LMFDB - Embedded newform 370.2.ba.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(17,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([9, 7]))

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

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

chi := DirichletCharacter("370.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.ba (of order $36$, degree $12$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$9$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	370.17
Dual form			370.2.ba.a.283.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(-2.53220 + 1.77306i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.871338 - 2.05931i) q^{5} +(-2.18584 - 2.18584i) q^{6} +(-0.146400 - 1.67336i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.24221 - 6.16042i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(-2.53220 + 1.77306i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.871338 - 2.05931i) q^{5} +(-2.18584 - 2.18584i) q^{6} +(-0.146400 - 1.67336i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.24221 - 6.16042i) q^{9} +(2.17933 + 0.500504i) q^{10} +(1.57628 - 0.910064i) q^{11} +(1.77306 - 2.53220i) q^{12} +(0.388334 - 0.141342i) q^{13} +(1.62251 - 0.434751i) q^{14} +(1.44489 + 6.75953i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.781019 - 2.14583i) q^{17} +(6.45619 + 1.13840i) q^{18} +(0.0141789 + 0.0202495i) q^{19} +(-0.114463 + 2.23314i) q^{20} +(3.33768 + 3.97770i) q^{21} +(1.16996 + 1.39430i) q^{22} +(-3.22036 + 5.57783i) q^{23} +(2.80162 + 1.30642i) q^{24} +(-3.48154 - 3.58871i) q^{25} +(0.206628 + 0.357891i) q^{26} +(2.84489 + 10.6173i) q^{27} +(0.709893 + 1.52237i) q^{28} +(1.43544 - 5.35715i) q^{29} +(-6.40593 + 2.59672i) q^{30} +(7.07748 - 7.07748i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-2.37785 + 5.09931i) q^{33} +(2.24886 + 0.396534i) q^{34} +(-3.57353 - 1.15658i) q^{35} +6.55579i q^{36} +(5.43589 + 2.72968i) q^{37} +(-0.0174798 + 0.0174798i) q^{38} +(-0.732730 + 1.04645i) q^{39} +(-2.21909 + 0.275056i) q^{40} +(-2.43898 - 6.70104i) q^{41} +(-3.33768 + 3.97770i) q^{42} -3.99954 q^{43} +(-1.16996 + 1.39430i) q^{44} +(-10.7325 - 9.98522i) q^{45} +(-6.05230 - 2.20286i) q^{46} +(12.2686 - 3.28735i) q^{47} +(-0.800073 + 2.98591i) q^{48} +(4.11496 - 0.725579i) q^{49} +(2.92963 - 4.05182i) q^{50} +(1.82700 + 6.81847i) q^{51} +(-0.316573 + 0.265636i) q^{52} +(0.723956 - 8.27486i) q^{53} +(-9.96195 + 4.64533i) q^{54} +(-0.500637 - 4.03902i) q^{55} +(-1.37597 + 0.963465i) q^{56} +(-0.0718074 - 0.0261358i) q^{57} +(5.52503 + 0.483377i) q^{58} +(-0.186306 + 2.12949i) q^{59} +(-3.66965 - 5.85769i) q^{60} +(-3.44856 + 7.39546i) q^{61} +(8.19894 + 5.74096i) q^{62} +(-10.6368 - 2.85014i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0473026 - 0.922858i) q^{65} +(-5.43474 - 1.45624i) q^{66} +(-11.5392 + 1.00955i) q^{67} +2.28355i q^{68} +(-1.73526 - 19.8341i) q^{69} +(0.518468 - 3.72008i) q^{70} +(1.09003 - 6.18185i) q^{71} +(-6.45619 + 1.13840i) q^{72} +(-4.95515 - 4.95515i) q^{73} +(-1.74428 + 5.82731i) q^{74} +(15.1790 + 2.91434i) q^{75} +(-0.0202495 - 0.0141789i) q^{76} +(-1.75363 - 2.50444i) q^{77} +(-1.15779 - 0.539885i) q^{78} +(-13.9435 + 1.21990i) q^{79} +(-0.656218 - 2.13761i) q^{80} +(-10.9628 - 9.19891i) q^{81} +(6.17571 - 3.56555i) q^{82} +(-4.78373 + 2.23069i) q^{83} +(-4.49685 - 2.59626i) q^{84} +(-3.73841 - 3.47811i) q^{85} +(-0.694513 - 3.93878i) q^{86} +(5.86375 + 16.1105i) q^{87} +(-1.57628 - 0.910064i) q^{88} +(-1.22019 - 0.106753i) q^{89} +(7.96984 - 12.3034i) q^{90} +(-0.293368 - 0.629129i) q^{91} +(1.11842 - 6.34288i) q^{92} +(-5.37275 + 30.4704i) q^{93} +(5.36782 + 11.5113i) q^{94} +(0.0540547 - 0.0115546i) q^{95} +(-3.07948 - 0.269420i) q^{96} +(-7.32860 - 4.23117i) q^{97} +(1.42911 + 3.92645i) q^{98} +(-2.07203 - 11.7511i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8}+O(q^{10}) $ 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8	$ 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8} - 12 q^{10} + 36 q^{11} - 6 q^{12} + 6 q^{13} + 12 q^{14} + 24 q^{15} + 12 q^{19} - 6 q^{20} - 42 q^{21} - 6 q^{22} - 6 q^{24} - 18 q^{25} - 6 q^{26} + 6 q^{27} - 12 q^{30} + 6 q^{33} - 54 q^{35} + 12 q^{37} + 48 q^{38} - 12 q^{40} + 48 q^{41} + 42 q^{42} + 6 q^{44} - 90 q^{45} + 6 q^{46} - 12 q^{47} - 12 q^{49} - 12 q^{50} - 12 q^{51} + 6 q^{52} + 36 q^{53} - 18 q^{54} + 36 q^{57} + 6 q^{58} + 24 q^{59} - 54 q^{60} - 36 q^{61} + 54 q^{62} - 96 q^{63} - 54 q^{64} - 18 q^{65} - 42 q^{67} - 96 q^{69} - 12 q^{70} - 48 q^{71} + 84 q^{73} + 42 q^{74} + 252 q^{75} - 6 q^{76} - 66 q^{77} - 24 q^{78} + 66 q^{79} + 6 q^{80} - 108 q^{81} + 36 q^{82} + 48 q^{83} - 36 q^{85} + 108 q^{87} - 36 q^{88} - 66 q^{89} + 6 q^{90} - 18 q^{91} - 12 q^{92} - 12 q^{93} + 18 q^{94} + 90 q^{95} + 12 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) $ 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8 - 12 * q^10 + 36 * q^11 - 6 * q^12 + 6 * q^13 + 12 * q^14 + 24 * q^15 + 12 * q^19 - 6 * q^20 - 42 * q^21 - 6 * q^22 - 6 * q^24 - 18 * q^25 - 6 * q^26 + 6 * q^27 - 12 * q^30 + 6 * q^33 - 54 * q^35 + 12 * q^37 + 48 * q^38 - 12 * q^40 + 48 * q^41 + 42 * q^42 + 6 * q^44 - 90 * q^45 + 6 * q^46 - 12 * q^47 - 12 * q^49 - 12 * q^50 - 12 * q^51 + 6 * q^52 + 36 * q^53 - 18 * q^54 + 36 * q^57 + 6 * q^58 + 24 * q^59 - 54 * q^60 - 36 * q^61 + 54 * q^62 - 96 * q^63 - 54 * q^64 - 18 * q^65 - 42 * q^67 - 96 * q^69 - 12 * q^70 - 48 * q^71 + 84 * q^73 + 42 * q^74 + 252 * q^75 - 6 * q^76 - 66 * q^77 - 24 * q^78 + 66 * q^79 + 6 * q^80 - 108 * q^81 + 36 * q^82 + 48 * q^83 - 36 * q^85 + 108 * q^87 - 36 * q^88 - 66 * q^89 + 6 * q^90 - 18 * q^91 - 12 * q^92 - 12 * q^93 + 18 * q^94 + 90 * q^95 + 12 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	−2.53220	+	1.77306i	−1.46197	+	1.02368i	−0.472119	+	0.881535i	$0.656511\pi$
$3$	−2.53220	+	1.77306i	−1.46197	+	1.02368i	−0.989846	+	0.142145i	$0.954600\pi$
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	0.871338	−	2.05931i	0.389674	−	0.920953i
$5$	0.871338	−	2.05931i	0.389674	−	0.920953i
$6$	−2.18584	−	2.18584i	−0.892365	−	0.892365i
$7$	−0.146400	−	1.67336i	−0.0553339	−	0.632470i	−0.972336	−	0.233587i	$-0.924954\pi$
$7$	−0.146400	−	1.67336i	−0.0553339	−	0.632470i	0.917002	−	0.398883i	$-0.130602\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.24221	−	6.16042i	0.747404	−	2.05347i
$10$	2.17933	+	0.500504i	0.689166	+	0.158273i
$11$	1.57628	−	0.910064i	0.475266	−	0.274395i	−0.243176	−	0.969982i	$-0.578189\pi$
$11$	1.57628	−	0.910064i	0.475266	−	0.274395i	0.718441	+	0.695588i	$0.244856\pi$
$12$	1.77306	−	2.53220i	0.511840	−	0.730983i
$13$	0.388334	−	0.141342i	0.107704	−	0.0392012i	−0.287606	−	0.957749i	$-0.592859\pi$
$13$	0.388334	−	0.141342i	0.107704	−	0.0392012i	0.395310	+	0.918548i	$0.370637\pi$
$14$	1.62251	−	0.434751i	0.433635	−	0.116192i
$15$	1.44489	+	6.75953i	0.373070	+	1.74530i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.781019	−	2.14583i	0.189425	−	0.520441i	−0.808231	−	0.588865i	$-0.799575\pi$
$17$	0.781019	−	2.14583i	0.189425	−	0.520441i	0.997656	+	0.0684242i	$0.0217971\pi$
$18$	6.45619	+	1.13840i	1.52174	+	0.268324i
$19$	0.0141789	+	0.0202495i	0.00325286	+	0.00464556i	0.820775	−	0.571251i	$-0.193542\pi$
$19$	0.0141789	+	0.0202495i	0.00325286	+	0.00464556i	−0.817522	+	0.575897i	$0.804653\pi$
$20$	−0.114463	+	2.23314i	−0.0255947	+	0.499344i
$21$	3.33768	+	3.97770i	0.728342	+	0.868005i
$22$	1.16996	+	1.39430i	0.249436	+	0.297266i
$23$	−3.22036	+	5.57783i	−0.671492	+	1.16306i	0.305989	+	0.952035i	$0.401013\pi$
$23$	−3.22036	+	5.57783i	−0.671492	+	1.16306i	−0.977481	+	0.211024i	$0.932320\pi$
$24$	2.80162	+	1.30642i	0.571878	+	0.266671i
$25$	−3.48154	−	3.58871i	−0.696308	−	0.717743i
$26$	0.206628	+	0.357891i	0.0405231	+	0.0701881i
$27$	2.84489	+	10.6173i	0.547499	+	2.04329i
$28$	0.709893	+	1.52237i	0.134157	+	0.287701i
$29$	1.43544	−	5.35715i	0.266555	−	0.994798i	−0.694736	−	0.719265i	$-0.744479\pi$
$29$	1.43544	−	5.35715i	0.266555	−	0.994798i	0.961291	−	0.275534i	$-0.0888545\pi$
$30$	−6.40593	+	2.59672i	−1.16956	+	0.474095i
$31$	7.07748	−	7.07748i	1.27115	−	1.27115i	0.325668	−	0.945484i	$-0.394411\pi$
$31$	7.07748	−	7.07748i	1.27115	−	1.27115i	0.945484	−	0.325668i	$-0.105589\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	−2.37785	+	5.09931i	−0.413930	+	0.887675i
$34$	2.24886	+	0.396534i	0.385675	+	0.0680050i
$35$	−3.57353	−	1.15658i	−0.604037	−	0.195497i
$36$			6.55579i			1.09263i
$37$	5.43589	+	2.72968i	0.893654	+	0.448757i
$37$	5.43589	+	2.72968i	0.893654	+	0.448757i
$38$	−0.0174798	+	0.0174798i	−0.00283559	+	0.00283559i
$39$	−0.732730	+	1.04645i	−0.117331	+	0.167566i
$40$	−2.21909	+	0.275056i	−0.350868	+	0.0434902i
$41$	−2.43898	−	6.70104i	−0.380905	−	1.04653i	−0.970976	−	0.239176i	$-0.923123\pi$
$41$	−2.43898	−	6.70104i	−0.380905	−	1.04653i	0.590072	−	0.807351i	$-0.299100\pi$
$42$	−3.33768	+	3.97770i	−0.515016	+	0.613772i
$43$	−3.99954			−0.609924			−0.304962	−	0.952365i	$-0.598644\pi$
$43$	−3.99954			−0.609924			−0.304962	+	0.952365i	$0.598644\pi$
$44$	−1.16996	+	1.39430i	−0.176378	+	0.210199i
$45$	−10.7325	−	9.98522i	−1.59991	−	1.48851i
$46$	−6.05230	−	2.20286i	−0.892364	−	0.324794i
$47$	12.2686	−	3.28735i	1.78955	−	0.479509i	0.797283	−	0.603606i	$-0.206270\pi$
$47$	12.2686	−	3.28735i	1.78955	−	0.479509i	0.992270	+	0.124097i	$0.0396033\pi$
$48$	−0.800073	+	2.98591i	−0.115481	+	0.430979i
$49$	4.11496	−	0.725579i	0.587852	−	0.103654i
$50$	2.92963	−	4.05182i	0.414312	−	0.573014i
$51$	1.82700	+	6.81847i	0.255832	+	0.954777i
$52$	−0.316573	+	0.265636i	−0.0439008	+	0.0368371i
$53$	0.723956	−	8.27486i	0.0994431	−	1.13664i	−0.768457	−	0.639901i	$-0.778975\pi$
$53$	0.723956	−	8.27486i	0.0994431	−	1.13664i	0.867900	−	0.496738i	$-0.165469\pi$
$54$	−9.96195	+	4.64533i	−1.35565	+	0.632150i
$55$	−0.500637	−	4.03902i	−0.0675059	−	0.544622i
$56$	−1.37597	+	0.963465i	−0.183872	+	0.128748i
$57$	−0.0718074	−	0.0261358i	−0.00951113	−	0.00346177i
$58$	5.52503	+	0.483377i	0.725472	+	0.0634706i
$59$	−0.186306	+	2.12949i	−0.0242550	+	0.277236i	0.974376	+	0.224926i	$0.0722139\pi$
$59$	−0.186306	+	2.12949i	−0.0242550	+	0.277236i	−0.998631	+	0.0523099i	$0.983342\pi$
$60$	−3.66965	−	5.85769i	−0.473750	−	0.756225i
$61$	−3.44856	+	7.39546i	−0.441543	+	0.946892i	0.552043	+	0.833815i	$0.313848\pi$
$61$	−3.44856	+	7.39546i	−0.441543	+	0.946892i	−0.993586	+	0.113076i	$0.963929\pi$
$62$	8.19894	+	5.74096i	1.04127	+	0.729103i
$63$	−10.6368	−	2.85014i	−1.34012	−	0.359083i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.0473026	−	0.922858i	0.00586716	−	0.114466i
$66$	−5.43474	−	1.45624i	−0.668971	−	0.179250i
$67$	−11.5392	+	1.00955i	−1.40973	+	0.123336i	−0.766456	−	0.642297i	$-0.777982\pi$
$67$	−11.5392	+	1.00955i	−1.40973	+	0.123336i	−0.643278	+	0.765633i	$0.722426\pi$
$68$			2.28355i			0.276921i
$69$	−1.73526	−	19.8341i	−0.208901	−	2.38774i
$70$	0.518468	−	3.72008i	0.0619688	−	0.444634i
$71$	1.09003	−	6.18185i	0.129362	−	0.733651i	−0.849258	−	0.527978i	$-0.822951\pi$
$71$	1.09003	−	6.18185i	0.129362	−	0.733651i	0.978621	−	0.205673i	$-0.0659384\pi$
$72$	−6.45619	+	1.13840i	−0.760869	+	0.134162i
$73$	−4.95515	−	4.95515i	−0.579956	−	0.579956i	0.354935	−	0.934891i	$-0.384503\pi$
$73$	−4.95515	−	4.95515i	−0.579956	−	0.579956i	−0.934891	+	0.354935i	$0.884503\pi$
$74$	−1.74428	+	5.82731i	−0.202768	+	0.677411i
$75$	15.1790	+	2.91434i	1.75272	+	0.336519i
$76$	−0.0202495	−	0.0141789i	−0.00232278	−	0.00162643i
$77$	−1.75363	−	2.50444i	−0.199845	−	0.285408i
$78$	−1.15779	−	0.539885i	−0.131094	−	0.0611299i
$79$	−13.9435	+	1.21990i	−1.56877	+	0.137250i	−0.838114	−	0.545495i	$-0.816342\pi$
$79$	−13.9435	+	1.21990i	−1.56877	+	0.137250i	−0.730657	+	0.682745i	$0.760786\pi$
$80$	−0.656218	−	2.13761i	−0.0733674	−	0.238992i
$81$	−10.9628	−	9.19891i	−1.21809	−	1.02210i
$82$	6.17571	−	3.56555i	0.681994	−	0.393749i
$83$	−4.78373	+	2.23069i	−0.525082	+	0.244850i	−0.667039	−	0.745023i	$-0.732438\pi$
$83$	−4.78373	+	2.23069i	−0.525082	+	0.244850i	0.141957	+	0.989873i	$0.454661\pi$
$84$	−4.49685	−	2.59626i	−0.490646	−	0.283275i
$85$	−3.73841	−	3.47811i	−0.405487	−	0.377254i
$86$	−0.694513	−	3.93878i	−0.0748912	−	0.424729i
$87$	5.86375	+	16.1105i	0.628660	+	1.72723i
$88$	−1.57628	−	0.910064i	−0.168032	−	0.0970132i
$89$	−1.22019	−	0.106753i	−0.129340	−	0.0113158i	0.0223019	−	0.999751i	$-0.492901\pi$
$89$	−1.22019	−	0.106753i	−0.129340	−	0.0113158i	−0.151642	+	0.988435i	$0.548456\pi$
$90$	7.96984	−	12.3034i	0.840095	−	1.29689i
$91$	−0.293368	−	0.629129i	−0.0307533	−	0.0659507i
$92$	1.11842	−	6.34288i	0.116603	−	0.661291i
$93$	−5.37275	+	30.4704i	−0.557128	+	3.15963i
$94$	5.36782	+	11.5113i	0.553648	+	1.18730i
$95$	0.0540547	−	0.0115546i	0.00554590	−	0.00118547i
$96$	−3.07948	−	0.269420i	−0.314298	−	0.0274975i
$97$	−7.32860	−	4.23117i	−0.744106	−	0.429610i	0.0794542	−	0.996839i	$-0.474682\pi$
$97$	−7.32860	−	4.23117i	−0.744106	−	0.429610i	−0.823560	+	0.567229i	$0.808016\pi$
$98$	1.42911	+	3.92645i	0.144362	+	0.396631i
$99$	−2.07203	−	11.7511i	−0.208247	−	1.18103i
$100$	4.49899	+	2.18153i	0.449899	+	0.218153i
$101$	12.2951	+	7.09859i	1.22341	+	0.706336i	0.965643	−	0.259871i	$-0.0836800\pi$
$101$	12.2951	+	7.09859i	1.22341	+	0.706336i	0.257767	+	0.966207i	$0.417013\pi$
$102$	−6.39763	+	2.98326i	−0.633460	+	0.295387i
$103$	6.60905	−	3.81573i	0.651209	−	0.375976i	−0.137710	−	0.990473i	$-0.543974\pi$
$103$	6.60905	−	3.81573i	0.651209	−	0.375976i	0.788919	+	0.614497i	$0.210641\pi$
$104$	−0.316573	−	0.265636i	−0.0310425	−	0.0260478i
$105$	11.0996	−	3.40742i	1.08321	−	0.332530i
$106$	8.27486	−	0.723956i	0.803725	−	0.0703169i
$107$	11.2211	+	5.23247i	1.08478	+	0.505842i	0.880972	−	0.473168i	$-0.156890\pi$
$107$	11.2211	+	5.23247i	1.08478	+	0.505842i	0.203810	+	0.979010i	$0.434668\pi$
$108$	−6.30464	−	9.00395i	−0.606664	−	0.866406i
$109$	9.19474	+	6.43823i	0.880697	+	0.616670i	0.924000	−	0.382392i	$-0.124899\pi$
$109$	9.19474	+	6.43823i	0.880697	+	0.616670i	−0.0433037	+	0.999062i	$0.513788\pi$
$110$	3.89073	−	1.19440i	0.370966	−	0.113882i
$111$	−18.6046	+	2.72608i	−1.76587	+	0.258748i
$112$	−1.18776	−	1.18776i	−0.112233	−	0.112233i
$113$	5.42819	−	0.957136i	0.510641	−	0.0900398i	0.0876098	−	0.996155i	$-0.472077\pi$
$113$	5.42819	−	0.957136i	0.510641	−	0.0900398i	0.423031	+	0.906115i	$0.360966\pi$
$114$	0.0132695	−	0.0752550i	0.00124280	−	0.00704827i
$115$	8.68048	+	11.4919i	0.809459	+	1.07163i
$116$	0.483377	+	5.52503i	0.0448805	+	0.512986i
$117$		−	2.70922i		−	0.250468i
$118$	−2.12949	+	0.186306i	−0.196035	+	0.0171509i
$119$	−3.70509	−	0.992775i	−0.339645	−	0.0910075i
$120$	5.13147	−	4.63108i	0.468437	−	0.422758i
$121$	−3.84357	+	6.65725i	−0.349415	+	0.605205i
$122$	−7.88194	−	2.11196i	−0.713598	−	0.191208i
$123$	18.0574	+	12.6439i	1.62818	+	1.14006i
$124$	−4.23001	+	9.07129i	−0.379866	+	0.814626i
$125$	−10.4239	+	4.04260i	−0.932341	+	0.361581i
$126$	0.959766	−	10.9702i	0.0855027	−	0.977301i
$127$	−15.4794	−	1.35427i	−1.37357	−	0.120172i	−0.623652	−	0.781702i	$-0.714352\pi$
$127$	−15.4794	−	1.35427i	−1.37357	−	0.120172i	−0.749918	+	0.661530i	$0.769907\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	10.1276	−	7.09144i	0.891688	−	0.624367i
$130$	0.917052	−	0.113669i	0.0804308	−	0.00996940i
$131$	10.5155	−	4.90345i	0.918741	−	0.428416i	0.0950615	−	0.995471i	$-0.469695\pi$
$131$	10.5155	−	4.90345i	0.918741	−	0.428416i	0.823680	+	0.567055i	$0.191917\pi$
$132$	0.490378	−	5.60505i	0.0426820	−	0.487857i
$133$	0.0318089	−	0.0266909i	0.00275818	−	0.00231439i
$134$	−2.99796	−	11.1886i	−0.258985	−	0.966544i
$135$	24.3431	+	3.39271i	2.09512	+	0.291998i
$136$	−2.24886	+	0.396534i	−0.192838	+	0.0340025i
$137$	2.92135	−	10.9026i	0.249587	−	0.931473i	−0.721435	−	0.692483i	$-0.756517\pi$
$137$	2.92135	−	10.9026i	0.249587	−	0.931473i	0.971022	−	0.238990i	$-0.0768164\pi$
$138$	19.2314	−	5.15305i	1.63709	−	0.438657i
$139$	12.4085	+	4.51633i	1.05248	+	0.383070i	0.809597	−	0.586986i	$-0.199686\pi$
$139$	12.4085	+	4.51633i	1.05248	+	0.383070i	0.242880	+	0.970056i	$0.421908\pi$
$140$	3.75359	−	0.135393i	0.317237	−	0.0114428i
$141$	−25.2377	+	30.0772i	−2.12540	+	2.53295i
$142$	6.27722			0.526772
$143$	0.483492	−	0.576203i	0.0404316	−	0.0481845i
$144$	−2.24221	−	6.16042i	−0.186851	−	0.513369i
$145$	−9.78130	−	7.62392i	−0.812293	−	0.633132i
$146$	4.01942	−	5.74032i	0.332649	−	0.475072i
$147$	−9.13340	+	9.13340i	−0.753310	+	0.753310i
$148$	−6.04167	−	0.705878i	−0.496622	−	0.0580228i
$149$			11.2199i			0.919170i	0.888134	+	0.459585i	$0.152002\pi$
$149$			11.2199i			0.919170i	−0.888134	+	0.459585i	$0.847998\pi$
$150$	−0.234263	+	15.4544i	−0.0191275	+	1.26185i
$151$	−22.8753	−	4.03353i	−1.86156	−	0.328244i	−0.874058	−	0.485821i	$-0.838521\pi$
$151$	−22.8753	−	4.03353i	−1.86156	−	0.328244i	−0.987507	+	0.157577i	$0.949632\pi$
$152$	0.0104472	−	0.0224040i	0.000847377	−	0.00181721i
$153$	−11.4680	−	9.62282i	−0.927135	−	0.777959i
$154$	2.16188	−	2.16188i	0.174209	−	0.174209i
$155$	−8.40787	−	20.7416i	−0.675336	−	1.66601i
$156$	0.330635	−	1.23395i	0.0264720	−	0.0987949i
$157$	5.86706	+	12.5819i	0.468242	+	1.00415i	0.988651	+	0.150231i	$0.0480018\pi$
$157$	5.86706	+	12.5819i	0.468242	+	1.00415i	−0.520409	+	0.853917i	$0.674220\pi$
$158$	−3.62264	−	13.5199i	−0.288202	−	1.07558i
$159$	12.8387	+	22.2372i	1.01817	+	1.76353i
$160$	1.99118	−	1.01744i	0.157417	−	0.0804357i
$161$	9.80517	+	4.57223i	0.772756	+	0.360342i
$162$	7.15548	−	12.3937i	0.562188	−	0.973738i
$163$	−5.06557	−	6.03691i	−0.396766	−	0.472848i	0.530265	−	0.847832i	$-0.322092\pi$
$163$	−5.06557	−	6.03691i	−0.396766	−	0.472848i	−0.927031	+	0.374984i	$0.877648\pi$
$164$	4.58378	+	5.46274i	0.357933	+	0.426568i
$165$	8.42916	+	9.33994i	0.656209	+	0.727114i
$166$	−3.02748	−	4.32369i	−0.234978	−	0.335584i
$167$	−6.09806	−	1.07525i	−0.471882	−	0.0832055i	−0.0673500	−	0.997729i	$-0.521454\pi$
$167$	−6.09806	−	1.07525i	−0.471882	−	0.0832055i	−0.404532	+	0.914524i	$0.632566\pi$
$168$	1.77594	−	4.87937i	0.137017	−	0.376451i
$169$	−9.82775	+	8.24646i	−0.755981	+	0.634343i
$170$	2.77610	−	4.28558i	0.212917	−	0.328689i
$171$	0.156538	−	0.0419442i	0.0119707	−	0.00320755i
$172$	3.75834	−	1.36792i	0.286571	−	0.104303i
$173$	7.69649	−	10.9917i	0.585153	−	0.835685i	−0.411993	−	0.911187i	$-0.635167\pi$
$173$	7.69649	−	10.9917i	0.585153	−	0.835685i	0.997146	+	0.0755021i	$0.0240560\pi$
$174$	−14.8475	+	8.57222i	−1.12559	+	0.649859i
$175$	−5.49551	+	6.35125i	−0.415421	+	0.480109i
$176$	0.622521	−	1.71036i	0.0469243	−	0.128923i
$177$	−3.30395	−	5.72261i	−0.248340	−	0.430138i
$178$	−0.106753	−	1.22019i	−0.00800147	−	0.0914572i
$179$	−2.56106	−	2.56106i	−0.191422	−	0.191422i	0.604888	−	0.796311i	$-0.293218\pi$
$179$	−2.56106	−	2.56106i	−0.191422	−	0.191422i	−0.796311	+	0.604888i	$0.793218\pi$
$180$	13.5004	+	5.71230i	1.00626	+	0.425770i
$181$	1.11180	−	0.404663i	0.0826397	−	0.0300784i	−0.300369	−	0.953823i	$-0.597110\pi$
$181$	1.11180	−	0.404663i	0.0826397	−	0.0300784i	0.383009	+	0.923745i	$0.374888\pi$
$182$	0.568629	−	0.398158i	0.0421496	−	0.0295134i
$183$	−4.38019	−	24.8413i	−0.323793	−	1.83632i
$184$	6.44073			0.474817
$185$	10.3578	−	8.81572i	0.761517	−	0.648144i
$186$	−30.9404			−2.26866
$187$	−0.721743	−	4.09321i	−0.0527791	−	0.299325i
$188$	−10.4043	+	7.28519i	−0.758814	+	0.531327i
$189$	17.3500	−	6.31488i	1.26203	−	0.459340i
$190$	0.0207655	+	0.0512271i	0.00150649	+	0.00371640i
$191$	2.98282	+	2.98282i	0.215830	+	0.215830i	0.806738	−	0.590909i	$-0.201231\pi$
$191$	2.98282	+	2.98282i	0.215830	+	0.215830i	−0.590909	+	0.806738i	$0.701231\pi$
$192$	−0.269420	−	3.07948i	−0.0194437	−	0.222242i
$193$	3.21269	+	5.56453i	0.231254	+	0.400544i	0.958177	−	0.286175i	$-0.0923838\pi$
$193$	3.21269	+	5.56453i	0.231254	+	0.400544i	−0.726923	+	0.686719i	$0.759050\pi$
$194$	2.89429	−	7.95199i	0.207798	−	0.570920i
$195$	1.51651	+	2.42073i	0.108599	+	0.173352i
$196$	−3.61864	+	2.08922i	−0.258474	+	0.149230i
$197$	−8.39170	+	11.9846i	−0.597884	+	0.853867i	−0.998040	−	0.0625801i	$-0.980067\pi$
$197$	−8.39170	+	11.9846i	−0.597884	+	0.853867i	0.400156	+	0.916447i	$0.368956\pi$
$198$	11.2128	−	4.08111i	0.796856	−	0.290032i
$199$	−6.24611	+	1.67364i	−0.442775	+	0.118641i	−0.473317	−	0.880892i	$-0.656943\pi$
$199$	−6.24611	+	1.67364i	−0.442775	+	0.118641i	0.0305417	+	0.999533i	$0.490277\pi$
$200$	−1.36715	+	4.80946i	−0.0966719	+	0.340080i
$201$	27.4295	−	23.0161i	1.93473	−	1.62343i
$202$	−4.85572	+	13.3410i	−0.341647	+	0.938669i
$203$	−9.17458	−	1.61773i	−0.643929	−	0.113542i
$204$	−4.04888	−	5.78240i	−0.283478	−	0.404849i
$205$	−15.9247	−	0.816247i	−1.11223	−	0.0570092i
$206$	4.90541	+	5.84605i	0.341776	+	0.407313i
$207$	27.1411	+	32.3455i	1.88644	+	2.24817i
$208$	0.206628	−	0.357891i	0.0143271	−	0.0248153i
$209$	0.0407782	+	0.0190152i	0.00282069	+	0.00131531i
$210$	5.28307	+	10.3393i	0.364567	+	0.713476i
$211$	8.83274	+	15.2988i	0.608071	+	1.05321i	0.991558	+	0.129664i	$0.0413898\pi$
$211$	8.83274	+	15.2988i	0.608071	+	1.05321i	−0.383487	+	0.923546i	$0.625277\pi$
$212$	2.14987	+	8.02343i	0.147654	+	0.551052i
$213$	8.20065	+	17.5864i	0.561900	+	1.20500i
$214$	−3.20446	+	11.9592i	−0.219052	+	0.817515i
$215$	−3.48495	+	8.23630i	−0.237672	+	0.561711i
$216$	7.77238	−	7.77238i	0.528843	−	0.528843i
$217$	−12.8793	−	10.8070i	−0.874303	−	0.733627i
$218$	−4.74377	+	10.1730i	−0.321288	+	0.689005i
$219$	21.3332	+	3.76162i	1.44156	+	0.254187i
$220$	1.85187	+	3.62421i	0.124853	+	0.244344i
$221$		−	0.943691i		−	0.0634795i
$222$	−5.91533	−	17.8486i	−0.397011	−	1.19792i
$223$	17.8501	−	17.8501i	1.19533	−	1.19533i	0.219783	−	0.975549i	$-0.429465\pi$
$223$	17.8501	−	17.8501i	1.19533	−	1.19533i	0.975549	−	0.219783i	$-0.0705351\pi$
$224$	0.963465	−	1.37597i	0.0643742	−	0.0919359i
$225$	−29.9143	+	13.4011i	−1.99429	+	0.893408i
$226$	1.88519	+	5.17952i	0.125401	+	0.344536i
$227$	13.5622	−	16.1628i	0.900156	−	1.07276i	−0.0968392	−	0.995300i	$-0.530873\pi$
$227$	13.5622	−	16.1628i	0.900156	−	1.07276i	0.996995	−	0.0774640i	$-0.0246823\pi$
$228$	0.0764159			0.00506077
$229$	−17.4245	+	20.7657i	−1.15144	+	1.37223i	−0.235034	+	0.971987i	$0.575520\pi$
$229$	−17.4245	+	20.7657i	−1.15144	+	1.37223i	−0.916407	+	0.400247i	$0.868924\pi$
$230$	−9.80998	+	10.5442i	−0.646851	+	0.695261i
$231$	8.88108	+	3.23245i	0.584332	+	0.212679i
$232$	−5.35715	+	1.43544i	−0.351714	+	0.0942416i
$233$	−1.82127	+	6.79707i	−0.119315	+	0.445291i	−0.999573	−	0.0292043i	$-0.990703\pi$
$233$	−1.82127	+	6.79707i	−0.119315	+	0.445291i	0.880258	+	0.474495i	$0.157369\pi$
$234$	2.66806	−	0.470451i	0.174417	−	0.0307544i
$235$	3.92037	−	28.1292i	0.255737	−	1.83495i
$236$	−0.553257	−	2.06478i	−0.0360140	−	0.134406i
$237$	33.1449	−	27.8118i	2.15299	−	1.80657i
$238$	0.334311	−	3.82119i	0.0216702	−	0.247691i
$239$	11.3923	−	5.31232i	0.736907	−	0.343625i	−0.0176638	−	0.999844i	$-0.505623\pi$
$239$	11.3923	−	5.31232i	0.736907	−	0.343625i	0.754571	+	0.656219i	$0.227845\pi$
$240$	5.45179	+	4.24934i	0.351912	+	0.274294i
$241$	−2.57375	+	1.80216i	−0.165790	+	0.116087i	−0.653527	−	0.756903i	$-0.726711\pi$
$241$	−2.57375	+	1.80216i	−0.165790	+	0.116087i	0.487737	+	0.872991i	$0.337823\pi$
$242$	−7.22354	−	2.62915i	−0.464347	−	0.169008i
$243$	11.2204	+	0.981660i	0.719791	+	0.0629735i
$244$	0.711190	−	8.12894i	0.0455293	−	0.520402i
$245$	2.09133	−	9.10622i	0.133610	−	0.581775i
$246$	−9.31618	+	19.9786i	−0.593978	+	1.27379i
$247$	0.00836825	+	0.00585951i	0.000532459	+	0.000372832i
$248$	−9.66801	−	2.59054i	−0.613919	−	0.164499i
$249$	8.15819	−	14.1304i	0.517004	−	0.895477i
$250$	−5.79127	−	9.56353i	−0.366272	−	0.604851i
$251$	−4.19290	−	1.12348i	−0.264653	−	0.0709137i	0.124052	−	0.992276i	$-0.460411\pi$
$251$	−4.19290	−	1.12348i	−0.264653	−	0.0709137i	−0.388706	+	0.921362i	$0.627078\pi$
$252$	10.9702	−	0.959766i	0.691056	−	0.0604596i
$253$			11.7230i			0.737016i
$254$	−1.35427	−	15.4794i	−0.0849743	−	0.971261i
$255$	15.6333	+	2.17882i	0.978996	+	0.136443i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	23.6879	−	4.17682i	1.47761	−	0.260543i	0.623990	−	0.781433i	$-0.285511\pi$
$257$	23.6879	−	4.17682i	1.47761	−	0.260543i	0.853624	+	0.520890i	$0.174400\pi$
$258$	8.74235	+	8.74235i	0.544275	+	0.544275i
$259$	3.77192	−	9.49580i	0.234376	−	0.590041i
$260$	0.271186	+	0.883381i	0.0168183	+	0.0547850i
$261$	−29.7838	−	20.8548i	−1.84357	−	1.29088i
$262$	6.65494	+	9.50425i	0.411144	+	0.587174i
$263$	−13.1569	−	6.13518i	−0.811292	−	0.378311i	−0.0277221	−	0.999616i	$-0.508825\pi$
$263$	−13.1569	−	6.13518i	−0.811292	−	0.378311i	−0.783569	+	0.621304i	$0.786603\pi$
$264$	5.60505	−	0.490378i	0.344967	−	0.0301807i
$265$	−16.4097	−	8.70105i	−1.00804	−	0.534501i
$266$	0.0318089	+	0.0266909i	0.00195033	+	0.00163652i
$267$	3.27905	−	1.89316i	0.200674	−	0.115859i
$268$	10.4980	−	4.89529i	0.641267	−	0.299028i
$269$	−10.5982	−	6.11889i	−0.646185	−	0.373075i	0.140808	−	0.990037i	$-0.455030\pi$
$269$	−10.5982	−	6.11889i	−0.646185	−	0.373075i	−0.786993	+	0.616962i	$0.788363\pi$
$270$	0.885974	+	24.5624i	0.0539187	+	1.49482i
$271$	4.34630	+	24.6491i	0.264019	+	1.49732i	0.771815	+	0.635847i	$0.219349\pi$
$271$	4.34630	+	24.6491i	0.264019	+	1.49732i	−0.507796	+	0.861477i	$0.669540\pi$
$272$	−0.781019	−	2.14583i	−0.0473562	−	0.130110i
$273$	1.85835	+	1.07292i	0.112473	+	0.0649361i
$274$	11.2443	+	0.983745i	0.679291	+	0.0594302i
$275$	−8.75384	−	2.48838i	−0.527876	−	0.150055i
$276$	8.41427	+	18.0445i	0.506479	+	1.08615i
$277$	−3.28592	+	18.6354i	−0.197432	+	1.11969i	0.711480	+	0.702706i	$0.248025\pi$
$277$	−3.28592	+	18.6354i	−0.197432	+	1.11969i	−0.908912	+	0.416987i	$0.863086\pi$
$278$	−2.29300	+	13.0043i	−0.137525	+	0.779944i
$279$	−27.7311	−	59.4694i	−1.66021	−	3.56034i
$280$	0.785141	+	3.67306i	0.0469211	+	0.219507i
$281$	18.8675	+	1.65069i	1.12554	+	0.0984721i	0.634687	−	0.772769i	$-0.281129\pi$
$281$	18.8675	+	1.65069i	1.12554	+	0.0984721i	0.490854	+	0.871242i	$0.336685\pi$
$282$	−34.0027	−	19.6315i	−2.02483	−	1.16904i
$283$	5.41634	+	14.8813i	0.321968	+	0.884599i	0.990076	+	0.140535i	$0.0448822\pi$
$283$	5.41634	+	14.8813i	0.321968	+	0.884599i	−0.668108	+	0.744064i	$0.732896\pi$
$284$	1.09003	+	6.18185i	0.0646812	+	0.366825i
$285$	−0.116390	+	0.125101i	−0.00689436	+	0.00741034i
$286$	0.651407	+	0.376090i	0.0385185	+	0.0222387i
$287$	−10.8562	+	5.06232i	−0.640820	+	0.298819i
$288$	5.67748	−	3.27789i	0.334549	−	0.193152i
$289$	9.02815	+	7.57552i	0.531068	+	0.445619i
$290$	5.80959	−	10.9566i	0.341151	−	0.643392i
$291$	26.0596	−	2.27992i	1.52764	−	0.133651i
$292$	6.35108	+	2.96156i	0.371669	+	0.173312i
$293$	0.0930551	+	0.132896i	0.00543634	+	0.00776389i	0.821861	−	0.569688i	$-0.192936\pi$
$293$	0.0930551	+	0.132896i	0.00543634	+	0.00776389i	−0.816425	+	0.577452i	$0.804047\pi$
$294$	−10.5806	−	7.40865i	−0.617076	−	0.432081i
$295$	4.22294	+	2.23916i	0.245869	+	0.130369i
$296$	−0.353971	−	6.07245i	−0.0205741	−	0.352954i
$297$	14.1467	+	14.1467i	0.820876	+	0.820876i
$298$	−11.0494	+	1.94831i	−0.640077	+	0.112863i
$299$	−0.462195	+	2.62124i	−0.0267294	+	0.151590i
$300$	−15.2603	+	2.45293i	−0.881056	+	0.141620i
$301$	0.585532	+	6.69266i	0.0337495	+	0.385758i
$302$		−	23.2282i		−	1.33663i
$303$	−43.7199	+	3.82500i	−2.51165	+	0.219741i
$304$	0.0238778	+	0.00639804i	0.00136949	+	0.000366953i
$305$	12.2247	+	13.5456i	0.699985	+	0.775619i
$306$	7.48522	−	12.9648i	0.427902	−	0.741148i
$307$	−24.3325	−	6.51987i	−1.38873	−	0.372109i	−0.514444	−	0.857524i	$-0.672002\pi$
$307$	−24.3325	−	6.51987i	−1.38873	−	0.372109i	−0.874284	+	0.485415i	$0.838668\pi$
$308$	2.50444	+	1.75363i	0.142704	+	0.0999223i
$309$	−9.96987	+	21.3805i	−0.567166	+	1.21629i
$310$	18.9665	−	11.8819i	1.07722	−	0.674845i
$311$	0.636400	−	7.27408i	0.0360869	−	0.412475i	−0.956569	−	0.291505i	$-0.905844\pi$
$311$	0.636400	−	7.27408i	0.0360869	−	0.412475i	0.992656	−	0.120970i	$-0.0386005\pi$
$312$	1.27262	+	0.111339i	0.0720477	+	0.00630335i
$313$	18.6169	+	6.77599i	1.05229	+	0.383001i	0.809526	−	0.587084i	$-0.199724\pi$
$313$	18.6169	+	6.77599i	1.05229	+	0.383001i	0.242762	+	0.970086i	$0.421947\pi$
$314$	−11.3720	+	7.96276i	−0.641759	+	0.449364i
$315$	−15.1376	+	19.4212i	−0.852908	+	1.09426i
$316$	12.6854	−	5.91531i	0.713610	−	0.332762i
$317$	−1.16616	+	13.3293i	−0.0654981	+	0.748647i	0.890444	+	0.455092i	$0.150394\pi$
$317$	−1.16616	+	13.3293i	−0.0654981	+	0.748647i	−0.955942	+	0.293555i	$0.905162\pi$
$318$	−19.6700	+	16.5051i	−1.10304	+	0.925558i
$319$	−2.61269	−	9.75071i	−0.146283	−	0.545935i
$320$	1.34775	+	1.78426i	0.0753414	+	0.0997430i
$321$	−37.6915	+	6.64603i	−2.10373	+	0.370945i
$322$	−2.80011	+	10.4502i	−0.156044	+	0.582365i
$323$	0.0545261	−	0.0146102i	0.00303391	−	0.000812934i
$324$	13.4479	+	4.89464i	0.747106	+	0.271924i
$325$	−1.85924	−	0.901532i	−0.103132	−	0.0500080i
$326$	5.06557	−	6.03691i	0.280556	−	0.334354i
$327$	−34.6983			−1.91882
$328$	−4.58378	+	5.46274i	−0.253097	+	0.301629i
$329$	−7.29703	−	20.0484i	−0.402298	−	1.10530i
$330$	−7.73434	+	9.92297i	−0.425761	+	0.546241i
$331$	13.6104	−	19.4376i	0.748094	−	1.06839i	−0.246957	−	0.969026i	$-0.579431\pi$
$331$	13.6104	−	19.4376i	0.748094	−	1.06839i	0.995051	−	0.0993625i	$-0.0316803\pi$
$332$	3.73229	−	3.73229i	0.204836	−	0.204836i
$333$	29.0044	−	27.3668i	1.58943	−	1.49969i
$334$		−	6.19213i		−	0.338818i
$335$	−7.97554	+	24.6424i	−0.435750	+	1.34636i
$336$	5.11363	+	0.901671i	0.278971	+	0.0491902i
$337$	2.67494	−	5.73643i	0.145713	−	0.312483i	−0.819882	−	0.572533i	$-0.805961\pi$
$337$	2.67494	−	5.73643i	0.145713	−	0.312483i	0.965595	+	0.260049i	$0.0837388\pi$
$338$	−9.82775	−	8.24646i	−0.534559	−	0.448548i
$339$	−12.0482	+	12.0482i	−0.654368	+	0.654368i
$340$	4.70254	+	1.98974i	0.255031	+	0.107909i
$341$	4.71511	−	17.5970i	0.255337	−	0.952932i
$342$	0.0684894	+	0.146876i	0.00370348	+	0.00794215i
$343$	−4.85984	−	18.1372i	−0.262407	−	0.979315i
$344$	1.99977	+	3.46370i	0.107820	+	0.186750i
$345$	−42.3566	−	13.7088i	−2.28040	−	0.738054i
$346$	12.1612	+	5.67087i	0.653791	+	0.304868i
$347$	−8.44865	+	14.6335i	−0.453547	+	0.785567i	−0.998603	−	0.0528327i	$-0.983175\pi$
$347$	−8.44865	+	14.6335i	−0.453547	+	0.785567i	0.545056	+	0.838400i	$0.316508\pi$
$348$	−11.0202	−	13.1334i	−0.590747	−	0.704025i
$349$	−0.244572	−	0.291469i	−0.0130916	−	0.0156020i	0.759459	−	0.650555i	$-0.225464\pi$
$349$	−0.244572	−	0.291469i	−0.0130916	−	0.0156020i	−0.772551	+	0.634953i	$0.781019\pi$
$350$	−7.20905	−	4.30913i	−0.385340	−	0.230333i
$351$	2.60543	+	3.72094i	0.139068	+	0.198609i
$352$	1.79248	+	0.316062i	0.0955393	+	0.0168462i
$353$	−10.1774	+	27.9621i	−0.541686	+	1.48827i	0.302990	+	0.952994i	$0.402015\pi$
$353$	−10.1774	+	27.9621i	−0.541686	+	1.48827i	−0.844676	+	0.535278i	$0.820207\pi$
$354$	5.06195	−	4.24748i	0.269040	−	0.225751i
$355$	−11.7806	−	7.63119i	−0.625248	−	0.405021i
$356$	1.18312	−	0.317015i	0.0627051	−	0.0168018i
$357$	11.1423	−	4.05545i	0.589711	−	0.214637i
$358$	2.07743	−	2.96687i	0.109795	−	0.156804i
$359$	−10.8886	+	6.28653i	−0.574677	+	0.331790i	−0.759015	−	0.651073i	$-0.774319\pi$
$359$	−10.8886	+	6.28653i	−0.574677	+	0.331790i	0.184338	+	0.982863i	$0.440986\pi$
$360$	−3.28120	+	14.2872i	−0.172934	+	0.753004i
$361$	6.49817	−	17.8536i	0.342009	−	0.939662i
$362$	0.591578	+	1.02464i	0.0310927	+	0.0538541i
$363$	−2.07106	−	23.6724i	−0.108703	−	1.24248i
$364$	0.490850	+	0.490850i	0.0257276	+	0.0257276i
$365$	−14.5218	+	5.88659i	−0.760106	+	0.308118i
$366$	23.7033	−	8.62729i	1.23899	−	0.450956i
$367$	10.3543	−	7.25013i	0.540488	−	0.378454i	−0.271220	−	0.962517i	$-0.587427\pi$
$367$	10.3543	−	7.25013i	0.540488	−	0.378454i	0.811708	+	0.584064i	$0.198538\pi$
$368$	1.11842	+	6.34288i	0.0583017	+	0.330645i
$369$	−46.7500			−2.43371
$370$	10.4804	+	8.66957i	0.544850	+	0.450709i
$371$	−13.9528			−0.724393
$372$	−5.37275	−	30.4704i	−0.278564	−	1.57982i
$373$	27.1782	−	19.0304i	1.40723	−	0.985355i	0.409918	−	0.912123i	$-0.365557\pi$
$373$	27.1782	−	19.0304i	1.40723	−	0.985355i	0.997315	−	0.0732322i	$-0.0233314\pi$
$374$	3.90569	−	1.42156i	0.201959	−	0.0735069i
$375$	19.2276	−	28.7189i	0.992906	−	1.48304i
$376$	−8.98121	−	8.98121i	−0.463170	−	0.463170i
$377$	−0.199759	−	2.28325i	−0.0102881	−	0.117594i
$378$	9.23173	+	15.9898i	0.474829	+	0.822428i
$379$	−8.56693	+	23.5374i	−0.440053	+	1.20904i	0.499403	+	0.866370i	$0.333553\pi$
$379$	−8.56693	+	23.5374i	−0.440053	+	1.20904i	−0.939457	+	0.342667i	$0.888670\pi$
$380$	−0.0468429	+	0.0293455i	−0.00240299	+	0.00150539i
$381$	41.5980	−	24.0166i	2.13113	−	1.23041i
$382$	−2.41955	+	3.45547i	−0.123795	+	0.176797i
$383$	−9.25571	+	3.36880i	−0.472945	+	0.172138i	−0.567486	−	0.823383i	$-0.692084\pi$
$383$	−9.25571	+	3.36880i	−0.472945	+	0.172138i	0.0945412	+	0.995521i	$0.469862\pi$
$384$	2.98591	−	0.800073i	0.152374	−	0.0408285i
$385$	−6.68544	+	1.42906i	−0.340721	+	0.0728315i
$386$	−4.92212	+	4.13015i	−0.250529	+	0.210219i
$387$	−8.96781	+	24.6389i	−0.455859	+	1.25246i
$388$	8.33377	+	1.46947i	0.423083	+	0.0746010i
$389$	−4.71402	−	6.73232i	−0.239010	−	0.341342i	0.681670	−	0.731660i	$-0.261254\pi$
$389$	−4.71402	−	6.73232i	−0.239010	−	0.341342i	−0.920680	+	0.390318i	$0.872365\pi$
$390$	−2.12062	+	1.91382i	−0.107382	+	0.0969102i
$391$	9.45393	+	11.2668i	0.478106	+	0.569784i
$392$	−2.68585	−	3.20087i	−0.135656	−	0.161668i
$393$	−17.9331	+	31.0611i	−0.904607	+	1.56683i
$394$	−13.2597	−	6.18311i	−0.668015	−	0.311501i
$395$	−9.63738	+	29.7771i	−0.484909	+	1.49825i
$396$	5.96619	+	10.3337i	0.299812	+	0.519290i
$397$	−3.73367	−	13.9342i	−0.187387	−	0.699339i	−0.994107	−	0.108404i	$-0.965426\pi$
$397$	−3.73367	−	13.9342i	−0.187387	−	0.699339i	0.806720	−	0.590934i	$-0.201241\pi$
$398$	−2.73284	−	5.86060i	−0.136985	−	0.293765i
$399$	−0.0332219	+	0.123986i	−0.00166317	+	0.00620705i
$400$	−4.97380	−	0.511223i	−0.248690	−	0.0255612i
$401$	8.51616	−	8.51616i	0.425277	−	0.425277i	−0.461739	−	0.887016i	$-0.652774\pi$
$401$	8.51616	−	8.51616i	0.425277	−	0.425277i	0.887016	+	0.461739i	$0.152774\pi$
$402$	27.4295	+	23.0161i	1.36806	+	1.14794i
$403$	1.74808	−	3.74877i	0.0870781	−	0.186740i
$404$	−13.9815	−	2.46532i	−0.695605	−	0.122654i
$405$	−28.4958	+	14.5606i	−1.41597	+	0.723520i
$406$		−	9.31611i		−	0.462351i
$407$	11.0526	−	0.644272i	0.547859	−	0.0319354i
$408$	4.99147	−	4.99147i	0.247114	−	0.247114i
$409$	1.30092	−	1.85790i	0.0643262	−	0.0918674i	−0.785700	−	0.618608i	$-0.787697\pi$
$409$	1.30092	−	1.85790i	0.0643262	−	0.0918674i	0.850026	+	0.526740i	$0.176586\pi$
$410$	−1.96145	−	15.8245i	−0.0968692	−	0.781518i
$411$	11.9336	+	32.7873i	0.588641	+	1.61728i
$412$	−4.90541	+	5.84605i	−0.241672	+	0.288014i
$413$	3.59067			0.176685
$414$	−27.1411	+	32.3455i	−1.33391	+	1.58969i
$415$	0.425444	+	11.7949i	0.0208842	+	0.578987i
$416$	0.388334	+	0.141342i	0.0190396	+	0.00692986i
$417$	−39.4286	+	10.5649i	−1.93083	+	0.517363i
$418$	−0.0116452	+	0.0434607i	−0.000569588	+	0.00212573i
$419$	23.2995	−	4.10833i	1.13826	−	0.200705i	0.427413	−	0.904056i	$-0.359425\pi$
$419$	23.2995	−	4.10833i	1.13826	−	0.200705i	0.710842	+	0.703351i	$0.248314\pi$
$420$	−9.26478	+	6.99820i	−0.452075	+	0.341477i
$421$	6.42054	+	23.9618i	0.312918	+	1.16782i	0.925913	+	0.377738i	$0.123298\pi$
$421$	6.42054	+	23.9618i	0.312918	+	1.16782i	−0.612995	+	0.790087i	$0.710035\pi$
$422$	−13.5325	+	11.3552i	−0.658754	+	0.552760i
$423$	7.25722	−	82.9504i	0.352858	−	4.03319i
$424$	−7.52822	+	3.51047i	−0.365603	+	0.170483i
$425$	−10.4199	+	4.66795i	−0.505441	+	0.226429i
$426$	−15.8952	+	11.1299i	−0.770123	+	0.539246i
$427$	12.8801	+	4.68798i	0.623313	+	0.226867i
$428$	−12.3340	−	1.07908i	−0.596185	−	0.0521594i
$429$	−0.202652	+	2.31632i	−0.00978413	+	0.111833i
$430$	−8.71633	−	2.00179i	−0.420339	−	0.0965347i
$431$	−5.97821	+	12.8203i	−0.287960	+	0.617533i	−0.996070	−	0.0885696i	$-0.971770\pi$
$431$	−5.97821	+	12.8203i	−0.287960	+	0.617533i	0.708110	+	0.706102i	$0.249548\pi$
$432$	9.00395	+	6.30464i	0.433203	+	0.303332i
$433$	7.12805	+	1.90995i	0.342552	+	0.0917866i	0.425994	−	0.904726i	$-0.359925\pi$
$433$	7.12805	+	1.90995i	0.342552	+	0.0917866i	−0.0834416	+	0.996513i	$0.526591\pi$
$434$	8.40636	−	14.5602i	0.403518	−	0.698914i
$435$	38.2859	+	1.96241i	1.83567	+	0.0940901i
$436$	−10.8422	−	2.90517i	−0.519249	−	0.139132i
$437$	−0.158610	+	0.0138765i	−0.00758733	+	0.000663805i
$438$			21.6623i			1.03507i
$439$	−0.0157779	−	0.180342i	−0.000753036	−	0.00860724i	0.995809	−	0.0914586i	$-0.0291529\pi$
$439$	−0.0157779	−	0.180342i	−0.000753036	−	0.00860724i	−0.996562	+	0.0828513i	$0.973597\pi$
$440$	−3.24758	+	2.45308i	−0.154822	+	0.116946i
$441$	4.75674	−	26.9768i	0.226511	−	1.28461i
$442$	0.929354	−	0.163870i	0.0442049	−	0.00779451i
$443$	10.8057	+	10.8057i	0.513393	+	0.513393i	0.915564	−	0.402171i	$-0.131744\pi$
$443$	10.8057	+	10.8057i	0.513393	+	0.513393i	−0.402171	+	0.915564i	$0.631744\pi$
$444$	16.5503	−	8.92484i	0.785441	−	0.423554i
$445$	−1.28304	+	2.41974i	−0.0608218	+	0.114707i
$446$	20.6786	+	14.4793i	0.979159	+	0.685614i
$447$	−19.8936	−	28.4110i	−0.940935	−	1.34379i
$448$	1.52237	+	0.709893i	0.0719252	+	0.0335393i
$449$	−7.34573	+	0.642668i	−0.346666	+	0.0303294i	−0.259159	−	0.965835i	$-0.583446\pi$
$449$	−7.34573	+	0.642668i	−0.346666	+	0.0303294i	−0.0875068	+	0.996164i	$0.527890\pi$
$450$	−18.3921	−	27.1328i	−0.867012	−	1.27905i
$451$	−9.94289	−	8.34308i	−0.468192	−	0.392860i
$452$	−4.77347	+	2.75596i	−0.224525	+	0.129630i
$453$	65.0765	−	30.3457i	3.05756	−	1.42576i
$454$	18.2723	+	10.5495i	0.857563	+	0.495114i
$455$	−1.55120	+	0.0559521i	−0.0727212	+	0.00262308i
$456$	0.0132695	+	0.0752550i	0.000621400	+	0.00352414i
$457$	−1.80104	−	4.94832i	−0.0842492	−	0.231473i	0.890414	−	0.455152i	$-0.150415\pi$
$457$	−1.80104	−	4.94832i	−0.0842492	−	0.231473i	−0.974663	+	0.223680i	$0.928193\pi$
$458$	−23.4759	−	13.5538i	−1.09696	−	0.633329i
$459$	25.0048	+	2.18763i	1.16712	+	0.102110i
$460$	−12.0875	−	7.82997i	−0.563580	−	0.365074i
$461$	−7.07392	−	15.1701i	−0.329465	−	0.706541i	0.669889	−	0.742461i	$-0.266342\pi$
$461$	−7.07392	−	15.1701i	−0.329465	−	0.706541i	−0.999355	+	0.0359203i	$0.988564\pi$
$462$	−1.64116	+	9.30746i	−0.0763535	+	0.433022i
$463$	−5.73984	+	32.5522i	−0.266753	+	1.51283i	0.497244	+	0.867611i	$0.334345\pi$
$463$	−5.73984	+	32.5522i	−0.266753	+	1.51283i	−0.763997	+	0.645220i	$0.776766\pi$
$464$	−2.34390	−	5.02650i	−0.108813	−	0.233350i
$465$	58.0666	+	37.6142i	2.69277	+	1.74432i
$466$	−7.01007	−	0.613301i	−0.324735	−	0.0284106i
$467$	−4.41441	−	2.54866i	−0.204274	−	0.117938i	0.394373	−	0.918950i	$-0.370962\pi$
$467$	−4.41441	−	2.54866i	−0.204274	−	0.117938i	−0.598648	+	0.801012i	$0.704295\pi$
$468$	0.926608	+	2.54584i	0.0428325	+	0.117681i
$469$	3.37866	+	19.1614i	0.156012	+	0.884789i
$470$	28.3826	−	1.02377i	1.30919	−	0.0472229i
$471$	−37.1652	−	21.4573i	−1.71248	−	0.988701i
$472$	1.93734	−	0.903398i	0.0891734	−	0.0415822i
$473$	−6.30438	+	3.63984i	−0.289876	+	0.167360i
$474$	33.1449	+	27.8118i	1.52239	+	1.27744i
$475$	0.0233054	−	0.121384i	0.00106933	−	0.00556946i
$476$	3.82119	−	0.334311i	0.175144	−	0.0153231i
$477$	−49.3534	−	23.0139i	−2.25974	−	1.05373i
$478$	7.20987	+	10.2968i	0.329772	+	0.470963i
$479$	32.3866	+	22.6773i	1.47978	+	1.03615i	0.986033	+	0.166550i	$0.0532626\pi$
$479$	32.3866	+	22.6773i	1.47978	+	1.03615i	0.493749	+	0.869605i	$0.335626\pi$
$480$	−3.23809	+	6.10686i	−0.147798	+	0.278739i
$481$	2.49676	+	0.291709i	0.113842	+	0.0133008i
$482$	−2.22171	−	2.22171i	−0.101196	−	0.101196i
$483$	−32.9355	+	5.80741i	−1.49862	+	0.264247i
$484$	1.33486	−	7.57035i	0.0606753	−	0.344107i
$485$	−15.0990	+	11.4051i	−0.685609	+	0.517879i
$486$	0.981660	+	11.2204i	0.0445290	+	0.508969i
$487$			11.1586i			0.505643i	0.967513	+	0.252822i	$0.0813586\pi$
$487$			11.1586i			0.505643i	−0.967513	+	0.252822i	$0.918641\pi$
$488$	8.12894	−	0.711190i	0.367980	−	0.0321941i
$489$	23.5309	+	6.30508i	1.06410	+	0.285125i
$490$	9.33103	+	0.478277i	0.421533	+	0.0216064i
$491$	−3.96425	+	6.86628i	−0.178904	+	0.309871i	−0.941505	−	0.336998i	$-0.890589\pi$
$491$	−3.96425	+	6.86628i	−0.178904	+	0.309871i	0.762601	+	0.646869i	$0.223922\pi$
$492$	−21.2928	−	5.70540i	−0.959955	−	0.257219i
$493$	−10.3744	−	7.26426i	−0.467241	−	0.327166i
$494$	−0.00431736	+	0.00925861i	−0.000194247	+	0.000416565i
$495$	−26.0046	−	5.97220i	−1.16882	−	0.268431i
$496$	0.872347	−	9.97097i	0.0391695	−	0.447710i
$497$	−10.5040	−	0.918983i	−0.471170	−	0.0412220i
$498$	15.3324	+	5.58053i	0.687060	+	0.250070i
$499$	12.6463	−	8.85506i	0.566128	−	0.396407i	−0.255179	−	0.966894i	$-0.582134\pi$
$499$	12.6463	−	8.85506i	0.566128	−	0.396407i	0.821307	+	0.570487i	$0.193246\pi$
$500$	8.41260	−	7.36398i	0.376223	−	0.329327i
$501$	17.3480	−	8.08950i	0.775051	−	0.361412i
$502$	0.378326	−	4.32429i	0.0168855	−	0.193002i
$503$	9.38780	−	7.87730i	0.418581	−	0.351232i	−0.409042	−	0.912516i	$-0.634137\pi$
$503$	9.38780	−	7.87730i	0.418581	−	0.351232i	0.827623	+	0.561284i	$0.189693\pi$
$504$	2.85014	+	10.6368i	0.126955	+	0.473803i
$505$	25.3314	−	19.1342i	1.12723	−	0.851462i
$506$	−11.5449	+	2.03567i	−0.513231	+	0.0904965i
$507$	10.2643	−	38.3069i	0.455854	−	1.70127i
$508$	15.0090	−	4.02165i	0.665917	−	0.178432i
$509$	5.80429	+	2.11259i	0.257271	+	0.0936388i	0.467436	−	0.884027i	$-0.345178\pi$
$509$	5.80429	+	2.11259i	0.257271	+	0.0936388i	−0.210165	+	0.977666i	$0.567400\pi$
$510$	0.568978	+	15.7741i	0.0251948	+	0.698491i
$511$	−7.56630	+	9.01717i	−0.334713	+	0.398896i
$512$	1.00000			0.0441942
$513$	−0.174657	+	0.208148i	−0.00771131	+	0.00918998i
$514$	8.22674	+	22.6028i	0.362866	+	0.996966i
$515$	−2.09908	−	16.9349i	−0.0924966	−	0.746240i
$516$	−7.09144	+	10.1276i	−0.312183	+	0.445844i
$517$	16.3470	−	16.3470i	0.718938	−	0.718938i
$518$	10.0065	+	2.06568i	0.439662	+	0.0907610i
$519$			41.4796i			1.82075i
$520$	−0.822870	+	0.420464i	−0.0360852	+	0.0184386i
$521$	37.5078	+	6.61364i	1.64325	+	0.289749i	0.917358	−	0.398063i	$-0.130318\pi$
$521$	37.5078	+	6.61364i	1.64325	+	0.289749i	0.725889	+	0.687812i	$0.241429\pi$
$522$	15.3661	−	32.9527i	0.672555	−	1.44230i
$523$	−4.23610	−	3.55451i	−0.185232	−	0.155428i	0.545457	−	0.838139i	$-0.316356\pi$
$523$	−4.23610	−	3.55451i	−0.185232	−	0.155428i	−0.730688	+	0.682711i	$0.760801\pi$
$524$	−8.20424	+	8.20424i	−0.358404	+	0.358404i
$525$	2.65453	−	25.8265i	0.115853	−	1.12716i
$526$	3.75730	−	14.0224i	0.163826	−	0.611407i
$527$	−9.65943	−	20.7147i	−0.420772	−	0.902348i
$528$	1.45624	+	5.43474i	0.0633745	+	0.236517i
$529$	−9.24148	−	16.0067i	−0.401804	−	0.695944i
$530$	5.71934	−	17.6713i	0.248432	−	0.767594i
$531$	12.7008	+	5.92248i	0.551168	+	0.257014i
$532$	−0.0207618	+	0.0359605i	−0.000900138	+	0.00155908i
$533$	−1.89428	−	2.25751i	−0.0820503	−	0.0977837i
$534$	2.43380	+	2.90049i	0.105321	+	0.125516i
$535$	20.5526	−	18.5484i	0.888568	−	0.801919i
$536$	6.64388	+	9.48844i	0.286972	+	0.409838i
$537$	11.0260	+	1.94419i	0.475808	+	0.0838978i
$538$	4.18557	−	11.4997i	0.180453	−	0.495789i
$539$	5.82600	−	4.88859i	0.250944	−	0.210567i
$540$	−24.0354	+	5.13774i	−1.03432	+	0.221093i
$541$	30.8486	−	8.26587i	1.32629	−	0.355377i	0.474957	−	0.880009i	$-0.342464\pi$
$541$	30.8486	−	8.26587i	1.32629	−	0.355377i	0.851329	+	0.524632i	$0.175797\pi$
$542$	−23.5199	+	8.56053i	−1.01026	+	0.367706i
$543$	−2.09781	+	2.99599i	−0.0900258	+	0.128570i
$544$	1.97761	−	1.14177i	0.0847893	−	0.0489531i
$545$	21.2701	−	13.3250i	0.911109	−	0.570780i
$546$	−0.733921	+	2.01643i	−0.0314089	+	0.0862953i
$547$	−2.54020	−	4.39976i	−0.108611	−	0.188120i	0.806597	−	0.591102i	$-0.201307\pi$
$547$	−2.54020	−	4.39976i	−0.108611	−	0.188120i	−0.915208	+	0.402982i	$0.867974\pi$
$548$	0.983745	+	11.2443i	0.0420235	+	0.480331i
$549$	37.8268	+	37.8268i	1.61441	+	1.61441i
$550$	0.930492	−	9.05295i	0.0396763	−	0.386019i
$551$	0.128833	−	0.0468913i	0.00548846	−	0.00199764i
$552$	−16.3092	+	11.4198i	−0.694166	+	0.486060i
$553$	4.08266	+	23.1539i	0.173613	+	0.984606i
$554$	−18.9229			−0.803956
$555$	−10.5971	+	40.6881i	−0.449820	+	1.72711i
$556$	−13.2049			−0.560011
$557$	1.36131	+	7.72035i	0.0576804	+	0.327122i	0.999971	−	0.00767565i	$-0.00244326\pi$
$557$	1.36131	+	7.72035i	0.0576804	+	0.327122i	−0.942290	+	0.334797i	$0.891332\pi$
$558$	53.7505	−	37.6365i	2.27544	−	1.59328i
$559$	−1.55316	+	0.565303i	−0.0656916	+	0.0239098i
$560$	−3.48092	+	1.41103i	−0.147096	+	0.0596270i
$561$	9.08511	+	9.08511i	0.383574	+	0.383574i
$562$	1.65069	+	18.8675i	0.0696303	+	0.795878i
$563$	19.0794	+	33.0464i	0.804099	+	1.39274i	0.916897	+	0.399123i	$0.130685\pi$
$563$	19.0794	+	33.0464i	0.804099	+	1.39274i	−0.112798	+	0.993618i	$0.535981\pi$
$564$	13.4287	−	36.8951i	0.565451	−	1.55356i
$565$	2.75874	−	12.0123i	0.116061	−	0.505362i
$566$	−13.7146	+	7.91815i	−0.576470	+	0.332825i
$567$	−13.7881	+	19.6915i	−0.579046	+	0.826964i
$568$	−5.89865	+	2.14693i	−0.247502	+	0.0900833i
$569$	26.1048	−	6.99477i	1.09437	−	0.293236i	0.333901	−	0.942608i	$-0.391635\pi$
$569$	26.1048	−	6.99477i	1.09437	−	0.293236i	0.760471	+	0.649372i	$0.224968\pi$
$570$	−0.143411	−	0.0928985i	−0.00600684	−	0.00389109i
$571$	−3.80445	+	3.19232i	−0.159211	+	0.133594i	−0.718913	−	0.695100i	$-0.755360\pi$
$571$	−3.80445	+	3.19232i	−0.159211	+	0.133594i	0.559702	+	0.828694i	$0.310916\pi$
$572$	−0.257261	+	0.706818i	−0.0107566	+	0.0295535i
$573$	−12.8418	−	2.26436i	−0.536476	−	0.0945951i
$574$	−6.87056	−	9.81218i	−0.286772	−	0.409553i
$575$	31.2291	−	7.86249i	1.30234	−	0.327889i
$576$	4.21398	+	5.02202i	0.175582	+	0.209251i
$577$	−5.41007	−	6.44747i	−0.225224	−	0.268412i	0.641585	−	0.767052i	$-0.278277\pi$
$577$	−5.41007	−	6.44747i	−0.225224	−	0.268412i	−0.866809	+	0.498641i	$0.833833\pi$
$578$	−5.89271	+	10.2065i	−0.245104	+	0.424533i
$579$	−18.0014	−	8.39421i	−0.748114	−	0.348851i
$580$	11.7989	+	3.81874i	0.489925	+	0.158565i
$581$	4.43307	+	7.67831i	0.183915	+	0.318550i
$582$	6.77048	+	25.2678i	0.280645	+	1.04738i
$583$	−6.38950	−	13.7023i	−0.264626	−	0.567492i
$584$	−1.81371	+	6.76886i	−0.0750519	+	0.280097i
$585$	−5.57913	−	2.36065i	−0.230669	−	0.0976007i
$586$	−0.114719	+	0.114719i	−0.00473898	+	0.00473898i
$587$	−20.8635	−	17.5066i	−0.861129	−	0.722573i	0.101082	−	0.994878i	$-0.467770\pi$
$587$	−20.8635	−	17.5066i	−0.861129	−	0.722573i	−0.962211	+	0.272305i	$0.912214\pi$
$588$	5.45878	−	11.7064i	0.225116	−	0.482764i
$589$	0.243666	+	0.0429649i	0.0100401	+	0.00177034i
$590$	−1.47184	+	4.54761i	−0.0605947	+	0.187222i
$591$		−	45.2264i		−	1.86037i
$592$	5.91873	−	1.40306i	0.243258	−	0.0576656i
$593$	2.66427	−	2.66427i	0.109408	−	0.109408i	−0.650283	−	0.759692i	$-0.725350\pi$
$593$	2.66427	−	2.66427i	0.109408	−	0.109408i	0.759692	+	0.650283i	$0.225350\pi$
$594$	−11.4753	+	16.3884i	−0.470835	+	0.672422i
$595$	−5.27282	+	6.76489i	−0.216164	+	0.277333i
$596$	−3.83743	−	10.5433i	−0.157187	−	0.431869i
$597$	12.8489	−	15.3128i	0.525871	−	0.626709i
$598$	−2.66167			−0.108844
$599$	−19.8793	+	23.6913i	−0.812247	+	0.967999i	−0.999899	−	0.0142371i	$-0.995468\pi$
$599$	−19.8793	+	23.6913i	−0.812247	+	0.967999i	0.187651	+	0.982236i	$0.439912\pi$
$600$	−5.06559	−	14.6025i	−0.206802	−	0.596146i
$601$	7.59007	+	2.76256i	0.309605	+	0.112687i	0.492150	−	0.870510i	$-0.336211\pi$
$601$	7.59007	+	2.76256i	0.309605	+	0.112687i	−0.182545	+	0.983198i	$0.558433\pi$
$602$	−6.48931	+	1.73880i	−0.264484	+	0.0708684i
$603$	−19.6540	+	73.3498i	−0.800373	+	2.98703i
$604$	22.8753	−	4.03353i	0.930782	−	0.164122i
$605$	10.3603	+	13.7158i	0.421207	+	0.557627i
$606$	−11.3588	−	42.3915i	−0.461419	−	1.72204i
$607$	23.2097	−	19.4752i	0.942051	−	0.790475i	−0.0358902	−	0.999356i	$-0.511427\pi$
$607$	23.2097	−	19.4752i	0.942051	−	0.790475i	0.977941	+	0.208881i	$0.0669822\pi$
$608$	−0.00215450	+	0.0246260i	−8.73765e−5	+	0.000998718i
$609$	26.1002	−	12.1707i	1.05763	−	0.493182i
$610$	−11.2170	+	14.3912i	−0.454164	+	0.582681i
$611$	4.29966	−	3.01065i	0.173946	−	0.121798i
$612$	14.0676	+	5.12019i	0.568650	+	0.206972i
$613$	−26.8620	−	2.35012i	−1.08495	−	0.0949205i	−0.469373	−	0.883000i	$-0.655520\pi$
$613$	−26.8620	−	2.35012i	−1.08495	−	0.0949205i	−0.615574	+	0.788079i	$0.711076\pi$
$614$	2.19553	−	25.0950i	0.0886042	−	1.01275i
$615$	41.7718	−	26.1687i	1.68440	−	1.05522i
$616$	−1.29210	+	2.77091i	−0.0520600	+	0.111643i
$617$	−12.0783	−	8.45733i	−0.486255	−	0.340479i	0.304603	−	0.952479i	$-0.401476\pi$
$617$	−12.0783	−	8.45733i	−0.486255	−	0.340479i	−0.790858	+	0.612000i	$0.790365\pi$
$618$	−22.7869	−	6.10573i	−0.916623	−	0.245608i
$619$	−5.35221	+	9.27029i	−0.215123	+	0.372604i	−0.953311	−	0.301991i	$-0.902349\pi$
$619$	−5.35221	+	9.27029i	−0.215123	+	0.372604i	0.738187	+	0.674596i	$0.235682\pi$
$620$	14.9949	+	16.6151i	0.602208	+	0.667278i
$621$	−68.3829	−	18.3231i	−2.74411	−	0.735282i
$622$	7.27408	−	0.636400i	0.291664	−	0.0255173i
$623$			2.05745i			0.0824298i
$624$	0.111339	+	1.27262i	0.00445714	+	0.0509454i
$625$	−0.757741	+	24.9885i	−0.0303096	+	0.999541i
$626$	−3.44026	+	19.5107i	−0.137500	+	0.779803i
$627$	−0.136974	+	0.0241522i	−0.00547020	+	0.000964544i
$628$	−9.81651	−	9.81651i	−0.391721	−	0.391721i
$629$	10.1030	−	9.53257i	0.402832	−	0.380088i
$630$	−21.7547	−	11.5352i	−0.866730	−	0.459573i
$631$	−30.3132	−	21.2255i	−1.20675	−	0.844975i	−0.215439	−	0.976517i	$-0.569118\pi$
$631$	−30.3132	−	21.2255i	−1.20675	−	0.844975i	−0.991311	+	0.131542i	$0.958007\pi$
$632$	8.02824	+	11.4655i	0.319346	+	0.456074i
$633$	−49.4919	−	23.0785i	−1.96713	−	0.917287i
$634$	−13.3293	+	1.16616i	−0.529373	+	0.0463142i
$635$	−16.2766	+	30.6968i	−0.645917	+	1.21817i
$636$	−19.6700	−	16.5051i	−0.779965	−	0.654468i
$637$	1.49543	−	0.863384i	0.0592509	−	0.0342085i
$638$	9.14888	−	4.26619i	0.362208	−	0.168900i
$639$	−35.6387	−	20.5760i	−1.40985	−	0.813975i
$640$	−1.52312	+	1.63711i	−0.0602065	+	0.0647123i
$641$	−4.50684	−	25.5596i	−0.178010	−	1.00954i	−0.934612	−	0.355668i	$-0.884253\pi$
$641$	−4.50684	−	25.5596i	−0.178010	−	1.00954i	0.756603	−	0.653875i	$-0.226858\pi$
$642$	−13.0901	−	35.9648i	−0.516626	−	1.41942i
$643$	4.90962	+	2.83457i	0.193616	+	0.111785i	0.593674	−	0.804705i	$-0.297677\pi$
$643$	4.90962	+	2.83457i	0.193616	+	0.111785i	−0.400058	+	0.916490i	$0.631010\pi$
$644$	−10.7776	−	0.942921i	−0.424698	−	0.0371563i
$645$	−5.77891	−	27.0350i	−0.227545	−	1.06450i
$646$	0.0238566	+	0.0511607i	0.000938626	+	0.00201289i
$647$	6.02255	−	34.1556i	0.236771	−	1.34280i	−0.602081	−	0.798435i	$-0.705661\pi$
$647$	6.02255	−	34.1556i	0.236771	−	1.34280i	0.838852	−	0.544360i	$-0.183227\pi$
$648$	−2.48507	+	14.0936i	−0.0976229	+	0.553647i
$649$	1.64430	+	3.52621i	0.0645444	+	0.138416i
$650$	0.564982	−	1.98754i	0.0221604	−	0.0779578i
$651$	51.7744	+	4.52968i	2.02920	+	0.177532i
$652$	6.82483	+	3.94032i	0.267281	+	0.154315i
$653$	12.3110	+	33.8242i	0.481767	+	1.32364i	0.907977	+	0.419019i	$0.137626\pi$
$653$	12.3110	+	33.8242i	0.481767	+	1.32364i	−0.426211	+	0.904624i	$0.640152\pi$
$654$	−6.02530	−	34.1712i	−0.235608	−	1.33620i
$655$	−0.935202	−	25.9272i	−0.0365414	−	1.01306i
$656$	−6.17571	−	3.56555i	−0.241121	−	0.139211i
$657$	−41.6363	+	19.4153i	−1.62439	+	0.757464i
$658$	18.4767	−	10.6675i	0.720297	−	0.415864i
$659$	−21.5123	−	18.0510i	−0.838000	−	0.703165i	0.119113	−	0.992881i	$-0.461995\pi$
$659$	−21.5123	−	18.0510i	−0.838000	−	0.703165i	−0.957113	+	0.289715i	$0.906439\pi$
$660$	−11.1153	−	5.89373i	−0.432661	−	0.229413i
$661$	−29.7502	+	2.60280i	−1.15715	+	0.101237i	−0.649524	−	0.760341i	$-0.725032\pi$
$661$	−29.7502	+	2.60280i	−1.15715	+	0.101237i	−0.507624	+	0.861579i	$0.669476\pi$
$662$	21.5057	+	10.0283i	0.835845	+	0.389761i
$663$	1.67322	+	2.38961i	0.0649827	+	0.0928049i
$664$	4.32369	+	3.02748i	0.167792	+	0.117489i
$665$	−0.0272485	−	0.0887613i	−0.00105665	−	0.00344201i
$666$	31.9876	+	23.8115i	1.23950	+	0.922678i
$667$	25.2587	+	25.2587i	0.978019	+	0.978019i
$668$	6.09806	−	1.07525i	0.235941	−	0.0416028i
$669$	−13.5506	+	76.8494i	−0.523898	+	2.97117i
$670$	−25.6530	−	3.57526i	−0.991061	−	0.138124i
$671$	1.29446	+	14.7957i	0.0499720	+	0.571182i
$672$			5.19251i			0.200306i
$673$	34.4456	−	3.01360i	1.32778	−	0.116166i	0.598908	−	0.800818i	$-0.295601\pi$
$673$	34.4456	−	3.01360i	1.32778	−	0.116166i	0.728870	+	0.684652i	$0.240046\pi$
$674$	6.11378	+	1.63818i	0.235494	+	0.0631005i
$675$	28.1977	−	47.1739i	1.08533	−	1.81573i
$676$	6.41461	−	11.1104i	0.246716	−	0.427324i
$677$	−3.79992	−	1.01819i	−0.146043	−	0.0391321i	0.185057	−	0.982728i	$-0.440753\pi$
$677$	−3.79992	−	1.01819i	−0.146043	−	0.0391321i	−0.331100	+	0.943596i	$0.607420\pi$
$678$	−13.9573	−	9.77300i	−0.536027	−	0.375330i
$679$	−6.00735	+	12.8828i	−0.230541	+	0.494397i
$680$	−1.14292	+	4.97661i	−0.0438292	+	0.190844i
$681$	−5.68450	+	64.9741i	−0.217831	+	2.48981i
$682$	18.1485	+	1.58778i	0.694940	+	0.0607994i
$683$	1.55704	+	0.566717i	0.0595786	+	0.0216848i	0.371638	−	0.928378i	$-0.378796\pi$
$683$	1.55704	+	0.566717i	0.0595786	+	0.0216848i	−0.312059	+	0.950063i	$0.601019\pi$
$684$	−0.132752	+	0.0929537i	−0.00507588	+	0.00355417i
$685$	−19.9064	−	15.5158i	−0.760585	−	0.592829i
$686$	17.0177	−	7.93550i	0.649740	−	0.302979i
$687$	7.30333	−	83.4775i	0.278640	−	3.18486i
$688$	−3.06382	+	2.57085i	−0.116807	+	0.0980129i
$689$	−0.888449	−	3.31574i	−0.0338472	−	0.126319i
$690$	6.14534	−	44.0936i	0.233949	−	1.67862i
$691$	20.7732	−	3.66287i	0.790249	−	0.139342i	0.236066	−	0.971737i	$-0.424142\pi$
$691$	20.7732	−	3.66287i	0.790249	−	0.139342i	0.554183	+	0.832395i	$0.313031\pi$
$692$	−3.47294	+	12.9612i	−0.132021	+	0.492711i
$693$	−19.3604	+	5.18761i	−0.735442	+	0.197061i
$694$	−15.8783	−	5.77922i	−0.602731	−	0.219376i
$695$	20.1126	−	21.6178i	0.762913	−	0.820009i
$696$	11.0202	−	13.1334i	0.417721	−	0.497821i
$697$	−16.2842			−0.616808
$698$	0.244572	−	0.291469i	0.00925718	−	0.0110323i
$699$	−7.43983	−	20.4408i	−0.281400	−	0.773140i
$700$	2.99183	−	7.84780i	0.113081	−	0.296619i
$701$	−16.2365	+	23.1881i	−0.613244	+	0.875804i	−0.998902	−	0.0468380i	$-0.985086\pi$
$701$	−16.2365	+	23.1881i	−0.613244	+	0.875804i	0.385658	+	0.922642i	$0.373974\pi$
$702$	−3.21198	+	3.21198i	−0.121229	+	0.121229i
$703$	0.0218000	+	0.148778i	0.000822202	+	0.00561127i
$704$			1.82013i			0.0685987i
$705$	39.9477	+	78.1798i	1.50452	+	2.94442i
$706$	−29.3046	−	5.16718i	−1.10289	−	0.194470i
$707$	10.0785	−	21.6134i	0.379040	−	0.812854i
$708$	5.06195	+	4.24748i	0.190240	+	0.159630i
$709$	−21.1439	+	21.1439i	−0.794076	+	0.794076i	−0.982154	−	0.188078i	$-0.939774\pi$
$709$	−21.1439	+	21.1439i	−0.794076	+	0.794076i	0.188078	+	0.982154i	$0.439774\pi$
$710$	5.46957	−	12.9268i	0.205269	−	0.485132i
$711$	−23.7493	+	88.6334i	−0.890667	+	3.32401i
$712$	0.517645	+	1.11009i	0.0193996	+	0.0416025i
$713$	16.6849	+	62.2690i	0.624856	+	2.33199i
$714$	5.92868	+	10.2688i	0.221875	+	0.384299i
$715$	−0.765298	−	1.49773i	−0.0286205	−	0.0560119i
$716$	3.28254	+	1.53067i	0.122674	+	0.0572040i
$717$	−19.4285	+	33.6511i	−0.725570	+	1.25672i
$718$	−8.08180	−	9.63152i	−0.301610	−	0.359445i
$719$	19.8970	+	23.7123i	0.742034	+	0.884321i	0.996571	−	0.0827418i	$-0.0263677\pi$
$719$	19.8970	+	23.7123i	0.742034	+	0.884321i	−0.254537	+	0.967063i	$0.581923\pi$
$720$	−14.6400	−	0.750395i	−0.545599	−	0.0279656i
$721$	−7.35265	−	10.5007i	−0.273827	−	0.391066i
$722$	18.7107	+	3.29921i	0.696342	+	0.122784i
$723$	3.32191	−	9.12687i	0.123543	−	0.339432i
$724$	−0.906351	+	0.760518i	−0.0336843	+	0.0282644i
$725$	−24.2229	+	13.4997i	−0.899614	+	0.501368i
$726$	22.9531	−	6.15026i	0.851869	−	0.228258i
$727$	−5.20601	+	1.89483i	−0.193080	+	0.0702755i	−0.436751	−	0.899583i	$-0.643871\pi$
$727$	−5.20601	+	1.89483i	−0.193080	+	0.0702755i	0.243670	+	0.969858i	$0.421649\pi$
$728$	−0.398158	+	0.568629i	−0.0147567	+	0.0210748i
$729$	7.02809	−	4.05767i	0.260300	−	0.150284i
$730$	−8.31885	−	13.2790i	−0.307894	−	0.491478i
$731$	−3.12372	+	8.58234i	−0.115535	+	0.317429i
$732$	12.6123	+	21.8451i	0.466162	+	0.807417i
$733$	−3.02904	−	34.6221i	−0.111880	−	1.27880i	−0.819860	−	0.572564i	$-0.805949\pi$
$733$	−3.02904	−	34.6221i	−0.111880	−	1.27880i	0.707980	−	0.706232i	$-0.249607\pi$
$734$	8.93799	+	8.93799i	0.329907	+	0.329907i
$735$	10.8503	+	26.7668i	0.400218	+	0.987309i
$736$	−6.05230	+	2.20286i	−0.223091	+	0.0811984i
$737$	−17.2702	+	12.0927i	−0.636155	+	0.445441i
$738$	−8.11805	−	46.0397i	−0.298829	−	1.69475i
$739$	−5.18614			−0.190775			−0.0953876	−	0.995440i	$-0.530409\pi$
$739$	−5.18614			−0.190775			−0.0953876	+	0.995440i	$0.530409\pi$
$740$	−6.71796	+	11.8266i	−0.246957	+	0.434755i
$741$	−0.0315794			−0.00116010
$742$	−2.42288	−	13.7408i	−0.0889466	−	0.504441i
$743$	1.36055	−	0.952668i	0.0499138	−	0.0349500i	−0.548353	−	0.836247i	$-0.684745\pi$
$743$	1.36055	−	0.952668i	0.0499138	−	0.0349500i	0.598267	+	0.801297i	$0.295856\pi$
$744$	29.0745	−	10.5823i	1.06592	−	0.387964i
$745$	23.1053	+	9.77632i	0.846512	+	0.358177i
$746$	23.4607	+	23.4607i	0.858957	+	0.858957i
$747$	3.01586	+	34.4714i	0.110345	+	1.26124i
$748$	2.07818	+	3.59951i	0.0759856	+	0.131611i
$749$	7.11303	−	19.5429i	0.259905	−	0.714082i
$750$	31.6214	+	13.9485i	1.15465	+	0.509326i
$751$	−10.9195	+	6.30436i	−0.398457	+	0.230049i	−0.685818	−	0.727773i	$-0.740555\pi$
$751$	−10.9195	+	6.30436i	−0.398457	+	0.230049i	0.287361	+	0.957822i	$0.407222\pi$
$752$	7.28519	−	10.4043i	0.265664	−	0.379407i
$753$	12.6093	−	4.58939i	0.459507	−	0.167247i
$754$	2.21388	−	0.593207i	0.0806247	−	0.0216033i
$755$	−28.2384	+	43.5928i	−1.02770	+	1.58651i
$756$	−14.1438	+	11.8681i	−0.514406	+	0.431638i
$757$	−8.46061	+	23.2453i	−0.307506	+	0.844866i	0.685635	+	0.727945i	$0.259525\pi$
$757$	−8.46061	+	23.2453i	−0.307506	+	0.844866i	−0.993141	+	0.116921i	$0.962698\pi$
$758$	−24.6675	−	4.34954i	−0.895963	−	0.157983i
$759$	−20.7855	−	29.6848i	−0.754468	−	1.07749i
$760$	−0.0370339	−	0.0410355i	−0.00134336	−	0.00148851i
$761$	15.6899	+	18.6985i	0.568758	+	0.677819i	0.971376	−	0.237549i	$-0.0763440\pi$
$761$	15.6899	+	18.6985i	0.568758	+	0.677819i	−0.402618	+	0.915368i	$0.631900\pi$
$762$	30.8752	+	36.7956i	1.11849	+	1.33296i
$763$	9.42735	−	16.3286i	0.341293	−	0.591137i
$764$	−3.82312	−	1.78275i	−0.138316	−	0.0644977i
$765$	−29.8089	+	15.2315i	−1.07774	+	0.550697i
$766$	−4.92486	−	8.53011i	−0.177942	−	0.308205i
$767$	0.228637	+	0.853285i	0.00825560	+	0.0308103i
$768$	1.30642	+	2.80162i	0.0471412	+	0.101095i
$769$	−9.02721	+	33.6900i	−0.325529	+	1.21489i	0.588249	+	0.808680i	$0.299817\pi$
$769$	−9.02721	+	33.6900i	−0.325529	+	1.21489i	−0.913779	+	0.406213i	$0.866849\pi$
$770$	−2.56826	−	6.33572i	−0.0925537	−	0.228323i
$771$	−52.5768	+	52.5768i	−1.89351	+	1.89351i
$772$	−4.92212	−	4.13015i	−0.177151	−	0.148647i
$773$	11.4168	−	24.4834i	0.410633	−	0.880605i	−0.586850	−	0.809696i	$-0.699632\pi$
$773$	11.4168	−	24.4834i	0.410633	−	0.880605i	0.997483	−	0.0709094i	$-0.0225901\pi$
$774$	−25.8218	−	4.55308i	−0.928145	−	0.163657i
$775$	−50.0396	−	0.758515i	−1.79747	−	0.0272467i
$776$			8.46233i			0.303780i
$777$	7.28543	+	30.7331i	0.261363	+	1.10254i
$778$	5.81146	−	5.81146i	0.208351	−	0.208351i
$779$	0.101111	−	0.144401i	0.00362268	−	0.00517372i
$780$	−2.25299	−	1.75607i	−0.0806700	−	0.0628773i
$781$	−3.90770	−	10.7363i	−0.139828	−	0.384175i
$782$	−9.45393	+	11.2668i	−0.338072	+	0.402898i
$783$	60.9620			2.17860
$784$	2.68585	−	3.20087i	0.0959232	−	0.114317i
$785$	31.0224	−	1.11899i	1.10724	−	0.0399383i
$786$	−33.7033	−	12.2670i	−1.20216	−	0.437549i
$787$	42.1778	−	11.3015i	1.50348	−	0.402855i	0.589213	−	0.807978i	$-0.299438\pi$
$787$	42.1778	−	11.3015i	1.50348	−	0.402855i	0.914262	+	0.405123i	$0.132771\pi$
$788$	3.78665	−	14.1320i	0.134894	−	0.503430i
$789$	44.1941	−	7.79260i	1.57335	−	0.277424i
$790$	−30.9982	−	4.32023i	−1.10287	−	0.153707i
$791$	−2.39632	−	8.94318i	−0.0852032	−	0.317983i
$792$	−9.14073	+	7.66998i	−0.324802	+	0.272541i
$793$	−0.293904	+	3.35934i	−0.0104368	+	0.119294i
$794$	13.0742	−	6.09660i	0.463986	−	0.216360i
$795$	56.9802	−	7.06270i	2.02088	−	0.250488i
$796$	5.29701	−	3.70900i	0.187747	−	0.131462i
$797$	48.5684	+	17.6774i	1.72038	+	0.626167i	0.997873	−	0.0651956i	$-0.0207671\pi$
$797$	48.5684	+	17.6774i	1.72038	+	0.626167i	0.722508	+	0.691363i	$0.242989\pi$
$798$	−0.127871	−	0.0111873i	−0.00452659	−	0.000396025i
$799$	2.52788	−	28.8938i	0.0894298	−	1.02219i
$800$	−0.360234	−	4.98701i	−0.0127362	−	0.176317i
$801$	−3.39357	+	7.27753i	−0.119906	+	0.257139i
$802$	9.86559	+	6.90796i	0.348366	+	0.243929i
$803$	−12.3202	−	3.30119i	−0.434770	−	0.116496i
$804$	−17.9033	+	31.0095i	−0.631401	+	1.09362i
$805$	17.9593	−	16.2080i	0.632981	−	0.571256i
$806$	3.99537	+	1.07056i	0.140731	+	0.0377087i
$807$	37.6860	−	3.29710i	1.32661	−	0.116063i
$808$		−	14.1972i		−	0.499455i
$809$	−3.19189	−	36.4835i	−0.112221	−	1.28269i	−0.818396	−	0.574655i	$-0.805136\pi$
$809$	−3.19189	−	36.4835i	−0.112221	−	1.28269i	0.706175	−	0.708038i	$-0.250419\pi$
$810$	−19.2876	−	25.5344i	−0.677697	−	0.897189i
$811$	0.828985	−	4.70141i	0.0291096	−	0.165089i	−0.966788	−	0.255582i	$-0.917733\pi$
$811$	0.828985	−	4.70141i	0.0291096	−	0.165089i	0.995897	+	0.0904927i	$0.0288442\pi$
$812$	9.17458	−	1.61773i	0.321965	−	0.0567711i
$813$	−54.7101	−	54.7101i	−1.91877	−	1.91877i
$814$	2.55376	+	10.7729i	0.0895091	+	0.377588i
$815$	−16.8457	+	5.17141i	−0.590080	+	0.181147i
$816$	5.78240	+	4.04888i	0.202424	+	0.141739i
$817$	−0.0567090	−	0.0809888i	−0.00198400	−	0.00283344i
$818$	2.05558	+	0.958532i	0.0718716	+	0.0335143i
$819$	−4.53350	+	0.396629i	−0.158413	+	0.0138594i
$820$	15.2435	−	4.67955i	0.532327	−	0.163417i
$821$	−37.1368	−	31.1615i	−1.29608	−	1.08754i	−0.990808	−	0.135279i	$-0.956807\pi$
$821$	−37.1368	−	31.1615i	−1.29608	−	1.08754i	−0.305276	−	0.952264i	$-0.598749\pi$
$822$	−30.2169	+	17.4458i	−1.05394	+	0.608491i
$823$	−3.05666	+	1.42535i	−0.106549	+	0.0496844i	−0.475162	−	0.879898i	$-0.657610\pi$
$823$	−3.05666	+	1.42535i	−0.106549	+	0.0496844i	0.368613	+	0.929583i	$0.379833\pi$
$824$	−6.60905	−	3.81573i	−0.230237	−	0.132927i
$825$	26.5785	−	9.22004i	0.925345	−	0.321000i
$826$	0.623513	+	3.53612i	0.0216948	+	0.123037i
$827$	−6.92128	−	19.0161i	−0.240677	−	0.661253i	−0.999945	−	0.0104759i	$-0.996665\pi$
$827$	−6.92128	−	19.0161i	−0.240677	−	0.661253i	0.759269	−	0.650777i	$-0.225557\pi$
$828$	−36.5671	−	21.1120i	−1.27079	−	0.733693i
$829$	−22.3400	−	1.95450i	−0.775901	−	0.0678826i	−0.307675	−	0.951491i	$-0.599551\pi$
$829$	−22.3400	−	1.95450i	−0.775901	−	0.0678826i	−0.468226	+	0.883609i	$0.655107\pi$
$830$	−11.5418	+	2.46714i	−0.400622	+	0.0856356i
$831$	−24.7212	−	53.0147i	−0.857568	−	1.83906i
$832$	−0.0717612	+	0.406978i	−0.00248787	+	0.0141094i
$833$	1.65689	−	9.39671i	0.0574080	−	0.325577i
$834$	−17.2511	−	36.9950i	−0.597355	−	1.28103i
$835$	−7.52775	+	11.6209i	−0.260508	+	0.402158i
$836$	−0.0448226	−	0.00392147i	−0.00155022	−	0.000135627i
$837$	95.2780	+	55.0088i	3.29329	+	1.90138i
$838$	8.09183	+	22.2321i	0.279528	+	0.767996i
$839$	−6.85457	−	38.8742i	−0.236646	−	1.34209i	−0.839119	−	0.543947i	$-0.816929\pi$
$839$	−6.85457	−	38.8742i	−0.236646	−	1.34209i	0.602473	−	0.798139i	$-0.294182\pi$
$840$	−8.50070	−	7.90880i	−0.293302	−	0.272880i
$841$	−1.52385	−	0.879794i	−0.0525465	−	0.0303377i
$842$	−22.4828	+	10.4839i	−0.774809	+	0.361299i
$843$	−50.7031	+	29.2734i	−1.74631	+	1.00823i
$844$	−13.5325	−	11.3552i	−0.465810	−	0.390861i
$845$	8.41876	+	27.4239i	0.289614	+	0.943410i
$846$	82.9504	−	7.25722i	2.85189	−	0.249508i
$847$	11.7027	+	5.45704i	0.402108	+	0.187506i
$848$	−4.76439	−	6.80426i	−0.163610	−	0.233659i
$849$	−40.1007	−	28.0788i	−1.37625	−	0.963662i
$850$	−6.40644	−	9.45105i	−0.219739	−	0.324168i
$851$	−32.7312	+	21.5299i	−1.12201	+	0.738035i
$852$	−13.7210	−	13.7210i	−0.470073	−	0.470073i
$853$	−40.5313	+	7.14676i	−1.38776	+	0.244700i	−0.817106	−	0.576487i	$-0.804423\pi$
$853$	−40.5313	+	7.14676i	−1.38776	+	0.244700i	−0.570659	+	0.821187i	$0.693312\pi$
$854$	−2.38015	+	13.4985i	−0.0814471	+	0.461909i
$855$	0.0500211	−	0.358908i	0.00171068	−	0.0122744i
$856$	−1.07908	−	12.3340i	−0.0368823	−	0.421566i
$857$			52.5711i			1.79579i	0.440205	+	0.897897i	$0.354906\pi$
$857$			52.5711i			1.79579i	−0.440205	+	0.897897i	$0.645094\pi$
$858$	−2.31632	+	0.202652i	−0.0790780	+	0.00691843i
$859$	−2.72195	−	0.729345i	−0.0928718	−	0.0248849i	0.212084	−	0.977251i	$-0.431975\pi$
$859$	−2.72195	−	0.729345i	−0.0928718	−	0.0248849i	−0.304956	+	0.952367i	$0.598642\pi$
$860$	0.457799	−	8.93152i	0.0156108	−	0.304562i
$861$	18.5142	−	32.0675i	0.630961	−	1.09286i
$862$	−13.6637	−	3.66116i	−0.465386	−	0.124700i
$863$	−31.6275	−	22.1458i	−1.07661	−	0.753851i	−0.105967	−	0.994370i	$-0.533794\pi$
$863$	−31.6275	−	22.1458i	−1.07661	−	0.753851i	−0.970645	+	0.240518i	$0.922683\pi$
$864$	−4.64533	+	9.96195i	−0.158037	+	0.338913i
$865$	−15.9292	−	25.4270i	−0.541608	−	0.864543i
$866$	−0.643166	+	7.35142i	−0.0218557	+	0.249811i
$867$	−36.2929	−	3.17522i	−1.23257	−	0.107836i
$868$	15.7988	+	5.75029i	0.536246	+	0.195177i
$869$	−20.8687	+	14.6124i	−0.707923	+	0.495693i
$870$	4.71568	+	38.0450i	0.159877	+	1.28985i
$871$	−4.33836	+	2.02301i	−0.147000	+	0.0685471i
$872$	0.978298	−	11.1820i	0.0331293	−	0.378670i
$873$	−42.4980	+	35.6601i	−1.43834	+	1.20691i
$874$	−0.0412080	−	0.153790i	−0.00139388	−	0.00520204i
$875$	8.29077	+	16.8510i	0.280279	+	0.569669i
$876$	−21.3332	+	3.76162i	−0.720782	+	0.127093i
$877$	0.889930	−	3.32127i	0.0300508	−	0.112151i	−0.949271	−	0.314458i	$-0.898177\pi$
$877$	0.889930	−	3.32127i	0.0300508	−	0.112151i	0.979322	+	0.202307i	$0.0648439\pi$
$878$	0.174862	−	0.0468542i	0.00590131	−	0.00158125i
$879$	−0.471268	−	0.171527i	−0.0158955	−	0.00578548i
$880$	−2.97974	−	2.77227i	−0.100447	−	0.0934531i
$881$	−14.0526	+	16.7473i	−0.473445	+	0.564230i	−0.948927	−	0.315496i	$-0.897829\pi$
$881$	−14.0526	+	16.7473i	−0.473445	+	0.564230i	0.475482	+	0.879725i	$0.342274\pi$
$882$	27.3930			0.922369
$883$	30.8318	−	36.7439i	1.03757	−	1.23653i	0.0664898	−	0.997787i	$-0.478820\pi$
$883$	30.8318	−	36.7439i	1.03757	−	1.23653i	0.971083	−	0.238744i	$-0.0767355\pi$
$884$	0.322761	+	0.886779i	0.0108556	+	0.0298256i
$885$	−14.6635	+	1.81754i	−0.492909	+	0.0610961i
$886$	−8.76513	+	12.5179i	−0.294470	+	0.420547i
$887$	−17.1029	+	17.1029i	−0.574260	+	0.574260i	−0.933316	−	0.359056i	$-0.883099\pi$
$887$	−17.1029	+	17.1029i	−0.574260	+	0.574260i	0.359056	+	0.933316i	$0.383099\pi$
$888$	11.6632	+	14.7490i	0.391391	+	0.494946i
$889$			26.1008i			0.875391i
$890$	−2.60577	−	0.843361i	−0.0873458	−	0.0282695i
$891$	−25.6521	−	4.52315i	−0.859377	−	0.151531i
$892$	−10.6685	+	22.8787i	−0.357209	+	0.766036i
$893$	0.240522	+	0.201822i	0.00804875	+	0.00675370i
$894$	24.5249	−	24.5249i	0.820235	−	0.820235i
$895$	−7.50557	+	3.04247i	−0.250883	+	0.101699i
$896$	−0.434751	+	1.62251i	−0.0145240	+	0.0542044i
$897$	−3.47725	−	7.45699i	−0.116102	−	0.248982i
$898$	−1.90848	−	7.12253i	−0.0636867	−	0.237682i
$899$	−27.7558	−	48.0744i	−0.925708	−	1.60337i
$900$	23.5268	−	22.8242i	0.784228	−	0.760808i
$901$	−17.1910	−	8.01631i	−0.572717	−	0.267062i
$902$	6.48976	−	11.2406i	0.216085	−	0.374271i
$903$	−13.3492	−	15.9090i	−0.444233	−	0.529417i
$904$	−3.54300	−	4.22238i	−0.117838	−	0.140434i
$905$	0.135428	−	2.64215i	0.00450177	−	0.0878280i
$906$	41.1851	+	58.8184i	1.36828	+	1.95411i
$907$	29.2439	+	5.15649i	0.971028	+	0.171219i	0.636593	−	0.771200i	$-0.280343\pi$
$907$	29.2439	+	5.15649i	0.971028	+	0.171219i	0.334436	+	0.942419i	$0.391454\pi$
$908$	−7.21630	+	19.8266i	−0.239481	+	0.657970i
$909$	71.2986	−	59.8266i	2.36482	−	1.98432i
$910$	−0.324465	−	1.51791i	−0.0107559	−	0.0503184i
$911$	30.8302	−	8.26093i	1.02145	−	0.273697i	0.291044	−	0.956710i	$-0.405997\pi$
$911$	30.8302	−	8.26093i	1.02145	−	0.273697i	0.730406	+	0.683013i	$0.239331\pi$
$912$	−0.0718074	+	0.0261358i	−0.00237778	+	0.000865442i
$913$	−5.51041	+	7.86968i	−0.182368	+	0.260448i
$914$	4.56040	−	2.63295i	0.150845	−	0.0870902i
$915$	−54.9726	−	12.6250i	−1.81734	−	0.417369i
$916$	9.27136	−	25.4729i	0.306334	−	0.841647i
$917$	−9.74468	−	16.8783i	−0.321798	−	0.557370i
$918$	2.18763	+	25.0048i	0.0722027	+	0.825281i
$919$	−4.96902	−	4.96902i	−0.163913	−	0.163913i	0.620385	−	0.784298i	$-0.286976\pi$
$919$	−4.96902	−	4.96902i	−0.163913	−	0.163913i	−0.784298	+	0.620385i	$0.786976\pi$
$920$	5.61205	−	13.2635i	0.185024	−	0.437284i
$921$	73.1748	−	26.6335i	2.41119	−	0.877602i
$922$	13.7112	−	9.60071i	0.451555	−	0.316182i
$923$	−0.450461	−	2.55469i	−0.0148271	−	0.0840886i
$924$	−9.45104			−0.310917
$925$	−9.12922	−	29.0113i	−0.300167	−	0.953887i
$926$	−33.0544			−1.08624
$927$	−8.68767	−	49.2702i	−0.285340	−	1.61825i
$928$	4.54313	−	3.18113i	0.149135	−	0.104426i
$929$	−0.519259	+	0.188995i	−0.0170363	+	0.00620072i	−0.350524	−	0.936554i	$-0.613997\pi$
$929$	−0.519259	+	0.188995i	−0.0170363	+	0.00620072i	0.333488	+	0.942754i	$0.391774\pi$
$930$	−26.9596	+	63.7161i	−0.884039	+	2.08933i
$931$	0.0730382	+	0.0730382i	0.00239373	+	0.00239373i
$932$	−0.613301	−	7.01007i	−0.0200894	−	0.229622i
$933$	11.2859	+	19.5478i	0.369485	+	0.639966i
$934$	1.74339	−	4.78991i	0.0570453	−	0.156731i
$935$	−9.05807	−	2.08027i	−0.296231	−	0.0680321i
$936$	−2.34625	+	1.35461i	−0.0766897	+	0.0442768i
$937$	3.19447	−	4.56218i	0.104359	−	0.149040i	−0.763576	−	0.645718i	$-0.776558\pi$
$937$	3.19447	−	4.56218i	0.104359	−	0.149040i	0.867935	+	0.496678i	$0.165447\pi$
$938$	−18.2836	+	6.65467i	−0.596979	+	0.217283i
$939$	−59.1559	+	15.8508i	−1.93048	+	0.517270i
$940$	5.93680	+	27.7736i	0.193637	+	0.905876i
$941$	1.54807	−	1.29899i	0.0504658	−	0.0423458i	−0.617206	−	0.786802i	$-0.711735\pi$
$941$	1.54807	−	1.29899i	0.0504658	−	0.0423458i	0.667672	+	0.744456i	$0.267291\pi$
$942$	14.6777	−	40.3266i	0.478224	−	1.31391i
$943$	45.2317	+	7.97557i	1.47295	+	0.259720i
$944$	1.22609	+	1.75104i	0.0399058	+	0.0569914i
$945$	2.11338	−	41.2314i	0.0687484	−	1.34126i
$946$	−4.67929	−	5.57656i	−0.152137	−	0.181309i
$947$	−13.6610	−	16.2805i	−0.443922	−	0.529045i	0.496963	−	0.867772i	$-0.334448\pi$
$947$	−13.6610	−	16.2805i	−0.443922	−	0.529045i	−0.940885	+	0.338726i	$0.890004\pi$
$948$	−21.6338	+	37.4708i	−0.702632	+	1.21699i
$949$	−2.62462	−	1.22388i	−0.0851989	−	0.0397289i
$950$	0.123586	+	0.00187336i	0.00400967	+	6.07798e-5i
$951$	−20.6807	−	35.8201i	−0.670618	−	1.16154i
$952$	0.992775	+	3.70509i	0.0321760	+	0.120083i
$953$	12.3564	+	26.4983i	0.400262	+	0.858365i	0.998377	+	0.0569545i	$0.0181390\pi$
$953$	12.3564	+	26.4983i	0.400262	+	0.858365i	−0.598115	+	0.801411i	$0.704083\pi$
$954$	14.0941	−	52.5999i	0.456313	−	1.70298i
$955$	8.74162	−	3.54352i	0.282872	−	0.114666i
$956$	−8.88835	+	8.88835i	−0.287470	+	0.287470i
$957$	23.9045	+	20.0583i	0.772723	+	0.648391i
$958$	−16.7090	+	35.8325i	−0.539842	+	1.15769i
$959$	−18.6716	−	3.29232i	−0.602939	−	0.106314i
$960$	−6.57637	−	2.12845i	−0.212251	−	0.0686954i
$961$		−	69.1813i		−	2.23166i
$962$	0.146281	+	2.50948i	0.00471628	+	0.0809089i
$963$	57.3942	−	57.3942i	1.84950	−	1.84950i
$964$	1.80216	−	2.57375i	0.0580437	−	0.0828951i
$965$	14.2585	−	1.76734i	0.458996	−	0.0568926i
$966$	−11.4384	−	31.4267i	−0.368024	−	1.01114i
$967$	−9.79049	+	11.6678i	−0.314841	+	0.375213i	−0.900137	−	0.435607i	$-0.856534\pi$
$967$	−9.79049	+	11.6678i	−0.314841	+	0.375213i	0.585296	+	0.810820i	$0.300978\pi$
$968$	7.68713			0.247074
$969$	−0.112166	+	0.133674i	−0.00360329	+	0.00429423i
$970$	−13.8537	−	12.8891i	−0.444817	−	0.413845i
$971$	−49.7545	−	18.1092i	−1.59670	−	0.581151i	−0.617950	−	0.786217i	$-0.712037\pi$
$971$	−49.7545	−	18.1092i	−1.59670	−	0.581151i	−0.978748	+	0.205066i	$0.934259\pi$
$972$	−10.8795	+	2.91515i	−0.348960	+	0.0935036i
$973$	5.74083	−	21.4251i	0.184043	−	0.686857i
$974$	−10.9891	+	1.93767i	−0.352112	+	0.0620868i
$975$	6.30643	−	1.01369i	0.201967	−	0.0324641i
$976$	2.11196	+	7.88194i	0.0676022	+	0.252295i
$977$	−26.1426	+	21.9362i	−0.836376	+	0.701803i	−0.956745	−	0.290926i	$-0.906037\pi$
$977$	−26.1426	+	21.9362i	−0.836376	+	0.701803i	0.120369	+	0.992729i	$0.461592\pi$
$978$	−2.12320	+	24.2682i	−0.0678923	+	0.776013i
$979$	−2.02051	+	0.942181i	−0.0645759	+	0.0301122i
$980$	1.14931	+	9.27232i	0.0367132	+	0.296193i
$981$	60.2788	−	42.2076i	1.92455	−	1.34759i
$982$	−7.45035	−	2.71171i	−0.237750	−	0.0865340i
$983$	−39.4487	−	3.45132i	−1.25822	−	0.110080i	−0.561532	−	0.827455i	$-0.689788\pi$
$983$	−39.4487	−	3.45132i	−1.25822	−	0.110080i	−0.696687	+	0.717375i	$0.745343\pi$
$984$	1.92126	−	21.9601i	0.0612475	−	0.700062i
$985$	17.3680	+	27.7238i	0.553391	+	0.883353i
$986$	5.35240	−	11.4783i	0.170455	−	0.365542i
$987$	54.0246	+	37.8285i	1.71962	+	1.20409i
$988$	−0.00986765	−	0.00264403i	−0.000313932	−	8.41178e-5i
$989$	12.8800	−	22.3088i	0.409559	−	0.709377i
$990$	1.36582	−	26.6466i	0.0434085	−	0.846885i
$991$	46.4977	+	12.4590i	1.47705	+	0.395774i	0.905341	−	0.424685i	$-0.139615\pi$
$991$	46.4977	+	12.4590i	1.47705	+	0.395774i	0.571706	+	0.820458i	$0.306282\pi$
$992$	9.97097	−	0.872347i	0.316579	−	0.0276971i
$993$			73.3520i			2.32776i
$994$	−0.918983	−	10.5040i	−0.0291484	−	0.333167i
$995$	−1.99592	+	14.3210i	−0.0632750	+	0.454007i
$996$	−2.83331	+	16.0685i	−0.0897768	+	0.509150i
$997$	−23.3299	+	4.11369i	−0.738865	+	0.130282i	−0.530400	−	0.847748i	$-0.677958\pi$
$997$	−23.3299	+	4.11369i	−0.738865	+	0.130282i	−0.208466	+	0.978030i	$0.566847\pi$
$998$	10.9165	+	10.9165i	0.345557	+	0.345557i
$999$	−13.5172	+	65.4798i	−0.427667	+	2.07169i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.ba.a.17.1	✓	108
5.3	odd	4		370.2.bd.a.313.1	yes	108
37.24	odd	36		370.2.bd.a.357.1	yes	108
185.98	even	36	inner	370.2.ba.a.283.1	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.ba.a.17.1	✓	108	1.1	even	1	trivial
370.2.ba.a.283.1	yes	108	185.98	even	36	inner
370.2.bd.a.313.1	yes	108	5.3	odd	4
370.2.bd.a.357.1	yes	108	37.24	odd	36

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-2.53220 + 1.77306i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.871338 - 2.05931i) q^{5} +(-2.18584 - 2.18584i) q^{6} +(-0.146400 - 1.67336i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.24221 - 6.16042i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(-2.53220 + 1.77306i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.871338 - 2.05931i) q^{5} +(-2.18584 - 2.18584i) q^{6} +(-0.146400 - 1.67336i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.24221 - 6.16042i) q^{9} +(2.17933 + 0.500504i) q^{10} +(1.57628 - 0.910064i) q^{11} +(1.77306 - 2.53220i) q^{12} +(0.388334 - 0.141342i) q^{13} +(1.62251 - 0.434751i) q^{14} +(1.44489 + 6.75953i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.781019 - 2.14583i) q^{17} +(6.45619 + 1.13840i) q^{18} +(0.0141789 + 0.0202495i) q^{19} +(-0.114463 + 2.23314i) q^{20} +(3.33768 + 3.97770i) q^{21} +(1.16996 + 1.39430i) q^{22} +(-3.22036 + 5.57783i) q^{23} +(2.80162 + 1.30642i) q^{24} +(-3.48154 - 3.58871i) q^{25} +(0.206628 + 0.357891i) q^{26} +(2.84489 + 10.6173i) q^{27} +(0.709893 + 1.52237i) q^{28} +(1.43544 - 5.35715i) q^{29} +(-6.40593 + 2.59672i) q^{30} +(7.07748 - 7.07748i) q^{31} +(0.766044 + 0.642788i) q^{32} +(-2.37785 + 5.09931i) q^{33} +(2.24886 + 0.396534i) q^{34} +(-3.57353 - 1.15658i) q^{35} +6.55579i q^{36} +(5.43589 + 2.72968i) q^{37} +(-0.0174798 + 0.0174798i) q^{38} +(-0.732730 + 1.04645i) q^{39} +(-2.21909 + 0.275056i) q^{40} +(-2.43898 - 6.70104i) q^{41} +(-3.33768 + 3.97770i) q^{42} -3.99954 q^{43} +(-1.16996 + 1.39430i) q^{44} +(-10.7325 - 9.98522i) q^{45} +(-6.05230 - 2.20286i) q^{46} +(12.2686 - 3.28735i) q^{47} +(-0.800073 + 2.98591i) q^{48} +(4.11496 - 0.725579i) q^{49} +(2.92963 - 4.05182i) q^{50} +(1.82700 + 6.81847i) q^{51} +(-0.316573 + 0.265636i) q^{52} +(0.723956 - 8.27486i) q^{53} +(-9.96195 + 4.64533i) q^{54} +(-0.500637 - 4.03902i) q^{55} +(-1.37597 + 0.963465i) q^{56} +(-0.0718074 - 0.0261358i) q^{57} +(5.52503 + 0.483377i) q^{58} +(-0.186306 + 2.12949i) q^{59} +(-3.66965 - 5.85769i) q^{60} +(-3.44856 + 7.39546i) q^{61} +(8.19894 + 5.74096i) q^{62} +(-10.6368 - 2.85014i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0473026 - 0.922858i) q^{65} +(-5.43474 - 1.45624i) q^{66} +(-11.5392 + 1.00955i) q^{67} +2.28355i q^{68} +(-1.73526 - 19.8341i) q^{69} +(0.518468 - 3.72008i) q^{70} +(1.09003 - 6.18185i) q^{71} +(-6.45619 + 1.13840i) q^{72} +(-4.95515 - 4.95515i) q^{73} +(-1.74428 + 5.82731i) q^{74} +(15.1790 + 2.91434i) q^{75} +(-0.0202495 - 0.0141789i) q^{76} +(-1.75363 - 2.50444i) q^{77} +(-1.15779 - 0.539885i) q^{78} +(-13.9435 + 1.21990i) q^{79} +(-0.656218 - 2.13761i) q^{80} +(-10.9628 - 9.19891i) q^{81} +(6.17571 - 3.56555i) q^{82} +(-4.78373 + 2.23069i) q^{83} +(-4.49685 - 2.59626i) q^{84} +(-3.73841 - 3.47811i) q^{85} +(-0.694513 - 3.93878i) q^{86} +(5.86375 + 16.1105i) q^{87} +(-1.57628 - 0.910064i) q^{88} +(-1.22019 - 0.106753i) q^{89} +(7.96984 - 12.3034i) q^{90} +(-0.293368 - 0.629129i) q^{91} +(1.11842 - 6.34288i) q^{92} +(-5.37275 + 30.4704i) q^{93} +(5.36782 + 11.5113i) q^{94} +(0.0540547 - 0.0115546i) q^{95} +(-3.07948 - 0.269420i) q^{96} +(-7.32860 - 4.23117i) q^{97} +(1.42911 + 3.92645i) q^{98} +(-2.07203 - 11.7511i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8}+O(q^{10}) \) 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8	\( 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8} - 12 q^{10} + 36 q^{11} - 6 q^{12} + 6 q^{13} + 12 q^{14} + 24 q^{15} + 12 q^{19} - 6 q^{20} - 42 q^{21} - 6 q^{22} - 6 q^{24} - 18 q^{25} - 6 q^{26} + 6 q^{27} - 12 q^{30} + 6 q^{33} - 54 q^{35} + 12 q^{37} + 48 q^{38} - 12 q^{40} + 48 q^{41} + 42 q^{42} + 6 q^{44} - 90 q^{45} + 6 q^{46} - 12 q^{47} - 12 q^{49} - 12 q^{50} - 12 q^{51} + 6 q^{52} + 36 q^{53} - 18 q^{54} + 36 q^{57} + 6 q^{58} + 24 q^{59} - 54 q^{60} - 36 q^{61} + 54 q^{62} - 96 q^{63} - 54 q^{64} - 18 q^{65} - 42 q^{67} - 96 q^{69} - 12 q^{70} - 48 q^{71} + 84 q^{73} + 42 q^{74} + 252 q^{75} - 6 q^{76} - 66 q^{77} - 24 q^{78} + 66 q^{79} + 6 q^{80} - 108 q^{81} + 36 q^{82} + 48 q^{83} - 36 q^{85} + 108 q^{87} - 36 q^{88} - 66 q^{89} + 6 q^{90} - 18 q^{91} - 12 q^{92} - 12 q^{93} + 18 q^{94} + 90 q^{95} + 12 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) \) 108 * q - 6 * q^3 + 6 * q^5 - 54 * q^8 - 12 * q^10 + 36 * q^11 - 6 * q^12 + 6 * q^13 + 12 * q^14 + 24 * q^15 + 12 * q^19 - 6 * q^20 - 42 * q^21 - 6 * q^22 - 6 * q^24 - 18 * q^25 - 6 * q^26 + 6 * q^27 - 12 * q^30 + 6 * q^33 - 54 * q^35 + 12 * q^37 + 48 * q^38 - 12 * q^40 + 48 * q^41 + 42 * q^42 + 6 * q^44 - 90 * q^45 + 6 * q^46 - 12 * q^47 - 12 * q^49 - 12 * q^50 - 12 * q^51 + 6 * q^52 + 36 * q^53 - 18 * q^54 + 36 * q^57 + 6 * q^58 + 24 * q^59 - 54 * q^60 - 36 * q^61 + 54 * q^62 - 96 * q^63 - 54 * q^64 - 18 * q^65 - 42 * q^67 - 96 * q^69 - 12 * q^70 - 48 * q^71 + 84 * q^73 + 42 * q^74 + 252 * q^75 - 6 * q^76 - 66 * q^77 - 24 * q^78 + 66 * q^79 + 6 * q^80 - 108 * q^81 + 36 * q^82 + 48 * q^83 - 36 * q^85 + 108 * q^87 - 36 * q^88 - 66 * q^89 + 6 * q^90 - 18 * q^91 - 12 * q^92 - 12 * q^93 + 18 * q^94 + 90 * q^95 + 12 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

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