LMFDB - Embedded newform 273.2.by.c.202.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(76,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("273.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.by (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			202.8
Character	$\chi$	$=$	273.202
Dual form			273.2.by.c.223.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.37607 - 0.636667i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(3.50833 - 2.02554i) q^{4} +(0.498430 - 0.498430i) q^{5} +(-2.37607 - 0.636667i) q^{6} +(-2.12397 - 1.57758i) q^{7} +(3.56765 - 3.56765i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(2.37607 - 0.636667i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(3.50833 - 2.02554i) q^{4} +(0.498430 - 0.498430i) q^{5} +(-2.37607 - 0.636667i) q^{6} +(-2.12397 - 1.57758i) q^{7} +(3.56765 - 3.56765i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.866973 - 1.50164i) q^{10} +(0.184478 + 0.688480i) q^{11} -4.05107 q^{12} +(3.17894 + 1.70127i) q^{13} +(-6.05110 - 2.39618i) q^{14} +(-0.680869 + 0.182438i) q^{15} +(2.15452 - 3.73174i) q^{16} +(2.27300 + 3.93695i) q^{17} +(1.73941 + 1.73941i) q^{18} +(-3.25000 - 0.870835i) q^{19} +(0.739070 - 2.75825i) q^{20} +(1.05062 + 2.42821i) q^{21} +(0.876665 + 1.51843i) q^{22} +(-1.67026 - 0.964326i) q^{23} +(-4.87350 + 1.30585i) q^{24} +4.50313i q^{25} +(8.63655 + 2.01842i) q^{26} -1.00000i q^{27} +(-10.6470 - 1.23248i) q^{28} +(0.185925 - 0.322032i) q^{29} +(-1.50164 + 0.866973i) q^{30} +(-3.53994 + 3.53994i) q^{31} +(0.131724 - 0.491600i) q^{32} +(0.184478 - 0.688480i) q^{33} +(7.90735 + 7.90735i) q^{34} +(-1.84496 + 0.272339i) q^{35} +(3.50833 + 2.02554i) q^{36} +(-0.545727 - 2.03668i) q^{37} -8.27667 q^{38} +(-1.90241 - 3.06282i) q^{39} -3.55645i q^{40} +(-3.11983 - 11.6434i) q^{41} +(4.04232 + 5.10070i) q^{42} +(6.38504 - 3.68640i) q^{43} +(2.04175 + 2.04175i) q^{44} +(0.680869 + 0.182438i) q^{45} +(-4.58262 - 1.22791i) q^{46} +(3.55898 + 3.55898i) q^{47} +(-3.73174 + 2.15452i) q^{48} +(2.02250 + 6.70145i) q^{49} +(2.86700 + 10.6998i) q^{50} -4.54600i q^{51} +(14.5988 - 0.470438i) q^{52} -4.97712 q^{53} +(-0.636667 - 2.37607i) q^{54} +(0.435109 + 0.251210i) q^{55} +(-13.2058 + 1.94934i) q^{56} +(2.37916 + 2.37916i) q^{57} +(0.236745 - 0.883543i) q^{58} +(1.03416 - 3.85953i) q^{59} +(-2.01918 + 2.01918i) q^{60} +(-10.0720 + 5.81509i) q^{61} +(-6.15739 + 10.6649i) q^{62} +(0.304236 - 2.62820i) q^{63} +7.36614i q^{64} +(2.43245 - 0.736516i) q^{65} -1.75333i q^{66} +(-12.5870 + 3.37267i) q^{67} +(15.9489 + 9.20809i) q^{68} +(0.964326 + 1.67026i) q^{69} +(-4.21038 + 1.82173i) q^{70} +(2.10681 - 7.86274i) q^{71} +(4.87350 + 1.30585i) q^{72} +(-0.608899 - 0.608899i) q^{73} +(-2.59337 - 4.49186i) q^{74} +(2.25157 - 3.89983i) q^{75} +(-13.1660 + 3.52781i) q^{76} +(0.694305 - 1.75334i) q^{77} +(-6.47026 - 6.06627i) q^{78} +9.81537 q^{79} +(-0.786133 - 2.93389i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-14.8259 - 25.6792i) q^{82} +(2.25452 - 2.25452i) q^{83} +(8.60436 + 6.39088i) q^{84} +(3.09523 + 0.829364i) q^{85} +(12.8243 - 12.8243i) q^{86} +(-0.322032 + 0.185925i) q^{87} +(3.11441 + 1.79810i) q^{88} +(17.5524 - 4.70315i) q^{89} +1.73395 q^{90} +(-4.06809 - 8.62848i) q^{91} -7.81311 q^{92} +(4.83565 - 1.29571i) q^{93} +(10.7223 + 6.19052i) q^{94} +(-2.05395 + 1.18585i) q^{95} +(-0.359876 + 0.359876i) q^{96} +(-8.73810 - 2.34137i) q^{97} +(9.07221 + 14.6355i) q^{98} +(-0.504002 + 0.504002i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9	$ 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9} - 2 q^{10} - 4 q^{11} - 32 q^{12} - 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} + 8 q^{17} + 2 q^{18} - 2 q^{19} - 44 q^{20} + 2 q^{21} - 4 q^{22} - 18 q^{23} - 4 q^{24} + 28 q^{26} - 18 q^{28} - 18 q^{29} + 14 q^{31} - 8 q^{32} - 4 q^{33} + 66 q^{34} - 20 q^{35} + 6 q^{36} - 24 q^{37} - 24 q^{38} + 8 q^{39} + 16 q^{42} - 6 q^{43} - 20 q^{44} - 4 q^{45} - 58 q^{46} + 28 q^{47} + 60 q^{48} + 10 q^{49} + 70 q^{50} - 28 q^{52} - 80 q^{53} + 4 q^{54} - 60 q^{55} - 120 q^{56} + 16 q^{57} - 4 q^{58} + 42 q^{59} - 58 q^{60} - 36 q^{61} - 52 q^{62} + 2 q^{63} + 14 q^{65} + 26 q^{67} + 72 q^{68} - 2 q^{69} + 68 q^{70} - 4 q^{71} + 4 q^{72} - 12 q^{73} - 18 q^{74} - 16 q^{75} + 48 q^{76} - 28 q^{77} - 14 q^{78} - 4 q^{79} + 98 q^{80} - 16 q^{81} - 20 q^{82} + 36 q^{83} + 32 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} + 54 q^{89} - 4 q^{90} - 54 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} - 22 q^{96} + 40 q^{97} + 4 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9 - 2 * q^10 - 4 * q^11 - 32 * q^12 - 6 * q^13 + 34 * q^14 + 4 * q^15 + 14 * q^16 + 8 * q^17 + 2 * q^18 - 2 * q^19 - 44 * q^20 + 2 * q^21 - 4 * q^22 - 18 * q^23 - 4 * q^24 + 28 * q^26 - 18 * q^28 - 18 * q^29 + 14 * q^31 - 8 * q^32 - 4 * q^33 + 66 * q^34 - 20 * q^35 + 6 * q^36 - 24 * q^37 - 24 * q^38 + 8 * q^39 + 16 * q^42 - 6 * q^43 - 20 * q^44 - 4 * q^45 - 58 * q^46 + 28 * q^47 + 60 * q^48 + 10 * q^49 + 70 * q^50 - 28 * q^52 - 80 * q^53 + 4 * q^54 - 60 * q^55 - 120 * q^56 + 16 * q^57 - 4 * q^58 + 42 * q^59 - 58 * q^60 - 36 * q^61 - 52 * q^62 + 2 * q^63 + 14 * q^65 + 26 * q^67 + 72 * q^68 - 2 * q^69 + 68 * q^70 - 4 * q^71 + 4 * q^72 - 12 * q^73 - 18 * q^74 - 16 * q^75 + 48 * q^76 - 28 * q^77 - 14 * q^78 - 4 * q^79 + 98 * q^80 - 16 * q^81 - 20 * q^82 + 36 * q^83 + 32 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 + 54 * q^89 - 4 * q^90 - 54 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 - 22 * q^96 + 40 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$

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 $

$2$	2.37607	−	0.636667i	1.68014	−	0.450192i	0.712322	−	0.701852i	$-0.247643\pi$
$2$	2.37607	−	0.636667i	1.68014	−	0.450192i	0.967816	+	0.251661i	$0.0809767\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	3.50833	−	2.02554i	1.75417	−	1.01277i
$5$	0.498430	−	0.498430i	0.222905	−	0.222905i	−0.586816	−	0.809721i	$-0.699619\pi$
$5$	0.498430	−	0.498430i	0.222905	−	0.222905i	0.809721	+	0.586816i	$0.199619\pi$
$6$	−2.37607	−	0.636667i	−0.970028	−	0.259918i
$7$	−2.12397	−	1.57758i	−0.802785	−	0.596268i
$7$	−2.12397	−	1.57758i	−0.802785	−	0.596268i
$8$	3.56765	−	3.56765i	1.26135	−	1.26135i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.866973	−	1.50164i	0.274161	−	0.474861i
$11$	0.184478	+	0.688480i	0.0556221	+	0.207585i	0.988144	−	0.153528i	$-0.0490636\pi$
$11$	0.184478	+	0.688480i	0.0556221	+	0.207585i	−0.932522	+	0.361113i	$0.882397\pi$
$12$	−4.05107			−1.16944
$13$	3.17894	+	1.70127i	0.881680	+	0.471848i
$13$	3.17894	+	1.70127i	0.881680	+	0.471848i
$14$	−6.05110	−	2.39618i	−1.61723	−	0.640405i
$15$	−0.680869	+	0.182438i	−0.175799	+	0.0471053i
$16$	2.15452	−	3.73174i	0.538630	−	0.932934i
$17$	2.27300	+	3.93695i	0.551284	+	0.954852i	0.998182	+	0.0602669i	$0.0191952\pi$
$17$	2.27300	+	3.93695i	0.551284	+	0.954852i	−0.446898	+	0.894585i	$0.647471\pi$
$18$	1.73941	+	1.73941i	0.409982	+	0.409982i
$19$	−3.25000	−	0.870835i	−0.745601	−	0.199783i	−0.134035	−	0.990977i	$-0.542793\pi$
$19$	−3.25000	−	0.870835i	−0.745601	−	0.199783i	−0.611566	+	0.791193i	$0.709460\pi$
$20$	0.739070	−	2.75825i	0.165261	−	0.616763i
$21$	1.05062	+	2.42821i	0.229265	+	0.529878i
$22$	0.876665	+	1.51843i	0.186906	+	0.323730i
$23$	−1.67026	−	0.964326i	−0.348274	−	0.201076i	0.315651	−	0.948875i	$-0.397777\pi$
$23$	−1.67026	−	0.964326i	−0.348274	−	0.201076i	−0.663925	+	0.747799i	$0.731110\pi$
$24$	−4.87350	+	1.30585i	−0.994799	+	0.266556i
$25$			4.50313i			0.900627i
$26$	8.63655	+	2.01842i	1.69377	+	0.395845i
$27$		−	1.00000i		−	0.192450i
$28$	−10.6470	−	1.23248i	−2.01210	−	0.232917i
$29$	0.185925	−	0.322032i	0.0345254	−	0.0597998i	−0.848246	−	0.529602i	$-0.822341\pi$
$29$	0.185925	−	0.322032i	0.0345254	−	0.0597998i	0.882772	+	0.469802i	$0.155675\pi$
$30$	−1.50164	+	0.866973i	−0.274161	+	0.158287i
$31$	−3.53994	+	3.53994i	−0.635792	+	0.635792i	−0.949515	−	0.313723i	$-0.898424\pi$
$31$	−3.53994	+	3.53994i	−0.635792	+	0.635792i	0.313723	+	0.949515i	$0.398424\pi$
$32$	0.131724	−	0.491600i	0.0232857	−	0.0869034i
$33$	0.184478	−	0.688480i	0.0321134	−	0.119849i
$34$	7.90735	+	7.90735i	1.35610	+	1.35610i
$35$	−1.84496	+	0.272339i	−0.311856	+	0.0460337i
$36$	3.50833	+	2.02554i	0.584722	+	0.337589i
$37$	−0.545727	−	2.03668i	−0.0897169	−	0.334828i	0.906449	−	0.422316i	$-0.138783\pi$
$37$	−0.545727	−	2.03668i	−0.0897169	−	0.334828i	−0.996166	+	0.0874879i	$0.972116\pi$
$38$	−8.27667			−1.34265
$39$	−1.90241	−	3.06282i	−0.304629	−	0.490443i
$40$		−	3.55645i		−	0.562324i
$41$	−3.11983	−	11.6434i	−0.487236	−	1.81839i	−0.569776	−	0.821800i	$-0.692970\pi$
$41$	−3.11983	−	11.6434i	−0.487236	−	1.81839i	0.0825406	−	0.996588i	$-0.473697\pi$
$42$	4.04232	+	5.10070i	0.623743	+	0.787055i
$43$	6.38504	−	3.68640i	0.973709	−	0.562171i	0.0733440	−	0.997307i	$-0.476633\pi$
$43$	6.38504	−	3.68640i	0.973709	−	0.562171i	0.900365	+	0.435136i	$0.143300\pi$
$44$	2.04175	+	2.04175i	0.307805	+	0.307805i
$45$	0.680869	+	0.182438i	0.101498	+	0.0271963i
$46$	−4.58262	−	1.22791i	−0.675671	−	0.181045i
$47$	3.55898	+	3.55898i	0.519131	+	0.519131i	0.917308	−	0.398177i	$-0.130357\pi$
$47$	3.55898	+	3.55898i	0.519131	+	0.519131i	−0.398177	+	0.917308i	$0.630357\pi$
$48$	−3.73174	+	2.15452i	−0.538630	+	0.310978i
$49$	2.02250	+	6.70145i	0.288929	+	0.957351i
$50$	2.86700	+	10.6998i	0.405455	+	1.51318i
$51$		−	4.54600i		−	0.636568i
$52$	14.5988	−	0.470438i	2.02449	−	0.0652380i
$53$	−4.97712			−0.683660			−0.341830	−	0.939762i	$-0.611047\pi$
$53$	−4.97712			−0.683660			−0.341830	+	0.939762i	$0.611047\pi$
$54$	−0.636667	−	2.37607i	−0.0866394	−	0.323343i
$55$	0.435109	+	0.251210i	0.0586700	+	0.0338732i
$56$	−13.2058	+	1.94934i	−1.76470	+	0.260492i
$57$	2.37916	+	2.37916i	0.315128	+	0.315128i
$58$	0.236745	−	0.883543i	0.0310861	−	0.116015i
$59$	1.03416	−	3.85953i	0.134636	−	0.502467i	−0.865363	−	0.501145i	$-0.832912\pi$
$59$	1.03416	−	3.85953i	0.134636	−	0.502467i	0.999999	−	0.00132252i	$-0.000420972\pi$
$60$	−2.01918	+	2.01918i	−0.260675	+	0.260675i
$61$	−10.0720	+	5.81509i	−1.28959	+	0.744546i	−0.978581	−	0.205860i	$-0.934001\pi$
$61$	−10.0720	+	5.81509i	−1.28959	+	0.744546i	−0.311011	+	0.950406i	$0.600667\pi$
$62$	−6.15739	+	10.6649i	−0.781990	+	1.35445i
$63$	0.304236	−	2.62820i	0.0383302	−	0.331122i
$64$			7.36614i			0.920767i
$65$	2.43245	−	0.736516i	0.301708	−	0.0913536i
$66$		−	1.75333i		−	0.215820i
$67$	−12.5870	+	3.37267i	−1.53774	+	0.412037i	−0.925536	−	0.378660i	$-0.876385\pi$
$67$	−12.5870	+	3.37267i	−1.53774	+	0.412037i	−0.612207	+	0.790697i	$0.709718\pi$
$68$	15.9489	+	9.20809i	1.93409	+	1.11665i
$69$	0.964326	+	1.67026i	0.116091	+	0.201076i
$70$	−4.21038	+	1.82173i	−0.503237	+	0.217738i
$71$	2.10681	−	7.86274i	0.250033	−	0.933135i	−0.720754	−	0.693191i	$-0.756204\pi$
$71$	2.10681	−	7.86274i	0.250033	−	0.933135i	0.970787	−	0.239944i	$-0.0771291\pi$
$72$	4.87350	+	1.30585i	0.574347	+	0.153896i
$73$	−0.608899	−	0.608899i	−0.0712663	−	0.0712663i	0.670575	−	0.741842i	$-0.266047\pi$
$73$	−0.608899	−	0.608899i	−0.0712663	−	0.0712663i	−0.741842	+	0.670575i	$0.766047\pi$
$74$	−2.59337	−	4.49186i	−0.301474	−	0.522168i
$75$	2.25157	−	3.89983i	0.259989	−	0.450313i
$76$	−13.1660	+	3.52781i	−1.51024	+	0.404668i
$77$	0.694305	−	1.75334i	0.0791234	−	0.199812i
$78$	−6.47026	−	6.06627i	−0.732612	−	0.686870i
$79$	9.81537			1.10432			0.552158	−	0.833740i	$-0.313805\pi$
$79$	9.81537			1.10432			0.552158	+	0.833740i	$0.313805\pi$
$80$	−0.786133	−	2.93389i	−0.0878924	−	0.328019i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−14.8259	−	25.6792i	−1.63725	−	2.83579i
$83$	2.25452	−	2.25452i	0.247465	−	0.247465i	−0.572464	−	0.819930i	$-0.694012\pi$
$83$	2.25452	−	2.25452i	0.247465	−	0.247465i	0.819930	+	0.572464i	$0.194012\pi$
$84$	8.60436	+	6.39088i	0.938812	+	0.697302i
$85$	3.09523	+	0.829364i	0.335725	+	0.0899572i
$86$	12.8243	−	12.8243i	1.38288	−	1.38288i
$87$	−0.322032	+	0.185925i	−0.0345254	+	0.0199333i
$88$	3.11441	+	1.79810i	0.331997	+	0.191678i
$89$	17.5524	−	4.70315i	1.86055	−	0.498533i	0.860609	−	0.509266i	$-0.170083\pi$
$89$	17.5524	−	4.70315i	1.86055	−	0.498533i	0.999942	+	0.0107329i	$0.00341645\pi$
$90$	1.73395			0.182774
$91$	−4.06809	−	8.62848i	−0.426452	−	0.904510i
$92$	−7.81311			−0.814573
$93$	4.83565	−	1.29571i	0.501433	−	0.134359i
$94$	10.7223	+	6.19052i	1.10592	+	0.638503i
$95$	−2.05395	+	1.18585i	−0.210731	+	0.121665i
$96$	−0.359876	+	0.359876i	−0.0367297	+	0.0367297i
$97$	−8.73810	−	2.34137i	−0.887220	−	0.237730i	−0.213700	−	0.976899i	$-0.568552\pi$
$97$	−8.73810	−	2.34137i	−0.887220	−	0.237730i	−0.673520	+	0.739169i	$0.735218\pi$
$98$	9.07221	+	14.6355i	0.916432	+	1.47841i
$99$	−0.504002	+	0.504002i	−0.0506541	+	0.0506541i
$100$	9.12126	+	15.7985i	0.912126	+	1.57985i
$101$	6.77353	−	11.7321i	0.673991	−	1.16739i	−0.302772	−	0.953063i	$-0.597912\pi$
$101$	6.77353	−	11.7321i	0.673991	−	1.16739i	0.976763	−	0.214324i	$-0.0687547\pi$
$102$	−2.89429	−	10.8016i	−0.286577	−	1.06952i
$103$	−16.4565			−1.62151			−0.810756	−	0.585385i	$-0.800944\pi$
$103$	−16.4565			−1.62151			−0.810756	+	0.585385i	$0.800944\pi$
$104$	17.4109	−	5.27181i	1.70728	−	0.516943i
$105$	1.73396	+	0.686629i	0.169217	+	0.0670081i
$106$	−11.8260	+	3.16877i	−1.14864	+	0.307778i
$107$	8.35835	−	14.4771i	0.808033	−	1.39955i	−0.106192	−	0.994346i	$-0.533866\pi$
$107$	8.35835	−	14.4771i	0.808033	−	1.39955i	0.914225	−	0.405208i	$-0.132801\pi$
$108$	−2.02554	−	3.50833i	−0.194907	−	0.337589i
$109$	1.77768	+	1.77768i	0.170271	+	0.170271i	0.787099	−	0.616827i	$-0.211582\pi$
$109$	1.77768	+	1.77768i	0.170271	+	0.170271i	−0.616827	+	0.787099i	$0.711582\pi$
$110$	1.19379	+	0.319874i	0.113823	+	0.0304988i
$111$	−0.545727	+	2.03668i	−0.0517981	+	0.193313i
$112$	−10.4632	+	4.52718i	−0.988683	+	0.427778i
$113$	−2.96252	−	5.13124i	−0.278691	−	0.482706i	0.692369	−	0.721544i	$-0.256567\pi$
$113$	−2.96252	−	5.13124i	−0.278691	−	0.482706i	−0.971060	+	0.238837i	$0.923234\pi$
$114$	7.16781	+	4.13833i	0.671326	+	0.387591i
$115$	−1.31316	+	0.351860i	−0.122453	+	0.0328111i
$116$		−	1.50639i		−	0.139865i
$117$	0.116127	+	3.60368i	0.0107359	+	0.333160i
$118$		−	9.82893i		−	0.904826i
$119$	1.38306	−	11.9478i	0.126785	−	1.09525i
$120$	−1.77822	+	3.07997i	−0.162329	+	0.281162i
$121$	9.08631	−	5.24598i	0.826028	−	0.476907i
$122$	−20.2296	+	20.2296i	−1.83150	+	1.83150i
$123$	−3.11983	+	11.6434i	−0.281306	+	1.04985i
$124$	−5.24901	+	19.5896i	−0.471375	+	1.75919i
$125$	4.73665	+	4.73665i	0.423659	+	0.423659i
$126$	−0.950401	−	6.43850i	−0.0846684	−	0.573587i
$127$	−17.4169	−	10.0556i	−1.54550	−	0.892293i	−0.998477	−	0.0551724i	$-0.982429\pi$
$127$	−17.4169	−	10.0556i	−1.54550	−	0.892293i	−0.547019	−	0.837120i	$-0.684238\pi$
$128$	4.95322	+	18.4857i	0.437807	+	1.63392i
$129$	−7.37281			−0.649139
$130$	5.31076	−	3.29868i	0.465784	−	0.289313i
$131$			12.0796i			1.05540i	0.849430	+	0.527702i	$0.176946\pi$
$131$			12.0796i			1.05540i	−0.849430	+	0.527702i	$0.823054\pi$
$132$	−0.747332	−	2.78908i	−0.0650469	−	0.242758i
$133$	5.52909	+	6.97675i	0.479433	+	0.604961i
$134$	−27.7603	+	16.0274i	−2.39813	+	1.38456i
$135$	−0.498430	−	0.498430i	−0.0428981	−	0.0428981i
$136$	22.1549	+	5.93640i	1.89977	+	0.509042i
$137$	−13.9883	−	3.74816i	−1.19510	−	0.320227i	−0.394202	−	0.919024i	$-0.628979\pi$
$137$	−13.9883	−	3.74816i	−1.19510	−	0.320227i	−0.800901	+	0.598797i	$0.795646\pi$
$138$	3.35471	+	3.35471i	0.285572	+	0.285572i
$139$	6.95647	−	4.01632i	0.590040	−	0.340660i	−0.175073	−	0.984555i	$-0.556016\pi$
$139$	6.95647	−	4.01632i	0.590040	−	0.340660i	0.765113	+	0.643896i	$0.222683\pi$
$140$	−5.92111	+	4.69250i	−0.500425	+	0.396588i
$141$	−1.30268	−	4.86166i	−0.109705	−	0.409426i
$142$		−	20.0238i		−	1.68036i
$143$	−0.584848	+	2.50248i	−0.0489074	+	0.209268i
$144$	4.30904			0.359087
$145$	−0.0678396	−	0.253181i	−0.00563378	−	0.0210255i
$146$	−1.83446	−	1.05912i	−0.151821	−	0.0876537i
$147$	1.59919	−	6.81488i	0.131899	−	0.562082i
$148$	−6.03996	−	6.03996i	−0.496481	−	0.496481i
$149$	−2.13325	+	7.96140i	−0.174763	+	0.652223i	0.821829	+	0.569734i	$0.192954\pi$
$149$	−2.13325	+	7.96140i	−0.174763	+	0.652223i	−0.996592	+	0.0824894i	$0.973713\pi$
$150$	2.86700	−	10.6998i	0.234089	−	0.873633i
$151$	−4.15300	+	4.15300i	−0.337966	+	0.337966i	−0.855601	−	0.517635i	$-0.826812\pi$
$151$	−4.15300	+	4.15300i	−0.337966	+	0.337966i	0.517635	+	0.855601i	$0.326812\pi$
$152$	−14.7017	+	8.48802i	−1.19246	+	0.688469i
$153$	−2.27300	+	3.93695i	−0.183761	+	0.318284i
$154$	0.533427	−	4.60810i	0.0429848	−	0.371332i
$155$			3.52883i			0.283442i
$156$	−12.8781	−	6.89197i	−1.03108	−	0.551800i
$157$			14.6163i			1.16651i	0.812291	+	0.583253i	$0.198220\pi$
$157$			14.6163i			1.16651i	−0.812291	+	0.583253i	$0.801780\pi$
$158$	23.3220	−	6.24912i	1.85540	−	0.497154i
$159$	4.31031	+	2.48856i	0.341830	+	0.197356i
$160$	−0.179373	−	0.310684i	−0.0141807	−	0.0245617i
$161$	2.02629	+	4.68317i	0.159694	+	0.369085i
$162$	−0.636667	+	2.37607i	−0.0500213	+	0.186682i
$163$	7.35195	+	1.96995i	0.575849	+	0.154298i	0.534978	−	0.844866i	$-0.320320\pi$
$163$	7.35195	+	1.96995i	0.575849	+	0.154298i	0.0408715	+	0.999164i	$0.486987\pi$
$164$	−34.5294	−	34.5294i	−2.69630	−	2.69630i
$165$	−0.251210	−	0.435109i	−0.0195567	−	0.0338732i
$166$	3.92152	−	6.79228i	0.304369	−	0.527183i
$167$	−7.60079	+	2.03663i	−0.588167	+	0.157599i	−0.540615	−	0.841270i	$-0.681809\pi$
$167$	−7.60079	+	2.03663i	−0.588167	+	0.157599i	−0.0475517	+	0.998869i	$0.515142\pi$
$168$	12.4112	+	4.91473i	0.957548	+	0.379180i
$169$	7.21135	+	10.8165i	0.554719	+	0.832038i
$170$	7.88252			0.604562
$171$	−0.870835	−	3.25000i	−0.0665944	−	0.248534i
$172$	14.9339	−	25.8662i	1.13870	−	1.97228i
$173$	−5.36019	−	9.28412i	−0.407528	−	0.705859i	0.587084	−	0.809526i	$-0.300276\pi$
$173$	−5.36019	−	9.28412i	−0.407528	−	0.705859i	−0.994612	+	0.103667i	$0.966942\pi$
$174$	−0.646798	+	0.646798i	−0.0490337	+	0.0490337i
$175$	7.10404	−	9.56453i	0.537015	−	0.723010i
$176$	2.96669	+	0.794922i	0.223623	+	0.0599195i
$177$	−2.82537	+	2.82537i	−0.212368	+	0.212368i
$178$	38.7115	−	22.3501i	2.90155	−	1.67521i
$179$	8.63169	+	4.98351i	0.645163	+	0.372485i	0.786601	−	0.617462i	$-0.211839\pi$
$179$	8.63169	+	4.98351i	0.645163	+	0.372485i	−0.141438	+	0.989947i	$0.545172\pi$
$180$	2.75825	−	0.739070i	0.205588	−	0.0550870i
$181$	3.96508			0.294722			0.147361	−	0.989083i	$-0.452922\pi$
$181$	3.96508			0.294722			0.147361	+	0.989083i	$0.452922\pi$
$182$	−15.1596	−	17.9119i	−1.12370	−	1.32772i
$183$	11.6302			0.859728
$184$	−9.39929	+	2.51853i	−0.692925	+	0.185669i
$185$	−1.28715	−	0.743136i	−0.0946331	−	0.0546365i
$186$	10.6649	−	6.15739i	0.781990	−	0.451482i
$187$	−2.29120	+	2.29120i	−0.167549	+	0.167549i
$188$	19.6949	+	5.27724i	1.43640	+	0.384882i
$189$	−1.57758	+	2.12397i	−0.114752	+	0.154496i
$190$	−4.12534	+	4.12534i	−0.299284	+	0.299284i
$191$	−9.17881	−	15.8982i	−0.664155	−	1.15035i	−0.979514	−	0.201378i	$-0.935458\pi$
$191$	−9.17881	−	15.8982i	−0.664155	−	1.15035i	0.315358	−	0.948973i	$-0.397875\pi$
$192$	3.68307	−	6.37926i	0.265803	−	0.460384i
$193$	4.24786	+	15.8532i	0.305767	+	1.14114i	0.932283	+	0.361731i	$0.117814\pi$
$193$	4.24786	+	15.8532i	0.305767	+	1.14114i	−0.626515	+	0.779409i	$0.715519\pi$
$194$	−22.2531			−1.59768
$195$	−2.47482	−	0.578382i	−0.177225	−	0.0414188i
$196$	20.6696	+	19.4143i	1.47640	+	1.38673i
$197$	5.69553	−	1.52611i	0.405790	−	0.108731i	−0.0501498	−	0.998742i	$-0.515970\pi$
$197$	5.69553	−	1.52611i	0.405790	−	0.108731i	0.455940	+	0.890011i	$0.349303\pi$
$198$	−0.876665	+	1.51843i	−0.0623019	+	0.107910i
$199$	9.61483	+	16.6534i	0.681578	+	1.18053i	0.974499	+	0.224391i	$0.0720391\pi$
$199$	9.61483	+	16.6534i	0.681578	+	1.18053i	−0.292922	+	0.956136i	$0.594628\pi$
$200$	16.0656	+	16.0656i	1.13601	+	1.13601i
$201$	12.5870	+	3.37267i	0.887816	+	0.237890i
$202$	8.62496	−	32.1888i	0.606850	−	2.26480i
$203$	−0.902929	+	0.390675i	−0.0633732	+	0.0274200i
$204$	−9.20809	−	15.9489i	−0.644695	−	1.11665i
$205$	−7.35842	−	4.24839i	−0.513935	−	0.296720i
$206$	−39.1020	+	10.4773i	−2.72436	+	0.729991i
$207$		−	1.92865i		−	0.134051i
$208$	13.1978	−	8.19756i	0.915102	−	0.568398i
$209$		−	2.39821i		−	0.165888i
$210$	4.55716	+	0.527529i	0.314474	+	0.0364030i
$211$	−4.61920	+	8.00070i	−0.317999	+	0.550791i	−0.980070	−	0.198650i	$-0.936344\pi$
$211$	−4.61920	+	8.00070i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$212$	−17.4614	+	10.0813i	−1.19925	+	0.692389i
$213$	−5.75592	+	5.75592i	−0.394389	+	0.394389i
$214$	10.6430	−	39.7201i	0.727539	−	2.71521i
$215$	1.34508	−	5.01991i	0.0917338	−	0.342355i
$216$	−3.56765	−	3.56765i	−0.242748	−	0.242748i
$217$	13.1033	−	1.93420i	0.889507	−	0.131302i
$218$	5.35570	+	3.09212i	0.362734	+	0.209425i
$219$	0.222873	+	0.831772i	0.0150603	+	0.0562060i
$220$	2.03534			0.137223
$221$	0.527913	+	16.3823i	0.0355112	+	1.10200i
$222$			5.18675i			0.348112i
$223$	−0.482353	−	1.80016i	−0.0323007	−	0.120548i	0.947893	−	0.318589i	$-0.103209\pi$
$223$	−0.482353	−	1.80016i	−0.0323007	−	0.120548i	−0.980194	+	0.198041i	$0.936542\pi$
$224$	−1.05531	+	0.836340i	−0.0705112	+	0.0558803i
$225$	−3.89983	+	2.25157i	−0.259989	+	0.150104i
$226$	−10.3061	−	10.3061i	−0.685549	−	0.685549i
$227$	−5.38143	−	1.44195i	−0.357178	−	0.0957056i	0.0757678	−	0.997125i	$-0.475859\pi$
$227$	−5.38143	−	1.44195i	−0.357178	−	0.0957056i	−0.432946	+	0.901420i	$0.642526\pi$
$228$	13.1660	+	3.52781i	0.871938	+	0.233635i
$229$	−0.153144	−	0.153144i	−0.0101200	−	0.0101200i	0.702029	−	0.712149i	$-0.252278\pi$
$229$	−0.153144	−	0.153144i	−0.0101200	−	0.0101200i	−0.712149	+	0.702029i	$0.752278\pi$
$230$	−2.89615	+	1.67209i	−0.190966	+	0.110254i
$231$	−1.47796	+	1.17128i	−0.0972423	+	0.0770648i
$232$	−0.485580	−	1.81221i	−0.0318799	−	0.118977i
$233$			19.7822i			1.29598i	0.761650	+	0.647989i	$0.224390\pi$
$233$			19.7822i			1.29598i	−0.761650	+	0.647989i	$0.775610\pi$
$234$	2.57027	+	8.48868i	0.168024	+	0.554922i
$235$	3.54781			0.231434
$236$	−4.18944	−	15.6352i	−0.272710	−	1.01777i
$237$	−8.50036	−	4.90769i	−0.552158	−	0.318788i
$238$	−4.32053	−	29.2694i	−0.280058	−	1.89726i
$239$	−0.636908	−	0.636908i	−0.0411982	−	0.0411982i	0.686208	−	0.727406i	$-0.259274\pi$
$239$	−0.636908	−	0.636908i	−0.0411982	−	0.0411982i	−0.727406	+	0.686208i	$0.759274\pi$
$240$	−0.786133	+	2.93389i	−0.0507447	+	0.189382i
$241$	5.16499	−	19.2760i	0.332706	−	1.24168i	−0.573629	−	0.819116i	$-0.694465\pi$
$241$	5.16499	−	19.2760i	0.332706	−	1.24168i	0.906335	−	0.422561i	$-0.138869\pi$
$242$	18.2498	−	18.2498i	1.17314	−	1.17314i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−23.5574	+	40.8025i	−1.50811	+	2.61212i
$245$	4.34828	+	2.33213i	0.277802	+	0.148994i
$246$			29.6518i			1.89053i
$247$	−8.85003	−	8.29746i	−0.563114	−	0.527955i
$248$			25.2585i			1.60392i
$249$	−3.07973	+	0.825211i	−0.195170	+	0.0522956i
$250$	14.2703	+	8.23896i	0.902533	+	0.521078i
$251$	14.0053	+	24.2580i	0.884010	+	1.53115i	0.846845	+	0.531840i	$0.178499\pi$
$251$	14.0053	+	24.2580i	0.884010	+	1.53115i	0.0371651	+	0.999309i	$0.488167\pi$
$252$	−4.25615	−	9.83684i	−0.268112	−	0.619663i
$253$	0.355793	−	1.32784i	0.0223685	−	0.0834805i
$254$	−47.7858	−	12.8042i	−2.99835	−	0.803405i
$255$	−2.26587	−	2.26587i	−0.141894	−	0.141894i
$256$	16.1723	+	28.0113i	1.01077	+	1.75070i
$257$	−4.51978	+	7.82849i	−0.281936	+	0.488328i	−0.971862	−	0.235553i	$-0.924310\pi$
$257$	−4.51978	+	7.82849i	−0.281936	+	0.488328i	0.689925	+	0.723880i	$0.257643\pi$
$258$	−17.5183	+	4.69402i	−1.09064	+	0.292237i
$259$	−2.05391	+	5.18677i	−0.127624	+	0.322290i
$260$	7.04199	−	7.51095i	0.436726	−	0.465809i
$261$	0.371850			0.0230169
$262$	7.69071	+	28.7021i	0.475134	+	1.77322i
$263$	−11.6573	+	20.1910i	−0.718819	+	1.24503i	0.242649	+	0.970114i	$0.421984\pi$
$263$	−11.6573	+	20.1910i	−0.718819	+	1.24503i	−0.961468	+	0.274917i	$0.911350\pi$
$264$	−1.79810	−	3.11441i	−0.110666	−	0.191678i
$265$	−2.48075	+	2.48075i	−0.152391	+	0.152391i
$266$	17.5794	+	13.0571i	1.07786	+	0.800581i
$267$	−17.5524	−	4.70315i	−1.07419	−	0.287828i
$268$	−37.3278	+	37.3278i	−2.28016	+	2.28016i
$269$	24.9574	−	14.4092i	1.52168	−	0.878543i	0.522010	−	0.852939i	$-0.325182\pi$
$269$	24.9574	−	14.4092i	1.52168	−	0.878543i	0.999672	−	0.0256040i	$-0.00815089\pi$
$270$	−1.50164	−	0.866973i	−0.0913870	−	0.0527623i
$271$	11.9008	−	3.18880i	0.722920	−	0.193706i	0.121446	−	0.992598i	$-0.461247\pi$
$271$	11.9008	−	3.18880i	0.722920	−	0.193706i	0.601474	+	0.798892i	$0.294580\pi$
$272$	19.5889			1.18775
$273$	−0.791166	+	9.50653i	−0.0478836	+	0.575361i
$274$	−35.6236			−2.15210
$275$	−3.10032	+	0.830728i	−0.186956	+	0.0500948i
$276$	6.76635	+	3.90656i	0.407287	+	0.235147i
$277$	−12.3959	+	7.15677i	−0.744797	+	0.430009i	−0.823811	−	0.566865i	$-0.808156\pi$
$277$	−12.3959	+	7.15677i	−0.744797	+	0.430009i	0.0790140	+	0.996874i	$0.474823\pi$
$278$	13.9720	−	13.9720i	0.837987	−	0.837987i
$279$	−4.83565	−	1.29571i	−0.289503	−	0.0775720i
$280$	−5.61057	+	7.55379i	−0.335296	+	0.451425i
$281$	−10.7886	+	10.7886i	−0.643591	+	0.643591i	−0.951437	−	0.307845i	$-0.900392\pi$
$281$	−10.7886	+	10.7886i	−0.643591	+	0.643591i	0.307845	+	0.951437i	$0.400392\pi$
$282$	−6.19052	−	10.7223i	−0.368640	−	0.638503i
$283$	6.96923	−	12.0711i	0.414278	−	0.717550i	−0.581075	−	0.813850i	$-0.697368\pi$
$283$	6.96923	−	12.0711i	0.414278	−	0.717550i	0.995352	+	0.0963004i	$0.0307009\pi$
$284$	−8.53485	−	31.8525i	−0.506450	−	1.89010i
$285$	2.37170			0.140487
$286$	0.203609	+	6.31844i	0.0120396	+	0.373617i
$287$	−11.7419	+	29.6519i	−0.693101	+	1.75030i
$288$	0.491600	−	0.131724i	0.0289678	−	0.00776190i
$289$	−1.83307	+	3.17497i	−0.107828	+	0.186763i
$290$	−0.322384	−	0.558385i	−0.0189310	−	0.0327895i
$291$	6.39674	+	6.39674i	0.374983	+	0.374983i
$292$	−3.36957	−	0.902873i	−0.197189	−	0.0528367i
$293$	4.49081	−	16.7599i	0.262356	−	0.979126i	−0.701493	−	0.712677i	$-0.747483\pi$
$293$	4.49081	−	16.7599i	0.262356	−	0.979126i	0.963849	−	0.266450i	$-0.0858506\pi$
$294$	−0.539020	−	17.2108i	−0.0314363	−	1.00375i
$295$	−1.40825	−	2.43916i	−0.0819915	−	0.142013i
$296$	−9.21312	−	5.31920i	−0.535502	−	0.309172i
$297$	0.688480	−	0.184478i	0.0399497	−	0.0107045i
$298$			20.2750i			1.17450i
$299$	−3.66909	−	5.90711i	−0.212189	−	0.341617i
$300$		−	18.2425i		−	1.05323i
$301$	−19.3772	−	2.24308i	−1.11688	−	0.129289i
$302$	−7.22375	+	12.5119i	−0.415680	+	0.719980i
$303$	−11.7321	+	6.77353i	−0.673991	+	0.389129i
$304$	−10.2519	+	10.2519i	−0.587988	+	0.587988i
$305$	−2.12179	+	7.91863i	−0.121493	+	0.453419i
$306$	−2.89429	+	10.8016i	−0.165456	+	0.617489i
$307$	14.5281	+	14.5281i	0.829164	+	0.829164i	0.987401	−	0.158237i	$-0.0505810\pi$
$307$	14.5281	+	14.5281i	0.829164	+	0.829164i	−0.158237	+	0.987401i	$0.550581\pi$
$308$	−1.11560	−	7.55763i	−0.0635672	−	0.430636i
$309$	14.2518	+	8.22827i	0.810756	+	0.468090i
$310$	2.24669	+	8.38475i	0.127603	+	0.476222i
$311$	−7.52888			−0.426924			−0.213462	−	0.976951i	$-0.568474\pi$
$311$	−7.52888			−0.426924			−0.213462	+	0.976951i	$0.568474\pi$
$312$	−17.7142	−	4.13992i	−1.00287	−	0.234377i
$313$			7.90713i			0.446938i	0.974711	+	0.223469i	$0.0717381\pi$
$313$			7.90713i			0.446938i	−0.974711	+	0.223469i	$0.928262\pi$
$314$	9.30570	+	34.7293i	0.525151	+	1.95989i
$315$	−1.15833	−	1.46162i	−0.0652648	−	0.0823527i
$316$	34.4356	−	19.8814i	1.93715	−	1.11842i
$317$	12.2598	+	12.2598i	0.688580	+	0.688580i	0.961918	−	0.273338i	$-0.0881278\pi$
$317$	12.2598	+	12.2598i	0.688580	+	0.688580i	−0.273338	+	0.961918i	$0.588128\pi$
$318$	11.8260	+	3.16877i	0.663169	+	0.177696i
$319$	0.256011	+	0.0685980i	0.0143339	+	0.00384075i
$320$	3.67151	+	3.67151i	0.205243	+	0.205243i
$321$	−14.4771	+	8.35835i	−0.808033	+	0.466518i
$322$	7.79623	+	9.83748i	0.434467	+	0.548221i
$323$	−3.95882	−	14.7745i	−0.220274	−	0.822075i
$324$			4.05107i			0.225060i
$325$	−7.66105	+	14.3152i	−0.424959	+	0.794065i
$326$	18.7230			1.03697
$327$	−0.650678	−	2.42836i	−0.0359826	−	0.134289i
$328$	−52.6699	−	30.4090i	−2.90821	−	1.67905i
$329$	−1.94461	−	13.1737i	−0.107210	−	0.726292i
$330$	−0.873913	−	0.873913i	−0.0481073	−	0.0481073i
$331$	1.27846	−	4.77126i	0.0702703	−	0.262252i	−0.921849	−	0.387549i	$-0.873322\pi$
$331$	1.27846	−	4.77126i	0.0702703	−	0.262252i	0.992119	+	0.125297i	$0.0399884\pi$
$332$	3.34299	−	12.4762i	0.183470	−	0.684720i
$333$	1.49095	−	1.49095i	0.0817037	−	0.0817037i
$334$	−16.7634	+	9.67835i	−0.917252	+	0.529576i
$335$	−4.59269	+	7.95477i	−0.250925	+	0.434615i
$336$	11.3250	+	1.31097i	0.617831	+	0.0715191i
$337$		−	7.35624i		−	0.400720i	−0.979722	−	0.200360i	$-0.935789\pi$
$337$		−	7.35624i		−	0.400720i	0.979722	−	0.200360i	$-0.0642112\pi$
$338$	24.0212	+	21.1095i	1.30658	+	1.14821i
$339$			5.92505i			0.321804i
$340$	12.5390	−	3.35982i	0.680023	−	0.182212i
$341$	−3.09022	−	1.78414i	−0.167345	−	0.0966165i
$342$	−4.13833	−	7.16781i	−0.223775	−	0.387591i
$343$	6.27632	−	17.4243i	0.338890	−	0.940826i
$344$	9.62778	−	35.9314i	0.519095	−	1.93729i
$345$	1.31316	+	0.351860i	0.0706981	+	0.0189435i
$346$	−18.6471	−	18.6471i	−1.00247	−	1.00247i
$347$	1.58494	+	2.74519i	0.0850839	+	0.147370i	0.905427	−	0.424502i	$-0.139551\pi$
$347$	1.58494	+	2.74519i	0.0850839	+	0.147370i	−0.820343	+	0.571872i	$0.806218\pi$
$348$	−0.753196	+	1.30457i	−0.0403755	+	0.0699325i
$349$	26.0697	−	6.98534i	1.39548	−	0.373917i	0.518758	−	0.854921i	$-0.326395\pi$
$349$	26.0697	−	6.98534i	1.39548	−	0.373917i	0.876718	+	0.481004i	$0.159728\pi$
$350$	10.7903	−	27.2489i	0.576766	−	1.45652i
$351$	1.70127	−	3.17894i	0.0908072	−	0.169679i
$352$	0.362757			0.0193350
$353$	1.36374	+	5.08954i	0.0725845	+	0.270889i	0.992675	−	0.120817i	$-0.0385516\pi$
$353$	1.36374	+	5.08954i	0.0725845	+	0.270889i	−0.920090	+	0.391706i	$0.871885\pi$
$354$	−4.91447	+	8.51210i	−0.261201	+	0.452413i
$355$	−2.86893	−	4.96913i	−0.152267	−	0.263734i
$356$	52.0533	−	52.0533i	2.75882	−	2.75882i
$357$	−7.17167	+	9.65558i	−0.379565	+	0.511027i
$358$	23.6824	+	6.34567i	1.25165	+	0.335379i
$359$	17.8470	−	17.8470i	0.941927	−	0.941927i	−0.0564767	−	0.998404i	$-0.517987\pi$
$359$	17.8470	−	17.8470i	0.941927	−	0.941927i	0.998404	+	0.0564767i	$0.0179867\pi$
$360$	3.07997	−	1.77822i	0.162329	−	0.0937206i
$361$	−6.65034	−	3.83958i	−0.350018	−	0.202083i
$362$	9.42133	−	2.52444i	0.495174	−	0.132682i
$363$	−10.4920			−0.550685
$364$	−31.7495	−	22.0315i	−1.66413	−	1.15476i
$365$	−0.606988			−0.0317712
$366$	27.6342	−	7.40456i	1.44446	−	0.387042i
$367$	−28.6206	−	16.5241i	−1.49398	−	0.862551i	−0.494006	−	0.869458i	$-0.664468\pi$
$367$	−28.6206	−	16.5241i	−1.49398	−	0.862551i	−0.999976	+	0.00690739i	$0.997801\pi$
$368$	−7.19723	+	4.15532i	−0.375181	+	0.216611i
$369$	8.52353	−	8.52353i	0.443717	−	0.443717i
$370$	−3.53149	−	0.946261i	−0.183594	−	0.0491938i
$371$	10.5713	+	7.85179i	0.548832	+	0.407645i
$372$	14.3405	−	14.3405i	0.743523	−	0.743523i
$373$	13.8983	+	24.0726i	0.719627	+	1.24643i	0.961148	+	0.276035i	$0.0890204\pi$
$373$	13.8983	+	24.0726i	0.719627	+	1.24643i	−0.241521	+	0.970396i	$0.577646\pi$
$374$	−3.98532	+	6.90278i	−0.206076	+	0.356934i
$375$	−1.73373	−	6.47039i	−0.0895297	−	0.334129i
$376$	25.3944			1.30962
$377$	1.13891	−	0.707411i	0.0586567	−	0.0364335i
$378$	−2.39618	+	6.05110i	−0.123246	+	0.311235i
$379$	14.6943	−	3.93733i	0.754797	−	0.202247i	0.139152	−	0.990271i	$-0.455562\pi$
$379$	14.6943	−	3.93733i	0.754797	−	0.202247i	0.615645	+	0.788024i	$0.288896\pi$
$380$	−4.80395	+	8.32069i	−0.246438	+	0.426843i
$381$	10.0556	+	17.4169i	0.515165	+	0.892293i
$382$	−31.9314	−	31.9314i	−1.63375	−	1.63375i
$383$	−8.30637	−	2.22568i	−0.424436	−	0.113727i	0.0402774	−	0.999189i	$-0.487176\pi$
$383$	−8.30637	−	2.22568i	−0.424436	−	0.113727i	−0.464713	+	0.885461i	$0.653842\pi$
$384$	4.95322	−	18.4857i	0.252768	−	0.943344i
$385$	−0.527855	−	1.21998i	−0.0269020	−	0.0621759i
$386$	20.1864	+	34.9639i	1.02746	+	1.77962i
$387$	6.38504	+	3.68640i	0.324570	+	0.187390i
$388$	−35.3987	+	9.48505i	−1.79710	+	0.481530i
$389$		−	11.3461i		−	0.575268i	−0.957740	−	0.287634i	$-0.907131\pi$
$389$		−	11.3461i		−	0.575268i	0.957740	−	0.287634i	$-0.0928686\pi$
$390$	−6.24859	+	0.201358i	−0.316410	+	0.0101961i
$391$		−	8.76766i		−	0.443400i
$392$	31.1240	+	16.6929i	1.57200	+	0.843116i
$393$	6.03982	−	10.4613i	0.304669	−	0.527702i
$394$	12.5614	−	7.25232i	0.632833	−	0.365366i
$395$	4.89228	−	4.89228i	0.246157	−	0.246157i
$396$	−0.747332	+	2.78908i	−0.0375549	+	0.140157i
$397$	4.16966	−	15.5614i	0.209269	−	0.781003i	−0.778836	−	0.627227i	$-0.784190\pi$
$397$	4.16966	−	15.5614i	0.209269	−	0.781003i	0.988106	−	0.153776i	$-0.0491435\pi$
$398$	33.4482	+	33.4482i	1.67661	+	1.67661i
$399$	−1.29996	−	8.80659i	−0.0650794	−	0.440881i
$400$	16.8045	+	9.70209i	0.840226	+	0.485105i
$401$	−9.35796	−	34.9244i	−0.467314	−	1.74404i	−0.649101	−	0.760702i	$-0.724855\pi$
$401$	−9.35796	−	34.9244i	−0.467314	−	1.74404i	0.181787	−	0.983338i	$-0.441812\pi$
$402$	32.0548			1.59875
$403$	−17.2757	+	5.23087i	−0.860562	+	0.260568i
$404$		−	54.8801i		−	2.73039i
$405$	0.182438	+	0.680869i	0.00906543	+	0.0338326i
$406$	−1.89670	+	1.50314i	−0.0941314	+	0.0745994i
$407$	1.30154	−	0.751444i	0.0645149	−	0.0372477i
$408$	−16.2185	−	16.2185i	−0.802937	−	0.802937i
$409$	−13.9857	−	3.74745i	−0.691547	−	0.185300i	−0.104106	−	0.994566i	$-0.533198\pi$
$409$	−13.9857	−	3.74745i	−0.691547	−	0.185300i	−0.587441	+	0.809267i	$0.699865\pi$
$410$	−20.1890	−	5.40962i	−0.997062	−	0.267162i
$411$	10.2402	+	10.2402i	0.505110	+	0.505110i
$412$	−57.7350	+	33.3333i	−2.84440	+	1.64221i
$413$	−8.28522	+	6.56606i	−0.407689	+	0.323095i
$414$	−1.22791	−	4.58262i	−0.0603485	−	0.225224i
$415$		−	2.24744i		−	0.110322i
$416$	1.25509	−	1.33867i	0.0615357	−	0.0656337i
$417$	−8.03264			−0.393360
$418$	−1.52686	−	5.69832i	−0.0746812	−	0.278714i
$419$	−19.0889	−	11.0210i	−0.932553	−	0.538410i	−0.0449347	−	0.998990i	$-0.514308\pi$
$419$	−19.0889	−	11.0210i	−0.932553	−	0.538410i	−0.887618	+	0.460580i	$0.847641\pi$
$420$	7.47408	−	1.10327i	0.364698	−	0.0538339i
$421$	−7.69603	−	7.69603i	−0.375082	−	0.375082i	0.494243	−	0.869324i	$-0.335445\pi$
$421$	−7.69603	−	7.69603i	−0.375082	−	0.375082i	−0.869324	+	0.494243i	$0.835445\pi$
$422$	−5.88179	+	21.9511i	−0.286321	+	1.06856i
$423$	−1.30268	+	4.86166i	−0.0633384	+	0.236382i
$424$	−17.7566	+	17.7566i	−0.862338	+	0.862338i
$425$	−17.7286	+	10.2356i	−0.859965	+	0.496501i
$426$	−10.0119	+	17.3411i	−0.485078	+	0.840179i
$427$	30.5665	+	3.53832i	1.47921	+	0.171232i
$428$		−	67.7206i		−	3.27340i
$429$	1.75774	−	1.87479i	0.0848643	−	0.0905158i
$430$		−	12.7840i		−	0.616502i
$431$	−26.2932	+	7.04525i	−1.26650	+	0.339358i	−0.828689	−	0.559709i	$-0.810913\pi$
$431$	−26.2932	+	7.04525i	−1.26650	+	0.339358i	−0.437812	+	0.899067i	$0.644246\pi$
$432$	−3.73174	−	2.15452i	−0.179543	−	0.103659i
$433$	6.55214	+	11.3486i	0.314876	+	0.545381i	0.979411	−	0.201876i	$-0.0647038\pi$
$433$	6.55214	+	11.3486i	0.314876	+	0.545381i	−0.664535	+	0.747257i	$0.731371\pi$
$434$	29.9029	−	12.9382i	1.43538	−	0.621054i
$435$	−0.0678396	+	0.253181i	−0.00325266	+	0.0121391i
$436$	9.83747	+	2.63594i	0.471129	+	0.126239i
$437$	4.58858	+	4.58858i	0.219502	+	0.219502i
$438$	1.05912	+	1.83446i	0.0506069	+	0.0876537i
$439$	−19.9333	+	34.5255i	−0.951364	+	1.64781i	−0.208887	+	0.977940i	$0.566984\pi$
$439$	−19.9333	+	34.5255i	−0.951364	+	1.64781i	−0.742477	+	0.669872i	$0.766349\pi$
$440$	2.44854	−	0.656085i	0.116730	−	0.0312776i
$441$	−4.79238	+	5.10227i	−0.228208	+	0.242965i
$442$	11.6845	+	38.5896i	0.555773	+	1.83552i
$443$	23.0066			1.09308			0.546539	−	0.837433i	$-0.315945\pi$
$443$	23.0066			1.09308			0.546539	+	0.837433i	$0.315945\pi$
$444$	2.21078	+	8.25074i	0.104919	+	0.391563i
$445$	6.40446	−	11.0928i	0.303600	−	0.525851i
$446$	−2.29221	−	3.97023i	−0.108539	−	0.187996i
$447$	5.82815	−	5.82815i	0.275662	−	0.275662i
$448$	11.6206	−	15.6455i	0.549024	−	0.739178i
$449$	15.6281	+	4.18754i	0.737536	+	0.197622i	0.607983	−	0.793950i	$-0.291979\pi$
$449$	15.6281	+	4.18754i	0.737536	+	0.197622i	0.129553	+	0.991572i	$0.458646\pi$
$450$	−7.83278	+	7.83278i	−0.369241	+	0.369241i
$451$	7.44068	−	4.29588i	0.350368	−	0.202285i
$452$	−20.7870	−	12.0014i	−0.977739	−	0.564498i
$453$	5.67310	−	1.52010i	0.266546	−	0.0714207i
$454$	−13.7047			−0.643194
$455$	−6.32836	−	2.27303i	−0.296678	−	0.106561i
$456$	16.9760			0.794976
$457$	0.658952	−	0.176566i	0.0308245	−	0.00825939i	−0.243374	−	0.969933i	$-0.578254\pi$
$457$	0.658952	−	0.176566i	0.0308245	−	0.00825939i	0.274198	+	0.961673i	$0.411588\pi$
$458$	−0.461383	−	0.266380i	−0.0215590	−	0.0124471i
$459$	3.93695	−	2.27300i	0.183761	−	0.106095i
$460$	−3.89429	+	3.89429i	−0.181572	+	0.181572i
$461$	−8.08252	−	2.16570i	−0.376440	−	0.100867i	0.0656375	−	0.997844i	$-0.479092\pi$
$461$	−8.08252	−	2.16570i	−0.376440	−	0.100867i	−0.442078	+	0.896977i	$0.645759\pi$
$462$	−2.76601	+	3.72402i	−0.128687	+	0.173257i
$463$	22.3879	−	22.3879i	1.04045	−	1.04045i	0.0413082	−	0.999146i	$-0.486847\pi$
$463$	22.3879	−	22.3879i	1.04045	−	1.04045i	0.999146	−	0.0413082i	$-0.0131525\pi$
$464$	−0.801158	−	1.38765i	−0.0371928	−	0.0644199i
$465$	1.76441	−	3.05605i	0.0818227	−	0.141721i
$466$	12.5947	+	47.0041i	0.583438	+	2.17742i
$467$	13.5832			0.628554			0.314277	−	0.949331i	$-0.398238\pi$
$467$	13.5832			0.628554			0.314277	+	0.949331i	$0.398238\pi$
$468$	7.70680	+	12.4077i	0.356247	+	0.573546i
$469$	32.0550	+	12.6935i	1.48016	+	0.586130i
$470$	8.42986	−	2.25877i	0.388840	−	0.104189i
$471$	7.30813	−	12.6581i	0.336741	−	0.583253i
$472$	−10.0799	−	17.4589i	−0.463966	−	0.803613i
$473$	3.71591	+	3.71591i	0.170858	+	0.170858i
$474$	−23.3220	−	6.24912i	−1.07122	−	0.287032i
$475$	3.92148	−	14.6352i	0.179930	−	0.671508i
$476$	−19.3485	−	44.7183i	−0.886836	−	2.04966i
$477$	−2.48856	−	4.31031i	−0.113943	−	0.197356i
$478$	−1.91884	−	1.10784i	−0.0877656	−	0.0506715i
$479$	4.03229	−	1.08045i	0.184240	−	0.0493669i	−0.165519	−	0.986207i	$-0.552930\pi$
$479$	4.03229	−	1.08045i	0.184240	−	0.0493669i	0.349759	+	0.936840i	$0.386263\pi$
$480$			0.358746i			0.0163745i
$481$	1.73011	−	7.40292i	0.0788863	−	0.337544i
$482$		−	49.0896i		−	2.23597i
$483$	0.586766	−	5.06889i	0.0266988	−	0.230642i
$484$	21.2518	−	36.8093i	0.965993	−	1.67315i
$485$	−5.52235	+	3.18833i	−0.250757	+	0.144775i
$486$	1.73941	−	1.73941i	0.0789011	−	0.0789011i
$487$	4.28159	−	15.9791i	0.194018	−	0.724083i	−0.798501	−	0.601993i	$-0.794374\pi$
$487$	4.28159	−	15.9791i	0.194018	−	0.724083i	0.992519	−	0.122090i	$-0.0389598\pi$
$488$	−15.1873	+	56.6797i	−0.687496	+	2.56577i
$489$	−5.38200	−	5.38200i	−0.243383	−	0.243383i
$490$	11.8166	+	2.77291i	0.533821	+	0.125267i
$491$	27.7156	+	16.0016i	1.25079	+	0.722143i	0.971266	−	0.237996i	$-0.0764905\pi$
$491$	27.7156	+	16.0016i	1.25079	+	0.722143i	0.279523	+	0.960139i	$0.409824\pi$
$492$	12.6387	+	47.1681i	0.569795	+	2.12650i
$493$	1.69043			0.0761332
$494$	−26.3111	−	14.0809i	−1.18379	−	0.633528i
$495$			0.502420i			0.0225821i
$496$	5.58326	+	20.8370i	0.250696	+	0.935609i
$497$	−16.8789	+	13.3766i	−0.757121	+	0.600021i
$498$	−6.79228	+	3.92152i	−0.304369	+	0.175728i
$499$	−14.4246	−	14.4246i	−0.645734	−	0.645734i	0.306225	−	0.951959i	$-0.400934\pi$
$499$	−14.4246	−	14.4246i	−0.645734	−	0.645734i	−0.951959	+	0.306225i	$0.900934\pi$
$500$	26.2120	+	7.02348i	1.17224	+	0.314100i
$501$	7.60079	+	2.03663i	0.339578	+	0.0909898i
$502$	48.7220	+	48.7220i	2.17457	+	2.17457i
$503$	−23.6349	+	13.6456i	−1.05383	+	0.608427i	−0.923718	−	0.383072i	$-0.874866\pi$
$503$	−23.6349	+	13.6456i	−1.05383	+	0.608427i	−0.130109	+	0.991500i	$0.541533\pi$
$504$	−8.29109	−	10.4619i	−0.369314	−	0.466010i
$505$	−2.47150	−	9.22376i	−0.109980	−	0.410452i
$506$		−	3.38157i		−	0.150329i
$507$	−0.836968	−	12.9730i	−0.0371710	−	0.576152i
$508$	−81.4721			−3.61474
$509$	−8.17110	−	30.4949i	−0.362177	−	1.35166i	−0.871207	−	0.490916i	$-0.836662\pi$
$509$	−8.17110	−	30.4949i	−0.362177	−	1.35166i	0.509030	−	0.860749i	$-0.330004\pi$
$510$	−6.82647	−	3.94126i	−0.302281	−	0.174522i
$511$	0.332699	+	2.25387i	0.0147177	+	0.0997054i
$512$	29.1956	+	29.1956i	1.29027	+	1.29027i
$513$	−0.870835	+	3.25000i	−0.0384483	+	0.143491i
$514$	−5.75519	+	21.4787i	−0.253851	+	0.947383i
$515$	−8.20244	+	8.20244i	−0.361443	+	0.361443i
$516$	−25.8662	+	14.9339i	−1.13870	+	0.657428i
$517$	−1.79374	+	3.10684i	−0.0788884	+	0.136639i
$518$	−1.57800	+	13.6318i	−0.0693332	+	0.598948i
$519$			10.7204i			0.470572i
$520$	6.05048	−	11.3057i	0.265331	−	0.495790i
$521$			13.1042i			0.574107i	0.957915	+	0.287054i	$0.0926758\pi$
$521$			13.1042i			0.574107i	−0.957915	+	0.287054i	$0.907324\pi$
$522$	0.883543	−	0.236745i	0.0386716	−	0.0103620i
$523$	−7.44365	−	4.29760i	−0.325488	−	0.187921i	0.328348	−	0.944557i	$-0.393508\pi$
$523$	−7.44365	−	4.29760i	−0.325488	−	0.187921i	−0.653836	+	0.756636i	$0.726841\pi$
$524$	24.4678	+	42.3794i	1.06888	+	1.85135i
$525$	−10.9345	+	4.73110i	−0.477223	+	0.206482i
$526$	−14.8436	+	55.3971i	−0.647212	+	2.41543i
$527$	−21.9829	−	5.89029i	−0.957589	−	0.256585i
$528$	−2.17177	−	2.17177i	−0.0945140	−	0.0945140i
$529$	−9.64015	−	16.6972i	−0.419137	−	0.725966i
$530$	−4.31503	+	7.47385i	−0.187433	+	0.324643i
$531$	3.85953	−	1.03416i	0.167489	−	0.0448786i
$532$	33.5295	+	13.2774i	1.45369	+	0.575647i
$533$	9.89076	−	42.3213i	0.428417	−	1.83314i
$534$	−44.7002			−1.93437
$535$	−3.04977	−	11.3819i	−0.131853	−	0.492082i
$536$	−32.8734	+	56.9384i	−1.41991	+	2.45936i
$537$	−4.98351	−	8.63169i	−0.215054	−	0.372485i
$538$	50.1269	−	50.1269i	2.16112	−	2.16112i
$539$	−4.24071	+	2.62872i	−0.182660	+	0.113227i
$540$	−2.75825	−	0.739070i	−0.118696	−	0.0318045i
$541$	6.09190	−	6.09190i	0.261911	−	0.261911i	−0.563919	−	0.825830i	$-0.690707\pi$
$541$	6.09190	−	6.09190i	0.261911	−	0.261911i	0.825830	+	0.563919i	$0.190707\pi$
$542$	26.2469	−	15.1537i	1.12740	−	0.650905i
$543$	−3.43386	−	1.98254i	−0.147361	−	0.0850790i
$544$	2.23482	−	0.598817i	0.0958169	−	0.0256741i
$545$	1.77210			0.0759086
$546$	4.17262	+	23.0919i	0.178572	+	0.988243i
$547$	30.2438			1.29313			0.646566	−	0.762858i	$-0.276205\pi$
$547$	30.2438			1.29313			0.646566	+	0.762858i	$0.276205\pi$
$548$	−56.6677	+	15.1841i	−2.42072	+	0.648631i
$549$	−10.0720	−	5.81509i	−0.429864	−	0.248182i
$550$	−6.83769	+	3.94774i	−0.291560	+	0.168332i
$551$	−0.884692	+	0.884692i	−0.0376892	+	0.0376892i
$552$	9.39929	+	2.51853i	0.400060	+	0.107196i
$553$	−20.8476	−	15.4845i	−0.886528	−	0.658468i
$554$	−24.8971	+	24.8971i	−1.05778	+	1.05778i
$555$	0.743136	+	1.28715i	0.0315444	+	0.0546365i
$556$	16.2704	−	28.1812i	0.690019	−	1.19515i
$557$	−11.7586	−	43.8837i	−0.498228	−	1.85941i	−0.511141	−	0.859497i	$-0.670777\pi$
$557$	−11.7586	−	43.8837i	−0.498228	−	1.85941i	0.0129131	−	0.999917i	$-0.495890\pi$
$558$	−12.3148			−0.521327
$559$	26.5692	−	0.856180i	1.12376	−	0.0362126i
$560$	−2.95871	+	7.47168i	−0.125028	+	0.315736i
$561$	3.12983	−	0.838636i	0.132142	−	0.0354072i
$562$	−18.7657	+	32.5031i	−0.791583	+	1.37106i
$563$	12.5992	+	21.8224i	0.530992	+	0.919704i	0.999346	+	0.0361636i	$0.0115137\pi$
$563$	12.5992	+	21.8224i	0.530992	+	0.919704i	−0.468354	+	0.883541i	$0.655153\pi$
$564$	−14.4177	−	14.4177i	−0.607095	−	0.607095i
$565$	−4.03418	−	1.08095i	−0.169719	−	0.0454761i
$566$	8.87415	−	33.1188i	0.373009	−	1.39209i
$567$	2.42821	−	1.05062i	0.101975	−	0.0441221i
$568$	−20.5351	−	35.5679i	−0.861634	−	1.49239i
$569$	13.9572	+	8.05819i	0.585116	+	0.337817i	0.763164	−	0.646205i	$-0.223645\pi$
$569$	13.9572	+	8.05819i	0.585116	+	0.337817i	−0.178048	+	0.984022i	$0.556978\pi$
$570$	5.63532	−	1.50998i	0.236038	−	0.0632461i
$571$			13.5825i			0.568409i	0.958764	+	0.284204i	$0.0917294\pi$
$571$			13.5825i			0.568409i	−0.958764	+	0.284204i	$0.908271\pi$
$572$	3.01703	+	9.96418i	0.126149	+	0.416623i
$573$			18.3576i			0.766900i
$574$	−9.02115	+	77.9308i	−0.376535	+	3.25277i
$575$	4.34249	−	7.52142i	0.181094	−	0.313665i
$576$	−6.37926	+	3.68307i	−0.265803	+	0.153461i
$577$	−33.5657	+	33.5657i	−1.39736	+	1.39736i	−0.589829	+	0.807528i	$0.700805\pi$
$577$	−33.5657	+	33.5657i	−1.39736	+	1.39736i	−0.807528	+	0.589829i	$0.799195\pi$
$578$	−2.33411	+	8.71103i	−0.0970863	+	0.362331i
$579$	4.24786	−	15.8532i	0.176535	−	0.658837i
$580$	−0.750831	−	0.750831i	−0.0311766	−	0.0311766i
$581$	−8.34520	+	1.23185i	−0.346217	+	0.0511059i
$582$	19.2717	+	11.1265i	0.798838	+	0.461209i
$583$	−0.918168	−	3.42665i	−0.0380266	−	0.141917i
$584$	−4.34468			−0.179784
$585$	1.85406	+	1.73830i	0.0766562	+	0.0718700i
$586$		−	42.6820i		−	1.76318i
$587$	6.29368	+	23.4883i	0.259768	+	0.969467i	0.965375	+	0.260864i	$0.0840076\pi$
$587$	6.29368	+	23.4883i	0.259768	+	0.969467i	−0.705607	+	0.708603i	$0.749326\pi$
$588$	−8.19330	−	27.1481i	−0.337886	−	1.11957i
$589$	14.5875	−	8.42210i	0.601067	−	0.347026i
$590$	−4.89904	−	4.89904i	−0.201690	−	0.201690i
$591$	−5.69553	−	1.52611i	−0.234283	−	0.0627759i
$592$	−8.77613	−	2.35156i	−0.360697	−	0.0966484i
$593$	10.0628	+	10.0628i	0.413231	+	0.413231i	0.882863	−	0.469631i	$-0.155613\pi$
$593$	10.0628	+	10.0628i	0.413231	+	0.413231i	−0.469631	+	0.882863i	$0.655613\pi$
$594$	1.51843	−	0.876665i	0.0623019	−	0.0359700i
$595$	−5.26579	−	6.64451i	−0.215876	−	0.272398i
$596$	8.64195	+	32.2522i	0.353988	+	1.32110i
$597$		−	19.2297i		−	0.787018i
$598$	−12.4789	−	11.6997i	−0.510299	−	0.478438i
$599$	15.7719			0.644422			0.322211	−	0.946668i	$-0.395574\pi$
$599$	15.7719			0.644422			0.322211	+	0.946668i	$0.395574\pi$
$600$	−5.88042	−	21.9460i	−0.240067	−	0.895942i
$601$	−18.2565	−	10.5404i	−0.744698	−	0.429952i	0.0790767	−	0.996869i	$-0.474803\pi$
$601$	−18.2565	−	10.5404i	−0.744698	−	0.429952i	−0.823775	+	0.566917i	$0.808136\pi$
$602$	−47.4698	+	7.00712i	−1.93472	+	0.285589i
$603$	−9.21430	−	9.21430i	−0.375235	−	0.375235i
$604$	−6.15805	+	22.9821i	−0.250567	+	0.935130i
$605$	1.91413	−	7.14365i	0.0778206	−	0.290431i
$606$	−23.5638	+	23.5638i	−0.957215	+	0.957215i
$607$	14.6360	−	8.45008i	0.594056	−	0.342978i	−0.172644	−	0.984984i	$-0.555231\pi$
$607$	14.6360	−	8.45008i	0.594056	−	0.342978i	0.766700	+	0.642006i	$0.221898\pi$
$608$	−0.856205	+	1.48299i	−0.0347237	+	0.0601432i
$609$	0.977297	+	0.113130i	0.0396021	+	0.00458427i
$610$			20.1661i			0.816502i
$611$	5.25901	+	17.3686i	0.212757	+	0.702658i
$612$			18.4162i			0.744430i
$613$	17.4644	−	4.67958i	0.705381	−	0.189006i	0.111742	−	0.993737i	$-0.464357\pi$
$613$	17.4644	−	4.67958i	0.705381	−	0.189006i	0.593640	+	0.804731i	$0.297690\pi$
$614$	43.7695	+	25.2703i	1.76639	+	1.01983i
$615$	4.24839	+	7.35842i	0.171312	+	0.296720i
$616$	−3.77826	−	8.73233i	−0.152230	−	0.351836i
$617$	5.54500	−	20.6942i	0.223233	−	0.833118i	−0.759871	−	0.650074i	$-0.774738\pi$
$617$	5.54500	−	20.6942i	0.223233	−	0.833118i	0.983105	−	0.183045i	$-0.0585952\pi$
$618$	39.1020	+	10.4773i	1.57291	+	0.421460i
$619$	−19.4756	−	19.4756i	−0.782790	−	0.782790i	0.197511	−	0.980301i	$-0.436714\pi$
$619$	−19.4756	−	19.4756i	−0.782790	−	0.782790i	−0.980301	+	0.197511i	$0.936714\pi$
$620$	7.14777	+	12.3803i	0.287061	+	0.497205i
$621$	−0.964326	+	1.67026i	−0.0386971	+	0.0670253i
$622$	−17.8892	+	4.79339i	−0.717291	+	0.192197i
$623$	−44.7004	−	17.7009i	−1.79088	−	0.709172i
$624$	−15.5284	+	0.500395i	−0.621634	+	0.0200318i
$625$	−17.7939			−0.711756
$626$	5.03421	+	18.7879i	0.201208	+	0.750917i
$627$	−1.19910	+	2.07691i	−0.0478876	+	0.0829438i
$628$	29.6058	+	51.2787i	1.18140	+	2.04624i
$629$	6.77788	−	6.77788i	0.270252	−	0.270252i
$630$	−3.68285	−	2.73543i	−0.146728	−	0.108982i
$631$	−20.8332	−	5.58224i	−0.829356	−	0.222225i	−0.180923	−	0.983497i	$-0.557909\pi$
$631$	−20.8332	−	5.58224i	−0.829356	−	0.222225i	−0.648433	+	0.761272i	$0.724575\pi$
$632$	35.0178	−	35.0178i	1.39293	−	1.39293i
$633$	8.00070	−	4.61920i	0.317999	−	0.183597i
$634$	36.9357	+	21.3248i	1.46690	+	0.846916i
$635$	−13.6931	+	3.66906i	−0.543395	+	0.145602i
$636$	20.1627			0.799502
$637$	−4.97157	+	24.7444i	−0.196981	+	0.980407i
$638$	0.651976			0.0258120
$639$	7.86274	−	2.10681i	0.311045	−	0.0833443i
$640$	11.6827	+	6.74499i	0.461798	+	0.266619i
$641$	25.3468	−	14.6340i	1.00114	−	0.578006i	0.0925521	−	0.995708i	$-0.470498\pi$
$641$	25.3468	−	14.6340i	1.00114	−	0.578006i	0.908584	+	0.417701i	$0.137164\pi$
$642$	−29.0772	+	29.0772i	−1.14758	+	1.14758i
$643$	−12.4873	−	3.34595i	−0.492449	−	0.131951i	0.00404423	−	0.999992i	$-0.498713\pi$
$643$	−12.4873	−	3.34595i	−0.492449	−	0.131951i	−0.496494	+	0.868040i	$0.665379\pi$
$644$	16.5948	+	12.3258i	0.653927	+	0.485704i
$645$	−3.67483	+	3.67483i	−0.144696	+	0.144696i
$646$	−18.8129	−	32.5849i	−0.740183	−	1.28203i
$647$	18.8428	−	32.6368i	0.740788	−	1.28308i	−0.211348	−	0.977411i	$-0.567785\pi$
$647$	18.8428	−	32.6368i	0.740788	−	1.28308i	0.952137	−	0.305672i	$-0.0988813\pi$
$648$	1.30585	+	4.87350i	0.0512986	+	0.191449i
$649$	2.84798			0.111793
$650$	−9.08921	+	38.8915i	−0.356508	+	1.52545i
$651$	−12.3149	−	4.87656i	−0.482657	−	0.191127i
$652$	29.7833	−	7.98041i	1.16640	−	0.312537i
$653$	−20.0158	+	34.6685i	−0.783280	+	1.35668i	0.146740	+	0.989175i	$0.453122\pi$
$653$	−20.0158	+	34.6685i	−0.783280	+	1.35668i	−0.930021	+	0.367507i	$0.880212\pi$
$654$	−3.09212	−	5.35570i	−0.120911	−	0.209425i
$655$	6.02086	+	6.02086i	0.235255	+	0.235255i
$656$	−50.1717	−	13.4435i	−1.95888	−	0.524879i
$657$	0.222873	−	0.831772i	0.00869509	−	0.0324505i
$658$	−13.0078	−	30.0637i	−0.507097	−	1.17201i
$659$	15.0023	+	25.9848i	0.584407	+	1.01222i	0.994949	+	0.100381i	$0.0320062\pi$
$659$	15.0023	+	25.9848i	0.584407	+	1.01222i	−0.410542	+	0.911842i	$0.634660\pi$
$660$	−1.76266	−	1.01767i	−0.0686113	−	0.0396128i
$661$	19.0751	−	5.11115i	0.741934	−	0.198801i	0.131996	−	0.991250i	$-0.457861\pi$
$661$	19.0751	−	5.11115i	0.741934	−	0.198801i	0.609937	+	0.792450i	$0.291195\pi$
$662$		−	12.1508i		−	0.472255i
$663$	7.73399	−	14.4515i	0.300363	−	0.561249i
$664$		−	16.0866i		−	0.624283i
$665$	6.23329	+	0.721556i	0.241717	+	0.0279807i
$666$	2.59337	−	4.49186i	0.100491	−	0.174056i
$667$	−0.621087	+	0.358585i	−0.0240486	+	0.0138845i
$668$	−22.5408	+	22.5408i	−0.872131	+	0.872131i
$669$	−0.482353	+	1.80016i	−0.0186488	+	0.0695984i
$670$	−5.84803	+	21.8251i	−0.225929	+	0.843178i
$671$	−5.86164	−	5.86164i	−0.226286	−	0.226286i
$672$	1.33210	−	0.196634i	0.0513868	−	0.00758533i
$673$	−39.4906	−	22.7999i	−1.52225	−	0.878872i	−0.999654	−	0.0262924i	$-0.991630\pi$
$673$	−39.4906	−	22.7999i	−1.52225	−	0.878872i	−0.522597	−	0.852580i	$-0.675037\pi$
$674$	−4.68348	−	17.4790i	−0.180401	−	0.673265i
$675$	4.50313			0.173326
$676$	47.2090	+	23.3410i	1.81573	+	0.897730i
$677$			6.55217i			0.251821i	0.992042	+	0.125910i	$0.0401851\pi$
$677$			6.55217i			0.251821i	−0.992042	+	0.125910i	$0.959815\pi$
$678$	3.77228	+	14.0783i	0.144874	+	0.540676i
$679$	14.8658	+	18.7580i	0.570497	+	0.719867i
$680$	14.0016	−	8.08381i	0.536936	−	0.310000i
$681$	3.93948	+	3.93948i	0.150961	+	0.150961i
$682$	−8.47849	−	2.27180i	−0.324658	−	0.0869919i
$683$	42.6432	+	11.4262i	1.63170	+	0.437212i	0.954408	−	0.298504i	$-0.0964875\pi$
$683$	42.6432	+	11.4262i	1.63170	+	0.437212i	0.677290	+	0.735716i	$0.263154\pi$
$684$	−9.63816	−	9.63816i	−0.368524	−	0.368524i
$685$	−8.84040	+	5.10401i	−0.337774	+	0.195014i
$686$	3.81950	−	45.3975i	0.145829	−	1.73328i
$687$	0.0560546	+	0.209199i	0.00213862	+	0.00798143i
$688$		−	31.7697i		−	1.21121i
$689$	−15.8220	−	8.46743i	−0.602769	−	0.322584i
$690$	3.34418			0.127311
$691$	−8.50701	−	31.7486i	−0.323622	−	1.20777i	−0.915690	−	0.401885i	$-0.868355\pi$
$691$	−8.50701	−	31.7486i	−0.323622	−	1.20777i	0.592068	−	0.805888i	$-0.298312\pi$
$692$	−37.6106	−	21.7145i	−1.42974	−	0.825462i
$693$	1.86559	−	0.275384i	0.0708679	−	0.0104610i
$694$	5.51370	+	5.51370i	0.209297	+	0.209297i
$695$	1.46546	−	5.46917i	0.0555881	−	0.207457i
$696$	−0.485580	+	1.81221i	−0.0184059	+	0.0686917i
$697$	38.7480	−	38.7480i	1.46769	−	1.46769i
$698$	57.4961	−	33.1954i	2.17626	−	1.25646i
$699$	9.89112	−	17.1319i	0.374116	−	0.647989i
$700$	5.55004	−	47.9450i	0.209772	−	1.81215i
$701$		−	8.83206i		−	0.333582i	−0.985992	−	0.166791i	$-0.946659\pi$
$701$		−	8.83206i		−	0.333582i	0.985992	−	0.166791i	$-0.0533406\pi$
$702$	2.01842	−	8.63655i	0.0761803	−	0.325965i
$703$			7.09444i			0.267572i
$704$	−5.07144	+	1.35889i	−0.191137	+	0.0512150i
$705$	−3.07249	−	1.77391i	−0.115717	−	0.0668091i
$706$	6.48069	+	11.2249i	0.243904	+	0.422454i
$707$	−32.8950	+	14.2329i	−1.23715	+	0.535282i
$708$	−4.18944	+	15.6352i	−0.157449	+	0.587607i
$709$	28.7065	+	7.69188i	1.07809	+	0.288874i	0.753815	−	0.657087i	$-0.228212\pi$
$709$	28.7065	+	7.69188i	1.07809	+	0.288874i	0.324279	+	0.945961i	$0.394878\pi$
$710$	−9.98046	−	9.98046i	−0.374560	−	0.374560i
$711$	4.90769	+	8.50036i	0.184053	+	0.318788i
$712$	45.8416	−	79.4000i	1.71799	−	2.97564i
$713$	9.32628	−	2.49897i	0.349272	−	0.0935872i
$714$	−10.8930	+	27.5083i	−0.407661	+	1.02947i
$715$	0.955809	+	1.53882i	0.0357452	+	0.0575486i
$716$	40.3771			1.50896
$717$	0.233125	+	0.870032i	0.00870619	+	0.0324920i
$718$	31.0431	−	53.7683i	1.15852	−	2.00662i
$719$	18.6597	+	32.3196i	0.695890	+	1.20532i	0.969880	+	0.243584i	$0.0783233\pi$
$719$	18.6597	+	32.3196i	0.695890	+	1.20532i	−0.273990	+	0.961733i	$0.588343\pi$
$720$	2.14776	−	2.14776i	0.0800421	−	0.0800421i
$721$	34.9532	+	25.9615i	1.30173	+	0.966855i
$722$	−18.2462	−	4.88907i	−0.679055	−	0.181952i
$723$	−14.1110	+	14.1110i	−0.524794	+	0.524794i
$724$	13.9108	−	8.03142i	0.516992	−	0.298485i
$725$	1.45015	+	0.837245i	0.0538573	+	0.0310945i
$726$	−24.9297	+	6.67989i	−0.925227	+	0.247914i
$727$	9.88660			0.366674			0.183337	−	0.983050i	$-0.441310\pi$
$727$	9.88660			0.366674			0.183337	+	0.983050i	$0.441310\pi$
$728$	−45.2969	−	16.2698i	−1.67881	−	0.603001i
$729$	−1.00000			−0.0370370
$730$	−1.44225	+	0.386449i	−0.0533800	+	0.0143031i
$731$	29.0264	+	16.7584i	1.07358	+	0.619832i
$732$	40.8025	−	23.5574i	1.50811	−	0.870705i
$733$	−14.5543	+	14.5543i	−0.537577	+	0.537577i	−0.922817	−	0.385240i	$-0.874119\pi$
$733$	−14.5543	+	14.5543i	−0.537577	+	0.537577i	0.385240	+	0.922817i	$0.374119\pi$
$734$	−78.5250	−	21.0407i	−2.89841	−	0.776626i
$735$	−2.59966	−	4.19383i	−0.0958899	−	0.154692i
$736$	−0.694076	+	0.694076i	−0.0255840	+	0.0255840i
$737$	−4.64403	−	8.04370i	−0.171065	−	0.296293i
$738$	14.8259	−	25.6792i	0.545749	−	0.945264i
$739$	13.1964	+	49.2497i	0.485438	+	1.81168i	0.578079	+	0.815981i	$0.303803\pi$
$739$	13.1964	+	49.2497i	0.485438	+	1.81168i	−0.0926405	+	0.995700i	$0.529531\pi$
$740$	−6.02100			−0.221336
$741$	3.51562	+	11.6108i	0.129150	+	0.426535i
$742$	30.1171	+	11.9261i	1.10563	+	0.437820i
$743$	−13.4007	+	3.59070i	−0.491623	+	0.131730i	−0.496109	−	0.868260i	$-0.665239\pi$
$743$	−13.4007	+	3.59070i	−0.491623	+	0.131730i	0.00448658	+	0.999990i	$0.498572\pi$
$744$	12.6293	−	21.8745i	0.463011	−	0.801959i
$745$	2.90493	+	5.03148i	0.106428	+	0.184339i
$746$	48.3496	+	48.3496i	1.77020	+	1.77020i
$747$	3.07973	+	0.825211i	0.112681	+	0.0301929i
$748$	−3.39737	+	12.6792i	−0.124220	+	0.463597i
$749$	−40.5916	+	17.5630i	−1.48319	+	0.641737i
$750$	−8.23896	−	14.2703i	−0.300844	−	0.521078i
$751$	−7.39608	−	4.27013i	−0.269887	−	0.155819i	0.358949	−	0.933357i	$-0.383135\pi$
$751$	−7.39608	−	4.27013i	−0.269887	−	0.155819i	−0.628836	+	0.777538i	$0.716468\pi$
$752$	20.9491	−	5.61329i	0.763935	−	0.204696i
$753$		−	28.0107i		−	1.02077i
$754$	2.25574	−	2.40597i	0.0821494	−	0.0876201i
$755$			4.13996i			0.150669i
$756$	−1.23248	+	10.6470i	−0.0448250	+	0.387229i
$757$	−5.08375	+	8.80531i	−0.184772	+	0.320034i	−0.943500	−	0.331374i	$-0.892488\pi$
$757$	−5.08375	+	8.80531i	−0.184772	+	0.320034i	0.758728	+	0.651408i	$0.225821\pi$
$758$	32.4080	−	18.7108i	1.17711	−	0.679606i
$759$	−0.972046	+	0.972046i	−0.0352830	+	0.0352830i
$760$	−3.09708	+	11.5585i	−0.112343	+	0.419269i
$761$	−0.975866	+	3.64198i	−0.0353751	+	0.132022i	−0.981355	−	0.192203i	$-0.938437\pi$
$761$	−0.975866	+	3.64198i	−0.0353751	+	0.132022i	0.945980	+	0.324225i	$0.105103\pi$
$762$	34.9816	+	34.9816i	1.26725	+	1.26725i
$763$	−0.971316	−	6.58019i	−0.0351640	−	0.238219i
$764$	−64.4046	−	37.1840i	−2.33008	−	1.34527i
$765$	0.829364	+	3.09523i	0.0299857	+	0.111908i
$766$	−21.1536			−0.764309
$767$	9.85363	−	10.5098i	0.355794	−	0.379488i
$768$		−	32.3446i		−	1.16714i
$769$	1.12134	+	4.18491i	0.0404367	+	0.150912i	0.983192	−	0.182572i	$-0.0584424\pi$
$769$	1.12134	+	4.18491i	0.0404367	+	0.150912i	−0.942756	+	0.333484i	$0.891776\pi$
$770$	−2.03094	−	2.56270i	−0.0731901	−	0.0923531i
$771$	7.82849	−	4.51978i	0.281936	−	0.162776i
$772$	47.0142	+	47.0142i	1.69208	+	1.69208i
$773$	−14.9644	−	4.00970i	−0.538233	−	0.144219i	−0.0205453	−	0.999789i	$-0.506540\pi$
$773$	−14.9644	−	4.00970i	−0.538233	−	0.144219i	−0.517687	+	0.855570i	$0.673207\pi$
$774$	17.5183	+	4.69402i	0.629683	+	0.168723i
$775$	−15.9408	−	15.9408i	−0.572611	−	0.572611i
$776$	−39.5277	+	22.8213i	−1.41896	+	0.819237i
$777$	4.37213	−	3.46492i	0.156849	−	0.124303i
$778$	−7.22366	−	26.9591i	−0.258981	−	0.966529i
$779$			40.5578i			1.45313i
$780$	−9.85402	+	2.98368i	−0.352830	+	0.106833i
$781$	5.80200			0.207612
$782$	−5.58208	−	20.8326i	−0.199615	−	0.744973i
$783$	−0.322032	−	0.185925i	−0.0115085	−	0.00664442i
$784$	29.3656	+	6.89097i	1.04877	+	0.246106i
$785$	7.28519	+	7.28519i	0.260020	+	0.260020i
$786$	7.69071	−	28.7021i	0.274319	−	1.02377i
$787$	−11.1122	+	41.4712i	−0.396106	+	1.47829i	0.423782	+	0.905764i	$0.360702\pi$
$787$	−11.1122	+	41.4712i	−0.396106	+	1.47829i	−0.819888	+	0.572524i	$0.805964\pi$
$788$	16.8906	−	16.8906i	0.601703	−	0.601703i
$789$	20.1910	−	11.6573i	0.718819	−	0.415010i
$790$	8.50966	−	14.7392i	0.302760	−	0.524396i
$791$	−1.80261	+	15.5722i	−0.0640936	+	0.553684i
$792$			3.59621i			0.127786i
$793$	−41.9115	+	1.35058i	−1.48832	+	0.0479604i
$794$		−	39.6297i		−	1.40640i
$795$	3.38876	−	0.908017i	0.120187	−	0.0322040i
$796$	67.4641	+	38.9504i	2.39120	+	1.38056i
$797$	−23.6527	−	40.9678i	−0.837823	−	1.45115i	−0.891711	−	0.452606i	$-0.850495\pi$
$797$	−23.6527	−	40.9678i	−0.837823	−	1.45115i	0.0538875	−	0.998547i	$-0.482839\pi$
$798$	−8.69567	−	20.0975i	−0.307823	−	0.711443i
$799$	−5.92198	+	22.1011i	−0.209505	+	0.781882i
$800$	2.21374	+	0.593170i	0.0782676	+	0.0209717i
$801$	12.8493	+	12.8493i	0.454006	+	0.454006i
$802$	−44.4704	−	77.0250i	−1.57030	−	2.71985i
$803$	0.306887	−	0.531543i	0.0108298	−	0.0187578i
$804$	50.9907	−	13.6629i	1.79830	−	0.481854i
$805$	3.34420	+	1.32427i	0.117867	+	0.0466744i
$806$	−37.7179	+	23.4278i	−1.32856	+	0.825208i
$807$	−28.8184			−1.01445
$808$	−17.6904	−	66.0215i	−0.622347	−	2.32263i
$809$	9.15672	−	15.8599i	0.321933	−	0.557604i	−0.658954	−	0.752183i	$-0.729001\pi$
$809$	9.15672	−	15.8599i	0.321933	−	0.557604i	0.980887	+	0.194579i	$0.0623341\pi$
$810$	0.866973	+	1.50164i	0.0304623	+	0.0527623i
$811$	7.95198	−	7.95198i	0.279232	−	0.279232i	−0.553571	−	0.832802i	$-0.686735\pi$
$811$	7.95198	−	7.95198i	0.279232	−	0.279232i	0.832802	+	0.553571i	$0.186735\pi$
$812$	−2.37645	+	3.19953i	−0.0833970	+	0.112282i
$813$	−11.9008	−	3.18880i	−0.417378	−	0.111836i
$814$	2.61413	−	2.61413i	0.0916253	−	0.0916253i
$815$	4.64632	−	2.68255i	0.162753	−	0.0939658i
$816$	−16.9645	−	9.79445i	−0.593876	−	0.342874i
$817$	−23.9616	+	6.42049i	−0.838311	+	0.224625i
$818$	−35.6169			−1.24532
$819$	5.43843	−	7.83731i	0.190034	−	0.273858i
$820$	−34.4210			−1.20204
$821$	−35.4162	+	9.48973i	−1.23603	+	0.331194i	−0.816926	−	0.576743i	$-0.804323\pi$
$821$	−35.4162	+	9.48973i	−1.23603	+	0.331194i	−0.419107	+	0.907937i	$0.637657\pi$
$822$	30.8509	+	17.8118i	1.07605	+	0.621258i
$823$	−14.5778	+	8.41649i	−0.508150	+	0.293380i	−0.732073	−	0.681226i	$-0.761447\pi$
$823$	−14.5778	+	8.41649i	−0.508150	+	0.293380i	0.223923	+	0.974607i	$0.428114\pi$
$824$	−58.7112	+	58.7112i	−2.04530	+	2.04530i
$825$	3.10032	+	0.830728i	0.107939	+	0.0289222i
$826$	−15.5059	+	20.8764i	−0.539519	+	0.726381i
$827$	−20.4920	+	20.4920i	−0.712578	+	0.712578i	−0.967074	−	0.254496i	$-0.918090\pi$
$827$	−20.4920	+	20.4920i	−0.712578	+	0.712578i	0.254496	+	0.967074i	$0.418090\pi$
$828$	−3.90656	−	6.76635i	−0.135762	−	0.235147i
$829$	2.04801	−	3.54725i	0.0711302	−	0.123201i	−0.828267	−	0.560334i	$-0.810673\pi$
$829$	2.04801	−	3.54725i	0.0711302	−	0.123201i	0.899397	+	0.437133i	$0.144006\pi$
$830$	−1.43087	−	5.34008i	−0.0496662	−	0.185357i
$831$	14.3135			0.496531
$832$	−12.5318	+	23.4165i	−0.434462	+	0.811822i
$833$	−21.7862	+	23.1949i	−0.754846	+	0.803656i
$834$	−19.0861	+	5.11412i	−0.660899	+	0.177087i
$835$	−2.77335	+	4.80358i	−0.0959757	+	0.166235i
$836$	−4.85766	−	8.41371i	−0.168006	−	0.290994i
$837$	3.53994	+	3.53994i	0.122358	+	0.122358i
$838$	−52.3733	−	14.0334i	−1.80920	−	0.484775i
$839$	−8.69536	+	32.4515i	−0.300197	+	1.12035i	0.636804	+	0.771026i	$0.280256\pi$
$839$	−8.69536	+	32.4515i	−0.300197	+	1.12035i	−0.937001	+	0.349326i	$0.886411\pi$
$840$	8.63579	−	3.73649i	0.297963	−	0.128921i
$841$	14.4309	+	24.9950i	0.497616	+	0.861896i
$842$	−23.1861	−	13.3865i	−0.799047	−	0.461330i
$843$	14.7374	−	3.94889i	0.507585	−	0.136007i
$844$			37.4255i			1.28824i
$845$	8.98562	+	1.79691i	0.309115	+	0.0618156i
$846$			12.3810i			0.425669i
$847$	−27.5750	−	3.19204i	−0.947488	−	0.109680i
$848$	−10.7233	+	18.5733i	−0.368240	+	0.637810i
$849$	−12.0711	+	6.96923i	−0.414278	+	0.239183i
$850$	−35.6079	+	35.6079i	−1.22134	+	1.22134i
$851$	−1.05252	+	3.92805i	−0.0360798	+	0.134652i
$852$	−8.53485	+	31.8525i	−0.292399	+	1.09125i
$853$	−6.65000	−	6.65000i	−0.227692	−	0.227692i	0.584036	−	0.811728i	$-0.301473\pi$
$853$	−6.65000	−	6.65000i	−0.227692	−	0.227692i	−0.811728	+	0.584036i	$0.801473\pi$
$854$	74.8809	−	11.0533i	2.56237	−	0.378237i
$855$	−2.05395	−	1.18585i	−0.0702436	−	0.0405551i
$856$	−21.8295	−	81.4688i	−0.746117	−	2.78455i
$857$	38.2819			1.30768			0.653842	−	0.756631i	$-0.273156\pi$
$857$	38.2819			1.30768			0.653842	+	0.756631i	$0.273156\pi$
$858$	2.98289	−	5.57374i	0.101834	−	0.190284i
$859$			16.5870i			0.565942i	0.959128	+	0.282971i	$0.0913201\pi$
$859$			16.5870i			0.565942i	−0.959128	+	0.282971i	$0.908680\pi$
$860$	−5.44902	−	20.3360i	−0.185810	−	0.693453i
$861$	24.9947	−	19.8084i	0.851818	−	0.675068i
$862$	−57.9892	+	33.4801i	−1.97512	+	1.14034i
$863$	−11.6109	−	11.6109i	−0.395240	−	0.395240i	0.481310	−	0.876550i	$-0.340161\pi$
$863$	−11.6109	−	11.6109i	−0.395240	−	0.395240i	−0.876550	+	0.481310i	$0.840161\pi$
$864$	−0.491600	−	0.131724i	−0.0167246	−	0.00448134i
$865$	−7.29917	−	1.95581i	−0.248179	−	0.0664994i
$866$	22.7937	+	22.7937i	0.774560	+	0.774560i
$867$	3.17497	−	1.83307i	0.107828	−	0.0622544i
$868$	42.0528	−	33.3269i	1.42736	−	1.13119i
$869$	1.81072	+	6.75769i	0.0614244	+	0.229239i
$870$			0.644768i			0.0218597i
$871$	−45.7511	−	10.6923i	−1.55022	−	0.362296i
$872$	12.6843			0.429545
$873$	−2.34137	−	8.73810i	−0.0792433	−	0.295740i
$874$	13.8242	+	7.98141i	0.467611	+	0.269975i
$875$	−2.58808	−	17.5329i	−0.0874929	−	0.592721i
$876$	2.46670	+	2.46670i	0.0833419	+	0.0833419i
$877$	−5.37931	+	20.0759i	−0.181646	+	0.677914i	0.813677	+	0.581317i	$0.197462\pi$
$877$	−5.37931	+	20.0759i	−0.181646	+	0.677914i	−0.995324	+	0.0965967i	$0.969204\pi$
$878$	−25.3817	+	94.7260i	−0.856592	+	3.19685i
$879$	−12.2691	+	12.2691i	−0.413827	+	0.413827i
$880$	1.87490	−	1.08247i	0.0632029	−	0.0364902i
$881$	6.22366	−	10.7797i	0.209680	−	0.363177i	−0.741934	−	0.670473i	$-0.766091\pi$
$881$	6.22366	−	10.7797i	0.209680	−	0.363177i	0.951614	+	0.307297i	$0.0994243\pi$
$882$	−8.13860	+	15.1745i	−0.274041	+	0.510952i
$883$			28.9456i			0.974097i	0.873375	+	0.487049i	$0.161927\pi$
$883$			28.9456i			0.974097i	−0.873375	+	0.487049i	$0.838073\pi$
$884$	35.0351	+	56.4054i	1.17836	+	1.89712i
$885$			2.81650i			0.0946756i
$886$	54.6655	−	14.6476i	1.83652	−	0.492095i
$887$	6.26961	+	3.61976i	0.210513	+	0.121540i	0.601550	−	0.798835i	$-0.294550\pi$
$887$	6.26961	+	3.61976i	0.210513	+	0.121540i	−0.391037	+	0.920375i	$0.627883\pi$
$888$	5.31920	+	9.21312i	0.178501	+	0.309172i
$889$	21.1294	+	48.8343i	0.708656	+	1.63785i
$890$	8.15502	−	30.4349i	0.273357	−	1.02018i
$891$	−0.688480	−	0.184478i	−0.0230649	−	0.00618023i
$892$	−5.33855	−	5.33855i	−0.178748	−	0.178748i
$893$	−8.46740	−	14.6660i	−0.283351	−	0.490778i
$894$	10.1375	−	17.5587i	0.339049	−	0.587251i
$895$	6.78623	−	1.81836i	0.226839	−	0.0607812i
$896$	18.6421	−	47.0771i	0.622788	−	1.57274i
$897$	0.223968	+	6.95025i	0.00747808	+	0.232062i
$898$	39.7996			1.32813
$899$	0.481809	+	1.79814i	0.0160692	+	0.0599712i
$900$	−9.12126	+	15.7985i	−0.304042	+	0.526616i
$901$	−11.3130	−	19.5947i	−0.376891	−	0.652794i
$902$	14.9446	−	14.9446i	0.497600	−	0.497600i
$903$	15.6596	+	11.6312i	0.521120	+	0.387061i
$904$	−28.8757	−	7.73722i	−0.960391	−	0.257336i
$905$	1.97632	−	1.97632i	0.0656950	−	0.0656950i
$906$	12.5119	−	7.22375i	0.415680	−	0.239993i
$907$	0.515467	+	0.297605i	0.0171158	+	0.00988182i	0.508533	−	0.861042i	$-0.330188\pi$
$907$	0.515467	+	0.297605i	0.0171158	+	0.00988182i	−0.491418	+	0.870924i	$0.663521\pi$
$908$	−21.8006	+	5.84144i	−0.723477	+	0.193855i
$909$	13.5471			0.449327
$910$	−16.4838	−	1.37184i	−0.546433	−	0.0454760i
$911$	−23.8117			−0.788915			−0.394458	−	0.918914i	$-0.629068\pi$
$911$	−23.8117			−0.788915			−0.394458	+	0.918914i	$0.629068\pi$
$912$	14.0044	−	3.75246i	0.463731	−	0.124256i
$913$	1.96810	+	1.13628i	0.0651345	+	0.0376054i
$914$	1.45331	−	0.839066i	0.0480711	−	0.0277538i
$915$	5.79684	−	5.79684i	0.191638	−	0.191638i
$916$	−0.847479	−	0.227081i	−0.0280015	−	0.00750297i
$917$	19.0566	−	25.6568i	0.629303	−	0.847263i
$918$	7.90735	−	7.90735i	0.260981	−	0.260981i
$919$	−2.86358	−	4.95987i	−0.0944609	−	0.163611i	0.814923	−	0.579570i	$-0.196779\pi$
$919$	−2.86358	−	4.95987i	−0.0944609	−	0.163611i	−0.909383	+	0.415959i	$0.863446\pi$
$920$	−3.42958	+	5.94020i	−0.113070	+	0.195843i
$921$	−5.31766	−	19.8458i	−0.175223	−	0.653941i
$922$	−20.5835			−0.677881
$923$	20.0741	−	21.4109i	0.660747	−	0.704749i
$924$	−2.81268	+	7.10290i	−0.0925304	+	0.233668i
$925$	9.17144	−	2.45748i	0.301555	−	0.0808015i
$926$	38.9417	−	67.4490i	1.27970	−	2.21651i
$927$	−8.22827	−	14.2518i	−0.270252	−	0.468090i
$928$	−0.133820	−	0.133820i	−0.00439286	−	0.00439286i
$929$	23.7758	+	6.37070i	0.780058	+	0.209016i	0.626810	−	0.779172i	$-0.284360\pi$
$929$	23.7758	+	6.37070i	0.780058	+	0.209016i	0.153247	+	0.988188i	$0.451027\pi$
$930$	2.24669	−	8.38475i	0.0736718	−	0.274947i
$931$	−0.737273	−	23.5410i	−0.0241631	−	0.771524i
$932$	40.0696	+	69.4026i	1.31252	+	2.27336i
$933$	6.52020	+	3.76444i	0.213462	+	0.123242i
$934$	32.2746	−	8.64795i	1.05606	−	0.282970i
$935$			2.28400i			0.0746949i
$936$	13.2710	+	12.4424i	0.433775	+	0.406691i
$937$		−	26.2867i		−	0.858749i	−0.903127	−	0.429374i	$-0.858734\pi$
$937$		−	26.2867i		−	0.858749i	0.903127	−	0.429374i	$-0.141266\pi$
$938$	84.2466	+	9.75225i	2.75075	+	0.318422i
$939$	3.95357	−	6.84778i	0.129020	−	0.223469i
$940$	12.4469	−	7.18622i	0.405973	−	0.234389i
$941$	2.11330	−	2.11330i	0.0688916	−	0.0688916i	−0.671821	−	0.740713i	$-0.734488\pi$
$941$	2.11330	−	2.11330i	0.0688916	−	0.0688916i	0.740713	+	0.671821i	$0.234488\pi$
$942$	9.30570	−	34.7293i	0.303196	−	1.13154i
$943$	−6.01707	+	22.4560i	−0.195943	+	0.731268i
$944$	−12.1746	−	12.1746i	−0.396250	−	0.396250i
$945$	0.272339	+	1.84496i	0.00885920	+	0.0600167i
$946$	11.1951	+	6.46348i	0.363983	+	0.210146i
$947$	−0.631600	−	2.35716i	−0.0205243	−	0.0765976i	0.954904	−	0.296914i	$-0.0959576\pi$
$947$	−0.631600	−	2.35716i	−0.0205243	−	0.0765976i	−0.975428	+	0.220317i	$0.929291\pi$
$948$	−39.7628			−1.29143
$949$	−0.899753	−	2.97156i	−0.0292072	−	0.0964609i
$950$		−	37.2709i		−	1.20923i
$951$	−4.48741	−	16.7472i	−0.145514	−	0.543066i
$952$	−37.6913	−	47.5599i	−1.22158	−	1.54142i
$953$	−11.0082	+	6.35559i	−0.356591	+	0.205878i	−0.667584	−	0.744534i	$-0.732672\pi$
$953$	−11.0082	+	6.35559i	−0.356591	+	0.205878i	0.310994	+	0.950412i	$0.399338\pi$
$954$	−8.65724	−	8.65724i	−0.280288	−	0.280288i
$955$	−12.4991	−	3.34913i	−0.404462	−	0.108375i
$956$	−3.52456	−	0.944404i	−0.113993	−	0.0305442i
$957$	−0.187413	−	0.187413i	−0.00605821	−	0.00605821i
$958$	8.89312	−	5.13445i	0.287324	−	0.165886i
$959$	23.7978	+	30.0286i	0.768470	+	0.969675i
$960$	−1.34386	−	5.01537i	−0.0433730	−	0.161870i
$961$			5.93766i			0.191537i
$962$	−0.602320	−	18.6914i	−0.0194196	−	0.602634i
$963$	16.7167			0.538688
$964$	−20.9237	−	78.0885i	−0.673908	−	2.51506i
$965$	10.0190	+	5.78446i	0.322523	+	0.186209i
$966$	−1.83299	−	12.4176i	−0.0589756	−	0.399531i
$967$	−12.3880	−	12.3880i	−0.398371	−	0.398371i	0.479287	−	0.877658i	$-0.340895\pi$
$967$	−12.3880	−	12.3880i	−0.398371	−	0.398371i	−0.877658	+	0.479287i	$0.840895\pi$
$968$	13.7009	−	51.1326i	0.440365	−	1.64346i
$969$	−3.95882	+	14.7745i	−0.127175	+	0.474625i
$970$	−11.0916	+	11.0916i	−0.356130	+	0.356130i
$971$	−6.20175	+	3.58058i	−0.199024	+	0.114906i	−0.596200	−	0.802836i	$-0.703323\pi$
$971$	−6.20175	+	3.58058i	−0.199024	+	0.114906i	0.397176	+	0.917742i	$0.369990\pi$
$972$	2.02554	−	3.50833i	0.0649691	−	0.112530i
$973$	−21.1114	−	2.44382i	−0.676800	−	0.0783453i
$974$		−	40.6935i		−	1.30390i
$975$	13.7923	−	8.56680i	0.441706	−	0.274357i
$976$			50.1149i			1.60414i
$977$	−3.17102	+	0.849671i	−0.101450	+	0.0271834i	−0.309187	−	0.951001i	$-0.600057\pi$
$977$	−3.17102	+	0.849671i	−0.101450	+	0.0271834i	0.207737	+	0.978185i	$0.433390\pi$
$978$	−16.2146	−	9.36149i	−0.518485	−	0.299348i
$979$	6.47605	+	11.2169i	0.206976	+	0.358492i
$980$	19.9790	−	0.625717i	0.638207	−	0.0199878i
$981$	−0.650678	+	2.42836i	−0.0207745	+	0.0775317i
$982$	76.0421	+	20.3754i	2.42660	+	0.650206i
$983$	10.1688	+	10.1688i	0.324335	+	0.324335i	0.850428	−	0.526092i	$-0.176343\pi$
$983$	10.1688	+	10.1688i	0.324335	+	0.324335i	−0.526092	+	0.850428i	$0.676343\pi$
$984$	30.4090	+	52.6699i	0.969402	+	1.67905i
$985$	2.07817	−	3.59949i	0.0662159	−	0.114689i
$986$	4.01659	−	1.07624i	0.127914	−	0.0342745i
$987$	−4.90279	+	12.3811i	−0.156058	+	0.394095i
$988$	−47.8557	−	11.1842i	−1.52249	−	0.355816i
$989$	−14.2196			−0.452156
$990$	0.319874	+	1.19379i	0.0101663	+	0.0379411i
$991$	−4.87954	+	8.45161i	−0.155004	+	0.268474i	−0.933060	−	0.359720i	$-0.882872\pi$
$991$	−4.87954	+	8.45161i	−0.155004	+	0.268474i	0.778057	+	0.628194i	$0.216206\pi$
$992$	1.27394	+	2.20653i	0.0404476	+	0.0700574i
$993$	−3.49281	+	3.49281i	−0.110841	+	0.110841i
$994$	−31.5891	+	42.5299i	−1.00194	+	1.34897i
$995$	13.0929	+	3.50823i	0.415072	+	0.111218i
$996$	−9.13321	+	9.13321i	−0.289397	+	0.289397i
$997$	−27.8354	+	16.0708i	−0.881555	+	0.508966i	−0.871171	−	0.490980i	$-0.836639\pi$
$997$	−27.8354	+	16.0708i	−0.881555	+	0.508966i	−0.0103840	+	0.999946i	$0.503305\pi$
$998$	−43.4576	−	25.0903i	−1.37563	−	0.794218i
$999$	−2.03668	+	0.545727i	−0.0644377	+	0.0172660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.by.c.202.8	✓	32
3.2	odd	2		819.2.fm.f.748.1		32
7.6	odd	2		273.2.by.d.202.8	yes	32
13.2	odd	12		273.2.by.d.223.8	yes	32
21.20	even	2		819.2.fm.e.748.1		32
39.2	even	12		819.2.fm.e.496.1		32
91.41	even	12	inner	273.2.by.c.223.8	yes	32
273.41	odd	12		819.2.fm.f.496.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.202.8	✓	32	1.1	even	1	trivial
273.2.by.c.223.8	yes	32	91.41	even	12	inner
273.2.by.d.202.8	yes	32	7.6	odd	2
273.2.by.d.223.8	yes	32	13.2	odd	12
819.2.fm.e.496.1		32	39.2	even	12
819.2.fm.e.748.1		32	21.20	even	2
819.2.fm.f.496.1		32	273.41	odd	12
819.2.fm.f.748.1		32	3.2	odd	2

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.37607 - 0.636667i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(3.50833 - 2.02554i) q^{4} +(0.498430 - 0.498430i) q^{5} +(-2.37607 - 0.636667i) q^{6} +(-2.12397 - 1.57758i) q^{7} +(3.56765 - 3.56765i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(2.37607 - 0.636667i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(3.50833 - 2.02554i) q^{4} +(0.498430 - 0.498430i) q^{5} +(-2.37607 - 0.636667i) q^{6} +(-2.12397 - 1.57758i) q^{7} +(3.56765 - 3.56765i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.866973 - 1.50164i) q^{10} +(0.184478 + 0.688480i) q^{11} -4.05107 q^{12} +(3.17894 + 1.70127i) q^{13} +(-6.05110 - 2.39618i) q^{14} +(-0.680869 + 0.182438i) q^{15} +(2.15452 - 3.73174i) q^{16} +(2.27300 + 3.93695i) q^{17} +(1.73941 + 1.73941i) q^{18} +(-3.25000 - 0.870835i) q^{19} +(0.739070 - 2.75825i) q^{20} +(1.05062 + 2.42821i) q^{21} +(0.876665 + 1.51843i) q^{22} +(-1.67026 - 0.964326i) q^{23} +(-4.87350 + 1.30585i) q^{24} +4.50313i q^{25} +(8.63655 + 2.01842i) q^{26} -1.00000i q^{27} +(-10.6470 - 1.23248i) q^{28} +(0.185925 - 0.322032i) q^{29} +(-1.50164 + 0.866973i) q^{30} +(-3.53994 + 3.53994i) q^{31} +(0.131724 - 0.491600i) q^{32} +(0.184478 - 0.688480i) q^{33} +(7.90735 + 7.90735i) q^{34} +(-1.84496 + 0.272339i) q^{35} +(3.50833 + 2.02554i) q^{36} +(-0.545727 - 2.03668i) q^{37} -8.27667 q^{38} +(-1.90241 - 3.06282i) q^{39} -3.55645i q^{40} +(-3.11983 - 11.6434i) q^{41} +(4.04232 + 5.10070i) q^{42} +(6.38504 - 3.68640i) q^{43} +(2.04175 + 2.04175i) q^{44} +(0.680869 + 0.182438i) q^{45} +(-4.58262 - 1.22791i) q^{46} +(3.55898 + 3.55898i) q^{47} +(-3.73174 + 2.15452i) q^{48} +(2.02250 + 6.70145i) q^{49} +(2.86700 + 10.6998i) q^{50} -4.54600i q^{51} +(14.5988 - 0.470438i) q^{52} -4.97712 q^{53} +(-0.636667 - 2.37607i) q^{54} +(0.435109 + 0.251210i) q^{55} +(-13.2058 + 1.94934i) q^{56} +(2.37916 + 2.37916i) q^{57} +(0.236745 - 0.883543i) q^{58} +(1.03416 - 3.85953i) q^{59} +(-2.01918 + 2.01918i) q^{60} +(-10.0720 + 5.81509i) q^{61} +(-6.15739 + 10.6649i) q^{62} +(0.304236 - 2.62820i) q^{63} +7.36614i q^{64} +(2.43245 - 0.736516i) q^{65} -1.75333i q^{66} +(-12.5870 + 3.37267i) q^{67} +(15.9489 + 9.20809i) q^{68} +(0.964326 + 1.67026i) q^{69} +(-4.21038 + 1.82173i) q^{70} +(2.10681 - 7.86274i) q^{71} +(4.87350 + 1.30585i) q^{72} +(-0.608899 - 0.608899i) q^{73} +(-2.59337 - 4.49186i) q^{74} +(2.25157 - 3.89983i) q^{75} +(-13.1660 + 3.52781i) q^{76} +(0.694305 - 1.75334i) q^{77} +(-6.47026 - 6.06627i) q^{78} +9.81537 q^{79} +(-0.786133 - 2.93389i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-14.8259 - 25.6792i) q^{82} +(2.25452 - 2.25452i) q^{83} +(8.60436 + 6.39088i) q^{84} +(3.09523 + 0.829364i) q^{85} +(12.8243 - 12.8243i) q^{86} +(-0.322032 + 0.185925i) q^{87} +(3.11441 + 1.79810i) q^{88} +(17.5524 - 4.70315i) q^{89} +1.73395 q^{90} +(-4.06809 - 8.62848i) q^{91} -7.81311 q^{92} +(4.83565 - 1.29571i) q^{93} +(10.7223 + 6.19052i) q^{94} +(-2.05395 + 1.18585i) q^{95} +(-0.359876 + 0.359876i) q^{96} +(-8.73810 - 2.34137i) q^{97} +(9.07221 + 14.6355i) q^{98} +(-0.504002 + 0.504002i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9	\( 32 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 16 q^{9} - 2 q^{10} - 4 q^{11} - 32 q^{12} - 6 q^{13} + 34 q^{14} + 4 q^{15} + 14 q^{16} + 8 q^{17} + 2 q^{18} - 2 q^{19} - 44 q^{20} + 2 q^{21} - 4 q^{22} - 18 q^{23} - 4 q^{24} + 28 q^{26} - 18 q^{28} - 18 q^{29} + 14 q^{31} - 8 q^{32} - 4 q^{33} + 66 q^{34} - 20 q^{35} + 6 q^{36} - 24 q^{37} - 24 q^{38} + 8 q^{39} + 16 q^{42} - 6 q^{43} - 20 q^{44} - 4 q^{45} - 58 q^{46} + 28 q^{47} + 60 q^{48} + 10 q^{49} + 70 q^{50} - 28 q^{52} - 80 q^{53} + 4 q^{54} - 60 q^{55} - 120 q^{56} + 16 q^{57} - 4 q^{58} + 42 q^{59} - 58 q^{60} - 36 q^{61} - 52 q^{62} + 2 q^{63} + 14 q^{65} + 26 q^{67} + 72 q^{68} - 2 q^{69} + 68 q^{70} - 4 q^{71} + 4 q^{72} - 12 q^{73} - 18 q^{74} - 16 q^{75} + 48 q^{76} - 28 q^{77} - 14 q^{78} - 4 q^{79} + 98 q^{80} - 16 q^{81} - 20 q^{82} + 36 q^{83} + 32 q^{84} - 10 q^{85} - 40 q^{86} + 96 q^{88} + 54 q^{89} - 4 q^{90} - 54 q^{91} - 4 q^{92} + 2 q^{93} + 60 q^{95} - 22 q^{96} + 40 q^{97} + 4 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 16 * q^9 - 2 * q^10 - 4 * q^11 - 32 * q^12 - 6 * q^13 + 34 * q^14 + 4 * q^15 + 14 * q^16 + 8 * q^17 + 2 * q^18 - 2 * q^19 - 44 * q^20 + 2 * q^21 - 4 * q^22 - 18 * q^23 - 4 * q^24 + 28 * q^26 - 18 * q^28 - 18 * q^29 + 14 * q^31 - 8 * q^32 - 4 * q^33 + 66 * q^34 - 20 * q^35 + 6 * q^36 - 24 * q^37 - 24 * q^38 + 8 * q^39 + 16 * q^42 - 6 * q^43 - 20 * q^44 - 4 * q^45 - 58 * q^46 + 28 * q^47 + 60 * q^48 + 10 * q^49 + 70 * q^50 - 28 * q^52 - 80 * q^53 + 4 * q^54 - 60 * q^55 - 120 * q^56 + 16 * q^57 - 4 * q^58 + 42 * q^59 - 58 * q^60 - 36 * q^61 - 52 * q^62 + 2 * q^63 + 14 * q^65 + 26 * q^67 + 72 * q^68 - 2 * q^69 + 68 * q^70 - 4 * q^71 + 4 * q^72 - 12 * q^73 - 18 * q^74 - 16 * q^75 + 48 * q^76 - 28 * q^77 - 14 * q^78 - 4 * q^79 + 98 * q^80 - 16 * q^81 - 20 * q^82 + 36 * q^83 + 32 * q^84 - 10 * q^85 - 40 * q^86 + 96 * q^88 + 54 * q^89 - 4 * q^90 - 54 * q^91 - 4 * q^92 + 2 * q^93 + 60 * q^95 - 22 * q^96 + 40 * q^97 + 4 * q^99

Introduction

L-functions

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