LMFDB - Embedded newform 85.2.l.a.66.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(26,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("85.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.l (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			66.2
Character	$\chi$	$=$	85.66
Dual form			85.2.l.a.76.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.528855 - 0.528855i) q^{2} +(1.17676 + 2.84096i) q^{3} -1.44062i q^{4} +(-0.923880 + 0.382683i) q^{5} +(0.880118 - 2.12479i) q^{6} +(2.98655 + 1.23707i) q^{7} +(-1.81959 + 1.81959i) q^{8} +(-4.56494 + 4.56494i) q^{9} +O(q^{10})$	\(q+(-0.528855 - 0.528855i) q^{2} +(1.17676 + 2.84096i) q^{3} -1.44062i q^{4} +(-0.923880 + 0.382683i) q^{5} +(0.880118 - 2.12479i) q^{6} +(2.98655 + 1.23707i) q^{7} +(-1.81959 + 1.81959i) q^{8} +(-4.56494 + 4.56494i) q^{9} +(0.690983 + 0.286214i) q^{10} +(1.04667 - 2.52689i) q^{11} +(4.09275 - 1.69527i) q^{12} -4.31833i q^{13} +(-0.925222 - 2.23368i) q^{14} +(-2.17437 - 2.17437i) q^{15} -0.956646 q^{16} +(-3.47152 - 2.22453i) q^{17} +4.82839 q^{18} +(-0.897260 - 0.897260i) q^{19} +(0.551303 + 1.33096i) q^{20} +9.94040i q^{21} +(-1.88990 + 0.782821i) q^{22} +(-0.188421 + 0.454888i) q^{23} +(-7.31061 - 3.02815i) q^{24} +(0.707107 - 0.707107i) q^{25} +(-2.28377 + 2.28377i) q^{26} +(-9.81779 - 4.06666i) q^{27} +(1.78215 - 4.30250i) q^{28} +(-0.410535 + 0.170049i) q^{29} +2.29986i q^{30} +(-2.11561 - 5.10754i) q^{31} +(4.14511 + 4.14511i) q^{32} +8.41047 q^{33} +(0.659477 + 3.01239i) q^{34} -3.23262 q^{35} +(6.57637 + 6.57637i) q^{36} +(4.09469 + 9.88545i) q^{37} +0.949042i q^{38} +(12.2682 - 5.08165i) q^{39} +(0.984756 - 2.37741i) q^{40} +(-2.00526 - 0.830608i) q^{41} +(5.25703 - 5.25703i) q^{42} +(1.52864 - 1.52864i) q^{43} +(-3.64030 - 1.50786i) q^{44} +(2.47053 - 5.96439i) q^{45} +(0.340217 - 0.140922i) q^{46} +8.39597i q^{47} +(-1.12575 - 2.71779i) q^{48} +(2.43940 + 2.43940i) q^{49} -0.747914 q^{50} +(2.23464 - 12.4802i) q^{51} -6.22109 q^{52} +(1.28480 + 1.28480i) q^{53} +(3.04152 + 7.34287i) q^{54} +2.73509i q^{55} +(-7.68527 + 3.18334i) q^{56} +(1.49321 - 3.60494i) q^{57} +(0.307045 + 0.127182i) q^{58} +(-2.13537 + 2.13537i) q^{59} +(-3.13246 + 3.13246i) q^{60} +(11.2928 + 4.67764i) q^{61} +(-1.58230 + 3.82000i) q^{62} +(-19.2806 + 7.98628i) q^{63} -2.47104i q^{64} +(1.65255 + 3.98962i) q^{65} +(-4.44792 - 4.44792i) q^{66} -4.21389 q^{67} +(-3.20471 + 5.00116i) q^{68} -1.51404 q^{69} +(1.70959 + 1.70959i) q^{70} +(-1.48927 - 3.59542i) q^{71} -16.6127i q^{72} +(-5.97807 + 2.47620i) q^{73} +(3.06247 - 7.39347i) q^{74} +(2.84096 + 1.17676i) q^{75} +(-1.29261 + 1.29261i) q^{76} +(6.25188 - 6.25188i) q^{77} +(-9.17555 - 3.80064i) q^{78} +(-2.76355 + 6.67180i) q^{79} +(0.883826 - 0.366093i) q^{80} -13.3100i q^{81} +(0.621223 + 1.49977i) q^{82} +(0.160866 + 0.160866i) q^{83} +14.3204 q^{84} +(4.05856 + 0.726705i) q^{85} -1.61686 q^{86} +(-0.966206 - 0.966206i) q^{87} +(2.69339 + 6.50243i) q^{88} -13.3408i q^{89} +(-4.46085 + 1.84774i) q^{90} +(5.34208 - 12.8969i) q^{91} +(0.655322 + 0.271443i) q^{92} +(12.0207 - 12.0207i) q^{93} +(4.44025 - 4.44025i) q^{94} +(1.17233 + 0.485594i) q^{95} +(-6.89827 + 16.6539i) q^{96} +(-13.6803 + 5.66657i) q^{97} -2.58018i q^{98} +(6.75711 + 16.3131i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 24 q^{9}+O(q^{10}) $ 24 * q - 8 * q^6 - 24 * q^9	$ 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35} - 24 q^{36} + 24 q^{37} + 8 q^{39} + 16 q^{40} + 16 q^{41} - 24 q^{42} + 8 q^{43} + 16 q^{44} + 16 q^{45} + 8 q^{46} + 80 q^{48} + 8 q^{50} - 56 q^{51} - 48 q^{52} + 24 q^{53} - 32 q^{54} + 64 q^{56} + 32 q^{57} - 64 q^{58} + 32 q^{59} + 24 q^{60} + 32 q^{61} - 32 q^{62} - 56 q^{63} + 8 q^{65} + 96 q^{66} + 16 q^{67} - 40 q^{68} + 96 q^{69} - 24 q^{71} - 64 q^{74} - 8 q^{75} - 8 q^{76} + 24 q^{77} - 112 q^{78} - 32 q^{80} - 80 q^{82} - 96 q^{83} - 64 q^{84} - 16 q^{86} - 48 q^{87} - 8 q^{88} - 24 q^{91} + 80 q^{92} + 64 q^{93} + 56 q^{94} - 16 q^{95} - 168 q^{96} - 40 q^{97} - 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$	−0.528855	−	0.528855i	−0.373957	−	0.373957i	0.494959	−	0.868916i	$-0.335183\pi$
$2$	−0.528855	−	0.528855i	−0.373957	−	0.373957i	−0.868916	+	0.494959i	$0.835183\pi$
$3$	1.17676	+	2.84096i	0.679404	+	1.64023i	0.765105	+	0.643906i	$0.222687\pi$
$3$	1.17676	+	2.84096i	0.679404	+	1.64023i	−0.0857002	+	0.996321i	$0.527313\pi$
$4$		−	1.44062i		−	0.720312i
$5$	−0.923880	+	0.382683i	−0.413171	+	0.171141i
$5$	−0.923880	+	0.382683i	−0.413171	+	0.171141i
$6$	0.880118	−	2.12479i	0.359307	−	0.867443i
$7$	2.98655	+	1.23707i	1.12881	+	0.467569i	0.867376	−	0.497653i	$-0.165805\pi$
$7$	2.98655	+	1.23707i	1.12881	+	0.467569i	0.261434	+	0.965221i	$0.415805\pi$
$8$	−1.81959	+	1.81959i	−0.643323	+	0.643323i
$9$	−4.56494	+	4.56494i	−1.52165	+	1.52165i
$10$	0.690983	+	0.286214i	0.218508	+	0.0905089i
$11$	1.04667	−	2.52689i	0.315584	−	0.761886i	−0.683894	−	0.729581i	$-0.739715\pi$
$11$	1.04667	−	2.52689i	0.315584	−	0.761886i	0.999478	−	0.0323052i	$-0.0102849\pi$
$12$	4.09275	−	1.69527i	1.18148	−	0.489383i
$13$		−	4.31833i		−	1.19769i	−0.800865	−	0.598845i	$-0.795627\pi$
$13$		−	4.31833i		−	1.19769i	0.800865	−	0.598845i	$-0.204373\pi$
$14$	−0.925222	−	2.23368i	−0.247276	−	0.596977i
$15$	−2.17437	−	2.17437i	−0.561421	−	0.561421i
$16$	−0.956646			−0.239162
$17$	−3.47152	−	2.22453i	−0.841968	−	0.539528i
$17$	−3.47152	−	2.22453i	−0.841968	−	0.539528i
$18$	4.82839			1.13806
$19$	−0.897260	−	0.897260i	−0.205846	−	0.205846i	0.596653	−	0.802499i	$-0.296497\pi$
$19$	−0.897260	−	0.897260i	−0.205846	−	0.205846i	−0.802499	+	0.596653i	$0.796497\pi$
$20$	0.551303	+	1.33096i	0.123275	+	0.297612i
$21$			9.94040i			2.16917i
$22$	−1.88990	+	0.782821i	−0.402928	+	0.166898i
$23$	−0.188421	+	0.454888i	−0.0392884	+	0.0948506i	−0.942306	−	0.334754i	$-0.891347\pi$
$23$	−0.188421	+	0.454888i	−0.0392884	+	0.0948506i	0.903017	+	0.429604i	$0.141347\pi$
$24$	−7.31061	−	3.02815i	−1.49227	−	0.618119i
$25$	0.707107	−	0.707107i	0.141421	−	0.141421i
$26$	−2.28377	+	2.28377i	−0.447884	+	0.447884i
$27$	−9.81779	−	4.06666i	−1.88943	−	0.782630i
$28$	1.78215	−	4.30250i	0.336795	−	0.813096i
$29$	−0.410535	+	0.170049i	−0.0762345	+	0.0315774i	−0.420475	−	0.907304i	$-0.638137\pi$
$29$	−0.410535	+	0.170049i	−0.0762345	+	0.0315774i	0.344240	+	0.938882i	$0.388137\pi$
$30$			2.29986i			0.419895i
$31$	−2.11561	−	5.10754i	−0.379975	−	0.917342i	−0.991969	−	0.126479i	$-0.959632\pi$
$31$	−2.11561	−	5.10754i	−0.379975	−	0.917342i	0.611994	−	0.790862i	$-0.290368\pi$
$32$	4.14511	+	4.14511i	0.732759	+	0.732759i
$33$	8.41047			1.46408
$34$	0.659477	+	3.01239i	0.113099	+	0.516620i
$35$	−3.23262			−0.546412
$36$	6.57637	+	6.57637i	1.09606	+	1.09606i
$37$	4.09469	+	9.88545i	0.673162	+	1.62516i	0.776205	+	0.630481i	$0.217142\pi$
$37$	4.09469	+	9.88545i	0.673162	+	1.62516i	−0.103043	+	0.994677i	$0.532858\pi$
$38$			0.949042i			0.153955i
$39$	12.2682	−	5.08165i	1.96448	−	0.813715i
$40$	0.984756	−	2.37741i	0.155704	−	0.375902i
$41$	−2.00526	−	0.830608i	−0.313170	−	0.129719i	0.220562	−	0.975373i	$-0.429211\pi$
$41$	−2.00526	−	0.830608i	−0.313170	−	0.129719i	−0.533732	+	0.845654i	$0.679211\pi$
$42$	5.25703	−	5.25703i	0.811178	−	0.811178i
$43$	1.52864	−	1.52864i	0.233115	−	0.233115i	−0.580876	−	0.813992i	$-0.697290\pi$
$43$	1.52864	−	1.52864i	0.233115	−	0.233115i	0.813992	+	0.580876i	$0.197290\pi$
$44$	−3.64030	−	1.50786i	−0.548796	−	0.227319i
$45$	2.47053	−	5.96439i	0.368285	−	0.889118i
$46$	0.340217	−	0.140922i	0.0501622	−	0.0207779i
$47$			8.39597i			1.22468i	0.790595	+	0.612339i	$0.209771\pi$
$47$			8.39597i			1.22468i	−0.790595	+	0.612339i	$0.790229\pi$
$48$	−1.12575	−	2.71779i	−0.162487	−	0.392279i
$49$	2.43940	+	2.43940i	0.348485	+	0.348485i
$50$	−0.747914			−0.105771
$51$	2.23464	−	12.4802i	0.312912	−	1.74758i
$52$	−6.22109			−0.862710
$53$	1.28480	+	1.28480i	0.176481	+	0.176481i	0.789820	−	0.613339i	$-0.210174\pi$
$53$	1.28480	+	1.28480i	0.176481	+	0.176481i	−0.613339	+	0.789820i	$0.710174\pi$
$54$	3.04152	+	7.34287i	0.413898	+	0.999238i
$55$			2.73509i			0.368799i
$56$	−7.68527	+	3.18334i	−1.02699	+	0.425392i
$57$	1.49321	−	3.60494i	0.197781	−	0.477486i
$58$	0.307045	+	0.127182i	0.0403170	+	0.0166999i
$59$	−2.13537	+	2.13537i	−0.278001	+	0.278001i	−0.832311	−	0.554309i	$-0.812982\pi$
$59$	−2.13537	+	2.13537i	−0.278001	+	0.278001i	0.554309	+	0.832311i	$0.312982\pi$
$60$	−3.13246	+	3.13246i	−0.404398	+	0.404398i
$61$	11.2928	+	4.67764i	1.44590	+	0.598910i	0.961220	−	0.275783i	$-0.0889371\pi$
$61$	11.2928	+	4.67764i	1.44590	+	0.598910i	0.484677	+	0.874693i	$0.338937\pi$
$62$	−1.58230	+	3.82000i	−0.200952	+	0.485141i
$63$	−19.2806	+	7.98628i	−2.42913	+	1.00618i
$64$		−	2.47104i		−	0.308880i
$65$	1.65255	+	3.98962i	0.204974	+	0.494851i
$66$	−4.44792	−	4.44792i	−0.547501	−	0.547501i
$67$	−4.21389			−0.514808			−0.257404	−	0.966304i	$-0.582867\pi$
$67$	−4.21389			−0.514808			−0.257404	+	0.966304i	$0.582867\pi$
$68$	−3.20471	+	5.00116i	−0.388629	+	0.606479i
$69$	−1.51404			−0.182269
$70$	1.70959	+	1.70959i	0.204335	+	0.204335i
$71$	−1.48927	−	3.59542i	−0.176744	−	0.426698i	0.810536	−	0.585689i	$-0.199176\pi$
$71$	−1.48927	−	3.59542i	−0.176744	−	0.426698i	−0.987280	+	0.158991i	$0.949176\pi$
$72$		−	16.6127i		−	1.95782i
$73$	−5.97807	+	2.47620i	−0.699680	+	0.289817i	−0.704027	−	0.710173i	$-0.748617\pi$
$73$	−5.97807	+	2.47620i	−0.699680	+	0.289817i	0.00434632	+	0.999991i	$0.498617\pi$
$74$	3.06247	−	7.39347i	0.356005	−	0.859473i
$75$	2.84096	+	1.17676i	0.328045	+	0.135881i
$76$	−1.29261	+	1.29261i	−0.148273	+	0.148273i
$77$	6.25188	−	6.25188i	0.712468	−	0.712468i
$78$	−9.17555	−	3.80064i	−1.03893	−	0.430338i
$79$	−2.76355	+	6.67180i	−0.310923	+	0.750636i	0.688748	+	0.725001i	$0.258161\pi$
$79$	−2.76355	+	6.67180i	−0.310923	+	0.750636i	−0.999671	+	0.0256347i	$0.991839\pi$
$80$	0.883826	−	0.366093i	0.0988147	−	0.0409304i
$81$		−	13.3100i		−	1.47889i
$82$	0.621223	+	1.49977i	0.0686026	+	0.165621i
$83$	0.160866	+	0.160866i	0.0176574	+	0.0176574i	0.715880	−	0.698223i	$-0.246026\pi$
$83$	0.160866	+	0.160866i	0.0176574	+	0.0176574i	−0.698223	+	0.715880i	$0.746026\pi$
$84$	14.3204			1.56248
$85$	4.05856	+	0.726705i	0.440213	+	0.0788222i
$86$	−1.61686			−0.174350
$87$	−0.966206	−	0.966206i	−0.103588	−	0.103588i
$88$	2.69339	+	6.50243i	0.287117	+	0.693161i
$89$		−	13.3408i		−	1.41413i	−0.707150	−	0.707064i	$-0.750019\pi$
$89$		−	13.3408i		−	1.41413i	0.707150	−	0.707064i	$-0.249981\pi$
$90$	−4.46085	+	1.84774i	−0.470215	+	0.194769i
$91$	5.34208	−	12.8969i	0.560002	−	1.35196i
$92$	0.655322	+	0.271443i	0.0683220	+	0.0282999i
$93$	12.0207	−	12.0207i	1.24649	−	1.24649i
$94$	4.44025	−	4.44025i	0.457977	−	0.457977i
$95$	1.17233	+	0.485594i	0.120278	+	0.0498209i
$96$	−6.89827	+	16.6539i	−0.704052	+	1.69973i
$97$	−13.6803	+	5.66657i	−1.38902	+	0.575353i	−0.946879	−	0.321591i	$-0.895782\pi$
$97$	−13.6803	+	5.66657i	−1.38902	+	0.575353i	−0.442145	+	0.896943i	$0.645782\pi$
$98$		−	2.58018i		−	0.260637i
$99$	6.75711	+	16.3131i	0.679115	+	1.63953i
$100$	−1.01868	−	1.01868i	−0.101868	−	0.101868i
$101$	−0.284213			−0.0282803			−0.0141401	−	0.999900i	$-0.504501\pi$
$101$	−0.284213			−0.0282803			−0.0141401	+	0.999900i	$0.504501\pi$
$102$	−7.78201	+	5.41841i	−0.770534	+	0.536503i
$103$	−14.0842			−1.38775			−0.693877	−	0.720093i	$-0.744099\pi$
$103$	−14.0842			−1.38775			−0.693877	+	0.720093i	$0.744099\pi$
$104$	7.85760	+	7.85760i	0.770501	+	0.770501i
$105$	−3.80403	−	9.18373i	−0.371235	−	0.896240i
$106$		−	1.35894i		−	0.131992i
$107$	17.2857	−	7.15995i	1.67107	−	0.692179i	0.672228	−	0.740344i	$-0.265337\pi$
$107$	17.2857	−	7.15995i	1.67107	−	0.692179i	0.998839	+	0.0481649i	$0.0153373\pi$
$108$	−5.85853	+	14.1437i	−0.563738	+	1.36098i
$109$	−3.26202	−	1.35117i	−0.312444	−	0.129419i	0.220951	−	0.975285i	$-0.429084\pi$
$109$	−3.26202	−	1.35117i	−0.312444	−	0.129419i	−0.533395	+	0.845866i	$0.679084\pi$
$110$	1.44647	−	1.44647i	0.137915	−	0.137915i
$111$	−23.2657	+	23.2657i	−2.20828	+	2.20828i
$112$	−2.85707	−	1.18344i	−0.269968	−	0.111824i
$113$	1.08741	−	2.62525i	0.102295	−	0.246963i	−0.864443	−	0.502731i	$-0.832329\pi$
$113$	1.08741	−	2.62525i	0.102295	−	0.246963i	0.966738	+	0.255769i	$0.0823285\pi$
$114$	−2.69619	+	1.11680i	−0.252521	+	0.104598i
$115$		−	0.492367i		−	0.0459134i
$116$	0.244977	+	0.591427i	0.0227456	+	0.0549126i
$117$	19.7129	+	19.7129i	1.82246	+	1.82246i
$118$	2.25860			0.207921
$119$	−7.61598	−	10.9382i	−0.698155	−	1.00270i
$120$	7.91295			0.722350
$121$	2.48852	+	2.48852i	0.226229	+	0.226229i
$122$	−3.49847	−	8.44606i	−0.316737	−	0.764670i
$123$		−	6.67430i		−	0.601801i
$124$	−7.35805	+	3.04780i	−0.660772	+	0.273701i
$125$	−0.382683	+	0.923880i	−0.0342282	+	0.0826343i
$126$	14.4202	+	5.97306i	1.28466	+	0.532122i
$127$	3.86444	−	3.86444i	0.342914	−	0.342914i	−0.514548	−	0.857462i	$-0.672040\pi$
$127$	3.86444	−	3.86444i	0.342914	−	0.342914i	0.857462	+	0.514548i	$0.172040\pi$
$128$	6.98340	−	6.98340i	0.617251	−	0.617251i
$129$	6.14164	+	2.54395i	0.540742	+	0.223983i
$130$	1.23597	−	2.98389i	0.108402	−	0.261705i
$131$	9.21986	−	3.81899i	0.805543	−	0.333667i	0.0583689	−	0.998295i	$-0.481410\pi$
$131$	9.21986	−	3.81899i	0.805543	−	0.333667i	0.747174	+	0.664628i	$0.231410\pi$
$132$		−	12.1163i		−	1.05459i
$133$	−1.56974	−	3.78969i	−0.136114	−	0.328608i
$134$	2.22854	+	2.22854i	0.192516	+	0.192516i
$135$	10.6267			0.914601
$136$	10.3645	−	2.26901i	0.888748	−	0.194566i
$137$	−3.07772			−0.262947			−0.131474	−	0.991320i	$-0.541971\pi$
$137$	−3.07772			−0.262947			−0.131474	+	0.991320i	$0.541971\pi$
$138$	0.800709	+	0.800709i	0.0681609	+	0.0681609i
$139$	−2.56777	−	6.19915i	−0.217796	−	0.525805i	0.776786	−	0.629765i	$-0.216849\pi$
$139$	−2.56777	−	6.19915i	−0.217796	−	0.525805i	−0.994582	+	0.103960i	$0.966849\pi$
$140$			4.65699i			0.393587i
$141$	−23.8526	+	9.88006i	−2.00875	+	0.832051i
$142$	−1.11385	+	2.68907i	−0.0934720	+	0.225661i
$143$	−10.9119	−	4.51988i	−0.912503	−	0.377971i
$144$	4.36704	−	4.36704i	0.363920	−	0.363920i
$145$	0.314210	−	0.314210i	0.0260937	−	0.0260937i
$146$	4.47109	+	1.85198i	0.370030	+	0.153271i
$147$	−4.05963	+	9.80082i	−0.334833	+	0.808358i
$148$	14.2412	−	5.89890i	1.17062	−	0.484887i
$149$			22.9914i			1.88353i	0.336276	+	0.941764i	$0.390833\pi$
$149$			22.9914i			1.88353i	−0.336276	+	0.941764i	$0.609167\pi$
$150$	−0.880118	−	2.12479i	−0.0718613	−	0.173489i
$151$	0.138411	+	0.138411i	0.0112638	+	0.0112638i	0.712716	−	0.701452i	$-0.247465\pi$
$151$	0.138411	+	0.138411i	0.0112638	+	0.0112638i	−0.701452	+	0.712716i	$0.747465\pi$
$152$	3.26530			0.264850
$153$	26.0022	−	5.69244i	2.10215	−	0.460207i
$154$	−6.61268			−0.532865
$155$	3.90914	+	3.90914i	0.313990	+	0.313990i
$156$	−7.32075	−	17.6738i	−0.586129	−	1.41504i
$157$			11.8582i			0.946391i	0.880957	+	0.473196i	$0.156900\pi$
$157$			11.8582i			0.946391i	−0.880957	+	0.473196i	$0.843100\pi$
$158$	4.98993	−	2.06690i	0.396978	−	0.164434i
$159$	−2.13815	+	5.16196i	−0.169567	+	0.409370i
$160$	−5.41585	−	2.24332i	−0.428161	−	0.177350i
$161$	−1.12546	+	1.12546i	−0.0886983	+	0.0886983i
$162$	−7.03907	+	7.03907i	−0.553041	+	0.553041i
$163$	−4.93787	−	2.04533i	−0.386764	−	0.160203i	0.180824	−	0.983515i	$-0.442123\pi$
$163$	−4.93787	−	2.04533i	−0.386764	−	0.160203i	−0.567588	+	0.823312i	$0.692123\pi$
$164$	−1.19659	+	2.88883i	−0.0934382	+	0.225580i
$165$	−7.77026	+	3.21855i	−0.604914	+	0.250564i
$166$		−	0.170150i		−	0.0132062i
$167$	−4.43529	−	10.7077i	−0.343213	−	0.828589i	−0.997387	−	0.0722453i	$-0.976984\pi$
$167$	−4.43529	−	10.7077i	−0.343213	−	0.828589i	0.654174	−	0.756344i	$-0.273016\pi$
$168$	−18.0875	−	18.0875i	−1.39548	−	1.39548i
$169$	−5.64797			−0.434459
$170$	−1.76207	−	2.53071i	−0.135144	−	0.194097i
$171$	8.19188			0.626449
$172$	−2.20220	−	2.20220i	−0.167916	−	0.167916i
$173$	4.21988	+	10.1877i	0.320832	+	0.774556i	0.999206	+	0.0398396i	$0.0126847\pi$
$173$	4.21988	+	10.1877i	0.320832	+	0.774556i	−0.678375	+	0.734716i	$0.737315\pi$
$174$			1.02197i			0.0774750i
$175$	2.98655	−	1.23707i	0.225762	−	0.0935137i
$176$	−1.00130	+	2.41734i	−0.0754755	+	0.182214i
$177$	−8.57932	−	3.55367i	−0.644861	−	0.267110i
$178$	−7.05538	+	7.05538i	−0.528823	+	0.528823i
$179$	14.9009	−	14.9009i	1.11375	−	1.11375i	0.121109	−	0.992639i	$-0.461355\pi$
$179$	14.9009	−	14.9009i	1.11375	−	1.11375i	0.992639	−	0.121109i	$-0.0386451\pi$
$180$	−8.59244	−	3.55910i	−0.640443	−	0.265280i
$181$	8.67131	−	20.9344i	0.644533	−	1.55604i	−0.175968	−	0.984396i	$-0.556305\pi$
$181$	8.67131	−	20.9344i	0.644533	−	1.55604i	0.820501	−	0.571645i	$-0.193695\pi$
$182$	−9.64579	+	3.99542i	−0.714993	+	0.296160i
$183$			37.5869i			2.77850i
$184$	−0.484861	−	1.17056i	−0.0357444	−	0.0862947i
$185$	−7.56599	−	7.56599i	−0.556263	−	0.556263i
$186$	−12.7145			−0.932269
$187$	−9.25469	+	6.44380i	−0.676770	+	0.471217i
$188$	12.0954			0.882150
$189$	−24.2906	−	24.2906i	−1.76688	−	1.76688i
$190$	−0.363182	−	0.876800i	−0.0263480	−	0.0636098i
$191$		−	3.50162i		−	0.253368i	−0.991943	−	0.126684i	$-0.959567\pi$
$191$		−	3.50162i		−	0.253368i	0.991943	−	0.126684i	$-0.0404335\pi$
$192$	7.02011	−	2.90782i	0.506633	−	0.209854i
$193$	−4.70480	+	11.3584i	−0.338659	+	0.817595i	0.659186	+	0.751980i	$0.270901\pi$
$193$	−4.70480	+	11.3584i	−0.338659	+	0.817595i	−0.997845	+	0.0656152i	$0.979099\pi$
$194$	10.2317	+	4.23811i	0.734593	+	0.304278i
$195$	−9.38966	+	9.38966i	−0.672408	+	0.672408i
$196$	3.51426	−	3.51426i	0.251018	−	0.251018i
$197$	15.6835	+	6.49632i	1.11740	+	0.462843i	0.863481	−	0.504381i	$-0.168279\pi$
$197$	15.6835	+	6.49632i	1.11740	+	0.462843i	0.253922	+	0.967225i	$0.418279\pi$
$198$	5.05374	−	12.2008i	0.359154	−	0.867074i
$199$	10.6966	−	4.43067i	0.758260	−	0.314082i	0.0301533	−	0.999545i	$-0.490400\pi$
$199$	10.6966	−	4.43067i	0.758260	−	0.314082i	0.728107	+	0.685464i	$0.240400\pi$
$200$			2.57329i			0.181959i
$201$	−4.95875	−	11.9715i	−0.349763	−	0.844403i
$202$	0.150308	+	0.150308i	0.0105756	+	0.0105756i
$203$	−1.43645			−0.100819
$204$	−17.9793	−	3.21928i	−1.25880	−	0.225394i
$205$	2.17048			0.151593
$206$	7.44849	+	7.44849i	0.518961	+	0.518961i
$207$	−1.21641	−	2.93667i	−0.0845461	−	0.204112i
$208$			4.13111i			0.286441i
$209$	−3.20642	+	1.32814i	−0.221792	+	0.0918694i
$210$	−2.84509	+	6.86865i	−0.196330	+	0.473982i
$211$	6.15655	+	2.55013i	0.423834	+	0.175558i	0.584397	−	0.811468i	$-0.301331\pi$
$211$	6.15655	+	2.55013i	0.423834	+	0.175558i	−0.160563	+	0.987026i	$0.551331\pi$
$212$	1.85091	−	1.85091i	0.127121	−	0.127121i
$213$	8.46191	−	8.46191i	0.579800	−	0.579800i
$214$	−12.9282	−	5.35503i	−0.883753	−	0.366063i
$215$	−0.827294	+	1.99726i	−0.0564210	+	0.136212i
$216$	25.2640	−	10.4647i	1.71900	−	0.712033i
$217$		−	17.8711i		−	1.21317i
$218$	1.01056	+	2.43971i	0.0684438	+	0.165238i
$219$	−14.0695	−	14.0695i	−0.950732	−	0.950732i
$220$	3.94023			0.265650
$221$	−9.60626	+	14.9912i	−0.646187	+	1.00842i
$222$	24.6083			1.65160
$223$	8.90442	+	8.90442i	0.596284	+	0.596284i	0.939322	−	0.343037i	$-0.111456\pi$
$223$	8.90442	+	8.90442i	0.596284	+	0.596284i	−0.343037	+	0.939322i	$0.611456\pi$
$224$	7.25180	+	17.5074i	0.484531	+	1.16976i
$225$			6.45581i			0.430387i
$226$	−1.96346	+	0.813292i	−0.130607	+	0.0540994i
$227$	3.07779	−	7.43044i	0.204280	−	0.493176i	−0.788224	−	0.615389i	$-0.788999\pi$
$227$	3.07779	−	7.43044i	0.204280	−	0.493176i	0.992504	+	0.122213i	$0.0389991\pi$
$228$	−5.19336	−	2.15116i	−0.343939	−	0.142464i
$229$	−15.2944	+	15.2944i	−1.01068	+	1.01068i	−0.0107373	+	0.999942i	$0.503418\pi$
$229$	−15.2944	+	15.2944i	−1.01068	+	1.01068i	−0.999942	+	0.0107373i	$0.996582\pi$
$230$	−0.260391	+	0.260391i	−0.0171697	+	0.0171697i
$231$	25.1183	+	10.4043i	1.65266	+	0.684555i
$232$	0.437587	−	1.05643i	0.0287290	−	0.0693579i
$233$	−20.2797	+	8.40011i	−1.32857	+	0.550310i	−0.930246	−	0.366937i	$-0.880406\pi$
$233$	−20.2797	+	8.40011i	−1.32857	+	0.550310i	−0.398320	+	0.917247i	$0.630406\pi$
$234$		−	20.8506i		−	1.36304i
$235$	−3.21300	−	7.75686i	−0.209593	−	0.506002i
$236$	3.07626	+	3.07626i	0.200248	+	0.200248i
$237$	−22.2063			−1.44246
$238$	−1.75697	+	9.81247i	−0.113888	+	0.636048i
$239$	5.90132			0.381725			0.190862	−	0.981617i	$-0.438872\pi$
$239$	5.90132			0.381725			0.190862	+	0.981617i	$0.438872\pi$
$240$	2.08011	+	2.08011i	0.134270	+	0.134270i
$241$	5.09407	+	12.2982i	0.328138	+	0.792195i	0.998731	+	0.0503696i	$0.0160399\pi$
$241$	5.09407	+	12.2982i	0.328138	+	0.792195i	−0.670593	+	0.741826i	$0.733960\pi$
$242$		−	2.63214i		−	0.169200i
$243$	8.35977	−	3.46273i	0.536279	−	0.222134i
$244$	6.73872	−	16.2687i	0.431402	−	1.04150i
$245$	−3.18723	−	1.32019i	−0.203624	−	0.0843440i
$246$	−3.52974	+	3.52974i	−0.225048	+	0.225048i
$247$	−3.87467	+	3.87467i	−0.246539	+	0.246539i
$248$	13.1432	+	5.44409i	0.834594	+	0.345700i
$249$	−0.267712	+	0.646315i	−0.0169656	+	0.0409586i
$250$	0.690983	−	0.286214i	0.0437016	−	0.0181018i
$251$		−	3.59367i		−	0.226831i	−0.993548	−	0.113415i	$-0.963821\pi$
$251$		−	3.59367i		−	0.226831i	0.993548	−	0.113415i	$-0.0361790\pi$
$252$	11.5052	+	27.7761i	0.724761	+	1.74973i
$253$	0.952236	+	0.952236i	0.0598666	+	0.0598666i
$254$	−4.08746			−0.256470
$255$	2.71142	+	12.3853i	0.169796	+	0.775601i
$256$	−12.3285			−0.770531
$257$	−17.3588	−	17.3588i	−1.08281	−	1.08281i	−0.996246	−	0.0865680i	$-0.972410\pi$
$257$	−17.3588	−	17.3588i	−1.08281	−	1.08281i	−0.0865680	−	0.996246i	$-0.527590\pi$
$258$	−1.90266	−	4.59342i	−0.118454	−	0.285974i
$259$			34.5888i			2.14924i
$260$	5.74754	−	2.38071i	0.356447	−	0.147645i
$261$	1.09781	−	2.65034i	0.0679524	−	0.164052i
$262$	−6.89567	−	2.85628i	−0.426016	−	0.176462i
$263$	10.3521	−	10.3521i	0.638340	−	0.638340i	−0.311806	−	0.950146i	$-0.600934\pi$
$263$	10.3521	−	10.3521i	0.638340	−	0.638340i	0.950146	+	0.311806i	$0.100934\pi$
$264$	−15.3036	+	15.3036i	−0.941873	+	0.941873i
$265$	−1.67867	−	0.695328i	−0.103120	−	0.0427136i
$266$	−1.17403	+	2.83436i	−0.0719845	+	0.173786i
$267$	37.9008	−	15.6990i	2.31949	−	0.960764i
$268$			6.07063i			0.370823i
$269$	−7.17904	−	17.3317i	−0.437714	−	1.05673i	−0.976736	−	0.214443i	$-0.931206\pi$
$269$	−7.17904	−	17.3317i	−0.437714	−	1.05673i	0.539023	−	0.842291i	$-0.318794\pi$
$270$	−5.61999	−	5.61999i	−0.342022	−	0.342022i
$271$	5.76388			0.350131			0.175065	−	0.984557i	$-0.443986\pi$
$271$	5.76388			0.350131			0.175065	+	0.984557i	$0.443986\pi$
$272$	3.32102	+	2.12809i	0.201366	+	0.129034i
$273$	42.9259			2.59800
$274$	1.62767	+	1.62767i	0.0983311	+	0.0983311i
$275$	−1.04667	−	2.52689i	−0.0631167	−	0.152377i
$276$			2.18117i			0.131291i
$277$	0.113870	−	0.0471663i	0.00684176	−	0.00283395i	−0.379260	−	0.925290i	$-0.623821\pi$
$277$	0.113870	−	0.0471663i	0.00684176	−	0.00283395i	0.386102	+	0.922456i	$0.373821\pi$
$278$	−1.92047	+	4.63643i	−0.115182	+	0.278075i
$279$	32.9733	+	13.6580i	1.97406	+	0.817682i
$280$	5.88205	−	5.88205i	0.351520	−	0.351520i
$281$	−1.28950	+	1.28950i	−0.0769253	+	0.0769253i	−0.744523	−	0.667597i	$-0.767323\pi$
$281$	−1.28950	+	1.28950i	−0.0769253	+	0.0769253i	0.667597	+	0.744523i	$0.267323\pi$
$282$	17.8397	+	7.38944i	1.06234	+	0.440035i
$283$	10.9554	−	26.4486i	0.651229	−	1.57221i	−0.159767	−	0.987155i	$-0.551074\pi$
$283$	10.9554	−	26.4486i	0.651229	−	1.57221i	0.810996	−	0.585052i	$-0.198926\pi$
$284$	−5.17965	+	2.14548i	−0.307355	+	0.127311i
$285$			3.90196i			0.231132i
$286$	3.38048	+	8.16120i	0.199892	+	0.482582i
$287$	−4.96130	−	4.96130i	−0.292856	−	0.292856i
$288$	−37.8444			−2.23000
$289$	7.10292	+	15.4450i	0.417819	+	0.908530i
$290$	−0.332343			−0.0195159
$291$	−32.1969	−	32.1969i	−1.88742	−	1.88742i
$292$	3.56727	+	8.61216i	0.208759	+	0.503988i
$293$		−	1.41607i		−	0.0827278i	−0.999144	−	0.0413639i	$-0.986830\pi$
$293$		−	1.41607i		−	0.0827278i	0.999144	−	0.0413639i	$-0.0131703\pi$
$294$	7.33017	−	3.03626i	0.427504	−	0.177078i
$295$	1.15565	−	2.78999i	0.0672848	−	0.162440i
$296$	−25.4381	−	10.5368i	−1.47856	−	0.612440i
$297$	−20.5520	+	20.5520i	−1.19255	+	1.19255i
$298$	12.1591	−	12.1591i	0.704358	−	0.704358i
$299$	1.96435	+	0.813662i	0.113602	+	0.0470553i
$300$	1.69527	−	4.09275i	0.0978766	−	0.236295i
$301$	6.45639	−	2.67433i	0.372140	−	0.154146i
$302$		−	0.146399i		−	0.00842433i
$303$	−0.334452	−	0.807438i	−0.0192138	−	0.0463861i
$304$	0.858361	+	0.858361i	0.0492304	+	0.0492304i
$305$	−12.2233			−0.699902
$306$	−16.7619	−	10.7409i	−0.958212	−	0.614017i
$307$	−21.7364			−1.24056			−0.620281	−	0.784379i	$-0.712982\pi$
$307$	−21.7364			−1.24056			−0.620281	+	0.784379i	$0.712982\pi$
$308$	−9.00661	−	9.00661i	−0.513199	−	0.513199i
$309$	−16.5737	−	40.0125i	−0.942846	−	2.27623i
$310$		−	4.13474i		−	0.234838i
$311$	7.99250	−	3.31060i	0.453213	−	0.187727i	−0.144387	−	0.989521i	$-0.546121\pi$
$311$	7.99250	−	3.31060i	0.453213	−	0.187727i	0.597600	+	0.801794i	$0.296121\pi$
$312$	−13.0766	+	31.5696i	−0.740315	+	1.78728i
$313$	9.49936	+	3.93476i	0.536936	+	0.222406i	0.634638	−	0.772810i	$-0.281149\pi$
$313$	9.49936	+	3.93476i	0.536936	+	0.222406i	−0.0977022	+	0.995216i	$0.531149\pi$
$314$	6.27130	−	6.27130i	0.353910	−	0.353910i
$315$	14.7567	−	14.7567i	0.831447	−	0.831447i
$316$	9.61155	+	3.98123i	0.540692	+	0.223962i
$317$	−0.431538	+	1.04183i	−0.0242376	+	0.0585147i	−0.935535	−	0.353234i	$-0.885082\pi$
$317$	−0.431538	+	1.04183i	−0.0242376	+	0.0585147i	0.911297	+	0.411749i	$0.135082\pi$
$318$	3.86070	−	1.59916i	0.216497	−	0.0896762i
$319$			1.21536i			0.0680473i
$320$	0.945625	+	2.28294i	0.0528620	+	0.127620i
$321$	40.6822	+	40.6822i	2.27066	+	2.27066i
$322$	1.19041			0.0663387
$323$	1.11887	+	5.11084i	0.0622559	+	0.284375i
$324$	−19.1747			−1.06526
$325$	−3.05352	−	3.05352i	−0.169379	−	0.169379i
$326$	1.52974	+	3.69311i	0.0847242	+	0.204542i
$327$		−	10.8573i		−	0.600407i
$328$	5.16013	−	2.13740i	0.284921	−	0.118018i
$329$	−10.3864	+	25.0750i	−0.572621	+	1.38243i
$330$	5.81149	+	2.40720i	0.319912	+	0.132512i
$331$	−24.2254	+	24.2254i	−1.33155	+	1.33155i	−0.427567	+	0.903984i	$0.640629\pi$
$331$	−24.2254	+	24.2254i	−1.33155	+	1.33155i	−0.903984	+	0.427567i	$0.859371\pi$
$332$	0.231748	−	0.231748i	0.0127188	−	0.0127188i
$333$	−63.8185	−	26.4345i	−3.49723	−	1.44860i
$334$	−3.31722	+	8.00847i	−0.181510	+	0.438204i
$335$	3.89312	−	1.61259i	0.212704	−	0.0881049i
$336$		−	9.50945i		−	0.518783i
$337$	−5.26046	−	12.6999i	−0.286556	−	0.691807i	0.713404	−	0.700753i	$-0.247152\pi$
$337$	−5.26046	−	12.6999i	−0.286556	−	0.691807i	−0.999960	+	0.00894611i	$0.997152\pi$
$338$	2.98696	+	2.98696i	0.162469	+	0.162469i
$339$	8.73784			0.474574
$340$	1.04691	−	5.84686i	0.0567766	−	0.317090i
$341$	−15.1206			−0.818824
$342$	−4.33232	−	4.33232i	−0.234265	−	0.234265i
$343$	−4.39181	−	10.6028i	−0.237135	−	0.572495i
$344$			5.56300i			0.299937i
$345$	1.39879	−	0.579399i	0.0753085	−	0.0311938i
$346$	3.15611	−	7.61952i	0.169673	−	0.409628i
$347$	17.4415	+	7.22453i	0.936311	+	0.387833i	0.798069	−	0.602566i	$-0.205855\pi$
$347$	17.4415	+	7.22453i	0.936311	+	0.387833i	0.138242	+	0.990398i	$0.455855\pi$
$348$	−1.39194	+	1.39194i	−0.0746158	+	0.0746158i
$349$	4.98501	−	4.98501i	0.266842	−	0.266842i	−0.560985	−	0.827826i	$-0.689577\pi$
$349$	4.98501	−	4.98501i	0.266842	−	0.266842i	0.827826	+	0.560985i	$0.189577\pi$
$350$	−2.23368	−	0.925222i	−0.119395	−	0.0494552i
$351$	−17.5612	+	42.3965i	−0.937347	+	2.26296i
$352$	14.8128	−	6.13567i	0.789526	−	0.327032i
$353$		−	8.60779i		−	0.458146i	−0.973409	−	0.229073i	$-0.926431\pi$
$353$		−	8.60779i		−	0.458146i	0.973409	−	0.229073i	$-0.0735695\pi$
$354$	2.65784	+	6.41659i	0.141263	+	0.341038i
$355$	2.75181	+	2.75181i	0.146051	+	0.146051i
$356$	−19.2191			−1.01861
$357$	22.1127	−	34.5083i	1.17033	−	1.82637i
$358$	−15.7609			−0.832988
$359$	−6.49195	−	6.49195i	−0.342632	−	0.342632i	0.514724	−	0.857356i	$-0.327894\pi$
$359$	−6.49195	−	6.49195i	−0.342632	−	0.342632i	−0.857356	+	0.514724i	$0.827894\pi$
$360$	6.35739	+	15.3481i	0.335064	+	0.808916i
$361$		−	17.3898i		−	0.915255i
$362$	−15.6571	+	6.48540i	−0.822921	+	0.340865i
$363$	−4.14138	+	9.99818i	−0.217366	+	0.524769i
$364$	−18.5796	−	7.69592i	−0.973836	−	0.403376i
$365$	4.57542	−	4.57542i	0.239488	−	0.239488i
$366$	19.8780	−	19.8780i	1.03904	−	1.03904i
$367$	−6.29722	−	2.60840i	−0.328712	−	0.136157i	0.212223	−	0.977221i	$-0.431930\pi$
$367$	−6.29722	−	2.60840i	−0.328712	−	0.136157i	−0.540935	+	0.841064i	$0.681930\pi$
$368$	0.180252	−	0.435166i	0.00939628	−	0.0226846i
$369$	12.9456	−	5.36224i	0.673921	−	0.279147i
$370$			8.00263i			0.416037i
$371$	2.24773	+	5.42650i	0.116696	+	0.281730i
$372$	−17.3174	−	17.3174i	−0.897863	−	0.897863i
$373$	10.4647			0.541841			0.270920	−	0.962602i	$-0.412672\pi$
$373$	10.4647			0.541841			0.270920	+	0.962602i	$0.412672\pi$
$374$	8.30223	+	1.48656i	0.429298	+	0.0768680i
$375$	−3.07503			−0.158794
$376$	−15.2772	−	15.2772i	−0.787863	−	0.787863i
$377$	0.734329	+	1.77283i	0.0378199	+	0.0913053i
$378$			25.6924i			1.32148i
$379$	23.4129	−	9.69794i	1.20264	−	0.498150i	0.310789	−	0.950479i	$-0.399407\pi$
$379$	23.4129	−	9.69794i	1.20264	−	0.498150i	0.891851	+	0.452330i	$0.149407\pi$
$380$	0.699558	−	1.68888i	0.0358866	−	0.0866378i
$381$	15.5263	+	6.43119i	0.795434	+	0.329480i
$382$	−1.85185	+	1.85185i	−0.0947489	+	0.0947489i
$383$	−5.43799	+	5.43799i	−0.277868	+	0.277868i	−0.832258	−	0.554389i	$-0.812952\pi$
$383$	−5.43799	+	5.43799i	−0.277868	+	0.277868i	0.554389	+	0.832258i	$0.312952\pi$
$384$	28.0574	+	11.6217i	1.43180	+	0.593069i
$385$	−3.38349	+	8.16848i	−0.172439	+	0.416304i
$386$	8.49511	−	3.51879i	0.432389	−	0.179102i
$387$			13.9563i			0.709439i
$388$	8.16339	+	19.7082i	0.414433	+	1.00053i
$389$	11.1991	+	11.1991i	0.567816	+	0.567816i	0.931516	−	0.363700i	$-0.118487\pi$
$389$	11.1991	+	11.1991i	0.567816	+	0.567816i	−0.363700	+	0.931516i	$0.618487\pi$
$390$	9.93155			0.502903
$391$	1.66602	−	1.16000i	0.0842541	−	0.0586639i
$392$	−8.87742			−0.448377
$393$	21.6992	+	21.6992i	1.09458	+	1.09458i
$394$	−4.85869	−	11.7299i	−0.244777	−	0.590944i
$395$		−	7.22150i		−	0.363353i
$396$	23.5011	−	9.73446i	1.18097	−	0.489175i
$397$	11.1606	−	26.9440i	0.560133	−	1.35228i	−0.349526	−	0.936927i	$-0.613657\pi$
$397$	11.1606	−	26.9440i	0.560133	−	1.35228i	0.909659	−	0.415355i	$-0.136343\pi$
$398$	−8.00012	−	3.31376i	−0.401010	−	0.166104i
$399$	8.91913	−	8.91913i	0.446515	−	0.446515i
$400$	−0.676451	+	0.676451i	−0.0338226	+	0.0338226i
$401$	−15.1386	−	6.27060i	−0.755984	−	0.313139i	−0.0288034	−	0.999585i	$-0.509170\pi$
$401$	−15.1386	−	6.27060i	−0.755984	−	0.313139i	−0.727181	+	0.686446i	$0.759170\pi$
$402$	−3.70872	+	8.95364i	−0.184974	+	0.446567i
$403$	−22.0561	+	9.13592i	−1.09869	+	0.455092i
$404$			0.409445i			0.0203706i
$405$	5.09352	+	12.2968i	0.253099	+	0.611035i
$406$	0.759673	+	0.759673i	0.0377019	+	0.0377019i
$407$	29.2652			1.45062
$408$	18.6427	+	26.7750i	0.922952	+	1.32556i
$409$	33.9971			1.68105			0.840525	−	0.541772i	$-0.182247\pi$
$409$	33.9971			1.68105			0.840525	+	0.541772i	$0.182247\pi$
$410$	−1.14787	−	1.14787i	−0.0566893	−	0.0566893i
$411$	−3.62175	−	8.74367i	−0.178648	−	0.431294i
$412$			20.2900i			0.999616i
$413$	−9.01899	+	3.73579i	−0.443796	+	0.183826i
$414$	−0.909768	+	2.19637i	−0.0447127	+	0.107946i
$415$	−0.210182	−	0.0870601i	−0.0103174	−	0.00427361i
$416$	17.9000	−	17.9000i	0.877618	−	0.877618i
$417$	14.5899	−	14.5899i	0.714468	−	0.714468i
$418$	2.39812	+	0.993336i	0.117296	+	0.0485856i
$419$	0.341711	−	0.824964i	0.0166937	−	0.0403021i	−0.915313	−	0.402743i	$-0.868057\pi$
$419$	0.341711	−	0.824964i	0.0166937	−	0.0403021i	0.932007	+	0.362441i	$0.118057\pi$
$420$	−13.2303	+	5.48017i	−0.645573	+	0.267405i
$421$		−	33.6725i		−	1.64110i	−0.571575	−	0.820550i	$-0.693668\pi$
$421$		−	33.6725i		−	1.64110i	0.571575	−	0.820550i	$-0.306332\pi$
$422$	−1.90728	−	4.60457i	−0.0928448	−	0.224147i
$423$	−38.3271	−	38.3271i	−1.86353	−	1.86353i
$424$	−4.67562			−0.227068
$425$	−4.02772	+	0.881755i	−0.195373	+	0.0427714i
$426$	−8.95025			−0.433641
$427$	27.9400	+	27.9400i	1.35211	+	1.35211i
$428$	−10.3148	−	24.9021i	−0.498585	−	1.20369i
$429$		−	36.3192i		−	1.75351i
$430$	1.49378	−	0.618745i	0.0720366	−	0.0298385i
$431$	−6.23658	+	15.0564i	−0.300405	+	0.725243i	0.699538	+	0.714595i	$0.253389\pi$
$431$	−6.23658	+	15.0564i	−0.300405	+	0.725243i	−0.999943	+	0.0106472i	$0.996611\pi$
$432$	9.39215	+	3.89036i	0.451880	+	0.187175i
$433$	−24.7450	+	24.7450i	−1.18917	+	1.18917i	−0.211871	+	0.977298i	$0.567956\pi$
$433$	−24.7450	+	24.7450i	−1.18917	+	1.18917i	−0.977298	+	0.211871i	$0.932044\pi$
$434$	−9.45122	+	9.45122i	−0.453673	+	0.453673i
$435$	1.26241	+	0.522907i	0.0605279	+	0.0250715i
$436$	−1.94653	+	4.69934i	−0.0932219	+	0.225057i
$437$	0.577215	−	0.239090i	0.0276119	−	0.0114372i
$438$			14.8815i			0.711066i
$439$	8.52530	+	20.5819i	0.406891	+	0.982321i	0.985951	+	0.167036i	$0.0534196\pi$
$439$	8.52530	+	20.5819i	0.406891	+	0.982321i	−0.579060	+	0.815285i	$0.696580\pi$
$440$	−4.97674	−	4.97674i	−0.237257	−	0.237257i
$441$	−22.2714			−1.06054
$442$	13.0085	−	2.84784i	0.618750	−	0.135458i
$443$	−8.79907			−0.418056			−0.209028	−	0.977910i	$-0.567030\pi$
$443$	−8.79907			−0.418056			−0.209028	+	0.977910i	$0.567030\pi$
$444$	33.5171	+	33.5171i	1.59065	+	1.59065i
$445$	5.10532	+	12.3253i	0.242015	+	0.584277i
$446$		−	9.41830i		−	0.445970i
$447$	−65.3175	+	27.0554i	−3.08941	+	1.27968i
$448$	3.05685	−	7.37988i	0.144422	−	0.348666i
$449$	−8.19189	−	3.39319i	−0.386599	−	0.160135i	0.180914	−	0.983499i	$-0.442094\pi$
$449$	−8.19189	−	3.39319i	−0.386599	−	0.160135i	−0.567513	+	0.823364i	$0.692094\pi$
$450$	3.41419	−	3.41419i	0.160946	−	0.160946i
$451$	−4.19771	+	4.19771i	−0.197662	+	0.197662i
$452$	−3.78200	−	1.56655i	−0.177890	−	0.0736845i
$453$	−0.230343	+	0.556098i	−0.0108225	+	0.0261278i
$454$	−5.55733	+	2.30192i	−0.260819	+	0.108035i
$455$			13.9595i			0.654432i
$456$	3.84248	+	9.27656i	0.179941	+	0.434415i
$457$	−13.0643	−	13.0643i	−0.611120	−	0.611120i	0.332118	−	0.943238i	$-0.392237\pi$
$457$	−13.0643	−	13.0643i	−0.611120	−	0.611120i	−0.943238	+	0.332118i	$0.892237\pi$
$458$	16.1770			0.755902
$459$	25.0363	+	35.9575i	1.16859	+	1.67835i
$460$	−0.709315			−0.0330720
$461$	17.3736	+	17.3736i	0.809169	+	0.809169i	0.984508	−	0.175339i	$-0.0561022\pi$
$461$	17.3736	+	17.3736i	0.809169	+	0.809169i	−0.175339	+	0.984508i	$0.556102\pi$
$462$	−7.78156	−	18.7863i	−0.362031	−	0.874020i
$463$		−	9.90931i		−	0.460525i	−0.973129	−	0.230262i	$-0.926042\pi$
$463$		−	9.90931i		−	0.460525i	0.973129	−	0.230262i	$-0.0739584\pi$
$464$	0.392737	−	0.162677i	0.0182324	−	0.00755209i
$465$	−6.50557	+	15.7058i	−0.301689	+	0.728341i
$466$	15.1675	+	6.28257i	0.702619	+	0.291034i
$467$	−20.7918	+	20.7918i	−0.962131	+	0.962131i	−0.999309	−	0.0371777i	$-0.988163\pi$
$467$	−20.7918	+	20.7918i	−0.962131	+	0.962131i	0.0371777	+	0.999309i	$0.488163\pi$
$468$	28.3989	−	28.3989i	1.31274	−	1.31274i
$469$	−12.5850	−	5.21287i	−0.581121	−	0.240708i
$470$	−2.40305	+	5.80147i	−0.110844	+	0.267602i
$471$	−33.6888	+	13.9543i	−1.55230	+	0.642982i
$472$		−	7.77100i		−	0.357689i
$473$	−2.26272	−	5.46269i	−0.104040	−	0.251175i
$474$	11.7439	+	11.7439i	0.539417	+	0.539417i
$475$	−1.26892			−0.0582219
$476$	−15.7578	+	10.9718i	−0.722259	+	0.502890i
$477$	−11.7301			−0.537083
$478$	−3.12095	−	3.12095i	−0.142749	−	0.142749i
$479$	−10.9449	−	26.4232i	−0.500083	−	1.20731i	−0.949438	−	0.313955i	$-0.898346\pi$
$479$	−10.9449	−	26.4232i	−0.500083	−	1.20731i	0.449354	−	0.893354i	$-0.351654\pi$
$480$		−	18.0260i		−	0.822773i
$481$	42.6886	−	17.6822i	1.94643	−	0.806239i
$482$	3.80993	−	9.19799i	0.173538	−	0.418957i
$483$	−4.52176	−	1.87298i	−0.205747	−	0.0852234i
$484$	3.58503	−	3.58503i	0.162956	−	0.162956i
$485$	10.4704	−	10.4704i	0.475439	−	0.475439i
$486$	−6.25239	−	2.58982i	−0.283614	−	0.117477i
$487$	−0.236454	+	0.570849i	−0.0107147	+	0.0258677i	−0.929146	−	0.369712i	$-0.879456\pi$
$487$	−0.236454	+	0.570849i	−0.0107147	+	0.0258677i	0.918432	+	0.395580i	$0.129456\pi$
$488$	−29.0597	+	12.0369i	−1.31547	+	0.544886i
$489$		−	16.4352i		−	0.743224i
$490$	0.987391	+	2.38377i	0.0446058	+	0.107688i
$491$	18.0077	+	18.0077i	0.812675	+	0.812675i	0.985034	−	0.172359i	$-0.0551390\pi$
$491$	18.0077	+	18.0077i	0.812675	+	0.812675i	−0.172359	+	0.985034i	$0.555139\pi$
$492$	−9.61515			−0.433485
$493$	1.80346	+	0.322919i	0.0812239	+	0.0145435i
$494$	4.09827			0.184390
$495$	−12.4855	−	12.4855i	−0.561182	−	0.561182i
$496$	2.02389	+	4.88611i	0.0908755	+	0.219393i
$497$		−	12.5802i		−	0.564301i
$498$	0.483388	−	0.200226i	0.0216611	−	0.00897234i
$499$	13.9527	−	33.6849i	0.624611	−	1.50794i	−0.221624	−	0.975132i	$-0.571136\pi$
$499$	13.9527	−	33.6849i	0.624611	−	1.50794i	0.846234	−	0.532811i	$-0.178864\pi$
$500$	1.33096	+	0.551303i	0.0595225	+	0.0246550i
$501$	25.2009	−	25.2009i	1.12589	−	1.12589i
$502$	−1.90053	+	1.90053i	−0.0848249	+	0.0848249i
$503$	27.8902	+	11.5525i	1.24356	+	0.515100i	0.904826	−	0.425781i	$-0.140001\pi$
$503$	27.8902	+	11.5525i	1.24356	+	0.515100i	0.338736	+	0.940881i	$0.390001\pi$
$504$	20.5510	−	49.6146i	0.915416	−	2.21001i
$505$	0.262579	−	0.108764i	0.0116846	−	0.00483992i
$506$		−	1.00719i		−	0.0447751i
$507$	−6.64632	−	16.0456i	−0.295174	−	0.712612i
$508$	−5.56721	−	5.56721i	−0.247005	−	0.247005i
$509$	−40.1857			−1.78120			−0.890600	−	0.454787i	$-0.849715\pi$
$509$	−40.1857			−1.78120			−0.890600	+	0.454787i	$0.849715\pi$
$510$	5.11611	−	7.98401i	0.226545	−	0.353538i
$511$	−20.9171			−0.925316
$512$	−7.44682	−	7.44682i	−0.329106	−	0.329106i
$513$	5.16026	+	12.4580i	0.227831	+	0.550033i
$514$			18.3606i			0.809852i
$515$	13.0121	−	5.38978i	0.573381	−	0.237502i
$516$	3.66488	−	8.84780i	0.161337	−	0.389503i
$517$	21.2157	+	8.78783i	0.933065	+	0.386488i
$518$	18.2925	−	18.2925i	0.803725	−	0.803725i
$519$	−23.9770	+	23.9770i	−1.05247	+	1.05247i
$520$	−10.2664	−	4.25250i	−0.450214	−	0.186485i
$521$	−13.5302	+	32.6647i	−0.592767	+	1.43107i	0.288053	+	0.957614i	$0.406992\pi$
$521$	−13.5302	+	32.6647i	−0.592767	+	1.43107i	−0.880820	+	0.473451i	$0.843008\pi$
$522$	−1.98222	+	0.821064i	−0.0867596	+	0.0359370i
$523$		−	24.5035i		−	1.07146i	−0.844388	−	0.535732i	$-0.820036\pi$
$523$		−	24.5035i		−	1.07146i	0.844388	−	0.535732i	$-0.179964\pi$
$524$	−5.50173	−	13.2824i	−0.240344	−	0.580243i
$525$	7.02892	+	7.02892i	0.306767	+	0.306767i
$526$	−10.9496			−0.477424
$527$	−4.01749	+	22.4372i	−0.175005	+	0.977379i
$528$	−8.04585			−0.350150
$529$	16.0920	+	16.0920i	0.699654	+	0.699654i
$530$	0.520046	+	1.25550i	0.0225893	+	0.0545355i
$531$		−	19.4957i		−	0.846041i
$532$	−5.45951	+	2.26140i	−0.236700	+	0.0980443i
$533$	−3.58684	+	8.65939i	−0.155363	+	0.375080i
$534$	−28.3465	−	11.7415i	−1.22667	−	0.508105i
$535$	−13.2299	+	13.2299i	−0.571977	+	0.571977i
$536$	7.66756	−	7.66756i	0.331188	−	0.331188i
$537$	59.8678	+	24.7981i	2.58349	+	1.07011i
$538$	−5.36930	+	12.9626i	−0.231487	+	0.558859i
$539$	8.71734	−	3.61084i	0.375483	−	0.155530i
$540$		−	15.3091i		−	0.658798i
$541$	9.77786	+	23.6058i	0.420383	+	1.01489i	0.982235	+	0.187657i	$0.0600892\pi$
$541$	9.77786	+	23.6058i	0.420383	+	1.01489i	−0.561852	+	0.827238i	$0.689911\pi$
$542$	−3.04826	−	3.04826i	−0.130934	−	0.130934i
$543$	69.6778			2.99016
$544$	−5.16891	−	23.6108i	−0.221615	−	1.01230i
$545$	3.53078			0.151242
$546$	−22.7016	−	22.7016i	−0.971539	−	0.971539i
$547$	−4.50103	−	10.8664i	−0.192450	−	0.464616i	0.797971	−	0.602696i	$-0.205907\pi$
$547$	−4.50103	−	10.8664i	−0.192450	−	0.464616i	−0.990421	+	0.138080i	$0.955907\pi$
$548$			4.43384i			0.189404i
$549$	−72.9042	+	30.1979i	−3.11148	+	1.28882i
$550$	−0.782821	+	1.88990i	−0.0333796	+	0.0805855i
$551$	0.520936	+	0.215779i	0.0221926	+	0.00919248i
$552$	2.75494	−	2.75494i	0.117258	−	0.117258i
$553$	−16.5070	+	16.5070i	−0.701947	+	0.701947i
$554$	−0.0851647	−	0.0352764i	−0.00361830	−	0.00149875i
$555$	12.5913	−	30.3980i	0.534470	−	1.29032i
$556$	−8.93065	+	3.69919i	−0.378744	+	0.156881i
$557$			35.6812i			1.51186i	0.654651	+	0.755931i	$0.272816\pi$
$557$			35.6812i			1.51186i	−0.654651	+	0.755931i	$0.727184\pi$
$558$	−10.2150	−	24.6612i	−0.432436	−	1.04399i
$559$	−6.60117	−	6.60117i	−0.279200	−	0.279200i
$560$	3.09247			0.130681
$561$	−29.1971	−	18.7094i	−1.23270	−	0.789910i
$562$	1.36392			0.0575335
$563$	−21.3003	−	21.3003i	−0.897702	−	0.897702i	0.0975306	−	0.995233i	$-0.468906\pi$
$563$	−21.3003	−	21.3003i	−0.897702	−	0.897702i	−0.995233	+	0.0975306i	$0.968906\pi$
$564$	14.2335	+	34.3626i	0.599337	+	1.44693i
$565$			2.84155i			0.119545i
$566$	−19.7813	+	8.19368i	−0.831470	+	0.344406i
$567$	16.4654	−	39.7510i	0.691482	−	1.66939i
$568$	9.25206	+	3.83233i	0.388208	+	0.160801i
$569$	−17.2524	+	17.2524i	−0.723257	+	0.723257i	−0.969267	−	0.246010i	$-0.920880\pi$
$569$	−17.2524	+	17.2524i	−0.723257	+	0.723257i	0.246010	+	0.969267i	$0.420880\pi$
$570$	2.06357	−	2.06357i	0.0864335	−	0.0864335i
$571$	−30.7483	−	12.7364i	−1.28678	−	0.533001i	−0.368755	−	0.929527i	$-0.620216\pi$
$571$	−30.7483	−	12.7364i	−1.28678	−	0.533001i	−0.918024	+	0.396526i	$0.870216\pi$
$572$	−6.51144	+	15.7200i	−0.272257	+	0.657287i
$573$	9.94795	−	4.12058i	0.415582	−	0.172140i
$574$			5.24762i			0.219032i
$575$	0.188421	+	0.454888i	0.00785768	+	0.0189701i
$576$	11.2801	+	11.2801i	0.470006	+	0.470006i
$577$	−18.0611			−0.751895			−0.375947	−	0.926641i	$-0.622683\pi$
$577$	−18.0611			−0.751895			−0.375947	+	0.926641i	$0.622683\pi$
$578$	4.41176	−	11.9246i	0.183505	−	0.495998i
$579$	−37.8051			−1.57113
$580$	−0.452659	−	0.452659i	−0.0187956	−	0.0187956i
$581$	0.281432	+	0.679438i	0.0116758	+	0.0281878i
$582$			34.0550i			1.41163i
$583$	4.59131	−	1.90178i	0.190152	−	0.0787637i
$584$	6.37198	−	15.3833i	0.263675	−	0.636567i
$585$	−25.7562	−	10.6686i	−1.06489	−	0.441091i
$586$	−0.748897	+	0.748897i	−0.0309366	+	0.0309366i
$587$	−29.5785	+	29.5785i	−1.22084	+	1.22084i	−0.253500	+	0.967335i	$0.581582\pi$
$587$	−29.5785	+	29.5785i	−1.22084	+	1.22084i	−0.967335	+	0.253500i	$0.918418\pi$
$588$	14.1193	+	5.84840i	0.582270	+	0.241184i
$589$	−2.68454	+	6.48105i	−0.110614	+	0.267047i
$590$	−2.08668	+	0.864330i	−0.0859071	+	0.0355839i
$591$			52.2008i			2.14725i
$592$	−3.91717	−	9.45688i	−0.160995	−	0.388675i
$593$	14.6130	+	14.6130i	0.600085	+	0.600085i	0.940335	−	0.340250i	$-0.110512\pi$
$593$	14.6130	+	14.6130i	0.600085	+	0.600085i	−0.340250	+	0.940335i	$0.610512\pi$
$594$	21.7381			0.891925
$595$	11.2221	+	7.19106i	0.460062	+	0.294805i
$596$	33.1219			1.35673
$597$	25.1747	+	25.1747i	1.03033	+	1.03033i
$598$	−0.608550	−	1.46917i	−0.0248854	−	0.0600788i
$599$			9.21817i			0.376644i	0.982107	+	0.188322i	$0.0603049\pi$
$599$			9.21817i			0.376644i	−0.982107	+	0.188322i	$0.939695\pi$
$600$	−7.31061	+	3.02815i	−0.298454	+	0.123624i
$601$	−0.620216	+	1.49733i	−0.0252991	+	0.0610775i	−0.936024	−	0.351936i	$-0.885524\pi$
$601$	−0.620216	+	1.49733i	−0.0252991	+	0.0610775i	0.910725	+	0.413013i	$0.135524\pi$
$602$	−4.82883	−	2.00017i	−0.196808	−	0.0815207i
$603$	19.2362	−	19.2362i	0.783357	−	0.783357i
$604$	0.199399	−	0.199399i	0.00811342	−	0.00811342i
$605$	−3.25141	−	1.34678i	−0.132189	−	0.0547543i
$606$	−0.250141	+	0.603894i	−0.0101613	+	0.0245315i
$607$	23.1115	−	9.57311i	0.938068	−	0.388560i	0.139334	−	0.990245i	$-0.455504\pi$
$607$	23.1115	−	9.57311i	0.938068	−	0.388560i	0.798733	+	0.601685i	$0.205504\pi$
$608$		−	7.43849i		−	0.301671i
$609$	−1.69036	−	4.08089i	−0.0684968	−	0.165366i
$610$	6.46434	+	6.46434i	0.261733	+	0.261733i
$611$	36.2566			1.46678
$612$	−8.20067	−	37.4593i	−0.331492	−	1.51420i
$613$	4.83538			0.195299			0.0976495	−	0.995221i	$-0.468868\pi$
$613$	4.83538			0.195299			0.0976495	+	0.995221i	$0.468868\pi$
$614$	11.4954	+	11.4954i	0.463917	+	0.463917i
$615$	2.55414	+	6.16625i	0.102993	+	0.248647i
$616$			22.7517i			0.916694i
$617$	15.5336	−	6.43422i	0.625358	−	0.259032i	−0.0474212	−	0.998875i	$-0.515100\pi$
$617$	15.5336	−	6.43422i	0.625358	−	0.259032i	0.672779	+	0.739843i	$0.265100\pi$
$618$	−12.3957	+	29.9259i	−0.498629	+	1.20380i
$619$	11.7540	+	4.86865i	0.472431	+	0.195687i	0.606179	−	0.795328i	$-0.292701\pi$
$619$	11.7540	+	4.86865i	0.472431	+	0.195687i	−0.133748	+	0.991015i	$0.542701\pi$
$620$	5.63161	−	5.63161i	0.226171	−	0.226171i
$621$	3.69975	−	3.69975i	0.148466	−	0.148466i
$622$	−5.97771	−	2.47605i	−0.239684	−	0.0992804i
$623$	16.5036	−	39.8431i	0.661201	−	1.59628i
$624$	−11.7363	+	4.86134i	−0.469829	+	0.194609i
$625$		−	1.00000i		−	0.0400000i
$626$	−2.94287	−	7.10471i	−0.117621	−	0.283961i
$627$	−7.54638	−	7.54638i	−0.301373	−	0.301373i
$628$	17.0833			0.681697
$629$	7.77569	−	43.4263i	0.310037	−	1.73152i
$630$	−15.6083			−0.621851
$631$	−2.99812	−	2.99812i	−0.119353	−	0.119353i	0.644907	−	0.764261i	$-0.276896\pi$
$631$	−2.99812	−	2.99812i	−0.119353	−	0.119353i	−0.764261	+	0.644907i	$0.776896\pi$
$632$	−7.11142	−	17.1685i	−0.282877	−	0.682925i
$633$			20.4914i			0.814459i
$634$	0.779196	−	0.322754i	0.0309458	−	0.0128182i
$635$	−2.09142	+	5.04914i	−0.0829956	+	0.200369i
$636$	7.43644	+	3.08028i	0.294874	+	0.122141i
$637$	10.5341	−	10.5341i	0.417377	−	0.417377i
$638$	0.642752	−	0.642752i	0.0254468	−	0.0254468i
$639$	23.2113	+	9.61444i	0.918226	+	0.380342i
$640$	−3.77939	+	9.12426i	−0.149394	+	0.360668i
$641$	19.6050	−	8.12065i	0.774350	−	0.320746i	0.0397171	−	0.999211i	$-0.487354\pi$
$641$	19.6050	−	8.12065i	0.774350	−	0.320746i	0.734633	+	0.678465i	$0.237354\pi$
$642$		−	43.0300i		−	1.69826i
$643$	−3.12525	−	7.54502i	−0.123248	−	0.297547i	0.850198	−	0.526462i	$-0.176482\pi$
$643$	−3.12525	−	7.54502i	−0.123248	−	0.297547i	−0.973446	+	0.228916i	$0.926482\pi$
$644$	1.62136	+	1.62136i	0.0638905	+	0.0638905i
$645$	−6.64767			−0.261752
$646$	2.11117	−	3.29462i	0.0830630	−	0.129625i
$647$	23.4331			0.921249			0.460624	−	0.887595i	$-0.347626\pi$
$647$	23.4331			0.921249			0.460624	+	0.887595i	$0.347626\pi$
$648$	24.2188	+	24.2188i	0.951404	+	0.951404i
$649$	3.16081	+	7.63088i	0.124073	+	0.299538i
$650$			3.22974i			0.126681i
$651$	50.7710	−	21.0300i	1.98987	−	0.824232i
$652$	−2.94656	+	7.11362i	−0.115396	+	0.278591i
$653$	15.5279	+	6.43188i	0.607655	+	0.251699i	0.665225	−	0.746643i	$-0.268335\pi$
$653$	15.5279	+	6.43188i	0.607655	+	0.251699i	−0.0575706	+	0.998341i	$0.518335\pi$
$654$	−5.74192	+	5.74192i	−0.224527	+	0.224527i
$655$	−7.05658	+	7.05658i	−0.275723	+	0.275723i
$656$	1.91833	+	0.794598i	0.0748981	+	0.0310238i
$657$	15.9859	−	38.5933i	0.623668	−	1.50567i
$658$	18.7539	−	7.76814i	0.731105	−	0.302833i
$659$		−	14.0972i		−	0.549150i	−0.961566	−	0.274575i	$-0.911463\pi$
$659$		−	14.0972i		−	0.549150i	0.961566	−	0.274575i	$-0.0885371\pi$
$660$	4.63672	+	11.1940i	0.180484	+	0.435727i
$661$	−7.34734	−	7.34734i	−0.285779	−	0.285779i	0.549630	−	0.835408i	$-0.314769\pi$
$661$	−7.34734	−	7.34734i	−0.285779	−	0.285779i	−0.835408	+	0.549630i	$0.814769\pi$
$662$	25.6235			0.995886
$663$	−53.8936	−	9.64991i	−2.09305	−	0.374771i
$664$	−0.585422			−0.0227188
$665$	2.90050	+	2.90050i	0.112477	+	0.112477i
$666$	19.7707	+	47.7308i	0.766101	+	1.84953i
$667$		−	0.218788i		−	0.00847151i
$668$	−15.4258	+	6.38959i	−0.596843	+	0.247220i
$669$	−14.8187	+	35.7755i	−0.572923	+	1.38316i
$670$	−2.91172	−	1.20608i	−0.112490	−	0.0465948i
$671$	23.6398	−	23.6398i	0.912603	−	0.912603i
$672$	−41.2041	+	41.2041i	−1.58948	+	1.58948i
$673$	−18.3153	−	7.58646i	−0.706005	−	0.292437i	0.000645530	−	1.00000i	$-0.499795\pi$
$673$	−18.3153	−	7.58646i	−0.706005	−	0.292437i	−0.706650	+	0.707563i	$0.749795\pi$
$674$	−3.93438	+	9.49842i	−0.151546	+	0.365866i
$675$	−9.81779	+	4.06666i	−0.377887	+	0.156526i
$676$			8.13660i			0.312946i
$677$	1.28043	+	3.09124i	0.0492111	+	0.118806i	0.946573	−	0.322489i	$-0.104519\pi$
$677$	1.28043	+	3.09124i	0.0492111	+	0.118806i	−0.897362	+	0.441295i	$0.854519\pi$
$678$	−4.62105	−	4.62105i	−0.177471	−	0.177471i
$679$	−47.8669			−1.83696
$680$	−8.70723	+	6.06262i	−0.333907	+	0.232491i
$681$	24.7314			0.947709
$682$	7.99658	+	7.99658i	0.306205	+	0.306205i
$683$	19.2424	+	46.4553i	0.736290	+	1.77756i	0.620380	+	0.784302i	$0.286978\pi$
$683$	19.2424	+	46.4553i	0.736290	+	1.77756i	0.115910	+	0.993260i	$0.463022\pi$
$684$		−	11.8014i		−	0.451239i
$685$	2.84344	−	1.17779i	0.108642	−	0.0450012i
$686$	−3.28470	+	7.92996i	−0.125410	+	0.302767i
$687$	−61.4484	−	25.4528i	−2.34440	−	0.971084i
$688$	−1.46237	+	1.46237i	−0.0557522	+	0.0557522i
$689$	5.54818	−	5.54818i	0.211369	−	0.211369i
$690$	−1.04618	−	0.433341i	−0.0398273	−	0.0164970i
$691$	−14.8926	+	35.9539i	−0.566540	+	1.36775i	0.337913	+	0.941177i	$0.390279\pi$
$691$	−14.8926	+	35.9539i	−0.566540	+	1.36775i	−0.904454	+	0.426572i	$0.859721\pi$
$692$	14.6766	−	6.07926i	0.557922	−	0.231099i
$693$			57.0790i			2.16825i
$694$	−5.40333	−	13.0448i	−0.205107	−	0.495173i
$695$	4.74462	+	4.74462i	0.179974	+	0.179974i
$696$	3.51620			0.133281
$697$	5.11360	+	7.34424i	0.193692	+	0.278183i
$698$	−5.27270			−0.199575
$699$	−47.7287	−	47.7287i	−1.80527	−	1.80527i
$700$	−1.78215	−	4.30250i	−0.0673590	−	0.162619i
$701$		−	37.5419i		−	1.41794i	−0.705239	−	0.708969i	$-0.749160\pi$
$701$		−	37.5419i		−	1.41794i	0.705239	−	0.708969i	$-0.250840\pi$
$702$	31.7089	−	13.1343i	1.19678	−	0.495721i
$703$	5.19582	−	12.5438i	0.195964	−	0.473099i
$704$	−6.24404	−	2.58637i	−0.235331	−	0.0974773i
$705$	18.2560	−	18.2560i	0.687560	−	0.687560i
$706$	−4.55227	+	4.55227i	−0.171327	+	0.171327i
$707$	−0.848818	−	0.351592i	−0.0319231	−	0.0132230i
$708$	−5.11950	+	12.3596i	−0.192403	+	0.464501i
$709$	12.7076	−	5.26367i	0.477245	−	0.197681i	−0.131076	−	0.991372i	$-0.541843\pi$
$709$	12.7076	−	5.26367i	0.477245	−	0.197681i	0.608321	+	0.793691i	$0.291843\pi$
$710$		−	2.91062i		−	0.109234i
$711$	−17.8409	−	43.0718i	−0.669087	−	1.61532i
$712$	24.2749	+	24.2749i	0.909741	+	0.909741i
$713$	2.72198			0.101939
$714$	−29.9443	+	6.55547i	−1.12064	+	0.245332i
$715$	11.8110			0.441707
$716$	−21.4667	−	21.4667i	−0.802246	−	0.802246i
$717$	6.94446	+	16.7654i	0.259346	+	0.626116i
$718$			6.86660i			0.256259i
$719$	−0.488717	+	0.202433i	−0.0182261	+	0.00754949i	−0.391778	−	0.920060i	$-0.628140\pi$
$719$	−0.488717	+	0.202433i	−0.0182261	+	0.00754949i	0.373552	+	0.927609i	$0.378140\pi$
$720$	−2.36342	+	5.70581i	−0.0880796	+	0.212643i
$721$	−42.0631	−	17.4231i	−1.56651	−	0.648870i
$722$	−9.19671	+	9.19671i	−0.342266	+	0.342266i
$723$	−28.9441	+	28.9441i	−1.07644	+	1.07644i
$724$	−30.1586	−	12.4921i	−1.12084	−	0.464265i
$725$	−0.170049	+	0.410535i	−0.00631547	+	0.0152469i
$726$	7.47778	−	3.09740i	0.277527	−	0.114955i
$727$		−	26.7632i		−	0.992591i	−0.868154	−	0.496296i	$-0.834693\pi$
$727$		−	26.7632i		−	0.992591i	0.868154	−	0.496296i	$-0.165307\pi$
$728$	13.7467	+	33.1875i	0.509487	+	1.23001i
$729$	−8.55986	−	8.55986i	−0.317032	−	0.317032i
$730$	−4.83947			−0.179117
$731$	−8.70721	+	1.90620i	−0.322048	+	0.0705033i
$732$	54.1486			2.00139
$733$	−12.2673	−	12.2673i	−0.453105	−	0.453105i	0.443279	−	0.896384i	$-0.353815\pi$
$733$	−12.2673	−	12.2673i	−0.453105	−	0.453105i	−0.896384	+	0.443279i	$0.853815\pi$
$734$	1.95086	+	4.70978i	0.0720074	+	0.173841i
$735$		−	10.6083i		−	0.391294i
$736$	−2.66658	+	1.10454i	−0.0982916	+	0.0407137i
$737$	−4.41056	+	10.6480i	−0.162465	+	0.392225i
$738$	−9.68219	−	4.01050i	−0.356407	−	0.147628i
$739$	21.3876	−	21.3876i	0.786757	−	0.786757i	−0.194204	−	0.980961i	$-0.562212\pi$
$739$	21.3876	−	21.3876i	0.786757	−	0.786757i	0.980961	+	0.194204i	$0.0622124\pi$
$740$	−10.8998	+	10.8998i	−0.400683	+	0.400683i
$741$	−15.5673	−	6.44819i	−0.571880	−	0.236880i
$742$	1.68111	−	4.05856i	0.0617155	−	0.148994i
$743$	6.63416	−	2.74796i	0.243384	−	0.100813i	−0.257657	−	0.966236i	$-0.582951\pi$
$743$	6.63416	−	2.74796i	0.243384	−	0.100813i	0.501041	+	0.865424i	$0.332951\pi$
$744$			43.7457i			1.60379i
$745$	−8.79842	−	21.2413i	−0.322349	−	0.778220i
$746$	−5.53430	−	5.53430i	−0.202625	−	0.202625i
$747$	−1.46869			−0.0537366
$748$	9.28309	+	13.3325i	0.339423	+	0.487486i
$749$	60.4819			2.20996
$750$	1.62625	+	1.62625i	0.0593821	+	0.0593821i
$751$	11.9767	+	28.9144i	0.437037	+	1.05510i	0.976967	+	0.213390i	$0.0684505\pi$
$751$	11.9767	+	28.9144i	0.437037	+	1.05510i	−0.539930	+	0.841710i	$0.681549\pi$
$752$		−	8.03197i		−	0.292896i
$753$	10.2095	−	4.22890i	0.372054	−	0.154110i
$754$	0.549215	−	1.32592i	0.0200012	−	0.0482873i
$755$	−0.180843	−	0.0749077i	−0.00658156	−	0.00272617i
$756$	−34.9936	+	34.9936i	−1.27271	+	1.27271i
$757$	−7.61956	+	7.61956i	−0.276938	+	0.276938i	−0.831885	−	0.554948i	$-0.812738\pi$
$757$	−7.61956	+	7.61956i	−0.276938	+	0.276938i	0.554948	+	0.831885i	$0.312738\pi$
$758$	−17.5108	−	7.25323i	−0.636022	−	0.263449i
$759$	−1.58471	+	3.82582i	−0.0575212	+	0.138868i
$760$	−3.01674	+	1.24957i	−0.109429	+	0.0453268i
$761$		−	33.1409i		−	1.20136i	−0.799491	−	0.600678i	$-0.794898\pi$
$761$		−	33.1409i		−	1.20136i	0.799491	−	0.600678i	$-0.205102\pi$
$762$	−4.80998	−	11.6123i	−0.174247	−	0.420670i
$763$	−8.07068	−	8.07068i	−0.292178	−	0.292178i
$764$	−5.04452			−0.182504
$765$	−21.8445	+	15.2097i	−0.789788	+	0.549909i
$766$	5.75182			0.207822
$767$	9.22123	+	9.22123i	0.332959	+	0.332959i
$768$	−14.5077	−	35.0247i	−0.523502	−	1.26385i
$769$		−	11.4864i		−	0.414210i	−0.978319	−	0.207105i	$-0.933596\pi$
$769$		−	11.4864i		−	0.414210i	0.978319	−	0.207105i	$-0.0664042\pi$
$770$	6.10932	−	2.53056i	0.220165	−	0.0911952i
$771$	28.8885	−	69.7429i	1.04039	−	2.51173i
$772$	16.3632	+	6.77785i	0.588924	+	0.243940i
$773$	−2.26913	+	2.26913i	−0.0816149	+	0.0816149i	−0.746736	−	0.665121i	$-0.768380\pi$
$773$	−2.26913	+	2.26913i	−0.0816149	+	0.0816149i	0.665121	+	0.746736i	$0.268380\pi$
$774$	7.38087	−	7.38087i	0.265300	−	0.265300i
$775$	−5.10754	−	2.11561i	−0.183468	−	0.0759951i
$776$	14.5817	−	35.2034i	0.523454	−	1.26373i
$777$	−98.2653	+	40.7028i	−3.52525	+	1.46021i
$778$		−	11.8454i		−	0.424678i
$779$	1.05397	+	2.54451i	0.0377625	+	0.0911667i
$780$	13.5270	+	13.5270i	0.484343	+	0.484343i
$781$	−10.6440			−0.380873
$782$	−1.49456	−	0.267608i	−0.0534452	−	0.00956963i
$783$	4.72208			0.168754
$784$	−2.33364	−	2.33364i	−0.0833443	−	0.0833443i
$785$	−4.53796	−	10.9556i	−0.161967	−	0.391022i
$786$		−	22.9515i		−	0.818651i
$787$	3.11375	−	1.28976i	0.110993	−	0.0459748i	−0.326496	−	0.945199i	$-0.605868\pi$
$787$	3.11375	−	1.28976i	0.110993	−	0.0459748i	0.437489	+	0.899224i	$0.355868\pi$
$788$	9.35875	−	22.5940i	0.333392	−	0.804879i
$789$	41.5920	+	17.2280i	1.48071	+	0.613332i
$790$	−3.81913	+	3.81913i	−0.135878	+	0.135878i
$791$	6.49523	−	6.49523i	0.230944	−	0.230944i
$792$	−41.9784	−	17.3880i	−1.49164	−	0.617857i
$793$	20.1996	−	48.7661i	0.717308	−	1.73174i
$794$	−20.1518	+	8.34716i	−0.715161	+	0.296230i
$795$		−	5.58726i		−	0.198160i
$796$	−6.38293	−	15.4097i	−0.226237	−	0.546184i
$797$	−15.0966	−	15.0966i	−0.534747	−	0.534747i	0.387234	−	0.921981i	$-0.373431\pi$
$797$	−15.0966	−	15.0966i	−0.534747	−	0.534747i	−0.921981	+	0.387234i	$0.873431\pi$
$798$	−9.43385			−0.333955
$799$	18.6771	−	29.1468i	0.660748	−	1.03114i
$800$	5.86207			0.207256
$801$	60.9002	+	60.9002i	2.15180	+	2.15180i
$802$	4.68987	+	11.3224i	0.165605	+	0.399806i
$803$			17.6977i			0.624538i
$804$	−17.2464	+	7.14369i	−0.608233	+	0.251939i
$805$	0.609092	−	1.47048i	0.0214677	−	0.0518276i
$806$	16.4960	+	6.83288i	0.581048	+	0.240678i
$807$	40.7907	−	40.7907i	1.43590	−	1.43590i
$808$	0.517153	−	0.517153i	0.0181934	−	0.0181934i
$809$	−2.52190	−	1.04460i	−0.0886652	−	0.0367263i	0.337910	−	0.941178i	$-0.390280\pi$
$809$	−2.52190	−	1.04460i	−0.0886652	−	0.0367263i	−0.426575	+	0.904452i	$0.640280\pi$
$810$	3.80952	−	9.19698i	0.133853	−	0.323149i
$811$	−34.4933	+	14.2876i	−1.21122	+	0.501705i	−0.894609	−	0.446849i	$-0.852546\pi$
$811$	−34.4933	+	14.2876i	−1.21122	+	0.501705i	−0.316614	+	0.948554i	$0.602546\pi$
$812$			2.06938i			0.0726211i
$813$	6.78272	+	16.3749i	0.237880	+	0.574294i
$814$	−15.4771	−	15.4771i	−0.542471	−	0.542471i
$815$	5.34472			0.187217
$816$	−2.13776	+	11.9391i	−0.0748365	+	0.417953i
$817$	−2.74317			−0.0959715
$818$	−17.9796	−	17.9796i	−0.628641	−	0.628641i
$819$	34.4874	+	83.2600i	1.20509	+	2.90934i
$820$		−	3.12685i		−	0.109194i
$821$	−39.0148	+	16.1605i	−1.36163	+	0.564004i	−0.939505	−	0.342536i	$-0.888714\pi$
$821$	−39.0148	+	16.1605i	−1.36163	+	0.564004i	−0.422121	+	0.906540i	$0.638714\pi$
$822$	−2.70876	+	6.53952i	−0.0944788	+	0.228092i
$823$	19.1803	+	7.94473i	0.668582	+	0.276936i	0.691045	−	0.722812i	$-0.257151\pi$
$823$	19.1803	+	7.94473i	0.668582	+	0.276936i	−0.0224627	+	0.999748i	$0.507151\pi$
$824$	25.6275	−	25.6275i	0.892775	−	0.892775i
$825$	5.94710	−	5.94710i	0.207051	−	0.207051i
$826$	6.74543	+	2.79405i	0.234704	+	0.0972174i
$827$	−4.40367	+	10.6314i	−0.153131	+	0.369690i	−0.981765	−	0.190101i	$-0.939119\pi$
$827$	−4.40367	+	10.6314i	−0.153131	+	0.369690i	0.828634	+	0.559791i	$0.189119\pi$
$828$	−4.23063	+	1.75238i	−0.147025	+	0.0608996i
$829$			11.7508i			0.408121i	0.978958	+	0.204060i	$0.0654139\pi$
$829$			11.7508i			0.408121i	−0.978958	+	0.204060i	$0.934586\pi$
$830$	0.0651135	+	0.157198i	0.00226012	+	0.00545642i
$831$	0.267995	+	0.267995i	0.00929664	+	0.00929664i
$832$	−10.6708			−0.369942
$833$	−3.04191	−	13.8949i	−0.105396	−	0.481431i
$834$	−15.4318			−0.534361
$835$	8.19535	+	8.19535i	0.283612	+	0.283612i
$836$	1.91335	+	4.61924i	0.0661747	+	0.159760i
$837$			58.7483i			2.03064i
$838$	−0.617003	+	0.255571i	−0.0213140	+	0.00882855i
$839$	−14.0060	+	33.8134i	−0.483540	+	1.16737i	0.474377	+	0.880322i	$0.342673\pi$
$839$	−14.0060	+	33.8134i	−0.483540	+	1.16737i	−0.957917	+	0.287046i	$0.907327\pi$
$840$	23.6324	+	9.78887i	0.815396	+	0.337748i
$841$	−20.3665	+	20.3665i	−0.702292	+	0.702292i
$842$	−17.8079	+	17.8079i	−0.613701	+	0.613701i
$843$	−5.18086	−	2.14598i	−0.178438	−	0.0739116i
$844$	3.67377	−	8.86927i	0.126457	−	0.305293i
$845$	5.21805	−	2.16139i	0.179506	−	0.0743539i
$846$			40.5390i			1.39376i
$847$	4.35362	+	10.5106i	0.149592	+	0.361148i
$848$	−1.22910	−	1.22910i	−0.0422074	−	0.0422074i
$849$	88.0312			3.02122
$850$	2.59640	+	1.66376i	0.0890558	+	0.0570665i
$851$	−5.26829			−0.180595
$852$	−12.1904	−	12.1904i	−0.417637	−	0.417637i
$853$	14.5715	+	35.1787i	0.498918	+	1.20450i	0.950067	+	0.312046i	$0.101014\pi$
$853$	14.5715	+	35.1787i	0.498918	+	1.20450i	−0.451149	+	0.892449i	$0.648986\pi$
$854$		−	29.5524i		−	1.01126i
$855$	−7.56831	+	3.13490i	−0.258831	+	0.107211i
$856$	−18.4247	+	44.4811i	−0.629742	+	1.52033i
$857$	−18.6880	−	7.74080i	−0.638368	−	0.264421i	0.0399356	−	0.999202i	$-0.487285\pi$
$857$	−18.6880	−	7.74080i	−0.638368	−	0.264421i	−0.678304	+	0.734781i	$0.737285\pi$
$858$	−19.2076	+	19.2076i	−0.655736	+	0.655736i
$859$	1.84360	−	1.84360i	0.0629028	−	0.0629028i	−0.674956	−	0.737858i	$-0.735837\pi$
$859$	1.84360	−	1.84360i	0.0629028	−	0.0629028i	0.737858	+	0.674956i	$0.235837\pi$
$860$	2.87731	+	1.19182i	0.0981153	+	0.0406407i
$861$	8.25657	−	19.9331i	0.281383	−	0.679319i
$862$	11.2609	−	4.66443i	0.383548	−	0.158871i
$863$		−	11.2563i		−	0.383169i	−0.981476	−	0.191584i	$-0.938637\pi$
$863$		−	11.2563i		−	0.383169i	0.981476	−	0.191584i	$-0.0613626\pi$
$864$	−23.8391	−	57.5526i	−0.811022	−	1.95798i
$865$	−7.79732	−	7.79732i	−0.265117	−	0.265117i
$866$	26.1730			0.889396
$867$	−35.5202	+	38.3542i	−1.20633	+	1.30258i
$868$	−25.7455			−0.873860
$869$	13.9664	+	13.9664i	0.473777	+	0.473777i
$870$	−0.391089	−	0.944173i	−0.0132592	−	0.0320105i
$871$			18.1970i			0.616580i
$872$	8.39412	−	3.47696i	0.284261	−	0.117745i
$873$	36.5822	−	88.3174i	1.23812	−	2.98909i
$874$	−0.431707	−	0.178819i	−0.0146027	−	0.00604864i
$875$	−2.28581	+	2.28581i	−0.0772744	+	0.0772744i
$876$	−20.2689	+	20.2689i	−0.684824	+	0.684824i
$877$	−5.54426	−	2.29651i	−0.187216	−	0.0775476i	0.287106	−	0.957899i	$-0.407307\pi$
$877$	−5.54426	−	2.29651i	−0.187216	−	0.0775476i	−0.474322	+	0.880351i	$0.657307\pi$
$878$	6.37620	−	15.3935i	0.215186	−	0.519506i
$879$	4.02300	−	1.66638i	0.135692	−	0.0562056i
$880$		−	2.61651i		−	0.0882025i
$881$	13.1380	+	31.7181i	0.442632	+	1.06861i	0.975022	+	0.222109i	$0.0712941\pi$
$881$	13.1380	+	31.7181i	0.442632	+	1.06861i	−0.532390	+	0.846499i	$0.678706\pi$
$882$	11.7784	+	11.7784i	0.396598	+	0.396598i
$883$	−11.8244			−0.397921			−0.198961	−	0.980007i	$-0.563757\pi$
$883$	−11.8244			−0.397921			−0.198961	+	0.980007i	$0.563757\pi$
$884$	21.5966	+	13.8390i	0.726374	+	0.465456i
$885$	9.28618			0.312152
$886$	4.65343	+	4.65343i	0.156335	+	0.156335i
$887$	−9.27440	−	22.3904i	−0.311404	−	0.751796i	−0.999654	−	0.0263216i	$-0.991621\pi$
$887$	−9.27440	−	22.3904i	−0.311404	−	0.751796i	0.688250	−	0.725474i	$-0.258379\pi$
$888$		−	84.6680i		−	2.84127i
$889$	16.3220	−	6.76077i	0.547421	−	0.226749i
$890$	3.81834	−	9.21830i	0.127991	−	0.308998i
$891$	−33.6329	−	13.9312i	−1.12675	−	0.466713i
$892$	12.8279	−	12.8279i	0.429511	−	0.429511i
$893$	7.53337	−	7.53337i	0.252095	−	0.252095i
$894$	48.8519	+	20.2351i	1.63385	+	0.676764i
$895$	−8.06433	+	19.4690i	−0.269561	+	0.650777i
$896$	29.4952	−	12.2173i	0.985367	−	0.408152i
$897$			6.53813i			0.218302i
$898$	2.53782	+	6.12683i	0.0846880	+	0.204455i
$899$	1.73707	+	1.73707i	0.0579345	+	0.0579345i
$900$	9.30039			0.310013
$901$	−1.60213	−	7.31828i	−0.0533747	−	0.243807i
$902$	4.43996			0.147835
$903$	15.1953	+	15.1953i	0.505668	+	0.505668i
$904$	2.79823	+	6.75553i	0.0930678	+	0.224686i
$905$			22.6592i			0.753218i
$906$	0.415914	−	0.172277i	0.0138178	−	0.00572353i
$907$	−17.1364	+	41.3709i	−0.569005	+	1.37370i	0.333390	+	0.942789i	$0.391808\pi$
$907$	−17.1364	+	41.3709i	−0.569005	+	1.37370i	−0.902395	+	0.430910i	$0.858192\pi$
$908$	−10.7045	−	4.43394i	−0.355240	−	0.147145i
$909$	1.29742	−	1.29742i	0.0430326	−	0.0430326i
$910$	7.38256	−	7.38256i	0.244730	−	0.244730i
$911$	9.19129	+	3.80716i	0.304521	+	0.126137i	0.529711	−	0.848178i	$-0.322300\pi$
$911$	9.19129	+	3.80716i	0.304521	+	0.126137i	−0.225190	+	0.974315i	$0.572300\pi$
$912$	−1.42848	+	3.44865i	−0.0473016	+	0.114196i
$913$	0.574865	−	0.238117i	0.0190253	−	0.00788052i
$914$			13.8182i			0.457066i
$915$	−14.3839	−	34.7257i	−0.475516	−	1.14800i
$916$	22.0334	+	22.0334i	0.728005	+	0.728005i
$917$	32.2600			1.06532
$918$	5.77575	−	32.2569i	0.190628	−	1.06464i
$919$	−33.3601			−1.10045			−0.550224	−	0.835017i	$-0.685458\pi$
$919$	−33.3601			−1.10045			−0.550224	+	0.835017i	$0.685458\pi$
$920$	0.895907	+	0.895907i	0.0295372	+	0.0295372i
$921$	−25.5786	−	61.7522i	−0.842844	−	2.03480i
$922$		−	18.3762i		−	0.605189i
$923$	−15.5262	+	6.43116i	−0.511051	+	0.211684i
$924$	14.9887	−	36.1860i	0.493094	−	1.19043i
$925$	9.88545	+	4.09469i	0.325032	+	0.134632i
$926$	−5.24059	+	5.24059i	−0.172217	+	0.172217i
$927$	64.2934	−	64.2934i	2.11167	−	2.11167i
$928$	−2.40659	−	0.996842i	−0.0790001	−	0.0327229i
$929$	−9.52731	+	23.0010i	−0.312581	+	0.754637i	0.687027	+	0.726632i	$0.258915\pi$
$929$	−9.52731	+	23.0010i	−0.312581	+	0.754637i	−0.999608	+	0.0280049i	$0.991085\pi$
$930$	11.7466	−	4.86561i	0.385187	−	0.159550i
$931$		−	4.37755i		−	0.143468i
$932$	12.1014	+	29.2154i	0.396395	+	0.956982i
$933$	18.8106	+	18.8106i	0.615830	+	0.615830i
$934$	21.9917			0.719592
$935$	6.08429	−	9.49491i	0.198977	−	0.310517i
$936$	−71.7390			−2.34486
$937$	−22.0943	−	22.0943i	−0.721788	−	0.721788i	0.247181	−	0.968969i	$-0.420496\pi$
$937$	−22.0943	−	22.0943i	−0.721788	−	0.721788i	−0.968969	+	0.247181i	$0.920496\pi$
$938$	3.89878	+	9.41250i	0.127300	+	0.307329i
$939$			31.6176i			1.03180i
$940$	−11.1747	+	4.62872i	−0.364479	+	0.150972i
$941$	−0.663467	+	1.60175i	−0.0216284	+	0.0522156i	−0.934325	−	0.356423i	$-0.883996\pi$
$941$	−0.663467	+	1.60175i	−0.0216284	+	0.0522156i	0.912696	+	0.408638i	$0.133996\pi$
$942$	25.1963	+	10.4367i	0.820940	+	0.340045i
$943$	0.755666	−	0.755666i	0.0246079	−	0.0246079i
$944$	2.04279	−	2.04279i	0.0664873	−	0.0664873i
$945$	31.7372	+	13.1460i	1.03241	+	0.427639i
$946$	−1.69232	+	4.08562i	−0.0550221	+	0.132835i
$947$	10.0253	−	4.15260i	0.325777	−	0.134941i	−0.213800	−	0.976877i	$-0.568584\pi$
$947$	10.0253	−	4.15260i	0.325777	−	0.134941i	0.539577	+	0.841936i	$0.318584\pi$
$948$			31.9910i			1.03902i
$949$	10.6930	+	25.8153i	0.347111	+	0.838000i
$950$	0.671074	+	0.671074i	0.0217725	+	0.0217725i
$951$	−3.46760			−0.112445
$952$	33.7610	+	6.04508i	1.09420	+	0.195922i
$953$	−16.9007			−0.547466			−0.273733	−	0.961806i	$-0.588258\pi$
$953$	−16.9007			−0.547466			−0.273733	+	0.961806i	$0.588258\pi$
$954$	6.20351	+	6.20351i	0.200846	+	0.200846i
$955$	1.34001	+	3.23508i	0.0433618	+	0.104685i
$956$		−	8.50159i		−	0.274961i
$957$	−3.45280	+	1.43020i	−0.111613	+	0.0462316i
$958$	−8.18582	+	19.7623i	−0.264472	+	0.638491i
$959$	−9.19177	−	3.80736i	−0.296818	−	0.122946i
$960$	−5.37296	+	5.37296i	−0.173411	+	0.173411i
$961$	0.309144	−	0.309144i	0.00997239	−	0.00997239i
$962$	−31.9274	−	13.2248i	−1.02938	−	0.426384i
$963$	−46.2233	+	111.593i	−1.48952	+	3.59603i
$964$	17.7171	−	7.33864i	0.570628	−	0.236362i
$965$		−	12.2942i		−	0.395765i
$966$	1.40083	+	3.38189i	0.0450708	+	0.108811i
$967$	22.0869	+	22.0869i	0.710267	+	0.710267i	0.966591	−	0.256324i	$-0.0825115\pi$
$967$	22.0869	+	22.0869i	0.710267	+	0.710267i	−0.256324	+	0.966591i	$0.582511\pi$
$968$	−9.05619			−0.291077
$969$	−13.2030	+	9.19292i	−0.424142	+	0.295319i
$970$	−11.0747			−0.355587
$971$	−12.2957	−	12.2957i	−0.394589	−	0.394589i	0.481731	−	0.876319i	$-0.340008\pi$
$971$	−12.2957	−	12.2957i	−0.394589	−	0.394589i	−0.876319	+	0.481731i	$0.840008\pi$
$972$	−4.98849	−	12.0433i	−0.160006	−	0.386288i
$973$		−	21.6906i		−	0.695368i
$974$	0.426947	−	0.176847i	0.0136802	−	0.00566654i
$975$	5.08165	−	12.2682i	0.162743	−	0.392896i
$976$	−10.8032	−	4.47485i	−0.345803	−	0.143236i
$977$	−6.48656	+	6.48656i	−0.207523	+	0.207523i	−0.803214	−	0.595691i	$-0.796878\pi$
$977$	−6.48656	+	6.48656i	−0.207523	+	0.207523i	0.595691	+	0.803214i	$0.296878\pi$
$978$	−8.69182	+	8.69182i	−0.277934	+	0.277934i
$979$	−33.7109	−	13.9635i	−1.07740	−	0.446275i
$980$	−1.90190	+	4.59160i	−0.0607540	+	0.146673i
$981$	21.0589	−	8.72290i	0.672360	−	0.278501i
$982$		−	19.0469i		−	0.607811i
$983$	14.2729	+	34.4578i	0.455235	+	1.09903i	0.970305	+	0.241886i	$0.0777660\pi$
$983$	14.2729	+	34.4578i	0.455235	+	1.09903i	−0.515070	+	0.857148i	$0.672234\pi$
$984$	12.1445	+	12.1445i	0.387152	+	0.387152i
$985$	−16.9757			−0.540891
$986$	−0.782993	−	1.12455i	−0.0249356	−	0.0358129i
$987$	−83.4593			−2.65654
$988$	5.58194	+	5.58194i	0.177585	+	0.177585i
$989$	0.407332	+	0.983386i	0.0129524	+	0.0312699i
$990$			13.2061i			0.419716i
$991$	−32.3988	+	13.4200i	−1.02918	+	0.426301i	−0.832417	−	0.554149i	$-0.813044\pi$
$991$	−32.3988	+	13.4200i	−1.02918	+	0.426301i	−0.196765	+	0.980451i	$0.563044\pi$
$992$	12.4019	−	29.9408i	0.393760	−	0.950621i
$993$	−97.3310	−	40.3158i	−3.08871	−	1.27938i
$994$	−6.65312	+	6.65312i	−0.211024	+	0.211024i
$995$	−8.18680	+	8.18680i	−0.259539	+	0.259539i
$996$	0.931097	+	0.385673i	0.0295029	+	0.0122205i
$997$	14.2961	−	34.5139i	0.452763	−	1.09307i	−0.518505	−	0.855075i	$-0.673511\pi$
$997$	14.2961	−	34.5139i	0.452763	−	1.09307i	0.971267	−	0.237991i	$-0.0764889\pi$
$998$	−25.1934	+	10.4355i	−0.797484	+	0.330329i
$999$		−	113.705i		−	3.59747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.l.a.66.2	✓	24
3.2	odd	2		765.2.be.b.406.5		24
5.2	odd	4		425.2.n.c.49.5		24
5.3	odd	4		425.2.n.f.49.2		24
5.4	even	2		425.2.m.b.151.5		24
17.3	odd	16		1445.2.d.j.866.7		24
17.5	odd	16		1445.2.a.p.1.9		12
17.8	even	8	inner	85.2.l.a.76.2	yes	24
17.12	odd	16		1445.2.a.q.1.9		12
17.14	odd	16		1445.2.d.j.866.8		24
51.8	odd	8		765.2.be.b.586.5		24
85.8	odd	8		425.2.n.c.399.5		24
85.29	odd	16		7225.2.a.bq.1.4		12
85.39	odd	16		7225.2.a.bs.1.4		12
85.42	odd	8		425.2.n.f.399.2		24
85.59	even	8		425.2.m.b.76.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.2	✓	24	1.1	even	1	trivial
85.2.l.a.76.2	yes	24	17.8	even	8	inner
425.2.m.b.76.5		24	85.59	even	8
425.2.m.b.151.5		24	5.4	even	2
425.2.n.c.49.5		24	5.2	odd	4
425.2.n.c.399.5		24	85.8	odd	8
425.2.n.f.49.2		24	5.3	odd	4
425.2.n.f.399.2		24	85.42	odd	8
765.2.be.b.406.5		24	3.2	odd	2
765.2.be.b.586.5		24	51.8	odd	8
1445.2.a.p.1.9		12	17.5	odd	16
1445.2.a.q.1.9		12	17.12	odd	16
1445.2.d.j.866.7		24	17.3	odd	16
1445.2.d.j.866.8		24	17.14	odd	16
7225.2.a.bq.1.4		12	85.29	odd	16
7225.2.a.bs.1.4		12	85.39	odd	16

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.528855 - 0.528855i) q^{2} +(1.17676 + 2.84096i) q^{3} -1.44062i q^{4} +(-0.923880 + 0.382683i) q^{5} +(0.880118 - 2.12479i) q^{6} +(2.98655 + 1.23707i) q^{7} +(-1.81959 + 1.81959i) q^{8} +(-4.56494 + 4.56494i) q^{9} +O(q^{10})\)	\(q+(-0.528855 - 0.528855i) q^{2} +(1.17676 + 2.84096i) q^{3} -1.44062i q^{4} +(-0.923880 + 0.382683i) q^{5} +(0.880118 - 2.12479i) q^{6} +(2.98655 + 1.23707i) q^{7} +(-1.81959 + 1.81959i) q^{8} +(-4.56494 + 4.56494i) q^{9} +(0.690983 + 0.286214i) q^{10} +(1.04667 - 2.52689i) q^{11} +(4.09275 - 1.69527i) q^{12} -4.31833i q^{13} +(-0.925222 - 2.23368i) q^{14} +(-2.17437 - 2.17437i) q^{15} -0.956646 q^{16} +(-3.47152 - 2.22453i) q^{17} +4.82839 q^{18} +(-0.897260 - 0.897260i) q^{19} +(0.551303 + 1.33096i) q^{20} +9.94040i q^{21} +(-1.88990 + 0.782821i) q^{22} +(-0.188421 + 0.454888i) q^{23} +(-7.31061 - 3.02815i) q^{24} +(0.707107 - 0.707107i) q^{25} +(-2.28377 + 2.28377i) q^{26} +(-9.81779 - 4.06666i) q^{27} +(1.78215 - 4.30250i) q^{28} +(-0.410535 + 0.170049i) q^{29} +2.29986i q^{30} +(-2.11561 - 5.10754i) q^{31} +(4.14511 + 4.14511i) q^{32} +8.41047 q^{33} +(0.659477 + 3.01239i) q^{34} -3.23262 q^{35} +(6.57637 + 6.57637i) q^{36} +(4.09469 + 9.88545i) q^{37} +0.949042i q^{38} +(12.2682 - 5.08165i) q^{39} +(0.984756 - 2.37741i) q^{40} +(-2.00526 - 0.830608i) q^{41} +(5.25703 - 5.25703i) q^{42} +(1.52864 - 1.52864i) q^{43} +(-3.64030 - 1.50786i) q^{44} +(2.47053 - 5.96439i) q^{45} +(0.340217 - 0.140922i) q^{46} +8.39597i q^{47} +(-1.12575 - 2.71779i) q^{48} +(2.43940 + 2.43940i) q^{49} -0.747914 q^{50} +(2.23464 - 12.4802i) q^{51} -6.22109 q^{52} +(1.28480 + 1.28480i) q^{53} +(3.04152 + 7.34287i) q^{54} +2.73509i q^{55} +(-7.68527 + 3.18334i) q^{56} +(1.49321 - 3.60494i) q^{57} +(0.307045 + 0.127182i) q^{58} +(-2.13537 + 2.13537i) q^{59} +(-3.13246 + 3.13246i) q^{60} +(11.2928 + 4.67764i) q^{61} +(-1.58230 + 3.82000i) q^{62} +(-19.2806 + 7.98628i) q^{63} -2.47104i q^{64} +(1.65255 + 3.98962i) q^{65} +(-4.44792 - 4.44792i) q^{66} -4.21389 q^{67} +(-3.20471 + 5.00116i) q^{68} -1.51404 q^{69} +(1.70959 + 1.70959i) q^{70} +(-1.48927 - 3.59542i) q^{71} -16.6127i q^{72} +(-5.97807 + 2.47620i) q^{73} +(3.06247 - 7.39347i) q^{74} +(2.84096 + 1.17676i) q^{75} +(-1.29261 + 1.29261i) q^{76} +(6.25188 - 6.25188i) q^{77} +(-9.17555 - 3.80064i) q^{78} +(-2.76355 + 6.67180i) q^{79} +(0.883826 - 0.366093i) q^{80} -13.3100i q^{81} +(0.621223 + 1.49977i) q^{82} +(0.160866 + 0.160866i) q^{83} +14.3204 q^{84} +(4.05856 + 0.726705i) q^{85} -1.61686 q^{86} +(-0.966206 - 0.966206i) q^{87} +(2.69339 + 6.50243i) q^{88} -13.3408i q^{89} +(-4.46085 + 1.84774i) q^{90} +(5.34208 - 12.8969i) q^{91} +(0.655322 + 0.271443i) q^{92} +(12.0207 - 12.0207i) q^{93} +(4.44025 - 4.44025i) q^{94} +(1.17233 + 0.485594i) q^{95} +(-6.89827 + 16.6539i) q^{96} +(-13.6803 + 5.66657i) q^{97} -2.58018i q^{98} +(6.75711 + 16.3131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 24 q^{9}+O(q^{10}) \) 24 * q - 8 * q^6 - 24 * q^9	\( 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35} - 24 q^{36} + 24 q^{37} + 8 q^{39} + 16 q^{40} + 16 q^{41} - 24 q^{42} + 8 q^{43} + 16 q^{44} + 16 q^{45} + 8 q^{46} + 80 q^{48} + 8 q^{50} - 56 q^{51} - 48 q^{52} + 24 q^{53} - 32 q^{54} + 64 q^{56} + 32 q^{57} - 64 q^{58} + 32 q^{59} + 24 q^{60} + 32 q^{61} - 32 q^{62} - 56 q^{63} + 8 q^{65} + 96 q^{66} + 16 q^{67} - 40 q^{68} + 96 q^{69} - 24 q^{71} - 64 q^{74} - 8 q^{75} - 8 q^{76} + 24 q^{77} - 112 q^{78} - 32 q^{80} - 80 q^{82} - 96 q^{83} - 64 q^{84} - 16 q^{86} - 48 q^{87} - 8 q^{88} - 24 q^{91} + 80 q^{92} + 64 q^{93} + 56 q^{94} - 16 q^{95} - 168 q^{96} - 40 q^{97} - 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

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