LMFDB - Embedded newform 196.2.p.a.103.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [196,2,Mod(3,196)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(196, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 1]))

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

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

chi := DirichletCharacter("196.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.p (of order $42$, 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:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$312$
Relative dimension:	$26$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			103.5
Character	$\chi$	$=$	196.103
Dual form			196.2.p.a.59.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20490 - 0.740415i) q^{2} +(1.89744 + 1.29365i) q^{3} +(0.903573 + 1.78425i) q^{4} +(0.459106 + 0.0344052i) q^{5} +(-1.32839 - 2.96362i) q^{6} +(-0.101996 - 2.64378i) q^{7} +(0.232371 - 2.81887i) q^{8} +(0.830721 + 2.11664i) q^{9} +O(q^{10})$	\(q+(-1.20490 - 0.740415i) q^{2} +(1.89744 + 1.29365i) q^{3} +(0.903573 + 1.78425i) q^{4} +(0.459106 + 0.0344052i) q^{5} +(-1.32839 - 2.96362i) q^{6} +(-0.101996 - 2.64378i) q^{7} +(0.232371 - 2.81887i) q^{8} +(0.830721 + 2.11664i) q^{9} +(-0.527703 - 0.381383i) q^{10} +(5.59412 + 2.19553i) q^{11} +(-0.593729 + 4.55442i) q^{12} +(-4.33422 + 3.45643i) q^{13} +(-1.83460 + 3.26102i) q^{14} +(0.826618 + 0.659206i) q^{15} +(-2.36711 + 3.22440i) q^{16} +(2.11293 + 2.27720i) q^{17} +(0.566257 - 3.16542i) q^{18} +(3.06297 - 5.30522i) q^{19} +(0.353448 + 0.850248i) q^{20} +(3.22661 - 5.14837i) q^{21} +(-5.11476 - 6.78737i) q^{22} +(-3.35196 + 3.61255i) q^{23} +(4.08755 - 5.04803i) q^{24} +(-4.73456 - 0.713620i) q^{25} +(7.78150 - 0.955531i) q^{26} +(0.371087 - 1.62584i) q^{27} +(4.62502 - 2.57084i) q^{28} +(0.395863 + 1.73439i) q^{29} +(-0.507907 - 1.40632i) q^{30} +(-1.92532 - 3.33475i) q^{31} +(5.23953 - 2.13244i) q^{32} +(7.77426 + 11.4027i) q^{33} +(-0.859803 - 4.30825i) q^{34} +(0.0441332 - 1.21729i) q^{35} +(-3.02601 + 3.39476i) q^{36} +(-2.78661 - 0.859554i) q^{37} +(-7.61863 + 4.12440i) q^{38} +(-12.6954 + 0.951386i) q^{39} +(0.203666 - 1.28616i) q^{40} +(-4.16086 - 8.64012i) q^{41} +(-7.69968 + 3.81425i) q^{42} +(-0.134323 + 0.278925i) q^{43} +(1.13731 + 11.9651i) q^{44} +(0.308565 + 1.00034i) q^{45} +(6.71356 - 1.87093i) q^{46} +(-3.46750 + 0.522642i) q^{47} +(-8.66272 + 3.05589i) q^{48} +(-6.97919 + 0.539309i) q^{49} +(5.17630 + 4.36538i) q^{50} +(1.06326 + 7.05426i) q^{51} +(-10.0834 - 4.61022i) q^{52} +(-0.191211 + 0.0589807i) q^{53} +(-1.65092 + 1.68421i) q^{54} +(2.49276 + 1.20045i) q^{55} +(-7.47617 - 0.326827i) q^{56} +(12.6749 - 6.10392i) q^{57} +(0.807192 - 2.38287i) q^{58} +(-0.0565834 - 0.755053i) q^{59} +(-0.429280 + 2.07053i) q^{60} +(0.954189 - 3.09340i) q^{61} +(-0.149279 + 5.44358i) q^{62} +(5.51122 - 2.41214i) q^{63} +(-7.89201 - 1.31005i) q^{64} +(-2.10879 + 1.43775i) q^{65} +(-0.924455 - 19.4954i) q^{66} +(-10.0103 + 5.77947i) q^{67} +(-2.15391 + 5.82762i) q^{68} +(-11.0335 + 2.51833i) q^{69} +(-0.954472 + 1.43403i) q^{70} +(10.3098 + 2.35315i) q^{71} +(6.15957 - 1.84985i) q^{72} +(-0.0295568 + 0.196097i) q^{73} +(2.72116 + 3.09892i) q^{74} +(-8.06037 - 7.47893i) q^{75} +(12.2335 + 0.671460i) q^{76} +(5.23394 - 15.0136i) q^{77} +(16.0011 + 8.25350i) q^{78} +(-3.05893 - 1.76607i) q^{79} +(-1.19769 + 1.39890i) q^{80} +(7.80788 - 7.24465i) q^{81} +(-1.38384 + 13.4913i) q^{82} +(3.10144 - 3.88908i) q^{83} +(12.1015 + 1.10516i) q^{84} +(0.891712 + 1.11817i) q^{85} +(0.368367 - 0.236623i) q^{86} +(-1.49257 + 3.80302i) q^{87} +(7.48882 - 15.2589i) q^{88} +(-8.95632 + 3.51510i) q^{89} +(0.368879 - 1.43378i) q^{90} +(9.58012 + 11.1062i) q^{91} +(-9.47444 - 2.71654i) q^{92} +(0.660832 - 8.81820i) q^{93} +(4.56497 + 1.93766i) q^{94} +(1.58875 - 2.33027i) q^{95} +(12.7003 + 2.73196i) q^{96} +4.04201i q^{97} +(8.80855 + 4.51768i) q^{98} +13.6646i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9	$ 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9} - 20 q^{10} + 9 q^{12} - 28 q^{13} - 51 q^{14} - 17 q^{16} - 22 q^{17} - 12 q^{18} - 14 q^{20} - 34 q^{21} - 18 q^{22} - 44 q^{24} - 48 q^{25} - 2 q^{26} - 36 q^{28} - 11 q^{30} - 13 q^{32} - 34 q^{33} - 98 q^{34} - 4 q^{36} - 58 q^{37} - 18 q^{38} + 30 q^{40} - 28 q^{41} - 26 q^{42} + 16 q^{44} - 28 q^{45} - 14 q^{46} - 24 q^{49} + 96 q^{50} - 14 q^{52} - 22 q^{53} - 17 q^{54} + 40 q^{56} + 34 q^{57} - 12 q^{58} + 98 q^{60} - 38 q^{61} - 4 q^{64} - 32 q^{65} - 176 q^{66} - 21 q^{68} + 28 q^{69} + 50 q^{70} - 120 q^{72} - 58 q^{73} - 14 q^{74} - 91 q^{76} - 18 q^{77} - 112 q^{78} + 66 q^{80} - 170 q^{81} + 114 q^{82} + 140 q^{84} - 24 q^{85} + 97 q^{86} + 127 q^{88} - 82 q^{89} + 266 q^{90} + 34 q^{92} + 226 q^{94} + 122 q^{96} + 183 q^{98}+O(q^{100}) $ 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9 - 20 * q^10 + 9 * q^12 - 28 * q^13 - 51 * q^14 - 17 * q^16 - 22 * q^17 - 12 * q^18 - 14 * q^20 - 34 * q^21 - 18 * q^22 - 44 * q^24 - 48 * q^25 - 2 * q^26 - 36 * q^28 - 11 * q^30 - 13 * q^32 - 34 * q^33 - 98 * q^34 - 4 * q^36 - 58 * q^37 - 18 * q^38 + 30 * q^40 - 28 * q^41 - 26 * q^42 + 16 * q^44 - 28 * q^45 - 14 * q^46 - 24 * q^49 + 96 * q^50 - 14 * q^52 - 22 * q^53 - 17 * q^54 + 40 * q^56 + 34 * q^57 - 12 * q^58 + 98 * q^60 - 38 * q^61 - 4 * q^64 - 32 * q^65 - 176 * q^66 - 21 * q^68 + 28 * q^69 + 50 * q^70 - 120 * q^72 - 58 * q^73 - 14 * q^74 - 91 * q^76 - 18 * q^77 - 112 * q^78 + 66 * q^80 - 170 * q^81 + 114 * q^82 + 140 * q^84 - 24 * q^85 + 97 * q^86 + 127 * q^88 - 82 * q^89 + 266 * q^90 + 34 * q^92 + 226 * q^94 + 122 * q^96 + 183 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{29}{42}\right)$

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 $

$2$	−1.20490	−	0.740415i	−0.851994	−	0.523552i
$2$	−1.20490	−	0.740415i	−0.851994	−	0.523552i
$3$	1.89744	+	1.29365i	1.09549	+	0.746891i	0.969488	−	0.245139i	$-0.0788336\pi$
$3$	1.89744	+	1.29365i	1.09549	+	0.746891i	0.126000	+	0.992030i	$0.459786\pi$
$4$	0.903573	+	1.78425i	0.451786	+	0.892126i
$5$	0.459106	+	0.0344052i	0.205318	+	0.0153865i	0.176992	−	0.984212i	$-0.443363\pi$
$5$	0.459106	+	0.0344052i	0.205318	+	0.0153865i	0.0283261	+	0.999599i	$0.490982\pi$
$6$	−1.32839	−	2.96362i	−0.542313	−	1.20989i
$7$	−0.101996	−	2.64378i	−0.0385507	−	0.999257i
$7$	−0.101996	−	2.64378i	−0.0385507	−	0.999257i
$8$	0.232371	−	2.81887i	0.0821556	−	0.996620i
$9$	0.830721	+	2.11664i	0.276907	+	0.705548i
$10$	−0.527703	−	0.381383i	−0.166874	−	0.120604i
$11$	5.59412	+	2.19553i	1.68669	+	0.661978i	0.998008	−	0.0630850i	$-0.0200939\pi$
$11$	5.59412	+	2.19553i	1.68669	+	0.661978i	0.688683	+	0.725063i	$0.258189\pi$
$12$	−0.593729	+	4.55442i	−0.171395	+	1.31475i
$13$	−4.33422	+	3.45643i	−1.20210	+	0.958641i	−0.999786	−	0.0206804i	$-0.993417\pi$
$13$	−4.33422	+	3.45643i	−1.20210	+	0.958641i	−0.202311	+	0.979321i	$0.564845\pi$
$14$	−1.83460	+	3.26102i	−0.490318	+	0.871544i
$15$	0.826618	+	0.659206i	0.213432	+	0.170206i
$16$	−2.36711	+	3.22440i	−0.591778	+	0.806101i
$17$	2.11293	+	2.27720i	0.512461	+	0.552302i	0.935278	−	0.353913i	$-0.115149\pi$
$17$	2.11293	+	2.27720i	0.512461	+	0.552302i	−0.422817	+	0.906215i	$0.638959\pi$
$18$	0.566257	−	3.16542i	0.133468	−	0.746098i
$19$	3.06297	−	5.30522i	0.702693	−	1.21710i	−0.264824	−	0.964297i	$-0.585314\pi$
$19$	3.06297	−	5.30522i	0.702693	−	1.21710i	0.967518	−	0.252804i	$-0.0813527\pi$
$20$	0.353448	+	0.850248i	0.0790333	+	0.190121i
$21$	3.22661	−	5.14837i	0.704104	−	1.12347i
$22$	−5.11476	−	6.78737i	−1.09047	−	1.44707i
$23$	−3.35196	+	3.61255i	−0.698932	+	0.753269i	−0.978363	−	0.206897i	$-0.933664\pi$
$23$	−3.35196	+	3.61255i	−0.698932	+	0.753269i	0.279431	+	0.960166i	$0.409854\pi$
$24$	4.08755	−	5.04803i	0.834367	−	1.03042i
$25$	−4.73456	−	0.713620i	−0.946912	−	0.142724i
$26$	7.78150	−	0.955531i	1.52608	−	0.187395i
$27$	0.371087	−	1.62584i	0.0714157	−	0.312892i
$28$	4.62502	−	2.57084i	0.874046	−	0.485843i
$29$	0.395863	+	1.73439i	0.0735100	+	0.322068i	0.998291	−	0.0584303i	$-0.0186095\pi$
$29$	0.395863	+	1.73439i	0.0735100	+	0.322068i	−0.924782	+	0.380499i	$0.875752\pi$
$30$	−0.507907	−	1.40632i	−0.0927307	−	0.256757i
$31$	−1.92532	−	3.33475i	−0.345798	−	0.598939i	0.639701	−	0.768624i	$-0.279058\pi$
$31$	−1.92532	−	3.33475i	−0.345798	−	0.598939i	−0.985498	+	0.169685i	$0.945725\pi$
$32$	5.23953	−	2.13244i	0.926227	−	0.376966i
$33$	7.77426	+	11.4027i	1.35333	+	1.98496i
$34$	−0.859803	−	4.30825i	−0.147455	−	0.738858i
$35$	0.0441332	−	1.21729i	0.00745987	−	0.205759i
$36$	−3.02601	+	3.39476i	−0.504335	+	0.565793i
$37$	−2.78661	−	0.859554i	−0.458115	−	0.141310i	0.0571041	−	0.998368i	$-0.481813\pi$
$37$	−2.78661	−	0.859554i	−0.458115	−	0.141310i	−0.515219	+	0.857058i	$0.672290\pi$
$38$	−7.61863	+	4.12440i	−1.23591	+	0.669065i
$39$	−12.6954	+	0.951386i	−2.03288	+	0.152344i
$40$	0.203666	−	1.28616i	0.0322025	−	0.203360i
$41$	−4.16086	−	8.64012i	−0.649818	−	1.34936i	−0.922028	−	0.387123i	$-0.873469\pi$
$41$	−4.16086	−	8.64012i	−0.649818	−	1.34936i	0.272210	−	0.962238i	$-0.412245\pi$
$42$	−7.69968	+	3.81425i	−1.18809	+	0.588552i
$43$	−0.134323	+	0.278925i	−0.0204841	+	0.0425357i	−0.910960	−	0.412495i	$-0.864657\pi$
$43$	−0.134323	+	0.278925i	−0.0204841	+	0.0425357i	0.890476	+	0.455031i	$0.150372\pi$
$44$	1.13731	+	11.9651i	0.171456	+	1.80381i
$45$	0.308565	+	1.00034i	0.0459982	+	0.149122i
$46$	6.71356	−	1.87093i	0.989861	−	0.275853i
$47$	−3.46750	+	0.522642i	−0.505787	+	0.0762351i	−0.396979	−	0.917828i	$-0.629941\pi$
$47$	−3.46750	+	0.522642i	−0.505787	+	0.0762351i	−0.108808	+	0.994063i	$0.534703\pi$
$48$	−8.66272	+	3.05589i	−1.25036	+	0.441080i
$49$	−6.97919	+	0.539309i	−0.997028	+	0.0770441i
$50$	5.17630	+	4.36538i	0.732040	+	0.617358i
$51$	1.06326	+	7.05426i	0.148886	+	0.987793i
$52$	−10.0834	−	4.61022i	−1.39832	−	0.639322i
$53$	−0.191211	+	0.0589807i	−0.0262648	+	0.00810162i	−0.307860	−	0.951432i	$-0.599613\pi$
$53$	−0.191211	+	0.0589807i	−0.0262648	+	0.00810162i	0.281595	+	0.959533i	$0.409137\pi$
$54$	−1.65092	+	1.68421i	−0.224661	+	0.229193i
$55$	2.49276	+	1.20045i	0.336123	+	0.161868i
$56$	−7.47617	−	0.326827i	−0.999046	−	0.0436741i
$57$	12.6749	−	6.10392i	1.67883	−	0.808484i
$58$	0.807192	−	2.38287i	0.105990	−	0.312886i
$59$	−0.0565834	−	0.755053i	−0.00736653	−	0.0982995i	0.992309	−	0.123789i	$-0.0395046\pi$
$59$	−0.0565834	−	0.755053i	−0.00736653	−	0.0982995i	−0.999675	+	0.0254895i	$0.991886\pi$
$60$	−0.429280	+	2.07053i	−0.0554198	+	0.267305i
$61$	0.954189	−	3.09340i	0.122171	−	0.396070i	−0.873741	−	0.486391i	$-0.838313\pi$
$61$	0.954189	−	3.09340i	0.122171	−	0.396070i	0.995913	+	0.0903211i	$0.0287893\pi$
$62$	−0.149279	+	5.44358i	−0.0189585	+	0.691336i
$63$	5.51122	−	2.41214i	0.694348	−	0.303901i
$64$	−7.89201	−	1.31005i	−0.986501	−	0.163756i
$65$	−2.10879	+	1.43775i	−0.261563	+	0.178330i
$66$	−0.924455	−	19.4954i	−0.113793	−	2.39971i
$67$	−10.0103	+	5.77947i	−1.22296	+	0.706075i	−0.965547	−	0.260227i	$-0.916203\pi$
$67$	−10.0103	+	5.77947i	−1.22296	+	0.706075i	−0.257411	+	0.966302i	$0.582869\pi$
$68$	−2.15391	+	5.82762i	−0.261200	+	0.706703i
$69$	−11.0335	+	2.51833i	−1.32828	+	0.303172i
$70$	−0.954472	+	1.43403i	−0.114081	+	0.171400i
$71$	10.3098	+	2.35315i	1.22355	+	0.279267i	0.785032	−	0.619456i	$-0.212647\pi$
$71$	10.3098	+	2.35315i	1.22355	+	0.279267i	0.438517	+	0.898723i	$0.355504\pi$
$72$	6.15957	−	1.84985i	0.725912	−	0.218006i
$73$	−0.0295568	+	0.196097i	−0.00345936	+	0.0229514i	−0.990494	−	0.137557i	$-0.956075\pi$
$73$	−0.0295568	+	0.196097i	−0.00345936	+	0.0229514i	0.987035	+	0.160508i	$0.0513132\pi$
$74$	2.72116	+	3.09892i	0.316328	+	0.360242i
$75$	−8.06037	−	7.47893i	−0.930732	−	0.863593i
$76$	12.2335	+	0.671460i	1.40327	+	0.0770218i
$77$	5.23394	−	15.0136i	0.596462	−	1.71096i
$78$	16.0011	+	8.25350i	1.81176	+	0.934525i
$79$	−3.05893	−	1.76607i	−0.344157	−	0.198699i	0.317952	−	0.948107i	$-0.397005\pi$
$79$	−3.05893	−	1.76607i	−0.344157	−	0.198699i	−0.662109	+	0.749408i	$0.730338\pi$
$80$	−1.19769	+	1.39890i	−0.133906	+	0.156402i
$81$	7.80788	−	7.24465i	0.867542	−	0.804961i
$82$	−1.38384	+	13.4913i	−0.152820	+	1.48986i
$83$	3.10144	−	3.88908i	0.340427	−	0.426882i	−0.581919	−	0.813247i	$-0.697698\pi$
$83$	3.10144	−	3.88908i	0.340427	−	0.426882i	0.922346	+	0.386365i	$0.126269\pi$
$84$	12.1015	+	1.10516i	1.32038	+	0.120583i
$85$	0.891712	+	1.11817i	0.0967197	+	0.121283i
$86$	0.368367	−	0.236623i	0.0397220	−	0.0255157i
$87$	−1.49257	+	3.80302i	−0.160021	+	0.407726i
$88$	7.48882	−	15.2589i	0.798311	−	1.62660i
$89$	−8.95632	+	3.51510i	−0.949368	+	0.372600i	−0.788955	−	0.614450i	$-0.789378\pi$
$89$	−8.95632	+	3.51510i	−0.949368	+	0.372600i	−0.160413	+	0.987050i	$0.551283\pi$
$90$	0.368879	−	1.43378i	0.0388832	−	0.151134i
$91$	9.58012	+	11.1062i	1.00427	+	1.16425i
$92$	−9.47444	−	2.71654i	−0.987779	−	0.283219i
$93$	0.660832	−	8.81820i	0.0685251	−	0.914404i
$94$	4.56497	+	1.93766i	0.470840	+	0.199854i
$95$	1.58875	−	2.33027i	0.163003	−	0.239081i
$96$	12.7003	+	2.73196i	1.29622	+	0.278829i
$97$			4.04201i			0.410404i	0.978720	+	0.205202i	$0.0657851\pi$
$97$			4.04201i			0.410404i	−0.978720	+	0.205202i	$0.934215\pi$
$98$	8.80855	+	4.51768i	0.889798	+	0.456355i
$99$			13.6646i			1.37335i
$100$	−3.00474	−	9.09246i	−0.300474	−	0.909246i
$101$	1.52853	−	2.24194i	0.152094	−	0.223081i	−0.742628	−	0.669704i	$-0.766421\pi$
$101$	1.52853	−	2.24194i	0.152094	−	0.223081i	0.894722	+	0.446623i	$0.147373\pi$
$102$	3.94195	−	9.28693i	0.390312	−	0.919543i
$103$	0.419882	−	5.60294i	0.0413722	−	0.552074i	−0.937551	−	0.347847i	$-0.886913\pi$
$103$	0.419882	−	5.60294i	0.0413722	−	0.552074i	0.978924	−	0.204227i	$-0.0654681\pi$
$104$	8.73606	+	13.0208i	0.856641	+	1.27679i
$105$	1.65849	−	2.25264i	0.161852	−	0.219835i
$106$	0.274060	+	0.0705093i	0.0266191	+	0.00684846i
$107$	1.91195	−	0.750387i	0.184836	−	0.0725426i	−0.271118	−	0.962546i	$-0.587393\pi$
$107$	1.91195	−	0.750387i	0.184836	−	0.0725426i	0.455954	+	0.890003i	$0.349298\pi$
$108$	3.23621	−	0.806949i	0.311404	−	0.0776487i
$109$	0.455150	−	1.15970i	0.0435955	−	0.111079i	−0.907418	−	0.420230i	$-0.861949\pi$
$109$	0.455150	−	1.15970i	0.0435955	−	0.111079i	0.951013	+	0.309150i	$0.100045\pi$
$110$	−2.11469	−	3.29209i	−0.201628	−	0.313889i
$111$	−4.17546	−	5.23586i	−0.396317	−	0.496965i
$112$	8.76606	+	5.92926i	0.828315	+	0.560263i
$113$	−4.31606	+	5.41217i	−0.406021	+	0.509134i	−0.942237	−	0.334947i	$-0.891282\pi$
$113$	−4.31606	+	5.41217i	−0.406021	+	0.509134i	0.536216	+	0.844081i	$0.319853\pi$
$114$	−19.7915	−	2.03008i	−1.85364	−	0.190134i
$115$	−1.66319	+	1.54322i	−0.155094	+	0.143906i
$116$	−2.73690	+	2.27347i	−0.254115	+	0.211086i
$117$	−10.9166	−	6.30268i	−1.00924	−	0.582683i
$118$	−0.490875	+	0.951659i	−0.0451887	+	0.0876073i
$119$	5.80491	−	5.81840i	0.532136	−	0.533372i
$120$	2.05029	−	2.17694i	0.187165	−	0.198727i
$121$	18.4103	+	17.0822i	1.67366	+	1.55293i
$122$	−3.44010	+	3.02075i	−0.311452	+	0.273486i
$123$	3.28233	−	21.7768i	0.295958	−	1.96355i
$124$	4.21037	−	6.44845i	0.378103	−	0.579088i
$125$	−4.39336	−	1.00276i	−0.392954	−	0.0896892i
$126$	−8.42645	−	1.17420i	−0.750688	−	0.104606i
$127$	9.99984	−	2.28240i	0.887342	−	0.202530i	0.245527	−	0.969390i	$-0.421039\pi$
$127$	9.99984	−	2.28240i	0.887342	−	0.202530i	0.641815	+	0.766860i	$0.278182\pi$
$128$	8.53911	+	7.42183i	0.754758	+	0.656003i
$129$	−0.615704	+	0.355477i	−0.0542097	+	0.0312980i
$130$	3.60541	−	0.170966i	0.316215	−	0.0149947i
$131$	−9.61994	+	6.55876i	−0.840498	+	0.573042i	−0.905260	−	0.424859i	$-0.860324\pi$
$131$	−9.61994	+	6.55876i	−0.840498	+	0.573042i	0.0647615	+	0.997901i	$0.479371\pi$
$132$	−13.3208	+	24.1745i	−1.15942	+	2.10412i
$133$	−14.3383	−	7.55672i	−1.24329	−	0.655251i
$134$	16.3407	+	0.448110i	1.41162	+	0.0387108i
$135$	0.226305	−	0.733663i	0.0194773	−	0.0631437i
$136$	6.91010	−	5.42692i	0.592536	−	0.465354i
$137$	1.53435	+	20.4745i	0.131089	+	1.74926i	0.544543	+	0.838733i	$0.316703\pi$
$137$	1.53435	+	20.4745i	0.131089	+	1.74926i	−0.413454	+	0.910525i	$0.635678\pi$
$138$	15.1589	+	5.13505i	1.29041	+	0.437124i
$139$	5.61736	−	2.70518i	0.476458	−	0.229450i	−0.180212	−	0.983628i	$-0.557679\pi$
$139$	5.61736	−	2.70518i	0.476458	−	0.229450i	0.656670	+	0.754178i	$0.271964\pi$
$140$	2.21182	−	1.02116i	0.186933	−	0.0863039i
$141$	−7.25550	−	3.49406i	−0.611023	−	0.294253i
$142$	−10.6800	−	10.4688i	−0.896245	−	0.878525i
$143$	−31.8349	+	9.81976i	−2.66217	+	0.821169i
$144$	−8.79132	−	2.33175i	−0.732610	−	0.194313i
$145$	0.122071	+	0.809888i	0.0101374	+	0.0672576i
$146$	0.180806	−	0.214393i	0.0149636	−	0.0177433i
$147$	−13.9403	−	8.00535i	−1.14978	−	0.660270i
$148$	−0.984239	−	5.74868i	−0.0809040	−	0.472538i
$149$	10.1068	−	1.52335i	0.827980	−	0.124798i	0.278639	−	0.960396i	$-0.410117\pi$
$149$	10.1068	−	1.52335i	0.827980	−	0.124798i	0.549341	+	0.835598i	$0.314879\pi$
$150$	4.17444	+	14.9794i	0.340842	+	1.22306i
$151$	2.51353	+	8.14865i	0.204548	+	0.663128i	0.998480	+	0.0551212i	$0.0175545\pi$
$151$	2.51353	+	8.14865i	0.204548	+	0.663128i	−0.793932	+	0.608007i	$0.791969\pi$
$152$	−14.2430	−	9.86688i	−1.15526	−	0.800309i
$153$	−3.06476	+	6.36404i	−0.247771	+	0.514502i
$154$	−17.4227	+	14.2146i	−1.40396	+	1.14545i
$155$	−0.769192	−	1.59724i	−0.0617830	−	0.128294i
$156$	−13.1687	−	21.7921i	−1.05434	−	1.74476i
$157$	−15.5026	+	1.16176i	−1.23724	+	0.0927186i	−0.677234	−	0.735768i	$-0.736822\pi$
$157$	−15.5026	+	1.16176i	−1.23724	+	0.0927186i	−0.560010	+	0.828486i	$0.689203\pi$
$158$	2.37808	+	4.39282i	0.189190	+	0.349474i
$159$	−0.439111	−	0.135448i	−0.0348238	−	0.0107417i
$160$	2.47887	−	0.798749i	0.195972	−	0.0631466i
$161$	9.89269	+	8.49339i	0.779653	+	0.669373i
$162$	−14.7718	+	2.94802i	−1.16058	+	0.231618i
$163$	−0.677667	−	0.993955i	−0.0530790	−	0.0778526i	0.798782	−	0.601621i	$-0.205478\pi$
$163$	−0.677667	−	0.993955i	−0.0530790	−	0.0778526i	−0.851861	+	0.523768i	$0.824526\pi$
$164$	11.6565	−	15.2310i	0.910221	−	1.18934i
$165$	3.17689	+	5.50254i	0.247321	+	0.428372i
$166$	−6.61645	+	2.38961i	−0.513536	+	0.185469i
$167$	−1.08347	−	4.74700i	−0.0838416	−	0.367334i	0.915550	−	0.402204i	$-0.131756\pi$
$167$	−1.08347	−	4.74700i	−0.0838416	−	0.367334i	−0.999392	+	0.0348695i	$0.988898\pi$
$168$	−13.7628	−	10.2917i	−1.06182	−	0.794023i
$169$	3.94583	−	17.2878i	0.303525	−	1.32983i
$170$	−0.246514	−	2.00752i	−0.0189068	−	0.153970i
$171$	13.7737	+	2.07606i	1.05330	+	0.158760i
$172$	−0.619044	+	0.0123625i	−0.0472017	+	0.000942632i
$173$	3.12885	−	3.37210i	0.237882	−	0.256376i	−0.602816	−	0.797880i	$-0.705955\pi$
$173$	3.12885	−	3.37210i	0.237882	−	0.256376i	0.840698	+	0.541504i	$0.182145\pi$
$174$	4.61421	−	3.47713i	0.349802	−	0.263601i
$175$	−1.40375	+	12.5899i	−0.106114	+	0.951710i
$176$	−20.3212	+	12.8406i	−1.53177	+	0.967899i
$177$	0.869413	−	1.50587i	0.0653491	−	0.113188i
$178$	13.3941	+	2.39605i	1.00393	+	0.179591i
$179$	1.11511	+	1.20180i	0.0833473	+	0.0898270i	0.773348	−	0.633981i	$-0.218580\pi$
$179$	1.11511	+	1.20180i	0.0833473	+	0.0898270i	−0.690001	+	0.723808i	$0.742390\pi$
$180$	−1.50606	+	1.45444i	−0.112255	+	0.108408i
$181$	9.79535	+	7.81153i	0.728082	+	0.580626i	0.915818	−	0.401593i	$-0.131543\pi$
$181$	9.79535	+	7.81153i	0.728082	+	0.580626i	−0.187736	+	0.982220i	$0.560115\pi$
$182$	−3.31990	−	20.4752i	−0.246087	−	1.51772i
$183$	5.81231	−	4.63516i	0.429658	−	0.342641i
$184$	9.40440	+	10.2882i	0.693302	+	0.758454i
$185$	−1.24977	−	0.490500i	−0.0918852	−	0.0360623i
$186$	−7.32536	+	10.1358i	−0.537121	+	0.743190i
$187$	6.82034	+	17.3779i	0.498753	+	1.27080i
$188$	−4.06566	−	5.71465i	−0.296519	−	0.416784i
$189$	−4.33621	−	0.815245i	−0.315413	−	0.0593003i
$190$	−3.63966	+	1.63141i	−0.264049	+	0.118355i
$191$	19.5997	+	1.46879i	1.41818	+	0.106278i	0.761634	−	0.648007i	$-0.224397\pi$
$191$	19.5997	+	1.46879i	1.41818	+	0.106278i	0.656547	+	0.754285i	$0.272016\pi$
$192$	−13.2799	−	12.6953i	−0.958393	−	0.916201i
$193$	15.0199	+	10.2404i	1.08116	+	0.737119i	0.966598	−	0.256297i	$-0.0825026\pi$
$193$	15.0199	+	10.2404i	1.08116	+	0.737119i	0.114558	+	0.993417i	$0.463455\pi$
$194$	2.99276	−	4.87022i	0.214868	−	0.349661i
$195$	−5.86124			−0.419732
$196$	−7.26847	−	11.9653i	−0.519177	−	0.854667i
$197$	18.7302			1.33447			0.667235	−	0.744847i	$-0.267478\pi$
$197$	18.7302			1.33447			0.667235	+	0.744847i	$0.267478\pi$
$198$	10.1175	−	16.4645i	0.719019	−	1.17008i
$199$	16.9839	+	11.5794i	1.20396	+	0.820844i	0.987832	−	0.155522i	$-0.0497059\pi$
$199$	16.9839	+	11.5794i	1.20396	+	0.820844i	0.216125	+	0.976366i	$0.430658\pi$
$200$	−3.11177	+	13.1803i	−0.220036	+	0.931985i
$201$	−26.4707	−	1.98370i	−1.86710	−	0.139920i
$202$	−3.50169	+	1.56957i	−0.246378	+	0.110435i
$203$	4.54498	−	1.22348i	0.318995	−	0.0858713i
$204$	−11.6258	+	8.27115i	−0.813972	+	0.579097i
$205$	−1.61301	−	4.10988i	−0.112658	−	0.287047i
$206$	−4.65442	+	6.44010i	−0.324289	+	0.448703i
$207$	−10.4310	−	4.09388i	−0.725007	−	0.284544i
$208$	−0.885319	−	22.1570i	−0.0613858	−	1.53631i
$209$	28.7824	−	22.9532i	1.99092	−	1.58771i
$210$	−3.66620	+	1.48623i	−0.252992	+	0.102560i
$211$	−14.1520	−	11.2859i	−0.974267	−	0.776952i	0.000540468	−	1.00000i	$-0.499828\pi$
$211$	−14.1520	−	11.2859i	−0.974267	−	0.776952i	−0.974808	+	0.223048i	$0.928399\pi$
$212$	−0.278009	−	0.287875i	−0.0190937	−	0.0197713i
$213$	16.5181	+	17.8023i	1.13180	+	1.21979i
$214$	−2.85931	−	0.511497i	−0.195459	−	0.0349652i
$215$	−0.0712651	+	0.123435i	−0.00486024	+	0.00841818i
$216$	−4.49679	−	1.42384i	−0.305968	−	0.0968801i
$217$	−8.61999	+	5.43026i	−0.585163	+	0.368630i
$218$	−1.40707	+	1.06033i	−0.0952990	+	0.0718145i
$219$	−0.309764	+	0.333846i	−0.0209319	+	0.0225592i
$220$	0.110484	+	5.53240i	0.00744881	+	0.372994i
$221$	−17.0289	−	2.56669i	−1.14549	−	0.172655i
$222$	1.15431	+	9.40026i	0.0774720	+	0.630904i
$223$	3.80609	−	16.6756i	0.254874	−	1.11668i	−0.671776	−	0.740754i	$-0.734468\pi$
$223$	3.80609	−	16.6756i	0.254874	−	1.11668i	0.926651	−	0.375924i	$-0.122675\pi$
$224$	−6.17212	−	13.6347i	−0.412392	−	0.911006i
$225$	−2.42262	−	10.6142i	−0.161508	−	0.707613i
$226$	9.20767	−	3.32545i	0.612485	−	0.221206i
$227$	−7.27865	−	12.6070i	−0.483101	−	0.836755i	0.516711	−	0.856160i	$-0.327156\pi$
$227$	−7.27865	−	12.6070i	−0.483101	−	0.836755i	−0.999812	+	0.0194049i	$0.993823\pi$
$228$	22.3436	+	17.0999i	1.47974	+	1.13247i
$229$	4.28828	+	6.28975i	0.283378	+	0.415639i	0.941365	−	0.337391i	$-0.109544\pi$
$229$	4.28828	+	6.28975i	0.283378	+	0.415639i	−0.657987	+	0.753029i	$0.728592\pi$
$230$	3.14660	−	0.627972i	0.207481	−	0.0414073i
$231$	29.3535	−	21.7165i	1.93132	−	1.42884i
$232$	4.98100	−	0.712864i	0.327019	−	0.0468018i
$233$	−5.65474	−	1.74426i	−0.370454	−	0.114270i	0.103937	−	0.994584i	$-0.466856\pi$
$233$	−5.65474	−	1.74426i	−0.370454	−	0.114270i	−0.474392	+	0.880314i	$0.657332\pi$
$234$	8.48678	+	15.6769i	0.554798	+	1.02483i
$235$	−1.60993	+	0.120648i	−0.105020	+	0.00787018i
$236$	1.29608	−	0.783204i	0.0843675	−	0.0509822i
$237$	−3.51945	−	7.30822i	−0.228613	−	0.474720i
$238$	−11.3024	+	2.71255i	−0.732624	+	0.175829i
$239$	−7.47961	+	15.5316i	−0.483816	+	1.00465i	0.506031	+	0.862515i	$0.331112\pi$
$239$	−7.47961	+	15.5316i	−0.483816	+	1.00465i	−0.989847	+	0.142139i	$0.954602\pi$
$240$	−4.08224	+	1.10493i	−0.263508	+	0.0713232i
$241$	3.04935	+	9.88577i	0.196426	+	0.636798i	0.999180	+	0.0404876i	$0.0128911\pi$
$241$	3.04935	+	9.88577i	0.196426	+	0.636798i	−0.802754	+	0.596311i	$0.796633\pi$
$242$	−9.53462	−	34.2136i	−0.612908	−	2.19934i
$243$	19.2400	−	2.89996i	1.23425	−	0.186033i
$244$	6.38159	−	1.09260i	0.408539	−	0.0699466i
$245$	−3.22274	+	0.00747910i	−0.205893	+	0.000477822i
$246$	−20.0788	+	23.8087i	−1.28018	+	1.51798i
$247$	5.06151	+	33.5809i	0.322056	+	2.13670i
$248$	−9.84761	+	4.65232i	−0.625324	+	0.295423i
$249$	10.9159	−	3.36711i	0.691768	−	0.213382i
$250$	4.55111	+	4.46113i	0.287837	+	0.282147i
$251$	10.7403	+	5.17227i	0.677924	+	0.326471i	0.740969	−	0.671540i	$-0.234367\pi$
$251$	10.7403	+	5.17227i	0.677924	+	0.326471i	−0.0630445	+	0.998011i	$0.520081\pi$
$252$	9.28365	+	7.65387i	0.584815	+	0.482148i
$253$	−26.6827	+	12.8497i	−1.67753	+	0.807855i
$254$	−13.7387	−	4.65396i	−0.862045	−	0.292015i
$255$	0.245445	+	3.27523i	0.0153703	+	0.205103i
$256$	−4.79355	−	15.2651i	−0.299597	−	0.954066i
$257$	−3.92974	+	12.7399i	−0.245131	+	0.794694i	0.746477	+	0.665411i	$0.231744\pi$
$257$	−3.92974	+	12.7399i	−0.245131	+	0.794694i	−0.991608	+	0.129283i	$0.958732\pi$
$258$	1.00506	+	0.0275618i	0.0625724	+	0.00171592i
$259$	−1.98825	+	7.45486i	−0.123544	+	0.463222i
$260$	−4.47074	−	2.46350i	−0.277264	−	0.152780i
$261$	−3.34223	+	2.27870i	−0.206879	+	0.141048i
$262$	16.4473	−	0.779917i	1.01612	−	0.0481835i
$263$	18.8488	−	10.8824i	1.16227	−	0.671036i	0.210422	−	0.977611i	$-0.432516\pi$
$263$	18.8488	−	10.8824i	1.16227	−	0.671036i	0.951847	+	0.306574i	$0.0991827\pi$
$264$	33.9493	−	19.2649i	2.08944	−	1.18567i
$265$	−0.0898151	+	0.0204997i	−0.00551730	+	0.00125929i
$266$	11.6811	+	19.7214i	0.716213	+	1.20919i
$267$	−21.5414	−	4.91669i	−1.31831	−	0.300896i
$268$	−19.3571	−	12.6388i	−1.18242	−	0.772038i
$269$	2.07411	−	13.7608i	0.126461	−	0.839014i	−0.832203	−	0.554472i	$-0.812920\pi$
$269$	2.07411	−	13.7608i	0.126461	−	0.839014i	0.958664	−	0.284542i	$-0.0918415\pi$
$270$	−0.815890	+	0.716432i	−0.0496535	+	0.0436007i
$271$	−6.77814	−	6.28920i	−0.411743	−	0.382042i	0.446927	−	0.894570i	$-0.352518\pi$
$271$	−6.77814	−	6.28920i	−0.411743	−	0.382042i	−0.858670	+	0.512529i	$0.828709\pi$
$272$	−12.3442	+	1.42256i	−0.748475	+	0.0862552i
$273$	3.81013	+	33.4668i	0.230600	+	2.02550i
$274$	13.3109	−	25.8058i	0.804141	−	1.55899i
$275$	−24.9189	−	14.3870i	−1.50267	−	0.867566i
$276$	−14.4629	−	17.4111i	−0.870567	−	1.04803i
$277$	−23.1473	+	21.4776i	−1.39079	+	1.29046i	−0.480196	+	0.877161i	$0.659434\pi$
$277$	−23.1473	+	21.4776i	−1.39079	+	1.29046i	−0.910594	+	0.413302i	$0.864375\pi$
$278$	−8.77131	−	0.899703i	−0.526068	−	0.0539606i
$279$	5.45908	−	6.84547i	0.326826	−	0.409827i
$280$	−3.42111	−	0.407267i	−0.204450	−	0.0243389i
$281$	6.51396	+	8.16825i	0.388590	+	0.487277i	0.937195	−	0.348805i	$-0.113412\pi$
$281$	6.51396	+	8.16825i	0.388590	+	0.487277i	−0.548605	+	0.836082i	$0.684841\pi$
$282$	6.15510	+	9.58207i	0.366531	+	0.570604i
$283$	−5.02488	+	12.8032i	−0.298698	+	0.761070i	0.700191	+	0.713955i	$0.253098\pi$
$283$	−5.02488	+	12.8032i	−0.298698	+	0.761070i	−0.998889	+	0.0471152i	$0.984997\pi$
$284$	5.11705	+	20.5215i	0.303641	+	1.21773i
$285$	6.02913	−	2.36626i	0.357135	−	0.140165i
$286$	45.6286	+	11.7392i	2.69807	+	0.694152i
$287$	−22.4182	+	11.8817i	−1.32331	+	0.701354i
$288$	8.86621	+	9.31876i	0.522446	+	0.549113i
$289$	0.549257	−	7.32933i	0.0323092	−	0.431137i
$290$	0.452570	−	1.06622i	0.0265758	−	0.0626105i
$291$	−5.22896	+	7.66947i	−0.306527	+	0.449592i
$292$	−0.376593	+	0.124451i	−0.0220384	+	0.00728293i
$293$		−	4.24335i		−	0.247899i	−0.992289	−	0.123949i	$-0.960444\pi$
$293$		−	4.24335i		−	0.247899i	0.992289	−	0.123949i	$-0.0395561\pi$
$294$	10.8694	+	19.9673i	0.633916	+	1.16451i
$295$		−	0.348596i		−	0.0202960i
$296$	−3.07049	+	7.65533i	−0.178469	+	0.444957i
$297$	5.64548	−	8.28040i	0.327584	−	0.480477i
$298$	−13.3056	−	5.64772i	−0.770772	−	0.327164i
$299$	2.04161	−	27.2434i	0.118069	−	1.57553i
$300$	6.06117	−	21.1395i	0.349942	−	1.22049i
$301$	0.751119	+	0.326673i	0.0432938	+	0.0188291i
$302$	3.00483	−	11.6794i	0.172909	−	0.672072i
$303$	5.80059	−	2.27656i	0.333235	−	0.130785i
$304$	9.85577	+	22.4343i	0.565267	+	1.28670i
$305$	0.544503	−	1.38737i	0.0311781	−	0.0794406i
$306$	8.40476	−	5.39885i	0.480468	−	0.308632i
$307$	−17.4235	−	21.8484i	−0.994412	−	1.24695i	−0.968945	−	0.247277i	$-0.920464\pi$
$307$	−17.4235	−	21.8484i	−0.994412	−	1.24695i	−0.0254669	−	0.999676i	$-0.508107\pi$
$308$	31.5173	−	4.22720i	1.79586	−	0.240867i
$309$	8.04497	−	10.0881i	0.457662	−	0.573890i
$310$	−0.255822	+	2.49404i	−0.0145297	+	0.141652i
$311$	4.38763	−	4.07113i	0.248800	−	0.230853i	−0.545907	−	0.837846i	$-0.683815\pi$
$311$	4.38763	−	4.07113i	0.248800	−	0.230853i	0.794707	+	0.606993i	$0.207624\pi$
$312$	−0.268205	+	36.0076i	−0.0151841	+	2.03853i
$313$	−12.0092	−	6.93349i	−0.678798	−	0.391904i	0.120604	−	0.992701i	$-0.461517\pi$
$313$	−12.0092	−	6.93349i	−0.678798	−	0.391904i	−0.799402	+	0.600797i	$0.794850\pi$
$314$	19.5393	+	10.0786i	1.10267	+	0.568766i
$315$	2.61322	−	0.917811i	0.147238	−	0.0517128i
$316$	0.387157	−	7.05368i	0.0217793	−	0.396801i
$317$	2.23450	+	2.07332i	0.125502	+	0.116449i	0.740427	−	0.672137i	$-0.234623\pi$
$317$	2.23450	+	2.07332i	0.125502	+	0.116449i	−0.614925	+	0.788586i	$0.710814\pi$
$318$	0.428798	+	0.488326i	0.0240458	+	0.0273840i
$319$	−1.59340	+	10.5715i	−0.0892133	+	0.591892i
$320$	−3.57819	−	0.872975i	−0.200027	−	0.0488008i
$321$	4.59856	+	1.04959i	0.256667	+	0.0585825i
$322$	−5.63109	−	17.5584i	−0.313808	−	0.978491i
$323$	18.5529	−	4.23458i	1.03231	−	0.235618i
$324$	19.9813	+	7.38516i	1.11007	+	0.410286i
$325$	22.9872	−	13.2717i	1.27510	−	0.736180i
$326$	0.0805829	+	1.69937i	0.00446308	+	0.0941195i
$327$	2.36388	−	1.61166i	0.130723	−	0.0891252i
$328$	−25.3222	+	9.72120i	−1.39819	+	0.536764i
$329$	1.73542	+	9.11402i	0.0956769	+	0.502472i
$330$	0.246319	−	8.98224i	0.0135594	−	0.494456i
$331$	3.11298	−	10.0920i	0.171105	−	0.554709i	−0.828884	−	0.559421i	$-0.811024\pi$
$331$	3.11298	−	10.0920i	0.171105	−	0.554709i	0.999989	+	0.00471200i	$0.00149988\pi$
$332$	9.74147	+	2.01968i	0.534633	+	0.110844i
$333$	−0.495523	−	6.61230i	−0.0271545	−	0.362352i
$334$	−2.20927	+	6.52189i	−0.120886	+	0.356862i
$335$	−4.79465	+	2.30898i	−0.261960	+	0.126153i
$336$	8.96268	+	22.5907i	0.488954	+	1.23242i
$337$	−26.2667	−	12.6494i	−1.43084	−	0.689055i	−0.451684	−	0.892178i	$-0.649177\pi$
$337$	−26.2667	−	12.6494i	−1.43084	−	0.689055i	−0.979153	+	0.203123i	$0.934891\pi$
$338$	−17.5545	+	17.9086i	−0.954838	+	0.974097i
$339$	−15.1909	+	4.68578i	−0.825059	+	0.254497i
$340$	−1.18937	+	2.60139i	−0.0645028	+	0.141080i
$341$	−3.44892	−	22.8821i	−0.186770	−	1.23914i
$342$	−15.0588	−	12.6997i	−0.814289	−	0.686722i
$343$	2.13766	+	18.3965i	0.115423	+	0.993316i
$344$	0.755041	+	0.443454i	0.0407091	+	0.0239094i
$345$	−5.15220	+	0.776569i	−0.277385	+	0.0418091i
$346$	−6.26671	+	1.74640i	−0.336900	+	0.0938870i
$347$	0.299949	+	0.972412i	0.0161021	+	0.0522018i	0.963267	−	0.268544i	$-0.0865426\pi$
$347$	0.299949	+	0.972412i	0.0161021	+	0.0522018i	−0.947165	+	0.320746i	$0.896066\pi$
$348$	−8.13419	+	0.773172i	−0.436038	+	0.0414464i
$349$	−1.03525	+	2.14971i	−0.0554155	+	0.115072i	−0.926838	−	0.375462i	$-0.877484\pi$
$349$	−1.03525	+	2.14971i	−0.0554155	+	0.115072i	0.871422	+	0.490534i	$0.163198\pi$
$350$	11.0132	−	14.1303i	0.588678	−	0.755295i
$351$	4.01122	+	8.32938i	0.214103	+	0.444589i
$352$	33.9924	−	0.425581i	1.81180	−	0.0226836i
$353$	−16.7757	+	1.25716i	−0.892878	+	0.0669120i	−0.513262	−	0.858232i	$-0.671563\pi$
$353$	−16.7757	+	1.25716i	−0.892878	+	0.0669120i	−0.379616	+	0.925144i	$0.623944\pi$
$354$	−2.16252	+	1.17070i	−0.114937	+	0.0622218i
$355$	4.65233	+	1.43505i	0.246920	+	0.0761647i
$356$	−14.3645	−	12.8042i	−0.761317	−	0.678621i
$357$	18.5415	−	3.53053i	0.981319	−	0.186855i
$358$	−0.453765	−	2.27370i	−0.0239822	−	0.120169i
$359$	6.38516	+	9.36531i	0.336996	+	0.494282i	0.956909	−	0.290389i	$-0.0937845\pi$
$359$	6.38516	+	9.36531i	0.336996	+	0.494282i	−0.619913	+	0.784670i	$0.712832\pi$
$360$	2.89154	−	0.637353i	0.152397	−	0.0335915i
$361$	−9.26356	−	16.0450i	−0.487556	−	0.844471i
$362$	−6.01865	−	16.6647i	−0.316333	−	0.875879i
$363$	12.8339	+	56.2291i	0.673606	+	2.95126i
$364$	−11.1600	+	27.1286i	−0.584940	+	1.42193i
$365$	−0.0203164	+	0.0890122i	−0.00106341	+	0.00465911i
$366$	−10.4352	+	1.28139i	−0.545457	+	0.0669795i
$367$	11.9730	+	1.80463i	0.624983	+	0.0942010i	0.453896	−	0.891055i	$-0.350034\pi$
$367$	11.9730	+	1.80463i	0.624983	+	0.0942010i	0.171087	+	0.985256i	$0.445272\pi$
$368$	−3.71386	−	19.3594i	−0.193598	−	1.00918i
$369$	14.8315	−	15.9846i	0.772099	−	0.832125i
$370$	1.14268	+	1.51635i	0.0594051	+	0.0788315i
$371$	0.175435	+	0.499504i	0.00910812	+	0.0259329i
$372$	16.3310	−	6.78879i	0.846723	−	0.351982i
$373$	14.3488	−	24.8529i	0.742954	−	1.28683i	−0.208190	−	0.978088i	$-0.566757\pi$
$373$	14.3488	−	24.8529i	0.742954	−	1.28683i	0.951145	−	0.308746i	$-0.0999093\pi$
$374$	4.64905	−	25.9886i	0.240396	−	1.34384i
$375$	−7.03893	−	7.58616i	−0.363489	−	0.391748i
$376$	0.667510	+	9.89586i	0.0344242	+	0.510340i
$377$	−7.71056	−	6.14897i	−0.397114	−	0.316688i
$378$	4.62109	+	4.19288i	0.237683	+	0.215659i
$379$	11.8209	−	9.42689i	0.607201	−	0.484227i	−0.270961	−	0.962590i	$-0.587341\pi$
$379$	11.8209	−	9.42689i	0.607201	−	0.484227i	0.878162	+	0.478364i	$0.158770\pi$
$380$	5.59335	+	0.729166i	0.286933	+	0.0374054i
$381$	21.9267	+	8.60561i	1.12334	+	0.440879i
$382$	−22.5281	−	16.2816i	−1.15264	−	0.833040i
$383$	−6.43889	−	16.4060i	−0.329012	−	0.838309i	−0.995671	−	0.0929462i	$-0.970372\pi$
$383$	−6.43889	−	16.4060i	−0.329012	−	0.838309i	0.666659	−	0.745363i	$-0.267724\pi$
$384$	6.60118	+	25.1291i	0.336865	+	1.28237i
$385$	2.91947	−	6.71275i	0.148790	−	0.342113i
$386$	−10.5154	−	23.4596i	−0.535217	−	1.19406i
$387$	−0.701971	−	0.0526055i	−0.0356832	−	0.00267409i
$388$	−7.21196	+	3.65225i	−0.366132	+	0.185415i
$389$	−25.9523	−	17.6939i	−1.31583	−	0.897119i	−0.317146	−	0.948377i	$-0.602724\pi$
$389$	−25.9523	−	17.6939i	−1.31583	−	0.897119i	−0.998685	+	0.0512581i	$0.983677\pi$
$390$	7.06222	+	4.33975i	0.357609	+	0.219752i
$391$	−15.3090			−0.774207
$392$	−0.101523	+	19.7987i	−0.00512768	+	0.999987i
$393$	−26.7380			−1.34876
$394$	−22.5680	−	13.8681i	−1.13696	−	0.698664i
$395$	−1.34361	−	0.916058i	−0.0676044	−	0.0460919i
$396$	−24.3812	+	12.3470i	−1.22520	+	0.620460i
$397$	39.3005	+	2.94516i	1.97243	+	0.147813i	0.997280	−	0.0737127i	$-0.0234848\pi$
$397$	39.3005	+	2.94516i	1.97243	+	0.147813i	0.975154	+	0.221526i	$0.0711038\pi$
$398$	−11.8903	−	26.5272i	−0.596009	−	1.32969i
$399$	−17.4302	−	32.8872i	−0.872603	−	1.64642i
$400$	13.5082	−	13.5769i	0.675412	−	0.678845i
$401$	10.3504	+	26.3723i	0.516874	+	1.31697i	0.916405	+	0.400253i	$0.131078\pi$
$401$	10.3504	+	26.3723i	0.516874	+	1.31697i	−0.399531	+	0.916720i	$0.630827\pi$
$402$	30.4258	+	21.9894i	1.51750	+	1.09673i
$403$	19.8711	+	7.79883i	0.989850	+	0.388488i
$404$	5.38133	+	0.701526i	0.267731	+	0.0349022i
$405$	3.83389	−	3.05743i	0.190508	−	0.151925i
$406$	−6.38213	−	1.89100i	−0.316740	−	0.0938487i
$407$	−13.7014	−	10.9265i	−0.679155	−	0.541608i
$408$	20.1321	−	1.35798i	0.996686	−	0.0672299i
$409$	−14.9138	−	16.0732i	−0.737439	−	0.794770i	0.247276	−	0.968945i	$-0.420465\pi$
$409$	−14.9138	−	16.0732i	−0.737439	−	0.794770i	−0.984715	+	0.174175i	$0.944274\pi$
$410$	−1.09950	+	6.14630i	−0.0543004	+	0.303544i
$411$	−23.5756	+	40.8342i	−1.16290	+	2.01420i
$412$	10.3765	−	4.31349i	0.511211	−	0.212510i
$413$	−1.99043	+	0.226606i	−0.0979424	+	0.0111506i
$414$	9.53719	+	12.6560i	0.468727	+	0.622008i
$415$	1.55769	−	1.67879i	0.0764641	−	0.0824087i
$416$	−15.3387	+	27.3525i	−0.752040	+	1.34107i
$417$	14.1582	+	2.13400i	0.693328	+	0.104502i
$418$	−51.6748	+	6.34542i	−2.52750	+	0.310365i
$419$	−6.44355	+	28.2310i	−0.314788	+	1.37918i	0.531774	+	0.846886i	$0.321525\pi$
$419$	−6.44355	+	28.2310i	−0.314788	+	1.37918i	−0.846562	+	0.532290i	$0.821332\pi$
$420$	5.51783	+	0.923739i	0.269243	+	0.0450738i
$421$	6.51895	+	28.5614i	0.317714	+	1.39200i	0.841551	+	0.540178i	$0.181643\pi$
$421$	6.51895	+	28.5614i	0.317714	+	1.39200i	−0.523836	+	0.851819i	$0.675500\pi$
$422$	8.69558	+	24.0767i	0.423294	+	1.17204i
$423$	−3.98677	−	6.90529i	−0.193843	−	0.335747i
$424$	0.121827	+	0.552702i	0.00591643	+	0.0268416i
$425$	−8.37875	−	12.2894i	−0.406429	−	0.596122i
$426$	−6.72161	−	33.6802i	−0.325663	−	1.63181i
$427$	−8.27562	−	2.20716i	−0.400485	−	0.106812i
$428$	3.06647	+	2.73338i	0.148223	+	0.132123i
$429$	−73.1082	−	22.5509i	−3.52970	−	1.08877i
$430$	0.177260	−	0.0959610i	0.00854825	−	0.00462765i
$431$	−32.8667	+	2.46302i	−1.58313	+	0.118639i	−0.837016	−	0.547178i	$-0.815702\pi$
$431$	−32.8667	+	2.46302i	−1.58313	+	0.118639i	−0.746115	+	0.665817i	$0.768083\pi$
$432$	4.36395	+	5.04507i	0.209961	+	0.242731i
$433$	9.65223	+	20.0431i	0.463857	+	0.963209i	0.993376	+	0.114910i	$0.0366581\pi$
$433$	9.65223	+	20.0431i	0.463857	+	0.963209i	−0.529519	+	0.848298i	$0.677628\pi$
$434$	14.4069	−	0.160560i	0.691552	−	0.00770711i
$435$	−0.816092	+	1.69463i	−0.0391286	+	0.0812515i
$436$	2.48046	−	0.235774i	0.118793	−	0.0112915i
$437$	8.89843	+	28.8480i	0.425670	+	1.37999i
$438$	0.620419	−	0.172898i	0.0296447	−	0.00826136i
$439$	−19.1569	+	2.88744i	−0.914309	+	0.137810i	−0.589312	−	0.807905i	$-0.700601\pi$
$439$	−19.1569	+	2.88744i	−0.914309	+	0.137810i	−0.324996	+	0.945715i	$0.605363\pi$
$440$	3.96314	−	6.74779i	0.188935	−	0.321688i
$441$	−6.93929	−	14.3244i	−0.330442	−	0.682117i
$442$	18.6177	+	15.7011i	0.885555	+	0.746823i
$443$	−3.11225	−	20.6484i	−0.147867	−	0.981036i	−0.932525	−	0.361106i	$-0.882399\pi$
$443$	−3.11225	−	20.6484i	−0.147867	−	0.981036i	0.784657	−	0.619930i	$-0.212839\pi$
$444$	5.56926	−	12.1810i	0.264305	−	0.578087i
$445$	−4.23284	+	1.30566i	−0.200656	+	0.0618941i
$446$	−16.9328	+	17.2743i	−0.801791	+	0.817962i
$447$	21.1477	+	10.1842i	1.00025	+	0.481696i
$448$	−2.65853	+	20.9984i	−0.125604	+	0.992081i
$449$	7.21061	−	3.47245i	0.340290	−	0.163875i	−0.255932	−	0.966695i	$-0.582382\pi$
$449$	7.21061	−	3.47245i	0.340290	−	0.163875i	0.596222	+	0.802820i	$0.296668\pi$
$450$	−4.93989	+	14.5828i	−0.232868	+	0.687440i
$451$	−4.30672	−	57.4692i	−0.202796	−	2.70612i
$452$	−13.5565	−	2.81065i	−0.637646	−	0.132202i
$453$	−5.77227	+	18.7132i	−0.271205	+	0.879224i
$454$	−0.564348	+	20.5794i	−0.0264861	+	0.965838i
$455$	4.01618	+	5.42853i	0.188281	+	0.254493i
$456$	−14.2608	−	37.1473i	−0.667825	−	1.73958i
$457$	31.3813	−	21.3954i	1.46796	−	1.00083i	0.475304	−	0.879822i	$-0.342338\pi$
$457$	31.3813	−	21.3954i	1.46796	−	1.00083i	0.992651	−	0.121013i	$-0.0386144\pi$
$458$	−0.509929	−	10.7536i	−0.0238274	−	0.502484i
$459$	4.48644	−	2.59024i	0.209409	−	0.120902i
$460$	−4.25631	−	1.57315i	−0.198451	−	0.0733484i
$461$	−10.1732	+	2.32198i	−0.473815	+	0.108145i	−0.452759	−	0.891633i	$-0.649560\pi$
$461$	−10.1732	+	2.32198i	−0.473815	+	0.108145i	−0.0210566	+	0.999778i	$0.506703\pi$
$462$	−51.4472	+	4.43250i	−2.39354	+	0.206219i
$463$	2.30682	+	0.526517i	0.107207	+	0.0244693i	0.275788	−	0.961219i	$-0.411061\pi$
$463$	2.30682	+	0.526517i	0.107207	+	0.0244693i	−0.168581	+	0.985688i	$0.553918\pi$
$464$	−6.52943	−	2.82908i	−0.303121	−	0.131337i
$465$	0.606784	−	4.02575i	0.0281389	−	0.186690i
$466$	5.52193	+	6.28851i	0.255798	+	0.291310i
$467$	19.8384	+	18.4073i	0.918012	+	0.851790i	0.989334	−	0.145663i	$-0.0465315\pi$
$467$	19.8384	+	18.4073i	0.918012	+	0.851790i	−0.0713226	+	0.997453i	$0.522722\pi$
$468$	1.38167	−	25.1728i	0.0638675	−	1.16361i
$469$	16.3007	+	25.8757i	0.752696	+	1.19483i
$470$	2.02914	+	1.04665i	0.0935971	+	0.0482782i
$471$	−30.9182	−	17.8506i	−1.42464	−	0.822514i
$472$	−2.14154	−	0.0159514i	−0.0985724	−	0.000734223i
$473$	−1.36381	+	1.26543i	−0.0627081	+	0.0581846i
$474$	−1.17052	+	11.4115i	−0.0537638	+	0.524149i
$475$	−18.2877	+	22.9321i	−0.839098	+	1.05220i
$476$	15.6267	+	5.10008i	0.716247	+	0.233762i
$477$	−0.283684	−	0.355728i	−0.0129890	−	0.0162877i
$478$	20.5120	−	13.1760i	0.938197	−	0.602656i
$479$	3.74300	−	9.53701i	0.171022	−	0.435757i	−0.819505	−	0.573071i	$-0.805752\pi$
$479$	3.74300	−	9.53701i	0.171022	−	0.435757i	0.990528	+	0.137314i	$0.0438470\pi$
$480$	5.73681	+	1.69122i	0.261848	+	0.0771931i
$481$	15.0488	−	5.90620i	0.686164	−	0.269300i
$482$	3.64539	−	14.1692i	0.166043	−	0.645387i
$483$	7.78330	+	28.9134i	0.354152	+	1.31561i
$484$	−13.8440	+	48.2836i	−0.629273	+	2.19471i
$485$	−0.139066	+	1.85571i	−0.00631467	+	0.0842634i
$486$	−25.3295	−	10.7514i	−1.14897	−	0.487694i
$487$	−3.63640	+	5.33362i	−0.164781	+	0.241689i	−0.899744	−	0.436418i	$-0.856247\pi$
$487$	−3.63640	+	5.33362i	−0.164781	+	0.241689i	0.734963	+	0.678107i	$0.237199\pi$
$488$	−8.49816	−	3.40855i	−0.384694	−	0.154298i
$489$		−	2.76264i		−	0.124931i
$490$	3.88862	+	2.37715i	0.175670	+	0.107389i
$491$			18.9214i			0.853913i	0.904272	+	0.426956i	$0.140414\pi$
$491$			18.9214i			0.853913i	−0.904272	+	0.426956i	$0.859586\pi$
$492$	41.8212	−	13.8205i	1.88545	−	0.623074i
$493$	−3.11312	+	4.56611i	−0.140208	+	0.205647i
$494$	18.7652	−	44.2093i	0.844286	−	1.98907i
$495$	−0.470135	+	6.27351i	−0.0211310	+	0.281973i
$496$	15.3100	+	1.68573i	0.687441	+	0.0756914i
$497$	5.16966	−	27.4969i	0.231891	−	1.23341i
$498$	−15.6457	−	4.02526i	−0.701099	−	0.180376i
$499$	10.9223	−	4.28670i	0.488951	−	0.191899i	−0.108041	−	0.994146i	$-0.534458\pi$
$499$	10.9223	−	4.28670i	0.488951	−	0.191899i	0.596992	+	0.802247i	$0.296363\pi$
$500$	−2.18055	−	8.74493i	−0.0975172	−	0.391085i
$501$	4.08515	−	10.4088i	0.182511	−	0.465031i
$502$	−9.11142	−	14.1844i	−0.406662	−	0.633080i
$503$	−16.0235	−	20.0928i	−0.714452	−	0.895894i	0.283558	−	0.958955i	$-0.408485\pi$
$503$	−16.0235	−	20.0928i	−0.714452	−	0.895894i	−0.998010	+	0.0630611i	$0.979914\pi$
$504$	−5.51884	−	16.0959i	−0.245829	−	0.716968i
$505$	0.778891	−	0.976698i	0.0346602	−	0.0434625i
$506$	41.6642	+	4.27364i	1.85220	+	0.189986i
$507$	29.8514	−	27.6981i	1.32575	−	1.23011i
$508$	13.1079	+	15.7799i	0.581571	+	0.700121i
$509$	25.7756	+	14.8815i	1.14248	+	0.659612i	0.947044	−	0.321104i	$-0.104054\pi$
$509$	25.7756	+	14.8815i	1.14248	+	0.659612i	0.195437	+	0.980716i	$0.437387\pi$
$510$	2.12929	−	4.12806i	0.0942866	−	0.182793i
$511$	0.521452	+	0.0581409i	0.0230677	+	0.00257200i
$512$	−5.52672	+	21.9421i	−0.244249	+	0.969713i
$513$	−7.48879	−	6.94858i	−0.330638	−	0.306787i
$514$	14.1678	−	12.4407i	0.624913	−	0.548735i
$515$	0.385541	−	2.55790i	0.0169890	−	0.112714i
$516$	−1.19059	−	0.777372i	−0.0524129	−	0.0342219i
$517$	−20.5451	−	4.68928i	−0.903572	−	0.206234i
$518$	7.91533	−	7.51023i	0.347780	−	0.329981i
$519$	10.2991	−	2.35071i	0.452082	−	0.103185i
$520$	3.56279	+	6.27847i	0.156239	+	0.275329i
$521$	−22.4340	+	12.9523i	−0.982852	+	0.567450i	−0.903130	−	0.429367i	$-0.858737\pi$
$521$	−22.4340	+	12.9523i	−0.982852	+	0.567450i	−0.0797224	+	0.996817i	$0.525403\pi$
$522$	5.71424	−	0.270965i	0.250106	−	0.0118598i
$523$	28.9503	−	19.7380i	1.26591	−	0.863082i	0.270875	−	0.962615i	$-0.412687\pi$
$523$	28.9503	−	19.7380i	1.26591	−	0.863082i	0.995034	+	0.0995326i	$0.0317347\pi$
$524$	−20.3948	−	11.2381i	−0.890951	−	0.490938i
$525$	−18.9506	+	22.0727i	−0.827071	+	0.963332i
$526$	−30.7685	−	0.843762i	−1.34157	−	0.0367898i
$527$	3.52582	−	11.4304i	0.153587	−	0.497918i
$528$	−55.1696	−	1.92424i	−2.40095	−	0.0837419i
$529$	−0.0961143	−	1.28256i	−0.00417888	−	0.0557633i
$530$	0.123397	+	0.0418003i	0.00536000	+	0.00181569i
$531$	1.55117	−	0.747005i	0.0673152	−	0.0324173i
$532$	0.527437	−	32.4111i	0.0228673	−	1.40520i
$533$	47.8981	+	23.0665i	2.07470	+	0.999121i
$534$	22.3149	+	21.8737i	0.965659	+	0.946568i
$535$	0.903606	−	0.278726i	0.0390663	−	0.0120504i
$536$	13.9654	+	29.5608i	0.603216	+	1.27683i
$537$	0.561140	+	3.72292i	0.0242150	+	0.160656i
$538$	−12.6878	+	15.0448i	−0.547011	+	0.648625i
$539$	−40.2265	−	12.3061i	−1.73268	−	0.530060i
$540$	1.51352	−	0.259133i	0.0651317	−	0.0111513i
$541$	−27.1615	+	4.09393i	−1.16776	+	0.176012i	−0.704167	−	0.710035i	$-0.748679\pi$
$541$	−27.1615	+	4.09393i	−1.16776	+	0.176012i	−0.463596	+	0.886047i	$0.653441\pi$
$542$	3.51038	+	12.5965i	0.150784	+	0.541066i
$543$	8.48069	+	27.4937i	0.363941	+	1.17987i
$544$	15.9268	+	7.42576i	0.682855	+	0.318377i
$545$	0.248862	−	0.516767i	0.0106601	−	0.0221359i
$546$	20.1884	−	43.1452i	0.863986	−	1.84644i
$547$	−9.19796	−	19.0998i	−0.393276	−	0.816647i	−0.999768	−	0.0215568i	$-0.993138\pi$
$547$	−9.19796	−	19.0998i	−0.393276	−	0.816647i	0.606491	−	0.795090i	$-0.292577\pi$
$548$	−35.1453	+	21.2379i	−1.50133	+	0.907238i
$549$	7.34030	−	0.550079i	0.313276	−	0.0234768i
$550$	19.3725	+	35.7852i	0.826048	+	1.52589i
$551$	10.4138	+	3.21224i	0.443644	+	0.136846i
$552$	4.53497	+	31.6872i	0.193021	+	1.34870i
$553$	−4.35712	+	8.26729i	−0.185284	+	0.351561i
$554$	43.7926	−	8.73975i	1.86057	−	0.371316i
$555$	−1.73683	−	2.54747i	−0.0737245	−	0.108134i
$556$	9.90241	+	7.57846i	0.419956	+	0.321398i
$557$	−8.93942	−	15.4835i	−0.378776	−	0.656059i	0.612109	−	0.790774i	$-0.290321\pi$
$557$	−8.93942	−	15.4835i	−0.378776	−	0.656059i	−0.990884	+	0.134715i	$0.956988\pi$
$558$	−11.6461	+	4.20613i	−0.493020	+	0.178060i
$559$	−0.381898	−	1.67320i	−0.0161526	−	0.0707690i
$560$	3.82055	+	3.02376i	0.161448	+	0.127777i
$561$	−9.53984	+	41.7968i	−0.402772	+	1.76466i
$562$	−1.80079	−	14.6650i	−0.0759617	−	0.618604i
$563$	37.3263	+	5.62603i	1.57312	+	0.237109i	0.876882	−	0.480706i	$-0.159620\pi$
$563$	37.3263	+	5.62603i	1.57312	+	0.237109i	0.696234	+	0.717815i	$0.254858\pi$
$564$	−0.321577	−	16.1028i	−0.0135409	−	0.678049i
$565$	−2.16773	+	2.33626i	−0.0911973	+	0.0982873i
$566$	15.5341	−	11.7061i	0.652949	−	0.492043i
$567$	−19.9497	−	19.9034i	−0.837807	−	0.835865i
$568$	9.02890	−	28.5152i	0.378844	−	1.19647i
$569$	−8.71952	+	15.1027i	−0.365541	+	0.633136i	−0.988863	−	0.148829i	$-0.952449\pi$
$569$	−8.71952	+	15.1027i	−0.365541	+	0.633136i	0.623322	+	0.781966i	$0.285783\pi$
$570$	−9.01652	−	1.61295i	−0.377661	−	0.0675590i
$571$	5.42913	+	5.85121i	0.227202	+	0.244865i	0.836356	−	0.548186i	$-0.184681\pi$
$571$	5.42913	+	5.85121i	0.227202	+	0.244865i	−0.609154	+	0.793052i	$0.708491\pi$
$572$	−46.2860	−	47.9286i	−1.93532	−	2.00399i
$573$	35.2891	+	28.1421i	1.47422	+	1.17565i
$574$	35.8091	+	2.28254i	1.49464	+	0.0952712i
$575$	18.4480	−	14.7118i	0.769336	−	0.613525i
$576$	−3.78316	−	17.7928i	−0.157632	−	0.741369i
$577$	−30.8394	−	12.1036i	−1.28386	−	0.503879i	−0.377354	−	0.926069i	$-0.623166\pi$
$577$	−30.8394	−	12.1036i	−1.28386	−	0.503879i	−0.906507	+	0.422190i	$0.861261\pi$
$578$	−6.08854	+	8.42444i	−0.253250	+	0.350410i
$579$	15.2519	+	38.8611i	0.633845	+	1.61501i
$580$	−1.33475	+	0.949598i	−0.0554223	+	0.0394299i
$581$	−10.5982	−	7.80286i	−0.439688	−	0.323717i
$582$	11.9790	−	5.36936i	0.496544	−	0.222567i
$583$	−1.19915	−	0.0898638i	−0.0496637	−	0.00372178i
$584$	0.545902	+	0.128884i	0.0225896	+	0.00533325i
$585$	−4.79501	−	3.26918i	−0.198249	−	0.135164i
$586$	−3.14184	+	5.11281i	−0.129788	+	0.211208i
$587$	20.0265			0.826583			0.413292	−	0.910599i	$-0.364379\pi$
$587$	20.0265			0.826583			0.413292	+	0.910599i	$0.364379\pi$
$588$	1.68751	−	32.1064i	0.0695916	−	1.32405i
$589$	−23.5888			−0.971959
$590$	−0.258105	+	0.420023i	−0.0106260	+	0.0172921i
$591$	35.5394	+	24.2304i	1.46190	+	0.996704i
$592$	9.36776	−	6.95048i	0.385013	−	0.285663i
$593$	11.7343	+	0.879368i	0.481872	+	0.0361113i	0.313452	−	0.949604i	$-0.398515\pi$
$593$	11.7343	+	0.879368i	0.481872	+	0.0361113i	0.168420	+	0.985715i	$0.446134\pi$
$594$	−12.9332	+	5.79706i	−0.530654	+	0.237856i
$595$	2.86525	−	2.47154i	0.117464	−	0.101323i
$596$	11.8503	+	16.6566i	0.485405	+	0.682280i
$597$	17.2462	+	43.9426i	0.705840	+	1.79845i
$598$	−22.6314	+	31.3140i	−0.925465	+	1.28052i
$599$	12.5049	+	4.90783i	0.510938	+	0.200528i	0.606783	−	0.794868i	$-0.292460\pi$
$599$	12.5049	+	4.90783i	0.510938	+	0.200528i	−0.0958444	+	0.995396i	$0.530555\pi$
$600$	−22.9551	+	20.9832i	−0.937138	+	0.856636i
$601$	−12.6546	+	10.0917i	−0.516193	+	0.411650i	−0.846633	−	0.532177i	$-0.821374\pi$
$601$	−12.6546	+	10.0917i	−0.516193	+	0.411650i	0.330440	+	0.943827i	$0.392803\pi$
$602$	−0.663151	−	0.949748i	−0.0270280	−	0.0387088i
$603$	−20.5489	−	16.3872i	−0.836816	−	0.667338i
$604$	−12.2681	+	11.8477i	−0.499182	+	0.482075i
$605$	7.86454	+	8.47596i	0.319739	+	0.344597i
$606$	−8.67474	−	1.55181i	−0.352387	−	0.0630379i
$607$	10.6147	−	18.3852i	0.430837	−	0.746231i	−0.566109	−	0.824331i	$-0.691552\pi$
$607$	10.6147	−	18.3852i	0.430837	−	0.746231i	0.996946	+	0.0780992i	$0.0248851\pi$
$608$	4.73546	−	34.3285i	0.192048	−	1.39220i
$609$	10.2066	+	3.55815i	0.413592	+	0.144184i
$610$	−1.68330	+	1.26849i	−0.0681548	+	0.0513595i
$611$	13.2224	−	14.2504i	0.534923	−	0.576510i
$612$	−14.1243	+	0.282067i	−0.570941	+	0.0114019i
$613$	25.9946	+	3.91805i	1.04991	+	0.158249i	0.651260	−	0.758854i	$-0.274241\pi$
$613$	25.9946	+	3.91805i	1.04991	+	0.158249i	0.398650	+	0.917103i	$0.369479\pi$
$614$	4.81673	+	39.2257i	0.194388	+	1.58302i
$615$	2.25617	−	9.88494i	0.0909777	−	0.398599i
$616$	−41.1051	−	18.2425i	−1.65617	−	0.735011i
$617$	0.594655	+	2.60535i	0.0239399	+	0.104888i	0.985486	−	0.169755i	$-0.0542976\pi$
$617$	0.594655	+	2.60535i	0.0239399	+	0.104888i	−0.961546	+	0.274643i	$0.911440\pi$
$618$	−17.1627	+	6.19851i	−0.690387	+	0.249341i
$619$	−6.06911	−	10.5120i	−0.243938	−	0.422513i	0.717895	−	0.696152i	$-0.245106\pi$
$619$	−6.06911	−	10.5120i	−0.243938	−	0.422513i	−0.961832	+	0.273639i	$0.911773\pi$
$620$	2.15487	−	2.81566i	0.0865415	−	0.113080i
$621$	4.62955	+	6.79031i	0.185778	+	0.272486i
$622$	−8.30099	+	1.65664i	−0.332839	+	0.0664252i
$623$	10.2067	+	23.3201i	0.408921	+	0.934298i
$624$	26.9837	−	43.1870i	1.08021	−	1.72886i
$625$	20.8941	+	6.44497i	0.835763	+	0.257799i
$626$	9.33619	+	17.2459i	0.373149	+	0.689286i
$627$	84.3064	−	6.31789i	3.36687	−	0.252312i
$628$	−16.0806	−	26.6108i	−0.641686	−	1.06189i
$629$	−3.93053	−	8.16184i	−0.156721	−	0.325434i
$630$	−3.82823	−	0.828996i	−0.152520	−	0.0330280i
$631$	−3.94442	+	8.19068i	−0.157025	+	0.326066i	−0.964608	−	0.263688i	$-0.915061\pi$
$631$	−3.94442	+	8.19068i	−0.157025	+	0.326066i	0.807583	+	0.589754i	$0.200775\pi$
$632$	−5.68913	+	8.21233i	−0.226302	+	0.326669i
$633$	−12.2527	−	39.7221i	−0.486999	−	1.57881i
$634$	−1.15724	−	4.15260i	−0.0459599	−	0.164921i
$635$	4.66951	−	0.703815i	0.185304	−	0.0279300i
$636$	−0.155096	−	0.905873i	−0.00614995	−	0.0359202i
$637$	28.3853	−	26.4606i	1.12467	−	1.04841i
$638$	9.74720	−	11.5579i	0.385895	−	0.457580i
$639$	3.58380	+	23.7770i	0.141773	+	0.940603i
$640$	3.66500	+	3.70119i	0.144872	+	0.146303i
$641$	14.9372	−	4.60753i	0.589985	−	0.181986i	0.0146341	−	0.999893i	$-0.495342\pi$
$641$	14.9372	−	4.60753i	0.589985	−	0.181986i	0.575351	+	0.817907i	$0.304865\pi$
$642$	−4.76368	−	4.66950i	−0.188007	−	0.184290i
$643$	16.5381	+	7.96433i	0.652199	+	0.314082i	0.730566	−	0.682842i	$-0.239256\pi$
$643$	16.5381	+	7.96433i	0.652199	+	0.314082i	−0.0783671	+	0.996925i	$0.524971\pi$
$644$	−6.21559	+	25.3255i	−0.244928	+	0.997963i
$645$	−0.294903	+	0.142018i	−0.0116118	+	0.00559195i
$646$	−25.4897	−	8.63458i	−1.00288	−	0.339723i
$647$	3.52257	+	47.0055i	0.138487	+	1.84798i	0.444293	+	0.895882i	$0.353455\pi$
$647$	3.52257	+	47.0055i	0.138487	+	1.84798i	−0.305806	+	0.952094i	$0.598926\pi$
$648$	−18.6074	−	23.6928i	−0.730967	−	0.930741i
$649$	1.34121	−	4.34809i	0.0526470	−	0.170677i
$650$	−37.5239	−	1.02902i	−1.47181	−	0.0403613i
$651$	−23.3808	−	0.847681i	−0.916366	−	0.0332232i
$652$	1.16115	−	2.10724i	0.0454740	−	0.0825259i
$653$	4.26910	−	2.91063i	0.167063	−	0.113902i	−0.476902	−	0.878956i	$-0.658240\pi$
$653$	4.26910	−	2.91063i	0.167063	−	0.113902i	0.643965	+	0.765055i	$0.277288\pi$
$654$	−4.04153	+	0.191646i	−0.158037	+	0.00749397i
$655$	−4.64222	+	2.68019i	−0.181387	+	0.104724i
$656$	37.7085	+	7.03585i	1.47227	+	0.274704i
$657$	−0.439620	+	0.100340i	−0.0171512	+	0.00391465i
$658$	4.65714	−	12.2664i	0.181554	−	0.478195i
$659$	−16.2591	−	3.71103i	−0.633364	−	0.144561i	−0.106228	−	0.994342i	$-0.533877\pi$
$659$	−16.2591	−	3.71103i	−0.633364	−	0.144561i	−0.527137	+	0.849781i	$0.676734\pi$
$660$	−6.94737	+	10.6403i	−0.270426	+	0.414174i
$661$	2.61186	−	17.3286i	0.101590	−	0.674003i	−0.878838	−	0.477121i	$-0.841680\pi$
$661$	2.61186	−	17.3286i	0.101590	−	0.674003i	0.980427	−	0.196882i	$-0.0630815\pi$
$662$	−11.2231	+	9.85501i	−0.436199	+	0.383026i
$663$	−28.9909	−	26.8997i	−1.12591	−	1.04470i
$664$	−10.2421	−	9.64624i	−0.397471	−	0.374347i
$665$	−6.32279	−	3.96264i	−0.245187	−	0.153665i
$666$	−4.29879	+	8.33406i	−0.166575	+	0.322938i
$667$	−7.59249	−	4.38353i	−0.293983	−	0.169731i
$668$	7.49085	−	6.22245i	0.289830	−	0.240754i
$669$	28.7942	−	26.7171i	1.11325	−	1.03294i
$670$	7.48668	+	0.767934i	0.289236	+	0.0296679i
$671$	12.1295	−	15.2099i	0.468255	−	0.587173i
$672$	5.92733	−	33.8556i	0.228652	−	1.30601i
$673$	−6.06793	−	7.60895i	−0.233902	−	0.293303i	0.651003	−	0.759075i	$-0.274348\pi$
$673$	−6.06793	−	7.60895i	−0.233902	−	0.293303i	−0.884905	+	0.465771i	$0.845777\pi$
$674$	22.2830	+	34.6895i	0.858308	+	1.33619i
$675$	−2.91716	+	7.43281i	−0.112282	+	0.286089i
$676$	34.4112	−	8.58044i	1.32351	−	0.330017i
$677$	−26.8971	+	10.5563i	−1.03374	+	0.405712i	−0.820717	−	0.571335i	$-0.806426\pi$
$677$	−26.8971	+	10.5563i	−1.03374	+	0.405712i	−0.213021	+	0.977048i	$0.568330\pi$
$678$	21.7730	+	5.60169i	0.836187	+	0.215132i
$679$	10.6862	−	0.412267i	0.410099	−	0.0158214i
$680$	3.35918	−	2.25378i	0.128819	−	0.0864287i
$681$	2.49827	−	33.3371i	0.0957338	−	1.27748i
$682$	−12.7866	+	30.1243i	−0.489626	+	1.15352i
$683$	5.42755	−	7.96075i	0.207679	−	0.304610i	−0.708240	−	0.705972i	$-0.750511\pi$
$683$	5.42755	−	7.96075i	0.207679	−	0.304610i	0.915920	+	0.401362i	$0.131463\pi$
$684$	8.74136	+	26.4517i	0.334234	+	1.01141i
$685$			9.45277i			0.361172i
$686$	11.0453	−	23.7487i	0.421713	−	0.906729i
$687$			17.4820i			0.666980i
$688$	−0.581409	−	1.09336i	−0.0221660	−	0.0416840i
$689$	0.624887	−	0.916541i	0.0238063	−	0.0349174i
$690$	6.78288	+	2.87908i	0.258220	+	0.109605i
$691$	−0.839293	+	11.1996i	−0.0319282	+	0.426052i	0.958220	+	0.286031i	$0.0923361\pi$
$691$	−0.839293	+	11.1996i	−0.0319282	+	0.426052i	−0.990149	+	0.140021i	$0.955283\pi$
$692$	8.84382	+	2.53572i	0.336192	+	0.0963937i
$693$	36.1264	−	1.39373i	1.37233	−	0.0529435i
$694$	0.358579	−	1.39375i	0.0136115	−	0.0529059i
$695$	2.67203	−	1.04870i	0.101356	−	0.0397793i
$696$	10.3734	+	5.09107i	0.393201	+	0.192977i
$697$	10.8837	−	27.7311i	0.412248	−	1.05039i
$698$	2.83905	−	1.82368i	0.107460	−	0.0690273i
$699$	−8.47308	−	10.6249i	−0.320481	−	0.401871i
$700$	−23.7320	+	8.87128i	−0.896986	+	0.335303i
$701$	−3.18350	+	3.99198i	−0.120239	+	0.150775i	−0.838308	−	0.545197i	$-0.816455\pi$
$701$	−3.18350	+	3.99198i	−0.120239	+	0.150775i	0.718069	+	0.695972i	$0.245026\pi$
$702$	1.33407	−	13.0060i	0.0503513	−	0.490881i
$703$	−13.0954	+	12.1508i	−0.493903	+	0.458275i
$704$	−41.2726	−	24.6557i	−1.55552	−	0.929247i
$705$	−3.21082	−	1.85377i	−0.120927	−	0.0698170i
$706$	21.1438	+	10.9062i	0.795758	+	0.410460i
$707$	−6.08311	−	3.81243i	−0.228779	−	0.143381i
$708$	3.47243	+	0.190592i	0.130502	+	0.00716287i
$709$	0.608331	+	0.564449i	0.0228464	+	0.0211983i	0.691513	−	0.722364i	$-0.256944\pi$
$709$	0.608331	+	0.564449i	0.0228464	+	0.0211983i	−0.668667	+	0.743562i	$0.733135\pi$
$710$	−4.54306	−	5.17375i	−0.170498	−	0.194167i
$711$	1.19703	−	7.94178i	0.0448922	−	0.297840i
$712$	7.82740	+	26.0635i	0.293344	+	0.976770i
$713$	18.5006	+	4.22263i	0.692851	+	0.158139i
$714$	−24.9547	−	9.47445i	−0.933906	−	0.354572i
$715$	−14.9534	+	3.41302i	−0.559226	+	0.127640i
$716$	−1.13674	+	3.07556i	−0.0424819	+	0.114939i
$717$	−34.2846	+	19.7942i	−1.28038	+	0.739229i
$718$	−0.759273	−	16.0119i	−0.0283358	−	0.597560i
$719$	4.16525	−	2.83982i	0.155338	−	0.105907i	−0.483157	−	0.875534i	$-0.660510\pi$
$719$	4.16525	−	2.83982i	0.155338	−	0.105907i	0.638494	+	0.769626i	$0.279558\pi$
$720$	−3.95592	−	1.37299i	−0.147428	−	0.0511683i
$721$	−14.8558	−	0.538603i	−0.553259	−	0.0200586i
$722$	−0.718247	+	26.1915i	−0.0267304	+	0.974745i
$723$	−7.00278	+	22.7025i	−0.260436	+	0.844314i
$724$	−5.08693	+	24.5357i	−0.189054	+	0.911860i
$725$	−0.636543	−	8.49407i	−0.0236406	−	0.315462i
$726$	26.1692	−	77.2529i	0.971231	−	2.86712i
$727$	−37.8488	+	18.2270i	−1.40373	+	0.676003i	−0.973915	−	0.226912i	$-0.927137\pi$
$727$	−37.8488	+	18.2270i	−1.40373	+	0.676003i	−0.429819	+	0.902915i	$0.641423\pi$
$728$	33.5331	−	24.4243i	1.24282	−	0.905226i
$729$	11.4691	+	5.52325i	0.424783	+	0.204565i
$730$	0.0903852	−	0.0922083i	0.00334531	−	0.00341278i
$731$	−0.918985	+	0.283469i	−0.0339899	+	0.0104845i
$732$	13.5221	+	6.18242i	0.499793	+	0.228509i
$733$	−5.88306	−	39.0316i	−0.217296	−	1.44166i	−0.785544	−	0.618806i	$-0.787617\pi$
$733$	−5.88306	−	39.0316i	−0.217296	−	1.44166i	0.568248	−	0.822858i	$-0.307622\pi$
$734$	−13.0900	−	11.0394i	−0.483162	−	0.407470i
$735$	−6.12464	−	4.15492i	−0.225911	−	0.153257i
$736$	−9.85914	+	26.0759i	−0.363413	+	0.961172i
$737$	−68.6881	+	10.3531i	−2.53016	+	0.381360i
$738$	−29.7058	+	8.27837i	−1.09348	+	0.304731i
$739$	−12.1056	−	39.2455i	−0.445313	−	1.44367i	−0.848815	−	0.528690i	$-0.822683\pi$
$739$	−12.1056	−	39.2455i	−0.445313	−	1.44367i	0.403502	−	0.914979i	$-0.367793\pi$
$740$	−0.254085	−	2.67311i	−0.00934036	−	0.0982656i
$741$	−33.8382	+	70.2657i	−1.24308	+	2.58128i
$742$	0.158458	−	0.731747i	0.00581719	−	0.0268633i
$743$	−2.78544	−	5.78402i	−0.102188	−	0.212195i	0.843606	−	0.536962i	$-0.180428\pi$
$743$	−2.78544	−	5.78402i	−0.102188	−	0.212195i	−0.945794	+	0.324767i	$0.894714\pi$
$744$	−24.7037	−	3.91189i	−0.905683	−	0.143417i
$745$	4.69249	−	0.351654i	0.171920	−	0.0128836i
$746$	−35.6904	+	19.3212i	−1.30672	+	0.707399i
$747$	10.8082	+	3.33389i	0.395452	+	0.121981i
$748$	−24.8440	+	27.8714i	−0.908385	+	1.01908i
$749$	−2.17887	−	4.97826i	−0.0796142	−	0.181902i
$750$	2.86431	+	14.3523i	0.104590	+	0.524072i
$751$	−24.2766	−	35.6072i	−0.885864	−	1.29932i	−0.953432	−	0.301609i	$-0.902476\pi$
$751$	−24.2766	−	35.6072i	−0.885864	−	1.29932i	0.0675677	−	0.997715i	$-0.478476\pi$
$752$	6.52276	−	12.4178i	0.237861	−	0.452829i
$753$	13.6880	+	23.7084i	0.498820	+	0.863981i
$754$	4.73768	+	13.1179i	0.172536	+	0.477726i
$755$	0.873618	+	3.82757i	0.0317942	+	0.139300i
$756$	−2.46348	−	8.47353i	−0.0895959	−	0.308179i
$757$	−2.54703	+	11.1593i	−0.0925735	+	0.405591i	−0.999890	−	0.0148582i	$-0.995270\pi$
$757$	−2.54703	+	11.1593i	−0.0925735	+	0.405591i	0.907316	+	0.420449i	$0.138127\pi$
$758$	−21.2229	+	2.60607i	−0.770849	+	0.0946566i
$759$	−67.2520	−	10.1366i	−2.44109	−	0.367936i
$760$	−6.19955	−	5.01997i	−0.224881	−	0.182093i
$761$	−15.7495	+	16.9739i	−0.570918	+	0.615303i	−0.950828	−	0.309720i	$-0.899765\pi$
$761$	−15.7495	+	16.9739i	−0.570918	+	0.615303i	0.379910	+	0.925024i	$0.375955\pi$
$762$	−20.0478	−	26.6038i	−0.726256	−	0.963753i
$763$	−3.11243	−	1.08503i	−0.112678	−	0.0392809i
$764$	15.0890	+	36.2979i	0.545901	+	1.31321i
$765$	−1.62601	+	2.81632i	−0.0587883	+	0.101824i
$766$	−4.38904	+	24.5351i	−0.158582	+	0.886489i
$767$	2.85503

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.p (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20490 - 0.740415i) q^{2} +(1.89744 + 1.29365i) q^{3} +(0.903573 + 1.78425i) q^{4} +(0.459106 + 0.0344052i) q^{5} +(-1.32839 - 2.96362i) q^{6} +(-0.101996 - 2.64378i) q^{7} +(0.232371 - 2.81887i) q^{8} +(0.830721 + 2.11664i) q^{9} +O(q^{10})\)	\(q+(-1.20490 - 0.740415i) q^{2} +(1.89744 + 1.29365i) q^{3} +(0.903573 + 1.78425i) q^{4} +(0.459106 + 0.0344052i) q^{5} +(-1.32839 - 2.96362i) q^{6} +(-0.101996 - 2.64378i) q^{7} +(0.232371 - 2.81887i) q^{8} +(0.830721 + 2.11664i) q^{9} +(-0.527703 - 0.381383i) q^{10} +(5.59412 + 2.19553i) q^{11} +(-0.593729 + 4.55442i) q^{12} +(-4.33422 + 3.45643i) q^{13} +(-1.83460 + 3.26102i) q^{14} +(0.826618 + 0.659206i) q^{15} +(-2.36711 + 3.22440i) q^{16} +(2.11293 + 2.27720i) q^{17} +(0.566257 - 3.16542i) q^{18} +(3.06297 - 5.30522i) q^{19} +(0.353448 + 0.850248i) q^{20} +(3.22661 - 5.14837i) q^{21} +(-5.11476 - 6.78737i) q^{22} +(-3.35196 + 3.61255i) q^{23} +(4.08755 - 5.04803i) q^{24} +(-4.73456 - 0.713620i) q^{25} +(7.78150 - 0.955531i) q^{26} +(0.371087 - 1.62584i) q^{27} +(4.62502 - 2.57084i) q^{28} +(0.395863 + 1.73439i) q^{29} +(-0.507907 - 1.40632i) q^{30} +(-1.92532 - 3.33475i) q^{31} +(5.23953 - 2.13244i) q^{32} +(7.77426 + 11.4027i) q^{33} +(-0.859803 - 4.30825i) q^{34} +(0.0441332 - 1.21729i) q^{35} +(-3.02601 + 3.39476i) q^{36} +(-2.78661 - 0.859554i) q^{37} +(-7.61863 + 4.12440i) q^{38} +(-12.6954 + 0.951386i) q^{39} +(0.203666 - 1.28616i) q^{40} +(-4.16086 - 8.64012i) q^{41} +(-7.69968 + 3.81425i) q^{42} +(-0.134323 + 0.278925i) q^{43} +(1.13731 + 11.9651i) q^{44} +(0.308565 + 1.00034i) q^{45} +(6.71356 - 1.87093i) q^{46} +(-3.46750 + 0.522642i) q^{47} +(-8.66272 + 3.05589i) q^{48} +(-6.97919 + 0.539309i) q^{49} +(5.17630 + 4.36538i) q^{50} +(1.06326 + 7.05426i) q^{51} +(-10.0834 - 4.61022i) q^{52} +(-0.191211 + 0.0589807i) q^{53} +(-1.65092 + 1.68421i) q^{54} +(2.49276 + 1.20045i) q^{55} +(-7.47617 - 0.326827i) q^{56} +(12.6749 - 6.10392i) q^{57} +(0.807192 - 2.38287i) q^{58} +(-0.0565834 - 0.755053i) q^{59} +(-0.429280 + 2.07053i) q^{60} +(0.954189 - 3.09340i) q^{61} +(-0.149279 + 5.44358i) q^{62} +(5.51122 - 2.41214i) q^{63} +(-7.89201 - 1.31005i) q^{64} +(-2.10879 + 1.43775i) q^{65} +(-0.924455 - 19.4954i) q^{66} +(-10.0103 + 5.77947i) q^{67} +(-2.15391 + 5.82762i) q^{68} +(-11.0335 + 2.51833i) q^{69} +(-0.954472 + 1.43403i) q^{70} +(10.3098 + 2.35315i) q^{71} +(6.15957 - 1.84985i) q^{72} +(-0.0295568 + 0.196097i) q^{73} +(2.72116 + 3.09892i) q^{74} +(-8.06037 - 7.47893i) q^{75} +(12.2335 + 0.671460i) q^{76} +(5.23394 - 15.0136i) q^{77} +(16.0011 + 8.25350i) q^{78} +(-3.05893 - 1.76607i) q^{79} +(-1.19769 + 1.39890i) q^{80} +(7.80788 - 7.24465i) q^{81} +(-1.38384 + 13.4913i) q^{82} +(3.10144 - 3.88908i) q^{83} +(12.1015 + 1.10516i) q^{84} +(0.891712 + 1.11817i) q^{85} +(0.368367 - 0.236623i) q^{86} +(-1.49257 + 3.80302i) q^{87} +(7.48882 - 15.2589i) q^{88} +(-8.95632 + 3.51510i) q^{89} +(0.368879 - 1.43378i) q^{90} +(9.58012 + 11.1062i) q^{91} +(-9.47444 - 2.71654i) q^{92} +(0.660832 - 8.81820i) q^{93} +(4.56497 + 1.93766i) q^{94} +(1.58875 - 2.33027i) q^{95} +(12.7003 + 2.73196i) q^{96} +4.04201i q^{97} +(8.80855 + 4.51768i) q^{98} +13.6646i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9	\( 312 q - 13 q^{2} - 13 q^{4} - 22 q^{5} - 14 q^{6} - 4 q^{8} - 4 q^{9} - 20 q^{10} + 9 q^{12} - 28 q^{13} - 51 q^{14} - 17 q^{16} - 22 q^{17} - 12 q^{18} - 14 q^{20} - 34 q^{21} - 18 q^{22} - 44 q^{24} - 48 q^{25} - 2 q^{26} - 36 q^{28} - 11 q^{30} - 13 q^{32} - 34 q^{33} - 98 q^{34} - 4 q^{36} - 58 q^{37} - 18 q^{38} + 30 q^{40} - 28 q^{41} - 26 q^{42} + 16 q^{44} - 28 q^{45} - 14 q^{46} - 24 q^{49} + 96 q^{50} - 14 q^{52} - 22 q^{53} - 17 q^{54} + 40 q^{56} + 34 q^{57} - 12 q^{58} + 98 q^{60} - 38 q^{61} - 4 q^{64} - 32 q^{65} - 176 q^{66} - 21 q^{68} + 28 q^{69} + 50 q^{70} - 120 q^{72} - 58 q^{73} - 14 q^{74} - 91 q^{76} - 18 q^{77} - 112 q^{78} + 66 q^{80} - 170 q^{81} + 114 q^{82} + 140 q^{84} - 24 q^{85} + 97 q^{86} + 127 q^{88} - 82 q^{89} + 266 q^{90} + 34 q^{92} + 226 q^{94} + 122 q^{96} + 183 q^{98}+O(q^{100}) \) 312 * q - 13 * q^2 - 13 * q^4 - 22 * q^5 - 14 * q^6 - 4 * q^8 - 4 * q^9 - 20 * q^10 + 9 * q^12 - 28 * q^13 - 51 * q^14 - 17 * q^16 - 22 * q^17 - 12 * q^18 - 14 * q^20 - 34 * q^21 - 18 * q^22 - 44 * q^24 - 48 * q^25 - 2 * q^26 - 36 * q^28 - 11 * q^30 - 13 * q^32 - 34 * q^33 - 98 * q^34 - 4 * q^36 - 58 * q^37 - 18 * q^38 + 30 * q^40 - 28 * q^41 - 26 * q^42 + 16 * q^44 - 28 * q^45 - 14 * q^46 - 24 * q^49 + 96 * q^50 - 14 * q^52 - 22 * q^53 - 17 * q^54 + 40 * q^56 + 34 * q^57 - 12 * q^58 + 98 * q^60 - 38 * q^61 - 4 * q^64 - 32 * q^65 - 176 * q^66 - 21 * q^68 + 28 * q^69 + 50 * q^70 - 120 * q^72 - 58 * q^73 - 14 * q^74 - 91 * q^76 - 18 * q^77 - 112 * q^78 + 66 * q^80 - 170 * q^81 + 114 * q^82 + 140 * q^84 - 24 * q^85 + 97 * q^86 + 127 * q^88 - 82 * q^89 + 266 * q^90 + 34 * q^92 + 226 * q^94 + 122 * q^96 + 183 * q^98

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