LMFDB - Embedded newform 670.2.e.j.171.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(171,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("670.171");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.e (of order $3$, 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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 17 x^{10} - 18 x^{9} + 172 x^{8} - 170 x^{7} + 887 x^{6} - 312 x^{5} + 2516 x^{4} + \cdots + 289 $ x^12 - 2x^11 + 17x^10 - 18x^9 + 172x^8 - 170x^7 + 887x^6 - 312x^5 + 2516x^4 - 1220x^3 + 3001x^2 + 816*x + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			171.4
Root			$-0.146964 + 0.254549i$ of defining polynomial
Character	$\chi$	$=$	670.171
Dual form			670.2.e.j.431.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +0.293928 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.146964 + 0.254549i) q^{6} +(1.88267 - 3.26088i) q^{7} -1.00000 q^{8} -2.91361 q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +0.293928 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.146964 + 0.254549i) q^{6} +(1.88267 - 3.26088i) q^{7} -1.00000 q^{8} -2.91361 q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.45680 - 4.25531i) q^{11} +(-0.146964 + 0.254549i) q^{12} +(-3.03588 - 5.25830i) q^{13} +3.76534 q^{14} -0.293928 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.426587 + 0.738870i) q^{17} +(-1.45680 - 2.52326i) q^{18} +(-2.23643 - 3.87360i) q^{19} +(0.500000 - 0.866025i) q^{20} +(0.553368 - 0.958462i) q^{21} +4.91361 q^{22} +(4.35552 + 7.54398i) q^{23} -0.293928 q^{24} +1.00000 q^{25} +(3.03588 - 5.25830i) q^{26} -1.73817 q^{27} +(1.88267 + 3.26088i) q^{28} +(-1.67267 + 2.89716i) q^{29} +(-0.146964 - 0.254549i) q^{30} +(1.71072 - 2.96305i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.722122 - 1.25075i) q^{33} +(-0.426587 + 0.738870i) q^{34} +(-1.88267 + 3.26088i) q^{35} +(1.45680 - 2.52326i) q^{36} +(0.515328 + 0.892573i) q^{37} +(2.23643 - 3.87360i) q^{38} +(-0.892329 - 1.54556i) q^{39} +1.00000 q^{40} +(-1.04496 + 1.80992i) q^{41} +1.10674 q^{42} +5.81820 q^{43} +(2.45680 + 4.25531i) q^{44} +2.91361 q^{45} +(-4.35552 + 7.54398i) q^{46} +(6.09748 - 10.5611i) q^{47} +(-0.146964 - 0.254549i) q^{48} +(-3.58888 - 6.21612i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.125386 + 0.217174i) q^{51} +6.07176 q^{52} -11.1024 q^{53} +(-0.869086 - 1.50530i) q^{54} +(-2.45680 + 4.25531i) q^{55} +(-1.88267 + 3.26088i) q^{56} +(-0.657347 - 1.13856i) q^{57} -3.34535 q^{58} +8.50495 q^{59} +(0.146964 - 0.254549i) q^{60} +(2.27747 + 3.94469i) q^{61} +3.42143 q^{62} +(-5.48535 + 9.50091i) q^{63} +1.00000 q^{64} +(3.03588 + 5.25830i) q^{65} +1.44424 q^{66} +(-6.39967 + 5.10335i) q^{67} -0.853174 q^{68} +(1.28021 + 2.21738i) q^{69} -3.76534 q^{70} +(5.07590 - 8.79171i) q^{71} +2.91361 q^{72} +(-3.16127 - 5.47548i) q^{73} +(-0.515328 + 0.892573i) q^{74} +0.293928 q^{75} +4.47285 q^{76} +(-9.25069 - 16.0227i) q^{77} +(0.892329 - 1.54556i) q^{78} +(-3.89284 + 6.74260i) q^{79} +(0.500000 + 0.866025i) q^{80} +8.22992 q^{81} -2.08992 q^{82} +(-1.79959 - 3.11699i) q^{83} +(0.553368 + 0.958462i) q^{84} +(-0.426587 - 0.738870i) q^{85} +(2.90910 + 5.03871i) q^{86} +(-0.491645 + 0.851555i) q^{87} +(-2.45680 + 4.25531i) q^{88} +6.38502 q^{89} +(1.45680 + 2.52326i) q^{90} -22.8622 q^{91} -8.71104 q^{92} +(0.502826 - 0.870921i) q^{93} +12.1950 q^{94} +(2.23643 + 3.87360i) q^{95} +(0.146964 - 0.254549i) q^{96} +(6.43873 + 11.1522i) q^{97} +(3.58888 - 6.21612i) q^{98} +(-7.15816 + 12.3983i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9	\( 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9} - 6 q^{10} + 2 q^{12} + 6 q^{14} + 4 q^{15} - 6 q^{16} + 13 q^{17} + 12 q^{18} - 9 q^{19} + 6 q^{20} + 11 q^{21} - 3 q^{23} + 4 q^{24} + 12 q^{25} - 16 q^{27} + 3 q^{28} - 5 q^{29} + 2 q^{30} + 14 q^{31} + 6 q^{32} + 10 q^{33} - 13 q^{34} - 3 q^{35} - 12 q^{36} + 2 q^{37} + 9 q^{38} + 14 q^{39} + 12 q^{40} + 15 q^{41} + 22 q^{42} + 4 q^{43} - 24 q^{45} + 3 q^{46} - 11 q^{47} + 2 q^{48} - 43 q^{49} + 6 q^{50} + 15 q^{51} - 52 q^{53} - 8 q^{54} - 3 q^{56} + 3 q^{57} - 10 q^{58} + 54 q^{59} - 2 q^{60} - 6 q^{61} + 28 q^{62} - 4 q^{63} + 12 q^{64} + 20 q^{66} - 5 q^{67} - 26 q^{68} + 13 q^{69} - 6 q^{70} - 6 q^{71} - 24 q^{72} - 15 q^{73} - 2 q^{74} - 4 q^{75} + 18 q^{76} - 10 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} + 12 q^{81} + 30 q^{82} - 15 q^{83} + 11 q^{84} - 13 q^{85} + 2 q^{86} + 5 q^{87} - 14 q^{89} - 12 q^{90} + 4 q^{91} + 6 q^{92} + 28 q^{93} - 22 q^{94} + 9 q^{95} - 2 q^{96} + 21 q^{97} + 43 q^{98} - 72 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9 - 6 * q^10 + 2 * q^12 + 6 * q^14 + 4 * q^15 - 6 * q^16 + 13 * q^17 + 12 * q^18 - 9 * q^19 + 6 * q^20 + 11 * q^21 - 3 * q^23 + 4 * q^24 + 12 * q^25 - 16 * q^27 + 3 * q^28 - 5 * q^29 + 2 * q^30 + 14 * q^31 + 6 * q^32 + 10 * q^33 - 13 * q^34 - 3 * q^35 - 12 * q^36 + 2 * q^37 + 9 * q^38 + 14 * q^39 + 12 * q^40 + 15 * q^41 + 22 * q^42 + 4 * q^43 - 24 * q^45 + 3 * q^46 - 11 * q^47 + 2 * q^48 - 43 * q^49 + 6 * q^50 + 15 * q^51 - 52 * q^53 - 8 * q^54 - 3 * q^56 + 3 * q^57 - 10 * q^58 + 54 * q^59 - 2 * q^60 - 6 * q^61 + 28 * q^62 - 4 * q^63 + 12 * q^64 + 20 * q^66 - 5 * q^67 - 26 * q^68 + 13 * q^69 - 6 * q^70 - 6 * q^71 - 24 * q^72 - 15 * q^73 - 2 * q^74 - 4 * q^75 + 18 * q^76 - 10 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 + 12 * q^81 + 30 * q^82 - 15 * q^83 + 11 * q^84 - 13 * q^85 + 2 * q^86 + 5 * q^87 - 14 * q^89 - 12 * q^90 + 4 * q^91 + 6 * q^92 + 28 * q^93 - 22 * q^94 + 9 * q^95 - 2 * q^96 + 21 * q^97 + 43 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	0.293928			0.169699			0.0848496	−	0.996394i	$-0.472959\pi$
$3$	0.293928			0.169699			0.0848496	+	0.996394i	$0.472959\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.146964	+	0.254549i	0.0599977	+	0.103919i
$7$	1.88267	−	3.26088i	0.711582	−	1.23250i	−0.252682	−	0.967549i	$-0.581313\pi$
$7$	1.88267	−	3.26088i	0.711582	−	1.23250i	0.964263	−	0.264946i	$-0.0853542\pi$
$8$	−1.00000			−0.353553
$9$	−2.91361			−0.971202
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	2.45680	−	4.25531i	0.740754	−	1.28302i	−0.211398	−	0.977400i	$-0.567802\pi$
$11$	2.45680	−	4.25531i	0.740754	−	1.28302i	0.952152	−	0.305624i	$-0.0988649\pi$
$12$	−0.146964	+	0.254549i	−0.0424248	+	0.0734819i
$13$	−3.03588	−	5.25830i	−0.842002	−	1.45839i	−0.888199	−	0.459458i	$-0.848044\pi$
$13$	−3.03588	−	5.25830i	−0.842002	−	1.45839i	0.0461970	−	0.998932i	$-0.485290\pi$
$14$	3.76534			1.00633
$15$	−0.293928			−0.0758918
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.426587	+	0.738870i	0.103463	+	0.179202i	0.913109	−	0.407715i	$-0.133674\pi$
$17$	0.426587	+	0.738870i	0.103463	+	0.179202i	−0.809646	+	0.586918i	$0.800341\pi$
$18$	−1.45680	−	2.52326i	−0.343372	−	0.594737i
$19$	−2.23643	−	3.87360i	−0.513071	−	0.888666i	−0.999885	−	0.0151599i	$-0.995174\pi$
$19$	−2.23643	−	3.87360i	−0.513071	−	0.888666i	0.486814	−	0.873506i	$-0.338159\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	0.553368	−	0.958462i	0.120755	−	0.209153i
$22$	4.91361			1.04758
$23$	4.35552	+	7.54398i	0.908189	+	1.57303i	0.816578	+	0.577234i	$0.195868\pi$
$23$	4.35552	+	7.54398i	0.908189	+	1.57303i	0.0916105	+	0.995795i	$0.470799\pi$
$24$	−0.293928			−0.0599977
$25$	1.00000			0.200000
$26$	3.03588	−	5.25830i	0.595386	−	1.03124i
$27$	−1.73817			−0.334511
$28$	1.88267	+	3.26088i	0.355791	+	0.616248i
$29$	−1.67267	+	2.89716i	−0.310608	+	0.537989i	−0.978494	−	0.206275i	$-0.933866\pi$
$29$	−1.67267	+	2.89716i	−0.310608	+	0.537989i	0.667886	+	0.744263i	$0.267199\pi$
$30$	−0.146964	−	0.254549i	−0.0268318	−	0.0464740i
$31$	1.71072	−	2.96305i	0.307254	−	0.532179i	−0.670507	−	0.741903i	$-0.733923\pi$
$31$	1.71072	−	2.96305i	0.307254	−	0.532179i	0.977761	+	0.209724i	$0.0672567\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.722122	−	1.25075i	0.125705	−	0.217728i
$34$	−0.426587	+	0.738870i	−0.0731591	+	0.126715i
$35$	−1.88267	+	3.26088i	−0.318229	+	0.551189i
$36$	1.45680	−	2.52326i	0.242801	−	0.420543i
$37$	0.515328	+	0.892573i	0.0847193	+	0.146738i	0.905272	−	0.424833i	$-0.139667\pi$
$37$	0.515328	+	0.892573i	0.0847193	+	0.146738i	−0.820552	+	0.571572i	$0.806334\pi$
$38$	2.23643	−	3.87360i	0.362796	−	0.628382i
$39$	−0.892329	−	1.54556i	−0.142887	−	0.247488i
$40$	1.00000			0.158114
$41$	−1.04496	+	1.80992i	−0.163195	+	0.282662i	−0.936013	−	0.351966i	$-0.885513\pi$
$41$	−1.04496	+	1.80992i	−0.163195	+	0.282662i	0.772818	+	0.634628i	$0.218847\pi$
$42$	1.10674			0.170773
$43$	5.81820			0.887268			0.443634	−	0.896208i	$-0.353689\pi$
$43$	5.81820			0.887268			0.443634	+	0.896208i	$0.353689\pi$
$44$	2.45680	+	4.25531i	0.370377	+	0.641512i
$45$	2.91361			0.434335
$46$	−4.35552	+	7.54398i	−0.642187	+	1.11230i
$47$	6.09748	−	10.5611i	0.889408	−	1.54050i	0.0488321	−	0.998807i	$-0.484450\pi$
$47$	6.09748	−	10.5611i	0.889408	−	1.54050i	0.840576	−	0.541693i	$-0.182217\pi$
$48$	−0.146964	−	0.254549i	−0.0212124	−	0.0367409i
$49$	−3.58888	−	6.21612i	−0.512697	−	0.888017i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	0.125386	+	0.217174i	0.0175575	+	0.0304105i
$52$	6.07176			0.842002
$53$	−11.1024			−1.52503			−0.762517	−	0.646968i	$-0.776037\pi$
$53$	−11.1024			−1.52503			−0.762517	+	0.646968i	$0.776037\pi$
$54$	−0.869086	−	1.50530i	−0.118268	−	0.204846i
$55$	−2.45680	+	4.25531i	−0.331275	+	0.573786i
$56$	−1.88267	+	3.26088i	−0.251582	+	0.435753i
$57$	−0.657347	−	1.13856i	−0.0870678	−	0.150806i
$58$	−3.34535			−0.439266
$59$	8.50495			1.10725			0.553625	−	0.832766i	$-0.313244\pi$
$59$	8.50495			1.10725			0.553625	+	0.832766i	$0.313244\pi$
$60$	0.146964	−	0.254549i	0.0189729	−	0.0328621i
$61$	2.27747	+	3.94469i	0.291600	+	0.505065i	0.974188	−	0.225738i	$-0.0724792\pi$
$61$	2.27747	+	3.94469i	0.291600	+	0.505065i	−0.682589	+	0.730803i	$0.739146\pi$
$62$	3.42143			0.434522
$63$	−5.48535	+	9.50091i	−0.691090	+	1.19700i
$64$	1.00000			0.125000
$65$	3.03588	+	5.25830i	0.376555	+	0.652212i
$66$	1.44424			0.177774
$67$	−6.39967	+	5.10335i	−0.781845	+	0.623473i
$67$	−6.39967	+	5.10335i	−0.781845	+	0.623473i
$68$	−0.853174			−0.103463
$69$	1.28021	+	2.21738i	0.154119	+	0.266942i
$70$	−3.76534			−0.450044
$71$	5.07590	−	8.79171i	0.602398	−	1.04338i	−0.390059	−	0.920790i	$-0.627545\pi$
$71$	5.07590	−	8.79171i	0.602398	−	1.04338i	0.992457	−	0.122594i	$-0.0391214\pi$
$72$	2.91361			0.343372
$73$	−3.16127	−	5.47548i	−0.369998	−	0.640856i	0.619566	−	0.784944i	$-0.287308\pi$
$73$	−3.16127	−	5.47548i	−0.369998	−	0.640856i	−0.989565	+	0.144088i	$0.953975\pi$
$74$	−0.515328	+	0.892573i	−0.0599056	+	0.103760i
$75$	0.293928			0.0339398
$76$	4.47285			0.513071
$77$	−9.25069	−	16.0227i	−1.05421	−	1.82595i
$78$	0.892329	−	1.54556i	0.101036	−	0.175000i
$79$	−3.89284	+	6.74260i	−0.437979	+	0.758601i	−0.997533	−	0.0701920i	$-0.977639\pi$
$79$	−3.89284	+	6.74260i	−0.437979	+	0.758601i	0.559555	+	0.828793i	$0.310972\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	8.22992			0.914436
$82$	−2.08992			−0.230793
$83$	−1.79959	−	3.11699i	−0.197531	−	0.342134i	0.750196	−	0.661215i	$-0.229959\pi$
$83$	−1.79959	−	3.11699i	−0.197531	−	0.342134i	−0.947727	+	0.319081i	$0.896626\pi$
$84$	0.553368	+	0.958462i	0.0603774	+	0.104577i
$85$	−0.426587	−	0.738870i	−0.0462699	−	0.0801417i
$86$	2.90910	+	5.03871i	0.313696	+	0.543338i
$87$	−0.491645	+	0.851555i	−0.0527099	+	0.0912962i
$88$	−2.45680	+	4.25531i	−0.261896	+	0.453617i
$89$	6.38502			0.676810			0.338405	−	0.941001i	$-0.390113\pi$
$89$	6.38502			0.676810			0.338405	+	0.941001i	$0.390113\pi$
$90$	1.45680	+	2.52326i	0.153561	+	0.265975i
$91$	−22.8622			−2.39661
$92$	−8.71104			−0.908189
$93$	0.502826	−	0.870921i	0.0521407	−	0.0903103i
$94$	12.1950			1.25781
$95$	2.23643	+	3.87360i	0.229453	+	0.397423i
$96$	0.146964	−	0.254549i	0.0149994	−	0.0259798i
$97$	6.43873	+	11.1522i	0.653754	+	1.13234i	0.982205	+	0.187814i	$0.0601403\pi$
$97$	6.43873	+	11.1522i	0.653754	+	1.13234i	−0.328450	+	0.944521i	$0.606526\pi$
$98$	3.58888	−	6.21612i	0.362531	−	0.627923i
$99$	−7.15816	+	12.3983i	−0.719422	+	1.24608i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	3.79523	−	6.57354i	0.377640	−	0.654092i	−0.613078	−	0.790022i	$-0.710069\pi$
$101$	3.79523	−	6.57354i	0.377640	−	0.654092i	0.990718	+	0.135931i	$0.0434024\pi$
$102$	−0.125386	+	0.217174i	−0.0124150	+	0.0215035i
$103$	−7.91855	+	13.7153i	−0.780238	+	1.35141i	0.151565	+	0.988447i	$0.451569\pi$
$103$	−7.91855	+	13.7153i	−0.780238	+	1.35141i	−0.931803	+	0.362965i	$0.881765\pi$
$104$	3.03588	+	5.25830i	0.297693	+	0.515619i
$105$	−0.553368	+	0.958462i	−0.0540032	+	0.0935363i
$106$	−5.55121	−	9.61498i	−0.539181	−	0.933889i
$107$	−16.1944			−1.56557			−0.782783	−	0.622294i	$-0.786201\pi$
$107$	−16.1944			−1.56557			−0.782783	+	0.622294i	$0.786201\pi$
$108$	0.869086	−	1.50530i	0.0836278	−	0.144848i
$109$	−0.560415			−0.0536781			−0.0268390	−	0.999640i	$-0.508544\pi$
$109$	−0.560415			−0.0536781			−0.0268390	+	0.999640i	$0.508544\pi$
$110$	−4.91361			−0.468494
$111$	0.151469	+	0.262352i	0.0143768	+	0.0249013i
$112$	−3.76534			−0.355791
$113$	0.373308	−	0.646588i	0.0351178	−	0.0608259i	−0.847932	−	0.530105i	$-0.822153\pi$
$113$	0.373308	−	0.646588i	0.0351178	−	0.0608259i	0.883050	+	0.469279i	$0.155486\pi$
$114$	0.657347	−	1.13856i	0.0615662	−	0.106636i
$115$	−4.35552	−	7.54398i	−0.406154	−	0.703480i
$116$	−1.67267	−	2.89716i	−0.155304	−	0.268994i
$117$	8.84537	+	15.3206i	0.817754	+	1.41639i
$118$	4.25248	+	7.36550i	0.391472	+	0.678050i
$119$	3.21249			0.294488
$120$	0.293928			0.0268318
$121$	−6.57176	−	11.3826i	−0.597433	−	1.03478i
$122$	−2.27747	+	3.94469i	−0.206192	+	0.357135i
$123$	−0.307142	+	0.531986i	−0.0276941	+	0.0479676i
$124$	1.71072	+	2.96305i	0.153627	+	0.266089i
$125$	−1.00000			−0.0894427
$126$	−10.9707			−0.977348
$127$	2.41818	−	4.18841i	0.214579	−	0.371661i	−0.738564	−	0.674184i	$-0.764496\pi$
$127$	2.41818	−	4.18841i	0.214579	−	0.371661i	0.953142	+	0.302523i	$0.0978288\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.71013			0.150569
$130$	−3.03588	+	5.25830i	−0.266265	+	0.461184i
$131$	11.1514			0.974300			0.487150	−	0.873318i	$-0.338037\pi$
$131$	11.1514			0.974300			0.487150	+	0.873318i	$0.338037\pi$
$132$	0.722122	+	1.25075i	0.0628527	+	0.108864i
$133$	−16.8418			−1.46037
$134$	−7.61947	−	2.99061i	−0.658222	−	0.258349i
$135$	1.73817			0.149598
$136$	−0.426587	−	0.738870i	−0.0365795	−	0.0633576i
$137$	16.8560			1.44011			0.720053	−	0.693919i	$-0.244117\pi$
$137$	16.8560			1.44011			0.720053	+	0.693919i	$0.244117\pi$
$138$	−1.28021	+	2.21738i	−0.108979	+	0.188756i
$139$	11.1821			0.948455			0.474228	−	0.880402i	$-0.342727\pi$
$139$	11.1821			0.948455			0.474228	+	0.880402i	$0.342727\pi$
$140$	−1.88267	−	3.26088i	−0.159114	−	0.275594i
$141$	1.79222	−	3.10421i	0.150932	−	0.261422i
$142$	10.1518			0.851920
$143$	−29.8343			−2.49487
$144$	1.45680	+	2.52326i	0.121400	+	0.210271i
$145$	1.67267	−	2.89716i	0.138908	−	0.240596i
$146$	3.16127	−	5.47548i	0.261628	−	0.453154i
$147$	−1.05487	−	1.82709i	−0.0870042	−	0.150696i
$148$	−1.03066			−0.0847193
$149$	21.0515			1.72460			0.862301	−	0.506396i	$-0.169022\pi$
$149$	21.0515			1.72460			0.862301	+	0.506396i	$0.169022\pi$
$150$	0.146964	+	0.254549i	0.0119995	+	0.0207838i
$151$	−2.76120	−	4.78254i	−0.224704	−	0.389198i	0.731527	−	0.681813i	$-0.238808\pi$
$151$	−2.76120	−	4.78254i	−0.224704	−	0.389198i	−0.956230	+	0.292615i	$0.905475\pi$
$152$	2.23643	+	3.87360i	0.181398	+	0.314191i
$153$	−1.24291	−	2.15278i	−0.100483	−	0.174042i
$154$	9.25069	−	16.0227i	0.745442	−	1.29114i
$155$	−1.71072	+	2.96305i	−0.137408	+	0.237998i
$156$	1.78466			0.142887
$157$	−6.79338	−	11.7665i	−0.542171	−	0.939067i	−0.998779	−	0.0493992i	$-0.984269\pi$
$157$	−6.79338	−	11.7665i	−0.542171	−	0.939067i	0.456609	−	0.889668i	$-0.349064\pi$
$158$	−7.78568			−0.619395
$159$	−3.26331			−0.258797
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	32.8000			2.58500
$162$	4.11496	+	7.12732i	0.323302	+	0.559975i
$163$	−1.52949	+	2.64916i	−0.119799	+	0.207498i	−0.919688	−	0.392650i	$-0.871558\pi$
$163$	−1.52949	+	2.64916i	−0.119799	+	0.207498i	0.799889	+	0.600148i	$0.204892\pi$
$164$	−1.04496	−	1.80992i	−0.0815976	−	0.141331i
$165$	−0.722122	+	1.25075i	−0.0562171	+	0.0973709i
$166$	1.79959	−	3.11699i	0.139676	−	0.241925i
$167$	−10.8507	+	18.7939i	−0.839652	+	1.45432i	0.0505343	+	0.998722i	$0.483908\pi$
$167$	−10.8507	+	18.7939i	−0.839652	+	1.45432i	−0.890186	+	0.455597i	$0.849426\pi$
$168$	−0.553368	+	0.958462i	−0.0426933	+	0.0739469i
$169$	−11.9332	+	20.6688i	−0.917936	+	1.58991i
$170$	0.426587	−	0.738870i	0.0327177	−	0.0566688i
$171$	6.51607	+	11.2862i	0.498296	+	0.863074i
$172$	−2.90910	+	5.03871i	−0.221817	+	0.384198i
$173$	−1.77454	−	3.07360i	−0.134916	−	0.233681i	0.790649	−	0.612269i	$-0.209743\pi$
$173$	−1.77454	−	3.07360i	−0.134916	−	0.233681i	−0.925565	+	0.378588i	$0.876410\pi$
$174$	−0.983290			−0.0745431
$175$	1.88267	−	3.26088i	0.142316	−	0.246499i
$176$	−4.91361			−0.370377
$177$	2.49984			0.187899
$178$	3.19251	+	5.52959i	0.239289	+	0.414460i
$179$	−10.6121			−0.793189			−0.396595	−	0.917994i	$-0.629808\pi$
$179$	−10.6121			−0.793189			−0.396595	+	0.917994i	$0.629808\pi$
$180$	−1.45680	+	2.52326i	−0.108584	+	0.188072i
$181$	2.50770	−	4.34347i	0.186396	−	0.322848i	−0.757650	−	0.652661i	$-0.773653\pi$
$181$	2.50770	−	4.34347i	0.186396	−	0.322848i	0.944046	+	0.329814i	$0.106986\pi$
$182$	−11.4311	−	19.7993i	−0.847331	−	1.46762i
$183$	0.669410	+	1.15945i	0.0494842	+	0.0857091i
$184$	−4.35552	−	7.54398i	−0.321093	−	0.556150i
$185$	−0.515328	−	0.892573i	−0.0378876	−	0.0656233i
$186$	1.00565			0.0737380
$187$	4.19216			0.306561
$188$	6.09748	+	10.5611i	0.444704	+	0.770250i
$189$	−3.27240	+	5.66796i	−0.238032	+	0.412284i
$190$	−2.23643	+	3.87360i	−0.162247	+	0.281021i
$191$	4.60449	+	7.97521i	0.333169	+	0.577066i	0.983131	−	0.182901i	$-0.0585486\pi$
$191$	4.60449	+	7.97521i	0.333169	+	0.577066i	−0.649962	+	0.759966i	$0.725215\pi$
$192$	0.293928			0.0212124
$193$	3.65934			0.263405			0.131703	−	0.991289i	$-0.457956\pi$
$193$	3.65934			0.263405			0.131703	+	0.991289i	$0.457956\pi$
$194$	−6.43873	+	11.1522i	−0.462274	+	0.800682i
$195$	0.892329	+	1.54556i	0.0639010	+	0.110680i
$196$	7.17776			0.512697
$197$	4.45209	−	7.71124i	0.317198	−	0.549403i	−0.662704	−	0.748881i	$-0.730591\pi$
$197$	4.45209	−	7.71124i	0.317198	−	0.549403i	0.979902	+	0.199478i	$0.0639247\pi$
$198$	−14.3163			−1.01742
$199$	−9.08723	−	15.7395i	−0.644177	−	1.11575i	−0.984491	−	0.175435i	$-0.943867\pi$
$199$	−9.08723	−	15.7395i	−0.644177	−	1.11575i	0.340314	−	0.940312i	$-0.389467\pi$
$200$	−1.00000			−0.0707107
$201$	−1.88104	+	1.50001i	−0.132678	+	0.105803i
$202$	7.59047			0.534063
$203$	6.29818	+	10.9088i	0.442046	+	0.765646i
$204$	−0.250771			−0.0175575
$205$	1.04496	−	1.80992i	0.0729831	−	0.126410i
$206$	−15.8371			−1.10342
$207$	−12.6903	−	21.9802i	−0.882035	−	1.52773i
$208$	−3.03588	+	5.25830i	−0.210501	+	0.364598i
$209$	−21.9778			−1.52024
$210$	−1.10674			−0.0763720
$211$	5.67989	+	9.83786i	0.391020	+	0.677266i	0.992584	−	0.121558i	$-0.0387890\pi$
$211$	5.67989	+	9.83786i	0.391020	+	0.677266i	−0.601564	+	0.798824i	$0.705456\pi$
$212$	5.55121	−	9.61498i	0.381259	−	0.660359i
$213$	1.49195	−	2.58413i	0.102226	−	0.177061i
$214$	−8.09718	−	14.0247i	−0.553511	−	0.958710i
$215$	−5.81820			−0.396798
$216$	1.73817			0.118268
$217$	−6.44142	−	11.1569i	−0.437272	−	0.757377i
$218$	−0.280208	−	0.485334i	−0.0189781	−	0.0328710i
$219$	−0.929184	−	1.60939i	−0.0627884	−	0.108753i
$220$	−2.45680	−	4.25531i	−0.165638	−	0.286893i
$221$	2.59014	−	4.48625i	0.174231	−	0.301778i
$222$	−0.151469	+	0.262352i	−0.0101659	+	0.0176079i
$223$	−8.65673			−0.579698			−0.289849	−	0.957072i	$-0.593605\pi$
$223$	−8.65673			−0.579698			−0.289849	+	0.957072i	$0.593605\pi$
$224$	−1.88267	−	3.26088i	−0.125791	−	0.217876i
$225$	−2.91361			−0.194240
$226$	0.746615			0.0496641
$227$	5.23701	−	9.07077i	0.347593	−	0.602048i	−0.638229	−	0.769847i	$-0.720333\pi$
$227$	5.23701	−	9.07077i	0.347593	−	0.602048i	0.985821	+	0.167799i	$0.0536659\pi$
$228$	1.31469			0.0870678
$229$	−2.44831	−	4.24060i	−0.161789	−	0.280227i	0.773721	−	0.633526i	$-0.218393\pi$
$229$	−2.44831	−	4.24060i	−0.161789	−	0.280227i	−0.935510	+	0.353299i	$0.885060\pi$
$230$	4.35552	−	7.54398i	0.287195	−	0.497436i
$231$	−2.71903	−	4.70950i	−0.178899	−	0.309863i
$232$	1.67267	−	2.89716i	0.109816	−	0.190208i
$233$	−7.75089	+	13.4249i	−0.507778	+	0.879497i	0.492182	+	0.870493i	$0.336200\pi$
$233$	−7.75089	+	13.4249i	−0.507778	+	0.879497i	−0.999959	+	0.00900462i	$0.997134\pi$
$234$	−8.84537	+	15.3206i	−0.578240	+	1.00154i
$235$	−6.09748	+	10.5611i	−0.397755	+	0.688933i
$236$	−4.25248	+	7.36550i	−0.276813	+	0.479454i
$237$	−1.14421	+	1.98183i	−0.0743246	+	0.128734i
$238$	1.60624	+	2.78210i	0.104117	+	0.180336i
$239$	2.15933	−	3.74006i	0.139675	−	0.241925i	−0.787698	−	0.616061i	$-0.788727\pi$
$239$	2.15933	−	3.74006i	0.139675	−	0.241925i	0.927374	+	0.374136i	$0.122061\pi$
$240$	0.146964	+	0.254549i	0.00948647	+	0.0164310i
$241$	2.21083			0.142412			0.0712061	−	0.997462i	$-0.477315\pi$
$241$	2.21083			0.142412			0.0712061	+	0.997462i	$0.477315\pi$
$242$	6.57176	−	11.3826i	0.422449	−	0.731703i
$243$	7.63352			0.489690
$244$	−4.55493			−0.291600
$245$	3.58888	+	6.21612i	0.229285	+	0.397133i
$246$	−0.614285			−0.0391654
$247$	−13.5791	+	23.5196i	−0.864015	+	1.49652i
$248$	−1.71072	+	2.96305i	−0.108631	+	0.188154i
$249$	−0.528950	−	0.916169i	−0.0335209	−	0.0580598i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	13.8314	+	23.9567i	0.873032	+	1.51214i	0.858844	+	0.512237i	$0.171183\pi$
$251$	13.8314	+	23.9567i	0.873032	+	1.51214i	0.0141884	+	0.999899i	$0.495484\pi$
$252$	−5.48535	−	9.50091i	−0.345545	−	0.598501i
$253$	42.8026			2.69098
$254$	4.83636			0.303460
$255$	−0.125386	−	0.217174i	−0.00785196	−	0.0136000i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.389331	−	0.674342i	0.0242858	−	0.0420643i	−0.853627	−	0.520885i	$-0.825602\pi$
$257$	0.389331	−	0.674342i	0.0242858	−	0.0420643i	0.877913	+	0.478820i	$0.158935\pi$
$258$	0.855065	+	1.48102i	0.0532340	+	0.0922040i
$259$	3.88076			0.241139
$260$	−6.07176			−0.376555
$261$	4.87352	−	8.44118i	0.301663	−	0.522496i
$262$	5.57569	+	9.65737i	0.344467	+	0.596634i
$263$	−3.41813			−0.210771			−0.105386	−	0.994431i	$-0.533608\pi$
$263$	−3.41813			−0.210771			−0.105386	+	0.994431i	$0.533608\pi$
$264$	−0.722122	+	1.25075i	−0.0444435	+	0.0769785i
$265$	11.1024			0.682016
$266$	−8.42090	−	14.5854i	−0.516318	−	0.894290i
$267$	1.87673			0.114854
$268$	−1.21979	−	8.09395i	−0.0745107	−	0.494417i
$269$	1.91880			0.116991			0.0584957	−	0.998288i	$-0.481370\pi$
$269$	1.91880			0.116991			0.0584957	+	0.998288i	$0.481370\pi$
$270$	0.869086	+	1.50530i	0.0528909	+	0.0916097i
$271$	−1.34023			−0.0814132			−0.0407066	−	0.999171i	$-0.512961\pi$
$271$	−1.34023			−0.0814132			−0.0407066	+	0.999171i	$0.512961\pi$
$272$	0.426587	−	0.738870i	0.0258656	−	0.0448006i
$273$	−6.71984			−0.406703
$274$	8.42801	+	14.5977i	0.509155	+	0.881882i
$275$	2.45680	−	4.25531i	0.148151	−	0.256605i
$276$	−2.56042			−0.154119
$277$	−6.77799			−0.407250			−0.203625	−	0.979049i	$-0.565272\pi$
$277$	−6.77799			−0.407250			−0.203625	+	0.979049i	$0.565272\pi$
$278$	5.59106	+	9.68400i	0.335330	+	0.580808i
$279$	−4.98435	+	8.63315i	−0.298405	+	0.516853i
$280$	1.88267	−	3.26088i	0.112511	−	0.194875i
$281$	6.48824	+	11.2380i	0.387056	+	0.670401i	0.992052	−	0.125828i	$-0.0401586\pi$
$281$	6.48824	+	11.2380i	0.387056	+	0.670401i	−0.604996	+	0.796229i	$0.706825\pi$
$282$	3.58443			0.213450
$283$	23.0369			1.36940			0.684702	−	0.728823i	$-0.259932\pi$
$283$	23.0369			1.36940			0.684702	+	0.728823i	$0.259932\pi$
$284$	5.07590	+	8.79171i	0.301199	+	0.521692i
$285$	0.657347	+	1.13856i	0.0389379	+	0.0674424i
$286$	−14.9171	−	25.8372i	−0.882069	−	1.52779i
$287$	3.93462	+	6.81497i	0.232253	+	0.402275i
$288$	−1.45680	+	2.52326i	−0.0858430	+	0.148684i
$289$	8.13605	−	14.0920i	0.478591	−	0.828944i
$290$	3.34535			0.196446
$291$	1.89252	+	3.27794i	0.110942	+	0.192156i
$292$	6.32254			0.369998
$293$	8.38906			0.490094			0.245047	−	0.969511i	$-0.421197\pi$
$293$	8.38906			0.490094			0.245047	+	0.969511i	$0.421197\pi$
$294$	1.05487	−	1.82709i	0.0615213	−	0.106558i
$295$	−8.50495			−0.495177
$296$	−0.515328	−	0.892573i	−0.0299528	−	0.0518798i
$297$	−4.27035	+	7.39646i	−0.247791	+	0.429186i
$298$	10.5257	+	18.2311i	0.609739	+	1.05610i
$299$	26.4457	−	45.8053i	1.52939	−	2.64899i
$300$	−0.146964	+	0.254549i	−0.00848496	+	0.0146964i
$301$	10.9537	−	18.9724i	0.631363	−	1.09355i
$302$	2.76120	−	4.78254i	0.158889	−	0.275204i
$303$	1.11552	−	1.93214i	0.0640852	−	0.110999i
$304$	−2.23643	+	3.87360i	−0.128268	+	0.222166i
$305$	−2.27747	−	3.94469i	−0.130407	−	0.225872i
$306$	1.24291	−	2.15278i	0.0710522	−	0.123066i
$307$	−12.5922	−	21.8104i	−0.718678	−	1.24479i	−0.961524	−	0.274721i	$-0.911414\pi$
$307$	−12.5922	−	21.8104i	−0.718678	−	1.24479i	0.242846	−	0.970065i	$-0.421919\pi$
$308$	18.5014			1.05421
$309$	−2.32748	+	4.03131i	−0.132406	+	0.229333i
$310$	−3.42143			−0.194324
$311$	33.4862			1.89883			0.949413	−	0.314030i	$-0.101679\pi$
$311$	33.4862			1.89883			0.949413	+	0.314030i	$0.101679\pi$
$312$	0.892329	+	1.54556i	0.0505182	+	0.0875001i
$313$	−2.48386			−0.140396			−0.0701980	−	0.997533i	$-0.522363\pi$
$313$	−2.48386			−0.140396			−0.0701980	+	0.997533i	$0.522363\pi$
$314$	6.79338	−	11.7665i	0.383372	−	0.664021i
$315$	5.48535	−	9.50091i	0.309065	−	0.535316i
$316$	−3.89284	−	6.74260i	−0.218989	−	0.379301i
$317$	3.33497	+	5.77635i	0.187311	+	0.324432i	0.944353	−	0.328934i	$-0.106690\pi$
$317$	3.33497	+	5.77635i	0.187311	+	0.324432i	−0.757042	+	0.653366i	$0.773356\pi$
$318$	−1.63165	−	2.82611i	−0.0914986	−	0.158480i
$319$	8.21887	+	14.2355i	0.460168	+	0.797035i
$320$	−1.00000			−0.0559017
$321$	−4.75997			−0.265675
$322$	16.4000	+	28.4056i	0.913936	+	1.58298i
$323$	1.90806	−	3.30486i	0.106167	−	0.183887i
$324$	−4.11496	+	7.12732i	−0.228609	+	0.395962i
$325$	−3.03588	−	5.25830i	−0.168400	−	0.291678i
$326$	−3.05899			−0.169422
$327$	−0.164721			−0.00910912
$328$	1.04496	−	1.80992i	0.0576982	−	0.0999363i
$329$	−22.9590	−	39.7662i	−1.26577	−	2.19238i
$330$	−1.44424			−0.0795030
$331$	6.34594	−	10.9915i	0.348805	−	0.604147i	−0.637233	−	0.770671i	$-0.719921\pi$
$331$	6.34594	−	10.9915i	0.348805	−	0.604147i	0.986037	+	0.166524i	$0.0532544\pi$
$332$	3.59919			0.197531
$333$	−1.50146	−	2.60061i	−0.0822796	−	0.142512i
$334$	−21.7014			−1.18745
$335$	6.39967	−	5.10335i	0.349652	−	0.278826i
$336$	−1.10674			−0.0603774
$337$	13.2511	+	22.9516i	0.721834	+	1.25025i	0.960264	+	0.279093i	$0.0900337\pi$
$337$	13.2511	+	22.9516i	0.721834	+	1.25025i	−0.238431	+	0.971160i	$0.576633\pi$
$338$	−23.8663			−1.29816
$339$	0.109725	−	0.190050i	0.00595947	−	0.0103221i
$340$	0.853174			0.0462699
$341$	−8.40578	−	14.5592i	−0.455199	−	0.788427i
$342$	−6.51607	+	11.2862i	−0.352349	+	0.610286i
$343$	−0.669313			−0.0361395
$344$	−5.81820			−0.313696
$345$	−1.28021	−	2.21738i	−0.0689241	−	0.119380i
$346$	1.77454	−	3.07360i	0.0953999	−	0.165238i
$347$	11.1663	−	19.3406i	0.599439	−	1.03826i	−0.393465	−	0.919340i	$-0.628724\pi$
$347$	11.1663	−	19.3406i	0.599439	−	1.03826i	0.992904	−	0.118920i	$-0.0379431\pi$
$348$	−0.491645	−	0.851555i	−0.0263550	−	0.0456481i
$349$	7.50950			0.401975			0.200987	−	0.979594i	$-0.435585\pi$
$349$	7.50950			0.401975			0.200987	+	0.979594i	$0.435585\pi$
$350$	3.76534			0.201266
$351$	5.27689	+	9.13983i	0.281659	+	0.487848i
$352$	−2.45680	−	4.25531i	−0.130948	−	0.226809i
$353$	16.8189	+	29.1311i	0.895178	+	1.55049i	0.833584	+	0.552392i	$0.186285\pi$
$353$	16.8189	+	29.1311i	0.895178	+	1.55049i	0.0615939	+	0.998101i	$0.480382\pi$
$354$	1.24992	+	2.16492i	0.0664325	+	0.115064i
$355$	−5.07590	+	8.79171i	−0.269401	+	0.466616i
$356$	−3.19251	+	5.52959i	−0.169203	+	0.293067i
$357$	0.944238			0.0499744
$358$	−5.30607	−	9.19039i	−0.280435	−	0.485727i
$359$	24.4378			1.28978			0.644890	−	0.764276i	$-0.276903\pi$
$359$	24.4378			1.28978			0.644890	+	0.764276i	$0.276903\pi$
$360$	−2.91361			−0.153561
$361$	−0.503207	+	0.871580i	−0.0264846	+	0.0458726i
$362$	5.01541			0.263604
$363$	−1.93162	−	3.34567i	−0.101384	−	0.175602i
$364$	11.4311	−	19.7993i	0.599153	−	1.03776i
$365$	3.16127	+	5.47548i	0.165468	+	0.286600i
$366$	−0.669410	+	1.15945i	−0.0349906	+	0.0606055i
$367$	−15.2402	+	26.3969i	−0.795534	+	1.37791i	0.126965	+	0.991907i	$0.459476\pi$
$367$	−15.2402	+	26.3969i	−0.795534	+	1.37791i	−0.922499	+	0.385999i	$0.873857\pi$
$368$	4.35552	−	7.54398i	0.227047	−	0.393257i
$369$	3.04460	−	5.27340i	0.158496	−	0.274522i
$370$	0.515328	−	0.892573i	0.0267906	−	0.0464027i
$371$	−20.9022	+	36.2036i	−1.08519	+	1.87960i
$372$	0.502826	+	0.870921i	0.0260703	+	0.0451551i
$373$	4.36823	−	7.56599i	0.226178	−	0.391752i	−0.730494	−	0.682919i	$-0.760710\pi$
$373$	4.36823	−	7.56599i	0.226178	−	0.391752i	0.956672	+	0.291167i	$0.0940435\pi$
$374$	2.09608	+	3.63052i	0.108386	+	0.187730i
$375$	−0.293928			−0.0151784
$376$	−6.09748	+	10.5611i	−0.314453	+	0.544649i
$377$	20.3122			1.04613
$378$	−6.54480			−0.336628
$379$	9.94781	+	17.2301i	0.510985	+	0.885051i	0.999919	+	0.0127308i	$0.00405245\pi$
$379$	9.94781	+	17.2301i	0.510985	+	0.885051i	−0.488934	+	0.872321i	$0.662614\pi$
$380$	−4.47285			−0.229453
$381$	0.710769	−	1.23109i	0.0364138	−	0.0630706i
$382$	−4.60449	+	7.97521i	−0.235586	+	0.408047i
$383$	−0.982910	−	1.70245i	−0.0502243	−	0.0869911i	0.839820	−	0.542865i	$-0.182660\pi$
$383$	−0.982910	−	1.70245i	−0.0502243	−	0.0869911i	−0.890045	+	0.455873i	$0.849327\pi$
$384$	0.146964	+	0.254549i	0.00749971	+	0.0129899i
$385$	9.25069	+	16.0227i	0.471459	+	0.816591i
$386$	1.82967	+	3.16909i	0.0931279	+	0.161302i
$387$	−16.9520			−0.861716
$388$	−12.8775			−0.653754
$389$	−14.3435	−	24.8437i	−0.727245	−	1.25962i	−0.958043	−	0.286623i	$-0.907467\pi$
$389$	−14.3435	−	24.8437i	−0.727245	−	1.25962i	0.230799	−	0.973002i	$-0.425866\pi$
$390$	−0.892329	+	1.54556i	−0.0451849	+	0.0782625i
$391$	−3.71602	+	6.43633i	−0.187927	+	0.325499i
$392$	3.58888	+	6.21612i	0.181266	+	0.313961i
$393$	3.27770			0.165338
$394$	8.90417			0.448586
$395$	3.89284	−	6.74260i	0.195870	−	0.339257i
$396$	−7.15816	−	12.3983i	−0.359711	−	0.623038i
$397$	−33.6587			−1.68928			−0.844640	−	0.535334i	$-0.820186\pi$
$397$	−33.6587			−1.68928			−0.844640	+	0.535334i	$0.820186\pi$
$398$	9.08723	−	15.7395i	0.455502	−	0.788952i
$399$	−4.95027			−0.247823
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	0.765061			0.0382053			0.0191027	−	0.999818i	$-0.493919\pi$
$401$	0.765061			0.0382053			0.0191027	+	0.999818i	$0.493919\pi$
$402$	−2.23957	−	0.879022i	−0.111700	−	0.0438416i
$403$	−20.7741			−1.03483
$404$	3.79523	+	6.57354i	0.188820	+	0.327046i
$405$	−8.22992			−0.408948
$406$	−6.29818	+	10.9088i	−0.312574	+	0.541393i
$407$	5.06423			0.251025
$408$	−0.125386	−	0.217174i	−0.00620752	−	0.0107517i
$409$	5.50070	−	9.52749i	0.271992	−	0.471104i	−0.697380	−	0.716702i	$-0.745651\pi$
$409$	5.50070	−	9.52749i	0.271992	−	0.471104i	0.969372	+	0.245598i	$0.0789842\pi$
$410$	2.08992			0.103214
$411$	4.95445			0.244385
$412$	−7.91855	−	13.7153i	−0.390119	−	0.675706i
$413$	16.0120	−	27.7336i	0.787899	−	1.36468i
$414$	12.6903	−	21.9802i	0.623693	−	1.08027i
$415$	1.79959	+	3.11699i	0.0883386	+	0.153007i
$416$	−6.07176			−0.297693
$417$	3.28673			0.160952
$418$	−10.9889	−	19.0334i	−0.537486	−	0.930952i
$419$	−7.29746	−	12.6396i	−0.356504	−	0.617484i	0.630870	−	0.775889i	$-0.282698\pi$
$419$	−7.29746	−	12.6396i	−0.356504	−	0.617484i	−0.987374	+	0.158405i	$0.949365\pi$
$420$	−0.553368	−	0.958462i	−0.0270016	−	0.0467681i
$421$	−5.76822	−	9.99086i	−0.281126	−	0.486925i	0.690536	−	0.723298i	$-0.257375\pi$
$421$	−5.76822	−	9.99086i	−0.281126	−	0.486925i	−0.971662	+	0.236373i	$0.924041\pi$
$422$	−5.67989	+	9.83786i	−0.276493	+	0.478900i
$423$	−17.7656	+	30.7710i	−0.863795	+	1.49614i
$424$	11.1024			0.539181
$425$	0.426587	+	0.738870i	0.0206925	+	0.0358405i
$426$	2.98389			0.144570
$427$	17.1508			0.829988
$428$	8.09718	−	14.0247i	0.391392	−	0.677910i
$429$	−8.76911			−0.423377
$430$	−2.90910	−	5.03871i	−0.140289	−	0.242988i
$431$	13.6845	−	23.7023i	0.659160	−	1.14170i	−0.321673	−	0.946851i	$-0.604245\pi$
$431$	13.6845	−	23.7023i	0.659160	−	1.14170i	0.980833	−	0.194848i	$-0.0624214\pi$
$432$	0.869086	+	1.50530i	0.0418139	+	0.0724238i
$433$	−9.05124	+	15.6772i	−0.434975	+	0.753398i	−0.997294	−	0.0735223i	$-0.976576\pi$
$433$	−9.05124	+	15.6772i	−0.434975	+	0.753398i	0.562319	+	0.826920i	$0.309909\pi$
$434$	6.44142	−	11.1569i	0.309198	−	0.535547i
$435$	0.491645	−	0.851555i	0.0235726	−	0.0408289i
$436$	0.280208	−	0.485334i	0.0134195	−	0.0232433i
$437$	19.4816	−	33.7431i	0.931932	−	1.61415i
$438$	0.929184	−	1.60939i	0.0443981	−	0.0768998i
$439$	−0.101583	−	0.175947i	−0.00484830	−	0.00839750i	0.863591	−	0.504193i	$-0.168210\pi$
$439$	−0.101583	−	0.175947i	−0.00484830	−	0.00839750i	−0.868439	+	0.495795i	$0.834877\pi$
$440$	2.45680	−	4.25531i	0.117124	−	0.202864i
$441$	10.4566	+	18.1113i	0.497932	+	0.862444i
$442$	5.18027			0.246400
$443$	−16.2337	+	28.1177i	−0.771288	+	1.33591i	0.165569	+	0.986198i	$0.447054\pi$
$443$	−16.2337	+	28.1177i	−0.771288	+	1.33591i	−0.936857	+	0.349712i	$0.886279\pi$
$444$	−0.302938			−0.0143768
$445$	−6.38502			−0.302679
$446$	−4.32837	−	7.49695i	−0.204954	−	0.354991i
$447$	6.18760			0.292664
$448$	1.88267	−	3.26088i	0.0889477	−	0.154062i
$449$	−20.8785	+	36.1626i	−0.985318	+	1.70662i	−0.344803	+	0.938675i	$0.612054\pi$
$449$	−20.8785	+	36.1626i	−0.985318	+	1.70662i	−0.640515	+	0.767945i	$0.721279\pi$
$450$	−1.45680	−	2.52326i	−0.0686744	−	0.118947i
$451$	5.13452	+	8.89325i	0.241775	+	0.418767i
$452$	0.373308	+	0.646588i	0.0175589	+	0.0304129i
$453$	−0.811594	−	1.40572i	−0.0381320	−	0.0660466i
$454$	10.4740			0.491570
$455$	22.8622			1.07180
$456$	0.657347	+	1.13856i	0.0307831	+	0.0533179i
$457$	12.0137	−	20.8083i	0.561976	−	0.973371i	−0.435348	−	0.900262i	$-0.643375\pi$
$457$	12.0137	−	20.8083i	0.561976	−	0.973371i	0.997324	−	0.0731087i	$-0.0232920\pi$
$458$	2.44831	−	4.24060i	0.114402	−	0.198150i
$459$	−0.741482	−	1.28428i	−0.0346094	−	0.0599452i
$460$	8.71104			0.406154
$461$	38.4560			1.79107			0.895537	−	0.444987i	$-0.146792\pi$
$461$	38.4560			1.79107			0.895537	+	0.444987i	$0.146792\pi$
$462$	2.71903	−	4.70950i	0.126501	−	0.219106i
$463$	−5.19044	−	8.99010i	−0.241220	−	0.417805i	0.719842	−	0.694138i	$-0.244214\pi$
$463$	−5.19044	−	8.99010i	−0.241220	−	0.417805i	−0.961062	+	0.276333i	$0.910881\pi$
$464$	3.34535			0.155304
$465$	−0.502826	+	0.870921i	−0.0233180	+	0.0403880i
$466$	−15.5018			−0.718106
$467$	19.5174	+	33.8052i	0.903159	+	1.56432i	0.823369	+	0.567506i	$0.192092\pi$
$467$	19.5174	+	33.8052i	0.903159	+	1.56432i	0.0797898	+	0.996812i	$0.474575\pi$
$468$	−17.6907			−0.817754
$469$	4.59293	+	30.4765i	0.212082	+	1.40727i
$470$	−12.1950			−0.562511
$471$	−1.99676	−	3.45849i	−0.0920059	−	0.159359i
$472$	−8.50495			−0.391472
$473$	14.2942	−	24.7582i	0.657247	−	1.13839i
$474$	−2.28843			−0.105111
$475$	−2.23643	−	3.87360i	−0.102614	−	0.177733i
$476$	−1.60624	+	2.78210i	−0.0736220	+	0.127517i
$477$	32.3481			1.48112
$478$	4.31865			0.197531
$479$	4.72042	+	8.17601i	0.215682	+	0.373571i	0.953483	−	0.301446i	$-0.0974694\pi$
$479$	4.72042	+	8.17601i	0.215682	+	0.373571i	−0.737802	+	0.675018i	$0.764136\pi$
$480$	−0.146964	+	0.254549i	−0.00670795	+	0.0116185i
$481$	3.12895	−	5.41950i	0.142668	−	0.247108i
$482$	1.10542	+	1.91464i	0.0503503	+	0.0872092i
$483$	9.64082			0.438673
$484$	13.1435			0.597433
$485$	−6.43873	−	11.1522i	−0.292368	−	0.506396i
$486$	3.81676	+	6.61082i	0.173132	+	0.299873i
$487$	−2.22657	−	3.85654i	−0.100896	−	0.174756i	0.811158	−	0.584827i	$-0.198837\pi$
$487$	−2.22657	−	3.85654i	−0.100896	−	0.174756i	−0.912054	+	0.410070i	$0.865504\pi$
$488$	−2.27747	−	3.94469i	−0.103096	−	0.178568i
$489$	−0.449560	+	0.778662i	−0.0203298	+	0.0352123i
$490$	−3.58888	+	6.21612i	−0.162129	+	0.280816i
$491$	−16.1998			−0.731085			−0.365542	−	0.930795i	$-0.619116\pi$
$491$	−16.1998			−0.731085			−0.365542	+	0.930795i	$0.619116\pi$
$492$	−0.307142	−	0.531986i	−0.0138470	−	0.0239838i
$493$	−2.85417			−0.128545
$494$	−27.1581			−1.22190
$495$	7.15816	−	12.3983i	0.321735	−	0.557262i
$496$	−3.42143			−0.153627
$497$	−19.1125	−	33.1038i	−0.857311	−	1.48491i
$498$	0.528950	−	0.916169i	0.0237028	−	0.0410545i
$499$	−1.82545	−	3.16177i	−0.0817184	−	0.141540i	0.822270	−	0.569098i	$-0.192707\pi$
$499$	−1.82545	−	3.16177i	−0.0817184	−	0.141540i	−0.903988	+	0.427558i	$0.859374\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−3.18932	+	5.52406i	−0.142488	+	0.246797i
$502$	−13.8314	+	23.9567i	−0.617327	+	1.06924i
$503$	11.6019	−	20.0951i	0.517303	−	0.895996i	−0.482495	−	0.875899i	$-0.660269\pi$
$503$	11.6019	−	20.0951i	0.517303	−	0.895996i	0.999798	−	0.0200969i	$-0.00639747\pi$
$504$	5.48535	−	9.50091i	0.244337	−	0.423204i
$505$	−3.79523	+	6.57354i	−0.168886	+	0.292519i
$506$	21.4013	+	37.0682i	0.951405	+	1.64788i
$507$	−3.50749	+	6.07514i	−0.155773	+	0.269807i
$508$	2.41818	+	4.18841i	0.107289	+	0.185831i
$509$	19.1287			0.847867			0.423933	−	0.905693i	$-0.360649\pi$
$509$	19.1287			0.847867			0.423933	+	0.905693i	$0.360649\pi$
$510$	0.125386	−	0.217174i	0.00555217	−	0.00961664i
$511$	−23.8065			−1.05314
$512$	−1.00000			−0.0441942
$513$	3.88729	+	6.73299i	0.171628	+	0.297269i
$514$	0.778663			0.0343453
$515$	7.91855	−	13.7153i	0.348933	−	0.604370i
$516$	−0.855065	+	1.48102i	−0.0376421	+	0.0651981i
$517$	−29.9606	−	51.8933i	−1.31767	−	2.28226i
$518$	1.94038	+	3.36084i	0.0852555	+	0.147667i
$519$	−0.521587	−	0.903415i	−0.0228951	−	0.0396555i
$520$	−3.03588	−	5.25830i	−0.133132	−	0.230592i
$521$	−25.1550			−1.10206			−0.551030	−	0.834485i	$-0.685765\pi$
$521$	−25.1550			−1.10206			−0.551030	+	0.834485i	$0.685765\pi$
$522$	9.74703			0.426616
$523$	−22.4324	−	38.8541i	−0.980900	−	1.69897i	−0.658901	−	0.752229i	$-0.728979\pi$
$523$	−22.4324	−	38.8541i	−0.980900	−	1.69897i	−0.321999	−	0.946740i	$-0.604355\pi$
$524$	−5.57569	+	9.65737i	−0.243575	+	0.421884i
$525$	0.553368	−	0.958462i	0.0241510	−	0.0418307i
$526$	−1.70907	−	2.96019i	−0.0745189	−	0.129070i
$527$	2.91908			0.127157
$528$	−1.44424			−0.0628527
$529$	−26.4411	+	45.7974i	−1.14961	+	1.99119i
$530$	5.55121	+	9.61498i	0.241129	+	0.417648i
$531$	−24.7801			−1.07536
$532$	8.42090	−	14.5854i	0.365092	−	0.632358i
$533$	12.6895			0.549643
$534$	0.938366	+	1.62530i	0.0406071	+	0.0703335i
$535$	16.1944			0.700143
$536$	6.39967	−	5.10335i	0.276424	−	0.220431i
$537$	−3.11920			−0.134604
$538$	0.959400	+	1.66173i	0.0413627	+	0.0716423i
$539$	−35.2687			−1.51913
$540$	−0.869086	+	1.50530i	−0.0373995	+	0.0647778i
$541$	−32.0762			−1.37906			−0.689531	−	0.724256i	$-0.742183\pi$
$541$	−32.0762			−1.37906			−0.689531	+	0.724256i	$0.742183\pi$
$542$	−0.670115	−	1.16067i	−0.0287839	−	0.0498552i
$543$	0.737083	−	1.27667i	0.0316313	−	0.0547870i
$544$	0.853174			0.0365795
$545$	0.560415			0.0240056
$546$	−3.35992	−	5.81955i	−0.143791	−	0.249054i
$547$	−11.4860	+	19.8944i	−0.491108	+	0.850624i	−0.999948	−	0.0102376i	$-0.996741\pi$
$547$	−11.4860	+	19.8944i	−0.491108	+	0.850624i	0.508840	+	0.860861i	$0.330075\pi$
$548$	−8.42801	+	14.5977i	−0.360027	+	0.623584i
$549$	−6.63564	−	11.4933i	−0.283202	−	0.490520i
$550$	4.91361			0.209517
$551$	14.9633			0.637456
$552$	−1.28021	−	2.21738i	−0.0544893	−	0.0943782i
$553$	14.6578	+	25.3881i	0.623315	+	1.07961i
$554$	−3.38899	−	5.86991i	−0.143985	−	0.249389i
$555$	−0.151469	−	0.262352i	−0.00642950	−	0.0111362i
$556$	−5.59106	+	9.68400i	−0.237114	+	0.410693i
$557$	−17.1606	+	29.7230i	−0.727118	+	1.25940i	0.230979	+	0.972959i	$0.425807\pi$
$557$	−17.1606	+	29.7230i	−0.727118	+	1.25940i	−0.958096	+	0.286446i	$0.907526\pi$
$558$	−9.96870			−0.422009
$559$	−17.6634	−	30.5939i	−0.747081	−	1.29398i
$560$	3.76534			0.159114
$561$	1.23219			0.0520232
$562$	−6.48824	+	11.2380i	−0.273690	+	0.474045i
$563$	−21.9578			−0.925410			−0.462705	−	0.886512i	$-0.653121\pi$
$563$	−21.9578			−0.925410			−0.462705	+	0.886512i	$0.653121\pi$
$564$	1.79222	+	3.10421i	0.0754659	+	0.130711i
$565$	−0.373308	+	0.646588i	−0.0157052	+	0.0272022i
$566$	11.5185	+	19.9506i	0.484157	+	0.838585i
$567$	15.4942	−	26.8368i	0.650696	−	1.12704i
$568$	−5.07590	+	8.79171i	−0.212980	+	0.368892i
$569$	2.99526	−	5.18795i	0.125568	−	0.217490i	−0.796387	−	0.604788i	$-0.793258\pi$
$569$	2.99526	−	5.18795i	0.125568	−	0.217490i	0.921955	+	0.387297i	$0.126591\pi$
$570$	−0.657347	+	1.13856i	−0.0275333	+	0.0476890i
$571$	0.383528	−	0.664290i	0.0160501	−	0.0277997i	−0.857889	−	0.513835i	$-0.828224\pi$
$571$	0.383528	−	0.664290i	0.0160501	−	0.0277997i	0.873939	+	0.486036i	$0.161558\pi$
$572$	14.9171	−	25.8372i	0.623717	−	1.08031i
$573$	1.35339	+	2.34413i	0.0565385	+	0.0979276i
$574$	−3.93462	+	6.81497i	−0.164228	+	0.284451i
$575$	4.35552	+	7.54398i	0.181638	+	0.314606i
$576$	−2.91361			−0.121400
$577$	−7.26957	+	12.5913i	−0.302636	+	0.524182i	−0.976732	−	0.214462i	$-0.931200\pi$
$577$	−7.26957	+	12.5913i	−0.302636	+	0.524182i	0.674096	+	0.738644i	$0.264533\pi$
$578$	16.2721			0.676830
$579$	1.07558			0.0446997
$580$	1.67267	+	2.89716i	0.0694540	+	0.120298i
$581$	−13.5522			−0.562238
$582$	−1.89252	+	3.27794i	−0.0784475	+	0.135875i
$583$	−27.2765	+	47.2442i	−1.12968	+	1.95666i
$584$	3.16127	+	5.47548i	0.130814	+	0.226577i
$585$	−8.84537	−	15.3206i	−0.365711	−	0.633430i
$586$	4.19453	+	7.26514i	0.173274	+	0.300120i
$587$	−0.862285	−	1.49352i	−0.0355903	−	0.0616442i	0.847682	−	0.530505i	$-0.177998\pi$
$587$	−0.862285	−	1.49352i	−0.0355903	−	0.0616442i	−0.883272	+	0.468861i	$0.844664\pi$
$588$	2.10974			0.0870042
$589$	−15.3036			−0.630572
$590$	−4.25248	−	7.36550i	−0.175072	−	0.303233i
$591$	1.30859	−	2.26655i	0.0538282	−	0.0932332i
$592$	0.515328	−	0.892573i	0.0211798	−	0.0366845i
$593$	−11.9463	−	20.6915i	−0.490574	−	0.849699i	0.509367	−	0.860549i	$-0.329880\pi$
$593$	−11.9463	−	20.6915i	−0.490574	−	0.849699i	−0.999941	+	0.0108502i	$0.996546\pi$
$594$	−8.54069			−0.350429
$595$	−3.21249			−0.131699
$596$	−10.5257	+	18.2311i	−0.431151	+	0.746775i
$597$	−2.67099	−	4.62629i	−0.109316	−	0.189341i
$598$	52.8914			2.16289
$599$	2.50174	−	4.33314i	0.102218	−	0.177047i	−0.810380	−	0.585905i	$-0.800739\pi$
$599$	2.50174	−	4.33314i	0.102218	−	0.177047i	0.912598	+	0.408857i	$0.134073\pi$
$600$	−0.293928			−0.0119995
$601$	14.6017	+	25.2909i	0.595616	+	1.03164i	0.993460	+	0.114184i	$0.0364255\pi$
$601$	14.6017	+	25.2909i	0.595616	+	1.03164i	−0.397843	+	0.917453i	$0.630241\pi$
$602$	21.9075			0.892883
$603$	18.6461	−	14.8692i	0.759329	−	0.605519i
$604$	5.52241			0.224704
$605$	6.57176	+	11.3826i	0.267180	+	0.462770i
$606$	2.23105			0.0906301
$607$	−12.9163	+	22.3717i	−0.524257	+	0.908041i	0.475344	+	0.879800i	$0.342324\pi$
$607$	−12.9163	+	22.3717i	−0.524257	+	0.908041i	−0.999601	+	0.0282404i	$0.991010\pi$
$608$	−4.47285			−0.181398
$609$	1.85121	+	3.20639i	0.0750148	+	0.129929i
$610$	2.27747	−	3.94469i	0.0922119	−	0.159716i
$611$	−74.0449			−2.99554
$612$	2.48581			0.100483
$613$	−14.5104	−	25.1328i	−0.586070	−	1.01510i	−0.994741	−	0.102421i	$-0.967341\pi$
$613$	−14.5104	−	25.1328i	−0.586070	−	1.01510i	0.408671	−	0.912682i	$-0.365992\pi$
$614$	12.5922	−	21.8104i	0.508182	−	0.880197i
$615$	0.307142	−	0.531986i	0.0123852	−	0.0214518i
$616$	9.25069	+	16.0227i	0.372721	+	0.645572i
$617$	−32.4899			−1.30799			−0.653997	−	0.756497i	$-0.726909\pi$
$617$	−32.4899			−1.30799			−0.653997	+	0.756497i	$0.726909\pi$
$618$	−4.65496			−0.187250
$619$	4.86902	+	8.43339i	0.195702	+	0.338967i	0.947131	−	0.320848i	$-0.103968\pi$
$619$	4.86902	+	8.43339i	0.195702	+	0.338967i	−0.751428	+	0.659815i	$0.770635\pi$
$620$	−1.71072	−	2.96305i	−0.0687040	−	0.118999i
$621$	−7.57064	−	13.1127i	−0.303799	−	0.526196i
$622$	16.7431	+	28.9999i	0.671337	+	1.16279i
$623$	12.0209	−	20.8207i	0.481606	−	0.834166i
$624$	−0.892329	+	1.54556i	−0.0357218	+	0.0618719i
$625$	1.00000			0.0400000
$626$	−1.24193	−	2.15108i	−0.0496375	−	0.0859746i
$627$	−6.45989			−0.257983
$628$	13.5868			0.542171
$629$	−0.439664	+	0.761520i	−0.0175306	+	0.0303638i
$630$	10.9707			0.437083
$631$	−10.0835	−	17.4652i	−0.401419	−	0.695278i	0.592479	−	0.805586i	$-0.298149\pi$
$631$	−10.0835	−	17.4652i	−0.401419	−	0.695278i	−0.993897	+	0.110309i	$0.964816\pi$
$632$	3.89284	−	6.74260i	0.154849	−	0.268206i
$633$	1.66948	+	2.89162i	0.0663557	+	0.114932i
$634$	−3.33497	+	5.77635i	−0.132449	+	0.229408i
$635$	−2.41818	+	4.18841i	−0.0959625	+	0.166212i
$636$	1.63165	−	2.82611i	0.0646993	−	0.112062i
$637$	−21.7908	+	37.7428i	−0.863384	+	1.49542i
$638$	−8.21887	+	14.2355i	−0.325388	+	0.563589i
$639$	−14.7892	+	25.6156i	−0.585051	+	1.01334i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−19.1907	+	33.2392i	−0.757986	+	1.31287i	0.185890	+	0.982571i	$0.440483\pi$
$641$	−19.1907	+	33.2392i	−0.757986	+	1.31287i	−0.943876	+	0.330300i	$0.892850\pi$
$642$	−2.37998	−	4.12225i	−0.0939304	−	0.162692i
$643$	20.7686			0.819032			0.409516	−	0.912303i	$-0.365698\pi$
$643$	20.7686			0.819032			0.409516	+	0.912303i	$0.365698\pi$
$644$	−16.4000	+	28.4056i	−0.646251	+	1.11934i
$645$	−1.71013			−0.0673363
$646$	3.81612			0.150143
$647$	−6.53671	−	11.3219i	−0.256984	−	0.445110i	0.708448	−	0.705763i	$-0.249396\pi$
$647$	−6.53671	−	11.3219i	−0.256984	−	0.445110i	−0.965433	+	0.260653i	$0.916062\pi$
$648$	−8.22992			−0.323302
$649$	20.8950	−	36.1912i	0.820200	−	1.42063i
$650$	3.03588	−	5.25830i	0.119077	−	0.206248i
$651$	−1.89331	−	3.27931i	−0.0742047	−	0.128526i
$652$	−1.52949	−	2.64916i	−0.0598996	−	0.103749i
$653$	−15.5002	−	26.8471i	−0.606568	−	1.05061i	−0.991802	−	0.127788i	$-0.959212\pi$
$653$	−15.5002	−	26.8471i	−0.606568	−	1.05061i	0.385233	−	0.922819i	$-0.374121\pi$
$654$	−0.0823607	−	0.142653i	−0.00322056	−	0.00557817i
$655$	−11.1514			−0.435720
$656$	2.08992			0.0815976
$657$	9.21069	+	15.9534i	0.359343	+	0.622401i
$658$	22.9590	−	39.7662i	0.895037	−	1.55025i
$659$	−5.30185	+	9.18308i	−0.206531	+	0.357722i	−0.950619	−	0.310359i	$-0.899551\pi$
$659$	−5.30185	+	9.18308i	−0.206531	+	0.357722i	0.744089	+	0.668081i	$0.232884\pi$
$660$	−0.722122	−	1.25075i	−0.0281086	−	0.0486855i
$661$	49.4825			1.92465			0.962323	−	0.271909i	$-0.0876548\pi$
$661$	49.4825			1.92465			0.962323	+	0.271909i	$0.0876548\pi$
$662$	12.6919			0.493284
$663$	0.761312	−	1.31863i	0.0295669	−	0.0512114i
$664$	1.79959	+	3.11699i	0.0698378	+	0.120963i
$665$	16.8418			0.653097
$666$	1.50146	−	2.60061i	0.0581805	−	0.100772i
$667$	−29.1415			−1.12836
$668$	−10.8507	−	18.7939i	−0.419826	−	0.727160i
$669$	−2.54445			−0.0983742
$670$	7.61947	+	2.99061i	0.294366	+	0.115537i
$671$	22.3811			0.864014
$672$	−0.553368	−	0.958462i	−0.0213466	−	0.0369735i
$673$	43.1990			1.66520			0.832599	−	0.553877i	$-0.186852\pi$
$673$	43.1990			1.66520			0.832599	+	0.553877i	$0.186852\pi$
$674$	−13.2511	+	22.9516i	−0.510413	+	0.884062i
$675$	−1.73817			−0.0669023
$676$	−11.9332	−	20.6688i	−0.458968	−	0.794956i
$677$	−12.2463	+	21.2111i	−0.470662	+	0.815210i	−0.999437	−	0.0335516i	$-0.989318\pi$
$677$	−12.2463	+	21.2111i	−0.470662	+	0.815210i	0.528775	+	0.848762i	$0.322652\pi$
$678$	0.219451			0.00842796
$679$	48.4880			1.86080
$680$	0.426587	+	0.738870i	0.0163589	+	0.0283344i
$681$	1.53930	−	2.66615i	0.0589862	−	0.102167i
$682$	8.40578	−	14.5592i	0.321874	−	0.557502i
$683$	14.8840	+	25.7799i	0.569522	+	0.986442i	0.996613	+	0.0822328i	$0.0262051\pi$
$683$	14.8840	+	25.7799i	0.569522	+	0.986442i	−0.427091	+	0.904209i	$0.640462\pi$
$684$	−13.0321			−0.498296
$685$	−16.8560			−0.644035
$686$	−0.334657	−	0.579642i	−0.0127773	−	0.0221308i
$687$	−0.719626	−	1.24643i	−0.0274554	−	0.0475542i
$688$	−2.90910	−	5.03871i	−0.110908	−	0.192099i
$689$	33.7056	+	58.3799i	1.28408	+	2.22410i
$690$	1.28021	−	2.21738i	0.0487367	−	0.0844144i
$691$	1.73419	−	3.00370i	0.0659717	−	0.114266i	−0.831153	−	0.556044i	$-0.812319\pi$
$691$	1.73419	−	3.00370i	0.0659717	−	0.114266i	0.897125	+	0.441778i	$0.145652\pi$
$692$	3.54908			0.134916
$693$	26.9529	+	46.6837i	1.02385	+	1.77337i
$694$	22.3326			0.847735
$695$	−11.1821			−0.424162
$696$	0.491645	−	0.851555i	0.0186358	−	0.0322781i
$697$	−1.78306			−0.0675384
$698$	3.75475	+	6.50342i	0.142119	+	0.246158i
$699$	−2.27820	+	3.94596i	−0.0861695	+	0.149250i
$700$	1.88267	+	3.26088i	0.0711582	+	0.123250i
$701$	−23.3554	+	40.4527i	−0.882120	+	1.52788i	−0.0331415	+	0.999451i	$0.510551\pi$
$701$	−23.3554	+	40.4527i	−0.882120	+	1.52788i	−0.848979	+	0.528427i	$0.822782\pi$
$702$	−5.27689	+	9.13983i	−0.199163	+	0.344961i
$703$	2.30498	−	3.99235i	0.0869341	−	0.150574i
$704$	2.45680	−	4.25531i	0.0925943	−	0.160378i
$705$	−1.79222	+	3.10421i	−0.0674988	+	0.116911i
$706$	−16.8189	+	29.1311i	−0.632986	+	1.09636i
$707$	−14.2903	−	24.7516i	−0.537443	−	0.930879i
$708$	−1.24992	+	2.16492i	−0.0469749	+	0.0813629i
$709$	−23.0221	−	39.8754i	−0.864612	−	1.49755i	−0.867432	−	0.497555i	$-0.834231\pi$
$709$	−23.0221	−	39.8754i	−0.864612	−	1.49755i	0.00282069	−	0.999996i	$-0.499102\pi$
$710$	−10.1518			−0.380990
$711$	11.3422	−	19.6453i	0.425366	−	0.736755i
$712$	−6.38502			−0.239289
$713$	29.8042			1.11618
$714$	0.472119	+	0.817734i	0.0176686	+	0.0306029i
$715$	29.8343			1.11574
$716$	5.30607	−	9.19039i	0.198297	−	0.343461i
$717$	0.634686	−	1.09931i	0.0237028	−	0.0410544i
$718$	12.2189	+	21.1638i	0.456006	+	0.789825i
$719$	−18.8000	−	32.5625i	−0.701120	−	1.21438i	−0.968074	−	0.250666i	$-0.919350\pi$
$719$	−18.8000	−	32.5625i	−0.701120	−	1.21438i	0.266954	−	0.963709i	$-0.413983\pi$
$720$	−1.45680	−	2.52326i	−0.0542919	−	0.0940362i
$721$	29.8160	+	51.6428i	1.11041	+	1.92328i
$722$	−1.00641			−0.0374549
$723$	0.649824			0.0241672
$724$	2.50770	+	4.34347i	0.0931981	+	0.161424i
$725$	−1.67267	+	2.89716i	−0.0621216	+	0.107598i
$726$	1.93162	−	3.34567i	0.0716892	−	0.124169i
$727$	23.2881	+	40.3362i	0.863709	+	1.49599i	0.868324	+	0.495998i	$0.165198\pi$
$727$	23.2881	+	40.3362i	0.863709	+	1.49599i	−0.00461500	+	0.999989i	$0.501469\pi$
$728$	22.8622			0.847331
$729$	−22.4461			−0.831336
$730$	−3.16127	+	5.47548i	−0.117004	+	0.202656i
$731$	2.48197	+	4.29890i	0.0917990	+	0.159000i
$732$	−1.33882			−0.0494842
$733$	12.9406	−	22.4137i	0.477971	−	0.827870i	−0.521710	−	0.853123i	$-0.674706\pi$
$733$	12.9406	−	22.4137i	0.477971	−	0.827870i	0.999681	+	0.0252527i	$0.00803905\pi$
$734$	−30.4805			−1.12506
$735$	1.05487	+	1.82709i	0.0389095	+	0.0673932i
$736$	8.71104			0.321093
$737$	5.99358	+	39.7705i	0.220776	+	1.46497i
$738$	6.08920			0.224147
$739$	−4.68527	−	8.11513i	−0.172351	−	0.298520i	0.766891	−	0.641778i	$-0.221803\pi$
$739$	−4.68527	−	8.11513i	−0.172351	−	0.298520i	−0.939241	+	0.343258i	$0.888470\pi$
$740$	1.03066			0.0378876
$741$	−3.99126	+	6.91306i	−0.146623	+	0.253958i
$742$	−41.8043			−1.53469
$743$	−16.2799	−	28.1976i	−0.597250	−	1.03447i	−0.993225	−	0.116207i	$-0.962927\pi$
$743$	−16.2799	−	28.1976i	−0.597250	−	1.03447i	0.395975	−	0.918261i	$-0.370407\pi$
$744$	−0.502826	+	0.870921i	−0.0184345	+	0.0319295i
$745$	−21.0515			−0.771266
$746$	8.73645			0.319864
$747$	5.24331	+	9.08168i	0.191843	+	0.332281i
$748$	−2.09608	+	3.63052i	−0.0766403	+	0.132745i
$749$	−30.4886	+	52.8078i	−1.11403	+	1.92955i
$750$	−0.146964	−	0.254549i	−0.00536636	−	0.00929481i
$751$	−39.6914			−1.44836			−0.724180	−	0.689611i	$-0.757781\pi$
$751$	−39.6914			−1.44836			−0.724180	+	0.689611i	$0.757781\pi$
$752$	−12.1950			−0.444704
$753$	4.06544	+	7.04155i	0.148153	+	0.256608i
$754$	10.1561	+	17.5909i	0.369863	+	0.640621i
$755$	2.76120	+	4.78254i	0.100490	+	0.174055i
$756$	−3.27240	−	5.66796i	−0.119016	−	0.206142i
$757$	−18.4000	+	31.8698i	−0.668761	+	1.15833i	0.309490	+	0.950903i	$0.399842\pi$
$757$	−18.4000	+	31.8698i	−0.668761	+	1.15833i	−0.978251	+	0.207425i	$0.933492\pi$
$758$	−9.94781	+	17.2301i	−0.361321	+	0.625826i
$759$	12.5809			0.456657
$760$	−2.23643	−	3.87360i	−0.0811237	−	0.140510i
$761$	−26.2664			−0.952157			−0.476079	−	0.879403i	$-0.657942\pi$
$761$	−26.2664			−0.952157			−0.476079	+	0.879403i	$0.657942\pi$
$762$	1.42154			0.0514969
$763$	−1.05508	+	1.82745i	−0.0381963	+	0.0661580i
$764$	−9.20898			−0.333169
$765$	1.24291	+	2.15278i	0.0449374	+	0.0778338i
$766$	0.982910	−	1.70245i	0.0355140	−	0.0615120i
$767$	−25.8200	−	44.7216i	−0.932307	−	1.61480i
$768$	−0.146964	+	0.254549i	−0.00530310	+	0.00918524i
$769$	1.21323	−	2.10137i	0.0437501	−	0.0757773i	−0.843321	−	0.537410i	$-0.819403\pi$
$769$	1.21323	−	2.10137i	0.0437501	−	0.0757773i	0.887071	+	0.461633i	$0.152736\pi$
$770$	−9.25069	+	16.0227i	−0.333372	+	0.577417i
$771$	0.114435	−	0.198208i	0.00412128	−	0.00713827i
$772$	−1.82967	+	3.16909i	−0.0658513	+	0.114058i
$773$	26.6011	−	46.0744i	0.956774	−	1.65718i	0.226519	−	0.974007i	$-0.427265\pi$
$773$	26.6011	−	46.0744i	0.956774	−	1.65718i	0.730255	−	0.683175i	$-0.239401\pi$
$774$	−8.47598	−	14.6808i	−0.304663	−	0.527691i
$775$	1.71072	−	2.96305i	0.0614507	−	0.106436i
$776$	−6.43873	−	11.1522i	−0.231137	−	0.400341i
$777$	1.14066			0.0409211
$778$	14.3435	−	24.8437i	0.514240	−	0.890689i
$779$	9.34790			0.334923
$780$	−1.78466			−0.0639010
$781$	−24.9410	−	43.1990i	−0.892458	−	1.54578i
$782$	−7.43203			−0.265769
$783$	2.90740	−	5.03576i	0.103902	−	0.179963i
$784$	−3.58888	+	6.21612i	−0.128174	+	0.222004i
$785$	6.79338	+	11.7665i	0.242466	+	0.419963i
$786$	1.63885	+	2.83857i	0.0584558	+	0.101248i
$787$	22.4318	+	38.8529i	0.799606	+	1.38496i	0.919873	+	0.392216i	$0.128291\pi$
$787$	22.4318	+	38.8529i	0.799606	+	1.38496i	−0.120268	+	0.992742i	$0.538375\pi$
$788$	4.45209	+	7.71124i	0.158599	+	0.274702i
$789$	−1.00468			−0.0357677
$790$	7.78568			0.277002
$791$	−1.40563	−	2.43462i	−0.0499784	−	0.0865652i
$792$	7.15816	−	12.3983i	0.254354	−	0.440554i
$793$	13.8282	−	23.9512i	0.491055	−	0.850532i
$794$	−16.8293	−	29.1493i	−0.597251	−	1.03447i
$795$	3.26331			0.115738
$796$	18.1745			0.644177
$797$	7.06426	−	12.2357i	0.250229	−	0.433409i	−0.713360	−	0.700798i	$-0.752827\pi$
$797$	7.06426	−	12.2357i	0.250229	−	0.433409i	0.963589	+	0.267389i	$0.0861608\pi$
$798$	−2.47513	−	4.28706i	−0.0876188	−	0.151760i
$799$	10.4044			0.368082
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−18.6034			−0.657320
$802$	0.382530	+	0.662562i	0.0135076	+	0.0233959i
$803$	−31.0665			−1.09631
$804$	−0.358531	−	2.37904i	−0.0126444	−	0.0839021i
$805$	−32.8000			−1.15605
$806$	−10.3871	−	17.9909i	−0.365869	−	0.633703i
$807$	0.563988			0.0198533
$808$	−3.79523	+	6.57354i	−0.133516	+	0.231256i
$809$	−25.9908			−0.913787			−0.456894	−	0.889521i	$-0.651038\pi$
$809$	−25.9908			−0.913787			−0.456894	+	0.889521i	$0.651038\pi$
$810$	−4.11496	−	7.12732i	−0.144585	−	0.250429i
$811$	−12.6677	+	21.9410i	−0.444821	+	0.770453i	−0.998040	−	0.0625830i	$-0.980066\pi$
$811$	−12.6677	+	21.9410i	−0.444821	+	0.770453i	0.553218	+	0.833036i	$0.313400\pi$
$812$	−12.5964			−0.442046
$813$	−0.393931			−0.0138158
$814$	2.53212	+	4.38575i	0.0887506	+	0.153721i
$815$	1.52949	−	2.64916i	0.0535758	−	0.0927961i
$816$	0.125386	−	0.217174i	0.00438938	−	0.00760262i
$817$	−13.0120	−	22.5374i	−0.455232	−	0.788484i
$818$	11.0014			0.384655
$819$	66.6116			2.32760
$820$	1.04496	+	1.80992i	0.0364916	+	0.0632052i
$821$	−9.90354	−	17.1534i	−0.345636	−	0.598659i	0.639833	−	0.768514i	$-0.279003\pi$
$821$	−9.90354	−	17.1534i	−0.345636	−	0.598659i	−0.985469	+	0.169855i	$0.945670\pi$
$822$	2.47722	+	4.29068i	0.0864031	+	0.149655i
$823$	17.3176	+	29.9949i	0.603653	+	1.04556i	0.992263	+	0.124155i	$0.0396221\pi$
$823$	17.3176	+	29.9949i	0.603653	+	1.04556i	−0.388610	+	0.921402i	$0.627045\pi$
$824$	7.91855	−	13.7153i	0.275856	−	0.477796i
$825$	0.722122	−	1.25075i	0.0251411	−	0.0435456i
$826$	32.0240			1.11426
$827$	16.7088	+	28.9405i	0.581022	+	1.00636i	0.995359	+	0.0962362i	$0.0306804\pi$
$827$	16.7088	+	28.9405i	0.581022	+	1.00636i	−0.414336	+	0.910124i	$0.635986\pi$
$828$	25.3806			0.882035
$829$	19.2488			0.668537			0.334269	−	0.942478i	$-0.391511\pi$
$829$	19.2488			0.668537			0.334269	+	0.942478i	$0.391511\pi$
$830$	−1.79959	+	3.11699i	−0.0624648	+	0.108192i
$831$	−1.99224			−0.0691099
$832$	−3.03588	−	5.25830i	−0.105250	−	0.182299i
$833$	3.06194	−	5.30343i	0.106090	−	0.183753i
$834$	1.64337	+	2.84640i	0.0569052	+	0.0985626i
$835$	10.8507	−	18.7939i	0.375504	−	0.650391i
$836$	10.9889	−	19.0334i	0.380060	−	0.658283i
$837$	−2.97352	+	5.15028i	−0.102780	+	0.178020i
$838$	7.29746	−	12.6396i	0.252087	−	0.436627i
$839$	1.57185	−	2.72252i	0.0542661	−	0.0939917i	−0.837616	−	0.546259i	$-0.816051\pi$
$839$	1.57185	−	2.72252i	0.0542661	−	0.0939917i	0.891882	+	0.452267i	$0.149385\pi$
$840$	0.553368	−	0.958462i	0.0190930	−	0.0330701i
$841$	8.90432	+	15.4227i	0.307045	+	0.531818i
$842$	5.76822	−	9.99086i	0.198786	−	0.344308i
$843$	1.90707	+	3.30315i	0.0656831	+	0.113766i
$844$	−11.3598			−0.391020
$845$	11.9332	−	20.6688i	0.410513	−	0.711030i
$846$	−35.5313			−1.22159
$847$	−49.4898			−1.70049
$848$	5.55121	+	9.61498i	0.190629	+	0.330180i
$849$	6.77119			0.232387
$850$	−0.426587	+	0.738870i	−0.0146318	+	0.0253430i
$851$	−4.48904	+	7.77525i	−0.153882	+	0.266532i
$852$	1.49195	+	2.58413i	0.0511132	+	0.0885307i
$853$	−24.7082	−	42.7959i	−0.845994	−	1.46530i	−0.884755	−	0.466056i	$-0.845675\pi$
$853$	−24.7082	−	42.7959i	−0.845994	−	1.46530i	0.0387616	−	0.999248i	$-0.487659\pi$
$854$	8.57542	+	14.8531i	0.293445	+	0.508261i
$855$	−6.51607	−	11.2862i	−0.222845	−	0.385978i
$856$	16.1944			0.553511
$857$	11.7664			0.401932			0.200966	−	0.979598i	$-0.435592\pi$
$857$	11.7664			0.401932			0.200966	+	0.979598i	$0.435592\pi$
$858$	−4.38456	−	7.59427i	−0.149686	−	0.259264i
$859$	−5.19062	+	8.99041i	−0.177102	+	0.306749i	−0.940887	−	0.338722i	$-0.890005\pi$
$859$	−5.19062	+	8.99041i	−0.177102	+	0.306749i	0.763785	+	0.645471i	$0.223339\pi$
$860$	2.90910	−	5.03871i	0.0991995	−	0.171819i
$861$	1.15649	+	2.00311i	0.0394132	+	0.0682657i
$862$	27.3690			0.932193
$863$	−30.4962			−1.03810			−0.519051	−	0.854743i	$-0.673715\pi$
$863$	−30.4962			−1.03810			−0.519051	+	0.854743i	$0.673715\pi$
$864$	−0.869086	+	1.50530i	−0.0295669	+	0.0512114i
$865$	1.77454	+	3.07360i	0.0603362	+	0.104505i
$866$	−18.1025			−0.615147
$867$	2.39141	−	4.14204i	0.0812165	−	0.140671i
$868$	12.8828			0.437272
$869$	19.1279	+	33.1305i	0.648869	+	1.12387i
$870$	0.983290			0.0333367
$871$	46.2636	+	18.1583i	1.56758	+	0.615269i
$872$	0.560415			0.0189781
$873$	−18.7599	−	32.4932i	−0.634928	−	1.09973i
$874$	38.9632			1.31795
$875$	−1.88267	+	3.26088i	−0.0636458	+	0.110238i
$876$	1.85837			0.0627884
$877$	−14.7924	−	25.6211i	−0.499502	−	0.865163i	0.500498	−	0.865738i	$-0.333150\pi$
$877$	−14.7924	−	25.6211i	−0.499502	−	0.865163i	−1.00000		0.000574729i	$0.999817\pi$
$878$	0.101583	−	0.175947i	0.00342827	−	0.00593793i
$879$	2.46577			0.0831685
$880$	4.91361			0.165638
$881$	−12.7727	−	22.1230i	−0.430324	−	0.745342i	0.566577	−	0.824008i	$-0.308267\pi$
$881$	−12.7727	−	22.1230i	−0.430324	−	0.745342i	−0.996901	+	0.0786662i	$0.974934\pi$
$882$	−10.4566	+	18.1113i	−0.352091	+	0.609840i
$883$	21.4177	−	37.0965i	0.720762	−	1.24840i	−0.239932	−	0.970790i	$-0.577125\pi$
$883$	21.4177	−	37.0965i	0.720762	−	1.24840i	0.960695	−	0.277607i	$-0.0895414\pi$
$884$	2.59014	+	4.48625i	0.0871157	+	0.150889i
$885$	−2.49984			−0.0840312
$886$	−32.4675			−1.09077
$887$	10.0906	+	17.4775i	0.338810	+	0.586836i	0.984209	−	0.177009i	$-0.0566423\pi$
$887$	10.0906	+	17.4775i	0.338810	+	0.586836i	−0.645399	+	0.763846i	$0.723309\pi$
$888$	−0.151469	−	0.262352i	−0.00508297	−	0.00880395i
$889$	−9.10525	−	15.7708i	−0.305380	−	0.528934i
$890$	−3.19251	−	5.52959i	−0.107013	−	0.185352i
$891$	20.2193	−	35.0209i	0.677372	−	1.17324i
$892$	4.32837	−	7.49695i	0.144924	−	0.251016i
$893$	−54.5462			−1.82532
$894$	3.09380	+	5.35862i	0.103472	+	0.179219i
$895$	10.6121			0.354725
$896$	3.76534			0.125791
$897$	7.77312	−	13.4634i	0.259537	−	0.449531i
$898$	−41.7570			−1.39345
$899$	5.72294	+	9.91243i	0.190871	+	0.330598i
$900$	1.45680	−	2.52326i	0.0485601	−	0.0841086i
$901$	−4.73615	−	8.20325i	−0.157784	−	0.273290i
$902$	−5.13452	+	8.89325i	−0.170961	+	0.296113i
$903$	3.21961	−	5.57652i	0.107142	−	0.185575i
$904$	−0.373308	+	0.646588i	−0.0124160	+	0.0215052i
$905$	−2.50770	+	4.34347i	−0.0833589	+	0.144382i
$906$	0.811594	−	1.40572i	0.0269634	−	0.0467020i
$907$	8.85001	−	15.3287i	0.293860	−	0.508980i	−0.680859	−	0.732414i	$-0.738393\pi$
$907$	8.85001	−	15.3287i	0.293860	−	0.508980i	0.974719	+	0.223434i	$0.0717268\pi$
$908$	5.23701	+	9.07077i	0.173796	+	0.301024i
$909$	−11.0578	+	19.1527i	−0.366765	+	0.635255i
$910$	11.4311	+	19.7993i	0.378938	+	0.656340i
$911$	35.2947			1.16937			0.584683	−	0.811262i	$-0.301219\pi$
$911$	35.2947			1.16937			0.584683	+	0.811262i	$0.301219\pi$
$912$	−0.657347	+	1.13856i	−0.0217669	+	0.0377015i
$913$	−17.6850			−0.585288
$914$	24.0273			0.794754
$915$	−0.669410	−	1.15945i	−0.0221300	−	0.0383303i
$916$	4.89662			0.161789
$917$	20.9943	−	36.3632i	0.693294	−	1.20082i
$918$	0.741482	−	1.28428i	0.0244725	−	0.0423877i
$919$	4.58463	+	7.94082i	0.151233	+	0.261943i	0.931681	−	0.363277i	$-0.118342\pi$
$919$	4.58463	+	7.94082i	0.151233	+	0.261943i	−0.780448	+	0.625221i	$0.785009\pi$
$920$	4.35552	+	7.54398i	0.143597	+	0.248718i
$921$	−3.70121	−	6.41068i	−0.121959	−	0.211239i
$922$	19.2280	+	33.3039i	0.633240	+	1.09680i
$923$	−61.6393			−2.02888
$924$	5.43807			0.178899
$925$	0.515328	+	0.892573i	0.0169439	+	0.0293476i
$926$	5.19044	−	8.99010i	0.170568	−	0.295433i
$927$	23.0715	−	39.9611i	0.757769	−	1.31249i
$928$	1.67267	+	2.89716i	0.0549082	+	0.0951039i
$929$	−16.8767			−0.553708			−0.276854	−	0.960912i	$-0.589292\pi$
$929$	−16.8767			−0.553708			−0.276854	+	0.960912i	$0.589292\pi$
$930$	−1.00565			−0.0329767
$931$	−16.0525	+	27.8038i	−0.526100	+	0.911232i
$932$	−7.75089	−	13.4249i	−0.253889	−	0.439749i
$933$	9.84251			0.322229
$934$	−19.5174	+	33.8052i	−0.638630	+	1.10614i
$935$	−4.19216			−0.137098
$936$	−8.84537	−	15.3206i	−0.289120	−	0.500770i
$937$	14.9529			0.488490			0.244245	−	0.969713i	$-0.421460\pi$
$937$	14.9529			0.488490			0.244245	+	0.969713i	$0.421460\pi$
$938$	−24.0969	+	19.2158i	−0.786793	+	0.627419i
$939$	−0.730075			−0.0238251
$940$	−6.09748	−	10.5611i	−0.198878	−	0.344466i
$941$	−3.16916			−0.103312			−0.0516559	−	0.998665i	$-0.516450\pi$
$941$	−3.16916			−0.103312			−0.0516559	+	0.998665i	$0.516450\pi$
$942$	1.99676	−	3.45849i	0.0650580	−	0.112684i
$943$	−18.2054			−0.592848
$944$	−4.25248	−	7.36550i	−0.138406	−	0.239727i
$945$	3.27240	−	5.66796i	0.106451	−	0.184379i
$946$	28.5884			0.929488
$947$	−30.9290			−1.00506			−0.502529	−	0.864560i	$-0.667597\pi$
$947$	−30.9290			−1.00506			−0.502529	+	0.864560i	$0.667597\pi$
$948$	−1.14421	−	1.98183i	−0.0371623	−	0.0643670i
$949$	−19.1945	+	33.2458i	−0.623079	+	1.07920i
$950$	2.23643	−	3.87360i	0.0725593	−	0.125676i
$951$	0.980241	+	1.69783i	0.0317865	+	0.0550558i
$952$	−3.21249			−0.104117
$953$	52.1525			1.68939			0.844693	−	0.535251i	$-0.179783\pi$
$953$	52.1525			1.68939			0.844693	+	0.535251i	$0.179783\pi$
$954$	16.1740	+	28.0143i	0.523654	+	0.906995i
$955$	−4.60449	−	7.97521i	−0.148998	−	0.258072i
$956$	2.15933	+	3.74006i	0.0698376	+	0.120962i
$957$	2.41575	+	4.18420i	0.0780901	+	0.135256i
$958$	−4.72042	+	8.17601i	−0.152510	+	0.264155i
$959$	31.7343	−	54.9654i	1.02475	−	1.77493i
$960$	−0.293928			−0.00948647
$961$	9.64691	+	16.7089i	0.311191	+	0.538998i
$962$	6.25790			0.201763
$963$	47.1840			1.52048
$964$	−1.10542	+	1.91464i	−0.0356030	+	0.0616663i
$965$	−3.65934			−0.117798
$966$	4.82041	+	8.34920i	0.155094	+	0.268631i
$967$	18.5008	−	32.0443i	0.594946	−	1.03048i	−0.398609	−	0.917121i	$-0.630507\pi$
$967$	18.5008	−	32.0443i	0.594946	−	1.03048i	0.993555	−	0.113355i	$-0.0361597\pi$
$968$	6.57176	+	11.3826i	0.211225	+	0.365852i
$969$	0.560832	−	0.971389i	0.0180165	−	0.0312055i
$970$	6.43873	−	11.1522i	0.206735	−	0.358076i
$971$	3.36263	−	5.82425i	0.107912	−	0.186909i	−0.807012	−	0.590535i	$-0.798917\pi$
$971$	3.36263	−	5.82425i	0.107912	−	0.186909i	0.914924	+	0.403626i	$0.132250\pi$
$972$	−3.81676	+	6.61082i	−0.122423	+	0.212042i
$973$	21.0522	−	36.4635i	0.674903	−	1.16897i
$974$	2.22657	−	3.85654i	0.0713440	−	0.123571i
$975$	−0.892329	−	1.54556i	−0.0285774	−	0.0494975i
$976$	2.27747	−	3.94469i	0.0728999	−	0.126266i
$977$	−19.8662	−	34.4093i	−0.635576	−	1.10085i	−0.986393	−	0.164406i	$-0.947429\pi$
$977$	−19.8662	−	34.4093i	−0.635576	−	1.10085i	0.350816	−	0.936444i	$-0.385904\pi$
$978$	−0.899121			−0.0287507
$979$	15.6867	−	27.1702i	0.501350	−	0.868364i
$980$	−7.17776			−0.229285
$981$	1.63283			0.0521322
$982$	−8.09988	−	14.0294i	−0.258477	−	0.447696i
$983$	−14.8427			−0.473409			−0.236704	−	0.971582i	$-0.576067\pi$
$983$	−14.8427			−0.473409			−0.236704	+	0.971582i	$0.576067\pi$
$984$	0.307142	−	0.531986i	0.00979134	−	0.0169591i
$985$	−4.45209	+	7.71124i	−0.141855	+	0.245701i
$986$	−1.42708	−	2.47178i	−0.0454476	−	0.0787175i
$987$	−6.74830	−	11.6884i	−0.214801	−	0.372046i
$988$	−13.5791	−	23.5196i	−0.432007	−	0.748259i
$989$	25.3413	+	43.8924i	0.805807	+	1.39570i
$990$	14.3163			0.455002
$991$	−8.70854			−0.276636			−0.138318	−	0.990388i	$-0.544170\pi$
$991$	−8.70854			−0.276636			−0.138318	+	0.990388i	$0.544170\pi$
$992$	−1.71072	−	2.96305i	−0.0543153	−	0.0940768i
$993$	1.86525	−	3.23070i	0.0591918	−	0.102523i
$994$	19.1125	−	33.1038i	0.606210	−	1.04999i
$995$	9.08723	+	15.7395i	0.288085	+	0.498977i
$996$	1.05790			0.0335209
$997$	14.0850			0.446077			0.223038	−	0.974810i	$-0.428402\pi$
$997$	14.0850			0.446077			0.223038	+	0.974810i	$0.428402\pi$
$998$	1.82545	−	3.16177i	0.0577836	−	0.100084i
$999$	−0.895728	−	1.55145i	−0.0283396	−	0.0490856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.j.171.4	✓	12
67.29	even	3	inner	670.2.e.j.431.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.j.171.4	✓	12	1.1	even	1	trivial
670.2.e.j.431.4	yes	12	67.29	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +0.293928 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.146964 + 0.254549i) q^{6} +(1.88267 - 3.26088i) q^{7} -1.00000 q^{8} -2.91361 q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +0.293928 q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.146964 + 0.254549i) q^{6} +(1.88267 - 3.26088i) q^{7} -1.00000 q^{8} -2.91361 q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.45680 - 4.25531i) q^{11} +(-0.146964 + 0.254549i) q^{12} +(-3.03588 - 5.25830i) q^{13} +3.76534 q^{14} -0.293928 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.426587 + 0.738870i) q^{17} +(-1.45680 - 2.52326i) q^{18} +(-2.23643 - 3.87360i) q^{19} +(0.500000 - 0.866025i) q^{20} +(0.553368 - 0.958462i) q^{21} +4.91361 q^{22} +(4.35552 + 7.54398i) q^{23} -0.293928 q^{24} +1.00000 q^{25} +(3.03588 - 5.25830i) q^{26} -1.73817 q^{27} +(1.88267 + 3.26088i) q^{28} +(-1.67267 + 2.89716i) q^{29} +(-0.146964 - 0.254549i) q^{30} +(1.71072 - 2.96305i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.722122 - 1.25075i) q^{33} +(-0.426587 + 0.738870i) q^{34} +(-1.88267 + 3.26088i) q^{35} +(1.45680 - 2.52326i) q^{36} +(0.515328 + 0.892573i) q^{37} +(2.23643 - 3.87360i) q^{38} +(-0.892329 - 1.54556i) q^{39} +1.00000 q^{40} +(-1.04496 + 1.80992i) q^{41} +1.10674 q^{42} +5.81820 q^{43} +(2.45680 + 4.25531i) q^{44} +2.91361 q^{45} +(-4.35552 + 7.54398i) q^{46} +(6.09748 - 10.5611i) q^{47} +(-0.146964 - 0.254549i) q^{48} +(-3.58888 - 6.21612i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.125386 + 0.217174i) q^{51} +6.07176 q^{52} -11.1024 q^{53} +(-0.869086 - 1.50530i) q^{54} +(-2.45680 + 4.25531i) q^{55} +(-1.88267 + 3.26088i) q^{56} +(-0.657347 - 1.13856i) q^{57} -3.34535 q^{58} +8.50495 q^{59} +(0.146964 - 0.254549i) q^{60} +(2.27747 + 3.94469i) q^{61} +3.42143 q^{62} +(-5.48535 + 9.50091i) q^{63} +1.00000 q^{64} +(3.03588 + 5.25830i) q^{65} +1.44424 q^{66} +(-6.39967 + 5.10335i) q^{67} -0.853174 q^{68} +(1.28021 + 2.21738i) q^{69} -3.76534 q^{70} +(5.07590 - 8.79171i) q^{71} +2.91361 q^{72} +(-3.16127 - 5.47548i) q^{73} +(-0.515328 + 0.892573i) q^{74} +0.293928 q^{75} +4.47285 q^{76} +(-9.25069 - 16.0227i) q^{77} +(0.892329 - 1.54556i) q^{78} +(-3.89284 + 6.74260i) q^{79} +(0.500000 + 0.866025i) q^{80} +8.22992 q^{81} -2.08992 q^{82} +(-1.79959 - 3.11699i) q^{83} +(0.553368 + 0.958462i) q^{84} +(-0.426587 - 0.738870i) q^{85} +(2.90910 + 5.03871i) q^{86} +(-0.491645 + 0.851555i) q^{87} +(-2.45680 + 4.25531i) q^{88} +6.38502 q^{89} +(1.45680 + 2.52326i) q^{90} -22.8622 q^{91} -8.71104 q^{92} +(0.502826 - 0.870921i) q^{93} +12.1950 q^{94} +(2.23643 + 3.87360i) q^{95} +(0.146964 - 0.254549i) q^{96} +(6.43873 + 11.1522i) q^{97} +(3.58888 - 6.21612i) q^{98} +(-7.15816 + 12.3983i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9	\( 12 q + 6 q^{2} - 4 q^{3} - 6 q^{4} - 12 q^{5} - 2 q^{6} + 3 q^{7} - 12 q^{8} + 24 q^{9} - 6 q^{10} + 2 q^{12} + 6 q^{14} + 4 q^{15} - 6 q^{16} + 13 q^{17} + 12 q^{18} - 9 q^{19} + 6 q^{20} + 11 q^{21} - 3 q^{23} + 4 q^{24} + 12 q^{25} - 16 q^{27} + 3 q^{28} - 5 q^{29} + 2 q^{30} + 14 q^{31} + 6 q^{32} + 10 q^{33} - 13 q^{34} - 3 q^{35} - 12 q^{36} + 2 q^{37} + 9 q^{38} + 14 q^{39} + 12 q^{40} + 15 q^{41} + 22 q^{42} + 4 q^{43} - 24 q^{45} + 3 q^{46} - 11 q^{47} + 2 q^{48} - 43 q^{49} + 6 q^{50} + 15 q^{51} - 52 q^{53} - 8 q^{54} - 3 q^{56} + 3 q^{57} - 10 q^{58} + 54 q^{59} - 2 q^{60} - 6 q^{61} + 28 q^{62} - 4 q^{63} + 12 q^{64} + 20 q^{66} - 5 q^{67} - 26 q^{68} + 13 q^{69} - 6 q^{70} - 6 q^{71} - 24 q^{72} - 15 q^{73} - 2 q^{74} - 4 q^{75} + 18 q^{76} - 10 q^{77} - 14 q^{78} - 2 q^{79} + 6 q^{80} + 12 q^{81} + 30 q^{82} - 15 q^{83} + 11 q^{84} - 13 q^{85} + 2 q^{86} + 5 q^{87} - 14 q^{89} - 12 q^{90} + 4 q^{91} + 6 q^{92} + 28 q^{93} - 22 q^{94} + 9 q^{95} - 2 q^{96} + 21 q^{97} + 43 q^{98} - 72 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - 4 * q^3 - 6 * q^4 - 12 * q^5 - 2 * q^6 + 3 * q^7 - 12 * q^8 + 24 * q^9 - 6 * q^10 + 2 * q^12 + 6 * q^14 + 4 * q^15 - 6 * q^16 + 13 * q^17 + 12 * q^18 - 9 * q^19 + 6 * q^20 + 11 * q^21 - 3 * q^23 + 4 * q^24 + 12 * q^25 - 16 * q^27 + 3 * q^28 - 5 * q^29 + 2 * q^30 + 14 * q^31 + 6 * q^32 + 10 * q^33 - 13 * q^34 - 3 * q^35 - 12 * q^36 + 2 * q^37 + 9 * q^38 + 14 * q^39 + 12 * q^40 + 15 * q^41 + 22 * q^42 + 4 * q^43 - 24 * q^45 + 3 * q^46 - 11 * q^47 + 2 * q^48 - 43 * q^49 + 6 * q^50 + 15 * q^51 - 52 * q^53 - 8 * q^54 - 3 * q^56 + 3 * q^57 - 10 * q^58 + 54 * q^59 - 2 * q^60 - 6 * q^61 + 28 * q^62 - 4 * q^63 + 12 * q^64 + 20 * q^66 - 5 * q^67 - 26 * q^68 + 13 * q^69 - 6 * q^70 - 6 * q^71 - 24 * q^72 - 15 * q^73 - 2 * q^74 - 4 * q^75 + 18 * q^76 - 10 * q^77 - 14 * q^78 - 2 * q^79 + 6 * q^80 + 12 * q^81 + 30 * q^82 - 15 * q^83 + 11 * q^84 - 13 * q^85 + 2 * q^86 + 5 * q^87 - 14 * q^89 - 12 * q^90 + 4 * q^91 + 6 * q^92 + 28 * q^93 - 22 * q^94 + 9 * q^95 - 2 * q^96 + 21 * q^97 + 43 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more