LMFDB - Embedded newform 41.2.g.a.33.2

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			33.2
Character	$\chi$	$=$	41.33
Dual form			41.2.g.a.5.2

$q$-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 $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{9}{20}\right)$

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	−0.952682	−	0.303969i	$-0.901688\pi$
$2$	−0.522120	+	0.718637i	−0.369195	+	0.508153i	0.583487	+	0.812123i	$0.301688\pi$
$3$	−0.983583	+	0.983583i	−0.567872	+	0.567872i	−0.931532	−	0.363660i	$-0.881527\pi$
$3$	−0.983583	+	0.983583i	−0.567872	+	0.567872i	0.363660	+	0.931532i	$0.381527\pi$
$4$	0.374204	+	1.15168i	0.187102	+	0.575841i
$5$	1.02071	−	0.331648i	0.456474	−	0.148318i	−0.0717495	−	0.997423i	$-0.522858\pi$
$5$	1.02071	−	0.331648i	0.456474	−	0.148318i	0.528224	+	0.849105i	$0.322858\pi$
$6$	−0.193291	−	1.22039i	−0.0789105	−	0.498222i
$7$	0.625712	−	3.95059i	0.236497	−	1.49318i	−0.528382	−	0.849007i	$-0.677201\pi$
$7$	0.625712	−	3.95059i	0.236497	−	1.49318i	0.764878	−	0.644175i	$-0.222799\pi$
$8$	−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	0.652499	−	0.757789i	$-0.273721\pi$
$11$	−1.14123	−	2.23980i	−0.344095	−	0.675324i	−0.996594	+	0.0824655i	$0.973721\pi$
$12$	−1.50084	−	0.764715i	−0.433254	−	0.220754i
$13$	4.25204	−	0.673457i	1.17930	−	0.186783i	0.464154	−	0.885755i	$-0.346359\pi$
$13$	4.25204	−	0.673457i	1.17930	−	0.186783i	0.715150	+	0.698971i	$0.246359\pi$
$14$	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	−0.886606	−	0.462525i	$-0.846944\pi$
$17$	−4.26144	+	2.17131i	−1.03355	+	0.526620i	−0.146944	+	0.989145i	$0.546944\pi$
$18$	−0.765440	−	0.556125i	−0.180416	−	0.131080i
$19$	0.967006	+	0.153159i	0.221846	+	0.0351370i	0.266368	−	0.963871i	$-0.414176\pi$
$19$	0.967006	+	0.153159i	0.221846	+	0.0351370i	−0.0445217	+	0.999008i	$0.514176\pi$
$20$	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	0.386013	−	0.922493i	$-0.373852\pi$
$23$	−1.78427	−	1.29635i	−0.372046	−	0.270307i	−0.758059	+	0.652186i	$0.773852\pi$
$24$	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	0.615735	−	0.787953i	$-0.288859\pi$
$29$	1.83197	+	0.933434i	0.340188	+	0.173334i	−0.275547	+	0.961287i	$0.588859\pi$
$30$	−0.602033	−	1.18156i	−0.109916	−	0.215722i
$31$	−2.02631	+	6.23635i	−0.363936	+	1.12008i	0.586708	+	0.809799i	$0.300424\pi$
$31$	−2.02631	+	6.23635i	−0.363936	+	1.12008i	−0.950644	+	0.310283i	$0.899576\pi$
$32$		−	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	−0.706976	−	0.707237i	$-0.749941\pi$
$37$	−3.34992	−	10.3100i	−0.550724	−	1.69495i	0.156252	−	0.987717i	$-0.450059\pi$
$38$	−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	−0.889770	−	0.456410i	$-0.849135\pi$
$43$	−1.18522	+	1.63132i	−0.180745	+	0.248773i	0.709025	+	0.705183i	$0.249135\pi$
$44$	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	0.792857	+	0.609408i	$0.208593\pi$
$47$	1.55707	+	9.83098i	0.227123	+	1.43400i	−0.565735	+	0.824587i	$0.691407\pi$
$48$	−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	0.859193	−	0.511652i	$-0.170966\pi$
$53$	6.91813	+	3.52496i	0.950278	+	0.484191i	0.0910855	+	0.995843i	$0.470966\pi$
$54$	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	0.964549	−	0.263902i	$-0.0850096\pi$
$59$	7.77045	+	5.64556i	1.01163	+	0.734989i	0.0470763	+	0.998891i	$0.485010\pi$
$60$	−1.78553	−	0.282801i	−0.230511	−	0.0365094i
$61$	−0.263416	−	0.362561i	−0.0337269	−	0.0464211i	0.791821	−	0.610754i	$-0.209134\pi$
$61$	−0.263416	−	0.362561i	−0.0337269	−	0.0464211i	−0.825547	+	0.564333i	$0.809134\pi$
$62$	−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	−0.967574	−	0.252587i	$-0.918718\pi$
$67$	−1.59206	+	3.12459i	−0.194501	+	0.381729i	0.773073	+	0.634317i	$0.218718\pi$
$68$	−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	−0.868452	−	0.495773i	$-0.834885\pi$
$71$	−6.39610	−	12.5531i	−0.759078	−	1.48977i	0.109374	−	0.994001i	$-0.465115\pi$
$72$	0.938792	−	2.88930i	0.110638	−	0.340508i
$73$			8.75882i			1.02514i	0.858645	+	0.512571i	$0.171307\pi$
$73$			8.75882i			1.02514i	−0.858645	+	0.512571i	$0.828693\pi$
$74$	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	−0.807400	−	0.590005i	$-0.799126\pi$
$79$	−1.93225	+	1.93225i	−0.217395	+	0.217395i	0.590005	+	0.807400i	$0.299126\pi$
$80$	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	−0.706326	−	0.707887i	$-0.749649\pi$
$89$	1.73754	−	10.9704i	0.184179	−	1.16286i	0.890505	−	0.454974i	$-0.150351\pi$
$90$	−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	−0.787962	−	0.615724i	$-0.788864\pi$
$97$	1.70702	−	3.35021i	0.173321	−	0.340162i	0.961283	+	0.275561i	$0.0888637\pi$
$98$	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	0.0659658	−	0.997822i	$-0.478987\pi$
$101$	−1.80537	−	0.285942i	−0.179641	−	0.0284523i	−0.245607	+	0.969370i	$0.578987\pi$
$102$	3.47354	+	4.78091i	0.343931	+	0.473381i
$103$	6.53693	+	8.99731i	0.644103	+	0.886531i	0.998826	−	0.0484399i	$-0.0154249\pi$
$103$	6.53693	+	8.99731i	0.644103	+	0.886531i	−0.354723	+	0.934971i	$0.615425\pi$
$104$	−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	0.0466060	−	0.998913i	$-0.485159\pi$
$107$	10.4582	−	7.59832i	1.01103	−	0.734557i	0.964425	+	0.264356i	$0.0851595\pi$
$108$	3.10866	−	6.10110i	0.299131	−	0.587078i
$109$	−4.71687	−	4.71687i	−0.451794	−	0.451794i	0.444156	−	0.895950i	$-0.353504\pi$
$109$	−4.71687	−	4.71687i	−0.451794	−	0.451794i	−0.895950	+	0.444156i	$0.853504\pi$
$110$	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	0.559991	+	0.828499i	$0.310805\pi$
$113$	−4.03978	+	12.4332i	−0.380031	+	1.16961i	−0.940021	+	0.341115i	$0.889195\pi$
$114$		−	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	0.994307	+	0.106554i	$0.0339816\pi$
$127$	2.84583	+	8.75856i	0.252526	+	0.777196i	−0.741781	+	0.670643i	$0.766018\pi$
$128$	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	0.316857	−	0.948473i	$-0.397373\pi$
$131$	0.179705	+	0.0583895i	0.0157009	+	0.00510152i	−0.301156	+	0.953575i	$0.597373\pi$
$132$			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	0.485746	−	0.874100i	$-0.338548\pi$
$137$	−4.54556	−	4.54556i	−0.388353	−	0.388353i	−0.874100	+	0.485746i	$0.838548\pi$
$138$	−1.23717	+	2.42807i	−0.105315	+	0.206691i
$139$	5.82631	−	4.23306i	0.494181	−	0.359043i	−0.312609	−	0.949882i	$-0.601203\pi$
$139$	5.82631	−	4.23306i	0.494181	−	0.359043i	0.806790	+	0.590838i	$0.201203\pi$
$140$	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	−0.963580	−	0.267420i	$-0.913829\pi$
$149$	−2.20761	+	4.33268i	−0.180855	+	0.354947i	0.782725	+	0.622367i	$0.213829\pi$
$150$	3.36215	+	3.36215i	0.274518	+	0.274518i
$151$	−9.40032	+	1.48886i	−0.764987	+	0.121162i	−0.526721	−	0.850038i	$-0.676579\pi$
$151$	−9.40032	+	1.48886i	−0.764987	+	0.121162i	−0.238266	+	0.971200i	$0.576579\pi$
$152$	−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	−0.888668	−	0.458551i	$-0.848369\pi$
$157$	1.23051	−	7.76915i	0.0982056	−	0.620046i	0.986874	−	0.161495i	$-0.0516314\pi$
$158$	−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	−0.701899	−	0.712277i	$-0.747664\pi$
$167$	0.134117	−	0.134117i	0.0103783	−	0.0103783i	0.712277	+	0.701899i	$0.247664\pi$
$168$	−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	$0.0648033\pi$
$173$			5.31858i			0.404364i	−0.979348	+	0.202182i	$0.935197\pi$
$174$	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	−0.414578	−	0.910014i	$-0.636071\pi$
$179$	7.56349	−	14.8442i	0.565322	−	1.10951i	0.979899	−	0.199492i	$-0.0639293\pi$
$180$	−1.11990	+	0.813658i	−0.0834727	+	0.0606465i
$181$	9.39816	−	4.78860i	0.698560	−	0.355934i	−0.0683744	−	0.997660i	$-0.521781\pi$
$181$	9.39816	−	4.78860i	0.698560	−	0.355934i	0.766934	+	0.641726i	$0.221781\pi$
$182$	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	0.984031	−	0.177999i	$-0.0569623\pi$
$191$	11.1396	+	11.1396i	0.806032	+	0.806032i	−0.177999	+	0.984031i	$0.556962\pi$
$192$	−7.14750	+	1.13205i	−0.515827	+	0.0816989i
$193$	−20.8262	−	10.6115i	−1.49910	−	0.763831i	−0.504097	−	0.863647i	$-0.668175\pi$
$193$	−20.8262	−	10.6115i	−1.49910	−	0.763831i	−0.995006	+	0.0998160i	$0.968175\pi$
$194$	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	0.681393	−	0.731918i	$-0.261374\pi$
$197$	11.2628	+	3.65951i	0.802442	+	0.260729i	0.121048	+	0.992647i	$0.461374\pi$
$198$	−0.372060	+	2.34910i	−0.0264412	+	0.166943i
$199$	1.32526	+	8.36737i	0.0939452	+	0.593147i	0.989083	+	0.147358i	$0.0470769\pi$
$199$	1.32526	+	8.36737i	0.0939452	+	0.593147i	−0.895138	+	0.445789i	$0.852923\pi$
$200$	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	−0.983840	−	0.179050i	$-0.942698\pi$
$211$	−1.50316	−	9.49061i	−0.103482	−	0.653360i	0.880358	−	0.474310i	$-0.157302\pi$
$212$	−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	0.433484	−	0.901161i	$-0.357284\pi$
$223$	−4.32492	−	3.14224i	−0.289618	−	0.210420i	−0.723102	+	0.690742i	$0.757284\pi$
$224$	−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	0.379704	−	0.925108i	$-0.376026\pi$
$227$	6.85453	+	1.08565i	0.454951	+	0.0720571i	0.0752464	+	0.997165i	$0.476026\pi$
$228$	−1.33420	−	0.969350i	−0.0883593	−	0.0641968i
$229$	15.9124	−	8.10777i	1.05152	−	0.535777i	0.159232	−	0.987241i	$-0.449098\pi$
$229$	15.9124	−	8.10777i	1.05152	−	0.535777i	0.892289	+	0.451465i	$0.149098\pi$
$230$	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	−0.295866	−	0.955230i	$-0.595608\pi$
$233$	−4.30559	+	0.681939i	−0.282069	+	0.0446753i	0.0137971	+	0.999905i	$0.495608\pi$
$234$	−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	−0.865368	−	0.501138i	$-0.832915\pi$
$239$	1.73930	−	10.9815i	0.112506	−	0.710334i	0.977874	−	0.209197i	$-0.0670850\pi$
$240$	0.0260850	+	0.164694i	0.00168378	+	0.0106310i
$241$	18.4604	−	5.99815i	1.18914	−	0.386375i	0.353385	−	0.935478i	$-0.385030\pi$
$241$	18.4604	−	5.99815i	1.18914	−	0.386375i	0.835755	+	0.549103i	$0.185030\pi$
$242$	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	−0.378040	−	0.925789i	$-0.623402\pi$
$251$	−2.21352	+	0.719217i	−0.139716	+	0.0453966i	0.238324	+	0.971186i	$0.423402\pi$
$252$	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	−0.983250	−	0.182263i	$-0.941658\pi$
$257$	−8.86149	−	17.3916i	−0.552764	−	1.08486i	0.430485	−	0.902597i	$-0.358342\pi$
$258$	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	−0.541559	−	0.840662i	$-0.682166\pi$
$263$	−2.91538	+	1.48546i	−0.179770	+	0.0915973i	0.361790	+	0.932260i	$0.382166\pi$
$264$	−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	0.277966	−	0.960591i	$-0.410340\pi$
$269$	−9.01598	−	6.55050i	−0.549714	−	0.399391i	−0.827680	+	0.561200i	$0.810340\pi$
$270$	4.80317	−	2.44734i	0.292312	−	0.148940i
$271$	−5.17280	+	3.75826i	−0.314225	+	0.228298i	−0.733707	−	0.679466i	$-0.762212\pi$
$271$	−5.17280	+	3.75826i	−0.314225	+	0.228298i	0.419482	+	0.907764i	$0.362212\pi$
$272$	−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	−0.387671	−	0.921798i	$-0.626720\pi$
$277$	7.78542	−	23.9611i	0.467781	−	1.43968i	0.855452	−	0.517883i	$-0.173280\pi$
$278$			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	0.966750	−	0.255723i	$-0.0823136\pi$
$281$	−0.531501	−	3.35577i	−0.0317067	−	0.200188i	−0.998457	+	0.0555350i	$0.982314\pi$
$282$	11.6966	−	3.80047i	0.696525	−	0.226315i
$283$	2.32829	+	7.16575i	0.138403	+	0.425959i	0.996104	−	0.0881892i	$-0.0281080\pi$
$283$	2.32829	+	7.16575i	0.138403	+	0.425959i	−0.857701	+	0.514149i	$0.828108\pi$
$284$	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	−0.999832	−	0.0183540i	$-0.994157\pi$
$293$	−0.934720	−	5.90159i	−0.0546069	−	0.344775i	0.945225	−	0.326421i	$-0.105843\pi$
$294$	−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	0.821189	−	0.570656i	$-0.193311\pi$
$307$	0.432807	+	0.595708i	0.0247016	+	0.0339988i	−0.796488	+	0.604655i	$0.793311\pi$
$308$	−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	−0.990051	−	0.140706i	$-0.955063\pi$
$311$	−25.7148	+	13.1024i	−1.45816	+	0.742967i	−0.468104	+	0.883673i	$0.655063\pi$
$312$	13.8181	−	10.0394i	0.782293	−	0.568369i
$313$	−7.45211	+	14.6256i	−0.421218	+	0.826687i	0.578720	+	0.815526i	$0.303553\pi$
$313$	−7.45211	+	14.6256i	−0.421218	+	0.826687i	−0.999938	+	0.0111603i	$0.996447\pi$
$314$	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	0.713174	+	0.700987i	$0.247257\pi$
$317$	15.3313	+	30.0894i	0.861091	+	1.68999i	0.147917	+	0.989000i	$0.452743\pi$
$318$	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	−0.901385	−	0.433018i	$-0.857449\pi$
$331$	−8.52119	+	8.52119i	−0.468367	+	0.468367i	0.433018	+	0.901385i	$0.357449\pi$
$332$	−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	$-0.966952\pi$
$337$		−	3.80509i		−	0.207276i	0.994615	−	0.103638i	$-0.0330484\pi$
$338$	−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	−0.287190	−	0.957874i	$-0.592721\pi$
$347$	−15.9515	−	2.52648i	−0.856324	−	0.135628i	−0.569134	+	0.822245i	$0.692721\pi$
$348$	−2.03568	−	2.80187i	−0.109124	−	0.150196i
$349$	−0.538696	−	0.741452i	−0.0288358	−	0.0396890i	0.794356	−	0.607453i	$-0.207809\pi$
$349$	−0.538696	−	0.741452i	−0.0288358	−	0.0396890i	−0.823191	+	0.567764i	$0.807809\pi$
$350$	−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	−0.676653	−	0.736302i	$-0.736570\pi$
$353$	−3.48494	+	2.53196i	−0.185485	+	0.134763i	0.491168	+	0.871065i	$0.336570\pi$
$354$	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	−0.480239	−	0.877138i	$-0.659450\pi$
$359$	8.03083	−	24.7164i	0.423851	−	1.30448i	0.904090	−	0.427342i	$-0.140550\pi$
$360$		−	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	−0.543473	−	0.839427i	$-0.682891\pi$
$367$	8.09990	−	11.1486i	0.422811	−	0.581950i	0.966285	+	0.257477i	$0.0828910\pi$
$368$	−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	0.697460	+	0.716624i	$0.254313\pi$
$373$	10.7077	+	32.9549i	0.554424	+	1.70634i	−0.143036	+	0.989717i	$0.545687\pi$
$374$	−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	−0.997752	−	0.0670121i	$-0.978653\pi$
$379$	−2.94287	+	9.05722i	−0.151165	+	0.465238i	0.846587	+	0.532250i	$0.178653\pi$
$380$	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	0.134262	−	0.990946i	$-0.457134\pi$
$383$	−16.7656	−	16.7656i	−0.856684	−	0.856684i	−0.990946	+	0.134262i	$0.957134\pi$
$384$	−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	0.613540	−	0.789664i	$-0.289745\pi$
$389$	−6.45082	−	8.87880i	−0.327070	−	0.450173i	−0.940609	+	0.339491i	$0.889745\pi$
$390$	−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	−0.755809	−	0.654792i	$-0.772756\pi$
$397$	−25.3501	+	4.01506i	−1.27228	+	0.201510i	−0.516476	+	0.856302i	$0.672756\pi$
$398$	−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	$0.232472\pi$
$401$			26.7180i			1.33423i	−0.744953	+	0.667117i	$0.767528\pi$
$402$	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	$0.245478\pi$
$419$			28.5341i			1.39398i	−0.717080	+	0.696991i	$0.754522\pi$
$420$	−2.23446	+	6.87695i	−0.109030	+	0.335561i
$421$	4.65405	+	9.13410i	0.226825	+	0.445169i	0.976169	−	0.217012i	$-0.0696311\pi$
$421$	4.65405	+	9.13410i	0.226825	+	0.445169i	−0.749344	+	0.662181i	$0.769631\pi$
$422$	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	0.994533	−	0.104425i	$-0.0333004\pi$
$431$	12.2049	+	16.7986i	0.587891	+	0.809162i	−0.406642	+	0.913588i	$0.633300\pi$
$432$	−0.623816	−	0.0988028i	−0.0300134	−	0.00475365i
$433$	−13.3108	−	9.67086i	−0.639676	−	0.464752i	0.220063	−	0.975486i	$-0.429374\pi$
$433$	−13.3108	−	9.67086i	−0.639676	−	0.464752i	−0.859739	+	0.510734i	$0.829374\pi$
$434$	−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	0.868470	−	0.495741i	$-0.165103\pi$
$439$	20.4889	+	10.4396i	0.977882	+	0.498256i	0.109411	+	0.993997i	$0.465103\pi$
$440$	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	0.316886	−	0.948464i	$-0.397363\pi$
$443$	0.331688	+	0.107772i	0.0157590	+	0.00512040i	−0.301127	+	0.953584i	$0.597363\pi$
$444$	−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	0.176183	+	0.984357i	$0.443625\pi$
$449$	−17.2577	+	23.7532i	−0.814440	+	1.12098i	−0.990623	+	0.136623i	$0.956375\pi$
$450$	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	−0.999021	−	0.0442385i	$-0.985914\pi$
$457$	−1.33751	−	8.44470i	−0.0625660	−	0.395026i	0.936455	−	0.350788i	$-0.114086\pi$
$458$	−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	−0.298337	−	0.954461i	$-0.596432\pi$
$461$	10.8222	−	33.3073i	0.504041	−	1.55128i	0.802378	−	0.596817i	$-0.203568\pi$
$462$	5.64020	+	11.0695i	0.262406	+	0.515000i
$463$	−4.11872	−	2.09859i	−0.191413	−	0.0975298i	0.355657	−	0.934616i	$-0.384257\pi$
$463$	−4.11872	−	2.09859i	−0.191413	−	0.0975298i	−0.547070	+	0.837087i	$0.684257\pi$
$464$	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	0.0663821	−	0.997794i	$-0.478854\pi$
$467$	22.3850	−	16.2637i	1.03585	−	0.752592i	0.969472	+	0.245202i	$0.0788544\pi$
$468$	−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	−0.0400274	−	0.999199i	$-0.512745\pi$
$479$	5.04854	−	0.799610i	0.230674	−	0.0365351i	0.270701	+	0.962663i	$0.412745\pi$
$480$	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	0.215819	−	0.976433i	$-0.430758\pi$
$487$	21.2814	−	6.91475i	0.964353	−	0.313337i	0.748534	+	0.663096i	$0.230758\pi$
$488$	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	0.584682	+	0.811263i	$0.301219\pi$
$499$	−4.96084	+	31.3215i	−0.222078	+	1.40214i	−0.806759	+	0.590880i	$0.798781\pi$
$500$	−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	0.924040	−	0.382295i	$-0.124866\pi$
$503$	1.60627	+	3.15248i	0.0716200	+	0.140562i	−0.852420	+	0.522857i	$0.824866\pi$
$504$	−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	−0.548812	−	0.835946i	$-0.684920\pi$
$509$	−4.40168	+	2.24277i	−0.195101	+	0.0994090i	0.353711	+	0.935355i	$0.384920\pi$
$510$	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	0.430823	−	0.902436i	$-0.358223\pi$
$521$	−1.05069	−	0.535356i	−0.0460318	−	0.0234544i	−0.476855	+	0.878982i	$0.658223\pi$
$522$	−0.883155	−	1.73329i	−0.0386547	−	0.0758640i
$523$	0.00907992	−	0.0279451i	0.000397037	−	0.00122195i	−0.950858	−	0.309628i	$-0.899796\pi$
$523$	0.00907992	−	0.0279451i	0.000397037	−	0.00122195i	0.951255	+	0.308406i	$0.0997955\pi$
$524$			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	0.928467	−	0.371414i	$-0.121127\pi$
$541$	33.9890	+	11.0437i	1.46130	+	0.474806i	0.532834	+	0.846220i	$0.321127\pi$
$542$		−	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	0.595960	−	0.803014i	$-0.296772\pi$
$547$	−4.84258	−	4.84258i	−0.207054	−	0.207054i	−0.803014	+	0.595960i	$0.796772\pi$
$548$	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	−0.846154	−	0.532938i	$-0.821088\pi$
$557$	−21.5323	+	10.9713i	−0.912355	+	0.464868i	−0.0662005	+	0.997806i	$0.521088\pi$
$558$	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	0.950844	−	0.309669i	$-0.100218\pi$
$563$	3.35567	+	6.58588i	0.141425	+	0.277562i	−0.809420	+	0.587231i	$0.800218\pi$
$564$	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	−0.384288	−	0.923213i	$-0.625553\pi$
$569$	−3.63848	+	1.18221i	−0.152533	+	0.0495609i	0.231755	+	0.972774i	$0.425553\pi$
$570$	−0.401203	−	1.23478i	−0.0168046	−	0.0517191i
$571$	−7.80695	+	7.80695i	−0.326710	+	0.326710i	−0.851334	−	0.524624i	$-0.824206\pi$
$571$	−7.80695	+	7.80695i	−0.326710	+	0.326710i	0.524624	+	0.851334i	$0.324206\pi$
$572$	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	−0.841416	−	0.540388i	$-0.818278\pi$
$577$	−7.23096	+	7.23096i	−0.301029	+	0.301029i	0.540388	+	0.841416i	$0.318278\pi$
$578$	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	0.0881260	−	0.996109i	$-0.471912\pi$
$587$	11.6235	−	1.84098i	0.479754	−	0.0759855i	0.391628	+	0.920124i	$0.371912\pi$
$588$	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	−0.424412	−	0.905469i	$-0.639519\pi$
$593$	−26.9781	−	4.27291i	−1.10786	−	0.175467i	−0.683445	+	0.730002i	$0.739519\pi$
$594$	−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	−0.408358	−	0.912822i	$-0.633898\pi$
$599$	8.16465	−	5.93196i	0.333598	−	0.242373i	0.741956	+	0.670449i	$0.233898\pi$
$600$	−6.93126	+	13.6034i	−0.282968	+	0.555355i
$601$	−9.88133	−	9.88133i	−0.403068	−	0.403068i	0.476245	−	0.879313i	$-0.341998\pi$
$601$	−9.88133	−	9.88133i	−0.403068	−	0.403068i	−0.879313	+	0.476245i	$0.841998\pi$
$602$	−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	0.427388	−	0.904068i	$-0.359434\pi$
$607$	5.95620	+	1.93529i	0.241755	+	0.0785509i	−0.185634	+	0.982619i	$0.559434\pi$
$608$	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	−0.431963	−	0.901891i	$-0.642179\pi$
$613$	13.8469	−	19.0586i	0.559270	−	0.769769i	0.991233	+	0.132122i	$0.0421790\pi$
$614$	−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	0.205492	+	0.978659i	$0.434121\pi$
$617$	−19.5926	+	26.9669i	−0.788768	+	1.08565i	−0.994260	+	0.106988i	$0.965879\pi$
$618$	9.71669	−	9.71669i	0.390863	−	0.390863i
$619$	−13.3135	−	40.9747i	−0.535115	−	1.64691i	−0.743401	−	0.668846i	$-0.766789\pi$
$619$	−13.3135	−	40.9747i	−0.535115	−	1.64691i	0.208286	−	0.978068i	$-0.433211\pi$
$620$	−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	−0.464444	−	0.885603i	$-0.653746\pi$
$631$	5.88538	−	4.27598i	0.234293	−	0.170224i	0.698737	+	0.715379i	$0.253746\pi$
$632$	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	−0.431070	−	0.902318i	$-0.641864\pi$
$641$	13.9831	−	27.4433i	0.552297	−	1.08394i	0.983368	−	0.181626i	$-0.0581361\pi$
$642$	−11.2944	−	11.2944i	−0.445753	−	0.445753i
$643$	15.0094	−	2.37726i	0.591914	−	0.0937500i	0.146711	−	0.989179i	$-0.453131\pi$
$643$	15.0094	−	2.37726i	0.591914	−	0.0937500i	0.445203	+	0.895429i	$0.353131\pi$
$644$	−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	$-0.963496\pi$
$647$		−	5.82135i		−	0.228861i	0.993431	−	0.114430i	$-0.0365043\pi$
$648$	−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	−0.845617	−	0.533790i	$-0.820767\pi$
$653$	−7.96838	+	7.96838i	−0.311827	+	0.311827i	0.533790	+	0.845617i	$0.320767\pi$
$654$	−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	−0.971049	−	0.238880i	$-0.923220\pi$
$659$	−18.7955	+	18.7955i	−0.732169	+	0.732169i	0.238880	+	0.971049i	$0.423220\pi$
$660$	1.40429	+	4.32197i	0.0546620	+	0.168232i
$661$	2.86486	−	0.930849i	0.111430	−	0.0362058i	−0.252771	−	0.967526i	$-0.581342\pi$
$661$	2.86486	−	0.930849i	0.111430	−	0.0362058i	0.364201	+	0.931320i	$0.381342\pi$
$662$	−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	−0.349361	−	0.936988i	$-0.613601\pi$
$673$	5.27484	−	2.68766i	0.203330	−	0.103602i	0.552691	+	0.833387i	$0.313601\pi$
$674$	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	0.675335	−	0.737512i	$-0.263999\pi$
$677$	−6.10855	−	8.40769i	−0.234770	−	0.323134i	−0.910105	+	0.414378i	$0.863999\pi$
$678$	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	0.999743	−	0.0226507i	$-0.00721056\pi$
$683$	25.5356	+	25.5356i	0.977093	+	0.977093i	−0.0226507	+	0.999743i	$0.507211\pi$
$684$	−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	0.996963	−	0.0778748i	$-0.0248134\pi$
$691$	0.650080	+	4.10445i	0.0247302	+	0.156140i	−0.972233	+	0.234015i	$0.924813\pi$
$692$	−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	0.882821	−	0.469710i	$-0.155642\pi$
$701$	−2.84581	−	8.75851i	−0.107485	−	0.330805i	−0.990306	+	0.138906i	$0.955642\pi$
$702$	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	−0.185342	−	0.982674i	$-0.559339\pi$
$709$	−29.0044	−	14.7785i	−1.08928	−	0.555018i	−0.903941	+	0.427656i	$0.859339\pi$
$710$	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	−0.0337427	−	0.999431i	$-0.510743\pi$
$719$	−10.0466	−	1.59122i	−0.374675	−	0.0593427i	−0.340932	+	0.940088i	$0.610743\pi$
$720$	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	0.853952	+	0.520352i	$0.174199\pi$
$727$	20.8419	+	40.9046i	0.772985	+	1.51707i	−0.0809673	+	0.996717i	$0.525801\pi$
$728$	−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	−0.884892	−	0.465797i	$-0.845768\pi$
$733$	−35.9271	+	11.6734i	−1.32700	+	0.431167i	−0.442104	+	0.896964i	$0.645768\pi$
$734$	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	0.0570164	−	0.998373i	$-0.481841\pi$
$743$	18.8073	−	6.11086i	0.689973	−	0.224186i	0.632956	+	0.774188i	$0.281841\pi$
$744$	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	0.135691	−	0.990751i	$-0.456675\pi$
$751$	15.6451	−	2.47795i	0.570899	−	0.0904216i	0.435209	+	0.900330i	$0.356675\pi$
$752$	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	0.554213	−	0.832375i	$-0.313019\pi$
$757$	22.6735	+	3.59113i	0.824083	+	0.130522i	0.269870	+	0.962897i	$0.413019\pi$
$758$	−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	0.999868	+	0.0162427i	$0.00517045\pi$
$761$	36.5322	+	26.5422i	1.32429	+	0.962155i	0.324424	+	0.945912i	$0.394830\pi$
$762$	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	0.744864	+	0.667216i	$0.232514\pi$
$769$	−6.93059	+	21.3302i	−0.249924	+	0.769186i	−0.994788	+	0.101969i	$0.967486\pi$
$770$		−	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	0.999252	+	0.0386657i	$0.0123108\pi$
$773$	1.69195	+	10.6826i	0.0608553	+	0.384225i	−0.938397	+	0.345559i	$0.887689\pi$
$774$	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	−0.230573	−	0.973055i	$-0.574060\pi$
$787$	−27.7465	−	9.01540i	−0.989057	−	0.321364i	−0.758485	+	0.651691i	$0.774060\pi$
$788$			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	0.230893	−	0.972979i	$-0.425835\pi$
$797$	−17.5913	−	12.7808i	−0.623115	−	0.452720i	−0.854008	+	0.520259i	$0.825835\pi$
$798$	−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	−0.872386	−	0.488817i	$-0.837429\pi$
$809$	−21.4765	−	42.1499i	−0.755072	−	1.48191i	0.117314	−	0.993095i	$-0.462571\pi$
$810$	−1.37581	+	4.23430i	−0.0483410	+	0.148778i
$811$		−	53.0392i		−	1.86246i	−0.364436	−	0.931228i	$-0.618738\pi$
$811$		−	53.0392i		−	1.86246i	0.364436	−	0.931228i	$-0.381262\pi$
$812$	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	−0.689027	−	0.724736i	$-0.741962\pi$
$823$	1.02441	−	1.02441i	0.0357087	−	0.0357087i	0.724736	+	0.689027i	$0.241962\pi$
$824$	−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	−0.536756	−	0.843737i	$-0.680351\pi$
$827$	6.74246	−	42.5702i	0.234458	−	1.48031i	0.771215	−	0.636575i	$-0.219649\pi$
$828$	2.70544	+	0.879049i	0.0940204	+	0.0305491i
$829$			12.8894i			0.447667i	0.974627	+	0.223834i	$0.0718572\pi$
$829$			12.8894i			0.447667i	−0.974627	+	0.223834i	$0.928143\pi$
$830$	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	−0.602825	−	0.797873i	$-0.705958\pi$
$839$	−41.2093	−	6.52691i	−1.42270	−	0.225334i	−0.819877	+	0.572539i	$0.805958\pi$
$840$	−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	0.804610	−	0.593803i	$-0.202374\pi$
$853$	32.3174	+	10.5005i	1.10653	+	0.359532i	0.301915	+	0.953335i	$0.402374\pi$
$854$	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	0.825278	−	0.564726i	$-0.191018\pi$
$857$	−5.10325	−	15.7062i	−0.174324	−	0.536513i	−0.999602	+	0.0282132i	$0.991018\pi$
$858$	−9.45514	+	9.45514i	−0.322793	+	0.322793i
$859$	−24.0112	+	33.0486i	−0.819252	+	1.12760i	0.170577	+	0.985344i	$0.445437\pi$
$859$	−24.0112	+	33.0486i	−0.819252	+	1.12760i	−0.989829	+	0.142260i	$0.954563\pi$
$860$	−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	−0.339214	−	0.940709i	$-0.610161\pi$
$863$	19.3968	−	26.6975i	0.660276	−	0.908792i	0.999491	+	0.0319168i	$0.0101612\pi$
$864$	−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	−0.729476	−	0.684006i	$-0.760236\pi$
$877$	−9.01360	+	6.54877i	−0.304368	+	0.221136i	0.425108	+	0.905143i	$0.360236\pi$
$878$	−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	0.980115	−	0.198428i	$-0.0635836\pi$
$881$	14.5003	+	19.9579i	0.488527	+	0.672400i	−0.491589	+	0.870828i	$0.663584\pi$
$882$	5.00437	+	6.88793i	0.168506	+	0.231929i
$883$	21.4782	+	3.40182i	0.722800	+	0.114480i	0.506986	−	0.861954i	$-0.330760\pi$
$883$	21.4782	+	3.40182i	0.722800	+	0.114480i	0.215814	+	0.976435i	$0.430760\pi$
$884$	−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	0.217189	+	0.976130i	$0.430311\pi$
$887$	−20.8531	+	40.9264i	−0.700177	+	1.37418i	−0.917366	+	0.398045i	$0.869689\pi$
$888$	−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	0.601121	−	0.799158i	$-0.294721\pi$
$907$	46.8965	−	15.2376i	1.55717	−	0.505956i	0.956050	+	0.293203i	$0.0947211\pi$
$908$	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	$-0.952989\pi$
$911$		−	8.88306i		−	0.294309i	0.989114	−	0.147154i	$-0.0470114\pi$
$912$	−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	−0.624693	−	0.780870i	$-0.714776\pi$
$919$	−10.9177	+	5.56284i	−0.360141	+	0.183501i	0.264552	+	0.964371i	$0.414776\pi$
$920$	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	0.954693	−	0.297593i	$-0.0961839\pi$
$929$	20.0281	+	20.0281i	0.657099	+	0.657099i	−0.297593	+	0.954693i	$0.596184\pi$
$930$	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	0.814558	+	0.580082i	$0.196979\pi$
$937$	6.70744	+	42.3491i	0.219122	+	1.38348i	−0.595436	+	0.803403i	$0.703021\pi$
$938$	−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	0.179727	+	0.983717i	$0.442479\pi$
$941$	−24.8897	+	34.2578i	−0.811382	+	1.11677i	−0.991109	+	0.133055i	$0.957521\pi$
$942$	−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	0.927473	−	0.373891i	$-0.121977\pi$
$947$	−1.31206	−	4.03811i	−0.0426362	−	0.131221i	−0.970109	+	0.242670i	$0.921977\pi$
$948$	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	−0.584557	−	0.811353i	$-0.698732\pi$
$953$	11.2759	−	34.7035i	0.365261	−	1.12416i	0.949818	−	0.312804i	$-0.101268\pi$
$954$	−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	0.224567	−	0.974459i	$-0.427903\pi$
$967$	35.6031	−	18.1407i	1.14492	−	0.583365i	0.920351	+	0.391094i	$0.127903\pi$
$968$	−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	−0.538281	−	0.842765i	$-0.680926\pi$
$971$	−24.6105	+	3.89792i	−0.789788	+	0.125090i	−0.251507	+	0.967855i	$0.580926\pi$
$972$	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	−0.952202	−	0.305469i	$-0.901187\pi$
$977$	1.49380	−	9.43148i	0.0477909	−	0.301740i	0.999993	+	0.00372882i	$0.00118692\pi$
$978$	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	−0.999741	−	0.0227378i	$-0.992762\pi$
$991$	−1.31916	+	8.32884i	−0.0419045	+	0.264574i	0.957837	+	0.287312i	$0.0927617\pi$
$992$	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	0.0357924	−	0.999359i	$-0.488604\pi$
$997$	11.9561	−	1.89365i	0.378652	−	0.0599726i	0.342860	+	0.939387i	$0.388604\pi$
$998$	−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.33.2	yes	24
3.2	odd	2		369.2.u.a.361.2		24
4.3	odd	2		656.2.bs.d.33.2		24
41.5	even	20	inner	41.2.g.a.5.2	✓	24
41.13	odd	40		1681.2.a.m.1.8		24
41.28	odd	40		1681.2.a.m.1.7		24
123.5	odd	20		369.2.u.a.46.2		24
164.87	odd	20		656.2.bs.d.497.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.5.2	✓	24	41.5	even	20	inner
41.2.g.a.33.2	yes	24	1.1	even	1	trivial
369.2.u.a.46.2		24	123.5	odd	20
369.2.u.a.361.2		24	3.2	odd	2
656.2.bs.d.33.2		24	4.3	odd	2
656.2.bs.d.497.2		24	164.87	odd	20
1681.2.a.m.1.7		24	41.28	odd	40
1681.2.a.m.1.8		24	41.13	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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