LMFDB - Embedded newform 41.2.g.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,2,Mod(2,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("41.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	41.g (of order $20$, degree $8$, 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:	$0.327386648287$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	41.5
Dual form			41.2.g.a.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.522120 - 0.718637i) q^{2} +(-0.983583 - 0.983583i) q^{3} +(0.374204 - 1.15168i) q^{4} +(1.02071 + 0.331648i) q^{5} +(-0.193291 + 1.22039i) q^{6} +(0.625712 + 3.95059i) q^{7} +(-2.71264 + 0.881390i) q^{8} -1.06513i q^{9} +O(q^{10})$	\(q+(-0.522120 - 0.718637i) q^{2} +(-0.983583 - 0.983583i) q^{3} +(0.374204 - 1.15168i) q^{4} +(1.02071 + 0.331648i) q^{5} +(-0.193291 + 1.22039i) q^{6} +(0.625712 + 3.95059i) q^{7} +(-2.71264 + 0.881390i) q^{8} -1.06513i q^{9} +(-0.294598 - 0.906679i) q^{10} +(-1.14123 + 2.23980i) q^{11} +(-1.50084 + 0.764715i) q^{12} +(4.25204 + 0.673457i) q^{13} +(2.51234 - 2.51234i) q^{14} +(-0.677748 - 1.33015i) q^{15} +(0.0903637 + 0.0656531i) q^{16} +(-4.26144 - 2.17131i) q^{17} +(-0.765440 + 0.556125i) q^{18} +(0.967006 - 0.153159i) q^{19} +(0.763907 - 1.05143i) q^{20} +(3.27029 - 4.50117i) q^{21} +(2.20546 - 0.349311i) q^{22} +(-1.78427 + 1.29635i) q^{23} +(3.53503 + 1.80119i) q^{24} +(-3.11323 - 2.26189i) q^{25} +(-1.73611 - 3.40730i) q^{26} +(-3.99839 + 3.99839i) q^{27} +(4.78397 + 0.757706i) q^{28} +(1.83197 - 0.933434i) q^{29} +(-0.602033 + 1.18156i) q^{30} +(-2.02631 - 6.23635i) q^{31} +5.60526i q^{32} +(3.32552 - 1.08053i) q^{33} +(0.664599 + 4.19611i) q^{34} +(-0.671536 + 4.23991i) q^{35} +(-1.22669 - 0.398575i) q^{36} +(-3.34992 + 10.3100i) q^{37} +(-0.614959 - 0.614959i) q^{38} +(-3.51983 - 4.84464i) q^{39} -3.06112 q^{40} +(6.18056 + 1.67354i) q^{41} -4.94220 q^{42} +(-1.18522 - 1.63132i) q^{43} +(2.15248 + 2.15248i) q^{44} +(0.353247 - 1.08718i) q^{45} +(1.86321 + 0.605393i) q^{46} +(1.55707 - 9.83098i) q^{47} +(-0.0243050 - 0.153456i) q^{48} +(-8.55823 + 2.78074i) q^{49} +3.41827i q^{50} +(2.05581 + 6.32714i) q^{51} +(2.36674 - 4.64499i) q^{52} +(6.91813 - 3.52496i) q^{53} +(4.96103 + 0.785751i) q^{54} +(-1.90769 + 1.90769i) q^{55} +(-5.17934 - 10.1650i) q^{56} +(-1.10177 - 0.800486i) q^{57} +(-1.62731 - 0.829155i) q^{58} +(7.77045 - 5.64556i) q^{59} +(-1.78553 + 0.282801i) q^{60} +(-0.263416 + 0.362561i) q^{61} +(-3.42369 + 4.71231i) q^{62} +(4.20788 - 0.666462i) q^{63} +(4.20887 - 3.05793i) q^{64} +(4.11674 + 2.09758i) q^{65} +(-2.51283 - 1.82568i) q^{66} +(-1.59206 - 3.12459i) q^{67} +(-4.09531 + 4.09531i) q^{68} +(3.03004 + 0.479912i) q^{69} +(3.39758 - 1.73115i) q^{70} +(-6.39610 + 12.5531i) q^{71} +(0.938792 + 2.88930i) q^{72} -8.75882i q^{73} +(9.15822 - 2.97568i) q^{74} +(0.837360 + 5.28689i) q^{75} +(0.185468 - 1.17100i) q^{76} +(-9.56259 - 3.10707i) q^{77} +(-1.64376 + 5.05897i) q^{78} +(-1.93225 - 1.93225i) q^{79} +(0.0704612 + 0.0969816i) q^{80} +4.67012 q^{81} +(-2.02433 - 5.31537i) q^{82} -2.79623 q^{83} +(-3.96016 - 5.45070i) q^{84} +(-3.62957 - 3.62957i) q^{85} +(-0.553497 + 1.70349i) q^{86} +(-2.72000 - 0.883783i) q^{87} +(1.12162 - 7.08163i) q^{88} +(1.73754 + 10.9704i) q^{89} +(-0.965728 + 0.313784i) q^{90} +17.2194i q^{91} +(0.825300 + 2.54001i) q^{92} +(-4.14092 + 8.12702i) q^{93} +(-7.87788 + 4.01398i) q^{94} +(1.03782 + 0.164375i) q^{95} +(5.51324 - 5.51324i) q^{96} +(1.70702 + 3.35021i) q^{97} +(6.46677 + 4.69838i) q^{98} +(2.38567 + 1.21556i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) $ 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{11}{20}\right)$

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 $

$2$	−0.522120	−	0.718637i	−0.369195	−	0.508153i	0.583487	−	0.812123i	$-0.301688\pi$
$2$	−0.522120	−	0.718637i	−0.369195	−	0.508153i	−0.952682	+	0.303969i	$0.901688\pi$
$3$	−0.983583	−	0.983583i	−0.567872	−	0.567872i	0.363660	−	0.931532i	$-0.381527\pi$
$3$	−0.983583	−	0.983583i	−0.567872	−	0.567872i	−0.931532	+	0.363660i	$0.881527\pi$
$4$	0.374204	−	1.15168i	0.187102	−	0.575841i
$5$	1.02071	+	0.331648i	0.456474	+	0.148318i	0.528224	−	0.849105i	$-0.322858\pi$
$5$	1.02071	+	0.331648i	0.456474	+	0.148318i	−0.0717495	+	0.997423i	$0.522858\pi$
$6$	−0.193291	+	1.22039i	−0.0789105	+	0.498222i
$7$	0.625712	+	3.95059i	0.236497	+	1.49318i	0.764878	+	0.644175i	$0.222799\pi$
$7$	0.625712	+	3.95059i	0.236497	+	1.49318i	−0.528382	+	0.849007i	$0.677201\pi$
$8$	−2.71264	+	0.881390i	−0.959063	+	0.311618i
$9$		−	1.06513i		−	0.355042i
$10$	−0.294598	−	0.906679i	−0.0931600	−	0.286717i
$11$	−1.14123	+	2.23980i	−0.344095	+	0.675324i	−0.996594	−	0.0824655i	$-0.973721\pi$
$11$	−1.14123	+	2.23980i	−0.344095	+	0.675324i	0.652499	+	0.757789i	$0.273721\pi$
$12$	−1.50084	+	0.764715i	−0.433254	+	0.220754i
$13$	4.25204	+	0.673457i	1.17930	+	0.186783i	0.715150	−	0.698971i	$-0.246359\pi$
$13$	4.25204	+	0.673457i	1.17930	+	0.186783i	0.464154	+	0.885755i	$0.346359\pi$
$14$	2.51234	−	2.51234i	0.671452	−	0.671452i
$15$	−0.677748	−	1.33015i	−0.174994	−	0.343444i
$16$	0.0903637	+	0.0656531i	0.0225909	+	0.0164133i
$17$	−4.26144	−	2.17131i	−1.03355	−	0.526620i	−0.146944	−	0.989145i	$-0.546944\pi$
$17$	−4.26144	−	2.17131i	−1.03355	−	0.526620i	−0.886606	+	0.462525i	$0.846944\pi$
$18$	−0.765440	+	0.556125i	−0.180416	+	0.131080i
$19$	0.967006	−	0.153159i	0.221846	−	0.0351370i	−0.0445217	−	0.999008i	$-0.514176\pi$
$19$	0.967006	−	0.153159i	0.221846	−	0.0351370i	0.266368	+	0.963871i	$0.414176\pi$
$20$	0.763907	−	1.05143i	0.170815	−	0.235106i
$21$	3.27029	−	4.50117i	0.713636	−	0.982236i
$22$	2.20546	−	0.349311i	0.470206	−	0.0744733i
$23$	−1.78427	+	1.29635i	−0.372046	+	0.270307i	−0.758059	−	0.652186i	$-0.773852\pi$
$23$	−1.78427	+	1.29635i	−0.372046	+	0.270307i	0.386013	+	0.922493i	$0.373852\pi$
$24$	3.53503	+	1.80119i	0.721584	+	0.367666i
$25$	−3.11323	−	2.26189i	−0.622646	−	0.452379i
$26$	−1.73611	−	3.40730i	−0.340478	−	0.668226i
$27$	−3.99839	+	3.99839i	−0.769491	+	0.769491i
$28$	4.78397	+	0.757706i	0.904085	+	0.143193i
$29$	1.83197	−	0.933434i	0.340188	−	0.173334i	−0.275547	−	0.961287i	$-0.588859\pi$
$29$	1.83197	−	0.933434i	0.340188	−	0.173334i	0.615735	+	0.787953i	$0.288859\pi$
$30$	−0.602033	+	1.18156i	−0.109916	+	0.215722i
$31$	−2.02631	−	6.23635i	−0.363936	−	1.12008i	−0.950644	−	0.310283i	$-0.899576\pi$
$31$	−2.02631	−	6.23635i	−0.363936	−	1.12008i	0.586708	−	0.809799i	$-0.300424\pi$
$32$			5.60526i			0.990879i
$33$	3.32552	−	1.08053i	0.578900	−	0.188096i
$34$	0.664599	+	4.19611i	0.113978	+	0.719627i
$35$	−0.671536	+	4.23991i	−0.113510	+	0.716676i
$36$	−1.22669	−	0.398575i	−0.204448	−	0.0664292i
$37$	−3.34992	+	10.3100i	−0.550724	+	1.69495i	0.156252	+	0.987717i	$0.450059\pi$
$37$	−3.34992	+	10.3100i	−0.550724	+	1.69495i	−0.706976	+	0.707237i	$0.749941\pi$
$38$	−0.614959	−	0.614959i	−0.0997595	−	0.0997595i
$39$	−3.51983	−	4.84464i	−0.563624	−	0.775763i
$40$	−3.06112			−0.484006
$41$	6.18056	+	1.67354i	0.965241	+	0.261363i
$41$	6.18056	+	1.67354i	0.965241	+	0.261363i
$42$	−4.94220			−0.762597
$43$	−1.18522	−	1.63132i	−0.180745	−	0.248773i	0.709025	−	0.705183i	$-0.249135\pi$
$43$	−1.18522	−	1.63132i	−0.180745	−	0.248773i	−0.889770	+	0.456410i	$0.849135\pi$
$44$	2.15248	+	2.15248i	0.324499	+	0.324499i
$45$	0.353247	−	1.08718i	0.0526590	−	0.162068i
$46$	1.86321	+	0.605393i	0.274715	+	0.0892603i
$47$	1.55707	−	9.83098i	0.227123	−	1.43400i	−0.565735	−	0.824587i	$-0.691407\pi$
$47$	1.55707	−	9.83098i	0.227123	−	1.43400i	0.792857	−	0.609408i	$-0.208593\pi$
$48$	−0.0243050	−	0.153456i	−0.00350812	−	0.0221494i
$49$	−8.55823	+	2.78074i	−1.22260	+	0.397248i
$50$			3.41827i			0.483416i
$51$	2.05581	+	6.32714i	0.287871	+	0.885977i
$52$	2.36674	−	4.64499i	0.328208	−	0.644144i
$53$	6.91813	−	3.52496i	0.950278	−	0.484191i	0.0910855	−	0.995843i	$-0.470966\pi$
$53$	6.91813	−	3.52496i	0.950278	−	0.484191i	0.859193	+	0.511652i	$0.170966\pi$
$54$	4.96103	+	0.785751i	0.675111	+	0.106927i
$55$	−1.90769	+	1.90769i	−0.257233	+	0.257233i
$56$	−5.17934	−	10.1650i	−0.692118	−	1.35836i
$57$	−1.10177	−	0.800486i	−0.145934	−	0.106027i
$58$	−1.62731	−	0.829155i	−0.213676	−	0.108873i
$59$	7.77045	−	5.64556i	1.01163	−	0.734989i	0.0470763	−	0.998891i	$-0.485010\pi$
$59$	7.77045	−	5.64556i	1.01163	−	0.734989i	0.964549	+	0.263902i	$0.0850096\pi$
$60$	−1.78553	+	0.282801i	−0.230511	+	0.0365094i
$61$	−0.263416	+	0.362561i	−0.0337269	+	0.0464211i	−0.825547	−	0.564333i	$-0.809134\pi$
$61$	−0.263416	+	0.362561i	−0.0337269	+	0.0464211i	0.791821	+	0.610754i	$0.209134\pi$
$62$	−3.42369	+	4.71231i	−0.434809	+	0.598464i
$63$	4.20788	−	0.666462i	0.530143	−	0.0839663i
$64$	4.20887	−	3.05793i	0.526109	−	0.382241i
$65$	4.11674	+	2.09758i	0.510618	+	0.260173i
$66$	−2.51283	−	1.82568i	−0.309308	−	0.224726i
$67$	−1.59206	−	3.12459i	−0.194501	−	0.381729i	0.773073	−	0.634317i	$-0.218718\pi$
$67$	−1.59206	−	3.12459i	−0.194501	−	0.381729i	−0.967574	+	0.252587i	$0.918718\pi$
$68$	−4.09531	+	4.09531i	−0.496629	+	0.496629i
$69$	3.03004	+	0.479912i	0.364775	+	0.0577746i
$70$	3.39758	−	1.73115i	0.406088	−	0.206912i
$71$	−6.39610	+	12.5531i	−0.759078	+	1.48977i	0.109374	+	0.994001i	$0.465115\pi$
$71$	−6.39610	+	12.5531i	−0.759078	+	1.48977i	−0.868452	+	0.495773i	$0.834885\pi$
$72$	0.938792	+	2.88930i	0.110638	+	0.340508i
$73$		−	8.75882i		−	1.02514i	−0.858645	−	0.512571i	$-0.828693\pi$
$73$		−	8.75882i		−	1.02514i	0.858645	−	0.512571i	$-0.171307\pi$
$74$	9.15822	−	2.97568i	1.06462	−	0.345916i
$75$	0.837360	+	5.28689i	0.0966901	+	0.610477i
$76$	0.185468	−	1.17100i	0.0212746	−	0.134322i
$77$	−9.56259	−	3.10707i	−1.08976	−	0.354084i
$78$	−1.64376	+	5.05897i	−0.186119	+	0.572815i
$79$	−1.93225	−	1.93225i	−0.217395	−	0.217395i	0.590005	−	0.807400i	$-0.299126\pi$
$79$	−1.93225	−	1.93225i	−0.217395	−	0.217395i	−0.807400	+	0.590005i	$0.799126\pi$
$80$	0.0704612	+	0.0969816i	0.00787781	+	0.0108429i
$81$	4.67012			0.518903
$82$	−2.02433	−	5.31537i	−0.223550	−	0.586984i
$83$	−2.79623			−0.306926			−0.153463	−	0.988154i	$-0.549043\pi$
$83$	−2.79623			−0.306926			−0.153463	+	0.988154i	$0.549043\pi$
$84$	−3.96016	−	5.45070i	−0.432089	−	0.594720i
$85$	−3.62957	−	3.62957i	−0.393682	−	0.393682i
$86$	−0.553497	+	1.70349i	−0.0596851	+	0.183692i
$87$	−2.72000	−	0.883783i	−0.291615	−	0.0947515i
$88$	1.12162	−	7.08163i	0.119565	−	0.754904i
$89$	1.73754	+	10.9704i	0.184179	+	1.16286i	0.890505	+	0.454974i	$0.150351\pi$
$89$	1.73754	+	10.9704i	0.184179	+	1.16286i	−0.706326	+	0.707887i	$0.749649\pi$
$90$	−0.965728	+	0.313784i	−0.101797	+	0.0330757i
$91$			17.2194i			1.80509i
$92$	0.825300	+	2.54001i	0.0860435	+	0.264815i
$93$	−4.14092	+	8.12702i	−0.429394	+	0.842732i
$94$	−7.87788	+	4.01398i	−0.812542	+	0.414011i
$95$	1.03782	+	0.164375i	0.106479	+	0.0168645i
$96$	5.51324	−	5.51324i	0.562693	−	0.562693i
$97$	1.70702	+	3.35021i	0.173321	+	0.340162i	0.961283	−	0.275561i	$-0.0888637\pi$
$97$	1.70702	+	3.35021i	0.173321	+	0.340162i	−0.787962	+	0.615724i	$0.788864\pi$
$98$	6.46677	+	4.69838i	0.653242	+	0.474608i
$99$	2.38567	+	1.21556i	0.239769	+	0.122168i
$100$	−3.76997	+	2.73904i	−0.376997	+	0.273904i
$101$	−1.80537	+	0.285942i	−0.179641	+	0.0284523i	−0.245607	−	0.969370i	$-0.578987\pi$
$101$	−1.80537	+	0.285942i	−0.179641	+	0.0284523i	0.0659658	+	0.997822i	$0.478987\pi$
$102$	3.47354	−	4.78091i	0.343931	−	0.473381i
$103$	6.53693	−	8.99731i	0.644103	−	0.886531i	−0.354723	−	0.934971i	$-0.615425\pi$
$103$	6.53693	−	8.99731i	0.644103	−	0.886531i	0.998826	+	0.0484399i	$0.0154249\pi$
$104$	−12.1278	+	1.92086i	−1.18923	+	0.188356i
$105$	4.83082	−	3.50979i	0.471440	−	0.342521i
$106$	−6.14527	−	3.13117i	−0.596881	−	0.304126i
$107$	10.4582	+	7.59832i	1.01103	+	0.734557i	0.964425	−	0.264356i	$-0.0851595\pi$
$107$	10.4582	+	7.59832i	1.01103	+	0.734557i	0.0466060	+	0.998913i	$0.485159\pi$
$108$	3.10866	+	6.10110i	0.299131	+	0.587078i
$109$	−4.71687	+	4.71687i	−0.451794	+	0.451794i	−0.895950	−	0.444156i	$-0.853504\pi$
$109$	−4.71687	+	4.71687i	−0.451794	+	0.451794i	0.444156	+	0.895950i	$0.353504\pi$
$110$	2.36698	+	0.374893i	0.225683	+	0.0357446i
$111$	13.4357	−	6.84582i	1.27526	−	0.649777i
$112$	−0.202827	+	0.398070i	−0.0191653	+	0.0376141i
$113$	−4.03978	−	12.4332i	−0.380031	−	1.16961i	−0.940021	−	0.341115i	$-0.889195\pi$
$113$	−4.03978	−	12.4332i	−0.380031	−	1.16961i	0.559991	−	0.828499i	$-0.310805\pi$
$114$			1.20973i			0.113301i
$115$	−2.25115	+	0.731443i	−0.209921	+	0.0682074i
$116$	−0.389490	−	2.45914i	−0.0361632	−	0.228326i
$117$	0.717317	−	4.52896i	0.0663160	−	0.418703i
$118$	−8.11422	−	2.63647i	−0.746974	−	0.242707i
$119$	5.91152	−	18.1938i	0.541908	−	1.66782i
$120$	3.01087	+	3.01087i	0.274854	+	0.274854i
$121$	2.75136	+	3.78693i	0.250124	+	0.344266i
$122$	0.398084			0.0360408
$123$	−4.43303	−	7.72516i	−0.399713	−	0.696554i
$124$	−7.94055			−0.713082
$125$	−5.58171	−	7.68256i	−0.499243	−	0.687149i
$126$	−2.67596	−	2.67596i	−0.238394	−	0.238394i
$127$	2.84583	−	8.75856i	0.252526	−	0.777196i	−0.741781	−	0.670643i	$-0.766018\pi$
$127$	2.84583	−	8.75856i	0.252526	−	0.777196i	0.994307	−	0.106554i	$-0.0339816\pi$
$128$	6.26676	+	2.03619i	0.553908	+	0.179976i
$129$	−0.438772	+	2.77030i	−0.0386318	+	0.243911i
$130$	−0.642032	−	4.05363i	−0.0563099	−	0.355527i
$131$	0.179705	−	0.0583895i	0.0157009	−	0.00510152i	−0.301156	−	0.953575i	$-0.597373\pi$
$131$	0.179705	−	0.0583895i	0.0157009	−	0.00510152i	0.316857	+	0.948473i	$0.397373\pi$
$132$		−	4.23429i		−	0.368547i
$133$	1.21013	+	3.72441i	0.104932	+	0.322947i
$134$	−1.41420	+	2.77552i	−0.122168	+	0.239769i
$135$	−5.40725	+	2.75513i	−0.465382	+	0.237124i
$136$	13.4735	+	2.13399i	1.15534	+	0.182988i
$137$	−4.54556	+	4.54556i	−0.388353	+	0.388353i	−0.874100	−	0.485746i	$-0.838548\pi$
$137$	−4.54556	+	4.54556i	−0.388353	+	0.388353i	0.485746	+	0.874100i	$0.338548\pi$
$138$	−1.23717	−	2.42807i	−0.105315	−	0.206691i
$139$	5.82631	+	4.23306i	0.494181	+	0.359043i	0.806790	−	0.590838i	$-0.201203\pi$
$139$	5.82631	+	4.23306i	0.494181	+	0.359043i	−0.312609	+	0.949882i	$0.601203\pi$
$140$	4.63174	+	2.35999i	0.391453	+	0.199456i
$141$	−11.2011	+	8.13807i	−0.943303	+	0.685349i
$142$	12.3606	−	1.95773i	1.03728	−	0.164289i
$143$	−6.36097	+	8.75513i	−0.531931	+	0.732141i
$144$	0.0699289	−	0.0962489i	0.00582741	−	0.00802074i
$145$	2.17948	−	0.345195i	0.180996	−	0.0286669i
$146$	−6.29441	+	4.57316i	−0.520929	+	0.378477i
$147$	11.1528	+	5.68264i	0.919869	+	0.468697i
$148$	10.6203	+	7.71610i	0.872983	+	0.634260i
$149$	−2.20761	−	4.33268i	−0.180855	−	0.354947i	0.782725	−	0.622367i	$-0.213829\pi$
$149$	−2.20761	−	4.33268i	−0.180855	−	0.354947i	−0.963580	+	0.267420i	$0.913829\pi$
$150$	3.36215	−	3.36215i	0.274518	−	0.274518i
$151$	−9.40032	−	1.48886i	−0.764987	−	0.121162i	−0.238266	−	0.971200i	$-0.576579\pi$
$151$	−9.40032	−	1.48886i	−0.764987	−	0.121162i	−0.526721	+	0.850038i	$0.676579\pi$
$152$	−2.48814	+	1.26777i	−0.201815	+	0.102830i
$153$	−2.31272	+	4.53897i	−0.186972	+	0.366954i
$154$	2.75997	+	8.49430i	0.222404	+	0.684490i
$155$		−	7.03751i		−	0.565266i
$156$	−6.89662	+	2.24085i	−0.552172	+	0.179411i
$157$	1.23051	+	7.76915i	0.0982056	+	0.620046i	0.986874	+	0.161495i	$0.0516314\pi$
$157$	1.23051	+	7.76915i	0.0982056	+	0.620046i	−0.888668	+	0.458551i	$0.848369\pi$
$158$	−0.379719	+	2.39745i	−0.0302088	+	0.190731i
$159$	−10.2717	−	3.33746i	−0.814595	−	0.264678i
$160$	−1.85897	+	5.72133i	−0.146965	+	0.452311i
$161$	−6.23777	−	6.23777i	−0.491605	−	0.491605i
$162$	−2.43837	−	3.35612i	−0.191576	−	0.263682i
$163$	−14.6310			−1.14599			−0.572994	−	0.819560i	$-0.694218\pi$
$163$	−14.6310			−1.14599			−0.572994	+	0.819560i	$0.694218\pi$
$164$	4.24018	−	6.49179i	0.331102	−	0.506924i
$165$	3.75274			0.292151
$166$	1.45997	+	2.00948i	0.113316	+	0.155966i
$167$	0.134117	+	0.134117i	0.0103783	+	0.0103783i	0.712277	−	0.701899i	$-0.247664\pi$
$167$	0.134117	+	0.134117i	0.0103783	+	0.0103783i	−0.701899	+	0.712277i	$0.747664\pi$
$168$	−4.90384	+	15.0925i	−0.378339	+	1.16441i
$169$	5.26255	+	1.70991i	0.404812	+	0.131531i
$170$	−0.713271	+	4.50342i	−0.0547054	+	0.345396i
$171$	−0.163133	−	1.02998i	−0.0124751	−	0.0787648i
$172$	−2.32227	+	0.754553i	−0.177072	+	0.0575341i
$173$		−	5.31858i		−	0.404364i	−0.979348	−	0.202182i	$-0.935197\pi$
$173$		−	5.31858i		−	0.404364i	0.979348	−	0.202182i	$-0.0648033\pi$
$174$	0.785050	+	2.41614i	0.0595145	+	0.183167i
$175$	6.98783	−	13.7144i	0.528230	−	1.03671i
$176$	−0.250176	+	0.127471i	−0.0188577	+	0.00960848i
$177$	−13.1958	−	2.09000i	−0.991854	−	0.157094i
$178$	6.97653	−	6.97653i	0.522913	−	0.522913i
$179$	7.56349	+	14.8442i	0.565322	+	1.10951i	0.979899	+	0.199492i	$0.0639293\pi$
$179$	7.56349	+	14.8442i	0.565322	+	1.10951i	−0.414578	+	0.910014i	$0.636071\pi$
$180$	−1.11990	−	0.813658i	−0.0834727	−	0.0606465i
$181$	9.39816	+	4.78860i	0.698560	+	0.355934i	0.766934	−	0.641726i	$-0.221781\pi$
$181$	9.39816	+	4.78860i	0.698560	+	0.355934i	−0.0683744	+	0.997660i	$0.521781\pi$
$182$	12.3745	−	8.99062i	0.917261	−	0.666429i
$183$	0.615700	−	0.0975173i	0.0455138	−	0.00720868i
$184$	3.69749	−	5.08916i	0.272583	−	0.375178i
$185$	−6.83859	+	9.41251i	−0.502783	+	0.692021i
$186$	8.00244	−	1.26746i	0.586767	−	0.0929348i
$187$	9.72658	−	7.06678i	0.711278	−	0.516774i
$188$	−10.7395	−	5.47205i	−0.783259	−	0.399090i
$189$	−18.2978	−	13.2942i	−1.33097	−	0.967007i
$190$	−0.423743	−	0.831643i	−0.0307416	−	0.0603337i
$191$	11.1396	−	11.1396i	0.806032	−	0.806032i	−0.177999	−	0.984031i	$-0.556962\pi$
$191$	11.1396	−	11.1396i	0.806032	−	0.806032i	0.984031	+	0.177999i	$0.0569623\pi$
$192$	−7.14750	−	1.13205i	−0.515827	−	0.0816989i
$193$	−20.8262	+	10.6115i	−1.49910	+	0.763831i	−0.995006	−	0.0998160i	$-0.968175\pi$
$193$	−20.8262	+	10.6115i	−1.49910	+	0.763831i	−0.504097	+	0.863647i	$0.668175\pi$
$194$	1.51632	−	2.97594i	0.108865	−	0.213660i
$195$	−1.98601	−	6.11230i	−0.142221	−	0.437711i
$196$			10.8969i			0.778352i
$197$	11.2628	−	3.65951i	0.802442	−	0.260729i	0.121048	−	0.992647i	$-0.461374\pi$
$197$	11.2628	−	3.65951i	0.802442	−	0.260729i	0.681393	+	0.731918i	$0.261374\pi$
$198$	−0.372060	−	2.34910i	−0.0264412	−	0.166943i
$199$	1.32526	−	8.36737i	0.0939452	−	0.593147i	−0.895138	−	0.445789i	$-0.852923\pi$
$199$	1.32526	−	8.36737i	0.0939452	−	0.593147i	0.989083	−	0.147358i	$-0.0470769\pi$
$200$	10.4387	+	3.39173i	0.738126	+	0.239832i
$201$	−1.50737	+	4.63921i	−0.106322	+	0.327225i
$202$	1.14811	+	1.14811i	0.0807806	+	0.0807806i
$203$	4.83390	+	6.65329i	0.339273	+	0.466969i
$204$	8.05616			0.564044
$205$	5.75351	+	3.75796i	0.401843	+	0.262468i
$206$	−9.87887			−0.688293
$207$	1.38078	+	1.90047i	0.0959705	+	0.132092i
$208$	0.340016	+	0.340016i	0.0235758	+	0.0235758i
$209$	−0.760535	+	2.34068i	−0.0526073	+	0.161909i
$210$	−5.04454	−	1.63907i	−0.348106	−	0.113107i
$211$	−1.50316	+	9.49061i	−0.103482	+	0.653360i	0.880358	+	0.474310i	$0.157302\pi$
$211$	−1.50316	+	9.49061i	−0.103482	+	0.653360i	−0.983840	+	0.179050i	$0.942698\pi$
$212$	−1.47084	−	9.28655i	−0.101018	−	0.637803i
$213$	18.6381	−	6.05588i	1.27706	−	0.414942i
$214$		−	11.4829i		−	0.784953i
$215$	−0.668741	−	2.05817i	−0.0456078	−	0.140366i
$216$	7.32205	−	14.3703i	0.498203	−	0.977777i
$217$	23.3693	−	11.9073i	1.58641	−	0.808319i
$218$	5.85249	+	0.926943i	0.396380	+	0.0627805i
$219$	−8.61503	+	8.61503i	−0.582150	+	0.582150i
$220$	1.48319	+	2.91092i	0.0999965	+	0.196254i
$221$	−16.6575	−	12.1024i	−1.12051	−	0.814095i
$222$	−11.9347	−	6.08104i	−0.801005	−	0.408132i
$223$	−4.32492	+	3.14224i	−0.289618	+	0.210420i	−0.723102	−	0.690742i	$-0.757284\pi$
$223$	−4.32492	+	3.14224i	−0.289618	+	0.210420i	0.433484	+	0.901161i	$0.357284\pi$
$224$	−22.1441	+	3.50727i	−1.47956	+	0.234340i
$225$	−2.40921	+	3.31599i	−0.160614	+	0.221066i
$226$	−6.82568	+	9.39475i	−0.454038	+	0.624929i
$227$	6.85453	−	1.08565i	0.454951	−	0.0720571i	0.0752464	−	0.997165i	$-0.476026\pi$
$227$	6.85453	−	1.08565i	0.454951	−	0.0720571i	0.379704	+	0.925108i	$0.376026\pi$
$228$	−1.33420	+	0.969350i	−0.0883593	+	0.0641968i
$229$	15.9124	+	8.10777i	1.05152	+	0.535777i	0.892289	−	0.451465i	$-0.149098\pi$
$229$	15.9124	+	8.10777i	1.05152	+	0.535777i	0.159232	+	0.987241i	$0.449098\pi$
$230$	1.70101	+	1.23586i	0.112161	+	0.0814901i
$231$	6.34954	+	12.4617i	0.417769	+	0.819918i
$232$	−4.14675	+	4.14675i	−0.272247	+	0.272247i
$233$	−4.30559	−	0.681939i	−0.282069	−	0.0446753i	0.0137971	−	0.999905i	$-0.495608\pi$
$233$	−4.30559	−	0.681939i	−0.282069	−	0.0446753i	−0.295866	+	0.955230i	$0.595608\pi$
$234$	−3.62921	+	1.84917i	−0.237249	+	0.120884i
$235$	4.84974	−	9.51815i	0.316362	−	0.620896i
$236$	−3.59416	−	11.0617i	−0.233960	−	0.720054i
$237$			3.80105i			0.246905i
$238$	−16.1613	+	5.25111i	−1.04758	+	0.340379i
$239$	1.73930	+	10.9815i	0.112506	+	0.710334i	0.977874	+	0.209197i	$0.0670850\pi$
$239$	1.73930	+	10.9815i	0.112506	+	0.710334i	−0.865368	+	0.501138i	$0.832915\pi$
$240$	0.0260850	−	0.164694i	0.00168378	−	0.0106310i
$241$	18.4604	+	5.99815i	1.18914	+	0.386375i	0.835755	−	0.549103i	$-0.185030\pi$
$241$	18.4604	+	5.99815i	1.18914	+	0.386375i	0.353385	+	0.935478i	$0.385030\pi$
$242$	1.28488	−	3.95446i	0.0825954	−	0.254203i
$243$	7.40172	+	7.40172i	0.474821	+	0.474821i
$244$	0.318983	+	0.439043i	0.0204208	+	0.0281068i
$245$	−9.65767			−0.617006
$246$	−3.23701	+	7.21920i	−0.206384	+	0.460279i
$247$	4.21489			0.268187
$248$	10.9933	+	15.1310i	0.698076	+	0.960819i
$249$	2.75033	+	2.75033i	0.174295	+	0.174295i
$250$	−2.60665	+	8.02244i	−0.164859	+	0.507384i
$251$	−2.21352	−	0.719217i	−0.139716	−	0.0453966i	0.238324	−	0.971186i	$-0.423402\pi$
$251$	−2.21352	−	0.719217i	−0.139716	−	0.0453966i	−0.378040	+	0.925789i	$0.623402\pi$
$252$	0.807053	−	5.09553i	0.0508396	−	0.320988i
$253$	−0.867287	−	5.47584i	−0.0545259	−	0.344263i
$254$	−7.78009	+	2.52790i	−0.488166	+	0.158615i
$255$			7.13997i			0.447122i
$256$	−5.02401	−	15.4623i	−0.314001	−	0.966395i
$257$	−8.86149	+	17.3916i	−0.552764	+	1.08486i	0.430485	+	0.902597i	$0.358342\pi$
$257$	−8.86149	+	17.3916i	−0.552764	+	1.08486i	−0.983250	+	0.182263i	$0.941658\pi$
$258$	2.21993	−	1.13111i	0.138207	−	0.0704200i
$259$	−42.8267	−	6.78308i	−2.66112	−	0.421480i
$260$	3.95625	−	3.95625i	0.245356	−	0.245356i
$261$	−0.994226	−	1.95128i	−0.0615410	−	0.120781i
$262$	−0.135788	−	0.0986560i	−0.00838903	−	0.00609499i
$263$	−2.91538	−	1.48546i	−0.179770	−	0.0915973i	0.361790	−	0.932260i	$-0.382166\pi$
$263$	−2.91538	−	1.48546i	−0.179770	−	0.0915973i	−0.541559	+	0.840662i	$0.682166\pi$
$264$	−8.06858	+	5.86217i	−0.496587	+	0.360791i
$265$	8.23043	−	1.30357i	0.505592	−	0.0800778i
$266$	2.04466	−	2.81423i	0.125366	−	0.172552i
$267$	9.08129	−	12.4993i	0.555766	−	0.764946i
$268$	−4.19429	+	0.664310i	−0.256207	+	0.0405792i
$269$	−9.01598	+	6.55050i	−0.549714	+	0.399391i	−0.827680	−	0.561200i	$-0.810340\pi$
$269$	−9.01598	+	6.55050i	−0.549714	+	0.399391i	0.277966	+	0.960591i	$0.410340\pi$
$270$	4.80317	+	2.44734i	0.292312	+	0.148940i
$271$	−5.17280	−	3.75826i	−0.314225	−	0.228298i	0.419482	−	0.907764i	$-0.362212\pi$
$271$	−5.17280	−	3.75826i	−0.314225	−	0.228298i	−0.733707	+	0.679466i	$0.762212\pi$
$272$	−0.242526	−	0.475984i	−0.0147053	−	0.0288608i
$273$	16.9368	−	16.9368i	1.02506	−	1.02506i
$274$	5.63994	+	0.893278i	0.340721	+	0.0539649i
$275$	8.61911	−	4.39165i	0.519752	−	0.264827i
$276$	1.68656	−	3.31007i	0.101519	−	0.199243i
$277$	7.78542	+	23.9611i	0.467781	+	1.43968i	0.855452	+	0.517883i	$0.173280\pi$
$277$	7.78542	+	23.9611i	0.467781	+	1.43968i	−0.387671	+	0.921798i	$0.626720\pi$
$278$		−	6.39717i		−	0.383677i
$279$	−6.64250	+	2.15828i	−0.397676	+	0.129213i
$280$	−1.91538	−	12.0932i	−0.114466	−	0.722709i
$281$	−0.531501	+	3.35577i	−0.0317067	+	0.200188i	−0.998457	−	0.0555350i	$-0.982314\pi$
$281$	−0.531501	+	3.35577i	−0.0317067	+	0.200188i	0.966750	+	0.255723i	$0.0823136\pi$
$282$	11.6966	+	3.80047i	0.696525	+	0.226315i
$283$	2.32829	−	7.16575i	0.138403	−	0.425959i	−0.857701	−	0.514149i	$-0.828108\pi$
$283$	2.32829	−	7.16575i	0.138403	−	0.425959i	0.996104	+	0.0881892i	$0.0281080\pi$
$284$	12.0637	+	12.0637i	0.715849	+	0.715849i
$285$	−0.859110	−	1.18246i	−0.0508893	−	0.0700431i
$286$	9.61295			0.568426
$287$	−2.74422	+	25.4640i	−0.161986	+	1.50309i
$288$	5.97031			0.351804
$289$	3.45290	+	4.75251i	0.203112	+	0.279559i
$290$	−1.38602	−	1.38602i	−0.0813898	−	0.0813898i
$291$	1.61622	−	4.97421i	0.0947443	−	0.291593i
$292$	−10.0874	−	3.27759i	−0.590319	−	0.191806i
$293$	−0.934720	+	5.90159i	−0.0546069	+	0.344775i	0.945225	+	0.326421i	$0.105843\pi$
$293$	−0.934720	+	5.90159i	−0.0546069	+	0.344775i	−0.999832	+	0.0183540i	$0.994157\pi$
$294$	−1.73935	−	10.9819i	−0.101441	−	0.640475i
$295$	9.80369	−	3.18541i	0.570793	−	0.185462i
$296$		−	30.9199i		−	1.79718i
$297$	−4.39249	−	13.5187i	−0.254878	−	0.784433i
$298$	−1.96099	+	3.84865i	−0.113597	+	0.222947i
$299$	−8.45982	+	4.31049i	−0.489244	+	0.249282i
$300$	6.40216	+	1.01400i	0.369629	+	0.0585435i
$301$	5.70305	−	5.70305i	0.328718	−	0.328718i
$302$	3.83814	+	7.53278i	0.220860	+	0.433463i
$303$	2.05698	+	1.49448i	0.118170	+	0.0858558i
$304$	0.0974376	+	0.0496469i	0.00558843	+	0.00284745i
$305$	−0.389113	+	0.282707i	−0.0222805	+	0.0161878i
$306$	4.46939	−	0.707882i	0.255498	−	0.0404669i
$307$	0.432807	−	0.595708i	0.0247016	−	0.0339988i	−0.796488	−	0.604655i	$-0.793311\pi$
$307$	0.432807	−	0.595708i	0.0247016	−	0.0339988i	0.821189	+	0.570656i	$0.193311\pi$
$308$	−7.15673	+	9.85039i	−0.407792	+	0.561278i
$309$	−15.2792	+	2.41999i	−0.869205	+	0.137668i
$310$	−5.05742	+	3.67443i	−0.287242	+	0.208693i
$311$	−25.7148	−	13.1024i	−1.45816	−	0.742967i	−0.468104	−	0.883673i	$-0.655063\pi$
$311$	−25.7148	−	13.1024i	−1.45816	−	0.742967i	−0.990051	+	0.140706i	$0.955063\pi$
$312$	13.8181	+	10.0394i	0.782293	+	0.568369i
$313$	−7.45211	−	14.6256i	−0.421218	−	0.826687i	−0.999938	−	0.0111603i	$-0.996447\pi$
$313$	−7.45211	−	14.6256i	−0.421218	−	0.826687i	0.578720	−	0.815526i	$-0.303553\pi$
$314$	4.94072	−	4.94072i	0.278821	−	0.278821i
$315$	4.51604	+	0.715271i	0.254450	+	0.0403010i
$316$	−2.94839	+	1.50228i	−0.165860	+	0.0845098i
$317$	15.3313	−	30.0894i	0.861091	−	1.68999i	0.147917	−	0.989000i	$-0.452743\pi$
$317$	15.3313	−	30.0894i	0.861091	−	1.68999i	0.713174	−	0.700987i	$-0.247257\pi$
$318$	2.96462	+	9.12415i	0.166247	+	0.511657i
$319$			5.16850i			0.289380i
$320$	5.31018	−	1.72538i	0.296848	−	0.0964519i
$321$	−2.81292	−	17.7601i	−0.157002	−	0.991271i
$322$	−1.22583	+	7.73956i	−0.0683126	+	0.431309i
$323$	−4.45339	−	1.44699i	−0.247793	−	0.0805129i
$324$	1.74758	−	5.37850i	0.0970878	−	0.298806i
$325$	−11.7143	−	11.7143i	−0.649792	−	0.649792i
$326$	7.63914	+	10.5144i	0.423093	+	0.582337i
$327$	9.27886			0.513122
$328$	−18.2407	+	0.907773i	−1.00717	+	0.0501234i
$329$	39.8124			2.19493
$330$	−1.95938	−	2.69686i	−0.107861	−	0.148457i
$331$	−8.52119	−	8.52119i	−0.468367	−	0.468367i	0.433018	−	0.901385i	$-0.357449\pi$
$331$	−8.52119	−	8.52119i	−0.468367	−	0.468367i	−0.901385	+	0.433018i	$0.857449\pi$
$332$	−1.04636	+	3.22037i	−0.0574266	+	0.176741i
$333$	10.9815	+	3.56809i	0.601781	+	0.195530i
$334$	0.0263562	−	0.166407i	0.00144215	−	0.00910537i
$335$	−0.588761	−	3.71729i	−0.0321675	−	0.203097i
$336$	0.591032	−	0.192038i	0.0322434	−	0.0104765i
$337$			3.80509i			0.207276i	0.994615	+	0.103638i	$0.0330484\pi$
$337$			3.80509i			0.207276i	−0.994615	+	0.103638i	$0.966952\pi$
$338$	−1.51888	−	4.67464i	−0.0826163	−	0.254267i
$339$	−8.25560	+	16.2025i	−0.448383	+	0.880000i
$340$	−5.53831	+	2.82191i	−0.300357	+	0.153040i
$341$	16.2806	+	2.57860i	0.881646	+	0.139639i
$342$	−0.655009	+	0.655009i	−0.0354188	+	0.0354188i
$343$	−3.62932	−	7.12295i	−0.195965	−	0.384603i
$344$	4.65290	+	3.38053i	0.250868	+	0.182266i
$345$	2.93363	+	1.49476i	0.157941	+	0.0804751i
$346$	−3.82213	+	2.77694i	−0.205479	+	0.149289i
$347$	−15.9515	+	2.52648i	−0.856324	+	0.135628i	−0.569134	−	0.822245i	$-0.692721\pi$
$347$	−15.9515	+	2.52648i	−0.856324	+	0.135628i	−0.287190	+	0.957874i	$0.592721\pi$
$348$	−2.03568	+	2.80187i	−0.109124	+	0.150196i
$349$	−0.538696	+	0.741452i	−0.0288358	+	0.0396890i	−0.823191	−	0.567764i	$-0.807809\pi$
$349$	−0.538696	+	0.741452i	−0.0288358	+	0.0396890i	0.794356	+	0.607453i	$0.207809\pi$
$350$	−13.5042	+	2.13885i	−0.721827	+	0.114326i
$351$	−19.6941	+	14.3086i	−1.05119	+	0.763735i
$352$	−12.5546	−	6.39691i	−0.669164	−	0.340956i
$353$	−3.48494	−	2.53196i	−0.185485	−	0.134763i	0.491168	−	0.871065i	$-0.336570\pi$
$353$	−3.48494	−	2.53196i	−0.185485	−	0.134763i	−0.676653	+	0.736302i	$0.736570\pi$
$354$	5.38782	+	10.5742i	0.286360	+	0.562012i
$355$	−10.6917	+	10.6917i	−0.567459	+	0.567459i
$356$	13.2846	+	2.10408i	0.704084	+	0.111516i
$357$	−23.7096	+	12.0806i	−1.25484	+	0.639375i
$358$	6.71853	−	13.1859i	0.355085	−	0.696894i
$359$	8.03083	+	24.7164i	0.423851	+	1.30448i	0.904090	+	0.427342i	$0.140550\pi$
$359$	8.03083	+	24.7164i	0.423851	+	1.30448i	−0.480239	+	0.877138i	$0.659450\pi$
$360$			3.26048i			0.171843i
$361$	−17.1584	+	5.57511i	−0.903075	+	0.293427i
$362$	−1.46570	−	9.25409i	−0.0770357	−	0.486384i
$363$	1.01856	−	6.43096i	0.0534607	−	0.337538i
$364$	19.8313	+	6.44359i	1.03944	+	0.337736i
$365$	2.90485	−	8.94020i	0.152047	−	0.467951i
$366$	−0.391549	−	0.391549i	−0.0204666	−	0.0204666i
$367$	8.09990	+	11.1486i	0.422811	+	0.581950i	0.966285	−	0.257477i	$-0.0828910\pi$
$367$	8.09990	+	11.1486i	0.422811	+	0.581950i	−0.543473	+	0.839427i	$0.682891\pi$
$368$	−0.246343			−0.0128415
$369$	1.78253	−	6.58308i	0.0927949	−	0.342701i
$370$	10.3347			0.537278
$371$	18.2544	+	25.1251i	0.947723	+	1.30443i
$372$	7.81019	+	7.81019i	0.404940	+	0.404940i
$373$	10.7077	−	32.9549i	0.554424	−	1.70634i	−0.143036	−	0.989717i	$-0.545687\pi$
$373$	10.7077	−	32.9549i	0.554424	−	1.70634i	0.697460	−	0.716624i	$-0.254313\pi$
$374$	−10.1569	−	3.30018i	−0.525201	−	0.170648i
$375$	−2.06636	+	13.0465i	−0.106707	+	0.673719i
$376$	4.44114	+	28.0403i	0.229034	+	1.44607i
$377$	8.41822	−	2.73525i	0.433561	−	0.140872i
$378$			20.0907i			1.03335i
$379$	−2.94287	−	9.05722i	−0.151165	−	0.465238i	0.846587	−	0.532250i	$-0.178653\pi$
$379$	−2.94287	−	9.05722i	−0.151165	−	0.465238i	−0.997752	+	0.0670121i	$0.978653\pi$
$380$	0.577667	−	1.13373i	0.0296337	−	0.0581594i
$381$	−11.4139	+	5.81566i	−0.584751	+	0.297945i
$382$	−13.8215	−	2.18911i	−0.707171	−	0.112005i
$383$	−16.7656	+	16.7656i	−0.856684	+	0.856684i	−0.990946	−	0.134262i	$-0.957134\pi$
$383$	−16.7656	+	16.7656i	−0.856684	+	0.856684i	0.134262	+	0.990946i	$0.457134\pi$
$384$	−4.16111	−	8.16664i	−0.212346	−	0.416752i
$385$	−8.73016	−	6.34283i	−0.444930	−	0.323261i
$386$	18.4996	+	9.42601i	0.941604	+	0.479771i
$387$	−1.73756	+	1.26241i	−0.0883251	+	0.0641720i
$388$	4.49715	−	0.712279i	0.228308	−	0.0361605i
$389$	−6.45082	+	8.87880i	−0.327070	+	0.450173i	−0.940609	−	0.339491i	$-0.889745\pi$
$389$	−6.45082	+	8.87880i	−0.327070	+	0.450173i	0.613540	+	0.789664i	$0.289745\pi$
$390$	−3.35559	+	4.61858i	−0.169917	+	0.233871i
$391$	10.4183	−	1.65010i	0.526877	−	0.0834492i
$392$	20.7645	−	15.0863i	1.04876	−	0.761972i
$393$	−0.234185	−	0.119323i	−0.0118131	−	0.00601907i
$394$	−8.51040	−	6.18317i	−0.428748	−	0.311503i
$395$	−1.33143	−	2.61308i	−0.0669916	−	0.131479i
$396$	2.29266	−	2.29266i	0.115211	−	0.115211i
$397$	−25.3501	−	4.01506i	−1.27228	−	0.201510i	−0.516476	−	0.856302i	$-0.672756\pi$
$397$	−25.3501	−	4.01506i	−1.27228	−	0.201510i	−0.755809	+	0.654792i	$0.772756\pi$
$398$	−6.70505	+	3.41639i	−0.336094	+	0.171248i
$399$	2.47300	−	4.85353i	0.123805	−	0.242980i
$400$	−0.132823	−	0.408787i	−0.00664114	−	0.0204393i
$401$		−	26.7180i		−	1.33423i	−0.744953	−	0.667117i	$-0.767528\pi$
$401$		−	26.7180i		−	1.33423i	0.744953	−	0.667117i	$-0.232472\pi$
$402$	4.12094	−	1.33897i	0.205534	−	0.0667820i
$403$	−4.41605	−	27.8818i	−0.219979	−	1.38889i
$404$	−0.346262	+	2.18621i	−0.0172272	+	0.108768i
$405$	4.76683	+	1.54884i	0.236866	+	0.0769623i
$406$	2.25742	−	6.94763i	0.112034	−	0.344805i
$407$	−19.2693	−	19.2693i	−0.955142	−	0.955142i
$408$	−11.1534	−	15.3513i	−0.552174	−	0.760002i
$409$	35.3318			1.74704			0.873522	−	0.486785i	$-0.161831\pi$
$409$	35.3318			1.74704			0.873522	+	0.486785i	$0.161831\pi$
$410$	−0.303416	−	6.09680i	−0.0149846	−	0.301099i
$411$	8.94188			0.441070
$412$	−7.91590	−	10.8953i	−0.389988	−	0.536773i
$413$	27.1653	+	27.1653i	1.33672	+	1.33672i
$414$	0.644820	−	1.98455i	0.0316912	−	0.0975354i
$415$	−2.85414	−	0.927365i	−0.140104	−	0.0455225i
$416$	−3.77490	+	23.8338i	−0.185080	+	1.16855i
$417$	−1.56709	−	9.89423i	−0.0767408	−	0.484522i
$418$	2.07919	−	0.675571i	0.101697	−	0.0330433i
$419$		−	28.5341i		−	1.39398i	−0.717080	−	0.696991i	$-0.754522\pi$
$419$		−	28.5341i		−	1.39398i	0.717080	−	0.696991i	$-0.245478\pi$
$420$	−2.23446	−	6.87695i	−0.109030	−	0.335561i
$421$	4.65405	−	9.13410i	0.226825	−	0.445169i	−0.749344	−	0.662181i	$-0.769631\pi$
$421$	4.65405	−	9.13410i	0.226825	−	0.445169i	0.976169	+	0.217012i	$0.0696311\pi$
$422$	7.60514	−	3.87501i	0.370212	−	0.188633i
$423$	−10.4712	−	1.65848i	−0.509129	−	0.0806381i
$424$	−15.6595	+	15.6595i	−0.760494	+	0.760494i
$425$	8.35556	+	16.3987i	0.405304	+	0.795454i
$426$	−14.0833	−	10.2321i	−0.682338	−	0.495748i
$427$	−1.59715	−	0.813788i	−0.0772915	−	0.0393820i
$428$	12.6644	−	9.20119i	0.612155	−	0.444756i
$429$	14.8679	−	2.35485i	0.717831	−	0.113693i
$430$	−1.12992	+	1.55520i	−0.0544894	+	0.0749982i
$431$	12.2049	−	16.7986i	0.587891	−	0.809162i	−0.406642	−	0.913588i	$-0.633300\pi$
$431$	12.2049	−	16.7986i	0.587891	−	0.809162i	0.994533	+	0.104425i	$0.0333004\pi$
$432$	−0.623816	+	0.0988028i	−0.0300134	+	0.00475365i
$433$	−13.3108	+	9.67086i	−0.639676	+	0.464752i	−0.859739	−	0.510734i	$-0.829374\pi$
$433$	−13.3108	+	9.67086i	−0.639676	+	0.464752i	0.220063	+	0.975486i	$0.429374\pi$
$434$	−20.7586	−	10.5770i	−0.996446	−	0.507715i
$435$	−2.48322	−	1.80417i	−0.119061	−	0.0865032i
$436$	3.66726	+	7.19741i	0.175630	+	0.344693i
$437$	−1.52685	+	1.52685i	−0.0730392	+	0.0730392i
$438$	10.6892	+	1.69300i	0.510748	+	0.0808945i
$439$	20.4889	−	10.4396i	0.977882	−	0.498256i	0.109411	−	0.993997i	$-0.465103\pi$
$439$	20.4889	−	10.4396i	0.977882	−	0.498256i	0.868470	+	0.495741i	$0.165103\pi$
$440$	3.49345	−	6.85629i	0.166544	−	0.326861i
$441$	2.96184	+	9.11560i	0.141040	+	0.434076i
$442$			18.2896i			0.869948i
$443$	0.331688	−	0.107772i	0.0157590	−	0.00512040i	−0.301127	−	0.953584i	$-0.597363\pi$
$443$	0.331688	−	0.107772i	0.0157590	−	0.00512040i	0.316886	+	0.948464i	$0.397363\pi$
$444$	−2.85652	−	18.0354i	−0.135565	−	0.855921i
$445$	−1.86479	+	11.7738i	−0.0883996	+	0.558133i
$446$	4.51626	+	1.46742i	0.213851	+	0.0694844i
$447$	−2.09018	+	6.43293i	−0.0988623	+	0.304267i
$448$	14.7141	+	14.7141i	0.695178	+	0.695178i
$449$	−17.2577	−	23.7532i	−0.814440	−	1.12098i	−0.990623	−	0.136623i	$-0.956375\pi$
$449$	−17.2577	−	23.7532i	−0.814440	−	1.12098i	0.176183	−	0.984357i	$-0.443625\pi$
$450$	3.64089			0.171633
$451$	−10.8018	+	11.9333i	−0.508639	+	0.561917i
$452$	−15.8308			−0.744617
$453$	7.78157	+	10.7104i	0.365610	+	0.503219i
$454$	−4.35908	−	4.35908i	−0.204582	−	0.204582i
$455$	−5.71079	+	17.5760i	−0.267726	+	0.823976i
$456$	3.69426	+	1.20034i	0.172999	+	0.0562109i
$457$	−1.33751	+	8.44470i	−0.0625660	+	0.395026i	0.936455	+	0.350788i	$0.114086\pi$
$457$	−1.33751	+	8.44470i	−0.0625660	+	0.395026i	−0.999021	+	0.0442385i	$0.985914\pi$
$458$	−2.48164	−	15.6685i	−0.115960	−	0.732140i
$459$	25.7206	−	8.35714i	1.20054	−	0.390078i
$460$			2.86632i			0.133643i
$461$	10.8222	+	33.3073i	0.504041	+	1.55128i	0.802378	+	0.596817i	$0.203568\pi$
$461$	10.8222	+	33.3073i	0.504041	+	1.55128i	−0.298337	+	0.954461i	$0.596432\pi$
$462$	5.64020	−	11.0695i	0.262406	−	0.515000i
$463$	−4.11872	+	2.09859i	−0.191413	+	0.0975298i	−0.547070	−	0.837087i	$-0.684257\pi$
$463$	−4.11872	+	2.09859i	−0.191413	+	0.0975298i	0.355657	+	0.934616i	$0.384257\pi$
$464$	0.226826	+	0.0359258i	0.0105301	+	0.00166781i
$465$	−6.92198	+	6.92198i	−0.320999	+	0.320999i
$466$	1.75797	+	3.45021i	0.0814364	+	0.159828i
$467$	22.3850	+	16.2637i	1.03585	+	0.752592i	0.969472	−	0.245202i	$-0.0788544\pi$
$467$	22.3850	+	16.2637i	1.03585	+	0.752592i	0.0663821	+	0.997794i	$0.478854\pi$
$468$	−4.94750	−	2.52088i	−0.228698	−	0.116528i
$469$	11.3478	−	8.24465i	0.523992	−	0.380703i
$470$	−9.37224	+	1.48442i	−0.432309	+	0.0684711i
$471$	6.43130	−	8.85192i	0.296338	−	0.407875i
$472$	−16.1025	+	22.1632i	−0.741176	+	1.02014i
$473$	5.00643	−	0.792941i	0.230196	−	0.0364595i
$474$	2.73158	−	1.98461i	0.125465	−	0.0911560i
$475$	−3.35694	−	1.71045i	−0.154027	−	0.0784807i
$476$	−18.7414	−	13.6164i	−0.859009	−	0.624106i
$477$	−3.75453	−	7.36869i	−0.171908	−	0.337389i
$478$	6.98359	−	6.98359i	0.319422	−	0.319422i
$479$	5.04854	+	0.799610i	0.230674	+	0.0365351i	0.270701	−	0.962663i	$-0.412745\pi$
$479$	5.04854	+	0.799610i	0.230674	+	0.0365351i	−0.0400274	+	0.999199i	$0.512745\pi$
$480$	7.45586	−	3.79895i	0.340312	−	0.173398i
$481$	−21.1873	+	41.5825i	−0.966060	+	1.89600i
$482$	−5.32807	−	16.3981i	−0.242687	−	0.746913i
$483$			12.2707i			0.558338i
$484$	5.39091	−	1.75161i	0.245041	−	0.0796188i
$485$	0.631275	+	3.98571i	0.0286647	+	0.180982i
$486$	1.45456	−	9.18374i	0.0659802	−	0.416583i
$487$	21.2814	+	6.91475i	0.964353	+	0.313337i	0.748534	−	0.663096i	$-0.230758\pi$
$487$	21.2814	+	6.91475i	0.964353	+	0.313337i	0.215819	+	0.976433i	$0.430758\pi$
$488$	0.394994	−	1.21567i	0.0178806	−	0.0550307i
$489$	14.3908	+	14.3908i	0.650774	+	0.650774i
$490$	5.04247	+	6.94036i	0.227796	+	0.313534i
$491$	−40.1125			−1.81025			−0.905125	−	0.425146i	$-0.860223\pi$
$491$	−40.1125			−1.81025			−0.905125	+	0.425146i	$0.860223\pi$
$492$	−10.5558	+	2.21465i	−0.475892	+	0.0998443i
$493$	−9.83359			−0.442883
$494$	−2.20068	−	3.02898i	−0.0990133	−	0.136280i
$495$	2.03193	+	2.03193i	0.0913285	+	0.0913285i
$496$	0.226330	−	0.696573i	0.0101625	−	0.0312771i
$497$	−53.5941	−	17.4138i	−2.40402	−	0.781114i
$498$	0.540485	−	3.41249i	0.0242197	−	0.152917i
$499$	−4.96084	−	31.3215i	−0.222078	−	1.40214i	−0.806759	−	0.590880i	$-0.798781\pi$
$499$	−4.96084	−	31.3215i	−0.222078	−	1.40214i	0.584682	−	0.811263i	$-0.301219\pi$
$500$	−10.9366	+	3.55351i	−0.489098	+	0.158918i
$501$		−	0.263831i		−	0.0117871i
$502$	0.638869	+	1.96624i	0.0285141	+	0.0877574i
$503$	1.60627	−	3.15248i	0.0716200	−	0.140562i	−0.852420	−	0.522857i	$-0.824866\pi$
$503$	1.60627	−	3.15248i	0.0716200	−	0.140562i	0.924040	+	0.382295i	$0.124866\pi$
$504$	−10.8270	+	5.51665i	−0.482275	+	0.245731i
$505$	−1.93759	−	0.306883i	−0.0862214	−	0.0136561i
$506$	−3.48231	+	3.48231i	−0.154808	+	0.154808i
$507$	−3.49432	−	6.85799i	−0.155188	−	0.304574i
$508$	−9.02216	−	6.55498i	−0.400294	−	0.290830i
$509$	−4.40168	−	2.24277i	−0.195101	−	0.0994090i	0.353711	−	0.935355i	$-0.384920\pi$
$509$	−4.40168	−	2.24277i	−0.195101	−	0.0994090i	−0.548812	+	0.835946i	$0.684920\pi$
$510$	5.13105	−	3.72792i	0.227207	−	0.165075i
$511$	34.6025	−	5.48050i	1.53072	−	0.242443i
$512$	−0.742519	+	1.02199i	−0.0328150	+	0.0451660i
$513$	−3.25408	+	4.47886i	−0.143671	+	0.197746i
$514$	17.1250	−	2.71234i	0.755353	−	0.119636i
$515$	9.65623	−	7.01567i	0.425505	−	0.309147i
$516$	3.02632	+	1.54199i	0.133226	+	0.0678821i
$517$	20.2424	+	14.7070i	0.890260	+	0.646811i
$518$	17.4861	+	34.3184i	0.768295	+	1.50786i
$519$	−5.23127	+	5.23127i	−0.229627	+	0.229627i
$520$	−13.0160	−	2.06153i	−0.570790	−	0.0904042i
$521$	−1.05069	+	0.535356i	−0.0460318	+	0.0234544i	−0.476855	−	0.878982i	$-0.658223\pi$
$521$	−1.05069	+	0.535356i	−0.0460318	+	0.0234544i	0.430823	+	0.902436i	$0.358223\pi$
$522$	−0.883155	+	1.73329i	−0.0386547	+	0.0758640i
$523$	0.00907992	+	0.0279451i	0.000397037	+	0.00122195i	0.951255	−	0.308406i	$-0.0997955\pi$
$523$	0.00907992	+	0.0279451i	0.000397037	+	0.00122195i	−0.950858	+	0.309628i	$0.899796\pi$
$524$		−	0.228812i		−	0.00999571i
$525$	−20.3624	+	6.61613i	−0.888686	+	0.288752i
$526$	0.454672	+	2.87069i	0.0198246	+	0.125168i
$527$	−4.90605	+	30.9756i	−0.213711	+	1.34932i
$528$	0.371447	+	0.120690i	0.0161652	+	0.00525238i
$529$	−5.60429	+	17.2482i	−0.243665	+	0.749923i
$530$	−5.23407	−	5.23407i	−0.227354	−	0.227354i
$531$	−6.01324	−	8.27651i	−0.260952	−	0.359170i
$532$	4.74217			0.205599
$533$	25.1529	+	11.2783i	1.08949	+	0.488517i
$534$	−13.7240			−0.593896
$535$	8.15478	+	11.2241i	0.352562	+	0.485260i
$536$	7.07266	+	7.07266i	0.305492	+	0.305492i
$537$	7.16117	−	22.0398i	0.309027	−	0.951088i
$538$	9.41486	+	3.05907i	0.405903	+	0.131886i
$539$	3.53865	−	22.3422i	0.152420	−	0.962345i
$540$	1.14962	+	7.25842i	0.0494718	+	0.312353i
$541$	33.9890	−	11.0437i	1.46130	−	0.474806i	0.532834	−	0.846220i	$-0.321127\pi$
$541$	33.9890	−	11.0437i	1.46130	−	0.474806i	0.928467	+	0.371414i	$0.121127\pi$
$542$			5.67963i			0.243961i
$543$	−4.53389	−	13.9539i	−0.194568	−	0.598818i
$544$	12.1708	−	23.8864i	0.521817	−	1.02412i
$545$	−6.37888	+	3.25020i	−0.273241	+	0.139223i
$546$	−21.0144	−	3.32835i	−0.899333	−	0.142440i
$547$	−4.84258	+	4.84258i	−0.207054	+	0.207054i	−0.803014	−	0.595960i	$-0.796772\pi$
$547$	−4.84258	+	4.84258i	−0.207054	+	0.207054i	0.595960	+	0.803014i	$0.296772\pi$
$548$	3.53407	+	6.93601i	0.150968	+	0.296292i
$549$	0.386173	+	0.280571i	0.0164815	+	0.0119745i
$550$	−7.65622	−	3.90104i	−0.326462	−	0.166341i
$551$	1.62856	−	1.18322i	0.0693790	−	0.0504068i
$552$	−8.64241	+	1.36882i	−0.367845	+	0.0582610i
$553$	6.42448	−	8.84253i	0.273197	−	0.376023i
$554$	13.1544	−	18.1054i	0.558876	−	0.769227i
$555$	15.9843	−	2.53167i	0.678496	−	0.107463i
$556$	7.05537	−	5.12603i	0.299214	−	0.217392i
$557$	−21.5323	−	10.9713i	−0.912355	−	0.464868i	−0.0662005	−	0.997806i	$-0.521088\pi$
$557$	−21.5323	−	10.9713i	−0.912355	−	0.464868i	−0.846154	+	0.532938i	$0.821088\pi$
$558$	5.01921	+	3.64667i	0.212480	+	0.154376i
$559$	−3.94098	−	7.73462i	−0.166686	−	0.327139i
$560$	−0.339046	+	0.339046i	−0.0143273	+	0.0143273i
$561$	−16.5177	−	2.61614i	−0.697377	−	0.110454i
$562$	2.68909	−	1.37016i	0.113432	−	0.0577966i
$563$	3.35567	−	6.58588i	0.141425	−	0.277562i	−0.809420	−	0.587231i	$-0.800218\pi$
$563$	3.35567	−	6.58588i	0.141425	−	0.277562i	0.950844	+	0.309669i	$0.100218\pi$
$564$	5.18098	+	15.9454i	0.218159	+	0.671423i
$565$		−	14.0304i		−	0.590264i
$566$	−6.36522	+	2.06819i	−0.267550	+	0.0869323i
$567$	2.92215	+	18.4497i	0.122719	+	0.774816i
$568$	6.28618	−	39.6894i	0.263762	−	1.66533i
$569$	−3.63848	−	1.18221i	−0.152533	−	0.0495609i	0.231755	−	0.972774i	$-0.425553\pi$
$569$	−3.63848	−	1.18221i	−0.152533	−	0.0495609i	−0.384288	+	0.923213i	$0.625553\pi$
$570$	−0.401203	+	1.23478i	−0.0168046	+	0.0517191i
$571$	−7.80695	−	7.80695i	−0.326710	−	0.326710i	0.524624	−	0.851334i	$-0.324206\pi$
$571$	−7.80695	−	7.80695i	−0.326710	−	0.326710i	−0.851334	+	0.524624i	$0.824206\pi$
$572$	7.70283	+	10.6020i	0.322071	+	0.443293i
$573$	−21.9134			−0.915446
$574$	19.7322	−	11.3232i	0.823605	−	0.472620i
$575$	8.48705			0.353934
$576$	−3.25708	−	4.48298i	−0.135712	−	0.186791i
$577$	−7.23096	−	7.23096i	−0.301029	−	0.301029i	0.540388	−	0.841416i	$-0.318278\pi$
$577$	−7.23096	−	7.23096i	−0.301029	−	0.301029i	−0.841416	+	0.540388i	$0.818278\pi$
$578$	1.61250	−	4.96276i	0.0670712	−	0.206424i
$579$	30.9216	+	10.0470i	1.28506	+	0.417540i
$580$	0.418014	−	2.63924i	0.0173571	−	0.109588i
$581$	−1.74963	−	11.0468i	−0.0725871	−	0.458297i
$582$	−4.41851	+	1.43566i	−0.183153	+	0.0595100i
$583$			19.5180i			0.808353i
$584$	7.71994	+	23.7595i	0.319453	+	0.983176i
$585$	2.23419	−	4.38485i	0.0923725	−	0.181291i
$586$	4.72914	−	2.40962i	0.195359	−	0.0995403i
$587$	11.6235	+	1.84098i	0.479754	+	0.0759855i	0.391628	−	0.920124i	$-0.371912\pi$
$587$	11.6235	+	1.84098i	0.479754	+	0.0759855i	0.0881260	+	0.996109i	$0.471912\pi$
$588$	10.7180	−	10.7180i	0.442004	−	0.442004i
$589$	−2.91461	−	5.72024i	−0.120094	−	0.235698i
$590$	−7.40786	−	5.38213i	−0.304977	−	0.221579i
$591$	−14.6773	−	7.47848i	−0.603745	−	0.307623i
$592$	−0.979595	+	0.711718i	−0.0402611	+	0.0292514i
$593$	−26.9781	+	4.27291i	−1.10786	+	0.175467i	−0.683445	−	0.730002i	$-0.739519\pi$
$593$	−26.9781	+	4.27291i	−1.10786	+	0.175467i	−0.424412	+	0.905469i	$0.639519\pi$
$594$	−7.42162	+	10.2150i	−0.304513	+	0.419126i
$595$	12.0679	−	16.6100i	0.494734	−	0.680943i
$596$	−5.81597	+	0.921160i	−0.238232	+	0.0377322i
$597$	−9.53351	+	6.92650i	−0.390181	+	0.283483i
$598$	7.51472	+	3.82894i	0.307300	+	0.156577i
$599$	8.16465	+	5.93196i	0.333598	+	0.242373i	0.741956	−	0.670449i	$-0.233898\pi$
$599$	8.16465	+	5.93196i	0.333598	+	0.242373i	−0.408358	+	0.912822i	$0.633898\pi$
$600$	−6.93126	−	13.6034i	−0.282968	−	0.555355i
$601$	−9.88133	+	9.88133i	−0.403068	+	0.403068i	−0.879313	−	0.476245i	$-0.841998\pi$
$601$	−9.88133	+	9.88133i	−0.403068	+	0.403068i	0.476245	+	0.879313i	$0.341998\pi$
$602$	−7.07611	−	1.12074i	−0.288401	−	0.0456782i
$603$	−3.32808	+	1.69574i	−0.135530	+	0.0690560i
$604$	−5.23234	+	10.2690i	−0.212901	+	0.417841i
$605$	1.55241	+	4.77783i	0.0631145	+	0.194246i
$606$		−	2.25852i		−	0.0917461i
$607$	5.95620	−	1.93529i	0.241755	−	0.0785509i	−0.185634	−	0.982619i	$-0.559434\pi$
$607$	5.95620	−	1.93529i	0.241755	−	0.0785509i	0.427388	+	0.904068i	$0.359434\pi$
$608$	0.858493	+	5.42031i	0.0348165	+	0.219823i
$609$	1.78952	−	11.2986i	0.0725151	−	0.457843i
$610$	0.406327	+	0.132024i	0.0164517	+	0.00534549i
$611$	13.2415	−	40.7531i	0.535693	−	1.64869i
$612$	4.36202	+	4.36202i	0.176324	+	0.176324i
$613$	13.8469	+	19.0586i	0.559270	+	0.769769i	0.991233	−	0.132122i	$-0.0421790\pi$
$613$	13.8469	+	19.0586i	0.559270	+	0.769769i	−0.431963	+	0.901891i	$0.642179\pi$
$614$	−0.654075			−0.0263963
$615$	−1.96279	−	9.35533i	−0.0791474	−	0.377243i
$616$	28.6784			1.15549
$617$	−19.5926	−	26.9669i	−0.788768	−	1.08565i	−0.994260	−	0.106988i	$-0.965879\pi$
$617$	−19.5926	−	26.9669i	−0.788768	−	1.08565i	0.205492	−	0.978659i	$-0.434121\pi$
$618$	9.71669	+	9.71669i	0.390863	+	0.390863i
$619$	−13.3135	+	40.9747i	−0.535115	+	1.64691i	0.208286	+	0.978068i	$0.433211\pi$
$619$	−13.3135	+	40.9747i	−0.535115	+	1.64691i	−0.743401	+	0.668846i	$0.766789\pi$
$620$	−8.10498	−	2.63347i	−0.325504	−	0.105763i
$621$	1.95090	−	12.3175i	0.0782870	−	0.494285i
$622$	4.01040	+	25.3207i	0.160802	+	1.01527i
$623$	−42.2523	+	13.7286i	−1.69280	+	0.550025i
$624$		−	0.668867i		−	0.0267761i
$625$	2.79636	+	8.60631i	0.111854	+	0.344252i
$626$	−6.61959	+	12.9917i	−0.264572	+	0.519252i
$627$	3.05031	−	1.55421i	0.121818	−	0.0620692i
$628$	9.40806	+	1.49009i	0.375422	+	0.0594611i
$629$	36.6617	−	36.6617i	1.46180	−	1.46180i
$630$	−1.84390	−	3.61885i	−0.0734627	−	0.144179i
$631$	5.88538	+	4.27598i	0.234293	+	0.170224i	0.698737	−	0.715379i	$-0.253746\pi$
$631$	5.88538	+	4.27598i	0.234293	+	0.170224i	−0.464444	+	0.885603i	$0.653746\pi$
$632$	6.94455	+	3.53842i	0.276239	+	0.140751i
$633$	10.8133	−	7.85632i	0.429790	−	0.312261i
$634$	−29.6281	+	4.69263i	−1.17668	+	0.186368i
$635$	5.80952	−	7.99611i	0.230544	−	0.317316i
$636$	−7.68740	+	10.5808i	−0.304825	+	0.419556i
$637$	−38.2626	+	6.06020i	−1.51602	+	0.240114i
$638$	3.71428	−	2.69858i	0.147050	−	0.106838i
$639$	13.3706	+	6.81266i	0.528933	+	0.269505i
$640$	5.72123	+	4.15671i	0.226151	+	0.164309i
$641$	13.9831	+	27.4433i	0.552297	+	1.08394i	0.983368	+	0.181626i	$0.0581361\pi$
$641$	13.9831	+	27.4433i	0.552297	+	1.08394i	−0.431070	+	0.902318i	$0.641864\pi$
$642$	−11.2944	+	11.2944i	−0.445753	+	0.445753i
$643$	15.0094	+	2.37726i	0.591914	+	0.0937500i	0.445203	−	0.895429i	$-0.353131\pi$
$643$	15.0094	+	2.37726i	0.591914	+	0.0937500i	0.146711	+	0.989179i	$0.453131\pi$
$644$	−9.51814	+	4.84973i	−0.375067	+	0.191106i
$645$	−1.36662	+	2.68215i	−0.0538107	+	0.105609i
$646$	1.28534	+	3.95587i	0.0505711	+	0.155642i
$647$			5.82135i			0.228861i	0.993431	+	0.114430i	$0.0365043\pi$
$647$			5.82135i			0.228861i	−0.993431	+	0.114430i	$0.963496\pi$
$648$	−12.6684	+	4.11620i	−0.497660	+	0.161700i
$649$	3.77701	+	23.8471i	0.148261	+	0.936081i
$650$	−2.30205	+	14.5346i	−0.0902940	+	0.570094i
$651$	−34.6975	−	11.2739i	−1.35990	−	0.441859i
$652$	−5.47498	+	16.8503i	−0.214417	+	0.659907i
$653$	−7.96838	−	7.96838i	−0.311827	−	0.311827i	0.533790	−	0.845617i	$-0.320767\pi$
$653$	−7.96838	−	7.96838i	−0.311827	−	0.311827i	−0.845617	+	0.533790i	$0.820767\pi$
$654$	−4.84468	−	6.66814i	−0.189442	−	0.260745i
$655$	0.202791			0.00792368
$656$	0.448625	+	0.557000i	0.0175159	+	0.0217472i
$657$	−9.32926			−0.363969
$658$	−20.7869	−	28.6107i	−0.810356	−	1.11536i
$659$	−18.7955	−	18.7955i	−0.732169	−	0.732169i	0.238880	−	0.971049i	$-0.423220\pi$
$659$	−18.7955	−	18.7955i	−0.732169	−	0.732169i	−0.971049	+	0.238880i	$0.923220\pi$
$660$	1.40429	−	4.32197i	0.0546620	−	0.168232i
$661$	2.86486	+	0.930849i	0.111430	+	0.0362058i	0.364201	−	0.931320i	$-0.381342\pi$
$661$	2.86486	+	0.930849i	0.111430	+	0.0362058i	−0.252771	+	0.967526i	$0.581342\pi$
$662$	−1.67456	+	10.5727i	−0.0650835	+	0.410921i
$663$	4.48034	+	28.2878i	0.174002	+	1.09861i
$664$	7.58517	−	2.46457i	0.294362	−	0.0956439i
$665$			4.20287i			0.162980i
$666$	−3.16948	−	9.75466i	−0.122815	−	0.377986i
$667$	−2.05867	+	4.04037i	−0.0797120	+	0.156444i
$668$	0.204647	−	0.104273i	0.00791805	−	0.00403445i
$669$	7.34458	+	1.16327i	0.283958	+	0.0449745i
$670$	−2.36398	+	2.36398i	−0.0913285	+	0.0913285i
$671$	−0.511443	−	1.00376i	−0.0197440	−	0.0387499i
$672$	25.2302	+	18.3308i	0.973277	+	0.707127i
$673$	5.27484	+	2.68766i	0.203330	+	0.103602i	0.552691	−	0.833387i	$-0.313601\pi$
$673$	5.27484	+	2.68766i	0.203330	+	0.103602i	−0.349361	+	0.936988i	$0.613601\pi$
$674$	2.73448	−	1.98671i	0.105328	−	0.0765253i
$675$	21.4919	−	3.40398i	0.827222	−	0.131019i
$676$	3.93854	−	5.42093i	0.151482	−	0.208497i
$677$	−6.10855	+	8.40769i	−0.234770	+	0.323134i	−0.910105	−	0.414378i	$-0.863999\pi$
$677$	−6.10855	+	8.40769i	−0.234770	+	0.323134i	0.675335	+	0.737512i	$0.263999\pi$
$678$	15.9541	−	2.52689i	0.612715	−	0.0970446i
$679$	−12.1672	+	8.83999i	−0.466934	+	0.339248i
$680$	13.0448	+	6.64665i	0.500244	+	0.254887i
$681$	−7.80983	−	5.67417i	−0.299273	−	0.217435i
$682$	−6.64738	−	13.0462i	−0.254541	−	0.499565i
$683$	25.5356	−	25.5356i	0.977093	−	0.977093i	−0.0226507	−	0.999743i	$-0.507211\pi$
$683$	25.5356	−	25.5356i	0.977093	−	0.977093i	0.999743	+	0.0226507i	$0.00721056\pi$
$684$	−1.24726	−	0.197547i	−0.0476902	−	0.00755338i
$685$	−6.14721	+	3.13216i	−0.234873	+	0.119674i
$686$	−3.22387	+	6.32720i	−0.123088	+	0.241574i
$687$	−7.67650	−	23.6258i	−0.292877	−	0.901382i
$688$		−	0.225225i		−	0.00858663i
$689$	31.7901	−	10.3292i	1.21110	−	0.393512i
$690$	−0.457518	−	2.88866i	−0.0174174	−	0.109969i
$691$	0.650080	−	4.10445i	0.0247302	−	0.156140i	−0.972233	−	0.234015i	$-0.924813\pi$
$691$	0.650080	−	4.10445i	0.0247302	−	0.156140i	0.996963	+	0.0778748i	$0.0248134\pi$
$692$	−6.12532	−	1.99024i	−0.232850	−	0.0756575i
$693$	−3.30943	+	10.1854i	−0.125715	+	0.386910i
$694$	10.1442	+	10.1442i	0.385070	+	0.385070i
$695$	4.54307	+	6.25300i	0.172328	+	0.237190i
$696$	8.15735			0.309203
$697$	−22.7043	−	20.5516i	−0.859986	−	0.778447i
$698$	0.814099			0.0308141
$699$	3.56417	+	4.90565i	0.134809	+	0.185549i
$700$	−13.1797	−	13.1797i	−0.498148	−	0.498148i
$701$	−2.84581	+	8.75851i	−0.107485	+	0.330805i	−0.990306	−	0.138906i	$-0.955642\pi$
$701$	−2.84581	+	8.75851i	−0.107485	+	0.330805i	0.882821	+	0.469710i	$0.155642\pi$
$702$	20.5653	+	6.68208i	0.776189	+	0.252199i
$703$	−1.66033	+	10.4829i	−0.0626205	+	0.395370i
$704$	2.04582	+	12.9168i	0.0771049	+	0.486821i
$705$	−14.1320	+	4.59177i	−0.532243	+	0.172936i
$706$			3.82640i			0.144008i
$707$	−2.25928	−	6.95335i	−0.0849689	−	0.261507i
$708$	−7.34493	+	14.4152i	−0.276039	+	0.541758i
$709$	−29.0044	+	14.7785i	−1.08928	+	0.555018i	−0.903941	−	0.427656i	$-0.859339\pi$
$709$	−29.0044	+	14.7785i	−1.08928	+	0.555018i	−0.185342	+	0.982674i	$0.559339\pi$
$710$	13.2659	+	2.10111i	0.497859	+	0.0788531i
$711$	−2.05809	+	2.05809i	−0.0771843	+	0.0771843i
$712$	−14.3825	−	28.2273i	−0.539008	−	1.05786i
$713$	11.7000	+	8.50052i	0.438167	+	0.318347i
$714$	21.0609	+	10.7310i	0.788183	+	0.401599i
$715$	−9.39631	+	6.82682i	−0.351402	+	0.255309i
$716$	19.9261	−	3.15598i	0.744673	−	0.117945i
$717$	9.09048	−	12.5120i	0.339490	−	0.467268i
$718$	13.5690	−	18.6762i	0.506392	−	0.696989i
$719$	−10.0466	+	1.59122i	−0.374675	+	0.0593427i	−0.340932	−	0.940088i	$-0.610743\pi$
$719$	−10.0466	+	1.59122i	−0.374675	+	0.0593427i	−0.0337427	+	0.999431i	$0.510743\pi$
$720$	0.103298	−	0.0750502i	0.00384968	−	0.00279695i
$721$	39.6349	+	20.1950i	1.47608	+	0.752101i
$722$	12.9653	+	9.41981i	0.482517	+	0.350569i
$723$	−12.2577	−	24.0570i	−0.455868	−	0.894691i
$724$	9.03178	−	9.03178i	0.335664	−	0.335664i
$725$	−7.81467	−	1.23772i	−0.290230	−	0.0459678i
$726$	−5.15334	+	2.62576i	−0.191258	+	0.0974509i
$727$	20.8419	−	40.9046i	0.772985	−	1.51707i	−0.0809673	−	0.996717i	$-0.525801\pi$
$727$	20.8419	−	40.9046i	0.772985	−	1.51707i	0.853952	−	0.520352i	$-0.174199\pi$
$728$	−15.1770	−	46.7101i	−0.562498	−	1.73119i
$729$		−	28.5708i		−	1.05818i
$730$	−7.94144	+	2.58033i	−0.293926	+	0.0955023i
$731$	1.50865	+	9.52523i	0.0557994	+	0.352304i
$732$	0.118089	−	0.745582i	0.00436468	−	0.0275575i
$733$	−35.9271	−	11.6734i	−1.32700	−	0.431167i	−0.442104	−	0.896964i	$-0.645768\pi$
$733$	−35.9271	−	11.6734i	−1.32700	−	0.431167i	−0.884892	+	0.465797i	$0.845768\pi$
$734$	3.78264	−	11.6418i	0.139620	−	0.429706i
$735$	9.49913	+	9.49913i	0.350381	+	0.350381i
$736$	−7.26636	−	10.0013i	−0.267842	−	0.368652i
$737$	8.81535			0.324718
$738$	−5.66154	+	2.15617i	−0.208404	+	0.0793696i
$739$	−37.9331			−1.39539			−0.697697	−	0.716393i	$-0.745792\pi$
$739$	−37.9331			−1.39539			−0.697697	+	0.716393i	$0.745792\pi$
$740$	8.28119	+	11.3981i	0.304423	+	0.419002i
$741$	−4.14570	−	4.14570i	−0.152296	−	0.152296i
$742$	8.52479	−	26.2366i	0.312955	−	0.963176i
$743$	18.8073	+	6.11086i	0.689973	+	0.224186i	0.632956	−	0.774188i	$-0.281841\pi$
$743$	18.8073	+	6.11086i	0.689973	+	0.224186i	0.0570164	+	0.998373i	$0.481841\pi$
$744$	4.06976	−	25.6954i	0.149204	−	0.942040i
$745$	−0.816401	−	5.15455i	−0.0299106	−	0.188848i
$746$	−29.2733	+	9.51148i	−1.07177	+	0.348240i
$747$			2.97834i			0.108972i
$748$	−4.49895	−	13.8464i	−0.164498	−	0.506273i
$749$	−23.4740	+	46.0703i	−0.857721	+	1.68337i
$750$	10.4546	−	5.32688i	0.381748	−	0.194510i
$751$	15.6451	+	2.47795i	0.570899	+	0.0904216i	0.435209	−	0.900330i	$-0.356675\pi$
$751$	15.6451	+	2.47795i	0.570899	+	0.0904216i	0.135691	+	0.990751i	$0.456675\pi$
$752$	0.786137	−	0.786137i	0.0286675	−	0.0286675i
$753$	1.46977	+	2.88459i	0.0535615	+	0.105120i
$754$	−6.36098	−	4.62152i	−0.231653	−	0.168306i
$755$	−9.10120	−	4.63729i	−0.331226	−	0.168768i
$756$	−22.1578	+	16.0986i	−0.805871	+	0.585499i
$757$	22.6735	−	3.59113i	0.824083	−	0.130522i	0.269870	−	0.962897i	$-0.413019\pi$
$757$	22.6735	−	3.59113i	0.824083	−	0.130522i	0.554213	+	0.832375i	$0.313019\pi$
$758$	−4.97232	+	6.84381i	−0.180603	+	0.248578i
$759$	−4.53289	+	6.23899i	−0.164534	+	0.226461i
$760$	−2.96012	+	0.468837i	−0.107375	+	0.0170065i
$761$	36.5322	−	26.5422i	1.32429	−	0.962155i	0.324424	−	0.945912i	$-0.394830\pi$
$761$	36.5322	−	26.5422i	1.32429	−	0.962155i	0.999868	−	0.0162427i	$-0.00517045\pi$
$762$	10.1388	+	5.16596i	0.367289	+	0.187143i
$763$	−21.5858	−	15.6830i	−0.781458	−	0.567762i
$764$	−8.66079	−	16.9978i	−0.313336	−	0.614957i
$765$	−3.86595	+	3.86595i	−0.139774	+	0.139774i
$766$	20.8021	+	3.29473i	0.751610	+	0.119043i
$767$	36.8423	−	18.7721i	1.33030	−	0.677820i
$768$	−10.2669	+	20.1500i	−0.370476	+	0.727101i
$769$	−6.93059	−	21.3302i	−0.249924	−	0.769186i	−0.994788	−	0.101969i	$-0.967486\pi$
$769$	−6.93059	−	21.3302i	−0.249924	−	0.769186i	0.744864	−	0.667216i	$-0.232514\pi$
$770$			9.58553i			0.345439i
$771$	25.8221	−	8.39012i	0.929962	−	0.302163i
$772$	4.42780	+	27.9560i	0.159360	+	1.00616i
$773$	1.69195	−	10.6826i	0.0608553	−	0.384225i	−0.938397	−	0.345559i	$-0.887689\pi$
$773$	1.69195	−	10.6826i	0.0608553	−	0.384225i	0.999252	−	0.0386657i	$-0.0123108\pi$
$774$	1.81443	+	0.589544i	0.0652184	+	0.0211907i
$775$	−7.79759	+	23.9985i	−0.280098	+	0.862052i
$776$	−7.58336	−	7.58336i	−0.272227	−	0.272227i
$777$	35.4519	+	48.7953i	1.27183	+	1.75052i
$778$	9.74874			0.349509
$779$	6.23295	+	0.671716i	0.223319	+	0.0240667i
$780$	−7.78261			−0.278662
$781$	−20.8169	−	28.6519i	−0.744885	−	1.02525i
$782$	−6.62544	−	6.62544i	−0.236925	−	0.236925i
$783$	−3.59269	+	11.0572i	−0.128392	+	0.395151i
$784$	−0.955917	−	0.310596i	−0.0341399	−	0.0110927i
$785$	−1.32063	+	8.33813i	−0.0471353	+	0.297601i
$786$	0.0365227	+	0.230596i	0.00130272	+	0.00822507i
$787$	−27.7465	+	9.01540i	−0.989057	+	0.321364i	−0.758485	−	0.651691i	$-0.774060\pi$
$787$	−27.7465	+	9.01540i	−0.989057	+	0.321364i	−0.230573	+	0.973055i	$0.574060\pi$
$788$		−	14.3406i		−	0.510862i
$789$	1.40644	+	4.32859i	0.0500707	+	0.154102i
$790$	−1.18269	+	2.32116i	−0.0420782	+	0.0825832i
$791$	46.5906	−	23.7391i	1.65657	−	0.844065i
$792$	−7.54284	−	1.19467i	−0.268023	−	0.0424507i
$793$	−1.36422	+	1.36422i	−0.0484449	+	0.0484449i
$794$	10.3504	+	20.3139i	0.367323	+	0.720912i
$795$	−9.37749	−	6.81315i	−0.332585	−	0.241637i
$796$	−9.14063	−	4.65739i	−0.323981	−	0.165077i
$797$	−17.5913	+	12.7808i	−0.623115	+	0.452720i	−0.854008	−	0.520259i	$-0.825835\pi$
$797$	−17.5913	+	12.7808i	−0.623115	+	0.452720i	0.230893	+	0.972979i	$0.425835\pi$
$798$	−4.77913	+	0.756940i	−0.169179	+	0.0267954i
$799$	−27.9815	+	38.5132i	−0.989913	+	1.36250i
$800$	12.6785	−	17.4505i	0.448253	−	0.616967i
$801$	11.6849	−	1.85070i	0.412865	−	0.0653913i
$802$	−19.2006	+	13.9500i	−0.677995	+	0.492592i
$803$	19.6180	+	9.99586i	0.692303	+	0.352746i
$804$	4.77884	+	3.47203i	0.168537	+	0.122449i
$805$	−4.29820	−	8.43569i	−0.151492	−	0.297319i
$806$	−17.7312	+	17.7312i	−0.624555	+	0.624555i
$807$	15.3109	+	2.42501i	0.538970	+	0.0853645i
$808$	4.64528	−	2.36689i	0.163421	−	0.0832669i
$809$	−21.4765	+	42.1499i	−0.755072	+	1.48191i	0.117314	+	0.993095i	$0.462571\pi$
$809$	−21.4765	+	42.1499i	−0.755072	+	1.48191i	−0.872386	+	0.488817i	$0.837429\pi$
$810$	−1.37581	−	4.23430i	−0.0483410	−	0.148778i
$811$			53.0392i			1.86246i	0.364436	+	0.931228i	$0.381262\pi$
$811$			53.0392i			1.86246i	−0.364436	+	0.931228i	$0.618738\pi$
$812$	9.47134	−	3.07743i	0.332379	−	0.107996i
$813$	1.39132	+	8.78445i	0.0487957	+	0.308084i
$814$	−3.78673	+	23.9085i	−0.132725	+	0.837992i
$815$	−14.9340	−	4.85234i	−0.523114	−	0.169970i
$816$	−0.229626	+	0.706715i	−0.00803850	+	0.0247400i
$817$	−1.39597	−	1.39597i	−0.0488386	−	0.0488386i
$818$	−18.4474	−	25.3907i	−0.645000	−	0.887766i
$819$	18.3409			0.640882
$820$	6.48097	−	5.21998i	0.226325	−	0.182290i
$821$	−38.9809			−1.36044			−0.680222	−	0.733006i	$-0.738117\pi$
$821$	−38.9809			−1.36044			−0.680222	+	0.733006i	$0.738117\pi$
$822$	−4.66874	−	6.42596i	−0.162841	−	0.224131i
$823$	1.02441	+	1.02441i	0.0357087	+	0.0357087i	0.724736	−	0.689027i	$-0.241962\pi$
$823$	1.02441	+	1.02441i	0.0357087	+	0.0357087i	−0.689027	+	0.724736i	$0.741962\pi$
$824$	−9.80219	+	30.1680i	−0.341475	+	1.05095i
$825$	−12.7972	−	4.15805i	−0.445540	−	0.144765i
$826$	5.33844	−	33.7056i	0.185748	−	1.17277i
$827$	6.74246	+	42.5702i	0.234458	+	1.48031i	0.771215	+	0.636575i	$0.219649\pi$
$827$	6.74246	+	42.5702i	0.234458	+	1.48031i	−0.536756	+	0.843737i	$0.680351\pi$
$828$	2.70544	−	0.879049i	0.0940204	−	0.0305491i
$829$		−	12.8894i		−	0.447667i	−0.974627	−	0.223834i	$-0.928143\pi$
$829$		−	12.8894i		−	0.447667i	0.974627	−	0.223834i	$-0.0718572\pi$
$830$	0.823763	+	2.53528i	0.0285932	+	0.0880010i
$831$	15.9101	−	31.2253i	0.551915	−	1.08319i
$832$	19.9557	−	10.1679i	0.691838	−	0.352509i
$833$	42.5082	+	6.73263i	1.47282	+	0.233272i
$834$	−6.29215	+	6.29215i	−0.217879	+	0.217879i
$835$	0.0924146	+	0.181374i	0.00319814	+	0.00627670i
$836$	2.41113	+	1.75179i	0.0833907	+	0.0605869i
$837$	33.0374	+	16.8334i	1.14194	+	0.581846i
$838$	−20.5057	+	14.8982i	−0.708356	+	0.514651i
$839$	−41.2093	+	6.52691i	−1.42270	+	0.225334i	−0.819877	−	0.572539i	$-0.805958\pi$
$839$	−41.2093	+	6.52691i	−1.42270	+	0.225334i	−0.602825	+	0.797873i	$0.705958\pi$
$840$	−10.0108	+	13.7786i	−0.345404	+	0.475408i
$841$	−14.5610	+	20.0414i	−0.502102	+	0.691084i
$842$	−8.99408	+	1.42452i	−0.309956	+	0.0490923i
$843$	3.82345	−	2.77790i	0.131687	−	0.0956760i
$844$	10.3677	+	5.28260i	0.356870	+	0.181834i
$845$	4.80444	+	3.49063i	0.165278	+	0.120081i
$846$	4.27540	+	8.39095i	0.146991	+	0.288487i
$847$	−13.2390	+	13.2390i	−0.454898	+	0.454898i
$848$	0.856573	+	0.135668i	0.0294148	+	0.00465885i
$849$	−9.33818	+	4.75804i	−0.320485	+	0.163295i
$850$	7.42211	−	14.5667i	0.254576	−	0.499634i
$851$	−7.38819	−	22.7385i	−0.253264	−	0.779466i
$852$		−	23.7313i		−	0.813021i
$853$	32.3174	−	10.5005i	1.10653	−	0.359532i	0.301915	−	0.953335i	$-0.402374\pi$
$853$	32.3174	−	10.5005i	1.10653	−	0.359532i	0.804610	+	0.593803i	$0.202374\pi$
$854$	0.249086	+	1.57267i	0.00852354	+	0.0538155i
$855$	0.175081	−	1.10542i	0.00598763	−	0.0378044i
$856$	−35.0664	−	11.3938i	−1.19854	−	0.389430i
$857$	−5.10325	+	15.7062i	−0.174324	+	0.536513i	−0.999602	−	0.0282132i	$-0.991018\pi$
$857$	−5.10325	+	15.7062i	−0.174324	+	0.536513i	0.825278	+	0.564726i	$0.191018\pi$
$858$	−9.45514	−	9.45514i	−0.322793	−	0.322793i
$859$	−24.0112	−	33.0486i	−0.819252	−	1.12760i	−0.989829	−	0.142260i	$-0.954563\pi$
$859$	−24.0112	−	33.0486i	−0.819252	−	1.12760i	0.170577	−	0.985344i	$-0.445437\pi$
$860$	−2.62061			−0.0893620
$861$	27.7451	−	22.3468i	0.945551	−	0.761576i
$862$	−18.4446			−0.628224
$863$	19.3968	+	26.6975i	0.660276	+	0.908792i	0.999491	−	0.0319168i	$-0.0101612\pi$
$863$	19.3968	+	26.6975i	0.660276	+	0.908792i	−0.339214	+	0.940709i	$0.610161\pi$
$864$	−22.4120	−	22.4120i	−0.762472	−	0.762472i
$865$	1.76390	−	5.42872i	0.0599743	−	0.184582i
$866$	13.8997	+	4.51628i	0.472330	+	0.153469i
$867$	1.27827	−	8.07071i	0.0434125	−	0.274096i
$868$	−4.96849	−	31.3698i	−0.168642	−	1.06476i
$869$	6.53298	−	2.12269i	0.221616	−	0.0720075i
$870$			2.72653i			0.0924380i
$871$	−4.66521	−	14.3580i	−0.158075	−	0.486504i
$872$	8.63776	−	16.9526i	0.292511	−	0.574086i
$873$	3.56840	−	1.81819i	0.120772	−	0.0615364i
$874$	1.89445	+	0.300052i	0.0640808	+	0.0101494i
$875$	26.8581	−	26.8581i	0.907969	−	0.907969i
$876$	6.69800	+	13.1456i	0.226304	+	0.444148i
$877$	−9.01360	−	6.54877i	−0.304368	−	0.221136i	0.425108	−	0.905143i	$-0.360236\pi$
$877$	−9.01360	−	6.54877i	−0.304368	−	0.221136i	−0.729476	+	0.684006i	$0.760236\pi$
$878$	−18.2000	−	9.27335i	−0.614219	−	0.312960i
$879$	6.72408	−	4.88533i	0.226798	−	0.164778i
$880$	−0.297632	+	0.0471402i	−0.0100332	+	0.00158910i
$881$	14.5003	−	19.9579i	0.488527	−	0.672400i	−0.491589	−	0.870828i	$-0.663584\pi$
$881$	14.5003	−	19.9579i	0.488527	−	0.672400i	0.980115	+	0.198428i	$0.0635836\pi$
$882$	5.00437	−	6.88793i	0.168506	−	0.231929i
$883$	21.4782	−	3.40182i	0.722800	−	0.114480i	0.215814	−	0.976435i	$-0.430760\pi$
$883$	21.4782	−	3.40182i	0.722800	−	0.114480i	0.506986	+	0.861954i	$0.330760\pi$
$884$	−20.1714	+	14.6554i	−0.678438	+	0.492914i
$885$	−12.7759	−	6.50963i	−0.429456	−	0.218819i
$886$	−0.250630	−	0.182093i	−0.00842008	−	0.00611755i
$887$	−20.8531	−	40.9264i	−0.700177	−	1.37418i	−0.917366	−	0.398045i	$-0.869689\pi$
$887$	−20.8531	−	40.9264i	−0.700177	−	1.37418i	0.217189	−	0.976130i	$-0.430311\pi$
$888$	−30.4123	+	30.4123i	−1.02057	+	1.02057i
$889$	36.3821	+	5.76236i	1.22022	+	0.193263i
$890$	9.43475	−	4.80725i	0.316254	−	0.161139i
$891$	−5.32970	+	10.4601i	−0.178552	+	0.350427i
$892$	2.00046	+	6.15678i	0.0669803	+	0.206144i
$893$		−	9.74509i		−	0.326107i
$894$	5.71427	−	1.85668i	0.191114	−	0.0620966i
$895$	2.79707	+	17.6600i	0.0934956	+	0.590308i
$896$	−4.12297	+	26.0314i	−0.137739	+	0.869649i
$897$	12.5607	+	4.08121i	0.419388	+	0.136268i
$898$	−8.05931	+	24.8040i	−0.268943	+	0.827721i
$899$	−9.53336	−	9.53336i	−0.317955	−	0.317955i
$900$	2.91743	+	4.01550i	0.0972477	+	0.133850i
$901$	−37.1350			−1.23714
$902$	14.2156	+	1.53199i	0.473327	+	0.0510097i
$903$	−11.2189			−0.373340
$904$	21.9169	+	30.1661i	0.728947	+	1.00331i
$905$	8.00464	+	8.00464i	0.266083	+	0.266083i
$906$	3.63399	−	11.1843i	0.120731	−	0.371572i
$907$	46.8965	+	15.2376i	1.55717	+	0.505956i	0.956050	−	0.293203i	$-0.0947211\pi$
$907$	46.8965	+	15.2376i	1.55717	+	0.505956i	0.601121	+	0.799158i	$0.294721\pi$
$908$	1.31467	−	8.30049i	0.0436288	−	0.275462i
$909$	0.304565	+	1.92295i	0.0101018	+	0.0637801i
$910$	15.6125	−	5.07281i	0.517549	−	0.168162i
$911$			8.88306i			0.294309i	0.989114	+	0.147154i	$0.0470114\pi$
$911$			8.88306i			0.294309i	−0.989114	+	0.147154i	$0.952989\pi$
$912$	−0.0470061	−	0.144670i	−0.00155653	−	0.00479050i
$913$	3.19115	−	6.26299i	0.105612	−	0.207275i
$914$	6.76701	−	3.44797i	0.223833	−	0.114049i
$915$	0.660791	+	0.104659i	0.0218451	+	0.00345992i
$916$	15.2921	−	15.2921i	0.505264	−	0.505264i
$917$	0.343116	+	0.673403i	0.0113307	+	0.0222377i
$918$	−19.4350	−	14.1204i	−0.641451	−	0.466042i
$919$	−10.9177	−	5.56284i	−0.360141	−	0.183501i	0.264552	−	0.964371i	$-0.414776\pi$
$919$	−10.9177	−	5.56284i	−0.360141	−	0.183501i	−0.624693	+	0.780870i	$0.714776\pi$
$920$	5.46187	−	3.96828i	0.180072	−	0.130830i
$921$	−1.01163	+	0.160226i	−0.0333343	+	0.00527964i
$922$	18.2854	−	25.1677i	0.602197	−	0.828854i
$923$	−35.6504	+	49.0686i	−1.17345	+	1.61511i
$924$	16.7279	−	2.64944i	0.550308	−	0.0871603i
$925$	33.7492	−	24.5203i	1.10967	−	0.806221i
$926$	3.65859	+	1.86415i	0.120229	+	0.0612596i
$927$	−9.58328	−	6.96266i	−0.314756	−	0.228684i
$928$	5.23214	+	10.2687i	0.171753	+	0.337085i
$929$	20.0281	−	20.0281i	0.657099	−	0.657099i	−0.297593	−	0.954693i	$-0.596184\pi$
$929$	20.0281	−	20.0281i	0.657099	−	0.657099i	0.954693	+	0.297593i	$0.0961839\pi$
$930$	8.58850	+	1.36028i	0.281628	+	0.0446055i
$931$	−7.84996	+	3.99975i	−0.257272	+	0.131087i
$932$	−2.39655	+	4.70349i	−0.0785016	+	0.154068i
$933$	12.4054	+	38.1800i	0.406135	+	1.24996i
$934$		−	24.5783i		−	0.804226i
$935$	12.2717	−	3.98731i	0.401327	−	0.130399i
$936$	2.04596	+	12.9177i	0.0668742	+	0.422227i
$937$	6.70744	−	42.3491i	0.219122	−	1.38348i	−0.595436	−	0.803403i	$-0.703021\pi$
$937$	6.70744	−	42.3491i	0.219122	−	1.38348i	0.814558	−	0.580082i	$-0.196979\pi$
$938$	−11.8498	−	3.85024i	−0.386910	−	0.125715i
$939$	−7.05571	+	21.7153i	−0.230254	+	0.708650i
$940$	−9.14710	−	9.14710i	−0.298345	−	0.298345i
$941$	−24.8897	−	34.2578i	−0.811382	−	1.11677i	−0.991109	−	0.133055i	$-0.957521\pi$
$941$	−24.8897	−	34.2578i	−0.811382	−	1.11677i	0.179727	−	0.983717i	$-0.442479\pi$
$942$	−9.71923			−0.316670
$943$	−13.1973	+	5.02611i	−0.429762	+	0.163673i
$944$	1.07281			0.0349172
$945$	−14.2678	−	19.6379i	−0.464130	−	0.638820i
$946$	−3.18380	−	3.18380i	−0.103514	−	0.103514i
$947$	−1.31206	+	4.03811i	−0.0426362	+	0.131221i	−0.970109	−	0.242670i	$-0.921977\pi$
$947$	−1.31206	+	4.03811i	−0.0426362	+	0.131221i	0.927473	+	0.373891i	$0.121977\pi$
$948$	4.37760	+	1.42237i	0.142178	+	0.0461964i
$949$	5.89869	−	37.2428i	0.191479	−	1.20895i
$950$	0.523537	+	3.30548i	0.0169858	+	0.107244i
$951$	−44.6750	+	14.5158i	−1.44869	+	0.470707i
$952$			54.5635i			1.76841i
$953$	11.2759	+	34.7035i	0.365261	+	1.12416i	0.949818	+	0.312804i	$0.101268\pi$
$953$	11.2759	+	34.7035i	0.365261	+	1.12416i	−0.584557	+	0.811353i	$0.698732\pi$
$954$	−3.33509	+	6.54549i	−0.107978	+	0.211918i
$955$	15.0647	−	7.67584i	0.487482	−	0.248384i
$956$	13.2981	+	2.10621i	0.430090	+	0.0681196i
$957$	5.08365	−	5.08365i	0.164331	−	0.164331i
$958$	−2.06132	−	4.04556i	−0.0665981	−	0.130706i
$959$	−20.8018	−	15.1134i	−0.671726	−	0.488038i
$960$	−6.92007	−	3.52595i	−0.223344	−	0.113800i
$961$	−9.70657	+	7.05224i	−0.313115	+	0.227491i
$962$	40.9451	−	6.48506i	1.32012	−	0.209087i
$963$	8.09317	−	11.1393i	0.260799	−	0.358959i
$964$	13.8159	−	19.0160i	0.444982	−	0.612464i
$965$	−24.7767	+	3.92425i	−0.797592	+	0.126326i
$966$	8.81821	−	6.40680i	0.283721	−	0.206136i
$967$	35.6031	+	18.1407i	1.14492	+	0.583365i	0.920351	−	0.391094i	$-0.127903\pi$
$967$	35.6031	+	18.1407i	1.14492	+	0.583365i	0.224567	+	0.974459i	$0.427903\pi$
$968$	−10.8012	−	7.84754i	−0.347164	−	0.252230i
$969$	2.95704	+	5.80352i	0.0949938	+	0.186436i
$970$	2.53468	−	2.53468i	0.0813837	−	0.0813837i
$971$	−24.6105	−	3.89792i	−0.789788	−	0.125090i	−0.251507	−	0.967855i	$-0.580926\pi$
$971$	−24.6105	−	3.89792i	−0.789788	−	0.125090i	−0.538281	+	0.842765i	$0.680926\pi$
$972$	11.2942	−	5.75468i	0.362261	−	0.184581i
$973$	−13.0775	+	25.6660i	−0.419245	+	0.822814i
$974$	−6.14227	−	18.9040i	−0.196811	−	0.605722i
$975$			23.0440i			0.737998i
$976$	−0.0476064	+	0.0154683i	−0.00152385	+	0.000495127i
$977$	1.49380	+	9.43148i	0.0477909	+	0.301740i	0.999993	−	0.00372882i	$-0.00118692\pi$
$977$	1.49380	+	9.43148i	0.0477909	+	0.301740i	−0.952202	+	0.305469i	$0.901187\pi$
$978$	2.82803	−	17.8555i	0.0904305	−	0.570956i
$979$	−26.5544	−	8.62805i	−0.848683	−	0.275754i
$980$	−3.61394	+	11.1226i	−0.115443	+	0.355298i
$981$	5.02406	+	5.02406i	0.160406	+	0.160406i
$982$	20.9435	+	28.8263i	0.668335	+	0.919884i
$983$	−21.0349			−0.670908			−0.335454	−	0.942057i	$-0.608890\pi$
$983$	−21.0349			−0.670908			−0.335454	+	0.942057i	$0.608890\pi$
$984$	18.8341	+	17.0483i	0.600408	+	0.543481i
$985$	12.7097			0.404965
$986$	5.13432	+	7.06678i	0.163510	+	0.225052i
$987$	−39.1588	−	39.1588i	−1.24644	−	1.24644i
$988$	1.57723	−	4.85422i	0.0501784	−	0.154433i
$989$	4.22951	+	1.37425i	0.134491	+	0.0436986i
$990$	0.399308	−	2.52113i	0.0126909	−	0.0801269i
$991$	−1.31916	−	8.32884i	−0.0419045	−	0.264574i	0.957837	−	0.287312i	$-0.0927617\pi$
$991$	−1.31916	−	8.32884i	−0.0419045	−	0.264574i	−0.999741	+	0.0227378i	$0.992762\pi$
$992$	34.9563	−	11.3580i	1.10986	−	0.360617i
$993$			16.7626i			0.531945i
$994$	15.4684	+	47.6068i	0.490627	+	1.51000i
$995$	4.12772	−	8.10111i	0.130858	−	0.256823i
$996$	4.19669	−	2.13832i	0.132977	−	0.0677553i
$997$	11.9561	+	1.89365i	0.378652	+	0.0599726i	0.342860	−	0.939387i	$-0.388604\pi$
$997$	11.9561	+	1.89365i	0.378652	+	0.0599726i	0.0357924	+	0.999359i	$0.488604\pi$
$998$	−19.9186	+	19.9186i	−0.630514	+	0.630514i
$999$	−27.8291	−	54.6178i	−0.880475	−	1.72803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.2.g.a.5.2	✓	24
3.2	odd	2		369.2.u.a.46.2		24
4.3	odd	2		656.2.bs.d.497.2		24
41.19	odd	40		1681.2.a.m.1.8		24
41.22	odd	40		1681.2.a.m.1.7		24
41.33	even	20	inner	41.2.g.a.33.2	yes	24
123.74	odd	20		369.2.u.a.361.2		24
164.115	odd	20		656.2.bs.d.33.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.5.2	✓	24	1.1	even	1	trivial
41.2.g.a.33.2	yes	24	41.33	even	20	inner
369.2.u.a.46.2		24	3.2	odd	2
369.2.u.a.361.2		24	123.74	odd	20
656.2.bs.d.33.2		24	164.115	odd	20
656.2.bs.d.497.2		24	4.3	odd	2
1681.2.a.m.1.7		24	41.22	odd	40
1681.2.a.m.1.8		24	41.19	odd	40

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:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	41.g (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.522120 - 0.718637i) q^{2} +(-0.983583 - 0.983583i) q^{3} +(0.374204 - 1.15168i) q^{4} +(1.02071 + 0.331648i) q^{5} +(-0.193291 + 1.22039i) q^{6} +(0.625712 + 3.95059i) q^{7} +(-2.71264 + 0.881390i) q^{8} -1.06513i q^{9} +O(q^{10})\)	\(q+(-0.522120 - 0.718637i) q^{2} +(-0.983583 - 0.983583i) q^{3} +(0.374204 - 1.15168i) q^{4} +(1.02071 + 0.331648i) q^{5} +(-0.193291 + 1.22039i) q^{6} +(0.625712 + 3.95059i) q^{7} +(-2.71264 + 0.881390i) q^{8} -1.06513i q^{9} +(-0.294598 - 0.906679i) q^{10} +(-1.14123 + 2.23980i) q^{11} +(-1.50084 + 0.764715i) q^{12} +(4.25204 + 0.673457i) q^{13} +(2.51234 - 2.51234i) q^{14} +(-0.677748 - 1.33015i) q^{15} +(0.0903637 + 0.0656531i) q^{16} +(-4.26144 - 2.17131i) q^{17} +(-0.765440 + 0.556125i) q^{18} +(0.967006 - 0.153159i) q^{19} +(0.763907 - 1.05143i) q^{20} +(3.27029 - 4.50117i) q^{21} +(2.20546 - 0.349311i) q^{22} +(-1.78427 + 1.29635i) q^{23} +(3.53503 + 1.80119i) q^{24} +(-3.11323 - 2.26189i) q^{25} +(-1.73611 - 3.40730i) q^{26} +(-3.99839 + 3.99839i) q^{27} +(4.78397 + 0.757706i) q^{28} +(1.83197 - 0.933434i) q^{29} +(-0.602033 + 1.18156i) q^{30} +(-2.02631 - 6.23635i) q^{31} +5.60526i q^{32} +(3.32552 - 1.08053i) q^{33} +(0.664599 + 4.19611i) q^{34} +(-0.671536 + 4.23991i) q^{35} +(-1.22669 - 0.398575i) q^{36} +(-3.34992 + 10.3100i) q^{37} +(-0.614959 - 0.614959i) q^{38} +(-3.51983 - 4.84464i) q^{39} -3.06112 q^{40} +(6.18056 + 1.67354i) q^{41} -4.94220 q^{42} +(-1.18522 - 1.63132i) q^{43} +(2.15248 + 2.15248i) q^{44} +(0.353247 - 1.08718i) q^{45} +(1.86321 + 0.605393i) q^{46} +(1.55707 - 9.83098i) q^{47} +(-0.0243050 - 0.153456i) q^{48} +(-8.55823 + 2.78074i) q^{49} +3.41827i q^{50} +(2.05581 + 6.32714i) q^{51} +(2.36674 - 4.64499i) q^{52} +(6.91813 - 3.52496i) q^{53} +(4.96103 + 0.785751i) q^{54} +(-1.90769 + 1.90769i) q^{55} +(-5.17934 - 10.1650i) q^{56} +(-1.10177 - 0.800486i) q^{57} +(-1.62731 - 0.829155i) q^{58} +(7.77045 - 5.64556i) q^{59} +(-1.78553 + 0.282801i) q^{60} +(-0.263416 + 0.362561i) q^{61} +(-3.42369 + 4.71231i) q^{62} +(4.20788 - 0.666462i) q^{63} +(4.20887 - 3.05793i) q^{64} +(4.11674 + 2.09758i) q^{65} +(-2.51283 - 1.82568i) q^{66} +(-1.59206 - 3.12459i) q^{67} +(-4.09531 + 4.09531i) q^{68} +(3.03004 + 0.479912i) q^{69} +(3.39758 - 1.73115i) q^{70} +(-6.39610 + 12.5531i) q^{71} +(0.938792 + 2.88930i) q^{72} -8.75882i q^{73} +(9.15822 - 2.97568i) q^{74} +(0.837360 + 5.28689i) q^{75} +(0.185468 - 1.17100i) q^{76} +(-9.56259 - 3.10707i) q^{77} +(-1.64376 + 5.05897i) q^{78} +(-1.93225 - 1.93225i) q^{79} +(0.0704612 + 0.0969816i) q^{80} +4.67012 q^{81} +(-2.02433 - 5.31537i) q^{82} -2.79623 q^{83} +(-3.96016 - 5.45070i) q^{84} +(-3.62957 - 3.62957i) q^{85} +(-0.553497 + 1.70349i) q^{86} +(-2.72000 - 0.883783i) q^{87} +(1.12162 - 7.08163i) q^{88} +(1.73754 + 10.9704i) q^{89} +(-0.965728 + 0.313784i) q^{90} +17.2194i q^{91} +(0.825300 + 2.54001i) q^{92} +(-4.14092 + 8.12702i) q^{93} +(-7.87788 + 4.01398i) q^{94} +(1.03782 + 0.164375i) q^{95} +(5.51324 - 5.51324i) q^{96} +(1.70702 + 3.35021i) q^{97} +(6.46677 + 4.69838i) q^{98} +(2.38567 + 1.21556i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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