LMFDB - Embedded newform 370.2.m.c.159.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(159,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("370.159");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.m (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 37x^{14} + 559x^{12} + 4431x^{10} + 19684x^{8} + 48248x^{6} + 58656x^{4} + 25392x^{2} + 256 $ x^16 + 37x^14 + 559x^12 + 4431x^10 + 19684x^8 + 48248x^6 + 58656x^4 + 25392*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			159.3
Root			$-1.93403i$ of defining polynomial
Character	$\chi$	$=$	370.159
Dual form			370.2.m.c.249.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.67492 - 0.967016i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.564048 + 2.16376i) q^{5} +1.93403i q^{6} +(0.358580 + 0.207027i) q^{7} +1.00000 q^{8} +(0.370239 + 0.641273i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.67492 - 0.967016i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.564048 + 2.16376i) q^{5} +1.93403i q^{6} +(0.358580 + 0.207027i) q^{7} +1.00000 q^{8} +(0.370239 + 0.641273i) q^{9} +(2.15589 - 0.593399i) q^{10} +4.06848 q^{11} +(1.67492 - 0.967016i) q^{12} +(1.51113 - 2.61735i) q^{13} -0.414053i q^{14} +(3.03712 - 3.07868i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.66400 - 4.61419i) q^{17} +(0.370239 - 0.641273i) q^{18} +(-2.74384 - 1.58416i) q^{19} +(-1.59185 - 1.57036i) q^{20} +(-0.400396 - 0.693506i) q^{21} +(-2.03424 - 3.52341i) q^{22} +9.34555 q^{23} +(-1.67492 - 0.967016i) q^{24} +(-4.36370 - 2.44093i) q^{25} -3.02226 q^{26} +4.36999i q^{27} +(-0.358580 + 0.207027i) q^{28} -6.14537i q^{29} +(-4.18478 - 1.09089i) q^{30} +4.98408i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-6.81439 - 3.93429i) q^{33} +(-2.66400 + 4.61419i) q^{34} +(-0.650212 + 0.659108i) q^{35} -0.740478 q^{36} +(6.08276 - 0.00221606i) q^{37} +3.16831i q^{38} +(-5.06204 + 2.92257i) q^{39} +(-0.564048 + 2.16376i) q^{40} +(4.42552 - 7.66522i) q^{41} +(-0.400396 + 0.693506i) q^{42} +2.04410 q^{43} +(-2.03424 + 3.52341i) q^{44} +(-1.59639 + 0.439399i) q^{45} +(-4.67277 - 8.09348i) q^{46} -11.1999i q^{47} +1.93403i q^{48} +(-3.41428 - 5.91371i) q^{49} +(0.0679436 + 4.99954i) q^{50} +10.3045i q^{51} +(1.51113 + 2.61735i) q^{52} +(-0.0502578 + 0.0290163i) q^{53} +(3.78452 - 2.18499i) q^{54} +(-2.29482 + 8.80321i) q^{55} +(0.358580 + 0.207027i) q^{56} +(3.06381 + 5.30667i) q^{57} +(-5.32204 + 3.07268i) q^{58} +(3.89814 - 2.25059i) q^{59} +(1.14765 + 4.16957i) q^{60} +(9.62137 + 5.55490i) q^{61} +(4.31634 - 2.49204i) q^{62} +0.306597i q^{63} +1.00000 q^{64} +(4.81097 + 4.74603i) q^{65} +7.86858i q^{66} +(2.76181 + 1.59453i) q^{67} +5.32800 q^{68} +(-15.6530 - 9.03729i) q^{69} +(0.895911 + 0.233546i) q^{70} +(-1.80052 + 3.11860i) q^{71} +(0.370239 + 0.641273i) q^{72} +12.3070i q^{73} +(-3.04330 - 5.26672i) q^{74} +(4.94843 + 8.30813i) q^{75} +(2.74384 - 1.58416i) q^{76} +(1.45888 + 0.842284i) q^{77} +(5.06204 + 2.92257i) q^{78} +(5.31138 + 3.06653i) q^{79} +(2.15589 - 0.593399i) q^{80} +(5.33656 - 9.24320i) q^{81} -8.85103 q^{82} +(1.46749 - 0.847254i) q^{83} +0.800792 q^{84} +(11.4866 - 3.16163i) q^{85} +(-1.02205 - 1.77024i) q^{86} +(-5.94267 + 10.2930i) q^{87} +4.06848 q^{88} +(-9.57915 + 5.53052i) q^{89} +(1.17873 + 1.16282i) q^{90} +(1.08372 - 0.625688i) q^{91} +(-4.67277 + 8.09348i) q^{92} +(4.81968 - 8.34794i) q^{93} +(-9.69944 + 5.59997i) q^{94} +(4.97539 - 5.04346i) q^{95} +(1.67492 - 0.967016i) q^{96} -4.73567 q^{97} +(-3.41428 + 5.91371i) q^{98} +(1.50631 + 2.60901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9}+O(q^{10}) $ 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9	$ 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} - 3 q^{12} + 6 q^{13} - 9 q^{15} - 8 q^{16} + 13 q^{18} - 3 q^{19} - 6 q^{21} + 3 q^{22} + 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{28} - 9 q^{30} - 8 q^{32} - 6 q^{33} + 12 q^{35} - 26 q^{36} - 16 q^{37} + 15 q^{39} + 6 q^{40} + 7 q^{41} - 6 q^{42} + 22 q^{43} + 3 q^{44} - 4 q^{45} - 11 q^{46} + 4 q^{49} - 6 q^{50} + 6 q^{52} - 3 q^{53} + 9 q^{54} - 25 q^{55} + 12 q^{56} - 18 q^{57} - 36 q^{58} + 15 q^{59} + 18 q^{60} + 12 q^{61} + 33 q^{62} + 16 q^{64} - 26 q^{65} - 24 q^{67} + 42 q^{69} - 18 q^{70} - 4 q^{71} + 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} + 24 q^{77} - 15 q^{78} - 6 q^{80} + 10 q^{81} - 14 q^{82} - 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} - 50 q^{87} - 6 q^{88} + 9 q^{89} + 5 q^{90} - 24 q^{91} - 11 q^{92} + 25 q^{93} - 27 q^{94} + 49 q^{95} - 3 q^{96} - 68 q^{97} + 4 q^{98} + 37 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 - 3 * q^12 + 6 * q^13 - 9 * q^15 - 8 * q^16 + 13 * q^18 - 3 * q^19 - 6 * q^21 + 3 * q^22 + 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 12 * q^28 - 9 * q^30 - 8 * q^32 - 6 * q^33 + 12 * q^35 - 26 * q^36 - 16 * q^37 + 15 * q^39 + 6 * q^40 + 7 * q^41 - 6 * q^42 + 22 * q^43 + 3 * q^44 - 4 * q^45 - 11 * q^46 + 4 * q^49 - 6 * q^50 + 6 * q^52 - 3 * q^53 + 9 * q^54 - 25 * q^55 + 12 * q^56 - 18 * q^57 - 36 * q^58 + 15 * q^59 + 18 * q^60 + 12 * q^61 + 33 * q^62 + 16 * q^64 - 26 * q^65 - 24 * q^67 + 42 * q^69 - 18 * q^70 - 4 * q^71 + 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 + 24 * q^77 - 15 * q^78 - 6 * q^80 + 10 * q^81 - 14 * q^82 - 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 - 50 * q^87 - 6 * q^88 + 9 * q^89 + 5 * q^90 - 24 * q^91 - 11 * q^92 + 25 * q^93 - 27 * q^94 + 49 * q^95 - 3 * q^96 - 68 * q^97 + 4 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.67492	−	0.967016i	−0.967016	−	0.558307i	−0.0686906	−	0.997638i	$-0.521882\pi$
$3$	−1.67492	−	0.967016i	−0.967016	−	0.558307i	−0.898325	+	0.439331i	$0.855215\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.564048	+	2.16376i	−0.252250	+	0.967662i
$5$	−0.564048	+	2.16376i	−0.252250	+	0.967662i
$6$			1.93403i			0.789565i
$7$	0.358580	+	0.207027i	0.135531	+	0.0782487i	0.566232	−	0.824246i	$-0.308401\pi$
$7$	0.358580	+	0.207027i	0.135531	+	0.0782487i	−0.430702	+	0.902494i	$0.641734\pi$
$8$	1.00000			0.353553
$9$	0.370239	+	0.641273i	0.123413	+	0.213758i
$10$	2.15589	−	0.593399i	0.681753	−	0.187649i
$11$	4.06848			1.22669			0.613347	−	0.789814i	$-0.289823\pi$
$11$	4.06848			1.22669			0.613347	+	0.789814i	$0.289823\pi$
$12$	1.67492	−	0.967016i	0.483508	−	0.279153i
$13$	1.51113	−	2.61735i	0.419112	−	0.725923i	−0.576738	−	0.816929i	$-0.695675\pi$
$13$	1.51113	−	2.61735i	0.419112	−	0.725923i	0.995850	+	0.0910056i	$0.0290081\pi$
$14$		−	0.414053i		−	0.110660i
$15$	3.03712	−	3.07868i	0.784182	−	0.794912i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.66400	−	4.61419i	−0.646115	−	1.11910i	−0.984043	−	0.177933i	$-0.943059\pi$
$17$	−2.66400	−	4.61419i	−0.646115	−	1.11910i	0.337927	−	0.941172i	$-0.390274\pi$
$18$	0.370239	−	0.641273i	0.0872662	−	0.151150i
$19$	−2.74384	−	1.58416i	−0.629480	−	0.363430i	0.151071	−	0.988523i	$-0.451728\pi$
$19$	−2.74384	−	1.58416i	−0.629480	−	0.363430i	−0.780551	+	0.625093i	$0.785061\pi$
$20$	−1.59185	−	1.57036i	−0.355947	−	0.351143i
$21$	−0.400396	−	0.693506i	−0.0873735	−	0.151335i
$22$	−2.03424	−	3.52341i	−0.433702	−	0.751193i
$23$	9.34555			1.94868			0.974340	−	0.225079i	$-0.0722641\pi$
$23$	9.34555			1.94868			0.974340	+	0.225079i	$0.0722641\pi$
$24$	−1.67492	−	0.967016i	−0.341892	−	0.197391i
$25$	−4.36370	−	2.44093i	−0.872740	−	0.488186i
$26$	−3.02226			−0.592714
$27$			4.36999i			0.841004i
$28$	−0.358580	+	0.207027i	−0.0677653	+	0.0391243i
$29$		−	6.14537i		−	1.14117i	−0.821240	−	0.570583i	$-0.806717\pi$
$29$		−	6.14537i		−	1.14117i	0.821240	−	0.570583i	$-0.193283\pi$
$30$	−4.18478	−	1.09089i	−0.764032	−	0.199168i
$31$			4.98408i			0.895167i	0.894242	+	0.447584i	$0.147715\pi$
$31$			4.98408i			0.895167i	−0.894242	+	0.447584i	$0.852285\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−6.81439	−	3.93429i	−1.18623	−	0.684872i
$34$	−2.66400	+	4.61419i	−0.456873	+	0.791327i
$35$	−0.650212	+	0.659108i	−0.109906	+	0.111410i
$36$	−0.740478			−0.123413
$37$	6.08276	−	0.00221606i	1.00000	−	0.000364319i
$37$	6.08276	−	0.00221606i	1.00000	−	0.000364319i
$38$			3.16831i			0.513968i
$39$	−5.06204	+	2.92257i	−0.810576	+	0.467986i
$40$	−0.564048	+	2.16376i	−0.0891839	+	0.342120i
$41$	4.42552	−	7.66522i	0.691150	−	1.19711i	−0.280312	−	0.959909i	$-0.590438\pi$
$41$	4.42552	−	7.66522i	0.691150	−	1.19711i	0.971462	−	0.237197i	$-0.0762287\pi$
$42$	−0.400396	+	0.693506i	−0.0617824	+	0.107010i
$43$	2.04410			0.311722			0.155861	−	0.987779i	$-0.450185\pi$
$43$	2.04410			0.311722			0.155861	+	0.987779i	$0.450185\pi$
$44$	−2.03424	+	3.52341i	−0.306673	+	0.531174i
$45$	−1.59639	+	0.439399i	−0.237976	+	0.0655017i
$46$	−4.67277	−	8.09348i	−0.688963	−	1.19332i
$47$		−	11.1999i		−	1.63368i	−0.576864	−	0.816840i	$-0.695724\pi$
$47$		−	11.1999i		−	1.63368i	0.576864	−	0.816840i	$-0.304276\pi$
$48$			1.93403i			0.279153i
$49$	−3.41428	−	5.91371i	−0.487754	−	0.844815i
$50$	0.0679436	+	4.99954i	0.00960868	+	0.707041i
$51$			10.3045i			1.44292i
$52$	1.51113	+	2.61735i	0.209556	+	0.362962i
$53$	−0.0502578	+	0.0290163i	−0.00690344	+	0.00398570i	−0.503448	−	0.864026i	$-0.667935\pi$
$53$	−0.0502578	+	0.0290163i	−0.00690344	+	0.00398570i	0.496544	+	0.868011i	$0.334602\pi$
$54$	3.78452	−	2.18499i	0.515008	−	0.297340i
$55$	−2.29482	+	8.80321i	−0.309434	+	1.18703i
$56$	0.358580	+	0.207027i	0.0479173	+	0.0276651i
$57$	3.06381	+	5.30667i	0.405811	+	0.702886i
$58$	−5.32204	+	3.07268i	−0.698819	+	0.403463i
$59$	3.89814	−	2.25059i	0.507495	−	0.293002i	−0.224308	−	0.974518i	$-0.572012\pi$
$59$	3.89814	−	2.25059i	0.507495	−	0.293002i	0.731803	+	0.681516i	$0.238679\pi$
$60$	1.14765	+	4.16957i	0.148161	+	0.538289i
$61$	9.62137	+	5.55490i	1.23189	+	0.711232i	0.967424	−	0.253163i	$-0.0814709\pi$
$61$	9.62137	+	5.55490i	1.23189	+	0.711232i	0.264466	+	0.964395i	$0.414804\pi$
$62$	4.31634	−	2.49204i	0.548176	−	0.316489i
$63$			0.306597i			0.0386276i
$64$	1.00000			0.125000
$65$	4.81097	+	4.74603i	0.596727	+	0.588673i
$66$			7.86858i			0.968555i
$67$	2.76181	+	1.59453i	0.337409	+	0.194803i	0.659125	−	0.752033i	$-0.270927\pi$
$67$	2.76181	+	1.59453i	0.337409	+	0.194803i	−0.321717	+	0.946836i	$0.604260\pi$
$68$	5.32800			0.646115
$69$	−15.6530	−	9.03729i	−1.88441	−	1.08796i
$70$	0.895911	+	0.233546i	0.107082	+	0.0279141i
$71$	−1.80052	+	3.11860i	−0.213683	+	0.370110i	−0.952864	−	0.303397i	$-0.901879\pi$
$71$	−1.80052	+	3.11860i	−0.213683	+	0.370110i	0.739181	+	0.673506i	$0.235213\pi$
$72$	0.370239	+	0.641273i	0.0436331	+	0.0755748i
$73$			12.3070i			1.44043i	0.693751	+	0.720215i	$0.255957\pi$
$73$			12.3070i			1.44043i	−0.693751	+	0.720215i	$0.744043\pi$
$74$	−3.04330	−	5.26672i	−0.353776	−	0.612244i
$75$	4.94843	+	8.30813i	0.571396	+	0.959340i
$76$	2.74384	−	1.58416i	0.314740	−	0.181715i
$77$	1.45888	+	0.842284i	0.166255	+	0.0959872i
$78$	5.06204	+	2.92257i	0.573164	+	0.330916i
$79$	5.31138	+	3.06653i	0.597577	+	0.345011i	0.768088	−	0.640344i	$-0.221208\pi$
$79$	5.31138	+	3.06653i	0.597577	+	0.345011i	−0.170511	+	0.985356i	$0.554542\pi$
$80$	2.15589	−	0.593399i	0.241036	−	0.0663440i
$81$	5.33656	−	9.24320i	0.592951	−	1.02702i
$82$	−8.85103			−0.977433
$83$	1.46749	−	0.847254i	0.161078	−	0.0929982i	−0.417294	−	0.908771i	$-0.637022\pi$
$83$	1.46749	−	0.847254i	0.161078	−	0.0929982i	0.578372	+	0.815773i	$0.303688\pi$
$84$	0.800792			0.0873735
$85$	11.4866	−	3.16163i	1.24590	−	0.342927i
$86$	−1.02205	−	1.77024i	−0.110210	−	0.190890i
$87$	−5.94267	+	10.2930i	−0.637121	+	1.10353i
$88$	4.06848			0.433702
$89$	−9.57915	+	5.53052i	−1.01539	+	0.586234i	−0.912765	−	0.408486i	$-0.866057\pi$
$89$	−9.57915	+	5.53052i	−1.01539	+	0.586234i	−0.102623	+	0.994720i	$0.532723\pi$
$90$	1.17873	+	1.16282i	0.124249	+	0.122572i
$91$	1.08372	−	0.625688i	0.113605	−	0.0655899i
$92$	−4.67277	+	8.09348i	−0.487170	+	0.843804i
$93$	4.81968	−	8.34794i	0.499778	−	0.865641i
$94$	−9.69944	+	5.59997i	−1.00042	+	0.577593i
$95$	4.97539	−	5.04346i	0.510464	−	0.517448i
$96$	1.67492	−	0.967016i	0.170946	−	0.0986956i
$97$	−4.73567			−0.480834			−0.240417	−	0.970670i	$-0.577284\pi$
$97$	−4.73567			−0.480834			−0.240417	+	0.970670i	$0.577284\pi$
$98$	−3.41428	+	5.91371i	−0.344894	+	0.597375i
$99$	1.50631	+	2.60901i	0.151390	+	0.262215i
$100$	4.29576	−	2.55861i	0.429576	−	0.255861i
$101$	−7.43544			−0.739854			−0.369927	−	0.929061i	$-0.620617\pi$
$101$	−7.43544			−0.739854			−0.369927	+	0.929061i	$0.620617\pi$
$102$	8.92398	−	5.15226i	0.883606	−	0.510150i
$103$	−19.2263			−1.89443			−0.947213	−	0.320606i	$-0.896114\pi$
$103$	−19.2263			−1.89443			−0.947213	+	0.320606i	$0.896114\pi$
$104$	1.51113	−	2.61735i	0.148178	−	0.256653i
$105$	1.72642	−	0.475189i	0.168481	−	0.0463737i
$106$	0.0502578	+	0.0290163i	0.00488147	+	0.00281832i
$107$	10.5779	+	6.10718i	1.02261	+	0.590403i	0.914858	−	0.403775i	$-0.132302\pi$
$107$	10.5779	+	6.10718i	1.02261	+	0.590403i	0.107750	+	0.994178i	$0.465635\pi$
$108$	−3.78452	−	2.18499i	−0.364166	−	0.210251i
$109$	−5.75115	+	3.32043i	−0.550860	+	0.318039i	−0.749469	−	0.662040i	$-0.769691\pi$
$109$	−5.75115	+	3.32043i	−0.550860	+	0.318039i	0.198609	+	0.980079i	$0.436358\pi$
$110$	8.77122	−	2.41423i	0.836303	−	0.230188i
$111$	−10.1903	−	5.87842i	−0.967219	−	0.557955i
$112$		−	0.414053i		−	0.0391243i
$113$	−2.06848	−	3.58272i	−0.194587	−	0.337034i	0.752178	−	0.658960i	$-0.229003\pi$
$113$	−2.06848	−	3.58272i	−0.194587	−	0.337034i	−0.946765	+	0.321926i	$0.895670\pi$
$114$	3.06381	−	5.30667i	0.286952	−	0.497015i
$115$	−5.27134	+	20.2215i	−0.491555	+	1.88566i
$116$	5.32204	+	3.07268i	0.494139	+	0.285292i
$117$	2.23792			0.206896
$118$	−3.89814	−	2.25059i	−0.358853	−	0.207184i
$119$		−	2.20608i		−	0.202231i
$120$	3.03712	−	3.07868i	0.277250	−	0.281044i
$121$	5.55256			0.504778
$122$		−	11.1098i		−	1.00583i
$123$	−14.8248	+	8.55909i	−1.33671	+	0.771747i
$124$	−4.31634	−	2.49204i	−0.387619	−	0.223792i
$125$	7.74292	−	8.06519i	0.692547	−	0.721372i
$126$	0.265521	−	0.153299i	0.0236545	−	0.0136569i
$127$	−2.47026	+	1.42621i	−0.219200	+	0.126555i	−0.605580	−	0.795784i	$-0.707059\pi$
$127$	−2.47026	+	1.42621i	−0.219200	+	0.126555i	0.386380	+	0.922340i	$0.373725\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−3.42370	−	1.97667i	−0.301440	−	0.174036i
$130$	1.70470	−	6.53944i	0.149512	−	0.573547i
$131$	4.93906	−	2.85157i	0.431528	−	0.249143i	−0.268469	−	0.963288i	$-0.586518\pi$
$131$	4.93906	−	2.85157i	0.431528	−	0.249143i	0.699997	+	0.714145i	$0.253185\pi$
$132$	6.81439	−	3.93429i	0.593116	−	0.342436i
$133$	−0.655925	−	1.13609i	−0.0568759	−	0.0985119i
$134$		−	3.18906i		−	0.275493i
$135$	−9.45559	−	2.46488i	−0.813808	−	0.212143i
$136$	−2.66400	−	4.61419i	−0.228436	−	0.395663i
$137$		−	2.56213i		−	0.218898i	−0.993992	−	0.109449i	$-0.965091\pi$
$137$		−	2.56213i		−	0.218898i	0.993992	−	0.109449i	$-0.0349086\pi$
$138$			18.0746i			1.53861i
$139$	0.0413318	+	0.0715888i	0.00350572	+	0.00607209i	0.867773	−	0.496961i	$-0.165551\pi$
$139$	0.0413318	+	0.0715888i	0.00350572	+	0.00607209i	−0.864267	+	0.503033i	$0.832217\pi$
$140$	−0.245699	−	0.892654i	−0.0207653	−	0.0754431i
$141$	−10.8305	+	18.7590i	−0.912095	+	1.57979i
$142$	3.60105			0.302193
$143$	6.14801	−	10.6487i	0.514122	−	0.890486i
$144$	0.370239	−	0.641273i	0.0308533	−	0.0534394i
$145$	13.2971	+	3.46628i	1.10426	+	0.287859i
$146$	10.6582	−	6.15352i	0.882080	−	0.509269i
$147$			13.2067i			1.08927i
$148$	−3.03946	+	5.26893i	−0.249842	+	0.433104i
$149$	−8.11569			−0.664864			−0.332432	−	0.943127i	$-0.607869\pi$
$149$	−8.11569			−0.664864			−0.332432	+	0.943127i	$0.607869\pi$
$150$	4.72083	−	8.43953i	0.385454	−	0.689085i
$151$	0.649772	−	1.12544i	0.0528777	−	0.0915869i	−0.838375	−	0.545094i	$-0.816494\pi$
$151$	0.649772	−	1.12544i	0.0528777	−	0.0915869i	0.891253	+	0.453507i	$0.149827\pi$
$152$	−2.74384	−	1.58416i	−0.222555	−	0.128492i
$153$	1.97264	−	3.41671i	0.159478	−	0.276224i
$154$		−	1.68457i		−	0.135746i
$155$	−10.7843	−	2.81126i	−0.866219	−	0.225806i
$156$		−	5.84515i		−	0.467986i
$157$	−2.93919	+	1.69694i	−0.234573	+	0.135431i	−0.612680	−	0.790331i	$-0.709909\pi$
$157$	−2.93919	+	1.69694i	−0.234573	+	0.135431i	0.378107	+	0.925762i	$0.376575\pi$
$158$		−	6.13306i		−	0.487920i
$159$	0.112237			0.00890098
$160$	−1.59185	−	1.57036i	−0.125846	−	0.124148i
$161$	3.35113	+	1.93478i	0.264106	+	0.152482i
$162$	−10.6731			−0.838560
$163$	−3.57110	−	6.18532i	−0.279710	−	0.484472i	0.691603	−	0.722278i	$-0.256905\pi$
$163$	−3.57110	−	6.18532i	−0.279710	−	0.484472i	−0.971313	+	0.237806i	$0.923572\pi$
$164$	4.42552	+	7.66522i	0.345575	+	0.598553i
$165$	12.3565	−	12.5256i	0.961951	−	0.975113i
$166$	−1.46749	−	0.847254i	−0.113899	−	0.0657597i
$167$	6.66644	−	11.5466i	0.515864	−	0.893503i	−0.483966	−	0.875087i	$-0.660804\pi$
$167$	6.66644	−	11.5466i	0.515864	−	0.893503i	0.999830	−	0.0184166i	$-0.00586253\pi$
$168$	−0.400396	−	0.693506i	−0.0308912	−	0.0535051i
$169$	1.93297	+	3.34801i	0.148690	+	0.257539i
$170$	−8.48136	−	8.36688i	−0.650491	−	0.641711i
$171$		−	2.34607i		−	0.179408i
$172$	−1.02205	+	1.77024i	−0.0779304	+	0.134979i
$173$	14.6374	−	8.45093i	1.11286	−	0.642512i	0.173294	−	0.984870i	$-0.444559\pi$
$173$	14.6374	−	8.45093i	1.11286	−	0.642512i	0.939570	+	0.342358i	$0.111225\pi$
$174$	11.8853			0.901025
$175$	−1.05940	−	1.77867i	−0.0800831	−	0.134455i
$176$	−2.03424	−	3.52341i	−0.153337	−	0.265587i
$177$	−8.70544			−0.654341
$178$	9.57915	+	5.53052i	0.717987	+	0.414530i
$179$			16.7109i			1.24903i	0.781011	+	0.624517i	$0.214704\pi$
$179$			16.7109i			1.24903i	−0.781011	+	0.624517i	$0.785296\pi$
$180$	0.417666	−	1.60222i	0.0311310	−	0.119422i
$181$	6.23719	−	10.8031i	0.463606	−	0.802990i	−0.535531	−	0.844516i	$-0.679888\pi$
$181$	6.23719	−	10.8031i	0.463606	−	0.802990i	0.999137	+	0.0415256i	$0.0132218\pi$
$182$	−1.08372	−	0.625688i	−0.0803309	−	0.0463791i
$183$	−10.7433	−	18.6080i	−0.794171	−	1.37554i
$184$	9.34555			0.688963
$185$	−3.42618	+	13.1629i	−0.251898	+	0.967754i
$186$	−9.63937			−0.706793
$187$	−10.8384	−	18.7727i	−0.792586	−	1.37280i
$188$	9.69944	+	5.59997i	0.707404	+	0.408420i
$189$	−0.904703	+	1.56699i	−0.0658075	+	0.113982i
$190$	−6.85546	−	1.78708i	−0.497348	−	0.129649i
$191$			7.93304i			0.574014i	0.957928	+	0.287007i	$0.0926604\pi$
$191$			7.93304i			0.574014i	−0.957928	+	0.287007i	$0.907340\pi$
$192$	−1.67492	−	0.967016i	−0.120877	−	0.0697884i
$193$	−24.3204			−1.75062			−0.875309	−	0.483564i	$-0.839342\pi$
$193$	−24.3204			−1.75062			−0.875309	+	0.483564i	$0.839342\pi$
$194$	2.36783	+	4.10121i	0.170001	+	0.294450i
$195$	−3.46850	−	12.6015i	−0.248385	−	0.902413i
$196$	6.82856			0.487754
$197$	−2.38098	+	1.37466i	−0.169638	+	0.0979406i	−0.582415	−	0.812891i	$-0.697892\pi$
$197$	−2.38098	+	1.37466i	−0.169638	+	0.0979406i	0.412777	+	0.910832i	$0.364559\pi$
$198$	1.50631	−	2.60901i	0.107049	−	0.185414i
$199$			21.3695i			1.51484i	0.652927	+	0.757421i	$0.273541\pi$
$199$			21.3695i			1.51484i	−0.652927	+	0.757421i	$0.726459\pi$
$200$	−4.36370	−	2.44093i	−0.308560	−	0.172600i
$201$	−3.08387	−	5.34142i	−0.217520	−	0.376755i
$202$	3.71772	+	6.43928i	0.261578	+	0.453066i
$203$	1.27225	−	2.20361i	0.0892947	−	0.154663i
$204$	−8.92398	−	5.15226i	−0.624804	−	0.360731i
$205$	14.0895	+	13.8993i	0.984052	+	0.970769i
$206$	9.61316	+	16.6505i	0.669781	+	1.16009i
$207$	3.46009	+	5.99305i	0.240493	+	0.416546i
$208$	−3.02226			−0.209556
$209$	−11.1633	−	6.44511i	−0.772179	−	0.445818i
$210$	−1.27474	−	1.25753i	−0.0879652	−	0.0867779i
$211$	11.6234			0.800186			0.400093	−	0.916475i	$-0.368978\pi$
$211$	11.6234			0.800186			0.400093	+	0.916475i	$0.368978\pi$
$212$		−	0.0580327i		−	0.00398570i
$213$	6.03147	−	3.48227i	0.413270	−	0.238601i
$214$		−	12.2144i		−	0.834956i
$215$	−1.15297	+	4.42293i	−0.0786318	+	0.301641i
$216$			4.36999i			0.297340i
$217$	−1.03184	+	1.78719i	−0.0700456	+	0.121323i
$218$	5.75115	+	3.32043i	0.389517	+	0.224888i
$219$	11.9011	−	20.6133i	0.804202	−	1.39292i
$220$	−6.47640	−	6.38898i	−0.436639	−	0.430745i
$221$	−16.1026			−1.08318
$222$	0.00428594	+	11.7643i	0.000287653	+	0.789565i
$223$		−	21.2933i		−	1.42590i	−0.701213	−	0.712952i	$-0.747358\pi$
$223$		−	21.2933i		−	1.42590i	0.701213	−	0.712952i	$-0.252642\pi$
$224$	−0.358580	+	0.207027i	−0.0239587	+	0.0138325i
$225$	−0.0503108	−	3.70205i	−0.00335405	−	0.246803i
$226$	−2.06848	+	3.58272i	−0.137593	+	0.238319i
$227$	−5.12241	+	8.87228i	−0.339987	+	0.588874i	−0.984430	−	0.175778i	$-0.943756\pi$
$227$	−5.12241	+	8.87228i	−0.339987	+	0.588874i	0.644443	+	0.764652i	$0.277089\pi$
$228$	−6.12762			−0.405811
$229$	3.42967	−	5.94037i	0.226639	−	0.392551i	−0.730171	−	0.683265i	$-0.760559\pi$
$229$	3.42967	−	5.94037i	0.226639	−	0.392551i	0.956810	+	0.290714i	$0.0938928\pi$
$230$	20.1480	−	5.54564i	1.32852	−	0.365668i
$231$	−1.62900	−	2.82152i	−0.107181	−	0.185642i
$232$		−	6.14537i		−	0.403463i
$233$		−	11.4152i		−	0.747838i	−0.927461	−	0.373919i	$-0.878014\pi$
$233$		−	11.4152i		−	0.747838i	0.927461	−	0.373919i	$-0.121986\pi$
$234$	−1.11896	−	1.93809i	−0.0731486	−	0.126697i
$235$	24.2340	+	6.31731i	1.58085	+	0.412096i
$236$			4.50119i			0.293002i
$237$	−5.93076	−	10.2724i	−0.385244	−	0.667263i
$238$	−1.91052	+	1.10304i	−0.123841	+	0.0714993i
$239$	7.03625	−	4.06238i	0.455137	−	0.262774i	−0.254860	−	0.966978i	$-0.582029\pi$
$239$	7.03625	−	4.06238i	0.455137	−	0.262774i	0.709997	+	0.704204i	$0.248696\pi$
$240$	−4.18478	−	1.09089i	−0.270126	−	0.0704165i
$241$	−19.7551	−	11.4056i	−1.27254	−	0.734701i	−0.297074	−	0.954855i	$-0.596011\pi$
$241$	−19.7551	−	11.4056i	−1.27254	−	0.734701i	−0.975465	+	0.220154i	$0.929344\pi$
$242$	−2.77628	−	4.80865i	−0.178466	−	0.309112i
$243$	−6.52308	+	3.76610i	−0.418456	+	0.241596i
$244$	−9.62137	+	5.55490i	−0.615945	+	0.355616i
$245$	14.7216	−	4.05206i	0.940532	−	0.258877i
$246$	14.8248	+	8.55909i	0.945193	+	0.545708i
$247$	−8.29259	+	4.78773i	−0.527645	+	0.304636i
$248$			4.98408i			0.316489i
$249$	−3.27723			−0.207686
$250$	−10.8561	−	2.67297i	−0.686601	−	0.169053i
$251$			26.7930i			1.69116i	0.533851	+	0.845579i	$0.320744\pi$
$251$			26.7930i			1.69116i	−0.533851	+	0.845579i	$0.679256\pi$
$252$	−0.265521	−	0.153299i	−0.0167263	−	0.00965691i
$253$	38.0222			2.39043
$254$	2.47026	+	1.42621i	0.154998	+	0.0894882i
$255$	−22.2965	−	5.81225i	−1.39626	−	0.363977i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.75782	−	15.1690i	−0.546298	−	0.946215i	−0.998524	−	0.0543120i	$-0.982703\pi$
$257$	−8.75782	−	15.1690i	−0.546298	−	0.946215i	0.452226	−	0.891903i	$-0.350630\pi$
$258$			3.95335i			0.246125i
$259$	2.18162	+	1.25850i	0.135559	+	0.0781993i
$260$	−6.51567	+	1.79341i	−0.404085	+	0.111222i
$261$	3.94086	−	2.27526i	0.243933	−	0.140835i
$262$	−4.93906	−	2.85157i	−0.305136	−	0.176171i
$263$	6.63293	+	3.82952i	0.409004	+	0.236138i	0.690362	−	0.723465i	$-0.257451\pi$
$263$	6.63293	+	3.82952i	0.409004	+	0.236138i	−0.281358	+	0.959603i	$0.590785\pi$
$264$	−6.81439	−	3.93429i	−0.419396	−	0.242139i
$265$	−0.0344365	−	0.125112i	−0.00211542	−	0.00768559i
$266$	−0.655925	+	1.13609i	−0.0402173	+	0.0696584i
$267$	21.3924			1.30919
$268$	−2.76181	+	1.59453i	−0.168704	+	0.0974015i
$269$	14.9782			0.913240			0.456620	−	0.889662i	$-0.349060\pi$
$269$	14.9782			0.913240			0.456620	+	0.889662i	$0.349060\pi$
$270$	2.59315	+	9.42123i	0.157814	+	0.573358i
$271$	−10.1678	−	17.6112i	−0.617650	−	1.06980i	−0.989913	−	0.141674i	$-0.954751\pi$
$271$	−10.1678	−	17.6112i	−0.617650	−	1.06980i	0.372263	−	0.928127i	$-0.378582\pi$
$272$	−2.66400	+	4.61419i	−0.161529	+	0.279776i
$273$	−2.42020			−0.146477
$274$	−2.21887	+	1.28107i	−0.134047	+	0.0773921i
$275$	−17.7536	−	9.93088i	−1.07058	−	0.598854i
$276$	15.6530	−	9.03729i	0.942203	−	0.543981i
$277$	−12.9118	+	22.3639i	−0.775795	+	1.34372i	0.158551	+	0.987351i	$0.449318\pi$
$277$	−12.9118	+	22.3639i	−0.775795	+	1.34372i	−0.934346	+	0.356366i	$0.884016\pi$
$278$	0.0413318	−	0.0715888i	0.00247892	−	0.00429361i
$279$	−3.19616	+	1.84530i	−0.191349	+	0.110475i
$280$	−0.650212	+	0.659108i	−0.0388576	+	0.0393893i
$281$	17.6512	−	10.1910i	1.05299	−	0.607941i	0.129502	−	0.991579i	$-0.458662\pi$
$281$	17.6512	−	10.1910i	1.05299	−	0.607941i	0.923484	+	0.383638i	$0.125329\pi$
$282$	21.6611			1.28990
$283$	−0.491609	+	0.851492i	−0.0292231	+	0.0506159i	−0.880267	−	0.474478i	$-0.842637\pi$
$283$	−0.491609	+	0.851492i	−0.0292231	+	0.0506159i	0.851044	+	0.525094i	$0.175970\pi$
$284$	−1.80052	−	3.11860i	−0.106841	−	0.185055i
$285$	−13.2105	+	3.63612i	−0.782522	+	0.215385i
$286$	−12.2960			−0.727078
$287$	3.17381	−	1.83240i	0.187344	−	0.108163i
$288$	−0.740478			−0.0436331
$289$	−5.69382	+	9.86198i	−0.334930	+	0.580117i
$290$	−3.64665	−	13.2488i	−0.214139	−	0.777994i
$291$	7.93187	+	4.57947i	0.464974	+	0.268453i
$292$	−10.6582	−	6.15352i	−0.623724	−	0.360107i
$293$	4.58109	+	2.64489i	0.267630	+	0.154516i	0.627810	−	0.778366i	$-0.283951\pi$
$293$	4.58109	+	2.64489i	0.267630	+	0.154516i	−0.360180	+	0.932883i	$0.617285\pi$
$294$	11.4373	−	6.60333i	0.667037	−	0.385114i
$295$	2.67100	+	9.70408i	0.155512	+	0.564993i
$296$	6.08276	−	0.00221606i	0.353553	−	0.000128806i
$297$			17.7792i			1.03165i
$298$	4.05785	+	7.02840i	0.235065	+	0.407144i
$299$	14.1223	−	24.4606i	0.816716	−	1.41459i
$300$	−9.66927	+	0.131405i	−0.558255	+	0.00758668i
$301$	0.732973	+	0.423182i	0.0422478	+	0.0243918i
$302$	−1.29954			−0.0747804
$303$	12.4538	+	7.19019i	0.715451	+	0.413066i
$304$			3.16831i			0.181715i
$305$	−17.4464	+	17.6851i	−0.998976	+	1.01264i
$306$	−3.94527			−0.225536
$307$			9.38404i			0.535575i	0.963478	+	0.267788i	$0.0862925\pi$
$307$			9.38404i			0.535575i	−0.963478	+	0.267788i	$0.913707\pi$
$308$	−1.45888	+	0.842284i	−0.0831273	+	0.0479936i
$309$	32.2026	+	18.5922i	1.83194	+	1.05767i
$310$	2.95755	+	10.7451i	0.167977	+	0.610283i
$311$	−21.1021	+	12.1833i	−1.19659	+	0.690851i	−0.959793	−	0.280708i	$-0.909431\pi$
$311$	−21.1021	+	12.1833i	−1.19659	+	0.690851i	−0.236796	+	0.971559i	$0.576097\pi$
$312$	−5.06204	+	2.92257i	−0.286582	+	0.165458i
$313$	12.7705	+	22.1191i	0.721829	+	1.25024i	0.960266	+	0.279086i	$0.0900315\pi$
$313$	12.7705	+	22.1191i	0.721829	+	1.25024i	−0.238437	+	0.971158i	$0.576635\pi$
$314$	2.93919	+	1.69694i	0.165868	+	0.0957641i
$315$	−0.663402	−	0.172936i	−0.0373785	−	0.00974382i
$316$	−5.31138	+	3.06653i	−0.298789	+	0.172506i
$317$	−9.11049	+	5.25994i	−0.511696	+	0.295428i	−0.733531	−	0.679657i	$-0.762129\pi$
$317$	−9.11049	+	5.25994i	−0.511696	+	0.295428i	0.221835	+	0.975084i	$0.428796\pi$
$318$	−0.0561185	−	0.0972001i	−0.00314697	−	0.00545071i
$319$		−	25.0023i		−	1.39986i
$320$	−0.564048	+	2.16376i	−0.0315313	+	0.120958i
$321$	−11.8115	−	20.4581i	−0.659252	−	1.14186i
$322$		−	3.86955i		−	0.215642i
$323$			16.8808i			0.939272i
$324$	5.33656	+	9.24320i	0.296476	+	0.513511i
$325$	−12.9829	+	7.73278i	−0.720161	+	0.428938i
$326$	−3.57110	+	6.18532i	−0.197785	+	0.342573i
$327$	12.8436			0.710254
$328$	4.42552	−	7.66522i	0.244358	−	0.423241i
$329$	2.31869	−	4.01608i	0.127833	−	0.221414i
$330$	−17.0257	−	4.43826i	−0.937234	−	0.244318i
$331$	−4.05217	+	2.33952i	−0.222728	+	0.128592i	−0.607213	−	0.794539i	$-0.707712\pi$
$331$	−4.05217	+	2.33952i	−0.222728	+	0.128592i	0.384485	+	0.923131i	$0.374379\pi$
$332$			1.69451i			0.0929982i
$333$	2.25350	+	3.89989i	0.123491	+	0.213713i
$334$	−13.3329			−0.729543
$335$	−5.00797	+	5.07649i	−0.273615	+	0.277358i
$336$	−0.400396	+	0.693506i	−0.0218434	+	0.0378338i
$337$	−4.20909	−	2.43012i	−0.229284	−	0.132377i	0.380958	−	0.924592i	$-0.375594\pi$
$337$	−4.20909	−	2.43012i	−0.229284	−	0.132377i	−0.610242	+	0.792215i	$0.708928\pi$
$338$	1.93297	−	3.34801i	0.105140	−	0.182108i
$339$			8.00102i			0.434556i
$340$	−3.00525	+	11.5285i	−0.162983	+	0.625221i
$341$			20.2776i			1.09810i
$342$	−2.03175	+	1.17303i	−0.109865	+	0.0634304i
$343$		−	5.72576i		−	0.309162i
$344$	2.04410			0.110210
$345$	28.3836	−	28.7719i	1.52812	−	1.54903i
$346$	−14.6374	−	8.45093i	−0.786914	−	0.454325i
$347$	26.4043			1.41745			0.708727	−	0.705483i	$-0.249270\pi$
$347$	26.4043			1.41745			0.708727	+	0.705483i	$0.249270\pi$
$348$	−5.94267	−	10.2930i	−0.318560	−	0.551763i
$349$	8.01159	+	13.8765i	0.428851	+	0.742791i	0.996771	−	0.0802921i	$-0.0255853\pi$
$349$	8.01159	+	13.8765i	0.428851	+	0.742791i	−0.567921	+	0.823083i	$0.692252\pi$
$350$	−1.01067	+	1.80680i	−0.0540228	+	0.0965777i
$351$	11.4378	+	6.60362i	0.610505	+	0.352475i
$352$	−2.03424	+	3.52341i	−0.108425	+	0.187798i
$353$	10.2140	+	17.6912i	0.543637	+	0.941608i	0.998691	+	0.0511437i	$0.0162866\pi$
$353$	10.2140	+	17.6912i	0.543637	+	0.941608i	−0.455054	+	0.890464i	$0.650380\pi$
$354$	4.35272	+	7.53913i	0.231344	+	0.400700i
$355$	−5.73231	−	5.65494i	−0.304240	−	0.300133i
$356$		−	11.0610i		−	0.586234i
$357$	−2.13331	+	3.69500i	−0.112907	+	0.195560i
$358$	14.4721	−	8.35547i	0.764874	−	0.441600i
$359$	27.0786			1.42915			0.714576	−	0.699558i	$-0.246620\pi$
$359$	27.0786			1.42915			0.714576	+	0.699558i	$0.246620\pi$
$360$	−1.59639	+	0.439399i	−0.0841373	+	0.0231584i
$361$	−4.48090	−	7.76114i	−0.235837	−	0.408481i
$362$	−12.4744			−0.655639
$363$	−9.30009	−	5.36941i	−0.488128	−	0.281821i
$364$			1.25138i			0.0655899i
$365$	−26.6295	−	6.94176i	−1.39385	−	0.363349i
$366$	−10.7433	+	18.6080i	−0.561564	+	0.972657i
$367$	12.5340	+	7.23652i	0.654270	+	0.377743i	0.790090	−	0.612990i	$-0.210034\pi$
$367$	12.5340	+	7.23652i	0.654270	+	0.377743i	−0.135820	+	0.990734i	$0.543367\pi$
$368$	−4.67277	−	8.09348i	−0.243585	−	0.421902i
$369$	6.55400			0.341187
$370$	13.1125	−	3.61428i	0.681685	−	0.187898i
$371$	−0.0240286			−0.00124750
$372$	4.81968	+	8.34794i	0.249889	+	0.432820i
$373$	−18.3963	−	10.6211i	−0.952523	−	0.549939i	−0.0586590	−	0.998278i	$-0.518682\pi$
$373$	−18.3963	−	10.6211i	−0.952523	−	0.549939i	−0.893864	+	0.448339i	$0.852016\pi$
$374$	−10.8384	+	18.7727i	−0.560443	+	0.970716i
$375$	−20.7679	+	6.02103i	−1.07245	+	0.310925i
$376$		−	11.1999i		−	0.577593i
$377$	−16.0846	−	9.28645i	−0.828399	−	0.478276i
$378$	1.80941			0.0930658
$379$	14.6888	+	25.4417i	0.754512	+	1.30685i	0.945617	+	0.325283i	$0.105460\pi$
$379$	14.6888	+	25.4417i	0.754512	+	1.30685i	−0.191105	+	0.981570i	$0.561207\pi$
$380$	1.88007	+	6.83055i	0.0964457	+	0.350400i
$381$	5.51666			0.282627
$382$	6.87021	−	3.96652i	0.351511	−	0.202945i
$383$	−10.5495	+	18.2722i	−0.539052	+	0.933666i	0.459903	+	0.887969i	$0.347884\pi$
$383$	−10.5495	+	18.2722i	−0.539052	+	0.933666i	−0.998955	+	0.0456966i	$0.985449\pi$
$384$			1.93403i			0.0986956i
$385$	−2.64538	+	2.68157i	−0.134821	+	0.136666i
$386$	12.1602	+	21.0621i	0.618937	+	1.07203i
$387$	0.756804	+	1.31082i	0.0384705	+	0.0666329i
$388$	2.36783	−	4.10121i	0.120209	−	0.208207i
$389$	6.18429	+	3.57050i	0.313556	+	0.181031i	0.648517	−	0.761201i	$-0.275390\pi$
$389$	6.18429	+	3.57050i	0.313556	+	0.181031i	−0.334961	+	0.942232i	$0.608723\pi$
$390$	−9.17898	+	9.30457i	−0.464796	+	0.471155i
$391$	−24.8966	−	43.1221i	−1.25907	−	2.18078i
$392$	−3.41428	−	5.91371i	−0.172447	−	0.298687i
$393$	−11.0300			−0.556392
$394$	2.38098	+	1.37466i	0.119952	+	0.0692545i
$395$	−9.63110	+	9.76288i	−0.484593	+	0.491224i
$396$	−3.01262			−0.151390
$397$			3.65365i			0.183371i	0.995788	+	0.0916857i	$0.0292255\pi$
$397$			3.65365i			0.183371i	−0.995788	+	0.0916857i	$0.970774\pi$
$398$	18.5065	−	10.6847i	0.927647	−	0.535577i
$399$			2.53716i			0.127017i
$400$	0.0679436	+	4.99954i	0.00339718	+	0.249977i
$401$			34.5602i			1.72586i	0.505327	+	0.862928i	$0.331372\pi$
$401$			34.5602i			1.72586i	−0.505327	+	0.862928i	$0.668628\pi$
$402$	−3.08387	+	5.34142i	−0.153810	+	0.266406i
$403$	13.0451	+	7.53159i	0.649823	+	0.375175i
$404$	3.71772	−	6.43928i	0.184964	−	0.320366i
$405$	16.9900	+	16.7606i	0.844238	+	0.832843i
$406$	−2.54451			−0.126282
$407$	24.7476	−	0.00901602i	1.22669	−	0.000446908i
$408$			10.3045i			0.510150i
$409$	8.77545	−	5.06651i	0.433918	−	0.250523i	−0.267096	−	0.963670i	$-0.586064\pi$
$409$	8.77545	−	5.06651i	0.433918	−	0.250523i	0.701014	+	0.713147i	$0.252731\pi$
$410$	4.99241	−	19.1515i	0.246558	−	0.945825i
$411$	−2.47762	+	4.29137i	−0.122212	+	0.211678i
$412$	9.61316	−	16.6505i	0.473606	−	0.820310i
$413$	1.86373			0.0917081
$414$	3.46009	−	5.99305i	0.170054	−	0.294542i
$415$	1.00552	+	3.65318i	0.0493590	+	0.179328i
$416$	1.51113	+	2.61735i	0.0740892	+	0.128326i
$417$		−	0.159874i		−	0.00782907i
$418$			12.8902i			0.630482i
$419$	4.65134	+	8.05636i	0.227233	+	0.393579i	0.956987	−	0.290131i	$-0.0936988\pi$
$419$	4.65134	+	8.05636i	0.227233	+	0.393579i	−0.729754	+	0.683710i	$0.760365\pi$
$420$	−0.451685	+	1.73272i	−0.0220400	+	0.0845481i
$421$		−	22.1257i		−	1.07834i	−0.842197	−	0.539170i	$-0.818738\pi$
$421$		−	22.1257i		−	1.07834i	0.842197	−	0.539170i	$-0.181262\pi$
$422$	−5.81169	−	10.0661i	−0.282908	−	0.490012i
$423$	7.18223	−	4.14666i	0.349212	−	0.201618i
$424$	−0.0502578	+	0.0290163i	−0.00244073	+	0.00140916i
$425$	0.362004	+	26.6376i	0.0175598	+	1.29211i
$426$	−6.03147	−	3.48227i	−0.292226	−	0.168717i
$427$	2.30002	+	3.98376i	0.111306	+	0.192787i
$428$	−10.5779	+	6.10718i	−0.511304	+	0.295202i
$429$	−20.5948	+	11.8904i	−0.994328	+	0.574076i
$430$	4.40685	−	1.21296i	0.212517	−	0.0584943i
$431$	−34.1354	−	19.7081i	−1.64424	−	0.949304i	−0.979301	−	0.202409i	$-0.935123\pi$
$431$	−34.1354	−	19.7081i	−1.64424	−	0.949304i	−0.664942	−	0.746895i	$-0.731544\pi$
$432$	3.78452	−	2.18499i	0.182083	−	0.105126i
$433$		−	4.61287i		−	0.221680i	−0.993838	−	0.110840i	$-0.964646\pi$
$433$		−	4.61287i		−	0.221680i	0.993838	−	0.110840i	$-0.0353542\pi$
$434$	2.06367			0.0990595
$435$	−18.9196	−	18.6642i	−0.907126	−	0.894882i
$436$		−	6.64085i		−	0.318039i
$437$	−25.6427	−	14.8048i	−1.22666	−	0.708210i
$438$	−23.8022			−1.13731
$439$	−14.0347	−	8.10294i	−0.669840	−	0.386732i	0.126176	−	0.992008i	$-0.459730\pi$
$439$	−14.0347	−	8.10294i	−0.669840	−	0.386732i	−0.796016	+	0.605276i	$0.793063\pi$
$440$	−2.29482	+	8.80321i	−0.109401	+	0.419677i
$441$	2.52820	−	4.37897i	0.120390	−	0.208522i
$442$	8.05131	+	13.9453i	0.382962	+	0.663309i
$443$		−	15.0950i		−	0.717184i	−0.933494	−	0.358592i	$-0.883257\pi$
$443$		−	15.0950i		−	0.717184i	0.933494	−	0.358592i	$-0.116743\pi$
$444$	10.1860	−	5.88584i	0.483406	−	0.279330i
$445$	−6.56361	−	23.8464i	−0.311145	−	1.13043i
$446$	−18.4405	+	10.6466i	−0.873185	+	0.504133i
$447$	13.5931	+	7.84801i	0.642934	+	0.371198i
$448$	0.358580	+	0.207027i	0.0169413	+	0.00978108i
$449$	−24.1648	−	13.9516i	−1.14041	−	0.658415i	−0.193876	−	0.981026i	$-0.562106\pi$
$449$	−24.1648	−	13.9516i	−1.14041	−	0.658415i	−0.946531	+	0.322612i	$0.895439\pi$
$450$	−3.18091	+	1.89460i	−0.149950	+	0.0893121i
$451$	18.0051	−	31.1858i	0.847829	−	1.46848i
$452$	4.13697			0.194587
$453$	−2.17663	+	1.25668i	−0.102267	+	0.0590440i
$454$	10.2448			0.480814
$455$	0.742565	+	2.69783i	0.0348120	+	0.126476i
$456$	3.06381	+	5.30667i	0.143476	+	0.248508i
$457$	8.58122	−	14.8631i	0.401412	−	0.695267i	−0.592484	−	0.805582i	$-0.701853\pi$
$457$	8.58122	−	14.8631i	0.401412	−	0.695267i	0.993897	+	0.110315i	$0.0351861\pi$
$458$	−6.85935			−0.320516
$459$	20.1639	−	11.6417i	0.941172	−	0.543386i
$460$	−14.8767	−	14.6759i	−0.693628	−	0.684266i
$461$	34.0409	−	19.6535i	1.58544	−	0.915355i	0.591396	−	0.806381i	$-0.298577\pi$
$461$	34.0409	−	19.6535i	1.58544	−	0.915355i	0.994045	−	0.108974i	$-0.0347564\pi$
$462$	−1.62900	+	2.82152i	−0.0757881	+	0.131269i
$463$	9.86106	−	17.0799i	0.458282	−	0.793768i	−0.540588	−	0.841287i	$-0.681798\pi$
$463$	9.86106	−	17.0799i	0.458282	−	0.793768i	0.998870	+	0.0475192i	$0.0151315\pi$
$464$	−5.32204	+	3.07268i	−0.247070	+	0.142646i
$465$	15.3444	+	15.1373i	0.711579	+	0.701974i
$466$	−9.88589	+	5.70762i	−0.457955	+	0.264401i
$467$	−35.9508			−1.66360			−0.831801	−	0.555074i	$-0.812690\pi$
$467$	−35.9508			−1.66360			−0.831801	+	0.555074i	$0.812690\pi$
$468$	−1.11896	+	1.93809i	−0.0517239	+	0.0895884i
$469$	0.660220	+	1.14354i	0.0304861	+	0.0528035i
$470$	−6.64604	−	24.1459i	−0.306559	−	1.11377i
$471$	6.56388			0.302448
$472$	3.89814	−	2.25059i	0.179427	−	0.103592i
$473$	8.31637			0.382387
$474$	−5.93076	+	10.2724i	−0.272409	+	0.471826i
$475$	8.10648	+	13.6103i	0.371951	+	0.624483i
$476$	1.91052	+	1.10304i	0.0875685	+	0.0505577i
$477$	−0.0372148	−	0.0214860i	−0.00170395	−	0.000983775i
$478$	−7.03625	−	4.06238i	−0.321831	−	0.185809i
$479$	−10.4535	+	6.03534i	−0.477634	+	0.275762i	−0.719430	−	0.694565i	$-0.755597\pi$
$479$	−10.4535	+	6.03534i	−0.477634	+	0.275762i	0.241796	+	0.970327i	$0.422263\pi$
$480$	1.14765	+	4.16957i	0.0523829	+	0.190314i
$481$	9.18604	−	15.9241i	0.418848	−	0.726076i
$482$			22.8112i			1.03902i
$483$	−3.74192	−	6.48119i	−0.170263	−	0.294904i
$484$	−2.77628	+	4.80865i	−0.126194	+	0.218575i
$485$	2.67115	−	10.2468i	0.121290	−	0.465285i
$486$	6.52308	+	3.76610i	0.295893	+	0.170834i
$487$	−9.34221			−0.423336			−0.211668	−	0.977342i	$-0.567890\pi$
$487$	−9.34221			−0.423336			−0.211668	+	0.977342i	$0.567890\pi$
$488$	9.62137	+	5.55490i	0.435539	+	0.251458i
$489$			13.8132i			0.624656i
$490$	−10.8700	−	10.7233i	−0.491057	−	0.484429i
$491$	22.9922			1.03763			0.518813	−	0.854888i	$-0.326374\pi$
$491$	22.9922			1.03763			0.518813	+	0.854888i	$0.326374\pi$
$492$		−	17.1182i		−	0.771747i
$493$	−28.3559	+	16.3713i	−1.27708	+	0.737325i
$494$	8.29259	+	4.78773i	0.373101	+	0.215410i
$495$	−6.49490	+	1.78769i	−0.291924	+	0.0803506i
$496$	4.31634	−	2.49204i	0.193809	−	0.111896i
$497$	−1.29127	+	0.745513i	−0.0579212	+	0.0334408i
$498$	1.63862	+	2.83817i	0.0734282	+	0.127181i
$499$	23.4214	+	13.5223i	1.04848	+	0.605343i	0.922225	−	0.386654i	$-0.126369\pi$
$499$	23.4214	+	13.5223i	1.04848	+	0.605343i	0.126260	+	0.991997i	$0.459703\pi$
$500$	3.11320	+	10.7382i	0.139227	+	0.480225i
$501$	−22.3315	+	12.8931i	−0.997698	+	0.576021i
$502$	23.2034	−	13.3965i	1.03562	−	0.597915i
$503$	14.0685	+	24.3674i	0.627283	+	1.08649i	0.988095	+	0.153848i	$0.0491665\pi$
$503$	14.0685	+	24.3674i	0.627283	+	1.08649i	−0.360811	+	0.932639i	$0.617500\pi$
$504$			0.306597i			0.0136569i
$505$	4.19395	−	16.0885i	0.186628	−	0.715929i
$506$	−19.0111	−	32.9282i	−0.845146	−	1.46384i
$507$		−	7.47686i		−	0.332059i
$508$		−	2.85241i		−	0.126555i
$509$	−11.1366	−	19.2892i	−0.493622	−	0.854979i	0.506351	−	0.862328i	$-0.330994\pi$
$509$	−11.1366	−	19.2892i	−0.493622	−	0.854979i	−0.999973	+	0.00734869i	$0.997661\pi$
$510$	6.11470	+	22.2155i	0.270763	+	0.983718i
$511$	−2.54788	+	4.41306i	−0.112712	+	0.195222i
$512$	1.00000			0.0441942
$513$	6.92274	−	11.9905i	0.305646	−	0.529395i
$514$	−8.75782	+	15.1690i	−0.386291	+	0.669075i
$515$	10.8446	−	41.6011i	0.477869	−	1.83316i
$516$	3.42370	−	1.97667i	0.150720	−	0.0870182i
$517$		−	45.5668i		−	2.00403i
$518$	−0.000917568	−	2.51859i	−4.03156e−5	−	0.110660i
$519$	−32.6887			−1.43488
$520$	4.81097	+	4.74603i	0.210975	+	0.208127i
$521$	3.46902	−	6.00852i	0.151981	−	0.263238i	−0.779975	−	0.625811i	$-0.784768\pi$
$521$	3.46902	−	6.00852i	0.151981	−	0.263238i	0.931955	+	0.362573i	$0.118102\pi$
$522$	−3.94086	−	2.27526i	−0.172487	−	0.0995852i
$523$	−2.48913	+	4.31130i	−0.108842	+	0.188520i	−0.915301	−	0.402769i	$-0.868048\pi$
$523$	−2.48913	+	4.31130i	−0.108842	+	0.188520i	0.806459	+	0.591290i	$0.201381\pi$
$524$			5.70314i			0.249143i
$525$	0.0544087	+	4.00359i	0.00237459	+	0.174731i
$526$		−	7.65904i		−	0.333950i
$527$	22.9975	−	13.2776i	1.00179	−	0.578381i
$528$			7.86858i			0.342436i
$529$	64.3392			2.79736
$530$	−0.0911322	+	0.0923791i	−0.00395853	+	0.00401269i
$531$	2.88649	+	1.66652i	0.125263	+	0.0723206i
$532$	1.31185			0.0568759
$533$	−13.3751	−	23.1663i	−0.579338	−	1.00344i
$534$	−10.6962	−	18.5264i	−0.462870	−	0.801714i
$535$	−19.1809	+	19.4434i	−0.829264	+	0.840610i
$536$	2.76181	+	1.59453i	0.119292	+	0.0688732i
$537$	16.1597	−	27.9895i	0.697344	−	1.20784i
$538$	−7.48912	−	12.9715i	−0.322879	−	0.559243i
$539$	−13.8909	−	24.0598i	−0.598325	−	1.03633i
$540$	6.86245	−	6.95634i	0.295313	−	0.299353i
$541$			25.8249i			1.11030i	0.831751	+	0.555149i	$0.187339\pi$
$541$			25.8249i			1.11030i	−0.831751	+	0.555149i	$0.812661\pi$
$542$	−10.1678	+	17.6112i	−0.436745	+	0.756464i
$543$	−20.8936	+	12.0629i	−0.896630	+	0.517669i
$544$	5.32800			0.228436
$545$	−3.94067	−	14.3170i	−0.168800	−	0.613272i
$546$	1.21010	+	2.09595i	0.0517875	+	0.0896986i
$547$	31.9838			1.36753			0.683765	−	0.729702i	$-0.260341\pi$
$547$	31.9838			1.36753			0.683765	+	0.729702i	$0.260341\pi$
$548$	2.21887	+	1.28107i	0.0947856	+	0.0547245i
$549$			8.22656i			0.351101i
$550$	0.276427	+	20.3405i	0.0117869	+	0.867323i
$551$	−9.73522	+	16.8619i	−0.414734	+	0.718341i
$552$	−15.6530	−	9.03729i	−0.666238	−	0.384653i
$553$	1.26971	+	2.19919i	0.0539934	+	0.0935192i
$554$	25.8236			1.09714
$555$	18.4673	−	18.7336i	0.783893	−	0.795197i
$556$	−0.0826637			−0.00350572
$557$	0.670638	+	1.16158i	0.0284159	+	0.0492177i	0.879884	−	0.475189i	$-0.157620\pi$
$557$	0.670638	+	1.16158i	0.0284159	+	0.0492177i	−0.851468	+	0.524407i	$0.824287\pi$
$558$	3.19616	+	1.84530i	0.135304	+	0.0781178i
$559$	3.08889	−	5.35012i	0.130646	−	0.226286i
$560$	0.895911	+	0.233546i	0.0378591	+	0.00986912i
$561$			41.9238i			1.77002i
$562$	−17.6512	−	10.1910i	−0.744573	−	0.429879i
$563$	−28.1948			−1.18827			−0.594135	−	0.804365i	$-0.702506\pi$
$563$	−28.1948			−1.18827			−0.594135	+	0.804365i	$0.702506\pi$
$564$	−10.8305	−	18.7590i	−0.456047	−	0.789897i
$565$	8.91886	−	2.45487i	0.375219	−	0.103277i
$566$	0.983218			0.0413277
$567$	3.82717	−	2.20962i	0.160726	−	0.0927953i
$568$	−1.80052	+	3.11860i	−0.0755483	+	0.130854i
$569$			45.0790i			1.88981i	0.327346	+	0.944904i	$0.393846\pi$
$569$			45.0790i			1.88981i	−0.327346	+	0.944904i	$0.606154\pi$
$570$	9.75422	+	9.62256i	0.408559	+	0.403045i
$571$	15.3395	+	26.5687i	0.641936	+	1.11187i	0.985000	+	0.172554i	$0.0552019\pi$
$571$	15.3395	+	26.5687i	0.641936	+	1.11187i	−0.343064	+	0.939312i	$0.611465\pi$
$572$	6.14801	+	10.6487i	0.257061	+	0.445243i
$573$	7.67137	−	13.2872i	0.320476	−	0.555081i
$574$	−3.17381	−	1.83240i	−0.132472	−	0.0764828i
$575$	−40.7811	−	22.8118i	−1.70069	−	0.951318i
$576$	0.370239	+	0.641273i	0.0154266	+	0.0267197i
$577$	5.96282	+	10.3279i	0.248235	+	0.429956i	0.963036	−	0.269372i	$-0.0868160\pi$
$577$	5.96282	+	10.3279i	0.248235	+	0.429956i	−0.714801	+	0.699328i	$0.753483\pi$
$578$	11.3876			0.473663
$579$	40.7347	+	23.5182i	1.69288	+	0.977382i
$580$	−9.65043	+	9.78247i	−0.400712	+	0.406195i
$581$	0.701616			0.0291079
$582$		−	9.15893i		−	0.379650i
$583$	−0.204473	+	0.118052i	−0.00846840	+	0.00488923i
$584$			12.3070i			0.509269i
$585$	−1.26229	+	4.84231i	−0.0521894	+	0.200205i
$586$		−	5.28979i		−	0.218519i
$587$	10.2387	−	17.7339i	0.422596	−	0.731957i	−0.573597	−	0.819138i	$-0.694452\pi$
$587$	10.2387	−	17.7339i	0.422596	−	0.731957i	0.996193	+	0.0871807i	$0.0277857\pi$
$588$	−11.4373	−	6.60333i	−0.471666	−	0.272317i
$589$	7.89556	−	13.6755i	0.325331	−	0.563490i
$590$	7.06848	−	7.16519i	0.291005	−	0.294986i
$591$	5.31728			0.218724
$592$	−3.04330	−	5.26672i	−0.125079	−	0.216461i
$593$			3.25794i			0.133788i	0.997760	+	0.0668938i	$0.0213089\pi$
$593$			3.25794i			0.133788i	−0.997760	+	0.0668938i	$0.978691\pi$
$594$	15.3973	−	8.88961i	0.631757	−	0.364745i
$595$	4.77342	+	1.24433i	0.195691	+	0.0510127i
$596$	4.05785	−	7.02840i	0.166216	−	0.287894i
$597$	20.6646	−	35.7922i	0.845746	−	1.46488i
$598$	−28.2447			−1.15501
$599$	8.50081	−	14.7238i	0.347334	−	0.601600i	−0.638441	−	0.769671i	$-0.720420\pi$
$599$	8.50081	−	14.7238i	0.347334	−	0.601600i	0.985775	+	0.168071i	$0.0537538\pi$
$600$	4.94843	+	8.30813i	0.202019	+	0.339178i
$601$	13.2637	+	22.9734i	0.541037	+	0.937104i	0.998845	+	0.0480525i	$0.0153015\pi$
$601$	13.2637	+	22.9734i	0.541037	+	0.937104i	−0.457808	+	0.889051i	$0.651365\pi$
$602$		−	0.846364i		−	0.0344952i
$603$			2.36143i			0.0961649i
$604$	0.649772	+	1.12544i	0.0264389	+	0.0457935i
$605$	−3.13191	+	12.0144i	−0.127330	+	0.488454i
$606$		−	14.3804i		−	0.584163i
$607$	10.6104	+	18.3777i	0.430662	+	0.745928i	0.996930	−	0.0782926i	$-0.0249469\pi$
$607$	10.6104	+	18.3777i	0.430662	+	0.745928i	−0.566269	+	0.824221i	$0.691614\pi$
$608$	2.74384	−	1.58416i	0.111277	−	0.0642460i
$609$	−4.26185	+	2.46058i	−0.172699	+	0.0997077i
$610$	24.0389	+	6.26646i	0.973307	+	0.253722i
$611$	−29.3142	−	16.9246i	−1.18593	−	0.684695i
$612$	1.97264	+	3.41671i	0.0797391	+	0.138112i
$613$	−30.2945	+	17.4905i	−1.22358	+	0.706435i	−0.965680	−	0.259736i	$-0.916364\pi$
$613$	−30.2945	+	17.4905i	−1.22358	+	0.706435i	−0.257902	+	0.966171i	$0.583031\pi$
$614$	8.12681	−	4.69202i	0.327971	−	0.189354i
$615$	−10.1579	−	36.9050i	−0.409606	−	1.48815i
$616$	1.45888	+	0.842284i	0.0587799	+	0.0339366i
$617$	−21.6307	+	12.4885i	−0.870820	+	0.502768i	−0.867621	−	0.497227i	$-0.834352\pi$
$617$	−21.6307	+	12.4885i	−0.870820	+	0.502768i	−0.00319933	+	0.999995i	$0.501018\pi$
$618$		−	37.1843i		−	1.49577i
$619$	−16.9508			−0.681309			−0.340654	−	0.940189i	$-0.610649\pi$
$619$	−16.9508			−0.681309			−0.340654	+	0.940189i	$0.610649\pi$
$620$	7.82680	−	7.93389i	0.314332	−	0.318632i
$621$			40.8399i			1.63885i
$622$	21.1021	+	12.1833i	0.846116	+	0.488506i
$623$	−4.57986			−0.183488
$624$	5.06204	+	2.92257i	0.202644	+	0.116997i
$625$	13.0837	+	21.3030i	0.523350	+	0.852118i
$626$	12.7705	−	22.1191i	0.510410	−	0.884056i
$627$	12.4651	+	21.5901i	0.497806	+	0.862226i
$628$		−	3.39389i		−	0.135431i
$629$	−16.2147	−	28.0611i	−0.646523	−	1.11887i
$630$	0.181935	+	0.660991i	0.00724844	+	0.0263345i
$631$	−6.24336	+	3.60461i	−0.248544	+	0.143497i	−0.619097	−	0.785314i	$-0.712501\pi$
$631$	−6.24336	+	3.60461i	−0.248544	+	0.143497i	0.370553	+	0.928811i	$0.379168\pi$
$632$	5.31138	+	3.06653i	0.211275	+	0.121980i
$633$	−19.4682	−	11.2400i	−0.773792	−	0.446749i
$634$	9.11049	+	5.25994i	0.361824	+	0.208899i
$635$	−1.69262	−	6.14950i	−0.0671695	−	0.244035i
$636$	−0.0561185	+	0.0972001i	−0.00222524	+	0.00385424i
$637$	−20.6377			−0.817695
$638$	−21.6526	+	12.5012i	−0.857236	+	0.494926i
$639$	−2.66650			−0.105485
$640$	2.15589	−	0.593399i	0.0852192	−	0.0234562i
$641$	−12.3044	−	21.3119i	−0.485996	−	0.841769i	0.513875	−	0.857865i	$-0.328210\pi$
$641$	−12.3044	−	21.3119i	−0.485996	−	0.841769i	−0.999870	+	0.0160962i	$0.994876\pi$
$642$	−11.8115	+	20.4581i	−0.466162	+	0.807416i
$643$	−24.7379			−0.975568			−0.487784	−	0.872964i	$-0.662195\pi$
$643$	−24.7379			−0.975568			−0.487784	+	0.872964i	$0.662195\pi$
$644$	−3.35113	+	1.93478i	−0.132053	+	0.0762408i
$645$	6.20817	−	6.29312i	0.244447	−	0.247791i
$646$	14.6192	−	8.44039i	0.575184	−	0.332083i
$647$	−7.94294	+	13.7576i	−0.312269	+	0.540866i	−0.978853	−	0.204564i	$-0.934422\pi$
$647$	−7.94294	+	13.7576i	−0.312269	+	0.540866i	0.666584	+	0.745430i	$0.267756\pi$
$648$	5.33656	−	9.24320i	0.209640	−	0.363107i
$649$	15.8595	−	9.15650i	0.622541	−	0.359424i
$650$	13.1882	+	7.37712i	0.517285	+	0.289354i
$651$	3.45649	−	1.99560i	0.135470	−	0.0782139i
$652$	7.14219			0.279710
$653$	−1.69247	+	2.93145i	−0.0662316	+	0.114717i	−0.897240	−	0.441544i	$-0.854431\pi$
$653$	−1.69247	+	2.93145i	−0.0662316	+	0.114717i	0.831008	+	0.556260i	$0.187764\pi$
$654$	−6.42181	−	11.1229i	−0.251113	−	0.434940i
$655$	3.38424	+	12.2954i	0.132233	+	0.480419i
$656$	−8.85103			−0.345575
$657$	−7.89217	+	4.55655i	−0.307903	+	0.177768i
$658$	−4.63737			−0.180784
$659$	5.44562	−	9.43209i	0.212131	−	0.367422i	−0.740250	−	0.672332i	$-0.765293\pi$
$659$	5.44562	−	9.43209i	0.212131	−	0.367422i	0.952381	+	0.304910i	$0.0986263\pi$
$660$	4.66920	+	16.9638i	0.181749	+	0.660315i
$661$	5.03518	+	2.90706i	0.195846	+	0.113072i	0.594716	−	0.803936i	$-0.297264\pi$
$661$	5.03518	+	2.90706i	0.195846	+	0.113072i	−0.398870	+	0.917007i	$0.630598\pi$
$662$	4.05217	+	2.33952i	0.157492	+	0.0909281i
$663$	26.9706	+	15.5715i	1.04745	+	0.604746i
$664$	1.46749	−	0.847254i	0.0569496	−	0.0328798i
$665$	2.82821	−	0.778450i	0.109673	−	0.0301870i
$666$	2.25066	−	3.90153i	0.0872111	−	0.151181i
$667$		−	57.4318i		−	2.22377i
$668$	6.66644	+	11.5466i	0.257932	+	0.446752i
$669$	−20.5910	+	35.6646i	−0.796092	+	1.37887i
$670$	6.90036	+	1.79878i	0.266584	+	0.0694931i
$671$	39.1444	+	22.6000i	1.51115	+	0.872464i
$672$	0.800792			0.0308912
$673$	35.0182	+	20.2178i	1.34985	+	0.779338i	0.988228	−	0.152986i	$-0.0488888\pi$
$673$	35.0182	+	20.2178i	1.34985	+	0.779338i	0.361625	+	0.932324i	$0.382222\pi$
$674$			4.86024i			0.187210i
$675$	10.6668	−	19.0693i	0.410566	−	0.733978i
$676$	−3.86595			−0.148690
$677$			30.3516i			1.16651i	0.812290	+	0.583254i	$0.198221\pi$
$677$			30.3516i			1.16651i	−0.812290	+	0.583254i	$0.801779\pi$
$678$	6.92909	−	4.00051i	0.266110	−	0.153639i
$679$	−1.69812	−	0.980409i	−0.0651678	−	0.0376246i
$680$	11.4866	−	3.16163i	0.440491	−	0.121243i
$681$	17.1593	−	9.90691i	0.657545	−	0.379634i
$682$	17.5610	−	10.1388i	0.672444	−	0.388236i
$683$	0.0753519	+	0.130513i	0.00288326	+	0.00499395i	0.867463	−	0.497501i	$-0.165749\pi$
$683$	0.0753519	+	0.130513i	0.00288326	+	0.00499395i	−0.864580	+	0.502495i	$0.832416\pi$
$684$	2.03175	+	1.17303i	0.0776860	+	0.0448521i
$685$	5.54384	+	1.44517i	0.211819	+	0.0552170i
$686$	−4.95865	+	2.86288i	−0.189322	+	0.109305i
$687$	−11.4889	+	6.63310i	−0.438327	+	0.253068i
$688$	−1.02205	−	1.77024i	−0.0389652	−	0.0674897i
$689$			0.175390i			0.00668182i
$690$	−39.1090	−	10.1949i	−1.48886	−	0.388115i
$691$	−20.2015	−	34.9900i	−0.768501	−	1.33108i	−0.938375	−	0.345617i	$-0.887669\pi$
$691$	−20.2015	−	34.9900i	−0.768501	−	1.33108i	0.169874	−	0.985466i	$-0.445664\pi$
$692$			16.9019i			0.642512i
$693$			1.24739i			0.0473843i
$694$	−13.2021	−	22.8668i	−0.501146	−	0.868010i
$695$	−0.178214	+	0.0490525i	−0.00676004	+	0.00186067i
$696$	−5.94267	+	10.2930i	−0.225256	+	0.390155i
$697$	−47.1583			−1.78625
$698$	8.01159	−	13.8765i	0.303243	−	0.525233i
$699$	−11.0387	+	19.1196i	−0.417523	+	0.723171i
$700$	2.07007	−	0.0281323i	0.0782414	−	0.00106330i
$701$	−39.8426	+	23.0031i	−1.50483	+	0.868816i	−0.504849	+	0.863208i	$0.668452\pi$
$701$	−39.8426	+	23.0031i	−1.50483	+	0.868816i	−0.999984	+	0.00560815i	$0.998215\pi$
$702$		−	13.2072i		−	0.498475i
$703$	−16.6936	−	9.62997i	−0.629612	−	0.363201i
$704$	4.06848			0.153337
$705$	−34.4811	−	34.0156i	−1.29863	−	1.28110i
$706$	10.2140	−	17.6912i	0.384410	−	0.665817i
$707$	−2.66620	−	1.53933i	−0.100273	−	0.0578926i
$708$	4.35272	−	7.53913i	0.163585	−	0.283338i
$709$		−	46.9042i		−	1.76152i	−0.473559	−	0.880762i	$-0.657031\pi$
$709$		−	46.9042i		−	1.76152i	0.473559	−	0.880762i	$-0.342969\pi$
$710$	−2.03117	+	7.79180i	−0.0762283	+	0.292421i
$711$			4.54140i			0.170316i
$712$	−9.57915	+	5.53052i	−0.358994	+	0.207265i
$713$			46.5789i			1.74440i
$714$	4.26662			0.159674
$715$	19.5734	+	19.3092i	0.732002	+	0.722122i
$716$	−14.4721	−	8.35547i	−0.540847	−	0.312258i
$717$	−15.7135			−0.586833
$718$	−13.5393	−	23.4507i	−0.505282	−	0.875173i
$719$	−16.3928	−	28.3931i	−0.611347	−	1.05888i	−0.991014	−	0.133761i	$-0.957295\pi$
$719$	−16.3928	−	28.3931i	−0.611347	−	1.05888i	0.379666	−	0.925123i	$-0.376039\pi$
$720$	1.17873	+	1.16282i	0.0439286	+	0.0433356i
$721$	−6.89418	−	3.98036i	−0.256753	−	0.148236i
$722$	−4.48090	+	7.76114i	−0.166762	+	0.288840i
$723$	22.0588	+	38.2070i	0.820377	+	1.42093i
$724$	6.23719	+	10.8031i	0.231803	+	0.401495i
$725$	−15.0004	+	26.8165i	−0.557101	+	0.995941i
$726$			10.7388i			0.398555i
$727$	−13.2163	+	22.8912i	−0.490164	+	0.848989i	−0.999936	−	0.0113208i	$-0.996396\pi$
$727$	−13.2163	+	22.8912i	−0.490164	+	0.848989i	0.509772	+	0.860309i	$0.329730\pi$
$728$	1.08372	−	0.625688i	0.0401655	−	0.0231895i
$729$	−17.4519			−0.646365
$730$	7.30298	+	26.5327i	0.270296	+	0.982018i
$731$	−5.44548	−	9.43184i	−0.201408	−	0.348849i
$732$	21.4867			0.794171
$733$	22.4801	+	12.9789i	0.830321	+	0.479386i	0.853963	−	0.520334i	$-0.174193\pi$
$733$	22.4801	+	12.9789i	0.830321	+	0.479386i	−0.0236414	+	0.999721i	$0.507526\pi$
$734$		−	14.4730i		−	0.534210i
$735$	−28.5760	−	7.44919i	−1.05404	−	0.274767i
$736$	−4.67277	+	8.09348i	−0.172241	+	0.298330i
$737$	11.2364	+	6.48732i	0.413897	+	0.238964i
$738$	−3.27700	−	5.67593i	−0.120628	−	0.208934i
$739$	−7.42521			−0.273141			−0.136570	−	0.990630i	$-0.543608\pi$
$739$	−7.42521			−0.273141			−0.136570	+	0.990630i	$0.543608\pi$
$740$	−9.68630	−	9.54859i	−0.356075	−	0.351013i
$741$	18.5192			0.680322
$742$	0.0120143	+	0.0208094i	0.000441059	+	0.000763937i
$743$	−15.1449	−	8.74394i	−0.555614	−	0.320784i	0.195769	−	0.980650i	$-0.437280\pi$
$743$	−15.1449	−	8.74394i	−0.555614	−	0.320784i	−0.751383	+	0.659866i	$0.770613\pi$
$744$	4.81968	−	8.34794i	0.176698	−	0.306050i
$745$	4.57764	−	17.5604i	0.167712	−	0.643363i
$746$			21.2422i			0.777732i
$747$	1.08664	+	0.627373i	0.0397582	+	0.0229544i
$748$	21.6769			0.792586
$749$	2.52870	+	4.37983i	0.0923965	+	0.160035i
$750$	15.5983	+	14.9750i	0.569570	+	0.546811i
$751$	−39.4824			−1.44073			−0.720367	−	0.693593i	$-0.756027\pi$
$751$	−39.4824			−1.44073			−0.720367	+	0.693593i	$0.756027\pi$
$752$	−9.69944	+	5.59997i	−0.353702	+	0.204210i
$753$	25.9092	−	44.8761i	0.944185	−	1.63538i
$754$			18.5729i			0.676385i
$755$	2.06867	+	2.04075i	0.0752868	+	0.0742706i
$756$	−0.904703	−	1.56699i	−0.0329037	−	0.0569909i
$757$	23.6852	+	41.0239i	0.860852	+	1.49104i	0.871108	+	0.491092i	$0.163402\pi$
$757$	23.6852	+	41.0239i	0.860852	+	1.49104i	−0.0102559	+	0.999947i	$0.503265\pi$
$758$	14.6888	−	25.4417i	0.533521	−	0.924085i
$759$	−63.6842	−	36.7681i	−2.31159	−	1.33460i
$760$	4.97539	−	5.04346i	0.180476	−	0.182946i
$761$	10.4993	+	18.1853i	0.380600	+	0.659218i	0.991148	−	0.132761i	$-0.0423842\pi$
$761$	10.4993	+	18.1853i	0.380600	+	0.659218i	−0.610548	+	0.791979i	$0.709051\pi$
$762$	−2.75833	−	4.77757i	−0.0999237	−	0.173073i
$763$	−2.74967			−0.0995446
$764$	−6.87021	−	3.96652i	−0.248556	−	0.143504i
$765$	6.28026	+	6.19549i	0.227063	+	0.223999i
$766$	21.0989			0.762335
$767$		−	13.6038i		−	0.491203i
$768$	1.67492	−	0.967016i	0.0604385	−	0.0348942i
$769$			9.46062i			0.341159i	0.985344	+	0.170579i	$0.0545639\pi$
$769$			9.46062i			0.341159i	−0.985344	+	0.170579i	$0.945436\pi$
$770$	3.64500	+	0.950178i	0.131357	+	0.0342420i
$771$			33.8758i			1.22001i
$772$	12.1602	−	21.0621i	0.437654	−	0.758040i
$773$	−23.5068	−	13.5717i	−0.845482	−	0.488140i	0.0136416	−	0.999907i	$-0.495658\pi$
$773$	−23.5068	−	13.5717i	−0.845482	−	0.488140i	−0.859124	+	0.511767i	$0.828991\pi$
$774$	0.756804	−	1.31082i	0.0272028	−	0.0471166i
$775$	12.1658	−	21.7490i	0.437008	−	0.781248i
$776$	−4.73567			−0.170001
$777$	−2.43705	−	4.21754i	−0.0874287	−	0.151304i
$778$		−	7.14100i		−	0.256017i
$779$	−24.2858	+	14.0214i	−0.870129	+	0.502369i
$780$	12.6475	+	3.29694i	0.452853	+	0.118050i
$781$	−7.32541	+	12.6880i	−0.262124	+	0.454011i
$782$	−24.8966	+	43.1221i	−0.890299	+	1.54204i
$783$	26.8552			0.959725
$784$	−3.41428	+	5.91371i	−0.121939	+	0.211204i
$785$	−2.01393	−	7.31686i	−0.0718802	−	0.261150i
$786$	5.51502	+	9.55230i	0.196714	+	0.340719i
$787$			32.3709i			1.15390i	0.816780	+	0.576949i	$0.195757\pi$
$787$			32.3709i			1.15390i	−0.816780	+	0.576949i	$0.804243\pi$
$788$		−	2.74932i		−	0.0979406i
$789$	−7.40642	−	12.8283i	−0.263675	−	0.456699i
$790$	13.2705	+	3.45934i	0.472141	+	0.123078i
$791$		−	1.71292i		−	0.0609045i
$792$	1.50631	+	2.60901i	0.0535245	+	0.0927071i
$793$	29.0783	−	16.7883i	1.03260	−	0.596172i
$794$	3.16415	−	1.82682i	0.112292	−	0.0648316i
$795$	−0.0633071	+	0.242854i	−0.00224527	+	0.00861314i
$796$	−18.5065	−	10.6847i	−0.655945	−	0.378710i
$797$	−8.83836	−	15.3085i	−0.313071	−	0.542254i	0.665955	−	0.745992i	$-0.268024\pi$
$797$	−8.83836	−	15.3085i	−0.313071	−	0.542254i	−0.979026	+	0.203738i	$0.934691\pi$
$798$	2.19724	−	1.26858i	0.0777816	−	0.0449072i
$799$	−51.6787	+	29.8367i	−1.82826	+	1.05555i
$800$	4.29576	−	2.55861i	0.151878	−	0.0904605i
$801$	−7.09315	−	4.09523i	−0.250624	−	0.144698i
$802$	29.9300	−	17.2801i	1.05687	−	0.610182i
$803$			50.0710i			1.76697i
$804$	6.16775			0.217520
$805$	−6.07659	+	6.15973i	−0.214172	+	0.217102i
$806$		−	15.0632i		−	0.530578i
$807$	−25.0874	−	14.4842i	−0.883117	−	0.509868i
$808$	−7.43544			−0.261578
$809$	−3.11773	−	1.80002i	−0.109613	−	0.0632854i	0.444191	−	0.895932i	$-0.353491\pi$
$809$	−3.11773	−	1.80002i	−0.109613	−	0.0632854i	−0.553804	+	0.832647i	$0.686824\pi$
$810$	6.02016	−	23.0941i	0.211527	−	0.811443i
$811$	3.45644	−	5.98673i	0.121372	−	0.210222i	−0.798937	−	0.601415i	$-0.794604\pi$
$811$	3.45644	−	5.98673i	0.121372	−	0.210222i	0.920309	+	0.391192i	$0.127937\pi$
$812$	1.27225	+	2.20361i	0.0446474	+	0.0773315i
$813$			39.3297i			1.37935i
$814$	−12.3816	−	21.4276i	−0.433975	−	0.751035i
$815$	15.3978	−	4.23817i	0.539362	−	0.148457i
$816$	8.92398	−	5.15226i	0.312402	−	0.180365i
$817$	−5.60867	−	3.23817i	−0.196223	−	0.113289i
$818$	−8.77545	−	5.06651i	−0.306826	−	0.177146i
$819$	0.802474	+	0.463308i	0.0280407	+	0.0161893i
$820$	−19.0819	+	5.25219i	−0.666368	+	0.183415i
$821$	10.9151	−	18.9055i	0.380939	−	0.659806i	−0.610258	−	0.792203i	$-0.708934\pi$
$821$	10.9151	−	18.9055i	0.380939	−	0.659806i	0.991197	+	0.132397i	$0.0422675\pi$
$822$	4.95525			0.172834
$823$	12.7491	−	7.36072i	0.444407	−	0.256579i	−0.261058	−	0.965323i	$-0.584071\pi$
$823$	12.7491	−	7.36072i	0.444407	−	0.256579i	0.705465	+	0.708744i	$0.250738\pi$
$824$	−19.2263			−0.669781
$825$	20.1326	+	33.8015i	0.700928	+	1.17682i
$826$	−0.931865	−	1.61404i	−0.0324237	−	0.0561595i
$827$	8.86959	−	15.3626i	0.308426	−	0.534209i	−0.669592	−	0.742729i	$-0.733531\pi$
$827$	8.86959	−	15.3626i	0.308426	−	0.534209i	0.978018	+	0.208520i	$0.0668645\pi$
$828$	−6.92017			−0.240493
$829$	−23.2324	+	13.4132i	−0.806894	+	0.465860i	−0.845876	−	0.533380i	$-0.820922\pi$
$829$	−23.2324	+	13.4132i	−0.806894	+	0.465860i	0.0389824	+	0.999240i	$0.487588\pi$
$830$	2.66099	−	2.69740i	0.0923642	−	0.0936280i
$831$	43.2525	−	24.9718i	1.50041	−	0.866264i
$832$	1.51113	−	2.61735i	0.0523890	−	0.0907404i
$833$	−18.1913	+	31.5083i	−0.630291	+	1.09170i
$834$	−0.138455	+	0.0799371i	−0.00479431	+	0.00276799i
$835$	21.2239	+	20.9374i	0.734483	+	0.724569i
$836$	11.1633	−	6.44511i	0.386090	−	0.222909i
$837$	−21.7804			−0.752839
$838$	4.65134	−	8.05636i	0.160678	−	0.278302i
$839$	−9.37267	−	16.2339i	−0.323580	−	0.560458i	0.657644	−	0.753329i	$-0.271553\pi$
$839$	−9.37267	−	16.2339i	−0.323580	−	0.560458i	−0.981224	+	0.192871i	$0.938220\pi$
$840$	1.72642	−	0.475189i	0.0595672	−	0.0163956i
$841$	−8.76554			−0.302260
$842$	−19.1614	+	11.0628i	−0.660345	+	0.381251i
$843$	−39.4192			−1.35767
$844$	−5.81169	+	10.0661i	−0.200046	+	0.346491i
$845$	−8.33457	+	2.29405i	−0.286718	+	0.0789177i
$846$	−7.18223	−	4.14666i	−0.246930	−	0.142565i
$847$	1.99104	+	1.14953i	0.0684129	+	0.0394982i
$848$	0.0502578	+	0.0290163i	0.00172586	+	0.000996425i
$849$	1.64681	−	0.950787i	0.0565184	−	0.0326309i
$850$	22.8878	−	13.6323i	0.785045	−	0.467584i
$851$	56.8467	−	0.0207103i	1.94868	−	0.000709941i
$852$			6.96454i			0.238601i
$853$	26.2865	+	45.5295i	0.900032	+	1.55890i	0.827450	+	0.561539i	$0.189791\pi$
$853$	26.2865	+	45.5295i	0.900032	+	1.55890i	0.0725818	+	0.997362i	$0.476876\pi$
$854$	2.30002	−	3.98376i	0.0787051	−	0.136321i
$855$	5.07632	+	1.32329i	0.173607	+	0.0452557i
$856$	10.5779	+	6.10718i	0.361547	+	0.208739i
$857$	46.2789			1.58086			0.790429	−	0.612553i	$-0.209858\pi$
$857$	46.2789			1.58086			0.790429	+	0.612553i	$0.209858\pi$
$858$	20.5948	+	11.8904i	0.703096	+	0.405933i
$859$			18.1021i			0.617636i	0.951121	+	0.308818i	$0.0999334\pi$
$859$			18.1021i			0.617636i	−0.951121	+	0.308818i	$0.900067\pi$
$860$	−3.25388	−	3.20996i	−0.110957	−	0.109459i
$861$	−7.08783			−0.241553
$862$			39.4161i			1.34252i
$863$	42.8832	−	24.7586i	1.45976	−	0.842793i	0.460761	−	0.887524i	$-0.347576\pi$
$863$	42.8832	−	24.7586i	1.45976	−	0.842793i	0.998999	+	0.0447311i	$0.0142431\pi$
$864$	−3.78452	−	2.18499i	−0.128752	−	0.0743350i
$865$	10.0295	+	36.4386i	0.341015	+	1.23895i
$866$	−3.99486	+	2.30644i	−0.135751	+	0.0783759i
$867$	19.0734	−	11.0120i	0.647766	−	0.373988i
$868$	−1.03184	−	1.78719i	−0.0350228	−	0.0606613i
$869$	21.6093	+	12.4761i	0.733044	+	0.423223i
$870$	−6.70390	+	25.7170i	−0.227284	+	0.871888i
$871$	8.34690	−	4.81909i	0.282824	−	0.163288i
$872$	−5.75115	+	3.32043i	−0.194758	+	0.112444i
$873$	−1.75333	−	3.03686i	−0.0593412	−	0.102782i
$874$			29.6096i			1.00156i
$875$	4.44617	−	1.28903i	0.150308	−	0.0435772i
$876$	11.9011	+	20.6133i	0.402101	+	0.696459i
$877$		−	22.6018i		−	0.763209i	−0.924326	−	0.381604i	$-0.875372\pi$
$877$		−	22.6018i		−	0.763209i	0.924326	−	0.381604i	$-0.124628\pi$
$878$			16.2059i			0.546922i
$879$	−5.11531	−	8.85997i	−0.172535	−	0.298839i
$880$	8.77122	−	2.41423i	0.295678	−	0.0813838i
$881$	−19.9147	+	34.4933i	−0.670943	+	1.16211i	0.306694	+	0.951808i	$0.400777\pi$
$881$	−19.9147	+	34.4933i	−0.670943	+	1.16211i	−0.977637	+	0.210300i	$0.932556\pi$
$882$	−5.05640			−0.170258
$883$	5.43593	−	9.41530i	0.182934	−	0.316850i	−0.759945	−	0.649988i	$-0.774774\pi$
$883$	5.43593	−	9.41530i	0.182934	−	0.316850i	0.942878	+	0.333138i	$0.108107\pi$
$884$	8.05131	−	13.9453i	0.270795	−	0.469030i
$885$	4.91029	−	18.8365i	0.165057	−	0.633181i
$886$	−13.0726	+	7.54749i	−0.439184	+	0.253563i
$887$			22.5448i			0.756981i	0.925605	+	0.378490i	$0.123557\pi$
$887$			22.5448i			0.756981i	−0.925605	+	0.378490i	$0.876443\pi$
$888$	−10.1903	−	5.87842i	−0.341964	−	0.197267i
$889$	−1.18105			−0.0396112
$890$	−17.3698	+	17.6075i	−0.582237	+	0.590204i
$891$	21.7117	−	37.6058i	0.727370	−	1.25984i
$892$	18.4405	+	10.6466i	0.617435	+	0.356476i
$893$	−17.7425	+	30.7309i	−0.593729	+	1.02837i
$894$		−	15.6960i		−	0.524953i
$895$	−36.1584	−	9.42577i	−1.20864	−	0.315069i
$896$		−	0.414053i		−	0.0138325i
$897$	−47.3076	+	27.3130i	−1.57955	+	0.911956i
$898$			27.9031i			0.931139i
$899$	30.6290			1.02153
$900$	3.23122	+	1.80745i	0.107707	+	0.0602485i
$901$	0.267774	+	0.154599i	0.00892083	+	0.00515045i
$902$	−36.0103			−1.19901
$903$	−0.818447	−	1.41759i	−0.0272362	−	0.0471745i
$904$	−2.06848	−	3.58272i	−0.0687967	−	0.119159i
$905$	19.8573	+	19.5893i	0.660078	+	0.651169i
$906$	2.17663	+	1.25668i	0.0723138	+	0.0417504i
$907$	−4.34143	+	7.51958i	−0.144155	+	0.249684i	−0.929057	−	0.369936i	$-0.879380\pi$
$907$	−4.34143	+	7.51958i	−0.144155	+	0.249684i	0.784902	+	0.619619i	$0.212713\pi$
$908$	−5.12241	−	8.87228i	−0.169993	−	0.294437i
$909$	−2.75289	−	4.76815i	−0.0913076	−	0.158149i
$910$	1.96511	−	1.99200i	0.0651427	−	0.0660340i
$911$		−	9.72325i		−	0.322146i	−0.986943	−	0.161073i	$-0.948505\pi$
$911$		−	9.72325i		−	0.322146i	0.986943	−	0.161073i	$-0.0514954\pi$
$912$	3.06381	−	5.30667i	0.101453	−	0.175721i
$913$	5.97045	−	3.44704i	0.197593	−	0.114080i
$914$	−17.1624			−0.567683
$915$	46.3230	−	12.7502i	1.53139	−	0.421508i
$916$	3.42967	+	5.94037i	0.113320	+	0.196275i
$917$	2.36140			0.0779803
$918$	−20.1639	−	11.6417i	−0.665509	−	0.384232i
$919$			1.54383i			0.0509264i	0.999676	+	0.0254632i	$0.00810607\pi$
$919$			1.54383i			0.0509264i	−0.999676	+	0.0254632i	$0.991894\pi$
$920$	−5.27134	+	20.2215i	−0.173791	+	0.666683i
$921$	9.07451	−	15.7175i	0.299015	−	0.517910i
$922$	−34.0409	−	19.6535i	−1.12108	−	0.647254i
$923$	5.44165	+	9.42522i	0.179114	+	0.310235i
$924$	3.25801			0.107181
$925$	−26.5488	−	14.8379i	−0.872918	−	0.487868i
$926$	−19.7221			−0.648109
$927$	−7.11834	−	12.3293i	−0.233797	−	0.404948i
$928$	5.32204	+	3.07268i	0.174705	+	0.100866i
$929$	−26.9069	+	46.6041i	−0.882786	+	1.52903i	−0.0345564	+	0.999403i	$0.511002\pi$
$929$	−26.9069	+	46.6041i	−0.882786	+	1.52903i	−0.848230	+	0.529628i	$0.822331\pi$
$930$	5.43707	−	20.8573i	0.178289	−	0.683937i
$931$			21.6350i			0.709059i
$932$	9.88589	+	5.70762i	0.323823	+	0.186959i
$933$	47.1257			1.54283
$934$	17.9754	+	31.1343i	0.588172	+	1.01874i
$935$	46.7331	−	12.8630i	1.52834	−	0.420667i
$936$	2.23792			0.0731486
$937$	−23.1112	+	13.3433i	−0.755011	+	0.435906i	−0.827502	−	0.561463i	$-0.810239\pi$
$937$	−23.1112	+	13.3433i	−0.755011	+	0.435906i	0.0724904	+	0.997369i	$0.476905\pi$
$938$	0.660220	−	1.14354i	0.0215570	−	0.0373377i
$939$		−	49.3969i		−	1.61201i
$940$	−17.5879	+	17.8286i	−0.573655	+	0.581504i
$941$	12.8031	+	22.1756i	0.417369	+	0.722905i	0.995674	−	0.0929161i	$-0.0296188\pi$
$941$	12.8031	+	22.1756i	0.417369	+	0.722905i	−0.578305	+	0.815821i	$0.696286\pi$
$942$	−3.28194	−	5.68449i	−0.106931	−	0.185211i
$943$	41.3589	−	71.6357i	1.34683	−	2.33278i
$944$	−3.89814	−	2.25059i	−0.126874	−	0.0732506i
$945$	−2.88029	−	2.84142i	−0.0936960	−	0.0924313i
$946$	−4.15818	−	7.20219i	−0.135194	−	0.234163i
$947$	12.5951	+	21.8154i	0.409286	+	0.708904i	0.994810	−	0.101751i	$-0.0324445\pi$
$947$	12.5951	+	21.8154i	0.409286	+	0.708904i	−0.585524	+	0.810655i	$0.699111\pi$
$948$	11.8615			0.385244
$949$	32.2119	+	18.5975i	1.04564	+	0.603701i
$950$	7.73362	−	13.8256i	0.250912	−	0.448560i
$951$	20.3458			0.659757
$952$		−	2.20608i		−	0.0714993i
$953$	28.2124	−	16.2884i	0.913889	−	0.527634i	0.0322087	−	0.999481i	$-0.489746\pi$
$953$	28.2124	−	16.2884i	0.913889	−	0.527634i	0.881680	+	0.471847i	$0.156413\pi$
$954$			0.0429719i			0.00139127i
$955$	−17.1652	−	4.47462i	−0.555452	−	0.144795i
$956$			8.12476i			0.262774i
$957$	−24.1776	+	41.8769i	−0.781552	+	1.35369i
$958$	10.4535	+	6.03534i	0.337738	+	0.194993i
$959$	0.530430	−	0.918731i	0.0171285	−	0.0296674i
$960$	3.03712	−	3.07868i	0.0980228	−	0.0993639i
$961$	6.15894			0.198676
$962$	−18.3837	+	0.00669752i	−0.592714	+	0.000215937i
$963$			9.04447i			0.291454i
$964$	19.7551	−	11.4056i	0.636269	−	0.367350i
$965$	13.7179	−	52.6234i	0.441593	−	1.69401i
$966$	−3.74192	+	6.48119i	−0.120394	+	0.208529i
$967$	−0.876800	+	1.51866i	−0.0281960	+	0.0488369i	−0.879779	−	0.475383i	$-0.842310\pi$
$967$	−0.876800	+	1.51866i	−0.0281960	+	0.0488369i	0.851583	+	0.524220i	$0.175643\pi$
$968$	5.55256			0.178466
$969$	16.3240	−	28.2740i	0.524402	−	0.908291i
$970$	−10.2096	+	2.81014i	−0.327810	+	0.0902282i
$971$	−26.8688	−	46.5382i	−0.862262	−	1.49348i	−0.869740	−	0.493510i	$-0.835714\pi$
$971$	−26.8688	−	46.5382i	−0.862262	−	1.49348i	0.00747776	−	0.999972i	$-0.497620\pi$
$972$		−	7.53221i		−	0.241596i
$973$			0.0342271i			0.00109727i
$974$	4.67110	+	8.09059i	0.149672	+	0.259239i
$975$	29.2230	−	0.397140i	0.935886	−	0.0127187i
$976$		−	11.1098i		−	0.355616i
$977$	20.4987	+	35.5047i	0.655810	+	1.13590i	0.981690	+	0.190485i	$0.0610062\pi$
$977$	20.4987	+	35.5047i	0.655810	+	1.13590i	−0.325880	+	0.945411i	$0.605660\pi$
$978$	11.9626	−	6.90662i	0.382522	−	0.220849i
$979$	−38.9726	+	22.5008i	−1.24557	+	0.719130i
$980$	−3.85164	+	14.7754i	−0.123036	+	0.471981i
$981$	−4.25860	−	2.45870i	−0.135967	−	0.0785004i
$982$	−11.4961	−	19.9119i	−0.366856	−	0.635413i
$983$	−14.5092	+	8.37689i	−0.462772	+	0.267181i	−0.713209	−	0.700951i	$-0.752759\pi$
$983$	−14.5092	+	8.37689i	−0.462772	+	0.267181i	0.250437	+	0.968133i	$0.419426\pi$
$984$	−14.8248	+	8.55909i	−0.472597	+	0.272854i
$985$	−1.63145	−	5.92725i	−0.0519822	−	0.188858i
$986$	28.3559	+	16.3713i	0.903035	+	0.521368i
$987$	−7.76723	+	4.48441i	−0.247234	+	0.142740i
$988$		−	9.57546i		−	0.304636i
$989$	19.1032			0.607446
$990$	4.79563	+	4.73090i	0.152415	+	0.150358i
$991$			53.8088i			1.70929i	0.519211	+	0.854646i	$0.326226\pi$
$991$			53.8088i			1.70929i	−0.519211	+	0.854646i	$0.673774\pi$
$992$	−4.31634	−	2.49204i	−0.137044	−	0.0791224i
$993$	9.04942			0.287175
$994$	1.29127	+	0.745513i	0.0409565	+	0.0236462i
$995$	−46.2384	−	12.0534i	−1.46585	−	0.382119i
$996$	1.63862	−	2.83817i	0.0519215	−	0.0899308i
$997$	−1.42860	−	2.47441i	−0.0452443	−	0.0783655i	0.842516	−	0.538671i	$-0.181073\pi$
$997$	−1.42860	−	2.47441i	−0.0452443	−	0.0783655i	−0.887761	+	0.460305i	$0.847740\pi$
$998$		−	27.0447i		−	0.856084i
$999$	0.00968417	+	26.5816i	0.000306394	+	0.841004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.m.c.159.3	✓	16
5.4	even	2		370.2.m.d.159.6	yes	16
37.27	even	6		370.2.m.d.249.6	yes	16
185.64	even	6	inner	370.2.m.c.249.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.m.c.159.3	✓	16	1.1	even	1	trivial
370.2.m.c.249.3	yes	16	185.64	even	6	inner
370.2.m.d.159.6	yes	16	5.4	even	2
370.2.m.d.249.6	yes	16	37.27	even	6

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.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.67492 - 0.967016i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.564048 + 2.16376i) q^{5} +1.93403i q^{6} +(0.358580 + 0.207027i) q^{7} +1.00000 q^{8} +(0.370239 + 0.641273i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.67492 - 0.967016i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.564048 + 2.16376i) q^{5} +1.93403i q^{6} +(0.358580 + 0.207027i) q^{7} +1.00000 q^{8} +(0.370239 + 0.641273i) q^{9} +(2.15589 - 0.593399i) q^{10} +4.06848 q^{11} +(1.67492 - 0.967016i) q^{12} +(1.51113 - 2.61735i) q^{13} -0.414053i q^{14} +(3.03712 - 3.07868i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.66400 - 4.61419i) q^{17} +(0.370239 - 0.641273i) q^{18} +(-2.74384 - 1.58416i) q^{19} +(-1.59185 - 1.57036i) q^{20} +(-0.400396 - 0.693506i) q^{21} +(-2.03424 - 3.52341i) q^{22} +9.34555 q^{23} +(-1.67492 - 0.967016i) q^{24} +(-4.36370 - 2.44093i) q^{25} -3.02226 q^{26} +4.36999i q^{27} +(-0.358580 + 0.207027i) q^{28} -6.14537i q^{29} +(-4.18478 - 1.09089i) q^{30} +4.98408i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-6.81439 - 3.93429i) q^{33} +(-2.66400 + 4.61419i) q^{34} +(-0.650212 + 0.659108i) q^{35} -0.740478 q^{36} +(6.08276 - 0.00221606i) q^{37} +3.16831i q^{38} +(-5.06204 + 2.92257i) q^{39} +(-0.564048 + 2.16376i) q^{40} +(4.42552 - 7.66522i) q^{41} +(-0.400396 + 0.693506i) q^{42} +2.04410 q^{43} +(-2.03424 + 3.52341i) q^{44} +(-1.59639 + 0.439399i) q^{45} +(-4.67277 - 8.09348i) q^{46} -11.1999i q^{47} +1.93403i q^{48} +(-3.41428 - 5.91371i) q^{49} +(0.0679436 + 4.99954i) q^{50} +10.3045i q^{51} +(1.51113 + 2.61735i) q^{52} +(-0.0502578 + 0.0290163i) q^{53} +(3.78452 - 2.18499i) q^{54} +(-2.29482 + 8.80321i) q^{55} +(0.358580 + 0.207027i) q^{56} +(3.06381 + 5.30667i) q^{57} +(-5.32204 + 3.07268i) q^{58} +(3.89814 - 2.25059i) q^{59} +(1.14765 + 4.16957i) q^{60} +(9.62137 + 5.55490i) q^{61} +(4.31634 - 2.49204i) q^{62} +0.306597i q^{63} +1.00000 q^{64} +(4.81097 + 4.74603i) q^{65} +7.86858i q^{66} +(2.76181 + 1.59453i) q^{67} +5.32800 q^{68} +(-15.6530 - 9.03729i) q^{69} +(0.895911 + 0.233546i) q^{70} +(-1.80052 + 3.11860i) q^{71} +(0.370239 + 0.641273i) q^{72} +12.3070i q^{73} +(-3.04330 - 5.26672i) q^{74} +(4.94843 + 8.30813i) q^{75} +(2.74384 - 1.58416i) q^{76} +(1.45888 + 0.842284i) q^{77} +(5.06204 + 2.92257i) q^{78} +(5.31138 + 3.06653i) q^{79} +(2.15589 - 0.593399i) q^{80} +(5.33656 - 9.24320i) q^{81} -8.85103 q^{82} +(1.46749 - 0.847254i) q^{83} +0.800792 q^{84} +(11.4866 - 3.16163i) q^{85} +(-1.02205 - 1.77024i) q^{86} +(-5.94267 + 10.2930i) q^{87} +4.06848 q^{88} +(-9.57915 + 5.53052i) q^{89} +(1.17873 + 1.16282i) q^{90} +(1.08372 - 0.625688i) q^{91} +(-4.67277 + 8.09348i) q^{92} +(4.81968 - 8.34794i) q^{93} +(-9.69944 + 5.59997i) q^{94} +(4.97539 - 5.04346i) q^{95} +(1.67492 - 0.967016i) q^{96} -4.73567 q^{97} +(-3.41428 + 5.91371i) q^{98} +(1.50631 + 2.60901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9}+O(q^{10}) \) 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9	\( 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} - 3 q^{12} + 6 q^{13} - 9 q^{15} - 8 q^{16} + 13 q^{18} - 3 q^{19} - 6 q^{21} + 3 q^{22} + 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{28} - 9 q^{30} - 8 q^{32} - 6 q^{33} + 12 q^{35} - 26 q^{36} - 16 q^{37} + 15 q^{39} + 6 q^{40} + 7 q^{41} - 6 q^{42} + 22 q^{43} + 3 q^{44} - 4 q^{45} - 11 q^{46} + 4 q^{49} - 6 q^{50} + 6 q^{52} - 3 q^{53} + 9 q^{54} - 25 q^{55} + 12 q^{56} - 18 q^{57} - 36 q^{58} + 15 q^{59} + 18 q^{60} + 12 q^{61} + 33 q^{62} + 16 q^{64} - 26 q^{65} - 24 q^{67} + 42 q^{69} - 18 q^{70} - 4 q^{71} + 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} + 24 q^{77} - 15 q^{78} - 6 q^{80} + 10 q^{81} - 14 q^{82} - 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} - 50 q^{87} - 6 q^{88} + 9 q^{89} + 5 q^{90} - 24 q^{91} - 11 q^{92} + 25 q^{93} - 27 q^{94} + 49 q^{95} - 3 q^{96} - 68 q^{97} + 4 q^{98} + 37 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 - 3 * q^12 + 6 * q^13 - 9 * q^15 - 8 * q^16 + 13 * q^18 - 3 * q^19 - 6 * q^21 + 3 * q^22 + 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 12 * q^28 - 9 * q^30 - 8 * q^32 - 6 * q^33 + 12 * q^35 - 26 * q^36 - 16 * q^37 + 15 * q^39 + 6 * q^40 + 7 * q^41 - 6 * q^42 + 22 * q^43 + 3 * q^44 - 4 * q^45 - 11 * q^46 + 4 * q^49 - 6 * q^50 + 6 * q^52 - 3 * q^53 + 9 * q^54 - 25 * q^55 + 12 * q^56 - 18 * q^57 - 36 * q^58 + 15 * q^59 + 18 * q^60 + 12 * q^61 + 33 * q^62 + 16 * q^64 - 26 * q^65 - 24 * q^67 + 42 * q^69 - 18 * q^70 - 4 * q^71 + 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 + 24 * q^77 - 15 * q^78 - 6 * q^80 + 10 * q^81 - 14 * q^82 - 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 - 50 * q^87 - 6 * q^88 + 9 * q^89 + 5 * q^90 - 24 * q^91 - 11 * q^92 + 25 * q^93 - 27 * q^94 + 49 * q^95 - 3 * q^96 - 68 * q^97 + 4 * q^98 + 37 * q^99

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