LMFDB - Embedded newform 507.2.p.b.25.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			25.8
Character	$\chi$	$=$	507.25
Dual form			507.2.p.b.142.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.103579 - 0.0392824i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.48784 - 1.31811i) q^{4} +(-1.67597 - 0.203500i) q^{5} +(0.0265109 + 0.107559i) q^{6} +(0.366680 + 0.698651i) q^{7} +(0.205293 + 0.391152i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})$	\(q+(-0.103579 - 0.0392824i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.48784 - 1.31811i) q^{4} +(-1.67597 - 0.203500i) q^{5} +(0.0265109 + 0.107559i) q^{6} +(0.366680 + 0.698651i) q^{7} +(0.205293 + 0.391152i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(0.165602 + 0.0869145i) q^{10} +(-3.94607 + 1.49655i) q^{11} +(-0.239594 + 1.97324i) q^{12} +(2.95276 - 2.06911i) q^{13} +(-0.0105358 - 0.0867698i) q^{14} +(0.784583 + 1.49490i) q^{15} +(0.473290 + 3.89789i) q^{16} +(-1.59829 + 0.838846i) q^{17} +(0.0734594 - 0.0829185i) q^{18} +2.59395i q^{19} +(2.22534 + 2.51188i) q^{20} +(0.366680 - 0.698651i) q^{21} +0.467518 q^{22} +6.75809 q^{23} +(0.205293 - 0.391152i) q^{24} +(-2.08724 - 0.514459i) q^{25} +(-0.387124 + 0.0983253i) q^{26} +(0.970942 - 0.239316i) q^{27} +(0.375337 - 1.52280i) q^{28} +(-2.66600 + 7.02966i) q^{29} +(-0.0225433 - 0.185661i) q^{30} +(2.10992 + 8.56026i) q^{31} +(0.315532 - 1.28016i) q^{32} +(3.47325 + 2.39741i) q^{33} +(0.198501 - 0.0241024i) q^{34} +(-0.472370 - 1.24554i) q^{35} +(1.76005 - 0.923743i) q^{36} +(0.655680 + 2.66020i) q^{37} +(0.101897 - 0.268680i) q^{38} +(-3.38020 - 1.25468i) q^{39} +(-0.264465 - 0.697337i) q^{40} +(-3.11397 + 2.14942i) q^{41} +(-0.0654251 + 0.0579616i) q^{42} +(2.07311 + 0.510976i) q^{43} +(7.84371 + 2.97473i) q^{44} +(0.784583 - 1.49490i) q^{45} +(-0.699998 - 0.265474i) q^{46} +(-0.813950 - 0.918759i) q^{47} +(2.93904 - 2.60376i) q^{48} +(3.62279 - 5.24852i) q^{49} +(0.195986 + 0.135279i) q^{50} +(1.59829 + 0.838846i) q^{51} +(-7.12053 - 0.813557i) q^{52} +(-10.4252 + 5.47157i) q^{53} +(-0.109970 - 0.0133528i) q^{54} +(6.91804 - 1.70514i) q^{55} +(-0.198002 + 0.286856i) q^{56} +(2.13478 - 1.47353i) q^{57} +(0.552284 - 0.623400i) q^{58} +(-11.4794 - 1.39385i) q^{59} +(0.803106 - 3.25833i) q^{60} +(-8.48800 - 4.45485i) q^{61} +(0.117724 - 0.969548i) q^{62} +(-0.783276 + 0.0951069i) q^{63} +(4.37806 - 6.34272i) q^{64} +(-5.36980 + 2.86688i) q^{65} +(-0.265581 - 0.384760i) q^{66} +(-2.93118 - 3.30862i) q^{67} +(3.48368 + 0.858650i) q^{68} +(-3.83903 - 5.56180i) q^{69} +0.147568i q^{70} +(-5.12174 + 3.53528i) q^{71} +(-0.438532 + 0.0532474i) q^{72} +(2.59240 - 0.983168i) q^{73} +(0.0365842 - 0.301298i) q^{74} +(0.762297 + 2.01001i) q^{75} +(3.41911 - 3.85938i) q^{76} +(-2.49251 - 2.20817i) q^{77} +(0.300832 + 0.262742i) q^{78} +(6.26327 - 5.54877i) q^{79} -6.62907i q^{80} +(-0.748511 - 0.663123i) q^{81} +(0.406976 - 0.100311i) q^{82} +(-0.207021 - 0.142896i) q^{83} +(-1.46646 + 0.556154i) q^{84} +(2.84939 - 1.08063i) q^{85} +(-0.194659 - 0.134363i) q^{86} +(7.29976 - 1.79923i) q^{87} +(-1.39548 - 1.23628i) q^{88} +8.34850i q^{89} +(-0.139990 + 0.124020i) q^{90} +(2.52830 + 1.30424i) q^{91} +(-10.0549 - 8.90789i) q^{92} +(5.84639 - 6.59921i) q^{93} +(0.0482172 + 0.127138i) q^{94} +(0.527869 - 4.34739i) q^{95} +(-1.23280 + 0.467538i) q^{96} +(-12.7824 + 1.55206i) q^{97} +(-0.581421 + 0.401326i) q^{98} -4.22032i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	$ 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) $ 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{3}{26}\right)$

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 $

$2$	−0.103579	−	0.0392824i	−0.0732416	−	0.0277769i	0.317712	−	0.948187i	$-0.397085\pi$
$2$	−0.103579	−	0.0392824i	−0.0732416	−	0.0277769i	−0.390954	+	0.920410i	$0.627855\pi$
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$3$	−0.568065	−	0.822984i	−0.327972	−	0.475150i
$4$	−1.48784	−	1.31811i	−0.743918	−	0.659054i
$5$	−1.67597	−	0.203500i	−0.749517	−	0.0910078i	−0.263141	−	0.964757i	$-0.584758\pi$
$5$	−1.67597	−	0.203500i	−0.749517	−	0.0910078i	−0.486376	+	0.873750i	$0.661682\pi$
$6$	0.0265109	+	0.107559i	0.0108230	+	0.0439108i
$7$	0.366680	+	0.698651i	0.138592	+	0.264065i	0.944853	−	0.327495i	$-0.106205\pi$
$7$	0.366680	+	0.698651i	0.138592	+	0.264065i	−0.806261	+	0.591560i	$0.798512\pi$
$8$	0.205293	+	0.391152i	0.0725819	+	0.138293i
$9$	−0.354605	+	0.935016i	−0.118202	+	0.311672i
$10$	0.165602	+	0.0869145i	0.0523679	+	0.0274848i
$11$	−3.94607	+	1.49655i	−1.18978	+	0.451225i	−0.868467	−	0.495746i	$-0.834895\pi$
$11$	−3.94607	+	1.49655i	−1.18978	+	0.451225i	−0.321316	+	0.946972i	$0.604125\pi$
$12$	−0.239594	+	1.97324i	−0.0691649	+	0.569624i
$13$	2.95276	−	2.06911i	0.818948	−	0.573868i
$13$	2.95276	−	2.06911i	0.818948	−	0.573868i
$14$	−0.0105358	−	0.0867698i	−0.00281580	−	0.0231902i
$15$	0.784583	+	1.49490i	0.202578	+	0.385981i
$16$	0.473290	+	3.89789i	0.118322	+	0.974473i
$17$	−1.59829	+	0.838846i	−0.387642	+	0.203450i	−0.647274	−	0.762258i	$-0.724091\pi$
$17$	−1.59829	+	0.838846i	−0.387642	+	0.203450i	0.259632	+	0.965708i	$0.416399\pi$
$18$	0.0734594	−	0.0829185i	0.0173145	−	0.0195441i
$19$			2.59395i			0.595094i	0.954707	+	0.297547i	$0.0961685\pi$
$19$			2.59395i			0.595094i	−0.954707	+	0.297547i	$0.903832\pi$
$20$	2.22534	+	2.51188i	0.497600	+	0.561674i
$21$	0.366680	−	0.698651i	0.0800162	−	0.152458i
$22$	0.467518			0.0996753
$23$	6.75809			1.40916			0.704580	−	0.709625i	$-0.251135\pi$
$23$	6.75809			1.40916			0.704580	+	0.709625i	$0.251135\pi$
$24$	0.205293	−	0.391152i	0.0419052	−	0.0798437i
$25$	−2.08724	−	0.514459i	−0.417448	−	0.102892i
$26$	−0.387124	+	0.0983253i	−0.0759213	+	0.0192832i
$27$	0.970942	−	0.239316i	0.186858	−	0.0460563i
$28$	0.375337	−	1.52280i	0.0709320	−	0.287782i
$29$	−2.66600	+	7.02966i	−0.495064	+	1.30538i	0.421986	+	0.906603i	$0.361333\pi$
$29$	−2.66600	+	7.02966i	−0.495064	+	1.30538i	−0.917049	+	0.398773i	$0.869436\pi$
$30$	−0.0225433	−	0.185661i	−0.00411582	−	0.0338969i
$31$	2.10992	+	8.56026i	0.378952	+	1.53747i	0.782583	+	0.622547i	$0.213902\pi$
$31$	2.10992	+	8.56026i	0.378952	+	1.53747i	−0.403630	+	0.914922i	$0.632252\pi$
$32$	0.315532	−	1.28016i	0.0557787	−	0.226303i
$33$	3.47325	+	2.39741i	0.604616	+	0.417336i
$34$	0.198501	−	0.0241024i	0.0340427	−	0.00413353i
$35$	−0.472370	−	1.24554i	−0.0798451	−	0.210534i
$36$	1.76005	−	0.923743i	0.293341	−	0.153957i
$37$	0.655680	+	2.66020i	0.107793	+	0.437334i	0.999895	−	0.0145006i	$-0.00461585\pi$
$37$	0.655680	+	2.66020i	0.107793	+	0.437334i	−0.892102	+	0.451835i	$0.850770\pi$
$38$	0.101897	−	0.268680i	0.0165298	−	0.0435856i
$39$	−3.38020	−	1.25468i	−0.541266	−	0.200910i
$40$	−0.264465	−	0.697337i	−0.0418156	−	0.110259i
$41$	−3.11397	+	2.14942i	−0.486320	+	0.335682i	−0.785863	−	0.618400i	$-0.787781\pi$
$41$	−3.11397	+	2.14942i	−0.486320	+	0.335682i	0.299543	+	0.954083i	$0.403166\pi$
$42$	−0.0654251	+	0.0579616i	−0.0100953	+	0.00894367i
$43$	2.07311	+	0.510976i	0.316146	+	0.0779231i	0.394196	−	0.919026i	$-0.371023\pi$
$43$	2.07311	+	0.510976i	0.316146	+	0.0779231i	−0.0780496	+	0.996949i	$0.524869\pi$
$44$	7.84371	+	2.97473i	1.18248	+	0.448457i
$45$	0.784583	−	1.49490i	0.116959	−	0.222846i
$46$	−0.699998	−	0.265474i	−0.103209	−	0.0391420i
$47$	−0.813950	−	0.918759i	−0.118727	−	0.134015i	0.686142	−	0.727468i	$-0.259303\pi$
$47$	−0.813950	−	0.918759i	−0.118727	−	0.134015i	−0.804869	+	0.593453i	$0.797764\pi$
$48$	2.93904	−	2.60376i	0.424214	−	0.375821i
$49$	3.62279	−	5.24852i	0.517542	−	0.749789i
$50$	0.195986	+	0.135279i	0.0277166	+	0.0191314i
$51$	1.59829	+	0.838846i	0.223805	+	0.117462i
$52$	−7.12053	−	0.813557i	−0.987440	−	0.112820i
$53$	−10.4252	+	5.47157i	−1.43201	+	0.751578i	−0.989411	−	0.145140i	$-0.953637\pi$
$53$	−10.4252	+	5.47157i	−1.43201	+	0.751578i	−0.442602	+	0.896718i	$0.645945\pi$
$54$	−0.109970	−	0.0133528i	−0.0149651	−	0.00181709i
$55$	6.91804	−	1.70514i	0.932828	−	0.229922i
$56$	−0.198002	+	0.286856i	−0.0264592	+	0.0383327i
$57$	2.13478	−	1.47353i	0.282759	−	0.195174i
$58$	0.552284	−	0.623400i	0.0725185	−	0.0818565i
$59$	−11.4794	−	1.39385i	−1.49449	−	0.181464i	−0.667892	−	0.744259i	$-0.732803\pi$
$59$	−11.4794	−	1.39385i	−1.49449	−	0.181464i	−0.826597	+	0.562795i	$0.809726\pi$
$60$	0.803106	−	3.25833i	0.103681	−	0.420648i
$61$	−8.48800	−	4.45485i	−1.08678	−	0.570385i	−0.176465	−	0.984307i	$-0.556466\pi$
$61$	−8.48800	−	4.45485i	−1.08678	−	0.570385i	−0.910312	+	0.413922i	$0.864159\pi$
$62$	0.117724	−	0.969548i	0.0149510	−	0.123133i
$63$	−0.783276	+	0.0951069i	−0.0986835	+	0.0119823i
$64$	4.37806	−	6.34272i	0.547258	−	0.792840i
$65$	−5.36980	+	2.86688i	−0.666042	+	0.355593i
$66$	−0.265581	−	0.384760i	−0.0326907	−	0.0473607i
$67$	−2.93118	−	3.30862i	−0.358101	−	0.404212i	0.541659	−	0.840599i	$-0.317797\pi$
$67$	−2.93118	−	3.30862i	−0.358101	−	0.404212i	−0.899759	+	0.436386i	$0.856258\pi$
$68$	3.48368	+	0.858650i	0.422458	+	0.104127i
$69$	−3.83903	−	5.56180i	−0.462165	−	0.669562i
$70$			0.147568i			0.0176377i
$71$	−5.12174	+	3.53528i	−0.607839	+	0.419561i	−0.831830	−	0.555030i	$-0.812707\pi$
$71$	−5.12174	+	3.53528i	−0.607839	+	0.419561i	0.223991	+	0.974591i	$0.428091\pi$
$72$	−0.438532	+	0.0532474i	−0.0516815	+	0.00627526i
$73$	2.59240	−	0.983168i	0.303417	−	0.115071i	−0.198197	−	0.980162i	$-0.563509\pi$
$73$	2.59240	−	0.983168i	0.303417	−	0.115071i	0.501615	+	0.865091i	$0.332739\pi$
$74$	0.0365842	−	0.301298i	0.00425283	−	0.0350252i
$75$	0.762297	+	2.01001i	0.0880225	+	0.232096i
$76$	3.41911	−	3.85938i	0.392199	−	0.442701i
$77$	−2.49251	−	2.20817i	−0.284047	−	0.251644i
$78$	0.300832	+	0.262742i	0.0340625	+	0.0297496i
$79$	6.26327	−	5.54877i	0.704673	−	0.624286i	−0.232727	−	0.972542i	$-0.574765\pi$
$79$	6.26327	−	5.54877i	0.704673	−	0.624286i	0.937399	+	0.348257i	$0.113226\pi$
$80$		−	6.62907i		−	0.741152i
$81$	−0.748511	−	0.663123i	−0.0831679	−	0.0736803i
$82$	0.406976	−	0.100311i	0.0449430	−	0.0110775i
$83$	−0.207021	−	0.142896i	−0.0227235	−	0.0156849i	0.556649	−	0.830748i	$-0.312087\pi$
$83$	−0.207021	−	0.142896i	−0.0227235	−	0.0156849i	−0.579372	+	0.815063i	$0.696702\pi$
$84$	−1.46646	+	0.556154i	−0.160004	+	0.0606813i
$85$	2.84939	−	1.08063i	0.309060	−	0.117211i
$86$	−0.194659	−	0.134363i	−0.0209906	−	0.0144888i
$87$	7.29976	−	1.79923i	0.782617	−	0.192898i
$88$	−1.39548	−	1.23628i	−0.148758	−	0.131788i
$89$			8.34850i			0.884939i	0.896784	+	0.442469i	$0.145897\pi$
$89$			8.34850i			0.884939i	−0.896784	+	0.442469i	$0.854103\pi$
$90$	−0.139990	+	0.124020i	−0.0147562	+	0.0130729i
$91$	2.52830	+	1.30424i	0.265038	+	0.136722i
$92$	−10.0549	−	8.90789i	−1.04830	−	0.928712i
$93$	5.84639	−	6.59921i	0.606243	−	0.684306i
$94$	0.0482172	+	0.127138i	0.00497322	+	0.0131133i
$95$	0.527869	−	4.34739i	0.0541582	−	0.446033i
$96$	−1.23280	+	0.467538i	−0.125822	+	0.0477179i
$97$	−12.7824	+	1.55206i	−1.29785	+	0.157588i	−0.740145	−	0.672448i	$-0.765243\pi$
$97$	−12.7824	+	1.55206i	−1.29785	+	0.157588i	−0.557710	+	0.830036i	$0.688320\pi$
$98$	−0.581421	+	0.401326i	−0.0587324	+	0.0405400i
$99$		−	4.22032i		−	0.424158i
$100$	2.42736	+	3.51664i	0.242736	+	0.351664i
$101$	10.8572	+	2.67606i	1.08033	+	0.266278i	0.739028	−	0.673675i	$-0.235285\pi$
$101$	10.8572	+	2.67606i	1.08033	+	0.266278i	0.341305	+	0.939953i	$0.389131\pi$
$102$	−0.132597	−	0.149672i	−0.0131291	−	0.0148197i
$103$	−2.58672	−	3.74751i	−0.254877	−	0.369254i	0.674568	−	0.738212i	$-0.264330\pi$
$103$	−2.58672	−	3.74751i	−0.254877	−	0.369254i	−0.929446	+	0.368959i	$0.879714\pi$
$104$	1.41552	+	0.730206i	0.138803	+	0.0716026i
$105$	−0.756720	+	1.09630i	−0.0738484	+	0.106988i
$106$	1.29477	−	0.157214i	0.125759	−	0.0152700i
$107$	−0.395131	+	3.25420i	−0.0381988	+	0.314595i	0.961068	+	0.276312i	$0.0891122\pi$
$107$	−0.395131	+	3.25420i	−0.0381988	+	0.314595i	−0.999267	+	0.0382838i	$0.987811\pi$
$108$	−1.76005	−	0.923743i	−0.169360	−	0.0888872i
$109$	−4.76813	+	19.3451i	−0.456704	+	1.85292i	0.0621613	+	0.998066i	$0.480201\pi$
$109$	−4.76813	+	19.3451i	−0.456704	+	1.85292i	−0.518866	+	0.854856i	$0.673645\pi$
$110$	−0.783547	−	0.0951399i	−0.0747083	−	0.00907123i
$111$	1.81683	−	2.05078i	0.172446	−	0.194651i
$112$	−2.54972	+	1.75994i	−0.240926	+	0.166299i
$113$	−10.0766	+	14.5985i	−0.947927	+	1.37331i	−0.0203033	+	0.999794i	$0.506463\pi$
$113$	−10.0766	+	14.5985i	−0.947927	+	1.37331i	−0.927624	+	0.373516i	$0.878152\pi$
$114$	−0.279003	+	0.0687681i	−0.0261310	+	0.00644072i
$115$	−11.3264	−	1.37527i	−1.05619	−	0.128245i
$116$	13.2324	−	6.94491i	1.22860	−	0.644819i
$117$	0.887589	+	3.49459i	0.0820576	+	0.323075i
$118$	1.13427	+	0.595312i	0.104418	+	0.0548029i
$119$	−1.17212	−	0.809056i	−0.107448	−	0.0741661i
$120$	−0.423664	+	0.613783i	−0.0386751	+	0.0560305i
$121$	5.09817	−	4.51659i	0.463470	−	0.410599i
$122$	0.704183	+	0.794859i	0.0637538	+	0.0719631i
$123$	3.53787	+	1.34174i	0.318999	+	0.120980i
$124$	8.14414	−	15.5174i	0.731366	−	1.39350i
$125$	11.2863	+	4.28033i	1.00948	+	0.382845i
$126$	0.0848672	+	0.0209179i	0.00756057	+	0.00186351i
$127$	8.84290	−	7.83413i	0.784681	−	0.695166i	−0.172388	−	0.985029i	$-0.555148\pi$
$127$	8.84290	−	7.83413i	0.784681	−	0.695166i	0.957068	+	0.289863i	$0.0936097\pi$
$128$	−2.87280	+	1.98295i	−0.253922	+	0.175270i
$129$	−0.757136	−	1.99640i	−0.0666621	−	0.175774i
$130$	0.668818	−	0.0860108i	0.0586592	−	0.00754364i
$131$	1.35505	−	3.57298i	0.118391	−	0.312173i	−0.862700	−	0.505715i	$-0.831229\pi$
$131$	1.35505	−	3.57298i	0.118391	−	0.312173i	0.981092	+	0.193543i	$0.0619978\pi$
$132$	−2.00758	−	8.14508i	−0.174738	−	0.708938i
$133$	−1.81227	+	0.951151i	−0.157144	+	0.0824753i
$134$	0.173639	+	0.457848i	0.0150001	+	0.0395521i
$135$	−1.67597	+	0.203500i	−0.144245	+	0.0175145i
$136$	−0.656233	−	0.452965i	−0.0562715	−	0.0388414i
$137$	4.11089	−	16.6785i	0.351217	−	1.42494i	−0.484021	−	0.875056i	$-0.660824\pi$
$137$	4.11089	−	16.6785i	0.351217	−	1.42494i	0.835239	−	0.549888i	$-0.185329\pi$
$138$	0.179163	+	0.726894i	0.0152514	+	0.0618773i
$139$	−2.41177	−	19.8627i	−0.204563	−	1.68473i	−0.627536	−	0.778588i	$-0.715936\pi$
$139$	−2.41177	−	19.8627i	−0.204563	−	1.68473i	0.422973	−	0.906142i	$-0.360987\pi$
$140$	−0.938943	+	2.47579i	−0.0793552	+	0.209242i
$141$	−0.293748	+	1.19178i	−0.0247380	+	0.100366i
$142$	0.669380	−	0.164987i	0.0561731	−	0.0138454i
$143$	−8.55526	+	12.5838i	−0.715427	+	1.05231i
$144$	−3.81242	−	0.939678i	−0.317702	−	0.0783065i
$145$	5.89867	−	11.2390i	0.489858	−	0.933347i
$146$	−0.307140			−0.0254191
$147$	−6.37743			−0.526002
$148$	2.53088	−	4.82220i	0.208037	−	0.396382i
$149$	−4.53059	−	5.11398i	−0.371161	−	0.418954i	0.533021	−	0.846102i	$-0.321057\pi$
$149$	−4.53059	−	5.11398i	−0.371161	−	0.418954i	−0.904182	+	0.427148i	$0.859518\pi$
$150$		−	0.238140i		−	0.0194441i
$151$	−2.05626	+	2.32104i	−0.167336	+	0.188884i	−0.826197	−	0.563381i	$-0.809500\pi$
$151$	−2.05626	+	2.32104i	−0.167336	+	0.188884i	0.658861	+	0.752265i	$0.271039\pi$
$152$	−1.01463	+	0.532520i	−0.0822975	+	0.0431931i
$153$	−0.217574	−	1.79188i	−0.0175898	−	0.144865i
$154$	0.171430	+	0.326632i	0.0138142	+	0.0263208i
$155$	−1.79415	−	14.7761i	−0.144109	−	1.18685i
$156$	3.37538	+	6.32223i	0.270247	+	0.506184i
$157$	−0.940178	+	7.74306i	−0.0750343	+	0.617963i	0.905882	+	0.423531i	$0.139210\pi$
$157$	−0.940178	+	7.74306i	−0.0750343	+	0.617963i	−0.980916	+	0.194432i	$0.937714\pi$
$158$	−0.866714	+	0.328701i	−0.0689520	+	0.0261501i
$159$	10.4252	+	5.47157i	0.826773	+	0.433924i
$160$	−0.789336	+	2.08131i	−0.0624025	+	0.164542i
$161$	2.47806	+	4.72155i	0.195298	+	0.372110i
$162$	0.0514811	+	0.0980890i	0.00404474	+	0.00770660i
$163$	6.05444	+	24.5638i	0.474220	+	1.92399i	0.368625	+	0.929578i	$0.379829\pi$
$163$	6.05444	+	24.5638i	0.474220	+	1.92399i	0.105596	+	0.994409i	$0.466325\pi$
$164$	7.46623	+	0.906565i	0.583015	+	0.0707908i
$165$	−5.33320	−	4.72480i	−0.415189	−	0.367825i
$166$	0.0158298	+	0.0229334i	0.00122863	+	0.00177998i
$167$	3.07652	+	1.16677i	0.238068	+	0.0902872i	0.470754	−	0.882265i	$-0.343982\pi$
$167$	3.07652	+	1.16677i	0.238068	+	0.0902872i	−0.232686	+	0.972552i	$0.574751\pi$
$168$	0.348556			0.0268916
$169$	4.43757	−	12.2192i	0.341351	−	0.939936i
$170$	−0.337587			−0.0258918
$171$	−2.42539	−	0.919829i	−0.185474	−	0.0703411i
$172$	−2.41093	−	3.49283i	−0.183831	−	0.266326i
$173$	−5.08348	−	4.50357i	−0.386490	−	0.342400i	0.447397	−	0.894335i	$-0.352351\pi$
$173$	−5.08348	−	4.50357i	−0.386490	−	0.342400i	−0.833887	+	0.551935i	$0.813889\pi$
$174$	−0.826782	−	0.100389i	−0.0626782	−	0.00761051i
$175$	−0.405923	−	1.64689i	−0.0306849	−	0.124494i
$176$	−7.70100	−	14.6730i	−0.580485	−	1.10602i
$177$	5.37392	+	10.2391i	0.403928	+	0.769621i
$178$	0.327949	−	0.864731i	0.0245808	−	0.0648143i
$179$	−3.54743	−	1.86183i	−0.265147	−	0.139160i	0.326911	−	0.945055i	$-0.393992\pi$
$179$	−3.54743	−	1.86183i	−0.265147	−	0.139160i	−0.592058	+	0.805895i	$0.701685\pi$
$180$	−3.13777	+	1.19000i	−0.233875	+	0.0886972i
$181$	−2.37147	+	19.5309i	−0.176270	+	1.45172i	0.589065	+	0.808085i	$0.299496\pi$
$181$	−2.37147	+	19.5309i	−0.176270	+	1.45172i	−0.765336	+	0.643631i	$0.777427\pi$
$182$	−0.210646	−	0.234411i	−0.0156141	−	0.0173757i
$183$	1.15547	+	9.51613i	0.0854146	+	0.703453i
$184$	1.38739	+	2.64344i	0.102280	+	0.194877i
$185$	−0.557551	−	4.59185i	−0.0409920	−	0.337599i
$186$	−0.864798	+	0.453881i	−0.0634100	+	0.0332802i
$187$	5.05158	−	5.70205i	0.369408	−	0.416975i
$188$			2.43984i			0.177943i
$189$	0.523223	+	0.590597i	0.0380589	+	0.0429596i
$190$	−0.225452	+	0.429564i	−0.0163560	+	0.0311638i
$191$	−3.90284			−0.282400			−0.141200	−	0.989981i	$-0.545096\pi$
$191$	−3.90284			−0.282400			−0.141200	+	0.989981i	$0.545096\pi$
$192$	−7.70698			−0.556203
$193$	−7.05116	+	13.4349i	−0.507553	+	0.967062i	0.487998	+	0.872845i	$0.337727\pi$
$193$	−7.05116	+	13.4349i	−0.507553	+	0.967062i	−0.995552	+	0.0942176i	$0.969965\pi$
$194$	1.38496	+	0.341362i	0.0994342	+	0.0245083i
$195$	5.40979	+	2.79068i	0.387403	+	0.199845i
$196$	−12.3082	+	3.03371i	−0.879160	+	0.216694i
$197$	−0.659781	+	2.67684i	−0.0470075	+	0.190717i	−0.989752	−	0.142800i	$-0.954389\pi$
$197$	−0.659781	+	2.67684i	−0.0470075	+	0.190717i	0.942744	+	0.333517i	$0.108235\pi$
$198$	−0.165784	+	0.437137i	−0.0117818	+	0.0310660i
$199$	−0.971826	−	8.00371i	−0.0688909	−	0.567368i	−0.985757	−	0.168174i	$-0.946213\pi$
$199$	−0.971826	−	8.00371i	−0.0688909	−	0.567368i	0.916866	−	0.399194i	$-0.130710\pi$
$200$	−0.227264	−	0.922045i	−0.0160700	−	0.0651984i
$201$	−1.05784	+	4.29182i	−0.0746143	+	0.302722i
$202$	−1.01946	−	0.703682i	−0.0717289	−	0.0495109i
$203$	−5.88885	+	0.715036i	−0.413316	+	0.0501857i
$204$	−1.27230	−	3.35478i	−0.0890788	−	0.234882i
$205$	5.65632	−	2.96867i	0.395055	−	0.207341i
$206$	0.120719	+	0.489777i	0.00841091	+	0.0341244i
$207$	−2.39645	+	6.31893i	−0.166565	+	0.439196i
$208$	9.46268	+	10.5302i	0.656119	+	0.730141i
$209$	−3.88197	−	10.2359i	−0.268522	−	0.708033i
$210$	0.121446	−	0.0838280i	0.00838056	−	0.00578468i
$211$	−7.13721	+	6.32302i	−0.491346	+	0.435294i	−0.872060	−	0.489398i	$-0.837216\pi$
$211$	−7.13721	+	6.32302i	−0.491346	+	0.435294i	0.380715	+	0.924693i	$0.375678\pi$
$212$	22.7231	+	5.60075i	1.56063	+	0.384661i
$213$	5.81896	+	2.20684i	0.398709	+	0.151210i
$214$	0.168760	−	0.321546i	0.0115362	−	0.0219804i
$215$	−3.37049	−	1.27826i	−0.229866	−	0.0871765i
$216$	0.292936	+	0.330657i	0.0199318	+	0.0224983i
$217$	−5.20697	+	4.61297i	−0.353472	+	0.313149i
$218$	1.25380	−	1.81644i	0.0849181	−	0.123025i
$219$	−2.28178	−	1.57500i	−0.154189	−	0.106429i
$220$	−12.5405	−	6.58175i	−0.845478	−	0.443741i
$221$	−2.98369	+	5.78394i	−0.200705	+	0.389070i
$222$	−0.268746	+	0.141049i	−0.0180370	+	0.00946656i
$223$	16.1329	+	1.95889i	1.08034	+	0.131177i	0.641300	−	0.767290i	$-0.278395\pi$
$223$	16.1329	+	1.95889i	1.08034	+	0.131177i	0.439041	+	0.898467i	$0.355318\pi$
$224$	1.01009	−	0.248964i	0.0674893	−	0.0166346i
$225$	1.22117	−	1.76918i	0.0814116	−	0.117945i
$226$	1.61719	−	1.11627i	0.107574	−	0.0742529i
$227$	6.37497	−	7.19585i	0.423122	−	0.477605i	−0.497834	−	0.867272i	$-0.665871\pi$
$227$	6.37497	−	7.19585i	0.423122	−	0.477605i	0.920956	+	0.389667i	$0.127410\pi$
$228$	−5.11848	−	0.621496i	−0.338980	−	0.0411596i
$229$	−1.27408	+	5.16914i	−0.0841934	+	0.341586i	−0.997899	−	0.0647910i	$-0.979362\pi$
$229$	−1.27408	+	5.16914i	−0.0841934	+	0.341586i	0.913705	+	0.406377i	$0.133208\pi$
$230$	1.11915	+	0.587377i	0.0737947	+	0.0387305i
$231$	−0.401382	+	3.30568i	−0.0264090	+	0.217497i
$232$	−3.29698	+	0.400326i	−0.216457	+	0.0262827i
$233$	8.48546	−	12.2933i	0.555901	−	0.805361i	−0.439790	−	0.898101i	$-0.644947\pi$
$233$	8.48546	−	12.2933i	0.555901	−	0.805361i	0.995690	+	0.0927394i	$0.0295623\pi$
$234$	0.0453403	−	0.396834i	0.00296399	−	0.0259418i
$235$	1.17719	+	1.70545i	0.0767913	+	0.111251i
$236$	15.2422	+	17.2049i	0.992182	+	1.11994i
$237$	−8.12449	−	2.00251i	−0.527742	−	0.130077i
$238$	0.0896256	+	0.129845i	0.00580957	+	0.00841661i
$239$		−	14.8922i		−	0.963299i	−0.876364	−	0.481649i	$-0.840038\pi$
$239$		−	14.8922i		−	0.963299i	0.876364	−	0.481649i	$-0.159962\pi$
$240$	−5.45562	+	3.76574i	−0.352158	+	0.243077i
$241$	8.04101	−	0.976355i	0.517967	−	0.0628926i	0.142621	−	0.989777i	$-0.454447\pi$
$241$	8.04101	−	0.976355i	0.517967	−	0.0628926i	0.375346	+	0.926885i	$0.377524\pi$
$242$	−0.705487	+	0.267556i	−0.0453504	+	0.0171992i
$243$	−0.120537	+	0.992709i	−0.00773243	+	0.0636823i
$244$	6.75679	+	17.8162i	0.432559	+	1.14056i
$245$	−7.13977	+	8.05914i	−0.456143	+	0.514879i
$246$	−0.313743	−	0.277952i	−0.0200035	−	0.0177216i
$247$	5.36718	+	7.65932i	0.341505	+	0.487351i
$248$	−2.91522	+	2.58266i	−0.185117	+	0.163999i
$249$			0.251549i			0.0159413i
$250$	−1.00089	−	0.886707i	−0.0633016	−	0.0560803i
$251$	5.54353	−	1.36636i	0.349904	−	0.0862437i	−0.0604464	−	0.998171i	$-0.519252\pi$
$251$	5.54353	−	1.36636i	0.349904	−	0.0862437i	0.410351	+	0.911928i	$0.365406\pi$
$252$	1.29075	+	0.890939i	0.0813095	+	0.0561239i
$253$	−26.6679	+	10.1138i	−1.67660	+	0.635849i
$254$	−1.22368	+	0.464082i	−0.0767808	+	0.0291191i
$255$	−2.50798	−	1.73113i	−0.157056	−	0.108408i
$256$	−14.5906	+	3.59626i	−0.911913	+	0.224766i
$257$	17.6619	+	15.6471i	1.10172	+	0.976037i	0.999824	−	0.0187581i	$-0.00597123\pi$
$257$	17.6619	+	15.6471i	1.10172	+	0.976037i	0.101894	+	0.994795i	$0.467510\pi$
$258$			0.236528i			0.0147256i
$259$	−1.61812	+	1.43353i	−0.100545	+	0.0890754i
$260$	11.7682	+	2.81252i	0.729836	+	0.174425i
$261$	−5.62747	−	4.98551i	−0.348332	−	0.308595i
$262$	−0.280711	+	0.316857i	−0.0173424	+	0.0195755i
$263$	6.86242	+	18.0947i	0.423155	+	1.11577i	0.961925	+	0.273314i	$0.0881200\pi$
$263$	6.86242	+	18.0947i	0.423155	+	1.11577i	−0.538770	+	0.842453i	$0.681111\pi$
$264$	−0.224721	+	1.85074i	−0.0138306	+	0.113905i
$265$	18.5858	−	7.04867i	1.14172	−	0.432996i
$266$	0.225077	−	0.0273293i	0.0138003	−	0.00167567i
$267$	6.87068	−	4.74249i	0.420479	−	0.290235i
$268$			8.78629i			0.536708i
$269$	−14.8571	−	21.5242i	−0.905853	−	1.31235i	−0.949650	−	0.313314i	$-0.898561\pi$
$269$	−14.8571	−	21.5242i	−0.905853	−	1.31235i	0.0437965	−	0.999040i	$-0.486055\pi$
$270$	0.181590	+	0.0447579i	0.0110512	+	0.00272388i
$271$	11.2187	+	12.6632i	0.681485	+	0.769237i	0.982877	−	0.184263i	$-0.0589898\pi$
$271$	11.2187	+	12.6632i	0.681485	+	0.769237i	−0.301392	+	0.953500i	$0.597451\pi$
$272$	−4.02618	−	5.83293i	−0.244123	−	0.353674i
$273$	−0.362867	−	2.82165i	−0.0219617	−	0.170774i
$274$	−1.08098	+	1.56606i	−0.0653042	+	0.0946094i
$275$	9.00631	−	1.09356i	0.543101	−	0.0659444i
$276$	−1.61920	+	13.3353i	−0.0974644	+	0.802691i
$277$	−26.6699	−	13.9974i	−1.60244	−	0.841024i	−0.999050	−	0.0435746i	$-0.986125\pi$
$277$	−26.6699	−	13.9974i	−1.60244	−	0.841024i	−0.603386	−	0.797449i	$-0.706182\pi$
$278$	−0.530445	+	2.15210i	−0.0318140	+	0.129074i
$279$	−8.75217	−	1.06271i	−0.523979	−	0.0636226i
$280$	0.390221	−	0.440468i	0.0233202	−	0.0263230i
$281$	−17.7370	+	12.2429i	−1.05810	+	0.730353i	−0.964186	−	0.265227i	$-0.914553\pi$
$281$	−17.7370	+	12.2429i	−1.05810	+	0.730353i	−0.0939131	+	0.995580i	$0.529938\pi$
$282$	0.0772423	−	0.111905i	0.00459971	−	0.00666383i
$283$	−6.55789	+	1.61637i	−0.389826	+	0.0960835i	−0.429357	−	0.903135i	$-0.641260\pi$
$283$	−6.55789	+	1.61637i	−0.389826	+	0.0960835i	0.0395310	+	0.999218i	$0.487414\pi$
$284$	12.2802	+	1.49108i	0.728695	+	0.0884796i
$285$	−3.87770	+	2.03517i	−0.229695	+	0.120553i
$286$	1.38047	−	0.967347i	0.0816288	−	0.0572004i
$287$	−2.64352	−	1.38743i	−0.156042	−	0.0818972i
$288$	1.08509	+	0.748980i	0.0639393	+	0.0441341i
$289$	−7.80624	+	11.3093i	−0.459191	+	0.665252i
$290$	−1.05247	+	0.932411i	−0.0618034	+	0.0547531i
$291$	8.53854	+	9.63802i	0.500538	+	0.564991i
$292$	−5.15299	−	1.95427i	−0.301556	−	0.114365i
$293$	−5.99163	+	11.4161i	−0.350035	+	0.666935i	−0.995281	−	0.0970397i	$-0.969063\pi$
$293$	−5.99163	+	11.4161i	−0.350035	+	0.666935i	0.645246	+	0.763975i	$0.276755\pi$
$294$	0.660570	+	0.250521i	0.0385252	+	0.0146107i
$295$	18.9555	+	4.67210i	1.10363	+	0.272020i
$296$	−0.905937	+	0.802590i	−0.0526565	+	0.0466496i
$297$	−3.47325	+	2.39741i	−0.201539	+	0.139112i
$298$	0.268386	+	0.707675i	0.0155472	+	0.0409945i
$299$	19.9550	−	13.9832i	1.15403	−	0.808672i
$300$	1.51524	−	3.99536i	0.0874824	−	0.230672i
$301$	0.403175	+	1.63574i	0.0232386	+	0.0942828i
$302$	0.304162	−	0.159637i	0.0175026	−	0.00918606i
$303$	−3.96524	−	10.4555i	−0.227797	−	0.600652i
$304$	−10.1110	+	1.22769i	−0.579903	+	0.0704130i
$305$	13.3191	+	9.19350i	0.762649	+	0.526418i
$306$	−0.0478534	+	0.194149i	−0.00273560	+	0.0110987i
$307$	6.25405	+	25.3737i	0.356937	+	1.44815i	0.825340	+	0.564636i	$0.190983\pi$
$307$	6.25405	+	25.3737i	0.356937	+	1.44815i	−0.468403	+	0.883515i	$0.655170\pi$
$308$	0.797838	+	6.57078i	0.0454610	+	0.374405i
$309$	−1.61472	+	4.25766i	−0.0918581	+	0.242210i
$310$	−0.394606	+	1.60098i	−0.0224121	+	0.0909294i
$311$	21.3087	−	5.25212i	1.20831	−	0.297820i	0.416809	−	0.908994i	$-0.363148\pi$
$311$	21.3087	−	5.25212i	1.20831	−	0.297820i	0.791496	+	0.611174i	$0.209302\pi$
$312$	−0.203158	−	1.57975i	−0.0115016	−	0.0894358i
$313$	−4.15464	−	1.02403i	−0.234834	−	0.0578814i	0.120142	−	0.992757i	$-0.461665\pi$
$313$	−4.15464	−	1.02403i	−0.234834	−	0.0578814i	−0.354976	+	0.934875i	$0.615511\pi$
$314$	0.401549	−	0.765088i	0.0226607	−	0.0431764i
$315$	1.33210			0.0750555
$316$	−16.6326			−0.935656
$317$	11.7766	−	22.4385i	0.661441	−	1.26027i	−0.291342	−	0.956619i	$-0.594102\pi$
$317$	11.7766	−	22.4385i	0.661441	−	1.26027i	0.952783	−	0.303652i	$-0.0982059\pi$
$318$	−0.864899	−	0.976269i	−0.0485011	−	0.0547464i
$319$		−	31.7293i		−	1.77650i
$320$	−8.62825	+	9.73928i	−0.482334	+	0.544442i
$321$	2.90261	−	1.52341i	0.162008	−	0.0850284i
$322$	−0.0712016	−	0.586398i	−0.00396791	−	0.0326787i
$323$	−2.17593	−	4.14588i	−0.121072	−	0.230683i
$324$	0.239594	+	1.97324i	0.0133108	+	0.109624i
$325$	−7.22759	+	2.79966i	−0.400915	+	0.155297i
$326$	0.337812	−	2.78214i	0.0187097	−	0.154088i
$327$	18.6293	−	7.06516i	1.03020	−	0.390704i
$328$	−1.48002	−	0.776776i	−0.0817206	−	0.0428903i
$329$	0.343433	−	0.905557i	0.0189340	−	0.0499250i
$330$	0.366807	+	0.698892i	0.0201921	+	0.0384728i
$331$	1.80845	+	3.44572i	0.0994015	+	0.189394i	0.930078	−	0.367361i	$-0.119739\pi$
$331$	1.80845	+	3.44572i	0.0994015	+	0.189394i	−0.830677	+	0.556755i	$0.812046\pi$
$332$	0.119661	+	0.485482i	0.00656723	+	0.0266443i
$333$	−2.71984	−	0.330248i	−0.149046	−	0.0180975i
$334$	−0.272830	−	0.241706i	−0.0149286	−	0.0132256i
$335$	4.23927	+	6.14164i	0.231616	+	0.335554i
$336$	2.89681	+	1.09862i	0.158034	+	0.0599344i
$337$	−19.0235			−1.03628			−0.518139	−	0.855297i	$-0.673375\pi$
$337$	−19.0235			−1.03628			−0.518139	+	0.855297i	$0.673375\pi$
$338$	−0.939638	+	1.09133i	−0.0511096	+	0.0593607i
$339$	17.7385			0.963422
$340$	−5.66381	−	2.14800i	−0.307163	−	0.116492i
$341$	−21.1367	−	30.6218i	−1.14462	−	1.65826i
$342$	0.215087	+	0.190550i	0.0116306	+	0.0103038i
$343$	10.4782	+	1.27229i	0.565771	+	0.0686970i
$344$	0.225725	+	0.915802i	0.0121703	+	0.0493767i
$345$	5.30229	+	10.1027i	0.285465	+	0.543909i
$346$	0.349632	+	0.666167i	0.0187963	+	0.0358134i
$347$	−3.34463	+	8.81905i	−0.179549	+	0.473432i	−0.994330	−	0.106337i	$-0.966088\pi$
$347$	−3.34463	+	8.81905i	−0.179549	+	0.473432i	0.814781	+	0.579768i	$0.196857\pi$
$348$	−13.2324	−	6.94491i	−0.709332	−	0.372286i
$349$	−5.86395	+	2.22390i	−0.313890	+	0.119043i	−0.506519	−	0.862229i	$-0.669068\pi$
$349$	−5.86395	+	2.22390i	−0.313890	+	0.119043i	0.192629	+	0.981272i	$0.438299\pi$
$350$	−0.0226488	+	0.186530i	−0.00121063	+	0.00997043i
$351$	2.37179	−	2.71563i	0.126597	−	0.144949i
$352$	0.670713	+	5.52382i	0.0357491	+	0.294421i
$353$	11.6483	+	22.1939i	0.619975	+	1.18126i	0.969674	+	0.244402i	$0.0785916\pi$
$353$	11.6483	+	22.1939i	0.619975	+	1.18126i	−0.349699	+	0.936862i	$0.613716\pi$
$354$	−0.154408	−	1.27166i	−0.00820668	−	0.0675881i
$355$	9.30332	−	4.88276i	0.493769	−	0.259150i
$356$	11.0042	−	12.4212i	0.583222	−	0.658322i
$357$			1.42423i			0.0753784i
$358$	0.294302	+	0.332199i	0.0155544	+	0.0175572i
$359$	14.3804	−	27.3995i	0.758966	−	1.44609i	−0.131632	−	0.991299i	$-0.542022\pi$
$359$	14.3804	−	27.3995i	0.758966	−	1.44609i	0.890598	−	0.454791i	$-0.150286\pi$
$360$	0.745802			0.0393072
$361$	12.2714			0.645863
$362$	1.01285	−	1.92983i	0.0532345	−	0.101430i
$363$	−6.61317	−	1.63000i	−0.347101	−	0.0855528i
$364$	−2.04256	−	5.27308i	−0.107059	−	0.276384i
$365$	−4.54486	+	1.12021i	−0.237889	+	0.0586344i
$366$	0.254134	−	1.03106i	0.0132838	−	0.0538945i
$367$	−1.04588	+	2.75775i	−0.0545944	+	0.143954i	−0.959539	−	0.281576i	$-0.909143\pi$
$367$	−1.04588	+	2.75775i	−0.0545944	+	0.143954i	0.904945	+	0.425529i	$0.139912\pi$
$368$	3.19854	+	26.3423i	0.166735	+	1.37319i
$369$	−0.905511	−	3.67380i	−0.0471390	−	0.191251i
$370$	−0.122628	+	0.497522i	−0.00637513	+	0.0258649i
$371$	−7.64544	−	5.27726i	−0.396931	−	0.273982i
$372$	−17.3969	+	2.11237i	−0.901989	+	0.109521i
$373$	−11.6307	−	30.6676i	−0.602214	−	1.58791i	−0.794963	−	0.606659i	$-0.792510\pi$
$373$	−11.6307	−	30.6676i	−0.602214	−	1.58791i	0.192749	−	0.981248i	$-0.438260\pi$
$374$	−0.747229	+	0.392176i	−0.0386383	+	0.0202789i
$375$	−2.88871	−	11.7200i	−0.149172	−	0.605216i
$376$	0.192277	−	0.506993i	0.00991593	−	0.0261462i
$377$	6.67310	+	26.2732i	0.343682	+	1.35314i
$378$	−0.0309950	−	0.0817270i	−0.00159421	−	0.00420358i
$379$	20.8370	−	14.3828i	1.07033	−	0.738793i	0.103603	−	0.994619i	$-0.466963\pi$
$379$	20.8370	−	14.3828i	1.07033	−	0.738793i	0.966723	+	0.255826i	$0.0823475\pi$
$380$	−6.51571	+	5.77242i	−0.334249	+	0.296119i
$381$	−11.4707	−	2.82727i	−0.587662	−	0.144846i
$382$	0.404253	+	0.153313i	0.0206834	+	0.00784417i
$383$	−1.71838	+	3.27409i	−0.0878050	+	0.167298i	−0.925398	−	0.378996i	$-0.876270\pi$
$383$	−1.71838	+	3.27409i	−0.0878050	+	0.167298i	0.837593	+	0.546294i	$0.183962\pi$
$384$	3.26388	+	1.23783i	0.166559	+	0.0631675i
$385$	3.72801	+	4.20805i	0.189997	+	0.214462i
$386$	1.25811	−	1.11459i	0.0640360	−	0.0567309i
$387$	−1.21291	+	1.75720i	−0.0616555	+	0.0893234i
$388$	21.0639	+	14.5393i	1.06936	+	0.738123i
$389$	−17.1257	−	8.98827i	−0.868308	−	0.455723i	−0.0291275	−	0.999576i	$-0.509273\pi$
$389$	−17.1257	−	8.98827i	−0.868308	−	0.455723i	−0.839181	+	0.543852i	$0.816965\pi$
$390$	−0.450717	−	0.501567i	−0.0228230	−	0.0253978i
$391$	−10.8014	+	5.66900i	−0.546249	+	0.286694i
$392$	2.79671	+	0.339582i	0.141255	+	0.0171515i
$393$	−3.71026	+	0.914498i	−0.187158	+	0.0461303i
$394$	0.173492	−	0.251347i	0.00874041	−	0.0126627i
$395$	−11.6262	+	8.02501i	−0.584979	+	0.403782i
$396$	−5.56283	+	6.27914i	−0.279543	+	0.315539i
$397$	2.41515	+	0.293252i	0.121213	+	0.0147179i	0.180918	−	0.983498i	$-0.442093\pi$
$397$	2.41515	+	0.293252i	0.121213	+	0.0147179i	−0.0597055	+	0.998216i	$0.519016\pi$
$398$	−0.213744	+	0.867193i	−0.0107140	+	0.0434685i
$399$	1.81227	+	0.951151i	0.0907269	+	0.0476171i
$400$	1.01744	−	8.37933i	0.0508718	−	0.418967i
$401$	−20.5504	+	2.49527i	−1.02624	+	0.124608i	−0.616305	−	0.787508i	$-0.711371\pi$
$401$	−20.5504	+	2.49527i	−1.02624	+	0.124608i	−0.409933	+	0.912116i	$0.634448\pi$
$402$	0.278163	−	0.402989i	0.0138735	−	0.0200993i
$403$	23.9422	+	20.9107i	1.19265	+	1.04164i
$404$	−12.6264	−	18.2925i	−0.628187	−	0.910087i
$405$	1.11954	+	1.26370i	0.0556302	+	0.0627936i
$406$	0.638051	+	0.157265i	0.0316659	+	0.00780495i
$407$	−6.56847	−	9.51607i	−0.325587	−	0.471694i
$408$			0.797383i			0.0394763i
$409$	−6.43825	+	4.44401i	−0.318351	+	0.219742i	−0.716514	−	0.697573i	$-0.754263\pi$
$409$	−6.43825	+	4.44401i	−0.318351	+	0.219742i	0.398163	+	0.917315i	$0.369648\pi$
$410$	−0.702494	+	0.0852982i	−0.0346937	+	0.00421258i
$411$	−16.0614	+	6.09129i	−0.792251	+	0.300461i
$412$	−1.09101	+	8.98526i	−0.0537501	+	0.442672i
$413$	−3.23545	−	8.53117i	−0.159206	−	0.419792i
$414$	0.496445	−	0.560371i	0.0243990	−	0.0275407i
$415$	0.317882	+	0.281619i	0.0156042	+	0.0138241i
$416$	−1.71711	−	4.43289i	−0.0841883	−	0.217340i
$417$	−14.9766	+	13.2681i	−0.733408	+	0.649743i
$418$			1.21272i			0.0593161i
$419$	13.0453	+	11.5571i	0.637303	+	0.564601i	0.918683	−	0.394995i	$-0.129254\pi$
$419$	13.0453	+	11.5571i	0.637303	+	0.564601i	−0.281380	+	0.959596i	$0.590792\pi$
$420$	2.57092	−	0.633674i	0.125448	−	0.0309201i
$421$	−15.4874	−	10.6902i	−0.754810	−	0.521007i	0.127407	−	0.991850i	$-0.459334\pi$
$421$	−15.4874	−	10.6902i	−0.754810	−	0.521007i	−0.882217	+	0.470843i	$0.843950\pi$
$422$	0.987650	−	0.374566i	0.0480780	−	0.0182336i
$423$	1.14769	−	0.435260i	0.0558024	−	0.0211630i
$424$	−4.28044	−	2.95457i	−0.207876	−	0.143487i
$425$	3.76757	−	0.928621i	0.182754	−	0.0450448i
$426$	−0.516033	−	0.457166i	−0.0250019	−	0.0221497i
$427$		−	7.56365i		−	0.366031i
$428$	4.87728	−	4.32089i	0.235752	−	0.208858i
$429$	15.2162	−	0.107560i	0.734645	−	0.00519307i
$430$	0.298900	+	0.264802i	0.0144142	+	0.0127699i
$431$	16.2408	−	18.3321i	0.782294	−	0.883027i	−0.213282	−	0.976991i	$-0.568415\pi$
$431$	16.2408	−	18.3321i	0.782294	−	0.883027i	0.995576	+	0.0939634i	$0.0299537\pi$
$432$	1.39236	+	3.67136i	0.0669901	+	0.176638i
$433$	3.90996	−	32.2014i	0.187901	−	1.54750i	−0.527967	−	0.849265i	$-0.677045\pi$
$433$	3.90996	−	32.2014i	0.187901	−	1.54750i	0.715867	−	0.698236i	$-0.246031\pi$
$434$	0.720543	−	0.273266i	0.0345872	−	0.0131172i
$435$	−12.6003	+	1.52996i	−0.604140	+	0.0733558i
$436$	32.5931	−	22.4974i	1.56093	−	1.07743i
$437$			17.5302i			0.838582i
$438$	0.174475	+	0.252771i	0.00833676	+	0.0120779i
$439$	−32.6609	−	8.05018i	−1.55882	−	0.384214i	−0.636697	−	0.771114i	$-0.719700\pi$
$439$	−32.6609	−	8.05018i	−1.55882	−	0.384214i	−0.922122	+	0.386900i	$0.873546\pi$
$440$	2.08719	+	2.35595i	0.0995031	+	0.112316i
$441$	3.62279	+	5.24852i	0.172514	+	0.249930i
$442$	0.536256	−	0.481890i	0.0255071	−	0.0229212i
$443$	7.34020	−	10.6341i	0.348744	−	0.505242i	−0.608881	−	0.793262i	$-0.708381\pi$
$443$	7.34020	−	10.6341i	0.348744	−	0.505242i	0.957625	+	0.288019i	$0.0929967\pi$
$444$	−5.40630	+	0.656443i	−0.256571	+	0.0311534i
$445$	1.69892	−	13.9918i	0.0805364	−	0.663277i
$446$	−1.59409	−	0.836641i	−0.0754822	−	0.0396161i
$447$	−1.63505	+	6.63368i	−0.0773354	+	0.313762i
$448$	6.03670	+	0.732988i	0.285207	+	0.0346304i
$449$	12.8683	−	14.5253i	0.607292	−	0.685491i	−0.361782	−	0.932263i	$-0.617831\pi$
$449$	12.8683	−	14.5253i	0.607292	−	0.685491i	0.969074	+	0.246772i	$0.0793698\pi$
$450$	−0.195986	+	0.135279i	−0.00923886	+	0.00637712i
$451$	9.07122	−	13.1419i	0.427147	−	0.618829i
$452$	34.2347	−	8.43810i	1.61027	−	0.396895i
$453$	3.07827	+	0.373770i	0.144630	+	0.0175612i
$454$	−0.942985	+	0.494917i	−0.0442565	+	0.0232276i
$455$	−3.97195	−	2.70039i	−0.186208	−	0.126596i
$456$	1.01463	+	0.532520i	0.0475145	+	0.0249375i
$457$	−14.6199	−	10.0914i	−0.683891	−	0.472056i	0.174764	−	0.984610i	$-0.444084\pi$
$457$	−14.6199	−	10.0914i	−0.683891	−	0.472056i	−0.858655	+	0.512554i	$0.828699\pi$
$458$	0.335024	−	0.485366i	0.0156547	−	0.0226797i
$459$	−1.35110	+	1.19697i	−0.0630637	+	0.0558696i
$460$	15.0390	+	16.9755i	0.701198	+	0.791489i
$461$	19.9283	+	7.55782i	0.928154	+	0.352003i	0.771922	−	0.635718i	$-0.219296\pi$
$461$	19.9283	+	7.55782i	0.928154	+	0.352003i	0.156233	+	0.987720i	$0.450065\pi$
$462$	0.171430	−	0.326632i	0.00797563	−	0.0151963i
$463$	4.41138	+	1.67302i	0.205014	+	0.0777516i	0.454975	−	0.890504i	$-0.349648\pi$
$463$	4.41138	+	1.67302i	0.205014	+	0.0777516i	−0.249960	+	0.968256i	$0.580418\pi$
$464$	−28.6627	−	7.06471i	−1.33063	−	0.327971i
$465$	−11.1413	+	9.87035i	−0.516666	+	0.457726i
$466$	−1.36183	+	0.940002i	−0.0630855	+	0.0435448i
$467$	−2.81003	−	7.40944i	−0.130033	−	0.342868i	0.854149	−	0.520028i	$-0.174078\pi$
$467$	−2.81003	−	7.40944i	−0.130033	−	0.342868i	−0.984182	+	0.177160i	$0.943309\pi$
$468$	3.28566	−	6.36932i	0.151880	−	0.294422i
$469$	1.23676	−	3.26108i	0.0571084	−	0.150583i
$470$	−0.0549380	−	0.222892i	−0.00253410	−	0.0102813i
$471$	6.90650	−	3.62481i	0.318234	−	0.167022i
$472$	−1.81143	−	4.77634i	−0.0833776	−	0.219849i
$473$	−8.94533	+	1.08616i	−0.411307	+	0.0499417i
$474$	0.762865	+	0.526568i	0.0350396	+	0.0241861i
$475$	1.33448	−	5.41421i	0.0612303	−	0.248421i
$476$	0.677500	+	2.74872i	0.0310531	+	0.125988i
$477$	−1.41918	−	11.6880i	−0.0649797	−	0.535156i
$478$	−0.585003	+	1.54253i	−0.0267574	+	0.0705535i
$479$	−1.45234	+	5.89238i	−0.0663591	+	0.269230i	−0.994744	−	0.102390i	$-0.967351\pi$
$479$	−1.45234	+	5.89238i	−0.0663591	+	0.269230i	0.928385	+	0.371619i	$0.121197\pi$
$480$	2.16128	−	0.532707i	0.0986483	−	0.0243146i
$481$	7.44031	+	6.49825i	0.339249	+	0.296295i
$482$	−0.871235	−	0.214740i	−0.0396837	−	0.00978115i
$483$	2.47806	−	4.72155i	0.112756	−	0.214838i
$484$	−13.5386			−0.615391
$485$	21.7388			0.987106
$486$	0.0514811	−	0.0980890i	0.00233523	−	0.00444941i
$487$	−2.79756	−	3.15779i	−0.126769	−	0.143093i	0.681699	−	0.731633i	$-0.261241\pi$
$487$	−2.79756	−	3.15779i	−0.126769	−	0.143093i	−0.808468	+	0.588540i	$0.799703\pi$
$488$		−	4.23465i		−	0.191694i
$489$	16.7763	−	18.9366i	0.758651	−	0.856340i
$490$	1.05611	−	0.554292i	0.0477104	−	0.0250403i
$491$	−2.88120	−	23.7288i	−0.130027	−	1.07087i	−0.900946	−	0.433932i	$-0.857126\pi$
$491$	−2.88120	−	23.7288i	−0.130027	−	1.07087i	0.770919	−	0.636933i	$-0.219797\pi$
$492$	−3.49522	−	6.65958i	−0.157576	−	0.300237i
$493$	−1.63577	−	13.4718i	−0.0736714	−	0.606739i
$494$	−0.255051	−	1.00418i	−0.0114753	−	0.0451803i
$495$	−0.858834	+	7.07313i	−0.0386017	+	0.317914i
$496$	−32.3684	+	12.2757i	−1.45338	+	0.551196i
$497$	−4.34797	−	2.28199i	−0.195033	−	0.102361i
$498$	0.00988147	−	0.0260553i	0.000442799	−	0.00116757i
$499$	−0.598717	−	1.14076i	−0.0268023	−	0.0510674i	0.871687	−	0.490064i	$-0.163026\pi$
$499$	−0.598717	−	1.14076i	−0.0268023	−	0.0510674i	−0.898489	+	0.438996i	$0.855334\pi$
$500$	−11.1502	−	21.2450i	−0.498654	−	0.950106i
$501$	−0.787428	−	3.19472i	−0.0351797	−	0.142730i
$502$	−0.627868	−	0.0762370i	−0.0280231	−	0.00340262i
$503$	−6.68197	−	5.91971i	−0.297934	−	0.263947i	0.500890	−	0.865511i	$-0.333006\pi$
$503$	−6.68197	−	5.91971i	−0.297934	−	0.263947i	−0.798825	+	0.601564i	$0.794545\pi$
$504$	−0.198002	−	0.286856i	−0.00881972	−	0.0127776i
$505$	−17.6518	−	6.69444i	−0.785495	−	0.297899i
$506$	3.15953			0.140458
$507$	−12.5770	+	3.28923i	−0.558564	+	0.146080i
$508$	−23.4830			−1.04189
$509$	9.60793	+	3.64381i	0.425864	+	0.161509i	0.558219	−	0.829693i	$-0.311485\pi$
$509$	9.60793	+	3.64381i	0.425864	+	0.161509i	−0.132355	+	0.991202i	$0.542254\pi$
$510$	0.191771	+	0.277829i	0.00849178	+	0.0123025i
$511$	1.63747	+	1.45067i	0.0724375	+	0.0641740i
$512$	8.58309	+	1.04218i	0.379322	+	0.0460581i
$513$	0.620774	+	2.51858i	0.0274078	+	0.111198i
$514$	−1.21475	−	2.31451i	−0.0535803	−	0.102089i
$515$	3.57265	+	6.80712i	0.157430	+	0.299958i
$516$	−1.50498	+	3.96831i	−0.0662531	+	0.174695i
$517$	4.58686	+	2.40737i	0.201730	+	0.105876i
$518$	0.223917	−	0.0849204i	0.00983834	−	0.00373119i
$519$	−0.818619	+	6.74194i	−0.0359334	+	0.295938i
$520$	−2.22377	−	1.51186i	−0.0975187	−	0.0662995i
$521$	−0.736802	−	6.06811i	−0.0322799	−	0.265849i	−0.999909	−	0.0134732i	$-0.995711\pi$
$521$	−0.736802	−	6.06811i	−0.0322799	−	0.265849i	0.967629	−	0.252376i	$-0.0812118\pi$
$522$	0.387047	+	0.737456i	0.0169406	+	0.0322776i
$523$	1.47861	+	12.1775i	0.0646552	+	0.532484i	0.988668	+	0.150121i	$0.0479663\pi$
$523$	1.47861	+	12.1775i	0.0646552	+	0.532484i	−0.924012	+	0.382362i	$0.875111\pi$
$524$	−6.72567	+	3.52990i	−0.293812	+	0.154205i
$525$	−1.12478	+	1.26961i	−0.0490893	+	0.0554104i
$526$		−	2.14381i		−	0.0934745i
$527$	−10.5530	−	11.9119i	−0.459696	−	0.518889i
$528$	−7.70100	+	14.6730i	−0.335143	+	0.638562i
$529$	22.6718			0.985732
$530$	−2.20199			−0.0956485
$531$	5.37392	−	10.2391i	0.233208	−	0.444341i
$532$	3.95008	+	0.973607i	0.171258	+	0.0422112i
$533$	−4.74741	+	12.7898i	−0.205633	+	0.553990i
$534$	−0.897956	+	0.221326i	−0.0388583	+	0.00957772i
$535$	1.32446	−	5.37353i	0.0572613	−	0.232318i
$536$	0.692425	−	1.82577i	0.0299082	−	0.0788614i
$537$	0.482909	+	3.97712i	0.0208391	+	0.171625i
$538$	0.693363	+	2.81308i	0.0298930	+	0.121281i
$539$	−6.44113	+	26.1327i	−0.277439	+	1.12562i
$540$	2.76180	+	1.90634i	0.118849	+	0.0820356i
$541$	5.66909	−	0.688352i	0.243733	−	0.0295946i	0.00224168	−	0.999997i	$-0.499286\pi$
$541$	5.66909	−	0.688352i	0.243733	−	0.0295946i	0.241492	+	0.970403i	$0.422363\pi$
$542$	−0.664577	−	1.75234i	−0.0285460	−	0.0752697i
$543$	17.4207	−	9.14310i	0.747595	−	0.392368i
$544$	0.569550	+	2.31075i	0.0244192	+	0.0990728i
$545$	11.9280	−	31.4515i	0.510938	−	1.34723i
$546$	−0.0732557	+	0.306518i	−0.00313505	+	0.0131178i
$547$	8.87034	+	23.3892i	0.379268	+	1.00005i	0.979717	+	0.200385i	$0.0642194\pi$
$547$	8.87034	+	23.3892i	0.379268	+	1.00005i	−0.600449	+	0.799663i	$0.705011\pi$
$548$	−28.1004	+	19.3963i	−1.20039	+	0.828570i
$549$	7.17524	−	6.35671i	0.306232	−	0.271298i
$550$	−0.975824	−	0.240519i	−0.0416093	−	0.0102558i
$551$	−18.2346	−	6.91548i	−0.776821	−	0.294609i
$552$	1.38739	−	2.64344i	0.0590511	−	0.112512i
$553$	6.17327	+	2.34121i	0.262514	+	0.0995585i
$554$	2.21259	+	2.49750i	0.0940040	+	0.106109i
$555$	−3.46229	+	3.06732i	−0.146966	+	0.130201i
$556$	−22.5928	+	32.7314i	−0.958150	+	1.38812i
$557$	−28.8014	−	19.8801i	−1.22035	−	0.842349i	−0.228981	−	0.973431i	$-0.573539\pi$
$557$	−28.8014	−	19.8801i	−1.22035	−	0.842349i	−0.991372	+	0.131082i	$0.958155\pi$
$558$	0.864798	+	0.453881i	0.0366098	+	0.0192143i
$559$	7.17866	−	2.78071i	0.303625	−	0.117611i
$560$	4.63140	−	2.43075i	0.195712	−	0.102718i
$561$	−7.56232	−	0.918232i	−0.319281	−	0.0387678i
$562$	2.31811	−	0.571364i	0.0977837	−	0.0241015i
$563$	9.76232	−	14.1432i	0.411433	−	0.596063i	−0.561408	−	0.827539i	$-0.689740\pi$
$563$	9.76232	−	14.1432i	0.411433	−	0.596063i	0.972841	+	0.231476i	$0.0743554\pi$
$564$	2.00795	−	1.38599i	0.0845498	−	0.0583605i
$565$	19.8589	−	22.4160i	0.835470	−	0.943050i
$566$	0.742756	+	0.0901869i	0.0312204	+	0.00379084i
$567$	0.188827	−	0.766101i	0.00792999	−	0.0321732i
$568$	−2.43429	−	1.27761i	−0.102141	−	0.0536075i
$569$	1.91702	−	15.7880i	0.0803655	−	0.661869i	−0.895741	−	0.444576i	$-0.853354\pi$
$569$	1.91702	−	15.7880i	0.0803655	−	0.661869i	0.976106	−	0.217293i	$-0.0697227\pi$
$570$	0.481595	−	0.0584763i	0.0201718	−	0.00244930i
$571$	3.53226	−	5.11736i	0.147820	−	0.214155i	−0.742078	−	0.670313i	$-0.766160\pi$
$571$	3.53226	−	5.11736i	0.147820	−	0.214155i	0.889898	+	0.456159i	$0.150775\pi$
$572$	29.3156	−	7.44585i	1.22575	−	0.311327i
$573$	2.21707	+	3.21197i	0.0926192	+	0.134182i
$574$	0.219312	+	0.247552i	0.00915392	+	0.0103326i
$575$	−14.1058	−	3.47676i	−0.588252	−	0.144991i
$576$	4.37806	+	6.34272i	0.182419	+	0.264280i
$577$			6.50638i			0.270864i	0.990787	+	0.135432i	$0.0432423\pi$
$577$			6.50638i			0.270864i	−0.990787	+	0.135432i	$0.956758\pi$
$578$	1.25282	−	0.864760i	0.0521105	−	0.0359693i
$579$	15.0622	−	1.82888i	0.625963	−	0.0760057i
$580$	−23.5905	+	8.94668i	−0.979540	+	0.371491i
$581$	0.0239241	−	0.197033i	0.000992539	−	0.00817429i
$582$	−0.505811	−	1.33371i	−0.0209665	−	0.0552842i
$583$	32.9501	−	37.1930i	1.36465	−	1.54038i
$584$	0.916769	+	0.812187i	0.0379362	+	0.0336085i
$585$	−0.776425	−	6.03746i	−0.0321012	−	0.249618i
$586$	1.06906	−	0.947104i	0.0441625	−	0.0391245i
$587$			2.22038i			0.0916449i	0.998950	+	0.0458224i	$0.0145908\pi$
$587$			2.22038i			0.0916449i	−0.998950	+	0.0458224i	$0.985409\pi$
$588$	9.48857	+	8.40614i	0.391302	+	0.346664i
$589$	−22.2049	+	5.47302i	−0.914938	+	0.225512i
$590$	−1.77986	−	1.22855i	−0.0732757	−	0.0505786i
$591$	2.57779	−	0.977628i	0.106036	−	0.0402142i
$592$	−10.0588	+	3.81481i	−0.413416	+	0.156788i
$593$	37.2662	+	25.7230i	1.53034	+	1.05632i	0.974326	+	0.225141i	$0.0722843\pi$
$593$	37.2662	+	25.7230i	1.53034	+	1.05632i	0.556011	+	0.831175i	$0.312331\pi$
$594$	0.453933	−	0.111884i	0.0186251	−	0.00459068i
$595$	1.79980	+	1.59448i	0.0737845	+	0.0653674i
$596$			13.5806i			0.556282i
$597$	−6.03486	+	5.34642i	−0.246990	+	0.218814i
$598$	−2.61622	+	0.664492i	−0.106985	+	0.0271731i
$599$	−19.4672	−	17.2464i	−0.795407	−	0.704669i	0.164073	−	0.986448i	$-0.447537\pi$
$599$	−19.4672	−	17.2464i	−0.795407	−	0.704669i	−0.959479	+	0.281779i	$0.909075\pi$
$600$	−0.629727	+	0.710815i	−0.0257085	+	0.0290189i
$601$	13.6521	+	35.9976i	0.556881	+	1.46837i	0.857426	+	0.514607i	$0.172062\pi$
$601$	13.6521	+	35.9976i	0.556881	+	1.46837i	−0.300545	+	0.953768i	$0.597169\pi$
$602$	0.0224955	−	0.185267i	0.000916847	−	0.00755091i
$603$	4.13302	−	1.56745i	0.168310	−	0.0638315i
$604$	6.11877	−	0.742953i	0.248969	−	0.0302303i
$605$	−9.46351	+	6.53219i	−0.384747	+	0.265571i
$606$			1.23874i			0.0503202i
$607$	22.0512	+	31.9466i	0.895029	+	1.29667i	0.954429	+	0.298439i	$0.0964660\pi$
$607$	22.0512	+	31.9466i	0.895029	+	1.29667i	−0.0593995	+	0.998234i	$0.518919\pi$
$608$	3.32069	+	0.818476i	0.134672	+	0.0331936i
$609$	3.93371	+	4.44024i	0.159402	+	0.179928i
$610$	−1.01844	−	1.47546i	−0.0412353	−	0.0597397i
$611$	−4.30441	−	1.02872i	−0.174138	−	0.0416177i
$612$	−2.03818	+	2.95282i	−0.0823886	+	0.119360i
$613$	−27.7771	+	3.37275i	−1.12190	+	0.136224i	−0.660400	−	0.750914i	$-0.729613\pi$
$613$	−27.7771	+	3.37275i	−1.12190	+	0.136224i	−0.461505	+	0.887138i	$0.652690\pi$
$614$	0.348950	−	2.87386i	0.0140825	−	0.115979i
$615$	−5.65632	−	2.96867i	−0.228085	−	0.119708i
$616$	0.352037	−	1.42827i	0.0141840	−	0.0575467i
$617$	11.5074	+	1.39725i	0.463271	+	0.0562513i	0.348845	−	0.937180i	$-0.386574\pi$
$617$	11.5074	+	1.39725i	0.463271	+	0.0562513i	0.114426	+	0.993432i	$0.463497\pi$
$618$	0.334502	−	0.377575i	0.0134557	−	0.0151883i
$619$	5.10982	−	3.52705i	0.205381	−	0.141764i	−0.460935	−	0.887434i	$-0.652486\pi$
$619$	5.10982	−	3.52705i	0.205381	−	0.141764i	0.666316	+	0.745670i	$0.267870\pi$
$620$	−16.8071	+	24.3493i	−0.674990	+	0.977892i
$621$	6.56172	−	1.61732i	0.263313	−	0.0649007i
$622$	−2.41345	−	0.293046i	−0.0967707	−	0.0117501i
$623$	−5.83268	+	3.06123i	−0.233681	+	0.122645i
$624$	3.29081	−	13.7695i	0.131738	−	0.551221i
$625$	−8.52713	−	4.47538i	−0.341085	−	0.179015i
$626$	0.390108	+	0.269272i	0.0155919	+	0.0107623i
$627$	−6.21878	+	9.00946i	−0.248354	+	0.359803i
$628$	11.6050	−	10.2811i	0.463091	−	0.410262i
$629$	−3.27946	−	3.70175i	−0.130761	−	0.147598i
$630$	−0.137978	−	0.0523282i	−0.00549718	−	0.00208481i
$631$	−11.6710	+	22.2372i	−0.464615	+	0.885249i	0.534580	+	0.845118i	$0.320470\pi$
$631$	−11.6710	+	22.2372i	−0.464615	+	0.885249i	−0.999194	+	0.0401313i	$0.987222\pi$
$632$	3.45622	+	1.31077i	0.137481	+	0.0521397i
$633$	9.25814	+	2.28193i	0.367978	+	0.0906984i
$634$	−2.10125	+	1.86155i	−0.0834514	+	0.0739314i
$635$	−16.4147	+	11.3302i	−0.651397	+	0.449627i
$636$	−8.29888	−	21.8824i	−0.329072	−	0.867692i
$637$	−0.162537	−	22.9936i	−0.00643996	−	0.911039i
$638$	−1.24640	+	3.28650i	−0.0493456	+	0.130114i
$639$	−1.48935	−	6.04254i	−0.0589178	−	0.239039i
$640$	5.21827	−	2.73876i	0.206270	−	0.108259i
$641$	2.38178	+	6.28024i	0.0940747	+	0.248055i	0.973791	−	0.227444i	$-0.0730369\pi$
$641$	2.38178	+	6.28024i	0.0940747	+	0.248055i	−0.879716	+	0.475499i	$0.842268\pi$
$642$	−0.360494	+	0.0437719i	−0.0142275	+	0.00172754i
$643$	−19.7808	−	13.6537i	−0.780079	−	0.538449i	0.110176	−	0.993912i	$-0.464858\pi$
$643$	−19.7808	−	13.6537i	−0.780079	−	0.538449i	−0.890255	+	0.455463i	$0.849474\pi$
$644$	2.53656	−	10.2912i	0.0999545	−	0.405531i
$645$	0.862671	+	3.49999i	0.0339676	+	0.137812i
$646$	0.0625206	+	0.514903i	0.00245984	+	0.0202586i
$647$	9.02014	−	23.7842i	0.354618	−	0.935052i	−0.632428	−	0.774619i	$-0.717942\pi$
$647$	9.02014	−	23.7842i	0.354618	−	0.935052i	0.987047	−	0.160433i	$-0.0512891\pi$
$648$	0.105718	−	0.428916i	0.00415301	−	0.0168494i
$649$	47.3844	−	11.6792i	1.86000	−	0.458449i
$650$	0.858606	−	0.00606933i	0.0336773	−	0.000238059i
$651$	6.75430	+	1.66478i	0.264722	+	0.0652481i
$652$	23.3698	−	44.5273i	0.915230	−	1.74383i
$653$	−33.6569			−1.31710			−0.658548	−	0.752538i	$-0.728829\pi$
$653$	−33.6569			−1.31710			−0.658548	+	0.752538i	$0.728829\pi$
$654$	−2.20714			−0.0863062
$655$	−2.99813	+	5.71246i	−0.117147	+	0.223204i
$656$	−9.85200	−	11.1206i	−0.384656	−	0.434187i
$657$			2.77257i			0.108168i
$658$	−0.0711450	+	0.0803061i	−0.00277352	+	0.00313066i
$659$	−33.9179	+	17.8015i	−1.32125	+	0.693447i	−0.970062	−	0.242857i	$-0.921916\pi$
$659$	−33.9179	+	17.8015i	−1.32125	+	0.693447i	−0.351191	+	0.936304i	$0.614223\pi$
$660$	1.70713	+	14.0595i	0.0664499	+	0.547264i
$661$	−23.2742	−	44.3453i	−0.905262	−	1.72483i	−0.653308	−	0.757092i	$-0.726619\pi$
$661$	−23.2742	−	44.3453i	−0.905262	−	1.72483i	−0.251954	−	0.967739i	$-0.581073\pi$
$662$	−0.0519619	−	0.427945i	−0.00201956	−	0.0166326i
$663$	6.45502	−	0.830123i	0.250692	−	0.0322393i
$664$	0.0133943	−	0.110312i	0.000519801	−	0.00428095i
$665$	3.23087	−	1.22531i	0.125288	−	0.0475153i
$666$	0.268746	+	0.141049i	0.0104137	+	0.00546552i
$667$	−18.0171	+	47.5071i	−0.697624	+	1.83948i
$668$	−3.03942	−	5.79114i	−0.117599	−	0.224066i
$669$	−7.55241	−	14.3899i	−0.291993	−	0.556346i
$670$	−0.197842	−	0.802676i	−0.00764329	−	0.0310101i
$671$	40.1611	+	4.87644i	1.55040	+	0.188253i
$672$	−0.778688	−	0.689858i	−0.0300386	−	0.0266118i
$673$	7.13269	+	10.3335i	0.274945	+	0.398327i	0.935994	−	0.352016i	$-0.114504\pi$
$673$	7.13269	+	10.3335i	0.274945	+	0.398327i	−0.661049	+	0.750343i	$0.729888\pi$
$674$	1.97044	+	0.747290i	0.0758986	+	0.0287845i
$675$	−2.14971			−0.0827423
$676$	−22.7085	+	12.3309i	−0.873406	+	0.474266i
$677$	40.1070			1.54144			0.770719	−	0.637176i	$-0.219897\pi$
$677$	40.1070			1.54144			0.770719	+	0.637176i	$0.219897\pi$
$678$	−1.83734	−	0.696810i	−0.0705625	−	0.0267608i
$679$	−5.77140	−	8.36131i	−0.221486	−	0.320878i
$680$	1.00765	+	0.892700i	0.0386416	+	0.0342335i
$681$	−9.54346	−	1.15879i	−0.365706	−	0.0444048i
$682$	0.986424	+	4.00208i	0.0377721	+	0.153248i
$683$	1.41335	+	2.69292i	0.0540805	+	0.103042i	0.910996	−	0.412415i	$-0.135315\pi$
$683$	1.41335	+	2.69292i	0.0540805	+	0.103042i	−0.856916	+	0.515457i	$0.827622\pi$
$684$	2.39615	+	4.56548i	0.0916190	+	0.174565i
$685$	−10.2838	+	27.1162i	−0.392924	+	1.03606i
$686$	−1.03535	−	0.543393i	−0.0395298	−	0.0207468i
$687$	4.97788	−	1.88786i	0.189918	−	0.0720263i
$688$	−1.01055	+	8.32260i	−0.0385267	+	0.317296i
$689$	−19.4618	+	37.7272i	−0.741437	+	1.43729i
$690$	−0.152350	−	1.25471i	−0.00579985	−	0.0477661i
$691$	15.3999	+	29.3420i	0.585839	+	1.11622i	0.980338	+	0.197327i	$0.0632261\pi$
$691$	15.3999	+	29.3420i	0.585839	+	1.11622i	−0.394498	+	0.918897i	$0.629082\pi$
$692$	1.62719	+	13.4011i	0.0618566	+	0.509435i
$693$	2.94853	−	1.54751i	0.112005	−	0.0587849i
$694$	0.692867	−	0.782086i	0.0263009	−	0.0296876i
$695$			33.7801i			1.28135i
$696$	2.20236	+	2.48595i	0.0834803	+	0.0942297i
$697$	3.17398	−	6.04752i	0.120223	−	0.229066i
$698$	0.694744			0.0262964
$699$	−14.9375			−0.564988
$700$	−1.56684	+	2.98536i	−0.0592209	+	0.112836i
$701$	−8.14327	−	2.00714i	−0.307567	−	0.0758085i	0.0825113	−	0.996590i	$-0.473706\pi$
$701$	−8.14327	−	2.00714i	−0.307567	−	0.0758085i	−0.390078	+	0.920782i	$0.627552\pi$
$702$	−0.352344	+	0.188113i	−0.0132984	+	0.00709987i
$703$	−6.90043	+	1.70080i	−0.260255	+	0.0641471i
$704$	−7.78396	+	31.5808i	−0.293369	+	1.19025i
$705$	0.734840	−	1.93761i	0.0276757	−	0.0729748i
$706$	−0.334688	−	2.75640i	−0.0125961	−	0.103739i
$707$	2.11149	+	8.56666i	0.0794108	+	0.322182i
$708$	5.50079	−	22.3176i	0.206732	−	0.838746i
$709$	39.1789	+	27.0433i	1.47140	+	1.01563i	0.990297	+	0.138964i	$0.0443773\pi$
$709$	39.1789	+	27.0433i	1.47140	+	1.01563i	0.481098	+	0.876667i	$0.340238\pi$
$710$	−1.15544	+	0.140295i	−0.0433628	+	0.00526519i
$711$	2.96721	+	7.82388i	0.111279	+	0.293418i
$712$	−3.26553	+	1.71388i	−0.122381	+	0.0642306i
$713$	14.2590	+	57.8511i	0.534004	+	2.16654i
$714$	0.0559473	−	0.147521i	0.00209378	−	0.00552083i
$715$	16.8992	−	19.3491i	0.631993	−	0.723614i
$716$	2.82389	+	7.44599i	0.105534	+	0.278270i
$717$	−12.2561	+	8.45975i	−0.457711	+	0.315935i
$718$	−2.56582	+	2.27312i	−0.0957557	+	0.0848322i
$719$	−19.5896	−	4.82840i	−0.730568	−	0.180069i	−0.143550	−	0.989643i	$-0.545852\pi$
$719$	−19.5896	−	4.82840i	−0.730568	−	0.180069i	−0.587018	+	0.809574i	$0.699698\pi$
$720$	6.19829	+	2.35070i	0.230996	+	0.0876054i
$721$	1.66970	−	3.18135i	0.0621830	−	0.118480i
$722$	−1.27106	−	0.482050i	−0.0473040	−	0.0179401i
$723$	−5.37134	−	6.06299i	−0.199762	−	0.225485i
$724$	29.2721	−	25.9328i	1.08789	−	0.963787i
$725$	9.18106	−	13.3011i	0.340976	−	0.493989i
$726$	0.620957	+	0.428615i	0.0230459	+	0.0159074i
$727$	17.7843	+	9.33394i	0.659585	+	0.346177i	0.761079	−	0.648659i	$-0.224670\pi$
$727$	17.7843	+	9.33394i	0.659585	+	0.346177i	−0.101494	+	0.994836i	$0.532362\pi$
$728$	0.00888340	+	1.25670i	0.000329241	+	0.0465765i
$729$	0.885456	−	0.464723i	0.0327947	−	0.0172120i
$730$	0.514758	+	0.0625029i	0.0190520	+	0.00231334i
$731$	−3.74206	+	0.922334i	−0.138405	+	0.0341138i
$732$	10.8241	−	15.6815i	0.400072	−	0.579604i
$733$	−20.1638	+	13.9181i	−0.744767	+	0.514076i	−0.878969	−	0.476878i	$-0.841768\pi$
$733$	−20.1638	+	13.9181i	−0.744767	+	0.514076i	0.134202	+	0.990954i	$0.457153\pi$
$734$	0.216662	−	0.244561i	0.00799716	−	0.00902692i
$735$	10.6884	+	1.29781i	0.394247	+	0.0478703i
$736$	2.13240	−	8.65147i	0.0786012	−	0.318897i
$737$	16.5181	+	8.66939i	0.608453	+	0.319341i
$738$	−0.0505237	+	0.416100i	−0.00185980	+	0.0153169i
$739$	−19.9368	+	2.42076i	−0.733386	+	0.0890492i	−0.478705	−	0.877976i	$-0.658894\pi$
$739$	−19.9368	+	2.42076i	−0.733386	+	0.0890492i	−0.254681	+	0.967025i	$0.581971\pi$
$740$	−5.22300	+	7.56683i	−0.192001	+	0.278162i
$741$	3.25459	−	8.76809i	0.119560	−	0.322104i
$742$	0.584605	+	0.846946i	0.0214615	+	0.0310924i
$743$	3.72264	+	4.20199i	0.136570	+	0.154156i	0.812817	−	0.582519i	$-0.197933\pi$
$743$	3.72264	+	4.20199i	0.136570	+	0.154156i	−0.676246	+	0.736675i	$0.736395\pi$
$744$	3.78152	+	0.932061i	0.138637	+	0.0341710i
$745$	6.55245	+	9.49286i	0.240063	+	0.347791i
$746$			3.63340i			0.133028i
$747$	0.207021	−	0.142896i	0.00757450	−	0.00522830i
$748$	−15.0318	+	1.82520i	−0.549618	+	0.0667358i
$749$	−2.41843	+	0.917191i	−0.0883677	+	0.0335134i
$750$	−0.161178	+	1.32742i	−0.00588539	+	0.0484705i
$751$	1.56310	+	4.12157i	0.0570385	+	0.150398i	0.960507	−	0.278257i	$-0.0897567\pi$
$751$	1.56310	+	4.12157i	0.0570385	+	0.150398i	−0.903468	+	0.428655i	$0.858988\pi$
$752$	3.19599	−	3.60753i	0.116546	−	0.131553i
$753$	−4.27357	−	3.78605i	−0.155738	−	0.137971i
$754$	0.340879	−	2.98349i	0.0124141	−	0.108652i
$755$	3.91857	−	3.47155i	0.142611	−	0.126343i
$756$		−	1.56838i		−	0.0570413i
$757$	15.4417	+	13.6802i	0.561239	+	0.497214i	0.895376	−	0.445310i	$-0.146907\pi$
$757$	15.4417	+	13.6802i	0.561239	+	0.497214i	−0.334138	+	0.942524i	$0.608445\pi$
$758$	−2.72327	+	0.671226i	−0.0989137	+	0.0243800i
$759$	23.4726	+	16.2019i	0.852000	+	0.588093i
$760$	1.80886	−	0.686010i	0.0656143	−	0.0248842i
$761$	−30.0272	+	11.3878i	−1.08849	+	0.412809i	−0.832587	−	0.553895i	$-0.813141\pi$
$761$	−30.0272	+	11.3878i	−1.08849	+	0.412809i	−0.255900	+	0.966703i	$0.582372\pi$
$762$	1.07706	+	0.743444i	0.0390179	+	0.0269321i
$763$	−15.2638	+	3.76220i	−0.552588	+	0.136201i
$764$	5.80678	+	5.14436i	0.210082	+	0.186117i
$765$			3.04742i			0.110180i
$766$	0.306603	−	0.271626i	0.0110780	−	0.00981425i
$767$	−36.7799	+	19.6364i	−1.32804	+	0.709030i
$768$	11.2481	+	9.96492i	0.405880	+	0.359578i
$769$	10.3148	−	11.6430i	0.371962	−	0.419858i	−0.532488	−	0.846437i	$-0.678743\pi$
$769$	10.3148	−	11.6430i	0.371962	−	0.419858i	0.904450	+	0.426579i	$0.140281\pi$
$770$	−0.220842	−	0.582312i	−0.00795858	−	0.0209851i
$771$	2.84419	−	23.4240i	0.102431	−	0.843595i
$772$	28.1996	−	10.6947i	1.01492	−	0.384910i
$773$	12.7283	−	1.54549i	0.457804	−	0.0555875i	0.111614	−	0.993752i	$-0.464398\pi$
$773$	12.7283	−	1.54549i	0.457804	−	0.0555875i	0.346191	+	0.938164i	$0.387475\pi$
$774$	0.194659	−	0.134363i	0.00699687	−	0.00482959i
$775$		−	18.9528i		−	0.680805i
$776$	−3.23122	−	4.68123i	−0.115994	−	0.168047i
$777$	2.09897	+	0.517351i	0.0753003	+	0.0185599i
$778$	1.42079	+	1.60374i	0.0509377	+	0.0574968i
$779$	−5.57549	−	8.07749i	−0.199763	−	0.289406i
$780$	−4.37046	−	11.2828i	−0.156488	−	0.403988i
$781$	14.9200	−	21.6154i	0.533880	−	0.773459i
$782$	1.34149	−	0.162886i	0.0479716	−	0.00582481i
$783$	−0.906222	+	7.46341i	−0.0323857	+	0.266721i
$784$	22.1728	+	11.6372i	0.791886	+	0.415614i
$785$	3.15142	−	12.7858i	0.112479	−	0.456345i
$786$	0.420230	+	0.0510251i	0.0149891	+	0.00182001i
$787$	−19.8440	+	22.3993i	−0.707363	+	0.798448i	−0.986839	−	0.161705i	$-0.948301\pi$
$787$	−19.8440	+	22.3993i	−0.707363	+	0.798448i	0.279476	+	0.960153i	$0.409839\pi$
$788$	4.51001	−	3.11303i	0.160662	−	0.110897i
$789$	10.9934	−	15.9266i	0.391374	−	0.567003i
$790$	1.51948	−	0.374518i	0.0540606	−	0.0133247i
$791$	−13.8941	−	1.68705i	−0.494018	−	0.0599847i
$792$	1.65079	−	0.866400i	0.0586582	−	0.0307862i
$793$	−34.2806	+	4.40852i	−1.21734	+	0.156551i
$794$	−0.238639	−	0.125248i	−0.00846899	−	0.00444487i
$795$	−16.3589	−	11.2917i	−0.580190	−	0.400476i
$796$	−9.10383	+	13.1892i	−0.322677	+	0.467478i
$797$	−23.0763	+	20.4439i	−0.817406	+	0.724159i	−0.964248	−	0.265001i	$-0.914628\pi$
$797$	−23.0763	+	20.4439i	−0.817406	+	0.724159i	0.146842	+	0.989160i	$0.453089\pi$
$798$	−0.150350	−	0.169710i	−0.00532232	−	0.00600766i
$799$	2.07162	+	0.785663i	0.0732888	+	0.0277948i
$800$	−1.31718	+	2.50969i	−0.0465695	+	0.0887308i
$801$	−7.80598	−	2.96042i	−0.275811	−	0.104601i
$802$	2.22661	+	0.548811i	0.0786245	+	0.0193792i
$803$	−8.75843	+	7.75929i	−0.309078	+	0.273819i
$804$	7.23098	−	4.99118i	0.255017	−	0.176025i
$805$	−3.19232	−	8.41746i	−0.112515	−	0.296676i
$806$	−1.65849	−	3.10643i	−0.0584178	−	0.109419i
$807$	−9.27429	+	24.4543i	−0.326471	+	0.860832i
$808$	1.18216	+	4.79620i	0.0415882	+	0.168730i
$809$	17.8631	−	9.37530i	0.628034	−	0.329618i	−0.120500	−	0.992713i	$-0.538450\pi$
$809$	17.8631	−	9.37530i	0.628034	−	0.329618i	0.748535	+	0.663095i	$0.230758\pi$
$810$	−0.0663197	−	0.174871i	−0.00233024	−	0.00614433i
$811$	46.1917	−	5.60869i	1.62201	−	0.196948i	0.741493	−	0.670960i	$-0.234118\pi$
$811$	46.1917	−	5.60869i	1.62201	−	0.196948i	0.880518	+	0.474013i	$0.157195\pi$
$812$	9.70413	+	6.69828i	0.340548	+	0.235064i
$813$	4.04872	−	16.4263i	0.141995	−	0.576096i
$814$	0.306543	+	1.24369i	0.0107443	+	0.0435914i
$815$	−5.14833	−	42.4003i	−0.180338	−	1.48522i
$816$	−2.51328	+	6.62697i	−0.0879823	+	0.231990i
$817$	−1.32545	+	5.37755i	−0.0463716	+	0.188137i
$818$	0.841441	−	0.207396i	0.0294203	−	0.00725145i
$819$	−2.11604	+	1.90151i	−0.0739404	+	0.0664442i
$820$	−12.3287	−	3.03875i	−0.430537	−	0.106118i
$821$	5.57389	−	10.6202i	0.194530	−	0.370646i	−0.768580	−	0.639754i	$-0.779036\pi$
$821$	5.57389	−	10.6202i	0.194530	−	0.370646i	0.963110	+	0.269107i	$0.0867287\pi$
$822$	1.90291			0.0663716
$823$	−14.6384			−0.510264			−0.255132	−	0.966906i	$-0.582119\pi$
$823$	−14.6384			−0.510264			−0.255132	+	0.966906i	$0.582119\pi$
$824$	0.934814	−	1.78114i	0.0325658	−	0.0620489i
$825$	−6.01615	−	6.79083i	−0.209455	−	0.236426i
$826$			1.01075i			0.0351684i
$827$	5.54165	−	6.25523i	0.192702	−	0.217516i	−0.644216	−	0.764843i	$-0.722816\pi$
$827$	5.54165	−	6.25523i	0.192702	−	0.217516i	0.836918	+	0.547328i	$0.184355\pi$
$828$	11.8946	−	6.24274i	0.413364	−	0.216950i
$829$	−1.22893	−	10.1212i	−0.0426827	−	0.351523i	−0.998367	−	0.0571293i	$-0.981805\pi$
$829$	−1.22893	−	10.1212i	−0.0426827	−	0.351523i	0.955684	−	0.294394i	$-0.0951178\pi$
$830$	−0.0218633	−	0.0416570i	−0.000758886	−	0.00144594i
$831$	3.63055	+	29.9003i	0.125943	+	1.03723i
$832$	−0.196423	−	27.7872i	−0.00680973	−	0.963349i
$833$	−1.38756	+	11.4276i	−0.0480762	+	0.395944i
$834$	2.07247	−	0.785985i	0.0717638	−	0.0272164i
$835$	−4.91871	−	2.58154i	−0.170219	−	0.0893379i
$836$	−7.71630	+	20.3462i	−0.266874	+	0.703689i
$837$	4.09721	+	7.80658i	0.141620	+	0.269835i
$838$	−0.897228	−	1.70952i	−0.0309942	−	0.0590546i
$839$	12.4840	+	50.6497i	0.430997	+	1.74862i	0.637764	+	0.770232i	$0.279859\pi$
$839$	12.4840	+	50.6497i	0.430997	+	1.74862i	−0.206768	+	0.978390i	$0.566294\pi$
$840$	−0.584169	−	0.0709310i	−0.0201557	−	0.00244735i
$841$	−20.6018	−	18.2516i	−0.710408	−	0.629366i
$842$	1.18424	+	1.71566i	0.0408115	+	0.0591256i
$843$	20.1515	+	7.64245i	0.694054	+	0.263220i
$844$	18.9534			0.652403
$845$	−9.92383	+	19.5759i	−0.341390	+	0.673432i
$846$	−0.135974			−0.00467490
$847$	5.02491	+	1.90570i	0.172658	+	0.0654806i
$848$	−26.2617	−	38.0467i	−0.901832	−	1.30653i
$849$	5.05556	+	4.47883i	0.173506	+	0.153713i
$850$	−0.426720	−	0.0518132i	−0.0146364	−	0.00177718i
$851$	4.43115	+	17.9779i	0.151898	+	0.616274i
$852$	−5.74880	−	10.9534i	−0.196951	−	0.375258i
$853$	−15.4664	−	29.4687i	−0.529559	−	1.00899i	−0.992459	−	0.122579i	$-0.960883\pi$
$853$	−15.4664	−	29.4687i	−0.529559	−	1.00899i	0.462900	−	0.886410i	$-0.346809\pi$
$854$	−0.297118	+	0.783437i	−0.0101672	+	0.0268087i
$855$	3.87770	+	2.03517i	0.132614	+	0.0696014i
$856$	−1.35401	+	0.513507i	−0.0462790	+	0.0175513i
$857$	−4.17878	+	34.4154i	−0.142744	+	1.17561i	0.728602	+	0.684937i	$0.240171\pi$
$857$	−4.17878	+	34.4154i	−0.142744	+	1.17561i	−0.871346	+	0.490669i	$0.836753\pi$
$858$	−1.58031	−	0.586588i	−0.0539508	−	0.0200258i
$859$	−0.371881	−	3.06272i	−0.0126884	−	0.104498i	0.984989	−	0.172619i	$-0.0552229\pi$
$859$	−0.371881	−	3.06272i	−0.0126884	−	0.104498i	−0.997677	+	0.0681204i	$0.978300\pi$
$860$	3.32985	+	6.34451i	0.113547	+	0.216346i
$861$	0.359861	+	2.96372i	0.0122640	+	0.101003i
$862$	−2.40234	+	1.26085i	−0.0818242	+	0.0429446i
$863$	−38.7448	+	43.7339i	−1.31889	+	1.48872i	−0.580716	+	0.814106i	$0.697227\pi$
$863$	−38.7448	+	43.7339i	−1.31889	+	1.48872i	−0.738173	+	0.674612i	$0.764311\pi$
$864$		−	1.31848i		−	0.0448555i
$865$	7.60328	+	8.58233i	0.258519	+	0.291808i
$866$	−1.66994	+	3.18180i	−0.0567469	+	0.108122i
$867$	13.7418			0.466696
$868$	13.8275			0.469336
$869$	−16.4113	+	31.2691i	−0.556715	+	1.06073i
$870$	1.36523	+	0.336500i	0.0462857	+	0.0114084i
$871$	−15.5010	−	3.70462i	−0.525230	−	0.125526i
$872$	−8.54574	+	2.10633i	−0.289395	+	0.0713295i
$873$	3.08149	−	12.5021i	0.104293	−	0.423132i
$874$	0.688628	−	1.81576i	0.0232932	−	0.0614191i
$875$	1.14801	+	9.45470i	0.0388098	+	0.319627i
$876$	1.31890	+	5.35098i	0.0445614	+	0.180793i
$877$	−12.8827	+	52.2671i	−0.435017	+	1.76494i	0.187434	+	0.982277i	$0.439983\pi$
$877$	−12.8827	+	52.2671i	−0.435017	+	1.76494i	−0.622452	+	0.782658i	$0.713863\pi$
$878$	3.06676	+	2.11683i	0.103498	+	0.0714396i
$879$	12.7989	−	1.55407i	0.431696	−	0.0524174i
$880$	9.92070	+	26.1587i	0.334427	+	0.881811i
$881$	17.3704	−	9.11671i	0.585225	−	0.307150i	−0.146002	−	0.989284i	$-0.546640\pi$
$881$	17.3704	−	9.11671i	0.585225	−	0.307150i	0.731227	+	0.682134i	$0.238948\pi$
$882$	−0.169072	−	0.685950i	−0.00569294	−	0.0230971i
$883$	−9.11857	+	24.0437i	−0.306864	+	0.809135i	0.689527	+	0.724260i	$0.257818\pi$
$883$	−9.11857	+	24.0437i	−0.306864	+	0.809135i	−0.996392	+	0.0848751i	$0.972951\pi$
$884$	12.0631	−	4.67273i	0.405726	−	0.157161i
$885$	−6.92287	−	18.2541i	−0.232710	−	0.613605i
$886$	−1.17803	+	0.813133i	−0.0395766	+	0.0273177i
$887$	17.9395	−	15.8930i	0.602348	−	0.533634i	−0.305901	−	0.952063i	$-0.598958\pi$
$887$	17.9395	−	15.8930i	0.602348	−	0.533634i	0.908249	+	0.418429i	$0.137419\pi$
$888$	1.17515	+	0.289648i	0.0394354	+	0.00971996i
$889$	8.71583	+	3.30548i	0.292320	+	0.110862i
$890$	−0.725606	+	1.38253i	−0.0243224	+	0.0463424i
$891$	3.94607	+	1.49655i	0.132198	+	0.0501362i
$892$	−21.4211	−	24.1794i	−0.717232	−	0.809588i
$893$	2.38322	−	2.11135i	0.0797514	−	0.0706536i
$894$	0.429945	−	0.622882i	0.0143795	−	0.0208323i
$895$	5.56650	+	3.84228i	0.186068	+	0.128433i
$896$	−2.43879	−	1.27998i	−0.0814743	−	0.0427610i
$897$	−22.8437	−	8.47927i	−0.762730	−	0.283115i
$898$	−1.90348	+	0.999021i	−0.0635198	+	0.0333378i
$899$	−65.8008	−	7.98967i	−2.19458	−	0.266470i
$900$	−4.14887	+	1.02260i	−0.138296	+	0.0340868i
$901$	12.0727	−	17.4903i	0.402199	−	0.582686i
$902$	−1.45584	+	1.00489i	−0.0484741	+	0.0334592i
$903$	1.11716	−	1.26102i	0.0371768	−	0.0419640i
$904$	−7.77888	−	0.944528i	−0.258722	−	0.0314145i
$905$	7.94905	−	32.2505i	0.264235	−	1.07204i
$906$	−0.304162	−	0.159637i	−0.0101051	−	0.00530358i
$907$	5.99625	−	49.3836i	0.199102	−	1.63975i	−0.460156	−	0.887838i	$-0.652207\pi$
$907$	5.99625	−	49.3836i	0.199102	−	1.63975i	0.659259	−	0.751916i	$-0.270870\pi$
$908$	−18.9698	+	2.30335i	−0.629535	+	0.0764394i
$909$	−6.35218	+	9.20272i	−0.210689	+	0.305235i
$910$	0.305334	+	0.435732i	0.0101217	+	0.0144444i
$911$	6.26982	+	9.08341i	0.207728	+	0.300947i	0.912975	−	0.408015i	$-0.133779\pi$
$911$	6.26982	+	9.08341i	0.207728	+	0.300947i	−0.705247	+	0.708962i	$0.749164\pi$
$912$	6.75405	+	7.62374i	0.223649	+	0.252447i
$913$	1.03077	+	0.254062i	0.0341135	+	0.00840822i
$914$	1.11791	+	1.61957i	0.0369770	+	0.0535705i
$915$		−	16.1839i		−	0.535023i
$916$	8.70910	−	6.01146i	0.287757	−	0.198624i
$917$	2.99314	−	0.363432i	0.0988420	−	0.0120016i
$918$	0.186965	−	0.0709065i	0.00617077	−	0.00234026i
$919$	1.93785	−	15.9596i	0.0639237	−	0.526459i	−0.925212	−	0.379451i	$-0.876113\pi$
$919$	1.93785	−	15.9596i	0.0639237	−	0.526459i	0.989135	−	0.147008i	$-0.0469642\pi$
$920$	−1.78728	−	4.71267i	−0.0589249	−	0.155372i
$921$	17.3294	−	19.5609i	0.571023	−	0.644552i
$922$	−1.76727	−	1.56567i	−0.0582020	−	0.0515624i
$923$	−7.80837	+	21.0363i	−0.257016	+	0.692417i
$924$	4.95443	−	4.38924i	0.162989	−	0.144395i
$925$		−	5.88980i		−	0.193655i
$926$	−0.391207	−	0.346579i	−0.0128559	−	0.0113893i
$927$	4.42125	−	1.08974i	0.145213	−	0.0357918i
$928$	8.15792	+	5.63100i	0.267797	+	0.184847i
$929$	41.7487	−	15.8332i	1.36973	−	0.519471i	0.443448	−	0.896300i	$-0.353755\pi$
$929$	41.7487	−	15.8332i	1.36973	−	0.519471i	0.926283	+	0.376829i	$0.122986\pi$
$930$	1.54174	−	0.584705i	0.0505557	−	0.0191732i
$931$	13.6144	+	9.39736i	0.446195	+	0.307986i
$932$	−28.8289	+	7.10568i	−0.944321	+	0.232754i
$933$	−16.4271	−	14.5532i	−0.537800	−	0.476449i
$934$			0.877848i			0.0287241i
$935$	−9.62666	+	8.52848i	−0.314826	+	0.278911i
$936$	−1.18470	+	1.06460i	−0.0387232	+	0.0347974i
$937$	40.8983	+	36.2327i	1.33609	+	1.18367i	0.967146	+	0.254220i	$0.0818188\pi$
$937$	40.8983	+	36.2327i	1.33609	+	1.18367i	0.368943	+	0.929452i	$0.379720\pi$
$938$	−0.256206	+	0.289197i	−0.00836542	+	0.00944261i
$939$	1.51735	+	4.00092i	0.0495168	+	0.130565i
$940$	0.496506	−	4.08910i	0.0161942	−	0.133372i
$941$	−41.6012	+	15.7772i	−1.35616	+	0.514323i	−0.922236	−	0.386627i	$-0.873640\pi$
$941$	−41.6012	+	15.7772i	−1.35616	+	0.514323i	−0.433923	+	0.900950i	$0.642871\pi$
$942$	−0.857761	+	0.104151i	−0.0279474	+	0.00339342i
$943$	−21.0445	+	14.5260i	−0.685302	+	0.473030i
$944$		−	45.4051i		−	1.47781i
$945$	−0.756720	−	1.09630i	−0.0246161	−	0.0356626i
$946$	0.969217	+	0.238891i	0.0315120	+	0.00776700i
$947$	−14.5021	−	16.3695i	−0.471254	−	0.531936i	0.464037	−	0.885816i	$-0.346401\pi$
$947$	−14.5021	−	16.3695i	−0.471254	−	0.531936i	−0.935291	+	0.353880i	$0.884862\pi$
$948$	9.44839	+	13.6884i	0.306869	+	0.444577i
$949$	5.62045	−	8.26702i	0.182447	−	0.268359i
$950$	−0.350908	+	0.508378i	−0.0113850	+	0.0164940i
$951$	−25.1564	+	3.05454i	−0.815752	+	0.0990502i
$952$	0.0758367	−	0.624571i	0.00245788	−	0.0202425i
$953$	9.43777	+	4.95333i	0.305719	+	0.160454i	0.610606	−	0.791935i	$-0.290926\pi$
$953$	9.43777	+	4.95333i	0.305719	+	0.160454i	−0.304886	+	0.952389i	$0.598618\pi$
$954$	−0.312135	+	1.26638i	−0.0101057	+	0.0410006i
$955$	6.54105	+	0.794227i	0.211663	+	0.0257006i
$956$	−19.6296	+	22.1572i	−0.634866	+	0.716615i
$957$	−26.1127	+	18.0243i	−0.844104	+	0.582643i
$958$	0.381899	−	0.553276i	0.0123386	−	0.0178755i
$959$	13.1599	−	3.24361i	0.424954	−	0.104742i
$960$	12.9167	+	1.56837i	0.416884	+	0.0506189i
$961$	−41.3773	+	21.7165i	−1.33475	+	0.700531i
$962$	−0.515395	−	0.965357i	−0.0166170	−	0.0311244i
$963$	−2.90261	−	1.52341i	−0.0935354	−	0.0490912i
$964$	−13.2506	−	9.14626i	−0.426774	−	0.294581i
$965$	14.5515	−	21.0815i	0.468430	−	0.678638i
$966$	−0.442149	+	0.391710i	−0.0142259	+	0.0126031i
$967$	−9.58185	−	10.8157i	−0.308132	−	0.347809i	0.573963	−	0.818881i	$-0.305405\pi$
$967$	−9.58185	−	10.8157i	−0.308132	−	0.347809i	−0.882094	+	0.471073i	$0.843867\pi$
$968$	2.81329	+	1.06694i	0.0904226	+	0.0342928i
$969$	−2.17593	+	4.14588i	−0.0699009	+	0.133185i
$970$	−2.25168	−	0.853951i	−0.0722972	−	0.0274187i
$971$	34.1475	+	8.41661i	1.09585	+	0.270102i	0.745491	−	0.666515i	$-0.232215\pi$
$971$	34.1475	+	8.41661i	1.09585	+	0.270102i	0.350355	+	0.936617i	$0.386061\pi$
$972$	1.48784	−	1.31811i	0.0477224	−	0.0422783i
$973$	12.9927	−	8.96823i	0.416528	−	0.287508i
$974$	0.165723	+	0.436976i	0.00531011	+	0.0140016i
$975$	6.40982	+	4.35780i	0.205278	+	0.139561i
$976$	13.3472	−	35.1937i	0.427234	−	1.12652i
$977$	4.96442	+	20.1414i	0.158826	+	0.644382i	0.995339	+	0.0964355i	$0.0307441\pi$
$977$	4.96442	+	20.1414i	0.158826	+	0.644382i	−0.836513	+	0.547947i	$0.815410\pi$
$978$	−2.48155	+	1.30242i	−0.0793513	+	0.0416468i
$979$	−12.4939	−	32.9437i	−0.399307	−	1.05289i
$980$	21.2456	−	2.57969i	0.678666	−	0.0824050i
$981$	−16.3972	−	11.3181i	−0.523521	−	0.361360i
$982$	−0.633692	+	2.57099i	−0.0202219	+	0.0820436i
$983$	−12.4032	−	50.3216i	−0.395600	−	1.60501i	−0.744346	−	0.667794i	$-0.767239\pi$
$983$	−12.4032	−	50.3216i	−0.395600	−	1.60501i	0.348746	−	0.937217i	$-0.386607\pi$
$984$	0.201475	+	1.65929i	0.00642278	+	0.0528964i
$985$	1.65051	−	4.35204i	0.0525896	−	0.138667i
$986$	−0.359773	+	1.45965i	−0.0114575	+	0.0464849i
$987$	−0.940351	+	0.231776i	−0.0299317	+	0.00737750i
$988$	2.11033	−	18.4703i	0.0671385	−	0.587619i
$989$	14.0103	+	3.45322i	0.445501	+	0.109806i
$990$	0.366807	−	0.698892i	0.0116579	−	0.0222123i
$991$	45.5447			1.44678			0.723388	−	0.690442i	$-0.242584\pi$
$991$	45.5447			1.44678			0.723388	+	0.690442i	$0.242584\pi$
$992$	11.6243			0.369072
$993$	1.80845	−	3.44572i	0.0573895	−	0.109347i
$994$	0.360717	+	0.407165i	0.0114412	+	0.0129145i
$995$			13.6117i			0.431521i
$996$	0.331569	−	0.374264i	0.0105062	−	0.0118590i
$997$	6.52491	−	3.42453i	0.206646	−	0.108456i	−0.358226	−	0.933635i	$-0.616618\pi$
$997$	6.52491	−	3.42453i	0.206646	−	0.108456i	0.564871	+	0.825179i	$0.308926\pi$
$998$	0.0172028	+	0.141678i	0.000544546	+	0.00448474i
$999$	1.27325	+	2.42598i	0.0402840	+	0.0767547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.b.25.8	✓	192
169.142	even	26	inner	507.2.p.b.142.8	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.b.25.8	✓	192	1.1	even	1	trivial
507.2.p.b.142.8	yes	192	169.142	even	26	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.103579 - 0.0392824i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.48784 - 1.31811i) q^{4} +(-1.67597 - 0.203500i) q^{5} +(0.0265109 + 0.107559i) q^{6} +(0.366680 + 0.698651i) q^{7} +(0.205293 + 0.391152i) q^{8} +(-0.354605 + 0.935016i) q^{9} +O(q^{10})\)	\(q+(-0.103579 - 0.0392824i) q^{2} +(-0.568065 - 0.822984i) q^{3} +(-1.48784 - 1.31811i) q^{4} +(-1.67597 - 0.203500i) q^{5} +(0.0265109 + 0.107559i) q^{6} +(0.366680 + 0.698651i) q^{7} +(0.205293 + 0.391152i) q^{8} +(-0.354605 + 0.935016i) q^{9} +(0.165602 + 0.0869145i) q^{10} +(-3.94607 + 1.49655i) q^{11} +(-0.239594 + 1.97324i) q^{12} +(2.95276 - 2.06911i) q^{13} +(-0.0105358 - 0.0867698i) q^{14} +(0.784583 + 1.49490i) q^{15} +(0.473290 + 3.89789i) q^{16} +(-1.59829 + 0.838846i) q^{17} +(0.0734594 - 0.0829185i) q^{18} +2.59395i q^{19} +(2.22534 + 2.51188i) q^{20} +(0.366680 - 0.698651i) q^{21} +0.467518 q^{22} +6.75809 q^{23} +(0.205293 - 0.391152i) q^{24} +(-2.08724 - 0.514459i) q^{25} +(-0.387124 + 0.0983253i) q^{26} +(0.970942 - 0.239316i) q^{27} +(0.375337 - 1.52280i) q^{28} +(-2.66600 + 7.02966i) q^{29} +(-0.0225433 - 0.185661i) q^{30} +(2.10992 + 8.56026i) q^{31} +(0.315532 - 1.28016i) q^{32} +(3.47325 + 2.39741i) q^{33} +(0.198501 - 0.0241024i) q^{34} +(-0.472370 - 1.24554i) q^{35} +(1.76005 - 0.923743i) q^{36} +(0.655680 + 2.66020i) q^{37} +(0.101897 - 0.268680i) q^{38} +(-3.38020 - 1.25468i) q^{39} +(-0.264465 - 0.697337i) q^{40} +(-3.11397 + 2.14942i) q^{41} +(-0.0654251 + 0.0579616i) q^{42} +(2.07311 + 0.510976i) q^{43} +(7.84371 + 2.97473i) q^{44} +(0.784583 - 1.49490i) q^{45} +(-0.699998 - 0.265474i) q^{46} +(-0.813950 - 0.918759i) q^{47} +(2.93904 - 2.60376i) q^{48} +(3.62279 - 5.24852i) q^{49} +(0.195986 + 0.135279i) q^{50} +(1.59829 + 0.838846i) q^{51} +(-7.12053 - 0.813557i) q^{52} +(-10.4252 + 5.47157i) q^{53} +(-0.109970 - 0.0133528i) q^{54} +(6.91804 - 1.70514i) q^{55} +(-0.198002 + 0.286856i) q^{56} +(2.13478 - 1.47353i) q^{57} +(0.552284 - 0.623400i) q^{58} +(-11.4794 - 1.39385i) q^{59} +(0.803106 - 3.25833i) q^{60} +(-8.48800 - 4.45485i) q^{61} +(0.117724 - 0.969548i) q^{62} +(-0.783276 + 0.0951069i) q^{63} +(4.37806 - 6.34272i) q^{64} +(-5.36980 + 2.86688i) q^{65} +(-0.265581 - 0.384760i) q^{66} +(-2.93118 - 3.30862i) q^{67} +(3.48368 + 0.858650i) q^{68} +(-3.83903 - 5.56180i) q^{69} +0.147568i q^{70} +(-5.12174 + 3.53528i) q^{71} +(-0.438532 + 0.0532474i) q^{72} +(2.59240 - 0.983168i) q^{73} +(0.0365842 - 0.301298i) q^{74} +(0.762297 + 2.01001i) q^{75} +(3.41911 - 3.85938i) q^{76} +(-2.49251 - 2.20817i) q^{77} +(0.300832 + 0.262742i) q^{78} +(6.26327 - 5.54877i) q^{79} -6.62907i q^{80} +(-0.748511 - 0.663123i) q^{81} +(0.406976 - 0.100311i) q^{82} +(-0.207021 - 0.142896i) q^{83} +(-1.46646 + 0.556154i) q^{84} +(2.84939 - 1.08063i) q^{85} +(-0.194659 - 0.134363i) q^{86} +(7.29976 - 1.79923i) q^{87} +(-1.39548 - 1.23628i) q^{88} +8.34850i q^{89} +(-0.139990 + 0.124020i) q^{90} +(2.52830 + 1.30424i) q^{91} +(-10.0549 - 8.90789i) q^{92} +(5.84639 - 6.59921i) q^{93} +(0.0482172 + 0.127138i) q^{94} +(0.527869 - 4.34739i) q^{95} +(-1.23280 + 0.467538i) q^{96} +(-12.7824 + 1.55206i) q^{97} +(-0.581421 + 0.401326i) q^{98} -4.22032i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9}+O(q^{10}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9	\( 192 q + 16 q^{3} + 18 q^{4} - 16 q^{9} - 18 q^{12} - 63 q^{13} - 10 q^{14} - 6 q^{16} + 12 q^{17} + 16 q^{22} - 52 q^{23} + 58 q^{25} + 51 q^{26} + 16 q^{27} - 49 q^{29} - 26 q^{31} - 13 q^{33} - 65 q^{34} + 39 q^{35} + 18 q^{36} + 77 q^{38} - 2 q^{39} - 55 q^{42} - 76 q^{43} + 39 q^{44} + 6 q^{48} - 58 q^{49} + 52 q^{50} - 12 q^{51} + 63 q^{52} - 73 q^{53} + 37 q^{55} - 10 q^{56} + 13 q^{57} - 26 q^{58} - 104 q^{59} - 13 q^{60} + 8 q^{61} + 53 q^{62} + 42 q^{64} + 52 q^{65} - 42 q^{66} + 26 q^{67} - 34 q^{68} - 39 q^{71} + 52 q^{73} + 59 q^{74} - 6 q^{75} - 130 q^{76} - 52 q^{77} + 53 q^{78} + 14 q^{79} - 16 q^{81} + 41 q^{82} - 78 q^{83} + 91 q^{85} + 169 q^{86} - 42 q^{87} - 270 q^{88} + 80 q^{91} - 54 q^{92} - 91 q^{93} + 25 q^{94} - 58 q^{95} - 65 q^{96} + 130 q^{97} + 104 q^{98}+O(q^{100}) \) 192 * q + 16 * q^3 + 18 * q^4 - 16 * q^9 - 18 * q^12 - 63 * q^13 - 10 * q^14 - 6 * q^16 + 12 * q^17 + 16 * q^22 - 52 * q^23 + 58 * q^25 + 51 * q^26 + 16 * q^27 - 49 * q^29 - 26 * q^31 - 13 * q^33 - 65 * q^34 + 39 * q^35 + 18 * q^36 + 77 * q^38 - 2 * q^39 - 55 * q^42 - 76 * q^43 + 39 * q^44 + 6 * q^48 - 58 * q^49 + 52 * q^50 - 12 * q^51 + 63 * q^52 - 73 * q^53 + 37 * q^55 - 10 * q^56 + 13 * q^57 - 26 * q^58 - 104 * q^59 - 13 * q^60 + 8 * q^61 + 53 * q^62 + 42 * q^64 + 52 * q^65 - 42 * q^66 + 26 * q^67 - 34 * q^68 - 39 * q^71 + 52 * q^73 + 59 * q^74 - 6 * q^75 - 130 * q^76 - 52 * q^77 + 53 * q^78 + 14 * q^79 - 16 * q^81 + 41 * q^82 - 78 * q^83 + 91 * q^85 + 169 * q^86 - 42 * q^87 - 270 * q^88 + 80 * q^91 - 54 * q^92 - 91 * q^93 + 25 * q^94 - 58 * q^95 - 65 * q^96 + 130 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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