LMFDB - Embedded newform 930.2.y.a.29.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(29,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("930.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.y (of order $10$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.11
Character	$\chi$	$=$	930.29
Dual form			930.2.y.a.449.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-1.01604 - 1.40273i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.08406 - 0.810354i) q^{5} +(-0.00251367 + 1.73205i) q^{6} +(2.70101 - 0.877611i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.935328 + 2.85047i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.01604 - 1.40273i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.08406 - 0.810354i) q^{5} +(-0.00251367 + 1.73205i) q^{6} +(2.70101 - 0.877611i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.935328 + 2.85047i) q^{9} +(1.20973 + 1.88057i) q^{10} +(0.682712 + 2.10117i) q^{11} +(1.02011 - 1.39978i) q^{12} +(3.46448 - 2.51709i) q^{13} +(-2.70101 - 0.877611i) q^{14} +(0.980780 + 3.74674i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.19758 + 0.714038i) q^{17} +(2.43216 - 1.75630i) q^{18} +(0.227369 + 0.165193i) q^{19} +(0.126681 - 2.23248i) q^{20} +(-3.97539 - 2.89711i) q^{21} +(0.682712 - 2.10117i) q^{22} +(0.615571 + 0.200011i) q^{23} +(-1.64805 + 0.532842i) q^{24} +(3.68665 + 3.37766i) q^{25} -4.28233 q^{26} +(4.94878 - 1.58417i) q^{27} +(1.66932 + 2.29762i) q^{28} +(7.56787 + 5.49838i) q^{29} +(1.40881 - 3.60767i) q^{30} +(4.69907 - 2.98642i) q^{31} +1.00000 q^{32} +(2.25372 - 3.09254i) q^{33} +(-1.35818 - 1.86938i) q^{34} +(-6.34025 - 0.359776i) q^{35} +(-2.99999 - 0.00870760i) q^{36} -7.71298 q^{37} +(-0.0868472 - 0.267288i) q^{38} +(-7.05085 - 2.30228i) q^{39} +(-1.41470 + 1.73165i) q^{40} +(3.76009 - 5.17532i) q^{41} +(1.51328 + 4.68049i) q^{42} +(-8.50897 - 6.18213i) q^{43} +(-1.78736 + 1.29860i) q^{44} +(4.25917 - 5.18261i) q^{45} +(-0.380444 - 0.523636i) q^{46} +(3.01546 - 2.19086i) q^{47} +(1.64650 + 0.537623i) q^{48} +(0.862129 - 0.626374i) q^{49} +(-0.997224 - 4.89955i) q^{50} +(-1.23122 - 3.80811i) q^{51} +(3.46448 + 2.51709i) q^{52} +(-0.420438 - 0.136608i) q^{53} +(-4.93480 - 1.62720i) q^{54} +(0.279877 - 4.93222i) q^{55} -2.84001i q^{56} +(0.000706450 - 0.486781i) q^{57} +(-2.89067 - 8.89657i) q^{58} +(-2.61334 - 3.59696i) q^{59} +(-3.26029 + 2.09058i) q^{60} -12.4400i q^{61} +(-5.55700 - 0.345977i) q^{62} +(-0.0247297 + 8.51999i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-9.25993 + 2.43832i) q^{65} +(-3.64105 + 1.17721i) q^{66} +5.64028i q^{67} +2.31067i q^{68} +(-0.344882 - 1.06670i) q^{69} +(4.91790 + 4.01777i) q^{70} +(4.43959 + 1.44251i) q^{71} +(2.42192 + 1.77039i) q^{72} +(2.66579 + 8.20445i) q^{73} +(6.23993 + 4.53357i) q^{74} +(0.992179 - 8.60323i) q^{75} +(-0.0868472 + 0.267288i) q^{76} +(3.68802 + 5.07613i) q^{77} +(4.35101 + 6.00697i) q^{78} +(1.37862 + 0.447940i) q^{79} +(2.16236 - 0.569392i) q^{80} +(-7.25032 - 5.33225i) q^{81} +(-6.08395 + 1.97679i) q^{82} +(2.60415 - 3.58431i) q^{83} +(1.52685 - 4.67607i) q^{84} +(-4.00128 - 3.26892i) q^{85} +(3.25014 + 10.0029i) q^{86} +(0.0235139 - 16.2023i) q^{87} +2.20930 q^{88} +(-5.37218 - 16.5339i) q^{89} +(-6.49201 + 1.68934i) q^{90} +(7.14856 - 9.83914i) q^{91} +0.647249i q^{92} +(-8.96360 - 3.55723i) q^{93} -3.72731 q^{94} +(-0.339986 - 0.528522i) q^{95} +(-1.01604 - 1.40273i) q^{96} +(-8.35086 + 2.71336i) q^{97} -1.06565 q^{98} +(-6.62788 - 0.0192377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9	$ 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9} + 2 q^{10} + 25 q^{15} - 32 q^{16} + 6 q^{18} - 8 q^{19} - 3 q^{20} - 20 q^{23} - 10 q^{25} - 48 q^{31} + 128 q^{32} - 8 q^{33} + 10 q^{34} + 16 q^{35} - 4 q^{36} + 12 q^{38} + 4 q^{39} - 3 q^{40} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 q^{60} - 8 q^{62} + 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} + 6 q^{72} + 5 q^{75} + 12 q^{76} + 50 q^{77} + 4 q^{78} - 10 q^{79} + 2 q^{80} - 24 q^{81} - 40 q^{83} - 30 q^{85} - 4 q^{87} - 53 q^{90} + 20 q^{91} - 26 q^{93} - 4 q^{94} - 26 q^{95} - 124 q^{98}+O(q^{100}) $ 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9 + 2 * q^10 + 25 * q^15 - 32 * q^16 + 6 * q^18 - 8 * q^19 - 3 * q^20 - 20 * q^23 - 10 * q^25 - 48 * q^31 + 128 * q^32 - 8 * q^33 + 10 * q^34 + 16 * q^35 - 4 * q^36 + 12 * q^38 + 4 * q^39 - 3 * q^40 + 37 * q^45 + 10 * q^46 + 6 * q^47 + 46 * q^49 - 5 * q^50 + 34 * q^51 - 20 * q^53 - 25 * q^60 - 8 * q^62 + 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 + 6 * q^72 + 5 * q^75 + 12 * q^76 + 50 * q^77 + 4 * q^78 - 10 * q^79 + 2 * q^80 - 24 * q^81 - 40 * q^83 - 30 * q^85 - 4 * q^87 - 53 * q^90 + 20 * q^91 - 26 * q^93 - 4 * q^94 - 26 * q^95 - 124 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−1.01604	−	1.40273i	−0.586611	−	0.809869i
$3$	−1.01604	−	1.40273i	−0.586611	−	0.809869i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−2.08406	−	0.810354i	−0.932022	−	0.362401i
$5$	−2.08406	−	0.810354i	−0.932022	−	0.362401i
$6$	−0.00251367	+	1.73205i	−0.00102620	+	0.707106i
$7$	2.70101	−	0.877611i	1.02089	−	0.331706i	0.249705	−	0.968322i	$-0.419666\pi$
$7$	2.70101	−	0.877611i	1.02089	−	0.331706i	0.771181	+	0.636616i	$0.219666\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.935328	+	2.85047i	−0.311776	+	0.950156i
$10$	1.20973	+	1.88057i	0.382550	+	0.594689i
$11$	0.682712	+	2.10117i	0.205845	+	0.633527i	0.999678	+	0.0253902i	$0.00808282\pi$
$11$	0.682712	+	2.10117i	0.205845	+	0.633527i	−0.793832	+	0.608137i	$0.791917\pi$
$12$	1.02011	−	1.39978i	0.294479	−	0.404082i
$13$	3.46448	−	2.51709i	0.960873	−	0.698115i	0.00751956	−	0.999972i	$-0.497606\pi$
$13$	3.46448	−	2.51709i	0.960873	−	0.698115i	0.953353	+	0.301857i	$0.0976064\pi$
$14$	−2.70101	−	0.877611i	−0.721875	−	0.234551i
$15$	0.980780	+	3.74674i	0.253236	+	0.967404i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.19758	+	0.714038i	0.532992	+	0.173180i	0.563133	−	0.826366i	$-0.309596\pi$
$17$	2.19758	+	0.714038i	0.532992	+	0.173180i	−0.0301413	+	0.999546i	$0.509596\pi$
$18$	2.43216	−	1.75630i	0.573265	−	0.413965i
$19$	0.227369	+	0.165193i	0.0521620	+	0.0378979i	0.613561	−	0.789648i	$-0.289737\pi$
$19$	0.227369	+	0.165193i	0.0521620	+	0.0378979i	−0.561399	+	0.827545i	$0.689737\pi$
$20$	0.126681	−	2.23248i	0.0283268	−	0.499197i
$21$	−3.97539	−	2.89711i	−0.867500	−	0.632202i
$22$	0.682712	−	2.10117i	0.145555	−	0.447971i
$23$	0.615571	+	0.200011i	0.128355	+	0.0417052i	0.372490	−	0.928036i	$-0.378504\pi$
$23$	0.615571	+	0.200011i	0.128355	+	0.0417052i	−0.244135	+	0.969741i	$0.578504\pi$
$24$	−1.64805	+	0.532842i	−0.336407	+	0.108766i
$25$	3.68665	+	3.37766i	0.737330	+	0.675532i
$26$	−4.28233			−0.839834
$27$	4.94878	−	1.58417i	0.952393	−	0.304873i
$28$	1.66932	+	2.29762i	0.315471	+	0.434209i
$29$	7.56787	+	5.49838i	1.40532	+	1.02102i	0.993982	+	0.109540i	$0.0349377\pi$
$29$	7.56787	+	5.49838i	1.40532	+	1.02102i	0.411336	+	0.911484i	$0.365062\pi$
$30$	1.40881	−	3.60767i	0.257213	−	0.658667i
$31$	4.69907	−	2.98642i	0.843978	−	0.536378i
$31$	4.69907	−	2.98642i	0.843978	−	0.536378i
$32$	1.00000			0.176777
$33$	2.25372	−	3.09254i	0.392323	−	0.538341i
$34$	−1.35818	−	1.86938i	−0.232926	−	0.320595i
$35$	−6.34025	−	0.359776i	−1.07170	−	0.0608132i
$36$	−2.99999	−	0.00870760i	−0.499998	−	0.00145127i
$37$	−7.71298			−1.26801			−0.634003	−	0.773331i	$-0.718589\pi$
$37$	−7.71298			−1.26801			−0.634003	+	0.773331i	$0.718589\pi$
$38$	−0.0868472	−	0.267288i	−0.0140885	−	0.0433599i
$39$	−7.05085	−	2.30228i	−1.12904	−	0.368660i
$40$	−1.41470	+	1.73165i	−0.223684	+	0.273798i
$41$	3.76009	−	5.17532i	0.587227	−	0.808249i	−0.407237	−	0.913322i	$-0.633508\pi$
$41$	3.76009	−	5.17532i	0.587227	−	0.808249i	0.994464	+	0.105074i	$0.0335079\pi$
$42$	1.51328	+	4.68049i	0.233504	+	0.722215i
$43$	−8.50897	−	6.18213i	−1.29761	−	0.942766i	−0.297677	−	0.954667i	$-0.596212\pi$
$43$	−8.50897	−	6.18213i	−1.29761	−	0.942766i	−0.999929	+	0.0119009i	$0.996212\pi$
$44$	−1.78736	+	1.29860i	−0.269455	+	0.195771i
$45$	4.25917	−	5.18261i	0.634920	−	0.772578i
$46$	−0.380444	−	0.523636i	−0.0560933	−	0.0772059i
$47$	3.01546	−	2.19086i	0.439849	−	0.319569i	−0.345726	−	0.938336i	$-0.612367\pi$
$47$	3.01546	−	2.19086i	0.439849	−	0.319569i	0.785575	+	0.618766i	$0.212367\pi$
$48$	1.64650	+	0.537623i	0.237652	+	0.0775992i
$49$	0.862129	−	0.626374i	0.123161	−	0.0894820i
$50$	−0.997224	−	4.89955i	−0.141029	−	0.692900i
$51$	−1.23122	−	3.80811i	−0.172406	−	0.533243i
$52$	3.46448	+	2.51709i	0.480436	+	0.349058i
$53$	−0.420438	−	0.136608i	−0.0577515	−	0.0187646i	0.279999	−	0.960000i	$-0.409666\pi$
$53$	−0.420438	−	0.136608i	−0.0577515	−	0.0187646i	−0.337750	+	0.941236i	$0.609666\pi$
$54$	−4.93480	−	1.62720i	−0.671541	−	0.221434i
$55$	0.279877	−	4.93222i	0.0377386	−	0.665060i
$56$		−	2.84001i		−	0.379512i
$57$	0.000706450	−	0.486781i	9.35717e−5	−	0.0644757i
$58$	−2.89067	−	8.89657i	−0.379564	−	1.16818i
$59$	−2.61334	−	3.59696i	−0.340228	−	0.468284i	0.604280	−	0.796772i	$-0.293461\pi$
$59$	−2.61334	−	3.59696i	−0.340228	−	0.468284i	−0.944508	+	0.328488i	$0.893461\pi$
$60$	−3.26029	+	2.09058i	−0.420901	+	0.269893i
$61$		−	12.4400i		−	1.59278i	−0.604787	−	0.796388i	$-0.706742\pi$
$61$		−	12.4400i		−	1.59278i	0.604787	−	0.796388i	$-0.293258\pi$
$62$	−5.55700	−	0.345977i	−0.705740	−	0.0439392i
$63$	−0.0247297	+	8.51999i	−0.00311565	+	1.07342i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−9.25993	+	2.43832i	−1.14855	+	0.302437i
$66$	−3.64105	+	1.17721i	−0.448182	+	0.144904i
$67$			5.64028i			0.689070i	0.938773	+	0.344535i	$0.111963\pi$
$67$			5.64028i			0.689070i	−0.938773	+	0.344535i	$0.888037\pi$
$68$			2.31067i			0.280210i
$69$	−0.344882	−	1.06670i	−0.0415189	−	0.128416i
$70$	4.91790	+	4.01777i	0.587802	+	0.480216i
$71$	4.43959	+	1.44251i	0.526882	+	0.171194i	0.560366	−	0.828245i	$-0.310660\pi$
$71$	4.43959	+	1.44251i	0.526882	+	0.171194i	−0.0334842	+	0.999439i	$0.510660\pi$
$72$	2.42192	+	1.77039i	0.285426	+	0.208643i
$73$	2.66579	+	8.20445i	0.312007	+	0.960258i	0.976969	+	0.213381i	$0.0684476\pi$
$73$	2.66579	+	8.20445i	0.312007	+	0.960258i	−0.664962	+	0.746877i	$0.731552\pi$
$74$	6.23993	+	4.53357i	0.725377	+	0.527017i
$75$	0.992179	−	8.60323i	0.114567	−	0.993416i
$76$	−0.0868472	+	0.267288i	−0.00996205	+	0.0306600i
$77$	3.68802	+	5.07613i	0.420289	+	0.578478i
$78$	4.35101	+	6.00697i	0.492655	+	0.680155i
$79$	1.37862	+	0.447940i	0.155106	+	0.0503972i	0.385541	−	0.922691i	$-0.374015\pi$
$79$	1.37862	+	0.447940i	0.155106	+	0.0503972i	−0.230435	+	0.973088i	$0.574015\pi$
$80$	2.16236	−	0.569392i	0.241759	−	0.0636600i
$81$	−7.25032	−	5.33225i	−0.805591	−	0.592472i
$82$	−6.08395	+	1.97679i	−0.671860	+	0.218300i
$83$	2.60415	−	3.58431i	0.285843	−	0.393429i	−0.641815	−	0.766859i	$-0.721818\pi$
$83$	2.60415	−	3.58431i	0.285843	−	0.393429i	0.927658	+	0.373430i	$0.121818\pi$
$84$	1.52685	−	4.67607i	0.166594	−	0.510201i
$85$	−4.00128	−	3.26892i	−0.434000	−	0.354564i
$86$	3.25014	+	10.0029i	0.350471	+	1.07864i
$87$	0.0235139	−	16.2023i	0.00252095	−	1.73707i
$88$	2.20930			0.235512
$89$	−5.37218	−	16.5339i	−0.569450	−	1.75259i	−0.654344	−	0.756197i	$-0.727055\pi$
$89$	−5.37218	−	16.5339i	−0.569450	−	1.75259i	0.0848946	−	0.996390i	$-0.472945\pi$
$90$	−6.49201	+	1.68934i	−0.684317	+	0.178072i
$91$	7.14856	−	9.83914i	0.749372	−	1.03142i
$92$			0.647249i			0.0674804i
$93$	−8.96360	−	3.55723i	−0.929482	−	0.368867i
$94$	−3.72731			−0.384442
$95$	−0.339986	−	0.528522i	−0.0348819	−	0.0542253i
$96$	−1.01604	−	1.40273i	−0.103699	−	0.143166i
$97$	−8.35086	+	2.71336i	−0.847901	+	0.275500i	−0.700567	−	0.713587i	$-0.747069\pi$
$97$	−8.35086	+	2.71336i	−0.847901	+	0.275500i	−0.147335	+	0.989087i	$0.547069\pi$
$98$	−1.06565			−0.107647
$99$	−6.62788	−	0.0192377i	−0.666127	−	0.00193346i
$100$	−2.07311	+	4.54997i	−0.207311	+	0.454997i
$101$	−3.99097	−	1.29674i	−0.397116	−	0.129031i	0.103649	−	0.994614i	$-0.466948\pi$
$101$	−3.99097	−	1.29674i	−0.397116	−	0.129031i	−0.500766	+	0.865583i	$0.666948\pi$
$102$	−1.24227	+	3.80453i	−0.123003	+	0.376704i
$103$	2.87681	−	3.95959i	0.283460	−	0.390150i	−0.643416	−	0.765517i	$-0.722483\pi$
$103$	2.87681	−	3.95959i	0.283460	−	0.390150i	0.926876	+	0.375367i	$0.122483\pi$
$104$	−1.32331	−	4.07274i	−0.129761	−	0.399365i
$105$	5.93728	+	9.25924i	0.579419	+	0.903609i
$106$	0.259845	+	0.357646i	0.0252383	+	0.0347376i
$107$	4.95353	−	15.2454i	0.478875	−	1.47383i	−0.361784	−	0.932262i	$-0.617832\pi$
$107$	4.95353	−	15.2454i	0.478875	−	1.47383i	0.840659	−	0.541565i	$-0.182168\pi$
$108$	3.03589	+	4.21703i	0.292129	+	0.405784i
$109$	−1.89084	+	1.37377i	−0.181109	+	0.131584i	−0.674646	−	0.738141i	$-0.735704\pi$
$109$	−1.89084	+	1.37377i	−0.181109	+	0.131584i	0.493537	+	0.869725i	$0.335704\pi$
$110$	−3.12551	+	3.82574i	−0.298006	+	0.364770i
$111$	7.83669	+	10.8193i	0.743826	+	1.02692i
$112$	−1.66932	+	2.29762i	−0.157735	+	0.217104i
$113$	3.89078	+	11.9746i	0.366014	+	1.12648i	0.949344	+	0.314240i	$0.101750\pi$
$113$	3.89078	+	11.9746i	0.366014	+	1.12648i	−0.583329	+	0.812236i	$0.698250\pi$
$114$	−0.286694	+	0.393399i	−0.0268514	+	0.0368452i
$115$	−1.12081	−	0.915666i	−0.104516	−	0.0853863i
$116$	−2.89067	+	8.89657i	−0.268392	+	0.826025i
$117$	3.93446	+	12.2297i	0.363741	+	1.13063i
$118$			4.44609i			0.409295i
$119$	6.56234			0.601568
$120$	3.86644	+	0.225030i	0.352956	+	0.0205423i
$121$	4.95036	−	3.59665i	0.450033	−	0.326968i
$122$	−7.31203	+	10.0641i	−0.662000	+	0.911165i
$123$	−11.0800	−	0.0160801i	−0.999049	−	0.00144989i
$124$	4.29235	+	3.54623i	0.385464	+	0.318461i
$125$	−4.94612	−	10.0268i	−0.442394	−	0.896821i
$126$	5.02793	−	6.87828i	0.447924	−	0.612766i
$127$	6.86015	−	4.98419i	0.608740	−	0.442275i	−0.240230	−	0.970716i	$-0.577223\pi$
$127$	6.86015	−	4.98419i	0.608740	−	0.442275i	0.848970	+	0.528440i	$0.177223\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−0.0264380	+	18.2171i	−0.00232773	+	1.60393i
$130$	8.92465	+	3.47020i	0.782744	+	0.304357i
$131$	−6.83740	+	2.22160i	−0.597386	+	0.194102i	−0.592074	−	0.805883i	$-0.701691\pi$
$131$	−6.83740	+	2.22160i	−0.597386	+	0.194102i	−0.00531174	+	0.999986i	$0.501691\pi$
$132$	3.63762	+	1.18777i	0.316614	+	0.103382i
$133$	0.759101	+	0.246647i	0.0658224	+	0.0213870i
$134$	3.31527	−	4.56308i	0.286396	−	0.394190i
$135$	−11.5973	−	0.708754i	−0.998138	−	0.0609998i
$136$	1.35818	−	1.86938i	0.116463	−	0.160298i
$137$	3.54766	+	4.88293i	0.303097	+	0.417177i	0.933213	−	0.359324i	$-0.116993\pi$
$137$	3.54766	+	4.88293i	0.303097	+	0.417177i	−0.630116	+	0.776501i	$0.716993\pi$
$138$	−0.347976	+	1.06570i	−0.0296217	+	0.0907180i
$139$	11.0537	+	15.2141i	0.937563	+	1.29045i	0.956835	+	0.290631i	$0.0938652\pi$
$139$	11.0537	+	15.2141i	0.937563	+	1.29045i	−0.0192718	+	0.999814i	$0.506135\pi$
$140$	−1.61708	−	6.14112i	−0.136668	−	0.519019i
$141$	−6.13701	−	2.00389i	−0.516830	−	0.168758i
$142$	−2.74382	−	3.77654i	−0.230256	−	0.316920i
$143$	7.65408	+	5.56101i	0.640066	+	0.465035i
$144$	−0.918766	−	2.85585i	−0.0765638	−	0.237987i
$145$	−11.3163	−	17.5916i	−0.939767	−	1.46091i
$146$	2.66579	−	8.20445i	0.220622	−	0.679005i
$147$	−1.75459	−	0.572919i	−0.144716	−	0.0472535i
$148$	−2.38344	−	7.33548i	−0.195918	−	0.602973i
$149$			23.7054i			1.94203i	0.239027	+	0.971013i	$0.423171\pi$
$149$			23.7054i			1.94203i	−0.239027	+	0.971013i	$0.576829\pi$
$150$	−5.85954	+	6.37697i	−0.478430	+	0.520678i
$151$	20.7062	−	6.72784i	1.68504	−	0.547504i	0.699164	−	0.714961i	$-0.253556\pi$
$151$	20.7062	−	6.72784i	1.68504	−	0.547504i	0.985879	+	0.167458i	$0.0535558\pi$
$152$	0.227369	−	0.165193i	0.0184420	−	0.0133989i
$153$	−4.09080	+	5.59628i	−0.330722	+	0.452432i
$154$		−	6.27444i		−	0.505609i
$155$	−12.2132	+	2.41599i	−0.980990	+	0.194057i
$156$	0.0107644	−	7.41720i	0.000861839	−	0.593851i
$157$	9.65025	−	13.2824i	0.770174	−	1.06005i	−0.226125	−	0.974098i	$-0.572606\pi$
$157$	9.65025	−	13.2824i	0.770174	−	1.06005i	0.996299	−	0.0859552i	$-0.0273942\pi$
$158$	−0.852032	−	1.17272i	−0.0677840	−	0.0932967i
$159$	0.235556	+	0.728562i	0.0186808	+	0.0577787i
$160$	−2.08406	−	0.810354i	−0.164760	−	0.0640641i
$161$	1.83819			0.144870
$162$	2.73142	+	8.57551i	0.214600	+	0.673756i
$163$	0.666709	+	0.216627i	0.0522206	+	0.0169675i	0.335011	−	0.942214i	$-0.391260\pi$
$163$	0.666709	+	0.216627i	0.0522206	+	0.0169675i	−0.282790	+	0.959182i	$0.591260\pi$
$164$	6.08395	+	1.97679i	0.475077	+	0.154362i
$165$	−7.20296	+	4.61873i	−0.560749	+	0.359568i
$166$	−4.21361	+	1.36908i	−0.327039	+	0.106262i
$167$	1.98562	−	2.73297i	0.153652	−	0.211484i	−0.725251	−	0.688485i	$-0.758276\pi$
$167$	1.98562	−	2.73297i	0.153652	−	0.211484i	0.878903	+	0.477001i	$0.158276\pi$
$168$	−3.98378	+	2.88556i	−0.307355	+	0.222626i
$169$	1.64964	−	5.07706i	0.126895	−	0.390543i
$170$	1.31568	+	4.99651i	0.100908	+	0.383215i
$171$	−0.683542	+	0.493597i	−0.0522718	+	0.0377463i
$172$	3.25014	−	10.0029i	0.247821	−	0.762714i
$173$	−3.72618	+	2.70723i	−0.283296	+	0.205827i	−0.720354	−	0.693607i	$-0.756021\pi$
$173$	−3.72618	+	2.70723i	−0.283296	+	0.205827i	0.437057	+	0.899434i	$0.356021\pi$
$174$	−9.54249	+	13.0941i	−0.723414	+	0.992661i
$175$	12.9220	+	5.88765i	0.976808	+	0.445064i
$176$	−1.78736	−	1.29860i	−0.134728	−	0.0978853i
$177$	−2.39032	+	7.32048i	−0.179667	+	0.550241i
$178$	−5.37218	+	16.5339i	−0.402662	+	1.23927i
$179$	−3.12349	−	9.61310i	−0.233460	−	0.718517i	−0.997322	−	0.0731368i	$-0.976699\pi$
$179$	−3.12349	−	9.61310i	−0.233460	−	0.718517i	0.763862	−	0.645380i	$-0.223301\pi$
$180$	6.24511	+	2.44920i	0.465483	+	0.182553i
$181$		−	16.5526i		−	1.23034i	−0.788393	−	0.615172i	$-0.789087\pi$
$181$		−	16.5526i		−	1.23034i	0.788393	−	0.615172i	$-0.210913\pi$
$182$	−11.5666	+	3.75822i	−0.857374	+	0.278578i
$183$	−17.4500	+	12.6395i	−1.28994	+	0.934339i
$184$	0.380444	−	0.523636i	0.0280467	−	0.0386029i
$185$	16.0743	+	6.25024i	1.18181	+	0.459527i
$186$	5.16082	+	8.14653i	0.378410	+	0.597332i
$187$			5.10498i			0.373313i
$188$	3.01546	+	2.19086i	0.219925	+	0.159785i
$189$	11.9764	−	8.62196i	0.871156	−	0.627155i
$190$	−0.0356029	+	0.627423i	−0.00258291	+	0.0455180i
$191$		−	18.9480i		−	1.37103i	−0.728059	−	0.685515i	$-0.759577\pi$
$191$		−	18.9480i		−	1.37103i	0.728059	−	0.685515i	$-0.240423\pi$
$192$	−0.00251367	+	1.73205i	−0.000181409	+	0.125000i
$193$	−13.1130	+	4.26067i	−0.943894	+	0.306690i	−0.740232	−	0.672352i	$-0.765284\pi$
$193$	−13.1130	+	4.26067i	−0.943894	+	0.306690i	−0.203662	+	0.979041i	$0.565284\pi$
$194$	8.35086	+	2.71336i	0.599557	+	0.194808i
$195$	12.8288	+	10.5118i	0.918687	+	0.752765i
$196$	0.862129	+	0.626374i	0.0615807	+	0.0447410i
$197$	−10.0418	+	3.26277i	−0.715447	+	0.232463i	−0.644048	−	0.764985i	$-0.722746\pi$
$197$	−10.0418	+	3.26277i	−0.715447	+	0.232463i	−0.0713989	+	0.997448i	$0.522746\pi$
$198$	5.35076	+	3.91133i	0.380262	+	0.277966i
$199$	15.5115	+	21.3497i	1.09958	+	1.51344i	0.835943	+	0.548816i	$0.184921\pi$
$199$	15.5115	+	21.3497i	1.09958	+	1.51344i	0.263635	+	0.964623i	$0.415079\pi$
$200$	4.35159	−	2.46246i	0.307704	−	0.174122i
$201$	7.91182	−	5.73075i	0.558057	−	0.404216i
$202$	2.46656	+	3.39492i	0.173546	+	0.238866i
$203$	25.2663	+	8.20953i	1.77335	+	0.576196i
$204$	3.24126	−	2.34774i	0.226934	−	0.164374i
$205$	−12.0301	+	7.73869i	−0.840219	+	0.540494i
$206$	−4.65477	+	1.51243i	−0.324313	+	0.105376i
$207$	−1.14589	+	1.56759i	−0.0796446	+	0.108955i
$208$	−1.32331	+	4.07274i	−0.0917552	+	0.282393i
$209$	−0.191872	+	0.590520i	−0.0132720	+	0.0408471i
$210$	0.639087	−	10.9807i	0.0441012	−	0.757742i
$211$	14.7248			1.01370			0.506850	−	0.862034i	$-0.330810\pi$
$211$	14.7248			1.01370			0.506850	+	0.862034i	$0.330810\pi$
$212$		−	0.442074i		−	0.0303618i
$213$	−2.48734	−	7.69321i	−0.170430	−	0.527130i
$214$	−12.9685	+	9.42217i	−0.886508	+	0.644086i
$215$	12.7235	+	19.7792i	0.867738	+	1.34893i
$216$	0.0226230	−	5.19610i	0.00153930	−	0.353550i
$217$	10.0713	−	12.1903i	0.683685	−	0.827532i
$218$	2.33720			0.158295
$219$	8.80012	−	12.0754i	0.594657	−	0.815982i
$220$	4.77730	−	1.25796i	0.322086	−	0.0848116i
$221$	9.41077	−	3.05774i	0.633037	−	0.205686i
$222$	0.0193879	−	13.3593i	0.00130123	−	0.896615i
$223$	15.5056			1.03833			0.519165	−	0.854674i	$-0.326243\pi$
$223$	15.5056			1.03833			0.519165	+	0.854674i	$0.326243\pi$
$224$	2.70101	−	0.877611i	0.180469	−	0.0586379i
$225$	−13.0761	+	7.34946i	−0.871743	+	0.489964i
$226$	3.89078	−	11.9746i	0.258811	−	0.796539i
$227$	1.62410	+	1.17998i	0.107795	+	0.0783179i	0.640377	−	0.768061i	$-0.278778\pi$
$227$	1.62410	+	1.17998i	0.107795	+	0.0783179i	−0.532582	+	0.846379i	$0.678778\pi$
$228$	0.463174	−	0.149752i	0.0306745	−	0.00991755i
$229$	−13.2180	+	18.1930i	−0.873470	+	1.20223i	0.104718	+	0.994502i	$0.466606\pi$
$229$	−13.2180	+	18.1930i	−0.873470	+	1.20223i	−0.978187	+	0.207726i	$0.933394\pi$
$230$	0.368539	+	1.39958i	0.0243007	+	0.0922859i
$231$	3.37328	−	10.3309i	0.221946	−	0.679721i
$232$	7.56787	−	5.49838i	0.496855	−	0.360986i
$233$	2.78712	−	2.02496i	0.182590	−	0.132659i	−0.492736	−	0.870179i	$-0.664003\pi$
$233$	2.78712	−	2.02496i	0.182590	−	0.132659i	0.675326	+	0.737520i	$0.264003\pi$
$234$	4.00538	−	12.2066i	0.261840	−	0.797973i
$235$	−8.05978	+	2.12230i	−0.525762	+	0.138444i
$236$	2.61334	−	3.59696i	0.170114	−	0.234142i
$237$	−0.772388	−	2.38896i	−0.0501720	−	0.155179i
$238$	−5.30904	−	3.85724i	−0.344134	−	0.250028i
$239$	−1.57128	+	4.83591i	−0.101638	+	0.312809i	−0.988927	−	0.148405i	$-0.952586\pi$
$239$	−1.57128	+	4.83591i	−0.101638	+	0.312809i	0.887289	+	0.461214i	$0.152586\pi$
$240$	−2.99575	−	2.45469i	−0.193375	−	0.158450i
$241$	5.92389	−	1.92479i	0.381591	−	0.123986i	−0.111939	−	0.993715i	$-0.535706\pi$
$241$	5.92389	−	1.92479i	0.381591	−	0.123986i	0.493530	+	0.869729i	$0.335706\pi$
$242$	−6.11898			−0.393343
$243$	−0.113114	+	15.5880i	−0.00725628	+	0.999974i
$244$	11.8311	−	3.84416i	0.757410	−	0.246097i
$245$	−2.30432	+	0.606773i	−0.147217	+	0.0387653i
$246$	8.95445	+	6.52566i	0.570915	+	0.416061i
$247$	1.20352			0.0765781
$248$	−1.38816	−	5.39194i	−0.0881486	−	0.342388i
$249$	−7.67375	−	0.0111367i	−0.486304	−	0.000705759i
$250$	−1.89209	+	11.0191i	−0.119666	+	0.696907i
$251$	−18.1029	+	13.1525i	−1.14264	+	0.830179i	−0.987485	−	0.157711i	$-0.949589\pi$
$251$	−18.1029	+	13.1525i	−1.14264	+	0.830179i	−0.155158	+	0.987890i	$0.549589\pi$
$252$	−8.11063	+	2.60930i	−0.510922	+	0.164371i
$253$			1.42997i			0.0899014i
$254$	−8.47961			−0.532058
$255$	−0.519971	+	8.93409i	−0.0325618	+	0.559474i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−4.41906	+	13.6005i	−0.275653	+	0.848373i	0.713393	+	0.700764i	$0.247158\pi$
$257$	−4.41906	+	13.6005i	−0.275653	+	0.848373i	−0.989046	+	0.147609i	$0.952842\pi$
$258$	10.7291	−	14.7224i	0.667967	−	0.916577i
$259$	−20.8328	+	6.76899i	−1.29449	+	0.420605i
$260$	−5.18046	−	8.05323i	−0.321278	−	0.499440i
$261$	−22.7514	+	16.4292i	−1.40828	+	1.01694i
$262$	6.83740	+	2.22160i	0.422416	+	0.137251i
$263$	13.3559	+	18.3829i	0.823563	+	1.13354i	0.989087	+	0.147332i	$0.0470684\pi$
$263$	13.3559	+	18.3829i	0.823563	+	1.13354i	−0.165524	+	0.986206i	$0.552932\pi$
$264$	−2.24474	−	3.09906i	−0.138154	−	0.190734i
$265$	0.765518	+	0.625404i	0.0470254	+	0.0384183i
$266$	−0.469150	−	0.645730i	−0.0287654	−	0.0395922i
$267$	−17.7343	+	24.3348i	−1.08532	+	1.48927i
$268$	−5.36423	+	1.74294i	−0.327672	+	0.106467i
$269$	−1.84977	−	1.34394i	−0.112783	−	0.0819414i	0.529964	−	0.848020i	$-0.322205\pi$
$269$	−1.84977	−	1.34394i	−0.112783	−	0.0819414i	−0.642747	+	0.766079i	$0.722205\pi$
$270$	8.96583	+	7.39012i	0.545643	+	0.449749i
$271$	−1.30005	−	0.422411i	−0.0789722	−	0.0256596i	0.269264	−	0.963066i	$-0.413219\pi$
$271$	−1.30005	−	0.422411i	−0.0789722	−	0.0256596i	−0.348237	+	0.937407i	$0.613219\pi$
$272$	−2.19758	+	0.714038i	−0.133248	+	0.0432949i
$273$	−21.0649	−	0.0305709i	−1.27491	−	0.00185023i
$274$		−	6.03564i		−	0.364626i
$275$	−4.58012	+	10.0523i	−0.276192	+	0.606174i
$276$	0.907919	−	0.657631i	0.0546503	−	0.0395847i
$277$	−13.0683	−	9.49469i	−0.785200	−	0.570481i	0.121335	−	0.992612i	$-0.461282\pi$
$277$	−13.0683	−	9.49469i	−0.785200	−	0.570481i	−0.906535	+	0.422131i	$0.861282\pi$
$278$		−	18.8057i		−	1.12789i
$279$	4.11753	+	16.1878i	0.246510	+	0.969140i
$280$	−2.30141	+	5.91876i	−0.137536	+	0.353714i
$281$	−0.889359	+	1.22410i	−0.0530547	+	0.0730236i	−0.834720	−	0.550675i	$-0.814371\pi$
$281$	−0.889359	+	1.22410i	−0.0530547	+	0.0730236i	0.781665	+	0.623698i	$0.214371\pi$
$282$	3.78709	+	5.22842i	0.225518	+	0.311348i
$283$	23.7491	−	7.71655i	1.41174	−	0.458701i	0.498770	−	0.866735i	$-0.333785\pi$
$283$	23.7491	−	7.71655i	1.41174	−	0.458701i	0.912967	+	0.408033i	$0.133785\pi$
$284$			4.66806i			0.276998i
$285$	−0.395937	+	1.01391i	−0.0234533	+	0.0600589i
$286$	−2.92360	−	8.99791i	−0.172876	−	0.532057i
$287$	5.61411	−	17.2785i	0.331391	−	1.01992i
$288$	−0.935328	+	2.85047i	−0.0551148	+	0.167965i
$289$	−9.43377	−	6.85404i	−0.554928	−	0.403179i
$290$	−1.18503	+	20.8835i	−0.0695872	+	1.22632i
$291$	12.2909	+	8.95716i	0.720507	+	0.525078i
$292$	−6.97912	+	5.07063i	−0.408422	+	0.296736i
$293$	4.32883	−	13.3228i	0.252893	−	0.778324i	−0.741345	−	0.671124i	$-0.765812\pi$
$293$	4.32883	−	13.3228i	0.252893	−	0.778324i	0.994238	−	0.107199i	$-0.0341883\pi$
$294$	1.08274	+	1.49483i	0.0631468	+	0.0871800i
$295$	2.53157	+	9.61403i	0.147394	+	0.559751i
$296$	−2.38344	+	7.33548i	−0.138535	+	0.426366i
$297$	6.70720	+	9.31670i	0.389191	+	0.540610i
$298$	13.9337	−	19.1781i	0.807158	−	1.11096i
$299$	2.63608	−	0.856513i	0.152448	−	0.0495334i
$300$	8.48876	−	1.71493i	0.490099	−	0.0990113i
$301$	−28.4083	−	9.23042i	−1.63743	−	0.532033i
$302$	−20.7062	−	6.72784i	−1.19151	−	0.387144i
$303$	2.23599	+	6.91582i	0.128454	+	0.397303i
$304$	−0.281043			−0.0161189
$305$	−10.0808	+	25.9257i	−0.577224	+	1.48450i
$306$	6.59894	−	2.12297i	0.377236	−	0.121362i
$307$	7.08027	+	9.74516i	0.404093	+	0.556186i	0.961765	−	0.273875i	$-0.0883055\pi$
$307$	7.08027	+	9.74516i	0.404093	+	0.556186i	−0.557673	+	0.830061i	$0.688306\pi$
$308$	−3.68802	+	5.07613i	−0.210145	+	0.289239i
$309$	−8.47720	−	0.0123027i	−0.482251	−	0.000699877i
$310$	11.3008	+	5.22418i	0.641842	+	0.296714i
$311$			1.13624i			0.0644303i	0.999481	+	0.0322151i	$0.0102562\pi$
$311$			1.13624i			0.0644303i	−0.999481	+	0.0322151i	$0.989744\pi$
$312$	−4.36843	+	5.99432i	−0.247314	+	0.339361i
$313$	−14.4885	+	10.5265i	−0.818937	+	0.594993i	−0.916408	−	0.400246i	$-0.868925\pi$
$313$	−14.4885	+	10.5265i	−0.818937	+	0.594993i	0.0974705	+	0.995238i	$0.468925\pi$
$314$	−15.6144	+	5.07344i	−0.881174	+	0.286311i
$315$	6.95575	−	17.7362i	0.391912	−	0.999320i
$316$			1.44956i			0.0815443i
$317$	−8.33623	−	25.6563i	−0.468209	−	1.44100i	−0.854901	−	0.518791i	$-0.826382\pi$
$317$	−8.33623	−	25.6563i	−0.468209	−	1.44100i	0.386692	−	0.922209i	$-0.373618\pi$
$318$	0.237669	−	0.727875i	0.0133278	−	0.0408172i
$319$	−6.38636	+	19.6552i	−0.357568	+	1.10048i
$320$	1.20973	+	1.88057i	0.0676259	+	0.105127i
$321$	−26.4182	+	8.54143i	−1.47452	+	0.476736i
$322$	−1.48713	−	1.08046i	−0.0828745	−	0.0602119i
$323$	0.381708	+	0.525375i	0.0212388	+	0.0292327i
$324$	2.83079	−	8.54322i	0.157266	−	0.474623i
$325$	21.2742	+	2.42220i	1.18008	+	0.134359i
$326$	−0.412049	−	0.567136i	−0.0228213	−	0.0314108i
$327$	3.84820	+	1.25653i	0.212806	+	0.0694865i
$328$	−3.76009	−	5.17532i	−0.207616	−	0.285759i
$329$	6.22205	−	8.56392i	0.343033	−	0.472144i
$330$	8.54214	+	0.497159i	0.470229	+	0.0273677i
$331$	9.89461	−	13.6188i	0.543857	−	0.748555i	−0.445305	−	0.895379i	$-0.646905\pi$
$331$	9.89461	−	13.6188i	0.543857	−	0.748555i	0.989163	+	0.146823i	$0.0469049\pi$
$332$	4.21361	+	1.36908i	0.231252	+	0.0751382i
$333$	7.21417	−	21.9856i	0.395334	−	1.20480i
$334$	−3.21280	+	1.04390i	−0.175797	+	0.0571198i
$335$	4.57063	−	11.7547i	0.249720	−	0.642229i
$336$	4.91903	+	0.00713885i	0.268355	+	0.000389456i
$337$	6.65129	+	20.4706i	0.362319	+	1.11510i	0.951643	+	0.307206i	$0.0993939\pi$
$337$	6.65129	+	20.4706i	0.362319	+	1.11510i	−0.589325	+	0.807896i	$0.700606\pi$
$338$	−4.31880	+	3.13780i	−0.234912	+	0.170674i
$339$	12.8440	−	17.6244i	0.697590	−	0.957226i
$340$	1.87247	−	4.81560i	0.101549	−	0.261162i
$341$	9.48310	+	7.83469i	0.513539	+	0.424272i
$342$	0.843126	+	0.00244721i	0.0455911	+	0.000132330i
$343$	−9.90630	+	13.6349i	−0.534890	+	0.736213i
$344$	−8.50897	+	6.18213i	−0.458773	+	0.333318i
$345$	−0.145650	+	2.50255i	−0.00784155	+	0.134733i
$346$	4.60582			0.247610
$347$		−	14.4000i		−	0.773031i	−0.922283	−	0.386516i	$-0.873679\pi$
$347$		−	14.4000i		−	0.773031i	0.922283	−	0.386516i	$-0.126321\pi$
$348$	15.4166	−	4.98442i	0.826414	−	0.267193i
$349$	1.58610	−	4.88151i	0.0849020	−	0.261301i	−0.899589	−	0.436738i	$-0.856134\pi$
$349$	1.58610	−	4.88151i	0.0849020	−	0.261301i	0.984491	+	0.175437i	$0.0561337\pi$
$350$	−6.99341	−	12.3585i	−0.373813	−	0.660592i
$351$	13.1574	−	17.9448i	0.702292	−	0.957824i
$352$	0.682712	+	2.10117i	0.0363887	+	0.111993i
$353$	2.96640	−	4.08290i	0.157886	−	0.217311i	−0.722744	−	0.691115i	$-0.757120\pi$
$353$	2.96640	−	4.08290i	0.157886	−	0.217311i	0.880630	+	0.473804i	$0.157120\pi$
$354$	6.23668	−	4.51740i	0.331476	−	0.240097i
$355$	−8.08344	−	6.60392i	−0.429025	−	0.350500i
$356$	14.0645	−	10.2185i	0.745420	−	0.541579i
$357$	−6.66759	−	9.20522i	−0.352886	−	0.487192i
$358$	−3.12349	+	9.61310i	−0.165081	+	0.508068i
$359$	7.78581	+	10.7163i	0.410920	+	0.565582i	0.963442	−	0.267916i	$-0.0863348\pi$
$359$	7.78581	+	10.7163i	0.410920	+	0.565582i	−0.552523	+	0.833498i	$0.686335\pi$
$360$	−3.61280	−	5.65223i	−0.190411	−	0.297899i
$361$	−5.84692	−	17.9950i	−0.307732	−	0.947103i
$362$	−9.72937	+	13.3913i	−0.511364	+	0.703832i
$363$	−10.0749	−	3.28971i	−0.528795	−	0.172665i
$364$	11.5666	+	3.75822i	0.606255	+	0.196984i
$365$	1.09284	−	19.2588i	0.0572017	−	1.00805i
$366$	21.5466	+	0.0312700i	1.12626	+	0.00163451i
$367$	−30.4492			−1.58944			−0.794718	−	0.606979i	$-0.792381\pi$
$367$	−30.4492			−1.58944			−0.794718	+	0.606979i	$0.792381\pi$
$368$	−0.615571	+	0.200011i	−0.0320888	+	0.0104263i
$369$	11.2351	+	15.5586i	0.584879	+	0.809950i
$370$	−9.33062	−	14.5048i	−0.485076	−	0.754070i
$371$	−1.25549			−0.0651820
$372$	0.613218	−	9.62413i	0.0317939	−	0.498988i
$373$		−	1.37935i		−	0.0714200i	−0.999362	−	0.0357100i	$-0.988631\pi$
$373$		−	1.37935i		−	0.0714200i	0.999362	−	0.0357100i	$-0.0113693\pi$
$374$	3.00063	−	4.13001i	0.155159	−	0.213558i
$375$	−9.03943	+	17.1257i	−0.466794	+	0.884366i
$376$	−1.15180	−	3.54488i	−0.0593996	−	0.182813i
$377$	40.0586			2.06312
$378$	−14.7570	−	0.0642494i	−0.759017	−	0.00330464i
$379$	−4.16004	−	12.8033i	−0.213687	−	0.657661i	−0.999244	−	0.0388719i	$-0.987624\pi$
$379$	−4.16004	−	12.8033i	−0.213687	−	0.657661i	0.785557	−	0.618789i	$-0.212376\pi$
$380$	0.397593	−	0.486669i	0.0203961	−	0.0249656i
$381$	−13.9617	−	4.55884i	−0.715279	−	0.233556i
$382$	−11.1374	+	15.3293i	−0.569837	+	0.784313i
$383$	−8.97486	+	2.91611i	−0.458594	+	0.149006i	−0.529198	−	0.848498i	$-0.677507\pi$
$383$	−8.97486	+	2.91611i	−0.458594	+	0.149006i	0.0706045	+	0.997504i	$0.477507\pi$
$384$	1.02011	−	1.39978i	0.0520571	−	0.0714322i
$385$	−3.57262	−	13.5676i	−0.182077	−	0.691468i
$386$	13.1130	+	4.26067i	0.667434	+	0.216862i
$387$	25.5806	−	18.4722i	1.30034	−	0.938996i
$388$	−5.16112	−	7.10367i	−0.262016	−	0.360634i
$389$	4.34119	−	13.3608i	0.220107	−	0.677420i	−0.778644	−	0.627466i	$-0.784092\pi$
$389$	4.34119	−	13.3608i	0.220107	−	0.677420i	0.998751	−	0.0499546i	$-0.0159077\pi$
$390$	−4.20002	−	16.0448i	−0.212676	−	0.812459i
$391$	1.20995	+	0.879081i	0.0611899	+	0.0444571i
$392$	−0.329304	−	1.01349i	−0.0166324	−	0.0511892i
$393$	10.0634	+	7.33381i	0.507631	+	0.369942i
$394$	10.0418	+	3.26277i	0.505897	+	0.164376i
$395$	−2.51014	−	2.05070i	−0.126299	−	0.103182i
$396$	−2.02983	−	6.30943i	−0.102003	−	0.317061i
$397$			7.03491i			0.353072i	0.984294	+	0.176536i	$0.0564892\pi$
$397$			7.03491i			0.353072i	−0.984294	+	0.176536i	$0.943511\pi$
$398$		−	26.3897i		−	1.32279i
$399$	−0.425296	−	1.31542i	−0.0212914	−	0.0658533i
$400$	−4.96790	−	0.565626i	−0.248395	−	0.0282813i
$401$	−25.5503	−	18.5634i	−1.27592	−	0.927011i	−0.276500	−	0.961014i	$-0.589174\pi$
$401$	−25.5503	−	18.5634i	−1.27592	−	0.927011i	−0.999422	+	0.0340028i	$0.989174\pi$
$402$	−9.76924	−	0.0141778i	−0.487246	−	0.000707125i
$403$	8.76273	−	22.1744i	0.436502	−	1.10458i
$404$		−	4.19635i		−	0.208776i
$405$	10.7891	+	16.9881i	0.536116	+	0.844144i
$406$	−15.6155	−	21.4928i	−0.774982	−	1.06667i
$407$	−5.26574	−	16.2063i	−0.261013	−	0.803316i
$408$	−4.00220	−	0.00580828i	−0.198139	−	0.000287553i
$409$			5.74750i			0.284195i	0.989853	+	0.142098i	$0.0453847\pi$
$409$			5.74750i			0.284195i	−0.989853	+	0.142098i	$0.954615\pi$
$410$	14.2812	+	0.810385i	0.705301	+	0.0400221i
$411$	3.24490	−	9.93767i	0.160059	−	0.490189i
$412$	4.65477	+	1.51243i	0.229324	+	0.0745120i
$413$	−10.2154	−	7.42192i	−0.502667	−	0.365209i
$414$	1.84845	−	0.594670i	0.0908462	−	0.0292265i
$415$	−8.33178	+	5.35964i	−0.408991	+	0.263095i
$416$	3.46448	−	2.51709i	0.169860	−	0.123410i
$417$	10.1104	−	30.9636i	0.495107	−	1.51629i
$418$	0.502327	−	0.364962i	0.0245696	−	0.0178509i
$419$	−8.72568	−	12.0099i	−0.426278	−	0.586721i	0.540816	−	0.841141i	$-0.318115\pi$
$419$	−8.72568	−	12.0099i	−0.426278	−	0.586721i	−0.967094	+	0.254420i	$0.918115\pi$
$420$	−6.97134	+	8.50795i	−0.340167	+	0.415145i
$421$	−20.9089	+	15.1912i	−1.01904	+	0.740374i	−0.966085	−	0.258223i	$-0.916863\pi$
$421$	−20.9089	+	15.1912i	−1.01904	+	0.740374i	−0.0529526	+	0.998597i	$0.516863\pi$
$422$	−11.9126	−	8.65504i	−0.579899	−	0.421321i
$423$	3.42452	+	10.6446i	0.166506	+	0.517559i
$424$	−0.259845	+	0.357646i	−0.0126192	+	0.0173688i
$425$	5.68994	+	10.0551i	0.276003	+	0.487744i
$426$	−2.50966	+	7.68596i	−0.121593	+	0.372386i
$427$	−10.9175	−	33.6005i	−0.528333	−	1.62604i
$428$	16.0299			0.774837
$429$	0.0237817	−	16.3868i	0.00114819	−	0.791164i
$430$	1.33239	−	23.4804i	0.0642536	−	1.13233i
$431$	6.52145	+	8.97601i	0.314127	+	0.432359i	0.936663	−	0.350232i	$-0.113897\pi$
$431$	6.52145	+	8.97601i	0.314127	+	0.432359i	−0.622536	+	0.782592i	$0.713897\pi$
$432$	−3.07250	+	4.19044i	−0.147825	+	0.201613i
$433$	−9.96900			−0.479080			−0.239540	−	0.970887i	$-0.576997\pi$
$433$	−9.96900			−0.479080			−0.239540	+	0.970887i	$0.576997\pi$
$434$	−15.3132	+	3.94240i	−0.735055	+	0.189241i
$435$	−13.1786	+	33.7476i	−0.631865	+	1.61807i
$436$	−1.89084	−	1.37377i	−0.0905547	−	0.0657918i
$437$	0.106921	+	0.147164i	0.00511473	+	0.00703982i
$438$	−14.2172	+	4.59665i	−0.679324	+	0.219636i
$439$	3.79627			0.181186			0.0905930	−	0.995888i	$-0.471124\pi$
$439$	3.79627			0.181186			0.0905930	+	0.995888i	$0.471124\pi$
$440$	−4.60433	−	1.79032i	−0.219503	−	0.0853500i
$441$	0.979083	+	3.04334i	0.0466230	+	0.144921i
$442$	−9.41077	−	3.05774i	−0.447625	−	0.145442i
$443$	10.9644	−	33.7449i	0.520933	−	1.60327i	−0.251287	−	0.967913i	$-0.580854\pi$
$443$	10.9644	−	33.7449i	0.520933	−	1.60327i	0.772220	−	0.635355i	$-0.219146\pi$
$444$	−7.86806	+	10.7965i	−0.373402	+	0.512378i
$445$	−2.20232	+	38.8110i	−0.104400	+	1.83982i
$446$	−12.5443	−	9.11395i	−0.593989	−	0.431558i
$447$	33.2524	−	24.0857i	1.57279	−	1.13921i
$448$	−2.70101	−	0.877611i	−0.127611	−	0.0414632i
$449$	10.1989	−	7.40997i	0.481318	−	0.349698i	−0.320518	−	0.947242i	$-0.603857\pi$
$449$	10.1989	−	7.40997i	0.481318	−	0.349698i	0.801836	+	0.597545i	$0.203857\pi$
$450$	14.8987	+	1.74013i	0.702333	+	0.0820305i
$451$	13.4413	+	4.36734i	0.632925	+	0.205650i
$452$	−10.1862	+	7.40071i	−0.479119	+	0.348100i
$453$	−30.4756	−	22.2095i	−1.43187	−	1.04349i
$454$	−0.620351	−	1.90925i	−0.0291145	−	0.0896053i
$455$	−22.8712	+	14.7126i	−1.07222	+	0.689735i
$456$	−0.462738	−	0.151095i	−0.0216697	−	0.00707569i
$457$	−6.00814	+	18.4912i	−0.281049	+	0.864980i	0.706506	+	0.707707i	$0.250270\pi$
$457$	−6.00814	+	18.4912i	−0.281049	+	0.864980i	−0.987555	+	0.157273i	$0.949730\pi$
$458$	21.3872	−	6.94911i	0.999356	−	0.324711i
$459$	12.0065	+	0.0522743i	0.560416	+	0.00243996i
$460$	0.524501	−	1.34891i	0.0244550	−	0.0628932i
$461$	9.03404	+	27.8039i	0.420757	+	1.29496i	0.906999	+	0.421133i	$0.138367\pi$
$461$	9.03404	+	27.8039i	0.420757	+	1.29496i	−0.486242	+	0.873824i	$0.661633\pi$
$462$	−8.80137	+	6.37508i	−0.409477	+	0.296595i
$463$	8.21913	+	5.97155i	0.381975	+	0.277521i	0.762159	−	0.647390i	$-0.224139\pi$
$463$	8.21913	+	5.97155i	0.381975	+	0.277521i	−0.380184	+	0.924911i	$0.624139\pi$
$464$	−9.35440			−0.434267
$465$	15.7981	+	14.6772i	0.732620	+	0.680638i
$466$	−3.44507			−0.159590
$467$	−5.79914	−	4.21332i	−0.268352	−	0.194969i	0.445469	−	0.895297i	$-0.353037\pi$
$467$	−5.79914	−	4.21332i	−0.268352	−	0.194969i	−0.713821	+	0.700328i	$0.753037\pi$
$468$	−10.4153	+	7.52107i	−0.481448	+	0.347662i
$469$	4.94997	+	15.2345i	0.228569	+	0.703462i
$470$	7.76795	+	3.02044i	0.358309	+	0.139323i
$471$	−28.4368	−	0.0412694i	−1.31030	−	0.00190159i
$472$	−4.22848	+	1.37392i	−0.194632	+	0.0632396i
$473$	7.18054	−	22.0994i	0.330161	−	1.01613i
$474$	−0.779319	+	2.38671i	−0.0357953	+	0.109625i
$475$	0.280263	+	1.37698i	0.0128594	+	0.0631804i
$476$	2.02787	+	6.24115i	0.0929474	+	0.286063i
$477$	0.782645	−	1.07067i	0.0358349	−	0.0490226i
$478$	4.11367	−	2.98876i	0.188155	−	0.136703i
$479$	−31.8710	−	10.3555i	−1.45623	−	0.473156i	−0.529311	−	0.848428i	$-0.677549\pi$
$479$	−31.8710	−	10.3555i	−1.45623	−	0.473156i	−0.926915	+	0.375272i	$0.877549\pi$
$480$	0.980780	+	3.74674i	0.0447663	+	0.171015i
$481$	−26.7214	+	19.4143i	−1.21839	+	0.885214i
$482$	−5.92389	−	1.92479i	−0.269826	−	0.0876717i
$483$	−1.86768	−	2.57850i	−0.0849822	−	0.117326i
$484$	4.95036	+	3.59665i	0.225016	+	0.163484i
$485$	19.6025	+	1.11234i	0.890104	+	0.0505087i
$486$	9.25394	−	12.5445i	0.419767	−	0.569030i
$487$	−5.92651	+	18.2399i	−0.268556	+	0.826529i	0.722297	+	0.691583i	$0.243086\pi$
$487$	−5.92651	+	18.2399i	−0.268556	+	0.826529i	−0.990853	+	0.134947i	$0.956914\pi$
$488$	−11.8311	−	3.84416i	−0.535569	−	0.174017i
$489$	−0.373532	−	1.15532i	−0.0168917	−	0.0522452i
$490$	2.22089	+	0.863555i	0.100329	+	0.0390114i
$491$	6.61166			0.298380			0.149190	−	0.988809i	$-0.452333\pi$
$491$	6.61166			0.298380			0.149190	+	0.988809i	$0.452333\pi$
$492$	−3.40861	−	10.5427i	−0.153672	−	0.475300i
$493$	12.7050	+	17.4869i	0.572203	+	0.787570i
$494$	−0.973668	−	0.707411i	−0.0438074	−	0.0318279i
$495$	13.7973	+	5.41102i	0.620144	+	0.243207i
$496$	−2.04625	+	5.17811i	−0.0918795	+	0.232504i
$497$	13.2573			0.594672
$498$	6.20165	+	4.51953i	0.277903	+	0.202525i
$499$	−3.23027	−	4.44609i	−0.144607	−	0.199034i	0.730569	−	0.682838i	$-0.239255\pi$
$499$	−3.23027	−	4.44609i	−0.144607	−	0.199034i	−0.875176	+	0.483804i	$0.839255\pi$
$500$	8.00758	−	7.80248i	0.358110	−	0.348937i
$501$	−5.85111	−	0.00849154i	−0.261408	−	0.000379374i
$502$	22.3764			0.998707
$503$	−8.47935	−	26.0968i	−0.378076	−	1.16360i	−0.941380	−	0.337348i	$-0.890470\pi$
$503$	−8.47935	−	26.0968i	−0.378076	−	1.16360i	0.563304	−	0.826249i	$-0.309530\pi$
$504$	8.09535	+	2.65634i	0.360596	+	0.118323i
$505$	7.26662	+	5.93660i	0.323360	+	0.264175i
$506$	0.840515	−	1.15687i	0.0373654	−	0.0514291i
$507$	−8.79786	+	2.84449i	−0.390727	+	0.126328i
$508$	6.86015	+	4.98419i	0.304370	+	0.221138i
$509$	−16.9783	+	12.3354i	−0.752549	+	0.546759i	−0.896616	−	0.442809i	$-0.853982\pi$
$509$	−16.9783	+	12.3354i	−0.752549	+	0.546759i	0.144067	+	0.989568i	$0.453982\pi$
$510$	5.67199	−	6.92220i	0.251160	−	0.306520i
$511$	14.4006	+	19.8208i	0.637046	+	0.876819i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	1.38689	+	0.457314i	0.0612328	+	0.0201909i
$514$	11.5692	−	8.40554i	0.510297	−	0.370753i
$515$	−9.20412	+	5.92080i	−0.405582	+	0.260902i
$516$	−17.3337	+	5.60425i	−0.763072	+	0.246714i
$517$	6.66205	+	4.84027i	0.292997	+	0.212875i
$518$	20.8328	+	6.76899i	0.915342	+	0.297413i
$519$	7.58347	+	2.47619i	0.332878	+	0.108693i
$520$	−0.542491	+	9.56020i	−0.0237898	+	0.419242i
$521$		−	18.7980i		−	0.823556i	−0.911284	−	0.411778i	$-0.864908\pi$
$521$		−	18.7980i		−	0.823556i	0.911284	−	0.411778i	$-0.135092\pi$
$522$	28.0631	+	0.0814544i	1.22829	+	0.00356516i
$523$	−7.18865	−	22.1244i	−0.314338	−	0.967431i	−0.976026	−	0.217653i	$-0.930160\pi$
$523$	−7.18865	−	22.1244i	−0.314338	−	0.967431i	0.661689	−	0.749779i	$-0.269840\pi$
$524$	−4.22574	−	5.81624i	−0.184602	−	0.254083i
$525$	−4.87040	−	24.1082i	−0.212562	−	1.05217i
$526$		−	22.7225i		−	0.990748i
$527$	12.4590	−	3.20760i	0.542723	−	0.139725i
$528$	−0.00555346	+	3.82662i	−0.000241683	+	0.166532i
$529$	−18.2685	−	13.2728i	−0.794281	−	0.577079i
$530$	−0.251714	−	0.955923i	−0.0109337	−	0.0415226i
$531$	12.6973	−	4.08491i	0.551018	−	0.177270i
$532$			0.798166i			0.0346049i
$533$		−	27.3942i		−	1.18658i
$534$	28.6510	−	9.26332i	1.23985	−	0.400863i
$535$	−22.6776	+	27.7583i	−0.980440	+	1.20009i
$536$	5.36423	+	1.74294i	0.231699	+	0.0752837i
$537$	−10.3110	+	14.1487i	−0.444954	+	0.610562i
$538$	0.706551	+	2.17454i	0.0304616	+	0.0937511i
$539$	1.90470	+	1.38385i	0.0820414	+	0.0596066i
$540$	−2.90970	−	11.2487i	−0.125214	−	0.484068i
$541$	4.76208	−	14.6562i	0.204738	−	0.630119i	−0.794986	−	0.606628i	$-0.792522\pi$
$541$	4.76208	−	14.6562i	0.204738	−	0.630119i	0.999724	−	0.0234910i	$-0.00747809\pi$
$542$	0.803473	+	1.10589i	0.0345121	+	0.0475019i
$543$	−23.2189	+	16.8181i	−0.996418	+	0.721733i
$544$	2.19758	+	0.714038i	0.0942206	+	0.0306141i
$545$	5.05387	−	1.33079i	0.216484	−	0.0570046i
$546$	17.0239	+	12.4064i	0.728556	+	0.530944i
$547$	1.34310	−	0.436400i	0.0574269	−	0.0186591i	−0.280163	−	0.959953i	$-0.590388\pi$
$547$	1.34310	−	0.436400i	0.0574269	−	0.0186591i	0.337590	+	0.941293i	$0.390388\pi$
$548$	−3.54766	+	4.88293i	−0.151548	+	0.208589i
$549$	35.4597	+	11.6355i	1.51338	+	0.496589i
$550$	9.61397	−	5.44032i	0.409941	−	0.231976i
$551$	0.812404	+	2.50032i	0.0346096	+	0.106517i
$552$	−1.12107	−	0.00162697i	−0.0477158	−	6.92485e-5i
$553$	4.11677			0.175063
$554$	4.99166	+	15.3627i	0.212075	+	0.652700i
$555$	−7.56473	−	28.8985i	−0.321105	−	1.22667i
$556$	−11.0537	+	15.2141i	−0.468782	+	0.645223i
$557$			13.2121i			0.559813i	0.960027	+	0.279906i	$0.0903035\pi$
$557$			13.2121i			0.559813i	−0.960027	+	0.279906i	$0.909697\pi$
$558$	6.18382	−	15.5165i	0.261782	−	0.656864i
$559$	−45.0401			−1.90499
$560$	5.34084	−	3.43564i	0.225692	−	0.145182i
$561$	7.16093	−	5.18686i	0.302335	−	0.218989i
$562$	1.43901	−	0.467564i	0.0607011	−	0.0197230i
$563$	45.5900			1.92139			0.960695	−	0.277606i	$-0.0895408\pi$
$563$	45.5900			1.92139			0.960695	+	0.277606i	$0.0895408\pi$
$564$	0.00936923	−	6.45588i	0.000394516	−	0.271842i
$565$	1.59502	−	28.1088i	0.0671032	−	1.18254i
$566$	−23.7491	−	7.71655i	−0.998249	−	0.324351i
$567$	−24.2628	−	8.03948i	−1.01894	−	0.337626i
$568$	2.74382	−	3.77654i	0.115128	−	0.158460i
$569$	8.79089	+	27.0556i	0.368533	+	1.13423i	0.947739	+	0.319047i	$0.103363\pi$
$569$	8.79089	+	27.0556i	0.368533	+	1.13423i	−0.579206	+	0.815181i	$0.696637\pi$
$570$	0.916281	−	0.587545i	0.0383788	−	0.0246095i
$571$	14.3410	+	19.7388i	0.600154	+	0.826041i	0.995722	−	0.0923953i	$-0.0294523\pi$
$571$	14.3410	+	19.7388i	0.600154	+	0.826041i	−0.395568	+	0.918437i	$0.629452\pi$
$572$	−2.92360	+	8.99791i	−0.122242	+	0.376221i
$573$	−26.5790	+	19.2519i	−1.11035	+	0.804260i
$574$	−14.6979	+	10.6787i	−0.613480	+	0.445720i
$575$	1.59383	+	2.81656i	0.0664671	+	0.117459i
$576$	2.43216	−	1.75630i	0.101340	−	0.0731793i
$577$	27.0091	−	37.1749i	1.12440	−	1.54761i	0.326120	−	0.945328i	$-0.394258\pi$
$577$	27.0091	−	37.1749i	1.12440	−	1.54761i	0.798284	−	0.602281i	$-0.205742\pi$
$578$	3.60338	+	11.0901i	0.149881	+	0.461286i
$579$	19.2999	+	14.0650i	0.802077	+	0.584523i
$580$	13.2337	−	16.1986i	0.549500	−	0.672608i
$581$	3.88821	−	11.9667i	0.161310	−	0.496462i
$582$	−4.67868	−	14.4709i	−0.193937	−	0.599839i
$583$		−	0.976676i		−	0.0404498i
$584$	8.62667			0.356974
$585$	1.71071	−	28.6757i	0.0707292	−	1.18560i
$586$	−11.3330	+	8.23391i	−0.468162	+	0.340140i
$587$	−17.5896	+	24.2100i	−0.726000	+	0.999253i	0.273304	+	0.961928i	$0.411884\pi$
$587$	−17.5896	+	24.2100i	−0.726000	+	0.999253i	−0.999303	+	0.0373249i	$0.988116\pi$
$588$	0.00267870	−	1.84576i	0.000110468	−	0.0761178i
$589$	1.56176	+	0.0972346i	0.0643512	+	0.00400648i
$590$	3.60291	−	9.26593i	0.148329	−	0.381472i
$591$	14.7796	+	10.7708i	0.607953	+	0.443053i
$592$	6.23993	−	4.53357i	0.256460	−	0.186329i
$593$	11.8443	+	36.4531i	0.486389	+	1.49695i	0.829960	+	0.557824i	$0.188363\pi$
$593$	11.8443	+	36.4531i	0.486389	+	1.49695i	−0.343571	+	0.939127i	$0.611637\pi$
$594$	0.0499810	−	11.4798i	0.00205074	−	0.471020i
$595$	−13.6763	−	5.31782i	−0.560675	−	0.218009i
$596$	−22.5452	+	7.32539i	−0.923488	+	0.300059i
$597$	14.1877	−	43.4506i	0.580664	−	1.77831i
$598$	−2.63608	−	0.856513i	−0.107797	−	0.0350254i
$599$	−8.32085	+	11.4527i	−0.339981	+	0.467943i	−0.944436	−	0.328696i	$-0.893391\pi$
$599$	−8.32085	+	11.4527i	−0.339981	+	0.467943i	0.604455	+	0.796639i	$0.293391\pi$
$600$	−7.87556	−	3.60216i	−0.321518	−	0.147058i
$601$	−18.7401	+	25.7936i	−0.764426	+	1.05214i	0.232407	+	0.972619i	$0.425340\pi$
$601$	−18.7401	+	25.7936i	−0.764426	+	1.05214i	−0.996833	+	0.0795235i	$0.974660\pi$
$602$	17.5573	+	24.1656i	0.715582	+	0.984914i
$603$	−16.0774	−	5.27552i	−0.654724	−	0.214836i
$604$	12.7971	+	17.6137i	0.520707	+	0.716692i
$605$	−13.2314	+	3.48410i	−0.537934	+	0.141649i
$606$	2.25606	−	6.90930i	0.0916461	−	0.280671i
$607$	19.9948	+	27.5204i	0.811563	+	1.11702i	0.991080	+	0.133266i	$0.0425464\pi$
$607$	19.9948	+	27.5204i	0.811563	+	1.11702i	−0.179517	+	0.983755i	$0.557454\pi$
$608$	0.227369	+	0.165193i	0.00922102	+	0.00669947i
$609$	−14.1558	−	43.7832i	−0.573622	−	1.77418i
$610$	23.3943	−	15.0490i	0.947206	−	0.609316i
$611$	4.93239	−	15.1803i	0.199543	−	0.614131i
$612$	−6.58650	−	2.16124i	−0.266244	−	0.0873629i
$613$	12.2107	+	37.5806i	0.493185	+	1.51787i	0.819766	+	0.572698i	$0.194103\pi$
$613$	12.2107	+	37.5806i	0.493185	+	1.51787i	−0.326581	+	0.945169i	$0.605897\pi$
$614$		−	12.0457i		−	0.486124i
$615$	23.0784	+	9.01223i	0.930610	+	0.363408i
$616$	5.96735	−	1.93891i	0.240431	−	0.0781208i
$617$	15.2958	−	11.1131i	0.615787	−	0.447395i	−0.235661	−	0.971835i	$-0.575725\pi$
$617$	15.2958	−	11.1131i	0.615787	−	0.447395i	0.851447	+	0.524440i	$0.175725\pi$
$618$	6.85097	+	4.99273i	0.275586	+	0.200837i
$619$		−	23.7475i		−	0.954491i	−0.878770	−	0.477246i	$-0.841635\pi$
$619$		−	23.7475i		−	0.954491i	0.878770	−	0.477246i	$-0.158365\pi$
$620$	−6.07184	−	10.8689i	−0.243851	−	0.436505i
$621$	3.36317	+	0.0146427i	0.134960	+	0.000587591i
$622$	0.667865	−	0.919238i	0.0267790	−	0.0368581i
$623$	−29.0206	−	39.9434i	−1.16269	−	1.60030i
$624$	7.05751	−	2.28180i	0.282526	−	0.0913453i
$625$	2.18281	+	24.9045i	0.0873122	+	0.996181i
$626$	17.9087			0.715778
$627$	1.02329	−	0.330847i	0.0408664	−	0.0132127i
$628$	15.6144	+	5.07344i	0.623084	+	0.202452i
$629$	−16.9499	−	5.50736i	−0.675837	−	0.219593i
$630$	−16.0524	+	10.2604i	−0.639542	+	0.408783i
$631$	−33.2235	+	10.7950i	−1.32261	+	0.429740i	−0.883389	−	0.468641i	$-0.844744\pi$
$631$	−33.2235	+	10.7950i	−1.32261	+	0.429740i	−0.439216	+	0.898381i	$0.644744\pi$
$632$	0.852032	−	1.17272i	0.0338920	−	0.0466483i
$633$	−14.9610	−	20.6550i	−0.594647	−	0.820964i
$634$	−8.33623	+	25.6563i	−0.331074	+	1.01894i
$635$	−18.3360	+	4.82823i	−0.727640	+	0.191602i
$636$	−0.620113	+	0.449165i	−0.0245891	+	0.0178105i
$637$	1.41019	−	4.34011i	0.0558737	−	0.171962i
$638$	16.7197	−	12.1476i	0.661940	−	0.480928i
$639$	−8.26430	+	11.3057i	−0.326931	+	0.447246i
$640$	0.126681	−	2.23248i	0.00500752	−	0.0882464i
$641$	21.0459	+	15.2907i	0.831262	+	0.603948i	0.919916	−	0.392115i	$-0.128256\pi$
$641$	21.0459	+	15.2907i	0.831262	+	0.603948i	−0.0886538	+	0.996063i	$0.528256\pi$
$642$	26.3933	+	8.61807i	1.04166	+	0.340128i
$643$	−10.5892	+	32.5902i	−0.417597	+	1.28523i	0.492311	+	0.870419i	$0.336152\pi$
$643$	−10.5892	+	32.5902i	−0.417597	+	1.28523i	−0.909908	+	0.414811i	$0.863848\pi$
$644$	0.568033	+	1.74823i	0.0223836	+	0.0688898i
$645$	14.8174	−	37.9442i	0.583435	−	1.49405i
$646$		−	0.649400i		−	0.0255503i
$647$	−9.11222	+	2.96074i	−0.358238	+	0.116399i	−0.482606	−	0.875837i	$-0.660310\pi$
$647$	−9.11222	+	2.96074i	−0.358238	+	0.116399i	0.124368	+	0.992236i	$0.460310\pi$
$648$	−7.31174	+	5.24771i	−0.287232	+	0.206150i
$649$	5.77367	−	7.94677i	0.226636	−	0.311938i
$650$	−15.7875	−	14.4643i	−0.619235	−	0.567335i
$651$	−27.3326	−	1.74154i	−1.07125	−	0.0682565i
$652$			0.701019i			0.0274540i
$653$	−0.319776	−	0.232331i	−0.0125138	−	0.00909180i	0.581511	−	0.813539i	$-0.302462\pi$
$653$	−0.319776	−	0.232331i	−0.0125138	−	0.00909180i	−0.594025	+	0.804447i	$0.702462\pi$
$654$	−2.37469	−	3.27848i	−0.0928577	−	0.128199i
$655$	16.0499	+	0.910745i	0.627120	+	0.0355857i
$656$			6.39704i			0.249763i
$657$	−25.8799	−	0.0751176i	−1.00967	−	0.00293062i
$658$	−10.0675	+	3.27113i	−0.392472	+	0.127522i
$659$	−19.4597	−	6.32284i	−0.758042	−	0.246303i	−0.0956039	−	0.995419i	$-0.530478\pi$
$659$	−19.4597	−	6.32284i	−0.758042	−	0.246303i	−0.662438	+	0.749117i	$0.730478\pi$
$660$	−6.61851	−	5.42315i	−0.257625	−	0.211096i
$661$	29.9248	+	21.7416i	1.16394	+	0.845651i	0.990271	−	0.139153i	$-0.0444379\pi$
$661$	29.9248	+	21.7416i	1.16394	+	0.845651i	0.173668	+	0.984804i	$0.444438\pi$
$662$	−16.0098	+	5.20191i	−0.622239	+	0.202178i
$663$	−13.8509	−	10.0940i	−0.537925	−	0.392019i
$664$	−2.60415	−	3.58431i	−0.101061	−	0.139098i
$665$	−1.38214	−	1.12917i	−0.0535972	−	0.0437873i
$666$	−18.7592	+	13.5463i	−0.726904	+	0.524910i
$667$	3.55882	+	4.89830i	0.137798	+	0.189663i
$668$	3.21280	+	1.04390i	0.124307	+	0.0403898i
$669$	−15.7543	−	21.7502i	−0.609095	−	0.840912i
$670$	−10.6070	+	6.82322i	−0.409783	+	0.263604i
$671$	26.1385	−	8.49292i	1.00907	−	0.327865i
$672$	−3.97539	−	2.89711i	−0.153354	−	0.111758i
$673$	3.74085	−	11.5131i	0.144199	−	0.443799i	−0.852708	−	0.522388i	$-0.825041\pi$
$673$	3.74085	−	11.5131i	0.144199	−	0.443799i	0.996907	+	0.0785886i	$0.0250413\pi$
$674$	6.65129	−	20.4706i	0.256198	−	0.788496i
$675$	23.5952	+	10.8750i	0.908180	+	0.418580i
$676$	5.33834			0.205321
$677$			25.9992i			0.999230i	0.866248	+	0.499615i	$0.166525\pi$
$677$			25.9992i			0.999230i	−0.866248	+	0.499615i	$0.833475\pi$
$678$	−20.7504	+	6.70893i	−0.796914	+	0.257655i
$679$	−20.1745	+	14.6576i	−0.774225	+	0.562508i
$680$	−4.34539	+	2.79529i	−0.166638	+	0.107195i
$681$	0.00504619	−	3.47709i	0.000193371	−	0.133242i
$682$	−3.06688	−	11.9124i	−0.117437	−	0.456150i
$683$	−4.24452			−0.162412			−0.0812060	−	0.996697i	$-0.525877\pi$
$683$	−4.24452			−0.162412			−0.0812060	+	0.996697i	$0.525877\pi$
$684$	−0.680665	−	0.497557i	−0.0260259	−	0.0190246i
$685$	−3.43664	−	13.0512i	−0.131307	−	0.498661i
$686$	16.0287	−	5.20805i	0.611980	−	0.198844i
$687$	38.9500	+	0.0565269i	1.48603	+	0.00215664i
$688$	10.5177			0.400982
$689$	−1.80045	+	0.585002i	−0.0685917	+	0.0222868i
$690$	1.58880	−	1.93899i	0.0604844	−	0.0738163i
$691$	6.00638	−	18.4857i	0.228493	−	0.703230i	−0.769425	−	0.638737i	$-0.779457\pi$
$691$	6.00638	−	18.4857i	0.228493	−	0.703230i	0.997918	−	0.0644930i	$-0.0205430\pi$
$692$	−3.72618	−	2.70723i	−0.141648	−	0.102913i
$693$	−17.9188	+	5.76474i	−0.680681	+	0.218984i
$694$	−8.46409	+	11.6498i	−0.321293	+	0.442221i
$695$	−10.7078	−	40.6646i	−0.406171	−	1.54250i
$696$	−15.4020	−	5.02914i	−0.583812	−	0.190629i
$697$	11.9585	−	8.68834i	0.452959	−	0.329094i
$698$	−4.15246	+	3.01694i	−0.157173	+	0.114193i
$699$	−5.67230	−	1.85215i	−0.214546	−	0.0700546i
$700$	−1.60638	+	14.1089i	−0.0607156	+	0.533266i
$701$	−21.9351	+	30.1910i	−0.828476	+	1.14030i	0.159728	+	0.987161i	$0.448938\pi$
$701$	−21.9351	+	30.1910i	−0.828476	+	1.14030i	−0.988205	+	0.153139i	$0.951062\pi$
$702$	−21.1923	+	6.78393i	−0.799852	+	0.256043i
$703$	−1.75369	−	1.27413i	−0.0661417	−	0.0480548i
$704$	0.682712	−	2.10117i	0.0257307	−	0.0791909i
$705$	11.1661	+	9.14939i	0.420539	+	0.344586i
$706$	−4.79974	+	1.55953i	−0.180641	+	0.0586937i
$707$	−11.9177			−0.448211
$708$	−7.70084	−	0.0111760i	−0.289415	−	0.000420020i
$709$	−32.5643	+	10.5808i	−1.22298	+	0.397370i	−0.848166	−	0.529730i	$-0.822293\pi$
$709$	−32.5643	+	10.5808i	−1.22298	+	0.397370i	−0.374813	+	0.927100i	$0.622293\pi$
$710$	2.65796	+	10.0940i	0.0997513	+	0.378822i
$711$	−2.56630	+	3.51073i	−0.0962436	+	0.131663i
$712$	−17.3847			−0.651521
$713$	3.48993	−	0.898489i	0.130699	−	0.0336487i
$714$	−0.0164956	+	11.3663i	−0.000617331	+	0.425373i
$715$	−11.4452	−	17.7920i	−0.428026	−	0.665384i
$716$	8.17739	−	5.94122i	0.305603	−	0.222034i
$717$	8.37999	−	2.70938i	0.312956	−	0.101184i
$718$		−	13.2460i		−	0.494337i
$719$	42.4478			1.58303			0.791517	−	0.611147i	$-0.209291\pi$
$719$	42.4478			1.58303			0.791517	+	0.611147i	$0.209291\pi$
$720$	−0.399482	+	6.69630i	−0.0148878	+	0.249556i
$721$	4.29531	−	13.2196i	0.159966	−	0.492324i
$722$	−5.84692	+	17.9950i	−0.217600	+	0.669703i
$723$	−8.71887	−	6.35398i	−0.324258	−	0.236307i
$724$	15.7424	−	5.11503i	0.585063	−	0.190099i
$725$	9.32844	+	45.8323i	0.346450	+	1.70217i
$726$	6.21713	+	8.58331i	0.230739	+	0.318556i
$727$	3.38853	+	1.10100i	0.125674	+	0.0408338i	0.371179	−	0.928562i	$-0.378954\pi$
$727$	3.38853	+	1.10100i	0.125674	+	0.0408338i	−0.245505	+	0.969395i	$0.578954\pi$
$728$	−7.14856	−	9.83914i	−0.264943	−	0.364663i
$729$	21.9808	−	15.6794i	0.814104	−	0.580718i
$730$	−12.2042	+	14.9384i	−0.451697	+	0.552894i
$731$	−14.2849	−	19.6615i	−0.528346	−	0.727205i
$732$	−17.4132	−	12.6901i	−0.643611	−	0.469039i
$733$	−20.4013	+	6.62878i	−0.753539	+	0.244840i	−0.660503	−	0.750823i	$-0.729657\pi$
$733$	−20.4013	+	6.62878i	−0.753539	+	0.244840i	−0.0930356	+	0.995663i	$0.529657\pi$
$734$	24.6339	+	17.8976i	0.909255	+	0.660612i
$735$	3.19242	+	2.61584i	0.117754	+	0.0964868i
$736$	0.615571	+	0.200011i	0.0226902	+	0.00737250i
$737$	−11.8512	+	3.85069i	−0.436545	+	0.141842i
$738$	0.0557029	−	19.1910i	0.00205045	−	0.706432i
$739$		−	50.2810i		−	1.84962i	−0.380434	−	0.924808i	$-0.624226\pi$
$739$		−	50.2810i		−	1.84962i	0.380434	−	0.924808i	$-0.375774\pi$
$740$	−0.977090	+	17.2190i	−0.0359185	+	0.632985i
$741$	−1.22282	−	1.68822i	−0.0449215	−	0.0620183i
$742$	1.01572	+	0.737961i	0.0372881	+	0.0270914i
$743$			21.4594i			0.787267i	0.919267	+	0.393634i	$0.128782\pi$
$743$			21.4594i			0.787267i	−0.919267	+	0.393634i	$0.871218\pi$
$744$	−6.15303	+	7.42565i	−0.225581	+	0.272237i
$745$	19.2098	−	49.4037i	0.703793	−	1.81001i
$746$	−0.810761	+	1.11592i	−0.0296841	+	0.0408566i
$747$	7.78121	+	10.7756i	0.284700	+	0.394257i
$748$	−4.85512	+	1.57753i	−0.177521	+	0.0576800i
$749$		−	45.5252i		−	1.66345i
$750$	17.3793	−	8.54172i	0.634601	−	0.311899i
$751$	12.3073	+	37.8779i	0.449099	+	1.38218i	0.877926	+	0.478797i	$0.158927\pi$
$751$	12.3073	+	37.8779i	0.449099	+	1.38218i	−0.428827	+	0.903387i	$0.641073\pi$
$752$	−1.15180	+	3.54488i	−0.0420019	+	0.129269i
$753$	36.8427	+	12.0301i	1.34262	+	0.438400i
$754$	−32.4081	−	23.5459i	−1.18023	−	0.857490i
$755$	−48.6049	−	2.75807i	−1.76891	−	0.100376i
$756$	11.9009	+	8.72591i	0.432831	+	0.317358i
$757$	−36.2582	+	26.3431i	−1.31783	+	0.957457i	−0.317870	+	0.948134i	$0.602968\pi$
$757$	−36.2582	+	26.3431i	−1.31783	+	0.957457i	−0.999957	+	0.00932278i	$0.997032\pi$
$758$	−4.16004	+	12.8033i	−0.151100	+	0.465036i
$759$	2.00587	−	1.45291i	0.0728084	−	0.0527371i
$760$	−0.607716	+	0.160024i	−0.0220442	+	0.00580468i
$761$	3.32639	−	10.2376i	0.120582	−	0.371112i	−0.872489	−	0.488634i	$-0.837495\pi$
$761$	3.32639	−	10.2376i	0.120582	−	0.371112i	0.993070	+	0.117522i	$0.0374952\pi$
$762$	8.61562	+	11.8946i	0.312111	+	0.430898i
$763$	−3.90153	+	5.36999i	−0.141245	+	0.194407i
$764$	18.0206	−	5.85525i	0.651963	−	0.211836i
$765$	13.0605	−	8.34800i	0.472202	−	0.301823i
$766$	8.97486	+	2.91611i	0.324275	+	0.105363i
$767$	−18.1077	−	5.88356i	−0.653833	−	0.212443i
$768$	−1.64805	+	0.532842i	−0.0594690	+	0.0192273i
$769$	−19.2632			−0.694648			−0.347324	−	0.937745i	$-0.612910\pi$
$769$	−19.2632			−0.694648			−0.347324	+	0.937745i	$0.612910\pi$
$770$	−5.08452	+	13.0763i	−0.183233	+	0.471238i
$771$	23.5678	−	7.61983i	0.848772	−	0.274422i
$772$	−8.10428	−	11.1546i	−0.291679	−	0.401462i
$773$	−12.5511	+	17.2750i	−0.451430	+	0.621340i	−0.972704	−	0.232049i	$-0.925457\pi$
$773$	−12.5511	+	17.2750i	−0.451430	+	0.621340i	0.521274	+	0.853389i	$0.325457\pi$
$774$	−31.5529	−	0.0915837i	−1.13414	−	0.00329191i
$775$	27.4110	+	4.86197i	0.984631	+	0.174647i
$776$			8.78061i			0.315206i
$777$	30.6621	+	22.3454i	1.10000	+	0.801635i
$778$	−11.3654	+	8.25744i	−0.407469	+	0.296043i
$779$	1.70985	−	0.555565i	0.0612619	−	0.0199052i
$780$	−6.03300	+	15.4492i	−0.216016	+	0.553170i
$781$			10.3132i			0.369034i
$782$	−0.462160	−	1.42238i	−0.0165268	−	0.0508643i
$783$	46.1621	+	15.2215i	1.64970	+	0.543972i
$784$	−0.329304	+	1.01349i	−0.0117609	+	0.0361962i
$785$	−30.8752	+	19.8613i	−1.10198	+	0.708881i
$786$	−3.83074	−	11.8483i	−0.136638	−	0.422614i
$787$	14.9637	+	10.8718i	0.533399	+	0.387537i	0.821627	−	0.570025i	$-0.193066\pi$
$787$	14.9637	+	10.8718i	0.533399	+	0.387537i	−0.288229	+	0.957562i	$0.593066\pi$
$788$	−6.20616	−	8.54205i	−0.221085	−	0.304298i
$789$	12.2161	−	37.4126i	0.434906	−	1.33192i
$790$	0.825370	+	3.13447i	0.0293653	+	0.111520i
$791$	21.0181	+	28.9289i	0.747317	+	1.02859i
$792$	−2.06642	+	6.29754i	−0.0734272	+	0.223773i
$793$	−31.3125	−	43.0980i	−1.11194	−	1.53045i
$794$	4.13502	−	5.69136i	0.146746	−	0.201979i
$795$	0.0994799	−	1.70925i	0.00352819	−	0.0606210i
$796$	−15.5115	+	21.3497i	−0.549789	+	0.756719i
$797$	44.6285	+	14.5007i	1.58082	+	0.513641i	0.962269	−	0.272101i	$-0.0877186\pi$
$797$	44.6285	+	14.5007i	1.58082	+	0.513641i	0.618554	+	0.785742i	$0.287719\pi$
$798$	−0.429112	+	1.31418i	−0.0151904	+	0.0465214i
$799$	8.19107	−	2.66144i	0.289779	−	0.0941549i
$800$	3.68665	+	3.37766i	0.130343	+	0.119418i
$801$	52.1540	+	0.151379i	1.84277	+	0.00534873i
$802$	9.75935	+	30.0362i	0.344615	+	1.06061i
$803$	−15.4190	+	11.2025i	−0.544124	+	0.395329i
$804$	7.89515	+	5.75369i	0.278441	+	0.202917i
$805$	−3.83091	−	1.48959i	−0.135022	−	0.0525011i
$806$	−20.1230	+	12.7888i	−0.708801	+	0.450468i
$807$	−0.00574737	+	3.96024i	−0.000202317	+	0.139407i
$808$	−2.46656	+	3.39492i	−0.0867731	+	0.119433i
$809$	−14.5843	+	10.5961i	−0.512757	+	0.372540i	−0.813869	−	0.581049i	$-0.802642\pi$
$809$	−14.5843	+	10.5961i	−0.512757	+	0.372540i	0.301111	+	0.953589i	$0.402642\pi$
$810$	1.25675	−	20.0853i	0.0441576	−	0.705727i
$811$	14.1097			0.495458			0.247729	−	0.968829i	$-0.420316\pi$
$811$	14.1097			0.495458			0.247729	+	0.968829i	$0.420316\pi$
$812$			26.5666i			0.932305i
$813$	0.728368	+	2.25281i	0.0255450	+	0.0790094i
$814$	−5.26574	+	16.2063i	−0.184564	+	0.568030i
$815$	−1.21392	−	0.991734i	−0.0425217	−	0.0347389i
$816$	3.23444	+	2.35713i	0.113228	+	0.0825162i
$817$	−0.913430	−	2.81125i	−0.0319569	−	0.0983531i
$818$	3.37829	−	4.64982i	0.118119	−	0.162577i
$819$	21.3599	+	29.5796i	0.746375	+	1.03359i
$820$	−11.0774	−	9.04992i	−0.386841	−	0.316037i
$821$	−6.88707	+	5.00375i	−0.240360	+	0.174632i	−0.701444	−	0.712725i	$-0.747461\pi$
$821$	−6.88707	+	5.00375i	−0.240360	+	0.174632i	0.461083	+	0.887357i	$0.347461\pi$
$822$	−8.46640	+	6.13244i	−0.295299	+	0.213894i
$823$	12.1792	−	37.4838i	0.424541	−	1.30660i	−0.478891	−	0.877874i	$-0.658961\pi$
$823$	12.1792	−	37.4838i	0.424541	−	1.30660i	0.903433	−	0.428730i	$-0.141039\pi$
$824$	−2.87681	−	3.95959i	−0.100218	−	0.137939i
$825$	18.7542	−	3.78879i	0.652939	−	0.131909i
$826$	3.90193	+	12.0089i	0.135766	+	0.417844i
$827$	−19.5392	+	26.8934i	−0.679445	+	0.935176i	−0.999927	−	0.0120784i	$-0.996155\pi$
$827$	−19.5392	+	26.8934i	−0.679445	+	0.935176i	0.320482	+	0.947255i	$0.396155\pi$
$828$	−1.84496	−	0.605391i	−0.0641169	−	0.0210388i
$829$	14.8295	+	4.81840i	0.515051	+	0.167350i	0.554998	−	0.831852i	$-0.312719\pi$
$829$	14.8295	+	4.81840i	0.515051	+	0.167350i	−0.0399473	+	0.999202i	$0.512719\pi$
$830$	9.89087	+	0.561255i	0.343317	+	0.0194814i
$831$	−0.0406042	+	27.9784i	−0.00140854	+	0.970559i
$832$	−4.28233			−0.148463
$833$	2.34185	−	0.760915i	0.0811405	−	0.0263641i
$834$	−26.3794	+	19.1073i	−0.913444	+	0.661632i
$835$	−6.35284	+	4.08664i	−0.219849	+	0.141424i
$836$	−0.620910			−0.0214746
$837$	18.5237	−	22.2233i	0.640272	−	0.768149i
$838$			14.8450i			0.512813i
$839$	−24.6816	+	33.9714i	−0.852105	+	1.17282i	0.131290	+	0.991344i	$0.458088\pi$
$839$	−24.6816	+	33.9714i	−0.852105	+	1.17282i	−0.983395	+	0.181478i	$0.941912\pi$
$840$	10.6408	−	2.78542i	0.367142	−	0.0961062i
$841$	18.0790	+	55.6414i	0.623414	+	1.91867i
$842$	25.8448			0.890672
$843$	2.62071	+	0.00380336i	0.0902620	+	0.000130995i
$844$	4.55023	+	14.0042i	0.156625	+	0.482043i
$845$	−7.55217	+	9.24413i	−0.259802	+	0.318008i
$846$	3.48626	−	10.6246i	0.119860	−	0.365280i
$847$	10.2145	−	14.0591i	0.350975	−	0.483075i
$848$	0.420438	−	0.136608i	0.0144379	−	0.00469115i
$849$	−34.9543	−	25.4734i	−1.19963	−	0.874243i
$850$	1.30698	−	11.4792i	0.0448290	−	0.393734i
$851$	−4.74788	−	1.54268i	−0.162755	−	0.0528824i
$852$	6.54805	−	4.74293i	0.224332	−	0.162490i
$853$	−18.3189	−	25.2138i	−0.627227	−	0.863304i	0.370627	−	0.928782i	$-0.379143\pi$
$853$	−18.3189	−	25.2138i	−0.627227	−	0.863304i	−0.997854	+	0.0654779i	$0.979143\pi$
$854$	−10.9175	+	33.6005i	−0.373588	+	1.14978i
$855$	1.82453	−	0.474778i	0.0623978	−	0.0162371i
$856$	−12.9685	−	9.42217i	−0.443254	−	0.322043i
$857$	16.2110	+	49.8922i	0.553756	+	1.70429i	0.699206	+	0.714921i	$0.253537\pi$
$857$	16.2110	+	49.8922i	0.553756	+	1.70429i	−0.145450	+	0.989366i	$0.546463\pi$
$858$	−9.65118	+	13.2433i	−0.329486	+	0.452117i
$859$	3.72949	+	1.21179i	0.127249	+	0.0413456i	0.371949	−	0.928253i	$-0.378690\pi$
$859$	3.72949	+	1.21179i	0.127249	+	0.0413456i	−0.244700	+	0.969599i	$0.578690\pi$
$860$	−14.8794	+	18.2129i	−0.507383	+	0.621055i
$861$	−29.9413	+	9.68049i	−1.02040	+	0.329910i
$862$		−	11.0950i		−	0.377896i
$863$			15.0898i			0.513663i	0.966456	+	0.256831i	$0.0826785\pi$
$863$			15.0898i			0.513663i	−0.966456	+	0.256831i	$0.917322\pi$
$864$	4.94878	−	1.58417i	0.168361	−	0.0538945i
$865$	9.95942	−	2.62252i	0.338631	−	0.0891682i
$866$	8.06509	+	5.85963i	0.274063	+	0.199118i
$867$	−0.0293114	+	20.1970i	−0.000995466	+	0.685928i
$868$	14.7059	+	5.81138i	0.499150	+	0.197251i
$869$			3.20252i			0.108638i
$870$	30.4980	−	19.5562i	1.03398	−	0.663016i
$871$	14.1971	+	19.5406i	0.481050	+	0.662109i
$872$	0.722235	+	2.22281i	0.0244580	+	0.0752739i
$873$	0.0764581	−	26.3417i	0.00258771	−	0.891532i
$874$		−	0.181905i		−	0.00615303i
$875$	−22.1591	−	22.7416i	−0.749115	−	0.768806i
$876$	14.2038	+	4.63790i	0.479902	+	0.156700i
$877$	−17.3533	−	5.63844i	−0.585980	−	0.190397i	0.000997653	−	1.00000i	$-0.499682\pi$
$877$	−17.3533	−	5.63844i	−0.585980	−	0.190397i	−0.586978	+	0.809603i	$0.699682\pi$
$878$	−3.07125	−	2.23139i	−0.103650	−	0.0753058i
$879$	−23.0865	+	7.46425i	−0.778690	+	0.251763i
$880$	2.67266	+	4.15475i	0.0900953	+	0.140057i
$881$	22.7784	−	16.5495i	0.767424	−	0.557566i	−0.133755	−	0.991014i	$-0.542703\pi$
$881$	22.7784	−	16.5495i	0.767424	−	0.557566i	0.901178	+	0.433448i	$0.142703\pi$
$882$	0.996733	−	3.03760i	0.0335618	−	0.102281i
$883$	−12.9833	+	9.43294i	−0.436924	+	0.317444i	−0.784411	−	0.620241i	$-0.787035\pi$
$883$	−12.9833	+	9.43294i	−0.436924	+	0.317444i	0.347488	+	0.937685i	$0.387035\pi$
$884$	5.81617	+	8.00528i	0.195619	+	0.269247i
$885$	10.9138	−	13.3193i	0.366862	−	0.447725i
$886$	−28.7051	+	20.8555i	−0.964367	+	0.700654i
$887$	25.5309	+	18.5493i	0.857243	+	0.622824i	0.927134	−	0.374731i	$-0.122265\pi$
$887$	25.5309	+	18.5493i	0.857243	+	0.622824i	−0.0698902	+	0.997555i	$0.522265\pi$
$888$	12.7114	−	4.10980i	0.426567	−	0.137916i
$889$	14.1551	−	19.4829i	0.474748	−	0.653435i
$890$	24.5943	−	30.1043i	0.824401	−	1.00910i
$891$	6.25408	−	18.8746i	0.209520	−	0.632321i
$892$	4.79149	+	14.7467i	0.160431	+	0.493755i
$893$	1.04754			0.0350544
$894$	−41.0590	−	0.0595877i	−1.37322	−	0.00199291i
$895$	−1.28047	+	22.5655i	−0.0428014	+	0.754280i
$896$	1.66932	+	2.29762i	0.0557679	+	0.0767579i
$897$	−3.87982	−	2.82746i	−0.129543	−	0.0944063i
$898$	−12.6066			−0.420687
$899$	51.9825	+	3.23641i	1.73371	+	0.107940i
$900$	−11.0305	−	10.1650i	−0.367683	−	0.338835i
$901$	−0.826402	−	0.600417i	−0.0275315	−	0.0200028i
$902$	−8.30717	−	11.4338i	−0.276598	−	0.380705i
$903$	15.9161	+	49.2278i	0.529656	+	1.63820i
$904$	12.5908			0.418765
$905$	−13.4135	+	34.4967i	−0.445878	+	1.14671i
$906$	11.6009	+	35.8810i	0.385414	+	1.19207i
$907$	−25.9715	−	8.43866i	−0.862370	−	0.280201i	−0.155752	−	0.987796i	$-0.549780\pi$
$907$	−25.9715	−	8.43866i	−0.862370	−	0.280201i	−0.706618	+	0.707595i	$0.749780\pi$
$908$	−0.620351	+	1.90925i	−0.0205871	+	0.0633605i
$909$	7.42920	−	10.1632i	0.246411	−	0.337094i
$910$	27.1510	+	1.54068i	0.900048	+	0.0510730i
$911$	−48.3287	−	35.1129i	−1.60120	−	1.16334i	−0.885164	−	0.465278i	$-0.845954\pi$
$911$	−48.3287	−	35.1129i	−1.60120	−	1.16334i	−0.716037	−	0.698062i	$-0.754046\pi$
$912$	0.285551	+	0.394229i	0.00945554	+	0.0130542i
$913$	9.30913	+	3.02472i	0.308087	+	0.100104i
$914$	15.7295	−	11.4282i	0.520286	−	0.378010i
$915$	46.6094	−	12.2009i	1.54086	−	0.403348i
$916$	−21.3872	−	6.94911i	−0.706652	−	0.229605i
$917$	−16.5182	+	12.0011i	−0.545478	+	0.396313i
$918$	−9.68274	−	7.09954i	−0.319578	−	0.234320i
$919$	−5.36573	−	16.5140i	−0.176999	−	0.544747i	0.822720	−	0.568447i	$-0.192455\pi$
$919$	−5.36573	−	16.5140i	−0.176999	−	0.544747i	−0.999719	+	0.0236998i	$0.992455\pi$
$920$	−1.21720	+	0.782997i	−0.0401299	+	0.0258146i
$921$	6.47604	−	19.8332i	0.213393	−	0.653527i
$922$	9.03404	−	27.8039i	0.297520	−	0.915673i
$923$	19.0118	−	6.17730i	0.625780	−	0.203328i
$924$	10.8676	+	0.0157719i	0.357519	+	0.000518857i
$925$	−28.4351	−	26.0518i	−0.934939	−	0.856579i
$926$	−3.13943	−	9.66217i	−0.103168	−	0.317519i
$927$	8.59591	+	11.9038i	0.282327	+	0.390971i
$928$	7.56787	+	5.49838i	0.248428	+	0.180493i
$929$	55.3503			1.81599			0.907993	−	0.418986i	$-0.137614\pi$
$929$	55.3503			1.81599			0.907993	+	0.418986i	$0.137614\pi$
$930$	−4.15391	−	21.1600i	−0.136212	−	0.693863i
$931$	0.299494			0.00981552
$932$	2.78712	+	2.02496i	0.0912950	+	0.0663297i
$933$	1.59384	−	1.15446i	0.0521801	−	0.0377955i
$934$	2.21507	+	6.81730i	0.0724794	+	0.223069i
$935$	4.13684	−	10.6391i	0.135289	−	0.347936i
$936$	12.8469	+	0.0372888i	0.419915	+	0.00121882i
$937$	−9.78902	+	3.18064i	−0.319793	+	0.103907i	−0.464515	−	0.885565i	$-0.653771\pi$
$937$	−9.78902	+	3.18064i	−0.319793	+	0.103907i	0.144722	+	0.989472i	$0.453771\pi$
$938$	4.94997	−	15.2345i	0.161622	−	0.497422i
$939$	29.4867	+	9.62816i	0.962264	+	0.314203i
$940$	−4.50903	−	7.00947i	−0.147069	−	0.228624i
$941$	3.88320	+	11.9513i	0.126589	+	0.389600i	0.994187	−	0.107666i	$-0.0343376\pi$
$941$	3.88320	+	11.9513i	0.126589	+	0.389600i	−0.867599	+	0.497265i	$0.834338\pi$
$942$	22.9816	+	16.7481i	0.748780	+	0.545682i
$943$	3.34972	−	2.43371i	0.109082	−	0.0792526i
$944$	4.22848	+	1.37392i	0.137625	+	0.0447172i
$945$	−31.9465	+	8.26358i	−1.03922	+	0.268814i
$946$	−18.7989	+	13.6582i	−0.611205	+	0.444066i
$947$	−13.4620	−	4.37407i	−0.437456	−	0.142138i	0.0820054	−	0.996632i	$-0.473868\pi$
$947$	−13.4620	−	4.37407i	−0.437456	−	0.142138i	−0.519462	+	0.854494i	$0.673868\pi$
$948$	2.03335	−	1.47281i	0.0660402	−	0.0478347i
$949$	29.8869	+	21.7141i	0.970169	+	0.704869i
$950$	0.582633	−	1.27874i	0.0189031	−	0.0414878i
$951$	−27.5190	+	37.7613i	−0.892365	+	1.22449i
$952$	2.02787	−	6.24115i	0.0657238	−	0.202277i
$953$	4.69230	+	1.52462i	0.151998	+	0.0493873i	0.384028	−	0.923321i	$-0.374537\pi$
$953$	4.69230	+	1.52462i	0.151998	+	0.0493873i	−0.232030	+	0.972709i	$0.574537\pi$
$954$	−1.26250	+	0.406163i	−0.0408748	+	0.0131500i
$955$	−15.3546	+	39.4889i	−0.496863	+	1.27783i
$956$	−5.08478			−0.164453
$957$	34.0598	−	11.0121i	1.10100	−	0.355970i
$958$	19.6974	+	27.1111i	0.636394	+	0.875921i
$959$	13.8676	+	10.0754i	0.447807	+	0.325351i
$960$	1.40881	−	3.60767i	0.0454692	−	0.116437i
$961$	13.1625	−	28.0668i	0.424598	−	0.905382i
$962$	33.0295			1.06491
$963$	38.8233	+	28.3793i	1.25106	+	0.914510i
$964$	3.66116	+	5.03916i	0.117918	+	0.162300i
$965$	30.7810	+	1.74666i	0.990875	+	0.0562269i
$966$	−0.00462061	+	3.18384i	−0.000148666	+	0.102438i
$967$	22.6637			0.728817			0.364408	−	0.931239i	$-0.381271\pi$
$967$	22.6637			0.728817			0.364408	+	0.931239i	$0.381271\pi$
$968$	−1.89087	−	5.81950i	−0.0607749	−	0.187046i
$969$	0.349132	−	1.06924i	0.0112157	−	0.0343488i
$970$	−15.2050	−	12.4220i	−0.488202	−	0.398845i
$971$	−16.7807	+	23.0967i	−0.538519	+	0.741208i	−0.988399	−	0.151881i	$-0.951467\pi$
$971$	−16.7807	+	23.0967i	−0.538519	+	0.741208i	0.449879	+	0.893089i	$0.351467\pi$
$972$	−14.8601	+	4.70939i	−0.476637	+	0.151054i
$973$	43.2083	+	31.3926i	1.38519	+	1.00640i
$974$	15.5158	−	11.2729i	0.497158	−	0.361207i
$975$	−18.2177	−	32.3031i	−0.583434	−	1.03453i
$976$	7.31203	+	10.0641i	0.234052	+	0.322146i
$977$	−26.0237	+	18.9073i	−0.832572	+	0.604899i	−0.920286	−	0.391247i	$-0.872044\pi$
$977$	−26.0237	+	18.9073i	−0.832572	+	0.604899i	0.0877136	+	0.996146i	$0.472044\pi$
$978$	−0.376884	+	1.15423i	−0.0120514	+	0.0369081i
$979$	31.0728	−	22.5757i	0.993092	−	0.721524i
$980$	−1.28915	−	2.00403i	−0.0411804	−	0.0640165i
$981$	−2.14734	−	6.67470i	−0.0685593	−	0.213107i
$982$	−5.34895	−	3.88624i	−0.170692	−	0.124015i
$983$	38.5354	+	12.5209i	1.22909	+	0.399355i	0.850384	−	0.526162i	$-0.176369\pi$
$983$	38.5354	+	12.5209i	1.22909	+	0.399355i	0.378705	+	0.925517i	$0.376369\pi$
$984$	−3.43920	+	10.5327i	−0.109638	+	0.335771i
$985$	23.5717	+	1.33757i	0.751057	+	0.0426185i
$986$		−	21.6150i		−	0.688361i
$987$	−18.3348	−	0.0266087i	−0.583602	−	0.000846964i
$988$	0.371908	+	1.14462i	0.0118320	+	0.0364151i
$989$	−4.00138	−	5.50743i	−0.127236	−	0.175126i
$990$	−7.98176	−	12.4875i	−0.253677	−	0.396878i
$991$		−	12.2502i		−	0.389141i	−0.980889	−	0.194571i	$-0.937669\pi$
$991$		−	12.2502i		−	0.389141i	0.980889	−	0.194571i	$-0.0623313\pi$
$992$	4.69907	−	2.98642i	0.149196	−	0.0948191i
$993$	−29.1568	−	0.0423144i	−0.925264	−	0.00134281i
$994$	−10.7254	−	7.79246i	−0.340189	−	0.247162i
$995$	−15.0261	−	57.0639i	−0.476358	−	1.80905i
$996$	−2.36073	−	7.30161i	−0.0748025	−	0.231361i
$997$		−	2.52746i		−	0.0800456i	−0.999199	−	0.0400228i	$-0.987257\pi$
$997$		−	2.52746i		−	0.0800456i	0.999199	−	0.0400228i	$-0.0127431\pi$
$998$			5.49567i			0.173962i
$999$	−38.1698	+	12.2187i	−1.20764	+	0.386581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.y.a.29.11	yes	128
3.2	odd	2		930.2.y.b.29.23	yes	128
5.4	even	2		930.2.y.b.29.22	yes	128
15.14	odd	2	inner	930.2.y.a.29.10	✓	128
31.15	odd	10	inner	930.2.y.a.449.10	yes	128
93.77	even	10		930.2.y.b.449.22	yes	128
155.139	odd	10		930.2.y.b.449.23	yes	128
465.449	even	10	inner	930.2.y.a.449.11	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.10	✓	128	15.14	odd	2	inner
930.2.y.a.29.11	yes	128	1.1	even	1	trivial
930.2.y.a.449.10	yes	128	31.15	odd	10	inner
930.2.y.a.449.11	yes	128	465.449	even	10	inner
930.2.y.b.29.22	yes	128	5.4	even	2
930.2.y.b.29.23	yes	128	3.2	odd	2
930.2.y.b.449.22	yes	128	93.77	even	10
930.2.y.b.449.23	yes	128	155.139	odd	10

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.01604 - 1.40273i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.08406 - 0.810354i) q^{5} +(-0.00251367 + 1.73205i) q^{6} +(2.70101 - 0.877611i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.935328 + 2.85047i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.01604 - 1.40273i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-2.08406 - 0.810354i) q^{5} +(-0.00251367 + 1.73205i) q^{6} +(2.70101 - 0.877611i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.935328 + 2.85047i) q^{9} +(1.20973 + 1.88057i) q^{10} +(0.682712 + 2.10117i) q^{11} +(1.02011 - 1.39978i) q^{12} +(3.46448 - 2.51709i) q^{13} +(-2.70101 - 0.877611i) q^{14} +(0.980780 + 3.74674i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.19758 + 0.714038i) q^{17} +(2.43216 - 1.75630i) q^{18} +(0.227369 + 0.165193i) q^{19} +(0.126681 - 2.23248i) q^{20} +(-3.97539 - 2.89711i) q^{21} +(0.682712 - 2.10117i) q^{22} +(0.615571 + 0.200011i) q^{23} +(-1.64805 + 0.532842i) q^{24} +(3.68665 + 3.37766i) q^{25} -4.28233 q^{26} +(4.94878 - 1.58417i) q^{27} +(1.66932 + 2.29762i) q^{28} +(7.56787 + 5.49838i) q^{29} +(1.40881 - 3.60767i) q^{30} +(4.69907 - 2.98642i) q^{31} +1.00000 q^{32} +(2.25372 - 3.09254i) q^{33} +(-1.35818 - 1.86938i) q^{34} +(-6.34025 - 0.359776i) q^{35} +(-2.99999 - 0.00870760i) q^{36} -7.71298 q^{37} +(-0.0868472 - 0.267288i) q^{38} +(-7.05085 - 2.30228i) q^{39} +(-1.41470 + 1.73165i) q^{40} +(3.76009 - 5.17532i) q^{41} +(1.51328 + 4.68049i) q^{42} +(-8.50897 - 6.18213i) q^{43} +(-1.78736 + 1.29860i) q^{44} +(4.25917 - 5.18261i) q^{45} +(-0.380444 - 0.523636i) q^{46} +(3.01546 - 2.19086i) q^{47} +(1.64650 + 0.537623i) q^{48} +(0.862129 - 0.626374i) q^{49} +(-0.997224 - 4.89955i) q^{50} +(-1.23122 - 3.80811i) q^{51} +(3.46448 + 2.51709i) q^{52} +(-0.420438 - 0.136608i) q^{53} +(-4.93480 - 1.62720i) q^{54} +(0.279877 - 4.93222i) q^{55} -2.84001i q^{56} +(0.000706450 - 0.486781i) q^{57} +(-2.89067 - 8.89657i) q^{58} +(-2.61334 - 3.59696i) q^{59} +(-3.26029 + 2.09058i) q^{60} -12.4400i q^{61} +(-5.55700 - 0.345977i) q^{62} +(-0.0247297 + 8.51999i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-9.25993 + 2.43832i) q^{65} +(-3.64105 + 1.17721i) q^{66} +5.64028i q^{67} +2.31067i q^{68} +(-0.344882 - 1.06670i) q^{69} +(4.91790 + 4.01777i) q^{70} +(4.43959 + 1.44251i) q^{71} +(2.42192 + 1.77039i) q^{72} +(2.66579 + 8.20445i) q^{73} +(6.23993 + 4.53357i) q^{74} +(0.992179 - 8.60323i) q^{75} +(-0.0868472 + 0.267288i) q^{76} +(3.68802 + 5.07613i) q^{77} +(4.35101 + 6.00697i) q^{78} +(1.37862 + 0.447940i) q^{79} +(2.16236 - 0.569392i) q^{80} +(-7.25032 - 5.33225i) q^{81} +(-6.08395 + 1.97679i) q^{82} +(2.60415 - 3.58431i) q^{83} +(1.52685 - 4.67607i) q^{84} +(-4.00128 - 3.26892i) q^{85} +(3.25014 + 10.0029i) q^{86} +(0.0235139 - 16.2023i) q^{87} +2.20930 q^{88} +(-5.37218 - 16.5339i) q^{89} +(-6.49201 + 1.68934i) q^{90} +(7.14856 - 9.83914i) q^{91} +0.647249i q^{92} +(-8.96360 - 3.55723i) q^{93} -3.72731 q^{94} +(-0.339986 - 0.528522i) q^{95} +(-1.01604 - 1.40273i) q^{96} +(-8.35086 + 2.71336i) q^{97} -1.06565 q^{98} +(-6.62788 - 0.0192377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9	\( 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9} + 2 q^{10} + 25 q^{15} - 32 q^{16} + 6 q^{18} - 8 q^{19} - 3 q^{20} - 20 q^{23} - 10 q^{25} - 48 q^{31} + 128 q^{32} - 8 q^{33} + 10 q^{34} + 16 q^{35} - 4 q^{36} + 12 q^{38} + 4 q^{39} - 3 q^{40} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 q^{60} - 8 q^{62} + 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} + 6 q^{72} + 5 q^{75} + 12 q^{76} + 50 q^{77} + 4 q^{78} - 10 q^{79} + 2 q^{80} - 24 q^{81} - 40 q^{83} - 30 q^{85} - 4 q^{87} - 53 q^{90} + 20 q^{91} - 26 q^{93} - 4 q^{94} - 26 q^{95} - 124 q^{98}+O(q^{100}) \) 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9 + 2 * q^10 + 25 * q^15 - 32 * q^16 + 6 * q^18 - 8 * q^19 - 3 * q^20 - 20 * q^23 - 10 * q^25 - 48 * q^31 + 128 * q^32 - 8 * q^33 + 10 * q^34 + 16 * q^35 - 4 * q^36 + 12 * q^38 + 4 * q^39 - 3 * q^40 + 37 * q^45 + 10 * q^46 + 6 * q^47 + 46 * q^49 - 5 * q^50 + 34 * q^51 - 20 * q^53 - 25 * q^60 - 8 * q^62 + 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 + 6 * q^72 + 5 * q^75 + 12 * q^76 + 50 * q^77 + 4 * q^78 - 10 * q^79 + 2 * q^80 - 24 * q^81 - 40 * q^83 - 30 * q^85 - 4 * q^87 - 53 * q^90 + 20 * q^91 - 26 * q^93 - 4 * q^94 - 26 * q^95 - 124 * q^98

Introduction

L-functions

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