i
$229$			13.4975i			0.891940i	0.895048	+	0.445970i	$0.147141\pi$
$229$			13.4975i			0.891940i	−0.895048	+	0.445970i	$0.852859\pi$
$230$	−6.06708	−	8.44682i	−0.400051	−	0.556967i
$231$	−5.07057			−0.333619
$232$	−3.33033	−	3.33033i	−0.218647	−	0.218647i
$233$	1.10924	+	1.10924i	0.0726687	+	0.0726687i	0.742507	−	0.669838i	$-0.233637\pi$
$233$	1.10924	+	1.10924i	0.0726687	+	0.0726687i	−0.669838	+	0.742507i	$0.733637\pi$
$234$			3.07874i			0.201264i
$235$	0.0724186	−	0.441676i	0.00472407	−	0.0288118i
$236$	−4.10789	−	4.10789i	−0.267401	−	0.267401i
$237$			23.9874i			1.55815i
$238$	−0.215416	+	0.215416i	−0.0139634	+	0.0139634i
$239$	−10.5161	−	10.5161i	−0.680230	−	0.680230i	0.279822	−	0.960052i	$-0.409725\pi$
$239$	−10.5161	−	10.5161i	−0.680230	−	0.680230i	−0.960052	+	0.279822i	$0.909725\pi$
$240$	−1.06980	+	6.52462i	−0.0690551	+	0.421163i
$241$	−18.7617	+	18.7617i	−1.20855	+	1.20855i	−0.237047	+	0.971498i	$0.576180\pi$
$241$	−18.7617	+	18.7617i	−1.20855	+	1.20855i	−0.971498	+	0.237047i	$0.923820\pi$
$242$		−	7.45037i		−	0.478928i
$243$	3.08553	+	3.08553i	0.197937	+	0.197937i
$244$	8.90180	+	8.90180i	0.569879	+	0.569879i
$245$	11.2084	−	8.05061i	0.716076	−	0.514334i
$246$	−17.2803	−	17.2803i	−1.10175	−	1.10175i
$247$	0.581747	−	0.581747i	0.0370157	−	0.0370157i
$248$	−4.90948	+	4.90948i	−0.311752	+	0.311752i
$249$	−33.0548			−2.09476
$250$	3.28101	+	10.6881i	0.207510	+	0.675973i
$251$	9.09164	+	9.09164i	0.573859	+	0.573859i	0.933205	−	0.359346i	$-0.117000\pi$
$251$	9.09164	+	9.09164i	0.573859	+	0.573859i	−0.359346	+	0.933205i	$0.617000\pi$
$252$	−3.69625	+	3.69625i	−0.232842	+	0.232842i
$253$	−8.76267			−0.550904
$254$	−3.59805	+	3.59805i	−0.225762	+	0.225762i
$255$	−0.358064	+	2.18381i	−0.0224228	+	0.136756i
$256$	1.00000			0.0625000
$257$	−2.08454			−0.130030			−0.0650151	−	0.997884i	$-0.520710\pi$
$257$	−2.08454			−0.130030			−0.0650151	+	0.997884i	$0.520710\pi$
$258$	−24.9052	−	24.9052i	−1.55053	−	1.55053i
$259$	−4.40672	−	3.35166i	−0.273820	−	0.208262i
$260$	0.973599	−	0.699305i	0.0603800	−	0.0433690i
$261$	−19.1262	−	19.1262i	−1.18388	−	1.18388i
$262$	7.63639	−	7.63639i	0.471778	−	0.471778i
$263$	6.41417	+	6.41417i	0.395515	+	0.395515i	0.876648	−	0.481133i	$-0.159775\pi$
$263$	6.41417	+	6.41417i	0.395515	+	0.395515i	−0.481133	+	0.876648i	$0.659775\pi$
$264$	3.93919	+	3.93919i	0.242441	+	0.242441i
$265$	−15.7059	−	2.57519i	−0.964806	−	0.158192i
$266$	1.39686			0.0856469
$267$	−5.08157			−0.310987
$268$	−3.61956	+	3.61956i	−0.221100	+	0.221100i
$269$		−	10.5529i		−	0.643424i	−0.946838	−	0.321712i	$-0.895742\pi$
$269$		−	10.5529i		−	0.643424i	0.946838	−	0.321712i	$-0.104258\pi$
$270$	−2.93449	+	17.8973i	−0.178588	+	1.08919i
$271$	19.2734			1.17078			0.585389	−	0.810753i	$-0.300942\pi$
$271$	19.2734			1.17078			0.585389	+	0.810753i	$0.300942\pi$
$272$	0.334703			0.0202943
$273$	1.44277			0.0873204
$274$	5.48037	−	5.48037i	0.331081	−	0.331081i
$275$	8.92698	+	3.00826i	0.538317	+	0.181405i
$276$	−9.72436	+	9.72436i	−0.585338	+	0.585338i
$277$			7.82056i			0.469892i	0.972008	+	0.234946i	$0.0754913\pi$
$277$			7.82056i			0.469892i	−0.972008	+	0.234946i	$0.924509\pi$
$278$			4.24414i			0.254546i
$279$	−28.1953	+	28.1953i	−1.68801	+	1.68801i
$280$	2.00844	+	0.329310i	0.120027	+	0.0196800i
$281$	−10.4788	+	10.4788i	−0.625110	+	0.625110i	−0.946834	−	0.321723i	$-0.895738\pi$
$281$	−10.4788	+	10.4788i	−0.625110	+	0.625110i	0.321723	+	0.946834i	$0.395738\pi$
$282$	−0.591849			−0.0352441
$283$	26.3960			1.56908			0.784539	−	0.620079i	$-0.212900\pi$
$283$	26.3960			1.56908			0.784539	+	0.620079i	$0.212900\pi$
$284$	−15.5121			−0.920477
$285$	8.24133	−	5.91948i	0.488174	−	0.350640i
$286$		−	1.01000i		−	0.0597228i
$287$	−5.31930	+	5.31930i	−0.313989	+	0.313989i
$288$	5.74304			0.338412
$289$	−16.8880			−0.993410
$290$	−1.70401	+	10.3927i	−0.100063	+	0.610278i
$291$	−35.9134	−	35.9134i	−2.10528	−	2.10528i
$292$	6.82739	+	6.82739i	0.399543	+	0.399543i
$293$	−22.4956	+	22.4956i	−1.31421	+	1.31421i	−0.395928	+	0.918281i	$0.629577\pi$
$293$	−22.4956	+	22.4956i	−1.31421	+	1.31421i	−0.918281	+	0.395928i	$0.870423\pi$
$294$	−12.9036	−	12.9036i	−0.752552	−	0.752552i
$295$	−2.10186	+	12.8191i	−0.122375	+	0.746359i
$296$	0.819646	+	6.02729i	0.0476410	+	0.350329i
$297$	10.8054	+	10.8054i	0.626990	+	0.626990i
$298$	20.3080			1.17641
$299$	2.49331			0.144192
$300$	13.2451	−	6.56829i	0.764708	−	0.379221i
$301$	−7.66643	+	7.66643i	−0.441886	+	0.441886i
$302$	−13.8362			−0.796183
$303$	−28.1584	+	28.1584i	−1.61766	+	1.61766i
$304$	−1.08518	−	1.08518i	−0.0622395	−	0.0622395i
$305$	4.55473	−	27.7790i	0.260803	−	1.59062i
$306$	1.92221			0.109885
$307$	17.4358	−	17.4358i	0.995111	−	0.995111i	−0.00487690	−	0.999988i	$-0.501552\pi$
$307$	17.4358	−	17.4358i	0.995111	−	0.995111i	0.999988	+	0.00487690i	$0.00155237\pi$
$308$	1.21258	−	1.21258i	0.0690932	−	0.0690932i
$309$	−26.3864	−	26.3864i	−1.50107	−	1.50107i
$310$	15.3206	+	2.51201i	0.870150	+	0.142672i
$311$	−3.97519	−	3.97519i	−0.225412	−	0.225412i	0.585361	−	0.810773i	$-0.300953\pi$
$311$	−3.97519	−	3.97519i	−0.225412	−	0.225412i	−0.810773	+	0.585361i	$0.800953\pi$
$312$	−1.12085	−	1.12085i	−0.0634557	−	0.0634557i
$313$		−	15.8472i		−	0.895735i	−0.894100	−	0.447867i	$-0.852184\pi$
$313$		−	15.8472i		−	0.895735i	0.894100	−	0.447867i	$-0.147816\pi$
$314$	13.2682	−	13.2682i	0.748770	−	0.748770i
$315$	11.5345	+	1.89124i	0.649898	+	0.106559i
$316$	−5.73637	−	5.73637i	−0.322696	−	0.322696i
$317$	−0.950144	+	0.950144i	−0.0533654	+	0.0533654i	−0.733286	−	0.679920i	$-0.762014\pi$
$317$	−0.950144	+	0.950144i	−0.0533654	+	0.0533654i	0.679920	+	0.733286i	$0.262014\pi$
$318$			21.0460i			1.18020i
$319$	6.27449	+	6.27449i	0.351304	+	0.351304i
$320$	−1.30447	−	1.81614i	−0.0729222	−	0.101525i
$321$		−	6.89116i		−	0.384627i
$322$	2.99340	+	2.99340i	0.166816	+	0.166816i
$323$	−0.363214	−	0.363214i	−0.0202097	−	0.0202097i
$324$	6.75336			0.375186
$325$	−2.54007	−	0.855965i	−0.140897	−	0.0474804i
$326$		−	1.48487i		−	0.0822394i
$327$		−	29.5309i		−	1.63306i
$328$	8.26486			0.456350
$329$			0.182186i			0.0100442i
$330$	2.01555	−	12.2927i	0.110952	−	0.676690i
$331$	−19.3735	+	19.3735i	−1.06486	+	1.06486i	−0.0671177	+	0.997745i	$0.521380\pi$
$331$	−19.3735	+	19.3735i	−1.06486	+	1.06486i	−0.997745	+	0.0671177i	$0.978620\pi$
$332$	7.90475	−	7.90475i	0.433829	−	0.433829i
$333$	4.70726	+	34.6149i	0.257956	+	1.89689i
$334$			4.69210i			0.256740i
$335$	11.2952	+	1.85200i	0.617124	+	0.101186i
$336$		−	2.69132i		−	0.146824i
$337$	3.21128	−	3.21128i	0.174929	−	0.174929i	−0.614212	−	0.789141i	$-0.710526\pi$
$337$	3.21128	−	3.21128i	0.174929	−	0.174929i	0.789141	+	0.614212i	$0.210526\pi$
$338$		−	12.7126i		−	0.691475i
$339$	−31.7180	−	31.7180i	−1.72268	−	1.72268i
$340$	−0.436611	−	0.607866i	−0.0236785	−	0.0329662i
$341$	9.24969	−	9.24969i	0.500899	−	0.500899i
$342$	−6.23224	−	6.23224i	−0.337001	−	0.337001i
$343$	−8.47727	+	8.47727i	−0.457730	+	0.457730i
$344$	11.9117			0.642236
$345$	30.3459	+	4.97561i	1.63377	+	0.267878i
$346$	1.68127	−	1.68127i	0.0903856	−	0.0903856i
$347$		−	18.4401i		−	0.989915i	−0.868917	−	0.494957i	$-0.835184\pi$
$347$		−	18.4401i		−	0.989915i	0.868917	−	0.494957i	$-0.164816\pi$
$348$	13.9262			0.746524
$349$			21.3314i			1.14184i	0.821005	+	0.570921i	$0.193414\pi$
$349$			21.3314i			1.14184i	−0.821005	+	0.570921i	$0.806586\pi$
$350$	−2.02188	−	4.07718i	−0.108074	−	0.217934i
$351$	−3.07453	−	3.07453i	−0.164106	−	0.164106i
$352$	−1.88405			−0.100420
$353$	−11.9150			−0.634173			−0.317086	−	0.948397i	$-0.602704\pi$
$353$	−11.9150			−0.634173			−0.317086	+	0.948397i	$0.602704\pi$
$354$	17.1777			0.912985
$355$	20.2352	+	28.1722i	1.07397	+	1.49522i
$356$	1.21521	−	1.21521i	0.0644061	−	0.0644061i
$357$		−	0.900793i		−	0.0476750i
$358$	−13.0168	−	13.0168i	−0.687959	−	0.687959i
$359$			24.9976i			1.31932i	0.751562	+	0.659662i	$0.229301\pi$
$359$			24.9976i			1.31932i	−0.751562	+	0.659662i	$0.770699\pi$
$360$	−7.49163	−	10.4301i	−0.394844	−	0.549717i
$361$		−	16.6448i		−	0.876040i
$362$		−	5.91911i		−	0.311101i
$363$	15.5774	+	15.5774i	0.817600	+	0.817600i
$364$	−0.345025	+	0.345025i	−0.0180842	+	0.0180842i
$365$	3.49333	−	21.3056i	0.182849	−	1.11519i
$366$	−37.2241			−1.94573
$367$	0.228241	+	0.228241i	0.0119141	+	0.0119141i	0.713039	−	0.701125i	$-0.247318\pi$
$367$	0.228241	+	0.228241i	0.0119141	+	0.0119141i	−0.701125	+	0.713039i	$0.747318\pi$
$368$		−	4.65098i		−	0.242449i
$369$	47.4654			2.47095
$370$	9.87717	−	9.35102i	0.513490	−	0.486136i
$371$	6.47848			0.336346
$372$		−	20.5297i		−	1.06441i
$373$	−5.32431	−	5.32431i	−0.275682	−	0.275682i	0.555700	−	0.831383i	$-0.312450\pi$
$373$	−5.32431	−	5.32431i	−0.275682	−	0.275682i	−0.831383	+	0.555700i	$0.812450\pi$
$374$	−0.630595			−0.0326073
$375$	−29.2068	−	15.4868i	−1.50823	−	0.799735i
$376$	0.141535	−	0.141535i	0.00729912	−	0.00729912i
$377$	−1.78533	−	1.78533i	−0.0919492	−	0.0919492i
$378$		−	7.38239i		−	0.379709i
$379$			7.62224i			0.391528i	0.980651	+	0.195764i	$0.0627187\pi$
$379$			7.62224i			0.391528i	−0.980651	+	0.195764i	$0.937281\pi$
$380$	−0.555249	+	3.38643i	−0.0284837	+	0.173720i
$381$		−	15.0457i		−	0.770816i
$382$	8.14150	+	8.14150i	0.416556	+	0.416556i
$383$		−	9.60774i		−	0.490933i	−0.969405	−	0.245466i	$-0.921059\pi$
$383$		−	9.60774i		−	0.490933i	0.969405	−	0.245466i	$-0.0789411\pi$
$384$	−2.09082	+	2.09082i	−0.106697	+	0.106697i
$385$	−3.78399	−	0.620435i	−0.192850	−	0.0316203i
$386$	−15.8717			−0.807848
$387$	68.4093			3.47744
$388$	17.1767			0.872016
$389$	12.3615	+	12.3615i	0.626751	+	0.626751i	0.947249	−	0.320498i	$-0.103850\pi$
$389$	12.3615	+	12.3615i	0.626751	+	0.626751i	−0.320498	+	0.947249i	$0.603850\pi$
$390$	−0.573499	+	3.49774i	−0.0290403	+	0.177115i
$391$		−	1.55670i		−	0.0787256i
$392$	6.17154			0.311710
$393$			31.9326i			1.61079i
$394$	3.60225	−	3.60225i	0.181479	−	0.181479i
$395$	−2.93510	+	17.9010i	−0.147681	+	0.900695i
$396$	−10.8201			−0.543732
$397$	−22.1034	+	22.1034i	−1.10934	+	1.10934i	−0.116100	+	0.993238i	$0.537039\pi$
$397$	−22.1034	+	22.1034i	−1.10934	+	1.10934i	−0.993238	+	0.116100i	$0.962961\pi$
$398$	−1.14697	−	1.14697i	−0.0574923	−	0.0574923i
$399$	−2.92058	+	2.92058i	−0.146212	+	0.146212i
$400$	−1.59670	+	4.73820i	−0.0798352	+	0.236910i
$401$	11.3365	+	11.3365i	0.566118	+	0.566118i	0.931039	−	0.364921i	$-0.118904\pi$
$401$	11.3365	+	11.3365i	0.566118	+	0.566118i	−0.364921	+	0.931039i	$0.618904\pi$
$402$		−	15.1357i		−	0.754899i
$403$	−2.63189	+	2.63189i	−0.131104	+	0.131104i
$404$		−	13.4676i		−	0.670041i
$405$	−8.80956	−	12.2650i	−0.437751	−	0.609454i
$406$		−	4.28683i		−	0.212752i
$407$	−1.54425	−	11.3557i	−0.0765456	−	0.562880i
$408$	−0.699803	+	0.699803i	−0.0346454	+	0.0346454i
$409$	10.2703	−	10.2703i	0.507834	−	0.507834i	−0.406027	−	0.913861i	$-0.633086\pi$
$409$	10.2703	−	10.2703i	0.507834	−	0.507834i	0.913861	+	0.406027i	$0.133086\pi$
$410$	−10.7813	−	15.0101i	−0.532449	−	0.741297i
$411$			22.9169i			1.13041i
$412$	12.6201			0.621749
$413$		−	5.28772i		−	0.260192i
$414$		−	26.7108i		−	1.31276i
$415$	−24.6676	−	4.04458i	−1.21089	−	0.198541i
$416$	0.536082			0.0262836
$417$	−8.87372	−	8.87372i	−0.434548	−	0.434548i
$418$	2.04453	+	2.04453i	0.100001	+	0.100001i
$419$		−	13.8549i		−	0.676854i	−0.940993	−	0.338427i	$-0.890105\pi$
$419$		−	13.8549i		−	0.676854i	0.940993	−	0.338427i	$-0.109895\pi$
$420$	−4.88781	+	3.51075i	−0.238501	+	0.171307i
$421$	−25.5907	−	25.5907i	−1.24722	−	1.24722i	−0.956944	−	0.290273i	$-0.906254\pi$
$421$	−25.5907	−	25.5907i	−1.24722	−	1.24722i	−0.290273	−	0.956944i	$-0.593746\pi$
$422$		−	3.19579i		−	0.155569i
$423$	0.812842	−	0.812842i	0.0395217	−	0.0395217i
$424$	−5.03296	−	5.03296i	−0.244422	−	0.244422i
$425$	−0.534422	+	1.58589i	−0.0259233	+	0.0769269i
$426$	32.4331	−	32.4331i	1.57139	−	1.57139i
$427$			11.4585i			0.554515i
$428$	1.64796	+	1.64796i	0.0796571	+	0.0796571i
$429$	2.11173	+	2.11173i	0.101955	+	0.101955i
$430$	−15.5385	−	21.6333i	−0.749332	−	1.04325i
$431$	16.4247	+	16.4247i	0.791148	+	0.791148i	0.981681	−	0.190533i	$-0.0610215\pi$
$431$	16.4247	+	16.4247i	0.791148	+	0.791148i	−0.190533	+	0.981681i	$0.561021\pi$
$432$	−5.73519	+	5.73519i	−0.275934	+	0.275934i
$433$	7.66855	−	7.66855i	0.368527	−	0.368527i	−0.498413	−	0.866940i	$-0.666084\pi$
$433$	7.66855	−	7.66855i	0.368527	−	0.368527i	0.866940	+	0.498413i	$0.166084\pi$
$434$	−6.31954			−0.303347
$435$	−18.1664	−	25.2919i	−0.871011	−	1.21265i
$436$	7.06206	+	7.06206i	0.338211	+	0.338211i
$437$	−5.04717	+	5.04717i	−0.241439	+	0.241439i
$438$	−28.5497			−1.36416
$439$	−22.6564	+	22.6564i	−1.08133	+	1.08133i	−0.0849471	+	0.996385i	$0.527072\pi$
$439$	−22.6564	+	22.6564i	−1.08133	+	1.08133i	−0.996385	+	0.0849471i	$0.972928\pi$
$440$	2.45768	+	3.42168i	0.117166	+	0.163122i
$441$	35.4434			1.68778
$442$	0.179428			0.00853453
$443$	−10.4105	−	10.4105i	−0.494616	−	0.494616i	0.415141	−	0.909757i	$-0.363732\pi$
$443$	−10.4105	−	10.4105i	−0.494616	−	0.494616i	−0.909757	+	0.415141i	$0.863732\pi$
$444$	−14.3157	−	10.8882i	−0.679392	−	0.516732i
$445$	−3.79220	−	0.621781i	−0.179768	−	0.0294753i
$446$	7.29909	+	7.29909i	0.345622	+	0.345622i
$447$	−42.4604	+	42.4604i	−2.00831	+	2.00831i
$448$	0.643605	+	0.643605i	0.0304075	+	0.0304075i
$449$	16.6573	+	16.6573i	0.786107	+	0.786107i	0.980854	−	0.194746i	$-0.0623884\pi$
$449$	16.6573	+	16.6573i	0.786107	+	0.786107i	−0.194746	+	0.980854i	$0.562388\pi$
$450$	−9.16993	+	27.2117i	−0.432275	+	1.28277i
$451$	−15.5714			−0.733227
$452$	15.1701			0.713543
$453$	28.9290	−	28.9290i	1.35920	−	1.35920i
$454$			19.6620i			0.922784i
$455$	1.07669	+	0.176537i	0.0504760	+	0.00827619i
$456$	4.53784			0.212504
$457$	39.7899			1.86129			0.930647	−	0.365919i	$-0.119245\pi$
$457$	39.7899			1.86129			0.930647	+	0.365919i	$0.119245\pi$
$458$	13.4975			0.630697
$459$	−1.91958	+	1.91958i	−0.0895985	+	0.0895985i
$460$	−8.44682	+	6.06708i	−0.393835	+	0.282879i
$461$	7.71541	−	7.71541i	0.359342	−	0.359342i	−0.504228	−	0.863570i	$-0.668223\pi$
$461$	7.71541	−	7.71541i	0.359342	−	0.359342i	0.863570	+	0.504228i	$0.168223\pi$
$462$			5.07057i			0.235904i
$463$		−	14.7430i		−	0.685164i	−0.939488	−	0.342582i	$-0.888698\pi$
$463$		−	14.7430i		−	0.685164i	0.939488	−	0.342582i	$-0.111302\pi$
$464$	−3.33033	+	3.33033i	−0.154607	+	0.154607i
$465$	−37.2847	+	26.7804i	−1.72904	+	1.24191i
$466$	1.10924	−	1.10924i	0.0513845	−	0.0513845i
$467$	−28.4840			−1.31808			−0.659041	−	0.752107i	$-0.729038\pi$
$467$	−28.4840			−1.31808			−0.659041	+	0.752107i	$0.729038\pi$
$468$	3.07874			0.142315
$469$	−4.65913			−0.215139
$470$	−0.441676	−	0.0724186i	−0.0203730	−	0.00334042i
$471$			55.4829i			2.55652i
$472$	−4.10789	+	4.10789i	−0.189081	+	0.189081i
$473$	−22.4422			−1.03189
$474$	23.9874			1.10178
$475$	6.87453	−	3.40909i	0.315425	−	0.156420i
$476$	0.215416	+	0.215416i	0.00987360	+	0.00987360i
$477$	−28.9045	−	28.9045i	−1.32344	−	1.32344i
$478$	−10.5161	+	10.5161i	−0.480995	+	0.480995i
$479$	−2.09957	−	2.09957i	−0.0959318	−	0.0959318i	0.657512	−	0.753444i	$-0.271609\pi$
$479$	−2.09957	−	2.09957i	−0.0959318	−	0.0959318i	−0.753444	+	0.657512i	$0.771609\pi$
$480$	6.52462	+	1.06980i	0.297807	+	0.0488293i
$481$	0.439398	+	3.23112i	0.0200348	+	0.147326i
$482$	18.7617	+	18.7617i	0.854571	+	0.854571i
$483$	−12.5173			−0.569557
$484$	−7.45037			−0.338653
$485$	−22.4066	−	31.1953i	−1.01743	−	1.41651i
$486$	3.08553	−	3.08553i	0.139962	−	0.139962i
$487$	17.7878			0.806044			0.403022	−	0.915190i	$-0.367960\pi$
$487$	17.7878			0.806044			0.403022	+	0.915190i	$0.367960\pi$
$488$	8.90180	−	8.90180i	0.402965	−	0.402965i
$489$	3.10459	+	3.10459i	0.140395	+	0.140395i
$490$	−8.05061	−	11.2084i	−0.363689	−	0.506342i
$491$	11.1728			0.504221			0.252110	−	0.967698i	$-0.418875\pi$
$491$	11.1728			0.504221			0.252110	+	0.967698i	$0.418875\pi$
$492$	−17.2803	+	17.2803i	−0.779056	+	0.779056i
$493$	−1.11467	+	1.11467i	−0.0502022	+	0.0502022i
$494$	−0.581747	−	0.581747i	−0.0261740	−	0.0261740i
$495$	14.1146	+	19.6509i	0.634403	+	0.883240i
$496$	4.90948	+	4.90948i	0.220442	+	0.220442i
$497$	−9.98370	−	9.98370i	−0.447830	−	0.447830i
$498$			33.0548i			1.48122i
$499$	−9.60201	+	9.60201i	−0.429845	+	0.429845i	−0.888576	−	0.458730i	$-0.848304\pi$
$499$	−9.60201	+	9.60201i	−0.429845	+	0.429845i	0.458730	+	0.888576i	$0.348304\pi$
$500$	10.6881	−	3.28101i	0.477985	−	0.146731i
$501$	−9.81033	−	9.81033i	−0.438293	−	0.438293i
$502$	9.09164	−	9.09164i	0.405780	−	0.405780i
$503$			14.7806i			0.659035i	0.944149	+	0.329518i	$0.106886\pi$
$503$			14.7806i			0.659035i	−0.944149	+	0.329518i	$0.893114\pi$
$504$	3.69625	+	3.69625i	0.164644	+	0.164644i
$505$	−24.4591	+	17.5682i	−1.08842	+	0.781773i
$506$			8.76267i			0.389548i
$507$	26.5798	+	26.5798i	1.18045	+	1.18045i
$508$	3.59805	+	3.59805i	0.159638	+	0.159638i
$509$	−4.49759			−0.199352			−0.0996760	−	0.995020i	$-0.531781\pi$
$509$	−4.49759			−0.199352			−0.0996760	+	0.995020i	$0.531781\pi$
$510$	2.18381	+	0.358064i	0.0967007	+	0.0158553i
$511$			8.78829i			0.388771i
$512$		−	1.00000i		−	0.0441942i
$513$	12.4475			0.549568
$514$			2.08454i			0.0919453i
$515$	−16.4626	−	22.9199i	−0.725429	−	1.00997i
$516$	−24.9052	+	24.9052i	−1.09639	+	1.09639i
$517$	−0.266659	+	0.266659i	−0.0117276	+	0.0117276i
$518$	−3.35166	+	4.40672i	−0.147264	+	0.193620i
$519$			7.03045i			0.308603i
$520$	−0.699305	−	0.973599i	−0.0306665	−	0.0426951i
$521$		−	14.5173i		−	0.636014i	−0.948088	−	0.318007i	$-0.896986\pi$
$521$		−	14.5173i		−	0.636014i	0.948088	−	0.318007i	$-0.103014\pi$
$522$	−19.1262	+	19.1262i	−0.837131	+	0.837131i
$523$		−	27.3756i		−	1.19705i	−0.801103	−	0.598526i	$-0.795753\pi$
$523$		−	27.3756i		−	1.19705i	0.801103	−	0.598526i	$-0.204247\pi$
$524$	−7.63639	−	7.63639i	−0.333597	−	0.333597i
$525$	12.7520	+	4.29725i	0.556544	+	0.187547i
$526$	6.41417	−	6.41417i	0.279671	−	0.279671i
$527$	1.64322	+	1.64322i	0.0715797	+	0.0715797i
$528$	3.93919	−	3.93919i	0.171431	−	0.171431i
$529$	1.36834			0.0594930
$530$	−2.57519	+	15.7059i	−0.111859	+	0.682221i
$531$	−23.5918	+	23.5918i	−1.02380	+	1.02380i
$532$		−	1.39686i		−	0.0605615i
$533$	4.43064			0.191913
$534$			5.08157i			0.219901i
$535$	0.843202	−	5.14264i	0.0364548	−	0.222336i
$536$	3.61956	+	3.61956i	0.156341	+	0.156341i
$537$	54.4315			2.34889
$538$	−10.5529			−0.454970
$539$	−11.6275			−0.500831
$540$	17.8973	+	2.93449i	0.770176	+	0.126280i
$541$	15.0886	−	15.0886i	0.648708	−	0.648708i	−0.303973	−	0.952681i	$-0.598313\pi$
$541$	15.0886	−	15.0886i	0.648708	−	0.648708i	0.952681	+	0.303973i	$0.0983133\pi$
$542$		−	19.2734i		−	0.827865i
$543$	12.3758	+	12.3758i	0.531095	+	0.531095i
$544$		−	0.334703i		−	0.0143503i
$545$	3.61340	−	22.0379i	0.154781	−	0.944001i
$546$		−	1.44277i		−	0.0617449i
$547$		−	24.9954i		−	1.06873i	−0.845255	−	0.534363i	$-0.820552\pi$
$547$		−	24.9954i		−	1.06873i	0.845255	−	0.534363i	$-0.179448\pi$
$548$	−5.48037	−	5.48037i	−0.234110	−	0.234110i
$549$	51.1233	−	51.1233i	2.18189	−	2.18189i
$550$	3.00826	−	8.92698i	0.128273	−	0.380648i
$551$	7.22803			0.307924
$552$	9.72436	+	9.72436i	0.413896	+	0.413896i
$553$		−	7.38391i		−	0.313996i
$554$	7.82056			0.332264
$555$	−1.10009	+	40.2026i	−0.0466963	+	1.70651i
$556$	4.24414			0.179991
$557$			12.4355i			0.526909i	0.964672	+	0.263455i	$0.0848620\pi$
$557$			12.4355i			0.526909i	−0.964672	+	0.263455i	$0.915138\pi$
$558$	28.1953	+	28.1953i	1.19360	+	1.19360i
$559$	6.38565			0.270084
$560$	0.329310	−	2.00844i	0.0139159	−	0.0848721i
$561$	1.31846	−	1.31846i	0.0556654	−	0.0556654i
$562$	10.4788	+	10.4788i	0.442020	+	0.442020i
$563$		−	9.73552i		−	0.410303i	−0.978730	−	0.205152i	$-0.934231\pi$
$563$		−	9.73552i		−	0.410303i	0.978730	−	0.205152i	$-0.0657688\pi$
$564$			0.591849i			0.0249213i
$565$	−19.7890	−	27.5510i	−0.832530	−	1.15908i
$566$		−	26.3960i		−	1.10951i
$567$	4.34649	+	4.34649i	0.182536	+	0.182536i
$568$			15.5121i			0.650875i
$569$	10.5582	−	10.5582i	0.442624	−	0.442624i	−0.450269	−	0.892893i	$-0.648672\pi$
$569$	10.5582	−	10.5582i	0.442624	−	0.442624i	0.892893	+	0.450269i	$0.148672\pi$
$570$	−5.91948	−	8.24133i	−0.247940	−	0.345191i
$571$	13.3170			0.557301			0.278650	−	0.960393i	$-0.410113\pi$
$571$	13.3170			0.557301			0.278650	+	0.960393i	$0.410113\pi$
$572$	−1.01000			−0.0422304
$573$	−34.0448			−1.42224
$574$	5.31930	+	5.31930i	0.222023	+	0.222023i
$575$	22.0373	+	7.42625i	0.919019	+	0.309696i
$576$		−	5.74304i		−	0.239293i
$577$	−4.76082			−0.198195			−0.0990977	−	0.995078i	$-0.531596\pi$
$577$	−4.76082			−0.198195			−0.0990977	+	0.995078i	$0.531596\pi$
$578$			16.8880i			0.702447i
$579$	33.1848	−	33.1848i	1.37911	−	1.37911i
$580$	10.3927	+	1.70401i	0.431532	+	0.0707552i
$581$	10.1751			0.422133
$582$	−35.9134	+	35.9134i	−1.48866	+	1.48866i
$583$	9.48232	+	9.48232i	0.392718	+	0.392718i
$584$	6.82739	−	6.82739i	0.282519	−	0.282519i
$585$	−4.01613	−	5.59141i	−0.166047	−	0.231177i
$586$	22.4956	+	22.4956i	0.929287	+	0.929287i
$587$		−	2.41574i		−	0.0997081i	−0.998757	−	0.0498540i	$-0.984124\pi$
$587$		−	2.41574i		−	0.0997081i	0.998757	−	0.0498540i	$-0.0158756\pi$
$588$	−12.9036	+	12.9036i	−0.532134	+	0.532134i
$589$		−	10.6554i		−	0.439047i
$590$	12.8191	+	2.10186i	0.527755	+	0.0865324i
$591$			15.0633i			0.619621i
$592$	6.02729	−	0.819646i	0.247720	−	0.0336872i
$593$	1.14068	−	1.14068i	0.0468420	−	0.0468420i	−0.683298	−	0.730140i	$-0.739455\pi$
$593$	1.14068	−	1.14068i	0.0468420	−	0.0468420i	0.730140	+	0.683298i	$0.239455\pi$
$594$	10.8054	−	10.8054i	0.443349	−	0.443349i
$595$	0.110221	−	0.672231i	0.00451862	−	0.0275588i
$596$		−	20.3080i		−	0.831849i
$597$	4.79620			0.196295
$598$		−	2.49331i		−	0.101959i
$599$		−	40.0185i		−	1.63511i	−0.575851	−	0.817555i	$-0.695329\pi$
$599$		−	40.0185i		−	1.63511i	0.575851	−	0.817555i	$-0.304671\pi$
$600$	−6.56829	−	13.2451i	−0.268149	−	0.540730i
$601$	−11.7034			−0.477393			−0.238696	−	0.971094i	$-0.576720\pi$
$601$	−11.7034			−0.477393			−0.238696	+	0.971094i	$0.576720\pi$
$602$	7.66643	+	7.66643i	0.312460	+	0.312460i
$603$	20.7873	+	20.7873i	0.846522	+	0.846522i
$604$			13.8362i			0.562987i
$605$	9.71881	+	13.5309i	0.395126	+	0.550109i
$606$	28.1584	+	28.1584i	1.14386	+	1.14386i
$607$			24.3851i			0.989761i	0.868961	+	0.494881i	$0.164788\pi$
$607$			24.3851i			0.989761i	−0.868961	+	0.494881i	$0.835212\pi$
$608$	−1.08518	+	1.08518i	−0.0440100	+	0.0440100i
$609$	8.96299	+	8.96299i	0.363199	+	0.363199i
$610$	−27.7790	−	4.55473i	−1.12474	−	0.184416i
$611$	0.0758746	−	0.0758746i	0.00306956	−	0.00306956i
$612$		−	1.92221i		−	0.0777008i
$613$	−18.3951	−	18.3951i	−0.742971	−	0.742971i	0.230178	−	0.973149i	$-0.426069\pi$
$613$	−18.3951	−	18.3951i	−0.742971	−	0.742971i	−0.973149	+	0.230178i	$0.926069\pi$
$614$	−17.4358	−	17.4358i	−0.703650	−	0.703650i
$615$	53.9251	+	8.84172i	2.17447	+	0.356533i
$616$	−1.21258	−	1.21258i	−0.0488563	−	0.0488563i
$617$	−31.2896	+	31.2896i	−1.25967	+	1.25967i	−0.308421	+	0.951250i	$0.599801\pi$
$617$	−31.2896	+	31.2896i	−1.25967	+	1.25967i	−0.951250	+	0.308421i	$0.900199\pi$
$618$	−26.3864	+	26.3864i	−1.06142	+	1.06142i
$619$	39.6915			1.59534			0.797669	−	0.603096i	$-0.206066\pi$
$619$	39.6915			1.59534			0.797669	+	0.603096i	$0.206066\pi$
$620$	2.51201	−	15.3206i	0.100885	−	0.615289i
$621$	26.6743	+	26.6743i	1.07040	+	1.07040i
$622$	−3.97519	+	3.97519i	−0.159391	+	0.159391i
$623$	1.56423			0.0626697
$624$	−1.12085	+	1.12085i	−0.0448699	+	0.0448699i
$625$	−19.9011	−	15.1310i	−0.796043	−	0.605240i
$626$	−15.8472			−0.633380
$627$	−8.54949			−0.341434
$628$	−13.2682	−	13.2682i	−0.529460	−	0.529460i
$629$	2.01735	−	0.274338i	0.0804370	−	0.0109386i
$630$	1.89124	−	11.5345i	0.0753488	−	0.459547i
$631$	−29.5138	−	29.5138i	−1.17493	−	1.17493i	−0.981020	−	0.193907i	$-0.937884\pi$
$631$	−29.5138	−	29.5138i	−1.17493	−	1.17493i	−0.193907	−	0.981020i	$-0.562116\pi$
$632$	−5.73637	+	5.73637i	−0.228181	+	0.228181i
$633$	6.68182	+	6.68182i	0.265579	+	0.265579i
$634$	0.950144	+	0.950144i	0.0377350	+	0.0377350i
$635$	1.84099	−	11.2281i	0.0730576	−	0.445574i
$636$	21.0460			0.834528
$637$	3.30846			0.131086
$638$	6.27449	−	6.27449i	0.248409	−	0.248409i
$639$			89.0868i			3.52422i
$640$	−1.81614	+	1.30447i	−0.0717891	+	0.0515638i
$641$	−36.0367			−1.42336			−0.711681	−	0.702503i	$-0.752066\pi$
$641$	−36.0367			−1.42336			−0.711681	+	0.702503i	$0.752066\pi$
$642$	−6.89116			−0.271973
$643$	−36.2733			−1.43048			−0.715239	−	0.698880i	$-0.753682\pi$
$643$	−36.2733			−1.43048			−0.715239	+	0.698880i	$0.753682\pi$
$644$	2.99340	−	2.99340i	0.117956	−	0.117956i
$645$	77.7194	+	12.7431i	3.06020	+	0.501759i
$646$	−0.363214	+	0.363214i	−0.0142905	+	0.0142905i
$647$			20.1761i			0.793203i	0.917991	+	0.396602i	$0.129811\pi$
$647$			20.1761i			0.793203i	−0.917991	+	0.396602i	$0.870189\pi$
$648$		−	6.75336i		−	0.265297i
$649$	7.73946	−	7.73946i	0.303800	−	0.303800i
$650$	−0.855965	+	2.54007i	−0.0335737	+	0.0996296i
$651$	13.2130	−	13.2130i	0.517858	−	0.517858i
$652$	−1.48487			−0.0581520
$653$	45.2272			1.76988			0.884939	−	0.465706i	$-0.154200\pi$
$653$	45.2272			1.76988			0.884939	+	0.465706i	$0.154200\pi$
$654$	−29.5309			−1.15475
$655$	−3.90727	+	23.8302i	−0.152670	+	0.931122i
$656$		−	8.26486i		−	0.322688i
$657$	39.2100	−	39.2100i	1.52973	−	1.52973i
$658$	0.182186			0.00710234
$659$	3.64301			0.141911			0.0709557	−	0.997479i	$-0.477395\pi$
$659$	3.64301			0.141911			0.0709557	+	0.997479i	$0.477395\pi$
$660$	−12.2927	−	2.01555i	−0.478492	−	0.0784550i
$661$	0.359733	+	0.359733i	0.0139920	+	0.0139920i	0.714068	−	0.700076i	$-0.246851\pi$
$661$	0.359733	+	0.359733i	0.0139920	+	0.0139920i	−0.700076	+	0.714068i	$0.746851\pi$
$662$	19.3735	+	19.3735i	0.752972	+	0.752972i
$663$	−0.375152	+	0.375152i	−0.0145697	+	0.0145697i
$664$	−7.90475	−	7.90475i	−0.306764	−	0.306764i
$665$	−2.53689	+	1.82216i	−0.0983762	+	0.0706604i
$666$	34.6149	−	4.70726i	1.34130	−	0.182402i
$667$	15.4893	+	15.4893i	0.599749	+	0.599749i
$668$	4.69210			0.181543
$669$	−30.5221			−1.18005
$670$	1.85200	−	11.2952i	0.0715490	−	0.436373i
$671$	−16.7714	+	16.7714i	−0.647452	+	0.647452i
$672$	−2.69132			−0.103820
$673$	12.3228	−	12.3228i	0.475011	−	0.475011i	−0.428521	−	0.903532i	$-0.640965\pi$
$673$	12.3228	−	12.3228i	0.475011	−	0.475011i	0.903532	+	0.428521i	$0.140965\pi$
$674$	−3.21128	−	3.21128i	−0.123694	−	0.123694i
$675$	−18.0171	−	36.3319i	−0.693477	−	1.39841i
$676$	−12.7126			−0.488947
$677$	−13.3890	+	13.3890i	−0.514579	+	0.514579i	−0.915926	−	0.401347i	$-0.868542\pi$
$677$	−13.3890	+	13.3890i	−0.514579	+	0.514579i	0.401347	+	0.915926i	$0.368542\pi$
$678$	−31.7180	+	31.7180i	−1.21812	+	1.21812i
$679$	11.0550	+	11.0550i	0.424253	+	0.424253i
$680$	−0.607866	+	0.436611i	−0.0233106	+	0.0167433i
$681$	−41.1097	−	41.1097i	−1.57533	−	1.57533i
$682$	−9.24969	−	9.24969i	−0.354189	−	0.354189i
$683$		−	26.4505i		−	1.01210i	−0.862504	−	0.506050i	$-0.831105\pi$
$683$		−	26.4505i		−	1.01210i	0.862504	−	0.506050i	$-0.168895\pi$
$684$	−6.23224	+	6.23224i	−0.238296	+	0.238296i
$685$	−2.80411	+	17.1021i	−0.107140	+	0.653437i
$686$	8.47727	+	8.47727i	0.323664	+	0.323664i
$687$	−28.2208	+	28.2208i	−1.07669	+	1.07669i
$688$		−	11.9117i		−	0.454129i
$689$	−2.69808	−	2.69808i	−0.102789	−	0.102789i
$690$	4.97561	−	30.3459i	0.189418	−	1.15525i
$691$			8.34143i			0.317323i	0.987333	+	0.158661i	$0.0507178\pi$
$691$			8.34143i			0.317323i	−0.987333	+	0.158661i	$0.949282\pi$
$692$	−1.68127	−	1.68127i	−0.0639123	−	0.0639123i
$693$	−6.96390	−	6.96390i	−0.264537	−	0.264537i
$694$	−18.4401			−0.699976
$695$	−5.53636	−	7.70793i	−0.210006	−	0.292379i
$696$		−	13.9262i		−	0.527872i
$697$		−	2.76627i		−	0.104780i
$698$	21.3314			0.807405
$699$			4.63843i			0.175442i
$700$	−4.07718	+	2.02188i	−0.154103	+	0.0764200i
$701$	15.0534	−	15.0534i	0.568560	−	0.568560i	−0.363165	−	0.931725i	$-0.618304\pi$
$701$	15.0534	−	15.0534i	0.568560	−	0.568560i	0.931725	+	0.363165i	$0.118304\pi$
$702$	−3.07453	+	3.07453i	−0.116041	+	0.116041i
$703$	−7.43017	−	5.65124i	−0.280234	−	0.213141i
$704$			1.88405i			0.0710076i
$705$	1.07488	−	0.772050i	0.0404823	−	0.0290771i
$706$			11.9150i			0.448428i
$707$	8.66785	−	8.66785i	0.325988	−	0.325988i
$708$		−	17.1777i		−	0.645578i
$709$	−26.5041	−	26.5041i	−0.995384	−	0.995384i	0.00460560	−	0.999989i	$-0.498534\pi$
$709$	−26.5041	−	26.5041i	−0.995384	−	0.995384i	−0.999989	+	0.00460560i	$0.998534\pi$
$710$	28.1722	−	20.2352i	1.05728	−	0.759412i
$711$	−32.9442	+	32.9442i	−1.23550	+	1.23550i
$712$	−1.21521	−	1.21521i	−0.0455420	−	0.0455420i
$713$	22.8339	−	22.8339i	0.855137	−	0.855137i
$714$	−0.900793			−0.0337113
$715$	1.31752	+	1.83430i	0.0492725	+	0.0685991i
$716$	−13.0168	+	13.0168i	−0.486461	+	0.486461i
$717$		−	43.9745i		−	1.64226i
$718$	24.9976			0.932903
$719$		−	17.0904i		−	0.637364i	−0.947862	−	0.318682i	$-0.896760\pi$
$719$		−	17.0904i		−	0.637364i	0.947862	−	0.318682i	$-0.103240\pi$
$720$	−10.4301	+	7.49163i	−0.388708	+	0.279197i
$721$	8.12238	+	8.12238i	0.302493	+	0.302493i
$722$	−16.6448			−0.619454
$723$	−78.4545			−2.91775
$724$	−5.91911			−0.219982
$725$	−10.4622	−	21.0973i	−0.388557	−	0.783535i
$726$	15.5774	−	15.5774i	0.578131	−	0.578131i
$727$		−	49.5068i		−	1.83611i	−0.396457	−	0.918053i	$-0.629760\pi$
$727$		−	49.5068i		−	1.83611i	0.396457	−	0.918053i	$-0.370240\pi$
$728$	0.345025	+	0.345025i	0.0127875	+	0.0127875i
$729$			33.1626i			1.22825i
$730$	−21.3056	−	3.49333i	−0.788556	−	0.129294i
$731$		−	3.98688i		−	0.147460i
$732$			37.2241i			1.37584i
$733$	−8.80945	−	8.80945i	−0.325385	−	0.325385i	0.525444	−	0.850828i	$-0.323899\pi$
$733$	−8.80945	−	8.80945i	−0.325385	−	0.325385i	−0.850828	+	0.525444i	$0.823899\pi$
$734$	0.228241	−	0.228241i	0.00842451	−	0.00842451i
$735$	40.2670	+	6.60230i	1.48527	+	0.243530i
$736$	−4.65098			−0.171438
$737$	−6.81941	−	6.81941i	−0.251196	−	0.251196i
$738$		−	47.4654i		−	1.74722i
$739$	44.3001			1.62961			0.814803	−	0.579738i	$-0.196845\pi$
$739$	44.3001			1.62961			0.814803	+	0.579738i	$0.196845\pi$
$740$	−9.35102	−	9.87717i	−0.343750	−	0.363092i
$741$	2.43265			0.0893658
$742$		−	6.47848i		−	0.237832i
$743$	16.9715	+	16.9715i	0.622623	+	0.622623i	0.946201	−	0.323579i	$-0.104886\pi$
$743$	16.9715	+	16.9715i	0.622623	+	0.622623i	−0.323579	+	0.946201i	$0.604886\pi$
$744$	−20.5297			−0.752654
$745$	−36.8822	+	26.4913i	−1.35126	+	0.970564i
$746$	−5.32431	+	5.32431i	−0.194937	+	0.194937i
$747$	−45.3972	−	45.3972i	−1.66100	−	1.66100i
$748$			0.630595i			0.0230568i
$749$			2.12127i			0.0775095i
$750$	−15.4868	+	29.2068i	−0.565498	+	1.06648i
$751$		−	10.2040i		−	0.372350i	−0.982517	−	0.186175i	$-0.940391\pi$
$751$		−	10.2040i		−	0.372350i	0.982517	−	0.186175i	$-0.0596091\pi$
$752$	−0.141535	−	0.141535i	−0.00516126	−	0.00516126i
$753$			38.0179i			1.38545i
$754$	−1.78533	+	1.78533i	−0.0650179	+	0.0650179i
$755$	25.1284	−	18.0489i	0.914517	−	0.656868i
$756$	−7.38239			−0.268495
$757$	6.71387			0.244020			0.122010	−	0.992529i	$-0.461066\pi$
$757$	6.71387			0.244020			0.122010	+	0.992529i	$0.461066\pi$
$758$	7.62224			0.276852
$759$	−18.3211	−	18.3211i	−0.665015	−	0.665015i
$760$	3.38643	+	0.555249i	0.122839	+	0.0201410i
$761$		−	1.33026i		−	0.0482218i	−0.999709	−	0.0241109i	$-0.992325\pi$
$761$		−	1.33026i		−	0.0482218i	0.999709	−	0.0241109i	$-0.00767549\pi$
$762$	−15.0457			−0.545049
$763$			9.09035i			0.329093i
$764$	8.14150	−	8.14150i	0.294549	−	0.294549i
$765$	−3.49100	+	2.50747i	−0.126217	+	0.0906578i
$766$	−9.60774			−0.347142
$767$	−2.20217	+	2.20217i	−0.0795157	+	0.0795157i
$768$	2.09082	+	2.09082i	0.0754459	+	0.0754459i
$769$	−18.1678	+	18.1678i	−0.655148	+	0.655148i	−0.954228	−	0.299080i	$-0.903320\pi$
$769$	−18.1678	+	18.1678i	−0.655148	+	0.655148i	0.299080	+	0.954228i	$0.403320\pi$
$770$	−0.620435	+	3.78399i	−0.0223589	+	0.136366i
$771$	−4.35840	−	4.35840i	−0.156964	−	0.156964i
$772$			15.8717i			0.571235i
$773$	19.9474	−	19.9474i	0.717458	−	0.717458i	−0.250626	−	0.968084i	$-0.580637\pi$
$773$	19.9474	−	19.9474i	0.717458	−	0.717458i	0.968084	+	0.250626i	$0.0806365\pi$
$774$		−	68.4093i		−	2.45892i
$775$	−31.1011	+	15.4231i	−1.11718	+	0.554015i
$776$		−	17.1767i		−	0.616609i
$777$	−2.20593	−	16.2214i	−0.0791373	−	0.581938i
$778$	12.3615	−	12.3615i	0.443180	−	0.443180i
$779$	−8.96888	+	8.96888i	−0.321343	+	0.321343i
$780$	3.49774	+	0.573499i	0.125239	+	0.0205346i
$781$		−	29.2256i		−	1.04577i
$782$	−1.55670			−0.0556674
$783$		−	38.2001i		−	1.36516i
$784$		−	6.17154i		−	0.220412i
$785$	−6.78889	+	41.4050i	−0.242306	+	1.47781i
$786$	31.9326			1.13900
$787$	34.1482	+	34.1482i	1.21725	+	1.21725i	0.968590	+	0.248663i	$0.0799912\pi$
$787$	34.1482	+	34.1482i	1.21725	+	1.21725i	0.248663	+	0.968590i	$0.420009\pi$
$788$	−3.60225	−	3.60225i	−0.128325	−	0.128325i
$789$			26.8217i			0.954878i
$790$	17.9010	+	2.93510i	0.636888	+	0.104426i
$791$	9.76357	+	9.76357i	0.347153	+	0.347153i
$792$			10.8201i			0.384477i
$793$	4.77210	−	4.77210i	0.169462	−	0.169462i
$794$	22.1034	+	22.1034i	0.784420	+	0.784420i
$795$	−27.4539	−	38.2224i	−0.973690	−	1.35561i
$796$	−1.14697	+	1.14697i	−0.0406532	+	0.0406532i
$797$		−	48.5605i		−	1.72010i	−0.510209	−	0.860050i	$-0.670432\pi$
$797$		−	48.5605i		−	1.72010i	0.510209	−	0.860050i	$-0.329568\pi$
$798$	2.92058	+	2.92058i	0.103387	+	0.103387i
$799$	−0.0473723	−	0.0473723i	−0.00167591	−	0.00167591i
$800$	4.73820	+	1.59670i	0.167521	+	0.0564520i
$801$	−6.97901	−	6.97901i	−0.246591	−	0.246591i
$802$	11.3365	−	11.3365i	0.400306	−	0.400306i
$803$	−12.8631	+	12.8631i	−0.453929	+	0.453929i
$804$	−15.1357			−0.533794
$805$	−9.34122	−	1.53162i	−0.329235	−	0.0539824i
$806$	2.63189	+	2.63189i	0.0927043	+	0.0927043i
$807$	22.0643	−	22.0643i	0.776699	−	0.776699i
$808$	−13.4676			−0.473790
$809$	−18.4675	+	18.4675i	−0.649284	+	0.649284i	−0.952820	−	0.303536i	$-0.901833\pi$
$809$	−18.4675	+	18.4675i	−0.649284	+	0.649284i	0.303536	+	0.952820i	$0.401833\pi$
$810$	−12.2650	+	8.80956i	−0.430949	+	0.309537i
$811$	−41.1929			−1.44648			−0.723238	−	0.690598i	$-0.757347\pi$
$811$	−41.1929			−1.44648			−0.723238	+	0.690598i	$0.757347\pi$
$812$	−4.28683			−0.150438
$813$	40.2972	+	40.2972i	1.41329	+	1.41329i
$814$	−11.3557	+	1.54425i	−0.398016	+	0.0541259i
$815$	1.93697	+	2.69673i	0.0678492	+	0.0944623i
$816$	0.699803	+	0.699803i	0.0244980	+	0.0244980i
$817$	−12.9264	+	12.9264i	−0.452236	+	0.452236i
$818$	−10.2703	−	10.2703i	−0.359093	−	0.359093i
$819$	1.98149	+	1.98149i	0.0692390	+	0.0692390i
$820$	−15.0101	+	10.7813i	−0.524176	+	0.376498i
$821$	54.6337			1.90673			0.953364	−	0.301822i	$-0.0975948\pi$
$821$	54.6337			1.90673			0.953364	+	0.301822i	$0.0975948\pi$
$822$	22.9169			0.799319
$823$	38.9987	−	38.9987i	1.35941	−	1.35941i	0.484768	−	0.874643i	$-0.338904\pi$
$823$	38.9987	−	38.9987i	1.35941	−	1.35941i	0.874643	−	0.484768i	$-0.161096\pi$
$824$		−	12.6201i		−	0.439643i
$825$	12.3750	+	24.9544i	0.430841	+	0.868801i
$826$	−5.28772			−0.183983
$827$	−1.62207			−0.0564050			−0.0282025	−	0.999602i	$-0.508978\pi$
$827$	−1.62207			−0.0564050			−0.0282025	+	0.999602i	$0.508978\pi$
$828$	−26.7108			−0.928264
$829$	−28.1215	+	28.1215i	−0.976699	+	0.976699i	−0.999735	−	0.0230357i	$-0.992667\pi$
$829$	−28.1215	+	28.1215i	−0.976699	+	0.976699i	0.0230357	+	0.999735i	$0.492667\pi$
$830$	−4.04458	+	24.6676i	−0.140389	+	0.856226i
$831$	−16.3514	+	16.3514i	−0.567222	+	0.567222i
$832$		−	0.536082i		−	0.0185853i
$833$		−	2.06563i		−	0.0715700i
$834$	−8.87372	+	8.87372i	−0.307272	+	0.307272i
$835$	−6.12071	−	8.52150i	−0.211816	−	0.294899i
$836$	2.04453	−	2.04453i	0.0707116	−	0.0707116i
$837$	−56.3136			−1.94648
$838$	−13.8549			−0.478608
$839$	35.3409			1.22010			0.610052	−	0.792361i	$-0.291149\pi$
$839$	35.3409			1.22010			0.610052	+	0.792361i	$0.291149\pi$
$840$	3.51075	+	4.88781i	0.121133	+	0.168645i
$841$			6.81781i			0.235097i
$842$	−25.5907	+	25.5907i	−0.881915	+	0.881915i
$843$	−43.8183			−1.50918
$844$	−3.19579			−0.110004
$845$	16.5833	+	23.0878i	0.570481	+	0.794246i
$846$	−0.812842	−	0.812842i	−0.0279461	−	0.0279461i
$847$	−4.79510	−	4.79510i	−0.164762	−	0.164762i
$848$	−5.03296	+	5.03296i	−0.172833	+	0.172833i
$849$	55.1892	+	55.1892i	1.89409	+	1.89409i
$850$	1.58589	+	0.534422i	0.0543955	+	0.0183305i
$851$	−3.81216	−	28.0328i	−0.130679	−	0.960953i
$852$	−32.4331	−	32.4331i	−1.11114	−	1.11114i
$853$	42.8331			1.46658			0.733289	−	0.679917i	$-0.237984\pi$
$853$	42.8331			1.46658			0.733289	+	0.679917i	$0.237984\pi$
$854$	11.4585			0.392101
$855$	19.4484	+	3.18882i	0.665121	+	0.109055i
$856$	1.64796	−	1.64796i	0.0563261	−	0.0563261i
$857$	−9.21841			−0.314895			−0.157447	−	0.987527i	$-0.550326\pi$
$857$	−9.21841			−0.314895			−0.157447	+	0.987527i	$0.550326\pi$
$858$	2.11173	−	2.11173i	0.0720934	−	0.0720934i
$859$	26.7930	+	26.7930i	0.914167	+	0.914167i	0.996597	−	0.0824302i	$-0.0262682\pi$
$859$	26.7930	+	26.7930i	0.914167	+	0.914167i	−0.0824302	+	0.996597i	$0.526268\pi$
$860$	−21.6333	+	15.5385i	−0.737689	+	0.529858i
$861$	−22.2434			−0.758053
$862$	16.4247	−	16.4247i	0.559426	−	0.559426i
$863$	−28.1937	+	28.1937i	−0.959726	+	0.959726i	−0.999220	−	0.0394943i	$-0.987425\pi$
$863$	−28.1937	+	28.1937i	−0.959726	+	0.959726i	0.0394943	+	0.999220i	$0.487425\pi$
$864$	5.73519	+	5.73519i	0.195115	+	0.195115i
$865$	−0.860246	+	5.24658i	−0.0292492	+	0.178389i
$866$	−7.66855	−	7.66855i	−0.260588	−	0.260588i
$867$	−35.3097	−	35.3097i	−1.19918	−	1.19918i
$868$			6.31954i			0.214499i
$869$	10.8076	−	10.8076i	0.366622	−	0.366622i
$870$	−25.2919	+	18.1664i	−0.857476	+	0.615898i
$871$	1.94038	+	1.94038i	0.0657473	+	0.0657473i
$872$	7.06206	−	7.06206i	0.239151	−	0.239151i
$873$		−	98.6466i		−	3.33868i
$874$	5.04717	+	5.04717i	0.170723	+	0.170723i
$875$	8.99058	+	4.76722i	0.303937	+	0.161162i
$876$			28.5497i			0.964604i
$877$	19.0689	+	19.0689i	0.643910	+	0.643910i	0.951514	−	0.307604i	$-0.0995274\pi$
$877$	19.0689	+	19.0689i	0.643910	+	0.643910i	−0.307604	+	0.951514i	$0.599527\pi$
$878$	22.6564	+	22.6564i	0.764618	+	0.764618i
$879$	−94.0686			−3.17285
$880$	3.42168	−	2.45768i	0.115345	−	0.0828485i
$881$			2.04078i			0.0687555i	0.999409	+	0.0343777i	$0.0109449\pi$
$881$			2.04078i			0.0687555i	−0.999409	+	0.0343777i	$0.989055\pi$
$882$		−	35.4434i		−	1.19344i
$883$	46.2566			1.55666			0.778329	−	0.627857i	$-0.216068\pi$
$883$	46.2566			1.55666			0.778329	+	0.627857i	$0.216068\pi$
$884$		−	0.179428i		−	0.00603483i
$885$	−31.1971	+	22.4078i	−1.04868	+	0.753232i
$886$	−10.4105	+	10.4105i	−0.349746	+	0.349746i
$887$	31.6807	−	31.6807i	1.06373	−	1.06373i	0.0659094	−	0.997826i	$-0.479005\pi$
$887$	31.6807	−	31.6807i	1.06373	−	1.06373i	0.997826	−	0.0659094i	$-0.0209948\pi$
$888$	−10.8882	+	14.3157i	−0.365385	+	0.480403i
$889$			4.63145i			0.155334i
$890$	−0.621781	+	3.79220i	−0.0208421	+	0.127115i
$891$			12.7236i			0.426258i
$892$	7.29909	−	7.29909i	0.244392	−	0.244392i
$893$			0.307183i			0.0102795i
$894$	42.4604	+	42.4604i	1.42009	+	1.42009i
$895$	40.6203	+	6.66024i	1.35779	+	0.222627i
$896$	0.643605	−	0.643605i	0.0215013	−	0.0215013i
$897$	5.21306	+	5.21306i	0.174059	+	0.174059i
$898$	16.6573	−	16.6573i	0.555862	−	0.555862i
$899$	−32.7004			−1.09062
$900$	27.2117	+	9.16993i	0.907055	+	0.305664i
$901$	−1.68455	+	1.68455i	−0.0561204	+	0.0561204i
$902$			15.5714i			0.518470i
$903$	−32.0582			−1.06683
$904$		−	15.1701i		−	0.504551i
$905$	7.72131	+	10.7499i	0.256665	+	0.357339i
$906$	−28.9290	−	28.9290i	−0.961100	−	0.961100i
$907$	−36.2975			−1.20524			−0.602620	−	0.798029i	$-0.705876\pi$
$907$	−36.2975			−1.20524			−0.602620	+	0.798029i	$0.705876\pi$
$908$	19.6620			0.652507
$909$	−77.3452			−2.56538
$910$	0.176537	−	1.07669i	0.00585215	−	0.0356919i
$911$	−5.83123	+	5.83123i	−0.193197	+	0.193197i	−0.797076	−	0.603879i	$-0.793621\pi$
$911$	−5.83123	+	5.83123i	−0.193197	+	0.193197i	0.603879	+	0.797076i	$0.293621\pi$
$912$		−	4.53784i		−	0.150263i
$913$	14.8929	+	14.8929i	0.492883	+	0.492883i
$914$		−	39.7899i		−	1.31613i
$915$	67.6040	−	48.5578i	2.23492	−	1.60527i
$916$		−	13.4975i		−	0.445970i
$917$		−	9.82963i		−	0.324603i
$918$	1.91958	+	1.91958i	0.0633557	+	0.0633557i
$919$	10.4404	−	10.4404i	0.344396	−	0.344396i	−0.513621	−	0.858017i	$-0.671696\pi$
$919$	10.4404	−	10.4404i	0.344396	−	0.344396i	0.858017	+	0.513621i	$0.171696\pi$
$920$	6.06708	+	8.44682i	0.200026	+	0.278484i
$921$	72.9100			2.40247
$922$	−7.71541	−	7.71541i	−0.254093	−	0.254093i
$923$			8.31579i			0.273718i
$924$	5.07057			0.166810
$925$	−5.74015	+	29.8672i	−0.188735	+	0.982028i
$926$	−14.7430			−0.484484
$927$		−	72.4779i		−	2.38049i
$928$	3.33033	+	3.33033i	0.109323	+	0.109323i
$929$	24.9525			0.818666			0.409333	−	0.912385i	$-0.365761\pi$
$929$	24.9525			0.818666			0.409333	+	0.912385i	$0.365761\pi$
$930$	26.7804	+	37.2847i	0.878163	+	1.22261i
$931$	−6.69725	+	6.69725i	−0.219494	+	0.219494i
$932$	−1.10924	−	1.10924i	−0.0363343	−	0.0363343i
$933$		−	16.6228i		−	0.544206i
$934$			28.4840i			0.932025i
$935$	1.14525	−	0.822594i	0.0374536	−	0.0269017i
$936$		−	3.07874i		−	0.100632i
$937$	−27.8220	−	27.8220i	−0.908904	−	0.908904i	0.0872802	−	0.996184i	$-0.472182\pi$
$937$	−27.8220	−	27.8220i	−0.908904	−	0.908904i	−0.996184	+	0.0872802i	$0.972182\pi$
$938$			4.65913i			0.152126i
$939$	33.1335	−	33.1335i	1.08127	−	1.08127i
$940$	−0.0724186	+	0.441676i	−0.00236203	+	0.0144059i
$941$	29.9817			0.977374			0.488687	−	0.872459i	$-0.337476\pi$
$941$	29.9817			0.977374			0.488687	+	0.872459i	$0.337476\pi$
$942$	55.4829			1.80773
$943$	−38.4397			−1.25177
$944$	4.10789	+	4.10789i	0.133701	+	0.133701i
$945$	9.63013	+	13.4074i	0.313268	+	0.436144i
$946$			22.4422i			0.729658i
$947$	−26.4941			−0.860941			−0.430471	−	0.902605i	$-0.641652\pi$
$947$	−26.4941			−0.860941			−0.430471	+	0.902605i	$0.641652\pi$
$948$		−	23.9874i		−	0.779075i
$949$	3.66004	−	3.66004i	0.118810	−	0.118810i
$950$	−3.40909	−	6.87453i	−0.110606	−	0.223039i
$951$	−3.97316			−0.128838
$952$	0.215416	−	0.215416i	0.00698169	−	0.00698169i
$953$	16.5640	+	16.5640i	0.536561	+	0.536561i	0.922517	−	0.385956i	$-0.126128\pi$
$953$	16.5640	+	16.5640i	0.536561	+	0.536561i	−0.385956	+	0.922517i	$0.626128\pi$
$954$	−28.9045	+	28.9045i	−0.935817	+	0.935817i
$955$	−25.4064	−	4.16572i	−0.822133	−	0.134800i
$956$	10.5161	+	10.5161i	0.340115	+	0.340115i
$957$			26.2376i			0.848142i
$958$	−2.09957	+	2.09957i	−0.0678340	+	0.0678340i
$959$		−	7.05439i		−	0.227798i
$960$	1.06980	−	6.52462i	0.0345276	−	0.210581i
$961$			17.2060i			0.555033i
$962$	3.23112	−	0.439398i	0.104176	−	0.0141668i
$963$	9.46429	−	9.46429i	0.304982	−	0.304982i
$964$	18.7617	−	18.7617i	0.604273	−	0.604273i
$965$	28.8252	−	20.7042i	0.927915	−	0.666491i
$966$			12.5173i			0.402737i
$967$	4.61124			0.148288			0.0741438	−	0.997248i	$-0.476378\pi$
$967$	4.61124			0.148288			0.0741438	+	0.997248i	$0.476378\pi$
$968$			7.45037i			0.239464i
$969$		−	1.51883i		−	0.0487918i
$970$	−31.1953	+	22.4066i	−1.00162	+	0.719432i
$971$	−27.9365			−0.896524			−0.448262	−	0.893902i	$-0.647957\pi$
$971$	−27.9365			−0.896524			−0.448262	+	0.893902i	$0.647957\pi$
$972$	−3.08553	−	3.08553i	−0.0989684	−	0.0989684i
$973$	2.73155	+	2.73155i	0.0875694	+	0.0875694i
$974$		−	17.7878i		−	0.569959i
$975$	−3.52115	−	7.10048i	−0.112767	−	0.227397i
$976$	−8.90180	−	8.90180i	−0.284940	−	0.284940i
$977$			6.07748i			0.194436i	0.995263	+	0.0972180i	$0.0309944\pi$
$977$			6.07748i			0.194436i	−0.995263	+	0.0972180i	$0.969006\pi$
$978$	3.10459	−	3.10459i	0.0992739	−	0.0992739i
$979$	2.28951	+	2.28951i	0.0731732	+	0.0731732i
$980$	−11.2084	+	8.05061i	−0.358038	+	0.257167i
$981$	40.5576	−	40.5576i	1.29491	−	1.29491i
$982$		−	11.1728i		−	0.356538i
$983$	−18.5414	−	18.5414i	−0.591379	−	0.591379i	0.346625	−	0.938004i	$-0.387328\pi$
$983$	−18.5414	−	18.5414i	−0.591379	−	0.591379i	−0.938004	+	0.346625i	$0.887328\pi$
$984$	17.2803	+	17.2803i	0.550876	+	0.550876i
$985$	−1.84314	+	11.2412i	−0.0587274	+	0.358175i
$986$	1.11467	+	1.11467i	0.0354983	+	0.0354983i
$987$	−0.380917	+	0.380917i	−0.0121247	+	0.0121247i
$988$	−0.581747	+	0.581747i	−0.0185078	+	0.0185078i
$989$	−55.4011			−1.76165
$990$	19.6509	−	14.1146i	0.624545	−	0.448590i
$991$	−8.80348	−	8.80348i	−0.279652	−	0.279652i	0.553318	−	0.832970i	$-0.313361\pi$
$991$	−8.80348	−	8.80348i	−0.279652	−	0.279652i	−0.832970	+	0.553318i	$0.813361\pi$
$992$	4.90948	−	4.90948i	0.155876	−	0.155876i
$993$	−81.0128			−2.57086
$994$	−9.98370	+	9.98370i	−0.316664	+	0.316664i
$995$	3.57924	+	0.586863i	0.113469	+	0.0186048i
$996$	33.0548			1.04738
$997$	−31.7260			−1.00477			−0.502386	−	0.864644i	$-0.667544\pi$
$997$	−31.7260			−1.00477			−0.502386	+	0.864644i	$0.667544\pi$
$998$	9.60201	+	9.60201i	0.303946	+	0.303946i
$999$	−29.8668	+	39.2684i	−0.944944	+	1.24240i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.g.e.327.10	yes	20
5.3	odd	4		370.2.h.e.253.1	yes	20
37.6	odd	4		370.2.h.e.117.1	yes	20
185.43	even	4	inner	370.2.g.e.43.10	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.10	✓	20	185.43	even	4	inner
370.2.g.e.327.10	yes	20	1.1	even	1	trivial
370.2.h.e.117.1	yes	20	37.6	odd	4
370.2.h.e.253.1	yes	20	5.3	odd	4

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(2.09082 + 2.09082i) q^{3} -1.00000 q^{4} +(1.30447 + 1.81614i) q^{5} +(2.09082 - 2.09082i) q^{6} +(-0.643605 - 0.643605i) q^{7} +1.00000i q^{8} +5.74304i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(2.09082 + 2.09082i) q^{3} -1.00000 q^{4} +(1.30447 + 1.81614i) q^{5} +(2.09082 - 2.09082i) q^{6} +(-0.643605 - 0.643605i) q^{7} +1.00000i q^{8} +5.74304i q^{9} +(1.81614 - 1.30447i) q^{10} -1.88405i q^{11} +(-2.09082 - 2.09082i) q^{12} +0.536082i q^{13} +(-0.643605 + 0.643605i) q^{14} +(-1.06980 + 6.52462i) q^{15} +1.00000 q^{16} +0.334703 q^{17} +5.74304 q^{18} +(-1.08518 - 1.08518i) q^{19} +(-1.30447 - 1.81614i) q^{20} -2.69132i q^{21} -1.88405 q^{22} -4.65098i q^{23} +(-2.09082 + 2.09082i) q^{24} +(-1.59670 + 4.73820i) q^{25} +0.536082 q^{26} +(-5.73519 + 5.73519i) q^{27} +(0.643605 + 0.643605i) q^{28} +(-3.33033 + 3.33033i) q^{29} +(6.52462 + 1.06980i) q^{30} +(4.90948 + 4.90948i) q^{31} -1.00000i q^{32} +(3.93919 - 3.93919i) q^{33} -0.334703i q^{34} +(0.329310 - 2.00844i) q^{35} -5.74304i q^{36} +(6.02729 - 0.819646i) q^{37} +(-1.08518 + 1.08518i) q^{38} +(-1.12085 + 1.12085i) q^{39} +(-1.81614 + 1.30447i) q^{40} -8.26486i q^{41} -2.69132 q^{42} -11.9117i q^{43} +1.88405i q^{44} +(-10.4301 + 7.49163i) q^{45} -4.65098 q^{46} +(-0.141535 - 0.141535i) q^{47} +(2.09082 + 2.09082i) q^{48} -6.17154i q^{49} +(4.73820 + 1.59670i) q^{50} +(0.699803 + 0.699803i) q^{51} -0.536082i q^{52} +(-5.03296 + 5.03296i) q^{53} +(5.73519 + 5.73519i) q^{54} +(3.42168 - 2.45768i) q^{55} +(0.643605 - 0.643605i) q^{56} -4.53784i q^{57} +(3.33033 + 3.33033i) q^{58} +(4.10789 + 4.10789i) q^{59} +(1.06980 - 6.52462i) q^{60} +(-8.90180 - 8.90180i) q^{61} +(4.90948 - 4.90948i) q^{62} +(3.69625 - 3.69625i) q^{63} -1.00000 q^{64} +(-0.973599 + 0.699305i) q^{65} +(-3.93919 - 3.93919i) q^{66} +(3.61956 - 3.61956i) q^{67} -0.334703 q^{68} +(9.72436 - 9.72436i) q^{69} +(-2.00844 - 0.329310i) q^{70} +15.5121 q^{71} -5.74304 q^{72} +(-6.82739 - 6.82739i) q^{73} +(-0.819646 - 6.02729i) q^{74} +(-13.2451 + 6.56829i) q^{75} +(1.08518 + 1.08518i) q^{76} +(-1.21258 + 1.21258i) q^{77} +(1.12085 + 1.12085i) q^{78} +(5.73637 + 5.73637i) q^{79} +(1.30447 + 1.81614i) q^{80} -6.75336 q^{81} -8.26486 q^{82} +(-7.90475 + 7.90475i) q^{83} +2.69132i q^{84} +(0.436611 + 0.607866i) q^{85} -11.9117 q^{86} -13.9262 q^{87} +1.88405 q^{88} +(-1.21521 + 1.21521i) q^{89} +(7.49163 + 10.4301i) q^{90} +(0.345025 - 0.345025i) q^{91} +4.65098i q^{92} +20.5297i q^{93} +(-0.141535 + 0.141535i) q^{94} +(0.555249 - 3.38643i) q^{95} +(2.09082 - 2.09082i) q^{96} -17.1767 q^{97} -6.17154 q^{98} +10.8201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} - 20 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7}+O(q^{10}) \) 20 * q - 4 * q^3 - 20 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7	\( 20 q - 4 q^{3} - 20 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{10} + 4 q^{12} - 2 q^{14} + 20 q^{16} + 20 q^{17} + 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{22} + 4 q^{24} - 10 q^{25} + 20 q^{27} + 2 q^{28} - 18 q^{29} - 4 q^{30} + 12 q^{31} + 4 q^{33} + 12 q^{35} - 6 q^{38} - 6 q^{39} - 4 q^{40} - 12 q^{42} - 18 q^{45} + 4 q^{46} - 22 q^{47} - 4 q^{48} + 4 q^{50} + 8 q^{51} - 4 q^{53} - 20 q^{54} - 34 q^{55} + 2 q^{56} + 18 q^{58} + 10 q^{59} + 10 q^{61} + 12 q^{62} - 2 q^{63} - 20 q^{64} - 20 q^{65} - 4 q^{66} - 8 q^{67} - 20 q^{68} + 34 q^{69} + 12 q^{70} + 16 q^{71} - 24 q^{72} + 6 q^{73} - 32 q^{74} - 26 q^{75} + 6 q^{76} + 4 q^{77} + 6 q^{78} - 12 q^{79} + 2 q^{80} - 28 q^{81} + 20 q^{82} + 6 q^{83} - 10 q^{85} - 16 q^{86} + 44 q^{87} + 8 q^{88} + 44 q^{89} - 22 q^{90} - 40 q^{91} - 22 q^{94} - 50 q^{95} - 4 q^{96} - 72 q^{97} + 52 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q - 4 * q^3 - 20 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^10 + 4 * q^12 - 2 * q^14 + 20 * q^16 + 20 * q^17 + 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^22 + 4 * q^24 - 10 * q^25 + 20 * q^27 + 2 * q^28 - 18 * q^29 - 4 * q^30 + 12 * q^31 + 4 * q^33 + 12 * q^35 - 6 * q^38 - 6 * q^39 - 4 * q^40 - 12 * q^42 - 18 * q^45 + 4 * q^46 - 22 * q^47 - 4 * q^48 + 4 * q^50 + 8 * q^51 - 4 * q^53 - 20 * q^54 - 34 * q^55 + 2 * q^56 + 18 * q^58 + 10 * q^59 + 10 * q^61 + 12 * q^62 - 2 * q^63 - 20 * q^64 - 20 * q^65 - 4 * q^66 - 8 * q^67 - 20 * q^68 + 34 * q^69 + 12 * q^70 + 16 * q^71 - 24 * q^72 + 6 * q^73 - 32 * q^74 - 26 * q^75 + 6 * q^76 + 4 * q^77 + 6 * q^78 - 12 * q^79 + 2 * q^80 - 28 * q^81 + 20 * q^82 + 6 * q^83 - 10 * q^85 - 16 * q^86 + 44 * q^87 + 8 * q^88 + 44 * q^89 - 22 * q^90 - 40 * q^91 - 22 * q^94 - 50 * q^95 - 4 * q^96 - 72 * q^97 + 52 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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