LMFDB - Embedded newform 429.2.bm.a.17.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(17,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 27, 5]))

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

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

chi := DirichletCharacter("429.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bm (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.20
Character	$\chi$	$=$	429.17
Dual form			429.2.bm.a.101.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.169208 + 0.796062i) q^{2} +(-1.73164 + 0.0376535i) q^{3} +(1.22201 + 0.544073i) q^{4} +(0.0210213 - 0.0646970i) q^{5} +(0.263033 - 1.38487i) q^{6} +(-0.681329 - 0.303347i) q^{7} +(-1.59662 + 2.19756i) q^{8} +(2.99716 - 0.130405i) q^{9} +O(q^{10})$	\(q+(-0.169208 + 0.796062i) q^{2} +(-1.73164 + 0.0376535i) q^{3} +(1.22201 + 0.544073i) q^{4} +(0.0210213 - 0.0646970i) q^{5} +(0.263033 - 1.38487i) q^{6} +(-0.681329 - 0.303347i) q^{7} +(-1.59662 + 2.19756i) q^{8} +(2.99716 - 0.130405i) q^{9} +(0.0479459 + 0.0276816i) q^{10} +(-3.02064 + 1.36957i) q^{11} +(-2.13657 - 0.896126i) q^{12} +(2.15862 + 2.88797i) q^{13} +(0.356770 - 0.491051i) q^{14} +(-0.0339654 + 0.112824i) q^{15} +(0.310895 + 0.345284i) q^{16} +(-0.573832 + 0.121972i) q^{17} +(-0.403335 + 2.40799i) q^{18} +(-0.472162 + 4.49232i) q^{19} +(0.0608881 - 0.0676231i) q^{20} +(1.19124 + 0.499634i) q^{21} +(-0.579148 - 2.63636i) q^{22} +(-5.10963 - 2.95005i) q^{23} +(2.68203 - 3.86551i) q^{24} +(4.04134 + 2.93621i) q^{25} +(-2.66426 + 1.22973i) q^{26} +(-5.18510 + 0.338668i) q^{27} +(-0.667546 - 0.741385i) q^{28} +(0.145099 + 1.38052i) q^{29} +(-0.0840674 - 0.0461292i) q^{30} +(-7.12737 + 2.31582i) q^{31} +(-5.03231 + 2.90540i) q^{32} +(5.17910 - 2.48535i) q^{33} -0.477444i q^{34} +(-0.0339481 + 0.0377032i) q^{35} +(3.73351 + 1.47132i) q^{36} +(-4.90780 + 0.515831i) q^{37} +(-3.49628 - 1.13601i) q^{38} +(-3.84669 - 4.91965i) q^{39} +(0.108613 + 0.149493i) q^{40} +(4.12387 + 9.26237i) q^{41} +(-0.599307 + 0.863758i) q^{42} +(6.74806 - 3.89599i) q^{43} +(-4.43639 + 0.0301795i) q^{44} +(0.0545676 - 0.196649i) q^{45} +(3.21301 - 3.56841i) q^{46} +(-3.22536 - 2.34336i) q^{47} +(-0.551360 - 0.586202i) q^{48} +(-4.31172 - 4.78866i) q^{49} +(-3.02123 + 2.72033i) q^{50} +(0.989078 - 0.232818i) q^{51} +(1.06658 + 4.70357i) q^{52} +(-5.37645 + 1.74691i) q^{53} +(0.607762 - 4.18497i) q^{54} +(0.0251094 + 0.224217i) q^{55} +(1.75445 - 1.01293i) q^{56} +(0.648464 - 7.79687i) q^{57} +(-1.12353 - 0.118088i) q^{58} +(13.5690 + 6.04132i) q^{59} +(-0.102890 + 0.119392i) q^{60} +(-0.152882 - 0.719253i) q^{61} +(-0.637529 - 6.06569i) q^{62} +(-2.08161 - 0.820333i) q^{63} +(-1.17422 - 3.61388i) q^{64} +(0.232220 - 0.0789471i) q^{65} +(1.10214 + 4.54342i) q^{66} +(6.21837 + 3.59017i) q^{67} +(-0.767588 - 0.163156i) q^{68} +(8.95912 + 4.91603i) q^{69} +(-0.0242698 - 0.0334045i) q^{70} +(11.4717 - 2.43839i) q^{71} +(-4.49877 + 6.79467i) q^{72} +(6.43699 - 4.67675i) q^{73} +(0.419807 - 3.99420i) q^{74} +(-7.10871 - 4.93229i) q^{75} +(-3.02114 + 5.23276i) q^{76} +(2.47351 - 0.0168266i) q^{77} +(4.56724 - 2.22976i) q^{78} +(7.55047 - 2.45330i) q^{79} +(0.0288743 - 0.0128557i) q^{80} +(8.96599 - 0.781688i) q^{81} +(-8.07121 + 1.71559i) q^{82} +(-4.02956 - 1.30928i) q^{83} +(1.18387 + 1.25868i) q^{84} +(-0.00417151 + 0.0396892i) q^{85} +(1.95962 + 6.03110i) q^{86} +(-0.303241 - 2.38511i) q^{87} +(1.81310 - 8.82474i) q^{88} +(1.53467 - 2.65813i) q^{89} +(0.147311 + 0.0767138i) q^{90} +(-0.594671 - 2.62247i) q^{91} +(-4.63896 - 6.38499i) q^{92} +(12.2549 - 4.27855i) q^{93} +(2.41122 - 2.17107i) q^{94} +(0.280715 + 0.124982i) q^{95} +(8.60476 - 5.22060i) q^{96} +(-10.1718 - 9.15874i) q^{97} +(4.54165 - 2.62212i) q^{98} +(-8.87476 + 4.49874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9}+O(q^{10}) $ 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9	$ 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9} - 36 q^{12} - 20 q^{13} - 9 q^{15} + 14 q^{16} - 30 q^{19} - 28 q^{22} + 15 q^{24} - 84 q^{25} - 24 q^{27} - 30 q^{28} - 5 q^{30} - 27 q^{33} - 73 q^{36} - 18 q^{37} - 65 q^{39} - 120 q^{40} - 25 q^{42} + 36 q^{45} + 30 q^{46} - 41 q^{48} + 14 q^{49} + 60 q^{51} + 20 q^{52} + 18 q^{55} - 126 q^{58} - 30 q^{61} + 105 q^{63} - 56 q^{64} + 170 q^{66} - 33 q^{69} - 195 q^{72} + 77 q^{75} + 4 q^{78} - 13 q^{81} + 36 q^{82} - 60 q^{84} - 30 q^{85} + 38 q^{88} - 190 q^{90} - 56 q^{91} + 24 q^{93} - 90 q^{94} + 54 q^{97}+O(q^{100}) $ 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9 - 36 * q^12 - 20 * q^13 - 9 * q^15 + 14 * q^16 - 30 * q^19 - 28 * q^22 + 15 * q^24 - 84 * q^25 - 24 * q^27 - 30 * q^28 - 5 * q^30 - 27 * q^33 - 73 * q^36 - 18 * q^37 - 65 * q^39 - 120 * q^40 - 25 * q^42 + 36 * q^45 + 30 * q^46 - 41 * q^48 + 14 * q^49 + 60 * q^51 + 20 * q^52 + 18 * q^55 - 126 * q^58 - 30 * q^61 + 105 * q^63 - 56 * q^64 + 170 * q^66 - 33 * q^69 - 195 * q^72 + 77 * q^75 + 4 * q^78 - 13 * q^81 + 36 * q^82 - 60 * q^84 - 30 * q^85 + 38 * q^88 - 190 * q^90 - 56 * q^91 + 24 * q^93 - 90 * q^94 + 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{10}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.169208	+	0.796062i	−0.119648	+	0.562901i	0.876957	+	0.480569i	$0.159570\pi$
$2$	−0.169208	+	0.796062i	−0.119648	+	0.562901i	−0.996605	+	0.0823315i	$0.973763\pi$
$3$	−1.73164	+	0.0376535i	−0.999764	+	0.0217392i
$3$	−1.73164	+	0.0376535i	−0.999764	+	0.0217392i
$4$	1.22201	+	0.544073i	0.611004	+	0.272036i
$5$	0.0210213	−	0.0646970i	0.00940103	−	0.0289334i	−0.946246	−	0.323448i	$-0.895158\pi$
$5$	0.0210213	−	0.0646970i	0.00940103	−	0.0289334i	0.955647	+	0.294515i	$0.0951579\pi$
$6$	0.263033	−	1.38487i	0.107383	−	0.565369i
$7$	−0.681329	−	0.303347i	−0.257518	−	0.114654i	0.273917	−	0.961753i	$-0.411681\pi$
$7$	−0.681329	−	0.303347i	−0.257518	−	0.114654i	−0.531435	+	0.847099i	$0.678347\pi$
$8$	−1.59662	+	2.19756i	−0.564492	+	0.776956i
$9$	2.99716	−	0.130405i	0.999055	−	0.0434682i
$10$	0.0479459	+	0.0276816i	0.0151618	+	0.00875368i
$11$	−3.02064	+	1.36957i	−0.910757	+	0.412942i
$11$	−3.02064	+	1.36957i	−0.910757	+	0.412942i
$12$	−2.13657	−	0.896126i	−0.616773	−	0.258689i
$13$	2.15862	+	2.88797i	0.598693	+	0.800979i
$13$	2.15862	+	2.88797i	0.598693	+	0.800979i
$14$	0.356770	−	0.491051i	0.0953507	−	0.131239i
$15$	−0.0339654	+	0.112824i	−0.00876982	+	0.0291309i
$16$	0.310895	+	0.345284i	0.0777238	+	0.0863210i
$17$	−0.573832	+	0.121972i	−0.139175	+	0.0295825i	−0.276972	−	0.960878i	$-0.589331\pi$
$17$	−0.573832	+	0.121972i	−0.139175	+	0.0295825i	0.137798	+	0.990460i	$0.455998\pi$
$18$	−0.403335	+	2.40799i	−0.0950669	+	0.567570i
$19$	−0.472162	+	4.49232i	−0.108321	+	1.03061i	0.796448	+	0.604708i	$0.206710\pi$
$19$	−0.472162	+	4.49232i	−0.108321	+	1.03061i	−0.904769	+	0.425902i	$0.859957\pi$
$20$	0.0608881	−	0.0676231i	0.0136150	−	0.0151210i
$21$	1.19124	+	0.499634i	0.259950	+	0.109029i
$22$	−0.579148	−	2.63636i	−0.123475	−	0.562074i
$23$	−5.10963	−	2.95005i	−1.06543	−	0.615127i	−0.138501	−	0.990362i	$-0.544229\pi$
$23$	−5.10963	−	2.95005i	−1.06543	−	0.615127i	−0.926930	+	0.375235i	$0.877562\pi$
$24$	2.68203	−	3.86551i	0.547468	−	0.789044i
$25$	4.04134	+	2.93621i	0.808268	+	0.587241i
$26$	−2.66426	+	1.22973i	−0.522504	+	0.241169i
$27$	−5.18510	+	0.338668i	−0.997874	+	0.0651766i
$28$	−0.667546	−	0.741385i	−0.126154	−	0.140109i
$29$	0.145099	+	1.38052i	0.0269442	+	0.256357i	0.999699	+	0.0245217i	$0.00780627\pi$
$29$	0.145099	+	1.38052i	0.0269442	+	0.256357i	−0.972755	+	0.231835i	$0.925527\pi$
$30$	−0.0840674	−	0.0461292i	−0.0153485	−	0.00842200i
$31$	−7.12737	+	2.31582i	−1.28011	+	0.415934i	−0.868620	−	0.495479i	$-0.834993\pi$
$31$	−7.12737	+	2.31582i	−1.28011	+	0.415934i	−0.411493	+	0.911413i	$0.634993\pi$
$32$	−5.03231	+	2.90540i	−0.889595	+	0.513608i
$33$	5.17910	−	2.48535i	0.901565	−	0.432643i
$34$		−	0.477444i		−	0.0818810i
$35$	−0.0339481	+	0.0377032i	−0.00573828	+	0.00637300i
$36$	3.73351	+	1.47132i	0.622251	+	0.245220i
$37$	−4.90780	+	0.515831i	−0.806838	+	0.0848021i	−0.498961	−	0.866624i	$-0.666285\pi$
$37$	−4.90780	+	0.515831i	−0.806838	+	0.0848021i	−0.307877	+	0.951426i	$0.599618\pi$
$38$	−3.49628	−	1.13601i	−0.567171	−	0.184285i
$39$	−3.84669	−	4.91965i	−0.615964	−	0.787774i
$40$	0.108613	+	0.149493i	0.0171732	+	0.0236368i
$41$	4.12387	+	9.26237i	0.644041	+	1.44654i	0.880094	+	0.474799i	$0.157479\pi$
$41$	4.12387	+	9.26237i	0.644041	+	1.44654i	−0.236054	+	0.971740i	$0.575854\pi$
$42$	−0.599307	+	0.863758i	−0.0924751	+	0.133281i
$43$	6.74806	−	3.89599i	1.02907	−	0.594133i	0.112351	−	0.993669i	$-0.464162\pi$
$43$	6.74806	−	3.89599i	1.02907	−	0.594133i	0.916718	+	0.399535i	$0.130829\pi$
$44$	−4.43639	+	0.0301795i	−0.668811	+	0.00454974i
$45$	0.0545676	−	0.196649i	0.00813446	−	0.0293147i
$46$	3.21301	−	3.56841i	0.473732	−	0.526133i
$47$	−3.22536	−	2.34336i	−0.470467	−	0.341814i	0.327156	−	0.944970i	$-0.393910\pi$
$47$	−3.22536	−	2.34336i	−0.470467	−	0.341814i	−0.797623	+	0.603156i	$0.793910\pi$
$48$	−0.551360	−	0.586202i	−0.0795819	−	0.0846109i
$49$	−4.31172	−	4.78866i	−0.615961	−	0.684094i
$50$	−3.02123	+	2.72033i	−0.427267	+	0.384712i
$51$	0.989078	−	0.232818i	0.138499	−	0.0326010i
$52$	1.06658	+	4.70357i	0.147908	+	0.652267i
$53$	−5.37645	+	1.74691i	−0.738512	+	0.239957i	−0.654031	−	0.756468i	$-0.726923\pi$
$53$	−5.37645	+	1.74691i	−0.738512	+	0.239957i	−0.0844813	+	0.996425i	$0.526923\pi$
$54$	0.607762	−	4.18497i	0.0827059	−	0.569502i
$55$	0.0251094	+	0.224217i	0.00338575	+	0.0302334i
$56$	1.75445	−	1.01293i	0.234448	−	0.135359i
$57$	0.648464	−	7.79687i	0.0858912	−	1.03272i
$58$	−1.12353	−	0.118088i	−0.147527	−	0.0155057i
$59$	13.5690	+	6.04132i	1.76654	+	0.786513i	0.987115	+	0.160015i	$0.0511541\pi$
$59$	13.5690	+	6.04132i	1.76654	+	0.786513i	0.779423	+	0.626498i	$0.215513\pi$
$60$	−0.102890	+	0.119392i	−0.0132831	+	0.0154134i
$61$	−0.152882	−	0.719253i	−0.0195745	−	0.0920910i	0.967276	−	0.253727i	$-0.0816564\pi$
$61$	−0.152882	−	0.719253i	−0.0195745	−	0.0920910i	−0.986850	+	0.161636i	$0.948323\pi$
$62$	−0.637529	−	6.06569i	−0.0809663	−	0.770343i
$63$	−2.08161	−	0.820333i	−0.262259	−	0.103352i
$64$	−1.17422	−	3.61388i	−0.146778	−	0.451735i
$65$	0.232220	−	0.0789471i	0.0288034	−	0.00979219i
$66$	1.10214	+	4.54342i	0.135665	+	0.559257i
$67$	6.21837	+	3.59017i	0.759694	+	0.438610i	0.829186	−	0.558973i	$-0.188804\pi$
$67$	6.21837	+	3.59017i	0.759694	+	0.438610i	−0.0694917	+	0.997583i	$0.522138\pi$
$68$	−0.767588	−	0.163156i	−0.0930838	−	0.0197856i
$69$	8.95912	+	4.91603i	1.07855	+	0.591820i
$70$	−0.0242698	−	0.0334045i	−0.00290079	−	0.00399260i
$71$	11.4717	−	2.43839i	1.36144	−	0.289383i	0.531416	−	0.847111i	$-0.321660\pi$
$71$	11.4717	−	2.43839i	1.36144	−	0.289383i	0.830024	+	0.557728i	$0.188327\pi$
$72$	−4.49877	+	6.79467i	−0.530185	+	0.800759i
$73$	6.43699	−	4.67675i	0.753393	−	0.547372i	−0.143484	−	0.989653i	$-0.545831\pi$
$73$	6.43699	−	4.67675i	0.753393	−	0.547372i	0.896877	+	0.442281i	$0.145831\pi$
$74$	0.419807	−	3.99420i	0.0488016	−	0.464316i
$75$	−7.10871	−	4.93229i	−0.820843	−	0.569531i
$76$	−3.02114	+	5.23276i	−0.346548	+	0.600239i
$77$	2.47351	−	0.0168266i	0.281882	−	0.00191756i
$78$	4.56724	−	2.22976i	0.517138	−	0.252471i
$79$	7.55047	−	2.45330i	0.849494	−	0.276017i	0.148260	−	0.988948i	$-0.452633\pi$
$79$	7.55047	−	2.45330i	0.849494	−	0.276017i	0.701234	+	0.712931i	$0.252633\pi$
$80$	0.0288743	−	0.0128557i	0.00322824	−	0.00143731i
$81$	8.96599	−	0.781688i	0.996221	−	0.0868543i
$82$	−8.07121	+	1.71559i	−0.891316	+	0.189455i
$83$	−4.02956	−	1.30928i	−0.442301	−	0.143712i	0.0793957	−	0.996843i	$-0.474701\pi$
$83$	−4.02956	−	1.30928i	−0.442301	−	0.143712i	−0.521697	+	0.853131i	$0.674701\pi$
$84$	1.18387	+	1.25868i	0.129170	+	0.137333i
$85$	−0.00417151	+	0.0396892i	−0.000452463	+	0.00430490i
$86$	1.95962	+	6.03110i	0.211312	+	0.650351i
$87$	−0.303241	−	2.38511i	−0.0325108	−	0.255710i
$88$	1.81310	−	8.82474i	0.193277	−	0.940721i
$89$	1.53467	−	2.65813i	0.162675	−	0.281761i	−0.773152	−	0.634220i	$-0.781321\pi$
$89$	1.53467	−	2.65813i	0.162675	−	0.281761i	0.935827	+	0.352459i	$0.114655\pi$
$90$	0.147311	+	0.0767138i	0.0155280	+	0.00808635i
$91$	−0.594671	−	2.62247i	−0.0623384	−	0.274909i
$92$	−4.63896	−	6.38499i	−0.483645	−	0.665681i
$93$	12.2549	−	4.27855i	1.27077	−	0.443665i
$94$	2.41122	−	2.17107i	0.248698	−	0.223929i
$95$	0.280715	+	0.124982i	0.0288007	+	0.0128229i
$96$	8.60476	−	5.22060i	0.878219	−	0.532826i
$97$	−10.1718	−	9.15874i	−1.03279	−	0.929929i	−0.0352053	−	0.999380i	$-0.511209\pi$
$97$	−10.1718	−	9.15874i	−1.03279	−	0.929929i	−0.997585	+	0.0694512i	$0.977875\pi$
$98$	4.54165	−	2.62212i	0.458776	−	0.264874i
$99$	−8.87476	+	4.49874i	−0.891947	+	0.452140i
$100$	3.34104	+	5.78685i	0.334104	+	0.578685i
$101$	11.4823	+	2.44065i	1.14254	+	0.242853i	0.740036	−	0.672567i	$-0.234808\pi$
$101$	11.4823	+	2.44065i	1.14254	+	0.242853i	0.402499	+	0.915420i	$0.368142\pi$
$102$	0.0179774	+	0.826762i	0.00178003	+	0.0818617i
$103$	−9.95049	+	7.22946i	−0.980451	+	0.712339i	−0.957809	−	0.287404i	$-0.907208\pi$
$103$	−9.95049	+	7.22946i	−0.980451	+	0.712339i	−0.0226417	+	0.999744i	$0.507208\pi$
$104$	−9.79300	+	0.132698i	−0.960282	+	0.0130121i
$105$	0.0573663	−	0.0665667i	0.00559838	−	0.00649624i
$106$	−0.480913	−	4.57558i	−0.0467104	−	0.444420i
$107$	15.8426	−	7.05357i	1.53156	−	0.681894i	0.543992	−	0.839090i	$-0.316912\pi$
$107$	15.8426	−	7.05357i	1.53156	−	0.681894i	0.987567	+	0.157196i	$0.0502453\pi$
$108$	−6.52050	−	2.40722i	−0.627435	−	0.231635i
$109$	10.8427			1.03854			0.519272	−	0.854609i	$-0.326203\pi$
$109$	10.8427			1.03854			0.519272	+	0.854609i	$0.326203\pi$
$110$	−0.182739	−	0.0179507i	−0.0174235	−	0.00171153i
$111$	8.47914	−	1.07803i	0.804804	−	0.102322i
$112$	−0.107081	−	0.329561i	−0.0101182	−	0.0311406i
$113$	12.2482	+	1.28733i	1.15221	+	0.121102i	0.661309	−	0.750113i	$-0.270001\pi$
$113$	12.2482	+	1.28733i	1.15221	+	0.121102i	0.490901	+	0.871216i	$0.336668\pi$
$114$	6.09707	+	1.83551i	0.571043	+	0.171912i
$115$	−0.298270	+	0.268564i	−0.0278139	+	0.0250437i
$116$	−0.573793	+	1.76595i	−0.0532753	+	0.163965i
$117$	6.84634	+	8.37423i	0.632944	+	0.774198i
$118$	−7.10526	+	9.77955i	−0.654092	+	0.900280i
$119$	0.427968	+	0.0909674i	0.0392318	+	0.00833897i
$120$	−0.193707	−	0.254778i	−0.0176830	−	0.0232579i
$121$	7.24854	−	8.27397i	0.658958	−	0.752179i
$122$	0.598439			0.0541801
$123$	−7.48983	−	15.8838i	−0.675335	−	1.43220i
$124$	−9.96968	−	1.04786i	−0.895303	−	0.0941002i
$125$	0.550091	−	0.399665i	0.0492017	−	0.0357471i
$126$	1.00526	−	1.51829i	0.0895558	−	0.135260i
$127$	−5.24260	+	4.72046i	−0.465206	+	0.418873i	−0.868112	−	0.496368i	$-0.834667\pi$
$127$	−5.24260	+	4.72046i	−0.465206	+	0.418873i	0.402906	+	0.915241i	$0.368000\pi$
$128$	−8.48240	+	0.891536i	−0.749745	+	0.0788014i
$129$	−11.5385	+	7.00055i	−1.01591	+	0.616364i
$130$	0.0235533	+	0.198220i	0.00206576	+	0.0173851i
$131$	−12.9813			−1.13418			−0.567091	−	0.823655i	$-0.691931\pi$
$131$	−12.9813			−1.13418			−0.567091	+	0.823655i	$0.691931\pi$
$132$	7.68111	−	0.219306i	0.668554	−	0.0190881i
$133$	1.68443	−	2.91752i	0.146059	−	0.252981i
$134$	−3.91020	+	4.34272i	−0.337790	+	0.375154i
$135$	−0.0870870	+	0.342580i	−0.00749526	+	0.0294846i
$136$	0.648153	−	1.45577i	0.0555786	−	0.124832i
$137$	−3.60092	+	0.765400i	−0.307648	+	0.0653925i	−0.359149	−	0.933280i	$-0.616933\pi$
$137$	−3.60092	+	0.765400i	−0.307648	+	0.0653925i	0.0515009	+	0.998673i	$0.483600\pi$
$138$	−5.42942	+	6.30019i	−0.462183	+	0.536307i
$139$	−4.76630	+	10.7053i	−0.404272	+	0.908010i	0.590609	+	0.806958i	$0.298888\pi$
$139$	−4.76630	+	10.7053i	−0.404272	+	0.908010i	−0.994881	+	0.101052i	$0.967779\pi$
$140$	−0.0619981	+	0.0276033i	−0.00523980	+	0.00233291i
$141$	5.67340	+	3.93642i	0.477787	+	0.331506i
$142$			9.54478i			0.800980i
$143$	−10.4757	−	5.76714i	−0.876021	−	0.482272i
$144$	0.976830	+	0.994330i	0.0814025	+	0.0828609i
$145$	0.0923659	+	0.0196330i	0.00767057	+	0.00163043i
$146$	2.63379	+	5.91559i	0.217974	+	0.489578i
$147$	7.64667	+	8.12988i	0.630687	+	0.670541i
$148$	−6.27802	−	2.03985i	−0.516050	−	0.167675i
$149$	0.841570	+	3.95927i	0.0689441	+	0.324356i	0.999081	−	0.0428559i	$-0.0136456\pi$
$149$	0.841570	+	3.95927i	0.0689441	+	0.324356i	−0.930137	+	0.367212i	$0.880312\pi$
$150$	5.12926	−	4.82439i	0.418802	−	0.393910i
$151$	−1.49726	−	1.08782i	−0.121845	−	0.0885256i	0.525194	−	0.850983i	$-0.323993\pi$
$151$	−1.49726	−	1.08782i	−0.121845	−	0.0885256i	−0.647039	+	0.762457i	$0.723993\pi$
$152$	−9.11830	−	8.21016i	−0.739592	−	0.665932i
$153$	−1.70396	+	0.440400i	−0.137757	+	0.0356042i
$154$	−0.405143	+	1.97191i	−0.0326473	+	0.158901i
$155$			0.509801i			0.0409482i
$156$	−2.02404	−	8.10473i	−0.162053	−	0.648898i
$157$	3.98267	+	2.89358i	0.317851	+	0.230933i	0.735258	−	0.677787i	$-0.237061\pi$
$157$	3.98267	+	2.89358i	0.317851	+	0.230933i	−0.417407	+	0.908720i	$0.637061\pi$
$158$	0.675374	+	6.42576i	0.0537299	+	0.511206i
$159$	9.24431	−	3.22747i	0.733121	−	0.255955i
$160$	0.0821852	+	0.386651i	0.00649731	+	0.0305674i
$161$	2.58645	+	3.55994i	0.203841	+	0.280563i
$162$	−0.894847	+	7.26975i	−0.0703058	+	0.571166i
$163$	−4.97515	−	4.47964i	−0.389683	−	0.350873i	0.450881	−	0.892584i	$-0.351110\pi$
$163$	−4.97515	−	4.47964i	−0.389683	−	0.350873i	−0.840564	+	0.541711i	$0.817777\pi$
$164$			13.5624i			1.05904i
$165$	−0.0519230	−	0.387318i	−0.00404220	−	0.0301526i
$166$	1.72410	−	2.98624i	0.133816	−	0.231777i
$167$	0.856713	−	4.03052i	0.0662945	−	0.311891i	−0.932489	−	0.361198i	$-0.882368\pi$
$167$	0.856713	−	4.03052i	0.0662945	−	0.311891i	0.998784	+	0.0493069i	$0.0157012\pi$
$168$	−2.99994	+	1.82010i	−0.231450	+	0.140424i
$169$	−3.68074	+	12.4680i	−0.283134	+	0.959080i
$170$	−0.0308892	−	0.0100365i	−0.00236910	−	0.000769766i
$171$	−0.829328	+	13.5258i	−0.0634203	+	1.03434i
$172$	10.3659	−	1.08950i	0.790391	−	0.0830734i
$173$	−1.89512	+	18.0308i	−0.144083	+	1.37086i	0.648556	+	0.761167i	$0.275373\pi$
$173$	−1.89512	+	18.0308i	−0.144083	+	1.37086i	−0.792639	+	0.609692i	$0.791293\pi$
$174$	1.95000	+	0.162181i	0.147829	+	0.0122949i
$175$	−1.86279	−	3.22645i	−0.140814	−	0.243897i
$176$	−1.41199	−	0.617185i	−0.106433	−	0.0465221i
$177$	−23.7242	−	9.95048i	−1.78322	−	0.747924i
$178$	1.85636	+	1.67147i	0.139140	+	0.125282i
$179$	−2.03169	−	4.56326i	−0.151856	−	0.341074i	0.821559	−	0.570124i	$-0.193105\pi$
$179$	−2.03169	−	4.56326i	−0.151856	−	0.341074i	−0.973415	+	0.229050i	$0.926438\pi$
$180$	0.173673	−	0.210618i	0.0129449	−	0.0156985i
$181$	5.92543	−	18.2366i	0.440434	−	1.35552i	−0.446981	−	0.894543i	$-0.647501\pi$
$181$	5.92543	−	18.2366i	0.440434	−	1.35552i	0.887415	−	0.460972i	$-0.152499\pi$
$182$	2.18827	−	0.0296518i	0.162205	−	0.00219794i
$183$	0.291819	+	1.23973i	0.0215719	+	0.0916437i
$184$	14.6411	−	6.51862i	1.07935	−	0.480559i
$185$	−0.0697959	+	0.328364i	−0.00513150	+	0.0241418i
$186$	1.33237	+	10.4796i	0.0976938	+	0.768401i
$187$	1.56629	−	1.15434i	0.114539	−	0.0844135i
$188$	−2.66646	−	4.61844i	−0.194471	−	0.336834i
$189$	3.63550	+	1.34214i	0.264443	+	0.0976265i
$190$	−0.146993	+	0.202318i	−0.0106640	+	0.0146777i
$191$	7.48755	−	16.8173i	0.541780	−	1.21686i	−0.410564	−	0.911832i	$-0.634668\pi$
$191$	7.48755	−	16.8173i	0.541780	−	1.21686i	0.952344	−	0.305026i	$-0.0986650\pi$
$192$	2.16940	+	6.21373i	0.156563	+	0.448437i
$193$	−13.6550	−	15.1654i	−0.982911	−	1.09163i	−0.995785	−	0.0917158i	$-0.970765\pi$
$193$	−13.6550	−	15.1654i	−0.982911	−	1.09163i	0.0128746	−	0.999917i	$-0.495902\pi$
$194$	9.01208	−	6.54766i	0.647029	−	0.470094i
$195$	−0.399149	+	0.145452i	−0.0285837	+	0.0104160i
$196$	−2.66358	−	8.19767i	−0.190256	−	0.585548i
$197$	12.1732	+	7.02819i	0.867303	+	0.500738i	0.866451	−	0.499262i	$-0.166396\pi$
$197$	12.1732	+	7.02819i	0.867303	+	0.500738i	0.000851880		1.00000i	$0.499729\pi$
$198$	−2.07959	−	7.82608i	−0.147790	−	0.556175i
$199$	−1.58662	−	2.74811i	−0.112473	−	0.194809i	0.804294	−	0.594232i	$-0.202544\pi$
$199$	−1.58662	−	2.74811i	−0.112473	−	0.194809i	−0.916767	+	0.399423i	$0.869210\pi$
$200$	−12.9050	+	4.19309i	−0.912521	+	0.296496i
$201$	−10.9032	−	5.98275i	−0.769050	−	0.421991i
$202$	−3.88581	+	8.72767i	−0.273405	+	0.614077i
$203$	0.319918	−	0.984605i	0.0224538	−	0.0691057i
$204$	1.33533	+	0.253625i	0.0934919	+	0.0177573i
$205$	0.685937	−	0.0720949i	0.0479079	−	0.00503533i
$206$	−4.07139	−	9.14449i	−0.283667	−	0.637127i
$207$	−15.6991	−	8.17545i	−1.09116	−	0.568233i
$208$	−0.326066	+	1.64319i	−0.0226086	+	0.113935i
$209$	−4.72633	−	14.2164i	−0.326927	−	0.983366i
$210$	0.0432844	+	0.0569308i	0.00298690	+	0.00392860i
$211$	3.68473	−	17.3353i	0.253667	−	1.19341i	−0.648224	−	0.761449i	$-0.724488\pi$
$211$	3.68473	−	17.3353i	0.253667	−	1.19341i	0.901892	−	0.431962i	$-0.142179\pi$
$212$	−7.52051	−	0.790437i	−0.516511	−	0.0542875i
$213$	−19.7731	+	4.65436i	−1.35483	+	0.318911i
$214$	2.93439	+	13.8052i	0.200590	+	0.943704i
$215$	−0.110206	−	0.518478i	−0.00751598	−	0.0353599i
$216$	7.53441	−	11.9353i	0.512652	−	0.812096i
$217$	5.55858	+	0.584231i	0.377341	+	0.0396602i
$218$	−1.83468	+	8.63148i	−0.124260	+	0.584598i
$219$	−10.9705	+	8.34083i	−0.741315	+	0.563621i
$220$	−0.0913064	+	0.287656i	−0.00615588	+	0.0193938i
$221$	−1.59093	−	1.39392i	−0.107018	−	0.0937651i
$222$	−0.576560	+	6.93233i	−0.0386962	+	0.465267i
$223$	4.12287	+	9.26011i	0.276088	+	0.620103i	0.997365	−	0.0725432i	$-0.0231115\pi$
$223$	4.12287	+	9.26011i	0.276088	+	0.620103i	−0.721278	+	0.692646i	$0.756445\pi$
$224$	4.31000	−	0.453000i	0.287974	−	0.0302673i
$225$	12.4955	+	8.27328i	0.833031	+	0.551552i
$226$	−3.09729	+	9.53247i	−0.206028	+	0.634090i
$227$	−5.04753	+	11.3369i	−0.335016	+	0.752459i	0.664968	+	0.746872i	$0.268445\pi$
$227$	−5.04753	+	11.3369i	−0.335016	+	0.752459i	−0.999984	+	0.00558712i	$0.998222\pi$
$228$	5.03450	−	9.17503i	0.333418	−	0.607631i
$229$	−16.4705	+	5.35158i	−1.08840	+	0.353643i	−0.797628	−	0.603150i	$-0.793912\pi$
$229$	−16.4705	+	5.35158i	−1.08840	+	0.353643i	−0.290772	+	0.956792i	$0.593912\pi$
$230$	−0.163324	−	0.282885i	−0.0107692	−	0.0186529i
$231$	−4.28259	+	0.122274i	−0.281774	+	0.00804502i
$232$	−3.26545	−	1.88531i	−0.214388	−	0.123777i
$233$	−3.56822	−	10.9818i	−0.233762	−	0.719444i	−0.997283	−	0.0736620i	$-0.976531\pi$
$233$	−3.56822	−	10.9818i	−0.233762	−	0.719444i	0.763522	−	0.645782i	$-0.223469\pi$
$234$	−7.82486	+	4.03312i	−0.511527	+	0.263653i
$235$	−0.219410	+	0.159411i	−0.0143127	+	0.0103988i
$236$	13.2945	+	14.7651i	0.865401	+	0.961125i
$237$	−12.9823	+	4.53253i	−0.843293	+	0.294419i
$238$	−0.144831	+	0.325297i	−0.00938802	+	0.0210858i
$239$	−6.97036	+	9.59388i	−0.450875	+	0.620577i	−0.972585	−	0.232546i	$-0.925294\pi$
$239$	−6.97036	+	9.59388i	−0.450875	+	0.620577i	0.521710	+	0.853123i	$0.325294\pi$
$240$	−0.0495158	+	0.0233486i	−0.00319623	+	0.00150715i
$241$	3.51157	+	6.08221i	0.226200	+	0.391790i	0.956679	−	0.291146i	$-0.0940364\pi$
$241$	3.51157	+	6.08221i	0.226200	+	0.391790i	−0.730479	+	0.682935i	$0.760703\pi$
$242$	5.36008	+	7.17031i	0.344559	+	0.460925i
$243$	−15.4964	+	1.69120i	−0.994097	+	0.108491i
$244$	0.204503	−	0.962112i	0.0130920	−	0.0615929i
$245$	−0.400450	+	0.178292i	−0.0255838	+	0.0113906i
$246$	13.9118	−	3.27469i	0.886987	−	0.208787i
$247$	−13.9929	+	8.33362i	−0.890348	+	0.530256i
$248$	6.29056	−	19.3603i	0.399451	−	1.22938i
$249$	7.02705	+	2.11548i	0.445321	+	0.134063i
$250$	0.225078	+	0.505533i	0.0142352	+	0.0319727i
$251$	6.73264	+	6.06210i	0.424961	+	0.382636i	0.853677	−	0.520803i	$-0.174367\pi$
$251$	6.73264	+	6.06210i	0.424961	+	0.382636i	−0.428716	+	0.903439i	$0.641034\pi$
$252$	−2.09743	−	2.13500i	−0.132125	−	0.134492i
$253$	19.4747	+	1.91302i	1.22436	+	0.120271i
$254$	−2.87069	−	4.97218i	−0.180123	−	0.311982i
$255$	0.00572912	−	0.0688846i	0.000358771	−	0.00431372i
$256$	1.51996	−	14.4615i	0.0949975	−	0.903841i
$257$	−7.16778	+	0.753364i	−0.447114	+	0.0469935i	−0.325410	−	0.945573i	$-0.605502\pi$
$257$	−7.16778	+	0.753364i	−0.447114	+	0.0469935i	−0.121703	+	0.992567i	$0.538836\pi$
$258$	−3.62046	−	10.3699i	−0.225400	−	0.645603i
$259$	3.50030	+	1.13732i	0.217498	+	0.0706695i
$260$	0.326728	+	0.0298707i	0.0202628	+	0.00185250i
$261$	0.614911	+	4.11873i	0.0380621	+	0.254943i
$262$	2.19654	−	10.3339i	0.135703	−	0.638432i
$263$	7.03449	−	12.1841i	0.433766	−	0.751304i	−0.563428	−	0.826165i	$-0.690518\pi$
$263$	7.03449	−	12.1841i	0.433766	−	0.751304i	0.997194	+	0.0748609i	$0.0238513\pi$
$264$	−2.80736	+	15.3496i	−0.172781	+	0.944700i
$265$			0.384563i			0.0236235i
$266$	2.03751	+	1.83458i	0.124928	+	0.112485i
$267$	−2.55741	+	4.66071i	−0.156511	+	0.285231i
$268$	5.64557	+	7.77046i	0.344858	+	0.474657i
$269$	−5.96472	−	28.0618i	−0.363675	−	1.71096i	−0.656104	−	0.754671i	$-0.727797\pi$
$269$	−5.96472	−	28.0618i	−0.363675	−	1.71096i	0.292428	−	0.956287i	$-0.405537\pi$
$270$	−0.257979	−	0.127294i	−0.0157001	−	0.00774687i
$271$	0.824942	+	7.84880i	0.0501116	+	0.476780i	0.990584	+	0.136909i	$0.0437168\pi$
$271$	0.824942	+	7.84880i	0.0501116	+	0.476780i	−0.940472	+	0.339871i	$0.889616\pi$
$272$	−0.220516	−	0.160214i	−0.0133708	−	0.00971443i
$273$	1.12850	+	4.51878i	0.0683000	+	0.273489i
$274$		−	2.99607i		−	0.180999i
$275$	−16.2288	−	3.33431i	−0.978633	−	0.201067i
$276$	8.27344	+	10.8818i	0.498003	+	0.655010i
$277$	6.36983	+	5.73542i	0.382726	+	0.344608i	0.837929	−	0.545780i	$-0.183766\pi$
$277$	6.36983	+	5.73542i	0.382726	+	0.344608i	−0.455203	+	0.890388i	$0.650433\pi$
$278$	−7.71557	−	5.60569i	−0.462749	−	0.336207i
$279$	−21.0599	+	7.87034i	−1.26082	+	0.471185i
$280$	−0.0286528	−	0.134801i	−0.00171233	−	0.00805590i
$281$	29.6606	+	9.63732i	1.76940	+	0.574914i	0.998104	−	0.0615575i	$-0.0196068\pi$
$281$	29.6606	+	9.63732i	1.76940	+	0.574914i	0.771300	+	0.636472i	$0.219607\pi$
$282$	−4.09362	+	3.85031i	−0.243771	+	0.229282i
$283$	9.21031	+	20.6867i	0.547496	+	1.22970i	0.949416	+	0.314022i	$0.101676\pi$
$283$	9.21031	+	20.6867i	0.547496	+	1.22970i	−0.401920	+	0.915675i	$0.631657\pi$
$284$	15.3452	+	3.26172i	0.910568	+	0.193547i
$285$	−0.490803	−	0.205854i	−0.0290727	−	0.0121938i
$286$	6.36357	−	7.36345i	0.376286	−	0.435410i
$287$		−	7.56168i		−	0.446352i
$288$	−14.7038	+	9.36421i	−0.866428	+	0.551792i
$289$	−15.2159	+	6.77454i	−0.895051	+	0.398502i
$290$	−0.0312581	+	0.0702069i	−0.00183554	+	0.00412269i
$291$	17.9588	+	15.4766i	1.05276	+	0.907257i
$292$	10.4105	−	2.21283i	0.609231	−	0.129496i
$293$	−0.0733963	+	0.164851i	−0.00428786	+	0.00963068i	−0.915677	−	0.401916i	$-0.868345\pi$
$293$	−0.0733963	+	0.164851i	−0.00428786	+	0.00963068i	0.911389	+	0.411546i	$0.135011\pi$
$294$	−7.76577	+	4.71158i	−0.452909	+	0.274785i
$295$	0.676095	−	0.750879i	0.0393638	−	0.0437179i
$296$	6.70234	−	11.6088i	0.389566	−	0.674748i
$297$	15.1985	−	8.12437i	0.881907	−	0.471424i
$298$	−3.29423			−0.190829
$299$	−2.51009	−	21.1245i	−0.145162	−	1.22166i
$300$	−6.00338	−	9.89495i	−0.346605	−	0.571285i
$301$	−5.77948	+	0.607448i	−0.333124	+	0.0350127i
$302$	1.11932	−	1.00784i	0.0644097	−	0.0579947i
$303$	−19.9752	−	3.79397i	−1.14754	−	0.217958i
$304$	−1.69792	+	1.23361i	−0.0973824	+	0.0707525i
$305$	−0.0497474	−	0.00522866i	−0.00284853	−	0.000299392i
$306$	−0.0622610	−	1.43098i	−0.00355922	−	0.0818036i
$307$	14.1840			0.809522			0.404761	−	0.914422i	$-0.367355\pi$
$307$	14.1840			0.809522			0.404761	+	0.914422i	$0.367355\pi$
$308$	3.03180	+	1.32521i	0.172753	+	0.0755106i
$309$	16.9585	−	12.8935i	0.964734	−	0.733485i
$310$	−0.405834	−	0.0862626i	−0.0230498	−	0.00489939i
$311$	−15.8195	+	21.7737i	−0.897042	+	1.23467i	0.0743602	+	0.997231i	$0.476309\pi$
$311$	−15.8195	+	21.7737i	−0.897042	+	1.23467i	−0.971402	+	0.237441i	$0.923691\pi$
$312$	16.9530	−	0.598526i	0.959773	−	0.0338849i
$313$	−4.19721	+	12.9177i	−0.237240	+	0.730150i	0.759576	+	0.650418i	$0.225406\pi$
$313$	−4.19721	+	12.9177i	−0.237240	+	0.730150i	−0.996816	+	0.0797320i	$0.974594\pi$
$314$	−2.97737	+	2.68083i	−0.168023	+	0.151288i
$315$	−0.0968314	+	0.117430i	−0.00545583	+	0.00661641i
$316$	10.5615	+	1.11006i	0.594131	+	0.0624456i
$317$	5.58956	+	17.2029i	0.313941	+	0.966211i	0.976188	+	0.216926i	$0.0696029\pi$
$317$	5.58956	+	17.2029i	0.313941	+	0.966211i	−0.662247	+	0.749286i	$0.730397\pi$
$318$	1.00505	+	7.90516i	0.0563607	+	0.443299i
$319$	−2.32902	−	3.97134i	−0.130400	−	0.222352i
$320$	−0.258491			−0.0144501
$321$	−27.1681	+	12.8108i	−1.51637	+	0.715028i
$322$	−3.27158	+	1.45660i	−0.182318	+	0.0811733i
$323$	−0.276995	−	2.63543i	−0.0154124	−	0.146639i
$324$	11.3818	+	3.92292i	0.632322	+	0.217940i
$325$	0.244034	+	18.0094i	0.0135365	+	0.998983i
$326$	4.40791	−	3.20253i	0.244131	−	0.177372i
$327$	−18.7757	+	0.408266i	−1.03830	+	0.0225772i
$328$	−26.9389	−	5.72604i	−1.48745	−	0.316168i
$329$	1.48668	+	2.57500i	0.0819633	+	0.141965i
$330$	0.317115	+	0.0242034i	0.0174566	+	0.00133235i
$331$	−1.11392	+	0.643120i	−0.0612264	+	0.0353491i	−0.530301	−	0.847810i	$-0.677921\pi$
$331$	−1.11392	+	0.643120i	−0.0612264	+	0.0353491i	0.469074	+	0.883159i	$0.344588\pi$
$332$	−4.21181	−	3.79233i	−0.231153	−	0.208131i
$333$	−14.6422	+	2.18603i	−0.802389	+	0.119794i
$334$	3.06358	+	1.36399i	0.167632	+	0.0746344i
$335$	0.362992	−	0.326840i	0.0198324	−	0.0178572i
$336$	0.197835	+	0.566650i	0.0107928	+	0.0309133i
$337$	10.7929	+	14.8552i	0.587927	+	0.809212i	0.994536	−	0.104390i	$-0.0332891\pi$
$337$	10.7929	+	14.8552i	0.587927	+	0.809212i	−0.406610	+	0.913602i	$0.633289\pi$
$338$	−9.30253	−	5.03979i	−0.505991	−	0.274129i
$339$	−21.2579	−	1.76801i	−1.15457	−	0.0960253i
$340$	−0.0266914	+	0.0462309i	−0.00144755	+	0.00250722i
$341$	18.3575	−	16.7567i	0.994116	−	0.907427i
$342$	−10.6271	−	2.94887i	−0.574645	−	0.159457i
$343$	3.09835	+	9.53573i	0.167295	+	0.514881i
$344$	−2.21241	+	21.0497i	−0.119285	+	1.13492i
$345$	0.506385	−	0.476287i	0.0272629	−	0.0256424i
$346$	−14.0330	−	4.55960i	−0.754418	−	0.245125i
$347$	30.8357	−	6.55432i	1.65535	−	0.351855i	0.716872	−	0.697205i	$-0.245573\pi$
$347$	30.8357	−	6.55432i	1.65535	−	0.351855i	0.938474	+	0.345350i	$0.112240\pi$
$348$	0.927110	−	3.07960i	0.0496983	−	0.165084i
$349$	−3.23888	+	1.44204i	−0.173373	+	0.0771908i	−0.491588	−	0.870828i	$-0.663583\pi$
$349$	−3.23888	+	1.44204i	−0.173373	+	0.0771908i	0.318215	+	0.948019i	$0.396917\pi$
$350$	2.88366	−	0.936956i	0.154138	−	0.0500824i
$351$	−12.1707	−	14.2434i	−0.649625	−	0.760255i
$352$	11.2216	−	15.6683i	0.598115	−	0.835123i
$353$	−0.0832275	+	0.144154i	−0.00442975	+	0.00767256i	−0.868232	−	0.496159i	$-0.834743\pi$
$353$	−0.0832275	+	0.144154i	−0.00442975	+	0.00767256i	0.863802	+	0.503831i	$0.168077\pi$
$354$	11.9355	−	17.2022i	0.634366	−	0.914287i
$355$	0.0833942	−	0.793443i	0.00442611	−	0.0421116i
$356$	3.32160	−	2.41328i	0.176044	−	0.127904i
$357$	−0.744512	−	0.141408i	−0.0394038	−	0.00748413i
$358$	3.97642	−	0.845214i	0.210160	−	0.0446709i
$359$	−16.7273	−	23.0231i	−0.882832	−	1.21511i	−0.975628	−	0.219429i	$-0.929580\pi$
$359$	−16.7273	−	23.0231i	−0.882832	−	1.21511i	0.0927960	−	0.995685i	$-0.470420\pi$
$360$	0.345025	+	0.433890i	0.0181844	+	0.0228680i
$361$	−1.37324	−	0.291891i	−0.0722759	−	0.0153627i
$362$	13.5148	+	7.80279i	0.710324	+	0.410105i
$363$	−12.2403	+	14.6005i	−0.642451	+	0.766327i
$364$	0.700121	−	3.52822i	0.0366963	−	0.184929i
$365$	−0.167258	−	0.514766i	−0.00875466	−	0.0269441i
$366$	−1.03628	+	0.0225333i	−0.0541673	+	0.00117784i
$367$	−2.60274	−	24.7634i	−0.135862	−	1.29264i	−0.823804	−	0.566875i	$-0.808152\pi$
$367$	−2.60274	−	24.7634i	−0.135862	−	1.29264i	0.687942	−	0.725765i	$-0.258514\pi$
$368$	−0.569955	−	2.68143i	−0.0297109	−	0.139779i
$369$	13.5678	+	27.2231i	0.706310	+	1.41718i
$370$	−0.249588	−	0.111124i	−0.0129755	−	0.00577705i
$371$	4.19305	+	0.440708i	0.217692	+	0.0228804i
$372$	17.3034	+	1.43912i	0.897138	+	0.0746147i
$373$	−1.26670	+	0.731329i	−0.0655872	+	0.0378668i	−0.532435	−	0.846471i	$-0.678723\pi$
$373$	−1.26670	+	0.731329i	−0.0655872	+	0.0378668i	0.466848	+	0.884338i	$0.345390\pi$
$374$	0.653895	+	1.44219i	0.0338121	+	0.0745738i
$375$	−0.937512	+	0.712789i	−0.0484129	+	0.0368083i
$376$	10.2994	−	3.34647i	0.531150	−	0.172581i
$377$	−3.67370	+	3.39906i	−0.189205	+	0.175061i
$378$	−1.68358	+	2.66698i	−0.0865942	+	0.137175i
$379$	−4.96154	+	4.46739i	−0.254857	+	0.229474i	−0.786649	−	0.617401i	$-0.788186\pi$
$379$	−4.96154	+	4.46739i	−0.254857	+	0.229474i	0.531792	+	0.846875i	$0.321519\pi$
$380$	0.275036	+	0.305458i	0.0141090	+	0.0156697i
$381$	8.90057	−	8.37155i	0.455990	−	0.428888i
$382$	12.1207	+	8.80618i	0.620147	+	0.450563i
$383$	0.778615	−	0.864740i	0.0397854	−	0.0441862i	−0.722924	−	0.690928i	$-0.757202\pi$
$383$	0.778615	−	0.864740i	0.0397854	−	0.0441862i	0.762709	+	0.646742i	$0.223869\pi$
$384$	14.6549	−	1.86321i	0.747855	−	0.0950816i
$385$	0.0509078	−	0.160382i	0.00259450	−	0.00817383i
$386$	14.3832	−	8.30413i	0.732085	−	0.422669i
$387$	19.7170	−	12.5569i	1.00227	−	0.638303i
$388$	−7.44701	−	16.7263i	−0.378064	−	0.849147i
$389$	−1.06218	−	1.46197i	−0.0538548	−	0.0741248i	0.781240	−	0.624231i	$-0.214587\pi$
$389$	−1.06218	−	1.46197i	−0.0538548	−	0.0741248i	−0.835095	+	0.550106i	$0.814587\pi$
$390$	−0.0482495	−	0.342359i	−0.00244321	−	0.0173360i
$391$	3.29189	+	1.06960i	0.166478	+	0.0540920i
$392$	17.4076	−	1.82961i	0.879215	−	0.0924093i
$393$	22.4790	−	0.488791i	1.13391	−	0.0246563i
$394$	−7.65467	+	8.50138i	−0.385637	+	0.428293i
$395$		−	0.540064i		−	0.0271736i
$396$	−13.2927	+	0.668979i	−0.667982	+	0.0336175i
$397$	15.8544	−	9.15351i	0.795707	−	0.459402i	−0.0462608	−	0.998929i	$-0.514731\pi$
$397$	15.8544	−	9.15351i	0.795707	−	0.459402i	0.841968	+	0.539528i	$0.181397\pi$
$398$	2.45614	−	0.798048i	0.123115	−	0.0400025i
$399$	−2.80698	+	5.11553i	−0.140525	+	0.256097i
$400$	0.242608	+	2.30826i	0.0121304	+	0.115413i
$401$	−8.06549	−	8.95763i	−0.402771	−	0.447323i	0.507303	−	0.861768i	$-0.330642\pi$
$401$	−8.06549	−	8.95763i	−0.402771	−	0.447323i	−0.910074	+	0.414445i	$0.863976\pi$
$402$	6.60755	−	7.66726i	0.329554	−	0.382408i
$403$	−22.0733	−	15.5847i	−1.09955	−	0.776327i
$404$	12.7036	+	9.22971i	0.632028	+	0.459195i
$405$	0.137904	−	0.596505i	0.00685252	−	0.0296406i
$406$	0.729674	+	0.421278i	0.0362131	+	0.0209077i
$407$	14.1182	−	8.27973i	0.699816	−	0.410411i
$408$	−1.06755	+	2.54529i	−0.0528518	+	0.126010i
$409$	3.12319	−	3.46865i	0.154432	−	0.171514i	−0.660964	−	0.750417i	$-0.729853\pi$
$409$	3.12319	−	3.46865i	0.154432	−	0.171514i	0.815396	+	0.578903i	$0.196519\pi$
$410$	−0.0586742	+	0.558247i	−0.00289771	+	0.0275699i
$411$	6.20669	−	1.46099i	0.306153	−	0.0720651i
$412$	−16.0929	+	3.42066i	−0.792842	+	0.168524i
$413$	−7.41235	−	8.23225i	−0.364738	−	0.405083i
$414$	9.16458	−	11.1141i	0.450415	−	0.546228i
$415$	−0.169413	+	0.233178i	−0.00831618	+	0.0114462i
$416$	−19.2536	−	8.26150i	−0.943983	−	0.405053i
$417$	7.85043	−	18.7172i	0.384437	−	0.916584i
$418$	12.1168	−	1.35693i	0.592654	−	0.0663696i
$419$	21.5399	+	12.4361i	1.05229	+	0.607541i	0.923290	−	0.384103i	$-0.125489\pi$
$419$	21.5399	+	12.4361i	1.05229	+	0.607541i	0.129002	+	0.991644i	$0.458823\pi$
$420$	0.106319	−	0.0501335i	0.00518784	−	0.00244627i
$421$	19.9420	−	27.4479i	0.971916	−	1.33773i	0.0308425	−	0.999524i	$-0.490181\pi$
$421$	19.9420	−	27.4479i	0.971916	−	1.33773i	0.941073	−	0.338203i	$-0.109819\pi$
$422$	13.1765	+	5.86655i	0.641421	+	0.285579i
$423$	−9.97252	−	6.60284i	−0.484881	−	0.321041i
$424$	4.74521	−	14.6043i	0.230448	−	0.709245i
$425$	−2.67718	−	1.19196i	−0.129863	−	0.0578185i
$426$	−0.359394	−	16.5281i	−0.0174127	−	0.800791i
$427$	−0.114021	+	0.536424i	−0.00551784	+	0.0259594i
$428$	23.1974			1.12129
$429$	18.3573	+	9.59217i	0.886299	+	0.463114i
$430$	0.431389			0.0208034
$431$	−3.39724	+	15.9828i	−0.163639	+	0.769862i	0.817403	+	0.576067i	$0.195413\pi$
$431$	−3.39724	+	15.9828i	−0.163639	+	0.769862i	−0.981042	+	0.193795i	$0.937920\pi$
$432$	−1.72896	−	1.68504i	−0.0831846	−	0.0810717i
$433$	10.6587	+	4.74554i	0.512222	+	0.228056i	0.646537	−	0.762883i	$-0.276217\pi$
$433$	10.6587	+	4.74554i	0.512222	+	0.228056i	−0.134315	+	0.990939i	$0.542883\pi$
$434$	−1.40564	+	4.32612i	−0.0674729	+	0.207660i
$435$	−0.160684	−	0.0305194i	−0.00770420	−	0.00146329i
$436$	13.2499	+	5.89923i	0.634555	+	0.282522i
$437$	15.6651	−	21.5612i	0.749365	−	1.03141i
$438$	−4.78352	−	10.1445i	−0.228566	−	0.484723i
$439$	3.59502	+	2.07558i	0.171581	+	0.0990622i	0.583331	−	0.812235i	$-0.301749\pi$
$439$	3.59502	+	2.07558i	0.171581	+	0.0990622i	−0.411750	+	0.911297i	$0.635082\pi$
$440$	−0.532821	−	0.302810i	−0.0254012	−	0.0144359i
$441$	−13.5474	−	13.7901i	−0.645115	−	0.656672i
$442$	1.37884	−	1.03062i	0.0655850	−	0.0490216i
$443$	4.14754	−	5.70859i	0.197055	−	0.271223i	−0.699042	−	0.715080i	$-0.746390\pi$
$443$	4.14754	−	5.70859i	0.197055	−	0.271223i	0.896098	+	0.443857i	$0.146390\pi$
$444$	10.9481	+	3.29591i	0.519574	+	0.156417i
$445$	−0.139712	−	0.155166i	−0.00662300	−	0.00735558i
$446$	−8.06924	+	1.71517i	−0.382090	+	0.0812157i
$447$	−1.60638	−	6.82435i	−0.0759790	−	0.322781i
$448$	−0.296230	+	2.81844i	−0.0139955	+	0.133159i
$449$	3.77403	−	4.19149i	0.178108	−	0.197808i	−0.647480	−	0.762082i	$-0.724177\pi$
$449$	3.77403	−	4.19149i	0.178108	−	0.197808i	0.825588	+	0.564274i	$0.190844\pi$
$450$	−8.70038	+	8.54725i	−0.410140	+	0.402921i
$451$	−25.1422	−	22.3303i	−1.18390	−	1.05149i
$452$	14.2669	+	8.23702i	0.671060	+	0.387437i
$453$	2.63367	+	1.82734i	0.123741	+	0.0858558i
$454$	−8.17082	−	5.93645i	−0.383476	−	0.278611i
$455$	−0.182167	−	0.0166544i	−0.00854011	−	0.000780768i
$456$	16.0988	+	13.8737i	0.753894	+	0.649696i
$457$	−16.6417	−	18.4825i	−0.778467	−	0.864575i	0.215243	−	0.976561i	$-0.430946\pi$
$457$	−16.6417	−	18.4825i	−0.778467	−	0.864575i	−0.993710	+	0.111986i	$0.964279\pi$
$458$	−1.47325	−	14.0171i	−0.0688405	−	0.654974i
$459$	2.93407	−	0.826774i	0.136951	−	0.0385905i
$460$	−0.510607	+	0.165906i	−0.0238072	+	0.00773542i
$461$	−14.2901	+	8.25040i	−0.665557	+	0.384260i	−0.794391	−	0.607407i	$-0.792210\pi$
$461$	−14.2901	+	8.25040i	−0.665557	+	0.384260i	0.128834	+	0.991666i	$0.458877\pi$
$462$	0.627312	−	3.42990i	0.0291852	−	0.159573i
$463$			28.8012i			1.33850i	0.743036	+	0.669252i	$0.233385\pi$
$463$			28.8012i			1.33850i	−0.743036	+	0.669252i	$0.766615\pi$
$464$	−0.431562	+	0.479298i	−0.0200348	+	0.0222508i
$465$	−0.0191958	−	0.882793i	−0.000890184	−	0.0409386i
$466$	9.34600	−	0.982304i	0.432945	−	0.0455043i
$467$	14.7999	+	4.80877i	0.684856	+	0.222523i	0.630720	−	0.776010i	$-0.282760\pi$
$467$	14.7999	+	4.80877i	0.684856	+	0.222523i	0.0541357	+	0.998534i	$0.482760\pi$
$468$	3.81008	+	13.9583i	0.176121	+	0.645221i
$469$	−3.14768	−	4.33241i	−0.145346	−	0.200052i
$470$	−0.0897748	−	0.201638i	−0.00414100	−	0.00930085i
$471$	−7.00550	−	4.86068i	−0.322797	−	0.223968i
$472$	−34.9408	+	20.1731i	−1.60828	+	0.928542i
$473$	−15.0476	+	21.0103i	−0.691890	+	0.966057i
$474$	−1.41146	−	11.1017i	−0.0648304	−	0.509917i
$475$	−15.0986	+	16.7687i	−0.692770	+	0.769398i
$476$	0.473487	+	0.344009i	0.0217023	+	0.0157676i
$477$	−15.8863	+	5.93690i	−0.727384	+	0.271832i
$478$	−6.45788	−	7.17220i	−0.295377	−	0.328049i
$479$	−25.1895	+	22.6807i	−1.15094	+	1.03631i	−0.152088	+	0.988367i	$0.548600\pi$
$479$	−25.1895	+	22.6807i	−1.15094	+	1.03631i	−0.998850	+	0.0479428i	$0.984733\pi$
$480$	−0.156874	−	0.666446i	−0.00716029	−	0.0304190i
$481$	−12.0838	−	13.0601i	−0.550973	−	0.595490i
$482$	−5.43600	+	1.76626i	−0.247603	+	0.0804511i
$483$	−4.61285	−	6.06715i	−0.209892	−	0.276065i
$484$	13.3594	−	6.16712i	0.607246	−	0.280324i
$485$	−0.806368	+	0.465557i	−0.0366153	+	0.0211399i
$486$	1.27582	−	12.6223i	0.0578725	−	0.572559i
$487$	3.33776	+	0.350813i	0.151248	+	0.0158968i	0.179850	−	0.983694i	$-0.442439\pi$
$487$	3.33776	+	0.350813i	0.151248	+	0.0158968i	−0.0286016	+	0.999591i	$0.509105\pi$
$488$	1.82470	+	0.812409i	0.0826003	+	0.0367760i
$489$	8.78384	+	7.56980i	0.397219	+	0.342318i
$490$	−0.0741719	−	0.348952i	−0.00335075	−	0.0157640i
$491$	3.49722	+	33.2738i	0.157827	+	1.50162i	0.731106	+	0.682264i	$0.239005\pi$
$491$	3.49722	+	33.2738i	0.157827	+	1.50162i	−0.573279	+	0.819361i	$0.694329\pi$
$492$	−0.510670	−	23.4852i	−0.0230228	−	1.05879i
$493$	−0.251647	−	0.774490i	−0.0113336	−	0.0348813i
$494$	−4.26636	−	12.5493i	−0.191953	−	0.564622i
$495$	0.104496	+	0.668740i	0.00469674	+	0.0300576i
$496$	−3.01548	−	1.74099i	−0.135399	−	0.0781727i
$497$	−8.55568	−	1.81857i	−0.383775	−	0.0815738i
$498$	−2.87309	+	5.23601i	−0.128746	+	0.234631i
$499$	−4.00567	−	5.51333i	−0.179318	−	0.246810i	0.709891	−	0.704312i	$-0.248744\pi$
$499$	−4.00567	−	5.51333i	−0.179318	−	0.246810i	−0.889209	+	0.457502i	$0.848744\pi$
$500$	0.889662	−	0.189104i	0.0397869	−	0.00845697i
$501$	−1.33176	+	7.01167i	−0.0594985	+	0.313258i
$502$	−5.96503	+	4.33384i	−0.266232	+	0.193429i
$503$	0.755973	−	7.19260i	0.0337072	−	0.320702i	−0.964656	−	0.263512i	$-0.915119\pi$
$503$	0.755973	−	7.19260i	0.0337072	−	0.320702i	0.998363	−	0.0571902i	$-0.0182142\pi$
$504$	5.12629	−	3.26471i	0.228343	−	0.145422i
$505$	0.399277	−	0.691567i	0.0177676	−	0.0307743i
$506$	−4.81815	+	15.1793i	−0.214193	+	0.674804i
$507$	5.90426	−	21.7288i	0.262217	−	0.965009i
$508$	−8.97478	+	2.91608i	−0.398191	+	0.129380i
$509$	−10.8340	+	4.82362i	−0.480209	+	0.213803i	−0.632542	−	0.774526i	$-0.717988\pi$
$509$	−10.8340	+	4.82362i	−0.480209	+	0.213803i	0.152332	+	0.988329i	$0.451322\pi$
$510$	0.0538670	+	0.0162166i	0.00238527	+	0.000718082i
$511$	−5.80439	+	1.23376i	−0.256771	+	0.0545783i
$512$	−4.96833	−	1.61431i	−0.219571	−	0.0713430i
$513$	0.926805	−	23.4531i	0.0409195	−	1.03548i
$514$	0.613122	−	5.83347i	0.0270437	−	0.257303i
$515$	0.258552	+	0.795740i	0.0113931	+	0.0350645i
$516$	−17.9090	+	2.27693i	−0.788398	+	0.100236i
$517$	12.9521	+	2.66109i	0.569631	+	0.117035i
$518$	−1.49766	+	2.59402i	−0.0658032	+	0.113975i
$519$	2.60274	−	31.2943i	0.114248	−	1.37367i
$520$	−0.197277	+	0.636367i	−0.00865116	+	0.0279066i
$521$	−13.3559	−	18.3828i	−0.585132	−	0.805366i	0.409114	−	0.912483i	$-0.365838\pi$
$521$	−13.3559	−	18.3828i	−0.585132	−	0.805366i	−0.994246	+	0.107118i	$0.965838\pi$
$522$	−3.38281	−	0.207416i	−0.148062	−	0.00907833i
$523$	27.8320	−	25.0601i	1.21701	−	1.09580i	0.224395	−	0.974498i	$-0.427960\pi$
$523$	27.8320	−	25.0601i	1.21701	−	1.09580i	0.992616	−	0.121302i	$-0.0387071\pi$
$524$	−15.8633	−	7.06278i	−0.692990	−	0.308539i
$525$	3.34718	+	5.51692i	0.146083	+	0.240778i
$526$	8.50901	+	7.66154i	0.371010	+	0.334059i
$527$	3.80745	−	2.19823i	0.165855	−	0.0957564i
$528$	2.46831	+	1.01558i	0.107419	+	0.0441973i
$529$	5.90553	+	10.2287i	0.256762	+	0.444725i
$530$	−0.306136	−	0.0650712i	−0.0132977	−	0.00282651i
$531$	41.4564	+	16.3374i	1.79906	+	0.708981i
$532$	3.64573	−	2.64878i	0.158063	−	0.114839i
$533$	−17.8476	+	31.9035i	−0.773064	+	1.38190i
$534$	−3.27748	−	2.82449i	−0.141830	−	0.122228i
$535$	−0.123313	−	1.17324i	−0.00533128	−	0.0507237i
$536$	−17.8180	+	7.93310i	−0.769621	+	0.342658i
$537$	3.68999	+	7.82543i	0.159235	+	0.337692i
$538$	23.3482			1.00661
$539$	19.5826	+	8.55959i	0.843482	+	0.368688i
$540$	−0.292810	+	0.371254i	−0.0126005	+	0.0159762i
$541$	12.8398	+	39.5168i	0.552026	+	1.69896i	0.703671	+	0.710526i	$0.251543\pi$
$541$	12.8398	+	39.5168i	0.552026	+	1.69896i	−0.151645	+	0.988435i	$0.548457\pi$
$542$	−6.38772	−	0.671376i	−0.274376	−	0.0288381i
$543$	−9.57405	+	31.8024i	−0.410862	+	1.36477i
$544$	2.53332	−	2.28101i	0.108615	−	0.0977976i
$545$	0.227929	−	0.701492i	0.00976339	−	0.0300486i
$546$	−3.78818	+	0.133742i	−0.162119	+	0.00572364i
$547$	−3.29279	+	4.53213i	−0.140789	+	0.193780i	−0.873589	−	0.486665i	$-0.838213\pi$
$547$	−3.29279	+	4.53213i	−0.140789	+	0.193780i	0.732799	+	0.680445i	$0.238213\pi$
$548$	−4.81679	−	1.02384i	−0.205763	−	0.0437363i
$549$	−0.552007	−	2.13578i	−0.0235591	−	0.0911531i
$550$	5.40037	−	12.3549i	0.230272	−	0.526816i
$551$	−6.27027			−0.267122
$552$	−25.1076	+	11.8392i	−1.06865	+	0.503910i
$553$	−5.88855	−	0.618912i	−0.250407	−	0.0263188i
$554$	−5.64358	+	4.10030i	−0.239773	+	0.174205i
$555$	0.108497	−	0.571237i	0.00460546	−	0.0242476i
$556$	−11.6489	+	10.4887i	−0.494024	+	0.444821i
$557$	3.04526	−	0.320069i	0.129032	−	0.0135618i	−0.0397925	−	0.999208i	$-0.512670\pi$
$557$	3.04526	−	0.320069i	0.129032	−	0.0135618i	0.168824	+	0.985646i	$0.446003\pi$
$558$	−2.70177	−	18.0967i	−0.114375	−	0.766095i
$559$	25.8180	+	11.0782i	1.09198	+	0.468559i
$560$	−0.0235726			−0.000996124
$561$	−2.66879	+	2.05787i	−0.112676	+	0.0868835i
$562$	−12.6907	+	21.9810i	−0.535326	+	0.927211i
$563$	−9.48997	+	10.5397i	−0.399954	+	0.444194i	−0.909158	−	0.416452i	$-0.863273\pi$
$563$	−9.48997	+	10.5397i	−0.399954	+	0.444194i	0.509203	+	0.860646i	$0.329940\pi$
$564$	4.79125	+	7.89708i	0.201748	+	0.332527i
$565$	0.340759	−	0.765358i	0.0143359	−	0.0321989i
$566$	−18.0264	+	3.83162i	−0.757704	+	0.161055i
$567$	−6.34591	−	2.18722i	−0.266503	−	0.0918546i
$568$	−12.9575	+	29.1030i	−0.543684	+	1.22113i
$569$	−30.9154	+	13.7644i	−1.29604	+	0.577035i	−0.934713	−	0.355404i	$-0.884343\pi$
$569$	−30.9154	+	13.7644i	−1.29604	+	0.577035i	−0.361329	+	0.932438i	$0.617677\pi$
$570$	0.246921	−	0.355877i	0.0103424	−	0.0149061i
$571$		−	11.1244i		−	0.465540i	−0.972532	−	0.232770i	$-0.925221\pi$
$571$		−	11.1244i		−	0.465540i	0.972532	−	0.232770i	$-0.0747789\pi$
$572$	−9.66363	−	12.7470i	−0.404057	−	0.532980i
$573$	−12.3325	+	29.4035i	−0.515198	+	1.22835i
$574$	6.01957	+	1.27950i	0.251252	+	0.0534053i
$575$	−11.9878	−	26.9251i	−0.499926	−	1.12285i
$576$	−3.99060	−	10.6783i	−0.166275	−	0.444928i
$577$	−5.43539	−	1.76607i	−0.226278	−	0.0735223i	0.193683	−	0.981064i	$-0.437957\pi$
$577$	−5.43539	−	1.76607i	−0.226278	−	0.0735223i	−0.419962	+	0.907542i	$0.637957\pi$
$578$	−2.81830	−	13.2591i	−0.117226	−	0.551505i
$579$	24.2167	+	25.7470i	1.00641	+	1.07001i
$580$	0.102190	+	0.0742454i	0.00424321	+	0.00308287i
$581$	2.34829	+	2.11441i	0.0974234	+	0.0877204i
$582$	−15.3591	+	11.6775i	−0.636657	+	0.484049i
$583$	13.8478	−	12.6402i	0.573517	−	0.523505i
$584$			21.6127i			0.894340i
$585$	0.685707	−	0.266900i	0.0283505	−	0.0110350i
$586$	−0.118812	−	0.0863221i	−0.00490809	−	0.00356593i
$587$	2.45280	+	23.3368i	0.101238	+	0.963215i	0.920750	+	0.390153i	$0.127578\pi$
$587$	2.45280	+	23.3368i	0.101238	+	0.963215i	−0.819512	+	0.573062i	$0.805755\pi$
$588$	4.92104	+	14.0951i	0.202940	+	0.581273i
$589$	−7.03815	−	33.1119i	−0.290002	−	1.36435i
$590$	0.483346	+	0.665268i	0.0198990	+	0.0273887i
$591$	−21.3442	−	11.7119i	−0.877984	−	0.481765i
$592$	−1.70392	−	1.53422i	−0.0700307	−	0.0630559i
$593$		−	31.1472i		−	1.27906i	−0.768765	−	0.639531i	$-0.779128\pi$
$593$		−	31.1472i		−	1.27906i	0.768765	−	0.639531i	$-0.220872\pi$
$594$	3.89579	+	13.4737i	0.159846	+	0.552831i
$595$	0.0148818	−	0.0257760i	0.000610094	−	0.00105671i
$596$	−1.12573	+	5.29614i	−0.0461116	+	0.216938i
$597$	2.85094	+	4.69901i	0.116681	+	0.192318i
$598$	17.2411	+	1.57625i	0.705042	+	0.0644575i
$599$	2.76077	+	0.897029i	0.112802	+	0.0366516i	0.364874	−	0.931057i	$-0.381112\pi$
$599$	2.76077	+	0.897029i	0.112802	+	0.0366516i	−0.252072	+	0.967708i	$0.581112\pi$
$600$	22.1889	−	7.74684i	0.905860	−	0.316264i
$601$	−19.1041	+	2.00792i	−0.779272	+	0.0819048i	−0.485808	−	0.874065i	$-0.661475\pi$
$601$	−19.1041	+	2.00792i	−0.779272	+	0.0819048i	−0.293464	+	0.955970i	$0.594808\pi$
$602$	0.494370	−	4.70361i	0.0201490	−	0.191705i
$603$	19.1056	+	9.94944i	0.778042	+	0.405173i
$604$	−1.23781	−	2.14394i	−0.0503656	−	0.0872357i
$605$	−0.382928	−	0.642889i	−0.0155682	−	0.0261372i
$606$	6.40020	−	15.2595i	0.259991	−	0.619875i
$607$	11.1839	+	10.0700i	0.453941	+	0.408730i	0.864129	−	0.503271i	$-0.167870\pi$
$607$	11.1839	+	10.0700i	0.453941	+	0.408730i	−0.410188	+	0.912001i	$0.634537\pi$
$608$	−10.6760	−	23.9786i	−0.432967	−	0.972460i
$609$	−0.516909	+	1.71703i	−0.0209462	+	0.0695775i
$610$	0.0125800	−	0.0387172i	0.000509349	−	0.00156762i
$611$	−0.194761	−	14.3732i	−0.00787919	−	0.581476i
$612$	−2.32186	−	0.388908i	−0.0938558	−	0.0157207i
$613$	−18.0794	+	8.04947i	−0.730220	+	0.325115i	−0.737950	−	0.674855i	$-0.764206\pi$
$613$	−18.0794	+	8.04947i	−0.730220	+	0.325115i	0.00773016	+	0.999970i	$0.497539\pi$
$614$	−2.40005	+	11.2913i	−0.0968579	+	0.455681i
$615$	−1.18508	+	0.150670i	−0.0477871	+	0.00607562i
$616$	−3.91228	+	5.46255i	−0.157630	+	0.220092i
$617$	2.98920	+	5.17745i	0.120341	+	0.208436i	0.919902	−	0.392148i	$-0.128268\pi$
$617$	2.98920	+	5.17745i	0.120341	+	0.208436i	−0.799561	+	0.600584i	$0.794935\pi$
$618$	7.39451	+	15.6817i	0.297451	+	0.630810i
$619$	3.43381	−	4.72623i	0.138016	−	0.189963i	−0.734414	−	0.678702i	$-0.762543\pi$
$619$	3.43381	−	4.72623i	0.138016	−	0.189963i	0.872430	+	0.488739i	$0.162543\pi$
$620$	−0.277369	+	0.622981i	−0.0111394	+	0.0250195i
$621$	27.4930	+	13.5658i	1.10326	+	0.544378i
$622$	−14.6564	−	16.2776i	−0.587669	−	0.652672i
$623$	−1.85195	+	1.34552i	−0.0741969	+	0.0539072i
$624$	0.502758	−	2.85770i	0.0201264	−	0.114399i
$625$	7.70398	+	23.7104i	0.308159	+	0.948417i
$626$	−9.57307	−	5.52702i	−0.382617	−	0.220904i
$627$	8.71961	+	24.4397i	0.348228	+	0.976027i
$628$	3.29253	+	5.70283i	0.131386	+	0.227568i
$629$	2.75334	−	0.894614i	0.109783	−	0.0356706i
$630$	−0.0770966	−	0.0969539i	−0.00307160	−	0.00386273i
$631$	−10.3004	+	23.1350i	−0.410051	+	0.920989i	0.583968	+	0.811777i	$0.301500\pi$
$631$	−10.3004	+	23.1350i	−0.410051	+	0.920989i	−0.994018	+	0.109212i	$0.965167\pi$
$632$	−6.66398	+	20.5096i	−0.265079	+	0.815829i
$633$	−5.72790	+	30.1573i	−0.227664	+	1.19864i
$634$	−14.6404	+	1.53877i	−0.581444	+	0.0611122i
$635$	0.195193	+	0.438411i	0.00774601	+	0.0173978i
$636$	13.0526	+	1.08558i	0.517569	+	0.0430461i
$637$	4.52213	−	22.7890i	0.179173	−	0.902933i
$638$	3.55552	−	1.18206i	0.140764	−	0.0467982i
$639$	34.0646	−	8.80421i	1.34757	−	0.348289i
$640$	−0.120632	+	0.567527i	−0.00476838	+	0.0224335i
$641$	45.4342	+	4.77533i	1.79454	+	0.188614i	0.942354	−	0.334618i	$-0.108607\pi$
$641$	45.4342	+	4.77533i	1.79454	+	0.188614i	0.852190	+	0.523232i	$0.175274\pi$
$642$	−5.60112	−	23.7952i	−0.221058	−	0.939120i
$643$	−6.32693	−	29.7659i	−0.249510	−	1.17385i	−0.907245	−	0.420603i	$-0.861819\pi$
$643$	−6.32693	−	29.7659i	−0.249510	−	1.17385i	0.657735	−	0.753249i	$-0.271515\pi$
$644$	1.22379	+	5.75749i	0.0482242	+	0.226877i
$645$	0.210360	+	0.893669i	0.00828290	+	0.0351882i
$646$	2.14484	+	0.225431i	0.0843874	+	0.00886947i
$647$	7.67306	−	36.0989i	0.301659	−	1.41919i	−0.522404	−	0.852698i	$-0.674965\pi$
$647$	7.67306	−	36.0989i	0.301659	−	1.41919i	0.824064	−	0.566497i	$-0.191702\pi$
$648$	−12.5975	+	20.9514i	−0.494876	+	0.823048i
$649$	−49.2612	+	0.335110i	−1.93367	+	0.0131542i
$650$	−14.3779	−	2.85308i	−0.563948	−	0.111907i
$651$	−9.64747	−	0.802378i	−0.378114	−	0.0314477i
$652$	−3.64241	−	8.18100i	−0.142648	−	0.320393i
$653$	−42.1667	+	4.43190i	−1.65011	+	0.173434i	−0.883419	−	0.468583i	$-0.844765\pi$
$653$	−42.1667	+	4.43190i	−1.65011	+	0.173434i	−0.766691	+	0.642017i	$0.778098\pi$
$654$	2.85200	−	15.0157i	0.111522	−	0.587161i
$655$	−0.272885	+	0.839852i	−0.0106625	+	0.0328157i
$656$	−1.91606	+	4.30353i	−0.0748094	+	0.168025i
$657$	18.6829	−	14.8564i	0.728887	−	0.579603i
$658$	−2.30142	+	0.747777i	−0.0897187	+	0.0291514i
$659$	3.03732	+	5.26079i	0.118317	+	0.204931i	0.919101	−	0.394022i	$-0.128917\pi$
$659$	3.03732	+	5.26079i	0.118317	+	0.204931i	−0.800784	+	0.598954i	$0.795583\pi$
$660$	0.147279	−	0.501555i	0.00573282	−	0.0195230i
$661$	2.28459	+	1.31901i	0.0888602	+	0.0513035i	0.543772	−	0.839233i	$-0.316996\pi$
$661$	2.28459	+	1.31901i	0.0888602	+	0.0513035i	−0.454911	+	0.890537i	$0.650329\pi$
$662$	−0.323480	−	0.995568i	−0.0125724	−	0.0386939i
$663$	2.80741	+	2.35386i	0.109031	+	0.0914165i
$664$	9.31092	−	6.76478i	0.361334	−	0.262524i
$665$	−0.153346	−	0.170308i	−0.00594650	−	0.00660426i
$666$	0.737369	−	12.0260i	0.0285725	−	0.465999i
$667$	3.33120	−	7.48201i	0.128985	−	0.289704i
$668$	3.23981	−	4.45921i	0.125352	−	0.172532i
$669$	−7.48800	−	15.8799i	−0.289503	−	0.613954i
$670$	0.198763	+	0.344268i	0.00767890	+	0.0133002i
$671$	1.44687	+	1.96322i	0.0558559	+	0.0757894i
$672$	−7.44632	+	0.946720i	−0.287248	+	0.0365205i
$673$	−5.46802	+	25.7250i	−0.210777	+	0.991626i	0.737786	+	0.675035i	$0.235871\pi$
$673$	−5.46802	+	25.7250i	−0.210777	+	0.991626i	−0.948562	+	0.316591i	$0.897462\pi$
$674$	−13.6519	+	6.07821i	−0.525850	+	0.234124i
$675$	−21.9492	−	13.8559i	−0.844824	−	0.533312i
$676$	−11.2814	+	13.2335i	−0.433901	+	0.508979i
$677$	−9.12759	+	28.0918i	−0.350802	+	1.07966i	0.607602	+	0.794241i	$0.292131\pi$
$677$	−9.12759	+	28.0918i	−0.350802	+	1.07966i	−0.958404	+	0.285415i	$0.907869\pi$
$678$	5.00446	−	16.6234i	0.192195	−	0.638419i
$679$	4.15207	+	9.32570i	0.159342	+	0.357888i
$680$	−0.0805593	−	0.0725359i	−0.00308931	−	0.00278162i
$681$	8.31364	−	19.8216i	0.318579	−	0.759564i
$682$	10.2331	+	17.4491i	0.391847	+	0.668161i
$683$	−7.47383	−	12.9451i	−0.285978	−	0.495329i	0.686868	−	0.726783i	$-0.258985\pi$
$683$	−7.47383	−	12.9451i	−0.285978	−	0.495329i	−0.972846	+	0.231454i	$0.925652\pi$
$684$	−8.37247	+	16.0774i	−0.320129	+	0.614736i
$685$	−0.0261771	+	0.249059i	−0.00100018	+	0.00951605i
$686$	−8.11530	+	0.852953i	−0.309844	+	0.0325659i
$687$	28.3195	−	9.88719i	1.08045	−	0.377220i
$688$	3.44316	+	1.11875i	0.131269	+	0.0426520i
$689$	−16.6507	−	11.7561i	−0.634342	−	0.447872i
$690$	0.293470	+	0.483706i	0.0111722	+	0.0184144i
$691$	−6.81895	+	32.0807i	−0.259405	+	1.22041i	0.634775	+	0.772697i	$0.281093\pi$
$691$	−6.81895	+	32.0807i	−0.259405	+	1.22041i	−0.894180	+	0.447708i	$0.852240\pi$
$692$	−12.1259	+	21.0027i	−0.460959	+	0.798404i
$693$	7.41131	−	0.372989i	0.281532	−	0.0141687i
$694$			25.6562i			0.973894i
$695$	0.592406	+	0.533405i	0.0224712	+	0.0202332i
$696$	5.72559	+	3.14173i	0.217028	+	0.119087i
$697$	−3.49616	−	4.81205i	−0.132426	−	0.182269i
$698$	−0.599910	−	2.82236i	−0.0227069	−	0.106828i
$699$	6.59237	+	18.8823i	0.249346	+	0.714192i
$700$	−0.520922	−	4.95624i	−0.0196890	−	0.187328i
$701$	21.8986	+	15.9103i	0.827099	+	0.600923i	0.918737	−	0.394870i	$-0.129210\pi$
$701$	21.8986	+	15.9103i	0.827099	+	0.600923i	−0.0916380	+	0.995792i	$0.529210\pi$
$702$	13.3980	−	7.27855i	0.505675	−	0.274711i
$703$		−	22.2910i		−	0.840721i
$704$	8.49637	+	9.30805i	0.320219	+	0.350810i
$705$	0.373937	−	0.284304i	0.0140833	−	0.0107075i
$706$	−0.100673	−	0.0906464i	−0.00378888	−	0.00341152i
$707$	−7.08288	−	5.14602i	−0.266379	−	0.193536i
$708$	−23.5773	−	25.0672i	−0.886090	−	0.942085i
$709$	−10.1381	−	47.6961i	−0.380745	−	1.79126i	−0.583585	−	0.812052i	$-0.698351\pi$
$709$	−10.1381	−	47.6961i	−0.380745	−	1.79126i	0.202840	−	0.979212i	$-0.434983\pi$
$710$	0.617519	+	0.200644i	0.0231751	+	0.00753004i
$711$	22.3101	−	8.33754i	0.836693	−	0.312682i
$712$	3.39112	+	7.61657i	0.127087	+	0.285443i
$713$	43.2500	+	9.19307i	1.61973	+	0.344283i
$714$	0.238547	−	0.568751i	0.00892742	−	0.0212850i
$715$	−0.593330	+	0.556513i	−0.0221893	+	0.0208124i
$716$		−	6.68173i		−	0.249708i
$717$	11.7089	−	16.8756i	0.437278	−	0.630232i
$718$	21.1582	−	9.42025i	0.789618	−	0.351561i
$719$	−10.0081	+	22.4785i	−0.373238	+	0.838306i	0.625093	+	0.780551i	$0.285061\pi$
$719$	−10.0081	+	22.4785i	−0.373238	+	0.838306i	−0.998331	+	0.0577559i	$0.981605\pi$
$720$	0.0848645	−	0.0422959i	0.00316271	−	0.00157627i
$721$	8.97259	−	1.90718i	0.334157	−	0.0710272i
$722$	0.464727	−	1.04379i	0.0172954	−	0.0388460i
$723$	−6.30979	−	10.4000i	−0.234664	−	0.386780i
$724$	17.1630	−	19.0614i	0.637856	−	0.708411i
$725$	−3.46711	+	6.00520i	−0.128765	+	0.223028i
$726$	−9.55173	−	12.2146i	−0.354498	−	0.453326i
$727$	26.3362			0.976757			0.488379	−	0.872632i	$-0.337588\pi$
$727$	26.3362			0.976757			0.488379	+	0.872632i	$0.337588\pi$
$728$	6.71251	+	2.88027i	0.248782	+	0.106750i
$729$	26.7706	−	3.51206i	0.991504	−	0.130076i
$730$	0.438087	−	0.0460448i	0.0162143	−	0.00170419i
$731$	−3.39705	+	3.05872i	−0.125644	+	0.113131i
$732$	−0.317899	+	1.67373i	−0.0117499	+	0.0618630i
$733$	−21.5779	+	15.6773i	−0.796999	+	0.579053i	−0.910032	−	0.414538i	$-0.863943\pi$
$733$	−21.5779	+	15.6773i	−0.796999	+	0.579053i	0.113033	+	0.993591i	$0.463943\pi$
$734$	20.1536	+	2.11823i	0.743884	+	0.0781853i
$735$	0.686723	−	0.323816i	0.0253301	−	0.0119441i
$736$	34.2843			1.26374
$737$	−23.7005	−	2.32813i	−0.873017	−	0.0857576i
$738$	−23.9670	+	6.19443i	−0.882239	+	0.228020i
$739$	5.43634	+	1.15553i	0.199979	+	0.0425068i	0.306812	−	0.951770i	$-0.400738\pi$
$739$	5.43634	+	1.15553i	0.199979	+	0.0425068i	−0.106833	+	0.994277i	$0.534071\pi$
$740$	−0.263945	+	0.363289i	−0.00970281	+	0.0133548i
$741$	23.9169	−	14.9577i	0.878610	−	0.549486i
$742$	−1.06033	+	3.26336i	−0.0389259	+	0.119802i
$743$	−21.2249	+	19.1110i	−0.778667	+	0.701114i	−0.959285	−	0.282439i	$-0.908857\pi$
$743$	−21.2249	+	19.1110i	−0.778667	+	0.701114i	0.180619	+	0.983553i	$0.442190\pi$
$744$	−10.1640	+	33.7620i	−0.372631	+	1.23778i
$745$	0.273844	+	0.0287822i	0.0100329	+	0.00105450i
$746$	−0.367847	−	1.13212i	−0.0134678	−	0.0414498i
$747$	−12.2480	−	3.39866i	−0.448130	−	0.124351i
$748$	2.54206	−	0.558432i	0.0929470	−	0.0204183i
$749$	−12.9337			−0.472587
$750$	−0.408789	−	0.866927i	−0.0149269	−	0.0316557i
$751$	10.8701	−	4.83969i	0.396657	−	0.176603i	−0.198708	−	0.980059i	$-0.563674\pi$
$751$	10.8701	−	4.83969i	0.396657	−	0.176603i	0.595364	+	0.803456i	$0.297008\pi$
$752$	−0.193623	−	1.84220i	−0.00706072	−	0.0671783i
$753$	−11.8868	−	10.2439i	−0.433178	−	0.373308i
$754$	−2.08424	−	3.49964i	−0.0759037	−	0.127449i
$755$	−0.101853	+	0.0740006i	−0.00370681	+	0.00269316i
$756$	3.71238	+	3.61808i	0.135018	+	0.131588i
$757$	2.50324	+	0.532081i	0.0909819	+	0.0193388i	0.253178	−	0.967420i	$-0.418524\pi$
$757$	2.50324	+	0.532081i	0.0909819	+	0.0193388i	−0.162196	+	0.986759i	$0.551858\pi$
$758$	−2.71679	−	4.70561i	−0.0986781	−	0.170915i
$759$	−33.7951	−	2.57938i	−1.22669	−	0.0936254i
$760$	−0.722852	+	0.417339i	−0.0262206	+	0.0151385i
$761$	−0.905039	−	0.814901i	−0.0328076	−	0.0295401i	0.652564	−	0.757734i	$-0.273693\pi$
$761$	−0.905039	−	0.814901i	−0.0328076	−	0.0295401i	−0.685371	+	0.728194i	$0.740360\pi$
$762$	5.15822	+	8.50194i	0.186863	+	0.307993i
$763$	−7.38746	−	3.28911i	−0.267444	−	0.119074i
$764$	18.2997	−	16.4771i	0.662059	−	0.596121i
$765$	−0.00732703	+	0.119499i	−0.000264909	+	0.00432050i
$766$	0.556639	+	0.766147i	0.0201122	+	0.0276820i
$767$	11.8432	+	52.2279i	0.427633	+	1.88584i
$768$	−2.08750	+	25.0993i	−0.0753262	+	0.905692i
$769$	13.7578	−	23.8293i	0.496121	−	0.859306i	−0.503869	−	0.863780i	$-0.668091\pi$
$769$	13.7578	−	23.8293i	0.496121	−	0.859306i	0.999990	+	0.00447365i	$0.00142401\pi$
$770$	0.119060	+	0.0676637i	0.00429063	+	0.00243843i
$771$	12.3837	−	1.57445i	0.445986	−	0.0567023i
$772$	−8.43544	−	25.9616i	−0.303598	−	0.934379i
$773$	1.54710	−	14.7197i	0.0556454	−	0.529430i	−0.930822	−	0.365473i	$-0.880907\pi$
$773$	1.54710	−	14.7197i	0.0556454	−	0.529430i	0.986467	−	0.163958i	$-0.0524260\pi$
$774$	6.65980	+	17.8207i	0.239382	+	0.640551i
$775$	−35.6039	−	11.5684i	−1.27893	−	0.415549i
$776$	36.3675	−	7.73014i	1.30552	−	0.277496i
$777$	−6.10410	−	1.83763i	−0.218983	−	0.0659246i
$778$	1.34355	−	0.598186i	0.0481685	−	0.0214460i
$779$	−43.5567	+	14.1524i	−1.56058	+	0.507063i
$780$	−0.566900	−	0.0394228i	−0.0202983	−	0.00141156i
$781$	−31.3123	+	23.0768i	−1.12044	+	0.825753i
$782$	−1.40848	+	2.43956i	−0.0503672	+	0.0872386i
$783$	−1.21989	−	7.10901i	−0.0435953	−	0.254055i
$784$	0.312952	−	2.97754i	0.0111769	−	0.106341i
$785$	0.270927	−	0.196840i	0.00966979	−	0.00702552i
$786$	−3.41452	+	17.9774i	−0.121792	+	0.641231i
$787$	21.0540	−	4.47516i	0.750494	−	0.159522i	0.183243	−	0.983068i	$-0.441340\pi$
$787$	21.0540	−	4.47516i	0.750494	−	0.159522i	0.567251	+	0.823545i	$0.308007\pi$
$788$	11.0519	+	15.2116i	0.393707	+	0.541891i
$789$	−11.7224	+	21.3634i	−0.417330	+	0.760556i
$790$	0.429925	+	0.0913833i	0.0152960	+	0.00325127i
$791$	−7.95452	−	4.59254i	−0.282830	−	0.163292i
$792$	4.28338	−	26.6856i	0.152203	−	0.948233i
$793$	1.74717	−	1.99411i	0.0620438	−	0.0708130i
$794$	4.60408	+	14.1699i	0.163393	+	0.502871i
$795$	−0.0144801	−	0.665925i	−0.000513557	−	0.0236179i
$796$	−0.443693	−	4.22146i	−0.0157263	−	0.149626i
$797$	−5.56748	−	26.1929i	−0.197210	−	0.927801i	−0.959749	−	0.280859i	$-0.909381\pi$
$797$	−5.56748	−	26.1929i	−0.197210	−	0.927801i	0.762539	−	0.646942i	$-0.223953\pi$
$798$	−3.59731	−	3.10012i	−0.127343	−	0.109743i
$799$	2.13664	+	0.951293i	0.0755888	+	0.0336543i
$800$	−28.8681	−	3.03416i	−1.02064	−	0.107274i
$801$	4.25303	−	8.16698i	0.150273	−	0.288566i
$802$	8.49558	−	4.90492i	0.299989	−	0.173199i
$803$	−13.0387	+	22.9427i	−0.460125	+	0.809630i
$804$	−10.0687	−	13.2431i	−0.355095	−	0.467048i
$805$	0.284688	−	0.0925009i	0.0100339	−	0.00326023i
$806$	16.1413	−	14.9347i	0.568554	−	0.526051i
$807$	11.3854	+	48.3684i	0.400784	+	1.70265i
$808$	−23.6964	+	21.3364i	−0.833638	+	0.750611i
$809$	−34.7806	−	38.6278i	−1.22282	−	1.35808i	−0.913353	−	0.407169i	$-0.866516\pi$
$809$	−34.7806	−	38.6278i	−1.22282	−	1.35808i	−0.309468	−	0.950910i	$-0.600151\pi$
$810$	0.451521	+	0.210714i	0.0158648	+	0.00740373i
$811$	−19.1746	−	13.9312i	−0.673312	−	0.489190i	0.197820	−	0.980238i	$-0.436614\pi$
$811$	−19.1746	−	13.9312i	−0.673312	−	0.489190i	−0.871132	+	0.491048i	$0.836614\pi$
$812$	0.926639	−	1.02914i	0.0325186	−	0.0361156i
$813$	−1.72404	−	13.5602i	−0.0604646	−	0.475578i
$814$	4.20226	+	12.6400i	0.147289	+	0.443032i
$815$	−0.394404	+	0.227709i	−0.0138154	+	0.00797630i
$816$	0.387888	+	0.269131i	0.0135788	+	0.00942146i
$817$	14.3159	+	32.1540i	0.500849	+	1.12493i
$818$	2.23279	+	3.07318i	0.0780678	+	0.107451i
$819$	−2.12431	−	7.78242i	−0.0742293	−	0.271940i
$820$	0.877445	+	0.285099i	0.0306417	+	0.00995610i
$821$	−22.6605	+	2.38171i	−0.790855	+	0.0831223i	−0.491338	−	0.870969i	$-0.663492\pi$
$821$	−22.6605	+	2.38171i	−0.790855	+	0.0831223i	−0.299517	+	0.954091i	$0.596826\pi$
$822$	0.112812	+	5.18812i	0.00393479	+	0.180956i
$823$	3.69818	−	4.10724i	0.128910	−	0.143169i	−0.675234	−	0.737604i	$-0.735957\pi$
$823$	3.69818	−	4.10724i	0.128910	−	0.143169i	0.804144	+	0.594434i	$0.202624\pi$
$824$		−	33.4096i		−	1.16388i
$825$	28.2280	+	5.16277i	0.982772	+	0.179744i
$826$	7.80762	−	4.50773i	0.271662	−	0.156844i
$827$	23.8814	−	7.75954i	0.830437	−	0.269825i	0.137208	−	0.990542i	$-0.456187\pi$
$827$	23.8814	−	7.75954i	0.830437	−	0.269825i	0.693230	+	0.720717i	$0.256187\pi$
$828$	−14.7364	−	18.5319i	−0.512124	−	0.644029i
$829$	−3.85206	−	36.6499i	−0.133788	−	1.27290i	−0.831095	−	0.556131i	$-0.812285\pi$
$829$	−3.85206	−	36.6499i	−0.133788	−	1.27290i	0.697307	−	0.716773i	$-0.254381\pi$
$830$	−0.156958	−	0.174319i	−0.00544808	−	0.00605071i
$831$	−11.2462	−	9.69185i	−0.390127	−	0.336207i
$832$	7.90208	−	11.1921i	0.273955	−	0.388016i
$833$	3.05829	+	2.22197i	0.105963	+	0.0769868i
$834$	13.5717	+	9.41653i	0.469949	+	0.326068i
$835$	−0.242753	−	0.140154i	−0.00840083	−	0.00485022i
$836$	1.95912	−	19.9440i	0.0677576	−	0.689777i
$837$	36.1719	−	14.4216i	1.25028	−	0.498483i
$838$	−13.5446	+	15.0428i	−0.467890	+	0.519645i
$839$	2.66052	−	25.3132i	0.0918514	−	0.873908i	−0.847464	−	0.530853i	$-0.821872\pi$
$839$	2.66052	−	25.3132i	0.0918514	−	0.873908i	0.939315	−	0.343055i	$-0.111462\pi$
$840$	0.0546921	+	0.232348i	0.00188706	+	0.00801677i
$841$	26.4815	−	5.62881i	0.913155	−	0.194097i
$842$	18.4758	+	20.5195i	0.636720	+	0.707149i
$843$	−51.7244	−	15.5716i	−1.78148	−	0.536313i
$844$	13.9344	−	19.1791i	0.479643	−	0.660172i
$845$	0.729271	+	0.500228i	0.0250877	+	0.0172084i
$846$	6.94370	−	6.82149i	0.238729	−	0.234528i
$847$	−7.44853	+	3.43847i	−0.255934	+	0.118147i
$848$	−2.27469	−	1.31329i	−0.0781133	−	0.0450987i
$849$	−16.7279	−	35.4751i	−0.574099	−	1.21750i
$850$	1.40188	−	1.92952i	0.0480839	−	0.0661818i
$851$	26.5988	+	11.8425i	0.911794	+	0.405957i
$852$	−26.6951	−	5.07032i	−0.914560	−	0.173706i
$853$	−1.20520	+	3.70924i	−0.0412654	+	0.127002i	−0.969567	−	0.244827i	$-0.921269\pi$
$853$	−1.20520	+	3.70924i	−0.0412654	+	0.127002i	0.928302	+	0.371828i	$0.121269\pi$
$854$	−0.407734	−	0.181535i	−0.0139524	−	0.00621199i
$855$	0.857646	+	0.337986i	0.0293309	+	0.0115589i
$856$	−9.79396	+	46.0770i	−0.334751	+	1.57488i
$857$	−23.6647			−0.808371			−0.404185	−	0.914677i	$-0.632445\pi$
$857$	−23.6647			−0.808371			−0.404185	+	0.914677i	$0.632445\pi$
$858$	−10.7422	+	12.9905i	−0.366731	+	0.443487i
$859$	−15.5235			−0.529655			−0.264828	−	0.964296i	$-0.585315\pi$
$859$	−15.5235			−0.529655			−0.264828	+	0.964296i	$0.585315\pi$
$860$	0.147417	−	0.693544i	0.00502689	−	0.0236497i
$861$	0.284724	+	13.0941i	0.00970336	+	0.446247i
$862$	−12.1484	−	5.40883i	−0.413777	−	0.184225i
$863$	8.49626	−	26.1488i	0.289216	−	0.890115i	−0.695887	−	0.718151i	$-0.744989\pi$
$863$	8.49626	−	26.1488i	0.289216	−	0.890115i	0.985103	−	0.171964i	$-0.0550113\pi$
$864$	25.1091	−	16.7691i	0.854228	−	0.570497i
$865$	1.12670	+	0.501641i	0.0383091	+	0.0170563i
$866$	−5.58128	+	7.68197i	−0.189660	+	0.261044i
$867$	26.0933	−	12.3040i	0.886176	−	0.417866i
$868$	6.47477	+	3.73821i	0.219768	+	0.126883i
$869$	−19.4473	+	17.7514i	−0.659704	+	0.602176i
$870$	0.0514844	−	0.122750i	0.00174548	−	0.00416162i
$871$	3.05475	+	25.7083i	0.103506	+	0.871091i
$872$	−17.3117	+	23.8276i	−0.586250	+	0.806904i
$873$	−31.6809	−	26.1238i	−1.07224	−	0.884156i
$874$	14.5134	+	16.1188i	0.490923	+	0.545225i
$875$	−0.496030	+	0.105434i	−0.0167689	+	0.00356434i
$876$	−17.9440	+	4.22382i	−0.606272	+	0.142710i
$877$	0.829848	−	7.89548i	0.0280220	−	0.266611i	−0.971536	−	0.236891i	$-0.923872\pi$
$877$	0.829848	−	7.89548i	0.0280220	−	0.266611i	0.999558	−	0.0297205i	$-0.00946171\pi$
$878$	−2.26060	+	2.51065i	−0.0762915	+	0.0847303i
$879$	0.120889	−	0.288226i	0.00407748	−	0.00972162i
$880$	−0.0696121	+	0.0783777i	−0.00234662	+	0.00264211i
$881$	8.62346	+	4.97876i	0.290532	+	0.167739i	0.638182	−	0.769886i	$-0.279687\pi$
$881$	8.62346	+	4.97876i	0.290532	+	0.167739i	−0.347650	+	0.937624i	$0.613020\pi$
$882$	13.2701	−	8.45118i	0.446828	−	0.284566i
$883$	27.1691	+	19.7395i	0.914313	+	0.664287i	0.942102	−	0.335326i	$-0.108847\pi$
$883$	27.1691	+	19.7395i	0.914313	+	0.664287i	−0.0277889	+	0.999614i	$0.508847\pi$
$884$	−1.18574	−	2.56896i	−0.0398808	−	0.0864036i
$885$	−1.14248	+	1.32571i	−0.0384041	+	0.0445633i
$886$	3.84260	+	4.26764i	0.129095	+	0.143374i
$887$	1.78027	+	16.9381i	0.0597756	+	0.568727i	0.982889	+	0.184199i	$0.0589690\pi$
$887$	1.78027	+	16.9381i	0.0597756	+	0.568727i	−0.923113	+	0.384528i	$0.874364\pi$
$888$	−11.1689	+	20.3546i	−0.374805	+	0.683057i
$889$	5.00388	−	1.62586i	0.167825	−	0.0545295i
$890$	0.147162	−	0.0849642i	0.00493289	−	0.00284801i
$891$	−26.0125	+	14.6408i	−0.871450	+	0.490484i
$892$			13.5591i			0.453991i
$893$	12.0500	−	13.3829i	0.403239	−	0.447842i
$894$	5.70442	−	0.124039i	0.190784	−	0.00414849i
$895$	−0.337938	+	0.0355188i	−0.0112960	+	0.00118726i
$896$	6.04975	+	1.96568i	0.202108	+	0.0656688i
$897$	5.14199	+	36.4855i	0.171686	+	1.21822i
$898$	2.69809	+	3.71360i	0.0900363	+	0.123924i
$899$	−4.23122	−	9.50347i	−0.141119	−	0.316959i
$900$	10.7683	+	16.9085i	0.358943	+	0.563615i
$901$	2.87210	−	1.65821i	0.0956836	−	0.0552430i
$902$	22.0306	−	16.2363i	0.733539	−	0.540609i
$903$	9.98512	−	1.26950i	0.332284	−	0.0422463i
$904$	−22.3847	+	24.8607i	−0.744504	+	0.826855i
$905$	−1.05529	−	0.766715i	−0.0350791	−	0.0254865i
$906$	−1.90031	+	1.78737i	−0.0631337	+	0.0593812i
$907$	−0.810559	−	0.900217i	−0.0269142	−	0.0298912i	0.729537	−	0.683941i	$-0.239735\pi$
$907$	−0.810559	−	0.900217i	−0.0269142	−	0.0298912i	−0.756452	+	0.654050i	$0.773069\pi$
$908$	−12.3362	+	11.1076i	−0.409392	+	0.368619i
$909$	34.7327	+	5.81767i	1.15201	+	0.192960i
$910$	0.0440820	−	0.142198i	0.00146130	−	0.00471382i
$911$	32.8652	−	10.6785i	1.08887	−	0.353796i	0.291062	−	0.956704i	$-0.405992\pi$
$911$	32.8652	−	10.6785i	1.08887	−	0.353796i	0.797811	+	0.602908i	$0.205992\pi$
$912$	2.89374	−	2.20011i	0.0958213	−	0.0728528i
$913$	13.9650	−	1.56390i	0.462174	−	0.0517575i
$914$	17.5291	−	10.1204i	0.579812	−	0.334755i
$915$	0.0863415	+	0.00718100i	0.00285436	+	0.000237397i
$916$	−23.0387	−	2.42146i	−0.761220	−	0.0800074i
$917$	8.84454	+	3.93784i	0.292072	+	0.130039i
$918$	0.161695	+	2.47560i	0.00533673	+	0.0817069i
$919$	−5.86638	−	27.5991i	−0.193514	−	0.910412i	−0.962529	−	0.271180i	$-0.912586\pi$
$919$	−5.86638	−	27.5991i	−0.193514	−	0.910412i	0.769015	−	0.639231i	$-0.220747\pi$
$920$	−0.113961	−	1.08426i	−0.00375717	−	0.0357471i
$921$	−24.5616	+	0.534076i	−0.809331	+	0.0175984i
$922$	−4.14983	−	12.7719i	−0.136667	−	0.420619i
$923$	31.8050	+	27.8664i	1.04687	+	0.917233i
$924$	−5.29989	−	2.18062i	−0.174353	−	0.0717372i
$925$	−21.3487	−	12.3257i	−0.701941	−	0.405266i
$926$	−22.9275	−	4.87339i	−0.753445	−	0.160150i
$927$	−28.8805	+	22.9655i	−0.948560	+	0.754285i
$928$	−4.74116	−	6.52565i	−0.155636	−	0.214215i
$929$	30.0200	−	6.38095i	0.984925	−	0.209352i	0.312823	−	0.949811i	$-0.398725\pi$
$929$	30.0200	−	6.38095i	0.984925	−	0.209352i	0.672101	+	0.740459i	$0.265392\pi$
$930$	0.706006	+	0.134095i	0.0231509	+	0.00439714i
$931$	23.5480	−	17.1086i	0.771756	−	0.560713i
$932$	1.61453	−	15.3613i	0.0528858	−	0.503175i
$933$	26.5739	−	38.2999i	0.869989	−	1.25388i
$934$	−6.33233	+	10.9679i	−0.207200	+	0.358881i
$935$	−0.0417567	−	0.125600i	−0.00136559	−	0.00410756i
$936$	−29.3339	+	1.67477i	−0.958809	+	0.0547416i
$937$	33.7666	−	10.9714i	1.10311	−	0.358421i	0.299809	−	0.953999i	$-0.403077\pi$
$937$	33.7666	−	10.9714i	1.10311	−	0.358421i	0.803297	+	0.595578i	$0.203077\pi$
$938$	3.98148	−	1.77267i	0.130000	−	0.0578798i
$939$	6.78167	−	22.5268i	0.221311	−	0.735135i
$940$	−0.354852	+	0.0754260i	−0.0115740	+	0.00246013i
$941$	23.9434	+	7.77967i	0.780531	+	0.253610i	0.672067	−	0.740490i	$-0.265407\pi$
$941$	23.9434	+	7.77967i	0.780531	+	0.253610i	0.108464	+	0.994100i	$0.465407\pi$
$942$	5.05479	−	4.75435i	0.164694	−	0.154905i
$943$	6.25295	−	59.4929i	0.203624	−	1.93735i
$944$	2.13257	+	6.56338i	0.0694093	+	0.213620i
$945$	0.163256	−	0.206992i	0.00531071	−	0.00673345i
$946$	−14.1794	−	15.5340i	−0.461011	−	0.505052i
$947$	2.53044	−	4.38285i	0.0822283	−	0.142424i	−0.821978	−	0.569519i	$-0.807130\pi$
$947$	2.53044	−	4.38285i	0.0822283	−	0.142424i	0.904207	+	0.427095i	$0.140463\pi$
$948$	−18.3305	−	1.52455i	−0.595348	−	0.0495149i
$949$	27.4013	+	8.49453i	0.889484	+	0.275744i
$950$	−10.7941	−	14.8568i	−0.350206	−	0.482018i
$951$	−10.3269	−	29.5788i	−0.334872	−	0.959158i
$952$	−0.883210	+	0.795246i	−0.0286250	+	0.0257741i
$953$	15.2816	+	6.80380i	0.495019	+	0.220397i	0.639033	−	0.769179i	$-0.279335\pi$
$953$	15.2816	+	6.80380i	0.495019	+	0.220397i	−0.144015	+	0.989576i	$0.546001\pi$
$954$	−2.03805	−	13.6511i	−0.0659844	−	0.441969i
$955$	−0.930631	−	0.837944i	−0.0301145	−	0.0271152i
$956$	−13.7376	+	7.93141i	−0.444306	+	0.256520i
$957$	4.18256	+	6.78924i	0.135203	+	0.219465i
$958$	−13.7930	−	23.8902i	−0.445632	−	0.771857i
$959$	2.68560	+	0.570841i	0.0867224	+	0.0184334i
$960$	0.447614	−	0.00973308i	0.0144467	−	0.000314134i
$961$	20.3568	−	14.7901i	0.656673	−	0.477101i
$962$	12.4413	−	7.40956i	0.401125	−	0.238894i
$963$	46.5630	−	23.2067i	1.50047	−	0.747824i
$964$	0.981995	+	9.34305i	0.0316279	+	0.300920i
$965$	−1.26821	+	0.564642i	−0.0408250	+	0.0181765i
$966$	5.61036	−	2.64550i	0.180510	−	0.0851176i
$967$	−17.5987			−0.565936			−0.282968	−	0.959129i	$-0.591319\pi$
$967$	−17.5987			−0.565936			−0.282968	+	0.959129i	$0.591319\pi$
$968$	6.60939	+	29.1396i	0.212434	+	0.936581i
$969$	0.578889	+	4.55319i	0.0185966	+	0.146270i
$970$	−0.234168	−	0.720695i	−0.00751868	−	0.0231401i
$971$	42.6845	+	4.48632i	1.36981	+	0.143973i	0.760696	−	0.649109i	$-0.224858\pi$
$971$	42.6845	+	4.48632i	1.36981	+	0.143973i	0.609115	+	0.793082i	$0.291525\pi$
$972$	−19.8569	−	6.36453i	−0.636911	−	0.204142i
$973$	6.49484	−	5.84798i	0.208215	−	0.187477i
$974$	−0.844045	+	2.59770i	−0.0270450	+	0.0832358i
$975$	−1.10070	−	31.1767i	−0.0352505	−	0.998452i
$976$	0.200816	−	0.276400i	0.00642798	−	0.00884735i
$977$	−12.3018	−	2.61483i	−0.393570	−	0.0836560i	0.00687557	−	0.999976i	$-0.497811\pi$
$977$	−12.3018	−	2.61483i	−0.393570	−	0.0836560i	−0.400446	+	0.916320i	$0.631145\pi$
$978$	−7.51233	+	5.71161i	−0.240218	+	0.182637i
$979$	−0.995191	+	10.1311i	−0.0318064	+	0.323791i
$980$	−0.586357			−0.0187305
$981$	32.4974	−	1.41394i	1.03756	−	0.0451437i
$982$	−27.0798	−	2.84620i	−0.864150	−	0.0908258i
$983$	45.2896	−	32.9048i	1.44451	−	1.04950i	0.457439	−	0.889241i	$-0.348767\pi$
$983$	45.2896	−	32.9048i	1.44451	−	1.04950i	0.987075	−	0.160259i	$-0.0512331\pi$
$984$	46.8641	+	8.90111i	1.49397	+	0.283757i
$985$	0.710599	−	0.639827i	0.0226416	−	0.0203866i
$986$	0.659123	−	0.0692766i	0.0209907	−	0.00220622i
$987$	−2.67135	−	4.40301i	−0.0850301	−	0.140149i
$988$	−21.6335	+	2.57058i	−0.688255	+	0.0817810i
$989$	−45.9734			−1.46187
$990$	−0.550040	−	0.0299712i	−0.0174814	−	0.000952546i
$991$	−28.2622	+	48.9516i	−0.897779	+	1.55500i	−0.0674513	+	0.997723i	$0.521487\pi$
$991$	−28.2622	+	48.9516i	−0.897779	+	1.55500i	−0.830327	+	0.557276i	$0.811847\pi$
$992$	29.1387	−	32.3618i	0.925156	−	1.02749i
$993$	1.90469	−	1.15560i	0.0604435	−	0.0366718i
$994$	2.89538	−	6.50314i	0.0918359	−	0.206267i
$995$	−0.211148	+	0.0448809i	−0.00669384	+	0.00142282i
$996$	7.43613	+	6.40836i	0.235623	+	0.203057i
$997$	−17.5680	+	39.4584i	−0.556384	+	1.24966i	0.388256	+	0.921552i	$0.373078\pi$
$997$	−17.5680	+	39.4584i	−0.556384	+	1.24966i	−0.944640	+	0.328108i	$0.893589\pi$
$998$	5.06674	−	2.25586i	0.160385	−	0.0714080i
$999$	25.2728	−	4.33675i	0.799595	−	0.137209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bm.a.17.20	✓	416
3.2	odd	2	inner	429.2.bm.a.17.33	yes	416
11.2	odd	10	inner	429.2.bm.a.134.20	yes	416
13.10	even	6	inner	429.2.bm.a.413.33	yes	416
33.2	even	10	inner	429.2.bm.a.134.33	yes	416
39.23	odd	6	inner	429.2.bm.a.413.20	yes	416
143.101	odd	30	inner	429.2.bm.a.101.33	yes	416
429.101	even	30	inner	429.2.bm.a.101.20	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bm.a.17.20	✓	416	1.1	even	1	trivial
429.2.bm.a.17.33	yes	416	3.2	odd	2	inner
429.2.bm.a.101.20	yes	416	429.101	even	30	inner
429.2.bm.a.101.33	yes	416	143.101	odd	30	inner
429.2.bm.a.134.20	yes	416	11.2	odd	10	inner
429.2.bm.a.134.33	yes	416	33.2	even	10	inner
429.2.bm.a.413.20	yes	416	39.23	odd	6	inner
429.2.bm.a.413.33	yes	416	13.10	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bm (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.169208 + 0.796062i) q^{2} +(-1.73164 + 0.0376535i) q^{3} +(1.22201 + 0.544073i) q^{4} +(0.0210213 - 0.0646970i) q^{5} +(0.263033 - 1.38487i) q^{6} +(-0.681329 - 0.303347i) q^{7} +(-1.59662 + 2.19756i) q^{8} +(2.99716 - 0.130405i) q^{9} +O(q^{10})\)	\(q+(-0.169208 + 0.796062i) q^{2} +(-1.73164 + 0.0376535i) q^{3} +(1.22201 + 0.544073i) q^{4} +(0.0210213 - 0.0646970i) q^{5} +(0.263033 - 1.38487i) q^{6} +(-0.681329 - 0.303347i) q^{7} +(-1.59662 + 2.19756i) q^{8} +(2.99716 - 0.130405i) q^{9} +(0.0479459 + 0.0276816i) q^{10} +(-3.02064 + 1.36957i) q^{11} +(-2.13657 - 0.896126i) q^{12} +(2.15862 + 2.88797i) q^{13} +(0.356770 - 0.491051i) q^{14} +(-0.0339654 + 0.112824i) q^{15} +(0.310895 + 0.345284i) q^{16} +(-0.573832 + 0.121972i) q^{17} +(-0.403335 + 2.40799i) q^{18} +(-0.472162 + 4.49232i) q^{19} +(0.0608881 - 0.0676231i) q^{20} +(1.19124 + 0.499634i) q^{21} +(-0.579148 - 2.63636i) q^{22} +(-5.10963 - 2.95005i) q^{23} +(2.68203 - 3.86551i) q^{24} +(4.04134 + 2.93621i) q^{25} +(-2.66426 + 1.22973i) q^{26} +(-5.18510 + 0.338668i) q^{27} +(-0.667546 - 0.741385i) q^{28} +(0.145099 + 1.38052i) q^{29} +(-0.0840674 - 0.0461292i) q^{30} +(-7.12737 + 2.31582i) q^{31} +(-5.03231 + 2.90540i) q^{32} +(5.17910 - 2.48535i) q^{33} -0.477444i q^{34} +(-0.0339481 + 0.0377032i) q^{35} +(3.73351 + 1.47132i) q^{36} +(-4.90780 + 0.515831i) q^{37} +(-3.49628 - 1.13601i) q^{38} +(-3.84669 - 4.91965i) q^{39} +(0.108613 + 0.149493i) q^{40} +(4.12387 + 9.26237i) q^{41} +(-0.599307 + 0.863758i) q^{42} +(6.74806 - 3.89599i) q^{43} +(-4.43639 + 0.0301795i) q^{44} +(0.0545676 - 0.196649i) q^{45} +(3.21301 - 3.56841i) q^{46} +(-3.22536 - 2.34336i) q^{47} +(-0.551360 - 0.586202i) q^{48} +(-4.31172 - 4.78866i) q^{49} +(-3.02123 + 2.72033i) q^{50} +(0.989078 - 0.232818i) q^{51} +(1.06658 + 4.70357i) q^{52} +(-5.37645 + 1.74691i) q^{53} +(0.607762 - 4.18497i) q^{54} +(0.0251094 + 0.224217i) q^{55} +(1.75445 - 1.01293i) q^{56} +(0.648464 - 7.79687i) q^{57} +(-1.12353 - 0.118088i) q^{58} +(13.5690 + 6.04132i) q^{59} +(-0.102890 + 0.119392i) q^{60} +(-0.152882 - 0.719253i) q^{61} +(-0.637529 - 6.06569i) q^{62} +(-2.08161 - 0.820333i) q^{63} +(-1.17422 - 3.61388i) q^{64} +(0.232220 - 0.0789471i) q^{65} +(1.10214 + 4.54342i) q^{66} +(6.21837 + 3.59017i) q^{67} +(-0.767588 - 0.163156i) q^{68} +(8.95912 + 4.91603i) q^{69} +(-0.0242698 - 0.0334045i) q^{70} +(11.4717 - 2.43839i) q^{71} +(-4.49877 + 6.79467i) q^{72} +(6.43699 - 4.67675i) q^{73} +(0.419807 - 3.99420i) q^{74} +(-7.10871 - 4.93229i) q^{75} +(-3.02114 + 5.23276i) q^{76} +(2.47351 - 0.0168266i) q^{77} +(4.56724 - 2.22976i) q^{78} +(7.55047 - 2.45330i) q^{79} +(0.0288743 - 0.0128557i) q^{80} +(8.96599 - 0.781688i) q^{81} +(-8.07121 + 1.71559i) q^{82} +(-4.02956 - 1.30928i) q^{83} +(1.18387 + 1.25868i) q^{84} +(-0.00417151 + 0.0396892i) q^{85} +(1.95962 + 6.03110i) q^{86} +(-0.303241 - 2.38511i) q^{87} +(1.81310 - 8.82474i) q^{88} +(1.53467 - 2.65813i) q^{89} +(0.147311 + 0.0767138i) q^{90} +(-0.594671 - 2.62247i) q^{91} +(-4.63896 - 6.38499i) q^{92} +(12.2549 - 4.27855i) q^{93} +(2.41122 - 2.17107i) q^{94} +(0.280715 + 0.124982i) q^{95} +(8.60476 - 5.22060i) q^{96} +(-10.1718 - 9.15874i) q^{97} +(4.54165 - 2.62212i) q^{98} +(-8.87476 + 4.49874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9}+O(q^{10}) \) 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9	\( 416 q - 3 q^{3} - 54 q^{4} - 15 q^{6} - 30 q^{7} - 9 q^{9} - 36 q^{12} - 20 q^{13} - 9 q^{15} + 14 q^{16} - 30 q^{19} - 28 q^{22} + 15 q^{24} - 84 q^{25} - 24 q^{27} - 30 q^{28} - 5 q^{30} - 27 q^{33} - 73 q^{36} - 18 q^{37} - 65 q^{39} - 120 q^{40} - 25 q^{42} + 36 q^{45} + 30 q^{46} - 41 q^{48} + 14 q^{49} + 60 q^{51} + 20 q^{52} + 18 q^{55} - 126 q^{58} - 30 q^{61} + 105 q^{63} - 56 q^{64} + 170 q^{66} - 33 q^{69} - 195 q^{72} + 77 q^{75} + 4 q^{78} - 13 q^{81} + 36 q^{82} - 60 q^{84} - 30 q^{85} + 38 q^{88} - 190 q^{90} - 56 q^{91} + 24 q^{93} - 90 q^{94} + 54 q^{97}+O(q^{100}) \) 416 * q - 3 * q^3 - 54 * q^4 - 15 * q^6 - 30 * q^7 - 9 * q^9 - 36 * q^12 - 20 * q^13 - 9 * q^15 + 14 * q^16 - 30 * q^19 - 28 * q^22 + 15 * q^24 - 84 * q^25 - 24 * q^27 - 30 * q^28 - 5 * q^30 - 27 * q^33 - 73 * q^36 - 18 * q^37 - 65 * q^39 - 120 * q^40 - 25 * q^42 + 36 * q^45 + 30 * q^46 - 41 * q^48 + 14 * q^49 + 60 * q^51 + 20 * q^52 + 18 * q^55 - 126 * q^58 - 30 * q^61 + 105 * q^63 - 56 * q^64 + 170 * q^66 - 33 * q^69 - 195 * q^72 + 77 * q^75 + 4 * q^78 - 13 * q^81 + 36 * q^82 - 60 * q^84 - 30 * q^85 + 38 * q^88 - 190 * q^90 - 56 * q^91 + 24 * q^93 - 90 * q^94 + 54 * q^97

Introduction

L-functions

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