LMFDB - Embedded newform 370.2.o.c.71.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (of order $9$, degree $6$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			71.2
Character	$\chi$	$=$	370.71
Dual form			370.2.o.c.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(0.204920 - 0.171948i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.939693 - 0.342020i) q^{5} -0.267503 q^{6} +(-3.03750 - 1.10556i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.508519 + 2.88395i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(0.204920 - 0.171948i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.939693 - 0.342020i) q^{5} -0.267503 q^{6} +(-3.03750 - 1.10556i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.508519 + 2.88395i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.746797 + 1.29349i) q^{11} +(0.204920 + 0.171948i) q^{12} +(0.0469699 + 0.266379i) q^{13} +(1.61622 + 2.79937i) q^{14} +(-0.251371 + 0.0914916i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.420456 + 2.38452i) q^{17} +(2.24332 - 1.88237i) q^{18} +(-5.39420 + 4.52627i) q^{19} +(0.173648 - 0.984808i) q^{20} +(-0.812541 + 0.295741i) q^{21} +(1.40352 - 0.510839i) q^{22} +(-1.46272 - 2.53351i) q^{23} +(-0.0464515 - 0.263439i) q^{24} +(0.766044 + 0.642788i) q^{25} +(0.135244 - 0.234250i) q^{26} +(0.792939 + 1.37341i) q^{27} +(0.561307 - 3.18333i) q^{28} +(-0.0380643 + 0.0659293i) q^{29} +(0.251371 + 0.0914916i) q^{30} -2.49861 q^{31} +(0.939693 + 0.342020i) q^{32} +(0.0693797 + 0.393472i) q^{33} +(1.85483 - 1.55639i) q^{34} +(2.47619 + 2.07777i) q^{35} -2.92844 q^{36} +(-5.96112 + 1.21041i) q^{37} +7.04163 q^{38} +(0.0554284 + 0.0465100i) q^{39} +(-0.766044 + 0.642788i) q^{40} +(0.903548 + 5.12428i) q^{41} +(0.812541 + 0.295741i) q^{42} -1.65852 q^{43} +(-1.40352 - 0.510839i) q^{44} +(1.46422 - 2.53611i) q^{45} +(-0.507999 + 2.88101i) q^{46} +(1.45021 + 2.51184i) q^{47} +(-0.133752 + 0.231665i) q^{48} +(2.64181 + 2.21674i) q^{49} +(-0.173648 - 0.984808i) q^{50} +(0.323854 + 0.560932i) q^{51} +(-0.254176 + 0.0925126i) q^{52} +(5.50298 - 2.00292i) q^{53} +(0.275385 - 1.56179i) q^{54} +(1.14416 - 0.960064i) q^{55} +(-2.47619 + 2.07777i) q^{56} +(-0.327094 + 1.85504i) q^{57} +(0.0715375 - 0.0260375i) q^{58} +(4.61755 - 1.68065i) q^{59} +(-0.133752 - 0.231665i) q^{60} +(0.0607858 + 0.344733i) q^{61} +(1.91404 + 1.60607i) q^{62} +(4.73300 - 8.19780i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.0469699 - 0.266379i) q^{65} +(0.199771 - 0.346013i) q^{66} +(-6.52776 - 2.37591i) q^{67} -2.42131 q^{68} +(-0.735373 - 0.267654i) q^{69} +(-0.561307 - 3.18333i) q^{70} +(3.03309 - 2.54507i) q^{71} +(2.24332 + 1.88237i) q^{72} -0.00494712 q^{73} +(5.34452 + 2.90450i) q^{74} +0.267503 q^{75} +(-5.39420 - 4.52627i) q^{76} +(3.69842 - 3.10334i) q^{77} +(-0.0125646 - 0.0712574i) q^{78} +(-14.6723 - 5.34027i) q^{79} +1.00000 q^{80} +(-7.85686 - 2.85966i) q^{81} +(2.60166 - 4.50621i) q^{82} +(2.80466 - 15.9060i) q^{83} +(-0.432344 - 0.748842i) q^{84} +(1.21065 - 2.09692i) q^{85} +(1.27050 + 1.06607i) q^{86} +(0.00353629 + 0.0200553i) q^{87} +(0.746797 + 1.29349i) q^{88} +(3.04991 - 1.11008i) q^{89} +(-2.75184 + 1.00159i) q^{90} +(0.151827 - 0.861054i) q^{91} +(2.24102 - 1.88044i) q^{92} +(-0.512013 + 0.429630i) q^{93} +(0.503654 - 2.85636i) q^{94} +(6.61696 - 2.40838i) q^{95} +(0.251371 - 0.0914916i) q^{96} +(-5.03969 - 8.72899i) q^{97} +(-0.598850 - 3.39625i) q^{98} +(-3.35060 - 2.81149i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{6} - 3 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 6 * q^6 - 3 * q^7 + 12 * q^8 + 12 * q^9	$ 24 q - 6 q^{6} - 3 q^{7} + 12 q^{8} + 12 q^{9} + 12 q^{10} - 15 q^{11} + 3 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 36 q^{21} + 9 q^{22} + 21 q^{23} - 6 q^{26} - 12 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{31} - 39 q^{33} - 21 q^{34} + 6 q^{35} + 54 q^{36} - 12 q^{37} - 36 q^{38} - 18 q^{39} + 27 q^{41} - 36 q^{42} - 24 q^{43} - 9 q^{44} - 27 q^{45} + 3 q^{46} - 6 q^{47} - 3 q^{48} - 27 q^{49} - 6 q^{51} - 9 q^{52} + 6 q^{53} + 9 q^{54} + 9 q^{55} - 6 q^{56} - 27 q^{57} + 27 q^{58} + 51 q^{59} - 3 q^{60} - 3 q^{62} - 27 q^{63} - 12 q^{64} + 15 q^{66} - 18 q^{69} + 3 q^{70} - 66 q^{71} + 6 q^{72} + 42 q^{73} - 42 q^{74} + 6 q^{75} - 6 q^{76} + 69 q^{77} + 36 q^{78} - 30 q^{79} + 24 q^{80} - 90 q^{81} + 24 q^{82} + 57 q^{83} + 6 q^{84} - 6 q^{86} + 6 q^{87} + 15 q^{88} - 57 q^{89} + 6 q^{90} + 3 q^{91} + 15 q^{92} - 72 q^{93} + 3 q^{94} - 15 q^{95} - 3 q^{97} - 72 q^{98} + 63 q^{99}+O(q^{100}) $ 24 * q - 6 * q^6 - 3 * q^7 + 12 * q^8 + 12 * q^9 + 12 * q^10 - 15 * q^11 + 3 * q^14 - 6 * q^17 + 6 * q^18 - 6 * q^19 + 36 * q^21 + 9 * q^22 + 21 * q^23 - 6 * q^26 - 12 * q^27 - 3 * q^28 + 12 * q^29 + 30 * q^31 - 39 * q^33 - 21 * q^34 + 6 * q^35 + 54 * q^36 - 12 * q^37 - 36 * q^38 - 18 * q^39 + 27 * q^41 - 36 * q^42 - 24 * q^43 - 9 * q^44 - 27 * q^45 + 3 * q^46 - 6 * q^47 - 3 * q^48 - 27 * q^49 - 6 * q^51 - 9 * q^52 + 6 * q^53 + 9 * q^54 + 9 * q^55 - 6 * q^56 - 27 * q^57 + 27 * q^58 + 51 * q^59 - 3 * q^60 - 3 * q^62 - 27 * q^63 - 12 * q^64 + 15 * q^66 - 18 * q^69 + 3 * q^70 - 66 * q^71 + 6 * q^72 + 42 * q^73 - 42 * q^74 + 6 * q^75 - 6 * q^76 + 69 * q^77 + 36 * q^78 - 30 * q^79 + 24 * q^80 - 90 * q^81 + 24 * q^82 + 57 * q^83 + 6 * q^84 - 6 * q^86 + 6 * q^87 + 15 * q^88 - 57 * q^89 + 6 * q^90 + 3 * q^91 + 15 * q^92 - 72 * q^93 + 3 * q^94 - 15 * q^95 - 3 * q^97 - 72 * q^98 + 63 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	0.204920	−	0.171948i	0.118310	−	0.0992742i	−0.581713	−	0.813394i	$-0.697617\pi$
$3$	0.204920	−	0.171948i	0.118310	−	0.0992742i	0.700023	+	0.714120i	$0.253173\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$5$	−0.939693	−	0.342020i	−0.420243	−	0.152956i
$6$	−0.267503			−0.109208
$7$	−3.03750	−	1.10556i	−1.14807	−	0.417862i	−0.303246	−	0.952912i	$-0.598070\pi$
$7$	−3.03750	−	1.10556i	−1.14807	−	0.417862i	−0.844820	+	0.535051i	$0.820292\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.508519	+	2.88395i	−0.169506	+	0.961317i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−0.746797	+	1.29349i	−0.225168	+	0.390002i	−0.956370	−	0.292159i	$-0.905626\pi$
$11$	−0.746797	+	1.29349i	−0.225168	+	0.390002i	0.731202	+	0.682161i	$0.238960\pi$
$12$	0.204920	+	0.171948i	0.0591552	+	0.0496371i
$13$	0.0469699	+	0.266379i	0.0130271	+	0.0738803i	0.990628	−	0.136586i	$-0.0436129\pi$
$13$	0.0469699	+	0.266379i	0.0130271	+	0.0738803i	−0.977601	+	0.210466i	$0.932502\pi$
$14$	1.61622	+	2.79937i	0.431952	+	0.748163i
$15$	−0.251371	+	0.0914916i	−0.0649037	+	0.0236230i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.420456	+	2.38452i	−0.101976	+	0.578332i	0.890410	+	0.455160i	$0.150418\pi$
$17$	−0.420456	+	2.38452i	−0.101976	+	0.578332i	−0.992385	+	0.123172i	$0.960693\pi$
$18$	2.24332	−	1.88237i	0.528755	−	0.443678i
$19$	−5.39420	+	4.52627i	−1.23751	+	1.03840i	−0.239800	+	0.970822i	$0.577082\pi$
$19$	−5.39420	+	4.52627i	−1.23751	+	1.03840i	−0.997714	+	0.0675753i	$0.978474\pi$
$20$	0.173648	−	0.984808i	0.0388289	−	0.220210i
$21$	−0.812541	+	0.295741i	−0.177311	+	0.0645359i
$22$	1.40352	−	0.510839i	0.299231	−	0.108911i
$23$	−1.46272	−	2.53351i	−0.304999	−	0.528274i	0.672262	−	0.740313i	$-0.265323\pi$
$23$	−1.46272	−	2.53351i	−0.304999	−	0.528274i	−0.977261	+	0.212039i	$0.931990\pi$
$24$	−0.0464515	−	0.263439i	−0.00948187	−	0.0537744i
$25$	0.766044	+	0.642788i	0.153209	+	0.128558i
$26$	0.135244	−	0.234250i	0.0265236	−	0.0459402i
$27$	0.792939	+	1.37341i	0.152601	+	0.264313i
$28$	0.561307	−	3.18333i	0.106077	−	0.601592i
$29$	−0.0380643	+	0.0659293i	−0.00706837	+	0.0122428i	−0.869538	−	0.493866i	$-0.835583\pi$
$29$	−0.0380643	+	0.0659293i	−0.00706837	+	0.0122428i	0.862470	+	0.506109i	$0.168917\pi$
$30$	0.251371	+	0.0914916i	0.0458939	+	0.0167040i
$31$	−2.49861			−0.448763			−0.224381	−	0.974501i	$-0.572036\pi$
$31$	−2.49861			−0.448763			−0.224381	+	0.974501i	$0.572036\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	0.0693797	+	0.393472i	0.0120774	+	0.0684946i
$34$	1.85483	−	1.55639i	0.318101	−	0.266918i
$35$	2.47619	+	2.07777i	0.418552	+	0.351207i
$36$	−2.92844			−0.488074
$37$	−5.96112	+	1.21041i	−0.980001	+	0.198991i
$37$	−5.96112	+	1.21041i	−0.980001	+	0.198991i
$38$	7.04163			1.14230
$39$	0.0554284	+	0.0465100i	0.00887565	+	0.00744755i
$40$	−0.766044	+	0.642788i	−0.121122	+	0.101634i
$41$	0.903548	+	5.12428i	0.141111	+	0.800277i	0.970408	+	0.241470i	$0.0776297\pi$
$41$	0.903548	+	5.12428i	0.141111	+	0.800277i	−0.829298	+	0.558807i	$0.811259\pi$
$42$	0.812541	+	0.295741i	0.125378	+	0.0456338i
$43$	−1.65852			−0.252921			−0.126461	−	0.991972i	$-0.540362\pi$
$43$	−1.65852			−0.252921			−0.126461	+	0.991972i	$0.540362\pi$
$44$	−1.40352	−	0.510839i	−0.211588	−	0.0770119i
$45$	1.46422	−	2.53611i	0.218273	−	0.378060i
$46$	−0.507999	+	2.88101i	−0.0749004	+	0.424781i
$47$	1.45021	+	2.51184i	0.211535	+	0.366390i	0.952195	−	0.305490i	$-0.0988203\pi$
$47$	1.45021	+	2.51184i	0.211535	+	0.366390i	−0.740660	+	0.671880i	$0.765487\pi$
$48$	−0.133752	+	0.231665i	−0.0193054	+	0.0334379i
$49$	2.64181	+	2.21674i	0.377402	+	0.316678i
$50$	−0.173648	−	0.984808i	−0.0245576	−	0.139273i
$51$	0.323854	+	0.560932i	0.0453487	+	0.0785462i
$52$	−0.254176	+	0.0925126i	−0.0352479	+	0.0128292i
$53$	5.50298	−	2.00292i	0.755893	−	0.275122i	0.0648095	−	0.997898i	$-0.479356\pi$
$53$	5.50298	−	2.00292i	0.755893	−	0.275122i	0.691083	+	0.722775i	$0.257134\pi$
$54$	0.275385	−	1.56179i	0.0374751	−	0.212532i
$55$	1.14416	−	0.960064i	0.154278	−	0.129455i
$56$	−2.47619	+	2.07777i	−0.330895	+	0.277654i
$57$	−0.327094	+	1.85504i	−0.0433247	+	0.245706i
$58$	0.0715375	−	0.0260375i	0.00939334	−	0.00341890i
$59$	4.61755	−	1.68065i	0.601154	−	0.218802i	−0.0234743	−	0.999724i	$-0.507473\pi$
$59$	4.61755	−	1.68065i	0.601154	−	0.218802i	0.624628	+	0.780922i	$0.285251\pi$
$60$	−0.133752	−	0.231665i	−0.0172673	−	0.0299078i
$61$	0.0607858	+	0.344733i	0.00778282	+	0.0441386i	0.988452	−	0.151535i	$-0.0484217\pi$
$61$	0.0607858	+	0.344733i	0.00778282	+	0.0441386i	−0.980669	+	0.195674i	$0.937311\pi$
$62$	1.91404	+	1.60607i	0.243084	+	0.203971i
$63$	4.73300	−	8.19780i	0.596302	−	1.03283i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.0469699	−	0.266379i	0.00582589	−	0.0330403i
$66$	0.199771	−	0.346013i	0.0245901	−	0.0425913i
$67$	−6.52776	−	2.37591i	−0.797493	−	0.290264i	−0.0890458	−	0.996028i	$-0.528382\pi$
$67$	−6.52776	−	2.37591i	−0.797493	−	0.290264i	−0.708447	+	0.705764i	$0.750604\pi$
$68$	−2.42131			−0.293627
$69$	−0.735373	−	0.267654i	−0.0885285	−	0.0322218i
$70$	−0.561307	−	3.18333i	−0.0670890	−	0.380480i
$71$	3.03309	−	2.54507i	0.359962	−	0.302044i	−0.444814	−	0.895623i	$-0.646730\pi$
$71$	3.03309	−	2.54507i	0.359962	−	0.302044i	0.804776	+	0.593579i	$0.202286\pi$
$72$	2.24332	+	1.88237i	0.264377	+	0.221839i
$73$	−0.00494712			−0.000579016			−0.000289508	−	1.00000i	$-0.500092\pi$
$73$	−0.00494712			−0.000579016			−0.000289508		1.00000i	$0.500092\pi$
$74$	5.34452	+	2.90450i	0.621288	+	0.337641i
$75$	0.267503			0.0308886
$76$	−5.39420	−	4.52627i	−0.618757	−	0.519199i
$77$	3.69842	−	3.10334i	0.421474	−	0.353659i
$78$	−0.0125646	−	0.0712574i	−0.00142266	−	0.00806831i
$79$	−14.6723	−	5.34027i	−1.65076	−	0.600828i	−0.661889	−	0.749602i	$-0.730245\pi$
$79$	−14.6723	−	5.34027i	−1.65076	−	0.600828i	−0.988871	+	0.148774i	$0.952467\pi$
$80$	1.00000			0.111803
$81$	−7.85686	−	2.85966i	−0.872985	−	0.317740i
$82$	2.60166	−	4.50621i	0.287306	−	0.497628i
$83$	2.80466	−	15.9060i	0.307851	−	1.74591i	−0.301920	−	0.953333i	$-0.597628\pi$
$83$	2.80466	−	15.9060i	0.307851	−	1.74591i	0.609771	−	0.792577i	$-0.291261\pi$
$84$	−0.432344	−	0.748842i	−0.0471726	−	0.0817053i
$85$	1.21065	−	2.09692i	0.131314	−	0.227442i
$86$	1.27050	+	1.06607i	0.137001	+	0.114958i
$87$	0.00353629	+	0.0200553i	0.000379130	+	0.00215015i
$88$	0.746797	+	1.29349i	0.0796088	+	0.137887i
$89$	3.04991	−	1.11008i	0.323290	−	0.117668i	−0.175277	−	0.984519i	$-0.556082\pi$
$89$	3.04991	−	1.11008i	0.323290	−	0.117668i	0.498567	+	0.866851i	$0.333860\pi$
$90$	−2.75184	+	1.00159i	−0.290069	+	0.105576i
$91$	0.151827	−	0.861054i	0.0159158	−	0.0902630i
$92$	2.24102	−	1.88044i	0.233643	−	0.196050i
$93$	−0.512013	+	0.429630i	−0.0530933	+	0.0445506i
$94$	0.503654	−	2.85636i	0.0519479	−	0.294611i
$95$	6.61696	−	2.40838i	0.678886	−	0.247094i
$96$	0.251371	−	0.0914916i	0.0256554	−	0.00933782i
$97$	−5.03969	−	8.72899i	−0.511703	−	0.886295i	−0.999908	−	0.0135663i	$-0.995682\pi$
$97$	−5.03969	−	8.72899i	−0.511703	−	0.886295i	0.488205	−	0.872729i	$-0.337652\pi$
$98$	−0.598850	−	3.39625i	−0.0604930	−	0.343073i
$99$	−3.35060	−	2.81149i	−0.336748	−	0.282565i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	2.95027	+	5.11001i	0.293562	+	0.508465i	0.974649	−	0.223737i	$-0.0718258\pi$
$101$	2.95027	+	5.11001i	0.293562	+	0.508465i	−0.681087	+	0.732202i	$0.738492\pi$
$102$	0.112473	−	0.637869i	0.0111365	−	0.0631584i
$103$	6.46552	−	11.1986i	0.637067	−	1.10343i	−0.349006	−	0.937120i	$-0.613481\pi$
$103$	6.46552	−	11.1986i	0.637067	−	1.10343i	0.986073	−	0.166312i	$-0.0531858\pi$
$104$	0.254176	+	0.0925126i	0.0249240	+	0.00907160i
$105$	0.864688			0.0843849
$106$	−5.50298	−	2.00292i	−0.534497	−	0.194541i
$107$	1.65481	+	9.38489i	0.159976	+	0.907271i	0.954094	+	0.299507i	$0.0968222\pi$
$107$	1.65481	+	9.38489i	0.159976	+	0.907271i	−0.794118	+	0.607764i	$0.792067\pi$
$108$	−1.21485	+	1.01938i	−0.116899	+	0.0980902i
$109$	5.82037	+	4.88387i	0.557490	+	0.467790i	0.877468	−	0.479635i	$-0.159231\pi$
$109$	5.82037	+	4.88387i	0.557490	+	0.467790i	−0.319978	+	0.947425i	$0.603676\pi$
$110$	−1.49359			−0.142409
$111$	−1.01342	+	1.27304i	−0.0961897	+	0.120831i
$112$	3.23244			0.305436
$113$	3.90890	+	3.27996i	0.367719	+	0.308553i	0.807858	−	0.589377i	$-0.200627\pi$
$113$	3.90890	+	3.27996i	0.367719	+	0.308553i	−0.440140	+	0.897929i	$0.645071\pi$
$114$	1.44297	−	1.21079i	0.135146	−	0.113401i
$115$	0.507999	+	2.88101i	0.0473712	+	0.268655i
$116$	−0.0715375	−	0.0260375i	−0.00664209	−	0.00241752i
$117$	−0.792110			−0.0732306
$118$	−4.61755	−	1.68065i	−0.425080	−	0.154716i
$119$	3.91336	−	6.77815i	0.358737	−	0.621352i
$120$	−0.0464515	+	0.263439i	−0.00424042	+	0.0240486i
$121$	4.38459	+	7.59433i	0.398599	+	0.690394i
$122$	0.175026	−	0.303153i	0.0158461	−	0.0274462i
$123$	1.06626	+	0.894701i	0.0961417	+	0.0806725i
$124$	−0.433878	−	2.46065i	−0.0389634	−	0.220973i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	−8.89513	+	3.23756i	−0.792441	+	0.288425i
$127$	−9.12946	+	3.32285i	−0.810109	+	0.294856i	−0.713669	−	0.700483i	$-0.752968\pi$
$127$	−9.12946	+	3.32285i	−0.810109	+	0.294856i	−0.0964400	+	0.995339i	$0.530746\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−0.339862	+	0.285178i	−0.0299232	+	0.0251085i
$130$	−0.207206	+	0.173867i	−0.0181732	+	0.0152491i
$131$	−0.355821	+	2.01796i	−0.0310882	+	0.176310i	−0.996398	−	0.0847960i	$-0.972976\pi$
$131$	−0.355821	+	2.01796i	−0.0310882	+	0.176310i	0.965310	+	0.261106i	$0.0840873\pi$
$132$	−0.375446	+	0.136651i	−0.0326784	+	0.0118940i
$133$	21.3889	−	7.78493i	1.85465	−	0.675039i
$134$	3.47335	+	6.01602i	0.300052	+	0.519705i
$135$	−0.275385	−	1.56179i	−0.0237014	−	0.134417i
$136$	1.85483	+	1.55639i	0.159050	+	0.133459i
$137$	−4.95296	+	8.57879i	−0.423160	+	0.732935i	−0.996247	−	0.0865598i	$-0.972413\pi$
$137$	−4.95296	+	8.57879i	−0.423160	+	0.732935i	0.573086	+	0.819495i	$0.305746\pi$
$138$	0.391284	+	0.677724i	0.0333083	+	0.0576917i
$139$	−2.53245	+	14.3622i	−0.214799	+	1.21819i	0.666455	+	0.745545i	$0.267811\pi$
$139$	−2.53245	+	14.3622i	−0.214799	+	1.21819i	−0.881254	+	0.472642i	$0.843300\pi$
$140$	−1.61622	+	2.79937i	−0.136595	+	0.236590i
$141$	0.729084	+	0.265365i	0.0613999	+	0.0223477i
$142$	−3.95942			−0.332267
$143$	−0.379636	−	0.138176i	−0.0317467	−	0.0115549i
$144$	−0.508519	−	2.88395i	−0.0423765	−	0.240329i
$145$	0.0583179	−	0.0489346i	0.00484304	−	0.00406379i
$146$	0.00378971	+	0.00317995i	0.000313639	+	0.000263174i
$147$	0.922523			0.0760884
$148$	−2.22716	−	5.66037i	−0.183071	−	0.465279i
$149$	−12.7148			−1.04163			−0.520817	−	0.853669i	$-0.674373\pi$
$149$	−12.7148			−1.04163			−0.520817	+	0.853669i	$0.674373\pi$
$150$	−0.204920	−	0.171948i	−0.0167316	−	0.0140395i
$151$	13.9080	−	11.6702i	1.13182	−	0.949707i	0.132676	−	0.991159i	$-0.457643\pi$
$151$	13.9080	−	11.6702i	1.13182	−	0.949707i	0.999140	+	0.0414527i	$0.0131986\pi$
$152$	1.22277	+	6.93465i	0.0991794	+	0.562474i
$153$	−6.66305	−	2.42515i	−0.538675	−	0.196062i
$154$	−4.82795			−0.389047
$155$	2.34792	+	0.854574i	0.188590	+	0.0686410i
$156$	−0.0361783	+	0.0626627i	−0.00289658	+	0.00501703i
$157$	0.985653	−	5.58992i	0.0786637	−	0.446124i	−0.919881	−	0.392197i	$-0.871715\pi$
$157$	0.985653	−	5.58992i	0.0786637	−	0.446124i	0.998545	−	0.0539268i	$-0.0171738\pi$
$158$	7.80696	+	13.5220i	0.621088	+	1.07576i
$159$	0.783270	−	1.35666i	0.0621174	−	0.107590i
$160$	−0.766044	−	0.642788i	−0.0605611	−	0.0508168i
$161$	1.64207	+	9.31267i	0.129414	+	0.733941i
$162$	4.18055	+	7.24092i	0.328455	+	0.568901i
$163$	−16.5644	+	6.02896i	−1.29743	+	0.472225i	−0.896158	−	0.443736i	$-0.853653\pi$
$163$	−16.5644	+	6.02896i	−1.29743	+	0.472225i	−0.401269	+	0.915960i	$0.631431\pi$
$164$	−4.88953	+	1.77964i	−0.381808	+	0.138967i
$165$	0.0693797	−	0.393472i	0.00540120	−	0.0306317i
$166$	−12.3727	+	10.3819i	−0.960306	+	0.805792i
$167$	−5.50871	+	4.62236i	−0.426277	+	0.357689i	−0.830545	−	0.556952i	$-0.811971\pi$
$167$	−5.50871	+	4.62236i	−0.426277	+	0.357689i	0.404268	+	0.914641i	$0.367526\pi$
$168$	−0.150151	+	0.851551i	−0.0115844	+	0.0656986i
$169$	12.1473	−	4.42124i	0.934404	−	0.340095i
$170$	−2.27529	+	0.828137i	−0.174507	+	0.0635152i
$171$	−10.3105	−	17.8583i	−0.788463	−	1.36566i
$172$	−0.287998	−	1.63332i	−0.0219597	−	0.124539i
$173$	18.0482	+	15.1443i	1.37218	+	1.15140i	0.972005	+	0.234958i	$0.0754954\pi$
$173$	18.0482	+	15.1443i	1.37218	+	1.15140i	0.400176	+	0.916438i	$0.368949\pi$
$174$	0.0101823	−	0.0176363i	0.000771921	−	0.00133701i
$175$	−1.61622	−	2.79937i	−0.122175	−	0.211613i
$176$	0.259360	−	1.47090i	0.0195500	−	0.110873i
$177$	0.657242	−	1.13838i	0.0494013	−	0.0855656i
$178$	−3.04991	−	1.11008i	−0.228601	−	0.0832039i
$179$	−6.51436			−0.486906			−0.243453	−	0.969913i	$-0.578280\pi$
$179$	−6.51436			−0.486906			−0.243453	+	0.969913i	$0.578280\pi$
$180$	2.75184	+	1.00159i	0.205110	+	0.0746538i
$181$	3.49494	+	19.8208i	0.259777	+	1.47327i	0.783507	+	0.621383i	$0.213429\pi$
$181$	3.49494	+	19.8208i	0.259777	+	1.47327i	−0.523730	+	0.851884i	$0.675460\pi$
$182$	−0.669781	+	0.562013i	−0.0496475	+	0.0416592i
$183$	0.0717324	+	0.0601906i	0.00530261	+	0.00444942i
$184$	−2.92545			−0.215667
$185$	6.01560	+	0.901406i	0.442276	+	0.0662727i
$186$	0.668386			0.0490084
$187$	−2.77036	−	2.32461i	−0.202589	−	0.169992i
$188$	−2.22186	+	1.86436i	−0.162046	+	0.135972i
$189$	−0.890164	−	5.04837i	−0.0647499	−	0.367215i
$190$	−6.61696	−	2.40838i	−0.480045	−	0.174722i
$191$	6.74888			0.488332			0.244166	−	0.969733i	$-0.421486\pi$
$191$	6.74888			0.488332			0.244166	+	0.969733i	$0.421486\pi$
$192$	−0.251371	−	0.0914916i	−0.0181411	−	0.00660284i
$193$	−12.6869	+	21.9744i	−0.913224	+	1.58175i	−0.103744	+	0.994604i	$0.533082\pi$
$193$	−12.6869	+	21.9744i	−0.913224	+	1.58175i	−0.809480	+	0.587147i	$0.800251\pi$
$194$	−1.75027	+	9.92625i	−0.125662	+	0.712663i
$195$	−0.0361783	−	0.0626627i	−0.00259078	−	0.00448737i
$196$	−1.72432	+	2.98661i	−0.123166	+	0.213329i
$197$	14.9434	+	12.5390i	1.06467	+	0.893365i	0.994559	−	0.104174i	$-0.0332200\pi$
$197$	14.9434	+	12.5390i	1.06467	+	0.893365i	0.0701116	+	0.997539i	$0.477664\pi$
$198$	0.759520	+	4.30745i	0.0539767	+	0.306117i
$199$	6.22234	+	10.7774i	0.441090	+	0.763990i	0.997771	−	0.0667365i	$-0.0212587\pi$
$199$	6.22234	+	10.7774i	0.441090	+	0.763990i	−0.556681	+	0.830726i	$0.687925\pi$
$200$	0.939693	−	0.342020i	0.0664463	−	0.0241845i
$201$	−1.74620	+	0.635564i	−0.123167	+	0.0448293i
$202$	1.02462	−	5.81089i	0.0720918	−	0.408853i
$203$	0.188509	−	0.158178i	0.0132307	−	0.0111019i
$204$	−0.496174	+	0.416339i	−0.0347391	+	0.0291496i
$205$	0.903548	−	5.12428i	0.0631065	−	0.357895i
$206$	−12.1512	+	4.42268i	−0.846615	+	0.308143i
$207$	8.05036	−	2.93009i	0.559538	−	0.203655i
$208$	−0.135244	−	0.234250i	−0.00937751	−	0.0162423i
$209$	−1.82632	−	10.3575i	−0.126329	−	0.716447i
$210$	−0.662389	−	0.555811i	−0.0457092	−	0.0383546i
$211$	−12.5850	+	21.7978i	−0.866384	+	1.50062i	−0.000718236		1.00000i	$0.500229\pi$
$211$	−12.5850	+	21.7978i	−0.866384	+	1.50062i	−0.865666	+	0.500622i	$0.833105\pi$
$212$	2.92808	+	5.07158i	0.201101	+	0.348317i
$213$	0.183921	−	1.04307i	0.0126021	−	0.0714698i
$214$	4.76483	−	8.25293i	0.325717	−	0.564159i
$215$	1.55849	+	0.567246i	0.106288	+	0.0386858i
$216$	1.58588			0.107905
$217$	7.58951	+	2.76235i	0.515209	+	0.187521i
$218$	−1.31937	−	7.48252i	−0.0893590	−	0.506780i
$219$	−0.00101376		0.000850647i	−6.85036e−5		5.74814e-5i
$220$	1.14416	+	0.960064i	0.0771392	+	0.0647275i
$221$	−0.654937			−0.0440558
$222$	1.59462	−	0.323789i	0.107024	−	0.0217313i
$223$	−7.47028			−0.500247			−0.250124	−	0.968214i	$-0.580471\pi$
$223$	−7.47028			−0.500247			−0.250124	+	0.968214i	$0.580471\pi$
$224$	−2.47619	−	2.07777i	−0.165447	−	0.138827i
$225$	−2.24332	+	1.88237i	−0.149554	+	0.125491i
$226$	−0.886076	−	5.02519i	−0.0589409	−	0.334271i
$227$	−21.9495	−	7.98898i	−1.45684	−	0.530247i	−0.512348	−	0.858778i	$-0.671224\pi$
$227$	−21.9495	−	7.98898i	−1.45684	−	0.530247i	−0.944493	+	0.328531i	$0.893447\pi$
$228$	−1.88366			−0.124748
$229$	−6.78526	−	2.46963i	−0.448383	−	0.163198i	0.107952	−	0.994156i	$-0.465571\pi$
$229$	−6.78526	−	2.46963i	−0.448383	−	0.163198i	−0.556335	+	0.830958i	$0.687793\pi$
$230$	1.46272	−	2.53351i	0.0964492	−	0.167055i
$231$	0.224265	−	1.27187i	0.0147556	−	0.0836830i
$232$	0.0380643	+	0.0659293i	0.00249905	+	0.00432847i
$233$	−11.9854	+	20.7593i	−0.785188	+	1.35998i	0.143699	+	0.989621i	$0.454100\pi$
$233$	−11.9854	+	20.7593i	−0.785188	+	1.35998i	−0.928887	+	0.370363i	$0.879233\pi$
$234$	0.606792	+	0.509159i	0.0396672	+	0.0332847i
$235$	−0.503654	−	2.85636i	−0.0328548	−	0.186329i
$236$	2.45695	+	4.25556i	0.159934	+	0.277013i
$237$	−3.92489	+	1.42854i	−0.254949	+	0.0927937i
$238$	−7.35472	+	2.67690i	−0.476736	+	0.173518i
$239$	2.80312	−	15.8973i	0.181319	−	1.02831i	−0.749276	−	0.662258i	$-0.769598\pi$
$239$	2.80312	−	15.8973i	0.181319	−	1.02831i	0.930595	−	0.366051i	$-0.119290\pi$
$240$	0.204920	−	0.171948i	0.0132275	−	0.0110992i
$241$	18.8870	−	15.8481i	1.21662	−	1.02086i	0.217624	−	0.976033i	$-0.430169\pi$
$241$	18.8870	−	15.8481i	1.21662	−	1.02086i	0.998995	−	0.0448316i	$-0.0142751\pi$
$242$	1.52275	−	8.63595i	0.0978862	−	0.555140i
$243$	−6.57245	+	2.39218i	−0.421623	+	0.153458i
$244$	−0.328941	+	0.119725i	−0.0210583	+	0.00766458i
$245$	−1.72432	−	2.98661i	−0.110163	−	0.190807i
$246$	−0.241702	−	1.37076i	−0.0154104	−	0.0873966i
$247$	−1.45907	−	1.22430i	−0.0928384	−	0.0779006i
$248$	−1.24930	+	2.16386i	−0.0793308	+	0.137405i
$249$	−2.16028	−	3.74171i	−0.136902	−	0.237121i
$250$	−0.173648	+	0.984808i	−0.0109825	+	0.0622847i
$251$	5.65061	−	9.78714i	0.356663	−	0.617759i	−0.630738	−	0.775996i	$-0.717248\pi$
$251$	5.65061	−	9.78714i	0.356663	−	0.617759i	0.987401	+	0.158237i	$0.0505810\pi$
$252$	8.89513	+	3.23756i	0.560341	+	0.203947i
$253$	4.36943			0.274704
$254$	9.12946	+	3.32285i	0.572833	+	0.208494i
$255$	−0.112473	−	0.637869i	−0.00704336	−	0.0399449i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−3.67791	−	3.08613i	−0.229422	−	0.192508i	0.520829	−	0.853661i	$-0.325623\pi$
$257$	−3.67791	−	3.08613i	−0.229422	−	0.192508i	−0.750251	+	0.661153i	$0.770067\pi$
$258$	0.443659			0.0276210
$259$	19.4450	+	2.91374i	1.20826	+	0.181051i
$260$	0.270489			0.0167750
$261$	−0.170781	−	0.143302i	−0.0105711	−	0.00887017i
$262$	1.56970	−	1.31713i	0.0969761	−	0.0813726i
$263$	0.699879	+	3.96921i	0.0431564	+	0.244752i	0.998753	−	0.0499263i	$-0.0158986\pi$
$263$	0.699879	+	3.96921i	0.0431564	+	0.244752i	−0.955597	+	0.294678i	$0.904788\pi$
$264$	0.375446	+	0.136651i	0.0231071	+	0.00841030i
$265$	−5.85615			−0.359741
$266$	−21.3889	−	7.78493i	−1.31144	−	0.477325i
$267$	0.434111	−	0.751903i	0.0265672	−	0.0460157i
$268$	1.20628	−	6.84116i	0.0736854	−	0.417890i
$269$	−6.62250	−	11.4705i	−0.403781	−	0.699369i	0.590398	−	0.807112i	$-0.298971\pi$
$269$	−6.62250	−	11.4705i	−0.403781	−	0.699369i	−0.994179	+	0.107743i	$0.965637\pi$
$270$	−0.792939	+	1.37341i	−0.0482568	+	0.0835832i
$271$	5.37556	+	4.51063i	0.326542	+	0.274001i	0.791289	−	0.611442i	$-0.209410\pi$
$271$	5.37556	+	4.51063i	0.326542	+	0.274001i	−0.464747	+	0.885443i	$0.653855\pi$
$272$	−0.420456	−	2.38452i	−0.0254939	−	0.144583i
$273$	−0.116944	−	0.202553i	−0.00707778	−	0.0122591i
$274$	9.30853	−	3.38803i	0.562349	−	0.204678i
$275$	−1.40352	+	0.510839i	−0.0846354	+	0.0308048i
$276$	0.135892	−	0.770679i	0.00817971	−	0.0463894i
$277$	−3.81923	+	3.20471i	−0.229475	+	0.192553i	−0.750274	−	0.661127i	$-0.770079\pi$
$277$	−3.81923	+	3.20471i	−0.229475	+	0.192553i	0.520799	+	0.853679i	$0.325634\pi$
$278$	11.1718	−	9.37427i	0.670042	−	0.562232i
$279$	1.27059	−	7.20586i	0.0760681	−	0.431404i
$280$	3.03750	−	1.10556i	0.181525	−	0.0660697i
$281$	23.5976	−	8.58881i	1.40771	−	0.512365i	0.477255	−	0.878765i	$-0.341632\pi$
$281$	23.5976	−	8.58881i	1.40771	−	0.512365i	0.930458	+	0.366400i	$0.119410\pi$
$282$	−0.387937	−	0.671927i	−0.0231013	−	0.0400127i
$283$	0.607403	+	3.44475i	0.0361064	+	0.204769i	0.997524	−	0.0703225i	$-0.0224029\pi$
$283$	0.607403	+	3.44475i	0.0361064	+	0.204769i	−0.961418	+	0.275092i	$0.911292\pi$
$284$	3.03309	+	2.54507i	0.179981	+	0.151022i
$285$	0.941830	−	1.63130i	0.0557892	−	0.0966297i
$286$	0.202000	+	0.349874i	0.0119445	+	0.0206885i
$287$	2.92066	−	16.5639i	0.172401	−	0.977736i
$288$	−1.46422	+	2.53611i	−0.0862800	+	0.149441i
$289$	10.4656	+	3.80917i	0.615624	+	0.224069i
$290$	−0.0761286			−0.00447043
$291$	−2.53366	−	0.922178i	−0.148526	−	0.0540590i
$292$	−0.000859058	−	0.00487196i	−5.02726e−5	−	0.000285110i
$293$	−20.5708	+	17.2610i	−1.20176	+	1.00840i	−0.202182	+	0.979348i	$0.564803\pi$
$293$	−20.5708	+	17.2610i	−1.20176	+	1.00840i	−0.999578	+	0.0290483i	$0.990752\pi$
$294$	−0.706694	−	0.592986i	−0.0412152	−	0.0345837i
$295$	−4.91389			−0.286098
$296$	−1.93231	+	5.76768i	−0.112313	+	0.335240i
$297$	−2.36866			−0.137444
$298$	9.74007	+	8.17289i	0.564227	+	0.473443i
$299$	0.606172	−	0.508638i	0.0350558	−	0.0294153i
$300$	0.0464515	+	0.263439i	0.00268188	+	0.0152097i
$301$	5.03773	+	1.83359i	0.290370	+	0.105686i
$302$	−18.1556			−1.04474
$303$	1.48322	+	0.539849i	0.0852089	+	0.0310135i
$304$	3.52081	−	6.09823i	0.201932	−	0.349757i
$305$	0.0607858	−	0.344733i	0.00348058	−	0.0197394i
$306$	3.54533	+	6.14070i	0.202673	+	0.351040i
$307$	2.72357	−	4.71737i	0.155443	−	0.269234i	−0.777778	−	0.628540i	$-0.783653\pi$
$307$	2.72357	−	4.71737i	0.155443	−	0.269234i	0.933220	+	0.359305i	$0.116986\pi$
$308$	3.69842	+	3.10334i	0.210737	+	0.176829i
$309$	−0.600666	−	3.40655i	−0.0341707	−	0.193792i
$310$	−1.24930	−	2.16386i	−0.0709556	−	0.122899i
$311$	22.9325	−	8.34673i	1.30038	−	0.473300i	0.403260	−	0.915085i	$-0.367877\pi$
$311$	22.9325	−	8.34673i	1.30038	−	0.473300i	0.897121	+	0.441786i	$0.145655\pi$
$312$	0.0679930	−	0.0247474i	0.00384935	−	0.00140105i
$313$	−1.09256	+	6.19624i	−0.0617554	+	0.350232i	0.938236	+	0.345997i	$0.112459\pi$
$313$	−1.09256	+	6.19624i	−0.0617554	+	0.350232i	−0.999991	+	0.00423525i	$0.998652\pi$
$314$	−4.34818	+	3.64856i	−0.245382	+	0.205900i
$315$	−7.25138	+	6.08463i	−0.408569	+	0.342830i
$316$	2.71133	−	15.3767i	0.152524	−	0.865007i
$317$	−22.5575	+	8.21024i	−1.26695	+	0.461133i	−0.886096	−	0.463501i	$-0.846593\pi$
$317$	−22.5575	+	8.21024i	−1.26695	+	0.461133i	−0.380857	+	0.924634i	$0.624371\pi$
$318$	−1.47207	+	0.535789i	−0.0825494	+	0.0300455i
$319$	−0.0568526	−	0.0984716i	−0.00318314	−	0.00551335i
$320$	0.173648	+	0.984808i	0.00970723	+	0.0550524i
$321$	1.95281	+	1.63861i	0.108995	+	0.0914581i
$322$	4.72816	−	8.18942i	0.263490	−	0.456379i
$323$	−8.52498	−	14.7657i	−0.474343	−	0.821585i
$324$	1.45189	−	8.23407i	0.0806605	−	0.457449i
$325$	−0.135244	+	0.234250i	−0.00750200	+	0.0129939i
$326$	16.5644	+	6.02896i	0.917419	+	0.333913i
$327$	2.03248			0.112396
$328$	4.88953	+	1.77964i	0.269979	+	0.0982643i
$329$	−1.62803	−	9.23301i	−0.0897562	−	0.509032i
$330$	−0.306067	+	0.256820i	−0.0168484	+	0.0141375i
$331$	−3.93650	−	3.30312i	−0.216370	−	0.181556i	0.528160	−	0.849145i	$-0.322882\pi$
$331$	−3.93650	−	3.30312i	−0.216370	−	0.181556i	−0.744530	+	0.667589i	$0.767326\pi$
$332$	16.1514			0.886422
$333$	−0.459433	−	17.8071i	−0.0251768	−	0.975823i
$334$	7.19111			0.393480
$335$	5.32148	+	4.46525i	0.290743	+	0.243963i
$336$	0.662389	−	0.555811i	0.0361363	−	0.0303220i
$337$	−5.30763	−	30.1011i	−0.289125	−	1.63971i	−0.690166	−	0.723651i	$-0.742463\pi$
$337$	−5.30763	−	30.1011i	−0.289125	−	1.63971i	0.401041	−	0.916060i	$-0.368648\pi$
$338$	−12.1473	−	4.42124i	−0.660723	−	0.240484i
$339$	1.36499			0.0741362
$340$	2.27529	+	0.828137i	0.123395	+	0.0449120i
$341$	1.86595	−	3.23192i	0.101047	−	0.175018i
$342$	−3.58080	+	20.3077i	−0.193627	+	1.09812i
$343$	5.73977	+	9.94158i	0.309919	+	0.536795i
$344$	−0.829258	+	1.43632i	−0.0447106	+	0.0774410i
$345$	0.599482	+	0.503025i	0.0322750	+	0.0270820i
$346$	−4.09120	−	23.2024i	−0.219944	−	1.24737i
$347$	5.26158	+	9.11333i	0.282457	+	0.489229i	0.971989	−	0.235026i	$-0.0755174\pi$
$347$	5.26158	+	9.11333i	0.282457	+	0.489229i	−0.689533	+	0.724255i	$0.742184\pi$
$348$	−0.0191365	+	0.00696513i	−0.00102583	+	0.000373370i
$349$	−14.7085	+	5.35346i	−0.787329	+	0.286564i	−0.704225	−	0.709977i	$-0.748706\pi$
$349$	−14.7085	+	5.35346i	−0.787329	+	0.286564i	−0.0831037	+	0.996541i	$0.526483\pi$
$350$	−0.561307	+	3.18333i	−0.0300031	+	0.170156i
$351$	−0.328604	+	0.275732i	−0.0175396	+	0.0147175i
$352$	−1.14416	+	0.960064i	−0.0609839	+	0.0511716i
$353$	2.16542	−	12.2807i	0.115253	−	0.653635i	−0.871371	−	0.490625i	$-0.836769\pi$
$353$	2.16542	−	12.2807i	0.115253	−	0.653635i	0.986624	−	0.163010i	$-0.0521203\pi$
$354$	−1.23521	+	0.449580i	−0.0656507	+	0.0238949i
$355$	−3.72064	+	1.35420i	−0.197471	+	0.0718736i
$356$	1.62283	+	2.81082i	0.0860096	+	0.148973i
$357$	−0.363563	−	2.06187i	−0.0192418	−	0.109126i
$358$	4.99029	+	4.18735i	0.263745	+	0.221308i
$359$	−17.0866	+	29.5949i	−0.901797	+	1.56196i	−0.0766363	+	0.997059i	$0.524418\pi$
$359$	−17.0866	+	29.5949i	−0.901797	+	1.56196i	−0.825160	+	0.564899i	$0.808915\pi$
$360$	−1.46422	−	2.53611i	−0.0771712	−	0.133664i
$361$	5.31094	−	30.1199i	0.279523	−	1.58526i
$362$	10.0633	−	17.4301i	0.528914	−	0.916106i
$363$	2.20432	+	0.802306i	0.115697	+	0.0421101i
$364$	0.874337			0.0458277
$365$	0.00464877	+	0.00169201i	0.000243328	+	8.85641e-5i
$366$	−0.0162604	−	0.0922173i	−0.000849945	−	0.00482028i
$367$	19.2219	−	16.1291i	1.00338	−	0.841933i	0.0159281	−	0.999873i	$-0.494930\pi$
$367$	19.2219	−	16.1291i	1.00338	−	0.841933i	0.987449	+	0.157940i	$0.0504853\pi$
$368$	2.24102	+	1.88044i	0.116821	+	0.0980249i
$369$	−15.2376			−0.793240
$370$	−4.02881	−	4.55727i	−0.209448	−	0.236921i
$371$	−18.9296			−0.982778
$372$	−0.512013	−	0.429630i	−0.0265467	−	0.0222753i
$373$	−17.0116	+	14.2744i	−0.880826	+	0.739101i	−0.966349	−	0.257235i	$-0.917188\pi$
$373$	−17.0116	+	14.2744i	−0.880826	+	0.739101i	0.0855225	+	0.996336i	$0.472744\pi$
$374$	0.627990	+	3.56151i	0.0324726	+	0.184161i
$375$	−0.251371	−	0.0914916i	−0.0129807	−	0.00472460i
$376$	2.90043			0.149578
$377$	−0.0193501	−	0.00704286i	−0.000996580	−	0.000362726i
$378$	−2.56313	+	4.43946i	−0.131833	+	0.228341i
$379$	−4.42627	+	25.1026i	−0.227362	+	1.28944i	0.630755	+	0.775982i	$0.282745\pi$
$379$	−4.42627	+	25.1026i	−0.227362	+	1.28944i	−0.858117	+	0.513454i	$0.828366\pi$
$380$	3.52081	+	6.09823i	0.180614	+	0.312832i
$381$	−1.29945	+	2.25071i	−0.0665727	+	0.115307i
$382$	−5.16995	−	4.33810i	−0.264517	−	0.221956i
$383$	−3.26798	−	18.5336i	−0.166986	−	0.947024i	−0.946993	−	0.321253i	$-0.895896\pi$
$383$	−3.26798	−	18.5336i	−0.166986	−	0.947024i	0.780007	−	0.625770i	$-0.215215\pi$
$384$	0.133752	+	0.231665i	0.00682549	+	0.0118221i
$385$	−4.53678	+	1.65125i	−0.231216	+	0.0841557i
$386$	23.8436	−	8.67836i	1.21361	−	0.441717i
$387$	0.843386	−	4.78308i	0.0428717	−	0.243138i
$388$	7.72125	−	6.47890i	0.391987	−	0.328916i
$389$	0.303594	−	0.254745i	0.0153928	−	0.0129161i	−0.635059	−	0.772464i	$-0.719024\pi$
$389$	0.303594	−	0.254745i	0.0153928	−	0.0129161i	0.650452	+	0.759548i	$0.274580\pi$
$390$	−0.0125646	+	0.0712574i	−0.000636233	+	0.00360826i
$391$	6.65624	−	2.42267i	0.336620	−	0.122520i
$392$	3.24066	−	1.17950i	0.163678	−	0.0595740i
$393$	0.274070	+	0.474703i	0.0138250	+	0.0239456i
$394$	−3.38739	−	19.2108i	−0.170654	−	0.967827i
$395$	11.9610	+	10.0364i	0.601821	+	0.504988i
$396$	2.18695	−	3.78791i	0.109898	−	0.190350i
$397$	6.40200	+	11.0886i	0.321307	+	0.556520i	0.980758	−	0.195227i	$-0.0625445\pi$
$397$	6.40200	+	11.0886i	0.321307	+	0.556520i	−0.659451	+	0.751748i	$0.729211\pi$
$398$	2.16100	−	12.2556i	0.108321	−	0.614318i
$399$	3.04440	−	5.27306i	0.152411	−	0.263983i
$400$	−0.939693	−	0.342020i	−0.0469846	−	0.0171010i
$401$	10.2774			0.513231			0.256615	−	0.966514i	$-0.417393\pi$
$401$	10.2774			0.513231			0.256615	+	0.966514i	$0.417393\pi$
$402$	1.74620	+	0.635564i	0.0870925	+	0.0316991i
$403$	−0.117359	−	0.665577i	−0.00584608	−	0.0331547i
$404$	−4.52007	+	3.79279i	−0.224882	+	0.188698i
$405$	6.40497	+	5.37441i	0.318266	+	0.267057i
$406$	−0.246081			−0.0122128
$407$	2.88609	−	8.61458i	0.143058	−	0.427009i
$408$	0.647709			0.0320664
$409$	−0.719521	−	0.603750i	−0.0355780	−	0.0298535i	0.624825	−	0.780765i	$-0.285170\pi$
$409$	−0.719521	−	0.603750i	−0.0355780	−	0.0298535i	−0.660403	+	0.750911i	$0.729615\pi$
$410$	−3.98598	+	3.34463i	−0.196853	+	0.165180i
$411$	0.460145	+	2.60961i	0.0226973	+	0.128723i
$412$	12.1512	+	4.42268i	0.598647	+	0.217890i
$413$	−15.8838			−0.781593
$414$	−8.05036	−	2.93009i	−0.395653	−	0.144006i
$415$	−8.07569	+	13.9875i	−0.396420	+	0.686620i
$416$	−0.0469699	+	0.266379i	−0.00230289	+	0.0130603i
$417$	1.95061	+	3.37855i	0.0955216	+	0.165448i
$418$	−5.25866	+	9.10827i	−0.257210	+	0.445500i
$419$	29.5828	+	24.8229i	1.44521	+	1.21268i	0.935982	+	0.352047i	$0.114514\pi$
$419$	29.5828	+	24.8229i	1.44521	+	1.21268i	0.509230	+	0.860630i	$0.329930\pi$
$420$	0.150151	+	0.851551i	0.00732664	+	0.0415514i
$421$	−13.1338	−	22.7485i	−0.640104	−	1.10869i	−0.985409	−	0.170203i	$-0.945558\pi$
$421$	−13.1338	−	22.7485i	−0.640104	−	1.10869i	0.345305	−	0.938491i	$-0.387776\pi$
$422$	23.6520	−	8.60862i	1.15136	−	0.419061i
$423$	−7.98150	+	2.90503i	−0.388074	+	0.141247i
$424$	1.01691	−	5.76718i	0.0493855	−	0.280079i
$425$	−1.85483	+	1.55639i	−0.0899725	+	0.0754959i
$426$	−0.811363	+	0.680814i	−0.0393107	+	0.0329856i
$427$	0.196486	−	1.11433i	0.00950863	−	0.0539261i
$428$	−8.95495	+	3.25934i	−0.432854	+	0.157546i
$429$	−0.101554	+	0.0369626i	−0.00490307	+	0.00178457i
$430$	−0.829258	−	1.43632i	−0.0399904	−	0.0692653i
$431$	−0.643283	−	3.64824i	−0.0309858	−	0.175729i	0.965387	−	0.260820i	$-0.0839930\pi$
$431$	−0.643283	−	3.64824i	−0.0309858	−	0.175729i	−0.996373	+	0.0850909i	$0.972882\pi$
$432$	−1.21485	−	1.01938i	−0.0584497	−	0.0490451i
$433$	2.02117	−	3.50077i	0.0971314	−	0.168237i	−0.813365	−	0.581754i	$-0.802367\pi$
$433$	2.02117	−	3.50077i	0.0971314	−	0.168237i	0.910496	+	0.413518i	$0.135700\pi$
$434$	−4.03829	−	6.99453i	−0.193844	−	0.335748i
$435$	0.00353629	−	0.0200553i	0.000169552	−	0.000961578i
$436$	−3.79897	+	6.58002i	−0.181938	+	0.315126i
$437$	19.3576	+	7.04559i	0.925999	+	0.337036i
$438$	0.00132337			6.32331e−5
$439$	35.1404	+	12.7901i	1.67716	+	0.610436i	0.992916	−	0.118818i	$-0.0379106\pi$
$439$	35.1404	+	12.7901i	1.67716	+	0.610436i	0.684243	+	0.729254i	$0.260133\pi$
$440$	−0.259360	−	1.47090i	−0.0123645	−	0.0701225i
$441$	−7.73639	+	6.49160i	−0.368400	+	0.309124i
$442$	0.501711	+	0.420985i	0.0238639	+	0.0200242i
$443$	−2.48851			−0.118233			−0.0591164	−	0.998251i	$-0.518828\pi$
$443$	−2.48851			−0.118233			−0.0591164	+	0.998251i	$0.518828\pi$
$444$	−1.42968	−	0.776964i	−0.0678495	−	0.0368731i
$445$	−3.24565			−0.153859
$446$	5.72257	+	4.80181i	0.270971	+	0.227372i
$447$	−2.60550	+	2.18628i	−0.123236	+	0.103407i
$448$	0.561307	+	3.18333i	0.0265192	+	0.150398i
$449$	−37.3024	−	13.5770i	−1.76041	−	0.640736i	−0.760446	−	0.649402i	$-0.775019\pi$
$449$	−37.3024	−	13.5770i	−1.76041	−	0.640736i	−0.999962	+	0.00866559i	$0.997242\pi$
$450$	2.92844			0.138048
$451$	−7.30297	−	2.65806i	−0.343883	−	0.125163i
$452$	−2.55135	+	4.41908i	−0.120006	+	0.207856i
$453$	0.843354	−	4.78290i	0.0396242	−	0.224720i
$454$	11.6791	+	20.2288i	0.548127	+	0.949384i
$455$	−0.437169	+	0.757198i	−0.0204948	+	0.0354980i
$456$	1.44297	+	1.21079i	0.0675731	+	0.0567006i
$457$	4.01670	+	22.7799i	0.187894	+	1.06560i	0.922181	+	0.386758i	$0.126405\pi$
$457$	4.01670	+	22.7799i	0.187894	+	1.06560i	−0.734288	+	0.678839i	$0.762484\pi$
$458$	3.61036	+	6.25333i	0.168701	+	0.292199i
$459$	−3.60833	+	1.31332i	−0.168422	+	0.0613007i
$460$	−2.74902	+	1.00056i	−0.128174	+	0.0466515i
$461$	−0.754226	+	4.27743i	−0.0351278	+	0.199220i	−0.997321	−	0.0731478i	$-0.976696\pi$
$461$	−0.754226	+	4.27743i	−0.0351278	+	0.199220i	0.962193	+	0.272367i	$0.0878066\pi$
$462$	−0.989340	+	0.830155i	−0.0460283	+	0.0386223i
$463$	−12.2426	+	10.2728i	−0.568962	+	0.477416i	−0.881301	−	0.472555i	$-0.843332\pi$
$463$	−12.2426	+	10.2728i	−0.568962	+	0.477416i	0.312339	+	0.949971i	$0.398887\pi$
$464$	0.0132196	−	0.0749721i	0.000613705	−	0.00348049i
$465$	0.628077	−	0.228601i	0.0291264	−	0.0106011i
$466$	22.5251	−	8.19848i	1.04346	−	0.379787i
$467$	7.11645	+	12.3261i	0.329310	+	0.570382i	0.982375	−	0.186920i	$-0.0598505\pi$
$467$	7.11645	+	12.3261i	0.329310	+	0.570382i	−0.653065	+	0.757302i	$0.726517\pi$
$468$	−0.137548	−	0.780076i	−0.00635818	−	0.0360590i
$469$	17.2013	+	14.4336i	0.794284	+	0.666483i
$470$	−1.45021	+	2.51184i	−0.0668934	+	0.115863i
$471$	−0.759195	−	1.31496i	−0.0349818	−	0.0605903i
$472$	0.853289	−	4.83924i	0.0392758	−	0.222744i
$473$	1.23857	−	2.14527i	0.0569497	−	0.0986398i
$474$	3.92489	+	1.42854i	0.180276	+	0.0656151i
$475$	−7.04163			−0.323092
$476$	7.35472	+	2.67690i	0.337103	+	0.122695i
$477$	2.97796	+	16.8889i	0.136352	+	0.773288i
$478$	−12.3659	+	10.3762i	−0.565602	+	0.474596i
$479$	−9.81824	−	8.23849i	−0.448607	−	0.376426i	0.390312	−	0.920683i	$-0.372367\pi$
$479$	−9.81824	−	8.23849i	−0.448607	−	0.376426i	−0.838919	+	0.544257i	$0.816812\pi$
$480$	−0.267503			−0.0122098
$481$	−0.602421	−	1.53106i	−0.0274681	−	0.0698105i
$482$	−24.6552			−1.12301
$483$	1.93779	+	1.62600i	0.0881723	+	0.0739854i
$484$	−6.71758	+	5.63672i	−0.305345	+	0.256214i
$485$	1.75027	+	9.92625i	0.0794754	+	0.450728i
$486$	6.57245	+	2.39218i	0.298133	+	0.108511i
$487$	−9.93859			−0.450360			−0.225180	−	0.974317i	$-0.572297\pi$
$487$	−9.93859			−0.450360			−0.225180	+	0.974317i	$0.572297\pi$
$488$	0.328941	+	0.119725i	0.0148904	+	0.00541968i
$489$	−2.35771	+	4.08367i	−0.106619	+	0.184670i
$490$	−0.598850	+	3.39625i	−0.0270533	+	0.153427i
$491$	−0.347494	−	0.601877i	−0.0156822	−	0.0271623i	0.858078	−	0.513520i	$-0.171659\pi$
$491$	−0.347494	−	0.601877i	−0.0156822	−	0.0271623i	−0.873760	+	0.486357i	$0.838325\pi$
$492$	−0.695954	+	1.20543i	−0.0313760	+	0.0543449i
$493$	−0.141206	−	0.118486i	−0.00635959	−	0.00533633i
$494$	0.330744	+	1.87574i	0.0148809	+	0.0843937i
$495$	2.18695	+	3.78791i	0.0982961	+	0.170254i
$496$	2.34792	−	0.854574i	0.105425	−	0.0383715i
$497$	−12.0267	+	4.37737i	−0.539472	+	0.196352i
$498$	−0.750256	+	4.25491i	−0.0336198	+	0.190667i
$499$	−27.0995	+	22.7392i	−1.21314	+	1.01794i	−0.213984	+	0.976837i	$0.568644\pi$
$499$	−27.0995	+	22.7392i	−1.21314	+	1.01794i	−0.999155	+	0.0411071i	$0.986912\pi$
$500$	0.766044	−	0.642788i	0.0342585	−	0.0287463i
$501$	−0.334038	+	1.89442i	−0.0149237	+	0.0846366i
$502$	−10.6197	+	3.86524i	−0.473979	+	0.172514i
$503$	19.0725	−	6.94184i	0.850403	−	0.309521i	0.120198	−	0.992750i	$-0.461647\pi$
$503$	19.0725	−	6.94184i	0.850403	−	0.309521i	0.730204	+	0.683229i	$0.239425\pi$
$504$	−4.73300	−	8.19780i	−0.210825	−	0.365159i
$505$	−1.02462	−	5.81089i	−0.0455948	−	0.258581i
$506$	−3.34718	−	2.80862i	−0.148800	−	0.124858i
$507$	1.72899	−	2.99469i	0.0767870	−	0.132999i
$508$	−4.85769	−	8.41376i	−0.215525	−	0.373300i
$509$	7.26892	−	41.2241i	0.322189	−	1.82723i	−0.206544	−	0.978437i	$-0.566222\pi$
$509$	7.26892	−	41.2241i	0.322189	−	1.82723i	0.528733	−	0.848788i	$-0.322667\pi$
$510$	−0.323854	+	0.560932i	−0.0143405	+	0.0248385i
$511$	0.0150269	+	0.00546933i	0.000664749	+	0.000241949i
$512$	−1.00000			−0.0441942
$513$	−10.4937	−	3.81940i	−0.463308	−	0.168630i
$514$	0.833714	+	4.72823i	0.0367736	+	0.208553i
$515$	−9.90576	+	8.31192i	−0.436500	+	0.366267i
$516$	−0.339862	−	0.285178i	−0.0149616	−	0.0125543i
$517$	−4.33206			−0.190524
$518$	−13.0229	−	14.7311i	−0.572191	−	0.647247i
$519$	6.30246			0.276647
$520$	−0.207206	−	0.173867i	−0.00908660	−	0.00762456i
$521$	26.0816	−	21.8851i	1.14266	−	0.958803i	0.143135	−	0.989703i	$-0.454282\pi$
$521$	26.0816	−	21.8851i	1.14266	−	0.958803i	0.999522	+	0.0308999i	$0.00983731\pi$
$522$	0.0387128	+	0.219551i	0.00169441	+	0.00960950i
$523$	−15.0241	−	5.46831i	−0.656956	−	0.239113i	−0.00803456	−	0.999968i	$-0.502558\pi$
$523$	−15.0241	−	5.46831i	−0.656956	−	0.239113i	−0.648922	+	0.760855i	$0.724780\pi$
$524$	−2.04909			−0.0895150
$525$	−0.812541	−	0.295741i	−0.0354622	−	0.0129072i
$526$	2.01522	−	3.49046i	0.0878678	−	0.152191i
$527$	1.05055	−	5.95799i	0.0457629	−	0.259534i
$528$	−0.199771	−	0.346013i	−0.00869391	−	0.0150583i
$529$	7.22087	−	12.5069i	0.313951	−	0.543779i
$530$	4.48607	+	3.76426i	0.194863	+	0.163509i
$531$	2.49881	+	14.1714i	0.108439	+	0.614988i
$532$	11.3808	+	19.7121i	0.493420	+	0.854629i
$533$	−1.32256	+	0.481373i	−0.0572865	+	0.0208506i
$534$	−0.815863	+	0.296950i	−0.0353058	+	0.0128503i
$535$	1.65481	−	9.38489i	0.0715436	−	0.405744i
$536$	−5.32148	+	4.46525i	−0.229853	+	0.192869i
$537$	−1.33492	+	1.12013i	−0.0576060	+	0.0483372i
$538$	−2.29997	+	13.0438i	−0.0991587	+	0.562357i
$539$	−4.84023	+	1.76170i	−0.208484	+	0.0758818i
$540$	1.49024	−	0.542403i	0.0641297	−	0.0233413i
$541$	−20.0626	−	34.7495i	−0.862560	−	1.49400i	−0.869449	−	0.494022i	$-0.835526\pi$
$541$	−20.0626	−	34.7495i	−0.862560	−	1.49400i	0.00688890	−	0.999976i	$-0.497807\pi$
$542$	−1.21854	−	6.91068i	−0.0523408	−	0.296839i
$543$	4.12432	+	3.46072i	0.176992	+	0.148514i
$544$	−1.21065	+	2.09692i	−0.0519064	+	0.0899045i
$545$	−3.79897	−	6.58002i	−0.162730	−	0.281857i
$546$	−0.0406143	+	0.230335i	−0.00173813	+	0.00985742i
$547$	15.8774	−	27.5004i	0.678867	−	1.17583i	−0.296456	−	0.955047i	$-0.595805\pi$
$547$	15.8774	−	27.5004i	0.678867	−	1.17583i	0.975322	−	0.220785i	$-0.0708619\pi$
$548$	−9.30853	−	3.38803i	−0.397641	−	0.144729i
$549$	−1.02510			−0.0437504
$550$	1.40352	+	0.510839i	0.0598462	+	0.0217823i
$551$	−0.0930875	−	0.527925i	−0.00396566	−	0.0224904i
$552$	−0.599482	+	0.503025i	−0.0255156	+	0.0214102i
$553$	38.6630	+	32.4421i	1.64412	+	1.37958i
$554$	4.98565			0.211820
$555$	1.38771	−	0.849654i	0.0589050	−	0.0360658i
$556$	−14.5838			−0.618490
$557$	−13.2860	−	11.1483i	−0.562945	−	0.472367i	0.316351	−	0.948642i	$-0.397542\pi$
$557$	−13.2860	−	11.1483i	−0.562945	−	0.472367i	−0.879296	+	0.476275i	$0.841987\pi$
$558$	−5.60516	+	4.70329i	−0.237286	+	0.199106i
$559$	−0.0779002	−	0.441794i	−0.00329483	−	0.0186859i
$560$	−3.03750	−	1.10556i	−0.128358	−	0.0467184i
$561$	−0.967414			−0.0408442
$562$	−23.5976	−	8.58881i	−0.995403	−	0.362297i
$563$	−14.7814	+	25.6022i	−0.622962	+	1.07900i	0.365969	+	0.930627i	$0.380738\pi$
$563$	−14.7814	+	25.6022i	−0.622962	+	1.07900i	−0.988931	+	0.148375i	$0.952596\pi$
$564$	−0.134729	+	0.764087i	−0.00567312	+	0.0321739i
$565$	−2.55135	−	4.41908i	−0.107336	−	0.185912i
$566$	1.74895	−	3.02926i	0.0735137	−	0.127329i
$567$	20.7037	+	17.3724i	0.869472	+	0.729574i
$568$	−0.687546	−	3.89927i	−0.0288488	−	0.163610i
$569$	−12.6854	−	21.9717i	−0.531798	−	0.921101i	−0.999311	−	0.0371147i	$-0.988183\pi$
$569$	−12.6854	−	21.9717i	−0.531798	−	0.921101i	0.467513	−	0.883986i	$-0.345150\pi$
$570$	−1.77006	+	0.644250i	−0.0741397	+	0.0269846i
$571$	−30.4770	+	11.0927i	−1.27542	+	0.464216i	−0.888916	−	0.458071i	$-0.848541\pi$
$571$	−30.4770	+	11.0927i	−1.27542	+	0.464216i	−0.386507	+	0.922286i	$0.626318\pi$
$572$	0.0701539	−	0.397862i	0.00293328	−	0.0166355i
$573$	1.38298	−	1.16046i	0.0577748	−	0.0484788i
$574$	−12.8844	+	10.8113i	−0.537785	+	0.451255i
$575$	0.507999	−	2.88101i	0.0211850	−	0.120146i
$576$	2.75184	−	1.00159i	0.114660	−	0.0417328i
$577$	41.9902	−	15.2832i	1.74807	−	0.636247i	0.748438	−	0.663204i	$-0.230804\pi$
$577$	41.9902	−	15.2832i	1.74807	−	0.636247i	0.999637	+	0.0269572i	$0.00858177\pi$
$578$	−5.56863	−	9.64515i	−0.231624	−	0.401185i
$579$	1.17865	+	6.68447i	0.0489831	+	0.277797i
$580$	0.0583179	+	0.0489346i	0.00242152	+	0.00203190i
$581$	−26.1041	+	45.2137i	−1.08298	+	1.87578i
$582$	1.34813	+	2.33504i	0.0558819	+	0.0967904i
$583$	−1.51885	+	8.61383i	−0.0629044	+	0.356748i
$584$	−0.00247356	+	0.00428433i	−0.000102357	+	0.000177287i
$585$	0.744340	+	0.270918i	0.0307747	+	0.0112011i
$586$	26.8533			1.10930
$587$	2.28996	+	0.833478i	0.0945168	+	0.0344013i	0.388846	−	0.921303i	$-0.372874\pi$
$587$	2.28996	+	0.833478i	0.0945168	+	0.0344013i	−0.294329	+	0.955704i	$0.595096\pi$
$588$	0.160194	+	0.908508i	0.00660631	+	0.0374662i
$589$	13.4780	−	11.3094i	0.555350	−	0.465994i
$590$	3.76426	+	3.15859i	0.154972	+	0.130037i
$591$	5.21824			0.214650
$592$	5.18763	−	3.17624i	0.213210	−	0.130543i
$593$	−42.2102			−1.73337			−0.866683	−	0.498859i	$-0.833753\pi$
$593$	−42.2102			−1.73337			−0.866683	+	0.498859i	$0.833753\pi$
$594$	1.81450	+	1.52254i	0.0744497	+	0.0624708i
$595$	−5.99562	+	5.03092i	−0.245797	+	0.206248i
$596$	−2.20789	−	12.5216i	−0.0904389	−	0.512904i
$597$	3.12823	+	1.13858i	0.128030	+	0.0465991i
$598$	−0.791301			−0.0323587
$599$	8.50720	+	3.09637i	0.347595	+	0.126514i	0.509917	−	0.860224i	$-0.329676\pi$
$599$	8.50720	+	3.09637i	0.347595	+	0.126514i	−0.162322	+	0.986738i	$0.551898\pi$
$600$	0.133752	−	0.231665i	0.00546039	−	0.00945768i
$601$	−7.14815	+	40.5391i	−0.291579	+	1.65363i	0.389212	+	0.921148i	$0.372747\pi$
$601$	−7.14815	+	40.5391i	−0.291579	+	1.65363i	−0.680791	+	0.732478i	$0.738364\pi$
$602$	−2.68052	−	4.64280i	−0.109250	−	0.189226i
$603$	10.1715	−	17.6176i	0.414216	−	0.717442i
$604$	13.9080	+	11.6702i	0.565908	+	0.474853i
$605$	−1.52275	−	8.63595i	−0.0619087	−	0.351101i
$606$	−0.789206	−	1.36695i	−0.0320593	−	0.0555284i
$607$	−20.8782	+	7.59905i	−0.847421	+	0.308436i	−0.728988	−	0.684526i	$-0.760009\pi$
$607$	−20.8782	+	7.59905i	−0.847421	+	0.308436i	−0.118432	+	0.992962i	$0.537787\pi$
$608$	−6.61696	+	2.40838i	−0.268353	+	0.0976726i
$609$	0.0114308	−	0.0648274i	0.000463200	−	0.00262694i
$610$	−0.268155	+	0.225009i	−0.0108573	+	0.00911033i
$611$	−0.600987	+	0.504288i	−0.0243133	+	0.0204013i
$612$	1.23128	−	6.98294i	0.0497716	−	0.282269i
$613$	31.3674	−	11.4168i	1.26692	−	0.461121i	0.380834	−	0.924644i	$-0.375637\pi$
$613$	31.3674	−	11.4168i	1.26692	−	0.461121i	0.886085	+	0.463523i	$0.153415\pi$
$614$	−5.11864	+	1.86303i	−0.206572	+	0.0751859i
$615$	−0.695954	−	1.20543i	−0.0280636	−	0.0486075i
$616$	−0.838364	−	4.75460i	−0.0337786	−	0.191568i
$617$	−1.28020	−	1.07422i	−0.0515389	−	0.0432463i	0.616654	−	0.787234i	$-0.288488\pi$
$617$	−1.28020	−	1.07422i	−0.0515389	−	0.0432463i	−0.668193	+	0.743988i	$0.732932\pi$
$618$	−1.72955	+	2.99567i	−0.0695727	+	0.120503i
$619$	13.6094	+	23.5722i	0.547008	+	0.947446i	0.998478	+	0.0551593i	$0.0175667\pi$
$619$	13.6094	+	23.5722i	0.547008	+	0.947446i	−0.451469	+	0.892287i	$0.649100\pi$
$620$	−0.433878	+	2.46065i	−0.0174250	+	0.0988220i
$621$	2.31970	−	4.01785i	0.0930865	−	0.161231i
$622$	−22.9325	−	8.34673i	−0.919508	−	0.334674i
$623$	−10.4914			−0.420327
$624$	−0.0679930	−	0.0247474i	−0.00272190	−	0.000990690i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	4.81982	−	4.04431i	0.192639	−	0.161643i
$627$	−2.15521	−	1.80843i	−0.0860707	−	0.0722219i
$628$	5.67615			0.226503
$629$	−0.379871	−	14.7234i	−0.0151464	−	0.587059i
$630$	9.46600			0.377134
$631$	−3.03268	−	2.54472i	−0.120729	−	0.101304i	0.580424	−	0.814314i	$-0.302887\pi$
$631$	−3.03268	−	2.54472i	−0.120729	−	0.101304i	−0.701153	+	0.713010i	$0.747331\pi$
$632$	−11.9610	+	10.0364i	−0.475781	+	0.399228i
$633$	1.16918	+	6.63075i	0.0464707	+	0.263549i
$634$	22.5575	+	8.21024i	0.895871	+	0.326070i
$635$	9.71537			0.385543
$636$	1.47207	+	0.535789i	0.0583712	+	0.0212454i
$637$	−0.466409	+	0.807844i	−0.0184798	+	0.0320079i
$638$	−0.0197447	+	0.111978i	−0.000781701	+	0.00443324i
$639$	5.79747	+	10.0415i	0.229344	+	0.397236i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−14.7145	−	12.3469i	−0.581188	−	0.487675i	0.304149	−	0.952624i	$-0.401628\pi$
$641$	−14.7145	−	12.3469i	−0.581188	−	0.487675i	−0.885337	+	0.464950i	$0.846072\pi$
$642$	−0.442667	−	2.51049i	−0.0174707	−	0.0990811i
$643$	6.72420	+	11.6467i	0.265177	+	0.459299i	0.967610	−	0.252450i	$-0.0812364\pi$
$643$	6.72420	+	11.6467i	0.265177	+	0.459299i	−0.702433	+	0.711750i	$0.747903\pi$
$644$	−8.88604	+	3.23425i	−0.350159	+	0.127447i
$645$	0.416903	−	0.151740i	0.0164155	−	0.00597476i
$646$	−2.96069	+	16.7909i	−0.116487	+	0.660630i
$647$	−22.9827	+	19.2848i	−0.903544	+	0.758163i	−0.970880	−	0.239567i	$-0.922994\pi$
$647$	−22.9827	+	19.2848i	−0.903544	+	0.758163i	0.0673362	+	0.997730i	$0.478550\pi$
$648$	−6.40497	+	5.37441i	−0.251611	+	0.211127i
$649$	−1.27447	+	7.22786i	−0.0500272	+	0.283718i
$650$	0.254176	−	0.0925126i	0.00996961	−	0.00362864i
$651$	2.03022	−	0.738939i	0.0795706	−	0.0289613i
$652$	−8.81375	−	15.2659i	−0.345173	−	0.597857i
$653$	4.58048	+	25.9772i	0.179248	+	1.01657i	0.933125	+	0.359551i	$0.117070\pi$
$653$	4.58048	+	25.9772i	0.179248	+	1.01657i	−0.753877	+	0.657015i	$0.771819\pi$
$654$	−1.55697	−	1.30645i	−0.0608823	−	0.0510863i
$655$	1.02455	−	1.77457i	0.0400323	−	0.0693380i
$656$	−2.60166	−	4.50621i	−0.101578	−	0.175938i
$657$	0.00251570	−	0.0142673i	9.81469e−5	−	0.000556619i
$658$	−4.68772	+	8.11938i	−0.182746	+	0.316526i
$659$	5.39128	+	1.96227i	0.210015	+	0.0764391i	0.444885	−	0.895588i	$-0.353244\pi$
$659$	5.39128	+	1.96227i	0.210015	+	0.0764391i	−0.234871	+	0.972027i	$0.575467\pi$
$660$	0.399542			0.0155521
$661$	−1.96655	−	0.715766i	−0.0764900	−	0.0278401i	0.303492	−	0.952834i	$-0.401848\pi$
$661$	−1.96655	−	0.715766i	−0.0764900	−	0.0278401i	−0.379982	+	0.924994i	$0.624070\pi$
$662$	0.892333	+	5.06067i	0.0346815	+	0.196689i
$663$	−0.134209	+	0.112615i	−0.00521226	+	0.00437360i
$664$	−12.3727	−	10.3819i	−0.480153	−	0.402896i
$665$	−22.7616			−0.882657
$666$	−11.0942	+	13.9363i	−0.429893	+	0.540022i
$667$	0.222711			0.00862339
$668$	−5.50871	−	4.62236i	−0.213138	−	0.178844i
$669$	−1.53081	+	1.28450i	−0.0591844	+	0.0496616i
$670$	−1.20628	−	6.84116i	−0.0466027	−	0.264297i
$671$	−0.491304	−	0.178820i	−0.0189666	−	0.00690327i
$672$	−0.864688			−0.0333561
$673$	15.1491	+	5.51381i	0.583954	+	0.212542i	0.617068	−	0.786910i	$-0.288320\pi$
$673$	15.1491	+	5.51381i	0.583954	+	0.212542i	−0.0331141	+	0.999452i	$0.510542\pi$
$674$	−15.2827	+	26.4705i	−0.588668	+	1.01960i
$675$	−0.275385	+	1.56179i	−0.0105996	+	0.0601132i
$676$	6.46342	+	11.1950i	0.248593	+	0.430576i
$677$	18.4193	−	31.9032i	0.707912	−	1.22614i	−0.257719	−	0.966220i	$-0.582971\pi$
$677$	18.4193	−	31.9032i	0.707912	−	1.22614i	0.965630	−	0.259919i	$-0.0836959\pi$
$678$	−1.04564	−	0.877400i	−0.0401578	−	0.0336964i
$679$	5.65762	+	32.0860i	0.217119	+	1.23135i
$680$	−1.21065	−	2.09692i	−0.0464265	−	0.0804131i
$681$	−5.87158	+	2.13708i	−0.224999	+	0.0818930i
$682$	−3.50684	+	1.27639i	−0.134284	+	0.0488753i
$683$	2.50768	−	14.2218i	0.0959537	−	0.544180i	−0.898497	−	0.438979i	$-0.855340\pi$
$683$	2.50768	−	14.2218i	0.0959537	−	0.544180i	0.994451	−	0.105201i	$-0.0335487\pi$
$684$	15.7966	−	13.2549i	0.603998	−	0.506815i
$685$	7.58838	−	6.36741i	0.289937	−	0.243286i
$686$	1.99340	−	11.3051i	0.0761084	−	0.431632i
$687$	−1.81508	+	0.660635i	−0.0692496	+	0.0252048i
$688$	1.55849	−	0.567246i	0.0594171	−	0.0216260i
$689$	0.792011	+	1.37180i	0.0301732	+	0.0522616i
$690$	−0.135892	−	0.770679i	−0.00517330	−	0.0293392i
$691$	14.0239	+	11.7675i	0.533495	+	0.447656i	0.869306	−	0.494274i	$-0.164566\pi$
$691$	14.0239	+	11.7675i	0.533495	+	0.447656i	−0.335811	+	0.941929i	$0.609010\pi$
$692$	−11.7801	+	20.4038i	−0.447814	+	0.775636i
$693$	7.06918	+	12.2442i	0.268536	+	0.465118i
$694$	1.82733	−	10.3633i	0.0693644	−	0.393385i
$695$	7.29189	−	12.6299i	0.276597	−	0.479080i
$696$	0.0191365	+	0.00696513i	0.000725369	+	0.000264013i
$697$	−12.5989			−0.477216
$698$	14.7085	+	5.35346i	0.556726	+	0.202632i
$699$	1.11348	+	6.31484i	0.0421156	+	0.238849i
$700$	2.47619	−	2.07777i	0.0935912	−	0.0785323i
$701$	24.6036	+	20.6449i	0.929267	+	0.779747i	0.975686	−	0.219175i	$-0.0703364\pi$
$701$	24.6036	+	20.6449i	0.929267	+	0.779747i	−0.0464188	+	0.998922i	$0.514781\pi$
$702$	0.428962			0.0161901
$703$	26.6768	−	33.5108i	1.00613	−	1.26388i
$704$	1.49359			0.0562919
$705$	−0.594354	−	0.498723i	−0.0223847	−	0.0187830i
$706$	−9.55268	+	8.01565i	−0.359520	+	0.301673i
$707$	−3.31201	−	18.7833i	−0.124561	−	0.706420i
$708$	1.23521	+	0.449580i	0.0464221	+	0.0168963i
$709$	10.4747			0.393387			0.196694	−	0.980465i	$-0.436980\pi$
$709$	10.4747			0.393387			0.196694	+	0.980465i	$0.436980\pi$
$710$	3.72064	+	1.35420i	0.139633	+	0.0508223i
$711$	22.8622	−	39.5985i	0.857400	−	1.48506i
$712$	0.563601	−	3.19634i	0.0211219	−	0.119788i
$713$	3.65477	+	6.33025i	0.136872	+	0.237070i
$714$	−1.04684	+	1.81318i	−0.0391769	+	0.0678565i
$715$	0.309482	+	0.259686i	0.0115740	+	0.00971171i
$716$	−1.13121	−	6.41539i	−0.0422752	−	0.239754i
$717$	−2.15909	−	3.73965i	−0.0806326	−	0.139660i
$718$	32.1123	−	11.6879i	1.19842	−	0.436190i
$719$	−7.25287	+	2.63983i	−0.270487	+	0.0984490i	−0.473703	−	0.880685i	$-0.657083\pi$
$719$	−7.25287	+	2.63983i	−0.270487	+	0.0984490i	0.203216	+	0.979134i	$0.434861\pi$
$720$	−0.508519	+	2.88395i	−0.0189514	+	0.107479i
$721$	−32.0197	+	26.8677i	−1.19248	+	1.00061i
$722$	−23.4291	+	19.6593i	−0.871941	+	0.731645i
$723$	1.14527	−	6.49516i	0.0425931	−	0.241558i
$724$	−18.9128	+	6.88369i	−0.702888	+	0.255830i
$725$	−0.0715375	+	0.0260375i	−0.00265684	+	0.000967010i
$726$	−1.17289	−	2.03151i	−0.0435301	−	0.0753964i
$727$	−1.27038	−	7.20470i	−0.0471159	−	0.267208i	0.952145	−	0.305647i	$-0.0988726\pi$
$727$	−1.27038	−	7.20470i	−0.0471159	−	0.267208i	−0.999261	+	0.0384389i	$0.987762\pi$
$728$	−0.669781	−	0.562013i	−0.0248237	−	0.0208296i
$729$	11.6062	−	20.1024i	0.429857	−	0.744535i
$730$	−0.00247356	−	0.00428433i	−9.15505e−5	−	0.000158570i
$731$	0.697333	−	3.95477i	0.0257918	−	0.146272i
$732$	−0.0468200	+	0.0810946i	−0.00173052	+	0.00299734i
$733$	−8.63900	−	3.14434i	−0.319089	−	0.116139i	0.177510	−	0.984119i	$-0.443196\pi$
$733$	−8.63900	−	3.14434i	−0.319089	−	0.116139i	−0.496599	+	0.867980i	$0.665418\pi$
$734$	−25.0925			−0.926179
$735$	−0.866888	−	0.315522i	−0.0319757	−	0.0116382i
$736$	−0.507999	−	2.88101i	−0.0187251	−	0.106195i
$737$	7.94813	−	6.66927i	0.292773	−	0.245666i
$738$	11.6727	+	9.79456i	0.429678	+	0.360543i
$739$	45.3962			1.66993			0.834964	−	0.550305i	$-0.185488\pi$
$739$	45.3962			1.66993			0.834964	+	0.550305i	$0.185488\pi$
$740$	0.156886	+	6.08074i	0.00576726	+	0.223532i
$741$	−0.509508			−0.0187173
$742$	14.5009	+	12.1677i	0.532346	+	0.446692i
$743$	25.3749	−	21.2921i	0.930915	−	0.781130i	−0.0450666	−	0.998984i	$-0.514350\pi$
$743$	25.3749	−	21.2921i	0.930915	−	0.781130i	0.975981	+	0.217854i	$0.0699056\pi$
$744$	0.116064	+	0.658232i	0.00425511	+	0.0241319i
$745$	11.9480	+	4.34870i	0.437739	+	0.159324i
$746$	22.2070			0.813058
$747$	44.4459	+	16.1770i	1.62619	+	0.591885i
$748$	1.80823	−	3.13194i	0.0661153	−	0.114515i
$749$	5.34906	−	30.3360i	0.195450	−	1.10845i
$750$	0.133752	+	0.231665i	0.00488392	+	0.00845920i
$751$	17.9905	−	31.1605i	0.656484	−	1.13706i	−0.325035	−	0.945702i	$-0.605376\pi$
$751$	17.9905	−	31.1605i	0.656484	−	1.13706i	0.981519	−	0.191362i	$-0.0612906\pi$
$752$	−2.22186	−	1.86436i	−0.0810228	−	0.0679862i
$753$	−0.524958	−	2.97719i	−0.0191306	−	0.108495i
$754$	0.0102960	+	0.0178331i	0.000374957	+	0.000649445i
$755$	−17.0607	+	6.20958i	−0.620902	+	0.225990i
$756$	4.81710	−	1.75328i	0.175196	−	0.0637662i
$757$	0.633850	−	3.59474i	0.0230377	−	0.130653i	−0.971120	−	0.238592i	$-0.923314\pi$
$757$	0.633850	−	3.59474i	0.0230377	−	0.130653i	0.994158	+	0.107939i	$0.0344252\pi$
$758$	19.5264	−	16.3846i	0.709230	−	0.595115i
$759$	0.895382	−	0.751315i	0.0325003	−	0.0272710i
$760$	1.22277	−	6.93465i	0.0443544	−	0.251546i
$761$	5.34768	−	1.94640i	0.193853	−	0.0705568i	−0.243269	−	0.969959i	$-0.578220\pi$
$761$	5.34768	−	1.94640i	0.193853	−	0.0705568i	0.437122	+	0.899402i	$0.355998\pi$
$762$	2.44216	−	0.888875i	0.0884702	−	0.0322005i
$763$	−12.2799	−	21.2695i	−0.444564	−	0.770007i
$764$	1.17193	+	6.64635i	0.0423990	+	0.240457i
$765$	5.43176	+	4.55779i	0.196386	+	0.164787i
$766$	−9.40976	+	16.2982i	−0.339989	+	0.588877i
$767$	0.664576	+	1.15108i	0.0239965	+	0.0415631i
$768$	0.0464515	−	0.263439i	0.00167617	−	0.00950605i
$769$	15.3203	−	26.5355i	0.552463	−	0.956894i	−0.445633	−	0.895216i	$-0.647021\pi$
$769$	15.3203	−	26.5355i	0.552463	−	0.956894i	0.998096	−	0.0616781i	$-0.0196452\pi$
$770$	4.53678	+	1.65125i	0.163494	+	0.0595071i
$771$	−1.28433			−0.0462540
$772$	−23.8436	−	8.67836i	−0.858150	−	0.312341i
$773$	−7.38747	−	41.8964i	−0.265709	−	1.50691i	−0.767010	−	0.641636i	$-0.778256\pi$
$773$	−7.38747	−	41.8964i	−0.265709	−	1.50691i	0.501301	−	0.865273i	$-0.332855\pi$
$774$	−3.72058	+	3.12193i	−0.133733	+	0.112216i
$775$	−1.91404	−	1.60607i	−0.0687545	−	0.0576918i
$776$	−10.0794			−0.361828
$777$	4.48568	−	2.74645i	0.160923	−	0.0985285i
$778$	−0.396313			−0.0142085
$779$	−28.0678	−	23.5517i	−1.00563	−	0.843826i
$780$	0.0554284	−	0.0465100i	0.00198466	−	0.00166532i
$781$	1.02691	+	5.82392i	0.0367459	+	0.208396i
$782$	−6.65624	−	2.42267i	−0.238027	−	0.0866346i
$783$	−0.120731			−0.00431457
$784$	−3.24066	−	1.17950i	−0.115738	−	0.0421252i
$785$	−2.83807	+	4.91569i	−0.101295	+	0.175448i
$786$	0.0951834	−	0.539812i	0.00339508	−	0.0192545i
$787$	16.5526	+	28.6700i	0.590037	+	1.02197i	0.994227	+	0.107299i	$0.0342203\pi$
$787$	16.5526	+	28.6700i	0.590037	+	1.02197i	−0.404189	+	0.914675i	$0.632446\pi$
$788$	−9.75359	+	16.8937i	−0.347457	+	0.601814i
$789$	0.825916	+	0.693026i	0.0294034	+	0.0246724i
$790$	−2.71133	−	15.3767i	−0.0964647	−	0.547078i
$791$	−8.24709	−	14.2844i	−0.293233	−	0.507894i
$792$	−4.11012	+	1.49596i	−0.146047	+	0.0531567i
$793$	−0.0889747	+	0.0323841i	−0.00315958	+	0.00114999i
$794$	2.22339	−	12.6095i	0.0789052	−	0.447494i
$795$	−1.20004	+	1.00695i	−0.0425610	+	0.0357129i
$796$	−9.53317	+	7.99928i	−0.337894	+	0.283527i
$797$	−0.314461	+	1.78340i	−0.0111388	+	0.0631712i	−0.989870	−	0.141973i	$-0.954655\pi$
$797$	−0.314461	+	1.78340i	−0.0111388	+	0.0631712i	0.978732	+	0.205144i	$0.0657664\pi$
$798$	−5.72161	+	2.08250i	−0.202543	+	0.0737195i
$799$	−6.59931	+	2.40195i	−0.233467	+	0.0849749i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	1.65047	+	9.36030i	0.0583166	+	0.330730i
$802$	−7.87297	−	6.60621i	−0.278004	−	0.233273i
$803$	0.00369449	−	0.00639905i	0.000130376	−	0.000225818i
$804$	−0.929133	−	1.60931i	−0.0327680	−	0.0567558i
$805$	1.64207	−	9.31267i	0.0578755	−	0.328228i
$806$	−0.337922	+	0.585299i	−0.0119028	+	0.0206163i
$807$	−3.32941	−	1.21181i	−0.117201	−	0.0426576i
$808$	5.90053			0.207580
$809$	−25.1968	−	9.17089i	−0.885873	−	0.322431i	−0.141296	−	0.989967i	$-0.545127\pi$
$809$	−25.1968	−	9.17089i	−0.885873	−	0.322431i	−0.744577	+	0.667536i	$0.767349\pi$
$810$	−1.45189	−	8.23407i	−0.0510142	−	0.289316i
$811$	−14.4035	+	12.0859i	−0.505774	+	0.424395i	−0.859639	−	0.510901i	$-0.829312\pi$
$811$	−14.4035	+	12.0859i	−0.505774	+	0.424395i	0.353865	+	0.935297i	$0.384867\pi$
$812$	0.188509	+	0.158178i	0.00661537	+	0.00555095i
$813$	1.87715			0.0658345
$814$	−7.74821	+	4.74401i	−0.271575	+	0.166277i
$815$	17.6275			0.617464
$816$	−0.496174	−	0.416339i	−0.0173696	−	0.0145748i
$817$	8.94636	−	7.50689i	0.312994	−	0.262633i
$818$	0.163102	+	0.924998i	0.00570273	+	0.0323418i
$819$	2.40603	+	0.875724i	0.0840735	+	0.0306003i
$820$	5.20333			0.181708
$821$	−50.0893	−	18.2310i	−1.74813	−	0.636266i	−0.748489	−	0.663147i	$-0.769220\pi$
$821$	−50.0893	−	18.2310i	−1.74813	−	0.636266i	−0.999639	+	0.0268806i	$0.991443\pi$
$822$	1.32494	−	2.29486i	0.0462124	−	0.0800423i
$823$	1.21373	−	6.88338i	0.0423078	−	0.239940i	−0.956319	−	0.292325i	$-0.905571\pi$
$823$	1.21373	−	6.88338i	0.0423078	−	0.239940i	0.998627	+	0.0523851i	$0.0166823\pi$
$824$	−6.46552	−	11.1986i	−0.225237	−	0.390122i
$825$	−0.199771	+	0.346013i	−0.00695512	+	0.0120466i
$826$	12.1677	+	10.2099i	0.423370	+	0.355249i
$827$	3.34612	+	18.9768i	0.116356	+	0.659887i	0.986070	+	0.166331i	$0.0531920\pi$
$827$	3.34612	+	18.9768i	0.116356	+	0.659887i	−0.869714	+	0.493556i	$0.835697\pi$
$828$	4.28350	+	7.41925i	0.148862	+	0.257837i
$829$	−36.3158	+	13.2179i	−1.26130	+	0.459076i	−0.884205	−	0.467098i	$-0.845299\pi$
$829$	−36.3158	+	13.2179i	−1.26130	+	0.459076i	−0.377096	+	0.926174i	$0.623077\pi$
$830$	15.1773	−	5.52410i	0.526813	−	0.191744i
$831$	−0.231591	+	1.31342i	−0.00803380	+	0.0455619i
$832$	0.207206	−	0.173867i	0.00718359	−	0.00602774i
$833$	−6.39664	+	5.36742i	−0.221631	+	0.185970i
$834$	0.677438	−	3.84194i	0.0234578	−	0.133036i
$835$	6.75743	−	2.45950i	0.233851	−	0.0851147i
$836$	9.88306	−	3.59714i	0.341813	−	0.124410i
$837$	−1.98124	−	3.43161i	−0.0684818	−	0.118614i
$838$	−6.70587	−	38.0309i	−0.231650	−	1.31375i
$839$	7.28639	+	6.11401i	0.251554	+	0.211079i	0.759841	−	0.650109i	$-0.225277\pi$
$839$	7.28639	+	6.11401i	0.251554	+	0.211079i	−0.508287	+	0.861188i	$0.669721\pi$
$840$	0.432344	−	0.748842i	0.0149173	−	0.0258375i
$841$	14.4971	+	25.1097i	0.499900	+	0.865852i
$842$	−4.56134	+	25.8686i	−0.157194	+	0.891492i
$843$	3.35877	−	5.81756i	0.115682	−	0.200368i
$844$	−23.6520	−	8.60862i	−0.814135	−	0.296321i
$845$	−12.9268			−0.444697
$846$	7.98150	+	2.90503i	0.274410	+	0.0998769i
$847$	−4.92220	−	27.9152i	−0.169129	−	0.959176i
$848$	−4.48607	+	3.76426i	−0.154052	+	0.129265i
$849$	0.716787	+	0.601456i	0.0246001	+	0.0206419i
$850$	2.42131			0.0830502
$851$	11.7861	+	13.3321i	0.404021	+	0.457017i
$852$	1.05916			0.0362862
$853$	−20.0424	−	16.8176i	−0.686240	−	0.575824i	0.231582	−	0.972815i	$-0.425610\pi$
$853$	−20.0424	−	16.8176i	−0.686240	−	0.575824i	−0.917822	+	0.396991i	$0.870054\pi$
$854$	−0.866793	+	0.727326i	−0.0296611	+	0.0248886i
$855$	3.58080	+	20.3077i	0.122461	+	0.694509i
$856$	8.95495	+	3.25934i	0.306074	+	0.111402i
$857$	38.1970			1.30478			0.652392	−	0.757882i	$-0.273766\pi$
$857$	38.1970			1.30478			0.652392	+	0.757882i	$0.273766\pi$
$858$	0.101554	+	0.0369626i	0.00346699	+	0.00126188i
$859$	3.36052	−	5.82060i	0.114660	−	0.198596i	−0.802984	−	0.596001i	$-0.796756\pi$
$859$	3.36052	−	5.82060i	0.114660	−	0.198596i	0.917644	+	0.397404i	$0.130089\pi$
$860$	−0.287998	+	1.63332i	−0.00982066	+	0.0556957i
$861$	−2.24963	−	3.89647i	−0.0766671	−	0.132791i
$862$	−1.85226	+	3.20821i	−0.0630882	+	0.109272i
$863$	21.1223	+	17.7237i	0.719012	+	0.603323i	0.927112	−	0.374785i	$-0.122283\pi$
$863$	21.1223	+	17.7237i	0.719012	+	0.603323i	−0.208100	+	0.978108i	$0.566728\pi$
$864$	0.275385	+	1.56179i	0.00936879	+	0.0531330i
$865$	−11.7801	−	20.4038i	−0.400537	−	0.693750i
$866$	−3.79856	+	1.38256i	−0.129080	+	0.0469814i
$867$	2.79958	−	1.01897i	0.0950789	−	0.0346059i
$868$	−1.40248	+	7.95388i	−0.0476034	+	0.269972i
$869$	17.8648	−	14.9903i	0.606022	−	0.508513i
$870$	−0.0156002	+	0.0130902i	−0.000528898	+	0.000443798i
$871$	0.326285	−	1.85046i	0.0110558	−	0.0627003i
$872$	7.13974	−	2.59865i	0.241782	−	0.0880014i
$873$	27.7368	−	10.0954i	0.938748	−	0.341676i
$874$	−10.3000	−	17.8401i	−0.348401	−	0.603449i
$875$	0.561307	+	3.18333i	0.0189756	+	0.107616i
$876$	−0.00101376		0.000850647i	−3.42518e−5		2.87407e-5i
$877$	1.49371	−	2.58718i	0.0504390	−	0.0873630i	−0.839704	−	0.543045i	$-0.817271\pi$
$877$	1.49371	−	2.58718i	0.0504390	−	0.0873630i	0.890143	+	0.455682i	$0.150605\pi$
$878$	−18.6978	−	32.3855i	−0.631020	−	1.09296i
$879$	−1.24738	+	7.07422i	−0.0420729	+	0.238607i
$880$	−0.746797	+	1.29349i	−0.0251745	+	0.0436035i
$881$	−49.3110	−	17.9478i	−1.66133	−	0.604675i	−0.670760	−	0.741675i	$-0.734032\pi$
$881$	−49.3110	−	17.9478i	−1.66133	−	0.604675i	−0.990571	+	0.136999i	$0.956254\pi$
$882$	10.0991			0.340056
$883$	11.0785	+	4.03223i	0.372820	+	0.135695i	0.521633	−	0.853170i	$-0.325323\pi$
$883$	11.0785	+	4.03223i	0.372820	+	0.135695i	−0.148813	+	0.988865i	$0.547545\pi$
$884$	−0.113729	−	0.644987i	−0.00382511	−	0.0216933i
$885$	−1.00695	+	0.844934i	−0.0338484	+	0.0284021i
$886$	1.90631	+	1.59959i	0.0640438	+	0.0537391i
$887$	22.3652			0.750950			0.375475	−	0.926833i	$-0.377480\pi$
$887$	22.3652			0.750950			0.375475	+	0.926833i	$0.377480\pi$
$888$	0.595773	+	1.51417i	0.0199928	+	0.0508121i
$889$	31.4043			1.05327
$890$	2.48631	+	2.08626i	0.0833414	+	0.0699317i
$891$	9.56643	−	8.02718i	0.320487	−	0.268921i
$892$	−1.29720	−	7.35679i	−0.0434335	−	0.246324i
$893$	−19.1920	−	6.98533i	−0.642237	−	0.233755i
$894$	3.40124			0.113755
$895$	6.12149	+	2.22804i	0.204619	+	0.0744752i
$896$	1.61622	−	2.79937i	0.0539940	−	0.0935204i
$897$	0.0367571	−	0.208460i	0.00122728	−	0.00696027i
$898$	19.8482	+	34.3781i	0.662342	+	1.14721i
$899$	0.0951078	−	0.164731i	0.00317202	−	0.00549410i
$900$	−2.24332	−	1.88237i	−0.0747772	−	0.0627455i
$901$	2.46225	+	13.9641i	0.0820296	+	0.465213i
$902$	3.88583	+	6.73045i	0.129384	+	0.224099i
$903$	1.34761	−	0.490490i	0.0448457	−	0.0163225i
$904$	4.79498	−	1.74523i	0.159479	−	0.0580455i
$905$	3.49494	−	19.8208i	0.116176	−	0.658865i
$906$	−3.72044	+	3.12182i	−0.123603	+	0.103715i
$907$	−28.5076	+	23.9207i	−0.946580	+	0.794275i	−0.978718	−	0.205209i	$-0.934213\pi$
$907$	−28.5076	+	23.9207i	−0.946580	+	0.794275i	0.0321386	+	0.999483i	$0.489768\pi$
$908$	4.05611	−	23.0033i	0.134607	−	0.763393i
$909$	−16.2373	+	5.90989i	−0.538557	+	0.196019i
$910$	0.821608	−	0.299041i	0.0272360	−	0.00991311i
$911$	−3.44465	−	5.96631i	−0.114126	−	0.197673i	0.803304	−	0.595569i	$-0.203074\pi$
$911$	−3.44465	−	5.96631i	−0.114126	−	0.197673i	−0.917430	+	0.397897i	$0.869740\pi$
$912$	−0.327094	−	1.85504i	−0.0108312	−	0.0614266i
$913$	18.4797	+	15.5063i	0.611590	+	0.513185i
$914$	11.5656	−	20.0323i	0.382557	−	0.662609i
$915$	−0.0468200	−	0.0810946i	−0.00154782	−	0.00268090i
$916$	1.25387	−	7.11102i	0.0414289	−	0.234955i
$917$	3.31178	−	5.73617i	0.109365	−	0.189425i
$918$	3.60833	+	1.31332i	0.119093	+	0.0433462i
$919$	−21.5072			−0.709455			−0.354728	−	0.934970i	$-0.615426\pi$
$919$	−21.5072			−0.709455			−0.354728	+	0.934970i	$0.615426\pi$
$920$	2.74902	+	1.00056i	0.0906326	+	0.0329876i
$921$	−0.253028	−	1.43499i	−0.00833756	−	0.0472846i
$922$	3.32725	−	2.79189i	0.109577	−	0.0919461i
$923$	0.820417	+	0.688412i	0.0270044	+	0.0226593i
$924$	1.29149			0.0424870
$925$	−5.34452	−	2.90450i	−0.175727	−	0.0954994i
$926$	15.9816			0.525188
$927$	29.0084	+	24.3410i	0.952762	+	0.799462i
$928$	−0.0583179	+	0.0489346i	−0.00191438	+	0.00160636i
$929$	−2.49488	−	14.1492i	−0.0818544	−	0.464220i	−0.997991	−	0.0633536i	$-0.979820\pi$
$929$	−2.49488	−	14.1492i	−0.0818544	−	0.464220i	0.916137	−	0.400866i	$-0.131291\pi$
$930$	−0.628077	−	0.228601i	−0.0205955	−	0.00749614i
$931$	−24.2840			−0.795877
$932$	−22.5251	−	8.19848i	−0.737835	−	0.268550i
$933$	3.26411	−	5.65360i	0.106862	−	0.185091i
$934$	2.47152	−	14.0167i	0.0808705	−	0.458640i
$935$	1.80823	+	3.13194i	0.0591353	+	0.102425i
$936$	−0.396055	+	0.685988i	−0.0129455	+	0.0224222i
$937$	−20.2188	−	16.9656i	−0.660519	−	0.554241i	0.249723	−	0.968317i	$-0.419660\pi$
$937$	−20.2188	−	16.9656i	−0.660519	−	0.554241i	−0.910242	+	0.414076i	$0.864105\pi$
$938$	−3.89923	−	22.1136i	−0.127314	−	0.722035i
$939$	0.841543	+	1.45759i	0.0274627	+	0.0475668i
$940$	2.72551	−	0.992005i	0.0888964	−	0.0323556i
$941$	−6.51450	+	2.37108i	−0.212366	+	0.0772951i	−0.446013	−	0.895027i	$-0.647156\pi$
$941$	−6.51450	+	2.37108i	−0.212366	+	0.0772951i	0.233646	+	0.972322i	$0.424934\pi$
$942$	−0.263666	+	1.49532i	−0.00859069	+	0.0487202i
$943$	11.6608	−	9.78456i	0.379727	−	0.318629i
$944$	−3.76426	+	3.15859i	−0.122516	+	0.102803i
$945$	−0.890164	+	5.04837i	−0.0289570	+	0.164224i
$946$	−2.32776	+	0.847235i	−0.0756819	+	0.0275460i
$947$	−21.1614	+	7.70212i	−0.687653	+	0.250285i	−0.662130	−	0.749389i	$-0.730347\pi$
$947$	−21.1614	+	7.70212i	−0.687653	+	0.250285i	−0.0255231	+	0.999674i	$0.508125\pi$
$948$	−2.08839	−	3.61719i	−0.0678277	−	0.117481i
$949$	−0.000232365	−	0.00131781i	−7.54290e−6	−	4.27779e-5i
$950$	5.39420	+	4.52627i	0.175011	+	0.146852i
$951$	−3.21073	+	5.56115i	−0.104115	+	0.180333i
$952$	−3.91336	−	6.77815i	−0.126833	−	0.219681i
$953$	−5.31077	+	30.1189i	−0.172033	+	0.975646i	0.769481	+	0.638670i	$0.220515\pi$
$953$	−5.31077	+	30.1189i	−0.172033	+	0.975646i	−0.941513	+	0.336976i	$0.890596\pi$
$954$	8.57470	−	14.8518i	0.277616	−	0.480845i
$955$	−6.34188	−	2.30825i	−0.205218	−	0.0746934i
$956$	16.1425			0.522086
$957$	−0.0285822	−	0.0104031i	−0.000923932	−	0.000336284i
$958$	2.22562	+	12.6221i	0.0719064	+	0.407801i
$959$	24.5290	−	20.5822i	0.792081	−	0.664635i
$960$	0.204920	+	0.171948i	0.00661375	+	0.00554960i
$961$	−24.7570			−0.798612
$962$	−0.522668	+	1.56009i	−0.0168515	+	0.0502994i
$963$	−27.9071			−0.899293
$964$	18.8870	+	15.8481i	0.608309	+	0.510432i
$965$	19.4375	−	16.3100i	0.625715	−	0.525037i
$966$	−0.439261	−	2.49117i	−0.0141330	−	0.0801521i
$967$	−36.2133	−	13.1805i	−1.16454	−	0.423858i	−0.313823	−	0.949482i	$-0.601610\pi$
$967$	−36.2133	−	13.1805i	−1.16454	−	0.423858i	−0.850717	+	0.525624i	$0.823832\pi$
$968$	8.76918			0.281852
$969$	−4.28587	−	1.55993i	−0.137682	−	0.0501121i
$970$	5.03969	−	8.72899i	0.161815	−	0.280271i
$971$	−9.80316	+	55.5965i	−0.314598	+	1.78418i	0.259864	+	0.965645i	$0.416322\pi$
$971$	−9.80316	+	55.5965i	−0.314598	+	1.78418i	−0.574462	+	0.818531i	$0.694789\pi$
$972$	−3.49713	−	6.05721i	−0.112170	−	0.194285i
$973$	23.5706	−	40.8254i	0.755638	−	1.30880i
$974$	7.61340	+	6.38840i	0.243949	+	0.204698i
$975$	0.0125646	+	0.0712574i	0.000402389	+	0.00228206i
$976$	−0.175026	−	0.303153i	−0.00560244	−	0.00970370i
$977$	8.02467	−	2.92074i	0.256732	−	0.0934428i	−0.210448	−	0.977605i	$-0.567492\pi$
$977$	8.02467	−	2.92074i	0.256732	−	0.0934428i	0.467180	+	0.884162i	$0.345270\pi$
$978$	4.43104	−	1.61277i	0.141689	−	0.0515706i
$979$	−0.841791	+	4.77404i	−0.0269038	+	0.152579i
$980$	2.64181	−	2.21674i	0.0843896	−	0.0708113i
$981$	−17.0446	+	14.3021i	−0.544192	+	0.456632i
$982$	−0.120683	+	0.684429i	−0.00385116	+	0.0218410i
$983$	−16.9067	+	6.15353i	−0.539240	+	0.196267i	−0.597259	−	0.802048i	$-0.703744\pi$
$983$	−16.9067	+	6.15353i	−0.539240	+	0.196267i	0.0580196	+	0.998315i	$0.481521\pi$
$984$	1.30797	−	0.476061i	0.0416964	−	0.0151763i
$985$	−9.75359	−	16.8937i	−0.310775	−	0.538278i
$986$	0.0320087	+	0.181531i	0.00101937	+	0.00578111i
$987$	−1.92121	−	1.61209i	−0.0611529	−	0.0513133i
$988$	0.952340	−	1.64950i	0.0302980	−	0.0524776i
$989$	2.42595	+	4.20187i	0.0771408	+	0.133612i
$990$	0.759520	−	4.30745i	0.0241391	−	0.136900i
$991$	−7.64964	+	13.2496i	−0.242999	+	0.420886i	−0.961567	−	0.274570i	$-0.911464\pi$
$991$	−7.64964	+	13.2496i	−0.242999	+	0.420886i	0.718568	+	0.695456i	$0.244798\pi$
$992$	−2.34792	−	0.854574i	−0.0745466	−	0.0271327i
$993$	−1.37463			−0.0436226
$994$	12.0267	+	4.37737i	0.381465	+	0.138842i
$995$	−2.16100	−	12.2556i	−0.0685082	−	0.388529i
$996$	3.30973	−	2.77720i	0.104873	−	0.0879988i
$997$	4.15851	+	3.48941i	0.131701	+	0.110511i	0.706259	−	0.707954i	$-0.250381\pi$
$997$	4.15851	+	3.48941i	0.131701	+	0.110511i	−0.574558	+	0.818464i	$0.694826\pi$
$998$	35.3758			1.11980
$999$	−6.38920	−	7.22728i	−0.202145	−	0.228661i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.c.71.2	✓	24
37.12	even	9	inner	370.2.o.c.271.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.c.71.2	✓	24	1.1	even	1	trivial
370.2.o.c.271.2	yes	24	37.12	even	9	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.204920 - 0.171948i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.939693 - 0.342020i) q^{5} -0.267503 q^{6} +(-3.03750 - 1.10556i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.508519 + 2.88395i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(0.204920 - 0.171948i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.939693 - 0.342020i) q^{5} -0.267503 q^{6} +(-3.03750 - 1.10556i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.508519 + 2.88395i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.746797 + 1.29349i) q^{11} +(0.204920 + 0.171948i) q^{12} +(0.0469699 + 0.266379i) q^{13} +(1.61622 + 2.79937i) q^{14} +(-0.251371 + 0.0914916i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.420456 + 2.38452i) q^{17} +(2.24332 - 1.88237i) q^{18} +(-5.39420 + 4.52627i) q^{19} +(0.173648 - 0.984808i) q^{20} +(-0.812541 + 0.295741i) q^{21} +(1.40352 - 0.510839i) q^{22} +(-1.46272 - 2.53351i) q^{23} +(-0.0464515 - 0.263439i) q^{24} +(0.766044 + 0.642788i) q^{25} +(0.135244 - 0.234250i) q^{26} +(0.792939 + 1.37341i) q^{27} +(0.561307 - 3.18333i) q^{28} +(-0.0380643 + 0.0659293i) q^{29} +(0.251371 + 0.0914916i) q^{30} -2.49861 q^{31} +(0.939693 + 0.342020i) q^{32} +(0.0693797 + 0.393472i) q^{33} +(1.85483 - 1.55639i) q^{34} +(2.47619 + 2.07777i) q^{35} -2.92844 q^{36} +(-5.96112 + 1.21041i) q^{37} +7.04163 q^{38} +(0.0554284 + 0.0465100i) q^{39} +(-0.766044 + 0.642788i) q^{40} +(0.903548 + 5.12428i) q^{41} +(0.812541 + 0.295741i) q^{42} -1.65852 q^{43} +(-1.40352 - 0.510839i) q^{44} +(1.46422 - 2.53611i) q^{45} +(-0.507999 + 2.88101i) q^{46} +(1.45021 + 2.51184i) q^{47} +(-0.133752 + 0.231665i) q^{48} +(2.64181 + 2.21674i) q^{49} +(-0.173648 - 0.984808i) q^{50} +(0.323854 + 0.560932i) q^{51} +(-0.254176 + 0.0925126i) q^{52} +(5.50298 - 2.00292i) q^{53} +(0.275385 - 1.56179i) q^{54} +(1.14416 - 0.960064i) q^{55} +(-2.47619 + 2.07777i) q^{56} +(-0.327094 + 1.85504i) q^{57} +(0.0715375 - 0.0260375i) q^{58} +(4.61755 - 1.68065i) q^{59} +(-0.133752 - 0.231665i) q^{60} +(0.0607858 + 0.344733i) q^{61} +(1.91404 + 1.60607i) q^{62} +(4.73300 - 8.19780i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.0469699 - 0.266379i) q^{65} +(0.199771 - 0.346013i) q^{66} +(-6.52776 - 2.37591i) q^{67} -2.42131 q^{68} +(-0.735373 - 0.267654i) q^{69} +(-0.561307 - 3.18333i) q^{70} +(3.03309 - 2.54507i) q^{71} +(2.24332 + 1.88237i) q^{72} -0.00494712 q^{73} +(5.34452 + 2.90450i) q^{74} +0.267503 q^{75} +(-5.39420 - 4.52627i) q^{76} +(3.69842 - 3.10334i) q^{77} +(-0.0125646 - 0.0712574i) q^{78} +(-14.6723 - 5.34027i) q^{79} +1.00000 q^{80} +(-7.85686 - 2.85966i) q^{81} +(2.60166 - 4.50621i) q^{82} +(2.80466 - 15.9060i) q^{83} +(-0.432344 - 0.748842i) q^{84} +(1.21065 - 2.09692i) q^{85} +(1.27050 + 1.06607i) q^{86} +(0.00353629 + 0.0200553i) q^{87} +(0.746797 + 1.29349i) q^{88} +(3.04991 - 1.11008i) q^{89} +(-2.75184 + 1.00159i) q^{90} +(0.151827 - 0.861054i) q^{91} +(2.24102 - 1.88044i) q^{92} +(-0.512013 + 0.429630i) q^{93} +(0.503654 - 2.85636i) q^{94} +(6.61696 - 2.40838i) q^{95} +(0.251371 - 0.0914916i) q^{96} +(-5.03969 - 8.72899i) q^{97} +(-0.598850 - 3.39625i) q^{98} +(-3.35060 - 2.81149i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{6} - 3 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 6 * q^6 - 3 * q^7 + 12 * q^8 + 12 * q^9	\( 24 q - 6 q^{6} - 3 q^{7} + 12 q^{8} + 12 q^{9} + 12 q^{10} - 15 q^{11} + 3 q^{14} - 6 q^{17} + 6 q^{18} - 6 q^{19} + 36 q^{21} + 9 q^{22} + 21 q^{23} - 6 q^{26} - 12 q^{27} - 3 q^{28} + 12 q^{29} + 30 q^{31} - 39 q^{33} - 21 q^{34} + 6 q^{35} + 54 q^{36} - 12 q^{37} - 36 q^{38} - 18 q^{39} + 27 q^{41} - 36 q^{42} - 24 q^{43} - 9 q^{44} - 27 q^{45} + 3 q^{46} - 6 q^{47} - 3 q^{48} - 27 q^{49} - 6 q^{51} - 9 q^{52} + 6 q^{53} + 9 q^{54} + 9 q^{55} - 6 q^{56} - 27 q^{57} + 27 q^{58} + 51 q^{59} - 3 q^{60} - 3 q^{62} - 27 q^{63} - 12 q^{64} + 15 q^{66} - 18 q^{69} + 3 q^{70} - 66 q^{71} + 6 q^{72} + 42 q^{73} - 42 q^{74} + 6 q^{75} - 6 q^{76} + 69 q^{77} + 36 q^{78} - 30 q^{79} + 24 q^{80} - 90 q^{81} + 24 q^{82} + 57 q^{83} + 6 q^{84} - 6 q^{86} + 6 q^{87} + 15 q^{88} - 57 q^{89} + 6 q^{90} + 3 q^{91} + 15 q^{92} - 72 q^{93} + 3 q^{94} - 15 q^{95} - 3 q^{97} - 72 q^{98} + 63 q^{99}+O(q^{100}) \) 24 * q - 6 * q^6 - 3 * q^7 + 12 * q^8 + 12 * q^9 + 12 * q^10 - 15 * q^11 + 3 * q^14 - 6 * q^17 + 6 * q^18 - 6 * q^19 + 36 * q^21 + 9 * q^22 + 21 * q^23 - 6 * q^26 - 12 * q^27 - 3 * q^28 + 12 * q^29 + 30 * q^31 - 39 * q^33 - 21 * q^34 + 6 * q^35 + 54 * q^36 - 12 * q^37 - 36 * q^38 - 18 * q^39 + 27 * q^41 - 36 * q^42 - 24 * q^43 - 9 * q^44 - 27 * q^45 + 3 * q^46 - 6 * q^47 - 3 * q^48 - 27 * q^49 - 6 * q^51 - 9 * q^52 + 6 * q^53 + 9 * q^54 + 9 * q^55 - 6 * q^56 - 27 * q^57 + 27 * q^58 + 51 * q^59 - 3 * q^60 - 3 * q^62 - 27 * q^63 - 12 * q^64 + 15 * q^66 - 18 * q^69 + 3 * q^70 - 66 * q^71 + 6 * q^72 + 42 * q^73 - 42 * q^74 + 6 * q^75 - 6 * q^76 + 69 * q^77 + 36 * q^78 - 30 * q^79 + 24 * q^80 - 90 * q^81 + 24 * q^82 + 57 * q^83 + 6 * q^84 - 6 * q^86 + 6 * q^87 + 15 * q^88 - 57 * q^89 + 6 * q^90 + 3 * q^91 + 15 * q^92 - 72 * q^93 + 3 * q^94 - 15 * q^95 - 3 * q^97 - 72 * q^98 + 63 * q^99

Introduction

L-functions

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