LMFDB - Embedded newform 418.2.f.h.229.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (of order $5$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 11 x^{18} - 3 x^{17} + 103 x^{16} + 50 x^{15} + 1002 x^{14} + 1120 x^{13} + \cdots + 1936 $ x^20 - x^19 + 11x^18 - 3x^17 + 103x^16 + 50x^15 + 1002x^14 + 1120x^13 + 7288x^12 + 5704x^11 + 24392x^10 + 10376x^9 + 48880x^8 + 21224x^7 + 77528x^6 + 44616x^5 + 147848x^4 + 67728x^3 + 115472x^2 - 24464x + 1936
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			229.3
Root			$-0.370901 - 1.14152i$ of defining polynomial
Character	$\chi$	$=$	418.229
Dual form			418.2.f.h.115.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.971032 + 0.705496i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.28699 - 3.96096i) q^{5} +(-0.370901 - 1.14152i) q^{6} +(0.280040 + 0.203461i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.481873 + 1.48305i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.971032 + 0.705496i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.28699 - 3.96096i) q^{5} +(-0.370901 - 1.14152i) q^{6} +(0.280040 + 0.203461i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.481873 + 1.48305i) q^{9} +4.16480 q^{10} +(0.00601040 + 3.31662i) q^{11} +1.20026 q^{12} +(-0.839381 + 2.58335i) q^{13} +(-0.280040 + 0.203461i) q^{14} +(4.04415 + 2.93825i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.41261 + 7.42525i) q^{17} +(-1.26156 - 0.916576i) q^{18} +(0.809017 - 0.587785i) q^{19} +(-1.28699 + 3.96096i) q^{20} -0.415468 q^{21} +(-3.15615 - 1.01918i) q^{22} +7.96455 q^{23} +(-0.370901 + 1.14152i) q^{24} +(-9.98775 + 7.25652i) q^{25} +(-2.19753 - 1.59660i) q^{26} +(-1.69108 - 5.20460i) q^{27} +(-0.106966 - 0.329206i) q^{28} +(6.18310 + 4.49229i) q^{29} +(-4.04415 + 2.93825i) q^{30} +(0.437738 - 1.34722i) q^{31} -1.00000 q^{32} +(-2.34570 - 3.21630i) q^{33} -7.80737 q^{34} +(0.445490 - 1.37108i) q^{35} +(1.26156 - 0.916576i) q^{36} +(-4.95093 - 3.59706i) q^{37} +(0.309017 + 0.951057i) q^{38} +(-1.00748 - 3.10069i) q^{39} +(-3.36939 - 2.44801i) q^{40} +(-5.40041 + 3.92362i) q^{41} +(0.128387 - 0.395134i) q^{42} +1.21044 q^{43} +(1.94460 - 2.68673i) q^{44} +6.49447 q^{45} +(-2.46118 + 7.57474i) q^{46} +(0.0345115 - 0.0250741i) q^{47} +(-0.971032 - 0.705496i) q^{48} +(-2.12609 - 6.54344i) q^{49} +(-3.81498 - 11.7413i) q^{50} +(-7.58120 - 5.50807i) q^{51} +(2.19753 - 1.59660i) q^{52} +(-2.65232 + 8.16301i) q^{53} +5.47244 q^{54} +(13.1293 - 4.29227i) q^{55} +0.346148 q^{56} +(-0.370901 + 1.14152i) q^{57} +(-6.18310 + 4.49229i) q^{58} +(-5.07313 - 3.68584i) q^{59} +(-1.54473 - 4.75418i) q^{60} +(0.139219 + 0.428471i) q^{61} +(1.14601 + 0.832626i) q^{62} +(-0.436686 + 0.317271i) q^{63} +(0.309017 - 0.951057i) q^{64} +11.3128 q^{65} +(3.78375 - 1.23700i) q^{66} +0.952714 q^{67} +(2.41261 - 7.42525i) q^{68} +(-7.73384 + 5.61896i) q^{69} +(1.16631 + 0.847373i) q^{70} +(4.38874 + 13.5072i) q^{71} +(0.481873 + 1.48305i) q^{72} +(11.4448 + 8.31517i) q^{73} +(4.95093 - 3.59706i) q^{74} +(4.57897 - 14.0926i) q^{75} -1.00000 q^{76} +(-0.673119 + 0.930008i) q^{77} +3.26026 q^{78} +(-3.95436 + 12.1703i) q^{79} +(3.36939 - 2.44801i) q^{80} +(1.52924 + 1.11105i) q^{81} +(-2.06277 - 6.34856i) q^{82} +(-1.85389 - 5.70569i) q^{83} +(0.336121 + 0.244206i) q^{84} +(26.3061 - 19.1125i) q^{85} +(-0.374047 + 1.15120i) q^{86} -9.17328 q^{87} +(1.95432 + 2.67967i) q^{88} -3.81546 q^{89} +(-2.00690 + 6.17661i) q^{90} +(-0.760670 + 0.552659i) q^{91} +(-6.44346 - 4.68145i) q^{92} +(0.525400 + 1.61701i) q^{93} +(0.0131822 + 0.0405707i) q^{94} +(-3.36939 - 2.44801i) q^{95} +(0.971032 - 0.705496i) q^{96} +(2.57651 - 7.92969i) q^{97} +6.88018 q^{98} +(-4.92161 - 1.58927i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) $ 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9} + 6 q^{10} + q^{11} + 4 q^{12} - 2 q^{13} - 13 q^{14} - 8 q^{15} - 5 q^{16} + 11 q^{17} + 6 q^{18} + 5 q^{19} - q^{20} + 2 q^{21} + 4 q^{22} + 28 q^{23} + q^{24} - 30 q^{25} - 13 q^{26} - 31 q^{27} - 2 q^{28} + 28 q^{29} + 8 q^{30} - q^{31} - 20 q^{32} + 9 q^{33} + 24 q^{34} - 11 q^{35} - 6 q^{36} + 8 q^{37} - 5 q^{38} + 18 q^{39} - 4 q^{40} - 5 q^{41} - 22 q^{42} - 44 q^{43} + 11 q^{44} - 4 q^{45} + 7 q^{46} - 39 q^{47} - q^{48} + 4 q^{49} - 25 q^{50} - 11 q^{51} + 13 q^{52} - q^{53} - 4 q^{54} + 8 q^{55} + 22 q^{56} + q^{57} - 28 q^{58} + 6 q^{59} + 7 q^{60} + 10 q^{61} + 11 q^{62} + 34 q^{63} - 5 q^{64} - 8 q^{65} + 41 q^{66} + 18 q^{67} + 11 q^{68} - 63 q^{69} + q^{70} - 3 q^{71} + 6 q^{72} + 5 q^{73} - 8 q^{74} + 5 q^{75} - 20 q^{76} + 36 q^{77} + 22 q^{78} + 19 q^{79} + 4 q^{80} + 63 q^{81} - 9 q^{83} - 23 q^{84} + 30 q^{85} - 26 q^{86} - 16 q^{87} - q^{88} + 44 q^{89} + 14 q^{90} - 68 q^{91} - 7 q^{92} + 27 q^{93} - 31 q^{94} - 4 q^{95} + q^{96} - 71 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9 + 6 * q^10 + q^11 + 4 * q^12 - 2 * q^13 - 13 * q^14 - 8 * q^15 - 5 * q^16 + 11 * q^17 + 6 * q^18 + 5 * q^19 - q^20 + 2 * q^21 + 4 * q^22 + 28 * q^23 + q^24 - 30 * q^25 - 13 * q^26 - 31 * q^27 - 2 * q^28 + 28 * q^29 + 8 * q^30 - q^31 - 20 * q^32 + 9 * q^33 + 24 * q^34 - 11 * q^35 - 6 * q^36 + 8 * q^37 - 5 * q^38 + 18 * q^39 - 4 * q^40 - 5 * q^41 - 22 * q^42 - 44 * q^43 + 11 * q^44 - 4 * q^45 + 7 * q^46 - 39 * q^47 - q^48 + 4 * q^49 - 25 * q^50 - 11 * q^51 + 13 * q^52 - q^53 - 4 * q^54 + 8 * q^55 + 22 * q^56 + q^57 - 28 * q^58 + 6 * q^59 + 7 * q^60 + 10 * q^61 + 11 * q^62 + 34 * q^63 - 5 * q^64 - 8 * q^65 + 41 * q^66 + 18 * q^67 + 11 * q^68 - 63 * q^69 + q^70 - 3 * q^71 + 6 * q^72 + 5 * q^73 - 8 * q^74 + 5 * q^75 - 20 * q^76 + 36 * q^77 + 22 * q^78 + 19 * q^79 + 4 * q^80 + 63 * q^81 - 9 * q^83 - 23 * q^84 + 30 * q^85 - 26 * q^86 - 16 * q^87 - q^88 + 44 * q^89 + 14 * q^90 - 68 * q^91 - 7 * q^92 + 27 * q^93 - 31 * q^94 - 4 * q^95 + q^96 - 71 * q^97 + 6 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−0.971032	+	0.705496i	−0.560626	+	0.407318i	−0.831688	−	0.555244i	$-0.812625\pi$
$3$	−0.971032	+	0.705496i	−0.560626	+	0.407318i	0.271062	+	0.962562i	$0.412625\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.28699	−	3.96096i	−0.575561	−	1.77139i	−0.634262	−	0.773118i	$-0.718696\pi$
$5$	−1.28699	−	3.96096i	−0.575561	−	1.77139i	0.0587009	−	0.998276i	$-0.481304\pi$
$6$	−0.370901	−	1.14152i	−0.151420	−	0.466022i
$7$	0.280040	+	0.203461i	0.105845	+	0.0769009i	0.639449	−	0.768834i	$-0.279163\pi$
$7$	0.280040	+	0.203461i	0.105845	+	0.0769009i	−0.533604	+	0.845735i	$0.679163\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−0.481873	+	1.48305i	−0.160624	+	0.494350i
$10$	4.16480			1.31702
$11$	0.00601040	+	3.31662i	0.00181221	+	0.999998i
$11$	0.00601040	+	3.31662i	0.00181221	+	0.999998i
$12$	1.20026			0.346486
$13$	−0.839381	+	2.58335i	−0.232802	+	0.716492i	0.764603	+	0.644502i	$0.222935\pi$
$13$	−0.839381	+	2.58335i	−0.232802	+	0.716492i	−0.997405	+	0.0719903i	$0.977065\pi$
$14$	−0.280040	+	0.203461i	−0.0748437	+	0.0543772i
$15$	4.04415	+	2.93825i	1.04420	+	0.758652i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.41261	+	7.42525i	0.585144	+	1.80089i	0.598693	+	0.800979i	$0.295687\pi$
$17$	2.41261	+	7.42525i	0.585144	+	1.80089i	−0.0135491	+	0.999908i	$0.504313\pi$
$18$	−1.26156	−	0.916576i	−0.297352	−	0.216039i
$19$	0.809017	−	0.587785i	0.185601	−	0.134847i
$19$	0.809017	−	0.587785i	0.185601	−	0.134847i
$20$	−1.28699	+	3.96096i	−0.287780	+	0.885697i
$21$	−0.415468			−0.0906626
$22$	−3.15615	−	1.01918i	−0.672893	−	0.217289i
$23$	7.96455			1.66072			0.830362	−	0.557224i	$-0.188134\pi$
$23$	7.96455			1.66072			0.830362	+	0.557224i	$0.188134\pi$
$24$	−0.370901	+	1.14152i	−0.0757099	+	0.233011i
$25$	−9.98775	+	7.25652i	−1.99755	+	1.45130i
$26$	−2.19753	−	1.59660i	−0.430971	−	0.313118i
$27$	−1.69108	−	5.20460i	−0.325448	−	1.00163i
$28$	−0.106966	−	0.329206i	−0.0202146	−	0.0622142i
$29$	6.18310	+	4.49229i	1.14817	+	0.834197i	0.988237	−	0.152930i	$-0.0488710\pi$
$29$	6.18310	+	4.49229i	1.14817	+	0.834197i	0.159937	+	0.987127i	$0.448871\pi$
$30$	−4.04415	+	2.93825i	−0.738358	+	0.536448i
$31$	0.437738	−	1.34722i	0.0786200	−	0.241967i	−0.904020	−	0.427490i	$-0.859398\pi$
$31$	0.437738	−	1.34722i	0.0786200	−	0.241967i	0.982640	+	0.185523i	$0.0593978\pi$
$32$	−1.00000			−0.176777
$33$	−2.34570	−	3.21630i	−0.408334	−	0.559886i
$34$	−7.80737			−1.33895
$35$	0.445490	−	1.37108i	0.0753016	−	0.231754i
$36$	1.26156	−	0.916576i	0.210260	−	0.152763i
$37$	−4.95093	−	3.59706i	−0.813928	−	0.591353i	0.101039	−	0.994883i	$-0.467783\pi$
$37$	−4.95093	−	3.59706i	−0.813928	−	0.591353i	−0.914967	+	0.403529i	$0.867783\pi$
$38$	0.309017	+	0.951057i	0.0501292	+	0.154282i
$39$	−1.00748	−	3.10069i	−0.161325	−	0.496508i
$40$	−3.36939	−	2.44801i	−0.532748	−	0.387064i
$41$	−5.40041	+	3.92362i	−0.843402	+	0.612767i	−0.923319	−	0.384034i	$-0.874534\pi$
$41$	−5.40041	+	3.92362i	−0.843402	+	0.612767i	0.0799172	+	0.996802i	$0.474534\pi$
$42$	0.128387	−	0.395134i	0.0198105	−	0.0609705i
$43$	1.21044			0.184591			0.0922954	−	0.995732i	$-0.470580\pi$
$43$	1.21044			0.184591			0.0922954	+	0.995732i	$0.470580\pi$
$44$	1.94460	−	2.68673i	0.293159	−	0.405040i
$45$	6.49447			0.968139
$46$	−2.46118	+	7.57474i	−0.362882	+	1.11683i
$47$	0.0345115	−	0.0250741i	0.00503402	−	0.00365743i	−0.585265	−	0.810842i	$-0.699010\pi$
$47$	0.0345115	−	0.0250741i	0.00503402	−	0.00365743i	0.590299	+	0.807184i	$0.299010\pi$
$48$	−0.971032	−	0.705496i	−0.140156	−	0.101830i
$49$	−2.12609	−	6.54344i	−0.303728	−	0.934777i
$50$	−3.81498	−	11.7413i	−0.539520	−	1.66047i
$51$	−7.58120	−	5.50807i	−1.06158	−	0.771283i
$52$	2.19753	−	1.59660i	0.304742	−	0.221408i
$53$	−2.65232	+	8.16301i	−0.364325	+	1.12128i	0.586078	+	0.810254i	$0.300671\pi$
$53$	−2.65232	+	8.16301i	−0.364325	+	1.12128i	−0.950403	+	0.311021i	$0.899329\pi$
$54$	5.47244			0.744705
$55$	13.1293	−	4.29227i	1.77035	−	0.578770i
$56$	0.346148			0.0462560
$57$	−0.370901	+	1.14152i	−0.0491271	+	0.151198i
$58$	−6.18310	+	4.49229i	−0.811881	+	0.589866i
$59$	−5.07313	−	3.68584i	−0.660465	−	0.479856i	0.206355	−	0.978477i	$-0.433840\pi$
$59$	−5.07313	−	3.68584i	−0.660465	−	0.479856i	−0.866820	+	0.498621i	$0.833840\pi$
$60$	−1.54473	−	4.75418i	−0.199424	−	0.613763i
$61$	0.139219	+	0.428471i	0.0178251	+	0.0548601i	0.959573	−	0.281458i	$-0.0908181\pi$
$61$	0.139219	+	0.428471i	0.0178251	+	0.0548601i	−0.941748	+	0.336318i	$0.890818\pi$
$62$	1.14601	+	0.832626i	0.145544	+	0.105744i
$63$	−0.436686	+	0.317271i	−0.0550173	+	0.0399724i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	11.3128			1.40318
$66$	3.78375	−	1.23700i	0.465747	−	0.152264i
$67$	0.952714			0.116393			0.0581963	−	0.998305i	$-0.481465\pi$
$67$	0.952714			0.116393			0.0581963	+	0.998305i	$0.481465\pi$
$68$	2.41261	−	7.42525i	0.292572	−	0.900443i
$69$	−7.73384	+	5.61896i	−0.931044	+	0.676443i
$70$	1.16631	+	0.847373i	0.139401	+	0.101280i
$71$	4.38874	+	13.5072i	0.520848	+	1.60301i	0.772383	+	0.635157i	$0.219065\pi$
$71$	4.38874	+	13.5072i	0.520848	+	1.60301i	−0.251535	+	0.967848i	$0.580935\pi$
$72$	0.481873	+	1.48305i	0.0567892	+	0.174779i
$73$	11.4448	+	8.31517i	1.33952	+	0.973217i	0.999462	+	0.0328122i	$0.0104463\pi$
$73$	11.4448	+	8.31517i	1.33952	+	0.973217i	0.340057	+	0.940405i	$0.389554\pi$
$74$	4.95093	−	3.59706i	0.575534	−	0.418150i
$75$	4.57897	−	14.0926i	0.528734	−	1.62728i
$76$	−1.00000			−0.114708
$77$	−0.673119	+	0.930008i	−0.0767090	+	0.105984i
$78$	3.26026			0.369152
$79$	−3.95436	+	12.1703i	−0.444901	+	1.36926i	0.437692	+	0.899125i	$0.355796\pi$
$79$	−3.95436	+	12.1703i	−0.444901	+	1.36926i	−0.882593	+	0.470139i	$0.844204\pi$
$80$	3.36939	−	2.44801i	0.376709	−	0.273695i
$81$	1.52924	+	1.11105i	0.169915	+	0.123451i
$82$	−2.06277	−	6.34856i	−0.227795	−	0.701081i
$83$	−1.85389	−	5.70569i	−0.203491	−	0.626281i	−0.999772	−	0.0213542i	$-0.993202\pi$
$83$	−1.85389	−	5.70569i	−0.203491	−	0.626281i	0.796281	−	0.604927i	$-0.206798\pi$
$84$	0.336121	+	0.244206i	0.0366738	+	0.0266451i
$85$	26.3061	−	19.1125i	2.85329	−	2.07304i
$86$	−0.374047	+	1.15120i	−0.0403346	+	0.124137i
$87$	−9.17328			−0.983479
$88$	1.95432	+	2.67967i	0.208331	+	0.285654i
$89$	−3.81546			−0.404438			−0.202219	−	0.979340i	$-0.564815\pi$
$89$	−3.81546			−0.404438			−0.202219	+	0.979340i	$0.564815\pi$
$90$	−2.00690	+	6.17661i	−0.211546	+	0.651072i
$91$	−0.760670	+	0.552659i	−0.0797399	+	0.0579344i
$92$	−6.44346	−	4.68145i	−0.671777	−	0.488075i
$93$	0.525400	+	1.61701i	0.0544814	+	0.167676i
$94$	0.0131822	+	0.0405707i	0.00135964	+	0.00418455i
$95$	−3.36939	−	2.44801i	−0.345692	−	0.251160i
$96$	0.971032	−	0.705496i	0.0991055	−	0.0720044i
$97$	2.57651	−	7.92969i	0.261605	−	0.805138i	−0.730851	−	0.682537i	$-0.760876\pi$
$97$	2.57651	−	7.92969i	0.261605	−	0.805138i	0.992456	−	0.122601i	$-0.0391236\pi$
$98$	6.88018			0.695003
$99$	−4.92161	−	1.58927i	−0.494641	−	0.159728i
$100$	12.3455			1.23455
$101$	−1.66251	+	5.11668i	−0.165426	+	0.509128i	−0.999067	−	0.0431774i	$-0.986252\pi$
$101$	−1.66251	+	5.11668i	−0.165426	+	0.509128i	0.833642	+	0.552306i	$0.186252\pi$
$102$	7.58120	−	5.50807i	0.750651	−	0.545380i
$103$	1.50110	+	1.09061i	0.147908	+	0.107461i	0.659278	−	0.751899i	$-0.270862\pi$
$103$	1.50110	+	1.09061i	0.147908	+	0.107461i	−0.511370	+	0.859360i	$0.670862\pi$
$104$	0.839381	+	2.58335i	0.0823080	+	0.253318i
$105$	0.534705	+	1.64565i	0.0521818	+	0.160599i
$106$	−6.94387	−	5.04502i	−0.674448	−	0.490015i
$107$	6.60724	−	4.80044i	0.638746	−	0.464076i	−0.220673	−	0.975348i	$-0.570825\pi$
$107$	6.60724	−	4.80044i	0.638746	−	0.464076i	0.859419	+	0.511271i	$0.170825\pi$
$108$	−1.69108	+	5.20460i	−0.162724	+	0.500813i
$109$	−12.3359			−1.18157			−0.590783	−	0.806830i	$-0.701181\pi$
$109$	−12.3359			−1.18157			−0.590783	+	0.806830i	$0.701181\pi$
$110$	0.0250321	+	13.8130i	0.00238672	+	1.31702i
$111$	7.34523			0.697178
$112$	−0.106966	+	0.329206i	−0.0101073	+	0.0311071i
$113$	−8.97854	+	6.52329i	−0.844630	+	0.613660i	−0.923660	−	0.383212i	$-0.874818\pi$
$113$	−8.97854	+	6.52329i	−0.844630	+	0.613660i	0.0790300	+	0.996872i	$0.474818\pi$
$114$	−0.971032	−	0.705496i	−0.0909455	−	0.0660757i
$115$	−10.2503	−	31.5473i	−0.955848	−	2.94180i
$116$	−2.36174	−	7.26867i	−0.219282	−	0.674880i
$117$	−3.42676	−	2.48969i	−0.316804	−	0.230172i
$118$	5.07313	−	3.68584i	0.467019	−	0.339309i
$119$	−0.835120	+	2.57023i	−0.0765553	+	0.235613i
$120$	4.99885			0.456330
$121$	−10.9999	+	0.0398685i	−0.999993	+	0.00362440i
$122$	−0.450521			−0.0407882
$123$	2.47586	−	7.61993i	0.223241	−	0.687066i
$124$	−1.14601	+	0.832626i	−0.102915	+	0.0747721i
$125$	24.7500	+	17.9819i	2.21371	+	1.60835i
$126$	−0.166799	−	0.513355i	−0.0148597	−	0.0457333i
$127$	−4.04538	−	12.4504i	−0.358969	−	1.10479i	−0.953672	−	0.300848i	$-0.902730\pi$
$127$	−4.04538	−	12.4504i	−0.358969	−	1.10479i	0.594703	−	0.803946i	$-0.297270\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−1.17538	+	0.853962i	−0.103486	+	0.0751872i
$130$	−3.49585	+	10.7591i	−0.306606	+	0.943637i
$131$	−0.111515			−0.00974312			−0.00487156	−	0.999988i	$-0.501551\pi$
$131$	−0.111515			−0.00974312			−0.00487156	+	0.999988i	$0.501551\pi$
$132$	0.00721406	+	3.98081i	0.000627903	+	0.346485i
$133$	0.346148			0.0300148
$134$	−0.294405	+	0.906085i	−0.0254327	+	0.0782738i
$135$	−18.4388	+	13.3966i	−1.58696	+	1.15299i
$136$	6.31629	+	4.58906i	0.541618	+	0.393508i
$137$	3.71399	+	11.4305i	0.317308	+	0.976573i	0.974794	+	0.223107i	$0.0716198\pi$
$137$	3.71399	+	11.4305i	0.317308	+	0.976573i	−0.657486	+	0.753467i	$0.728380\pi$
$138$	−2.95406	−	9.09167i	−0.251466	−	0.773934i
$139$	2.37522	+	1.72570i	0.201463	+	0.146372i	0.683943	−	0.729535i	$-0.260264\pi$
$139$	2.37522	+	1.72570i	0.201463	+	0.146372i	−0.482479	+	0.875907i	$0.660264\pi$
$140$	−1.16631	+	0.847373i	−0.0985711	+	0.0716161i
$141$	−0.0158221	+	0.0486954i	−0.00133246	+	0.00410090i
$142$	−14.2023			−1.19183
$143$	−8.57303	−	2.76838i	−0.716913	−	0.231503i
$144$	−1.55937			−0.129948
$145$	9.83615	−	30.2726i	0.816848	−	2.51400i
$146$	−11.4448	+	8.31517i	−0.947183	+	0.688168i
$147$	6.68088	+	4.85394i	0.551029	+	0.400346i
$148$	1.89109	+	5.82017i	0.155446	+	0.478415i
$149$	−3.24372	−	9.98314i	−0.265736	−	0.817851i	−0.991523	−	0.129931i	$-0.958524\pi$
$149$	−3.24372	−	9.98314i	−0.265736	−	0.817851i	0.725787	−	0.687919i	$-0.241476\pi$
$150$	11.9879	+	8.70972i	0.978809	+	0.711146i
$151$	−0.461827	+	0.335537i	−0.0375829	+	0.0273056i	−0.606418	−	0.795146i	$-0.707394\pi$
$151$	−0.461827	+	0.335537i	−0.0375829	+	0.0273056i	0.568835	+	0.822452i	$0.307394\pi$
$152$	0.309017	−	0.951057i	0.0250646	−	0.0771409i
$153$	−12.1746			−0.984258
$154$	−0.676485	−	0.927562i	−0.0545127	−	0.0747451i
$155$	−5.89964			−0.473870
$156$	−1.00748	+	3.10069i	−0.0806627	+	0.248254i
$157$	12.2606	−	8.90782i	0.978500	−	0.710922i	0.0211268	−	0.999777i	$-0.493275\pi$
$157$	12.2606	−	8.90782i	0.978500	−	0.710922i	0.957373	+	0.288855i	$0.0932746\pi$
$158$	−10.3527	−	7.52165i	−0.823613	−	0.598390i
$159$	−3.18348	−	9.79775i	−0.252466	−	0.777012i
$160$	1.28699	+	3.96096i	0.101746	+	0.313141i
$161$	2.23039	+	1.62047i	0.175779	+	0.127711i
$162$	−1.52924	+	1.11105i	−0.120148	+	0.0872927i
$163$	0.0882778	−	0.271691i	0.00691445	−	0.0212805i	−0.947540	−	0.319638i	$-0.896439\pi$
$163$	0.0882778	−	0.271691i	0.00691445	−	0.0212805i	0.954454	+	0.298357i	$0.0964387\pi$
$164$	6.67527			0.521251
$165$	−9.72074	+	13.4306i	−0.756759	+	1.04557i
$166$	5.99932			0.465638
$167$	5.06664	−	15.5935i	0.392068	−	1.20666i	−0.539153	−	0.842208i	$-0.681256\pi$
$167$	5.06664	−	15.5935i	0.392068	−	1.20666i	0.931221	−	0.364454i	$-0.118744\pi$
$168$	−0.336121	+	0.244206i	−0.0259323	+	0.0188409i
$169$	4.54809	+	3.30438i	0.349853	+	0.254183i
$170$	10.0480	+	30.9246i	0.770649	+	2.37181i
$171$	0.481873	+	1.48305i	0.0368497	+	0.113412i
$172$	−0.979268	−	0.711480i	−0.0746685	−	0.0542498i
$173$	2.44757	−	1.77826i	0.186085	−	0.135199i	−0.490842	−	0.871248i	$-0.663311\pi$
$173$	2.44757	−	1.77826i	0.186085	−	0.135199i	0.676928	+	0.736049i	$0.263311\pi$
$174$	2.83470	−	8.72431i	0.214898	−	0.661388i
$175$	−4.27338			−0.323037
$176$	−3.15244	+	1.03061i	−0.237624	+	0.0776850i
$177$	7.52652			0.565728
$178$	1.17904	−	3.62872i	0.0883730	−	0.271984i
$179$	10.2269	−	7.43027i	0.764394	−	0.555364i	−0.135861	−	0.990728i	$-0.543380\pi$
$179$	10.2269	−	7.43027i	0.764394	−	0.555364i	0.900255	+	0.435363i	$0.143380\pi$
$180$	−5.25414	−	3.81735i	−0.391620	−	0.284529i
$181$	4.30676	+	13.2549i	0.320119	+	0.985226i	0.973596	+	0.228279i	$0.0733098\pi$
$181$	4.30676	+	13.2549i	0.320119	+	0.985226i	−0.653477	+	0.756947i	$0.726690\pi$
$182$	−0.290550	−	0.894221i	−0.0215370	−	0.0662841i
$183$	−0.437470	−	0.317841i	−0.0323387	−	0.0234955i
$184$	6.44346	−	4.68145i	0.475018	−	0.345121i
$185$	−7.87600	+	24.2398i	−0.579055	+	1.78215i
$186$	−1.70023			−0.124667
$187$	−24.6122	+	8.04633i	−1.79982	+	0.588406i
$188$	−0.0426586			−0.00311120
$189$	0.585363	−	1.80156i	0.0425789	−	0.131044i
$190$	3.36939	−	2.44801i	0.244441	−	0.177597i
$191$	21.5923	+	15.6877i	1.56237	+	1.13512i	0.934037	+	0.357176i	$0.116260\pi$
$191$	21.5923	+	15.6877i	1.56237	+	1.13512i	0.628328	+	0.777948i	$0.283740\pi$
$192$	0.370901	+	1.14152i	0.0267675	+	0.0823819i
$193$	−1.85808	−	5.71857i	−0.133747	−	0.411632i	0.861646	−	0.507510i	$-0.169434\pi$
$193$	−1.85808	−	5.71857i	−0.133747	−	0.411632i	−0.995393	+	0.0958782i	$0.969434\pi$
$194$	6.74540	+	4.90082i	0.484292	+	0.351858i
$195$	−10.9851	+	7.98114i	−0.786659	+	0.571541i
$196$	−2.12609	+	6.54344i	−0.151864	+	0.467389i
$197$	6.48402			0.461968			0.230984	−	0.972958i	$-0.425806\pi$
$197$	6.48402			0.461968			0.230984	+	0.972958i	$0.425806\pi$
$198$	3.03235	−	4.18962i	0.215500	−	0.297743i
$199$	−22.9729			−1.62850			−0.814251	−	0.580513i	$-0.802852\pi$
$199$	−22.9729			−1.62850			−0.814251	+	0.580513i	$0.802852\pi$
$200$	−3.81498	+	11.7413i	−0.269760	+	0.830235i
$201$	−0.925115	+	0.672136i	−0.0652526	+	0.0474088i
$202$	−4.35251	−	3.16228i	−0.306241	−	0.222497i
$203$	0.817510	+	2.51604i	0.0573780	+	0.176591i
$204$	2.89576	+	8.91224i	0.202744	+	0.623981i
$205$	22.4916	+	16.3411i	1.57088	+	1.14131i
$206$	−1.50110	+	1.09061i	−0.104587	+	0.0759866i
$207$	−3.83790	+	11.8118i	−0.266753	+	0.820980i
$208$	−2.71629			−0.188341
$209$	1.95432	+	2.67967i	0.135183	+	0.185357i
$210$	−1.73034			−0.119405
$211$	−5.22190	+	16.0713i	−0.359490	+	1.10640i	0.593870	+	0.804561i	$0.297600\pi$
$211$	−5.22190	+	16.0713i	−0.359490	+	1.10640i	−0.953360	+	0.301836i	$0.902400\pi$
$212$	6.94387	−	5.04502i	0.476907	−	0.346493i
$213$	−13.7909	−	10.0196i	−0.944934	−	0.686535i
$214$	2.52374	+	7.76728i	0.172520	+	0.530960i
$215$	−1.55783	−	4.79451i	−0.106243	−	0.326983i
$216$	−4.42730	−	3.21662i	−0.301239	−	0.218863i
$217$	0.396690	−	0.288212i	0.0269291	−	0.0195651i
$218$	3.81201	−	11.7322i	0.258182	−	0.794602i
$219$	−16.9796			−1.14738
$220$	−13.1447	−	4.24466i	−0.886217	−	0.286175i
$221$	−21.2071			−1.42654
$222$	−2.26980	+	6.98573i	−0.152339	+	0.468851i
$223$	10.4374	−	7.58321i	0.698940	−	0.507809i	−0.180647	−	0.983548i	$-0.557819\pi$
$223$	10.4374	−	7.58321i	0.698940	−	0.507809i	0.879587	+	0.475739i	$0.157819\pi$
$224$	−0.280040	−	0.203461i	−0.0187109	−	0.0135943i
$225$	−5.94898	−	18.3091i	−0.396598	−	1.22060i
$226$	−3.42950	−	10.5549i	−0.228127	−	0.702102i
$227$	−10.7965	−	7.84413i	−0.716590	−	0.520633i	0.168703	−	0.985667i	$-0.446042\pi$
$227$	−10.7965	−	7.84413i	−0.716590	−	0.520633i	−0.885293	+	0.465034i	$0.846042\pi$
$228$	0.971032	−	0.705496i	0.0643082	−	0.0467226i
$229$	4.99435	−	15.3710i	0.330036	−	1.01575i	−0.639080	−	0.769140i	$-0.720685\pi$
$229$	4.99435	−	15.3710i	0.330036	−	1.01575i	0.969116	−	0.246606i	$-0.0793153\pi$
$230$	33.1708			2.18721
$231$	−0.00249713	−	1.37795i	−0.000164299	−	0.0906624i
$232$	7.64274			0.501770
$233$	1.19981	−	3.69264i	0.0786022	−	0.241913i	−0.904032	−	0.427464i	$-0.859407\pi$
$233$	1.19981	−	3.69264i	0.0786022	−	0.241913i	0.982635	+	0.185551i	$0.0594071\pi$
$234$	3.42676	−	2.48969i	0.224015	−	0.162756i
$235$	−0.143733	−	0.104428i	−0.00937613	−	0.00681216i
$236$	1.93776	+	5.96382i	0.126138	+	0.388212i
$237$	−4.74627	−	14.6075i	−0.308303	−	0.948860i
$238$	−2.18637	−	1.58849i	−0.141721	−	0.102967i
$239$	9.93994	−	7.22179i	0.642961	−	0.467139i	−0.217905	−	0.975970i	$-0.569922\pi$
$239$	9.93994	−	7.22179i	0.642961	−	0.467139i	0.860866	+	0.508831i	$0.169922\pi$
$240$	−1.54473	+	4.75418i	−0.0997118	+	0.306881i
$241$	−18.7769			−1.20953			−0.604763	−	0.796406i	$-0.706732\pi$
$241$	−18.7769			−1.20953			−0.604763	+	0.796406i	$0.706732\pi$
$242$	3.36125	−	10.4739i	0.216069	−	0.673286i
$243$	14.1485			0.907629
$244$	0.139219	−	0.428471i	0.00891256	−	0.0274300i
$245$	−23.1820	+	16.8427i	−1.48105	+	1.07604i
$246$	6.48190	+	4.70937i	0.413271	+	0.300259i
$247$	0.839381	+	2.58335i	0.0534085	+	0.164375i
$248$	−0.437738	−	1.34722i	−0.0277964	−	0.0855484i
$249$	5.82553	+	4.23250i	0.369178	+	0.268224i
$250$	−24.7500	+	17.9819i	−1.56533	+	1.13728i
$251$	−2.92028	+	8.98770i	−0.184326	+	0.567299i	−0.999936	−	0.0113040i	$-0.996402\pi$
$251$	−2.92028	+	8.98770i	−0.184326	+	0.567299i	0.815610	+	0.578603i	$0.196402\pi$
$252$	0.539774			0.0340026
$253$	0.0478702	+	26.4154i	0.00300957	+	1.66072i
$254$	13.0911			0.821410
$255$	−12.0603	+	37.1177i	−0.755243	+	2.32440i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−4.29144	−	3.11791i	−0.267693	−	0.194490i	0.445839	−	0.895113i	$-0.352905\pi$
$257$	−4.29144	−	3.11791i	−0.267693	−	0.194490i	−0.713531	+	0.700623i	$0.752905\pi$
$258$	−0.448954	−	1.38174i	−0.0279507	−	0.0860234i
$259$	−0.654596	−	2.01464i	−0.0406746	−	0.125184i
$260$	−9.15225	−	6.64950i	−0.567599	−	0.412385i
$261$	−9.64176	+	7.00515i	−0.596810	+	0.433608i
$262$	0.0344601	−	0.106057i	0.00212895	−	0.00655223i
$263$	11.1970			0.690435			0.345217	−	0.938523i	$-0.387805\pi$
$263$	11.1970			0.690435			0.345217	+	0.938523i	$0.387805\pi$
$264$	−3.78820	−	1.22328i	−0.233148	−	0.0752875i
$265$	35.7469			2.19591
$266$	−0.106966	+	0.329206i	−0.00655848	+	0.0201849i
$267$	3.70493	−	2.69179i	0.226738	−	0.164735i
$268$	−0.770762	−	0.559991i	−0.0470818	−	0.0342069i
$269$	−3.30962	−	10.1859i	−0.201791	−	0.621048i	−0.999830	−	0.0184426i	$-0.994129\pi$
$269$	−3.30962	−	10.1859i	−0.201791	−	0.621048i	0.798039	−	0.602606i	$-0.205871\pi$
$270$	−7.04299	−	21.6761i	−0.428623	−	1.31917i
$271$	−4.41649	−	3.20877i	−0.268283	−	0.194919i	0.445508	−	0.895278i	$-0.353023\pi$
$271$	−4.41649	−	3.20877i	−0.268283	−	0.194919i	−0.713791	+	0.700359i	$0.753023\pi$
$272$	−6.31629	+	4.58906i	−0.382981	+	0.278252i
$273$	0.348736	−	1.07330i	0.0211065	−	0.0649590i
$274$	−12.0187			−0.726078
$275$	−24.1272	−	33.0819i	−1.45492	−	1.99492i
$276$	9.55955			0.575417
$277$	3.18257	−	9.79495i	0.191222	−	0.588522i	−0.808778	−	0.588115i	$-0.799870\pi$
$277$	3.18257	−	9.79495i	0.191222	−	0.588522i	1.00000		0.000407101i	$-0.000129584\pi$
$278$	−2.37522	+	1.72570i	−0.142456	+	0.103500i
$279$	1.78706	+	1.29837i	0.106988	+	0.0777317i
$280$	−0.445490	−	1.37108i	−0.0266231	−	0.0819376i
$281$	5.81431	+	17.8946i	0.346853	+	1.06750i	0.960584	+	0.277989i	$0.0896678\pi$
$281$	5.81431	+	17.8946i	0.346853	+	1.06750i	−0.613731	+	0.789515i	$0.710332\pi$
$282$	−0.0414228	−	0.0300954i	−0.00246669	−	0.00179216i
$283$	25.8941	−	18.8131i	1.53924	−	1.11832i	0.588433	−	0.808546i	$-0.299745\pi$
$283$	25.8941	−	18.8131i	1.53924	−	1.11832i	0.950809	−	0.309779i	$-0.100255\pi$
$284$	4.38874	−	13.5072i	0.260424	−	0.801503i
$285$	4.99885			0.296106
$286$	5.28210	−	7.29796i	0.312337	−	0.431537i
$287$	−2.31063			−0.136392
$288$	0.481873	−	1.48305i	0.0283946	−	0.0873896i
$289$	−35.5603	+	25.8361i	−2.09178	+	1.51977i
$290$	25.7514	+	18.7095i	1.51217	+	1.09866i
$291$	3.09249	+	9.51771i	0.181285	+	0.557938i
$292$	−4.37154	−	13.4542i	−0.255825	−	0.787349i
$293$	5.52729	+	4.01581i	0.322908	+	0.234606i	0.737415	−	0.675440i	$-0.236046\pi$
$293$	5.52729	+	4.01581i	0.322908	+	0.234606i	−0.414508	+	0.910046i	$0.636046\pi$
$294$	−6.68088	+	4.85394i	−0.389637	+	0.283088i
$295$	−8.07039	+	24.8381i	−0.469876	+	1.44613i
$296$	−6.11969			−0.355700
$297$	17.2515	−	5.63994i	1.00103	−	0.327262i
$298$	10.4969			0.608069
$299$	−6.68529	+	20.5752i	−0.386620	+	1.18990i
$300$	−11.9879	+	8.70972i	−0.692122	+	0.502856i
$301$	0.338972	+	0.246277i	0.0195380	+	0.0141952i
$302$	−0.176402	−	0.542910i	−0.0101508	−	0.0312410i
$303$	−1.99545	−	6.14135i	−0.114635	−	0.352811i
$304$	0.809017	+	0.587785i	0.0464003	+	0.0337118i
$305$	1.51798	−	1.10288i	0.0869193	−	0.0631506i
$306$	3.76216	−	11.5787i	0.215068	−	0.661912i
$307$	32.1423			1.83446			0.917229	−	0.398361i	$-0.130421\pi$
$307$	32.1423			1.83446			0.917229	+	0.398361i	$0.130421\pi$
$308$	1.09121	−	0.356743i	0.0621774	−	0.0203273i
$309$	−2.22704			−0.126692
$310$	1.82309	−	5.61089i	0.103544	−	0.318677i
$311$	21.4139	−	15.5581i	1.21427	−	0.882220i	0.218660	−	0.975801i	$-0.429832\pi$
$311$	21.4139	−	15.5581i	1.21427	−	0.882220i	0.995612	+	0.0935816i	$0.0298316\pi$
$312$	−2.63761	−	1.91633i	−0.149325	−	0.108491i
$313$	3.79189	+	11.6702i	0.214330	+	0.659641i	0.999200	+	0.0399807i	$0.0127296\pi$
$313$	3.79189	+	11.6702i	0.214330	+	0.659641i	−0.784870	+	0.619660i	$0.787270\pi$
$314$	4.68312	+	14.4132i	0.264284	+	0.813382i
$315$	1.81871	+	1.32137i	0.102473	+	0.0744507i
$316$	10.3527	−	7.52165i	0.582383	−	0.423126i
$317$	−0.188901	+	0.581378i	−0.0106098	+	0.0326535i	−0.956221	−	0.292645i	$-0.905465\pi$
$317$	−0.188901	+	0.581378i	−0.0106098	+	0.0326535i	0.945611	+	0.325298i	$0.105465\pi$
$318$	10.3020			0.577705
$319$	−14.8620	+	20.5340i	−0.832115	+	1.14968i
$320$	−4.16480			−0.232819
$321$	−3.02915	+	9.32277i	−0.169071	+	0.520346i
$322$	−2.23039	+	1.62047i	−0.124295	+	0.0903055i
$323$	6.31629	+	4.58906i	0.351448	+	0.255342i
$324$	−0.584116	−	1.79772i	−0.0324509	−	0.0998736i
$325$	−10.3626	−	31.8928i	−0.574814	−	1.76910i
$326$	0.231114	+	0.167914i	0.0128002	+	0.00929992i
$327$	11.9786	−	8.70294i	0.662416	−	0.481274i
$328$	−2.06277	+	6.34856i	−0.113897	+	0.350540i
$329$	0.0147662			0.000814086
$330$	−9.76936	−	13.3952i	−0.537785	−	0.737384i
$331$	−23.7725			−1.30665			−0.653327	−	0.757076i	$-0.726627\pi$
$331$	−23.7725			−1.30665			−0.653327	+	0.757076i	$0.726627\pi$
$332$	−1.85389	+	5.70569i	−0.101746	+	0.313141i
$333$	7.72035	−	5.60916i	0.423072	−	0.307380i
$334$	13.2646	+	9.63732i	0.725808	+	0.527331i
$335$	−1.22614	−	3.77366i	−0.0669910	−	0.206177i
$336$	−0.128387	−	0.395134i	−0.00700407	−	0.0215563i
$337$	−15.6042	−	11.3371i	−0.850016	−	0.617573i	0.0751344	−	0.997173i	$-0.476061\pi$
$337$	−15.6042	−	11.3371i	−0.850016	−	0.617573i	−0.925150	+	0.379601i	$0.876061\pi$
$338$	−4.54809	+	3.30438i	−0.247384	+	0.179735i
$339$	4.11629	−	12.6687i	0.223566	−	0.688067i
$340$	−32.5161			−1.76343
$341$	4.47084	+	1.44371i	0.242110	+	0.0781814i
$342$	−1.55937			−0.0843212
$343$	1.48470	−	4.56944i	0.0801664	−	0.246727i
$344$	0.979268	−	0.711480i	0.0527986	−	0.0383604i
$345$	32.2099	+	23.4018i	1.73412	+	1.25991i
$346$	0.934889	+	2.87729i	0.0502600	+	0.154684i
$347$	−1.21295	−	3.73307i	−0.0651145	−	0.200402i	0.913206	−	0.407498i	$-0.133599\pi$
$347$	−1.21295	−	3.73307i	−0.0651145	−	0.200402i	−0.978321	+	0.207096i	$0.933599\pi$
$348$	7.42134	+	5.39192i	0.397826	+	0.289037i
$349$	7.13272	−	5.18223i	0.381806	−	0.277398i	−0.380284	−	0.924870i	$-0.624174\pi$
$349$	7.13272	−	5.18223i	0.381806	−	0.277398i	0.762089	+	0.647472i	$0.224174\pi$
$350$	1.32055	−	4.06423i	0.0705863	−	0.217242i
$351$	14.8647			0.793421
$352$	−0.00601040	−	3.31662i	−0.000320356	−	0.176776i
$353$	6.23196			0.331694			0.165847	−	0.986152i	$-0.446964\pi$
$353$	6.23196			0.331694			0.165847	+	0.986152i	$0.446964\pi$
$354$	−2.32582	+	7.15814i	−0.123616	+	0.380451i
$355$	47.8530	−	34.7673i	2.53977	−	1.84525i
$356$	3.08677	+	2.24267i	0.163599	+	0.118861i
$357$	−1.00236	−	3.08495i	−0.0530506	−	0.163273i
$358$	3.90632	+	12.0224i	0.206456	+	0.635405i
$359$	0.880116	+	0.639442i	0.0464507	+	0.0337484i	0.610768	−	0.791809i	$-0.290861\pi$
$359$	0.880116	+	0.639442i	0.0464507	+	0.0337484i	−0.564318	+	0.825558i	$0.690861\pi$
$360$	5.25414	−	3.81735i	0.276917	−	0.201192i
$361$	0.309017	−	0.951057i	0.0162641	−	0.0500556i
$362$	−13.9370			−0.732511
$363$	10.6532	−	7.79912i	0.559146	−	0.409348i
$364$	0.940240			0.0492819
$365$	18.2066	−	56.0341i	0.952977	−	2.93296i
$366$	0.437470	−	0.317841i	0.0228669	−	0.0166138i
$367$	0.166896	+	0.121257i	0.00871191	+	0.00632957i	0.592133	−	0.805840i	$-0.298286\pi$
$367$	0.166896	+	0.121257i	0.00871191	+	0.00632957i	−0.583421	+	0.812170i	$0.698286\pi$
$368$	2.46118	+	7.57474i	0.128298	+	0.394861i
$369$	−3.21663	−	9.89977i	−0.167451	−	0.515361i
$370$	−20.6196	−	14.9810i	−1.07196	−	0.778827i
$371$	−2.40361	+	1.74632i	−0.124789	+	0.0906646i
$372$	0.525400	−	1.61701i	0.0272407	−	0.0838382i
$373$	0.426626			0.0220899			0.0110449	−	0.999939i	$-0.496484\pi$
$373$	0.426626			0.0220899			0.0110449	+	0.999939i	$0.496484\pi$
$374$	−0.0469254	−	25.8941i	−0.00242646	−	1.33895i
$375$	−36.7192			−1.89617
$376$	0.0131822	−	0.0405707i	0.000679821	−	0.00209227i
$377$	−16.7951	+	12.2024i	−0.864993	+	0.628454i
$378$	1.53250	+	1.11343i	0.0788233	+	0.0572685i
$379$	−2.37700	−	7.31564i	−0.122098	−	0.375779i	0.871263	−	0.490816i	$-0.163301\pi$
$379$	−2.37700	−	7.31564i	−0.122098	−	0.375779i	−0.993361	+	0.115037i	$0.963301\pi$
$380$	1.28699	+	3.96096i	0.0660214	+	0.203193i
$381$	12.7119	+	9.23573i	0.651250	+	0.473161i
$382$	−21.5923	+	15.6877i	−1.10476	+	0.802654i
$383$	8.67238	−	26.6908i	0.443138	−	1.36384i	−0.441375	−	0.897323i	$-0.645509\pi$
$383$	8.67238	−	26.6908i	0.443138	−	1.36384i	0.884513	−	0.466516i	$-0.154491\pi$
$384$	−1.20026			−0.0612506
$385$	4.55002	+	1.46928i	0.231891	+	0.0748815i
$386$	6.01287			0.306047
$387$	−0.583279	+	1.79515i	−0.0296497	+	0.0912525i
$388$	−6.74540	+	4.90082i	−0.342446	+	0.248801i
$389$	2.19164	+	1.59232i	0.111120	+	0.0807337i	0.641958	−	0.766740i	$-0.278122\pi$
$389$	2.19164	+	1.59232i	0.111120	+	0.0807337i	−0.530837	+	0.847474i	$0.678122\pi$
$390$	−4.19593	−	12.9138i	−0.212469	−	0.653914i
$391$	19.2154	+	59.1388i	0.971762	+	2.99078i
$392$	−5.56618	−	4.04407i	−0.281135	−	0.204256i
$393$	0.108285	−	0.0786734i	0.00546224	−	0.00396855i
$394$	−2.00367	+	6.16667i	−0.100944	+	0.310672i
$395$	53.2952			2.68157
$396$	3.04752	+	4.17860i	0.153143	+	0.209983i
$397$	−23.9064			−1.19983			−0.599914	−	0.800065i	$-0.704798\pi$
$397$	−23.9064			−1.19983			−0.599914	+	0.800065i	$0.704798\pi$
$398$	7.09900	−	21.8485i	0.355841	−	1.09517i
$399$	−0.336121	+	0.244206i	−0.0168271	+	0.0122256i
$400$	−9.98775	−	7.25652i	−0.499387	−	0.362826i
$401$	0.598211	+	1.84110i	0.0298732	+	0.0919403i	0.964881	−	0.262686i	$-0.0846082\pi$
$401$	0.598211	+	1.84110i	0.0298732	+	0.0919403i	−0.935008	+	0.354626i	$0.884608\pi$
$402$	−0.353363	−	1.08754i	−0.0176241	−	0.0542415i
$403$	3.11290	+	2.26166i	0.155065	+	0.112661i
$404$	4.35251	−	3.16228i	0.216545	−	0.157329i
$405$	2.43272	−	7.48716i	0.120883	−	0.372040i
$406$	−2.64552			−0.131295
$407$	11.9003	−	16.4420i	0.589878	−	0.814999i
$408$	−9.37088			−0.463928
$409$	−0.363888	+	1.11993i	−0.0179931	+	0.0553771i	−0.959650	−	0.281197i	$-0.909268\pi$
$409$	−0.363888	+	1.11993i	−0.0179931	+	0.0553771i	0.941657	+	0.336575i	$0.109268\pi$
$410$	−22.4916	+	16.3411i	−1.11078	+	0.807029i
$411$	−11.6706	−	8.47917i	−0.575667	−	0.418246i
$412$	−0.573369	−	1.76465i	−0.0282479	−	0.0869380i
$413$	−0.670753	−	2.06436i	−0.0330056	−	0.101581i
$414$	−10.0478	−	7.30012i	−0.493820	−	0.358781i
$415$	−20.2141	+	14.6864i	−0.992269	+	0.720926i
$416$	0.839381	−	2.58335i	0.0411540	−	0.126659i
$417$	−3.52389			−0.172565
$418$	−3.15244	+	1.03061i	−0.154191	+	0.0504087i
$419$	−3.84131			−0.187660			−0.0938301	−	0.995588i	$-0.529911\pi$
$419$	−3.84131			−0.187660			−0.0938301	+	0.995588i	$0.529911\pi$
$420$	0.534705	−	1.64565i	0.0260909	−	0.0802996i
$421$	−3.77633	+	2.74366i	−0.184047	+	0.133718i	−0.675994	−	0.736907i	$-0.736285\pi$
$421$	−3.77633	+	2.74366i	−0.184047	+	0.133718i	0.491947	+	0.870625i	$0.336285\pi$
$422$	−13.6711	−	9.93264i	−0.665499	−	0.483513i
$423$	0.0205560	+	0.0632648i	0.000999467	+	0.00307604i
$424$	2.65232	+	8.16301i	0.128808	+	0.396431i
$425$	−77.9780	−	56.6543i	−3.78249	−	2.74814i
$426$	13.7909	−	10.0196i	0.668169	−	0.485453i
$427$	−0.0481902	+	0.148314i	−0.00233209	+	0.00717743i
$428$	−8.16700			−0.394767
$429$	10.2778	−	3.36005i	0.496215	−	0.162225i
$430$	5.04125			0.243110
$431$	2.91519	−	8.97202i	0.140420	−	0.432167i	−0.855974	−	0.517019i	$-0.827042\pi$
$431$	2.91519	−	8.97202i	0.140420	−	0.432167i	0.996394	+	0.0848518i	$0.0270417\pi$
$432$	4.42730	−	3.21662i	0.213008	−	0.154760i
$433$	−2.69835	−	1.96047i	−0.129675	−	0.0942141i	0.521057	−	0.853522i	$-0.325538\pi$
$433$	−2.69835	−	1.96047i	−0.129675	−	0.0942141i	−0.650732	+	0.759308i	$0.725538\pi$
$434$	0.151522	+	0.466337i	0.00727329	+	0.0223849i
$435$	11.8060	+	36.3350i	0.566052	+	1.74213i
$436$	9.97997	+	7.25087i	0.477954	+	0.347254i
$437$	6.44346	−	4.68145i	0.308232	−	0.223944i
$438$	5.24700	−	16.1486i	0.250711	−	0.771609i
$439$	−7.86715			−0.375479			−0.187739	−	0.982219i	$-0.560116\pi$
$439$	−7.86715			−0.375479			−0.187739	+	0.982219i	$0.560116\pi$
$440$	8.09885	−	11.1897i	0.386098	−	0.533448i
$441$	10.7288			0.510894
$442$	6.55335	−	20.1691i	0.311711	−	0.959348i
$443$	−11.4065	+	8.28729i	−0.541938	+	0.393741i	−0.824804	−	0.565418i	$-0.808715\pi$
$443$	−11.4065	+	8.28729i	−0.541938	+	0.393741i	0.282866	+	0.959159i	$0.408715\pi$
$444$	−5.94241	−	4.31742i	−0.282014	−	0.204895i
$445$	4.91047	+	15.1129i	0.232779	+	0.716419i
$446$	3.98673	+	12.2699i	0.188777	+	0.580996i
$447$	10.1928	+	7.40552i	0.482104	+	0.350269i
$448$	0.280040	−	0.203461i	0.0132306	−	0.00961262i
$449$	1.04220	−	3.20757i	0.0491845	−	0.151374i	−0.923448	−	0.383724i	$-0.874641\pi$
$449$	1.04220	−	3.20757i	0.0491845	−	0.151374i	0.972632	+	0.232350i	$0.0746414\pi$
$450$	19.2513			0.907514
$451$	−13.0456	−	17.8875i	−0.614295	−	0.842290i
$452$	11.0981			0.522010
$453$	0.211729	−	0.651634i	0.00994788	−	0.0306164i
$454$	10.7965	−	7.84413i	0.506706	−	0.368143i
$455$	3.16804	+	2.30171i	0.148520	+	0.107906i
$456$	0.370901	+	1.14152i	0.0173690	+	0.0534564i
$457$	−7.52073	−	23.1464i	−0.351805	−	1.08274i	−0.957839	−	0.287306i	$-0.907240\pi$
$457$	−7.52073	−	23.1464i	−0.351805	−	1.08274i	0.606034	−	0.795439i	$-0.292760\pi$
$458$	13.0754	+	9.49982i	0.610972	+	0.443897i
$459$	34.5655	−	25.1133i	1.61338	−	1.17219i
$460$	−10.2503	+	31.5473i	−0.477924	+	1.47090i
$461$	11.7644			0.547922			0.273961	−	0.961741i	$-0.411666\pi$
$461$	11.7644			0.547922			0.273961	+	0.961741i	$0.411666\pi$
$462$	1.31128	+	0.423435i	0.0610063	+	0.0197000i
$463$	−13.7929			−0.641009			−0.320504	−	0.947247i	$-0.603852\pi$
$463$	−13.7929			−0.641009			−0.320504	+	0.947247i	$0.603852\pi$
$464$	−2.36174	+	7.26867i	−0.109641	+	0.337440i
$465$	5.72874	−	4.16217i	0.265664	−	0.193016i
$466$	3.14115	+	2.28218i	0.145511	+	0.105720i
$467$	4.35352	+	13.3988i	0.201457	+	0.620021i	0.999840	+	0.0178712i	$0.00568887\pi$
$467$	4.35352	+	13.3988i	0.201457	+	0.620021i	−0.798383	+	0.602149i	$0.794311\pi$
$468$	1.30891	+	4.02840i	0.0605043	+	0.186213i
$469$	0.266798	+	0.193840i	0.0123196	+	0.00895069i
$470$	0.143733	−	0.104428i	0.00662993	−	0.00481692i
$471$	−5.62097	+	17.2996i	−0.259000	+	0.797121i
$472$	−6.27073			−0.288634
$473$	0.00727525	+	4.01458i	0.000334516	+	0.184590i
$474$	15.3593			0.705474
$475$	−3.81498	+	11.7413i	−0.175043	+	0.538728i
$476$	2.18637	−	1.58849i	0.100212	−	0.0728084i
$477$	−10.8281	−	7.86706i	−0.495784	−	0.360208i
$478$	3.79672	+	11.6851i	0.173658	+	0.534464i
$479$	−4.02676	−	12.3931i	−0.183987	−	0.566255i	0.815942	−	0.578134i	$-0.196219\pi$
$479$	−4.02676	−	12.3931i	−0.183987	−	0.566255i	−0.999929	+	0.0118788i	$0.996219\pi$
$480$	−4.04415	−	2.93825i	−0.184589	−	0.134112i
$481$	13.4482	−	9.77068i	0.613184	−	0.445504i
$482$	5.80238	−	17.8579i	0.264291	−	0.813404i
$483$	−3.30902			−0.150566
$484$	8.92256	+	6.43334i	0.405571	+	0.292425i
$485$	−34.7251			−1.57679
$486$	−4.37214	+	13.4561i	−0.198324	+	0.610379i
$487$	9.74418	−	7.07956i	0.441551	−	0.320806i	−0.344700	−	0.938713i	$-0.612019\pi$
$487$	9.74418	−	7.07956i	0.441551	−	0.320806i	0.786251	+	0.617907i	$0.212019\pi$
$488$	0.364479	+	0.264809i	0.0164992	+	0.0119874i
$489$	0.105956	+	0.326100i	0.00479152	+	0.0147468i
$490$	−8.85475	−	27.2521i	−0.400017	−	1.23112i
$491$	7.01639	+	5.09771i	0.316645	+	0.230056i	0.734743	−	0.678346i	$-0.237303\pi$
$491$	7.01639	+	5.09771i	0.316645	+	0.230056i	−0.418097	+	0.908402i	$0.637303\pi$
$492$	−6.48190	+	4.70937i	−0.292227	+	0.212315i
$493$	−18.4389	+	56.7492i	−0.830448	+	2.55586i
$494$	−2.71629			−0.122212
$495$	0.0390344	+	21.5397i	0.00175447	+	0.968137i
$496$	1.41655			0.0636049
$497$	−1.51916	+	4.67548i	−0.0681434	+	0.209724i
$498$	−5.82553	+	4.23250i	−0.261048	+	0.189663i
$499$	−13.3679	−	9.71234i	−0.598429	−	0.434784i	0.246892	−	0.969043i	$-0.420591\pi$
$499$	−13.3679	−	9.71234i	−0.598429	−	0.434784i	−0.845321	+	0.534259i	$0.820591\pi$
$500$	−9.45365	−	29.0954i	−0.422780	−	1.30118i
$501$	6.08129	+	18.7163i	0.271692	+	0.836182i
$502$	−7.64539	−	5.55470i	−0.341231	−	0.247919i
$503$	2.21161	−	1.60683i	0.0986109	−	0.0716450i	−0.537387	−	0.843336i	$-0.680589\pi$
$503$	2.21161	−	1.60683i	0.0986109	−	0.0716450i	0.635998	+	0.771691i	$0.280589\pi$
$504$	−0.166799	+	0.513355i	−0.00742983	+	0.0228667i
$505$	22.4066			0.997080
$506$	−25.1373	−	8.11728i	−1.11749	−	0.360857i
$507$	−6.74757			−0.299670
$508$	−4.04538	+	12.4504i	−0.179485	+	0.552397i
$509$	−28.0262	+	20.3623i	−1.24224	+	0.902541i	−0.997746	−	0.0671091i	$-0.978622\pi$
$509$	−28.0262	+	20.3623i	−1.24224	+	0.902541i	−0.244496	+	0.969650i	$0.578622\pi$
$510$	−31.5742	−	22.9400i	−1.39813	−	1.01580i
$511$	1.51320	+	4.65716i	0.0669401	+	0.206020i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−4.42730	−	3.21662i	−0.195470	−	0.142017i
$514$	4.29144	−	3.11791i	0.189287	−	0.137525i
$515$	2.38797	−	7.34941i	0.105226	−	0.323853i
$516$	1.45285			0.0639580
$517$	0.0833686	+	0.114311i	0.00366655	+	0.00502738i
$518$	2.11832			0.0930736
$519$	−1.12211	+	3.45350i	−0.0492552	+	0.151592i
$520$	9.15225	−	6.64950i	0.401353	−	0.291600i
$521$	8.05470	+	5.85208i	0.352883	+	0.256384i	0.750077	−	0.661350i	$-0.230016\pi$
$521$	8.05470	+	5.85208i	0.352883	+	0.256384i	−0.397195	+	0.917734i	$0.630016\pi$
$522$	−3.68283	−	11.3346i	−0.161193	−	0.496101i
$523$	1.04635	+	3.22032i	0.0457536	+	0.140815i	0.971324	−	0.237762i	$-0.0764137\pi$
$523$	1.04635	+	3.22032i	0.0457536	+	0.140815i	−0.925570	+	0.378577i	$0.876414\pi$
$524$	0.0902176	+	0.0655469i	0.00394117	+	0.00286343i
$525$	4.14959	−	3.01485i	0.181103	−	0.131579i
$526$	−3.46005	+	10.6490i	−0.150866	+	0.464316i
$527$	11.0595			0.481760
$528$	2.33403	−	3.22478i	0.101575	−	0.140341i
$529$	40.4341			1.75801
$530$	−11.0464	+	33.9973i	−0.479824	+	1.47675i
$531$	7.91090	−	5.74760i	0.343304	−	0.249425i
$532$	−0.280040	−	0.203461i	−0.0121413	−	0.00882114i
$533$	−5.60309	−	17.2445i	−0.242697	−	0.746944i
$534$	1.41516	+	4.35541i	0.0612399	+	0.188477i
$535$	−27.5178	−	19.9929i	−1.18970	−	0.864367i
$536$	0.770762	−	0.559991i	0.0332918	−	0.0241879i
$537$	−4.68861	+	14.4301i	−0.202328	+	0.622703i
$538$	10.7101			0.461747
$539$	21.6893	−	7.09077i	0.934225	−	0.305421i
$540$	22.7916			0.980794
$541$	−5.37237	+	16.5345i	−0.230976	+	0.710872i	0.766654	+	0.642061i	$0.221920\pi$
$541$	−5.37237	+	16.5345i	−0.230976	+	0.710872i	−0.997630	+	0.0688106i	$0.978080\pi$
$542$	4.41649	−	3.20877i	0.189704	−	0.137828i
$543$	−13.5333	−	9.83248i	−0.580767	−	0.421952i
$544$	−2.41261	−	7.42525i	−0.103440	−	0.318355i
$545$	15.8762	+	48.8620i	0.680063	+	2.09302i
$546$	0.913003	+	0.663335i	0.0390729	+	0.0283881i
$547$	20.1472	−	14.6378i	0.861433	−	0.625867i	−0.0668418	−	0.997764i	$-0.521292\pi$
$547$	20.1472	−	14.6378i	0.861433	−	0.625867i	0.928274	+	0.371896i	$0.121292\pi$
$548$	3.71399	−	11.4305i	0.158654	−	0.488287i
$549$	−0.702530			−0.0299832
$550$	38.9185	−	12.7234i	1.65949	−	0.542528i
$551$	7.64274			0.325592
$552$	−2.95406	+	9.09167i	−0.125733	+	0.386967i
$553$	−3.58355	+	2.60360i	−0.152388	+	0.110717i
$554$	8.33208	+	6.05361i	0.353996	+	0.257193i
$555$	−9.45326	−	29.0941i	−0.401268	−	1.23498i
$556$	−0.907253	−	2.79224i	−0.0384761	−	0.118417i
$557$	20.9023	+	15.1864i	0.885660	+	0.643469i	0.934743	−	0.355325i	$-0.115630\pi$
$557$	20.9023	+	15.1864i	0.885660	+	0.643469i	−0.0490830	+	0.998795i	$0.515630\pi$
$558$	−1.78706	+	1.29837i	−0.0756523	+	0.0549646i
$559$	−1.01602	+	3.12699i	−0.0429731	+	0.132258i
$560$	1.44164			0.0609203
$561$	18.2226	−	25.1771i	0.769358	−	1.06298i
$562$	−18.8155			−0.793685
$563$	−5.21630	+	16.0541i	−0.219841	+	0.676600i	0.778934	+	0.627106i	$0.215761\pi$
$563$	−5.21630	+	16.0541i	−0.219841	+	0.676600i	−0.998774	+	0.0494939i	$0.984239\pi$
$564$	0.0414228	−	0.0300954i	0.00174422	−	0.00126725i
$565$	37.3938	+	27.1682i	1.57317	+	1.14297i
$566$	9.89065	+	30.4403i	0.415735	+	1.27950i
$567$	0.202191	+	0.622279i	0.00849121	+	0.0261333i
$568$	11.4899	+	8.34789i	0.482105	+	0.350270i
$569$	−23.1738	+	16.8368i	−0.971496	+	0.705833i	−0.955792	−	0.294043i	$-0.904999\pi$
$569$	−23.1738	+	16.8368i	−0.971496	+	0.705833i	−0.0157043	+	0.999877i	$0.504999\pi$
$570$	−1.54473	+	4.75418i	−0.0647015	+	0.199131i
$571$	−20.4773			−0.856949			−0.428474	−	0.903554i	$-0.640949\pi$
$571$	−20.4773			−0.856949			−0.428474	+	0.903554i	$0.640949\pi$
$572$	5.30851	+	7.27876i	0.221960	+	0.304340i
$573$	−32.0345			−1.33826
$574$	0.714024	−	2.19754i	0.0298028	−	0.0917236i
$575$	−79.5480	+	57.7950i	−3.31738	+	2.41022i
$576$	1.26156	+	0.916576i	0.0525650	+	0.0381907i
$577$	−1.33846	−	4.11937i	−0.0557209	−	0.171491i	0.919323	−	0.393504i	$-0.128737\pi$
$577$	−1.33846	−	4.11937i	−0.0557209	−	0.171491i	−0.975044	+	0.222013i	$0.928737\pi$
$578$	−13.5828	−	41.8037i	−0.564971	−	1.73880i
$579$	5.83868	+	4.24205i	0.242647	+	0.176294i
$580$	−25.7514	+	18.7095i	−1.06927	+	0.776868i
$581$	0.641721	−	1.97501i	0.0266231	−	0.0819374i
$582$	−10.0075			−0.414825
$583$	−27.0895	−	8.74768i	−1.12193	−	0.362292i
$584$	14.1466			0.585391
$585$	−5.45133	+	16.7775i	−0.225385	+	0.693663i
$586$	−5.52729	+	4.01581i	−0.228330	+	0.165892i
$587$	−0.746356	−	0.542260i	−0.0308054	−	0.0223815i	0.572276	−	0.820061i	$-0.306061\pi$
$587$	−0.746356	−	0.542260i	−0.0308054	−	0.0223815i	−0.603081	+	0.797680i	$0.706061\pi$
$588$	−2.55187	−	7.85384i	−0.105237	−	0.323887i
$589$	−0.437738	−	1.34722i	−0.0180367	−	0.0555111i
$590$	−21.1285	−	15.3508i	−0.869849	−	0.631982i
$591$	−6.29619	+	4.57445i	−0.258991	+	0.188168i
$592$	1.89109	−	5.82017i	0.0777232	−	0.239208i
$593$	−8.81885			−0.362147			−0.181073	−	0.983470i	$-0.557957\pi$
$593$	−8.81885			−0.362147			−0.181073	+	0.983470i	$0.557957\pi$
$594$	0.0328916	+	18.1500i	0.00134956	+	0.744703i
$595$	11.2554			0.461426
$596$	−3.24372	+	9.98314i	−0.132868	+	0.408925i
$597$	22.3074	−	16.2073i	0.912980	−	0.663319i
$598$	−17.5023	−	12.7162i	−0.715723	−	0.520003i
$599$	3.11067	+	9.57365i	0.127098	+	0.391169i	0.994278	−	0.106828i	$-0.0340693\pi$
$599$	3.11067	+	9.57365i	0.127098	+	0.391169i	−0.867179	+	0.497996i	$0.834069\pi$
$600$	−4.57897	−	14.0926i	−0.186936	−	0.575329i
$601$	20.9340	+	15.2094i	0.853916	+	0.620406i	0.926223	−	0.376976i	$-0.123036\pi$
$601$	20.9340	+	15.2094i	0.853916	+	0.620406i	−0.0723073	+	0.997382i	$0.523036\pi$
$602$	−0.338972	+	0.246277i	−0.0138155	+	0.0100375i
$603$	−0.459087	+	1.41292i	−0.0186955	+	0.0575387i
$604$	0.570849			0.0232275
$605$	14.3147	+	43.5189i	0.581977	+	1.76930i
$606$	6.45740			0.262314
$607$	−14.7056	+	45.2591i	−0.596880	+	1.83701i	−0.0517465	+	0.998660i	$0.516479\pi$
$607$	−14.7056	+	45.2591i	−0.596880	+	1.83701i	−0.545134	+	0.838349i	$0.683521\pi$
$608$	−0.809017	+	0.587785i	−0.0328100	+	0.0238378i
$609$	−2.56888	−	1.86640i	−0.104096	−	0.0756305i
$610$	0.579817	+	1.78449i	0.0234761	+	0.0722520i
$611$	0.0358068	+	0.110202i	0.00144859	+	0.00445829i
$612$	9.84945	+	7.15605i	0.398141	+	0.289266i
$613$	16.2626	−	11.8155i	0.656840	−	0.477222i	−0.208754	−	0.977968i	$-0.566941\pi$
$613$	16.2626	−	11.8155i	0.656840	−	0.477222i	0.865594	+	0.500746i	$0.166941\pi$
$614$	−9.93252	+	30.5691i	−0.400844	+	1.23367i
$615$	−33.3686			−1.34555
$616$	0.00208049	+	1.14804i	8.38253e−5	+	0.0462559i
$617$	−10.4403			−0.420312			−0.210156	−	0.977668i	$-0.567397\pi$
$617$	−10.4403			−0.420312			−0.210156	+	0.977668i	$0.567397\pi$
$618$	0.688193	−	2.11804i	0.0276832	−	0.0852001i
$619$	31.4537	−	22.8524i	1.26423	−	0.918516i	0.265272	−	0.964174i	$-0.414538\pi$
$619$	31.4537	−	22.8524i	1.26423	−	0.918516i	0.998957	+	0.0456572i	$0.0145382\pi$
$620$	4.77291	+	3.46772i	0.191685	+	0.139267i
$621$	−13.4687	−	41.4523i	−0.540479	−	1.66342i
$622$	8.17938	+	25.1736i	0.327963	+	1.00937i
$623$	−1.06848	−	0.776297i	−0.0428078	−	0.0311017i
$624$	2.63761	−	1.91633i	0.105589	−	0.0767147i
$625$	20.2976	−	62.4697i	0.811906	−	2.49879i
$626$	−12.2708			−0.490441
$627$	−3.78820	−	1.22328i	−0.151286	−	0.0488530i
$628$	−15.1549			−0.604746
$629$	14.7644	−	45.4402i	0.588696	−	1.81182i
$630$	−1.81871	+	1.32137i	−0.0724591	+	0.0526446i
$631$	7.48118	+	5.43539i	0.297821	+	0.216380i	0.726653	−	0.687005i	$-0.241075\pi$
$631$	7.48118	+	5.43539i	0.297821	+	0.216380i	−0.428832	+	0.903384i	$0.641075\pi$
$632$	3.95436	+	12.1703i	0.157296	+	0.484108i
$633$	−6.26764	−	19.2898i	−0.249116	−	0.766702i
$634$	−0.494550	−	0.359312i	−0.0196411	−	0.0142701i
$635$	−44.1091	+	32.0471i	−1.75042	+	1.27175i
$636$	−3.18348	+	9.79775i	−0.126233	+	0.388506i
$637$	18.6886			0.740469
$638$	−14.9364	−	20.4800i	−0.591337	−	0.810811i
$639$	−22.1466			−0.876107
$640$	1.28699	−	3.96096i	0.0508729	−	0.156571i
$641$	26.7929	−	19.4662i	1.05826	−	0.768868i	0.0844908	−	0.996424i	$-0.473074\pi$
$641$	26.7929	−	19.4662i	1.05826	−	0.768868i	0.973765	+	0.227557i	$0.0730737\pi$
$642$	−7.93042	−	5.76179i	−0.312989	−	0.227400i
$643$	4.82865	+	14.8610i	0.190423	+	0.586062i	1.00000		0.000952218i	$-0.000303101\pi$
$643$	4.82865	+	14.8610i	0.190423	+	0.586062i	−0.809576	+	0.587015i	$0.800303\pi$
$644$	−0.851934	−	2.62198i	−0.0335709	−	0.103321i
$645$	4.89521	+	3.55658i	0.192749	+	0.140040i
$646$	−6.31629	+	4.58906i	−0.248511	+	0.180554i
$647$	−5.79838	+	17.8456i	−0.227958	+	0.701582i	0.770020	+	0.638019i	$0.220246\pi$
$647$	−5.79838	+	17.8456i	−0.227958	+	0.701582i	−0.997978	+	0.0635620i	$0.979754\pi$
$648$	1.89024			0.0742556
$649$	12.1940	−	16.8478i	0.478658	−	0.661334i
$650$	33.5341			1.31532
$651$	−0.181866	+	0.559726i	−0.00712789	+	0.0219374i
$652$	−0.231114	+	0.167914i	−0.00905113	+	0.00657603i
$653$	19.2059	+	13.9539i	0.751583	+	0.546057i	0.896317	−	0.443413i	$-0.146233\pi$
$653$	19.2059	+	13.9539i	0.751583	+	0.546057i	−0.144734	+	0.989471i	$0.546233\pi$
$654$	4.57541	+	14.0817i	0.178913	+	0.550636i
$655$	0.143519	+	0.441706i	0.00560776	+	0.0172589i
$656$	−5.40041	−	3.92362i	−0.210850	−	0.153192i
$657$	−17.8468	+	12.9664i	−0.696269	+	0.505869i
$658$	−0.00456300	+	0.0140435i	−0.000177884	+	0.000547471i
$659$	27.7968			1.08281			0.541405	−	0.840762i	$-0.317893\pi$
$659$	27.7968			1.08281			0.541405	+	0.840762i	$0.317893\pi$
$660$	15.7585	−	5.15185i	0.613400	−	0.200535i
$661$	0.628471			0.0244447			0.0122224	−	0.999925i	$-0.496109\pi$
$661$	0.628471			0.0244447			0.0122224	+	0.999925i	$0.496109\pi$
$662$	7.34610	−	22.6090i	0.285514	−	0.878722i
$663$	20.5928	−	14.9615i	0.799757	−	0.581057i
$664$	−4.85355	−	3.52631i	−0.188354	−	0.136847i
$665$	−0.445490	−	1.37108i	−0.0172754	−	0.0531681i
$666$	2.94891	+	9.07581i	0.114268	+	0.351681i
$667$	49.2457	+	35.7791i	1.90680	+	1.38537i
$668$	−13.2646	+	9.63732i	−0.513224	+	0.372879i
$669$	−4.78512	+	14.7271i	−0.185003	+	0.569382i
$670$	3.96786			0.153292
$671$	−1.42024	+	0.464310i	−0.0548277	+	0.0179245i
$672$	0.415468			0.0160270
$673$	−7.97374	+	24.5406i	−0.307365	+	0.945972i	0.671419	+	0.741078i	$0.265685\pi$
$673$	−7.97374	+	24.5406i	−0.307365	+	0.945972i	−0.978784	+	0.204894i	$0.934315\pi$
$674$	15.6042	−	11.3371i	0.601052	−	0.436690i
$675$	54.6573	+	39.7109i	2.10376	+	1.52847i
$676$	−1.73722	−	5.34660i	−0.0668160	−	0.205639i
$677$	1.01644	+	3.12829i	0.0390651	+	0.120230i	0.968687	−	0.248284i	$-0.0798666\pi$
$677$	1.01644	+	3.12829i	0.0390651	+	0.120230i	−0.929622	+	0.368514i	$0.879867\pi$
$678$	10.7766	+	7.82966i	0.413873	+	0.300696i
$679$	2.33491	−	1.69641i	0.0896055	−	0.0651022i
$680$	10.0480	−	30.9246i	0.385324	−	1.18591i
$681$	16.0178			0.613802
$682$	−2.75462	+	3.80589i	−0.105480	+	0.145735i
$683$	−42.7897			−1.63730			−0.818651	−	0.574291i	$-0.805278\pi$
$683$	−42.7897			−1.63730			−0.818651	+	0.574291i	$0.805278\pi$
$684$	0.481873	−	1.48305i	0.0184249	−	0.0567059i
$685$	40.4958	−	29.4219i	1.54727	−	1.12415i
$686$	3.88700	+	2.82407i	0.148406	+	0.107824i
$687$	5.99453	+	18.4493i	0.228705	+	0.703883i
$688$	0.374047	+	1.15120i	0.0142604	+	0.0438891i
$689$	−18.8616	−	13.7037i	−0.718569	−	0.522071i
$690$	−32.2099	+	23.4018i	−1.22621	+	0.890892i
$691$	8.39214	−	25.8283i	0.319252	−	0.982557i	−0.654717	−	0.755874i	$-0.727212\pi$
$691$	8.39214	−	25.8283i	0.319252	−	0.982557i	0.973969	−	0.226682i	$-0.0727879\pi$
$692$	−3.02537			−0.115007
$693$	−1.05489	−	1.44641i	−0.0400720	−	0.0549448i
$694$	3.92519			0.148998
$695$	3.77852	−	11.6291i	0.143328	−	0.441117i
$696$	−7.42134	+	5.39192i	−0.281305	+	0.204380i
$697$	−42.1629	−	30.6332i	−1.59704	−	1.16031i
$698$	2.72446	+	8.38502i	0.103122	+	0.317378i
$699$	1.44009	+	4.43213i	0.0544691	+	0.167639i
$700$	3.45724	+	2.51183i	0.130671	+	0.0949383i
$701$	11.7838	−	8.56143i	0.445068	−	0.323361i	−0.342577	−	0.939490i	$-0.611300\pi$
$701$	11.7838	−	8.56143i	0.445068	−	0.323361i	0.787645	+	0.616129i	$0.211300\pi$
$702$	−4.59346	+	14.1372i	−0.173369	+	0.533575i
$703$	−6.11969			−0.230808
$704$	3.15615	+	1.01918i	0.118952	+	0.0384116i
$705$	0.213244			0.00803122
$706$	−1.92578	+	5.92694i	−0.0724777	+	0.223063i
$707$	−1.50661	+	1.09462i	−0.0566620	+	0.0411673i
$708$	−6.08908	−	4.42398i	−0.228842	−	0.166263i
$709$	−9.73702	−	29.9675i	−0.365681	−	1.12545i	−0.949553	−	0.313606i	$-0.898463\pi$
$709$	−9.73702	−	29.9675i	−0.365681	−	1.12545i	0.583872	−	0.811846i	$-0.301537\pi$
$710$	18.2782	+	56.2546i	0.685970	+	2.11120i
$711$	−16.1437	−	11.7291i	−0.605434	−	0.439874i
$712$	−3.08677	+	2.24267i	−0.115682	+	0.0840477i
$713$	3.48638	−	10.7300i	0.130566	−	0.401841i
$714$	3.24371			0.121393
$715$	0.0679946	+	37.5203i	0.00254285	+	1.40318i
$716$	−12.6411			−0.472421
$717$	−4.55706	+	14.0252i	−0.170186	+	0.523780i
$718$	−0.880116	+	0.639442i	−0.0328456	+	0.0238638i
$719$	−20.4461	−	14.8550i	−0.762512	−	0.553997i	0.137168	−	0.990548i	$-0.456200\pi$
$719$	−20.4461	−	14.8550i	−0.762512	−	0.553997i	−0.899680	+	0.436550i	$0.856200\pi$
$720$	2.00690	+	6.17661i	0.0747928	+	0.230189i
$721$	0.198471	+	0.610830i	0.00739143	+	0.0227485i
$722$	0.809017	+	0.587785i	0.0301085	+	0.0218751i
$723$	18.2330	−	13.2470i	0.678091	−	0.492662i
$724$	4.30676	−	13.2549i	0.160060	−	0.492613i
$725$	−94.3537			−3.50421
$726$	4.12540	+	12.5418i	0.153108	+	0.465470i
$727$	−19.1962			−0.711947			−0.355974	−	0.934496i	$-0.615851\pi$
$727$	−19.1962			−0.711947			−0.355974	+	0.934496i	$0.615851\pi$
$728$	−0.290550	+	0.894221i	−0.0107685	+	0.0331420i
$729$	−18.3264	+	13.3149i	−0.678755	+	0.493144i
$730$	47.6655	+	34.6310i	1.76418	+	1.28175i
$731$	2.92032	+	8.98783i	0.108012	+	0.332427i
$732$	0.167099	+	0.514277i	0.00617614	+	0.0190082i
$733$	0.383606	+	0.278706i	0.0141688	+	0.0102942i	0.594847	−	0.803839i	$-0.297213\pi$
$733$	0.383606	+	0.278706i	0.0141688	+	0.0102942i	−0.580678	+	0.814133i	$0.697213\pi$
$734$	−0.166896	+	0.121257i	−0.00616025	+	0.00447568i
$735$	10.6280	−	32.7097i	0.392020	−	1.20651i
$736$	−7.96455			−0.293577
$737$	0.00572620	+	3.15979i	0.000210927	+	0.116392i
$738$	10.4092			0.383169
$739$	−3.96135	+	12.1918i	−0.145721	+	0.448482i	−0.997103	−	0.0760635i	$-0.975765\pi$
$739$	−3.96135	+	12.1918i	−0.145721	+	0.448482i	0.851382	+	0.524546i	$0.175765\pi$
$740$	20.6196	−	14.9810i	0.757993	−	0.550714i
$741$	−2.63761	−	1.91633i	−0.0968949	−	0.0703983i
$742$	−0.918097	−	2.82561i	−0.0337044	−	0.103731i
$743$	2.00295	+	6.16444i	0.0734810	+	0.226151i	0.981051	−	0.193749i	$-0.0620649\pi$
$743$	2.00295	+	6.16444i	0.0734810	+	0.226151i	−0.907570	+	0.419901i	$0.862065\pi$
$744$	1.37551	+	0.999369i	0.0504288	+	0.0366387i
$745$	−35.3681	+	25.6965i	−1.29579	+	0.941446i
$746$	−0.131835	+	0.405746i	−0.00482681	+	0.0148554i
$747$	9.35518			0.342288
$748$	24.6412	+	7.95708i	0.900972	+	0.290940i
$749$	2.82699			0.103296
$750$	11.3469	−	34.9220i	0.414329	−	1.27517i
$751$	35.5608	−	25.8365i	1.29763	−	0.942786i	0.297704	−	0.954658i	$-0.403779\pi$
$751$	35.5608	−	25.8365i	1.29763	−	0.942786i	0.999930	+	0.0118725i	$0.00377921\pi$
$752$	0.0345115	+	0.0250741i	0.00125850	+	0.000914357i
$753$	−3.50510	−	10.7876i	−0.127733	−	0.393122i
$754$	−6.41517	−	19.7438i	−0.233627	−	0.719029i
$755$	1.92341	+	1.39744i	0.0700002	+	0.0508581i
$756$	−1.53250	+	1.11343i	−0.0557365	+	0.0404949i
$757$	6.96262	−	21.4287i	0.253061	−	0.778841i	−0.741145	−	0.671345i	$-0.765717\pi$
$757$	6.96262	−	21.4287i	0.253061	−	0.778841i	0.994206	−	0.107496i	$-0.0342832\pi$
$758$	7.69212			0.279390
$759$	−18.6824	−	25.6164i	−0.678129	−	0.929817i
$760$	−4.16480			−0.151073
$761$	−3.75602	+	11.5598i	−0.136156	+	0.419044i	−0.995768	−	0.0919030i	$-0.970705\pi$
$761$	−3.75602	+	11.5598i	−0.136156	+	0.419044i	0.859612	+	0.510947i	$0.170705\pi$
$762$	−12.7119	+	9.23573i	−0.460503	+	0.334575i
$763$	−3.45455	−	2.50987i	−0.125063	−	0.0908636i
$764$	−8.24753	−	25.3833i	−0.298385	−	0.918335i
$765$	15.6686	+	48.2231i	0.566500	+	1.74351i
$766$	22.7046	+	16.4959i	0.820350	+	0.596019i
$767$	13.7801	−	10.0118i	0.497571	−	0.361506i
$768$	0.370901	−	1.14152i	0.0133837	−	0.0411909i
$769$	31.1071			1.12175			0.560876	−	0.827900i	$-0.310465\pi$
$769$	31.1071			1.12175			0.560876	+	0.827900i	$0.310465\pi$
$770$	−2.80340	+	3.87329i	−0.101028	+	0.139584i
$771$	6.36680			0.229295
$772$	−1.85808	+	5.71857i	−0.0668737	+	0.205816i
$773$	20.5055	−	14.8981i	0.737531	−	0.535848i	−0.154406	−	0.988008i	$-0.549346\pi$
$773$	20.5055	−	14.8981i	0.737531	−	0.535848i	0.891937	+	0.452160i	$0.149346\pi$
$774$	−1.52704	−	1.10946i	−0.0548885	−	0.0398788i
$775$	5.40410	+	16.6321i	0.194121	+	0.597444i
$776$	−2.57651	−	7.92969i	−0.0924915	−	0.284659i
$777$	2.05695	+	1.49447i	0.0737928	+	0.0536136i
$778$	−2.19164	+	1.59232i	−0.0785740	+	0.0570873i
$779$	−2.06277	+	6.34856i	−0.0739065	+	0.227461i
$780$	13.5783			0.486182
$781$	−44.7717	+	14.6370i	−1.60206	+	0.523752i
$782$	−62.1822			−2.22363
$783$	12.9245	−	39.7774i	0.461882	−	1.42153i
$784$	5.56618	−	4.04407i	0.198792	−	0.144431i
$785$	−51.0628	−	37.0993i	−1.82251	−	1.32413i
$786$	0.0413611	+	0.127296i	0.00147530	+	0.00454051i
$787$	11.5258	+	35.4727i	0.410849	+	1.26446i	0.915911	+	0.401381i	$0.131470\pi$
$787$	11.5258	+	35.4727i	0.410849	+	1.26446i	−0.505062	+	0.863083i	$0.668530\pi$
$788$	−5.24569	−	3.81121i	−0.186870	−	0.135769i
$789$	−10.8726	+	7.89942i	−0.387075	+	0.281227i
$790$	−16.4691	+	50.6868i	−0.585945	+	1.80335i
$791$	−3.84158			−0.136591
$792$	−4.91582	+	1.60710i	−0.174676	+	0.0571059i
$793$	−1.22375			−0.0434565
$794$	7.38748	−	22.7363i	0.262172	−	0.806882i
$795$	−34.7113	+	25.2193i	−1.23108	+	0.894435i
$796$	18.5854	+	13.5031i	0.658743	+	0.478605i
$797$	−5.55547	−	17.0980i	−0.196785	−	0.605642i	−0.999951	−	0.00988661i	$-0.996853\pi$
$797$	−5.55547	−	17.0980i	−0.196785	−	0.605642i	0.803166	−	0.595755i	$-0.203147\pi$
$798$	−0.128387	−	0.395134i	−0.00454484	−	0.0139876i
$799$	0.269444	+	0.195762i	0.00953224	+	0.00692558i
$800$	9.98775	−	7.25652i	0.353120	−	0.256557i
$801$	1.83857	−	5.65853i	0.0649626	−	0.199934i
$802$	−1.93585			−0.0683573
$803$	−27.5095	+	38.0082i	−0.970788	+	1.34128i
$804$	1.14351			0.0403283
$805$	3.54813	−	10.9200i	0.125055	−	0.384880i
$806$	−3.11290	+	2.26166i	−0.109647	+	0.0796635i
$807$	10.3999	+	7.55596i	0.366093	+	0.265982i
$808$	1.66251	+	5.11668i	0.0584869	+	0.180004i
$809$	−9.11535	−	28.0542i	−0.320479	−	0.986332i	−0.973440	−	0.228941i	$-0.926474\pi$
$809$	−9.11535	−	28.0542i	−0.320479	−	0.986332i	0.652962	−	0.757391i	$-0.273526\pi$
$810$	6.36896	+	4.62732i	0.223782	+	0.162587i
$811$	−14.3277	+	10.4096i	−0.503112	+	0.365532i	−0.810204	−	0.586147i	$-0.800644\pi$
$811$	−14.3277	+	10.4096i	−0.503112	+	0.365532i	0.307092	+	0.951680i	$0.400644\pi$
$812$	0.817510	−	2.51604i	0.0286890	−	0.0882956i
$813$	6.55232			0.229800
$814$	11.9598	+	16.3987i	0.419192	+	0.574775i
$815$	−1.18977			−0.0416758
$816$	2.89576	−	8.91224i	0.101372	−	0.311991i
$817$	0.979268	−	0.711480i	0.0342603	−	0.0248915i
$818$	−0.952671	−	0.692156i	−0.0333094	−	0.0242007i
$819$	−0.453076	−	1.39442i	−0.0158317	−	0.0487251i
$820$	−8.59102	−	26.4405i	−0.300012	−	0.923341i
$821$	0.406789	+	0.295549i	0.0141970	+	0.0103147i	0.594861	−	0.803828i	$-0.297207\pi$
$821$	0.406789	+	0.295549i	0.0141970	+	0.0103147i	−0.580664	+	0.814143i	$0.697207\pi$
$822$	11.6706	−	8.47917i	0.407058	−	0.295745i
$823$	0.572100	−	1.76074i	0.0199422	−	0.0613757i	−0.940590	−	0.339544i	$-0.889727\pi$
$823$	0.572100	−	1.76074i	0.0199422	−	0.0613757i	0.960532	+	0.278168i	$0.0897273\pi$
$824$	1.85546			0.0646381
$825$	46.7674	+	15.1020i	1.62823	+	0.525784i
$826$	2.17060			0.0755249
$827$	9.77923	−	30.0974i	0.340057	−	1.04659i	−0.624120	−	0.781329i	$-0.714542\pi$
$827$	9.77923	−	30.0974i	0.340057	−	1.04659i	0.964177	−	0.265260i	$-0.0854577\pi$
$828$	10.0478	−	7.30012i	0.349184	−	0.253697i
$829$	−41.6008	−	30.2247i	−1.44485	−	1.04975i	−0.987000	−	0.160721i	$-0.948618\pi$
$829$	−41.6008	−	30.2247i	−1.44485	−	1.04975i	−0.457854	−	0.889027i	$-0.651382\pi$
$830$	−7.72109	−	23.7631i	−0.268003	−	0.824828i
$831$	3.81992	+	11.7565i	0.132512	+	0.407829i
$832$	2.19753	+	1.59660i	0.0761855	+	0.0553520i
$833$	43.4572	−	31.5735i	1.50570	−	1.09396i
$834$	1.08894	−	3.35141i	0.0377069	−	0.116050i
$835$	−68.2859			−2.36313
$836$	−0.00601040	−	3.31662i	−0.000207874	−	0.114708i
$837$	−7.75198			−0.267947
$838$	1.18703	−	3.65330i	0.0410053	−	0.126201i
$839$	31.5476	−	22.9207i	1.08914	−	0.791310i	0.109890	−	0.993944i	$-0.464950\pi$
$839$	31.5476	−	22.9207i	1.08914	−	0.791310i	0.979255	+	0.202634i	$0.0649501\pi$
$840$	1.39987	+	1.01707i	0.0483003	+	0.0350922i
$841$	9.08863	+	27.9719i	0.313401	+	0.964549i
$842$	−1.44243	−	4.43934i	−0.0497094	−	0.152990i
$843$	−18.2705	−	13.2743i	−0.629268	−	0.457190i
$844$	13.6711	−	9.93264i	0.470579	−	0.341896i
$845$	7.23516	−	22.2675i	0.248897	−	0.766026i
$846$	−0.0665206			−0.00228703
$847$	−3.08853	−	2.22689i	−0.106123	−	0.0765168i
$848$	−8.58310			−0.294745
$849$	−11.8714	+	36.5363i	−0.407424	+	1.25392i
$850$	77.9780	−	56.6543i	2.67462	−	1.94323i
$851$	−39.4320	−	28.6490i	−1.35171	−	0.982075i
$852$	5.26764	+	16.2121i	0.180466	+	0.555418i
$853$	1.65583	+	5.09612i	0.0566945	+	0.174488i	0.975394	−	0.220470i	$-0.0707592\pi$
$853$	1.65583	+	5.09612i	0.0566945	+	0.174488i	−0.918699	+	0.394958i	$0.870759\pi$
$854$	−0.126164	−	0.0916633i	−0.00431723	−	0.00313665i
$855$	5.25414	−	3.81735i	0.179688	−	0.130551i
$856$	2.52374	−	7.76728i	0.0862598	−	0.265480i
$857$	−40.5766			−1.38607			−0.693035	−	0.720904i	$-0.743727\pi$
$857$	−40.5766			−1.38607			−0.693035	+	0.720904i	$0.743727\pi$
$858$	0.0195955	+	10.8130i	0.000668979	+	0.369151i
$859$	44.1951			1.50792			0.753959	−	0.656922i	$-0.228142\pi$
$859$	44.1951			1.50792			0.753959	+	0.656922i	$0.228142\pi$
$860$	−1.55783	+	4.79451i	−0.0531216	+	0.163491i
$861$	2.24370	−	1.63014i	0.0764650	−	0.0555551i
$862$	7.63206	+	5.54501i	0.259949	+	0.188864i
$863$	−5.84767	−	17.9973i	−0.199057	−	0.612635i	−0.999905	−	0.0137672i	$-0.995618\pi$
$863$	−5.84767	−	17.9973i	−0.199057	−	0.612635i	0.800848	−	0.598867i	$-0.204382\pi$
$864$	1.69108	+	5.20460i	0.0575316	+	0.177064i
$865$	−10.1936	−	7.40611i	−0.346594	−	0.251815i
$866$	2.69835	−	1.96047i	0.0916938	−	0.0666194i
$867$	16.3030	−	50.1753i	0.553677	−	1.70404i
$868$	−0.490336			−0.0166431
$869$	−40.3880	−	13.0420i	−1.37007	−	0.442419i
$870$	−38.2049			−1.29527
$871$	−0.799690	+	2.46119i	−0.0270964	+	0.0833943i
$872$	−9.97997	+	7.25087i	−0.337964	+	0.245545i
$873$	10.5186	+	7.64221i	0.356000	+	0.258649i
$874$	2.46118	+	7.57474i	0.0832507	+	0.256219i
$875$	3.27236	+	10.0713i	0.110626	+	0.340472i
$876$	13.7368	+	9.98038i	0.464124	+	0.337206i
$877$	−4.36869	+	3.17404i	−0.147520	+	0.107180i	−0.659097	−	0.752058i	$-0.729061\pi$
$877$	−4.36869	+	3.17404i	−0.147520	+	0.107180i	0.511577	+	0.859237i	$0.329061\pi$
$878$	2.43108	−	7.48210i	0.0820451	−	0.252509i
$879$	−8.20031			−0.276590
$880$	8.13936	+	11.1603i	0.274378	+	0.376213i
$881$	−18.4155			−0.620435			−0.310218	−	0.950666i	$-0.600402\pi$
$881$	−18.4155			−0.620435			−0.310218	+	0.950666i	$0.600402\pi$
$882$	−3.31537	+	10.2037i	−0.111634	+	0.343575i
$883$	8.23790	−	5.98518i	0.277227	−	0.201417i	−0.440480	−	0.897763i	$-0.645192\pi$
$883$	8.23790	−	5.98518i	0.277227	−	0.201417i	0.717707	+	0.696345i	$0.245192\pi$
$884$	17.1569	+	12.4652i	0.577049	+	0.419251i
$885$	−9.68657	−	29.8122i	−0.325611	−	1.00213i
$886$	−4.35689	−	13.4091i	−0.146372	−	0.450488i
$887$	14.2626	+	10.3624i	0.478890	+	0.347934i	0.800896	−	0.598804i	$-0.204357\pi$
$887$	14.2626	+	10.3624i	0.478890	+	0.347934i	−0.322006	+	0.946738i	$0.604357\pi$
$888$	5.94241	−	4.31742i	0.199414	−	0.144883i
$889$	1.40030	−	4.30968i	0.0469646	−	0.144542i
$890$	−15.8906			−0.532655
$891$	−3.67575	+	5.07857i	−0.123142	+	0.170139i
$892$	−12.9013			−0.431969
$893$	0.0131822	−	0.0405707i	0.000441126	−	0.00135765i
$894$	−10.1928	+	7.40552i	−0.340899	+	0.247678i
$895$	−42.5929	−	30.9456i	−1.42372	−	1.03440i
$896$	0.106966	+	0.329206i	0.00357347	+	0.0109980i
$897$	−8.02410	−	24.6956i	−0.267917	−	0.824563i
$898$	2.72852	+	1.98239i	0.0910519	+	0.0661531i
$899$	8.75867	−	6.36354i	0.292118	−	0.212236i
$900$	−5.94898	+	18.3091i	−0.198299	+	0.610302i
$901$	−67.0114			−2.23247
$902$	21.0434	−	6.87958i	0.700667	−	0.229065i
$903$	−0.502900			−0.0167355
$904$	−3.42950	+	10.5549i	−0.114063	+	0.351051i
$905$	46.9591	−	34.1178i	1.56097	−	1.13411i
$906$	0.554313	+	0.402732i	0.0184158	+	0.0133799i
$907$	−17.9020	−	55.0967i	−0.594426	−	1.82945i	−0.557564	−	0.830134i	$-0.688264\pi$
$907$	−17.9020	−	55.0967i	−0.594426	−	1.82945i	−0.0368620	−	0.999320i	$-0.511736\pi$
$908$	4.12390	+	12.6921i	0.136857	+	0.421201i
$909$	−6.78718	−	4.93117i	−0.225116	−	0.163557i
$910$	−3.16804	+	2.30171i	−0.105019	+	0.0763010i
$911$	−8.40778	+	25.8765i	−0.278562	+	0.857327i	0.709692	+	0.704512i	$0.248834\pi$
$911$	−8.40778	+	25.8765i	−0.278562	+	0.857327i	−0.988255	+	0.152815i	$0.951166\pi$
$912$	−1.20026			−0.0397446
$913$	18.9125	−	6.18295i	0.625911	−	0.204626i
$914$	24.3376			0.805016
$915$	−0.695932	+	2.14186i	−0.0230068	+	0.0708077i
$916$	−13.0754	+	9.49982i	−0.432023	+	0.313883i
$917$	−0.0312286	−	0.0226889i	−0.00103126	−	0.000749255i
$918$	13.2029	+	40.6342i	0.435759	+	1.34113i
$919$	−1.70005	−	5.23223i	−0.0560796	−	0.172595i	0.919093	−	0.394040i	$-0.128923\pi$
$919$	−1.70005	−	5.23223i	−0.0560796	−	0.172595i	−0.975173	+	0.221445i	$0.928923\pi$
$920$	−26.8357	−	19.4973i	−0.884747	−	0.642806i
$921$	−31.2112	+	22.6763i	−1.02844	+	0.747208i
$922$	−3.63539	+	11.1886i	−0.119725	+	0.368477i
$923$	−38.5775			−1.26980
$924$	−0.807918	+	1.11625i	−0.0265786	+	0.0367220i
$925$	75.5508			2.48410
$926$	4.26223	−	13.1178i	0.140066	−	0.431078i
$927$	−2.34077	+	1.70067i	−0.0768811	+	0.0558574i
$928$	−6.18310	−	4.49229i	−0.202970	−	0.147467i
$929$	11.4182	+	35.1416i	0.374619	+	1.15296i	0.943735	+	0.330701i	$0.107285\pi$
$929$	11.4182	+	35.1416i	0.374619	+	1.15296i	−0.569117	+	0.822257i	$0.692715\pi$
$930$	2.18818	+	6.73453i	0.0717533	+	0.220834i
$931$	−5.56618	−	4.04407i	−0.182424	−	0.132539i
$932$	−3.14115	+	2.28218i	−0.102892	+	0.0747551i
$933$	−9.81740	+	30.2148i	−0.321407	+	0.989190i
$934$	−14.0883			−0.460983
$935$	63.5469	+	87.1324i	2.07821	+	2.84953i
$936$	−4.23571			−0.138449
$937$	13.4908	−	41.5203i	0.440724	−	1.35641i	−0.446381	−	0.894843i	$-0.647287\pi$
$937$	13.4908	−	41.5203i	0.440724	−	1.35641i	0.887105	−	0.461567i	$-0.152713\pi$
$938$	−0.266798	+	0.193840i	−0.00871125	+	0.00632910i
$939$	−11.9154	−	8.65701i	−0.388843	−	0.282511i
$940$	0.0549013	+	0.168969i	0.00179068	+	0.00551115i
$941$	6.42068	+	19.7608i	0.209308	+	0.644184i	0.999509	+	0.0313360i	$0.00997619\pi$
$941$	6.42068	+	19.7608i	0.209308	+	0.644184i	−0.790201	+	0.612848i	$0.790024\pi$
$942$	−14.7159	−	10.6917i	−0.479469	−	0.348355i
$943$	−43.0118	+	31.2499i	−1.40066	+	1.01764i
$944$	1.93776	−	5.96382i	0.0630688	−	0.194106i
$945$	−7.88927			−0.256638
$946$	−3.82034	−	1.23365i	−0.124210	−	0.0401095i
$947$	53.1819			1.72818			0.864090	−	0.503338i	$-0.167895\pi$
$947$	53.1819			1.72818			0.864090	+	0.503338i	$0.167895\pi$
$948$	−4.74627	+	14.6075i	−0.154152	+	0.474430i
$949$	−31.0876	+	22.5864i	−1.00915	+	0.733187i
$950$	−9.98775	−	7.25652i	−0.324045	−	0.235433i
$951$	−0.226731	−	0.697806i	−0.00735225	−	0.0226279i
$952$	0.835120	+	2.57023i	0.0270664	+	0.0833018i
$953$	0.667926	+	0.485277i	0.0216363	+	0.0157197i	0.598551	−	0.801085i	$-0.295743\pi$
$953$	0.667926	+	0.485277i	0.0216363	+	0.0157197i	−0.576915	+	0.816804i	$0.695743\pi$
$954$	10.8281	−	7.86706i	0.350572	−	0.254706i
$955$	34.3493	−	105.716i	1.11152	−	3.42090i
$956$	−12.2864			−0.397372
$957$	−0.0551351	−	30.4243i	−0.00178227	−	0.983477i
$958$	13.0309			0.421008
$959$	−1.28559	+	3.95664i	−0.0415139	+	0.127767i
$960$	4.04415	−	2.93825i	0.130524	−	0.0948315i
$961$	23.4561	+	17.0419i	0.756650	+	0.549738i
$962$	5.13675	+	15.8093i	0.165615	+	0.509712i
$963$	3.93546	+	12.1121i	0.126818	+	0.390307i
$964$	15.1908	+	11.0368i	0.489263	+	0.355471i
$965$	−20.2597	+	14.7195i	−0.652183	+	0.473839i
$966$	1.02254	−	3.14706i	0.0328998	−	0.101255i
$967$	8.88350			0.285674			0.142837	−	0.989746i	$-0.454378\pi$
$967$	8.88350			0.285674			0.142837	+	0.989746i	$0.454378\pi$
$968$	−8.87569	+	6.49785i	−0.285276	+	0.208849i
$969$	−9.37088			−0.301036
$970$	10.7307	−	33.0256i	0.344541	−	1.06039i
$971$	−22.4303	+	16.2966i	−0.719823	+	0.522982i	−0.886328	−	0.463059i	$-0.846752\pi$
$971$	−22.4303	+	16.2966i	−0.719823	+	0.522982i	0.166505	+	0.986041i	$0.446752\pi$
$972$	−11.4464	−	8.31630i	−0.367144	−	0.266745i
$973$	0.314044	+	0.966528i	0.0100678	+	0.0309855i
$974$	3.72195	+	11.4550i	0.119259	+	0.367041i
$975$	32.5627	+	23.6582i	1.04284	+	0.757668i
$976$	−0.364479	+	0.264809i	−0.0116667	+	0.00847634i
$977$	7.53976	−	23.2050i	0.241218	−	0.742393i	−0.755017	−	0.655705i	$-0.772372\pi$
$977$	7.53976	−	23.2050i	0.241218	−	0.742393i	0.996235	−	0.0866883i	$-0.0276284\pi$
$978$	−0.342882			−0.0109642
$979$	−0.0229325	−	12.6544i	−0.000732925	−	0.404437i
$980$	28.6546			0.915336
$981$	5.94434	−	18.2948i	0.189788	−	0.584108i
$982$	−7.01639	+	5.09771i	−0.223902	+	0.162674i
$983$	29.4709	+	21.4119i	0.939976	+	0.682933i	0.948415	−	0.317032i	$-0.102686\pi$
$983$	29.4709	+	21.4119i	0.939976	+	0.682933i	−0.00843886	+	0.999964i	$0.502686\pi$
$984$	−2.47586	−	7.61993i	−0.0789277	−	0.242914i
$985$	−8.34489	−	25.6829i	−0.265890	−	0.818327i
$986$	−48.2738	−	35.0729i	−1.53735	−	1.11695i
$987$	−0.0143384	+	0.0104175i	−0.000456397	+	0.000331592i
$988$	0.839381	−	2.58335i	0.0267043	−	0.0821873i
$989$	9.64063			0.306554
$990$	−20.4975	−	6.61901i	−0.651454	−	0.210366i
$991$	39.3576			1.25023			0.625117	−	0.780531i	$-0.285051\pi$
$991$	39.3576			1.25023			0.625117	+	0.780531i	$0.285051\pi$
$992$	−0.437738	+	1.34722i	−0.0138982	+	0.0427742i
$993$	23.0838	−	16.7714i	0.732543	−	0.532224i
$994$	−3.97720	−	2.88960i	−0.126149	−	0.0916527i
$995$	29.5659	+	90.9945i	0.937302	+	2.88472i
$996$	−2.22516	−	6.84832i	−0.0705067	−	0.216997i
$997$	44.8485	+	32.5844i	1.42037	+	1.03196i	0.991711	+	0.128489i	$0.0410128\pi$
$997$	44.8485	+	32.5844i	1.42037	+	1.03196i	0.428656	+	0.903468i	$0.358987\pi$
$998$	13.3679	−	9.71234i	0.423153	−	0.307439i
$999$	−10.3489	+	31.8505i	−0.327424	+	1.00771i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.h.229.3	yes	20
11.4	even	5		4598.2.a.cc.1.6		10
11.5	even	5	inner	418.2.f.h.115.3	✓	20
11.7	odd	10		4598.2.a.cd.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.115.3	✓	20	11.5	even	5	inner
418.2.f.h.229.3	yes	20	1.1	even	1	trivial
4598.2.a.cc.1.6		10	11.4	even	5
4598.2.a.cd.1.6		10	11.7	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.971032 + 0.705496i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.28699 - 3.96096i) q^{5} +(-0.370901 - 1.14152i) q^{6} +(0.280040 + 0.203461i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.481873 + 1.48305i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.971032 + 0.705496i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-1.28699 - 3.96096i) q^{5} +(-0.370901 - 1.14152i) q^{6} +(0.280040 + 0.203461i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.481873 + 1.48305i) q^{9} +4.16480 q^{10} +(0.00601040 + 3.31662i) q^{11} +1.20026 q^{12} +(-0.839381 + 2.58335i) q^{13} +(-0.280040 + 0.203461i) q^{14} +(4.04415 + 2.93825i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.41261 + 7.42525i) q^{17} +(-1.26156 - 0.916576i) q^{18} +(0.809017 - 0.587785i) q^{19} +(-1.28699 + 3.96096i) q^{20} -0.415468 q^{21} +(-3.15615 - 1.01918i) q^{22} +7.96455 q^{23} +(-0.370901 + 1.14152i) q^{24} +(-9.98775 + 7.25652i) q^{25} +(-2.19753 - 1.59660i) q^{26} +(-1.69108 - 5.20460i) q^{27} +(-0.106966 - 0.329206i) q^{28} +(6.18310 + 4.49229i) q^{29} +(-4.04415 + 2.93825i) q^{30} +(0.437738 - 1.34722i) q^{31} -1.00000 q^{32} +(-2.34570 - 3.21630i) q^{33} -7.80737 q^{34} +(0.445490 - 1.37108i) q^{35} +(1.26156 - 0.916576i) q^{36} +(-4.95093 - 3.59706i) q^{37} +(0.309017 + 0.951057i) q^{38} +(-1.00748 - 3.10069i) q^{39} +(-3.36939 - 2.44801i) q^{40} +(-5.40041 + 3.92362i) q^{41} +(0.128387 - 0.395134i) q^{42} +1.21044 q^{43} +(1.94460 - 2.68673i) q^{44} +6.49447 q^{45} +(-2.46118 + 7.57474i) q^{46} +(0.0345115 - 0.0250741i) q^{47} +(-0.971032 - 0.705496i) q^{48} +(-2.12609 - 6.54344i) q^{49} +(-3.81498 - 11.7413i) q^{50} +(-7.58120 - 5.50807i) q^{51} +(2.19753 - 1.59660i) q^{52} +(-2.65232 + 8.16301i) q^{53} +5.47244 q^{54} +(13.1293 - 4.29227i) q^{55} +0.346148 q^{56} +(-0.370901 + 1.14152i) q^{57} +(-6.18310 + 4.49229i) q^{58} +(-5.07313 - 3.68584i) q^{59} +(-1.54473 - 4.75418i) q^{60} +(0.139219 + 0.428471i) q^{61} +(1.14601 + 0.832626i) q^{62} +(-0.436686 + 0.317271i) q^{63} +(0.309017 - 0.951057i) q^{64} +11.3128 q^{65} +(3.78375 - 1.23700i) q^{66} +0.952714 q^{67} +(2.41261 - 7.42525i) q^{68} +(-7.73384 + 5.61896i) q^{69} +(1.16631 + 0.847373i) q^{70} +(4.38874 + 13.5072i) q^{71} +(0.481873 + 1.48305i) q^{72} +(11.4448 + 8.31517i) q^{73} +(4.95093 - 3.59706i) q^{74} +(4.57897 - 14.0926i) q^{75} -1.00000 q^{76} +(-0.673119 + 0.930008i) q^{77} +3.26026 q^{78} +(-3.95436 + 12.1703i) q^{79} +(3.36939 - 2.44801i) q^{80} +(1.52924 + 1.11105i) q^{81} +(-2.06277 - 6.34856i) q^{82} +(-1.85389 - 5.70569i) q^{83} +(0.336121 + 0.244206i) q^{84} +(26.3061 - 19.1125i) q^{85} +(-0.374047 + 1.15120i) q^{86} -9.17328 q^{87} +(1.95432 + 2.67967i) q^{88} -3.81546 q^{89} +(-2.00690 + 6.17661i) q^{90} +(-0.760670 + 0.552659i) q^{91} +(-6.44346 - 4.68145i) q^{92} +(0.525400 + 1.61701i) q^{93} +(0.0131822 + 0.0405707i) q^{94} +(-3.36939 - 2.44801i) q^{95} +(0.971032 - 0.705496i) q^{96} +(2.57651 - 7.92969i) q^{97} +6.88018 q^{98} +(-4.92161 - 1.58927i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} - q^{3} - 5 q^{4} - q^{5} + q^{6} + 13 q^{7} + 5 q^{8} - 6 q^{9} + 6 q^{10} + q^{11} + 4 q^{12} - 2 q^{13} - 13 q^{14} - 8 q^{15} - 5 q^{16} + 11 q^{17} + 6 q^{18} + 5 q^{19} - q^{20} + 2 q^{21} + 4 q^{22} + 28 q^{23} + q^{24} - 30 q^{25} - 13 q^{26} - 31 q^{27} - 2 q^{28} + 28 q^{29} + 8 q^{30} - q^{31} - 20 q^{32} + 9 q^{33} + 24 q^{34} - 11 q^{35} - 6 q^{36} + 8 q^{37} - 5 q^{38} + 18 q^{39} - 4 q^{40} - 5 q^{41} - 22 q^{42} - 44 q^{43} + 11 q^{44} - 4 q^{45} + 7 q^{46} - 39 q^{47} - q^{48} + 4 q^{49} - 25 q^{50} - 11 q^{51} + 13 q^{52} - q^{53} - 4 q^{54} + 8 q^{55} + 22 q^{56} + q^{57} - 28 q^{58} + 6 q^{59} + 7 q^{60} + 10 q^{61} + 11 q^{62} + 34 q^{63} - 5 q^{64} - 8 q^{65} + 41 q^{66} + 18 q^{67} + 11 q^{68} - 63 q^{69} + q^{70} - 3 q^{71} + 6 q^{72} + 5 q^{73} - 8 q^{74} + 5 q^{75} - 20 q^{76} + 36 q^{77} + 22 q^{78} + 19 q^{79} + 4 q^{80} + 63 q^{81} - 9 q^{83} - 23 q^{84} + 30 q^{85} - 26 q^{86} - 16 q^{87} - q^{88} + 44 q^{89} + 14 q^{90} - 68 q^{91} - 7 q^{92} + 27 q^{93} - 31 q^{94} - 4 q^{95} + q^{96} - 71 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 - q^3 - 5 * q^4 - q^5 + q^6 + 13 * q^7 + 5 * q^8 - 6 * q^9 + 6 * q^10 + q^11 + 4 * q^12 - 2 * q^13 - 13 * q^14 - 8 * q^15 - 5 * q^16 + 11 * q^17 + 6 * q^18 + 5 * q^19 - q^20 + 2 * q^21 + 4 * q^22 + 28 * q^23 + q^24 - 30 * q^25 - 13 * q^26 - 31 * q^27 - 2 * q^28 + 28 * q^29 + 8 * q^30 - q^31 - 20 * q^32 + 9 * q^33 + 24 * q^34 - 11 * q^35 - 6 * q^36 + 8 * q^37 - 5 * q^38 + 18 * q^39 - 4 * q^40 - 5 * q^41 - 22 * q^42 - 44 * q^43 + 11 * q^44 - 4 * q^45 + 7 * q^46 - 39 * q^47 - q^48 + 4 * q^49 - 25 * q^50 - 11 * q^51 + 13 * q^52 - q^53 - 4 * q^54 + 8 * q^55 + 22 * q^56 + q^57 - 28 * q^58 + 6 * q^59 + 7 * q^60 + 10 * q^61 + 11 * q^62 + 34 * q^63 - 5 * q^64 - 8 * q^65 + 41 * q^66 + 18 * q^67 + 11 * q^68 - 63 * q^69 + q^70 - 3 * q^71 + 6 * q^72 + 5 * q^73 - 8 * q^74 + 5 * q^75 - 20 * q^76 + 36 * q^77 + 22 * q^78 + 19 * q^79 + 4 * q^80 + 63 * q^81 - 9 * q^83 - 23 * q^84 + 30 * q^85 - 26 * q^86 - 16 * q^87 - q^88 + 44 * q^89 + 14 * q^90 - 68 * q^91 - 7 * q^92 + 27 * q^93 - 31 * q^94 - 4 * q^95 + q^96 - 71 * q^97 + 6 * q^98 + 20 * q^99

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