LMFDB - Embedded newform 147.2.m.a.121.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [147,2,Mod(4,147)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(147, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([0, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("147.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.m (of order $21$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [48] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			121.1
Character	$\chi$	$=$	147.121
Dual form			147.2.m.a.130.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.206956 + 2.76163i) q^{2} +(-0.955573 + 0.294755i) q^{3} +(-5.60611 - 0.844986i) q^{4} +(-0.116448 - 0.108048i) q^{5} +(-0.616244 - 2.69994i) q^{6} +(-1.85394 + 1.88756i) q^{7} +(2.26127 - 9.90726i) q^{8} +(0.826239 - 0.563320i) q^{9} +(0.322487 - 0.299224i) q^{10} +(1.22138 + 0.832720i) q^{11} +(5.60611 - 0.844986i) q^{12} +(-4.48658 + 2.16062i) q^{13} +(-4.82907 - 5.51055i) q^{14} +(0.143122 + 0.0689238i) q^{15} +(16.0571 + 4.95296i) q^{16} +(-0.262423 + 0.668642i) q^{17} +(1.38469 + 2.39835i) q^{18} +(-2.79266 + 4.83703i) q^{19} +(0.561520 + 0.704124i) q^{20} +(1.21521 - 2.35016i) q^{21} +(-2.55244 + 3.20065i) q^{22} +(1.20493 + 3.07011i) q^{23} +(0.759411 + 10.1336i) q^{24} +(-0.371765 - 4.96086i) q^{25} +(-5.03832 - 12.8374i) q^{26} +(-0.623490 + 0.781831i) q^{27} +(11.9884 - 9.01534i) q^{28} +(2.33749 + 2.93113i) q^{29} +(-0.219962 + 0.380985i) q^{30} +(0.368945 + 0.639031i) q^{31} +(-9.57613 + 24.3996i) q^{32} +(-1.41256 - 0.435718i) q^{33} +(-1.79223 - 0.863094i) q^{34} +(0.419834 - 0.0194881i) q^{35} +(-5.10799 + 2.45988i) q^{36} +(-3.44919 + 0.519882i) q^{37} +(-12.7801 - 8.71335i) q^{38} +(3.65040 - 3.38708i) q^{39} +(-1.33377 + 0.909352i) q^{40} +(0.880638 - 3.85833i) q^{41} +(6.23879 + 3.84234i) q^{42} +(1.46276 + 6.40876i) q^{43} +(-6.14353 - 5.70037i) q^{44} +(-0.157079 - 0.0236758i) q^{45} +(-8.72787 + 2.69219i) q^{46} +(-0.771974 + 10.3013i) q^{47} -16.8036 q^{48} +(-0.125788 - 6.99887i) q^{49} +13.7770 q^{50} +(0.0536783 - 0.716287i) q^{51} +(26.9780 - 8.32160i) q^{52} +(10.7834 + 1.62534i) q^{53} +(-2.03010 - 1.88365i) q^{54} +(-0.0522529 - 0.228935i) q^{55} +(14.5083 + 22.6358i) q^{56} +(1.24285 - 5.44528i) q^{57} +(-8.57844 + 5.84868i) q^{58} +(9.45312 - 8.77121i) q^{59} +(-0.744117 - 0.507330i) q^{60} +(3.56105 - 0.536742i) q^{61} +(-1.84112 + 0.886639i) q^{62} +(-0.468498 + 2.60394i) q^{63} +(-35.1217 - 16.9137i) q^{64} +(0.755902 + 0.233165i) q^{65} +(1.49563 - 3.81080i) q^{66} +(3.13450 + 5.42912i) q^{67} +(2.03616 - 3.52674i) q^{68} +(-2.05633 - 2.57855i) q^{69} +(-0.0330681 + 1.16346i) q^{70} +(0.474231 - 0.594667i) q^{71} +(-3.71261 - 9.45958i) q^{72} +(0.0447067 + 0.596570i) q^{73} +(-0.721892 - 9.63298i) q^{74} +(1.81749 + 4.63088i) q^{75} +(19.7432 - 24.7572i) q^{76} +(-3.83617 + 0.761608i) q^{77} +(8.59838 + 10.7820i) q^{78} +(0.0318244 - 0.0551215i) q^{79} +(-1.33466 - 2.31169i) q^{80} +(0.365341 - 0.930874i) q^{81} +(10.4730 + 3.23050i) q^{82} +(-7.67321 - 3.69522i) q^{83} +(-8.79845 + 12.1484i) q^{84} +(0.102804 - 0.0495076i) q^{85} +(-18.0014 + 2.71327i) q^{86} +(-3.09761 - 2.11191i) q^{87} +(11.0118 - 10.2175i) q^{88} +(0.703926 - 0.479929i) q^{89} +(0.0978923 - 0.428894i) q^{90} +(4.23955 - 12.4744i) q^{91} +(-4.16077 - 18.2295i) q^{92} +(-0.540912 - 0.501893i) q^{93} +(-28.2886 - 4.26382i) q^{94} +(0.847828 - 0.261520i) q^{95} +(1.95879 - 26.1382i) q^{96} -10.8136 q^{97} +(19.3543 + 1.10108i) q^{98} +1.47824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 4 q^{3} + 3 q^{4} - 2 q^{6} + 6 q^{8} + 4 q^{9} + 30 q^{10} - 9 q^{11} - 3 q^{12} - 42 q^{14} - 7 q^{15} + 29 q^{16} - 5 q^{17} + 6 q^{18} - 26 q^{19} - 5 q^{20} + 7 q^{21} + q^{22} - 4 q^{23}+ \cdots - 24 q^{99}+O(q^{100}) $ 48 * q - q^2 - 4 * q^3 + 3 * q^4 - 2 * q^6 + 6 * q^8 + 4 * q^9 + 30 * q^10 - 9 * q^11 - 3 * q^12 - 42 * q^14 - 7 * q^15 + 29 * q^16 - 5 * q^17 + 6 * q^18 - 26 * q^19 - 5 * q^20 + 7 * q^21 + q^22 - 4 * q^23 - 18 * q^24 - 56 * q^25 - 62 * q^26 + 8 * q^27 + 7 * q^28 + 12 * q^29 + 12 * q^30 - 36 * q^31 - 14 * q^32 + 16 * q^33 - 76 * q^34 + 7 * q^35 - 6 * q^36 - 20 * q^37 - 60 * q^38 + 14 * q^39 + 28 * q^40 + 41 * q^41 + 28 * q^42 + 12 * q^43 + 44 * q^44 + 14 * q^45 + 16 * q^46 + 13 * q^47 - 12 * q^48 - 84 * q^49 - 12 * q^50 - 2 * q^51 + 92 * q^52 + 14 * q^53 + q^54 - 38 * q^55 + 105 * q^56 + 18 * q^57 + 3 * q^58 + 57 * q^59 + 36 * q^60 + 11 * q^61 - 16 * q^62 - 7 * q^63 - 110 * q^64 + 21 * q^65 + 11 * q^66 + 34 * q^67 + 22 * q^68 - 8 * q^69 + 6 * q^71 - 24 * q^72 - 69 * q^73 - 90 * q^74 - 42 * q^75 - 49 * q^76 + 2 * q^78 + 34 * q^79 + 55 * q^80 + 4 * q^81 + 91 * q^82 + 28 * q^83 + 28 * q^84 - 44 * q^85 - 26 * q^86 - 29 * q^87 + 45 * q^88 + 11 * q^89 + 24 * q^90 + 84 * q^92 + q^93 + 90 * q^94 + 150 * q^95 - 35 * q^96 + 124 * q^97 + 119 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$1$	$e\left(\frac{19}{21}\right)$

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 $

$2$	−0.206956	+	2.76163i	−0.146340	+	1.95277i	0.129536	+	0.991575i	$0.458651\pi$
$2$	−0.206956	+	2.76163i	−0.146340	+	1.95277i	−0.275876	+	0.961193i	$0.588968\pi$
$3$	−0.955573	+	0.294755i	−0.551700	+	0.170177i
$3$	−0.955573	+	0.294755i	−0.551700	+	0.170177i
$4$	−5.60611	−	0.844986i	−2.80306	−	0.422493i
$5$	−0.116448	−	0.108048i	−0.0520769	−	0.0483203i	0.653705	−	0.756749i	$-0.273214\pi$
$5$	−0.116448	−	0.108048i	−0.0520769	−	0.0483203i	−0.705782	+	0.708429i	$0.749404\pi$
$6$	−0.616244	−	2.69994i	−0.251581	−	1.10225i
$7$	−1.85394	+	1.88756i	−0.700725	+	0.713432i
$7$	−1.85394	+	1.88756i	−0.700725	+	0.713432i
$8$	2.26127	−	9.90726i	0.799479	−	3.50275i
$9$	0.826239	−	0.563320i	0.275413	−	0.187773i
$10$	0.322487	−	0.299224i	0.101979	−	0.0946230i
$11$	1.22138	+	0.832720i	0.368259	+	0.251074i	0.733283	−	0.679923i	$-0.237987\pi$
$11$	1.22138	+	0.832720i	0.368259	+	0.251074i	−0.365025	+	0.930998i	$0.618939\pi$
$12$	5.60611	−	0.844986i	1.61835	−	0.243926i
$13$	−4.48658	+	2.16062i	−1.24435	+	0.599249i	−0.935992	−	0.352020i	$-0.885495\pi$
$13$	−4.48658	+	2.16062i	−1.24435	+	0.599249i	−0.308361	+	0.951269i	$0.599781\pi$
$14$	−4.82907	−	5.51055i	−1.29062	−	1.47276i
$15$	0.143122	+	0.0689238i	0.0369539	+	0.0177960i
$16$	16.0571	+	4.95296i	4.01428	+	1.23824i
$17$	−0.262423	+	0.668642i	−0.0636468	+	0.162169i	−0.959159	−	0.282868i	$-0.908714\pi$
$17$	−0.262423	+	0.668642i	−0.0636468	+	0.162169i	0.895512	+	0.445037i	$0.146810\pi$
$18$	1.38469	+	2.39835i	0.326374	+	0.565296i
$19$	−2.79266	+	4.83703i	−0.640680	+	1.10969i	0.344601	+	0.938749i	$0.388014\pi$
$19$	−2.79266	+	4.83703i	−0.640680	+	1.10969i	−0.985281	+	0.170941i	$0.945319\pi$
$20$	0.561520	+	0.704124i	0.125560	+	0.157447i
$21$	1.21521	−	2.35016i	0.265180	−	0.512848i
$22$	−2.55244	+	3.20065i	−0.544181	+	0.682381i
$23$	1.20493	+	3.07011i	0.251245	+	0.640162i	0.999736	−	0.0229833i	$-0.00731647\pi$
$23$	1.20493	+	3.07011i	0.251245	+	0.640162i	−0.748491	+	0.663145i	$0.769221\pi$
$24$	0.759411	+	10.1336i	0.155014	+	2.06852i
$25$	−0.371765	−	4.96086i	−0.0743529	−	0.992171i
$26$	−5.03832	−	12.8374i	−0.988096	−	2.51763i
$27$	−0.623490	+	0.781831i	−0.119991	+	0.150464i
$28$	11.9884	−	9.01534i	2.26559	−	1.70374i
$29$	2.33749	+	2.93113i	0.434062	+	0.544296i	0.949967	−	0.312349i	$-0.101116\pi$
$29$	2.33749	+	2.93113i	0.434062	+	0.544296i	−0.515906	+	0.856645i	$0.672544\pi$
$30$	−0.219962	+	0.380985i	−0.0401594	+	0.0695581i
$31$	0.368945	+	0.639031i	0.0662645	+	0.114773i	0.897254	−	0.441514i	$-0.145559\pi$
$31$	0.368945	+	0.639031i	0.0662645	+	0.114773i	−0.830990	+	0.556288i	$0.812225\pi$
$32$	−9.57613	+	24.3996i	−1.69284	+	4.31328i
$33$	−1.41256	−	0.435718i	−0.245895	−	0.0758487i
$34$	−1.79223	−	0.863094i	−0.307365	−	0.148019i
$35$	0.419834	−	0.0194881i	0.0709649	−	0.00329409i
$36$	−5.10799	+	2.45988i	−0.851331	+	0.409979i
$37$	−3.44919	+	0.519882i	−0.567043	+	0.0854680i	−0.426306	−	0.904579i	$-0.640185\pi$
$37$	−3.44919	+	0.519882i	−0.567043	+	0.0854680i	−0.140737	+	0.990047i	$0.544947\pi$
$38$	−12.7801	−	8.71335i	−2.07321	−	1.41349i
$39$	3.65040	−	3.38708i	0.584532	−	0.542366i
$40$	−1.33377	+	0.909352i	−0.210888	+	0.143781i
$41$	0.880638	−	3.85833i	0.137533	−	0.602570i	−0.858440	−	0.512914i	$-0.828566\pi$
$41$	0.880638	−	3.85833i	0.137533	−	0.602570i	0.995973	−	0.0896560i	$-0.0285768\pi$
$42$	6.23879	+	3.84234i	0.962666	+	0.592886i
$43$	1.46276	+	6.40876i	0.223069	+	0.977327i	0.955153	+	0.296113i	$0.0956905\pi$
$43$	1.46276	+	6.40876i	0.223069	+	0.977327i	−0.732084	+	0.681214i	$0.761452\pi$
$44$	−6.14353	−	5.70037i	−0.926173	−	0.859363i
$45$	−0.157079	−	0.0236758i	−0.0234159	−	0.00352938i
$46$	−8.72787	+	2.69219i	−1.28685	+	0.396942i
$47$	−0.771974	+	10.3013i	−0.112604	+	1.50260i	0.599416	+	0.800437i	$0.295399\pi$
$47$	−0.771974	+	10.3013i	−0.112604	+	1.50260i	−0.712020	+	0.702159i	$0.752220\pi$
$48$	−16.8036			−2.42540
$49$	−0.125788	−	6.99887i	−0.0179697	−	0.999839i
$50$	13.7770			1.94836
$51$	0.0536783	−	0.716287i	0.00751646	−	0.100300i
$52$	26.9780	−	8.32160i	3.74117	−	1.15400i
$53$	10.7834	+	1.62534i	1.48122	+	0.223258i	0.839364	−	0.543570i	$-0.182928\pi$
$53$	10.7834	+	1.62534i	1.48122	+	0.223258i	0.641853	+	0.766828i	$0.278166\pi$
$54$	−2.03010	−	1.88365i	−0.276261	−	0.256333i
$55$	−0.0522529	−	0.228935i	−0.00704578	−	0.0308696i
$56$	14.5083	+	22.6358i	1.93876	+	3.02483i
$57$	1.24285	−	5.44528i	0.164620	−	0.721245i
$58$	−8.57844	+	5.84868i	−1.12640	+	0.767970i
$59$	9.45312	−	8.77121i	1.23069	−	1.14191i	0.245693	−	0.969348i	$-0.420984\pi$
$59$	9.45312	−	8.77121i	1.23069	−	1.14191i	0.984998	−	0.172567i	$-0.0552060\pi$
$60$	−0.744117	−	0.507330i	−0.0960651	−	0.0654961i
$61$	3.56105	−	0.536742i	0.455946	−	0.0687228i	0.0829458	−	0.996554i	$-0.473567\pi$
$61$	3.56105	−	0.536742i	0.455946	−	0.0687228i	0.373000	+	0.927831i	$0.378329\pi$
$62$	−1.84112	+	0.886639i	−0.233823	+	0.112603i
$63$	−0.468498	+	2.60394i	−0.0590252	+	0.328066i
$64$	−35.1217	−	16.9137i	−4.39021	−	2.11422i
$65$	0.755902	+	0.233165i	0.0937581	+	0.0289205i
$66$	1.49563	−	3.81080i	0.184099	−	0.469077i
$67$	3.13450	+	5.42912i	0.382940	+	0.663272i	0.991481	−	0.130250i	$-0.0415782\pi$
$67$	3.13450	+	5.42912i	0.382940	+	0.663272i	−0.608541	+	0.793523i	$0.708245\pi$
$68$	2.03616	−	3.52674i	0.246921	−	0.427680i
$69$	−2.05633	−	2.57855i	−0.247553	−	0.310421i
$70$	−0.0330681	+	1.16346i	−0.00395239	+	0.139060i
$71$	0.474231	−	0.594667i	0.0562809	−	0.0705740i	−0.752894	−	0.658141i	$-0.771343\pi$
$71$	0.474231	−	0.594667i	0.0562809	−	0.0705740i	0.809175	+	0.587567i	$0.199914\pi$
$72$	−3.71261	−	9.45958i	−0.437536	−	1.11482i
$73$	0.0447067	+	0.596570i	0.00523253	+	0.0698232i	0.999209	−	0.0397727i	$-0.0126634\pi$
$73$	0.0447067	+	0.596570i	0.00523253	+	0.0698232i	−0.993976	+	0.109596i	$0.965044\pi$
$74$	−0.721892	−	9.63298i	−0.0839183	−	1.11981i
$75$	1.81749	+	4.63088i	0.209865	+	0.534728i
$76$	19.7432	−	24.7572i	2.26470	−	2.83984i
$77$	−3.83617	+	0.761608i	−0.437172	+	0.0867933i
$78$	8.59838	+	10.7820i	0.973575	+	1.22082i
$79$	0.0318244	−	0.0551215i	0.00358053	−	0.00620166i	−0.864230	−	0.503098i	$-0.832194\pi$
$79$	0.0318244	−	0.0551215i	0.00358053	−	0.00620166i	0.867810	+	0.496896i	$0.165527\pi$
$80$	−1.33466	−	2.31169i	−0.149219	−	0.258455i
$81$	0.365341	−	0.930874i	0.0405934	−	0.103430i
$82$	10.4730	+	3.23050i	1.15655	+	0.356749i
$83$	−7.67321	−	3.69522i	−0.842244	−	0.405603i	−0.0375512	−	0.999295i	$-0.511956\pi$
$83$	−7.67321	−	3.69522i	−0.842244	−	0.405603i	−0.804693	+	0.593691i	$0.797670\pi$
$84$	−8.79845	+	12.1484i	−0.959990	+	1.32550i
$85$	0.102804	−	0.0495076i	0.0111506	−	0.00536986i
$86$	−18.0014	+	2.71327i	−1.94114	+	0.292579i
$87$	−3.09761	−	2.11191i	−0.332099	−	0.226421i
$88$	11.0118	−	10.2175i	1.17387	−	1.08919i
$89$	0.703926	−	0.479929i	0.0746160	−	0.0508724i	−0.525437	−	0.850832i	$-0.676098\pi$
$89$	0.703926	−	0.479929i	0.0746160	−	0.0508724i	0.600054	+	0.799960i	$0.295146\pi$
$90$	0.0978923	−	0.428894i	0.0103188	−	0.0452094i
$91$	4.23955	−	12.4744i	0.444426	−	1.30767i
$92$	−4.16077	−	18.2295i	−0.433790	−	1.90056i
$93$	−0.540912	−	0.501893i	−0.0560899	−	0.0520438i
$94$	−28.2886	−	4.26382i	−2.91774	−	0.439779i
$95$	0.847828	−	0.261520i	0.0869853	−	0.0268314i
$96$	1.95879	−	26.1382i	0.199918	−	2.66772i
$97$	−10.8136			−1.09796			−0.548978	−	0.835837i	$-0.684983\pi$
$97$	−10.8136			−1.09796			−0.548978	+	0.835837i	$0.684983\pi$
$98$	19.3543	+	1.10108i	1.95508	+	0.111225i
$99$	1.47824			0.148568
$100$	−2.10770	+	28.1253i	−0.210770	+	2.81253i
$101$	−11.6947	+	3.60735i	−1.16367	+	0.358945i	−0.815652	−	0.578543i	$-0.803622\pi$
$101$	−11.6947	+	3.60735i	−1.16367	+	0.358945i	−0.348018	+	0.937488i	$0.613145\pi$
$102$	1.96701	+	0.296479i	0.194763	+	0.0293558i
$103$	3.78643	+	3.51329i	0.373088	+	0.346175i	0.844325	−	0.535832i	$-0.180002\pi$
$103$	3.78643	+	3.51329i	0.373088	+	0.346175i	−0.471237	+	0.882007i	$0.656192\pi$
$104$	11.2605	+	49.3355i	1.10418	+	4.83774i
$105$	−0.395438	+	0.142370i	−0.0385908	+	0.0138939i
$106$	−6.72028	+	29.4435i	−0.652731	+	2.85980i
$107$	3.17320	−	2.16345i	0.306765	−	0.209149i	−0.400146	−	0.916451i	$-0.631041\pi$
$107$	3.17320	−	2.16345i	0.306765	−	0.209149i	0.706911	+	0.707303i	$0.250088\pi$
$108$	4.15599	−	3.85620i	0.399910	−	0.371063i
$109$	2.08946	+	1.42457i	0.200134	+	0.136449i	0.659240	−	0.751932i	$-0.270878\pi$
$109$	2.08946	+	1.42457i	0.200134	+	0.136449i	−0.459106	+	0.888381i	$0.651830\pi$
$110$	0.643048	−	0.0969238i	0.0613122	−	0.00924133i
$111$	3.14271	−	1.51345i	0.298293	−	0.143650i
$112$	−39.1180	+	21.1263i	−3.69630	+	1.99625i
$113$	2.75985	+	1.32907i	0.259625	+	0.125029i	0.559169	−	0.829054i	$-0.311120\pi$
$113$	2.75985	+	1.32907i	0.259625	+	0.125029i	−0.299544	+	0.954082i	$0.596835\pi$
$114$	14.7806	+	4.55923i	1.38433	+	0.427011i
$115$	0.191407	−	0.487696i	0.0178488	−	0.0454779i
$116$	−10.6275	−	18.4074i	−0.986739	−	1.70908i
$117$	−2.48986	+	4.31257i	−0.230188	+	0.398697i
$118$	22.2665	+	27.9213i	2.04979	+	2.57036i
$119$	−0.775587	−	1.73496i	−0.0710980	−	0.159044i
$120$	1.00648	−	1.26209i	0.0918789	−	0.115212i
$121$	−3.22042	−	8.20548i	−0.292765	−	0.745953i
$122$	0.745304	+	9.94539i	0.0674767	+	0.900414i
$123$	0.295748	+	3.94649i	0.0266667	+	0.355843i
$124$	−1.52838	−	3.89424i	−0.137252	−	0.349713i
$125$	−0.987934	+	1.23883i	−0.0883635	+	0.110804i
$126$	−7.09417	−	1.83272i	−0.631999	−	0.163272i
$127$	−5.24676	−	6.57923i	−0.465575	−	0.583813i	0.492506	−	0.870309i	$-0.336081\pi$
$127$	−5.24676	−	6.57923i	−0.465575	−	0.583813i	−0.958081	+	0.286496i	$0.907509\pi$
$128$	27.7666	−	48.0932i	2.45425	−	4.25088i
$129$	−3.28679	−	5.69288i	−0.289386	−	0.501230i
$130$	−0.800353	+	2.03927i	−0.0701956	+	0.178856i
$131$	−3.77801	−	1.16536i	−0.330086	−	0.101818i	0.125282	−	0.992121i	$-0.460016\pi$
$131$	−3.77801	−	1.16536i	−0.330086	−	0.101818i	−0.455369	+	0.890303i	$0.650493\pi$
$132$	7.55081	+	3.63628i	0.657213	+	0.316497i
$133$	−3.95276	−	14.2389i	−0.342748	−	1.23467i
$134$	−15.6419	+	7.53275i	−1.35126	+	0.650731i
$135$	0.157079	−	0.0236758i	0.0135192	−	0.00203769i
$136$	6.03100	+	4.11187i	0.517154	+	0.352590i
$137$	10.2139	−	9.47709i	0.872630	−	0.809683i	−0.110255	−	0.993903i	$-0.535167\pi$
$137$	10.2139	−	9.47709i	0.872630	−	0.809683i	0.982885	+	0.184221i	$0.0589761\pi$
$138$	7.54658	−	5.14517i	0.642408	−	0.437986i
$139$	−4.36479	+	19.1234i	−0.370217	+	1.62203i	0.355949	+	0.934505i	$0.384158\pi$
$139$	−4.36479	+	19.1234i	−0.370217	+	1.62203i	−0.726165	+	0.687520i	$0.758699\pi$
$140$	−2.37010	−	0.245501i	−0.200310	−	0.0207486i
$141$	−2.29868	−	10.0712i	−0.193584	−	0.848145i
$142$	1.54411	+	1.43272i	0.129578	+	0.120231i
$143$	−7.27899	−	1.09713i	−0.608700	−	0.0917468i
$144$	16.0571	−	4.95296i	1.33809	−	0.412747i
$145$	0.0445054	−	0.593883i	0.00369597	−	0.0493193i
$146$	−1.65676			−0.137114
$147$	2.18315	+	6.65085i	0.180063	+	0.548553i
$148$	19.7758			1.62556
$149$	−0.213722	+	2.85193i	−0.0175088	+	0.233639i	0.981583	+	0.191035i	$0.0611844\pi$
$149$	−0.213722	+	2.85193i	−0.0175088	+	0.233639i	−0.999092	+	0.0426039i	$0.986435\pi$
$150$	−13.1649	+	4.06084i	−1.07491	+	0.331566i
$151$	−5.21225	−	0.785621i	−0.424167	−	0.0639329i	−0.0665097	−	0.997786i	$-0.521186\pi$
$151$	−5.21225	−	0.785621i	−0.424167	−	0.0639329i	−0.357657	+	0.933853i	$0.616424\pi$
$152$	41.6068	+	38.6054i	3.37475	+	3.13131i
$153$	0.159836	+	0.700286i	0.0129219	+	0.0566148i
$154$	−1.30936	−	10.7517i	−0.105511	−	0.866398i
$155$	0.0260830	−	0.114277i	0.00209504	−	0.00917897i
$156$	−23.3266	+	15.9038i	−1.86762	+	1.27332i
$157$	11.5645	−	10.7303i	0.922951	−	0.856373i	−0.0670048	−	0.997753i	$-0.521344\pi$
$157$	11.5645	−	10.7303i	0.922951	−	0.856373i	0.989955	+	0.141380i	$0.0451538\pi$
$158$	0.145639	+	0.0992950i	0.0115864	+	0.00789949i
$159$	−10.7834	+	1.62534i	−0.855181	+	0.128898i
$160$	3.75143	−	1.80660i	0.296577	−	0.142824i
$161$	−8.02889	−	3.41743i	−0.632765	−	0.269331i
$162$	2.49512	+	1.20159i	0.196035	+	0.0944056i
$163$	−14.9512	−	4.61184i	−1.17107	−	0.361227i	−0.352599	−	0.935775i	$-0.614702\pi$
$163$	−14.9512	−	4.61184i	−1.17107	−	0.361227i	−0.818471	+	0.574547i	$0.805178\pi$
$164$	−8.19719	+	20.8861i	−0.640093	+	1.63093i
$165$	0.117411	+	0.203362i	0.00914045	+	0.0158317i
$166$	11.7929	−	20.4258i	0.915303	−	1.58535i
$167$	−6.32373	−	7.92971i	−0.489345	−	0.613619i	0.474444	−	0.880286i	$-0.342649\pi$
$167$	−6.32373	−	7.92971i	−0.489345	−	0.613619i	−0.963789	+	0.266667i	$0.914078\pi$
$168$	−20.5358	−	17.3537i	−1.58437	−	1.33887i
$169$	7.35574	−	9.22381i	0.565826	−	0.709524i
$170$	0.115446	+	0.294152i	0.00885430	+	0.0225604i
$171$	0.417391	+	5.56970i	0.0319187	+	0.425926i
$172$	−2.78508	−	37.1643i	−0.212360	−	2.83375i
$173$	8.99650	+	22.9227i	0.683991	+	1.74278i	0.669417	+	0.742887i	$0.266544\pi$
$173$	8.99650	+	22.9227i	0.683991	+	1.74278i	0.0145746	+	0.999894i	$0.495361\pi$
$174$	6.47340	−	8.11738i	0.490747	−	0.615377i
$175$	10.0532	+	8.49542i	0.759947	+	0.642193i
$176$	15.4873	+	19.4205i	1.16740	+	1.46387i
$177$	−6.44778	+	11.1679i	−0.484645	+	0.839430i
$178$	1.17970	+	2.04331i	0.0884226	+	0.153152i
$179$	−6.51764	+	16.6067i	−0.487151	+	1.24124i	0.450223	+	0.892916i	$0.351345\pi$
$179$	−6.51764	+	16.6067i	−0.487151	+	1.24124i	−0.937374	+	0.348325i	$0.886751\pi$
$180$	0.860596	+	0.265459i	0.0641451	+	0.0197861i
$181$	0.380366	+	0.183174i	0.0282724	+	0.0136153i	0.447967	−	0.894050i	$-0.352148\pi$
$181$	0.380366	+	0.183174i	0.0282724	+	0.0136153i	−0.419694	+	0.907666i	$0.637863\pi$
$182$	33.5722	+	14.2897i	2.48854	+	1.05922i
$183$	−3.24464	+	1.56253i	−0.239850	+	0.115506i
$184$	33.1410	−	4.99521i	2.44319	−	0.368252i
$185$	0.457822	+	0.312138i	0.0336597	+	0.0229488i
$186$	1.49799	−	1.38993i	0.109838	−	0.101915i
$187$	−0.877308	+	0.598138i	−0.0641551	+	0.0437402i
$188$	13.0322	−	57.0978i	0.950472	−	4.16429i
$189$	−0.319841	−	2.62635i	−0.0232650	−	0.191039i
$190$	0.546760	+	2.39551i	0.0396661	+	0.173789i
$191$	7.21918	+	6.69842i	0.522361	+	0.484681i	0.896717	−	0.442605i	$-0.145946\pi$
$191$	7.21918	+	6.69842i	0.522361	+	0.484681i	−0.374355	+	0.927285i	$0.622136\pi$
$192$	38.5468	+	5.80999i	2.78187	+	0.419300i
$193$	−6.56280	+	2.02436i	−0.472401	+	0.145716i	−0.521809	−	0.853062i	$-0.674743\pi$
$193$	−6.56280	+	2.02436i	−0.472401	+	0.145716i	0.0494082	+	0.998779i	$0.484266\pi$
$194$	2.23794	−	29.8632i	0.160675	−	2.14405i
$195$	−0.791046			−0.0566479
$196$	−5.20876	+	39.3428i	−0.372054	+	2.81020i
$197$	−13.9994			−0.997417			−0.498709	−	0.866770i	$-0.666192\pi$
$197$	−13.9994			−0.997417			−0.498709	+	0.866770i	$0.666192\pi$
$198$	−0.305929	+	4.08234i	−0.0217414	+	0.290119i
$199$	16.7080	−	5.15374i	1.18440	−	0.365339i	0.360872	−	0.932615i	$-0.382479\pi$
$199$	16.7080	−	5.15374i	1.18440	−	0.365339i	0.823528	+	0.567276i	$0.192003\pi$
$200$	−49.9892	−	7.53465i	−3.53477	−	0.532780i
$201$	−4.59550	−	4.26401i	−0.324142	−	0.300760i
$202$	−7.54188	−	33.0431i	−0.530645	−	2.32491i
$203$	−9.86627	−	1.02197i	−0.692476	−	0.0717284i
$204$	−0.906178	+	3.97023i	−0.0634452	+	0.277971i
$205$	−0.519431	+	0.354142i	−0.0362787	+	0.0247344i
$206$	−10.4860	+	9.72962i	−0.730597	+	0.677895i
$207$	2.72501	+	1.85788i	0.189401	+	0.129132i
$208$	−82.7430	+	12.4715i	−5.73719	+	0.864743i
$209$	−7.43877	+	3.58232i	−0.514551	+	0.247795i
$210$	−0.311337	−	1.12152i	−0.0214843	−	0.0773920i
$211$	20.3687	+	9.80905i	1.40224	+	0.675283i	0.973614	−	0.228199i	$-0.0732838\pi$
$211$	20.3687	+	9.80905i	1.40224	+	0.675283i	0.428625	+	0.903482i	$0.358998\pi$
$212$	−59.0797	−	18.2237i	−4.05761	−	1.25161i
$213$	−0.277881	+	0.708029i	−0.0190401	+	0.0485134i
$214$	5.31795	+	9.21095i	0.363527	+	0.629648i
$215$	0.522117	−	0.904332i	0.0356081	−	0.0616750i
$216$	6.33593	+	7.94501i	0.431106	+	0.540589i
$217$	−1.89022	−	0.488321i	−0.128316	−	0.0331494i
$218$	−4.36656	+	5.47550i	−0.295741	+	0.370847i
$219$	−0.218563	−	0.556888i	−0.0147691	−	0.0376310i
$220$	0.0994890	+	1.32759i	0.00670754	+	0.0895060i
$221$	−0.267303	−	3.56691i	−0.0179808	−	0.239936i
$222$	3.52919	+	8.99224i	0.236864	+	0.603519i
$223$	−0.940902	+	1.17985i	−0.0630075	+	0.0790089i	−0.812337	−	0.583189i	$-0.801805\pi$
$223$	−0.940902	+	1.17985i	−0.0630075	+	0.0790089i	0.749329	+	0.662198i	$0.230376\pi$
$224$	−28.3022	−	63.3110i	−1.89102	−	4.23015i
$225$	−3.10172	−	3.88943i	−0.206781	−	0.259295i
$226$	−4.24157	+	7.34662i	−0.282145	+	0.488690i
$227$	−0.927526	−	1.60652i	−0.0615620	−	0.106629i	0.833602	−	0.552366i	$-0.186275\pi$
$227$	−0.927526	−	1.60652i	−0.0615620	−	0.106629i	−0.895164	+	0.445737i	$0.852942\pi$
$228$	−11.5687	+	29.4767i	−0.766159	+	1.95214i
$229$	14.3472	+	4.42553i	0.948091	+	0.292447i	0.729974	−	0.683475i	$-0.239532\pi$
$229$	14.3472	+	4.42553i	0.948091	+	0.292447i	0.218117	+	0.975923i	$0.430008\pi$
$230$	1.30722	+	0.629526i	0.0861958	+	0.0415097i
$231$	3.44125	−	1.85850i	0.226418	−	0.122281i
$232$	34.3251	−	16.5301i	2.25356	−	1.08525i
$233$	14.6739	−	2.21173i	0.961318	−	0.144895i	0.350409	−	0.936597i	$-0.386042\pi$
$233$	14.6739	−	2.21173i	0.961318	−	0.144895i	0.610908	+	0.791701i	$0.290804\pi$
$234$	−11.3944	−	7.76860i	−0.744878	−	0.507849i
$235$	1.20292	−	1.11615i	0.0784700	−	0.0728095i
$236$	−60.4068	+	41.1847i	−3.93215	+	2.68089i
$237$	−0.0141632	+	0.0620530i	−0.000919999	+	0.00403078i
$238$	4.95184	−	1.78283i	0.320980	−	0.115563i
$239$	−1.62551	−	7.12184i	−0.105146	−	0.460673i	−0.999900	−	0.0141153i	$-0.995507\pi$
$239$	−1.62551	−	7.12184i	−0.105146	−	0.460673i	0.894755	−	0.446558i	$-0.147350\pi$
$240$	1.95674	+	1.81559i	0.126307	+	0.117196i
$241$	−5.69057	−	0.857715i	−0.366562	−	0.0552503i	−0.0368211	−	0.999322i	$-0.511723\pi$
$241$	−5.69057	−	0.857715i	−0.366562	−	0.0552503i	−0.329741	+	0.944072i	$0.606961\pi$
$242$	23.3270	−	7.19543i	1.49952	−	0.462540i
$243$	−0.0747301	+	0.997204i	−0.00479394	+	0.0639707i
$244$	−20.4172			−1.30708
$245$	−0.741563	+	0.828593i	−0.0473767	+	0.0529368i
$246$	−10.9599			−0.698781
$247$	2.07850	−	27.7356i	0.132252	−	1.76477i
$248$	7.16534	−	2.21021i	0.454999	−	0.140349i
$249$	8.42150	+	1.26934i	0.533691	+	0.0804409i
$250$	−3.21673	−	2.98469i	−0.203444	−	0.188768i
$251$	−0.655661	−	2.87264i	−0.0413849	−	0.181319i	0.950011	−	0.312216i	$-0.101071\pi$
$251$	−0.655661	−	2.87264i	−0.0413849	−	0.181319i	−0.991396	+	0.130897i	$0.958214\pi$
$252$	4.82675	−	14.2021i	0.304056	−	0.894649i
$253$	−1.08487	+	4.75312i	−0.0682051	+	0.298826i
$254$	19.2553	−	13.1280i	1.20818	−	0.823725i
$255$	−0.0836437	+	0.0776100i	−0.00523797	+	0.00486013i
$256$	62.6521	+	42.7154i	3.91575	+	2.66972i
$257$	8.90974	−	1.34293i	0.555774	−	0.0837695i	0.134851	−	0.990866i	$-0.456944\pi$
$257$	8.90974	−	1.34293i	0.555774	−	0.0837695i	0.420923	+	0.907096i	$0.361706\pi$
$258$	16.4019	−	7.89872i	1.02114	−	0.491753i
$259$	5.41329	−	7.47440i	0.336366	−	0.464436i
$260$	−4.04065	−	1.94587i	−0.250590	−	0.120678i
$261$	3.58249	+	1.10505i	0.221751	+	0.0684010i
$262$	4.00018	−	10.1923i	0.247132	−	0.629682i
$263$	7.66738	+	13.2803i	0.472791	+	0.818898i	0.999515	−	0.0311383i	$-0.00991324\pi$
$263$	7.66738	+	13.2803i	0.472791	+	0.818898i	−0.526724	+	0.850036i	$0.676580\pi$
$264$	−7.51095	+	13.0093i	−0.462267	+	0.800670i
$265$	−1.08009	−	1.35439i	−0.0663494	−	0.0831995i
$266$	40.1406	−	7.96925i	2.46118	−	0.488626i
$267$	−0.531191	+	0.666093i	−0.0325084	+	0.0407642i
$268$	−12.9848	−	33.0849i	−0.793176	−	2.02098i
$269$	0.714185	+	9.53014i	0.0435447	+	0.581063i	0.975715	+	0.219043i	$0.0702936\pi$
$269$	0.714185	+	9.53014i	0.0435447	+	0.581063i	−0.932170	+	0.362020i	$0.882087\pi$
$270$	0.0328756	+	0.438694i	0.00200074	+	0.0266981i
$271$	−5.98378	−	15.2464i	−0.363489	−	0.926154i	−0.989263	−	0.146149i	$-0.953312\pi$
$271$	−5.98378	−	15.2464i	−0.363489	−	0.926154i	0.625774	−	0.780004i	$-0.284783\pi$
$272$	−7.52550	+	9.43668i	−0.456301	+	0.572183i
$273$	−0.374315	+	13.1698i	−0.0226546	+	0.797073i
$274$	24.0584	+	30.1683i	1.45342	+	1.82253i
$275$	3.67694	−	6.36864i	0.221728	−	0.384044i
$276$	9.34916	+	16.1932i	0.562754	+	0.974718i
$277$	−7.23614	+	18.4374i	−0.434778	+	1.10780i	0.530758	+	0.847524i	$0.321907\pi$
$277$	−7.23614	+	18.4374i	−0.434778	+	1.10780i	−0.965535	+	0.260272i	$0.916188\pi$
$278$	−51.9085	−	16.0116i	−3.11326	−	0.960314i
$279$	0.664816	+	0.320158i	0.0398015	+	0.0191674i
$280$	0.756283	−	4.20347i	0.0451966	−	0.251206i
$281$	1.83386	−	0.883140i	0.109399	−	0.0526837i	−0.378384	−	0.925649i	$-0.623520\pi$
$281$	1.83386	−	0.883140i	0.109399	−	0.0526837i	0.487783	+	0.872965i	$0.337806\pi$
$282$	28.2886	−	4.26382i	1.68456	−	0.253907i
$283$	19.8825	+	13.5557i	1.18189	+	0.805802i	0.984648	−	0.174552i	$-0.0558476\pi$
$283$	19.8825	+	13.5557i	1.18189	+	0.805802i	0.197247	+	0.980354i	$0.436800\pi$
$284$	−3.16108	+	2.93305i	−0.187575	+	0.174045i
$285$	−0.733077	+	0.499803i	−0.0434237	+	0.0296058i
$286$	4.53630	−	19.8748i	0.268237	−	1.17522i
$287$	5.65018	+	8.81538i	0.333520	+	0.520356i
$288$	5.83261	+	25.5543i	0.343690	+	1.50580i
$289$	12.0837	+	11.2120i	0.710804	+	0.659530i
$290$	1.63088	+	0.245815i	0.0957683	+	0.0144347i
$291$	10.3332	−	3.18737i	0.605742	−	0.186847i
$292$	0.253462	−	3.38222i	0.0148327	−	0.197929i
$293$	26.0006			1.51897			0.759487	−	0.650523i	$-0.225450\pi$
$293$	26.0006			1.51897			0.759487	+	0.650523i	$0.225450\pi$
$294$	−18.8190	+	4.65263i	−1.09755	+	0.271347i
$295$	−2.04850			−0.119268
$296$	−2.64894	+	35.3476i	−0.153966	+	2.05454i
$297$	−1.41256	+	0.435718i	−0.0819651	+	0.0252829i
$298$	−7.83173	−	1.18044i	−0.453680	−	0.0683813i
$299$	−12.0394	−	11.1709i	−0.696254	−	0.646029i
$300$	−6.27601	−	27.4970i	−0.362345	−	1.58754i
$301$	−14.8088	−	9.12043i	−0.853566	−	0.525693i
$302$	3.24830	−	14.2317i	0.186919	−	0.818944i
$303$	10.1119	−	6.89417i	0.580913	−	0.396060i
$304$	−68.7996	+	63.8367i	−3.94593	+	3.66129i
$305$	−0.472670	−	0.322261i	−0.0270650	−	0.0184526i
$306$	−1.96701	+	0.296479i	−0.112446	+	0.0169486i
$307$	−5.79149	+	2.78904i	−0.330538	+	0.159179i	−0.591791	−	0.806092i	$-0.701579\pi$
$307$	−5.79149	+	2.78904i	−0.330538	+	0.159179i	0.261253	+	0.965270i	$0.415864\pi$
$308$	22.1496	−	1.02815i	1.26209	−	0.0585843i
$309$	−4.65377	−	2.24114i	−0.264744	−	0.127494i
$310$	0.310194	+	0.0956821i	0.0176178	+	0.00543438i
$311$	11.4931	−	29.2840i	0.651715	−	1.66054i	−0.0950645	−	0.995471i	$-0.530306\pi$
$311$	11.4931	−	29.2840i	0.651715	−	1.66054i	0.746779	−	0.665072i	$-0.231599\pi$
$312$	−25.3021	−	43.8246i	−1.43245	−	2.48108i
$313$	9.77989	−	16.9393i	0.552792	−	0.957464i	−0.445280	−	0.895392i	$-0.646896\pi$
$313$	9.77989	−	16.9393i	0.552792	−	0.957464i	0.998072	−	0.0620724i	$-0.0197710\pi$
$314$	27.2399	+	34.1577i	1.53723	+	1.92763i
$315$	0.335905	−	0.252603i	0.0189261	−	0.0142325i
$316$	−0.224988	+	0.282126i	−0.0126566	+	0.0158708i
$317$	9.40932	+	23.9746i	0.528480	+	1.34655i	0.907070	+	0.420981i	$0.138314\pi$
$317$	9.40932	+	23.9746i	0.528480	+	1.34655i	−0.378589	+	0.925565i	$0.623591\pi$
$318$	−2.25690	−	30.1162i	−0.126561	−	1.68883i
$319$	0.414153	+	5.52648i	0.0231881	+	0.309424i
$320$	2.26235	+	5.76438i	0.126469	+	0.322239i
$321$	−2.39454	+	3.00265i	−0.133650	+	0.167592i
$322$	11.0993	−	21.4656i	0.618540	−	1.19623i
$323$	−2.50138	−	3.13664i	−0.139181	−	0.174527i
$324$	−2.83472	+	4.90988i	−0.157484	+	0.272771i
$325$	12.3865	+	21.4540i	0.687079	+	1.19006i
$326$	15.8304	−	40.3353i	0.876767	−	2.23397i
$327$	−2.41653	−	0.745401i	−0.133635	−	0.0412208i
$328$	−36.2341	−	17.4494i	−2.00069	−	0.963484i
$329$	−18.0131	−	20.5551i	−0.993095	−	1.13324i
$330$	−0.585910	+	0.282159i	−0.0322533	+	0.0155324i
$331$	−13.0158	+	1.96182i	−0.715415	+	0.107831i	−0.496656	−	0.867948i	$-0.665439\pi$
$331$	−13.0158	+	1.96182i	−0.715415	+	0.107831i	−0.218759	+	0.975779i	$0.570201\pi$
$332$	39.8945	+	27.1996i	2.18949	+	1.49277i
$333$	−2.55699	+	2.37254i	−0.140122	+	0.130015i
$334$	23.2077	−	15.8227i	1.26987	−	0.865780i
$335$	0.221598	−	0.970883i	0.0121072	−	0.0530450i
$336$	31.1530	−	31.7179i	1.69954	−	1.73036i
$337$	−3.06582	−	13.4322i	−0.167006	−	0.731700i	−0.987183	−	0.159591i	$-0.948982\pi$
$337$	−3.06582	−	13.4322i	−0.167006	−	0.731700i	0.820177	−	0.572109i	$-0.193875\pi$
$338$	23.9504	+	22.2228i	1.30273	+	1.20876i
$339$	−3.02899	−	0.456546i	−0.164512	−	0.0247962i
$340$	−0.618162	+	0.190678i	−0.0335245	+	0.0103410i
$341$	−0.0815137	+	1.08773i	−0.00441422	+	0.0589036i
$342$	−15.4678			−0.836405
$343$	13.4440	+	12.7381i	0.725908	+	0.687791i
$344$	66.8010			3.60167
$345$	−0.0391520	+	0.522447i	−0.00210787	+	0.0281276i
$346$	−65.1659	+	20.1010i	−3.50334	+	1.08064i
$347$	−14.4821	−	2.18282i	−0.777439	−	0.117180i	−0.251677	−	0.967811i	$-0.580982\pi$
$347$	−14.4821	−	2.18282i	−0.777439	−	0.117180i	−0.525763	+	0.850631i	$0.676220\pi$
$348$	15.5810	+	14.4571i	0.835230	+	0.774980i
$349$	4.39555	+	19.2582i	0.235289	+	1.03087i	0.945179	+	0.326554i	$0.105887\pi$
$349$	4.39555	+	19.2582i	0.235289	+	1.03087i	−0.709890	+	0.704313i	$0.751255\pi$
$350$	−25.5418	+	26.0049i	−1.36526	+	1.39002i
$351$	1.10809	−	4.85488i	0.0591457	−	0.259134i
$352$	−32.0141	+	21.8268i	−1.70636	+	1.16337i
$353$	7.02774	−	6.52079i	0.374049	−	0.347067i	−0.470639	−	0.882326i	$-0.655977\pi$
$353$	7.02774	−	6.52079i	0.374049	−	0.347067i	0.844688	+	0.535259i	$0.179786\pi$
$354$	−29.5072	−	20.1176i	−1.56829	−	1.06924i
$355$	−0.119475	+	0.0180080i	−0.00634109	+	0.000955766i
$356$	−4.35182	+	2.09573i	−0.230646	+	0.111073i
$357$	1.25252	+	1.42928i	0.0662904	+	0.0756453i
$358$	−44.5126	−	21.4362i	−2.35257	−	1.13294i
$359$	−15.4279	−	4.75887i	−0.814252	−	0.251164i	−0.140462	−	0.990086i	$-0.544859\pi$
$359$	−15.4279	−	4.75887i	−0.814252	−	0.251164i	−0.673790	+	0.738922i	$0.735335\pi$
$360$	−0.589760	+	1.50268i	−0.0310831	+	0.0791984i
$361$	−6.09789	−	10.5619i	−0.320942	−	0.555888i
$362$	−0.584579	+	1.01252i	−0.0307248	+	0.0532169i
$363$	5.49595	+	6.89170i	0.288463	+	0.361721i
$364$	−34.3081	+	66.3504i	−1.79823	+	3.47771i
$365$	0.0592519	−	0.0742996i	0.00310139	−	0.00388902i
$366$	−3.64365	−	9.28387i	−0.190457	−	0.485275i
$367$	1.44595	+	19.2948i	0.0754777	+	1.00718i	0.898443	+	0.439089i	$0.144699\pi$
$367$	1.44595	+	19.2948i	0.0754777	+	1.00718i	−0.822966	+	0.568091i	$0.807682\pi$
$368$	4.14154	+	55.2650i	0.215893	+	2.88089i
$369$	−1.44586	−	3.68398i	−0.0752683	−	0.191780i
$370$	−0.956758	+	1.19974i	−0.0497395	+	0.0623713i
$371$	−23.0598	+	17.3411i	−1.19720	+	0.900305i
$372$	2.60832	+	3.27073i	0.135235	+	0.169579i
$373$	−4.78444	+	8.28690i	−0.247729	+	0.429079i	−0.962895	−	0.269875i	$-0.913018\pi$
$373$	−4.78444	+	8.28690i	−0.247729	+	0.429079i	0.715166	+	0.698954i	$0.246351\pi$
$374$	−1.47027	−	2.54659i	−0.0760260	−	0.131681i
$375$	0.578891	−	1.47499i	0.0298938	−	0.0761682i
$376$	100.312	+	30.9421i	5.17319	+	1.59572i
$377$	−16.8204	−	8.10028i	−0.866295	−	0.417186i
$378$	7.31920	−	0.339747i	0.376459	−	0.0174747i
$379$	−19.8820	+	9.57467i	−1.02127	+	0.491818i	−0.868104	−	0.496383i	$-0.834661\pi$
$379$	−19.8820	+	9.57467i	−1.02127	+	0.491818i	−0.153166	+	0.988200i	$0.548947\pi$
$380$	−4.97400	+	0.749710i	−0.255161	+	0.0384593i
$381$	6.95293	+	4.74043i	0.356209	+	0.242859i
$382$	−19.9926	+	18.5504i	−1.02291	+	0.949123i
$383$	2.22696	−	1.51832i	0.113792	−	0.0775824i	−0.505087	−	0.863069i	$-0.668539\pi$
$383$	2.22696	−	1.51832i	0.113792	−	0.0775824i	0.618879	+	0.785486i	$0.287587\pi$
$384$	−12.3573	+	54.1409i	−0.630606	+	2.76287i
$385$	0.529003	+	0.325802i	0.0269605	+	0.0166044i
$386$	−4.23232	−	18.5430i	−0.215419	−	0.943814i
$387$	4.81877	+	4.47117i	0.244952	+	0.227282i
$388$	60.6223	+	9.13734i	3.07763	+	0.463878i
$389$	−24.0751	+	7.42619i	−1.22066	+	0.376523i	−0.837129	−	0.547006i	$-0.815768\pi$
$389$	−24.0751	+	7.42619i	−1.22066	+	0.376523i	−0.383529	+	0.923529i	$0.625291\pi$
$390$	0.163711	−	2.18458i	0.00828985	−	0.110620i
$391$	−2.36900			−0.119806
$392$	−69.6241	−	14.5801i	−3.51655	−	0.736406i
$393$	3.95366			0.199436
$394$	2.89726	−	38.6612i	0.145962	−	1.94772i
$395$	−0.00966162	+	0.00298022i	−0.000486129	+	0.000149951i
$396$	−8.28716	−	1.24909i	−0.416445	−	0.0627690i
$397$	−6.55527	−	6.08240i	−0.329000	−	0.305267i	0.498326	−	0.866990i	$-0.333948\pi$
$397$	−6.55527	−	6.08240i	−0.329000	−	0.305267i	−0.827326	+	0.561723i	$0.810139\pi$
$398$	10.7749	+	47.2080i	0.540098	+	2.36632i
$399$	7.97414	+	12.4412i	0.399206	+	0.622839i
$400$	18.6015	−	81.4983i	0.930073	−	4.07492i
$401$	31.2139	−	21.2813i	1.55875	−	1.06274i	0.592349	−	0.805681i	$-0.298200\pi$
$401$	31.2139	−	21.2813i	1.55875	−	1.06274i	0.966397	−	0.257054i	$-0.0827519\pi$
$402$	12.7267	−	11.8086i	0.634749	−	0.588961i
$403$	−3.03601	−	2.06991i	−0.151234	−	0.103110i
$404$	68.6102	−	10.3413i	3.41349	−	0.514500i
$405$	−0.143122	+	0.0689238i	−0.00711178	+	0.00342485i
$406$	4.86419	−	27.0355i	0.241406	−	1.34175i
$407$	−4.64567	−	2.23724i	−0.230277	−	0.110896i
$408$	−6.97506	−	2.15152i	−0.345317	−	0.106516i
$409$	−2.52891	+	6.44357i	−0.125047	+	0.318614i	−0.979664	−	0.200644i	$-0.935696\pi$
$409$	−2.52891	+	6.44357i	−0.125047	+	0.318614i	0.854617	+	0.519258i	$0.173792\pi$
$410$	−0.870511	−	1.50777i	−0.0429915	−	0.0744634i
$411$	−6.96668	+	12.0666i	−0.343641	+	0.595204i
$412$	−18.2585	−	22.8954i	−0.899530	−	1.12797i
$413$	−0.969330	+	34.1047i	−0.0476976	+	1.67818i
$414$	−5.69474	+	7.14098i	−0.279881	+	0.350960i
$415$	0.494267	+	1.25937i	0.0242626	+	0.0618201i
$416$	−9.75423	−	130.161i	−0.478240	−	6.38167i
$417$	−1.46585	−	19.5603i	−0.0717827	−	0.957874i
$418$	−8.35356	−	21.2845i	−0.408586	−	1.04106i
$419$	21.7028	−	27.2144i	1.06025	−	1.32951i	0.118592	−	0.992943i	$-0.462162\pi$
$419$	21.7028	−	27.2144i	1.06025	−	1.32951i	0.941659	−	0.336569i	$-0.109267\pi$
$420$	2.33717	−	0.464006i	0.114042	−	0.0226412i
$421$	5.44856	+	6.83228i	0.265547	+	0.332985i	0.896672	−	0.442696i	$-0.145978\pi$
$421$	5.44856	+	6.83228i	0.265547	+	0.332985i	−0.631125	+	0.775681i	$0.717406\pi$
$422$	−31.3044	+	54.2208i	−1.52387	+	2.63943i
$423$	5.16508	+	8.94619i	0.251135	+	0.434978i
$424$	40.4869	−	103.159i	1.96622	−	5.00984i
$425$	3.41460	+	1.05326i	0.165632	+	0.0510908i
$426$	−1.89781	−	0.913936i	−0.0919491	−	0.0442803i
$427$	−5.58885	+	7.71680i	−0.270464	+	0.373442i
$428$	−19.6174	+	9.44725i	−0.948244	+	0.456650i
$429$	7.27899	−	1.09713i	0.351433	−	0.0529700i
$430$	2.38938	+	1.62905i	0.115226	+	0.0785598i
$431$	1.36907	−	1.27031i	0.0659456	−	0.0611886i	−0.646512	−	0.762904i	$-0.723773\pi$
$431$	1.36907	−	1.27031i	0.0659456	−	0.0611886i	0.712457	+	0.701716i	$0.247582\pi$
$432$	−13.8838	+	9.46583i	−0.667986	+	0.455425i
$433$	−7.94869	+	34.8255i	−0.381990	+	1.67361i	0.309250	+	0.950981i	$0.399922\pi$
$433$	−7.94869	+	34.8255i	−0.381990	+	1.67361i	−0.691240	+	0.722625i	$0.742935\pi$
$434$	1.73975	−	5.11902i	0.0835109	−	0.245721i
$435$	0.132522	+	0.580617i	0.00635394	+	0.0278384i
$436$	−10.5100	−	9.75187i	−0.503338	−	0.467030i
$437$	−18.2152	−	2.74549i	−0.871349	−	0.131335i
$438$	1.58315	−	0.488338i	0.0756460	−	0.0233337i
$439$	−0.406215	+	5.42056i	−0.0193876	+	0.258709i	0.979085	+	0.203453i	$0.0652165\pi$
$439$	−0.406215	+	5.42056i	−0.0193876	+	0.258709i	−0.998472	+	0.0552558i	$0.982403\pi$
$440$	−2.38628			−0.113761
$441$	−4.04653	−	5.71188i	−0.192692	−	0.271994i
$442$	9.90582			0.471172
$443$	2.30793	−	30.7971i	0.109653	−	1.46322i	−0.622791	−	0.782388i	$-0.714001\pi$
$443$	2.30793	−	30.7971i	0.109653	−	1.46322i	0.732444	−	0.680828i	$-0.238380\pi$
$444$	−18.8973	+	5.82903i	−0.896824	+	0.276634i
$445$	−0.133826	−	0.0201710i	−0.00634394	−	0.000956196i
$446$	−3.06360	−	2.84260i	−0.145065	−	0.134601i
$447$	−0.636393	−	2.78822i	−0.0301003	−	0.131878i
$448$	97.0394	−	34.9374i	4.58468	−	1.65064i
$449$	1.41120	−	6.18287i	0.0665986	−	0.291788i	−0.930651	−	0.365909i	$-0.880758\pi$
$449$	1.41120	−	6.18287i	0.0665986	−	0.291788i	0.997249	+	0.0741215i	$0.0236153\pi$
$450$	11.3831	−	7.76086i	0.536604	−	0.365850i
$451$	4.28850	−	3.97914i	0.201937	−	0.187371i
$452$	−14.3490	−	9.78296i	−0.674919	−	0.460152i
$453$	5.21225	−	0.785621i	0.244893	−	0.0369117i
$454$	4.62858	−	2.22901i	0.217230	−	0.104612i
$455$	−1.84151	+	0.994538i	−0.0863314	+	0.0466246i
$456$	−51.1374	−	24.6265i	−2.39473	−	1.15324i
$457$	−25.9268	−	7.99736i	−1.21281	−	0.374101i	−0.378603	−	0.925559i	$-0.623595\pi$
$457$	−25.9268	−	7.99736i	−1.21281	−	0.374101i	−0.834202	+	0.551458i	$0.814072\pi$
$458$	−15.1909	+	38.7058i	−0.709825	+	1.80861i
$459$	−0.359148	−	0.622062i	−0.0167636	−	0.0290354i
$460$	−1.48514	+	2.57235i	−0.0692452	+	0.119936i
$461$	2.03252	+	2.54870i	0.0946641	+	0.118705i	0.826907	−	0.562338i	$-0.190098\pi$
$461$	2.03252	+	2.54870i	0.0946641	+	0.118705i	−0.732243	+	0.681043i	$0.761527\pi$
$462$	4.42031	+	9.88810i	0.205652	+	0.460036i
$463$	−18.4772	+	23.1697i	−0.858709	+	1.07679i	0.137561	+	0.990493i	$0.456074\pi$
$463$	−18.4772	+	23.1697i	−0.858709	+	1.07679i	−0.996270	+	0.0862933i	$0.972498\pi$
$464$	23.0156	+	58.6429i	1.06847	+	2.72243i
$465$	0.00875957	+	0.116888i	0.000406215	+	0.00542057i
$466$	3.07114	+	40.9816i	0.142268	+	1.89843i
$467$	−12.6796	−	32.3070i	−0.586740	−	1.49499i	−0.848147	−	0.529760i	$-0.822282\pi$
$467$	−12.6796	−	32.3070i	−0.586740	−	1.49499i	0.261408	−	0.965228i	$-0.415813\pi$
$468$	17.6025	−	22.0729i	0.813677	−	1.02032i
$469$	−16.0590	−	4.14870i	−0.741535	−	0.191569i
$470$	2.83344	+	3.55302i	0.130697	+	0.163889i
$471$	−7.88794	+	13.6623i	−0.363457	+	0.629526i
$472$	−65.5227	−	113.489i	−3.01592	−	5.22373i
$473$	−3.55013	+	9.04557i	−0.163235	+	0.415916i
$474$	−0.168436	−	0.0519558i	−0.00773654	−	0.00238641i
$475$	25.0340	+	12.0557i	1.14864	+	0.553155i
$476$	2.88201	+	10.3818i	0.132097	+	0.475847i
$477$	9.82527	−	4.73160i	0.449868	−	0.216645i
$478$	20.0043	−	3.01516i	0.914975	−	0.137910i
$479$	−18.7408	−	12.7773i	−0.856289	−	0.583808i	0.0536456	−	0.998560i	$-0.482916\pi$
$479$	−18.7408	−	12.7773i	−0.856289	−	0.583808i	−0.909934	+	0.414752i	$0.863868\pi$
$480$	−3.05227	+	2.83209i	−0.139316	+	0.129267i
$481$	14.3518	−	9.78489i	0.654386	−	0.446153i
$482$	3.54639	−	15.5377i	0.161534	−	0.707725i
$483$	8.67949	+	0.899044i	0.394931	+	0.0409079i
$484$	11.1205	+	48.7221i	0.505477	+	2.21464i
$485$	1.25922	+	1.16838i	0.0571782	+	0.0530536i
$486$	−2.73844	−	0.412754i	−0.124218	−	0.0187229i
$487$	−29.2489	+	9.02210i	−1.32540	+	0.408830i	−0.875054	−	0.484026i	$-0.839174\pi$
$487$	−29.2489	+	9.02210i	−1.32540	+	0.408830i	−0.450342	+	0.892856i	$0.648698\pi$
$488$	2.73485	−	36.4940i	0.123801	−	1.65201i
$489$	15.6463			0.707552
$490$	−2.13480	−	2.21941i	−0.0964403	−	0.100263i
$491$	−7.93412			−0.358062			−0.179031	−	0.983843i	$-0.557296\pi$
$491$	−7.93412			−0.358062			−0.179031	+	0.983843i	$0.557296\pi$
$492$	1.67673	−	22.3744i	0.0755927	−	1.00871i
$493$	−2.57328	+	0.793753i	−0.115895	+	0.0357488i
$494$	76.1653	+	11.4801i	3.42684	+	0.516513i
$495$	−0.172137	−	0.159720i	−0.00773698	−	0.00717887i
$496$	2.75909	+	12.0884i	0.123887	+	0.542784i
$497$	0.243274	+	1.99762i	0.0109123	+	0.0896055i
$498$	−5.24831	+	22.9944i	−0.235183	+	1.03040i
$499$	27.8754	−	19.0052i	1.24788	−	0.850788i	0.254656	−	0.967032i	$-0.418038\pi$
$499$	27.8754	−	19.0052i	1.24788	−	0.850788i	0.993221	+	0.116244i	$0.0370855\pi$
$500$	6.58526	−	6.11023i	0.294502	−	0.273258i
$501$	8.38011	+	5.71346i	0.374395	+	0.255259i
$502$	8.06886	−	1.21618i	0.360131	−	0.0542810i
$503$	18.3233	−	8.82406i	0.816997	−	0.393445i	0.0217749	−	0.999763i	$-0.493068\pi$
$503$	18.3233	−	8.82406i	0.816997	−	0.393445i	0.795223	+	0.606318i	$0.207354\pi$
$504$	24.7385	+	10.5297i	1.10194	+	0.469032i
$505$	1.75159	+	0.843521i	0.0779447	+	0.0375362i
$506$	−12.9019	−	3.97969i	−0.573557	−	0.176919i
$507$	−4.31018	+	10.9822i	−0.191422	+	0.487735i
$508$	23.8546	+	41.3174i	1.05838	+	1.83316i
$509$	−10.0193	+	17.3539i	−0.444097	+	0.769199i	−0.997989	−	0.0633901i	$-0.979809\pi$
$509$	−10.0193	+	17.3539i	−0.444097	+	0.769199i	0.553892	+	0.832589i	$0.313142\pi$
$510$	−0.197020	−	0.247055i	−0.00872418	−	0.0109398i
$511$	−1.20895	−	1.02162i	−0.0534807	−	0.0451938i
$512$	−61.6817	+	77.3464i	−2.72597	+	3.41826i
$513$	−2.04055	−	5.19923i	−0.0900923	−	0.229551i
$514$	1.86475	+	24.8833i	0.0822505	+	1.09756i
$515$	−0.0613177	−	0.818228i	−0.00270198	−	0.0360555i
$516$	13.6157	+	34.6922i	0.599398	+	1.52724i
$517$	−9.52095	+	11.9389i	−0.418731	+	0.525072i
$518$	19.5212	+	16.4964i	0.857713	+	0.724810i
$519$	−15.3534	−	19.2525i	−0.673939	−	0.845093i
$520$	4.01932	−	6.96167i	0.176259	−	0.305289i
$521$	18.7782	+	32.5248i	0.822687	+	1.42494i	0.903674	+	0.428221i	$0.140859\pi$
$521$	18.7782	+	32.5248i	0.822687	+	1.42494i	−0.0809869	+	0.996715i	$0.525807\pi$
$522$	−3.79316	+	9.66482i	−0.166022	+	0.423018i
$523$	−30.8956	−	9.53003i	−1.35097	−	0.416719i	−0.466998	−	0.884258i	$-0.654665\pi$
$523$	−30.8956	−	9.53003i	−1.35097	−	0.416719i	−0.883972	+	0.467539i	$0.845141\pi$
$524$	20.1952	+	9.72552i	0.882233	+	0.424861i
$525$	−12.1106	−	5.15477i	−0.528550	−	0.224972i
$526$	−38.2621	+	18.4260i	−1.66831	+	0.803414i
$527$	−0.524103	+	0.0789958i	−0.0228303	+	0.00344111i
$528$	−20.5236	−	13.9927i	−0.893173	−	0.608955i
$529$	8.88648	−	8.24545i	0.386369	−	0.358498i
$530$	3.96386	−	2.70251i	0.172179	−	0.117390i
$531$	2.86953	−	12.5722i	0.124527	−	0.545589i
$532$	10.1280	+	83.1649i	0.439103	+	3.60566i
$533$	4.38534	+	19.2134i	0.189950	+	0.832226i
$534$	−1.72957	−	1.60481i	−0.0748458	−	0.0694468i
$535$	−0.603268	−	0.0909280i	−0.0260815	−	0.00393116i
$536$	60.8756	−	18.7776i	2.62943	−	0.811071i
$537$	1.33318	−	17.7900i	0.0575308	−	0.767695i
$538$	−26.4665			−1.14105
$539$	5.67446	−	8.65299i	0.244416	−	0.372711i
$540$	−0.900608			−0.0387560
$541$	1.49211	−	19.9108i	0.0641506	−	0.856030i	−0.868601	−	0.495512i	$-0.834981\pi$
$541$	1.49211	−	19.9108i	0.0641506	−	0.856030i	0.932752	−	0.360519i	$-0.117400\pi$
$542$	43.3433	−	13.3697i	1.86176	−	0.574276i
$543$	−0.417459	−	0.0629218i	−0.0179149	−	0.00270023i
$544$	−13.8016	−	12.8060i	−0.591739	−	0.549053i
$545$	−0.0893913	−	0.391649i	−0.00382910	−	0.0167764i
$546$	−36.2927	−	3.75929i	−1.55318	−	0.160883i
$547$	3.83205	−	16.7893i	0.163846	−	0.717858i	−0.824528	−	0.565821i	$-0.808559\pi$
$547$	3.83205	−	16.7893i	0.163846	−	0.717858i	0.988375	−	0.152037i	$-0.0485834\pi$
$548$	−65.2682	+	44.4991i	−2.78812	+	1.90091i
$549$	2.63992	−	2.44949i	0.112669	−	0.104542i
$550$	16.8269	+	11.4724i	0.717501	+	0.489184i
$551$	−20.7058	+	3.12089i	−0.882095	+	0.132954i
$552$	−30.1963	+	14.5418i	−1.28524	+	0.618939i
$553$	0.0450447	+	0.162263i	0.00191549	+	0.00690012i
$554$	−49.4197	−	23.7993i	−2.09964	−	1.01113i
$555$	−0.529486	−	0.163325i	−0.0224754	−	0.00693276i
$556$	40.6285	−	103.520i	1.72303	−	4.39022i
$557$	−3.01437	−	5.22104i	−0.127723	−	0.221222i	0.795071	−	0.606516i	$-0.207433\pi$
$557$	−3.01437	−	5.22104i	−0.127723	−	0.221222i	−0.922794	+	0.385294i	$0.874100\pi$
$558$	−1.02175	+	1.76972i	−0.0432540	+	0.0749181i
$559$	−20.4097	−	25.5930i	−0.863238	−	1.08247i
$560$	6.83784	+	1.76650i	0.288951	+	0.0746482i
$561$	0.662027	−	0.830156i	0.0279508	−	0.0350492i
$562$	2.05938	+	5.24721i	0.0868697	+	0.221340i
$563$	−0.713440	−	9.52019i	−0.0300679	−	0.401228i	−0.991850	−	0.127412i	$-0.959333\pi$
$563$	−0.713440	−	9.52019i	−0.0300679	−	0.401228i	0.961782	−	0.273816i	$-0.0882860\pi$
$564$	4.37666	+	58.4025i	0.184291	+	2.45919i
$565$	−0.177775	−	0.452962i	−0.00747903	−	0.0190563i
$566$	−41.5506	+	52.1028i	−1.74650	+	2.19005i
$567$	1.07976	+	2.41539i	0.0453457	+	0.101437i
$568$	−4.81916	−	6.04303i	−0.202207	−	0.253560i
$569$	−9.26009	+	16.0389i	−0.388203	+	0.672387i	−0.992208	−	0.124593i	$-0.960237\pi$
$569$	−9.26009	+	16.0389i	−0.388203	+	0.672387i	0.604005	+	0.796981i	$0.293571\pi$
$570$	−1.22856	−	2.12792i	−0.0514586	−	0.0891289i
$571$	−0.0465428	+	0.118589i	−0.00194776	+	0.00496280i	−0.931844	−	0.362858i	$-0.881801\pi$
$571$	−0.0465428	+	0.118589i	−0.00194776	+	0.00496280i	0.929897	+	0.367821i	$0.119896\pi$
$572$	39.8798	+	12.3013i	1.66746	+	0.514343i
$573$	−8.87284	−	4.27294i	−0.370668	−	0.178504i
$574$	−25.5142	+	13.7793i	−1.06494	+	0.575138i
$575$	14.7824	−	7.11883i	0.616469	−	0.296876i
$576$	−38.5468	+	5.80999i	−1.60612	+	0.242083i
$577$	−7.07883	−	4.82626i	−0.294695	−	0.200920i	0.406942	−	0.913454i	$-0.366595\pi$
$577$	−7.07883	−	4.82626i	−0.294695	−	0.200920i	−0.701638	+	0.712534i	$0.747547\pi$
$578$	−33.4642	+	31.0502i	−1.39193	+	1.29152i
$579$	5.67455	−	3.86884i	0.235826	−	0.160784i
$580$	−0.751325	+	3.29177i	−0.0311971	+	0.136683i
$581$	21.2007	−	7.63293i	0.879552	−	0.316667i
$582$	6.66382	+	29.1961i	0.276224	+	1.21022i
$583$	11.8172	+	10.9647i	0.489417	+	0.454112i
$584$	6.01147	+	0.906083i	0.248756	+	0.0374940i
$585$	0.755902	−	0.233165i	0.0312527	−	0.00964018i
$586$	−5.38098	+	71.8042i	−0.222286	+	2.96620i
$587$	37.2781			1.53863			0.769317	−	0.638868i	$-0.220597\pi$
$587$	37.2781			1.53863			0.769317	+	0.638868i	$0.220597\pi$
$588$	−6.61913	−	39.1302i	−0.272968	−	1.61370i
$589$	−4.12135			−0.169817
$590$	0.423949	−	5.65720i	0.0174537	−	0.232903i
$591$	13.3775	−	4.12640i	0.550275	−	0.169737i
$592$	−57.9590	−	8.73591i	−2.38210	−	0.359044i
$593$	15.2016	+	14.1050i	0.624255	+	0.579224i	0.927562	−	0.373669i	$-0.121900\pi$
$593$	15.2016	+	14.1050i	0.624255	+	0.579224i	−0.303307	+	0.952893i	$0.598091\pi$
$594$	−0.910954	−	3.99115i	−0.0373769	−	0.163759i
$595$	−0.0971434	+	0.285833i	−0.00398249	+	0.0117180i
$596$	3.60799	−	15.8076i	0.147789	−	0.647506i
$597$	−14.4466	+	9.84955i	−0.591261	+	0.403115i
$598$	33.3415	−	30.9364i	1.36343	−	1.26508i
$599$	−9.05227	−	6.17173i	−0.369866	−	0.252170i	0.364095	−	0.931362i	$-0.381378\pi$
$599$	−9.05227	−	6.17173i	−0.369866	−	0.252170i	−0.733961	+	0.679191i	$0.762331\pi$
$600$	49.9892	−	7.53465i	2.04080	−	0.307601i
$601$	34.4798	−	16.6046i	1.40646	−	0.677315i	0.431999	−	0.901874i	$-0.357809\pi$
$601$	34.4798	−	16.6046i	1.40646	−	0.677315i	0.974460	+	0.224559i	$0.0720942\pi$
$602$	28.2520	−	39.0090i	1.15147	−	1.58989i
$603$	5.64818	+	2.72002i	0.230012	+	0.110768i
$604$	28.5566	+	8.80856i	1.16195	+	0.358415i
$605$	−0.511573	+	1.30347i	−0.0207984	+	0.0529935i
$606$	16.9464	+	29.3521i	0.688402	+	1.19235i
$607$	3.50859	−	6.07705i	0.142409	−	0.246660i	−0.785994	−	0.618234i	$-0.787848\pi$
$607$	3.50859	−	6.07705i	0.142409	−	0.246660i	0.928403	+	0.371574i	$0.121182\pi$
$608$	−91.2786	−	114.460i	−3.70184	−	4.64196i
$609$	9.72917	−	1.93156i	0.394246	−	0.0782709i
$610$	0.987787	−	1.23865i	0.0399943	−	0.0501513i
$611$	−18.7937	−	47.8855i	−0.760310	−	1.93724i
$612$	−0.304325	−	4.06094i	−0.0123016	−	0.164154i
$613$	−2.56850	−	34.2742i	−0.103741	−	1.38432i	−0.769734	−	0.638365i	$-0.779611\pi$
$613$	−2.56850	−	34.2742i	−0.103741	−	1.38432i	0.665993	−	0.745958i	$-0.268008\pi$
$614$	−6.50371	−	16.5712i	−0.262468	−	0.668758i
$615$	0.391969	−	0.491514i	0.0158057	−	0.0198197i
$616$	−1.12916	+	39.7282i	−0.0454952	+	1.60069i
$617$	−21.5991	−	27.0844i	−0.869548	−	1.09038i	−0.995157	−	0.0982984i	$-0.968660\pi$
$617$	−21.5991	−	27.0844i	−0.869548	−	1.09038i	0.125609	−	0.992080i	$-0.459911\pi$
$618$	7.15231	−	12.3882i	0.287708	−	0.498325i
$619$	7.97891	+	13.8199i	0.320699	+	0.555468i	0.980633	−	0.195857i	$-0.0627487\pi$
$619$	7.97891	+	13.8199i	0.320699	+	0.555468i	−0.659933	+	0.751324i	$0.729415\pi$
$620$	−0.242787	+	0.618612i	−0.00975057	+	0.0248440i
$621$	−3.15157	−	0.972130i	−0.126468	−	0.0390102i
$622$	78.4930	+	37.8002i	3.14728	+	1.51565i
$623$	−0.399144	+	2.21847i	−0.0159913	+	0.0888810i
$624$	75.3909	−	36.3063i	3.01805	−	1.45342i
$625$	−24.3471	+	3.66974i	−0.973885	+	0.146789i
$626$	44.7560	+	30.5141i	1.78881	+	1.21959i
$627$	6.05238	−	5.61579i	0.241709	−	0.224273i
$628$	−73.8991	+	50.3836i	−2.94890	+	2.01052i
$629$	0.557531	−	2.44270i	0.0222302	−	0.0973969i
$630$	0.628078	+	0.979923i	0.0250232	+	0.0390411i
$631$	−1.01937	−	4.46616i	−0.0405805	−	0.177795i	0.950576	−	0.310491i	$-0.100494\pi$
$631$	−1.01937	−	4.46616i	−0.0405805	−	0.177795i	−0.991157	+	0.132696i	$0.957636\pi$
$632$	−0.474140	−	0.439937i	−0.0188603	−	0.0174998i
$633$	−22.3551	−	3.36948i	−0.888533	−	0.133925i
$634$	−68.1562	+	21.0234i	−2.70683	+	0.834946i
$635$	−0.0998972	+	1.33304i	−0.00396430	+	0.0528999i
$636$	61.8265			2.45158
$637$	15.6863	+	31.1292i	0.621513	+	1.23338i
$638$	−15.3478			−0.607626
$639$	0.0568403	−	0.758481i	0.00224857	−	0.0300050i
$640$	−8.42971	+	2.60022i	−0.333213	+	0.102783i
$641$	0.955720	+	0.144052i	0.0377487	+	0.00568970i	0.167889	−	0.985806i	$-0.446305\pi$
$641$	0.955720	+	0.144052i	0.0377487	+	0.00568970i	−0.130141	+	0.991496i	$0.541543\pi$
$642$	−7.79666	−	7.23424i	−0.307710	−	0.285513i
$643$	−7.16570	−	31.3950i	−0.282588	−	1.23810i	−0.894463	−	0.447143i	$-0.852442\pi$
$643$	−7.16570	−	31.3950i	−0.282588	−	1.23810i	0.611875	−	0.790954i	$-0.290416\pi$
$644$	42.1232	+	25.9428i	1.65989	+	1.02229i
$645$	−0.232364	+	1.01805i	−0.00914931	+	0.0400858i
$646$	9.17990	−	6.25875i	0.361179	−	0.246247i
$647$	4.50360	−	4.17873i	0.177055	−	0.164283i	−0.586667	−	0.809828i	$-0.699560\pi$
$647$	4.50360	−	4.17873i	0.177055	−	0.164283i	0.763722	+	0.645545i	$0.223370\pi$
$648$	−8.39628	−	5.72448i	−0.329837	−	0.224879i
$649$	18.8498	−	2.84114i	0.739918	−	0.111525i
$650$	−61.8116	+	29.7669i	−2.42445	+	1.16755i
$651$	1.95017	−	0.0905243i	0.0764333	−	0.00354793i
$652$	79.9213	+	38.4881i	3.12996	+	1.50731i
$653$	21.1621	+	6.52765i	0.828137	+	0.255447i	0.679714	−	0.733477i	$-0.262104\pi$
$653$	21.1621	+	6.52765i	0.828137	+	0.255447i	0.148423	+	0.988924i	$0.452580\pi$
$654$	2.55864	−	6.51930i	0.100051	−	0.254925i
$655$	0.314026	+	0.543908i	0.0122700	+	0.0212523i
$656$	33.2506	−	57.5918i	1.29822	−	2.24858i
$657$	0.372998	+	0.467725i	0.0145520	+	0.0182477i
$658$	60.4936	−	45.4916i	2.35829	−	1.77345i
$659$	−12.7464	+	15.9834i	−0.496528	+	0.622627i	−0.965442	−	0.260617i	$-0.916074\pi$
$659$	−12.7464	+	15.9834i	−0.496528	+	0.622627i	0.468914	+	0.883244i	$0.344645\pi$
$660$	−0.486382	−	1.23928i	−0.0189324	−	0.0482390i
$661$	2.01235	+	26.8529i	0.0782712	+	1.04446i	0.888661	+	0.458565i	$0.151636\pi$
$661$	2.01235	+	26.8529i	0.0782712	+	1.04446i	−0.810390	+	0.585891i	$0.800745\pi$
$662$	−2.72413	−	36.3509i	−0.105876	−	1.41282i
$663$	1.30679	+	3.32966i	0.0507517	+	0.129313i
$664$	−53.9607	+	67.6646i	−2.09408	+	2.62590i
$665$	−1.07819	+	2.08517i	−0.0418104	+	0.0808595i
$666$	−6.02291	−	7.55249i	−0.233383	−	0.292653i
$667$	−6.18236	+	10.7082i	−0.239382	+	0.414621i
$668$	28.7511	+	49.7983i	1.11241	+	1.92675i
$669$	0.551332	−	1.40477i	0.0213157	−	0.0543116i
$670$	2.63536	+	0.812901i	0.101813	+	0.0314051i
$671$	4.79634	+	2.30979i	0.185161	+	0.0891686i
$672$	45.7060	+	52.1561i	1.76315	+	2.01196i
$673$	25.2078	−	12.1395i	0.971691	−	0.467942i	0.120451	−	0.992719i	$-0.461566\pi$
$673$	25.2078	−	12.1395i	0.971691	−	0.467942i	0.851239	+	0.524778i	$0.175852\pi$
$674$	37.7294	−	5.68679i	1.45328	−	0.219047i
$675$	4.11034	+	2.80239i	0.158207	+	0.107864i
$676$	−49.0311	+	45.4942i	−1.88581	+	1.74978i
$677$	26.7394	−	18.2306i	1.02768	−	0.700660i	0.0727063	−	0.997353i	$-0.476836\pi$
$677$	26.7394	−	18.2306i	1.02768	−	0.700660i	0.954973	+	0.296694i	$0.0958840\pi$
$678$	1.88768	−	8.27046i	0.0724958	−	0.317625i
$679$	20.0478	−	20.4114i	0.769365	−	0.783316i
$680$	−0.258018	−	1.13045i	−0.00989455	−	0.0433509i
$681$	1.35985	+	1.26176i	0.0521095	+	0.0483506i
$682$	−2.98703	−	0.450222i	−0.114379	−	0.0172399i
$683$	2.58965	−	0.798802i	0.0990903	−	0.0305653i	−0.244814	−	0.969570i	$-0.578727\pi$
$683$	2.58965	−	0.798802i	0.0990903	−	0.0305653i	0.343904	+	0.939005i	$0.388251\pi$
$684$	2.36637	−	31.5771i	0.0904806	−	1.20738i
$685$	−2.21336			−0.0845681
$686$	−37.9602	+	34.4912i	−1.44933	+	1.31688i
$687$	−15.0143			−0.572830
$688$	−8.25469	+	110.151i	−0.314707	+	4.19947i
$689$	−51.8924	+	16.0067i	−1.97694	+	0.609807i
$690$	−1.43470	−	0.216247i	−0.0546183	−	0.00823238i
$691$	−2.29213	−	2.12679i	−0.0871968	−	0.0809068i	0.635370	−	0.772208i	$-0.280847\pi$
$691$	−2.29213	−	2.12679i	−0.0871968	−	0.0809068i	−0.722567	+	0.691301i	$0.757038\pi$
$692$	−31.0660	−	136.109i	−1.18095	−	5.17410i
$693$	−2.74056	+	2.79026i	−0.104105	+	0.105993i
$694$	9.02531	−	39.5424i	0.342596	−	1.50101i
$695$	2.57451	−	1.75527i	0.0976566	−	0.0665811i
$696$	−27.9278	+	25.9132i	−1.05860	+	0.982239i
$697$	2.34874	+	1.60134i	0.0889649	+	0.0606552i
$698$	−54.0937	+	8.15331i	−2.04748	+	0.308607i
$699$	−13.3700	+	6.43867i	−0.505701	+	0.243533i
$700$	−49.1806	−	56.1210i	−1.85885	−	2.12118i
$701$	25.1584	+	12.1157i	0.950220	+	0.457602i	0.843763	−	0.536715i	$-0.180335\pi$
$701$	25.1584	+	12.1157i	0.950220	+	0.457602i	0.106457	+	0.994317i	$0.466049\pi$
$702$	13.1781	+	4.06489i	0.497373	+	0.153419i
$703$	7.11773	−	18.1357i	0.268450	−	0.684000i
$704$	−28.8124	−	49.9046i	−1.08591	−	1.88085i
$705$	−0.820490	+	1.42113i	−0.0309014	+	0.0535228i
$706$	16.5536	+	20.7575i	0.623002	+	0.781220i
$707$	14.8723	−	28.7624i	0.559330	−	1.08172i
$708$	45.5837	−	57.1602i	1.71314	−	2.14821i
$709$	14.5618	+	37.1029i	0.546880	+	1.39343i	0.890786	+	0.454423i	$0.150155\pi$
$709$	14.5618	+	37.1029i	0.546880	+	1.39343i	−0.343906	+	0.939004i	$0.611750\pi$
$710$	−0.0250054	−	0.333674i	−0.000938436	−	0.0125226i
$711$	−0.00475648	−	0.0634709i	−0.000178382	−	0.00238034i
$712$	−3.16302	−	8.05923i	−0.118539	−	0.302032i
$713$	−1.51734	+	1.90269i	−0.0568250	+	0.0712562i
$714$	−4.20635	+	3.16320i	−0.157419	+	0.118380i
$715$	0.729079	+	0.914236i	0.0272660	+	0.0341905i
$716$	50.5710	−	87.5916i	1.88993	−	3.27345i
$717$	3.65249	+	6.32631i	0.136405	+	0.236260i
$718$	16.3351	−	41.6212i	0.609622	−	1.55329i
$719$	41.0406	+	12.6593i	1.53056	+	0.472114i	0.941793	−	0.336193i	$-0.109139\pi$
$719$	41.0406	+	12.6593i	1.53056	+	0.472114i	0.588762	+	0.808306i	$0.299615\pi$
$720$	−2.40497	−	1.15817i	−0.0896278	−	0.0431625i
$721$	−13.6514	+	0.633677i	−0.508404	+	0.0235994i
$722$	30.4300	−	14.6543i	1.13249	−	0.545376i
$723$	5.69057	−	0.857715i	0.211634	−	0.0318988i
$724$	−1.97759	−	1.34830i	−0.0734967	−	0.0501092i
$725$	13.6719	−	12.6857i	0.507761	−	0.471134i
$726$	−20.1698	+	13.7515i	−0.748570	+	0.510366i
$727$	0.0236792	−	0.103745i	0.000878213	−	0.00384770i	−0.974487	−	0.224444i	$-0.927943\pi$
$727$	0.0236792	−	0.103745i	0.000878213	−	0.00384770i	0.975365	+	0.220597i	$0.0708004\pi$
$728$	−114.000	−	70.2103i	−4.22513	−	2.60217i
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$	0.192926	+	0.179009i	0.00714049	+	0.00662541i
$731$	−4.66903	−	0.703743i	−0.172690	−	0.0260289i
$732$	19.5101	−	6.01808i	0.721115	−	0.222435i
$733$	−0.0587855	+	0.784438i	−0.00217129	+	0.0289739i	−0.998184	−	0.0602353i	$-0.980815\pi$
$733$	−0.0587855	+	0.784438i	−0.00217129	+	0.0289739i	0.996013	+	0.0892092i	$0.0284340\pi$
$734$	−53.5844			−1.97783
$735$	0.464386	−	1.01036i	0.0171291	−	0.0372677i
$736$	−86.4479			−3.18651
$737$	−0.692528	+	9.24115i	−0.0255096	+	0.340402i
$738$	10.4730	−	3.23050i	0.385517	−	0.118916i
$739$	12.5382	+	1.88984i	0.461227	+	0.0695187i	0.375546	−	0.926804i	$-0.377455\pi$
$739$	12.5382	+	1.88984i	0.461227	+	0.0695187i	0.0856810	+	0.996323i	$0.472693\pi$
$740$	−2.30285	−	2.13673i	−0.0846544	−	0.0785478i
$741$	6.18906	+	27.1160i	0.227361	+	0.996132i
$742$	−43.1174	−	67.2715i	−1.58289	−	2.46961i
$743$	−8.81831	+	38.6356i	−0.323513	+	1.41740i	0.507742	+	0.861509i	$0.330480\pi$
$743$	−8.81831	+	38.6356i	−0.323513	+	1.41740i	−0.831255	+	0.555892i	$0.812377\pi$
$744$	−6.19553	+	4.22404i	−0.227139	+	0.154861i
$745$	0.333031	−	0.309008i	0.0122013	−	0.0113212i
$746$	−21.8952	−	14.9279i	−0.801640	−	0.546549i
$747$	−8.42150	+	1.26934i	−0.308126	+	0.0464426i
$748$	5.42371	−	2.61192i	0.198310	−	0.0955012i
$749$	−1.79928	+	10.0005i	−0.0657444	+	0.365412i
$750$	3.95358	+	1.90394i	0.144364	+	0.0695221i
$751$	−15.5823	−	4.80651i	−0.568607	−	0.175392i	−0.00289640	−	0.999996i	$-0.500922\pi$
$751$	−15.5823	−	4.80651i	−0.568607	−	0.175392i	−0.565711	+	0.824604i	$0.691398\pi$
$752$	−63.4175	+	161.585i	−2.31260	+	5.89240i
$753$	1.47326	+	2.55176i	0.0536885	+	0.0929911i
$754$	25.8511	−	44.7754i	0.941441	−	1.63062i
$755$	0.522070	+	0.654655i	0.0190001	+	0.0238253i
$756$	−0.426159	+	14.9939i	−0.0154992	+	0.545322i
$757$	2.42579	−	3.04185i	0.0881669	−	0.110558i	−0.735791	−	0.677208i	$-0.763190\pi$
$757$	2.42579	−	3.04185i	0.0881669	−	0.110558i	0.823958	+	0.566651i	$0.191761\pi$
$758$	−22.3270	−	56.8883i	−0.810954	−	2.06628i
$759$	−0.364336	−	4.86173i	−0.0132246	−	0.176469i
$760$	−0.673784	−	8.99102i	−0.0244407	−	0.326139i
$761$	12.2832	+	31.2970i	0.445264	+	1.13451i	0.960701	+	0.277586i	$0.0895345\pi$
$761$	12.2832	+	31.2970i	0.445264	+	1.13451i	−0.515437	+	0.856928i	$0.672370\pi$
$762$	−14.5303	+	18.2204i	−0.526376	+	0.660054i
$763$	−6.56271	+	1.30292i	−0.237586	+	0.0471687i
$764$	−34.8115	−	43.6522i	−1.25943	−	1.57928i
$765$	0.0570517	−	0.0988165i	0.00206271	−	0.00357272i
$766$	3.73215	+	6.46427i	0.134848	+	0.233564i
$767$	−23.4609	+	59.7774i	−0.847123	+	2.15844i
$768$	−72.4592	−	22.3507i	−2.61465	−	0.806511i
$769$	16.1710	+	7.78754i	0.583141	+	0.280826i	0.702106	−	0.712072i	$-0.252243\pi$
$769$	16.1710	+	7.78754i	0.583141	+	0.280826i	−0.118965	+	0.992898i	$0.537958\pi$
$770$	−1.00922	+	1.39348i	−0.0363699	+	0.0502177i
$771$	−8.11807	+	3.90946i	−0.292365	+	0.140796i
$772$	38.5024	−	5.80330i	1.38573	−	0.208865i
$773$	−39.1048	−	26.6612i	−1.40650	−	0.958936i	−0.998953	−	0.0457515i	$-0.985432\pi$
$773$	−39.1048	−	26.6612i	−1.40650	−	0.958936i	−0.407547	−	0.913184i	$-0.633616\pi$
$774$	−13.3450	+	12.3823i	−0.479676	+	0.445074i
$775$	3.03298	−	2.06785i	0.108948	−	0.0742794i
$776$	−24.4525	+	107.133i	−0.877792	+	3.84586i
$777$	−2.96968	+	8.73793i	−0.106537	+	0.313471i
$778$	−15.5259	−	68.0235i	−0.556631	−	2.43876i
$779$	16.2035	+	15.0347i	0.580551	+	0.538673i
$780$	4.43469	+	0.668422i	0.158787	+	0.0239334i
$781$	1.07440	−	0.331410i	0.0384452	−	0.0118588i
$782$	0.490279	−	6.54231i	0.0175323	−	0.233953i
$783$	−3.74905			−0.133980
$784$	32.6453	−	113.005i	1.16590	−	4.03588i
$785$	−2.50605			−0.0894447
$786$	−0.818232	+	10.9186i	−0.0291854	+	0.389452i
$787$	8.74001	−	2.69594i	0.311548	−	0.0960997i	−0.135038	−	0.990840i	$-0.543116\pi$
$787$	8.74001	−	2.69594i	0.311548	−	0.0960997i	0.446586	+	0.894741i	$0.352640\pi$
$788$	78.4823	+	11.8293i	2.79582	+	0.421402i
$789$	−11.2412	−	10.4303i	−0.400196	−	0.371328i
$790$	−0.00623073	−	0.0272986i	−0.000221679	−	0.000971241i
$791$	−7.62531	+	2.74536i	−0.271125	+	0.0976138i
$792$	3.34269	−	14.6453i	0.118777	−	0.520397i
$793$	−14.8172	+	10.1022i	−0.526176	+	0.358741i
$794$	18.1540	−	16.8444i	0.644261	−	0.597787i
$795$	1.43132	+	0.975856i	0.0507636	+	0.0346100i
$796$	−98.0219	+	14.7744i	−3.47429	+	0.523666i
$797$	−7.37350	+	3.55089i	−0.261183	+	0.125779i	−0.559893	−	0.828565i	$-0.689158\pi$
$797$	−7.37350	+	3.55089i	−0.261183	+	0.125779i	0.298710	+	0.954344i	$0.403444\pi$
$798$	−36.0083	+	19.4469i	−1.27468	+	0.688411i
$799$	−6.68528	−	3.21946i	−0.236508	−	0.113896i
$800$	124.603	+	38.4349i	4.40538	+	1.35888i
$801$	0.311258	−	0.793072i	0.0109977	−	0.0280218i
$802$	52.3111	+	90.6055i	1.84717	+	3.19939i
$803$	−0.442172	+	0.765864i	−0.0156039	+	0.0270268i
$804$	22.1599	+	27.7876i	0.781519	+	0.979994i
$805$	0.565700	+	1.26545i	0.0199383	+	0.0446014i
$806$	6.34466	−	7.95595i	0.223481	−	0.280236i
$807$	−3.49151	−	8.89623i	−0.122907	−	0.313162i
$808$	9.29402	+	124.020i	0.326963	+	4.36301i
$809$	−0.0625196	−	0.834265i	−0.00219807	−	0.0293312i	0.995997	−	0.0893876i	$-0.0284910\pi$
$809$	−0.0625196	−	0.834265i	−0.00219807	−	0.0293312i	−0.998195	+	0.0600564i	$0.980872\pi$
$810$	−0.160722	−	0.409514i	−0.00564720	−	0.0143888i
$811$	18.1407	−	22.7477i	0.637005	−	0.798779i	−0.353620	−	0.935389i	$-0.615049\pi$
$811$	18.1407	−	22.7477i	0.637005	−	0.798779i	0.990625	+	0.136610i	$0.0436207\pi$
$812$	54.4479	+	14.0661i	1.91075	+	0.493625i
$813$	10.2119	+	12.8053i	0.358147	+	0.449102i
$814$	7.13987	−	12.3666i	0.250252	−	0.433450i
$815$	1.24274	+	2.15248i	0.0435311	+	0.0753981i
$816$	4.40966	−	11.2356i	0.154369	−	0.393325i
$817$	−35.0844	−	10.8221i	−1.22745	−	0.378617i
$818$	−17.2714	−	8.31746i	−0.603880	−	0.290813i
$819$	−3.52418	−	12.6950i	−0.123145	−	0.443601i
$820$	3.21124	−	1.54645i	0.112141	−	0.0540044i
$821$	31.4921	−	4.74666i	1.09908	−	0.165660i	0.425634	−	0.904896i	$-0.360051\pi$
$821$	31.4921	−	4.74666i	1.09908	−	0.165660i	0.673447	+	0.739236i	$0.264813\pi$
$822$	−31.8818	−	21.7367i	−1.11201	−	0.758153i
$823$	24.3761	−	22.6178i	0.849699	−	0.788405i	−0.129442	−	0.991587i	$-0.541319\pi$
$823$	24.3761	−	22.6178i	0.849699	−	0.788405i	0.979141	+	0.203182i	$0.0651282\pi$
$824$	43.3692	−	29.5686i	1.51084	−	1.03007i
$825$	−1.63639	+	7.16950i	−0.0569718	+	0.249610i
$826$	−93.9839	−	9.73509i	−3.27012	−	0.338727i
$827$	7.79416	+	34.1485i	0.271030	+	1.18746i	0.908800	+	0.417232i	$0.137000\pi$
$827$	7.79416	+	34.1485i	0.271030	+	1.18746i	−0.637770	+	0.770227i	$0.720143\pi$
$828$	−13.7068	−	12.7181i	−0.476346	−	0.441984i
$829$	−41.6779	−	6.28194i	−1.44753	−	0.218181i	−0.622215	−	0.782847i	$-0.713767\pi$
$829$	−41.6779	−	6.28194i	−1.44753	−	0.218181i	−0.825319	+	0.564666i	$0.809005\pi$
$830$	−3.58021	+	1.10435i	−0.124271	+	0.0383325i
$831$	1.48014	−	19.7512i	0.0513456	−	0.685160i
$832$	194.121			6.72992
$833$	4.71275	+	1.75255i	0.163287	+	0.0607224i
$834$	54.3218			1.88101
$835$	−0.120402	+	1.60666i	−0.00416670	+	0.0556007i
$836$	44.7296	−	13.7973i	1.54701	−	0.477188i
$837$	−0.729648	−	0.109977i	−0.0252203	−	0.00380135i
$838$	70.6647	+	65.5673i	2.44107	+	2.26498i
$839$	0.399501	+	1.75033i	0.0137923	+	0.0604281i	0.981356	−	0.192200i	$-0.0615622\pi$
$839$	0.399501	+	1.75033i	0.0137923	+	0.0604281i	−0.967563	+	0.252628i	$0.918705\pi$
$840$	0.516311	+	4.23964i	0.0178144	+	0.146282i
$841$	3.32549	−	14.5699i	0.114672	−	0.502411i
$842$	−19.9959	+	13.6329i	−0.689103	+	0.469822i
$843$	−1.49208	+	1.38444i	−0.0513898	+	0.0476828i
$844$	−105.901	−	72.2019i	−3.64526	−	2.48529i
$845$	−1.85317	+	0.279320i	−0.0637509	+	0.00960891i
$846$	−25.7750	+	12.4126i	−0.886163	+	0.426754i
$847$	21.4588	+	9.13377i	0.737334	+	0.313840i
$848$	165.100	+	79.5081i	5.66957	+	2.73032i
$849$	−22.9948	−	7.09297i	−0.789181	−	0.243430i
$850$	−3.61539	+	9.21187i	−0.124007	+	0.315965i
$851$	−5.75212	−	9.96297i	−0.197180	−	0.341526i
$852$	2.15611	−	3.73449i	0.0738670	−	0.127941i
$853$	−14.1630	−	17.7599i	−0.484933	−	0.608086i	0.477824	−	0.878456i	$-0.341426\pi$
$853$	−14.1630	−	17.7599i	−0.484933	−	0.608086i	−0.962757	+	0.270369i	$0.912854\pi$
$854$	−20.1543	−	17.0314i	−0.689666	−	0.582802i
$855$	0.553188	−	0.693676i	0.0189186	−	0.0237232i
$856$	−14.2584	−	36.3299i	−0.487343	−	1.24173i
$857$	1.60926	+	21.4740i	0.0549711	+	0.733538i	0.954791	+	0.297277i	$0.0960786\pi$
$857$	1.60926	+	21.4740i	0.0549711	+	0.733538i	−0.899820	+	0.436261i	$0.856302\pi$
$858$	1.52344	+	20.3290i	0.0520095	+	0.694019i
$859$	8.12797	+	20.7097i	0.277323	+	0.706607i	0.999883	+	0.0152989i	$0.00486999\pi$
$859$	8.12797	+	20.7097i	0.277323	+	0.706607i	−0.722560	+	0.691308i	$0.757035\pi$
$860$	−3.69119	+	4.62861i	−0.125869	+	0.157834i
$861$	−7.99754	−	6.75832i	−0.272556	−	0.230323i
$862$	3.22479	+	4.04375i	0.109837	+	0.137731i
$863$	−27.4119	+	47.4788i	−0.933113	+	1.61620i	−0.155148	+	0.987891i	$0.549585\pi$
$863$	−27.4119	+	47.4788i	−0.933113	+	1.61620i	−0.777965	+	0.628307i	$0.783748\pi$
$864$	−13.1057	−	22.6998i	−0.445867	−	0.772264i
$865$	1.42912	−	3.64134i	0.0485916	−	0.123809i
$866$	−94.5301	−	29.1587i	−3.21226	−	0.990852i
$867$	−14.8516	−	7.15216i	−0.504387	−	0.242900i
$868$	10.1841	+	4.33479i	0.345672	+	0.147132i
$869$	0.0847703	−	0.0408232i	0.00287564	−	0.00138483i
$870$	−1.63088	+	0.245815i	−0.0552919	+	0.00833391i
$871$	−25.7935	−	17.5857i	−0.873978	−	0.595868i
$872$	18.8384	−	17.4795i	0.637950	−	0.591931i
$873$	−8.93462	+	6.09152i	−0.302391	+	0.206167i
$874$	11.3518	−	49.7353i	0.383979	−	1.68232i
$875$	−0.506796	−	4.16151i	−0.0171328	−	0.140685i
$876$	0.754724	+	3.30666i	0.0254998	+	0.111722i
$877$	40.3652	+	37.4535i	1.36304	+	1.26471i	0.932037	+	0.362362i	$0.118030\pi$
$877$	40.3652	+	37.4535i	1.36304	+	1.26471i	0.431000	+	0.902352i	$0.358161\pi$
$878$	−14.8855	−	2.24363i	−0.502362	−	0.0757188i
$879$	−24.8455	+	7.66382i	−0.838018	+	0.258494i
$880$	0.294875	−	3.93484i	0.00994024	−	0.132643i
$881$	−37.6398			−1.26812			−0.634058	−	0.773286i	$-0.718612\pi$
$881$	−37.6398			−1.26812			−0.634058	+	0.773286i	$0.718612\pi$
$882$	16.6116	−	9.99293i	0.559340	−	0.336479i
$883$	−22.5780			−0.759809			−0.379905	−	0.925026i	$-0.624043\pi$
$883$	−22.5780			−0.759809			−0.379905	+	0.925026i	$0.624043\pi$
$884$	−1.51546	+	20.2224i	−0.0509704	+	0.680152i
$885$	1.95749	−	0.603806i	0.0658004	−	0.0202967i
$886$	84.5727	+	12.7473i	2.84127	+	0.428253i
$887$	−9.19397	−	8.53076i	−0.308703	−	0.286435i	0.510572	−	0.859835i	$-0.329434\pi$
$887$	−9.19397	−	8.53076i	−0.308703	−	0.286435i	−0.819276	+	0.573400i	$0.805624\pi$
$888$	−7.88764	−	34.5580i	−0.264692	−	1.15969i
$889$	22.1459	+	2.29393i	0.742750	+	0.0769359i
$890$	0.0834008	−	0.365403i	0.00279560	−	0.0122483i
$891$	1.22138	−	0.832720i	0.0409176	−	0.0278972i
$892$	6.27176	−	5.81935i	0.209994	−	0.194846i
$893$	−47.6717	−	32.5020i	−1.59527	−	1.08764i
$894$	7.83173	−	1.18044i	0.261932	−	0.0394800i
$895$	2.55327	−	1.22959i	0.0853465	−	0.0411007i
$896$	39.3012	+	141.573i	1.31296	+	4.72963i
$897$	14.7972	+	7.12594i	0.494063	+	0.237928i
$898$	16.7827	+	5.17679i	0.560047	+	0.172752i
$899$	−1.01067	+	2.57516i	−0.0337079	+	0.0858863i
$900$	14.1021	+	24.4255i	0.470069	+	0.814183i
$901$	−3.91658	+	6.78372i	−0.130480	+	0.225999i
$902$	10.1014	+	12.6668i	0.336340	+	0.421757i
$903$	16.8392	+	4.35026i	0.560373	+	0.144768i
$904$	19.4082	−	24.3371i	0.645508	−	0.809441i
$905$	−0.0245011	−	0.0624278i	−0.000814445	−	0.00207517i
$906$	1.09089	+	14.5569i	0.0362424	+	0.483621i
$907$	−0.269698	−	3.59887i	−0.00895518	−	0.119499i	0.990935	−	0.134345i	$-0.0428931\pi$
$907$	−0.269698	−	3.59887i	−0.00895518	−	0.119499i	−0.999890	+	0.0148465i	$0.995274\pi$
$908$	3.84233	+	9.79009i	0.127512	+	0.324896i
$909$	−7.63056	+	9.56842i	−0.253090	+	0.317364i
$910$	−2.36543	−	5.29140i	−0.0784134	−	0.175408i
$911$	17.7004	+	22.1956i	0.586440	+	0.735373i	0.983196	−	0.182551i	$-0.0584355\pi$
$911$	17.7004	+	22.1956i	0.586440	+	0.735373i	−0.396756	+	0.917924i	$0.629864\pi$
$912$	46.9269	−	81.2797i	1.55390	−	2.69144i
$913$	−6.29478	−	10.9029i	−0.208327	−	0.360833i
$914$	27.4515	−	69.9452i	0.908014	−	2.31358i
$915$	0.546658	+	0.168622i	0.0180720	+	0.00557446i
$916$	−76.6927	−	36.9332i	−2.53400	−	1.22031i
$917$	9.20391	−	4.97072i	0.303940	−	0.164148i
$918$	1.79223	−	0.863094i	0.0591525	−	0.0284863i
$919$	−38.5354	+	5.80828i	−1.27117	+	0.191597i	−0.749759	−	0.661711i	$-0.769831\pi$
$919$	−38.5354	+	5.80828i	−1.27117	+	0.191597i	−0.521407	+	0.853308i	$0.674593\pi$
$920$	−4.39891	−	2.99913i	−0.145028	−	0.0988783i
$921$	4.71211	−	4.37220i	0.155269	−	0.144069i
$922$	−7.45922	+	5.08561i	−0.245656	+	0.167486i
$923$	−0.842824	+	3.69265i	−0.0277419	+	0.121545i
$924$	−20.8625	+	7.51117i	−0.686325	+	0.247099i
$925$	3.86135	+	16.9177i	0.126960	+	0.556249i
$926$	−60.1622	−	55.8223i	−1.97705	−	1.83444i
$927$	5.10760	+	0.769847i	0.167756	+	0.0252851i
$928$	−93.9024	+	28.9651i	−3.08250	+	0.950825i
$929$	−0.357723	+	4.77348i	−0.0117365	+	0.156613i	0.988256	+	0.152806i	$0.0488309\pi$
$929$	−0.357723	+	4.77348i	−0.0117365	+	0.156613i	−0.999993	+	0.00380713i	$0.998788\pi$
$930$	−0.324615			−0.0106446
$931$	34.2050	+	18.9370i	1.12102	+	0.620636i
$932$	−84.1323			−2.75585
$933$	−2.35090	+	31.3706i	−0.0769652	+	1.02703i
$934$	91.8441	−	28.3301i	3.00523	−	0.926991i
$935$	0.166788	+	0.0251392i	0.00545454	+	0.000822140i
$936$	37.0955	+	34.4196i	1.21251	+	1.12504i
$937$	2.04967	+	8.98021i	0.0669599	+	0.293371i	0.997310	−	0.0733026i	$-0.0233539\pi$
$937$	2.04967	+	8.98021i	0.0669599	+	0.293371i	−0.930350	+	0.366673i	$0.880497\pi$
$938$	14.7807	−	43.4904i	0.482607	−	1.42001i
$939$	−4.35246	+	19.0694i	−0.142037	+	0.622306i
$940$	−7.68685	+	5.24081i	−0.250717	+	0.170936i
$941$	18.6257	−	17.2821i	0.607180	−	0.563381i	−0.315511	−	0.948922i	$-0.602176\pi$
$941$	18.6257	−	17.2821i	0.607180	−	0.563381i	0.922691	+	0.385541i	$0.125985\pi$
$942$	−36.0978	−	24.6111i	−1.17613	−	0.801872i
$943$	12.9066	−	1.94536i	0.420296	−	0.0633495i
$944$	195.233	−	94.0193i	6.35430	−	3.06007i
$945$	−0.246526	+	0.340390i	−0.00801948	+	0.0110729i
$946$	−24.2458	−	11.6762i	−0.788300	−	0.379625i
$947$	−29.2549	−	9.02394i	−0.950656	−	0.293239i	−0.219626	−	0.975584i	$-0.570484\pi$
$947$	−29.2549	−	9.02394i	−0.950656	−	0.293239i	−0.731030	+	0.682345i	$0.760960\pi$
$948$	0.131834	−	0.335909i	0.00428178	−	0.0109098i
$949$	−1.48954	−	2.57996i	−0.0483526	−	0.0837492i
$950$	−38.4744	+	66.6397i	−1.24828	+	2.16208i
$951$	−16.0579	−	20.1360i	−0.520714	−	0.652954i
$952$	−18.9426	+	3.76073i	−0.613932	+	0.121886i
$953$	24.2399	−	30.3958i	0.785207	−	0.984618i	−0.214762	−	0.976666i	$-0.568898\pi$
$953$	24.2399	−	30.3958i	0.785207	−	0.984618i	0.999968	−	0.00795142i	$-0.00253104\pi$
$954$	11.0335	+	28.1130i	0.357224	+	0.910192i
$955$	−0.116908	−	1.56003i	−0.00378306	−	0.0504814i
$956$	3.09496	+	41.2994i	0.100098	+	1.33572i
$957$	−2.02471	−	5.15888i	−0.0654496	−	0.166763i
$958$	39.1646	−	49.1108i	1.26535	−	1.58670i
$959$	−1.04734	+	36.8493i	−0.0338203	+	1.18993i
$960$	−3.86092	−	4.84144i	−0.124611	−	0.156257i
$961$	15.2278	−	26.3753i	0.491218	−	0.850815i
$962$	24.0521	+	41.6594i	0.775470	+	1.34315i
$963$	1.40311	−	3.57506i	0.0452145	−	0.115205i
$964$	31.1772	+	9.61690i	1.00415	+	0.309739i
$965$	0.982950	+	0.473364i	0.0316423	+	0.0152381i
$966$	−4.27910	+	23.7835i	−0.137678	+	0.765222i
$967$	2.40379	−	1.15760i	0.0773005	−	0.0372260i	−0.394834	−	0.918752i	$-0.629198\pi$
$967$	2.40379	−	1.15760i	0.0773005	−	0.0372260i	0.472135	+	0.881526i	$0.343484\pi$
$968$	−88.5761	+	13.3507i	−2.84694	+	0.429108i
$969$	3.31479	+	2.25999i	0.106486	+	0.0726013i
$970$	−3.48725	+	3.23569i	−0.111969	+	0.103892i
$971$	−34.8274	+	23.7449i	−1.11766	+	0.762010i	−0.973759	−	0.227582i	$-0.926918\pi$
$971$	−34.8274	+	23.7449i	−1.11766	+	0.762010i	−0.143904	+	0.989592i	$0.545966\pi$
$972$	1.26157	−	5.52729i	0.0404648	−	0.177288i
$973$	−28.0045	−	43.6925i	−0.897784	−	1.40072i
$974$	−18.8625	−	82.6419i	−0.604393	−	2.64802i
$975$	−18.1599	−	16.8499i	−0.581582	−	0.539629i
$976$	59.8387	+	9.01923i	1.91539	+	0.288698i
$977$	−3.60479	+	1.11193i	−0.115327	+	0.0355738i	−0.351882	−	0.936044i	$-0.614458\pi$
$977$	−3.60479	+	1.11193i	−0.115327	+	0.0355738i	0.236554	+	0.971618i	$0.423982\pi$
$978$	−3.23810	+	43.2094i	−0.103543	+	1.38169i
$979$	1.25940			0.0402507
$980$	4.85744	−	4.01857i	0.155165	−	0.128369i
$981$	2.52888			0.0807410
$982$	1.64201	−	21.9111i	0.0523987	−	0.699212i
$983$	57.6292	−	17.7763i	1.83809	−	0.566975i	0.838324	−	0.545172i	$-0.183536\pi$
$983$	57.6292	−	17.7763i	1.83809	−	0.566975i	0.999762	−	0.0218029i	$-0.00694064\pi$
$984$	39.7676	+	5.99401i	1.26775	+	0.191082i
$985$	1.63020	+	1.51260i	0.0519424	+	0.0481955i
$986$	−1.65950	−	7.27073i	−0.0528492	−	0.231547i
$987$	23.2716	+	14.3325i	0.740743	+	0.456208i
$988$	−35.0885	+	153.733i	−1.11631	+	4.89089i
$989$	−17.9131	+	12.2129i	−0.569603	+	0.388348i
$990$	0.476712	−	0.442324i	0.0151509	−	0.0140580i
$991$	22.3240	+	15.2202i	0.709145	+	0.483487i	0.863384	−	0.504547i	$-0.168340\pi$
$991$	22.3240	+	15.2202i	0.709145	+	0.483487i	−0.154239	+	0.988034i	$0.549293\pi$
$992$	−19.1252	+	2.88266i	−0.607225	+	0.0915244i
$993$	11.8593	−	5.71115i	0.376344	−	0.181238i
$994$	−5.56703	+	0.258414i	−0.176576	+	0.00819639i
$995$	−2.50246	−	1.20512i	−0.0793332	−	0.0382049i
$996$	−46.1393	−	14.2321i	−1.46198	−	0.450961i
$997$	16.1618	−	41.1795i	0.511848	−	1.30417i	−0.408389	−	0.912808i	$-0.633909\pi$
$997$	16.1618	−	41.1795i	0.511848	−	1.30417i	0.920238	−	0.391360i	$-0.127995\pi$
$998$	46.7163	+	80.9149i	1.47878	+	2.56132i
$999$	1.74407	−	3.02083i	0.0551801	−	0.0955747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.2.m.a.121.1	✓	48
3.2	odd	2		441.2.bb.c.415.4		48
49.9	even	21		7203.2.a.i.1.1		24
49.32	even	21	inner	147.2.m.a.130.1	yes	48
49.40	odd	42		7203.2.a.k.1.1		24
147.32	odd	42		441.2.bb.c.424.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.121.1	✓	48	1.1	even	1	trivial
147.2.m.a.130.1	yes	48	49.32	even	21	inner
441.2.bb.c.415.4		48	3.2	odd	2
441.2.bb.c.424.4		48	147.32	odd	42
7203.2.a.i.1.1		24	49.9	even	21
7203.2.a.k.1.1		24	49.40	odd	42

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.m (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.206956 + 2.76163i) q^{2} +(-0.955573 + 0.294755i) q^{3} +(-5.60611 - 0.844986i) q^{4} +(-0.116448 - 0.108048i) q^{5} +(-0.616244 - 2.69994i) q^{6} +(-1.85394 + 1.88756i) q^{7} +(2.26127 - 9.90726i) q^{8} +(0.826239 - 0.563320i) q^{9} +(0.322487 - 0.299224i) q^{10} +(1.22138 + 0.832720i) q^{11} +(5.60611 - 0.844986i) q^{12} +(-4.48658 + 2.16062i) q^{13} +(-4.82907 - 5.51055i) q^{14} +(0.143122 + 0.0689238i) q^{15} +(16.0571 + 4.95296i) q^{16} +(-0.262423 + 0.668642i) q^{17} +(1.38469 + 2.39835i) q^{18} +(-2.79266 + 4.83703i) q^{19} +(0.561520 + 0.704124i) q^{20} +(1.21521 - 2.35016i) q^{21} +(-2.55244 + 3.20065i) q^{22} +(1.20493 + 3.07011i) q^{23} +(0.759411 + 10.1336i) q^{24} +(-0.371765 - 4.96086i) q^{25} +(-5.03832 - 12.8374i) q^{26} +(-0.623490 + 0.781831i) q^{27} +(11.9884 - 9.01534i) q^{28} +(2.33749 + 2.93113i) q^{29} +(-0.219962 + 0.380985i) q^{30} +(0.368945 + 0.639031i) q^{31} +(-9.57613 + 24.3996i) q^{32} +(-1.41256 - 0.435718i) q^{33} +(-1.79223 - 0.863094i) q^{34} +(0.419834 - 0.0194881i) q^{35} +(-5.10799 + 2.45988i) q^{36} +(-3.44919 + 0.519882i) q^{37} +(-12.7801 - 8.71335i) q^{38} +(3.65040 - 3.38708i) q^{39} +(-1.33377 + 0.909352i) q^{40} +(0.880638 - 3.85833i) q^{41} +(6.23879 + 3.84234i) q^{42} +(1.46276 + 6.40876i) q^{43} +(-6.14353 - 5.70037i) q^{44} +(-0.157079 - 0.0236758i) q^{45} +(-8.72787 + 2.69219i) q^{46} +(-0.771974 + 10.3013i) q^{47} -16.8036 q^{48} +(-0.125788 - 6.99887i) q^{49} +13.7770 q^{50} +(0.0536783 - 0.716287i) q^{51} +(26.9780 - 8.32160i) q^{52} +(10.7834 + 1.62534i) q^{53} +(-2.03010 - 1.88365i) q^{54} +(-0.0522529 - 0.228935i) q^{55} +(14.5083 + 22.6358i) q^{56} +(1.24285 - 5.44528i) q^{57} +(-8.57844 + 5.84868i) q^{58} +(9.45312 - 8.77121i) q^{59} +(-0.744117 - 0.507330i) q^{60} +(3.56105 - 0.536742i) q^{61} +(-1.84112 + 0.886639i) q^{62} +(-0.468498 + 2.60394i) q^{63} +(-35.1217 - 16.9137i) q^{64} +(0.755902 + 0.233165i) q^{65} +(1.49563 - 3.81080i) q^{66} +(3.13450 + 5.42912i) q^{67} +(2.03616 - 3.52674i) q^{68} +(-2.05633 - 2.57855i) q^{69} +(-0.0330681 + 1.16346i) q^{70} +(0.474231 - 0.594667i) q^{71} +(-3.71261 - 9.45958i) q^{72} +(0.0447067 + 0.596570i) q^{73} +(-0.721892 - 9.63298i) q^{74} +(1.81749 + 4.63088i) q^{75} +(19.7432 - 24.7572i) q^{76} +(-3.83617 + 0.761608i) q^{77} +(8.59838 + 10.7820i) q^{78} +(0.0318244 - 0.0551215i) q^{79} +(-1.33466 - 2.31169i) q^{80} +(0.365341 - 0.930874i) q^{81} +(10.4730 + 3.23050i) q^{82} +(-7.67321 - 3.69522i) q^{83} +(-8.79845 + 12.1484i) q^{84} +(0.102804 - 0.0495076i) q^{85} +(-18.0014 + 2.71327i) q^{86} +(-3.09761 - 2.11191i) q^{87} +(11.0118 - 10.2175i) q^{88} +(0.703926 - 0.479929i) q^{89} +(0.0978923 - 0.428894i) q^{90} +(4.23955 - 12.4744i) q^{91} +(-4.16077 - 18.2295i) q^{92} +(-0.540912 - 0.501893i) q^{93} +(-28.2886 - 4.26382i) q^{94} +(0.847828 - 0.261520i) q^{95} +(1.95879 - 26.1382i) q^{96} -10.8136 q^{97} +(19.3543 + 1.10108i) q^{98} +1.47824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 4 q^{3} + 3 q^{4} - 2 q^{6} + 6 q^{8} + 4 q^{9} + 30 q^{10} - 9 q^{11} - 3 q^{12} - 42 q^{14} - 7 q^{15} + 29 q^{16} - 5 q^{17} + 6 q^{18} - 26 q^{19} - 5 q^{20} + 7 q^{21} + q^{22} - 4 q^{23}+ \cdots - 24 q^{99}+O(q^{100}) \) 48 * q - q^2 - 4 * q^3 + 3 * q^4 - 2 * q^6 + 6 * q^8 + 4 * q^9 + 30 * q^10 - 9 * q^11 - 3 * q^12 - 42 * q^14 - 7 * q^15 + 29 * q^16 - 5 * q^17 + 6 * q^18 - 26 * q^19 - 5 * q^20 + 7 * q^21 + q^22 - 4 * q^23 - 18 * q^24 - 56 * q^25 - 62 * q^26 + 8 * q^27 + 7 * q^28 + 12 * q^29 + 12 * q^30 - 36 * q^31 - 14 * q^32 + 16 * q^33 - 76 * q^34 + 7 * q^35 - 6 * q^36 - 20 * q^37 - 60 * q^38 + 14 * q^39 + 28 * q^40 + 41 * q^41 + 28 * q^42 + 12 * q^43 + 44 * q^44 + 14 * q^45 + 16 * q^46 + 13 * q^47 - 12 * q^48 - 84 * q^49 - 12 * q^50 - 2 * q^51 + 92 * q^52 + 14 * q^53 + q^54 - 38 * q^55 + 105 * q^56 + 18 * q^57 + 3 * q^58 + 57 * q^59 + 36 * q^60 + 11 * q^61 - 16 * q^62 - 7 * q^63 - 110 * q^64 + 21 * q^65 + 11 * q^66 + 34 * q^67 + 22 * q^68 - 8 * q^69 + 6 * q^71 - 24 * q^72 - 69 * q^73 - 90 * q^74 - 42 * q^75 - 49 * q^76 + 2 * q^78 + 34 * q^79 + 55 * q^80 + 4 * q^81 + 91 * q^82 + 28 * q^83 + 28 * q^84 - 44 * q^85 - 26 * q^86 - 29 * q^87 + 45 * q^88 + 11 * q^89 + 24 * q^90 + 84 * q^92 + q^93 + 90 * q^94 + 150 * q^95 - 35 * q^96 + 124 * q^97 + 119 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

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