LMFDB - Embedded newform 370.2.m.c.249.3

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			249.3
Root			$1.93403i$ of defining polynomial
Character	$\chi$	$=$	370.249
Dual form			370.2.m.c.159.3

$q$-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 $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

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

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	−0.898325	−	0.439331i	$-0.855215\pi$
$3$	−1.67492	+	0.967016i	−0.967016	+	0.558307i	−0.0686906	+	0.997638i	$0.521882\pi$
$4$	−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	−0.430702	−	0.902494i	$-0.641734\pi$
$7$	0.358580	−	0.207027i	0.135531	−	0.0782487i	0.566232	+	0.824246i	$0.308401\pi$
$8$	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	0.995850	−	0.0910056i	$-0.0290081\pi$
$13$	1.51113	+	2.61735i	0.419112	+	0.725923i	−0.576738	+	0.816929i	$0.695675\pi$
$14$			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	0.337927	+	0.941172i	$0.390274\pi$
$17$	−2.66400	+	4.61419i	−0.646115	+	1.11910i	−0.984043	+	0.177933i	$0.943059\pi$
$18$	0.370239	+	0.641273i	0.0872662	+	0.151150i
$19$	−2.74384	+	1.58416i	−0.629480	+	0.363430i	−0.780551	−	0.625093i	$-0.785061\pi$
$19$	−2.74384	+	1.58416i	−0.629480	+	0.363430i	0.151071	+	0.988523i	$0.451728\pi$
$20$	−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	$0.193283\pi$
$29$			6.14537i			1.14117i	−0.821240	+	0.570583i	$0.806717\pi$
$30$	−4.18478	+	1.09089i	−0.764032	+	0.199168i
$31$		−	4.98408i		−	0.895167i	−0.894242	−	0.447584i	$-0.852285\pi$
$31$		−	4.98408i		−	0.895167i	0.894242	−	0.447584i	$-0.147715\pi$
$32$	−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	0.971462	+	0.237197i	$0.0762287\pi$
$41$	4.42552	+	7.66522i	0.691150	+	1.19711i	−0.280312	+	0.959909i	$0.590438\pi$
$42$	−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	$0.304276\pi$
$47$			11.1999i			1.63368i	−0.576864	+	0.816840i	$0.695724\pi$
$48$		−	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	0.496544	−	0.868011i	$-0.334602\pi$
$53$	−0.0502578	−	0.0290163i	−0.00690344	−	0.00398570i	−0.503448	+	0.864026i	$0.667935\pi$
$54$	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	0.731803	−	0.681516i	$-0.238679\pi$
$59$	3.89814	+	2.25059i	0.507495	+	0.293002i	−0.224308	+	0.974518i	$0.572012\pi$
$60$	1.14765	−	4.16957i	0.148161	−	0.538289i
$61$	9.62137	−	5.55490i	1.23189	−	0.711232i	0.264466	−	0.964395i	$-0.414804\pi$
$61$	9.62137	−	5.55490i	1.23189	−	0.711232i	0.967424	+	0.253163i	$0.0814709\pi$
$62$	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	−0.321717	−	0.946836i	$-0.604260\pi$
$67$	2.76181	−	1.59453i	0.337409	−	0.194803i	0.659125	+	0.752033i	$0.270927\pi$
$68$	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	0.739181	−	0.673506i	$-0.235213\pi$
$71$	−1.80052	−	3.11860i	−0.213683	−	0.370110i	−0.952864	+	0.303397i	$0.901879\pi$
$72$	0.370239	−	0.641273i	0.0436331	−	0.0755748i
$73$		−	12.3070i		−	1.44043i	−0.693751	−	0.720215i	$-0.744043\pi$
$73$		−	12.3070i		−	1.44043i	0.693751	−	0.720215i	$-0.255957\pi$
$74$	−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	−0.170511	−	0.985356i	$-0.554542\pi$
$79$	5.31138	−	3.06653i	0.597577	−	0.345011i	0.768088	+	0.640344i	$0.221208\pi$
$80$	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	0.578372	−	0.815773i	$-0.303688\pi$
$83$	1.46749	+	0.847254i	0.161078	+	0.0929982i	−0.417294	+	0.908771i	$0.637022\pi$
$84$	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	−0.102623	−	0.994720i	$-0.532723\pi$
$89$	−9.57915	−	5.53052i	−1.01539	−	0.586234i	−0.912765	+	0.408486i	$0.866057\pi$
$90$	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	0.107750	−	0.994178i	$-0.465635\pi$
$107$	10.5779	−	6.10718i	1.02261	−	0.590403i	0.914858	+	0.403775i	$0.132302\pi$
$108$	−3.78452	+	2.18499i	−0.364166	+	0.210251i
$109$	−5.75115	−	3.32043i	−0.550860	−	0.318039i	0.198609	−	0.980079i	$-0.436358\pi$
$109$	−5.75115	−	3.32043i	−0.550860	−	0.318039i	−0.749469	+	0.662040i	$0.769691\pi$
$110$	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	−0.946765	−	0.321926i	$-0.895670\pi$
$113$	−2.06848	+	3.58272i	−0.194587	+	0.337034i	0.752178	+	0.658960i	$0.229003\pi$
$114$	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	0.386380	−	0.922340i	$-0.373725\pi$
$127$	−2.47026	−	1.42621i	−0.219200	−	0.126555i	−0.605580	+	0.795784i	$0.707059\pi$
$128$	−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	0.699997	−	0.714145i	$-0.253185\pi$
$131$	4.93906	+	2.85157i	0.431528	+	0.249143i	−0.268469	+	0.963288i	$0.586518\pi$
$132$	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	$0.0349086\pi$
$137$			2.56213i			0.218898i	−0.993992	+	0.109449i	$0.965091\pi$
$138$		−	18.0746i		−	1.53861i
$139$	0.0413318	−	0.0715888i	0.00350572	−	0.00607209i	−0.864267	−	0.503033i	$-0.832217\pi$
$139$	0.0413318	−	0.0715888i	0.00350572	−	0.00607209i	0.867773	+	0.496961i	$0.165551\pi$
$140$	−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	0.891253	−	0.453507i	$-0.149827\pi$
$151$	0.649772	+	1.12544i	0.0528777	+	0.0915869i	−0.838375	+	0.545094i	$0.816494\pi$
$152$	−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	0.378107	−	0.925762i	$-0.376575\pi$
$157$	−2.93919	−	1.69694i	−0.234573	−	0.135431i	−0.612680	+	0.790331i	$0.709909\pi$
$158$			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	−0.971313	−	0.237806i	$-0.923572\pi$
$163$	−3.57110	+	6.18532i	−0.279710	+	0.484472i	0.691603	+	0.722278i	$0.256905\pi$
$164$	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	0.999830	+	0.0184166i	$0.00586253\pi$
$167$	6.66644	+	11.5466i	0.515864	+	0.893503i	−0.483966	+	0.875087i	$0.660804\pi$
$168$	−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	0.939570	−	0.342358i	$-0.111225\pi$
$173$	14.6374	+	8.45093i	1.11286	+	0.642512i	0.173294	+	0.984870i	$0.444559\pi$
$174$	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	$-0.785296\pi$
$179$		−	16.7109i		−	1.24903i	0.781011	−	0.624517i	$-0.214704\pi$
$180$	0.417666	+	1.60222i	0.0311310	+	0.119422i
$181$	6.23719	+	10.8031i	0.463606	+	0.802990i	0.999137	−	0.0415256i	$-0.0132218\pi$
$181$	6.23719	+	10.8031i	0.463606	+	0.802990i	−0.535531	+	0.844516i	$0.679888\pi$
$182$	−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	$-0.907340\pi$
$191$		−	7.93304i		−	0.574014i	0.957928	−	0.287007i	$-0.0926604\pi$
$192$	−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	0.412777	−	0.910832i	$-0.364559\pi$
$197$	−2.38098	−	1.37466i	−0.169638	−	0.0979406i	−0.582415	+	0.812891i	$0.697892\pi$
$198$	1.50631	+	2.60901i	0.107049	+	0.185414i
$199$		−	21.3695i		−	1.51484i	−0.652927	−	0.757421i	$-0.726459\pi$
$199$		−	21.3695i		−	1.51484i	0.652927	−	0.757421i	$-0.273541\pi$
$200$	−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	$0.252642\pi$
$223$			21.2933i			1.42590i	−0.701213	+	0.712952i	$0.747358\pi$
$224$	−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	0.644443	−	0.764652i	$-0.277089\pi$
$227$	−5.12241	−	8.87228i	−0.339987	−	0.588874i	−0.984430	+	0.175778i	$0.943756\pi$
$228$	−6.12762			−0.405811
$229$	3.42967	+	5.94037i	0.226639	+	0.392551i	0.956810	−	0.290714i	$-0.0938928\pi$
$229$	3.42967	+	5.94037i	0.226639	+	0.392551i	−0.730171	+	0.683265i	$0.760559\pi$
$230$	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	$0.121986\pi$
$233$			11.4152i			0.747838i	−0.927461	+	0.373919i	$0.878014\pi$
$234$	−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	0.709997	−	0.704204i	$-0.248696\pi$
$239$	7.03625	+	4.06238i	0.455137	+	0.262774i	−0.254860	+	0.966978i	$0.582029\pi$
$240$	−4.18478	+	1.09089i	−0.270126	+	0.0704165i
$241$	−19.7551	+	11.4056i	−1.27254	+	0.734701i	−0.975465	−	0.220154i	$-0.929344\pi$
$241$	−19.7551	+	11.4056i	−1.27254	+	0.734701i	−0.297074	+	0.954855i	$0.596011\pi$
$242$	−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	$-0.679256\pi$
$251$		−	26.7930i		−	1.69116i	0.533851	−	0.845579i	$-0.320744\pi$
$252$	−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	0.452226	+	0.891903i	$0.350630\pi$
$257$	−8.75782	+	15.1690i	−0.546298	+	0.946215i	−0.998524	+	0.0543120i	$0.982703\pi$
$258$		−	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	−0.281358	−	0.959603i	$-0.590785\pi$
$263$	6.63293	−	3.82952i	0.409004	−	0.236138i	0.690362	+	0.723465i	$0.257451\pi$
$264$	−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	0.372263	+	0.928127i	$0.378582\pi$
$271$	−10.1678	+	17.6112i	−0.617650	+	1.06980i	−0.989913	+	0.141674i	$0.954751\pi$
$272$	−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	−0.934346	−	0.356366i	$-0.884016\pi$
$277$	−12.9118	−	22.3639i	−0.775795	−	1.34372i	0.158551	−	0.987351i	$-0.449318\pi$
$278$	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	0.923484	−	0.383638i	$-0.125329\pi$
$281$	17.6512	+	10.1910i	1.05299	+	0.607941i	0.129502	+	0.991579i	$0.458662\pi$
$282$	21.6611			1.28990
$283$	−0.491609	−	0.851492i	−0.0292231	−	0.0506159i	0.851044	−	0.525094i	$-0.175970\pi$
$283$	−0.491609	−	0.851492i	−0.0292231	−	0.0506159i	−0.880267	+	0.474478i	$0.842637\pi$
$284$	−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	−0.360180	−	0.932883i	$-0.617285\pi$
$293$	4.58109	−	2.64489i	0.267630	−	0.154516i	0.627810	+	0.778366i	$0.283951\pi$
$294$	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	$-0.913707\pi$
$307$		−	9.38404i		−	0.535575i	0.963478	−	0.267788i	$-0.0862925\pi$
$308$	−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	−0.236796	−	0.971559i	$-0.576097\pi$
$311$	−21.1021	−	12.1833i	−1.19659	−	0.690851i	−0.959793	+	0.280708i	$0.909431\pi$
$312$	−5.06204	−	2.92257i	−0.286582	−	0.165458i
$313$	12.7705	−	22.1191i	0.721829	−	1.25024i	−0.238437	−	0.971158i	$-0.576635\pi$
$313$	12.7705	−	22.1191i	0.721829	−	1.25024i	0.960266	−	0.279086i	$-0.0900315\pi$
$314$	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	0.221835	−	0.975084i	$-0.428796\pi$
$317$	−9.11049	−	5.25994i	−0.511696	−	0.295428i	−0.733531	+	0.679657i	$0.762129\pi$
$318$	−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	0.384485	−	0.923131i	$-0.374379\pi$
$331$	−4.05217	−	2.33952i	−0.222728	−	0.128592i	−0.607213	+	0.794539i	$0.707712\pi$
$332$		−	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	−0.610242	−	0.792215i	$-0.708928\pi$
$337$	−4.20909	+	2.43012i	−0.229284	+	0.132377i	0.380958	+	0.924592i	$0.375594\pi$
$338$	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	−0.567921	−	0.823083i	$-0.692252\pi$
$349$	8.01159	−	13.8765i	0.428851	−	0.742791i	0.996771	+	0.0802921i	$0.0255853\pi$
$350$	−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	−0.455054	−	0.890464i	$-0.650380\pi$
$353$	10.2140	−	17.6912i	0.543637	−	0.941608i	0.998691	−	0.0511437i	$-0.0162866\pi$
$354$	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	−0.135820	−	0.990734i	$-0.543367\pi$
$367$	12.5340	−	7.23652i	0.654270	−	0.377743i	0.790090	+	0.612990i	$0.210034\pi$
$368$	−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	−0.893864	−	0.448339i	$-0.852016\pi$
$373$	−18.3963	+	10.6211i	−0.952523	+	0.549939i	−0.0586590	+	0.998278i	$0.518682\pi$
$374$	−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	−0.191105	−	0.981570i	$-0.561207\pi$
$379$	14.6888	−	25.4417i	0.754512	−	1.30685i	0.945617	−	0.325283i	$-0.105460\pi$
$380$	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	−0.998955	−	0.0456966i	$-0.985449\pi$
$383$	−10.5495	−	18.2722i	−0.539052	−	0.933666i	0.459903	−	0.887969i	$-0.347884\pi$
$384$		−	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	−0.334961	−	0.942232i	$-0.608723\pi$
$389$	6.18429	−	3.57050i	0.313556	−	0.181031i	0.648517	+	0.761201i	$0.275390\pi$
$390$	−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	$-0.970774\pi$
$397$		−	3.65365i		−	0.183371i	0.995788	−	0.0916857i	$-0.0292255\pi$
$398$	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	$-0.668628\pi$
$401$		−	34.5602i		−	1.72586i	0.505327	−	0.862928i	$-0.331372\pi$
$402$	−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	0.701014	−	0.713147i	$-0.252731\pi$
$409$	8.77545	+	5.06651i	0.433918	+	0.250523i	−0.267096	+	0.963670i	$0.586064\pi$
$410$	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	−0.729754	−	0.683710i	$-0.760365\pi$
$419$	4.65134	−	8.05636i	0.227233	−	0.393579i	0.956987	+	0.290131i	$0.0936988\pi$
$420$	−0.451685	−	1.73272i	−0.0220400	−	0.0845481i
$421$			22.1257i			1.07834i	0.842197	+	0.539170i	$0.181262\pi$
$421$			22.1257i			1.07834i	−0.842197	+	0.539170i	$0.818738\pi$
$422$	−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	−0.664942	+	0.746895i	$0.731544\pi$
$431$	−34.1354	+	19.7081i	−1.64424	+	0.949304i	−0.979301	+	0.202409i	$0.935123\pi$
$432$	3.78452	+	2.18499i	0.182083	+	0.105126i
$433$			4.61287i			0.221680i	0.993838	+	0.110840i	$0.0353542\pi$
$433$			4.61287i			0.221680i	−0.993838	+	0.110840i	$0.964646\pi$
$434$	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	−0.796016	−	0.605276i	$-0.793063\pi$
$439$	−14.0347	+	8.10294i	−0.669840	+	0.386732i	0.126176	+	0.992008i	$0.459730\pi$
$440$	−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	$0.116743\pi$
$443$			15.0950i			0.717184i	−0.933494	+	0.358592i	$0.883257\pi$
$444$	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	−0.946531	−	0.322612i	$-0.895439\pi$
$449$	−24.1648	+	13.9516i	−1.14041	+	0.658415i	−0.193876	+	0.981026i	$0.562106\pi$
$450$	−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	0.993897	−	0.110315i	$-0.0351861\pi$
$457$	8.58122	+	14.8631i	0.401412	+	0.695267i	−0.592484	+	0.805582i	$0.701853\pi$
$458$	−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	0.994045	+	0.108974i	$0.0347564\pi$
$461$	34.0409	+	19.6535i	1.58544	+	0.915355i	0.591396	+	0.806381i	$0.298577\pi$
$462$	−1.62900	−	2.82152i	−0.0757881	−	0.131269i
$463$	9.86106	+	17.0799i	0.458282	+	0.793768i	0.998870	−	0.0475192i	$-0.0151315\pi$
$463$	9.86106	+	17.0799i	0.458282	+	0.793768i	−0.540588	+	0.841287i	$0.681798\pi$
$464$	−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	0.241796	−	0.970327i	$-0.422263\pi$
$479$	−10.4535	−	6.03534i	−0.477634	−	0.275762i	−0.719430	+	0.694565i	$0.755597\pi$
$480$	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	0.126260	−	0.991997i	$-0.459703\pi$
$499$	23.4214	−	13.5223i	1.04848	−	0.605343i	0.922225	+	0.386654i	$0.126369\pi$
$500$	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	−0.360811	−	0.932639i	$-0.617500\pi$
$503$	14.0685	−	24.3674i	0.627283	−	1.08649i	0.988095	−	0.153848i	$-0.0491665\pi$
$504$		−	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	−0.999973	−	0.00734869i	$-0.997661\pi$
$509$	−11.1366	+	19.2892i	−0.493622	+	0.854979i	0.506351	+	0.862328i	$0.330994\pi$
$510$	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	0.931955	−	0.362573i	$-0.118102\pi$
$521$	3.46902	+	6.00852i	0.151981	+	0.263238i	−0.779975	+	0.625811i	$0.784768\pi$
$522$	−3.94086	+	2.27526i	−0.172487	+	0.0995852i
$523$	−2.48913	−	4.31130i	−0.108842	−	0.188520i	0.806459	−	0.591290i	$-0.201381\pi$
$523$	−2.48913	−	4.31130i	−0.108842	−	0.188520i	−0.915301	+	0.402769i	$0.868048\pi$
$524$		−	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	$-0.812661\pi$
$541$		−	25.8249i		−	1.11030i	0.831751	−	0.555149i	$-0.187339\pi$
$542$	−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	−0.851468	−	0.524407i	$-0.824287\pi$
$557$	0.670638	−	1.16158i	0.0284159	−	0.0492177i	0.879884	+	0.475189i	$0.157620\pi$
$558$	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	$-0.606154\pi$
$569$		−	45.0790i		−	1.88981i	0.327346	−	0.944904i	$-0.393846\pi$
$570$	9.75422	−	9.62256i	0.408559	−	0.403045i
$571$	15.3395	−	26.5687i	0.641936	−	1.11187i	−0.343064	−	0.939312i	$-0.611465\pi$
$571$	15.3395	−	26.5687i	0.641936	−	1.11187i	0.985000	−	0.172554i	$-0.0552019\pi$
$572$	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	−0.714801	−	0.699328i	$-0.753483\pi$
$577$	5.96282	−	10.3279i	0.248235	−	0.429956i	0.963036	+	0.269372i	$0.0868160\pi$
$578$	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	0.996193	−	0.0871807i	$-0.0277857\pi$
$587$	10.2387	+	17.7339i	0.422596	+	0.731957i	−0.573597	+	0.819138i	$0.694452\pi$
$588$	−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	$-0.978691\pi$
$593$		−	3.25794i		−	0.133788i	0.997760	−	0.0668938i	$-0.0213089\pi$
$594$	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	0.985775	−	0.168071i	$-0.0537538\pi$
$599$	8.50081	+	14.7238i	0.347334	+	0.601600i	−0.638441	+	0.769671i	$0.720420\pi$
$600$	4.94843	−	8.30813i	0.202019	−	0.339178i
$601$	13.2637	−	22.9734i	0.541037	−	0.937104i	−0.457808	−	0.889051i	$-0.651365\pi$
$601$	13.2637	−	22.9734i	0.541037	−	0.937104i	0.998845	−	0.0480525i	$-0.0153015\pi$
$602$			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	−0.566269	−	0.824221i	$-0.691614\pi$
$607$	10.6104	−	18.3777i	0.430662	−	0.745928i	0.996930	+	0.0782926i	$0.0249469\pi$
$608$	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	−0.257902	−	0.966171i	$-0.583031\pi$
$613$	−30.2945	−	17.4905i	−1.22358	−	0.706435i	−0.965680	+	0.259736i	$0.916364\pi$
$614$	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	−0.00319933	−	0.999995i	$-0.501018\pi$
$617$	−21.6307	−	12.4885i	−0.870820	−	0.502768i	−0.867621	+	0.497227i	$0.834352\pi$
$618$			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	0.370553	−	0.928811i	$-0.379168\pi$
$631$	−6.24336	−	3.60461i	−0.248544	−	0.143497i	−0.619097	+	0.785314i	$0.712501\pi$
$632$	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	−0.999870	−	0.0160962i	$-0.994876\pi$
$641$	−12.3044	+	21.3119i	−0.485996	+	0.841769i	0.513875	+	0.857865i	$0.328210\pi$
$642$	−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	0.666584	−	0.745430i	$-0.267756\pi$
$647$	−7.94294	−	13.7576i	−0.312269	−	0.540866i	−0.978853	+	0.204564i	$0.934422\pi$
$648$	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	0.831008	−	0.556260i	$-0.187764\pi$
$653$	−1.69247	−	2.93145i	−0.0662316	−	0.114717i	−0.897240	+	0.441544i	$0.854431\pi$
$654$	−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	0.952381	−	0.304910i	$-0.0986263\pi$
$659$	5.44562	+	9.43209i	0.212131	+	0.367422i	−0.740250	+	0.672332i	$0.765293\pi$
$660$	4.66920	−	16.9638i	0.181749	−	0.660315i
$661$	5.03518	−	2.90706i	0.195846	−	0.113072i	−0.398870	−	0.917007i	$-0.630598\pi$
$661$	5.03518	−	2.90706i	0.195846	−	0.113072i	0.594716	+	0.803936i	$0.297264\pi$
$662$	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	0.361625	−	0.932324i	$-0.382222\pi$
$673$	35.0182	−	20.2178i	1.34985	−	0.779338i	0.988228	+	0.152986i	$0.0488888\pi$
$674$		−	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	$-0.801779\pi$
$677$		−	30.3516i		−	1.16651i	0.812290	−	0.583254i	$-0.198221\pi$
$678$	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	−0.864580	−	0.502495i	$-0.832416\pi$
$683$	0.0753519	−	0.130513i	0.00288326	−	0.00499395i	0.867463	+	0.497501i	$0.165749\pi$
$684$	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	0.169874	+	0.985466i	$0.445664\pi$
$691$	−20.2015	+	34.9900i	−0.768501	+	1.33108i	−0.938375	+	0.345617i	$0.887669\pi$
$692$		−	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	−0.999984	−	0.00560815i	$-0.998215\pi$
$701$	−39.8426	−	23.0031i	−1.50483	−	0.868816i	−0.504849	−	0.863208i	$-0.668452\pi$
$702$			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	$0.342969\pi$
$709$			46.9042i			1.76152i	−0.473559	+	0.880762i	$0.657031\pi$
$710$	−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	0.379666	+	0.925123i	$0.376039\pi$
$719$	−16.3928	+	28.3931i	−0.611347	+	1.05888i	−0.991014	+	0.133761i	$0.957295\pi$
$720$	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	0.509772	−	0.860309i	$-0.329730\pi$
$727$	−13.2163	−	22.8912i	−0.490164	−	0.848989i	−0.999936	+	0.0113208i	$0.996396\pi$
$728$	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	−0.0236414	−	0.999721i	$-0.507526\pi$
$733$	22.4801	−	12.9789i	0.830321	−	0.479386i	0.853963	+	0.520334i	$0.174193\pi$
$734$			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	−0.751383	−	0.659866i	$-0.770613\pi$
$743$	−15.1449	+	8.74394i	−0.555614	+	0.320784i	0.195769	+	0.980650i	$0.437280\pi$
$744$	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	−0.0102559	−	0.999947i	$-0.503265\pi$
$757$	23.6852	−	41.0239i	0.860852	−	1.49104i	0.871108	−	0.491092i	$-0.163402\pi$
$758$	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	−0.610548	−	0.791979i	$-0.709051\pi$
$761$	10.4993	−	18.1853i	0.380600	−	0.659218i	0.991148	+	0.132761i	$0.0423842\pi$
$762$	−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	$-0.945436\pi$
$769$		−	9.46062i		−	0.341159i	0.985344	−	0.170579i	$-0.0545639\pi$
$770$	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	−0.859124	−	0.511767i	$-0.828991\pi$
$773$	−23.5068	+	13.5717i	−0.845482	+	0.488140i	0.0136416	+	0.999907i	$0.495658\pi$
$774$	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	$-0.804243\pi$
$787$		−	32.3709i		−	1.15390i	0.816780	−	0.576949i	$-0.195757\pi$
$788$			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	−0.979026	−	0.203738i	$-0.934691\pi$
$797$	−8.83836	+	15.3085i	−0.313071	+	0.542254i	0.665955	+	0.745992i	$0.268024\pi$
$798$	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	−0.553804	−	0.832647i	$-0.686824\pi$
$809$	−3.11773	+	1.80002i	−0.109613	+	0.0632854i	0.444191	+	0.895932i	$0.353491\pi$
$810$	6.02016	+	23.0941i	0.211527	+	0.811443i
$811$	3.45644	+	5.98673i	0.121372	+	0.210222i	0.920309	−	0.391192i	$-0.127937\pi$
$811$	3.45644	+	5.98673i	0.121372	+	0.210222i	−0.798937	+	0.601415i	$0.794604\pi$
$812$	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	0.991197	−	0.132397i	$-0.0422675\pi$
$821$	10.9151	+	18.9055i	0.380939	+	0.659806i	−0.610258	+	0.792203i	$0.708934\pi$
$822$	4.95525			0.172834
$823$	12.7491	+	7.36072i	0.444407	+	0.256579i	0.705465	−	0.708744i	$-0.250738\pi$
$823$	12.7491	+	7.36072i	0.444407	+	0.256579i	−0.261058	+	0.965323i	$0.584071\pi$
$824$	−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	0.978018	−	0.208520i	$-0.0668645\pi$
$827$	8.86959	+	15.3626i	0.308426	+	0.534209i	−0.669592	+	0.742729i	$0.733531\pi$
$828$	−6.92017			−0.240493
$829$	−23.2324	−	13.4132i	−0.806894	−	0.465860i	0.0389824	−	0.999240i	$-0.487588\pi$
$829$	−23.2324	−	13.4132i	−0.806894	−	0.465860i	−0.845876	+	0.533380i	$0.820922\pi$
$830$	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	−0.981224	−	0.192871i	$-0.938220\pi$
$839$	−9.37267	+	16.2339i	−0.323580	+	0.560458i	0.657644	+	0.753329i	$0.271553\pi$
$840$	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	0.0725818	−	0.997362i	$-0.476876\pi$
$853$	26.2865	−	45.5295i	0.900032	−	1.55890i	0.827450	−	0.561539i	$-0.189791\pi$
$854$	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	$-0.900067\pi$
$859$		−	18.1021i		−	0.617636i	0.951121	−	0.308818i	$-0.0999334\pi$
$860$	−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	0.998999	−	0.0447311i	$-0.0142431\pi$
$863$	42.8832	+	24.7586i	1.45976	+	0.842793i	0.460761	+	0.887524i	$0.347576\pi$
$864$	−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	$0.124628\pi$
$877$			22.6018i			0.763209i	−0.924326	+	0.381604i	$0.875372\pi$
$878$		−	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	−0.977637	−	0.210300i	$-0.932556\pi$
$881$	−19.9147	−	34.4933i	−0.670943	−	1.16211i	0.306694	−	0.951808i	$-0.400777\pi$
$882$	−5.05640			−0.170258
$883$	5.43593	+	9.41530i	0.182934	+	0.316850i	0.942878	−	0.333138i	$-0.108107\pi$
$883$	5.43593	+	9.41530i	0.182934	+	0.316850i	−0.759945	+	0.649988i	$0.774774\pi$
$884$	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	$-0.876443\pi$
$887$		−	22.5448i		−	0.756981i	0.925605	−	0.378490i	$-0.123557\pi$
$888$	−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	0.784902	−	0.619619i	$-0.212713\pi$
$907$	−4.34143	−	7.51958i	−0.144155	−	0.249684i	−0.929057	+	0.369936i	$0.879380\pi$
$908$	−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	$0.0514954\pi$
$911$			9.72325i			0.322146i	−0.986943	+	0.161073i	$0.948505\pi$
$912$	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	$-0.991894\pi$
$919$		−	1.54383i		−	0.0509264i	0.999676	−	0.0254632i	$-0.00810607\pi$
$920$	−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	−0.848230	−	0.529628i	$-0.822331\pi$
$929$	−26.9069	−	46.6041i	−0.882786	−	1.52903i	−0.0345564	−	0.999403i	$-0.511002\pi$
$930$	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	0.0724904	−	0.997369i	$-0.476905\pi$
$937$	−23.1112	−	13.3433i	−0.755011	−	0.435906i	−0.827502	+	0.561463i	$0.810239\pi$
$938$	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	−0.578305	−	0.815821i	$-0.696286\pi$
$941$	12.8031	−	22.1756i	0.417369	−	0.722905i	0.995674	+	0.0929161i	$0.0296188\pi$
$942$	−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	−0.585524	−	0.810655i	$-0.699111\pi$
$947$	12.5951	−	21.8154i	0.409286	−	0.708904i	0.994810	+	0.101751i	$0.0324445\pi$
$948$	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	0.881680	−	0.471847i	$-0.156413\pi$
$953$	28.2124	+	16.2884i	0.913889	+	0.527634i	0.0322087	+	0.999481i	$0.489746\pi$
$954$		−	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	0.851583	−	0.524220i	$-0.175643\pi$
$967$	−0.876800	−	1.51866i	−0.0281960	−	0.0488369i	−0.879779	+	0.475383i	$0.842310\pi$
$968$	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	0.00747776	+	0.999972i	$0.497620\pi$
$971$	−26.8688	+	46.5382i	−0.862262	+	1.49348i	−0.869740	+	0.493510i	$0.835714\pi$
$972$			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	−0.325880	−	0.945411i	$-0.605660\pi$
$977$	20.4987	−	35.5047i	0.655810	−	1.13590i	0.981690	−	0.190485i	$-0.0610062\pi$
$978$	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	0.250437	−	0.968133i	$-0.419426\pi$
$983$	−14.5092	−	8.37689i	−0.462772	−	0.267181i	−0.713209	+	0.700951i	$0.752759\pi$
$984$	−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	$-0.673774\pi$
$991$		−	53.8088i		−	1.70929i	0.519211	−	0.854646i	$-0.326226\pi$
$992$	−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	−0.887761	−	0.460305i	$-0.847740\pi$
$997$	−1.42860	+	2.47441i	−0.0452443	+	0.0783655i	0.842516	+	0.538671i	$0.181073\pi$
$998$			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.249.3	yes	16
5.4	even	2		370.2.m.d.249.6	yes	16
37.11	even	6		370.2.m.d.159.6	yes	16
185.159	even	6	inner	370.2.m.c.159.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.m.c.159.3	✓	16	185.159	even	6	inner
370.2.m.c.249.3	yes	16	1.1	even	1	trivial
370.2.m.d.159.6	yes	16	37.11	even	6
370.2.m.d.249.6	yes	16	5.4	even	2

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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