LMFDB - Embedded newform 770.2.bi.a.27.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(27,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 10, 8]))

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

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

chi := DirichletCharacter("770.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bi (of order $20$, degree $8$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$48$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			27.16
Character	$\chi$	$=$	770.27
Dual form			770.2.bi.a.713.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(0.160862 + 1.01564i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-2.16890 + 0.543949i) q^{5} +(-0.977976 - 0.317764i) q^{6} +(2.46967 + 0.949081i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.84751 - 0.600293i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(0.160862 + 1.01564i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-2.16890 + 0.543949i) q^{5} +(-0.977976 - 0.317764i) q^{6} +(2.46967 + 0.949081i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.84751 - 0.600293i) q^{9} +(0.499997 - 2.17945i) q^{10} +(-0.0358649 + 3.31643i) q^{11} +(0.727121 - 0.727121i) q^{12} +(-1.04729 + 2.05542i) q^{13} +(-1.96684 + 1.76961i) q^{14} +(-0.901353 - 2.11533i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-1.97947 - 3.88492i) q^{17} +(-0.303888 + 1.91867i) q^{18} +(4.54891 + 3.30498i) q^{19} +(1.71491 + 1.43495i) q^{20} +(-0.566653 + 2.66097i) q^{21} +(-2.93868 - 1.53758i) q^{22} +(-3.13114 + 3.13114i) q^{23} +(0.317764 + 0.977976i) q^{24} +(4.40824 - 2.35954i) q^{25} +(-1.35593 - 1.86628i) q^{26} +(2.30740 + 4.52853i) q^{27} +(-0.683810 - 2.55586i) q^{28} +(-0.210267 - 0.289407i) q^{29} +(2.29398 + 0.157228i) q^{30} +(-5.17399 + 1.68113i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.37408 + 0.497063i) q^{33} +4.36015 q^{34} +(-5.87270 - 0.715087i) q^{35} +(-1.57159 - 1.14183i) q^{36} +(0.779305 + 0.123430i) q^{37} +(-5.00992 + 2.55268i) q^{38} +(-2.25605 - 0.733034i) q^{39} +(-2.05710 + 0.876543i) q^{40} +(0.121500 - 0.167231i) q^{41} +(-2.11369 - 1.71295i) q^{42} +(-7.64117 + 7.64117i) q^{43} +(2.70413 - 1.92033i) q^{44} +(-3.68054 + 2.30693i) q^{45} +(-1.36836 - 4.21138i) q^{46} +(-8.67139 + 1.37341i) q^{47} +(-1.01564 - 0.160862i) q^{48} +(5.19849 + 4.68782i) q^{49} +(0.101069 + 4.99898i) q^{50} +(3.62728 - 2.63537i) q^{51} +(2.27845 - 0.360871i) q^{52} +(-6.80148 - 3.46553i) q^{53} -5.08249 q^{54} +(-1.72618 - 7.21251i) q^{55} +(2.58773 + 0.551055i) q^{56} +(-2.62494 + 5.15173i) q^{57} +(0.353323 - 0.0559608i) q^{58} +(-3.33635 + 2.42400i) q^{59} +(-1.18153 + 1.97257i) q^{60} +(4.19738 + 1.36381i) q^{61} +(0.851043 - 5.37327i) q^{62} +(5.13246 + 0.270915i) q^{63} +(0.951057 - 0.309017i) q^{64} +(1.15342 - 5.02767i) q^{65} +(1.08892 - 3.23199i) q^{66} +(-0.245219 - 0.245219i) q^{67} +(-1.97947 + 3.88492i) q^{68} +(-3.68381 - 2.67645i) q^{69} +(3.30330 - 4.90797i) q^{70} +(1.58411 - 4.87540i) q^{71} +(1.73086 - 0.881917i) q^{72} +(-12.0637 - 1.91070i) q^{73} +(-0.463774 + 0.638330i) q^{74} +(3.10558 + 4.09764i) q^{75} -5.62277i q^{76} +(-3.23613 + 8.15643i) q^{77} +(1.67736 - 1.67736i) q^{78} +(11.7927 - 3.83167i) q^{79} +(0.152900 - 2.23083i) q^{80} +(0.486560 - 0.353506i) q^{81} +(0.0938438 + 0.184179i) q^{82} +(13.7484 - 7.00514i) q^{83} +(2.48584 - 1.10565i) q^{84} +(6.40646 + 7.34927i) q^{85} +(-3.33931 - 10.2774i) q^{86} +(0.260111 - 0.260111i) q^{87} +(0.483381 + 3.28121i) q^{88} +4.66473 q^{89} +(-0.384559 - 4.32671i) q^{90} +(-4.53722 + 4.08224i) q^{91} +(4.37359 + 0.692708i) q^{92} +(-2.53973 - 4.98450i) q^{93} +(2.71301 - 8.34978i) q^{94} +(-11.6639 - 4.69379i) q^{95} +(0.604422 - 0.831916i) q^{96} +(12.0347 + 6.13196i) q^{97} +(-6.53695 + 2.50366i) q^{98} +(1.92457 + 6.14868i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 4 q^{7}+O(q^{10}) $ 384 * q - 4 * q^7	$ 384 q - 4 q^{7} + 24 q^{15} + 96 q^{16} + 16 q^{22} + 16 q^{23} - 40 q^{25} + 4 q^{28} + 16 q^{30} - 32 q^{35} + 80 q^{36} - 64 q^{37} + 44 q^{42} - 80 q^{43} - 16 q^{46} - 64 q^{50} - 136 q^{51} + 80 q^{53} + 8 q^{56} - 112 q^{57} - 96 q^{58} + 68 q^{63} - 272 q^{65} + 160 q^{67} - 8 q^{70} + 16 q^{71} + 96 q^{77} + 24 q^{81} - 80 q^{85} - 16 q^{88} - 84 q^{91} + 16 q^{92} + 88 q^{93} - 184 q^{95} - 32 q^{98}+O(q^{100}) $ 384 * q - 4 * q^7 + 24 * q^15 + 96 * q^16 + 16 * q^22 + 16 * q^23 - 40 * q^25 + 4 * q^28 + 16 * q^30 - 32 * q^35 + 80 * q^36 - 64 * q^37 + 44 * q^42 - 80 * q^43 - 16 * q^46 - 64 * q^50 - 136 * q^51 + 80 * q^53 + 8 * q^56 - 112 * q^57 - 96 * q^58 + 68 * q^63 - 272 * q^65 + 160 * q^67 - 8 * q^70 + 16 * q^71 + 96 * q^77 + 24 * q^81 - 80 * q^85 - 16 * q^88 - 84 * q^91 + 16 * q^92 + 88 * q^93 - 184 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	0.160862	+	1.01564i	0.0928739	+	0.586383i	0.989606	+	0.143808i	$0.0459348\pi$
$3$	0.160862	+	1.01564i	0.0928739	+	0.586383i	−0.896732	+	0.442575i	$0.854065\pi$
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$	−2.16890	+	0.543949i	−0.969961	+	0.243262i
$5$	−2.16890	+	0.543949i	−0.969961	+	0.243262i
$6$	−0.977976	−	0.317764i	−0.399257	−	0.129726i
$7$	2.46967	+	0.949081i	0.933446	+	0.358719i
$7$	2.46967	+	0.949081i	0.933446	+	0.358719i
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	1.84751	−	0.600293i	0.615837	−	0.200098i
$10$	0.499997	−	2.17945i	0.158113	−	0.689203i
$11$	−0.0358649	+	3.31643i	−0.0108137	+	0.999942i
$11$	−0.0358649	+	3.31643i	−0.0108137	+	0.999942i
$12$	0.727121	−	0.727121i	0.209902	−	0.209902i
$13$	−1.04729	+	2.05542i	−0.290466	+	0.570071i	−0.989417	−	0.145098i	$-0.953650\pi$
$13$	−1.04729	+	2.05542i	−0.290466	+	0.570071i	0.698951	+	0.715169i	$0.253650\pi$
$14$	−1.96684	+	1.76961i	−0.525661	+	0.472949i
$15$	−0.901353	−	2.11533i	−0.232728	−	0.546176i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−1.97947	−	3.88492i	−0.480091	−	0.942232i	−0.996314	−	0.0857777i	$-0.972663\pi$
$17$	−1.97947	−	3.88492i	−0.480091	−	0.942232i	0.516223	−	0.856454i	$-0.327337\pi$
$18$	−0.303888	+	1.91867i	−0.0716271	+	0.452236i
$19$	4.54891	+	3.30498i	1.04359	+	0.758214i	0.970984	−	0.239146i	$-0.0768675\pi$
$19$	4.54891	+	3.30498i	1.04359	+	0.758214i	0.0726090	+	0.997360i	$0.476867\pi$
$20$	1.71491	+	1.43495i	0.383466	+	0.320865i
$21$	−0.566653	+	2.66097i	−0.123654	+	0.580672i
$22$	−2.93868	−	1.53758i	−0.626529	−	0.327814i
$23$	−3.13114	+	3.13114i	−0.652888	+	0.652888i	−0.953688	−	0.300799i	$-0.902747\pi$
$23$	−3.13114	+	3.13114i	−0.652888	+	0.652888i	0.300799	+	0.953688i	$0.402747\pi$
$24$	0.317764	+	0.977976i	0.0648632	+	0.199629i
$25$	4.40824	−	2.35954i	0.881648	−	0.471908i
$26$	−1.35593	−	1.86628i	−0.265921	−	0.366008i
$27$	2.30740	+	4.52853i	0.444060	+	0.871516i
$28$	−0.683810	−	2.55586i	−0.129228	−	0.483012i
$29$	−0.210267	−	0.289407i	−0.0390455	−	0.0537416i	0.789048	−	0.614332i	$-0.210574\pi$
$29$	−0.210267	−	0.289407i	−0.0390455	−	0.0537416i	−0.828093	+	0.560590i	$0.810574\pi$
$30$	2.29398	+	0.157228i	0.418821	+	0.0287057i
$31$	−5.17399	+	1.68113i	−0.929275	+	0.301940i	−0.734266	−	0.678862i	$-0.762474\pi$
$31$	−5.17399	+	1.68113i	−0.929275	+	0.301940i	−0.195009	+	0.980801i	$0.562474\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−3.37408	+	0.497063i	−0.587353	+	0.0865275i
$34$	4.36015			0.747759
$35$	−5.87270	−	0.715087i	−0.992668	−	0.120872i
$36$	−1.57159	−	1.14183i	−0.261931	−	0.190304i
$37$	0.779305	+	0.123430i	0.128117	+	0.0202917i	0.220164	−	0.975463i	$-0.429341\pi$
$37$	0.779305	+	0.123430i	0.128117	+	0.0202917i	−0.0920466	+	0.995755i	$0.529341\pi$
$38$	−5.00992	+	2.55268i	−0.812717	+	0.414100i
$39$	−2.25605	−	0.733034i	−0.361257	−	0.117379i
$40$	−2.05710	+	0.876543i	−0.325257	+	0.138594i
$41$	0.121500	−	0.167231i	0.0189752	−	0.0261171i	−0.799424	−	0.600767i	$-0.794862\pi$
$41$	0.121500	−	0.167231i	0.0189752	−	0.0261171i	0.818399	+	0.574650i	$0.194862\pi$
$42$	−2.11369	−	1.71295i	−0.326149	−	0.264314i
$43$	−7.64117	+	7.64117i	−1.16527	+	1.16527i	−0.181962	+	0.983306i	$0.558245\pi$
$43$	−7.64117	+	7.64117i	−1.16527	+	1.16527i	−0.983306	+	0.181962i	$0.941755\pi$
$44$	2.70413	−	1.92033i	0.407663	−	0.289501i
$45$	−3.68054	+	2.30693i	−0.548662	+	0.343896i
$46$	−1.36836	−	4.21138i	−0.201754	−	0.620934i
$47$	−8.67139	+	1.37341i	−1.26485	+	0.200333i	−0.752586	−	0.658494i	$-0.771194\pi$
$47$	−8.67139	+	1.37341i	−1.26485	+	0.200333i	−0.512266	+	0.858827i	$0.671194\pi$
$48$	−1.01564	−	0.160862i	−0.146596	−	0.0232185i
$49$	5.19849	+	4.68782i	0.742642	+	0.669689i
$50$	0.101069	+	4.99898i	0.0142933	+	0.706962i
$51$	3.62728	−	2.63537i	0.507921	−	0.369026i
$52$	2.27845	−	0.360871i	0.315965	−	0.0500439i
$53$	−6.80148	−	3.46553i	−0.934255	−	0.476027i	−0.0805310	−	0.996752i	$-0.525662\pi$
$53$	−6.80148	−	3.46553i	−0.934255	−	0.476027i	−0.853724	+	0.520725i	$0.825662\pi$
$54$	−5.08249			−0.691639
$55$	−1.72618	−	7.21251i	−0.232758	−	0.972535i
$56$	2.58773	+	0.551055i	0.345800	+	0.0736379i
$57$	−2.62494	+	5.15173i	−0.347681	+	0.682363i
$58$	0.353323	−	0.0559608i	0.0463936	−	0.00734802i
$59$	−3.33635	+	2.42400i	−0.434356	+	0.315578i	−0.783388	−	0.621533i	$-0.786510\pi$
$59$	−3.33635	+	2.42400i	−0.434356	+	0.315578i	0.349032	+	0.937111i	$0.386510\pi$
$60$	−1.18153	+	1.97257i	−0.152535	+	0.254658i
$61$	4.19738	+	1.36381i	0.537419	+	0.174618i	0.565136	−	0.824998i	$-0.308824\pi$
$61$	4.19738	+	1.36381i	0.537419	+	0.174618i	−0.0277169	+	0.999616i	$0.508824\pi$
$62$	0.851043	−	5.37327i	0.108083	−	0.682406i
$63$	5.13246	+	0.270915i	0.646630	+	0.0341321i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$	1.15342	−	5.02767i	0.143064	−	0.623606i
$66$	1.08892	−	3.23199i	0.134036	−	0.397831i
$67$	−0.245219	−	0.245219i	−0.0299582	−	0.0299582i	0.691969	−	0.721927i	$-0.256743\pi$
$67$	−0.245219	−	0.245219i	−0.0299582	−	0.0299582i	−0.721927	+	0.691969i	$0.756743\pi$
$68$	−1.97947	+	3.88492i	−0.240046	+	0.471116i
$69$	−3.68381	−	2.67645i	−0.443479	−	0.322206i
$70$	3.30330	−	4.90797i	0.394820	−	0.586615i
$71$	1.58411	−	4.87540i	0.188000	−	0.578604i	−0.811987	−	0.583675i	$-0.801614\pi$
$71$	1.58411	−	4.87540i	0.188000	−	0.578604i	0.999987	+	0.00507131i	$0.00161425\pi$
$72$	1.73086	−	0.881917i	0.203984	−	0.103935i
$73$	−12.0637	−	1.91070i	−1.41194	−	0.223630i	−0.596569	−	0.802562i	$-0.703470\pi$
$73$	−12.0637	−	1.91070i	−1.41194	−	0.223630i	−0.815376	+	0.578932i	$0.803470\pi$
$74$	−0.463774	+	0.638330i	−0.0539126	+	0.0742044i
$75$	3.10558	+	4.09764i	0.358601	+	0.473155i
$76$		−	5.62277i		−	0.644976i
$77$	−3.23613	+	8.15643i	−0.368792	+	0.929512i
$78$	1.67736	−	1.67736i	0.189924	−	0.189924i
$79$	11.7927	−	3.83167i	1.32678	−	0.431096i	0.441961	−	0.897034i	$-0.354283\pi$
$79$	11.7927	−	3.83167i	1.32678	−	0.431096i	0.884818	+	0.465938i	$0.154283\pi$
$80$	0.152900	−	2.23083i	0.0170947	−	0.249415i
$81$	0.486560	−	0.353506i	0.0540622	−	0.0392785i
$82$	0.0938438	+	0.184179i	0.0103633	+	0.0203392i
$83$	13.7484	−	7.00514i	1.50908	−	0.768914i	0.513084	−	0.858338i	$-0.328503\pi$
$83$	13.7484	−	7.00514i	1.50908	−	0.768914i	0.995994	+	0.0894246i	$0.0285028\pi$
$84$	2.48584	−	1.10565i	0.271228	−	0.120636i
$85$	6.40646	+	7.34927i	0.694878	+	0.797140i
$86$	−3.33931	−	10.2774i	−0.360087	−	1.10824i
$87$	0.260111	−	0.260111i	0.0278868	−	0.0278868i
$88$	0.483381	+	3.28121i	0.0515286	+	0.349778i
$89$	4.66473			0.494460			0.247230	−	0.968957i	$-0.420480\pi$
$89$	4.66473			0.494460			0.247230	+	0.968957i	$0.420480\pi$
$90$	−0.384559	−	4.32671i	−0.0405361	−	0.456075i
$91$	−4.53722	+	4.08224i	−0.475629	+	0.427935i
$92$	4.37359	+	0.692708i	0.455978	+	0.0722198i
$93$	−2.53973	−	4.98450i	−0.263358	−	0.516869i
$94$	2.71301	−	8.34978i	0.279826	−	0.861214i
$95$	−11.6639	−	4.69379i	−1.19669	−	0.481572i
$96$	0.604422	−	0.831916i	0.0616886	−	0.0849071i
$97$	12.0347	+	6.13196i	1.22193	+	0.622607i	0.941418	−	0.337243i	$-0.109494\pi$
$97$	12.0347	+	6.13196i	1.22193	+	0.622607i	0.280516	+	0.959849i	$0.409494\pi$
$98$	−6.53695	+	2.50366i	−0.660331	+	0.252908i
$99$	1.92457	+	6.14868i	0.193427	+	0.617965i
$100$	−4.50001	−	2.17944i	−0.450001	−	0.217944i
$101$	−8.78018	+	2.85285i	−0.873661	+	0.283870i	−0.711323	−	0.702866i	$-0.751904\pi$
$101$	−8.78018	+	2.85285i	−0.873661	+	0.283870i	−0.162338	+	0.986735i	$0.551904\pi$
$102$	0.701384	+	4.42836i	0.0694473	+	0.438473i
$103$	16.0239	+	2.53793i	1.57888	+	0.250070i	0.883450	−	0.468526i	$-0.155215\pi$
$103$	16.0239	+	2.53793i	1.57888	+	0.250070i	0.695428	+	0.718595i	$0.255215\pi$
$104$	−0.712857	+	2.19395i	−0.0699014	+	0.215134i
$105$	−0.218423	−	6.07961i	−0.0213159	−	0.593309i
$106$	6.17562	−	4.48685i	0.599829	−	0.435801i
$107$	2.79764	+	17.6636i	0.270458	+	1.70761i	0.631766	+	0.775159i	$0.282330\pi$
$107$	2.79764	+	17.6636i	0.270458	+	1.70761i	−0.361308	+	0.932447i	$0.617670\pi$
$108$	2.30740	−	4.52853i	0.222030	−	0.435758i
$109$		−	7.66400i		−	0.734078i	−0.930205	−	0.367039i	$-0.880371\pi$
$109$		−	7.66400i		−	0.734078i	0.930205	−	0.367039i	$-0.119629\pi$
$110$	7.21006	+	1.73637i	0.687453	+	0.165556i
$111$			0.811352i			0.0770102i
$112$	−1.66580	+	2.05551i	−0.157403	+	0.194227i
$113$	−1.85223	+	0.293364i	−0.174243	+	0.0275974i	−0.242946	−	0.970040i	$-0.578114\pi$
$113$	−1.85223	+	0.293364i	−0.174243	+	0.0275974i	0.0687032	+	0.997637i	$0.478114\pi$
$114$	−3.39853	−	4.67767i	−0.318301	−	0.438104i
$115$	5.08795	−	8.49431i	0.474453	−	0.792099i
$116$	−0.110544	+	0.340219i	−0.0102637	+	0.0315885i
$117$	−0.701025	+	4.42610i	−0.0648098	+	0.409193i
$118$	−0.645129	−	4.07319i	−0.0593890	−	0.374967i
$119$	−1.20151	−	11.4731i	−0.110143	−	1.05174i
$120$	−1.22117	−	1.94828i	−0.111477	−	0.177853i
$121$	−10.9974	−	0.237887i	−0.999766	−	0.0216261i
$122$	−3.12073	+	3.12073i	−0.282538	+	0.282538i
$123$	0.189392	+	0.0965000i	0.0170769	+	0.00870112i
$124$	4.40126	+	3.19770i	0.395244	+	0.287162i
$125$	−8.27755	+	7.51546i	−0.740366	+	0.672203i
$126$	−2.57148	+	4.45007i	−0.229085	+	0.396443i
$127$	−17.3009	+	8.81526i	−1.53521	+	0.782228i	−0.998120	−	0.0612976i	$-0.980476\pi$
$127$	−17.3009	+	8.81526i	−1.53521	+	0.782228i	−0.537089	+	0.843526i	$0.680476\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	−8.98989	−	6.53154i	−0.791516	−	0.575070i
$130$	3.95605	+	3.31022i	0.346968	+	0.290325i
$131$			6.70771i			0.586055i	0.956104	+	0.293028i	$0.0946628\pi$
$131$			6.70771i			0.586055i	−0.956104	+	0.293028i	$0.905337\pi$
$132$	2.38537	+	2.43753i	0.207620	+	0.212159i
$133$	8.09760	+	12.4795i	0.702151	+	1.08211i
$134$	0.329818	−	0.107164i	0.0284920	−	0.00925760i
$135$	−7.46781	−	8.56681i	−0.642727	−	0.737314i
$136$	−2.56283	−	3.52743i	−0.219761	−	0.302475i
$137$	13.1868	−	6.71901i	1.12662	−	0.574043i	0.211565	−	0.977364i	$-0.432144\pi$
$137$	13.1868	−	6.71901i	1.12662	−	0.574043i	0.915059	+	0.403321i	$0.132144\pi$
$138$	4.05715	−	2.06722i	0.345367	−	0.175973i
$139$	8.39268	−	6.09764i	0.711858	−	0.517195i	−0.171915	−	0.985112i	$-0.554995\pi$
$139$	8.39268	−	6.09764i	0.711858	−	0.517195i	0.883773	+	0.467917i	$0.154995\pi$
$140$	2.87337	+	5.17143i	0.242844	+	0.437066i
$141$	−2.78980	−	8.58612i	−0.234944	−	0.723082i
$142$	3.62484	+	3.62484i	0.304190	+	0.304190i
$143$	−6.77910	−	3.54698i	−0.566897	−	0.296613i
$144$			1.94259i			0.161882i
$145$	0.613470	+	0.513320i	0.0509459	+	0.0426289i
$146$	7.17923	−	9.88136i	0.594157	−	0.817787i
$147$	−3.92492	+	6.03391i	−0.323722	+	0.497669i
$148$	−0.358207	−	0.703021i	−0.0294445	−	0.0577880i
$149$	5.38531	+	1.74979i	0.441182	+	0.143349i	0.521181	−	0.853446i	$-0.325492\pi$
$149$	5.38531	+	1.74979i	0.441182	+	0.143349i	−0.0799989	+	0.996795i	$0.525492\pi$
$150$	−5.06093	+	0.906797i	−0.413223	+	0.0740397i
$151$	−5.80168	−	4.21517i	−0.472134	−	0.343025i	0.326139	−	0.945322i	$-0.394252\pi$
$151$	−5.80168	−	4.21517i	−0.472134	−	0.343025i	−0.798272	+	0.602297i	$0.794252\pi$
$152$	5.00992	+	2.55268i	0.406358	+	0.207050i
$153$	−5.98918	−	5.98918i	−0.484196	−	0.484196i
$154$	−5.79826	−	6.58636i	−0.467237	−	0.530744i
$155$	10.3074	−	6.46059i	0.827910	−	0.518927i
$156$	0.733034	+	2.25605i	0.0586897	+	0.180628i
$157$	−1.01674	+	0.161036i	−0.0811449	+	0.0128521i	−0.196875	−	0.980429i	$-0.563079\pi$
$157$	−1.01674	+	0.161036i	−0.0811449	+	0.0128521i	0.115730	+	0.993281i	$0.463079\pi$
$158$	−1.93972	+	12.2469i	−0.154316	+	0.974310i
$159$	2.42564	−	7.46536i	0.192366	−	0.592042i
$160$	1.91827	+	1.14901i	0.151653	+	0.0908374i
$161$	−10.7046	+	4.76117i	−0.843639	+	0.375233i
$162$	0.0940830	+	0.594017i	0.00739186	+	0.0466703i
$163$	8.08558	+	4.11981i	0.633311	+	0.322688i	0.741009	−	0.671496i	$-0.234348\pi$
$163$	8.08558	+	4.11981i	0.633311	+	0.322688i	−0.107697	+	0.994184i	$0.534348\pi$
$164$	−0.206709			−0.0161412
$165$	7.04767	−	2.91341i	0.548660	−	0.226809i
$166$			15.4301i			1.19761i
$167$	13.3189	+	6.78631i	1.03065	+	0.525140i	0.885680	−	0.464296i	$-0.153693\pi$
$167$	13.3189	+	6.78631i	1.03065	+	0.525140i	0.144966	+	0.989437i	$0.453693\pi$
$168$	−0.143408	+	2.71686i	−0.0110642	+	0.209610i
$169$	4.51327	+	6.21198i	0.347174	+	0.477844i
$170$	−9.45672	+	2.37170i	−0.725297	+	0.181901i
$171$	10.3881	+	3.37531i	0.794400	+	0.258116i
$172$	10.6732	+	1.69047i	0.813824	+	0.128897i
$173$	−1.72036	−	10.8619i	−0.130797	−	0.825817i	−0.962636	−	0.270800i	$-0.912712\pi$
$173$	−1.72036	−	10.8619i	−0.130797	−	0.825817i	0.831839	−	0.555017i	$-0.187288\pi$
$174$	0.113673	+	0.349848i	0.00861750	+	0.0265219i
$175$	13.1263	−	1.64350i	0.992253	−	0.124237i
$176$	−3.14303	−	1.05894i	−0.236915	−	0.0798208i
$177$	−2.99862	−	2.99862i	−0.225390	−	0.225390i
$178$	−2.11774	+	4.15630i	−0.158732	+	0.311528i
$179$	−2.56706	+	3.53325i	−0.191871	+	0.264088i	−0.894104	−	0.447859i	$-0.852186\pi$
$179$	−2.56706	+	3.53325i	−0.191871	+	0.264088i	0.702233	+	0.711947i	$0.252186\pi$
$180$	4.02971	+	1.62164i	0.300357	+	0.120870i
$181$	21.7493	+	7.06679i	1.61662	+	0.525270i	0.971140	−	0.238511i	$-0.0766593\pi$
$181$	21.7493	+	7.06679i	1.61662	+	0.525270i	0.645475	+	0.763781i	$0.276659\pi$
$182$	−1.57745	−	5.89599i	−0.116928	−	0.437040i
$183$	−0.709947	+	4.48243i	−0.0524808	+	0.331351i
$184$	−2.60277	+	3.58241i	−0.191879	+	0.264099i
$185$	−1.75737	+	0.156196i	−0.129205	+	0.0114837i
$186$	5.59424			0.410189
$187$	12.9551	−	6.42543i	0.947368	−	0.469874i
$188$	6.20803	+	6.20803i	0.452767	+	0.452767i
$189$	1.40057	+	13.3739i	0.101876	+	0.972805i
$190$	9.47748	−	8.26165i	0.687569	−	0.599363i
$191$	1.08582	−	0.788896i	0.0785674	−	0.0570825i	−0.547808	−	0.836604i	$-0.684538\pi$
$191$	1.08582	−	0.788896i	0.0785674	−	0.0570825i	0.626376	+	0.779521i	$0.284538\pi$
$192$	0.466841	+	0.916226i	0.0336913	+	0.0661229i
$193$	−2.73544	−	5.36861i	−0.196902	−	0.386441i	0.771353	−	0.636408i	$-0.219580\pi$
$193$	−2.73544	−	5.36861i	−0.196902	−	0.386441i	−0.968254	+	0.249966i	$0.919580\pi$
$194$	−10.9272	+	7.93910i	−0.784530	+	0.569994i
$195$	5.29187	+	0.362701i	0.378959	+	0.0259736i
$196$	0.736932	−	6.96110i	0.0526380	−	0.497222i
$197$	8.51802	+	8.51802i	0.606883	+	0.606883i	0.942130	−	0.335247i	$-0.108820\pi$
$197$	8.51802	+	8.51802i	0.606883	+	0.606883i	−0.335247	+	0.942130i	$0.608820\pi$
$198$	−6.35225	−	1.07664i	−0.451435	−	0.0765132i
$199$	16.6390			1.17951			0.589753	−	0.807584i	$-0.299225\pi$
$199$	16.6390			1.17951			0.589753	+	0.807584i	$0.299225\pi$
$200$	3.98485	−	3.02009i	0.281772	−	0.213553i
$201$	0.209609	−	0.288501i	0.0147846	−	0.0203493i
$202$	1.44421	−	9.11837i	0.101614	−	0.641566i
$203$	−0.244617	−	0.914299i	−0.0171688	−	0.0641712i
$204$	−4.26412	−	1.38550i	−0.298548	−	0.0970042i
$205$	−0.172557	+	0.428797i	−0.0120519	+	0.0299485i
$206$	−9.53599	+	13.1252i	−0.664404	+	0.914474i
$207$	−3.90522	+	7.66443i	−0.271432	+	0.532715i
$208$	−1.63119	−	1.63119i	−0.113103	−	0.113103i
$209$	−11.1239	+	14.9676i	−0.769455	+	1.03533i
$210$	5.51613	+	2.56547i	0.380649	+	0.177034i
$211$	−6.83561	−	21.0379i	−0.470583	−	1.44831i	−0.851823	−	0.523830i	$-0.824503\pi$
$211$	−6.83561	−	21.0379i	−0.470583	−	1.44831i	0.381240	−	0.924476i	$-0.375497\pi$
$212$	1.19414	+	7.53950i	0.0820138	+	0.517815i
$213$	5.20650	+	0.824628i	0.356743	+	0.0565026i
$214$	−17.0085	−	5.52639i	−1.16268	−	0.377777i
$215$	12.4165	−	20.7293i	0.846799	−	1.41373i
$216$	2.98741	+	4.11182i	0.203268	+	0.279774i
$217$	−14.3735	−	0.758702i	−0.975740	−	0.0515041i
$218$	6.82868	+	3.47938i	0.462496	+	0.235654i
$219$		−	12.5598i		−	0.848709i
$220$	−4.82042	+	5.63592i	−0.324992	+	0.379974i
$221$	10.0582			0.676590
$222$	−0.722920	−	0.368346i	−0.0485192	−	0.0247218i
$223$	0.334916	+	2.11458i	0.0224277	+	0.141603i	0.996361	−	0.0852307i	$-0.0271627\pi$
$223$	0.334916	+	2.11458i	0.0224277	+	0.141603i	−0.973934	+	0.226833i	$0.927163\pi$
$224$	−1.07522	−	2.41742i	−0.0718409	−	0.161521i
$225$	6.72786	−	7.00552i	0.448524	−	0.467034i
$226$	0.579505	−	1.78353i	0.0385481	−	0.118639i
$227$	3.25353	−	20.5420i	0.215945	−	1.36342i	−0.606730	−	0.794908i	$-0.707519\pi$
$227$	3.25353	−	20.5420i	0.215945	−	1.36342i	0.822675	−	0.568513i	$-0.192481\pi$
$228$	5.71073	−	0.904491i	0.378203	−	0.0599014i
$229$	1.20630	+	3.71262i	0.0797148	+	0.245337i	0.982970	−	0.183767i	$-0.0588293\pi$
$229$	1.20630	+	3.71262i	0.0797148	+	0.245337i	−0.903255	+	0.429104i	$0.858829\pi$
$230$	5.25861	+	8.38973i	0.346742	+	0.553202i
$231$	−8.80461	−	1.97470i	−0.579301	−	0.129926i
$232$	−0.252951	−	0.252951i	−0.0166071	−	0.0166071i
$233$	−5.57220	−	2.83918i	−0.365047	−	0.186001i	0.261840	−	0.965111i	$-0.415671\pi$
$233$	−5.57220	−	2.83918i	−0.365047	−	0.186001i	−0.626886	+	0.779111i	$0.715671\pi$
$234$	−3.62542	−	2.63402i	−0.237001	−	0.172192i
$235$	18.0603	−	7.69559i	1.17812	−	0.502005i
$236$	3.92212	+	1.27437i	0.255308	+	0.0829546i
$237$	5.78861	+	11.3608i	0.376011	+	0.737962i
$238$	10.7681	+	4.13813i	0.697993	+	0.268235i
$239$	11.9547	−	16.4543i	0.773287	−	1.06434i	−0.222704	−	0.974886i	$-0.571488\pi$
$239$	11.9547	−	16.4543i	0.773287	−	1.06434i	0.995991	−	0.0894525i	$-0.0285117\pi$
$240$	2.29033	−	0.203565i	0.147840	−	0.0131401i
$241$		−	22.3418i		−	1.43916i	−0.694407	−	0.719582i	$-0.744333\pi$
$241$		−	22.3418i		−	1.43916i	0.694407	−	0.719582i	$-0.255667\pi$
$242$	5.20469	−	9.69078i	0.334570	−	0.622947i
$243$	11.2189	+	11.2189i	0.719692	+	0.719692i
$244$	−1.36381	−	4.19738i	−0.0873090	−	0.268710i
$245$	−13.8249	−	7.33969i	−0.883243	−	0.468916i
$246$	−0.171964	+	0.124939i	−0.0109640	+	0.00796585i
$247$	−11.5572	+	5.88867i	−0.735364	+	0.374687i
$248$	−4.84730	+	2.46982i	−0.307804	+	0.156834i
$249$	9.32632	+	12.8366i	0.591032	+	0.813485i
$250$	−2.93840	−	10.7873i	−0.185841	−	0.682249i
$251$	24.0606	−	7.81775i	1.51869	−	0.493452i	0.573286	−	0.819355i	$-0.305668\pi$
$251$	24.0606	−	7.81775i	1.51869	−	0.493452i	0.945403	+	0.325903i	$0.105668\pi$
$252$	−2.79761	−	4.31149i	−0.176233	−	0.271598i
$253$	−10.2719	−	10.4965i	−0.645790	−	0.659910i
$254$		−	19.4173i		−	1.21835i
$255$	−6.43369	+	7.68891i	−0.402893	+	0.481498i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	1.10424	−	6.97192i	0.0688808	−	0.434896i	−0.929014	−	0.370044i	$-0.879342\pi$
$257$	1.10424	−	6.97192i	0.0688808	−	0.434896i	0.997895	−	0.0648519i	$-0.0206575\pi$
$258$	9.90097	−	5.04479i	0.616407	−	0.314075i
$259$	1.80748	+	1.04445i	0.112311	+	0.0648992i
$260$	−4.74544	+	2.02206i	−0.294299	+	0.125403i
$261$	−0.562199	−	0.408462i	−0.0347993	−	0.0252831i
$262$	−5.97661	−	3.04524i	−0.369236	−	0.188135i
$263$	−12.2063	+	12.2063i	−0.752673	+	0.752673i	−0.974977	−	0.222304i	$-0.928642\pi$
$263$	−12.2063	+	12.2063i	−0.752673	+	0.752673i	0.222304	+	0.974977i	$0.428642\pi$
$264$	−3.25479	+	1.01877i	−0.200318	+	0.0627007i
$265$	16.6368	+	3.81672i	1.02199	+	0.234459i
$266$	−14.7955	+	1.54945i	−0.907172	+	0.0950029i
$267$	0.750379	+	4.73771i	0.0459224	+	0.289943i
$268$	−0.0542501	+	0.342522i	−0.00331385	+	0.0209229i
$269$	3.63173	−	11.1773i	0.221431	−	0.681494i	−0.777204	−	0.629249i	$-0.783363\pi$
$269$	3.63173	−	11.1773i	0.221431	−	0.681494i	0.998634	−	0.0522444i	$-0.0166375\pi$
$270$	11.0234	−	2.76462i	0.670863	−	0.168249i
$271$	−16.8141	−	23.1427i	−1.02139	−	1.40582i	−0.911228	−	0.411903i	$-0.864864\pi$
$271$	−16.8141	−	23.1427i	−1.02139	−	1.40582i	−0.110158	−	0.993914i	$-0.535136\pi$
$272$	4.30647	−	0.682078i	0.261118	−	0.0413570i
$273$	−4.87597	−	3.95152i	−0.295107	−	0.239157i
$274$			14.7999i			0.894094i
$275$	7.66716	+	14.7042i	0.462347	+	0.886699i
$276$			4.55344i			0.274085i
$277$	−8.23690	+	16.1658i	−0.494908	+	0.971311i	0.499561	+	0.866279i	$0.333495\pi$
$277$	−8.23690	+	16.1658i	−0.494908	+	0.971311i	−0.994469	+	0.105032i	$0.966505\pi$
$278$	1.62284	+	10.2462i	0.0973314	+	0.614526i
$279$	−8.54983	+	6.21182i	−0.511865	+	0.371892i
$280$	−5.91227	+	0.212411i	−0.353325	+	0.0126940i
$281$	−6.17672	+	19.0100i	−0.368472	+	1.13404i	0.579305	+	0.815111i	$0.303324\pi$
$281$	−6.17672	+	19.0100i	−0.368472	+	1.13404i	−0.947778	+	0.318931i	$0.896676\pi$
$282$	8.91683	+	1.41229i	0.530990	+	0.0841005i
$283$	0.666181	+	4.20610i	0.0396003	+	0.250027i	0.999545	−	0.0301630i	$-0.00960262\pi$
$283$	0.666181	+	4.20610i	0.0396003	+	0.250027i	−0.959945	+	0.280190i	$0.909603\pi$
$284$	−4.87540	+	1.58411i	−0.289302	+	0.0939999i
$285$	2.89094	−	12.6014i	0.171245	−	0.746443i
$286$	6.23803	−	4.42993i	0.368863	−	0.261947i
$287$	0.458781	−	0.297691i	0.0270810	−	0.0175721i
$288$	−1.73086	−	0.881917i	−0.101992	−	0.0519675i
$289$	−1.18198	+	1.62685i	−0.0695281	+	0.0956972i
$290$	−0.735881	+	0.313563i	−0.0432124	+	0.0184131i
$291$	−4.29197	+	13.2093i	−0.251600	+	0.774345i
$292$	5.54506	+	10.8828i	0.324500	+	0.636867i
$293$	−28.2749	−	4.47830i	−1.65184	−	0.261625i	−0.740129	−	0.672464i	$-0.765236\pi$
$293$	−28.2749	−	4.47830i	−1.65184	−	0.261625i	−0.911708	+	0.410839i	$0.865236\pi$
$294$	−3.59438	−	6.23647i	−0.209628	−	0.363718i
$295$	5.91768	−	7.07222i	0.344540	−	0.411761i
$296$	0.789019			0.0458608
$297$	−15.1013	+	7.48992i	−0.876267	+	0.434609i
$298$	−4.00396	+	4.00396i	−0.231943	+	0.231943i
$299$	−3.15661	−	9.71503i	−0.182551	−	0.561835i
$300$	1.48965	−	4.92100i	0.0860050	−	0.284114i
$301$	−26.1232	+	11.6190i	−1.50572	+	0.669711i
$302$	6.38965	−	3.25569i	0.367683	−	0.187344i
$303$	−4.30989	−	8.45863i	−0.247597	−	0.485936i
$304$	−4.54891	+	3.30498i	−0.260898	+	0.189554i
$305$	−9.84553	−	0.674806i	−0.563753	−	0.0386393i
$306$	8.05543	−	2.61737i	0.460498	−	0.149625i
$307$	12.8400	−	12.8400i	0.732818	−	0.732818i	−0.238359	−	0.971177i	$-0.576609\pi$
$307$	12.8400	−	12.8400i	0.732818	−	0.732818i	0.971177	+	0.238359i	$0.0766094\pi$
$308$	8.50085	−	2.17614i	0.484381	−	0.123997i
$309$			16.6828i			0.949052i
$310$	1.07696	+	12.1170i	0.0611674	+	0.688200i
$311$	−13.4901	+	18.5675i	−0.764952	+	1.05287i	0.231834	+	0.972755i	$0.425527\pi$
$311$	−13.4901	+	18.5675i	−0.764952	+	1.05287i	−0.996786	+	0.0801105i	$0.974473\pi$
$312$	−2.34294	−	0.371086i	−0.132643	−	0.0210086i
$313$	−2.16323	+	1.10222i	−0.122273	+	0.0623012i	−0.514057	−	0.857756i	$-0.671858\pi$
$313$	−2.16323	+	1.10222i	−0.122273	+	0.0623012i	0.391784	+	0.920057i	$0.371858\pi$
$314$	0.318107	−	0.979033i	0.0179518	−	0.0552500i
$315$	−11.2792	+	2.20421i	−0.635508	+	0.124193i
$316$	−10.0314	−	7.28827i	−0.564313	−	0.409997i
$317$	−3.88395	+	7.62267i	−0.218144	+	0.428132i	−0.973982	−	0.226627i	$-0.927230\pi$
$317$	−3.88395	+	7.62267i	−0.218144	+	0.428132i	0.755837	+	0.654759i	$0.227230\pi$
$318$	5.55047	+	5.55047i	0.311255	+	0.311255i
$319$	0.967340	−	0.686955i	0.0541606	−	0.0384621i
$320$	−1.89466	+	1.18755i	−0.105914	+	0.0663862i
$321$	−17.4899	+	5.68282i	−0.976192	+	0.317184i
$322$	0.617548	−	11.6994i	0.0344146	−	0.651981i
$323$	3.83516	−	24.2143i	0.213394	−	1.34732i
$324$	−0.571985	−	0.185849i	−0.0317770	−	0.0103250i
$325$	0.233151	+	11.5319i	0.0129329	+	0.639675i
$326$	−7.34155	+	5.33395i	−0.406611	+	0.295420i
$327$	7.78390	−	1.23285i	0.430451	−	0.0681767i
$328$	0.0938438	−	0.184179i	0.00518166	−	0.0101696i
$329$	−22.7189	−	4.83798i	−1.25253	−	0.266726i
$330$	−0.603708	+	7.60218i	−0.0332330	+	0.418486i
$331$	23.5480			1.29431			0.647157	−	0.762357i	$-0.275958\pi$
$331$	23.5480			1.29431			0.647157	+	0.762357i	$0.275958\pi$
$332$	−13.7484	−	7.00514i	−0.754539	−	0.384457i
$333$	1.51387	−	0.239773i	0.0829596	−	0.0131395i
$334$	−12.0933	+	8.78629i	−0.661715	+	0.480764i
$335$	0.665241	+	0.398468i	0.0363460	+	0.0217706i
$336$	−2.35563	−	1.36120i	−0.128510	−	0.0742598i
$337$	−28.9386	−	4.58342i	−1.57639	−	0.249675i	−0.693920	−	0.720052i	$-0.744118\pi$
$337$	−28.9386	−	4.58342i	−1.57639	−	0.249675i	−0.882466	+	0.470377i	$0.844118\pi$
$338$	−7.58389	+	1.20117i	−0.412509	+	0.0653351i
$339$	−0.595908	−	1.83401i	−0.0323653	−	0.0996100i
$340$	2.18006	−	9.50273i	0.118230	−	0.515358i
$341$	−5.38979	−	17.2195i	−0.291873	−	0.932486i
$342$	−7.72353	+	7.72353i	−0.417641	+	0.417641i
$343$	8.38941	+	16.5111i	0.452986	+	0.891518i
$344$	−6.35175	+	8.74244i	−0.342464	+	0.471361i
$345$	9.44566	+	3.80113i	0.508537	+	0.204646i
$346$	10.4591	+	3.39836i	0.562284	+	0.182697i
$347$	16.3825	−	8.34731i	0.879460	−	0.448107i	0.0448789	−	0.998992i	$-0.485710\pi$
$347$	16.3825	−	8.34731i	0.879460	−	0.448107i	0.834581	+	0.550885i	$0.185710\pi$
$348$	−0.363323	−	0.0575448i	−0.0194762	−	0.00308472i
$349$	5.65201	+	4.10643i	0.302545	+	0.219812i	0.728691	−	0.684842i	$-0.240129\pi$
$349$	5.65201	+	4.10643i	0.302545	+	0.219812i	−0.426146	+	0.904654i	$0.640129\pi$
$350$	−4.49483	+	12.4417i	−0.240259	+	0.665038i
$351$	−11.7246			−0.625811
$352$	2.37043	−	2.31971i	0.126344	−	0.123641i
$353$	5.43225	+	5.43225i	0.289130	+	0.289130i	0.836736	−	0.547606i	$-0.184461\pi$
$353$	5.43225	+	5.43225i	0.289130	+	0.289130i	−0.547606	+	0.836736i	$0.684461\pi$
$354$	4.03313	−	1.31044i	0.214359	−	0.0696493i
$355$	−0.783810	+	11.4359i	−0.0416003	+	0.606956i
$356$	−2.74186	−	3.77384i	−0.145318	−	0.200013i
$357$	11.4593	−	3.06591i	0.606493	−	0.162265i
$358$	−1.98273	−	3.89133i	−0.104791	−	0.205663i
$359$	−8.12589	−	11.1843i	−0.428868	−	0.590286i	0.538825	−	0.842418i	$-0.318868\pi$
$359$	−8.12589	−	11.1843i	−0.428868	−	0.590286i	−0.967693	+	0.252132i	$0.918868\pi$
$360$	−3.27434	+	2.85429i	−0.172573	+	0.150434i
$361$	3.89841	+	11.9981i	0.205179	+	0.631477i
$362$	−16.1705	+	16.1705i	−0.849905	+	0.849905i
$363$	−1.52746	−	11.2077i	−0.0801710	−	0.588254i
$364$	5.96951	+	1.27120i	0.312887	+	0.0666292i
$365$	27.2042	−	2.41792i	1.42393	−	0.126559i
$366$	−3.67157	−	2.66755i	−0.191916	−	0.139435i
$367$	5.21229	−	32.9091i	0.272080	−	1.71784i	−0.351590	−	0.936154i	$-0.614359\pi$
$367$	5.21229	−	32.9091i	0.272080	−	1.71784i	0.623669	−	0.781688i	$-0.285641\pi$
$368$	−2.01032	−	3.94547i	−0.104795	−	0.205672i
$369$	0.124086	−	0.381897i	0.00645965	−	0.0198808i
$370$	0.658659	−	1.63674i	0.0342421	−	0.0850902i
$371$	−13.5083	−	15.0138i	−0.701317	−	0.779480i
$372$	−2.53973	+	4.98450i	−0.131679	+	0.258434i
$373$	−8.14928	+	8.14928i	−0.421954	+	0.421954i	−0.885876	−	0.463922i	$-0.846442\pi$
$373$	−8.14928	+	8.14928i	−0.421954	+	0.421954i	0.463922	+	0.885876i	$0.346442\pi$
$374$	−0.156376	+	14.4601i	−0.00808602	+	0.747716i
$375$	−8.96459	−	7.19809i	−0.462929	−	0.371708i
$376$	−8.34978	+	2.71301i	−0.430607	+	0.139913i
$377$	0.815064	−	0.129093i	0.0419779	−	0.00664865i
$378$	−12.5520	−	4.82369i	−0.645607	−	0.248104i
$379$	11.8128	+	3.83820i	0.606782	+	0.197155i	0.596263	−	0.802789i	$-0.296652\pi$
$379$	11.8128	+	3.83820i	0.606782	+	0.197155i	0.0105189	+	0.999945i	$0.496652\pi$
$380$	3.05850	+	12.1952i	0.156898	+	0.625601i
$381$	−11.7362	−	16.1535i	−0.601266	−	0.827571i
$382$	0.209959	+	1.32563i	0.0107424	+	0.0678250i
$383$	6.22641	−	12.2200i	0.318155	−	0.624414i	−0.675440	−	0.737415i	$-0.736046\pi$
$383$	6.22641	−	12.2200i	0.318155	−	0.624414i	0.993595	+	0.113001i	$0.0360463\pi$
$384$	−1.02830			−0.0524755
$385$	2.58216	−	19.4508i	0.131599	−	0.991303i
$386$	6.02534			0.306681
$387$	−9.53021	+	18.7041i	−0.484448	+	0.950783i
$388$	−2.11293	−	13.3405i	−0.107268	−	0.677262i
$389$	−1.12182	−	1.54405i	−0.0568783	−	0.0782863i	0.779630	−	0.626240i	$-0.215407\pi$
$389$	−1.12182	−	1.54405i	−0.0568783	−	0.0782863i	−0.836509	+	0.547954i	$0.815407\pi$
$390$	−2.72563	+	4.55043i	−0.138018	+	0.230420i
$391$	18.3622	+	5.96625i	0.928618	+	0.301726i
$392$	5.86783	+	3.81689i	0.296370	+	0.192782i
$393$	−6.81265	+	1.07902i	−0.343653	+	0.0544292i
$394$	−11.4567	+	3.72251i	−0.577180	+	0.187537i
$395$	−23.4929	+	14.7251i	−1.18205	+	0.740901i
$396$	3.84315	−	5.17111i	0.193126	−	0.259858i
$397$	10.8930	−	10.8930i	0.546702	−	0.546702i	−0.378783	−	0.925485i	$-0.623657\pi$
$397$	10.8930	−	10.8930i	0.546702	−	0.546702i	0.925485	+	0.378783i	$0.123657\pi$
$398$	−7.55394	+	14.8254i	−0.378645	+	0.743132i
$399$	−11.3721	+	10.2318i	−0.569318	+	0.512229i
$400$	0.881837	+	4.92162i	0.0440918	+	0.246081i
$401$	−4.50769	+	13.8733i	−0.225104	+	0.692797i	0.773178	+	0.634190i	$0.218666\pi$
$401$	−4.50769	+	13.8733i	−0.225104	+	0.692797i	−0.998281	+	0.0586078i	$0.981334\pi$
$402$	0.161896	+	0.317739i	0.00807465	+	0.0158474i
$403$	1.96323	−	12.3954i	0.0977955	−	0.617457i
$404$	7.46887	+	5.42645i	0.371590	+	0.269976i
$405$	−0.863009	+	1.03138i	−0.0428833	+	0.0512498i
$406$	0.925700	+	0.197127i	0.0459417	+	0.00978326i
$407$	−0.437296	+	2.58008i	−0.0216760	+	0.127890i
$408$	3.17036	−	3.17036i	0.156956	−	0.156956i
$409$	1.83542	+	5.64883i	0.0907555	+	0.279317i	0.986124	−	0.166009i	$-0.0530880\pi$
$409$	1.83542	+	5.64883i	0.0907555	+	0.279317i	−0.895369	+	0.445325i	$0.853088\pi$
$410$	−0.303722	−	0.348419i	−0.0149997	−	0.0172072i
$411$	8.94538	+	12.3123i	0.441243	+	0.607319i
$412$	−7.36536	−	14.4553i	−0.362865	−	0.712163i
$413$	−10.5402	+	2.82001i	−0.518652	+	0.138763i
$414$	−5.05612	−	6.95915i	−0.248495	−	0.342024i
$415$	−26.0083	+	22.6718i	−1.27670	+	1.11292i
$416$	2.19395	−	0.712857i	0.107567	−	0.0349507i
$417$	7.54310	+	7.54310i	0.369387	+	0.369387i
$418$	−8.28612	−	16.7066i	−0.405287	−	0.817147i
$419$	−3.59258			−0.175509			−0.0877545	−	0.996142i	$-0.527969\pi$
$419$	−3.59258			−0.175509			−0.0877545	+	0.996142i	$0.527969\pi$
$420$	−4.79012	+	3.75021i	−0.233734	+	0.182992i
$421$	6.46985	+	4.70062i	0.315321	+	0.229094i	0.734176	−	0.678959i	$-0.237569\pi$
$421$	6.46985	+	4.70062i	0.315321	+	0.229094i	−0.418855	+	0.908053i	$0.637569\pi$
$422$	21.8482	+	3.46041i	1.06355	+	0.168450i
$423$	−15.1961	+	7.74278i	−0.738857	+	0.376467i
$424$	−7.25987	−	2.35888i	−0.352571	−	0.114557i
$425$	−17.8926	−	12.4550i	−0.867918	−	0.604157i
$426$	−3.09845	+	4.26465i	−0.150120	+	0.206623i
$427$	9.07175	+	7.35181i	0.439013	+	0.355779i
$428$	12.6457	−	12.6457i	0.611255	−	0.611255i
$429$	2.51197	−	7.45574i	0.121279	−	0.359966i
$430$	12.8330	+	20.4741i	0.618862	+	0.987349i
$431$	5.22173	+	16.0708i	0.251522	+	0.774104i	0.994495	+	0.104783i	$0.0334149\pi$
$431$	5.22173	+	16.0708i	0.251522	+	0.774104i	−0.742973	+	0.669321i	$0.766585\pi$
$432$	−5.01991	+	0.795076i	−0.241521	+	0.0382531i
$433$	−26.7428	−	4.23564i	−1.28518	−	0.203552i	−0.523788	−	0.851849i	$-0.675482\pi$
$433$	−26.7428	−	4.23564i	−1.28518	−	0.203552i	−0.761388	+	0.648297i	$0.775482\pi$
$434$	7.20146	−	12.4625i	0.345681	−	0.598218i
$435$	−0.422667	+	0.705641i	−0.0202653	+	0.0338329i
$436$	−6.20031	+	4.50479i	−0.296941	+	0.215740i
$437$	−24.5917	+	3.89494i	−1.17638	+	0.186320i
$438$	11.1908	+	5.70201i	0.534718	+	0.272452i
$439$	−6.33165			−0.302193			−0.151097	−	0.988519i	$-0.548280\pi$
$439$	−6.33165			−0.302193			−0.151097	+	0.988519i	$0.548280\pi$
$440$	−2.83322	−	6.85368i	−0.135068	−	0.326736i
$441$	12.4183	+	5.54019i	0.591350	+	0.263819i
$442$	−4.56634	+	8.96195i	−0.217199	+	0.426276i
$443$	9.86364	−	1.56225i	0.468636	−	0.0742246i	0.0823494	−	0.996604i	$-0.473758\pi$
$443$	9.86364	−	1.56225i	0.468636	−	0.0742246i	0.386286	+	0.922379i	$0.373758\pi$
$444$	0.656398	−	0.476901i	0.0311513	−	0.0226327i
$445$	−10.1173	+	2.53738i	−0.479607	+	0.120283i
$446$	−2.03615	−	0.661586i	−0.0964146	−	0.0313270i
$447$	−0.910875	+	5.75104i	−0.0430829	+	0.272015i
$448$	2.64207	+	0.139461i	0.124826	+	0.00658891i
$449$	19.5490	−	6.35186i	0.922574	−	0.299763i	0.191052	−	0.981580i	$-0.438810\pi$
$449$	19.5490	−	6.35186i	0.922574	−	0.299763i	0.731522	+	0.681817i	$0.238810\pi$
$450$	3.18758	+	9.17500i	0.150264	+	0.432514i
$451$	0.550252	+	0.408945i	0.0259104	+	0.0192565i
$452$	1.32605	+	1.32605i	0.0623721	+	0.0623721i
$453$	3.34784	−	6.57050i	0.157295	−	0.308709i
$454$	16.8260	+	12.2248i	0.789683	+	0.573738i
$455$	7.62023	−	11.3220i	0.357242	−	0.530783i
$456$	−1.78671	+	5.49893i	−0.0836704	+	0.257511i
$457$	29.2142	−	14.8854i	1.36658	−	0.696308i	0.391921	−	0.919999i	$-0.371811\pi$
$457$	29.2142	−	14.8854i	1.36658	−	0.696308i	0.974660	+	0.223691i	$0.0718107\pi$
$458$	−3.85562	−	0.610670i	−0.180161	−	0.0285347i
$459$	13.0256	−	17.9281i	0.607981	−	0.836814i
$460$	−9.86266	+	0.876597i	−0.459849	+	0.0408715i
$461$		−	9.57736i		−	0.446062i	−0.974811	−	0.223031i	$-0.928405\pi$
$461$		−	9.57736i		−	0.446062i	0.974811	−	0.223031i	$-0.0715951\pi$
$462$	5.75668	−	6.94847i	0.267825	−	0.323272i
$463$	8.04925	−	8.04925i	0.374080	−	0.374080i	−0.494881	−	0.868961i	$-0.664788\pi$
$463$	8.04925	−	8.04925i	0.374080	−	0.374080i	0.868961	+	0.494881i	$0.164788\pi$
$464$	0.340219	−	0.110544i	0.0157943	−	0.00513186i
$465$	8.21973	+	9.42939i	0.381181	+	0.437277i
$466$	5.05945	−	3.67590i	0.234374	−	0.170283i
$467$	−3.37106	−	6.61608i	−0.155994	−	0.306156i	0.799761	−	0.600318i	$-0.204959\pi$
$467$	−3.37106	−	6.61608i	−0.155994	−	0.306156i	−0.955755	+	0.294162i	$0.904959\pi$
$468$	3.99284	−	2.03445i	0.184569	−	0.0940427i
$469$	−0.372876	−	0.838340i	−0.0172178	−	0.0387109i
$470$	−1.34238	+	19.5856i	−0.0619194	+	0.903415i
$471$	−0.327111	−	1.00674i	−0.0150725	−	0.0463883i
$472$	−2.91608	+	2.91608i	−0.134223	+	0.134223i
$473$	−25.0674	−	25.6155i	−1.15260	−	1.17780i
$474$	−12.7505			−0.585650
$475$	27.8509	+	3.83579i	1.27789	+	0.175998i
$476$	−8.57572	+	7.71578i	−0.393068	+	0.353652i
$477$	−14.6462	−	2.31972i	−0.670601	−	0.106213i
$478$	9.23353	+	18.1218i	0.422332	+	0.828873i
$479$	5.79012	−	17.8202i	0.264557	−	0.814224i	−0.727238	−	0.686386i	$-0.759196\pi$
$479$	5.79012	−	17.8202i	0.264557	−	0.814224i	0.991795	−	0.127838i	$-0.0408039\pi$
$480$	−0.858410	+	2.13312i	−0.0391809	+	0.0973630i
$481$	−1.06986	+	1.47253i	−0.0487814	+	0.0671418i
$482$	19.9067	+	10.1430i	0.906727	+	0.462000i
$483$	−6.55762	−	10.1062i	−0.298382	−	0.459846i
$484$	6.27167	+	9.03693i	0.285076	+	0.410770i
$485$	−29.4374	−	6.75336i	−1.33668	−	0.306654i
$486$	−15.0894	+	4.90284i	−0.684468	+	0.222397i
$487$	−3.30948	−	20.8953i	−0.149967	−	0.946854i	−0.941814	−	0.336135i	$-0.890880\pi$
$487$	−3.30948	−	20.8953i	−0.149967	−	0.946854i	0.791847	−	0.610720i	$-0.209120\pi$
$488$	4.35905	+	0.690405i	0.197325	+	0.0312532i
$489$	−2.88360	+	8.87479i	−0.130401	+	0.401332i
$490$	12.8161	−	8.98596i	0.578973	−	0.405944i
$491$	−14.2293	+	10.3382i	−0.642161	+	0.466557i	−0.860592	−	0.509295i	$-0.829906\pi$
$491$	−14.2293	+	10.3382i	−0.642161	+	0.466557i	0.218431	+	0.975852i	$0.429906\pi$
$492$	−0.0332517	−	0.209943i	−0.00149910	−	0.00946495i
$493$	−0.708108	+	1.38974i	−0.0318916	+	0.0625908i
$494$		−	12.9709i		−	0.583588i
$495$	−7.51876	−	12.2890i	−0.337943	−	0.552349i
$496$		−	5.44025i		−	0.244274i
$497$	8.53938	−	10.5372i	0.383044	−	0.472656i
$498$	−15.6715	+	2.48213i	−0.702258	+	0.111227i
$499$	−2.19901	−	3.02668i	−0.0984412	−	0.135493i	0.756955	−	0.653467i	$-0.226686\pi$
$499$	−2.19901	−	3.02668i	−0.0984412	−	0.135493i	−0.855396	+	0.517974i	$0.826686\pi$
$500$	10.9456	+	2.27920i	0.489500	+	0.101929i
$501$	−4.74997	+	14.6189i	−0.212213	+	0.653125i
$502$	−3.95760	+	24.9873i	−0.176636	+	1.11524i
$503$	4.19892	+	26.5110i	0.187221	+	1.18207i	0.884944	+	0.465698i	$0.154197\pi$
$503$	4.19892	+	26.5110i	0.187221	+	1.18207i	−0.697723	+	0.716368i	$0.745803\pi$
$504$	5.11165	−	0.535314i	0.227691	−	0.0238448i
$505$	17.4915	−	10.9635i	0.778362	−	0.487870i
$506$	14.0158	−	4.38703i	0.623079	−	0.195027i
$507$	−5.58315	+	5.58315i	−0.247956	+	0.247956i
$508$	17.3009	+	8.81526i	0.767604	+	0.391114i
$509$	20.6427	+	14.9978i	0.914971	+	0.664765i	0.942267	−	0.334862i	$-0.108690\pi$
$509$	20.6427	+	14.9978i	0.914971	+	0.664765i	−0.0272964	+	0.999627i	$0.508690\pi$
$510$	−3.93003	−	9.22315i	−0.174025	−	0.408408i
$511$	−27.9798	−	16.1682i	−1.23775	−	0.715238i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	−4.47053	+	28.2258i	−0.197379	+	1.24620i
$514$	5.71071	+	4.14907i	0.251889	+	0.183008i
$515$	−36.1346	+	3.21166i	−1.59228	+	0.141523i
$516$			11.1121i			0.489184i
$517$	−4.24383	−	28.8073i	−0.186644	−	1.26694i
$518$	−1.75119	+	1.13630i	−0.0769430	+	0.0499263i
$519$	10.7551	−	3.49455i	0.472097	−	0.153394i
$520$	0.352717	−	5.14621i	0.0154677	−	0.225676i
$521$	23.3217	+	32.0995i	1.02174	+	1.40631i	0.910976	+	0.412459i	$0.135330\pi$
$521$	23.3217	+	32.0995i	1.02174	+	1.40631i	0.110765	+	0.993847i	$0.464670\pi$
$522$	0.619175	−	0.315486i	0.0271006	−	0.0138084i
$523$	−6.21147	+	3.16490i	−0.271609	+	0.138391i	−0.584490	−	0.811401i	$-0.698706\pi$
$523$	−6.21147	+	3.16490i	−0.271609	+	0.138391i	0.312882	+	0.949792i	$0.398706\pi$
$524$	5.42665	−	3.94269i	0.237064	−	0.172237i
$525$	3.78074	+	13.0672i	0.165005	+	0.570301i
$526$	−5.33435	−	16.4175i	−0.232589	−	0.715835i
$527$	16.7728	+	16.7728i	0.730634	+	0.730634i
$528$	0.569915	−	3.36255i	0.0248024	−	0.146336i
$529$			3.39189i			0.147473i
$530$	−10.9537	+	13.0907i	−0.475797	+	0.568625i
$531$	−4.70884	+	6.48116i	−0.204346	+	0.281259i
$532$	5.33646	−	13.8864i	0.231365	−	0.602050i
$533$	0.216484	+	0.424874i	0.00937696	+	0.0184033i
$534$	−4.56199	−	1.48228i	−0.197417	−	0.0641446i
$535$	−15.6759	−	36.7888i	−0.677729	−	1.59052i
$536$	−0.280560	−	0.203839i	−0.0121184	−	0.00880450i
$537$	−4.00147	−	2.03885i	−0.172676	−	0.0879830i
$538$	8.31030	+	8.31030i	0.358282	+	0.358282i
$539$	−15.7333	+	17.0723i	−0.677681	+	0.735356i
$540$	−2.54123	+	11.0770i	−0.109357	+	0.476679i
$541$	−7.14062	−	21.9766i	−0.306999	−	0.944846i	−0.978924	−	0.204227i	$-0.934532\pi$
$541$	−7.14062	−	21.9766i	−0.306999	−	0.944846i	0.671924	−	0.740620i	$-0.265468\pi$
$542$	28.2537	−	4.47495i	1.21360	−	0.192216i
$543$	−3.67870	+	23.2264i	−0.157868	+	0.996739i
$544$	−1.34736	+	4.14675i	−0.0577676	+	0.177790i
$545$	4.16883	+	16.6224i	0.178573	+	0.712027i
$546$	5.73448	−	2.55057i	0.245413	−	0.109154i
$547$	−4.97138	−	31.3881i	−0.212561	−	1.34206i	−0.831021	−	0.556240i	$-0.812243\pi$
$547$	−4.97138	−	31.3881i	−0.212561	−	1.34206i	0.618461	−	0.785816i	$-0.287757\pi$
$548$	−13.1868	−	6.71901i	−0.563312	−	0.287022i
$549$	8.57339			0.365903
$550$	−16.5824	+	0.155899i	−0.707076	+	0.00664757i
$551$		−	2.01142i		−	0.0856892i
$552$	−4.05715	−	2.06722i	−0.172684	−	0.0879867i
$553$	32.7605	+	1.72925i	1.39312	+	0.0735353i
$554$	−10.6644	−	14.6783i	−0.453086	−	0.623620i
$555$	−0.441335	−	1.75974i	−0.0187336	−	0.0746968i
$556$	−9.86619	−	3.20572i	−0.418420	−	0.135953i
$557$	12.7916	+	2.02599i	0.541998	+	0.0858440i	0.421430	−	0.906861i	$-0.361528\pi$
$557$	12.7916	+	2.02599i	0.541998	+	0.0858440i	0.120568	+	0.992705i	$0.461528\pi$
$558$	−1.65323	−	10.4381i	−0.0699867	−	0.441878i
$559$	−7.70331	−	23.7083i	−0.325815	−	1.00276i
$560$	2.49485	−	5.36430i	0.105427	−	0.226683i
$561$	8.60994	+	12.1241i	0.363512	+	0.511881i
$562$	−14.1339	−	14.1339i	−0.596201	−	0.596201i
$563$	−11.9651	+	23.4829i	−0.504271	+	0.989687i	0.488825	+	0.872382i	$0.337426\pi$
$563$	−11.9651	+	23.4829i	−0.504271	+	0.989687i	−0.993096	+	0.117305i	$0.962574\pi$
$564$	−5.30652	+	7.30379i	−0.223445	+	0.307545i
$565$	3.85772	−	1.64380i	0.162296	−	0.0691550i
$566$	−4.05010	−	1.31596i	−0.170239	−	0.0553139i
$567$	1.53715	−	0.411258i	0.0645541	−	0.0172712i
$568$	0.801930	−	5.06319i	0.0336482	−	0.212447i
$569$	12.7549	−	17.5556i	0.534714	−	0.735971i	−0.453126	−	0.891447i	$-0.649691\pi$
$569$	12.7549	−	17.5556i	0.534714	−	0.735971i	0.987840	+	0.155476i	$0.0496911\pi$
$570$	9.91547	+	8.29676i	0.415313	+	0.347513i
$571$	−39.4887			−1.65255			−0.826276	−	0.563266i	$-0.809545\pi$
$571$	−39.4887			−1.65255			−0.826276	+	0.563266i	$0.809545\pi$
$572$	1.11509	+	7.56927i	0.0466242	+	0.316487i
$573$	0.975906	+	0.975906i	0.0407691	+	0.0407691i
$574$	0.0569622	+	0.543925i	0.00237756	+	0.0227030i
$575$	−6.41476	+	21.1909i	−0.267514	+	0.883721i
$576$	1.57159	−	1.14183i	0.0654828	−	0.0475761i
$577$	12.4012	+	24.3387i	0.516268	+	1.01323i	0.991095	+	0.133155i	$0.0425107\pi$
$577$	12.4012	+	24.3387i	0.516268	+	1.01323i	−0.474827	+	0.880079i	$0.657489\pi$
$578$	−0.912929	−	1.79172i	−0.0379729	−	0.0745259i
$579$	5.01257	−	3.64185i	0.208315	−	0.151350i
$580$	0.0546964	−	0.798030i	0.00227114	−	0.0331364i
$581$	40.6023	−	4.25204i	1.68447	−	0.176404i
$582$	−9.82109	−	9.82109i	−0.407097	−	0.407097i
$583$	11.7371	−	22.4324i	0.486102	−	0.929053i
$584$	−12.2140			−0.505420
$585$	−0.887121	−	9.98108i	−0.0366779	−	0.412667i
$586$	16.8267	−	23.1600i	0.695106	−	0.956731i
$587$	−6.54344	+	41.3137i	−0.270077	+	1.70520i	0.363563	+	0.931570i	$0.381560\pi$
$587$	−6.54344	+	41.3137i	−0.270077	+	1.70520i	−0.633640	+	0.773628i	$0.718440\pi$
$588$	7.18855	−	0.371318i	0.296451	−	0.0153129i
$589$	−29.0921	−	9.45260i	−1.19872	−	0.389488i
$590$	3.61483	+	8.48341i	0.148820	+	0.349256i
$591$	−7.28105	+	10.0215i	−0.299502	+	0.412230i
$592$	−0.358207	+	0.703021i	−0.0147222	+	0.0288940i
$593$	17.0815	+	17.0815i	0.701452	+	0.701452i	0.964722	−	0.263270i	$-0.0848012\pi$
$593$	17.0815	+	17.0815i	0.701452	+	0.701452i	−0.263270	+	0.964722i	$0.584801\pi$
$594$	0.182283	−	16.8557i	0.00747915	−	0.691599i
$595$	8.84676	+	24.2305i	0.362682	+	0.993353i
$596$	−1.74979	−	5.38531i	−0.0716744	−	0.220591i
$597$	2.67658	+	16.8993i	0.109545	+	0.691642i
$598$	10.0892	+	1.59798i	0.412579	+	0.0653461i
$599$	9.05396	+	2.94181i	0.369935	+	0.120199i	0.488084	−	0.872797i	$-0.337696\pi$
$599$	9.05396	+	2.94181i	0.369935	+	0.120199i	−0.118149	+	0.992996i	$0.537696\pi$
$600$	3.70835	+	3.56137i	0.151393	+	0.145393i
$601$	1.68823	+	2.32365i	0.0688642	+	0.0947835i	0.842060	−	0.539384i	$-0.181343\pi$
$601$	1.68823	+	2.32365i	0.0688642	+	0.0947835i	−0.773196	+	0.634168i	$0.781343\pi$
$602$	1.50705	−	28.5509i	0.0614227	−	1.16365i
$603$	−0.600247	−	0.305841i	−0.0244440	−	0.0124548i
$604$			7.17127i			0.291795i
$605$	23.9817	−	5.46609i	0.974995	−	0.222228i
$606$	9.49334			0.385641
$607$	2.80803	+	1.43076i	0.113974	+	0.0580729i	0.510048	−	0.860146i	$-0.329628\pi$
$607$	2.80803	+	1.43076i	0.113974	+	0.0580729i	−0.396074	+	0.918219i	$0.629628\pi$
$608$	−0.879595	−	5.55354i	−0.0356723	−	0.225226i
$609$	0.889253	−	0.395521i	0.0360344	−	0.0160273i
$610$	5.07103	−	8.46608i	0.205320	−	0.342781i
$611$	6.25852	−	19.2617i	0.253192	−	0.779246i
$612$	−1.32500	+	8.36570i	−0.0535598	+	0.338163i
$613$	9.39099	−	1.48739i	0.379299	−	0.0600750i	0.0361257	−	0.999347i	$-0.488498\pi$
$613$	9.39099	−	1.48739i	0.379299	−	0.0600750i	0.343173	+	0.939272i	$0.388498\pi$
$614$	5.61129	+	17.2698i	0.226453	+	0.696952i
$615$	−0.463263	−	0.106279i	−0.0186806	−	0.00428559i
$616$	−1.92035	+	8.56226i	−0.0773729	+	0.344983i
$617$	−28.7891	−	28.7891i	−1.15901	−	1.15901i	−0.984689	−	0.174318i	$-0.944228\pi$
$617$	−28.7891	−	28.7891i	−1.15901	−	1.15901i	−0.174318	−	0.984689i	$-0.555772\pi$
$618$	−14.8645	−	7.57384i	−0.597938	−	0.304664i
$619$	13.2039	+	9.59317i	0.530708	+	0.385582i	0.820623	−	0.571471i	$-0.193627\pi$
$619$	13.2039	+	9.59317i	0.530708	+	0.385582i	−0.289914	+	0.957053i	$0.593627\pi$
$620$	−11.2853	−	4.54142i	−0.453227	−	0.182388i
$621$	−21.4043	−	6.95467i	−0.858924	−	0.279081i
$622$	−10.4194	−	20.4492i	−0.417780	−	0.819939i
$623$	11.5203	+	4.42720i	0.461552	+	0.177372i
$624$	1.39431	−	1.91911i	0.0558172	−	0.0768258i
$625$	13.8651	−	20.8028i	0.554605	−	0.832114i
$626$		−	2.42785i		−	0.0970363i
$627$	−16.9912	−	8.89019i	−0.678563	−	0.355040i
$628$	0.727907	+	0.727907i	0.0290467	+	0.0290467i
$629$	−1.06309	−	3.27186i	−0.0423883	−	0.130458i
$630$	3.15666	−	11.0505i	0.125764	−	0.440262i
$631$	−14.0971	+	10.2421i	−0.561196	+	0.407733i	−0.831896	−	0.554931i	$-0.812745\pi$
$631$	−14.0971	+	10.2421i	−0.561196	+	0.407733i	0.270701	+	0.962664i	$0.412745\pi$
$632$	11.0481	−	5.62927i	0.439469	−	0.223921i
$633$	20.2674	−	10.3268i	0.805557	−	0.410452i
$634$	−5.02858	−	6.92124i	−0.199710	−	0.274878i
$635$	32.7289	−	28.5302i	1.29881	−	1.13219i
$636$	−7.46536	+	2.42564i	−0.296021	+	0.0961830i
$637$	−15.0798	+	5.77558i	−0.597483	+	0.228837i
$638$	0.172918	+	1.17378i	0.00684590	+	0.0464703i
$639$		−	9.95829i		−	0.393944i
$640$	−0.197962	−	2.22729i	−0.00782514	−	0.0880413i
$641$	34.2378	+	24.8752i	1.35231	+	0.982511i	0.998893	+	0.0470457i	$0.0149806\pi$
$641$	34.2378	+	24.8752i	1.35231	+	0.982511i	0.353418	+	0.935466i	$0.385019\pi$
$642$	2.87683	−	18.1636i	0.113539	−	0.716859i
$643$	42.5949	−	21.7032i	1.67978	−	0.855891i	0.688331	−	0.725397i	$-0.258344\pi$
$643$	42.5949	−	21.7032i	1.67978	−	0.855891i	0.991449	−	0.130494i	$-0.0416564\pi$
$644$	10.1439	+	5.86164i	0.399724	+	0.230981i
$645$	23.0510	+	9.27619i	0.907631	+	0.365250i
$646$	19.8339	+	14.4102i	0.780356	+	0.566962i
$647$	−24.0003	−	12.2288i	−0.943551	−	0.480763i	−0.0866468	−	0.996239i	$-0.527615\pi$
$647$	−24.0003	−	12.2288i	−0.943551	−	0.480763i	−0.856904	+	0.515476i	$0.827615\pi$
$648$	0.425269	−	0.425269i	0.0167061	−	0.0167061i
$649$	−7.91938	−	11.1517i	−0.310863	−	0.437743i
$650$	−10.3809	−	5.02764i	−0.407171	−	0.197200i
$651$	−1.54159	−	14.7205i	−0.0604196	−	0.576940i
$652$	−1.41959	−	8.96293i	−0.0555954	−	0.351015i
$653$	−0.978791	+	6.17984i	−0.0383030	+	0.241836i	−0.999410	−	0.0343398i	$-0.989067\pi$
$653$	−0.978791	+	6.17984i	−0.0383030	+	0.241836i	0.961107	+	0.276176i	$0.0890672\pi$
$654$	−2.43534	+	7.49521i	−0.0952294	+	0.293086i
$655$	−3.64865	−	14.5483i	−0.142565	−	0.568451i
$656$	0.121500	+	0.167231i	0.00474379	+	0.00652927i
$657$	−23.4347	+	3.71170i	−0.914276	+	0.144807i
$658$	14.6248	−	18.0463i	0.570136	−	0.703518i
$659$			33.0309i			1.28670i	0.765572	+	0.643350i	$0.222456\pi$
$659$			33.0309i			1.28670i	−0.765572	+	0.643350i	$0.777544\pi$
$660$	−6.49951	−	3.98922i	−0.252993	−	0.155280i
$661$			3.54453i			0.137866i	0.997621	+	0.0689331i	$0.0219595\pi$
$661$			3.54453i			0.137866i	−0.997621	+	0.0689331i	$0.978041\pi$
$662$	−10.6906	+	20.9814i	−0.415500	+	0.815466i
$663$	1.61799	+	10.2156i	0.0628375	+	0.396740i
$664$	12.4832	−	9.06961i	0.484444	−	0.351969i
$665$	−24.3511	−	22.6620i	−0.944294	−	0.878796i
$666$	−0.473643	+	1.45772i	−0.0183533	+	0.0564856i
$667$	1.56455	+	0.247800i	0.0605796	+	0.00959487i
$668$	−2.33840	−	14.7641i	−0.0904755	−	0.571240i
$669$	−2.09378	+	0.680312i	−0.0809504	+	0.0263024i
$670$	−0.657050	+	0.411833i	−0.0253841	+	0.0159105i
$671$	−4.67352	+	13.8714i	−0.180419	+	0.535499i
$672$	2.28228	−	1.48091i	0.0880407	−	0.0571273i
$673$	5.92537	+	3.01913i	0.228406	+	0.116379i	0.564449	−	0.825468i	$-0.309089\pi$
$673$	5.92537	+	3.01913i	0.228406	+	0.116379i	−0.336043	+	0.941847i	$0.609089\pi$
$674$	17.2217	−	23.7036i	0.663355	−	0.913030i
$675$	20.8568	+	14.5184i	0.802780	+	0.558815i
$676$	2.37276	−	7.30262i	0.0912602	−	0.280870i
$677$	5.42138	+	10.6401i	0.208360	+	0.408930i	0.971410	−	0.237410i	$-0.0762985\pi$
$677$	5.42138	+	10.6401i	0.208360	+	0.408930i	−0.763049	+	0.646341i	$0.776299\pi$
$678$	1.90466	+	0.301668i	0.0731479	+	0.0115855i
$679$	23.9018	+	26.5658i	0.917269	+	1.01950i
$680$	7.47727	+	6.25660i	0.286740	+	0.239930i
$681$	21.3867			0.819542
$682$	17.7896	+	3.01514i	0.681198	+	0.115456i
$683$	−6.51376	+	6.51376i	−0.249242	+	0.249242i	−0.820659	−	0.571418i	$-0.806394\pi$
$683$	−6.51376	+	6.51376i	−0.249242	+	0.249242i	0.571418	+	0.820659i	$0.306394\pi$
$684$	−3.37531	−	10.3881i	−0.129058	−	0.397200i
$685$	−24.9460	+	21.7458i	−0.953138	+	0.830864i
$686$	−18.5202	−	0.0208820i	−0.707106	−	0.000797277i
$687$	−3.57665	+	1.82240i	−0.136458	+	0.0695288i
$688$	−4.90593	−	9.62844i	−0.187037	−	0.367081i
$689$	14.2462	−	10.3505i	0.542739	−	0.394323i
$690$	−7.67507	+	6.69047i	−0.292185	+	0.254702i
$691$	10.4178	−	3.38496i	0.396313	−	0.128770i	−0.104078	−	0.994569i	$-0.533189\pi$
$691$	10.4178	−	3.38496i	0.396313	−	0.128770i	0.500392	+	0.865799i	$0.333189\pi$
$692$	−7.77628	+	7.77628i	−0.295610	+	0.295610i
$693$	−1.08255	+	17.0117i	−0.0411226	+	0.646223i
$694$			18.3865i			0.697943i
$695$	−14.8861	+	17.7904i	−0.564661	+	0.674827i
$696$	0.216218	−	0.297599i	0.00819573	−	0.0112805i
$697$	−0.890185	−	0.140991i	−0.0337182	−	0.00534043i
$698$	−6.22481	+	3.17170i	−0.235613	+	0.120051i
$699$	1.98724	−	6.11609i	0.0751642	−	0.231332i
$700$	−9.04505	−	9.65335i	−0.341871	−	0.364862i
$701$	20.4378	+	14.8489i	0.771925	+	0.560836i	0.902545	−	0.430596i	$-0.141697\pi$
$701$	20.4378	+	14.8489i	0.771925	+	0.560836i	−0.130620	+	0.991433i	$0.541697\pi$
$702$	5.32284	−	10.4467i	0.200898	−	0.394284i
$703$	3.13706	+	3.13706i	0.118316	+	0.118316i
$704$	0.990724	+	3.16520i	0.0373393	+	0.119293i
$705$	10.7212	+	17.1049i	0.403784	+	0.644208i
$706$	−7.30636	+	2.37398i	−0.274979	+	0.0893459i
$707$	−24.3917	−	1.28751i	−0.917344	−	0.0484217i
$708$	−0.663390	+	4.18848i	−0.0249317	+	0.157413i
$709$	−49.7290	−	16.1579i	−1.86761	−	0.606824i	−0.992395	−	0.123091i	$-0.960719\pi$
$709$	−49.7290	−	16.1579i	−1.86761	−	0.606824i	−0.875216	−	0.483733i	$-0.839281\pi$
$710$	−9.83364	−	5.89018i	−0.369050	−	0.221055i
$711$	19.4870	−	14.1581i	0.730818	−	0.530971i
$712$	4.60730	−	0.729724i	0.172666	−	0.0273476i
$713$	10.9366	−	21.4643i	0.409580	−	0.803846i
$714$	−2.47069	+	11.6022i	−0.0924633	+	0.434203i
$715$	16.6326	+	4.00555i	0.622023	+	0.149799i
$716$	4.36734			0.163215
$717$	18.6348	+	9.49489i	0.695928	+	0.354593i
$718$	13.6544	−	2.16264i	0.509577	−	0.0807091i
$719$	−5.51161	+	4.00442i	−0.205548	+	0.149340i	−0.685797	−	0.727793i	$-0.740546\pi$
$719$	−5.51161	+	4.00442i	−0.205548	+	0.149340i	0.480249	+	0.877132i	$0.340546\pi$
$720$	−1.05667	−	4.21328i	−0.0393798	−	0.157020i
$721$	37.1649	+	21.4758i	1.38409	+	0.799800i
$722$	−12.4602	−	1.97350i	−0.463720	−	0.0734461i
$723$	22.6914	−	3.59396i	0.843901	−	0.133661i
$724$	−7.06679	−	21.7493i	−0.262635	−	0.808308i
$725$	−1.60977	−	0.779643i	−0.0597855	−	0.0289552i
$726$	10.6796	+	3.72723i	0.396358	+	0.138330i
$727$	−20.9755	+	20.9755i	−0.777937	+	0.777937i	−0.979480	−	0.201543i	$-0.935405\pi$
$727$	−20.9755	+	20.9755i	−0.777937	+	0.777937i	0.201543	+	0.979480i	$0.435405\pi$
$728$	−3.84275	+	4.74176i	−0.142422	+	0.175741i
$729$	−8.52919	+	11.7394i	−0.315896	+	0.434793i
$730$	−10.1961	+	25.3368i	−0.377373	+	0.937757i
$731$	44.8108	+	14.5599i	1.65739	+	0.538518i
$732$	4.04366	−	2.06035i	0.149458	−	0.0761526i
$733$	−39.8900	−	6.31795i	−1.47337	−	0.233359i	−0.632485	−	0.774573i	$-0.717965\pi$
$733$	−39.8900	−	6.31795i	−1.47337	−	0.233359i	−0.840885	+	0.541214i	$0.817965\pi$
$734$	26.9559	+	19.5846i	0.994961	+	0.722882i
$735$	5.23061	−	15.2219i	0.192934	−	0.561468i
$736$	4.42810			0.163222
$737$	0.822045	−	0.804456i	0.0302804	−	0.0296325i
$738$	0.283939	+	0.283939i	0.0104519	+	0.0104519i
$739$	−4.66841	+	1.51686i	−0.171730	+	0.0557986i	−0.393620	−	0.919273i	$-0.628777\pi$
$739$	−4.66841	+	1.51686i	−0.171730	+	0.0557986i	0.221890	+	0.975072i	$0.428777\pi$
$740$	1.15932	+	1.32994i	0.0426176	+	0.0488894i
$741$	−7.83990	−	10.7907i	−0.288006	−	0.396406i
$742$	19.5101	−	5.21985i	0.716238	−	0.191627i
$743$	−22.7517	−	44.6526i	−0.834677	−	1.63815i	−0.768069	−	0.640368i	$-0.778782\pi$
$743$	−22.7517	−	44.6526i	−0.834677	−	1.63815i	−0.0666088	−	0.997779i	$-0.521218\pi$
$744$	−3.28821	−	4.52583i	−0.120552	−	0.165925i
$745$	−12.6320	−	0.865788i	−0.462800	−	0.0317200i
$746$	−3.56137	−	10.9608i	−0.130391	−	0.401302i
$747$	21.1951	−	21.1951i	0.775489	−	0.775489i
$748$	−12.8131	−	6.70410i	−0.468493	−	0.245126i
$749$	−9.85496	+	46.2784i	−0.360092	+	1.69098i
$750$	10.4834	−	4.71964i	0.382799	−	0.172337i
$751$	16.3432	+	11.8740i	0.596370	+	0.433289i	0.844589	−	0.535416i	$-0.179845\pi$
$751$	16.3432	+	11.8740i	0.596370	+	0.433289i	−0.248218	+	0.968704i	$0.579845\pi$
$752$	1.37341	−	8.67139i	0.0500832	−	0.316213i
$753$	11.8105	+	23.1794i	0.430398	+	0.844704i
$754$	−0.255008	+	0.784834i	−0.00928685	+	0.0285820i
$755$	14.8761	+	5.98645i	0.541396	+	0.217869i
$756$	9.99645	−	8.99404i	0.363567	−	0.327110i
$757$	1.87208	−	3.67417i	0.0680420	−	0.133540i	−0.854480	−	0.519484i	$-0.826124\pi$
$757$	1.87208	−	3.67417i	0.0680420	−	0.133540i	0.922522	+	0.385944i	$0.126124\pi$
$758$	−8.78275	+	8.78275i	−0.319004	+	0.319004i
$759$	9.00837	−	12.1211i	0.326983	−	0.439969i
$760$	−12.2545	−	2.81137i	−0.444519	−	0.101979i
$761$	22.2013	−	7.21364i	0.804796	−	0.261494i	0.122404	−	0.992480i	$-0.460940\pi$
$761$	22.2013	−	7.21364i	0.804796	−	0.261494i	0.682392	+	0.730986i	$0.260940\pi$
$762$	19.7211	−	3.12351i	0.714418	−	0.113153i
$763$	7.27376	−	18.9275i	0.263328	−	0.685222i
$764$	−1.27646	−	0.414747i	−0.0461808	−	0.0150050i
$765$	16.2477	+	9.73211i	0.587438	+	0.351865i
$766$	8.06139	+	11.0955i	0.291270	+	0.400898i
$767$	−1.48822	−	9.39624i	−0.0537365	−	0.339279i
$768$	0.466841	−	0.916226i	0.0168457	−	0.0330615i
$769$	24.0278			0.866465			0.433232	−	0.901282i	$-0.357373\pi$
$769$	24.0278			0.866465			0.433232	+	0.901282i	$0.357373\pi$
$770$	16.1585	+	11.1312i	0.582311	+	0.401140i
$771$	7.25862			0.261413
$772$	−2.73544	+	5.36861i	−0.0984508	+	0.193221i
$773$	−2.61693	−	16.5227i	−0.0941245	−	0.594279i	−0.988995	−	0.147952i	$-0.952732\pi$
$773$	−2.61693	−	16.5227i	−0.0941245	−	0.594279i	0.894870	−	0.446327i	$-0.147268\pi$
$774$	−12.3388	−	16.9830i	−0.443511	−	0.610440i
$775$	−18.8415	+	19.6191i	−0.676805	+	0.704737i
$776$	12.8457	+	4.17383i	0.461135	+	0.149832i
$777$	−0.770039	+	2.00377i	−0.0276250	+	0.0718848i
$778$	1.88505	−	0.298563i	0.0675823	−	0.0107040i
$779$	1.10539	−	0.359163i	0.0396047	−	0.0128683i
$780$	−2.81705	−	4.49440i	−0.100867	−	0.160925i
$781$	16.1121	+	5.42846i	0.576537	+	0.194246i
$782$	−13.6522	+	13.6522i	−0.488203	+	0.488203i
$783$	0.825420	−	1.61998i	0.0294981	−	0.0578933i
$784$	−6.06481	+	3.49544i	−0.216600	+	0.124837i
$785$	2.11762	−	0.902327i	0.0755809	−	0.0322054i
$786$	2.13147	−	6.55998i	0.0760269	−	0.233987i
$787$	16.9153	+	33.1981i	0.602965	+	1.18338i	0.967660	+	0.252258i	$0.0811731\pi$
$787$	16.9153	+	33.1981i	0.602965	+	1.18338i	−0.364695	+	0.931127i	$0.618827\pi$
$788$	1.88446	−	11.8980i	0.0671309	−	0.423848i
$789$	−14.3608	−	10.4337i	−0.511258	−	0.371451i
$790$	−2.45464	−	27.6174i	−0.0873321	−	0.982581i
$791$	−4.85281	−	1.03340i	−0.172546	−	0.0367436i
$792$	2.86274	+	5.77191i	0.101723	+	0.205096i
$793$	−7.19908	+	7.19908i	−0.255647	+	0.255647i
$794$	4.76040	+	14.6510i	0.168940	+	0.519945i
$795$	−1.20019	+	17.5110i	−0.0425665	+	0.621052i
$796$	−9.78014	−	13.4612i	−0.346648	−	0.477120i
$797$	5.78472	+	11.3532i	0.204905	+	0.402149i	0.970474	−	0.241204i	$-0.0775424\pi$
$797$	5.78472	+	11.3532i	0.204905	+	0.402149i	−0.765569	+	0.643354i	$0.777542\pi$
$798$	−3.95374	−	14.7778i	−0.139961	−	0.523127i
$799$	22.5003	+	30.9690i	0.796005	+	1.09561i
$800$	−4.78554	−	1.44865i	−0.169194	−	0.0512174i
$801$	8.61814	−	2.80020i	0.304507	−	0.0989404i
$802$	−10.3147	−	10.3147i	−0.364225	−	0.364225i
$803$	6.76935	−	39.9398i	0.238885	−	1.40944i
$804$	−0.356607			−0.0125766
$805$	20.6273	−	16.1492i	0.727017	−	0.569186i
$806$	10.1531	+	7.37662i	0.357626	+	0.259831i
$807$	11.9364	+	1.89054i	0.420181	+	0.0665502i
$808$	−8.22580	+	4.19125i	−0.289383	+	0.147448i
$809$	27.5885	+	8.96404i	0.969959	+	0.315159i	0.750800	−	0.660530i	$-0.229668\pi$
$809$	27.5885	+	8.96404i	0.969959	+	0.315159i	0.219160	+	0.975689i	$0.429668\pi$
$810$	−0.527171	−	1.23718i	−0.0185229	−	0.0434702i
$811$	−27.0021	+	37.1652i	−0.948171	+	1.30505i	0.00416435	+	0.999991i	$0.498674\pi$
$811$	−27.0021	+	37.1652i	−0.948171	+	1.30505i	−0.952335	+	0.305054i	$0.901326\pi$
$812$	−0.595901	+	0.735311i	−0.0209120	+	0.0258044i
$813$	20.8000	−	20.8000i	0.729487	−	0.729487i
$814$	−2.10034	−	1.56097i	−0.0736170	−	0.0547119i
$815$	−19.7778	−	4.53730i	−0.692785	−	0.158935i
$816$	1.38550	+	4.26412i	0.0485021	+	0.149274i
$817$	−60.0129	+	9.50512i	−2.09959	+	0.332542i
$818$	−5.86641	−	0.929148i	−0.205114	−	0.0324869i
$819$	−5.93202	+	10.2656i	−0.207282	+	0.358711i
$820$	0.448330	−	0.112439i	0.0156564	−	0.00392654i
$821$	18.0411	−	13.1076i	0.629638	−	0.457459i	−0.226637	−	0.973979i	$-0.572773\pi$
$821$	18.0411	−	13.1076i	0.629638	−	0.457459i	0.856275	+	0.516521i	$0.172773\pi$
$822$	−15.0314	+	2.38074i	−0.524281	+	0.0830380i
$823$	29.5597	+	15.0614i	1.03039	+	0.525008i	0.885597	−	0.464455i	$-0.153750\pi$
$823$	29.5597	+	15.0614i	1.03039	+	0.525008i	0.144789	+	0.989463i	$0.453750\pi$
$824$	16.2236			0.565176
$825$	−13.7009	+	10.1525i	−0.477005	+	0.353463i
$826$	2.27253	−	10.6717i	0.0790714	−	0.371315i
$827$	−4.99001	+	9.79345i	−0.173520	+	0.340552i	−0.961345	−	0.275347i	$-0.911207\pi$
$827$	−4.99001	+	9.79345i	−0.173520	+	0.340552i	0.787825	+	0.615899i	$0.211207\pi$
$828$	8.49608	−	1.34565i	0.295259	−	0.0467645i
$829$	−10.4620	+	7.60110i	−0.363361	+	0.263997i	−0.754453	−	0.656355i	$-0.772098\pi$
$829$	−10.4620	+	7.60110i	−0.363361	+	0.263997i	0.391092	+	0.920352i	$0.372098\pi$
$830$	−8.39321	−	33.4664i	−0.291333	−	1.16164i
$831$	−17.7438	−	5.76529i	−0.615524	−	0.199996i
$832$	−0.360871	+	2.27845i	−0.0125110	+	0.0789911i
$833$	7.92159	−	29.4751i	0.274467	−	1.02125i
$834$	−10.1454	+	3.29646i	−0.351308	+	0.114147i
$835$	−32.5787	−	7.47401i	−1.12743	−	0.258649i
$836$	18.6475	+	0.201660i	0.644938	+	0.00697455i
$837$	−19.5515	−	19.5515i	−0.675799	−	0.675799i
$838$	1.63100	−	3.20101i	0.0563419	−	0.110577i
$839$	−13.1696	−	9.56829i	−0.454666	−	0.330334i	0.336769	−	0.941587i	$-0.390666\pi$
$839$	−13.1696	−	9.56829i	−0.454666	−	0.330334i	−0.791435	+	0.611253i	$0.790666\pi$
$840$	−1.16679	−	5.97059i	−0.0402582	−	0.206005i
$841$	8.92195	−	27.4589i	0.307653	−	0.946860i
$842$	−7.12553	+	3.63064i	−0.245562	+	0.125120i
$843$	−20.3010	−	3.21536i	−0.699204	−	0.110743i
$844$	−13.0021	+	17.8959i	−0.447551	+	0.616001i
$845$	−13.1678	−	11.0182i	−0.452987	−	0.379036i
$846$		−	17.0549i		−	0.586361i
$847$	−26.9342	−	11.0249i	−0.925470	−	0.378822i
$848$	5.39769	−	5.39769i	0.185357	−	0.185357i
$849$	−4.16474	+	1.35321i	−0.142934	+	0.0464419i
$850$	19.2206	−	10.2880i	0.659260	−	0.352874i
$851$	−2.82659	+	2.05364i	−0.0968943	+	0.0703979i
$852$	−2.39316	−	4.69685i	−0.0819885	−	0.160911i
$853$	−0.0418935	+	0.0213458i	−0.00143441	+	0.000730867i	−0.454708	−	0.890641i	$-0.650256\pi$
$853$	−0.0418935	+	0.0213458i	−0.00143441	+	0.000730867i	0.453273	+	0.891372i	$0.350256\pi$
$854$	−10.6690	+	4.74534i	−0.365086	+	0.162382i
$855$	−24.3668	−	1.67008i	−0.833327	−	0.0571156i
$856$	5.52639	+	17.0085i	0.188888	+	0.581338i
$857$	18.6000	−	18.6000i	0.635363	−	0.635363i	−0.314045	−	0.949408i	$-0.601684\pi$
$857$	18.6000	−	18.6000i	0.635363	−	0.635363i	0.949408	+	0.314045i	$0.101684\pi$
$858$	5.50270	+	5.62302i	0.187859	+	0.191967i
$859$	−19.3604			−0.660567			−0.330284	−	0.943882i	$-0.607144\pi$
$859$	−19.3604			−0.660567			−0.330284	+	0.943882i	$0.607144\pi$
$860$	−24.0686	+	2.13923i	−0.820733	+	0.0729470i
$861$	0.376149	+	0.418071i	0.0128191	+	0.0142478i
$862$	−16.6898	−	2.64341i	−0.568458	−	0.0900348i
$863$	19.4199	+	38.1137i	0.661060	+	1.29740i	0.941332	+	0.337483i	$0.109576\pi$
$863$	19.4199	+	38.1137i	0.661060	+	1.29740i	−0.280271	+	0.959921i	$0.590424\pi$
$864$	1.57058	−	4.83373i	0.0534321	−	0.164447i
$865$	9.63963	+	22.6226i	0.327757	+	0.769193i
$866$	15.9149	−	21.9050i	0.540812	−	0.744364i
$867$	−1.84244	−	0.938770i	−0.0625725	−	0.0318823i
$868$	7.83475	+	12.0744i	0.265929	+	0.409832i
$869$	12.2845	+	39.2470i	0.416724	+	1.33136i
$870$	−0.436844	−	0.696953i	−0.0148104	−	0.0236289i
$871$	0.760842	−	0.247213i	0.0257802	−	0.00837648i
$872$	−1.19891	−	7.56965i	−0.0406004	−	0.256341i
$873$	25.9152	+	4.10456i	0.877095	+	0.138918i
$874$	7.69397	−	23.6796i	0.260252	−	0.800974i
$875$	−27.5756	+	10.7046i	−0.932224	+	0.361882i
$876$	−10.1611	+	7.38244i	−0.343310	+	0.249429i
$877$	0.729150	+	4.60367i	0.0246216	+	0.155455i	0.996936	−	0.0782218i	$-0.0249242\pi$
$877$	0.729150	+	4.60367i	0.0246216	+	0.155455i	−0.972314	+	0.233677i	$0.924924\pi$
$878$	2.87451	−	5.64154i	0.0970100	−	0.190393i
$879$		−	29.4376i		−	0.992907i
$880$	7.39292	+	0.587090i	0.249215	+	0.0197908i
$881$		−	29.2508i		−	0.985484i	−0.870176	−	0.492742i	$-0.835995\pi$
$881$		−	29.2508i		−	0.985484i	0.870176	−	0.492742i	$-0.164005\pi$
$882$	−10.5742	+	8.54963i	−0.356050	+	0.287881i
$883$	2.18684	−	0.346362i	0.0735932	−	0.0116560i	−0.119529	−	0.992831i	$-0.538139\pi$
$883$	2.18684	−	0.346362i	0.0735932	−	0.0116560i	0.193122	+	0.981175i	$0.438139\pi$
$884$	−5.91208	−	8.13728i	−0.198845	−	0.273686i
$885$	8.13479	+	4.87260i	0.273448	+	0.163791i
$886$	−3.08603	+	9.49781i	−0.103677	+	0.319085i
$887$	2.72261	−	17.1899i	0.0914162	−	0.577179i	−0.898879	−	0.438197i	$-0.855617\pi$
$887$	2.72261	−	17.1899i	0.0914162	−	0.577179i	0.990295	−	0.138982i	$-0.0443829\pi$
$888$	0.126923	+	0.801363i	0.00425927	+	0.0268920i
$889$	−51.0939	+	5.35077i	−1.71363	+	0.179459i
$890$	2.33235	−	10.1665i	0.0781805	−	0.340783i
$891$	1.15493	+	1.62632i	0.0386916	+	0.0544838i
$892$	1.51387	−	1.51387i	0.0506881	−	0.0506881i
$893$	−43.9845	−	22.4112i	−1.47189	−	0.749963i
$894$	−4.71069	−	3.42251i	−0.157549	−	0.114466i
$895$	3.64578	−	9.05962i	0.121865	−	0.302830i
$896$	−1.32374	+	2.29079i	−0.0442229	+	0.0765299i
$897$	9.35924	−	4.76877i	0.312496	−	0.159225i
$898$	−3.21552	+	20.3020i	−0.107303	+	0.677486i
$899$	1.57445	+	1.14390i	0.0525108	+	0.0381513i
$900$	−9.62212	−	1.32521i	−0.320737	−	0.0441737i
$901$			33.2831i			1.10882i
$902$	−0.614182	+	0.304621i	−0.0204500	+	0.0101428i
$903$	−16.0031	−	24.6628i	−0.532549	−	0.820728i
$904$	−1.78353	+	0.579505i	−0.0593194	+	0.0192740i
$905$	−51.0161	−	3.49660i	−1.69583	−	0.116231i
$906$	4.33447	+	5.96589i	0.144003	+	0.198203i
$907$	42.2150	−	21.5096i	1.40173	−	0.714215i	0.420539	−	0.907275i	$-0.361841\pi$
$907$	42.2150	−	21.5096i	1.40173	−	0.714215i	0.981187	+	0.193060i	$0.0618411\pi$
$908$	−18.5312	+	9.44212i	−0.614980	+	0.313348i
$909$	−14.5089	+	10.5414i	−0.481231	+	0.349635i
$910$	6.62845	+	11.9297i	0.219731	+	0.395467i
$911$	−8.10450	−	24.9431i	−0.268514	−	0.826401i	−0.990863	−	0.134873i	$-0.956938\pi$
$911$	−8.10450	−	24.9431i	−0.268514	−	0.826401i	0.722349	−	0.691529i	$-0.243062\pi$
$912$	−4.08843	−	4.08843i	−0.135382	−	0.135382i
$913$	22.7390	+	45.8467i	0.752550	+	1.51730i
$914$			32.7878i			1.08452i
$915$	−0.898412	−	10.1081i	−0.0297006	−	0.334164i
$916$	2.29453	−	3.15814i	0.0758133	−	0.104348i
$917$	−6.36616	+	16.5658i	−0.210229	+	0.547051i
$918$	10.0606	+	19.7451i	0.332050	+	0.651684i
$919$	7.51384	+	2.44139i	0.247859	+	0.0805342i	0.430312	−	0.902680i	$-0.358404\pi$
$919$	7.51384	+	2.44139i	0.247859	+	0.0805342i	−0.182453	+	0.983215i	$0.558404\pi$
$920$	3.69650	−	9.18566i	0.121870	−	0.302842i
$921$	15.1064	+	10.9754i	0.497772	+	0.361652i
$922$	8.53349	+	4.34803i	0.281036	+	0.143195i
$923$	8.36198	+	8.36198i	0.275238	+	0.275238i
$924$	3.57765	+	8.28378i	0.117696	+	0.272516i
$925$	3.72660	−	1.29469i	0.122530	−	0.0425693i
$926$	3.51765	+	10.8262i	0.115597	+	0.355772i
$927$	31.1278	−	4.93016i	1.02237	−	0.161928i
$928$	−0.0559608	+	0.353323i	−0.00183700	+	0.0115984i
$929$	15.3949	−	47.3807i	0.505091	−	1.55451i	−0.295528	−	0.955334i	$-0.595495\pi$
$929$	15.3949	−	47.3807i	0.505091	−	1.55451i	0.800618	−	0.599175i	$-0.204505\pi$
$930$	−12.1333	+	3.04298i	−0.397867	+	0.0997833i
$931$	8.15433	+	38.5054i	0.267247	+	1.26196i
$932$	0.978313	+	6.17683i	0.0320457	+	0.202329i
$933$	−21.0280	−	10.7143i	−0.688426	−	0.350771i
$934$	7.42540			0.242966
$935$	−24.6031	+	20.9830i	−0.804608	+	0.686218i
$936$			4.48127i			0.146475i
$937$	−30.9579	−	15.7738i	−1.01135	−	0.515308i	−0.131881	−	0.991266i	$-0.542102\pi$
$937$	−30.9579	−	15.7738i	−1.01135	−	0.515308i	−0.879468	+	0.475957i	$0.842102\pi$
$938$	0.916248	+	0.0483639i	0.0299166	+	0.00157914i
$939$	−1.46745	−	2.01977i	−0.0478883	−	0.0659126i
$940$	−16.8414	−	10.0877i	−0.549307	−	0.329026i
$941$	−1.46850	−	0.477143i	−0.0478716	−	0.0155544i	0.284983	−	0.958532i	$-0.408012\pi$
$941$	−1.46850	−	0.477143i	−0.0478716	−	0.0155544i	−0.332855	+	0.942978i	$0.608012\pi$
$942$	1.04552	+	0.165594i	0.0340649	+	0.00539535i
$943$	0.143189	+	0.904059i	0.00466287	+	0.0294402i
$944$	−1.27437	−	3.92212i	−0.0414773	−	0.127654i
$945$	−10.3124	−	28.2447i	−0.335462	−	0.918800i
$946$	34.2039	−	10.7060i	1.11206	−	0.348082i
$947$	−39.1303	−	39.1303i	−1.27156	−	1.27156i	−0.945267	−	0.326297i	$-0.894199\pi$
$947$	−39.1303	−	39.1303i	−1.27156	−	1.27156i	−0.326297	−	0.945267i	$-0.605801\pi$
$948$	5.78861	−	11.3608i	0.188005	−	0.368981i
$949$	16.5614	−	22.7949i	0.537607	−	0.739952i
$950$	−16.0618	+	23.0740i	−0.521113	+	0.748618i
$951$	−8.36671	−	2.71851i	−0.271309	−	0.0881537i
$952$	−2.98151	−	11.1439i	−0.0966314	−	0.361176i
$953$	6.32127	−	39.9109i	0.204766	−	1.29284i	−0.644389	−	0.764698i	$-0.722888\pi$
$953$	6.32127	−	39.9109i	0.204766	−	1.29284i	0.849155	−	0.528143i	$-0.177112\pi$
$954$	8.71610	−	11.9967i	0.282194	−	0.388407i
$955$	−1.92592	+	2.30167i	−0.0623213	+	0.0744803i
$956$	−20.3386			−0.657797
$957$	0.853311	+	0.871969i	0.0275836	+	0.0281867i
$958$	13.2492	+	13.2492i	0.428063	+	0.428063i
$959$	38.9438	−	4.07836i	1.25756	−	0.131697i
$960$	−1.51091	−	1.73326i	−0.0487644	−	0.0559408i
$961$	−1.13559	+	0.825057i	−0.0366320	+	0.0266147i
$962$	−0.826332	−	1.62177i	−0.0266420	−	0.0522879i
$963$	15.7720	+	30.9543i	0.508246	+	0.997489i
$964$	−18.0749	+	13.1322i	−0.582154	+	0.422960i
$965$	8.85315	+	10.1560i	0.284993	+	0.326934i
$966$	11.9817	−	1.25478i	0.385506	−	0.0403719i
$967$	26.4177	+	26.4177i	0.849537	+	0.849537i	0.990075	−	0.140538i	$-0.0448832\pi$
$967$	26.4177	+	26.4177i	0.849537	+	0.849537i	−0.140538	+	0.990075i	$0.544883\pi$
$968$	−10.8992	+	1.48542i	−0.350315	+	0.0477432i
$969$	25.2100			0.809863
$970$	19.3816	−	23.1630i	0.622306	−	0.743718i
$971$	−13.8849	+	19.1110i	−0.445589	+	0.613300i	−0.971443	−	0.237275i	$-0.923746\pi$
$971$	−13.8849	+	19.1110i	−0.445589	+	0.613300i	0.525854	+	0.850575i	$0.323746\pi$
$972$	2.48197	−	15.6706i	0.0796094	−	0.502634i
$973$	26.5143	−	7.09380i	0.850008	−	0.227417i
$974$	20.1203	+	6.53748i	0.644695	+	0.209474i
$975$	−11.6748	+	2.09185i	−0.373893	+	0.0669928i
$976$	−2.59412	+	3.57050i	−0.0830358	+	0.114289i
$977$	14.6194	−	28.6922i	0.467716	−	0.917945i	−0.529841	−	0.848097i	$-0.677749\pi$
$977$	14.6194	−	28.6922i	0.467716	−	0.917945i	0.997558	−	0.0698482i	$-0.0222515\pi$
$978$	−6.59837	−	6.59837i	−0.210993	−	0.210993i
$979$	−0.167300	+	15.4702i	−0.00534693	+	0.494431i
$980$	2.18816	+	15.4988i	0.0698981	+	0.495090i
$981$	−4.60065	−	14.1593i	−0.146887	−	0.452073i
$982$	−2.75144	−	17.3719i	−0.0878018	−	0.554359i
$983$	2.25667	+	0.357422i	0.0719766	+	0.0114000i	0.192319	−	0.981332i	$-0.438399\pi$
$983$	2.25667	+	0.357422i	0.0719766	+	0.0114000i	−0.120342	+	0.992732i	$0.538399\pi$
$984$	0.202156	+	0.0656845i	0.00644450	+	0.00209395i
$985$	−23.1081	−	13.8413i	−0.736285	−	0.441022i
$986$	−0.916794	−	1.26186i	−0.0291967	−	0.0401858i
$987$	1.25905	−	23.8526i	0.0400760	−	0.759236i
$988$	11.5572	+	5.88867i	0.367682	+	0.187343i
$989$		−	47.8512i		−	1.52158i
$990$	14.3630	−	1.12019i	0.456486	−	0.0356019i
$991$	45.2257			1.43664			0.718321	−	0.695711i	$-0.244911\pi$
$991$	45.2257			1.43664			0.718321	+	0.695711i	$0.244911\pi$
$992$	4.84730	+	2.46982i	0.153902	+	0.0784169i
$993$	3.78798	+	23.9164i	0.120208	+	0.758964i
$994$	5.51188	+	12.3924i	0.174826	+	0.393063i
$995$	−36.0882	+	9.05076i	−1.14407	+	0.286928i
$996$	4.90314	−	15.0903i	0.155362	−	0.478155i
$997$	2.88350	−	18.2057i	0.0913214	−	0.576581i	−0.899017	−	0.437913i	$-0.855718\pi$
$997$	2.88350	−	18.2057i	0.0913214	−	0.576581i	0.990339	−	0.138668i	$-0.0442821\pi$
$998$	3.69512	−	0.585249i	0.116967	−	0.0185257i
$999$	1.23921	+	3.81391i	0.0392070	+	0.120667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bi.a.27.16	yes	384
5.3	odd	4	inner	770.2.bi.a.643.33	yes	384
7.6	odd	2	inner	770.2.bi.a.27.9	✓	384
11.9	even	5	inner	770.2.bi.a.97.40	yes	384
35.13	even	4	inner	770.2.bi.a.643.40	yes	384
55.53	odd	20	inner	770.2.bi.a.713.9	yes	384
77.20	odd	10	inner	770.2.bi.a.97.33	yes	384
385.328	even	20	inner	770.2.bi.a.713.16	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bi.a.27.9	✓	384	7.6	odd	2	inner
770.2.bi.a.27.16	yes	384	1.1	even	1	trivial
770.2.bi.a.97.33	yes	384	77.20	odd	10	inner
770.2.bi.a.97.40	yes	384	11.9	even	5	inner
770.2.bi.a.643.33	yes	384	5.3	odd	4	inner
770.2.bi.a.643.40	yes	384	35.13	even	4	inner
770.2.bi.a.713.9	yes	384	55.53	odd	20	inner
770.2.bi.a.713.16	yes	384	385.328	even	20	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(0.160862 + 1.01564i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-2.16890 + 0.543949i) q^{5} +(-0.977976 - 0.317764i) q^{6} +(2.46967 + 0.949081i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.84751 - 0.600293i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(0.160862 + 1.01564i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-2.16890 + 0.543949i) q^{5} +(-0.977976 - 0.317764i) q^{6} +(2.46967 + 0.949081i) q^{7} +(0.987688 - 0.156434i) q^{8} +(1.84751 - 0.600293i) q^{9} +(0.499997 - 2.17945i) q^{10} +(-0.0358649 + 3.31643i) q^{11} +(0.727121 - 0.727121i) q^{12} +(-1.04729 + 2.05542i) q^{13} +(-1.96684 + 1.76961i) q^{14} +(-0.901353 - 2.11533i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-1.97947 - 3.88492i) q^{17} +(-0.303888 + 1.91867i) q^{18} +(4.54891 + 3.30498i) q^{19} +(1.71491 + 1.43495i) q^{20} +(-0.566653 + 2.66097i) q^{21} +(-2.93868 - 1.53758i) q^{22} +(-3.13114 + 3.13114i) q^{23} +(0.317764 + 0.977976i) q^{24} +(4.40824 - 2.35954i) q^{25} +(-1.35593 - 1.86628i) q^{26} +(2.30740 + 4.52853i) q^{27} +(-0.683810 - 2.55586i) q^{28} +(-0.210267 - 0.289407i) q^{29} +(2.29398 + 0.157228i) q^{30} +(-5.17399 + 1.68113i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.37408 + 0.497063i) q^{33} +4.36015 q^{34} +(-5.87270 - 0.715087i) q^{35} +(-1.57159 - 1.14183i) q^{36} +(0.779305 + 0.123430i) q^{37} +(-5.00992 + 2.55268i) q^{38} +(-2.25605 - 0.733034i) q^{39} +(-2.05710 + 0.876543i) q^{40} +(0.121500 - 0.167231i) q^{41} +(-2.11369 - 1.71295i) q^{42} +(-7.64117 + 7.64117i) q^{43} +(2.70413 - 1.92033i) q^{44} +(-3.68054 + 2.30693i) q^{45} +(-1.36836 - 4.21138i) q^{46} +(-8.67139 + 1.37341i) q^{47} +(-1.01564 - 0.160862i) q^{48} +(5.19849 + 4.68782i) q^{49} +(0.101069 + 4.99898i) q^{50} +(3.62728 - 2.63537i) q^{51} +(2.27845 - 0.360871i) q^{52} +(-6.80148 - 3.46553i) q^{53} -5.08249 q^{54} +(-1.72618 - 7.21251i) q^{55} +(2.58773 + 0.551055i) q^{56} +(-2.62494 + 5.15173i) q^{57} +(0.353323 - 0.0559608i) q^{58} +(-3.33635 + 2.42400i) q^{59} +(-1.18153 + 1.97257i) q^{60} +(4.19738 + 1.36381i) q^{61} +(0.851043 - 5.37327i) q^{62} +(5.13246 + 0.270915i) q^{63} +(0.951057 - 0.309017i) q^{64} +(1.15342 - 5.02767i) q^{65} +(1.08892 - 3.23199i) q^{66} +(-0.245219 - 0.245219i) q^{67} +(-1.97947 + 3.88492i) q^{68} +(-3.68381 - 2.67645i) q^{69} +(3.30330 - 4.90797i) q^{70} +(1.58411 - 4.87540i) q^{71} +(1.73086 - 0.881917i) q^{72} +(-12.0637 - 1.91070i) q^{73} +(-0.463774 + 0.638330i) q^{74} +(3.10558 + 4.09764i) q^{75} -5.62277i q^{76} +(-3.23613 + 8.15643i) q^{77} +(1.67736 - 1.67736i) q^{78} +(11.7927 - 3.83167i) q^{79} +(0.152900 - 2.23083i) q^{80} +(0.486560 - 0.353506i) q^{81} +(0.0938438 + 0.184179i) q^{82} +(13.7484 - 7.00514i) q^{83} +(2.48584 - 1.10565i) q^{84} +(6.40646 + 7.34927i) q^{85} +(-3.33931 - 10.2774i) q^{86} +(0.260111 - 0.260111i) q^{87} +(0.483381 + 3.28121i) q^{88} +4.66473 q^{89} +(-0.384559 - 4.32671i) q^{90} +(-4.53722 + 4.08224i) q^{91} +(4.37359 + 0.692708i) q^{92} +(-2.53973 - 4.98450i) q^{93} +(2.71301 - 8.34978i) q^{94} +(-11.6639 - 4.69379i) q^{95} +(0.604422 - 0.831916i) q^{96} +(12.0347 + 6.13196i) q^{97} +(-6.53695 + 2.50366i) q^{98} +(1.92457 + 6.14868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 4 q^{7}+O(q^{10}) \) 384 * q - 4 * q^7	\( 384 q - 4 q^{7} + 24 q^{15} + 96 q^{16} + 16 q^{22} + 16 q^{23} - 40 q^{25} + 4 q^{28} + 16 q^{30} - 32 q^{35} + 80 q^{36} - 64 q^{37} + 44 q^{42} - 80 q^{43} - 16 q^{46} - 64 q^{50} - 136 q^{51} + 80 q^{53} + 8 q^{56} - 112 q^{57} - 96 q^{58} + 68 q^{63} - 272 q^{65} + 160 q^{67} - 8 q^{70} + 16 q^{71} + 96 q^{77} + 24 q^{81} - 80 q^{85} - 16 q^{88} - 84 q^{91} + 16 q^{92} + 88 q^{93} - 184 q^{95} - 32 q^{98}+O(q^{100}) \) 384 * q - 4 * q^7 + 24 * q^15 + 96 * q^16 + 16 * q^22 + 16 * q^23 - 40 * q^25 + 4 * q^28 + 16 * q^30 - 32 * q^35 + 80 * q^36 - 64 * q^37 + 44 * q^42 - 80 * q^43 - 16 * q^46 - 64 * q^50 - 136 * q^51 + 80 * q^53 + 8 * q^56 - 112 * q^57 - 96 * q^58 + 68 * q^63 - 272 * q^65 + 160 * q^67 - 8 * q^70 + 16 * q^71 + 96 * q^77 + 24 * q^81 - 80 * q^85 - 16 * q^88 - 84 * q^91 + 16 * q^92 + 88 * q^93 - 184 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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