LMFDB - Embedded newform 352.2.bc.a.19.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(19,352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(40))

chi = DirichletCharacter(H, H._module([20, 35, 12]))

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

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

chi := DirichletCharacter("352.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.bc (of order $40$, degree $16$, 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:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$736$
Relative dimension:	$46$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			19.20
Character	$\chi$	$=$	352.19
Dual form			352.2.bc.a.315.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.362021 + 1.36709i) q^{2} +(-0.202587 + 2.57412i) q^{3} +(-1.73788 - 0.989833i) q^{4} +(-1.06398 - 0.255438i) q^{5} +(-3.44571 - 1.20884i) q^{6} +(-1.31451 - 2.57988i) q^{7} +(1.98234 - 2.01750i) q^{8} +(-3.62197 - 0.573664i) q^{9} +(0.734389 - 1.36208i) q^{10} +(-2.94173 - 1.53174i) q^{11} +(2.90002 - 4.27298i) q^{12} +(-0.0277744 - 0.115689i) q^{13} +(4.00281 - 0.863091i) q^{14} +(0.873075 - 2.68705i) q^{15} +(2.04046 + 3.44042i) q^{16} +(-4.27993 - 3.10955i) q^{17} +(2.09548 - 4.74389i) q^{18} +(-0.357602 + 4.54377i) q^{19} +(1.59622 + 1.49708i) q^{20} +(6.90721 - 2.86106i) q^{21} +(3.15900 - 3.46709i) q^{22} +(-3.99612 + 3.99612i) q^{23} +(4.79169 + 5.51150i) q^{24} +(-3.38824 - 1.72639i) q^{25} +(0.168212 + 0.00391160i) q^{26} +(0.402124 - 1.67497i) q^{27} +(-0.269179 + 5.78467i) q^{28} +(3.27549 - 3.83511i) q^{29} +(3.35737 + 2.16634i) q^{30} +(3.90097 + 5.36922i) q^{31} +(-5.44207 + 1.54399i) q^{32} +(4.53884 - 7.26205i) q^{33} +(5.80046 - 4.72533i) q^{34} +(0.739611 + 3.08070i) q^{35} +(5.72673 + 4.58211i) q^{36} +(0.0721150 + 0.916308i) q^{37} +(-6.08229 - 2.13382i) q^{38} +(0.303423 - 0.0480575i) q^{39} +(-2.62451 + 1.64021i) q^{40} +(-9.09645 - 4.63487i) q^{41} +(1.41078 + 10.4786i) q^{42} +(0.367663 + 0.887618i) q^{43} +(3.59621 + 5.57380i) q^{44} +(3.70715 + 1.53555i) q^{45} +(-4.01638 - 6.90975i) q^{46} +(-0.627294 - 1.93061i) q^{47} +(-9.26942 + 4.55540i) q^{48} +(-0.813329 + 1.11945i) q^{49} +(3.58675 - 4.00704i) q^{50} +(8.87140 - 10.3871i) q^{51} +(-0.0662438 + 0.228545i) q^{52} +(6.28322 + 3.85036i) q^{53} +(2.14426 + 1.15611i) q^{54} +(2.73866 + 2.38116i) q^{55} +(-7.81073 - 2.46217i) q^{56} +(-11.6237 - 1.84102i) q^{57} +(4.05715 + 5.86628i) q^{58} +(-14.5037 + 1.14147i) q^{59} +(-4.17703 + 3.80557i) q^{60} +(-3.23201 - 5.27416i) q^{61} +(-8.75246 + 3.38921i) q^{62} +(3.28115 + 10.0983i) q^{63} +(-0.140640 - 7.99876i) q^{64} +0.130184i q^{65} +(8.28473 + 8.83402i) q^{66} +(3.62404 + 1.50113i) q^{67} +(4.36007 + 9.64044i) q^{68} +(-9.47692 - 11.0960i) q^{69} +(-4.47936 - 0.104163i) q^{70} +(-2.10127 - 13.2669i) q^{71} +(-8.33736 + 6.17015i) q^{72} +(1.03684 + 2.03491i) q^{73} +(-1.27878 - 0.233135i) q^{74} +(5.13035 - 8.37198i) q^{75} +(5.11904 - 7.54256i) q^{76} +(-0.0847600 + 9.60280i) q^{77} +(-0.0441465 + 0.432205i) q^{78} +(0.571234 + 0.786237i) q^{79} +(-1.29219 - 4.18174i) q^{80} +(-6.23283 - 2.02517i) q^{81} +(9.62940 - 10.7578i) q^{82} +(5.92620 + 9.67069i) q^{83} +(-14.8359 - 1.86480i) q^{84} +(3.75944 + 4.40174i) q^{85} +(-1.34656 + 0.181293i) q^{86} +(9.20844 + 9.20844i) q^{87} +(-8.92181 + 2.89852i) q^{88} +(-8.56698 + 8.56698i) q^{89} +(-3.44131 + 4.51212i) q^{90} +(-0.261953 + 0.223729i) q^{91} +(10.9003 - 2.98929i) q^{92} +(-14.6113 + 8.95382i) q^{93} +(2.86642 - 0.158646i) q^{94} +(1.54113 - 4.74311i) q^{95} +(-2.87193 - 14.3213i) q^{96} +(-0.470991 + 0.342195i) q^{97} +(-1.23595 - 1.51716i) q^{98} +(9.77616 + 7.23549i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 736 q - 20 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} - 12 q^{9} - 16 q^{11} - 20 q^{13} - 28 q^{14} - 24 q^{15} - 52 q^{16} - 120 q^{18} - 20 q^{19} + 4 q^{20} - 4 q^{22} - 48 q^{23}+ \cdots - 68 q^{99}+O(q^{100}) $ 736 * q - 20 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 20 * q^6 - 20 * q^7 - 20 * q^8 - 12 * q^9 - 16 * q^11 - 20 * q^13 - 28 * q^14 - 24 * q^15 - 52 * q^16 - 120 * q^18 - 20 * q^19 + 4 * q^20 - 4 * q^22 - 48 * q^23 - 20 * q^24 - 12 * q^25 + 48 * q^26 - 12 * q^27 - 20 * q^28 - 20 * q^29 - 20 * q^30 - 32 * q^33 + 24 * q^34 - 20 * q^35 - 12 * q^36 - 12 * q^37 - 12 * q^38 - 20 * q^39 - 20 * q^40 - 20 * q^41 - 52 * q^42 + 24 * q^44 - 8 * q^45 - 20 * q^46 - 24 * q^47 - 12 * q^48 - 20 * q^50 - 20 * q^51 - 20 * q^52 - 60 * q^53 + 16 * q^55 - 248 * q^56 - 20 * q^57 - 12 * q^58 + 20 * q^59 + 68 * q^60 - 20 * q^61 - 20 * q^62 + 132 * q^64 - 8 * q^66 - 112 * q^67 - 20 * q^68 - 12 * q^69 + 36 * q^70 + 20 * q^71 - 320 * q^72 - 20 * q^73 - 20 * q^74 + 124 * q^75 - 32 * q^77 - 80 * q^78 - 40 * q^79 + 124 * q^80 + 28 * q^82 - 20 * q^83 - 20 * q^84 - 20 * q^85 - 116 * q^86 - 20 * q^88 - 32 * q^89 - 20 * q^90 - 156 * q^91 + 148 * q^92 - 36 * q^93 - 160 * q^94 - 20 * q^96 - 24 * q^97 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−0.362021	+	1.36709i	−0.255988	+	0.966680i
$2$	−0.362021	+	1.36709i	−0.255988	+	0.966680i
$3$	−0.202587	+	2.57412i	−0.116964	+	1.48617i	0.606101	+	0.795388i	$0.292733\pi$
$3$	−0.202587	+	2.57412i	−0.116964	+	1.48617i	−0.723065	+	0.690780i	$0.757267\pi$
$4$	−1.73788	−	0.989833i	−0.868941	−	0.494916i
$5$	−1.06398	−	0.255438i	−0.475824	−	0.114235i	−0.0115621	−	0.999933i	$-0.503680\pi$
$5$	−1.06398	−	0.255438i	−0.475824	−	0.114235i	−0.464262	+	0.885698i	$0.653680\pi$
$6$	−3.44571	−	1.20884i	−1.40671	−	0.493507i
$7$	−1.31451	−	2.57988i	−0.496839	−	0.975102i	−0.994199	−	0.107558i	$-0.965697\pi$
$7$	−1.31451	−	2.57988i	−0.496839	−	0.975102i	0.497359	−	0.867545i	$-0.334303\pi$
$8$	1.98234	−	2.01750i	0.700864	−	0.713295i
$9$	−3.62197	−	0.573664i	−1.20732	−	0.191221i
$10$	0.734389	−	1.36208i	0.232234	−	0.430727i
$11$	−2.94173	−	1.53174i	−0.886965	−	0.461837i
$11$	−2.94173	−	1.53174i	−0.886965	−	0.461837i
$12$	2.90002	−	4.27298i	0.837163	−	1.23350i
$13$	−0.0277744	−	0.115689i	−0.00770323	−	0.0320862i	0.968386	−	0.249457i	$-0.0802520\pi$
$13$	−0.0277744	−	0.115689i	−0.00770323	−	0.0320862i	−0.976089	+	0.217370i	$0.930252\pi$
$14$	4.00281	−	0.863091i	1.06980	−	0.230671i
$15$	0.873075	−	2.68705i	0.225427	−	0.693793i
$16$	2.04046	+	3.44042i	0.510116	+	0.860106i
$17$	−4.27993	−	3.10955i	−1.03803	−	0.754176i	−0.0681337	−	0.997676i	$-0.521704\pi$
$17$	−4.27993	−	3.10955i	−1.03803	−	0.754176i	−0.969901	+	0.243500i	$0.921704\pi$
$18$	2.09548	−	4.74389i	0.493910	−	1.11815i
$19$	−0.357602	+	4.54377i	−0.0820396	+	1.04241i	0.808797	+	0.588088i	$0.200119\pi$
$19$	−0.357602	+	4.54377i	−0.0820396	+	1.04241i	−0.890837	+	0.454324i	$0.849881\pi$
$20$	1.59622	+	1.49708i	0.356926	+	0.334757i
$21$	6.90721	−	2.86106i	1.50728	−	0.624335i
$22$	3.15900	−	3.46709i	0.673501	−	0.739187i
$23$	−3.99612	+	3.99612i	−0.833249	+	0.833249i	−0.987960	−	0.154711i	$-0.950555\pi$
$23$	−3.99612	+	3.99612i	−0.833249	+	0.833249i	0.154711	+	0.987960i	$0.450555\pi$
$24$	4.79169	+	5.51150i	0.978100	+	1.12503i
$25$	−3.38824	−	1.72639i	−0.677648	−	0.345279i
$26$	0.168212	+	0.00391160i	0.0329891	+	0.000767127i
$27$	0.402124	−	1.67497i	0.0773888	−	0.322347i
$28$	−0.269179	+	5.78467i	−0.0508700	+	1.09320i
$29$	3.27549	−	3.83511i	0.608243	−	0.712161i	−0.367759	−	0.929921i	$-0.619875\pi$
$29$	3.27549	−	3.83511i	0.608243	−	0.712161i	0.976002	+	0.217760i	$0.0698750\pi$
$30$	3.35737	+	2.16634i	0.612969	+	0.395518i
$31$	3.90097	+	5.36922i	0.700635	+	0.964341i	0.999948	+	0.0101863i	$0.00324246\pi$
$31$	3.90097	+	5.36922i	0.700635	+	0.964341i	−0.299313	+	0.954155i	$0.596758\pi$
$32$	−5.44207	+	1.54399i	−0.962030	+	0.272942i
$33$	4.53884	−	7.26205i	0.790110	−	1.26416i
$34$	5.80046	−	4.72533i	0.994771	−	0.810388i
$35$	0.739611	+	3.08070i	0.125017	+	0.520734i
$36$	5.72673	+	4.58211i	0.954455	+	0.763685i
$37$	0.0721150	+	0.916308i	0.0118556	+	0.150640i	0.999996	−	0.00291479i	$-0.000927808\pi$
$37$	0.0721150	+	0.916308i	0.0118556	+	0.150640i	−0.988140	+	0.153555i	$0.950928\pi$
$38$	−6.08229	−	2.13382i	−0.986677	−	0.346151i
$39$	0.303423	−	0.0480575i	0.0485865	−	0.00769535i
$40$	−2.62451	+	1.64021i	−0.414971	+	0.259340i
$41$	−9.09645	−	4.63487i	−1.42063	−	0.723845i	−0.436234	−	0.899833i	$-0.643688\pi$
$41$	−9.09645	−	4.63487i	−1.42063	−	0.723845i	−0.984392	+	0.175988i	$0.943688\pi$
$42$	1.41078	+	10.4786i	0.217688	+	1.61688i
$43$	0.367663	+	0.887618i	0.0560682	+	0.135360i	0.949431	−	0.313975i	$-0.101661\pi$
$43$	0.367663	+	0.887618i	0.0560682	+	0.135360i	−0.893363	+	0.449335i	$0.851661\pi$
$44$	3.59621	+	5.57380i	0.542149	+	0.840282i
$45$	3.70715	+	1.53555i	0.552630	+	0.228907i
$46$	−4.01638	−	6.90975i	−0.592184	−	1.01879i
$47$	−0.627294	−	1.93061i	−0.0915003	−	0.281609i	0.894826	−	0.446416i	$-0.147300\pi$
$47$	−0.627294	−	1.93061i	−0.0915003	−	0.281609i	−0.986326	+	0.164807i	$0.947300\pi$
$48$	−9.26942	+	4.55540i	−1.33793	+	0.657516i
$49$	−0.813329	+	1.11945i	−0.116190	+	0.159922i
$50$	3.58675	−	4.00704i	0.507243	−	0.566681i
$51$	8.87140	−	10.3871i	1.24224	−	1.45448i
$52$	−0.0662438	+	0.228545i	−0.00918636	+	0.0316935i
$53$	6.28322	+	3.85036i	0.863066	+	0.528888i	0.882171	−	0.470930i	$-0.156082\pi$
$53$	6.28322	+	3.85036i	0.863066	+	0.528888i	−0.0191046	+	0.999817i	$0.506082\pi$
$54$	2.14426	+	1.15611i	0.291796	+	0.157327i
$55$	2.73866	+	2.38116i	0.369281	+	0.321076i
$56$	−7.81073	−	2.46217i	−1.04375	−	0.329021i
$57$	−11.6237	−	1.84102i	−1.53960	−	0.243849i
$58$	4.05715	+	5.86628i	0.532729	+	0.770281i
$59$	−14.5037	+	1.14147i	−1.88822	+	0.148606i	−0.969308	−	0.245850i	$-0.920933\pi$
$59$	−14.5037	+	1.14147i	−1.88822	+	0.148606i	−0.918915	+	0.394457i	$0.870933\pi$
$60$	−4.17703	+	3.80557i	−0.539252	+	0.491297i
$61$	−3.23201	−	5.27416i	−0.413816	−	0.675287i	0.576030	−	0.817429i	$-0.304601\pi$
$61$	−3.23201	−	5.27416i	−0.413816	−	0.675287i	−0.989846	+	0.142142i	$0.954601\pi$
$62$	−8.75246	+	3.38921i	−1.11156	+	0.430430i
$63$	3.28115	+	10.0983i	0.413386	+	1.27227i
$64$	−0.140640	−	7.99876i	−0.0175800	−	0.999845i
$65$			0.130184i			0.0161474i
$66$	8.28473	+	8.83402i	1.01978	+	1.08739i
$67$	3.62404	+	1.50113i	0.442747	+	0.183392i	0.592909	−	0.805270i	$-0.297980\pi$
$67$	3.62404	+	1.50113i	0.442747	+	0.183392i	−0.150162	+	0.988661i	$0.547980\pi$
$68$	4.36007	+	9.64044i	0.528736	+	1.16907i
$69$	−9.47692	−	11.0960i	−1.14089	−	1.33581i
$70$	−4.47936	−	0.104163i	−0.535386	−	0.0124499i
$71$	−2.10127	−	13.2669i	−0.249375	−	1.57449i	−0.721153	−	0.692776i	$-0.756388\pi$
$71$	−2.10127	−	13.2669i	−0.249375	−	1.57449i	0.471778	−	0.881717i	$-0.343612\pi$
$72$	−8.33736	+	6.17015i	−0.982567	+	0.727159i
$73$	1.03684	+	2.03491i	0.121353	+	0.238168i	0.943689	−	0.330834i	$-0.107330\pi$
$73$	1.03684	+	2.03491i	0.121353	+	0.238168i	−0.822337	+	0.569001i	$0.807330\pi$
$74$	−1.27878	−	0.233135i	−0.148656	−	0.0271014i
$75$	5.13035	−	8.37198i	0.592402	−	0.966713i
$76$	5.11904	−	7.54256i	0.587194	−	0.865191i
$77$	−0.0847600	+	9.60280i	−0.00965930	+	1.09434i
$78$	−0.0441465	+	0.432205i	−0.00499861	+	0.0489375i
$79$	0.571234	+	0.786237i	0.0642689	+	0.0884585i	0.839942	−	0.542677i	$-0.182589\pi$
$79$	0.571234	+	0.786237i	0.0642689	+	0.0884585i	−0.775673	+	0.631135i	$0.782589\pi$
$80$	−1.29219	−	4.18174i	−0.144471	−	0.467532i
$81$	−6.23283	−	2.02517i	−0.692536	−	0.225019i
$82$	9.62940	−	10.7578i	1.06339	−	1.18800i
$83$	5.92620	+	9.67069i	0.650485	+	1.06150i	0.992552	+	0.121820i	$0.0388731\pi$
$83$	5.92620	+	9.67069i	0.650485	+	1.06150i	−0.342067	+	0.939676i	$0.611127\pi$
$84$	−14.8359	−	1.86480i	−1.61873	−	0.203466i
$85$	3.75944	+	4.40174i	0.407768	+	0.477435i
$86$	−1.34656	+	0.181293i	−0.145203	+	0.0195494i
$87$	9.20844	+	9.20844i	0.987248	+	0.987248i
$88$	−8.92181	+	2.89852i	−0.951068	+	0.308983i
$89$	−8.56698	+	8.56698i	−0.908098	+	0.908098i	−0.996119	−	0.0880202i	$-0.971946\pi$
$89$	−8.56698	+	8.56698i	−0.908098	+	0.908098i	0.0880202	+	0.996119i	$0.471946\pi$
$90$	−3.44131	+	4.51212i	−0.362746	+	0.475619i
$91$	−0.261953	+	0.223729i	−0.0274601	+	0.0234531i
$92$	10.9003	−	2.98929i	1.13643	−	0.311655i
$93$	−14.6113	+	8.95382i	−1.51512	+	0.928468i
$94$	2.86642	−	0.158646i	0.295649	−	0.0163631i
$95$	1.54113	−	4.74311i	0.158117	−	0.486633i
$96$	−2.87193	−	14.3213i	−0.293115	−	1.46166i
$97$	−0.470991	+	0.342195i	−0.0478219	+	0.0347446i	−0.611439	−	0.791291i	$-0.709409\pi$
$97$	−0.470991	+	0.342195i	−0.0478219	+	0.0347446i	0.563618	+	0.826036i	$0.309409\pi$
$98$	−1.23595	−	1.51716i	−0.124850	−	0.153256i
$99$	9.77616	+	7.23549i	0.982541	+	0.727194i
$100$	4.17951	+	6.35406i	0.417951	+	0.635406i
$101$	10.0542	+	6.16124i	1.00043	+	0.613066i	0.923350	−	0.383959i	$-0.125440\pi$
$101$	10.0542	+	6.16124i	1.00043	+	0.613066i	0.0770824	+	0.997025i	$0.475440\pi$
$102$	10.9885	+	15.8884i	1.08802	+	1.57318i
$103$	−14.6882	+	7.48402i	−1.44727	+	0.737422i	−0.988513	−	0.151138i	$-0.951706\pi$
$103$	−14.6882	+	7.48402i	−1.44727	+	0.737422i	−0.458760	+	0.888560i	$0.651706\pi$
$104$	−0.288460	−	0.173299i	−0.0282859	−	0.0169934i
$105$	−8.07993	+	1.27973i	−0.788520	+	0.124889i
$106$	−7.53845	+	7.19582i	−0.732199	+	0.698920i
$107$	−8.12392	+	6.93848i	−0.785369	+	0.670769i	−0.948832	−	0.315781i	$-0.897734\pi$
$107$	−8.12392	+	6.93848i	−0.785369	+	0.670769i	0.163463	+	0.986549i	$0.447734\pi$
$108$	−2.35678	+	2.51286i	−0.226781	+	0.241800i
$109$	1.77824	−	4.29306i	0.170325	−	0.411201i	−0.815549	−	0.578687i	$-0.803565\pi$
$109$	1.77824	−	4.29306i	0.170325	−	0.411201i	0.985874	+	0.167487i	$0.0535651\pi$
$110$	−4.24672	+	2.88197i	−0.404909	+	0.274785i
$111$	−2.37329			−0.225263
$112$	6.19366	−	9.78663i	0.585245	−	0.924750i
$113$	3.92589	−	1.27560i	0.369317	−	0.119998i	−0.118478	−	0.992957i	$-0.537801\pi$
$113$	3.92589	−	1.27560i	0.369317	−	0.119998i	0.487795	+	0.872958i	$0.337801\pi$
$114$	6.72489	−	15.2242i	0.629843	−	1.42588i
$115$	5.27253	−	3.23101i	0.491666	−	0.301294i
$116$	−9.48852	+	3.42277i	−0.880987	+	0.317796i
$117$	0.0342316	+	0.434954i	0.00316472	+	0.0402115i
$118$	3.69016	−	20.2411i	0.339707	−	1.86335i
$119$	−2.39624	+	15.1292i	−0.219663	+	1.38689i
$120$	−3.69040	−	7.08808i	−0.336886	−	0.647050i
$121$	6.30754	+	9.01193i	0.573413	+	0.819266i
$122$	8.38032	−	2.50910i	0.758718	−	0.227163i
$123$	13.7735	−	22.4764i	1.24192	−	2.02663i
$124$	−1.46479	−	13.1924i	−0.131542	−	1.18471i
$125$	7.32423	+	6.25548i	0.655099	+	0.559507i
$126$	−14.9932	+	0.829821i	−1.33570	+	0.0739263i
$127$	6.90551	+	5.01715i	0.612765	+	0.445200i	0.850387	−	0.526158i	$-0.176368\pi$
$127$	6.90551	+	5.01715i	0.612765	+	0.445200i	−0.237622	+	0.971358i	$0.576368\pi$
$128$	10.9860	+	2.70345i	0.971031	+	0.238954i
$129$	−2.35932	+	0.766589i	−0.207726	+	0.0674944i
$130$	−0.177974	−	0.0471295i	−0.0156094	−	0.00413353i
$131$	2.25458	−	5.44303i	0.196983	−	0.475560i	−0.794265	−	0.607572i	$-0.792144\pi$
$131$	2.25458	−	5.44303i	0.196983	−	0.475560i	0.991248	+	0.132012i	$0.0421438\pi$
$132$	−15.0762	+	8.12789i	−1.31221	+	0.707442i
$133$	12.1924	−	5.05027i	1.05722	−	0.437914i
$134$	−3.36416	+	4.41095i	−0.290619	+	0.381048i
$135$	−0.855699	+	1.67940i	−0.0736469	+	0.144540i
$136$	−14.7578	+	2.47058i	−1.26547	+	0.211850i
$137$	0.549392	+	3.46873i	0.0469378	+	0.296353i	0.999979	−	0.00648736i	$-0.00206500\pi$
$137$	0.549392	+	3.46873i	0.0469378	+	0.296353i	−0.953041	+	0.302841i	$0.902065\pi$
$138$	18.6002	−	8.93882i	1.58335	−	0.760923i
$139$	16.1468	−	1.27078i	1.36955	−	0.107786i	0.627755	−	0.778411i	$-0.283974\pi$
$139$	16.1468	−	1.27078i	1.36955	−	0.107786i	0.741796	+	0.670625i	$0.233974\pi$
$140$	1.76402	−	6.08599i	0.149087	−	0.514360i
$141$	5.09671	−	1.22361i	0.429220	−	0.103047i
$142$	18.8978	+	1.93027i	1.58587	+	0.161985i
$143$	−0.0955002	+	0.382868i	−0.00798613	+	0.0320170i
$144$	−5.41686	−	13.6317i	−0.451405	−	1.13597i
$145$	−4.46467	+	3.24377i	−0.370771	+	0.269381i
$146$	−3.15726	+	0.680772i	−0.261297	+	0.0563411i
$147$	−2.71683	−	2.32039i	−0.224080	−	0.191383i
$148$	0.781664	−	1.66382i	0.0642524	−	0.136765i
$149$	−16.5878	−	3.98238i	−1.35892	−	0.326249i	−0.512468	−	0.858707i	$-0.671269\pi$
$149$	−16.5878	−	3.98238i	−1.35892	−	0.326249i	−0.846457	+	0.532458i	$0.821269\pi$
$150$	9.58797	+	10.0445i	0.782854	+	0.820130i
$151$	7.99746	−	15.6959i	0.650824	−	1.27731i	−0.295885	−	0.955224i	$-0.595614\pi$
$151$	7.99746	−	15.6959i	0.650824	−	1.27731i	0.946709	−	0.322091i	$-0.104386\pi$
$152$	8.45818	+	9.72876i	0.686049	+	0.789107i
$153$	13.7179	+	13.7179i	1.10903	+	1.10903i
$154$	−13.0972	−	3.59229i	−1.05540	−	0.289475i
$155$	−2.77903	−	6.70918i	−0.223217	−	0.538894i
$156$	−0.574882	−	0.216820i	−0.0460274	−	0.0173595i
$157$	−17.8619	−	1.40576i	−1.42553	−	0.112192i	−0.657911	−	0.753096i	$-0.728560\pi$
$157$	−17.8619	−	1.40576i	−1.42553	−	0.112192i	−0.767621	+	0.640904i	$0.778560\pi$
$158$	−1.28166	+	0.496296i	−0.101963	+	0.0394832i
$159$	−11.1842	+	15.3937i	−0.886963	+	1.22080i
$160$	6.18462	−	0.252663i	0.488937	−	0.0199747i
$161$	15.5625	+	5.05655i	1.22649	+	0.398512i
$162$	5.02501	−	7.78769i	0.394802	−	0.611859i
$163$	−5.38790	+	1.29352i	−0.422013	+	0.101316i	−0.438889	−	0.898541i	$-0.644628\pi$
$163$	−5.38790	+	1.29352i	−0.422013	+	0.101316i	0.0168760	+	0.999858i	$0.494628\pi$
$164$	11.2208	+	17.0588i	0.876197	+	1.33207i
$165$	−6.68421	+	6.56725i	−0.520365	+	0.511259i
$166$	−15.3661	+	4.60067i	−1.19264	+	0.357082i
$167$	−0.604906	+	3.81923i	−0.0468091	+	0.295541i	−0.999976	−	0.00690334i	$-0.997803\pi$
$167$	−0.604906	+	3.81923i	−0.0468091	+	0.295541i	0.953167	+	0.302444i	$0.0978026\pi$
$168$	7.92026	−	19.6069i	0.611061	−	1.51271i
$169$	11.5705	−	5.89545i	0.890036	−	0.453496i
$170$	−7.37858	+	3.54598i	−0.565911	+	0.271964i
$171$	3.90182	−	16.2523i	0.298380	−	1.24284i
$172$	0.239638	−	1.90650i	0.0182722	−	0.145369i
$173$	6.78708	+	0.534155i	0.516012	+	0.0406110i	0.333792	−	0.942647i	$-0.391672\pi$
$173$	6.78708	+	0.534155i	0.516012	+	0.0406110i	0.182220	+	0.983258i	$0.441672\pi$
$174$	−15.9224	+	9.25513i	−1.20708	+	0.701630i
$175$			11.0106i			0.832324i
$176$	−0.732656	−	13.2463i	−0.0552260	−	0.998474i
$177$		−	37.5655i		−	2.82360i
$178$	−8.61043	−	14.8133i	−0.645379	−	1.11030i
$179$	−22.3063	−	1.75554i	−1.66725	−	0.131216i	−0.790597	−	0.612336i	$-0.790230\pi$
$179$	−22.3063	−	1.75554i	−1.66725	−	0.131216i	−0.876654	+	0.481121i	$0.840230\pi$
$180$	−4.92265	−	6.33807i	−0.366913	−	0.472412i
$181$	3.34531	−	13.9342i	0.248655	−	1.03572i	−0.698669	−	0.715445i	$-0.746224\pi$
$181$	3.34531	−	13.9342i	0.248655	−	1.03572i	0.947324	−	0.320277i	$-0.103776\pi$
$182$	−0.211025	−	0.439108i	−0.0156422	−	0.0325489i
$183$	14.2311	−	7.25109i	1.05199	−	0.536016i
$184$	0.140509	+	15.9839i	0.0103585	+	1.17835i
$185$	0.157331	−	0.993350i	0.0115672	−	0.0730325i
$186$	−6.95109	−	23.2165i	−0.509679	−	1.70231i
$187$	7.82736	+	15.7032i	0.572394	+	1.14833i
$188$	−0.820821	+	3.97609i	−0.0598645	+	0.289986i
$189$	−4.84981	+	1.16434i	−0.352771	+	0.0846929i
$190$	5.92635	+	3.82397i	0.429942	+	0.277420i
$191$	−1.01596	−	0.330104i	−0.0735120	−	0.0238855i	0.272030	−	0.962289i	$-0.412305\pi$
$191$	−1.01596	−	0.330104i	−0.0735120	−	0.0238855i	−0.345542	+	0.938403i	$0.612305\pi$
$192$	20.6182	+	1.25843i	1.48799	+	0.0908190i
$193$	−3.77387	+	5.19429i	−0.271649	+	0.373893i	−0.922946	−	0.384930i	$-0.874225\pi$
$193$	−3.77387	+	5.19429i	−0.271649	+	0.373893i	0.651296	+	0.758823i	$0.274225\pi$
$194$	−0.297303	−	0.767769i	−0.0213451	−	0.0551226i
$195$	−0.335110	−	0.0263737i	−0.0239977	−	0.00188866i
$196$	2.52154	−	1.14041i	0.180110	−	0.0814581i
$197$	0.168425	+	0.406614i	0.0119998	+	0.0289701i	0.929766	−	0.368151i	$-0.120009\pi$
$197$	0.168425	+	0.406614i	0.0119998	+	0.0289701i	−0.917766	+	0.397121i	$0.870009\pi$
$198$	−13.4308	+	10.7455i	−0.954482	+	0.763650i
$199$	5.61607	+	5.61607i	0.398112	+	0.398112i	0.877567	−	0.479454i	$-0.159165\pi$
$199$	5.61607	+	5.61607i	0.398112	+	0.398112i	−0.479454	+	0.877567i	$0.659165\pi$
$200$	−10.1997	+	3.41348i	−0.721224	+	0.241369i
$201$	−4.59826	+	9.02459i	−0.324336	+	0.636546i
$202$	−12.0628	+	11.5146i	−0.848737	+	0.810161i
$203$	−14.1998	−	3.40907i	−0.996629	−	0.239269i
$204$	−25.6989	+	9.27031i	−1.79928	+	0.649051i
$205$	8.49447	+	7.25497i	0.593280	+	0.506709i
$206$	−4.91390	−	22.7895i	−0.342367	−	1.58782i
$207$	16.7663	−	12.1814i	1.16534	−	0.846667i
$208$	0.341345	−	0.331614i	0.0236680	−	0.0229933i
$209$	8.01184	−	12.8188i	0.554191	−	0.886694i
$210$	1.17559	−	11.5093i	0.0811234	−	0.794217i
$211$	−0.0863746	+	0.0207367i	−0.00594627	+	0.00142757i	−0.236417	−	0.971652i	$-0.575973\pi$
$211$	−0.0863746	+	0.0207367i	−0.00594627	+	0.00142757i	0.230471	+	0.973079i	$0.425973\pi$
$212$	−7.10827	−	12.9108i	−0.488198	−	0.886717i
$213$	34.5763	−	2.72121i	2.36913	−	0.186454i
$214$	−6.54452	−	13.6180i	−0.447374	−	0.930909i
$215$	−0.164454	−	1.03832i	−0.0112156	−	0.0708128i
$216$	−2.58210	−	4.13164i	−0.175690	−	0.281123i
$217$	8.72407	−	17.1219i	0.592228	−	1.16231i
$218$	5.22525	+	3.98520i	0.353898	+	0.269912i
$219$	−5.44814	+	2.25669i	−0.368151	+	0.152493i
$220$	−2.40252	−	6.84900i	−0.161978	−	0.461759i
$221$	−0.240867	+	0.581505i	−0.0162025	+	0.0391162i
$222$	0.859183	−	3.24451i	0.0576646	−	0.217757i
$223$	−6.92410	+	2.24978i	−0.463672	+	0.150656i	−0.531531	−	0.847039i	$-0.678383\pi$
$223$	−6.92410	+	2.24978i	−0.463672	+	0.150656i	0.0678592	+	0.997695i	$0.478383\pi$
$224$	11.1370	+	12.0103i	0.744121	+	0.802470i
$225$	11.2817	+	8.19666i	0.752116	+	0.546444i
$226$	0.322606	+	5.82885i	0.0214594	+	0.387729i
$227$	9.70629	+	8.28996i	0.644229	+	0.550224i	0.910414	−	0.413698i	$-0.135763\pi$
$227$	9.70629	+	8.28996i	0.644229	+	0.550224i	−0.266185	+	0.963922i	$0.585763\pi$
$228$	18.3784	+	14.7050i	1.21714	+	0.973865i
$229$	7.41373	−	12.0981i	0.489913	−	0.799466i	−0.508176	−	0.861253i	$-0.669680\pi$
$229$	7.41373	−	12.0981i	0.489913	−	0.799466i	0.998089	+	0.0617876i	$0.0196801\pi$
$230$	2.50832	+	8.37773i	0.165394	+	0.552411i
$231$	−24.7016	−	2.16359i	−1.62524	−	0.142354i
$232$	−1.24420	−	14.2108i	−0.0816856	−	0.932985i
$233$	2.77399	−	17.5143i	0.181730	−	1.14740i	−0.713124	−	0.701038i	$-0.752720\pi$
$233$	2.77399	−	17.5143i	0.181730	−	1.14740i	0.894854	−	0.446359i	$-0.147280\pi$
$234$	−0.607015	−	0.110665i	−0.0396818	−	0.00723439i
$235$	0.174274	+	2.21436i	0.0113684	+	0.144449i
$236$	26.3356	+	12.3725i	1.71430	+	0.805382i
$237$	−2.13959	+	1.31114i	−0.138981	+	0.0851679i
$238$	−19.8156	−	8.75298i	−1.28445	−	0.567371i
$239$	−21.6255	+	7.02655i	−1.39884	+	0.454510i	−0.908814	−	0.417200i	$-0.863011\pi$
$239$	−21.6255	+	7.02655i	−1.39884	+	0.454510i	−0.490022	+	0.871710i	$0.663011\pi$
$240$	11.0261	−	2.47908i	0.711729	−	0.160024i
$241$	24.2870			1.56446			0.782232	−	0.622987i	$-0.214081\pi$
$241$	24.2870			1.56446			0.782232	+	0.622987i	$0.214081\pi$
$242$	−14.6036	+	5.36048i	−0.938755	+	0.344585i
$243$	8.45330	−	20.4081i	0.542279	−	1.30918i
$244$	0.396314	+	12.3650i	0.0253714	+	0.791589i
$245$	1.15131	−	0.983313i	0.0735546	−	0.0628216i
$246$	25.7409	+	26.9666i	1.64118	+	1.71933i
$247$	0.535594	−	0.0848298i	0.0340790	−	0.00539759i
$248$	18.5655	+	2.77342i	1.17891	+	0.176112i
$249$	−26.0941	+	13.2956i	−1.65364	+	0.842574i
$250$	−11.2033	+	7.74828i	−0.708562	+	0.490044i
$251$	−18.0845	−	11.0822i	−1.14149	−	0.699504i	−0.182570	−	0.983193i	$-0.558442\pi$
$251$	−18.0845	−	11.0822i	−1.14149	−	0.699504i	−0.958916	+	0.283689i	$0.908442\pi$
$252$	4.29342	−	20.7975i	0.270460	−	1.31012i
$253$	17.8765	−	5.63449i	1.12389	−	0.354237i
$254$	−9.35885	+	7.62416i	−0.587226	+	0.478382i
$255$	−12.0922	+	8.78550i	−0.757243	+	0.550169i
$256$	−7.67302	+	14.0401i	−0.479564	+	0.877507i
$257$	−7.17370	+	22.0784i	−0.447483	+	1.37721i	0.432255	+	0.901751i	$0.357718\pi$
$257$	−7.17370	+	22.0784i	−0.447483	+	1.37721i	−0.879738	+	0.475459i	$0.842282\pi$
$258$	−0.193874	−	3.50293i	−0.0120701	−	0.218083i
$259$	2.26917	−	1.39055i	0.140999	−	0.0864044i
$260$	0.128861	−	0.226245i	0.00799161	−	0.0140311i
$261$	−14.0638	+	12.0116i	−0.870527	+	0.743501i
$262$	6.62492	+	5.05271i	0.409289	+	0.312157i
$263$	16.4884	−	16.4884i	1.01672	−	1.01672i	0.0168603	−	0.999858i	$-0.494633\pi$
$263$	16.4884	−	16.4884i	1.01672	−	1.01672i	0.999858	−	0.0168603i	$-0.00536705\pi$
$264$	−5.65367	−	23.5530i	−0.347960	−	1.44959i
$265$	−5.70166	−	5.70166i	−0.350250	−	0.350250i
$266$	2.49027	+	18.4965i	0.152688	+	1.13409i
$267$	−20.3169	−	23.7880i	−1.24337	−	1.45580i
$268$	−4.81229	−	6.19597i	−0.293957	−	0.378479i
$269$	14.9508	+	24.3975i	0.911567	+	1.48754i	0.872676	+	0.488299i	$0.162382\pi$
$269$	14.9508	+	24.3975i	0.911567	+	1.48754i	0.0388907	+	0.999243i	$0.487618\pi$
$270$	−1.98612	−	1.77780i	−0.120871	−	0.108193i
$271$	−4.39954	−	1.42950i	−0.267253	−	0.0868358i	0.172325	−	0.985040i	$-0.444872\pi$
$271$	−4.39954	−	1.42950i	−0.267253	−	0.0868358i	−0.439578	+	0.898204i	$0.644872\pi$
$272$	1.96513	−	21.0697i	0.119154	−	1.27754i
$273$	−0.522836	−	0.719622i	−0.0316435	−	0.0435535i
$274$	−4.94096	−	0.504683i	−0.298494	−	0.0304890i
$275$	7.32289	+	10.2685i	0.441587	+	0.619213i
$276$	5.48653	+	28.6642i	0.330251	+	1.72538i
$277$	−15.2422	+	24.8731i	−0.915817	+	1.49448i	−0.0472627	+	0.998882i	$0.515050\pi$
$277$	−15.2422	+	24.8731i	−0.915817	+	1.49448i	−0.868554	+	0.495595i	$0.834950\pi$
$278$	−4.10820	+	22.5342i	−0.246394	+	1.35151i
$279$	−11.0491	−	21.6850i	−0.661491	−	1.29825i
$280$	7.68149	+	4.61484i	0.459057	+	0.275789i
$281$	−1.63195	−	10.3037i	−0.0973540	−	0.614669i	−0.987332	−	0.158666i	$-0.949281\pi$
$281$	−1.63195	−	10.3037i	−0.0973540	−	0.614669i	0.889978	−	0.456003i	$-0.150719\pi$
$282$	−0.172327	+	7.41064i	−0.0102619	+	0.441297i
$283$	5.97955	+	7.00115i	0.355447	+	0.416175i	0.909104	−	0.416570i	$-0.136768\pi$
$283$	5.97955	+	7.00115i	0.355447	+	0.416175i	−0.553657	+	0.832745i	$0.686768\pi$
$284$	−9.48026	+	25.1362i	−0.562550	+	1.49156i
$285$	11.8971	+	4.92794i	0.704724	+	0.291906i
$286$	−0.488842	−	0.269164i	−0.0289059	−	0.0159160i
$287$			29.5603i			1.74489i
$288$	20.5968	−	2.47039i	1.21368	−	0.145569i
$289$	3.39519	+	10.4493i	0.199717	+	0.614666i
$290$	−2.81823	−	7.27793i	−0.165492	−	0.427375i
$291$	−0.785433	−	1.28171i	−0.0460429	−	0.0751351i
$292$	0.212318	−	4.56272i	0.0124249	−	0.267013i
$293$	−5.33376	+	0.419776i	−0.311602	+	0.0245236i	−0.233296	−	0.972406i	$-0.574951\pi$
$293$	−5.33376	+	0.419776i	−0.311602	+	0.0245236i	−0.0783058	+	0.996929i	$0.524951\pi$
$294$	4.15574	−	2.87412i	0.242367	−	0.167622i
$295$	15.7232	+	2.49030i	0.915438	+	0.144991i
$296$	1.99161	+	1.67094i	0.115760	+	0.0971216i
$297$	−3.74855	+	4.31135i	−0.217513	+	0.250170i
$298$	11.4494	−	21.2353i	0.663246	−	1.23013i
$299$	0.573295	+	0.351316i	0.0331545	+	0.0203171i
$300$	−17.2028	+	9.47131i	−0.993204	+	0.546826i
$301$	1.80665	−	2.11531i	0.104133	−	0.121925i
$302$	18.5625	+	16.6155i	1.06815	+	0.956115i
$303$	−17.8966	+	24.6326i	−1.02813	+	1.41510i
$304$	−16.3622	+	8.04109i	−0.938434	+	0.461188i
$305$	2.09156	+	6.43715i	0.119762	+	0.368590i
$306$	−23.7199	+	13.7875i	−1.35598	+	0.788179i
$307$	−13.9434	−	5.77556i	−0.795793	−	0.329628i	−0.0525232	−	0.998620i	$-0.516726\pi$
$307$	−13.9434	−	5.77556i	−0.795793	−	0.329628i	−0.743270	+	0.668991i	$0.766726\pi$
$308$	9.65246	−	16.6046i	0.550000	−	0.946136i
$309$	−16.2891	−	39.3253i	−0.926654	−	2.23714i
$310$	10.1781	−	1.37033i	0.578079	−	0.0778294i
$311$	17.2023	+	8.76502i	0.975454	+	0.497019i	0.867662	−	0.497155i	$-0.165622\pi$
$311$	17.2023	+	8.76502i	0.975454	+	0.497019i	0.107792	+	0.994173i	$0.465622\pi$
$312$	0.504532	−	0.707423i	0.0285635	−	0.0400499i
$313$	−19.4602	+	3.08220i	−1.09996	+	0.174216i	−0.679917	−	0.733289i	$-0.737984\pi$
$313$	−19.4602	+	3.08220i	−1.09996	+	0.174216i	−0.420040	+	0.907506i	$0.637984\pi$
$314$	8.38817	−	23.9099i	0.473372	−	1.34931i
$315$	−0.911564	−	11.5825i	−0.0513608	−	0.652601i
$316$	−0.214495	−	1.93181i	−0.0120663	−	0.108673i
$317$	0.568056	+	2.36612i	0.0319052	+	0.132895i	0.986050	−	0.166452i	$-0.0532312\pi$
$317$	0.568056	+	2.36612i	0.0319052	+	0.132895i	−0.954144	+	0.299347i	$0.903231\pi$
$318$	−16.9957	−	20.8626i	−0.953071	−	1.16992i
$319$	−15.5100	+	6.26464i	−0.868393	+	0.350753i
$320$	−1.89355	+	8.54641i	−0.105853	+	0.477759i
$321$	−16.2147	−	22.3176i	−0.905015	−	1.24565i
$322$	−12.5467	+	19.4447i	−0.699201	+	1.08361i
$323$	15.6596	−	18.3350i	0.871322	−	1.02019i
$324$	8.82734	+	9.68896i	0.490408	+	0.538275i
$325$	−0.105618	+	0.439930i	−0.00585862	+	0.0244029i
$326$	0.182173	−	7.83404i	0.0100896	−	0.433888i
$327$	10.6906	+	5.44713i	0.591191	+	0.301227i
$328$	−27.3831	+	9.16421i	−1.51198	+	0.506009i
$329$	−4.15616	+	4.15616i	−0.229137	+	0.229137i
$330$	−6.55820	−	11.5154i	−0.361017	−	0.633903i
$331$	−17.3218	+	7.17491i	−0.952090	+	0.394369i	−0.804016	−	0.594608i	$-0.797307\pi$
$331$	−17.3218	+	7.17491i	−0.952090	+	0.394369i	−0.148074	+	0.988976i	$0.547307\pi$
$332$	−0.726680	−	22.6725i	−0.0398817	−	1.24431i
$333$	0.264455	−	3.36021i	0.0144920	−	0.184139i
$334$	−5.00225	−	2.20960i	−0.273711	−	0.120904i
$335$	−3.47244	−	2.52288i	−0.189720	−	0.137840i
$336$	23.9372	+	17.9258i	1.30588	+	0.977935i
$337$	−3.42782	+	10.5497i	−0.186725	+	0.574681i	−0.999974	−	0.00723550i	$-0.997697\pi$
$337$	−3.42782	+	10.5497i	−0.186725	+	0.574681i	0.813249	+	0.581916i	$0.197697\pi$
$338$	3.87087	+	17.9522i	0.210547	+	0.976470i
$339$	2.48821	+	10.3641i	0.135141	+	0.562902i
$340$	−2.17648	−	11.3709i	−0.118036	−	0.616674i
$341$	−3.25134	−	21.7701i	−0.176070	−	1.17892i
$342$	20.8058	+	11.2178i	1.12505	+	0.606590i
$343$	−16.0615	−	2.54390i	−0.867242	−	0.137358i
$344$	2.51961	+	1.01780i	0.135848	+	0.0548761i
$345$	7.24886	+	14.2267i	0.390265	+	0.765939i
$346$	−3.18731	+	9.08519i	−0.171351	+	0.488423i
$347$	18.5350	+	4.44987i	0.995013	+	0.238882i	0.698082	−	0.716017i	$-0.254037\pi$
$347$	18.5350	+	4.44987i	0.995013	+	0.238882i	0.296931	+	0.954899i	$0.404037\pi$
$348$	−6.88836	−	25.1180i	−0.369255	−	1.34647i
$349$	−0.577522	+	7.33812i	−0.0309141	+	0.392800i	0.961923	+	0.273322i	$0.0881223\pi$
$349$	−0.577522	+	7.33812i	−0.0309141	+	0.392800i	−0.992837	+	0.119479i	$0.961878\pi$
$350$	−15.0525	−	3.98607i	−0.804591	−	0.213065i
$351$	−0.204943			−0.0109391
$352$	18.3741	+	3.79382i	0.979342	+	0.202211i
$353$	−7.52255			−0.400385			−0.200192	−	0.979757i	$-0.564157\pi$
$353$	−7.52255			−0.400385			−0.200192	+	0.979757i	$0.564157\pi$
$354$	51.3555	+	13.5995i	2.72951	+	0.722806i
$355$	−1.15317	+	14.6524i	−0.0612039	+	0.777669i
$356$	23.3683	−	6.40852i	1.23852	−	0.339651i
$357$	−38.4590	−	9.23318i	−2.03546	−	0.488672i
$358$	10.4753	−	29.8592i	0.553639	−	1.57811i
$359$	−16.1833	−	31.7616i	−0.854123	−	1.67631i	−0.729366	−	0.684124i	$-0.760185\pi$
$359$	−16.1833	−	31.7616i	−0.854123	−	1.67631i	−0.124758	−	0.992187i	$-0.539815\pi$
$360$	10.4468	−	4.43520i	0.550596	−	0.233756i
$361$	−1.75186	−	0.277468i	−0.0922034	−	0.0146036i
$362$	17.8383	+	9.61783i	0.937559	+	0.505502i
$363$	−24.4756	+	14.4107i	−1.28464	+	0.756363i
$364$	0.676697	−	0.129525i	0.0354685	−	0.00678894i
$365$	−0.583376	−	2.42994i	−0.0305353	−	0.127189i
$366$	4.76096	+	22.0802i	0.248860	+	1.15415i
$367$	6.88641	−	21.1942i	0.359468	−	1.10633i	−0.593906	−	0.804535i	$-0.702415\pi$
$367$	6.88641	−	21.1942i	0.359468	−	1.10633i	0.953373	−	0.301793i	$-0.0975851\pi$
$368$	−21.9023	−	5.59441i	−1.14174	−	0.291629i
$369$	30.2882	+	22.0057i	1.57674	+	1.14557i
$370$	1.30104	+	0.574700i	0.0676380	+	0.0298772i
$371$	1.67409	−	21.2713i	0.0869142	−	1.10435i
$372$	34.2555	−	1.09793i	1.77606	−	0.0569250i
$373$	−8.95372	+	3.70875i	−0.463606	+	0.192032i	−0.602245	−	0.798311i	$-0.705727\pi$
$373$	−8.95372	+	3.70875i	−0.463606	+	0.192032i	0.138639	+	0.990343i	$0.455727\pi$
$374$	−24.3014	+	5.01584i	−1.25659	+	0.259363i
$375$	−17.5861	+	17.5861i	−0.908144	+	0.908144i
$376$	−5.13853	−	2.56157i	−0.264999	−	0.132103i
$377$	−0.534653	−	0.272419i	−0.0275360	−	0.0140303i
$378$	0.163979	−	7.05164i	0.00843416	−	0.362697i
$379$	−1.58072	+	6.58417i	−0.0811961	+	0.338206i	−0.998151	−	0.0607851i	$-0.980640\pi$
$379$	−1.58072	+	6.58417i	−0.0811961	+	0.338206i	0.916955	+	0.398991i	$0.130640\pi$
$380$	−7.37319	+	6.71750i	−0.378236	+	0.344601i
$381$	−14.3137	+	16.7592i	−0.733313	+	0.858599i
$382$	0.819081	−	1.26940i	0.0419078	−	0.0649482i
$383$	−15.6020	−	21.4743i	−0.797226	−	1.09729i	−0.993170	−	0.116673i	$-0.962777\pi$
$383$	−15.6020	−	21.4743i	−0.797226	−	1.09729i	0.195944	−	0.980615i	$-0.437223\pi$
$384$	−9.18463	+	27.7315i	−0.468701	+	1.41517i
$385$	2.54310	−	10.1955i	0.129608	−	0.519610i
$386$	−5.73485	−	7.03967i	−0.291896	−	0.358310i
$387$	−0.822473	−	3.42584i	−0.0418086	−	0.174145i
$388$	1.15724	−	0.128492i	0.0587500	−	0.00652319i
$389$	1.78961	+	22.7392i	0.0907370	+	1.15292i	0.858717	+	0.512450i	$0.171262\pi$
$389$	1.78961	+	22.7392i	0.0907370	+	1.15292i	−0.767980	+	0.640473i	$0.778738\pi$
$390$	0.157372	−	0.448578i	0.00796885	−	0.0227147i
$391$	29.5292	−	4.67697i	1.49336	−	0.236525i
$392$	0.646200	+	3.86003i	0.0326380	+	0.194961i
$393$	13.5542	+	6.90623i	0.683721	+	0.348373i
$394$	−0.616852	+	0.0830497i	−0.0310766	+	0.00418398i
$395$	−0.406945	−	0.982451i	−0.0204756	−	0.0494325i
$396$	−9.82789	−	22.2512i	−0.493870	−	1.11816i
$397$	22.4019	+	9.27916i	1.12432	+	0.465708i	0.865846	−	0.500311i	$-0.166781\pi$
$397$	22.4019	+	9.27916i	1.12432	+	0.465708i	0.258472	+	0.966019i	$0.416781\pi$
$398$	−9.71081	+	5.64454i	−0.486759	+	0.282935i
$399$	10.5300	+	32.4079i	0.527157	+	1.62242i
$400$	−0.974051	−	15.1796i	−0.0487025	−	0.758981i
$401$	−1.68605	+	2.32065i	−0.0841972	+	0.115887i	−0.849038	−	0.528332i	$-0.822818\pi$
$401$	−1.68605	+	2.32065i	−0.0841972	+	0.115887i	0.764841	+	0.644219i	$0.222818\pi$
$402$	−10.6728	−	9.55334i	−0.532310	−	0.476477i
$403$	0.512811	−	0.600425i	0.0255449	−	0.0299093i
$404$	−11.3745	−	20.6595i	−0.565900	−	1.02785i
$405$	6.11427	+	3.74683i	0.303820	+	0.186181i
$406$	9.80113	−	18.1783i	0.486422	−	0.902171i
$407$	1.19140	−	2.80599i	0.0590557	−	0.139088i
$408$	−3.36981	−	38.4888i	−0.166830	−	1.90548i
$409$	−28.3673	−	4.49293i	−1.40267	−	0.222161i	−0.591187	−	0.806535i	$-0.701340\pi$
$409$	−28.3673	−	4.49293i	−1.40267	−	0.222161i	−0.811485	+	0.584374i	$0.801340\pi$
$410$	−12.9934	+	8.98628i	−0.641698	+	0.443801i
$411$	−9.04021	+	0.711480i	−0.445921	+	0.0350947i
$412$	32.9343	+	1.53254i	1.62256	+	0.0755026i
$413$	22.0102	+	35.9173i	1.08305	+	1.76738i
$414$	10.5834	+	27.3310i	0.520144	+	1.34324i
$415$	−3.83508	−	11.8031i	−0.188256	−	0.579394i
$416$	0.329773	+	0.586702i	0.0161684	+	0.0287654i
$417$			41.8211i			2.04799i
$418$	14.6240	+	15.5936i	0.715283	+	0.762708i
$419$	5.85844	+	2.42664i	0.286203	+	0.118549i	0.521167	−	0.853455i	$-0.325497\pi$
$419$	5.85844	+	2.42664i	0.286203	+	0.118549i	−0.234963	+	0.972004i	$0.575497\pi$
$420$	15.3087	+	5.77375i	0.746987	+	0.281730i
$421$	−17.2401	−	20.1856i	−0.840231	−	0.983784i	0.159764	−	0.987155i	$-0.448927\pi$
$421$	−17.2401	−	20.1856i	−0.840231	−	0.983784i	−0.999994	+	0.00337175i	$0.998927\pi$
$422$	0.00292045	−	0.125589i	0.000142165	−	0.00611359i
$423$	1.16452	+	7.35249i	0.0566209	+	0.357490i
$424$	20.2236	−	5.04368i	0.982145	−	0.244943i
$425$	9.13310	+	17.9247i	0.443021	+	0.869477i
$426$	−8.79720	+	48.2541i	−0.426226	+	2.33792i
$427$	−9.35817	+	15.2711i	−0.452874	+	0.739023i
$428$	20.9863	−	4.01694i	1.01441	−	0.194166i
$429$	−0.966199	−	0.323393i	−0.0466485	−	0.0156136i
$430$	1.47901	+	0.151070i	0.0713243	+	0.00728526i
$431$	−20.3265	−	27.9770i	−0.979091	−	1.34760i	−0.937317	−	0.348477i	$-0.886699\pi$
$431$	−20.3265	−	27.9770i	−0.979091	−	1.34760i	−0.0417739	−	0.999127i	$-0.513301\pi$
$432$	6.58311	−	2.03423i	0.316730	−	0.0978720i
$433$	−10.0078	−	3.25175i	−0.480946	−	0.156269i	0.0585025	−	0.998287i	$-0.481367\pi$
$433$	−10.0078	−	3.25175i	−0.480946	−	0.156269i	−0.539449	+	0.842018i	$0.681367\pi$
$434$	20.2490	+	18.1251i	0.971982	+	0.870033i
$435$	−7.44537	−	12.1497i	−0.356978	−	0.582535i
$436$	−7.33979	+	5.70067i	−0.351512	+	0.273012i
$437$	−16.7284	−	19.5865i	−0.800229	−	0.936948i
$438$	−1.11277	−	8.26508i	−0.0531700	−	0.394921i
$439$	5.45429	+	5.45429i	0.260319	+	0.260319i	0.825184	−	0.564865i	$-0.191072\pi$
$439$	5.45429	+	5.45429i	0.260319	+	0.260319i	−0.564865	+	0.825184i	$0.691072\pi$
$440$	10.2330	−	0.804982i	0.487838	−	0.0383760i
$441$	3.58804	−	3.58804i	0.170859	−	0.170859i
$442$	−0.707771	−	0.539804i	−0.0336652	−	0.0256759i
$443$	14.1440	−	12.0801i	0.672000	−	0.573942i	−0.246607	−	0.969116i	$-0.579316\pi$
$443$	14.1440	−	12.0801i	0.672000	−	0.573942i	0.918606	+	0.395174i	$0.129316\pi$
$444$	4.12450	+	2.34916i	0.195740	+	0.111486i
$445$	11.3034	−	6.92673i	0.535832	−	0.328358i
$446$	−0.568980	−	10.2803i	−0.0269420	−	0.486788i
$447$	13.6116	−	41.8921i	0.643806	−	1.98143i
$448$	−20.4510	+	10.8773i	−0.966217	+	0.513905i
$449$	19.9427	−	14.4892i	0.941155	−	0.683789i	−0.00754325	−	0.999972i	$-0.502401\pi$
$449$	19.9427	−	14.4892i	0.941155	−	0.683789i	0.948698	+	0.316182i	$0.102401\pi$
$450$	−15.2898	+	12.4558i	−0.720769	+	0.587172i
$451$	19.6599	+	27.5679i	0.925747	+	1.29812i
$452$	−8.08536	−	1.66913i	−0.380303	−	0.0785095i
$453$	38.7829	+	23.7662i	1.82218	+	1.11663i
$454$	−14.8470	+	10.2683i	−0.696805	+	0.481913i
$455$	0.335860	−	0.171129i	0.0157454	−	0.00802266i
$456$	−26.7565	+	19.8014i	−1.25299	+	0.927286i
$457$	28.1383	−	4.45667i	1.31625	−	0.208474i	0.541481	−	0.840713i	$-0.317864\pi$
$457$	28.1383	−	4.45667i	1.31625	−	0.208474i	0.774773	+	0.632239i	$0.217864\pi$
$458$	13.8553	+	14.5150i	0.647416	+	0.678243i
$459$	−6.92945	+	5.91831i	−0.323439	+	0.276243i
$460$	−12.3612	+	0.396191i	−0.576344	+	0.0184725i
$461$	12.3500	−	29.8156i	0.575199	−	1.38865i	−0.321879	−	0.946781i	$-0.604315\pi$
$461$	12.3500	−	29.8156i	0.575199	−	1.38865i	0.897078	−	0.441872i	$-0.145685\pi$
$462$	11.9003	−	32.9860i	0.553653	−	1.53465i
$463$	18.5549			0.862321			0.431160	−	0.902275i	$-0.358104\pi$
$463$	18.5549			0.862321			0.431160	+	0.902275i	$0.358104\pi$
$464$	19.8779	+	3.44368i	0.922808	+	0.159869i
$465$	17.8332	−	5.79436i	0.826995	−	0.268707i
$466$	22.9394	+	10.1328i	1.06265	+	0.469394i
$467$	−6.51854	+	3.99457i	−0.301642	+	0.184847i	−0.665080	−	0.746772i	$-0.731603\pi$
$467$	−6.51854	+	3.99457i	−0.301642	+	0.184847i	0.363438	+	0.931618i	$0.381603\pi$
$468$	0.371041	−	0.789782i	0.0171514	−	0.0365077i
$469$	−0.891126	−	11.3228i	−0.0411484	−	0.522840i
$470$	−3.09032	−	0.563397i	−0.142546	−	0.0259875i
$471$	7.23718	−	45.6937i	0.333472	−	2.10546i
$472$	−26.4484	+	31.5241i	−1.21739	+	1.45101i
$473$	0.278034	−	3.17430i	0.0127840	−	0.145954i
$474$	−1.01788	−	3.39968i	−0.0467526	−	0.156152i
$475$	9.05597	−	14.7780i	0.415516	−	0.678061i
$476$	19.1398	−	23.9209i	0.877270	−	1.09641i
$477$	−20.5488	−	17.5504i	−0.940866	−	0.803576i
$478$	−1.77705	−	32.1078i	−0.0812805	−	1.46858i
$479$	−34.1796	−	24.8330i	−1.56171	−	1.13465i	−0.934592	−	0.355721i	$-0.884235\pi$
$479$	−34.1796	−	24.8330i	−1.56171	−	1.13465i	−0.627116	−	0.778926i	$-0.715765\pi$
$480$	−0.602543	+	15.9711i	−0.0275022	+	0.728978i
$481$	0.104003	−	0.0337928i	0.00474215	−	0.00154082i
$482$	−8.79241	+	33.2026i	−0.400483	+	1.51234i
$483$	−16.1689	+	39.0352i	−0.735711	+	1.77616i
$484$	−2.04146	−	21.9051i	−0.0927936	−	0.995685i
$485$	0.588532	−	0.243778i	0.0267239	−	0.0110694i
$486$	24.8394	+	18.9446i	1.12674	+	0.859344i
$487$	12.0721	−	23.6929i	0.547041	−	1.07363i	−0.437622	−	0.899159i	$-0.644179\pi$
$487$	12.0721	−	23.6929i	0.547041	−	1.07363i	0.984663	−	0.174469i	$-0.0558209\pi$
$488$	−17.0476	−	3.93460i	−0.771708	−	0.178111i
$489$	−2.23815	−	14.1311i	−0.101213	−	0.639033i
$490$	0.927480	+	1.92993i	0.0418993	+	0.0871853i
$491$	9.58267	−	0.754172i	0.432460	−	0.0340353i	0.139639	−	0.990203i	$-0.455406\pi$
$491$	9.58267	−	0.754172i	0.432460	−	0.0340353i	0.292821	+	0.956167i	$0.405406\pi$
$492$	−46.1846	+	25.4278i	−2.08216	+	1.14637i
$493$	−25.9443	+	6.22868i	−1.16847	+	0.280525i
$494$	−0.0779263	+	0.762917i	−0.00350607	+	0.0343253i
$495$	−8.55338	−	10.1956i	−0.384446	−	0.458257i
$496$	−10.5126	+	24.3767i	−0.472031	+	1.09455i
$497$	−31.4649	+	22.8606i	−1.41139	+	1.02544i
$498$	−8.72969	−	40.4863i	−0.391187	−	1.81423i
$499$	−29.7851	−	25.4389i	−1.33337	−	1.13880i	−0.979037	−	0.203681i	$-0.934709\pi$
$499$	−29.7851	−	25.4389i	−1.33337	−	1.13880i	−0.354329	−	0.935121i	$-0.615291\pi$
$500$	−6.53676	−	18.1210i	−0.292333	−	0.810398i
$501$	−9.70860	−	2.33083i	−0.433748	−	0.104134i
$502$	21.6974	−	20.7112i	0.968403	−	0.924388i
$503$	18.2327	−	35.7837i	0.812957	−	1.59552i	0.00964960	−	0.999953i	$-0.496928\pi$
$503$	18.2327	−	35.7837i	0.812957	−	1.59552i	0.803307	−	0.595565i	$-0.203072\pi$
$504$	26.8778	+	13.3986i	1.19723	+	0.596823i
$505$	−9.12363	−	9.12363i	−0.405996	−	0.405996i
$506$	1.23118	+	26.4787i	0.0547327	+	1.17712i
$507$	12.8315	+	30.9781i	0.569869	+	1.37579i
$508$	−7.03482	−	15.5545i	−0.312120	−	0.690120i
$509$	−4.31265	−	0.339413i	−0.191155	−	0.0150442i	−0.0174797	−	0.999847i	$-0.505564\pi$
$509$	−4.31265	−	0.339413i	−0.191155	−	0.0150442i	−0.173675	+	0.984803i	$0.555564\pi$
$510$	−7.63295	−	19.7117i	−0.337993	−	0.872849i
$511$	3.88687	−	5.34982i	0.171945	−	0.236662i
$512$	−16.4163	−	15.5725i	−0.725506	−	0.688216i
$513$	7.46686	+	2.42613i	0.329670	+	0.107116i
$514$	−27.5861	−	17.7999i	−1.21677	−	0.785122i
$515$	17.5396	−	4.21088i	0.772887	−	0.185554i
$516$	4.85901	+	1.00309i	0.213906	+	0.0441585i
$517$	−1.11187	+	6.64019i	−0.0488999	+	0.292035i
$518$	1.07952	+	3.60557i	0.0474314	+	0.158420i
$519$	−2.74995	+	17.3625i	−0.120710	+	0.762130i
$520$	0.262648	+	0.258070i	0.0115179	+	0.0113171i
$521$	14.5999	−	7.43903i	0.639634	−	0.325910i	−0.103920	−	0.994586i	$-0.533139\pi$
$521$	14.5999	−	7.43903i	0.639634	−	0.325910i	0.743554	+	0.668676i	$0.233139\pi$
$522$	−11.3296	−	23.5750i	−0.495883	−	1.03185i
$523$	−10.5482	+	43.9364i	−0.461240	+	1.92120i	−0.0797963	+	0.996811i	$0.525427\pi$
$523$	−10.5482	+	43.9364i	−0.461240	+	1.92120i	−0.381444	+	0.924392i	$0.624573\pi$
$524$	−9.30587	+	7.22769i	−0.406529	+	0.315743i
$525$	−28.3426	−	2.23061i	−1.23697	−	0.0973518i
$526$	16.5720	+	28.5103i	0.722574	+	1.24311i
$527$		−	35.1101i		−	1.52942i
$528$	34.2458	+	0.797583i	1.49036	+	0.0347103i
$529$		−	8.93797i		−	0.388607i
$530$	9.85881	−	5.73057i	0.428239	−	0.248920i
$531$	53.1869	+	4.18590i	2.30811	+	0.181652i
$532$	−26.1879	−	3.29170i	−1.13539	−	0.142713i
$533$	−0.283554	+	1.18109i	−0.0122821	+	0.0511585i
$534$	39.8755	−	19.1633i	1.72558	−	0.829275i
$535$	10.4160	−	5.30722i	0.450323	−	0.229451i
$536$	10.2126	−	4.33576i	0.441118	−	0.187277i
$537$	9.03795	−	57.0634i	0.390017	−	2.46247i
$538$	−38.7662	+	11.6067i	−1.67133	+	0.500401i
$539$	4.10730	−	2.04731i	0.176914	−	0.0881840i
$540$	3.14943	−	2.07161i	0.135530	−	0.0891478i
$541$	20.2708	−	4.86658i	0.871509	−	0.209231i	0.227062	−	0.973880i	$-0.427088\pi$
$541$	20.2708	−	4.86658i	0.871509	−	0.209231i	0.644446	+	0.764649i	$0.277088\pi$
$542$	3.54698	−	5.49707i	0.152356	−	0.236119i
$543$	35.1906	+	11.4341i	1.51017	+	0.490685i
$544$	28.0928	+	10.3142i	1.20447	+	0.442217i
$545$	−2.98862	+	4.11348i	−0.128018	+	0.176202i
$546$	1.17307	−	0.454246i	0.0502026	−	0.0194399i
$547$	−28.8476	−	2.27036i	−1.23344	−	0.0970735i	−0.555074	−	0.831801i	$-0.687310\pi$
$547$	−28.8476	−	2.27036i	−1.23344	−	0.0970735i	−0.678362	+	0.734728i	$0.737310\pi$
$548$	2.47868	−	6.57204i	0.105884	−	0.280744i
$549$	8.68066	+	20.9570i	0.370481	+	0.894421i
$550$	−16.6890	+	6.29366i	−0.711621	+	0.268363i
$551$	16.2545	+	16.2545i	0.692465	+	0.692465i
$552$	−41.1728	−	2.87644i	−1.75243	−	0.122430i
$553$	1.27750	−	2.50723i	0.0543248	−	0.106618i
$554$	−28.4857	−	29.8421i	−1.21024	−	1.26787i
$555$	2.52513	+	0.606229i	0.107186	+	0.0257330i
$556$	−29.3190	−	13.7741i	−1.24340	−	0.584153i
$557$	3.78741	+	3.23475i	0.160478	+	0.137061i	0.726061	−	0.687630i	$-0.241349\pi$
$557$	3.78741	+	3.23475i	0.160478	+	0.137061i	−0.565583	+	0.824691i	$0.691349\pi$
$558$	33.6454	−	7.25466i	1.42433	−	0.307114i
$559$	0.0924757	−	0.0671875i	0.00391130	−	0.00284173i
$560$	−9.08977	+	8.83064i	−0.384113	+	0.373162i
$561$	−42.0076	+	16.9673i	−1.77356	+	0.716359i
$562$	14.6769	+	1.49914i	0.619109	+	0.0632375i
$563$	−33.4998	+	8.04260i	−1.41185	+	0.338955i	−0.866468	−	0.499233i	$-0.833615\pi$
$563$	−33.4998	+	8.04260i	−1.41185	+	0.338955i	−0.545382	+	0.838188i	$0.683615\pi$
$564$	−10.0686	−	2.91840i	−0.423966	−	0.122887i
$565$	−4.50289	+	0.354385i	−0.189438	+	0.0149091i
$566$	−11.7359	+	5.64003i	−0.493298	+	0.237068i
$567$	2.96845	+	18.7420i	0.124663	+	0.787092i
$568$	−30.9315	−	22.0602i	−1.29786	−	0.925627i
$569$	9.35633	−	18.3628i	0.392238	−	0.769810i	−0.607461	−	0.794350i	$-0.707812\pi$
$569$	9.35633	−	18.3628i	0.392238	−	0.769810i	0.999699	+	0.0245393i	$0.00781188\pi$
$570$	−11.0440	+	14.4804i	−0.462581	+	0.606518i
$571$	−21.3464	+	8.84198i	−0.893320	+	0.370025i	−0.781648	−	0.623720i	$-0.785621\pi$
$571$	−21.3464	+	8.84198i	−0.893320	+	0.370025i	−0.111672	+	0.993745i	$0.535621\pi$
$572$	0.544943	−	0.570849i	0.0227852	−	0.0238684i
$573$	1.05555	−	2.54832i	0.0440961	−	0.106457i
$574$	−40.4117	−	10.7015i	−1.68675	−	0.446671i
$575$	20.4387	−	6.64093i	0.852352	−	0.276946i
$576$	−4.07921	+	29.0520i	−0.169967	+	1.21050i
$577$	2.07976	+	1.51103i	0.0865816	+	0.0629052i	0.630234	−	0.776405i	$-0.282959\pi$
$577$	2.07976	+	1.51103i	0.0865816	+	0.0629052i	−0.543652	+	0.839311i	$0.682959\pi$
$578$	−15.5143	+	0.858662i	−0.645310	+	0.0357156i
$579$	−12.6062	−	10.7667i	−0.523895	−	0.447448i
$580$	10.9699	−	1.21802i	0.455499	−	0.0505754i
$581$	17.1591	−	28.0011i	0.711880	−	1.16168i
$582$	2.03656	−	0.609753i	0.0844180	−	0.0252751i
$583$	−12.5858	−	20.9510i	−0.521249	−	0.867700i
$584$	6.16079	+	1.94206i	0.254935	+	0.0803630i
$585$	0.0746822	−	0.471525i	0.00308773	−	0.0194951i
$586$	1.35706	−	7.44371i	0.0560597	−	0.307497i
$587$	2.58971	+	32.9054i	0.106889	+	1.35815i	0.783307	+	0.621634i	$0.213531\pi$
$587$	2.58971	+	32.9054i	0.106889	+	1.35815i	−0.676419	+	0.736517i	$0.736469\pi$
$588$	2.42473	+	6.72177i	0.0999940	+	0.277201i
$589$	−25.7915	+	15.8051i	−1.06272	+	0.651236i
$590$	−9.09659	+	20.5935i	−0.374501	+	0.847820i
$591$	−1.08079	+	0.351171i	−0.0444579	+	0.0144452i
$592$	−3.00534	+	2.11780i	−0.123519	+	0.0870410i
$593$	−17.1726			−0.705196			−0.352598	−	0.935775i	$-0.614702\pi$
$593$	−17.1726			−0.705196			−0.352598	+	0.935775i	$0.614702\pi$
$594$	−4.53695	−	6.68541i	−0.186153	−	0.274306i
$595$	6.41411	−	15.4850i	0.262953	−	0.634825i
$596$	24.8857	+	23.3400i	1.01936	+	0.956045i
$597$	−15.5942	+	13.3187i	−0.638226	+	0.545097i
$598$	−0.687826	+	0.656564i	−0.0281273	+	0.0268489i
$599$	−9.98131	+	1.58088i	−0.407825	+	0.0645932i	−0.356977	−	0.934113i	$-0.616193\pi$
$599$	−9.98131	+	1.58088i	−0.407825	+	0.0645932i	−0.0508485	+	0.998706i	$0.516193\pi$
$600$	−6.72037	−	26.9466i	−0.274358	−	1.10009i
$601$	−6.21978	+	3.16914i	−0.253710	+	0.129272i	−0.576221	−	0.817294i	$-0.695473\pi$
$601$	−6.21978	+	3.16914i	−0.253710	+	0.129272i	0.322511	+	0.946566i	$0.395473\pi$
$602$	2.23778	+	3.23564i	0.0912052	+	0.131875i
$603$	−12.2650	−	7.51602i	−0.499471	−	0.306076i
$604$	−29.4349	+	19.3615i	−1.19769	+	0.787807i
$605$	−4.40908	−	11.1997i	−0.179255	−	0.455331i
$606$	−27.1960	−	33.3838i	−1.10476	−	1.35612i
$607$	8.97868	−	6.52339i	0.364433	−	0.264776i	−0.390465	−	0.920618i	$-0.627686\pi$
$607$	8.97868	−	6.52339i	0.364433	−	0.264776i	0.754899	+	0.655841i	$0.227686\pi$
$608$	−5.06946	−	25.2796i	−0.205594	−	1.02522i
$609$	11.6520	−	35.8613i	0.472164	−	1.45317i
$610$	−9.55737	+	0.528966i	−0.386967	+	0.0214172i
$611$	−0.205927	+	0.126192i	−0.00833092	+	0.00510520i
$612$	−10.2617	−	37.4186i	−0.414804	−	1.51256i
$613$	4.85410	−	4.14579i	0.196055	−	0.167447i	−0.546001	−	0.837784i	$-0.683851\pi$
$613$	4.85410	−	4.14579i	0.196055	−	0.167447i	0.742056	+	0.670337i	$0.233851\pi$
$614$	12.9435	−	16.9711i	0.522359	−	0.684897i
$615$	−20.3960	+	20.3960i	−0.822446	+	0.822446i
$616$	19.2057	+	19.2070i	0.773818	+	0.773873i
$617$	−16.8497	−	16.8497i	−0.678345	−	0.678345i	0.281280	−	0.959626i	$-0.409241\pi$
$617$	−16.8497	−	16.8497i	−0.678345	−	0.678345i	−0.959626	+	0.281280i	$0.909241\pi$
$618$	59.6584	−	8.03208i	2.39981	−	0.323098i
$619$	10.0134	+	11.7242i	0.402474	+	0.471237i	0.924218	−	0.381866i	$-0.124718\pi$
$619$	10.0134	+	11.7242i	0.402474	+	0.471237i	−0.521744	+	0.853102i	$0.674718\pi$
$620$	−1.81133	+	14.4105i	−0.0727449	+	0.578741i
$621$	5.08643	+	8.30030i	0.204111	+	0.333080i
$622$	−18.2102	+	20.3440i	−0.730162	+	0.815721i
$623$	33.3632	+	10.8404i	1.33667	+	0.434310i
$624$	0.784461	+	0.945843i	0.0314036	+	0.0378640i
$625$	4.98097	+	6.85572i	0.199239	+	0.274229i
$626$	2.83137	−	27.7197i	0.113164	−	1.10790i
$627$	31.3739	+	23.2203i	1.25295	+	0.927331i
$628$	29.6503	+	20.1233i	1.18318	+	0.803007i
$629$	2.54066	−	4.14598i	0.101303	−	0.165311i
$630$	16.1644	+	2.94692i	0.644004	+	0.117408i
$631$	1.03214	+	2.02568i	0.0410887	+	0.0806410i	0.910638	−	0.413205i	$-0.135591\pi$
$631$	1.03214	+	2.02568i	0.0410887	+	0.0806410i	−0.869549	+	0.493846i	$0.835591\pi$
$632$	2.71862	+	0.406123i	0.108141	+	0.0161547i
$633$	−0.0358803	−	0.226539i	−0.00142611	−	0.00900413i
$634$	−3.44035	−	0.0800019i	−0.136634	−	0.00317728i
$635$	−6.06572	−	7.10205i	−0.240711	−	0.281836i
$636$	34.6740	−	15.6820i	1.37491	−	0.621830i
$637$	0.152097	+	0.0630008i	0.00602632	+	0.00249618i
$638$	−2.94940	−	23.4715i	−0.116768	−	0.929246i
$639$			49.2578i			1.94861i
$640$	−10.9982	−	5.68264i	−0.434743	−	0.224626i
$641$	6.49719	+	19.9963i	0.256624	+	0.789806i	0.993505	+	0.113785i	$0.0362974\pi$
$641$	6.49719	+	19.9963i	0.256624	+	0.789806i	−0.736882	+	0.676022i	$0.763703\pi$
$642$	36.3802	−	14.0875i	1.43581	−	0.555990i
$643$	−1.65145	−	2.69492i	−0.0651268	−	0.106277i	0.818419	−	0.574621i	$-0.194851\pi$
$643$	−1.65145	−	2.69492i	−0.0651268	−	0.106277i	−0.883546	+	0.468344i	$0.844851\pi$
$644$	−22.0406	−	24.1919i	−0.868520	−	0.953295i
$645$	2.70607	−	0.212972i	0.106551	−	0.00838578i
$646$	19.3965	+	28.0457i	0.763147	+	1.10345i
$647$	36.3920	+	5.76393i	1.43072	+	0.226604i	0.823222	−	0.567719i	$-0.192174\pi$
$647$	36.3920	+	5.76393i	1.43072	+	0.226604i	0.607496	+	0.794323i	$0.292174\pi$
$648$	−16.4414	+	8.56017i	−0.645878	+	0.336275i
$649$	44.4144	+	18.8580i	1.74342	+	0.740242i
$650$	−0.563189	−	0.303653i	−0.0220901	−	0.0119103i
$651$	42.3065	+	25.9255i	1.65812	+	1.01610i
$652$	10.6439	+	3.08514i	0.416848	+	0.120823i
$653$	1.44049	−	1.68659i	0.0563706	−	0.0660015i	−0.731504	−	0.681837i	$-0.761181\pi$
$653$	1.44049	−	1.68659i	0.0563706	−	0.0660015i	0.787875	+	0.615835i	$0.211181\pi$
$654$	−11.3169	+	12.6430i	−0.442528	+	0.494382i
$655$	−3.78917	+	5.21534i	−0.148055	+	0.203780i
$656$	−2.61505	−	40.7529i	−0.102100	−	1.59113i
$657$	−2.58804	−	7.96517i	−0.100969	−	0.310751i
$658$	−4.17724	−	7.18647i	−0.162846	−	0.280158i
$659$	−0.486375	−	0.201463i	−0.0189465	−	0.00784789i	0.373190	−	0.927755i	$-0.378264\pi$
$659$	−0.486375	−	0.201463i	−0.0189465	−	0.00784789i	−0.392137	+	0.919907i	$0.628264\pi$
$660$	18.1168	−	4.79684i	0.705197	−	0.186717i
$661$	6.83039	+	16.4900i	0.265671	+	0.641387i	0.999270	−	0.0381952i	$-0.0121609\pi$
$661$	6.83039	+	16.4900i	0.265671	+	0.641387i	−0.733599	+	0.679583i	$0.762161\pi$
$662$	−3.53792	−	26.2779i	−0.137505	−	1.02132i
$663$	−1.44806	−	0.737826i	−0.0562382	−	0.0286548i
$664$	31.2584	+	7.21447i	1.21306	+	0.279976i
$665$	−14.2625	+	2.25896i	−0.553075	+	0.0875985i
$666$	4.49798	+	1.57800i	0.174293	+	0.0611463i
$667$	2.23629	+	28.4148i	0.0865896	+	1.10023i
$668$	4.83165	−	6.03861i	0.186942	−	0.233641i
$669$	−4.38845	−	18.2792i	−0.169667	−	0.706715i
$670$	4.70610	−	3.83381i	0.181813	−	0.148113i
$671$	1.42905	+	20.4658i	0.0551680	+	0.790072i
$672$	−33.1720	+	26.2348i	−1.27964	+	1.01203i
$673$	−13.4206	−	18.4718i	−0.517325	−	0.712037i	0.467808	−	0.883830i	$-0.345044\pi$
$673$	−13.4206	−	18.4718i	−0.517325	−	0.712037i	−0.985133	+	0.171793i	$0.945044\pi$
$674$	−13.1815	−	8.50537i	−0.507733	−	0.327615i
$675$	−4.25414	+	4.98096i	−0.163742	+	0.191717i
$676$	−25.9436	−	1.20724i	−0.997831	−	0.0464322i
$677$	1.50466	−	6.26737i	0.0578288	−	0.240874i	−0.935968	−	0.352085i	$-0.885473\pi$
$677$	1.50466	−	6.26737i	0.0578288	−	0.240874i	0.993797	+	0.111211i	$0.0354728\pi$
$678$	−15.0695	−	0.350426i	−0.578741	−	0.0134580i
$679$	1.50194	+	0.765279i	0.0576393	+	0.0293687i
$680$	16.3330	+	1.14107i	0.626343	+	0.0437580i
$681$	−23.3057	+	23.3057i	−0.893076	+	0.893076i
$682$	30.9388	+	3.43635i	1.18471	+	0.131585i
$683$	−20.1847	+	8.36078i	−0.772346	+	0.319916i	−0.733822	−	0.679341i	$-0.762266\pi$
$683$	−20.1847	+	8.36078i	−0.772346	+	0.319916i	−0.0385240	+	0.999258i	$0.512266\pi$
$684$	−22.8679	+	24.3824i	−0.874377	+	0.932283i
$685$	0.301504	−	3.83097i	0.0115199	−	0.146374i
$686$	9.29236	−	21.0367i	0.354784	−	0.803183i
$687$	29.6400	+	21.5347i	1.13084	+	0.821601i
$688$	−2.30358	+	3.07607i	−0.0878231	+	0.117274i
$689$	0.270930	−	0.833838i	0.0103216	−	0.0317667i
$690$	−22.0734	+	4.75949i	−0.840321	+	0.181191i
$691$	8.78838	+	36.6062i	0.334326	+	1.39257i	0.845906	+	0.533332i	$0.179060\pi$
$691$	8.78838	+	36.6062i	0.334326	+	1.39257i	−0.511580	+	0.859235i	$0.670940\pi$
$692$	−11.2664	−	7.64637i	−0.428285	−	0.290671i
$693$	5.81578	−	34.7325i	0.220923	−	1.31938i
$694$	−12.7935	+	23.7282i	−0.485633	+	0.900709i
$695$	−17.5044	−	2.77242i	−0.663978	−	0.105164i
$696$	36.8323	−	0.323781i	1.39613	−	0.0122729i
$697$	24.5198	+	48.1228i	0.928753	+	1.82278i
$698$	−9.82281	−	3.44608i	−0.371799	−	0.130436i
$699$	44.5218	+	10.6887i	1.68397	+	0.404285i
$700$	10.8987	−	19.1351i	0.411931	−	0.723240i
$701$	−2.67852	+	34.0338i	−0.101166	+	1.28544i	0.711490	+	0.702696i	$0.248021\pi$
$701$	−2.67852	+	34.0338i	−0.101166	+	1.28544i	−0.812657	+	0.582743i	$0.801979\pi$
$702$	0.0741938	−	0.280176i	0.00280026	−	0.0105746i
$703$	−4.18928			−0.158002
$704$	−11.8383	+	23.7456i	−0.446173	+	0.894947i
$705$	−5.73533			−0.216005
$706$	2.72332	−	10.2840i	0.102494	−	0.387044i
$707$	2.67883	−	34.0377i	0.100748	−	1.28012i
$708$	−37.1836	+	65.2844i	−1.39744	+	2.45354i
$709$	3.19011	+	0.765879i	0.119807	+	0.0287632i	0.292906	−	0.956141i	$-0.405378\pi$
$709$	3.19011	+	0.765879i	0.119807	+	0.0287632i	−0.173098	+	0.984905i	$0.555378\pi$
$710$	−19.6137	−	6.88097i	−0.736090	−	0.258238i
$711$	−1.61796	−	3.17542i	−0.0606782	−	0.119088i
$712$	0.301227	+	34.2666i	0.0112889	+	1.28420i
$713$	−37.0448	−	5.86732i	−1.38734	−	0.219733i
$714$	26.5456	−	49.2344i	0.993443	−	1.84255i
$715$	0.199409	−	0.382967i	0.00745746	−	0.0143222i
$716$	37.0280	+	25.1304i	1.38380	+	0.939168i
$717$	−13.7061	−	57.0900i	−0.511864	−	2.13207i
$718$	49.2797	−	10.6257i	1.83910	−	0.396549i
$719$	−8.40768	+	25.8762i	−0.313553	+	0.965018i	0.662792	+	0.748803i	$0.269371\pi$
$719$	−8.40768	+	25.8762i	−0.313553	+	0.965018i	−0.976346	+	0.216215i	$0.930629\pi$
$720$	2.28136	+	15.8874i	0.0850212	+	0.592089i
$721$	38.6157	+	28.0560i	1.43812	+	1.04486i
$722$	1.01354	−	2.29451i	0.0377199	−	0.0853928i
$723$	−4.92024	+	62.5176i	−0.182986	+	2.32506i
$724$	−19.6063	+	20.9047i	−0.728662	+	0.776918i
$725$	−17.7190	+	7.33947i	−0.658069	+	0.272581i
$726$	−10.8400	−	38.6774i	−0.402310	−	1.43545i
$727$	27.4529	−	27.4529i	1.01817	−	1.01817i	0.0183388	−	0.999832i	$-0.494162\pi$
$727$	27.4529	−	27.4529i	1.01817	−	1.01817i	0.999832	−	0.0183388i	$-0.00583773\pi$
$728$	−0.0679064	+	0.971997i	−0.00251678	+	0.0360246i
$729$	33.3024	+	16.9684i	1.23342	+	0.628460i
$730$	3.53314	+	0.0821596i	0.130767	+	0.00304086i
$731$	1.18652	−	4.94221i	0.0438850	−	0.182794i
$732$	−31.9093	−	1.48484i	−1.17940	−	0.0548812i
$733$	1.12638	−	1.31882i	0.0416037	−	0.0487117i	−0.739214	−	0.673471i	$-0.764803\pi$
$733$	1.12638	−	1.31882i	0.0416037	−	0.0487117i	0.780818	+	0.624759i	$0.214803\pi$
$734$	26.4814	+	17.0871i	0.977445	+	0.630696i
$735$	2.29792	+	3.16282i	0.0847601	+	0.116662i
$736$	15.5772	−	27.9171i	0.574182	−	1.02904i
$737$	−8.36161	−	9.96699i	−0.308004	−	0.367139i
$738$	−41.0488	+	33.4403i	−1.51103	+	1.23095i
$739$	0.871338	+	3.62938i	0.0320527	+	0.133509i	0.986102	−	0.166140i	$-0.0531304\pi$
$739$	0.871338	+	3.62938i	0.0320527	+	0.133509i	−0.954049	+	0.299649i	$0.903130\pi$
$740$	−1.25667	+	1.57059i	−0.0461962	+	0.0577361i
$741$	0.109857	+	1.39587i	0.00403571	+	0.0512785i
$742$	28.4737	+	9.98928i	1.04530	+	0.366718i
$743$	−28.5116	+	4.51579i	−1.04599	+	0.165668i	−0.655698	−	0.755024i	$-0.727625\pi$
$743$	−28.5116	+	4.51579i	−1.04599	+	0.165668i	−0.390290	+	0.920692i	$0.627625\pi$
$744$	−10.9002	+	47.2279i	−0.399622	+	1.73146i
$745$	16.6317	+	8.47430i	0.609340	+	0.310474i
$746$	−1.82877	−	13.5832i	−0.0669560	−	0.497317i
$747$	−15.9168	−	38.4266i	−0.582366	−	1.40596i
$748$	1.94049	−	35.0381i	0.0709515	−	1.28112i
$749$	28.5794	+	11.8380i	1.04427	+	0.432551i
$750$	−17.6753	−	30.4084i	−0.645411	−	1.11036i
$751$	3.55350	+	10.9366i	0.129669	+	0.399081i	0.994723	−	0.102599i	$-0.0327157\pi$
$751$	3.55350	+	10.9366i	0.129669	+	0.399081i	−0.865054	+	0.501679i	$0.832716\pi$
$752$	5.36215	−	6.09750i	0.195538	−	0.222353i
$753$	32.1906	−	44.3066i	1.17309	−	1.61462i
$754$	0.565978	−	0.632298i	0.0206117	−	0.0230269i
$755$	−12.5184	+	14.6572i	−0.455592	+	0.533430i
$756$	9.58088	+	2.77702i	0.348453	+	0.100999i
$757$	−23.6075	−	14.4667i	−0.858031	−	0.525802i	0.0225239	−	0.999746i	$-0.492830\pi$
$757$	−23.6075	−	14.4667i	−0.858031	−	0.525802i	−0.880555	+	0.473944i	$0.842830\pi$
$758$	−8.42891	−	4.54460i	−0.306152	−	0.165067i
$759$	10.8823	+	47.1578i	0.395001	+	1.71172i
$760$	−6.51419	−	12.5117i	−0.236295	−	0.453847i
$761$	38.4003	+	6.08201i	1.39201	+	0.220473i	0.806999	−	0.590553i	$-0.201090\pi$
$761$	38.4003	+	6.08201i	1.39201	+	0.220473i	0.585010	+	0.811026i	$0.301090\pi$
$762$	−17.7295	−	25.6353i	−0.642272	−	0.928670i
$763$	−13.4131	+	1.05563i	−0.485587	+	0.0382165i
$764$	1.43886	+	1.57931i	0.0520563	+	0.0571374i
$765$	−11.0915	−	18.0996i	−0.401013	−	0.654394i
$766$	35.0057	−	13.5552i	1.26481	−	0.489771i
$767$	0.534886	+	1.64621i	0.0193136	+	0.0594412i
$768$	−34.5864	−	22.5956i	−1.24803	−	0.815349i
$769$		−	11.2297i		−	0.404952i	−0.979287	−	0.202476i	$-0.935101\pi$
$769$		−	11.2297i		−	0.404952i	0.979287	−	0.202476i	$-0.0648988\pi$
$770$	13.0175	+	7.16763i	0.469119	+	0.258304i
$771$	−55.3790	−	22.9387i	−1.99443	−	0.826118i
$772$	11.7000	−	5.29156i	0.421093	−	0.190447i
$773$	−1.54335	−	1.80703i	−0.0555104	−	0.0649943i	0.731956	−	0.681352i	$-0.238608\pi$
$773$	−1.54335	−	1.80703i	−0.0555104	−	0.0649943i	−0.787466	+	0.616358i	$0.788608\pi$
$774$	4.98120	+	0.115833i	0.179045	+	0.00416352i
$775$	−3.94802	−	24.9268i	−0.141817	−	0.895398i
$776$	−0.243286	+	1.62857i	−0.00873344	+	0.0584623i
$777$	3.11973	+	6.12281i	0.111920	+	0.219655i
$778$	−31.7345	−	5.78550i	−1.13774	−	0.207420i
$779$	24.3127	−	39.6747i	0.871093	−	1.42149i
$780$	0.556276	+	0.377537i	0.0199179	+	0.0135180i
$781$	−14.1401	+	42.2463i	−0.505972	+	1.51169i
$782$	−4.29636	+	42.0623i	−0.153637	+	1.50415i
$783$	−5.10652	−	7.02852i	−0.182492	−	0.251179i
$784$	−5.51095	−	0.513997i	−0.196820	−	0.0183570i
$785$	18.6455	+	6.05829i	0.665486	+	0.216230i
$786$	−14.3484	+	16.0297i	−0.511790	+	0.571760i
$787$	9.18242	+	14.9844i	0.327318	+	0.534135i	0.973394	−	0.229139i	$-0.0735910\pi$
$787$	9.18242	+	14.9844i	0.327318	+	0.534135i	−0.646076	+	0.763273i	$0.723591\pi$
$788$	0.109777	−	0.873360i	0.00391065	−	0.0311122i
$789$	39.1027	+	45.7834i	1.39209	+	1.62993i
$790$	1.49042	−	0.200663i	0.0530269	−	0.00713925i
$791$	−8.45153	−	8.45153i	−0.300502	−	0.300502i
$792$	33.9773	−	5.38023i	1.20733	−	0.191178i
$793$	−0.520393	+	0.520393i	−0.0184797	+	0.0184797i
$794$	−20.7954	+	27.2662i	−0.738002	+	0.967640i
$795$	15.8318	−	13.5217i	0.561497	−	0.479564i
$796$	−4.20109	−	15.3190i	−0.148904	−	0.542968i
$797$	39.9782	−	24.4987i	1.41610	−	0.867787i	0.416947	−	0.908931i	$-0.363100\pi$
$797$	39.9782	−	24.4987i	1.41610	−	0.867787i	0.999153	+	0.0411434i	$0.0131001\pi$
$798$	−48.1166	+	2.66308i	−1.70331	+	0.0942722i
$799$	−3.31856	+	10.2135i	−0.117402	+	0.361327i
$800$	21.1046	+	4.16372i	0.746159	+	0.147210i
$801$	35.9440	−	26.1148i	1.27002	−	0.922722i
$802$	−2.56215	−	3.14510i	−0.0904727	−	0.111058i
$803$	0.0668553	−	7.57431i	0.00235927	−	0.267292i
$804$	16.9241	−	11.1322i	0.596866	−	0.392601i
$805$	−15.2664	−	9.35529i	−0.538071	−	0.329730i
$806$	0.635187	+	0.918426i	0.0223735	+	0.0323502i
$807$	−65.8309	+	33.5425i	−2.31736	+	1.18075i
$808$	32.3612	−	8.07075i	1.13846	−	0.283928i
$809$	−5.34683	+	0.846854i	−0.187984	+	0.0297738i	−0.249717	−	0.968319i	$-0.580337\pi$
$809$	−5.34683	+	0.846854i	−0.187984	+	0.0297738i	0.0617323	+	0.998093i	$0.480337\pi$
$810$	−7.33575	+	7.00234i	−0.257752	+	0.246037i
$811$	6.65568	−	5.68449i	0.233712	−	0.199609i	−0.524877	−	0.851178i	$-0.675889\pi$
$811$	6.65568	−	5.68449i	0.233712	−	0.199609i	0.758590	+	0.651569i	$0.225889\pi$
$812$	21.3031	+	19.9800i	0.747593	+	0.701159i
$813$	4.57099	−	11.0353i	0.160312	−	0.387026i
$814$	3.40474	+	2.64459i	0.119336	+	0.0926927i
$815$	6.06301			0.212378
$816$	53.8377	+	9.32693i	1.88470	+	0.326508i
$817$	−4.16461	+	1.35316i	−0.145701	+	0.0473412i
$818$	16.4118	−	37.1541i	0.573825	−	1.29906i
$819$	1.07713	−	0.660067i	0.0376380	−	0.0230646i
$820$	−7.58119	−	21.0164i	−0.264747	−	0.733924i
$821$	−0.0680188	−	0.864261i	−0.00237387	−	0.0301629i	0.995616	−	0.0935316i	$-0.0298156\pi$
$821$	−0.0680188	−	0.864261i	−0.00237387	−	0.0301629i	−0.997990	+	0.0633687i	$0.979816\pi$
$822$	2.30009	−	12.6164i	0.0802248	−	0.440046i
$823$	−8.06359	+	50.9115i	−0.281079	+	1.77466i	0.293247	+	0.956037i	$0.405264\pi$
$823$	−8.06359	+	50.9115i	−0.281079	+	1.77466i	−0.574326	+	0.818626i	$0.694736\pi$
$824$	−14.0180	+	44.4694i	−0.488341	+	1.54916i
$825$	−27.9158	+	16.7697i	−0.971904	+	0.583847i
$826$	−57.0704	+	17.0871i	−1.98573	+	0.594536i
$827$	−14.6890	+	23.9703i	−0.510788	+	0.833531i	−0.999237	−	0.0390620i	$-0.987563\pi$
$827$	−14.6890	+	23.9703i	−0.510788	+	0.833531i	0.488449	+	0.872593i	$0.337563\pi$
$828$	−41.1954	+	4.57404i	−1.43164	+	0.158959i
$829$	−32.7943	−	28.0089i	−1.13899	−	0.972791i	−0.139145	−	0.990272i	$-0.544435\pi$
$829$	−32.7943	−	28.0089i	−1.13899	−	0.972791i	−0.999847	+	0.0174812i	$0.994435\pi$
$830$	17.5244	−	0.969911i	0.608280	−	0.0336661i
$831$	−60.9383	−	44.2743i	−2.11393	−	1.53586i
$832$	−0.921460	+	0.238431i	−0.0319459	+	0.00826611i
$833$	6.96197	−	2.26208i	0.241218	−	0.0783765i
$834$	−57.1733	−	15.1401i	−1.97975	−	0.524260i
$835$	1.61918	−	3.90905i	0.0560341	−	0.135278i
$836$	−26.6121	+	14.3471i	−0.920398	+	0.496206i
$837$	10.5619	−	4.37490i	0.365074	−	0.151219i
$838$	−5.43833	+	7.13053i	−0.187864	+	0.246320i
$839$	−11.7072	+	22.9767i	−0.404178	+	0.793244i	−0.999951	−	0.00990864i	$-0.996846\pi$
$839$	−11.7072	+	22.9767i	−0.404178	+	0.793244i	0.595773	+	0.803153i	$0.296846\pi$
$840$	−13.4353	+	18.8382i	−0.463562	+	0.649978i
$841$	0.557397	+	3.51927i	0.0192206	+	0.121354i
$842$	33.8368	−	16.2612i	1.16609	−	0.560398i
$843$	26.8536	−	2.11343i	0.924888	−	0.0727902i
$844$	0.170635	+	0.0494585i	0.00587349	+	0.00170243i
$845$	−13.8166	+	3.31708i	−0.475306	+	0.114111i
$846$	−10.4731	−	1.06975i	−0.360073	−	0.0367788i
$847$	14.9583	−	28.1190i	0.513974	−	0.966180i
$848$	−0.426196	+	29.4734i	−0.0146356	+	1.01212i
$849$	−19.2332	+	13.9737i	−0.660080	+	0.479576i
$850$	−27.8111	+	5.99666i	−0.953914	+	0.205684i
$851$	−3.94986	−	3.37350i	−0.135399	−	0.115642i
$852$	−62.7830	−	29.4956i	−2.15091	−	1.01050i
$853$	9.51267	+	2.28379i	0.325708	+	0.0781955i	0.393002	−	0.919538i	$-0.371437\pi$
$853$	9.51267	+	2.28379i	0.325708	+	0.0781955i	−0.0672942	+	0.997733i	$0.521437\pi$
$854$	−17.4892	−	18.3220i	−0.598468	−	0.626965i
$855$	−8.30289	+	16.2953i	−0.283953	+	0.557289i
$856$	−2.10598	+	30.1445i	−0.0719808	+	1.03032i
$857$	0.717245	+	0.717245i	0.0245006	+	0.0245006i	0.719251	−	0.694750i	$-0.244485\pi$
$857$	0.717245	+	0.717245i	0.0245006	+	0.0245006i	−0.694750	+	0.719251i	$0.744485\pi$
$858$	0.791892	−	1.20381i	0.0270348	−	0.0410973i
$859$	−3.68915	−	8.90639i	−0.125872	−	0.303882i	0.848364	−	0.529414i	$-0.177588\pi$
$859$	−3.68915	−	8.90639i	−0.125872	−	0.303882i	−0.974236	+	0.225532i	$0.927588\pi$
$860$	−0.741961	+	1.96726i	−0.0253007	+	0.0670829i
$861$	−76.0918	−	5.98855i	−2.59320	−	0.204089i
$862$	45.6057	−	17.6599i	1.55334	−	0.601498i
$863$	−8.84439	+	12.1733i	−0.301067	+	0.414383i	−0.932569	−	0.360991i	$-0.882438\pi$
$863$	−8.84439	+	12.1733i	−0.301067	+	0.414383i	0.631503	+	0.775374i	$0.282438\pi$
$864$	0.397755	+	9.73615i	0.0135319	+	0.331231i
$865$	−7.08484	−	2.30200i	−0.240892	−	0.0782705i
$866$	8.06849	−	12.5044i	0.274178	−	0.424918i
$867$	−27.5856	+	6.62272i	−0.936856	+	0.224919i
$868$	−32.1093	+	21.1205i	−1.08986	+	0.716878i
$869$	−0.476107	−	3.18788i	−0.0161508	−	0.108141i
$870$	19.3052	−	5.78004i	0.654507	−	0.195962i
$871$	0.0730077	−	0.460953i	0.00247377	−	0.0156188i
$872$	−5.13618	−	12.0979i	−0.173933	−	0.409688i
$873$	1.90222	−	0.969230i	0.0643804	−	0.0328035i
$874$	32.8325	−	15.7786i	1.11058	−	0.533718i
$875$	6.51058	−	27.1185i	0.220098	−	0.916774i
$876$	11.7020	+	1.47088i	0.395373	+	0.0496964i
$877$	−32.8166	−	2.58272i	−1.10814	−	0.0872123i	−0.488844	−	0.872371i	$-0.662581\pi$
$877$	−32.8166	−	2.58272i	−1.10814	−	0.0872123i	−0.619294	+	0.785159i	$0.712581\pi$
$878$	−9.43109	+	5.48195i	−0.318284	+	0.185007i
$879$		−	13.8148i		−	0.465961i
$880$	−2.60407	+	14.2808i	−0.0877831	+	0.481407i
$881$			21.8136i			0.734920i	0.930039	+	0.367460i	$0.119773\pi$
$881$			21.8136i			0.734920i	−0.930039	+	0.367460i	$0.880227\pi$
$882$	3.60624	+	6.20413i	0.121428	+	0.208904i
$883$	26.1205	+	2.05573i	0.879025	+	0.0691808i	0.509935	−	0.860213i	$-0.329669\pi$
$883$	26.1205	+	2.05573i	0.879025	+	0.0691808i	0.369090	+	0.929394i	$0.379669\pi$
$884$	0.994190	−	0.772168i	0.0334382	−	0.0259708i
$885$	−9.59565	+	39.9688i	−0.322554	+	1.34354i
$886$	11.3942	+	23.7093i	0.382795	+	0.796531i
$887$	20.7816	−	10.5887i	0.697776	−	0.355535i	−0.0688510	−	0.997627i	$-0.521933\pi$
$887$	20.7816	−	10.5887i	0.697776	−	0.355535i	0.766628	+	0.642092i	$0.221933\pi$
$888$	−4.70468	+	4.78813i	−0.157879	+	0.160679i
$889$	3.86624	−	24.4105i	0.129670	−	0.818702i
$890$	5.37741	+	17.9604i	0.180251	+	0.602034i
$891$	15.2333	+	15.5046i	0.510333	+	0.519423i
$892$	14.2602	+	2.94385i	0.477465	+	0.0985675i
$893$	8.99658	−	2.15989i	0.301059	−	0.0722779i
$894$	52.3427	+	33.7741i	1.75060	+	1.12958i
$895$	23.2849	+	7.56573i	0.778329	+	0.252894i
$896$	−7.46661	−	31.8962i	−0.249442	−	1.06558i
$897$	−1.02047	+	1.40456i	−0.0340725	+	0.0468968i
$898$	12.5884	+	32.5089i	0.420081	+	1.08484i
$899$	33.3691	+	2.62621i	1.11292	+	0.0875889i
$900$	−11.4930	−	25.4119i	−0.383100	−	0.847062i
$901$	−14.9188	−	36.0172i	−0.497018	−	1.19991i
$902$	−44.8052	+	16.8967i	−1.49185	+	0.562598i
$903$	5.07906	+	5.07906i	0.169021	+	0.169021i
$904$	5.20893	−	10.4492i	0.173247	−	0.347534i
$905$	−7.11865	+	13.9711i	−0.236632	+	0.464416i
$906$	−46.5308	+	44.4159i	−1.54588	+	1.47562i
$907$	−15.4423	−	3.70737i	−0.512753	−	0.123101i	−0.0311917	−	0.999513i	$-0.509930\pi$
$907$	−15.4423	−	3.70737i	−0.512753	−	0.123101i	−0.481562	+	0.876412i	$0.659930\pi$
$908$	−8.66271	−	24.0146i	−0.287482	−	0.796951i
$909$	−32.8817	−	28.0836i	−1.09062	−	0.931474i
$910$	0.112361	+	0.521104i	0.00372473	+	0.0172744i
$911$	−43.9746	+	31.9494i	−1.45694	+	1.05853i	−0.472799	+	0.881170i	$0.656756\pi$
$911$	−43.9746	+	31.9494i	−1.45694	+	1.05853i	−0.984146	+	0.177362i	$0.943244\pi$
$912$	−17.3839	−	43.7471i	−0.575640	−	1.44861i
$913$	−2.62031	−	37.5259i	−0.0867196	−	1.24193i
$914$	−4.09398	+	40.0811i	−0.135417	+	1.32576i
$915$	−16.9937	+	4.07983i	−0.561795	+	0.134875i
$916$	−24.8593	+	13.6867i	−0.821374	+	0.452222i
$917$	−17.0060	+	1.33840i	−0.561588	+	0.0441980i
$918$	−5.58226	−	11.6157i	−0.184242	−	0.383377i
$919$	−3.14788	−	19.8749i	−0.103839	−	0.655613i	−0.983623	−	0.180239i	$-0.942313\pi$
$919$	−3.14788	−	19.8749i	−0.103839	−	0.655613i	0.879784	−	0.475374i	$-0.157687\pi$
$920$	3.93339	−	17.0423i	0.129680	−	0.561869i
$921$	17.6917	−	34.7220i	0.582962	−	1.14413i
$922$	36.2897	+	27.6775i	1.19514	+	0.911511i
$923$	−1.47647	+	0.611574i	−0.0485986	+	0.0201302i
$924$	40.7868	+	28.2105i	1.34179	+	0.928056i
$925$	1.33757	−	3.22917i	0.0439789	−	0.106174i
$926$	−6.71728	+	25.3663i	−0.220743	+	0.833588i
$927$	57.4936	−	18.6808i	1.88834	−	0.613558i
$928$	−11.9040	+	25.9282i	−0.390769	+	0.851136i
$929$	18.2389	+	13.2513i	0.598399	+	0.434763i	0.845310	−	0.534275i	$-0.179416\pi$
$929$	18.2389	+	13.2513i	0.598399	+	0.434763i	−0.246911	+	0.969038i	$0.579416\pi$
$930$	1.46543	+	26.4773i	0.0480532	+	0.868225i
$931$	−4.79568	−	4.09589i	−0.157172	−	0.134238i
$932$	−22.1570	+	27.6919i	−0.725778	+	0.907079i
$933$	−26.0472	+	42.5051i	−0.852746	+	1.39155i
$934$	−3.10109	−	10.3576i	−0.101471	−	0.338910i
$935$	−4.31693	−	18.7072i	−0.141179	−	0.611791i
$936$	0.945381	+	0.793166i	0.0309007	+	0.0259254i
$937$	4.44449	−	28.0614i	0.145195	−	0.916726i	−0.802292	−	0.596932i	$-0.796386\pi$
$937$	4.44449	−	28.0614i	0.145195	−	0.916726i	0.947487	−	0.319794i	$-0.103614\pi$
$938$	15.8020	+	2.88085i	0.515952	+	0.0940632i
$939$	−3.99154	−	50.7173i	−0.130259	−	1.65510i
$940$	1.88898	−	4.02080i	0.0616117	−	0.131144i
$941$	−19.3007	+	11.8275i	−0.629183	+	0.385564i	−0.800225	−	0.599700i	$-0.795287\pi$
$941$	−19.3007	+	11.8275i	−0.629183	+	0.385564i	0.171042	+	0.985264i	$0.445287\pi$
$942$	59.8475	+	26.4360i	1.94994	+	0.861331i
$943$	54.8720	−	17.8290i	1.78688	−	0.580592i
$944$	−33.5214	−	47.5698i	−1.09103	−	1.54826i
$945$	5.45749			0.177532
$946$	4.23890	+	1.52926i	0.137819	+	0.0497206i
$947$	10.4163	−	25.1472i	0.338485	−	0.817175i	−0.659376	−	0.751813i	$-0.729180\pi$
$947$	10.4163	−	25.1472i	0.338485	−	0.817175i	0.997862	−	0.0653625i	$-0.0208204\pi$
$948$	5.01617	−	0.160774i	0.162917	−	0.00522170i
$949$	0.206618	−	0.176468i	0.00670710	−	0.00572841i
$950$	16.9244	+	17.7303i	0.549101	+	0.575247i
$951$	−6.20576	+	0.982895i	−0.201235	+	0.0318726i
$952$	25.7731	+	34.8257i	0.835312	+	1.12871i
$953$	−47.0659	+	23.9813i	−1.52461	+	0.776830i	−0.997342	−	0.0728660i	$-0.976785\pi$
$953$	−47.0659	+	23.9813i	−1.52461	+	0.776830i	−0.527273	+	0.849696i	$0.676785\pi$
$954$	31.4321	−	21.7385i	1.01765	−	0.703811i
$955$	0.996631	+	0.610737i	0.0322502	+	0.0197630i
$956$	44.5376	+	9.19431i	1.44045	+	0.297365i
$957$	−12.9838	−	41.1937i	−0.419707	−	1.33160i
$958$	46.3227	−	37.7367i	1.49662	−	1.21922i
$959$	8.22671	−	5.97705i	0.265654	−	0.193009i
$960$	−21.6159	−	6.60561i	−0.697649	−	0.213195i
$961$	−4.03148	+	12.4076i	−0.130048	+	0.400246i
$962$	0.00854637	+	0.154416i	0.000275546	+	0.00497857i
$963$	33.4050	−	20.4706i	1.07646	−	0.659656i
$964$	−42.2079	−	24.0401i	−1.35943	−	0.774279i
$965$	5.34212	−	4.56261i	0.171969	−	0.146875i
$966$	−47.5112	−	36.2360i	−1.52865	−	1.16587i
$967$	−4.83385	+	4.83385i	−0.155446	+	0.155446i	−0.780545	−	0.625099i	$-0.785059\pi$
$967$	−4.83385	+	4.83385i	−0.155446	+	0.155446i	0.625099	+	0.780545i	$0.285059\pi$
$968$	30.6853	+	5.13924i	0.986263	+	0.165181i
$969$	44.0240	+	44.0240i	1.41426	+	1.41426i
$970$	0.120206	+	0.892830i	0.00385958	+	0.0286670i
$971$	−35.1267	−	41.1281i	−1.12727	−	1.31986i	−0.941402	−	0.337288i	$-0.890490\pi$
$971$	−35.1267	−	41.1281i	−1.12727	−	1.31986i	−0.185868	−	0.982575i	$-0.559510\pi$
$972$	−34.8914	+	27.0995i	−1.11914	+	0.869215i
$973$	−24.5036	−	39.9862i	−0.785549	−	1.28190i
$974$	28.0200	+	25.0811i	0.897819	+	0.803649i
$975$	−1.11103	−	0.360997i	−0.0355816	−	0.0115612i
$976$	11.5505	−	21.8812i	0.369724	−	0.700400i
$977$	−26.6885	−	36.7336i	−0.853842	−	1.17521i	−0.983003	−	0.183589i	$-0.941228\pi$
$977$	−26.6885	−	36.7336i	−0.853842	−	1.17521i	0.129161	−	0.991624i	$-0.458772\pi$
$978$	20.1288	+	2.05601i	0.643649	+	0.0657440i
$979$	38.3241	−	12.0794i	1.22484	−	0.386058i
$980$	−2.97416	+	0.569276i	−0.0950060	+	0.0181848i
$981$	−8.90353	+	14.5292i	−0.284268	+	0.463883i
$982$	−2.43811	+	13.3734i	−0.0778031	+	0.426763i
$983$	8.96508	+	17.5950i	0.285942	+	0.561192i	0.988641	−	0.150294i	$-0.0480222\pi$
$983$	8.96508	+	17.5950i	0.285942	+	0.561192i	−0.702700	+	0.711487i	$0.748022\pi$
$984$	−18.0423	−	72.3440i	−0.575167	−	2.30624i
$985$	−0.0753355	−	0.475650i	−0.00240039	−	0.0151555i
$986$	0.877214	−	37.7232i	0.0279362	−	1.20135i
$987$	−9.85646	−	11.5404i	−0.313734	−	0.367336i
$988$	−1.01477	−	0.382725i	−0.0322840	−	0.0121761i
$989$	−5.01626	−	2.07780i	−0.159508	−	0.0660702i
$990$	17.0348	−	8.00224i	0.541402	−	0.254328i
$991$		−	45.2710i		−	1.43808i	−0.694968	−	0.719041i	$-0.744581\pi$
$991$		−	45.2710i		−	1.43808i	0.694968	−	0.719041i	$-0.255419\pi$
$992$	−29.5194	−	23.1966i	−0.937242	−	0.736493i
$993$	−14.9599	−	46.0418i	−0.474738	−	1.46109i
$994$	−19.8615	−	51.2914i	−0.629970	−	1.62686i
$995$	−4.54080	−	7.40991i	−0.143953	−	0.234910i
$996$	58.5088	+	2.72260i	1.85392	+	0.0862688i
$997$	−6.25879	+	0.492577i	−0.198218	+	0.0156001i	−0.177179	−	0.984179i	$-0.556697\pi$
$997$	−6.25879	+	0.492577i	−0.198218	+	0.0156001i	−0.0210385	+	0.999779i	$0.506697\pi$
$998$	45.5602	−	31.5096i	1.44218	−	0.997419i
$999$	1.56378	+	0.247679i	0.0494759	+	0.00783622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.bc.a.19.20	✓	736
11.7	odd	10	inner	352.2.bc.a.51.46	yes	736
32.27	odd	8	inner	352.2.bc.a.283.46	yes	736
352.315	even	40	inner	352.2.bc.a.315.20	yes	736

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.bc.a.19.20	✓	736	1.1	even	1	trivial
352.2.bc.a.51.46	yes	736	11.7	odd	10	inner
352.2.bc.a.283.46	yes	736	32.27	odd	8	inner
352.2.bc.a.315.20	yes	736	352.315	even	40	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:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.bc (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.362021 + 1.36709i) q^{2} +(-0.202587 + 2.57412i) q^{3} +(-1.73788 - 0.989833i) q^{4} +(-1.06398 - 0.255438i) q^{5} +(-3.44571 - 1.20884i) q^{6} +(-1.31451 - 2.57988i) q^{7} +(1.98234 - 2.01750i) q^{8} +(-3.62197 - 0.573664i) q^{9} +(0.734389 - 1.36208i) q^{10} +(-2.94173 - 1.53174i) q^{11} +(2.90002 - 4.27298i) q^{12} +(-0.0277744 - 0.115689i) q^{13} +(4.00281 - 0.863091i) q^{14} +(0.873075 - 2.68705i) q^{15} +(2.04046 + 3.44042i) q^{16} +(-4.27993 - 3.10955i) q^{17} +(2.09548 - 4.74389i) q^{18} +(-0.357602 + 4.54377i) q^{19} +(1.59622 + 1.49708i) q^{20} +(6.90721 - 2.86106i) q^{21} +(3.15900 - 3.46709i) q^{22} +(-3.99612 + 3.99612i) q^{23} +(4.79169 + 5.51150i) q^{24} +(-3.38824 - 1.72639i) q^{25} +(0.168212 + 0.00391160i) q^{26} +(0.402124 - 1.67497i) q^{27} +(-0.269179 + 5.78467i) q^{28} +(3.27549 - 3.83511i) q^{29} +(3.35737 + 2.16634i) q^{30} +(3.90097 + 5.36922i) q^{31} +(-5.44207 + 1.54399i) q^{32} +(4.53884 - 7.26205i) q^{33} +(5.80046 - 4.72533i) q^{34} +(0.739611 + 3.08070i) q^{35} +(5.72673 + 4.58211i) q^{36} +(0.0721150 + 0.916308i) q^{37} +(-6.08229 - 2.13382i) q^{38} +(0.303423 - 0.0480575i) q^{39} +(-2.62451 + 1.64021i) q^{40} +(-9.09645 - 4.63487i) q^{41} +(1.41078 + 10.4786i) q^{42} +(0.367663 + 0.887618i) q^{43} +(3.59621 + 5.57380i) q^{44} +(3.70715 + 1.53555i) q^{45} +(-4.01638 - 6.90975i) q^{46} +(-0.627294 - 1.93061i) q^{47} +(-9.26942 + 4.55540i) q^{48} +(-0.813329 + 1.11945i) q^{49} +(3.58675 - 4.00704i) q^{50} +(8.87140 - 10.3871i) q^{51} +(-0.0662438 + 0.228545i) q^{52} +(6.28322 + 3.85036i) q^{53} +(2.14426 + 1.15611i) q^{54} +(2.73866 + 2.38116i) q^{55} +(-7.81073 - 2.46217i) q^{56} +(-11.6237 - 1.84102i) q^{57} +(4.05715 + 5.86628i) q^{58} +(-14.5037 + 1.14147i) q^{59} +(-4.17703 + 3.80557i) q^{60} +(-3.23201 - 5.27416i) q^{61} +(-8.75246 + 3.38921i) q^{62} +(3.28115 + 10.0983i) q^{63} +(-0.140640 - 7.99876i) q^{64} +0.130184i q^{65} +(8.28473 + 8.83402i) q^{66} +(3.62404 + 1.50113i) q^{67} +(4.36007 + 9.64044i) q^{68} +(-9.47692 - 11.0960i) q^{69} +(-4.47936 - 0.104163i) q^{70} +(-2.10127 - 13.2669i) q^{71} +(-8.33736 + 6.17015i) q^{72} +(1.03684 + 2.03491i) q^{73} +(-1.27878 - 0.233135i) q^{74} +(5.13035 - 8.37198i) q^{75} +(5.11904 - 7.54256i) q^{76} +(-0.0847600 + 9.60280i) q^{77} +(-0.0441465 + 0.432205i) q^{78} +(0.571234 + 0.786237i) q^{79} +(-1.29219 - 4.18174i) q^{80} +(-6.23283 - 2.02517i) q^{81} +(9.62940 - 10.7578i) q^{82} +(5.92620 + 9.67069i) q^{83} +(-14.8359 - 1.86480i) q^{84} +(3.75944 + 4.40174i) q^{85} +(-1.34656 + 0.181293i) q^{86} +(9.20844 + 9.20844i) q^{87} +(-8.92181 + 2.89852i) q^{88} +(-8.56698 + 8.56698i) q^{89} +(-3.44131 + 4.51212i) q^{90} +(-0.261953 + 0.223729i) q^{91} +(10.9003 - 2.98929i) q^{92} +(-14.6113 + 8.95382i) q^{93} +(2.86642 - 0.158646i) q^{94} +(1.54113 - 4.74311i) q^{95} +(-2.87193 - 14.3213i) q^{96} +(-0.470991 + 0.342195i) q^{97} +(-1.23595 - 1.51716i) q^{98} +(9.77616 + 7.23549i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 736 q - 20 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 20 q^{6} - 20 q^{7} - 20 q^{8} - 12 q^{9} - 16 q^{11} - 20 q^{13} - 28 q^{14} - 24 q^{15} - 52 q^{16} - 120 q^{18} - 20 q^{19} + 4 q^{20} - 4 q^{22} - 48 q^{23}+ \cdots - 68 q^{99}+O(q^{100}) \) 736 * q - 20 * q^2 - 12 * q^3 - 12 * q^4 - 12 * q^5 - 20 * q^6 - 20 * q^7 - 20 * q^8 - 12 * q^9 - 16 * q^11 - 20 * q^13 - 28 * q^14 - 24 * q^15 - 52 * q^16 - 120 * q^18 - 20 * q^19 + 4 * q^20 - 4 * q^22 - 48 * q^23 - 20 * q^24 - 12 * q^25 + 48 * q^26 - 12 * q^27 - 20 * q^28 - 20 * q^29 - 20 * q^30 - 32 * q^33 + 24 * q^34 - 20 * q^35 - 12 * q^36 - 12 * q^37 - 12 * q^38 - 20 * q^39 - 20 * q^40 - 20 * q^41 - 52 * q^42 + 24 * q^44 - 8 * q^45 - 20 * q^46 - 24 * q^47 - 12 * q^48 - 20 * q^50 - 20 * q^51 - 20 * q^52 - 60 * q^53 + 16 * q^55 - 248 * q^56 - 20 * q^57 - 12 * q^58 + 20 * q^59 + 68 * q^60 - 20 * q^61 - 20 * q^62 + 132 * q^64 - 8 * q^66 - 112 * q^67 - 20 * q^68 - 12 * q^69 + 36 * q^70 + 20 * q^71 - 320 * q^72 - 20 * q^73 - 20 * q^74 + 124 * q^75 - 32 * q^77 - 80 * q^78 - 40 * q^79 + 124 * q^80 + 28 * q^82 - 20 * q^83 - 20 * q^84 - 20 * q^85 - 116 * q^86 - 20 * q^88 - 32 * q^89 - 20 * q^90 - 156 * q^91 + 148 * q^92 - 36 * q^93 - 160 * q^94 - 20 * q^96 - 24 * q^97 - 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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