LMFDB - Embedded newform 25.2.e.a.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,2,Mod(4,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("25.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	25.e (of order $10$, degree $4$, 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:	$0.199626005053$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.58140625.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 $ x^8 - 3x^7 + 4x^6 - 7x^5 + 11x^4 + 5x^3 - 10x^2 - 25*x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			4.2
Root			$1.17421 + 0.0566033i$ of defining polynomial
Character	$\chi$	$=$	25.4
Dual form			25.2.e.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.174207 + 0.0566033i) q^{2} +(-0.865190 + 1.19083i) q^{3} +(-1.59089 - 1.15585i) q^{4} +(0.107666 - 2.23347i) q^{5} +(-0.218127 + 0.158479i) q^{6} +3.26086i q^{7} +(-0.427051 - 0.587785i) q^{8} +(0.257524 + 0.792578i) q^{9} +O(q^{10})$	\(q+(0.174207 + 0.0566033i) q^{2} +(-0.865190 + 1.19083i) q^{3} +(-1.59089 - 1.15585i) q^{4} +(0.107666 - 2.23347i) q^{5} +(-0.218127 + 0.158479i) q^{6} +3.26086i q^{7} +(-0.427051 - 0.587785i) q^{8} +(0.257524 + 0.792578i) q^{9} +(0.145178 - 0.382993i) q^{10} +(0.618034 - 1.90211i) q^{11} +(2.75284 - 0.894453i) q^{12} +(0.281873 - 0.0915860i) q^{13} +(-0.184575 + 0.568064i) q^{14} +(2.56654 + 2.06059i) q^{15} +(1.17421 + 3.61384i) q^{16} +(-3.03472 - 4.17693i) q^{17} +0.152649i q^{18} +(1.39991 - 1.01709i) q^{19} +(-2.75284 + 3.42877i) q^{20} +(-3.88313 - 2.82126i) q^{21} +(0.215332 - 0.296379i) q^{22} +(0.836161 + 0.271685i) q^{23} +1.06943 q^{24} +(-4.97682 - 0.480938i) q^{25} +0.0542883 q^{26} +(-5.36635 - 1.74363i) q^{27} +(3.76906 - 5.18766i) q^{28} +(4.78304 + 3.47508i) q^{29} +(0.330473 + 0.504244i) q^{30} +(-4.93462 + 3.58521i) q^{31} +2.14910i q^{32} +(1.73038 + 2.38166i) q^{33} +(-0.292241 - 0.899425i) q^{34} +(7.28304 + 0.351083i) q^{35} +(0.506408 - 1.55856i) q^{36} +(7.69215 - 2.49933i) q^{37} +(0.301444 - 0.0979452i) q^{38} +(-0.134810 + 0.414902i) q^{39} +(-1.35878 + 0.890523i) q^{40} +(-0.313697 - 0.965461i) q^{41} +(-0.516776 - 0.711281i) q^{42} -3.24199i q^{43} +(-3.18178 + 2.31170i) q^{44} +(1.79793 - 0.489840i) q^{45} +(0.130287 + 0.0946589i) q^{46} +(-2.48043 + 3.41402i) q^{47} +(-5.31939 - 1.72837i) q^{48} -3.63318 q^{49} +(-0.839774 - 0.365487i) q^{50} +7.59963 q^{51} +(-0.554288 - 0.180099i) q^{52} +(-4.76148 + 6.55362i) q^{53} +(-0.836161 - 0.607507i) q^{54} +(-4.18178 - 1.58516i) q^{55} +(1.91668 - 1.39255i) q^{56} +2.54703i q^{57} +(0.636538 + 0.876119i) q^{58} +(-1.83443 - 5.64581i) q^{59} +(-1.70135 - 6.24471i) q^{60} +(0.282941 - 0.870802i) q^{61} +(-1.06258 + 0.345253i) q^{62} +(-2.58448 + 0.839749i) q^{63} +(2.22677 - 6.85329i) q^{64} +(-0.174207 - 0.639416i) q^{65} +(0.166634 + 0.512848i) q^{66} +(4.04870 + 5.57255i) q^{67} +10.1527i q^{68} +(-1.04697 + 0.760668i) q^{69} +(1.24888 + 0.473405i) q^{70} +(4.82884 + 3.50836i) q^{71} +(0.355890 - 0.489840i) q^{72} +(8.40107 + 2.72967i) q^{73} +1.48150 q^{74} +(4.87861 - 5.51045i) q^{75} -3.40270 q^{76} +(6.20252 + 2.01532i) q^{77} +(-0.0469697 + 0.0646482i) q^{78} +(-6.27851 - 4.56161i) q^{79} +(8.19784 - 2.23347i) q^{80} +(4.69667 - 3.41233i) q^{81} -0.185946i q^{82} +(-8.53192 - 11.7432i) q^{83} +(2.91668 + 8.97663i) q^{84} +(-9.65580 + 6.32825i) q^{85} +(0.183507 - 0.564778i) q^{86} +(-8.27647 + 2.68919i) q^{87} +(-1.38197 + 0.449028i) q^{88} +(-2.32579 + 7.15805i) q^{89} +(0.340938 + 0.0164351i) q^{90} +(0.298649 + 0.919147i) q^{91} +(-1.01621 - 1.39870i) q^{92} -8.97820i q^{93} +(-0.625353 + 0.454345i) q^{94} +(-2.12093 - 3.23616i) q^{95} +(-2.55922 - 1.85938i) q^{96} +(3.95373 - 5.44184i) q^{97} +(-0.632925 - 0.205650i) q^{98} +1.66673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} - 5 q^{3} - q^{4} - 9 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 - 5 * q^3 - q^4 - 9 * q^6 + 10 * q^8 + q^9	$ 8 q - 5 q^{2} - 5 q^{3} - q^{4} - 9 q^{6} + 10 q^{8} + q^{9} - 5 q^{10} - 4 q^{11} + 15 q^{12} - 5 q^{13} + 13 q^{14} + 15 q^{15} + 3 q^{16} - 10 q^{17} - 5 q^{19} - 15 q^{20} - 4 q^{21} + 5 q^{23} - 20 q^{24} - 10 q^{25} + 6 q^{26} - 5 q^{27} - 15 q^{28} - 5 q^{29} + 15 q^{30} - 9 q^{31} + 10 q^{33} + 13 q^{34} + 15 q^{35} + 23 q^{36} + 30 q^{37} + 15 q^{38} - 3 q^{39} + 10 q^{40} - 4 q^{41} - 15 q^{42} - 2 q^{44} - 15 q^{45} - 19 q^{46} - 30 q^{48} + 14 q^{49} - 15 q^{50} - 4 q^{51} - 10 q^{52} - 10 q^{53} - 5 q^{54} - 10 q^{55} + 10 q^{56} + 20 q^{58} - 10 q^{60} - 9 q^{61} - 30 q^{62} + 10 q^{63} + 4 q^{64} + 5 q^{65} + 12 q^{66} + 20 q^{67} + 17 q^{69} + 30 q^{70} + 6 q^{71} + 5 q^{72} + 15 q^{73} - 12 q^{74} - 10 q^{75} - 20 q^{76} + 10 q^{77} + 25 q^{78} + 15 q^{79} + 20 q^{80} + 28 q^{81} - 45 q^{83} + 18 q^{84} - 15 q^{85} - 9 q^{86} - 20 q^{87} - 20 q^{88} - 25 q^{89} - 25 q^{90} + 6 q^{91} + 30 q^{92} - 27 q^{94} + 15 q^{95} + 16 q^{96} - 60 q^{97} - 10 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q - 5 * q^2 - 5 * q^3 - q^4 - 9 * q^6 + 10 * q^8 + q^9 - 5 * q^10 - 4 * q^11 + 15 * q^12 - 5 * q^13 + 13 * q^14 + 15 * q^15 + 3 * q^16 - 10 * q^17 - 5 * q^19 - 15 * q^20 - 4 * q^21 + 5 * q^23 - 20 * q^24 - 10 * q^25 + 6 * q^26 - 5 * q^27 - 15 * q^28 - 5 * q^29 + 15 * q^30 - 9 * q^31 + 10 * q^33 + 13 * q^34 + 15 * q^35 + 23 * q^36 + 30 * q^37 + 15 * q^38 - 3 * q^39 + 10 * q^40 - 4 * q^41 - 15 * q^42 - 2 * q^44 - 15 * q^45 - 19 * q^46 - 30 * q^48 + 14 * q^49 - 15 * q^50 - 4 * q^51 - 10 * q^52 - 10 * q^53 - 5 * q^54 - 10 * q^55 + 10 * q^56 + 20 * q^58 - 10 * q^60 - 9 * q^61 - 30 * q^62 + 10 * q^63 + 4 * q^64 + 5 * q^65 + 12 * q^66 + 20 * q^67 + 17 * q^69 + 30 * q^70 + 6 * q^71 + 5 * q^72 + 15 * q^73 - 12 * q^74 - 10 * q^75 - 20 * q^76 + 10 * q^77 + 25 * q^78 + 15 * q^79 + 20 * q^80 + 28 * q^81 - 45 * q^83 + 18 * q^84 - 15 * q^85 - 9 * q^86 - 20 * q^87 - 20 * q^88 - 25 * q^89 - 25 * q^90 + 6 * q^91 + 30 * q^92 - 27 * q^94 + 15 * q^95 + 16 * q^96 - 60 * q^97 - 10 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.174207	+	0.0566033i	0.123183	+	0.0400246i	0.369960	−	0.929048i	$-0.379371\pi$
$2$	0.174207	+	0.0566033i	0.123183	+	0.0400246i	−0.246777	+	0.969072i	$0.579371\pi$
$3$	−0.865190	+	1.19083i	−0.499518	+	0.687527i	−0.982108	−	0.188319i	$-0.939696\pi$
$3$	−0.865190	+	1.19083i	−0.499518	+	0.687527i	0.482590	+	0.875846i	$0.339696\pi$
$4$	−1.59089	−	1.15585i	−0.795445	−	0.577925i
$5$	0.107666	−	2.23347i	0.0481496	−	0.998840i
$5$	0.107666	−	2.23347i	0.0481496	−	0.998840i
$6$	−0.218127	+	0.158479i	−0.0890500	+	0.0646986i
$7$			3.26086i			1.23249i	0.787555	+	0.616244i	$0.211346\pi$
$7$			3.26086i			1.23249i	−0.787555	+	0.616244i	$0.788654\pi$
$8$	−0.427051	−	0.587785i	−0.150985	−	0.207813i
$9$	0.257524	+	0.792578i	0.0858414	+	0.264193i
$10$	0.145178	−	0.382993i	0.0459094	−	0.121113i
$11$	0.618034	−	1.90211i	0.186344	−	0.573509i	−0.813625	−	0.581390i	$-0.802509\pi$
$11$	0.618034	−	1.90211i	0.186344	−	0.573509i	0.999969	+	0.00788181i	$0.00250889\pi$
$12$	2.75284	−	0.894453i	0.794678	−	0.258206i
$13$	0.281873	−	0.0915860i	0.0781775	−	0.0254014i	−0.269667	−	0.962954i	$-0.586914\pi$
$13$	0.281873	−	0.0915860i	0.0781775	−	0.0254014i	0.347845	+	0.937552i	$0.386914\pi$
$14$	−0.184575	+	0.568064i	−0.0493298	+	0.151821i
$15$	2.56654	+	2.06059i	0.662678	+	0.532042i
$16$	1.17421	+	3.61384i	0.293552	+	0.903459i
$17$	−3.03472	−	4.17693i	−0.736027	−	1.01305i	−0.998837	−	0.0482067i	$-0.984649\pi$
$17$	−3.03472	−	4.17693i	−0.736027	−	1.01305i	0.262810	−	0.964847i	$-0.415351\pi$
$18$			0.152649i			0.0359798i
$19$	1.39991	−	1.01709i	0.321161	−	0.233337i	−0.415510	−	0.909589i	$-0.636397\pi$
$19$	1.39991	−	1.01709i	0.321161	−	0.233337i	0.736671	+	0.676252i	$0.236397\pi$
$20$	−2.75284	+	3.42877i	−0.615555	+	0.766695i
$21$	−3.88313	−	2.82126i	−0.847369	−	0.615649i
$22$	0.215332	−	0.296379i	0.0459089	−	0.0631881i
$23$	0.836161	+	0.271685i	0.174352	+	0.0566503i	0.394892	−	0.918728i	$-0.370782\pi$
$23$	0.836161	+	0.271685i	0.174352	+	0.0566503i	−0.220540	+	0.975378i	$0.570782\pi$
$24$	1.06943			0.218297
$25$	−4.97682	−	0.480938i	−0.995363	−	0.0961876i
$26$	0.0542883			0.0106468
$27$	−5.36635	−	1.74363i	−1.03276	−	0.335563i
$28$	3.76906	−	5.18766i	0.712285	−	0.980376i
$29$	4.78304	+	3.47508i	0.888188	+	0.645306i	0.935405	−	0.353578i	$-0.115035\pi$
$29$	4.78304	+	3.47508i	0.888188	+	0.645306i	−0.0472171	+	0.998885i	$0.515035\pi$
$30$	0.330473	+	0.504244i	0.0603359	+	0.0920620i
$31$	−4.93462	+	3.58521i	−0.886285	+	0.643923i	−0.934907	−	0.354894i	$-0.884517\pi$
$31$	−4.93462	+	3.58521i	−0.886285	+	0.643923i	0.0486220	+	0.998817i	$0.484517\pi$
$32$			2.14910i			0.379912i
$33$	1.73038	+	2.38166i	0.301220	+	0.414594i
$34$	−0.292241	−	0.899425i	−0.0501189	−	0.154250i
$35$	7.28304	+	0.351083i	1.23106	+	0.0593438i
$36$	0.506408	−	1.55856i	0.0844013	−	0.259761i
$37$	7.69215	−	2.49933i	1.26458	−	0.410887i	0.401457	−	0.915878i	$-0.368504\pi$
$37$	7.69215	−	2.49933i	1.26458	−	0.410887i	0.863125	+	0.504991i	$0.168504\pi$
$38$	0.301444	−	0.0979452i	0.0489007	−	0.0158888i
$39$	−0.134810	+	0.414902i	−0.0215869	+	0.0664376i
$40$	−1.35878	+	0.890523i	−0.214842	+	0.140804i
$41$	−0.313697	−	0.965461i	−0.0489913	−	0.150780i	0.923568	−	0.383434i	$-0.125259\pi$
$41$	−0.313697	−	0.965461i	−0.0489913	−	0.150780i	−0.972559	+	0.232655i	$0.925259\pi$
$42$	−0.516776	−	0.711281i	−0.0797403	−	0.109753i
$43$		−	3.24199i		−	0.494399i	−0.968965	−	0.247200i	$-0.920490\pi$
$43$		−	3.24199i		−	0.494399i	0.968965	−	0.247200i	$-0.0795103\pi$
$44$	−3.18178	+	2.31170i	−0.479671	+	0.348502i
$45$	1.79793	−	0.489840i	0.268019	−	0.0730210i
$46$	0.130287	+	0.0946589i	0.0192097	+	0.0139567i
$47$	−2.48043	+	3.41402i	−0.361808	+	0.497986i	−0.950651	−	0.310261i	$-0.899583\pi$
$47$	−2.48043	+	3.41402i	−0.361808	+	0.497986i	0.588844	+	0.808247i	$0.299583\pi$
$48$	−5.31939	−	1.72837i	−0.767787	−	0.249469i
$49$	−3.63318			−0.519026
$50$	−0.839774	−	0.365487i	−0.118762	−	0.0516877i
$51$	7.59963			1.06416
$52$	−0.554288	−	0.180099i	−0.0768660	−	0.0249753i
$53$	−4.76148	+	6.55362i	−0.654040	+	0.900209i	−0.999266	−	0.0383106i	$-0.987802\pi$
$53$	−4.76148	+	6.55362i	−0.654040	+	0.900209i	0.345226	+	0.938520i	$0.387802\pi$
$54$	−0.836161	−	0.607507i	−0.113787	−	0.0826712i
$55$	−4.18178	−	1.58516i	−0.563871	−	0.213742i
$56$	1.91668	−	1.39255i	0.256128	−	0.186088i
$57$			2.54703i			0.337363i
$58$	0.636538	+	0.876119i	0.0835815	+	0.115040i
$59$	−1.83443	−	5.64581i	−0.238823	−	0.735021i	−0.996591	−	0.0824976i	$-0.973710\pi$
$59$	−1.83443	−	5.64581i	−0.238823	−	0.735021i	0.757768	−	0.652524i	$-0.226290\pi$
$60$	−1.70135	−	6.24471i	−0.219643	−	0.806188i
$61$	0.282941	−	0.870802i	0.0362268	−	0.111495i	−0.931308	−	0.364233i	$-0.881331\pi$
$61$	0.282941	−	0.870802i	0.0362268	−	0.111495i	0.967535	+	0.252738i	$0.0813312\pi$
$62$	−1.06258	+	0.345253i	−0.134948	+	0.0438472i
$63$	−2.58448	+	0.839749i	−0.325614	+	0.105798i
$64$	2.22677	−	6.85329i	0.278346	−	0.856661i
$65$	−0.174207	−	0.639416i	−0.0216077	−	0.0793099i
$66$	0.166634	+	0.512848i	0.0205113	+	0.0631272i
$67$	4.04870	+	5.57255i	0.494627	+	0.680796i	0.981233	−	0.192826i	$-0.0617652\pi$
$67$	4.04870	+	5.57255i	0.494627	+	0.680796i	−0.486606	+	0.873622i	$0.661765\pi$
$68$			10.1527i			1.23120i
$69$	−1.04697	+	0.760668i	−0.126040	+	0.0915737i
$70$	1.24888	+	0.473405i	0.149270	+	0.0565827i
$71$	4.82884	+	3.50836i	0.573078	+	0.416366i	0.836222	−	0.548391i	$-0.184759\pi$
$71$	4.82884	+	3.50836i	0.573078	+	0.416366i	−0.263144	+	0.964757i	$0.584759\pi$
$72$	0.355890	−	0.489840i	0.0419420	−	0.0577282i
$73$	8.40107	+	2.72967i	0.983271	+	0.319484i	0.756161	−	0.654385i	$-0.227072\pi$
$73$	8.40107	+	2.72967i	0.983271	+	0.319484i	0.227110	+	0.973869i	$0.427072\pi$
$74$	1.48150			0.172220
$75$	4.87861	−	5.51045i	0.563333	−	0.636292i
$76$	−3.40270			−0.390317
$77$	6.20252	+	2.01532i	0.706842	+	0.229667i
$78$	−0.0469697	+	0.0646482i	−0.00531827	+	0.00731997i
$79$	−6.27851	−	4.56161i	−0.706388	−	0.513221i	0.175618	−	0.984458i	$-0.443808\pi$
$79$	−6.27851	−	4.56161i	−0.706388	−	0.513221i	−0.882006	+	0.471237i	$0.843808\pi$
$80$	8.19784	−	2.23347i	0.916546	−	0.249710i
$81$	4.69667	−	3.41233i	0.521852	−	0.379148i
$82$		−	0.185946i		−	0.0205343i
$83$	−8.53192	−	11.7432i	−0.936500	−	1.28898i	−0.957269	−	0.289197i	$-0.906612\pi$
$83$	−8.53192	−	11.7432i	−0.936500	−	1.28898i	0.0207694	−	0.999784i	$-0.493388\pi$
$84$	2.91668	+	8.97663i	0.318236	+	0.979430i
$85$	−9.65580	+	6.32825i	−1.04732	+	0.686395i
$86$	0.183507	−	0.564778i	0.0197881	−	0.0609015i
$87$	−8.27647	+	2.68919i	−0.887331	+	0.288311i
$88$	−1.38197	+	0.449028i	−0.147318	+	0.0478665i
$89$	−2.32579	+	7.15805i	−0.246534	+	0.758752i	0.748847	+	0.662743i	$0.230608\pi$
$89$	−2.32579	+	7.15805i	−0.246534	+	0.758752i	−0.995380	+	0.0960092i	$0.969392\pi$
$90$	0.340938	+	0.0164351i	0.0359381	+	0.00173241i
$91$	0.298649	+	0.919147i	0.0313069	+	0.0963528i
$92$	−1.01621	−	1.39870i	−0.105948	−	0.145824i
$93$		−	8.97820i		−	0.930996i
$94$	−0.625353	+	0.454345i	−0.0645002	+	0.0468621i
$95$	−2.12093	−	3.23616i	−0.217602	−	0.332023i
$96$	−2.55922	−	1.85938i	−0.261200	−	0.189773i
$97$	3.95373	−	5.44184i	0.401440	−	0.552535i	−0.559664	−	0.828719i	$-0.689070\pi$
$97$	3.95373	−	5.44184i	0.401440	−	0.552535i	0.961105	+	0.276184i	$0.0890699\pi$
$98$	−0.632925	−	0.205650i	−0.0639351	−	0.0207738i
$99$	1.66673			0.167513
$100$	7.36167	+	6.51757i	0.736167	+	0.651757i
$101$	−12.1955			−1.21350			−0.606748	−	0.794894i	$-0.707526\pi$
$101$	−12.1955			−1.21350			−0.606748	+	0.794894i	$0.707526\pi$
$102$	1.32391	+	0.430164i	0.131086	+	0.0425926i
$103$	0.811969	−	1.11758i	0.0800057	−	0.110118i	−0.767138	−	0.641482i	$-0.778320\pi$
$103$	0.811969	−	1.11758i	0.0800057	−	0.110118i	0.847144	+	0.531363i	$0.178320\pi$
$104$	−0.174207	−	0.126569i	−0.0170824	−	0.0124111i
$105$	−6.71929	+	8.36912i	−0.655736	+	0.816742i
$106$	−1.20044	+	0.872171i	−0.116597	+	0.0847127i
$107$		−	15.8285i		−	1.53020i	−0.643911	−	0.765101i	$-0.722689\pi$
$107$		−	15.8285i		−	1.53020i	0.643911	−	0.765101i	$-0.277311\pi$
$108$	6.52190	+	8.97663i	0.627570	+	0.863776i
$109$	0.619199	+	1.90570i	0.0593085	+	0.182533i	0.976322	−	0.216324i	$-0.0694069\pi$
$109$	0.619199	+	1.90570i	0.0593085	+	0.182533i	−0.917013	+	0.398857i	$0.869407\pi$
$110$	−0.638770	−	0.512848i	−0.0609044	−	0.0488981i
$111$	−3.67889	+	11.3225i	−0.349185	+	1.07468i
$112$	−11.7842	+	3.82892i	−1.11350	+	0.361799i
$113$	9.91713	−	3.22227i	0.932925	−	0.303126i	0.197167	−	0.980370i	$-0.436826\pi$
$113$	9.91713	−	3.22227i	0.932925	−	0.303126i	0.735758	+	0.677244i	$0.236826\pi$
$114$	−0.144170	+	0.443711i	−0.0135028	+	0.0415573i
$115$	0.696828	−	1.83829i	0.0649795	−	0.171422i
$116$	−3.59262	−	11.0569i	−0.333566	−	1.02661i
$117$	0.145178	+	0.199821i	0.0134217	+	0.0184734i
$118$		−	1.08737i		−	0.100101i
$119$	13.6204	−	9.89577i	1.24858	−	0.907144i
$120$	0.115141	−	2.38855i	0.0105109	−	0.218044i
$121$	5.66312	+	4.11450i	0.514829	+	0.374045i
$122$	0.0985805	−	0.135684i	0.00892506	−	0.0122843i
$123$	1.42111	+	0.461746i	0.128137	+	0.0416343i
$124$	11.9944			1.07713
$125$	−1.61000	+	11.0638i	−0.144002	+	0.989577i
$126$	−0.497767			−0.0443446
$127$	5.56375	+	1.80777i	0.493703	+	0.160414i	0.545278	−	0.838255i	$-0.316424\pi$
$127$	5.56375	+	1.80777i	0.493703	+	0.160414i	−0.0515752	+	0.998669i	$0.516424\pi$
$128$	3.30226	−	4.54517i	0.291881	−	0.401740i
$129$	3.86067	+	2.80494i	0.339913	+	0.246961i
$130$	0.00584500	−	0.121252i	0.000512640	−	0.0106345i
$131$	1.21081	−	0.879704i	0.105789	−	0.0768601i	−0.533633	−	0.845716i	$-0.679174\pi$
$131$	1.21081	−	0.879704i	0.105789	−	0.0768601i	0.639422	+	0.768856i	$0.279174\pi$
$132$		−	5.78902i		−	0.503870i
$133$	3.31659	+	4.56489i	0.287585	+	0.395827i
$134$	0.389887	+	1.19995i	0.0336811	+	0.103660i
$135$	−4.47214	+	11.7979i	−0.384900	+	1.01540i
$136$	−1.15916	+	3.56752i	−0.0993970	+	0.305913i
$137$	−7.46472	+	2.42543i	−0.637754	+	0.207219i	−0.610007	−	0.792396i	$-0.708833\pi$
$137$	−7.46472	+	2.42543i	−0.637754	+	0.207219i	−0.0277472	+	0.999615i	$0.508833\pi$
$138$	−0.225446	+	0.0732518i	−0.0191912	+	0.00623560i
$139$	−1.66607	+	5.12764i	−0.141314	+	0.434921i	−0.996519	−	0.0833702i	$-0.973432\pi$
$139$	−1.66607	+	5.12764i	−0.141314	+	0.434921i	0.855204	+	0.518291i	$0.173432\pi$
$140$	−11.1807	−	8.97663i	−0.944943	−	0.758663i
$141$	−1.91948	−	5.90755i	−0.161649	−	0.497505i
$142$	0.642634	+	0.884509i	0.0539286	+	0.0742264i
$143$		−	0.592757i		−	0.0495689i
$144$	−2.56186	+	1.86130i	−0.213488	+	0.155108i
$145$	8.27647	−	10.3086i	0.687324	−	0.856086i
$146$	1.30902	+	0.951057i	0.108335	+	0.0787100i
$147$	3.14339	−	4.32651i	0.259262	−	0.356844i
$148$	−15.1262	−	4.91480i	−1.24337	−	0.403994i
$149$	−18.8229			−1.54203			−0.771015	−	0.636817i	$-0.780251\pi$
$149$	−18.8229			−1.54203			−0.771015	+	0.636817i	$0.780251\pi$
$150$	1.16180	−	0.683814i	0.0948603	−	0.0558331i
$151$	−3.88797			−0.316398			−0.158199	−	0.987407i	$-0.550569\pi$
$151$	−3.88797			−0.316398			−0.158199	+	0.987407i	$0.550569\pi$
$152$	−1.19566	−	0.388495i	−0.0969811	−	0.0315111i
$153$	2.52903	−	3.48091i	0.204460	−	0.281415i
$154$	0.966448	+	0.702166i	0.0778786	+	0.0565821i
$155$	7.47619	+	11.4074i	0.600502	+	0.916261i
$156$	0.694033	−	0.504244i	0.0555671	−	0.0403718i
$157$		−	4.28378i		−	0.341883i	−0.985281	−	0.170941i	$-0.945319\pi$
$157$		−	4.28378i		−	0.341883i	0.985281	−	0.170941i	$-0.0546808\pi$
$158$	−0.835559	−	1.15005i	−0.0664735	−	0.0914930i
$159$	−3.68467	−	11.3403i	−0.292214	−	0.899341i
$160$	4.79997	+	0.231385i	0.379471	+	0.0182926i
$161$	−0.885926	+	2.72660i	−0.0698208	+	0.214886i
$162$	1.01134	−	0.328605i	0.0794585	−	0.0258176i
$163$	−14.9566	+	4.85970i	−1.17149	+	0.380641i	−0.829200	−	0.558952i	$-0.811204\pi$
$163$	−14.9566	+	4.85970i	−1.17149	+	0.380641i	−0.342293	+	0.939593i	$0.611204\pi$
$164$	−0.616869	+	1.89853i	−0.0481694	+	0.148250i
$165$	5.50569	−	3.60834i	0.428617	−	0.280909i
$166$	−0.821618	−	2.52868i	−0.0637699	−	0.196264i
$167$	12.3629	+	17.0161i	0.956670	+	1.31674i	0.948500	+	0.316777i	$0.102601\pi$
$167$	12.3629	+	17.0161i	0.956670	+	1.31674i	0.00816967	+	0.999967i	$0.497399\pi$
$168$			3.48727i			0.269049i
$169$	−10.4462	+	7.58958i	−0.803551	+	0.583814i
$170$	−2.04031	+	0.555875i	−0.156484	+	0.0426337i
$171$	1.16663	+	0.847609i	0.0892148	+	0.0648183i
$172$	−3.74725	+	5.15765i	−0.285725	+	0.393267i
$173$	6.81587	+	2.21461i	0.518201	+	0.168374i	0.556429	−	0.830895i	$-0.312171\pi$
$173$	6.81587	+	2.21461i	0.518201	+	0.168374i	−0.0382277	+	0.999269i	$0.512171\pi$
$174$	−1.59404			−0.120844
$175$	1.56827	−	16.2287i	0.118550	−	1.22677i
$176$	7.59963			0.572843
$177$	8.31034	+	2.70019i	0.624643	+	0.202959i
$178$	−0.810339	+	1.11534i	−0.0607375	+	0.0835979i
$179$	6.50396	+	4.72540i	0.486129	+	0.353193i	0.803694	−	0.595043i	$-0.202865\pi$
$179$	6.50396	+	4.72540i	0.486129	+	0.353193i	−0.317565	+	0.948237i	$0.602865\pi$
$180$	−3.42649	−	1.29885i	−0.255395	−	0.0968108i
$181$	16.6796	−	12.1184i	1.23978	−	0.900756i	0.242200	−	0.970226i	$-0.422131\pi$
$181$	16.6796	−	12.1184i	1.23978	−	0.900756i	0.997584	+	0.0694707i	$0.0221310\pi$
$182$			0.177026i			0.0131221i
$183$	0.792181	+	1.09034i	0.0585597	+	0.0806005i
$184$	−0.197391	−	0.607507i	−0.0145518	−	0.0447860i
$185$	−4.75401	−	17.4493i	−0.349522	−	1.28290i
$186$	0.508196	−	1.56407i	0.0372627	−	0.114683i
$187$	−9.82055	+	3.19089i	−0.718150	+	0.233341i
$188$	7.89218	−	2.56432i	0.575596	−	0.187023i
$189$	5.68574	−	17.4989i	0.413577	−	1.27286i
$190$	−0.186303	−	0.683814i	−0.0135158	−	0.0496090i
$191$	5.57167	+	17.1478i	0.403152	+	1.24077i	0.922429	+	0.386167i	$0.126201\pi$
$191$	5.57167	+	17.1478i	0.403152	+	1.24077i	−0.519277	+	0.854606i	$0.673799\pi$
$192$	6.23453	+	8.58110i	0.449939	+	0.619288i
$193$			6.78859i			0.488653i	0.969693	+	0.244327i	$0.0785669\pi$
$193$			6.78859i			0.488653i	−0.969693	+	0.244327i	$0.921433\pi$
$194$	0.996793	−	0.724213i	0.0715656	−	0.0519955i
$195$	0.912160	+	0.345766i	0.0653211	+	0.0247608i
$196$	5.77999	+	4.19941i	0.412856	+	0.299958i
$197$	−4.69956	+	6.46839i	−0.334830	+	0.460854i	−0.942923	−	0.333012i	$-0.891935\pi$
$197$	−4.69956	+	6.46839i	−0.334830	+	0.460854i	0.608092	+	0.793866i	$0.291935\pi$
$198$	0.290356	+	0.0943425i	0.0206347	+	0.00670463i
$199$	5.20485			0.368962			0.184481	−	0.982836i	$-0.440940\pi$
$199$	5.20485			0.368962			0.184481	+	0.982836i	$0.440940\pi$
$200$	1.84267	+	3.13068i	0.130296	+	0.221373i
$201$	−10.1389			−0.715141
$202$	−2.12454	−	0.690305i	−0.149482	−	0.0485697i
$203$	−11.3317	+	15.5968i	−0.795332	+	1.09468i
$204$	−12.0902	−	8.78402i	−0.846481	−	0.615005i
$205$	−2.19011	+	0.596687i	−0.152964	+	0.0416745i
$206$	0.204709	−	0.148730i	0.0142628	−	0.0103625i
$207$			0.732688i			0.0509254i
$208$	0.661954	+	0.911102i	0.0458983	+	0.0631735i
$209$	−1.06943	−	3.29138i	−0.0739743	−	0.227669i
$210$	−1.64427	+	1.07763i	−0.113465	+	0.0743632i
$211$	5.13029	−	15.7894i	0.353184	−	1.08699i	−0.603872	−	0.797082i	$-0.706376\pi$
$211$	5.13029	−	15.7894i	0.353184	−	1.08699i	0.957055	−	0.289906i	$-0.0936239\pi$
$212$	15.1500	−	4.92253i	1.04051	−	0.338081i
$213$	−8.35573	+	2.71494i	−0.572525	+	0.186025i
$214$	0.895947	−	2.75744i	0.0612456	−	0.188495i
$215$	−7.24091	−	0.349052i	−0.493826	−	0.0238051i
$216$	1.26682	+	3.89889i	0.0861965	+	0.265286i
$217$	−11.6909	−	16.0911i	−0.793628	−	1.09233i
$218$			0.367035i			0.0248587i
$219$	−10.5191	+	7.64258i	−0.710815	+	0.516438i
$220$	4.82055	+	7.35531i	0.325001	+	0.495895i
$221$	−1.23795	−	0.899425i	−0.0832737	−	0.0605019i
$222$	−1.28178	+	1.76421i	−0.0860272	+	0.118406i
$223$	6.30368	+	2.04819i	0.422126	+	0.137157i	0.512374	−	0.858762i	$-0.328766\pi$
$223$	6.30368	+	2.04819i	0.422126	+	0.137157i	−0.0902485	+	0.995919i	$0.528766\pi$
$224$	−7.00792			−0.468236
$225$	−0.900470	−	4.06837i	−0.0600313	−	0.271224i
$226$	1.91002			0.127053
$227$	−12.7365	−	4.13833i	−0.845350	−	0.274671i	−0.145853	−	0.989306i	$-0.546593\pi$
$227$	−12.7365	−	4.13833i	−0.845350	−	0.274671i	−0.699497	+	0.714636i	$0.746593\pi$
$228$	2.94398	−	4.05205i	0.194970	−	0.268353i
$229$	8.16032	+	5.92882i	0.539249	+	0.391788i	0.823806	−	0.566872i	$-0.191846\pi$
$229$	8.16032	+	5.92882i	0.539249	+	0.391788i	−0.284557	+	0.958659i	$0.591846\pi$
$230$	0.225446	−	0.280801i	0.0148655	−	0.0185155i
$231$	−7.76626	+	5.64252i	−0.510983	+	0.371251i
$232$		−	4.29544i		−	0.282009i
$233$	−12.9345	−	17.8028i	−0.847368	−	1.16630i	−0.984437	−	0.175740i	$-0.943768\pi$
$233$	−12.9345	−	17.8028i	−0.847368	−	1.16630i	0.137069	−	0.990562i	$-0.456232\pi$
$234$	0.0139805	+	0.0430277i	0.000913937	+	0.00281281i
$235$	7.35806	+	5.90755i	0.479987	+	0.385366i
$236$	−3.60732	+	11.1022i	−0.234816	+	0.722691i
$237$	10.8642	−	3.53000i	0.705707	−	0.229298i
$238$	2.93290	−	0.952956i	0.190111	−	0.0617709i
$239$	−2.33626	+	7.19026i	−0.151120	+	0.465099i	−0.997747	−	0.0670870i	$-0.978629\pi$
$239$	−2.33626	+	7.19026i	−0.151120	+	0.465099i	0.846627	+	0.532187i	$0.178629\pi$
$240$	−4.43299	+	11.6946i	−0.286148	+	0.754885i
$241$	−6.30226	−	19.3964i	−0.405964	−	1.24943i	−0.920087	−	0.391713i	$-0.871883\pi$
$241$	−6.30226	−	19.3964i	−0.405964	−	1.24943i	0.514123	−	0.857716i	$-0.328117\pi$
$242$	0.753661	+	1.03733i	0.0484472	+	0.0666818i
$243$		−	8.38230i		−	0.537725i
$244$	−1.45664	+	1.05831i	−0.0932520	+	0.0677515i
$245$	−0.391169	+	8.11461i	−0.0249909	+	0.518424i
$246$	0.221431	+	0.160879i	0.0141179	+	0.0102573i
$247$	0.301444	−	0.414902i	0.0191804	−	0.0263996i
$248$	4.21467	+	1.36943i	0.267632	+	0.0869589i
$249$	21.3659			1.35401
$250$	−0.906721	+	1.83626i	−0.0573460	+	0.116135i
$251$	10.5717			0.667278			0.333639	−	0.942701i	$-0.391723\pi$
$251$	10.5717			0.667278			0.333639	+	0.942701i	$0.391723\pi$
$252$	5.08225	+	1.65132i	0.320152	+	0.104024i
$253$	1.03355	−	1.42256i	0.0649789	−	0.0894357i
$254$	0.866918	+	0.629853i	0.0543953	+	0.0395205i
$255$	0.818220	−	16.9736i	0.0512389	−	1.06293i
$256$	−10.8270	+	7.86625i	−0.676685	+	0.491640i
$257$			20.2700i			1.26441i	0.774801	+	0.632205i	$0.217850\pi$
$257$			20.2700i			1.26441i	−0.774801	+	0.632205i	$0.782150\pi$
$258$	0.513786	+	0.707166i	0.0319869	+	0.0440263i
$259$	8.14996	+	25.0830i	0.506414	+	1.55858i
$260$	−0.461925	+	1.21860i	−0.0286474	+	0.0755743i
$261$	−1.52252	+	4.68585i	−0.0942419	+	0.290047i
$262$	0.260725	−	0.0847148i	0.0161077	−	0.00523370i
$263$	26.7160	−	8.68056i	1.64738	−	0.535267i	0.669211	−	0.743072i	$-0.266632\pi$
$263$	26.7160	−	8.68056i	1.64738	−	0.535267i	0.978170	+	0.207806i	$0.0666323\pi$
$264$	0.660946	−	2.03418i	0.0406784	−	0.125195i
$265$	14.1247	+	11.3403i	0.867673	+	0.696626i
$266$	0.319385	+	0.982966i	0.0195828	+	0.0602695i
$267$	−6.51179	−	8.96271i	−0.398515	−	0.548509i
$268$		−	13.5450i		−	0.827393i
$269$	16.4416	−	11.9455i	1.00246	−	0.728333i	0.0398490	−	0.999206i	$-0.487312\pi$
$269$	16.4416	−	11.9455i	1.00246	−	0.728333i	0.962615	+	0.270873i	$0.0873123\pi$
$270$	−1.44688	+	1.80214i	−0.0880541	+	0.109675i
$271$	−25.4409	−	18.4839i	−1.54543	−	1.12282i	−0.946816	−	0.321777i	$-0.895720\pi$
$271$	−25.4409	−	18.4839i	−1.54543	−	1.12282i	−0.598610	−	0.801041i	$-0.704280\pi$
$272$	11.5314	−	15.8716i	0.699191	−	0.962354i
$273$	−1.35294	−	0.439596i	−0.0818835	−	0.0266056i
$274$	−1.43769			−0.0868543
$275$	−3.99064	+	9.16923i	−0.240645	+	0.552925i
$276$	2.54483			0.153181
$277$	−13.2487	−	4.30475i	−0.796035	−	0.258648i	−0.117363	−	0.993089i	$-0.537444\pi$
$277$	−13.2487	−	4.30475i	−0.796035	−	0.258648i	−0.678672	+	0.734441i	$0.737444\pi$
$278$	−0.580483	+	0.798966i	−0.0348150	+	0.0479188i
$279$	−4.11235	−	2.98779i	−0.246200	−	0.178875i
$280$	−2.90387	−	4.43079i	−0.173539	−	0.264790i
$281$	−20.9355	+	15.2105i	−1.24891	+	0.907383i	−0.998158	−	0.0606690i	$-0.980677\pi$
$281$	−20.9355	+	15.2105i	−1.24891	+	0.907383i	−0.250748	+	0.968052i	$0.580677\pi$
$282$		−	1.13778i		−	0.0677541i
$283$	13.9491	+	19.1993i	0.829188	+	1.14128i	0.988074	+	0.153983i	$0.0492101\pi$
$283$	13.9491	+	19.1993i	0.829188	+	1.14128i	−0.158885	+	0.987297i	$0.550790\pi$
$284$	−3.62702	−	11.1628i	−0.215224	−	0.662392i
$285$	5.68873	+	0.274228i	0.336971	+	0.0162439i
$286$	0.0335520	−	0.103262i	0.00198397	−	0.00610604i
$287$	3.14823	−	1.02292i	0.185834	−	0.0603811i
$288$	−1.70333	+	0.553446i	−0.100370	+	0.0326121i
$289$	−2.98394	+	9.18363i	−0.175526	+	0.540214i
$290$	2.02532	−	1.32736i	0.118931	−	0.0779454i
$291$	3.05959	+	9.41645i	0.179356	+	0.552002i
$292$	−10.2101	−	14.0530i	−0.597500	−	0.822389i
$293$			12.3029i			0.718742i	0.933195	+	0.359371i	$0.117009\pi$
$293$			12.3029i			0.718742i	−0.933195	+	0.359371i	$0.882991\pi$
$294$	0.792495	−	0.575781i	0.0462193	−	0.0335803i
$295$	−12.8073	+	3.48930i	−0.745668	+	0.203155i
$296$	−4.75401	−	3.45399i	−0.276321	−	0.200759i
$297$	−6.63318	+	9.12979i	−0.384896	+	0.529764i
$298$	−3.27908	−	1.06544i	−0.189952	−	0.0617191i
$299$	0.260574			0.0150694
$300$	−14.1306	+	3.12758i	−0.815829	+	0.180571i
$301$	10.5717			0.609341
$302$	−0.677311	−	0.220072i	−0.0389749	−	0.0126637i
$303$	10.5514	−	14.5228i	0.606163	−	0.834311i
$304$	5.31939	+	3.86476i	0.305088	+	0.221659i
$305$	−1.91445	−	0.725696i	−0.109621	−	0.0415532i
$306$	0.637605	−	0.463247i	0.0364495	−	0.0264821i
$307$			4.28249i			0.244415i	0.992505	+	0.122207i	$0.0389973\pi$
$307$			4.28249i			0.244415i	−0.992505	+	0.122207i	$0.961003\pi$
$308$	−7.53811	−	10.3753i	−0.429524	−	0.591189i
$309$	0.628342	+	1.93384i	0.0357451	+	0.110012i
$310$	0.656711	+	2.41042i	0.0372987	+	0.136903i
$311$	7.92526	−	24.3915i	0.449400	−	1.38311i	−0.428185	−	0.903691i	$-0.640847\pi$
$311$	7.92526	−	24.3915i	0.449400	−	1.38311i	0.877585	−	0.479421i	$-0.159153\pi$
$312$	0.301444	−	0.0979452i	0.0170659	−	0.00554505i
$313$	−21.2573	+	6.90692i	−1.20153	+	0.390402i	−0.840325	−	0.542083i	$-0.817636\pi$
$313$	−21.2573	+	6.90692i	−1.20153	+	0.390402i	−0.361209	+	0.932485i	$0.617636\pi$
$314$	0.242476	−	0.746264i	0.0136837	−	0.0421141i
$315$	1.59730	+	5.86279i	0.0899975	+	0.330331i
$316$	4.71589	+	14.5140i	0.265290	+	0.816478i
$317$	−12.8859	−	17.7360i	−0.723746	−	0.996151i	−0.999391	−	0.0348911i	$-0.988892\pi$
$317$	−12.8859	−	17.7360i	−0.723746	−	0.996151i	0.275645	−	0.961259i	$-0.411108\pi$
$318$		−	2.18412i		−	0.122479i
$319$	9.56608	−	6.95016i	0.535597	−	0.389134i
$320$	−15.0669	−	5.71129i	−0.842265	−	0.319271i
$321$	18.8491	+	13.6947i	1.05205	+	0.764363i
$322$	−0.308669	+	0.424847i	−0.0172015	+	0.0236758i
$323$	−8.49664	−	2.76073i	−0.472766	−	0.153611i
$324$	−11.4160			−0.634224
$325$	−1.44688	+	0.320244i	−0.0802583	+	0.0177639i
$326$	−2.88062			−0.159543
$327$	−2.80509	−	0.911429i	−0.155122	−	0.0504021i
$328$	−0.433519	+	0.596687i	−0.0239371	+	0.0329466i
$329$	−11.1326	−	8.08832i	−0.613761	−	0.445923i
$330$	1.16337	−	0.316957i	0.0640416	−	0.0174479i
$331$	7.25121	−	5.26831i	0.398563	−	0.289573i	−0.370393	−	0.928875i	$-0.620777\pi$
$331$	7.25121	−	5.26831i	0.398563	−	0.289573i	0.768955	+	0.639303i	$0.220777\pi$
$332$			28.5437i			1.56654i
$333$	3.96183	+	5.45299i	0.217107	+	0.298822i
$334$	1.19054	+	3.66410i	0.0651433	+	0.200491i
$335$	12.8821	−	8.44269i	0.703822	−	0.461273i
$336$	5.63597	−	17.3457i	0.307468	−	0.946288i
$337$	27.6601	−	8.98731i	1.50674	−	0.489570i	0.564766	−	0.825251i	$-0.308966\pi$
$337$	27.6601	−	8.98731i	1.50674	−	0.489570i	0.941976	+	0.335681i	$0.108966\pi$
$338$	−2.24939	+	0.730871i	−0.122351	+	0.0397541i
$339$	−4.74302	+	14.5975i	−0.257605	+	0.792828i
$340$	22.6758	+	1.09310i	1.22977	+	0.0592817i
$341$	3.76972	+	11.6020i	0.204142	+	0.628283i
$342$	0.155258	+	0.213695i	0.00839541	+	0.0115553i
$343$			10.9787i			0.592795i
$344$	−1.90559	+	1.38450i	−0.102743	+	0.0746470i
$345$	1.58621	+	2.42028i	0.0853987	+	0.130303i
$346$	1.06202	+	0.771601i	0.0570944	+	0.0414815i
$347$	8.40368	−	11.5667i	0.451133	−	0.620931i	−0.521508	−	0.853247i	$-0.674630\pi$
$347$	8.40368	−	11.5667i	0.451133	−	0.620931i	0.972641	+	0.232315i	$0.0746302\pi$
$348$	16.2753	+	5.28815i	0.872445	+	0.283475i
$349$	−5.62382			−0.301036			−0.150518	−	0.988607i	$-0.548094\pi$
$349$	−5.62382			−0.301036			−0.150518	+	0.988607i	$0.548094\pi$
$350$	1.19180	−	2.73838i	0.0637044	−	0.146373i
$351$	−1.67232			−0.0892620
$352$	4.08784	+	1.32822i	0.217883	+	0.0707944i
$353$	−1.12265	+	1.54520i	−0.0597529	+	0.0822427i	−0.837848	−	0.545904i	$-0.816186\pi$
$353$	−1.12265	+	1.54520i	−0.0597529	+	0.0822427i	0.778095	+	0.628147i	$0.216186\pi$
$354$	1.29488	+	0.940785i	0.0688221	+	0.0500022i
$355$	8.35573	−	10.4074i	0.443476	−	0.552366i
$356$	11.9737	−	8.69941i	0.634605	−	0.461068i
$357$			24.7813i			1.31156i
$358$	0.865562	+	1.19134i	0.0457464	+	0.0629645i
$359$	−6.86161	−	21.1179i	−0.362142	−	1.11456i	−0.951751	−	0.306870i	$-0.900718\pi$
$359$	−6.86161	−	21.1179i	−0.362142	−	1.11456i	0.589609	−	0.807689i	$-0.299282\pi$
$360$	−1.05573	−	0.847609i	−0.0556418	−	0.0446729i
$361$	−4.94606	+	15.2224i	−0.260319	+	0.801179i
$362$	3.59164	−	1.16700i	0.188773	−	0.0613359i
$363$	−9.79935	+	3.18400i	−0.514332	+	0.167117i
$364$	0.587277	−	1.80745i	0.0307817	−	0.0947363i
$365$	7.00116	−	18.4697i	0.366458	−	0.966748i
$366$	0.0762864	+	0.234786i	0.00398756	+	0.0122724i
$367$	12.6050	+	17.3493i	0.657978	+	0.905629i	0.999412	−	0.0342768i	$-0.0109128\pi$
$367$	12.6050	+	17.3493i	0.657978	+	0.905629i	−0.341435	+	0.939906i	$0.610913\pi$
$368$			3.34077i			0.174149i
$369$	0.684418	−	0.497259i	0.0356294	−	0.0258863i
$370$	0.159507	−	3.30888i	0.00829235	−	0.172021i
$371$	−21.3704	−	15.5265i	−1.10950	−	0.806096i
$372$	−10.3774	+	14.2833i	−0.538045	+	0.740556i
$373$	−22.0074	−	7.15063i	−1.13950	−	0.370245i	−0.322320	−	0.946631i	$-0.604463\pi$
$373$	−22.0074	−	7.15063i	−1.13950	−	0.370245i	−0.817178	+	0.576385i	$0.804463\pi$
$374$	−1.89142			−0.0978032
$375$	−11.7822	−	11.4895i	−0.608430	−	0.593317i
$376$	3.06598			0.158116
$377$	1.66648	+	0.541471i	0.0858279	+	0.0278872i
$378$	1.98099	−	2.72660i	0.101891	−	0.140241i
$379$	−17.5153	−	12.7256i	−0.899702	−	0.653672i	0.0386872	−	0.999251i	$-0.487682\pi$
$379$	−17.5153	−	12.7256i	−0.899702	−	0.653672i	−0.938390	+	0.345579i	$0.887682\pi$
$380$	−0.366355	+	7.59985i	−0.0187936	+	0.389864i
$381$	−6.96645	+	5.06142i	−0.356902	+	0.259304i
$382$			3.30265i			0.168978i
$383$	3.32381	+	4.57484i	0.169839	+	0.233763i	0.885449	−	0.464737i	$-0.153851\pi$
$383$	3.32381	+	4.57484i	0.169839	+	0.233763i	−0.715610	+	0.698500i	$0.753851\pi$
$384$	2.55545	+	7.86488i	0.130407	+	0.401353i
$385$	5.16896	−	13.6362i	0.263435	−	0.694964i
$386$	−0.384257	+	1.18262i	−0.0195581	+	0.0601938i
$387$	2.56953	−	0.834891i	0.130617	−	0.0424399i
$388$	−12.5799	+	4.08746i	−0.638647	+	0.207509i
$389$	2.51109	−	7.72833i	0.127317	−	0.391842i	−0.866999	−	0.498310i	$-0.833954\pi$
$389$	2.51109	−	7.72833i	0.127317	−	0.391842i	0.994316	+	0.106468i	$0.0339541\pi$
$390$	0.139333	+	0.111866i	0.00705541	+	0.00566456i
$391$	−1.40270	−	4.31707i	−0.0709377	−	0.218324i
$392$	1.55155	+	2.13553i	0.0783653	+	0.107861i
$393$			2.20298i			0.111126i
$394$	−1.18483	+	0.860829i	−0.0596908	+	0.0433679i
$395$	−10.8642	+	13.5318i	−0.546638	+	0.680857i
$396$	−2.65159	−	1.92649i	−0.133247	−	0.0968098i
$397$	−12.2076	+	16.8024i	−0.612684	+	0.843287i	−0.996795	−	0.0799998i	$-0.974508\pi$
$397$	−12.2076	+	16.8024i	−0.612684	+	0.843287i	0.384111	+	0.923287i	$0.374508\pi$
$398$	0.906721	+	0.294611i	0.0454498	+	0.0147675i
$399$	−8.30550			−0.415795
$400$	−4.10578	−	18.5501i	−0.205289	−	0.927506i
$401$	30.1195			1.50410			0.752049	−	0.659107i	$-0.229066\pi$
$401$	30.1195			1.50410			0.752049	+	0.659107i	$0.229066\pi$
$402$	−1.76626	−	0.573893i	−0.0880931	−	0.0286232i
$403$	−1.06258	+	1.46252i	−0.0529309	+	0.0728532i
$404$	19.4017	+	14.0961i	0.965269	+	0.701309i
$405$	−7.11568	−	10.8573i	−0.353581	−	0.539503i
$406$	−2.85690	+	2.07566i	−0.141785	+	0.103013i
$407$		−	16.1760i		−	0.801815i
$408$	−3.24543	−	4.46695i	−0.160673	−	0.221147i
$409$	−3.41317	−	10.5046i	−0.168770	−	0.519421i	0.830524	−	0.556983i	$-0.188041\pi$
$409$	−3.41317	−	10.5046i	−0.168770	−	0.519421i	−0.999294	+	0.0375613i	$0.988041\pi$
$410$	−0.415306	−	0.0200201i	−0.0205105	−	0.000988721i
$411$	3.57012	−	10.9877i	0.176101	−	0.541983i
$412$	−2.58351	+	0.839433i	−0.127280	+	0.0413559i
$413$	18.4102	−	5.98182i	0.905905	−	0.294346i
$414$	−0.0414726	+	0.127639i	−0.00203827	+	0.00627314i
$415$	−27.1467	+	17.7915i	−1.33258	+	0.873350i
$416$	0.196828	+	0.605774i	0.00965029	+	0.0297005i
$417$	−4.66469	−	6.42039i	−0.228431	−	0.314408i
$418$		−	0.633915i		−	0.0310058i
$419$	−26.6338	+	19.3506i	−1.30115	+	0.945337i	−0.999966	−	0.00823011i	$-0.997380\pi$
$419$	−26.6338	+	19.3506i	−1.30115	+	0.945337i	−0.301179	+	0.953568i	$0.597380\pi$
$420$	20.3631	−	5.54786i	0.993617	−	0.270708i
$421$	16.3945	+	11.9113i	0.799019	+	0.580522i	0.910626	−	0.413231i	$-0.135600\pi$
$421$	16.3945	+	11.9113i	0.799019	+	0.580522i	−0.111607	+	0.993752i	$0.535600\pi$
$422$	1.78746	−	2.46023i	0.0870124	−	0.119762i
$423$	−3.34464	−	1.08674i	−0.162622	−	0.0528392i
$424$	5.88552			0.285826
$425$	13.0944	+	22.2473i	0.635171	+	1.07915i
$426$	−1.60930			−0.0779709
$427$	2.83956	+	0.922629i	0.137416	+	0.0446491i
$428$	−18.2954	+	25.1814i	−0.884341	+	1.21719i
$429$	0.705874	+	0.512848i	0.0340799	+	0.0247605i
$430$	−1.24166	−	0.470666i	−0.0598781	−	0.0226975i
$431$	−5.78873	+	4.20576i	−0.278833	+	0.202584i	−0.718408	−	0.695622i	$-0.755129\pi$
$431$	−5.78873	+	4.20576i	−0.278833	+	0.202584i	0.439575	+	0.898206i	$0.355129\pi$
$432$		−	21.4405i		−	1.03156i
$433$	−3.22262	−	4.43555i	−0.154869	−	0.213159i	0.724531	−	0.689242i	$-0.242056\pi$
$433$	−3.22262	−	4.43555i	−0.154869	−	0.213159i	−0.879400	+	0.476083i	$0.842056\pi$
$434$	−1.12582	−	3.46492i	−0.0540412	−	0.166322i
$435$	5.11514	+	18.7748i	0.245252	+	0.900184i
$436$	1.21762	−	3.74746i	0.0583135	−	0.179471i
$437$	1.44688	−	0.470119i	0.0692135	−	0.0224888i
$438$	−2.26510	+	0.735975i	−0.108231	+	0.0351662i
$439$	9.50415	−	29.2508i	0.453609	−	1.39606i	−0.419153	−	0.907916i	$-0.637673\pi$
$439$	9.50415	−	29.2508i	0.453609	−	1.39606i	0.872761	−	0.488148i	$-0.162327\pi$
$440$	0.854102	+	3.13493i	0.0407177	+	0.149452i
$441$	−0.935631	−	2.87958i	−0.0445539	−	0.137123i
$442$	−0.164750	−	0.226758i	−0.00783634	−	0.0107858i
$443$		−	11.3527i		−	0.539381i	−0.962947	−	0.269691i	$-0.913079\pi$
$443$		−	11.3527i		−	0.539381i	0.962947	−	0.269691i	$-0.0869214\pi$
$444$	18.9397	−	13.7605i	0.898841	−	0.653046i
$445$	15.7369	+	5.96528i	0.746002	+	0.282781i
$446$	0.982211	+	0.713618i	0.0465090	+	0.0337908i
$447$	16.2854	−	22.4149i	0.770271	−	1.06019i
$448$	22.3476	+	7.26117i	1.05582	+	0.343058i
$449$	15.7661			0.744050			0.372025	−	0.928223i	$-0.378664\pi$
$449$	15.7661			0.744050			0.372025	+	0.928223i	$0.378664\pi$
$450$	0.0734148	−	0.759708i	0.00346081	−	0.0358130i
$451$	−2.03029			−0.0956027
$452$	−19.5015	−	6.33643i	−0.917274	−	0.298040i
$453$	3.36383	−	4.62992i	0.158047	−	0.217532i
$454$	−1.98454	−	1.44185i	−0.0931391	−	0.0676695i
$455$	2.08504	−	0.568064i	0.0977484	−	0.0266312i
$456$	1.49711	−	1.08771i	0.0701085	−	0.0509368i
$457$		−	4.16714i		−	0.194931i	−0.995239	−	0.0974653i	$-0.968926\pi$
$457$		−	4.16714i		−	0.194931i	0.995239	−	0.0974653i	$-0.0310735\pi$
$458$	1.08599	+	1.49474i	0.0507452	+	0.0698448i
$459$	9.00233	+	27.7063i	0.420193	+	1.29322i
$460$	−3.23337	+	2.11909i	−0.150756	+	0.0988033i
$461$	−7.40758	+	22.7982i	−0.345005	+	1.06182i	0.616576	+	0.787296i	$0.288519\pi$
$461$	−7.40758	+	22.7982i	−0.345005	+	1.06182i	−0.961581	+	0.274521i	$0.911481\pi$
$462$	−1.67232	+	0.543370i	−0.0778035	+	0.0252799i
$463$	39.3021	−	12.7700i	1.82652	−	0.593473i	0.827013	−	0.562183i	$-0.190038\pi$
$463$	39.3021	−	12.7700i	1.82652	−	0.593473i	0.999510	−	0.0312899i	$-0.00996151\pi$
$464$	−6.94210	+	21.3656i	−0.322279	+	0.991872i
$465$	−20.0526	−	0.966645i	−0.929916	−	0.0448271i
$466$	−1.24558	−	3.83351i	−0.0577005	−	0.177584i
$467$	6.11096	+	8.41102i	0.282782	+	0.389216i	0.926653	−	0.375918i	$-0.122673\pi$
$467$	6.11096	+	8.41102i	0.282782	+	0.389216i	−0.643871	+	0.765134i	$0.722673\pi$
$468$		−	0.485697i		−	0.0224513i
$469$	−18.1713	+	13.2022i	−0.839072	+	0.609622i
$470$	0.947439	+	1.44563i	0.0437021	+	0.0666818i
$471$	5.10126	+	3.70628i	0.235054	+	0.170776i
$472$	−2.53512	+	3.48930i	−0.116689	+	0.160608i
$473$	−6.16663	−	2.00366i	−0.283542	−	0.0921284i
$474$	2.09243			0.0961086
$475$	−7.45624	+	4.38861i	−0.342116	+	0.201363i
$476$	−33.1065			−1.51743
$477$	−6.42045	−	2.08613i	−0.293972	−	0.0955174i
$478$	−0.813985	+	1.12035i	−0.0372308	+	0.0512438i
$479$	29.1312	+	21.1650i	1.33104	+	0.967055i	0.999723	+	0.0235349i	$0.00749208\pi$
$479$	29.1312	+	21.1650i	1.33104	+	0.967055i	0.331314	+	0.943520i	$0.392508\pi$
$480$	−4.42843	+	5.51577i	−0.202129	+	0.251759i
$481$	1.93930	−	1.40899i	0.0884246	−	0.0642443i
$482$		−	3.73571i		−	0.170157i
$483$	−2.48043	−	3.41402i	−0.112863	−	0.155343i
$484$	−4.25366	−	13.0914i	−0.193348	−	0.595065i
$485$	−11.7285	−	9.41645i	−0.532565	−	0.427579i
$486$	0.474466	−	1.46025i	0.0215222	−	0.0662385i
$487$	−10.1172	+	3.28726i	−0.458452	+	0.148960i	−0.529133	−	0.848539i	$-0.677483\pi$
$487$	−10.1172	+	3.28726i	−0.458452	+	0.148960i	0.0706809	+	0.997499i	$0.477483\pi$
$488$	−0.632674	+	0.205568i	−0.0286398	+	0.00930564i
$489$	7.15323	−	22.0154i	0.323480	−	0.995570i
$490$	−0.527458	+	1.39148i	−0.0238281	+	0.0628607i
$491$	−5.46010	−	16.8045i	−0.246411	−	0.758375i	−0.995401	−	0.0957938i	$-0.969461\pi$
$491$	−5.46010	−	16.8045i	−0.246411	−	0.758375i	0.748990	−	0.662581i	$-0.230539\pi$
$492$	−1.72712	−	2.37718i	−0.0778645	−	0.107171i
$493$		−	30.5243i		−	1.37475i
$494$	0.0759986	−	0.0552162i	0.00341934	−	0.00248429i
$495$	0.179450	−	3.72260i	0.00806568	−	0.167319i
$496$	−18.7507	−	13.6231i	−0.841929	−	0.611697i
$497$	−11.4403	+	15.7462i	−0.513166	+	0.706312i
$498$	3.72209	+	1.20938i	0.166791	+	0.0541936i
$499$	9.41734			0.421578			0.210789	−	0.977532i	$-0.432397\pi$
$499$	9.41734			0.421578			0.210789	+	0.977532i	$0.432397\pi$
$500$	15.3494	−	15.7404i	0.686447	−	0.703932i
$501$	−30.9595			−1.38317
$502$	1.84166	+	0.598391i	0.0821972	+	0.0267075i
$503$	10.5879	−	14.5730i	0.472093	−	0.649780i	−0.504869	−	0.863196i	$-0.668459\pi$
$503$	10.5879	−	14.5730i	0.472093	−	0.649780i	0.976961	+	0.213416i	$0.0684590\pi$
$504$	1.59730	+	1.16050i	0.0711493	+	0.0516930i
$505$	−1.31304	+	27.2383i	−0.0584294	+	1.21209i
$506$	0.260574	−	0.189318i	0.0115839	−	0.00841621i
$507$		−	19.0060i		−	0.844088i
$508$	−6.76180	−	9.30681i	−0.300006	−	0.412923i
$509$	4.95926	+	15.2630i	0.219815	+	0.676522i	0.998777	+	0.0494500i	$0.0157469\pi$
$509$	4.95926	+	15.2630i	0.219815	+	0.676522i	−0.778961	+	0.627072i	$0.784253\pi$
$510$	1.10330	−	2.91060i	0.0488549	−	0.128884i
$511$	−8.90107	+	27.3947i	−0.393760	+	1.21187i
$512$	−13.0177	+	4.22972i	−0.575308	+	0.186929i
$513$	−9.28583	+	3.01715i	−0.409980	+	0.133210i
$514$	−1.14735	+	3.53118i	−0.0506075	+	0.155754i
$515$	−2.40867	−	1.93384i	−0.106138	−	0.0852151i
$516$	−2.89981	−	8.92470i	−0.127657	−	0.392888i
$517$	4.96086	+	6.82803i	0.218178	+	0.300297i
$518$			4.83095i			0.212260i
$519$	−8.53425	+	6.20050i	−0.374612	+	0.272172i
$520$	−0.301444	+	0.375460i	−0.0132192	+	0.0164650i
$521$	1.78040	+	1.29354i	0.0780007	+	0.0566708i	0.626102	−	0.779741i	$-0.284649\pi$
$521$	1.78040	+	1.29354i	0.0780007	+	0.0566708i	−0.548102	+	0.836412i	$0.684649\pi$
$522$	−0.530469	+	0.730127i	−0.0232180	+	0.0319568i
$523$	7.07194	+	2.29781i	0.309234	+	0.100476i	0.459523	−	0.888166i	$-0.348020\pi$
$523$	7.07194	+	2.29781i	0.309234	+	0.100476i	−0.150289	+	0.988642i	$0.548020\pi$
$524$	−2.94307			−0.128569
$525$	17.9688	+	15.9084i	0.784222	+	0.694301i
$526$	5.14547			0.224353
$527$	29.9504	+	9.73147i	1.30466	+	0.423909i
$528$	−6.57512	+	9.04988i	−0.286145	+	0.393845i
$529$	−17.9820	−	13.0647i	−0.781828	−	0.568031i
$530$	1.81873	+	2.77506i	0.0790004	+	0.120541i
$531$	4.00233	−	2.90786i	0.173686	−	0.126190i
$532$		−	11.0957i		−	0.481061i
$533$	−0.176845	−	0.243407i	−0.00766003	−	0.0105431i
$534$	−0.627080	−	1.92995i	−0.0271364	−	0.0835173i
$535$	−35.3526	−	1.70419i	−1.52843	−	0.0736786i
$536$	1.54646	−	4.75953i	0.0667971	−	0.205580i
$537$	−11.2543	+	3.65675i	−0.485660	+	0.157800i
$538$	3.54040	−	1.15035i	0.152638	−	0.0495950i
$539$	−2.24543	+	6.91072i	−0.0967174	+	0.297666i
$540$	20.7513	−	13.6000i	0.892992	−	0.585252i
$541$	6.38040	+	19.6368i	0.274315	+	0.844254i	0.989400	+	0.145216i	$0.0463878\pi$
$541$	6.38040	+	19.6368i	0.274315	+	0.844254i	−0.715085	+	0.699037i	$0.753612\pi$
$542$	−3.38574	−	4.66007i	−0.145430	−	0.200167i
$543$			30.3473i			1.30233i
$544$	8.97666	−	6.52192i	0.384871	−	0.279625i
$545$	4.32299	−	1.17779i	0.185177	−	0.0504508i
$546$	−0.210809	−	0.153161i	−0.00902177	−	0.00655470i
$547$	18.4424	−	25.3839i	0.788542	−	1.08534i	−0.205746	−	0.978605i	$-0.565962\pi$
$547$	18.4424	−	25.3839i	0.788542	−	1.08534i	0.994288	−	0.106730i	$-0.0340379\pi$
$548$	14.6790	+	4.76949i	0.627055	+	0.203743i
$549$	0.763042			0.0325658
$550$	−1.21421	+	1.37146i	−0.0517739	+	0.0584793i
$551$	10.2303			0.435825
$552$	0.894219	+	0.290549i	0.0380605	+	0.0123666i
$553$	14.8747	−	20.4733i	0.632538	−	0.870615i
$554$	−2.06435	−	1.49984i	−0.0877057	−	0.0637219i
$555$	24.8923	+	9.43574i	1.05662	+	0.400525i
$556$	8.57732	−	6.23178i	0.363759	−	0.264287i
$557$		−	22.3515i		−	0.947064i	−0.880776	−	0.473532i	$-0.842979\pi$
$557$		−	22.3515i		−	0.947064i	0.880776	−	0.473532i	$-0.157021\pi$
$558$	−0.547280	−	0.753267i	−0.0231682	−	0.0318883i
$559$	−0.296921	−	0.913829i	−0.0125584	−	0.0386509i
$560$	7.28304	+	26.7320i	0.307765	+	1.12963i
$561$	4.69683	−	14.4554i	0.198300	−	0.610305i
$562$	−4.50807	+	1.46476i	−0.190162	+	0.0617872i
$563$	−32.6843	+	10.6198i	−1.37748	+	0.447570i	−0.901840	−	0.432070i	$-0.857783\pi$
$563$	−32.6843	+	10.6198i	−1.37748	+	0.447570i	−0.475639	+	0.879640i	$0.657783\pi$
$564$	−3.77455	+	11.6169i	−0.158937	+	0.489159i
$565$	−6.12912	−	22.4966i	−0.257854	−	0.946438i
$566$	1.34329	+	4.13422i	0.0564626	+	0.173774i
$567$	11.1271	+	15.3152i	0.467295	+	0.643177i
$568$		−	4.33657i		−	0.181958i
$569$	26.0230	−	18.9068i	1.09094	−	0.792615i	0.111383	−	0.993778i	$-0.464472\pi$
$569$	26.0230	−	18.9068i	1.09094	−	0.792615i	0.979558	+	0.201162i	$0.0644718\pi$
$570$	0.975494	+	0.369773i	0.0408590	+	0.0154881i
$571$	21.9784	+	15.9683i	0.919768	+	0.668251i	0.943466	−	0.331468i	$-0.107544\pi$
$571$	21.9784	+	15.9683i	0.919768	+	0.668251i	−0.0236979	+	0.999719i	$0.507544\pi$
$572$	−0.685138	+	0.943012i	−0.0286471	+	0.0394293i
$573$	−25.2407	−	8.20121i	−1.05445	−	0.342610i
$574$	0.606344			0.0253083
$575$	−4.03076	−	1.75427i	−0.168094	−	0.0731581i
$576$	6.00521			0.250217
$577$	13.1724	+	4.27998i	0.548375	+	0.178178i	0.570084	−	0.821586i	$-0.306911\pi$
$577$	13.1724	+	4.27998i	0.548375	+	0.178178i	−0.0217089	+	0.999764i	$0.506911\pi$
$578$	−1.03965	+	1.43095i	−0.0432436	+	0.0595198i
$579$	−8.08407	−	5.87342i	−0.335963	−	0.244091i
$580$	−25.0822	+	6.83356i	−1.04148	+	0.283748i
$581$	38.2928	−	27.8214i	1.58865	−	1.15422i
$582$			1.81360i			0.0751759i
$583$	9.52297	+	13.1072i	0.394401	+	0.542847i
$584$	−1.98322	−	6.10374i	−0.0820664	−	0.252574i
$585$	0.461925	−	0.302738i	0.0190982	−	0.0125167i
$586$	−0.696383	+	2.14325i	−0.0287673	+	0.0885367i
$587$	−41.9890	+	13.6431i	−1.73307	+	0.563110i	−0.993888	−	0.110392i	$-0.964789\pi$
$587$	−41.9890	+	13.6431i	−1.73307	+	0.563110i	−0.739185	+	0.673502i	$0.764789\pi$
$588$	−10.0016	+	3.24971i	−0.412458	+	0.134016i
$589$	−3.26152	+	10.0379i	−0.134389	+	0.413606i
$590$	−2.42862	−	0.117073i	−0.0999848	−	0.00481982i
$591$	−3.63675	−	11.1928i	−0.149596	−	0.460409i
$592$	18.0643	+	24.8634i	0.742440	+	1.02188i
$593$			16.2531i			0.667437i	0.942673	+	0.333718i	$0.108303\pi$
$593$			16.2531i			0.667437i	−0.942673	+	0.333718i	$0.891697\pi$
$594$	−1.67232	+	1.21501i	−0.0686162	+	0.0498526i
$595$	−20.6355	−	31.4862i	−0.845973	−	1.29081i
$596$	29.9451	+	21.7564i	1.22660	+	0.891177i
$597$	−4.50318	+	6.19810i	−0.184303	+	0.253671i
$598$	0.0453938	+	0.0147493i	0.00185629	+	0.000603145i
$599$	−30.4822			−1.24547			−0.622734	−	0.782433i	$-0.713978\pi$
$599$	−30.4822			−1.24547			−0.622734	+	0.782433i	$0.713978\pi$
$600$	−5.32237	−	0.514331i	−0.217285	−	0.0209975i
$601$	−28.9162			−1.17952			−0.589758	−	0.807580i	$-0.700777\pi$
$601$	−28.9162			−1.17952			−0.589758	+	0.807580i	$0.700777\pi$
$602$	1.84166	+	0.598391i	0.0750604	+	0.0243886i
$603$	−3.37405	+	4.64398i	−0.137402	+	0.189117i
$604$	6.18533	+	4.49390i	0.251677	+	0.182854i
$605$	9.79935	−	12.2054i	0.398400	−	0.496222i
$606$	2.66017	−	1.93272i	0.108062	−	0.0785115i
$607$			8.23276i			0.334157i	0.985944	+	0.167079i	$0.0534334\pi$
$607$			8.23276i			0.334157i	−0.985944	+	0.167079i	$0.946567\pi$
$608$	2.18584	+	3.00855i	0.0886474	+	0.122013i
$609$	−8.76906	−	26.9884i	−0.355340	−	1.09362i
$610$	−0.292434	−	0.234786i	−0.0118403	−	0.00950619i
$611$	−0.386489	+	1.18949i	−0.0156357	+	0.0481217i
$612$	−8.04681	+	2.61457i	−0.325273	+	0.105688i
$613$	4.56327	−	1.48270i	0.184309	−	0.0598856i	−0.215408	−	0.976524i	$-0.569108\pi$
$613$	4.56327	−	1.48270i	0.184309	−	0.0598856i	0.399717	+	0.916638i	$0.369108\pi$
$614$	−0.242403	+	0.746040i	−0.00978259	+	0.0301077i
$615$	1.18430	−	3.12430i	0.0477557	−	0.125984i
$616$	−1.46422	−	4.50639i	−0.0589949	−	0.181568i
$617$	1.19428	+	1.64379i	0.0480800	+	0.0661765i	0.832380	−	0.554205i	$-0.186978\pi$
$617$	1.19428	+	1.64379i	0.0480800	+	0.0661765i	−0.784300	+	0.620382i	$0.786978\pi$
$618$			0.372454i			0.0149823i
$619$	6.58621	−	4.78516i	0.264722	−	0.192332i	−0.447504	−	0.894282i	$-0.647687\pi$
$619$	6.58621	−	4.78516i	0.264722	−	0.192332i	0.712226	+	0.701950i	$0.247687\pi$
$620$	1.29139	−	26.7892i	0.0518634	−	1.07588i
$621$	−4.01342	−	2.91592i	−0.161053	−	0.117012i
$622$	2.76127	−	3.80057i	0.110717	−	0.152389i
$623$	−23.3414	−	7.58408i	−0.935153	−	0.303850i
$624$	−1.65769			−0.0663605
$625$	24.5374	+	4.78708i	0.981496	+	0.191483i
$626$	−4.09413			−0.163634
$627$	4.84474	+	1.57415i	0.193480	+	0.0628656i
$628$	−4.95140	+	6.81502i	−0.197582	+	0.271949i
$629$	−33.7830	−	24.5448i	−1.34702	−	0.978665i
$630$	−0.0535925	+	1.11175i	−0.00213518	+	0.0442932i
$631$	−26.9279	+	19.5643i	−1.07198	+	0.778841i	−0.976268	−	0.216567i	$-0.930514\pi$
$631$	−26.9279	+	19.5643i	−1.07198	+	0.778841i	−0.0957154	+	0.995409i	$0.530514\pi$
$632$			5.63846i			0.224286i
$633$	14.3638	+	19.7701i	0.570912	+	0.785793i
$634$	−1.24091	−	3.81911i	−0.0492826	−	0.151676i
$635$	4.63663	−	12.2318i	0.183999	−	0.485406i
$636$	−7.24572	+	22.3000i	−0.287311	+	0.884253i
$637$	−1.02409	+	0.332749i	−0.0405761	+	0.0131840i
$638$	2.05988	−	0.669295i	0.0815514	−	0.0264977i
$639$	−1.53710	+	4.73072i	−0.0608069	+	0.187144i
$640$	−9.79599	−	7.86488i	−0.387220	−	0.310887i
$641$	−12.3755	−	38.0880i	−0.488804	−	1.50439i	−0.826394	−	0.563092i	$-0.809612\pi$
$641$	−12.3755	−	38.0880i	−0.488804	−	1.50439i	0.337590	−	0.941293i	$-0.390388\pi$
$642$	2.50848	+	3.45263i	0.0990019	+	0.136264i
$643$			11.6870i			0.460890i	0.973085	+	0.230445i	$0.0740182\pi$
$643$			11.6870i			0.460890i	−0.973085	+	0.230445i	$0.925982\pi$
$644$	4.56095	−	3.31372i	0.179727	−	0.130579i
$645$	6.68042	−	8.32070i	0.263041	−	0.327627i
$646$	−1.32391	−	0.961876i	−0.0520885	−	0.0378445i
$647$	−4.67252	+	6.43117i	−0.183696	+	0.252835i	−0.890927	−	0.454147i	$-0.849944\pi$
$647$	−4.67252	+	6.43117i	−0.183696	+	0.252835i	0.707231	+	0.706982i	$0.249944\pi$
$648$	−4.01144	−	1.30339i	−0.157584	−	0.0512022i
$649$	−11.8727			−0.466044
$650$	−0.270183	−	0.0261093i	−0.0105974	−	0.00102409i
$651$	29.2766			1.14744
$652$	29.4114	+	9.55635i	1.15184	+	0.374256i
$653$	−1.96165	+	2.69998i	−0.0767653	+	0.105658i	−0.845673	−	0.533702i	$-0.820801\pi$
$653$	−1.96165	+	2.69998i	−0.0767653	+	0.105658i	0.768908	+	0.639360i	$0.220801\pi$
$654$	−0.437077	−	0.317555i	−0.0170910	−	0.0124174i
$655$	−1.83443	−	2.79902i	−0.0716772	−	0.109367i
$656$	3.12067	−	2.26730i	0.121842	−	0.0885232i
$657$			7.36146i			0.287198i
$658$	−1.48155	−	2.03918i	−0.0577570	−	0.0794957i
$659$	9.28621	+	28.5800i	0.361739	+	1.11332i	0.951998	+	0.306105i	$0.0990257\pi$
$659$	9.28621	+	28.5800i	0.361739	+	1.11332i	−0.590259	+	0.807214i	$0.700974\pi$
$660$	−12.9296	−	0.623280i	−0.503285	−	0.0242611i
$661$	−2.03462	+	6.26192i	−0.0791375	+	0.243560i	−0.982796	−	0.184693i	$-0.940871\pi$
$661$	−2.03462	+	6.26192i	−0.0791375	+	0.243560i	0.903659	+	0.428253i	$0.140871\pi$
$662$	1.56142	−	0.507335i	0.0606862	−	0.0197181i
$663$	2.14213	−	0.696020i	0.0831934	−	0.0270312i
$664$	−3.25890	+	10.0299i	−0.126470	+	0.389235i
$665$	10.5527	−	6.91604i	0.409215	−	0.268192i
$666$	0.381521	+	1.17420i	0.0147836	+	0.0454994i
$667$	3.05526	+	4.20521i	0.118300	+	0.162826i
$668$		−	41.3603i		−	1.60028i
$669$	−7.89293	+	5.73455i	−0.305158	+	0.221711i
$670$	2.72203	−	0.741608i	0.105161	−	0.0286508i
$671$	−1.48150	−	1.07637i	−0.0571925	−	0.0415528i
$672$	6.06318	−	8.34526i	0.233892	−	0.321925i
$673$	−6.40194	−	2.08012i	−0.246777	−	0.0801826i	0.183017	−	0.983110i	$-0.441414\pi$
$673$	−6.40194	−	2.08012i	−0.246777	−	0.0801826i	−0.429794	+	0.902927i	$0.641414\pi$
$674$	5.32730			0.205200
$675$	25.8688	+	11.2586i	0.995690	+	0.433345i
$676$	25.3911			0.976580
$677$	12.9799	+	4.21741i	0.498857	+	0.162088i	0.547629	−	0.836722i	$-0.315531\pi$
$677$	12.9799	+	4.21741i	0.498857	+	0.162088i	−0.0487718	+	0.998810i	$0.515531\pi$
$678$	−1.65253	+	2.27452i	−0.0634652	+	0.0873523i
$679$	17.7451	+	12.8925i	0.680993	+	0.494770i
$680$	7.84317	+	2.97305i	0.300772	+	0.114011i
$681$	15.9475	−	11.5866i	0.611111	−	0.443998i
$682$			2.23453i			0.0855645i
$683$	0.689001	+	0.948329i	0.0263639	+	0.0362868i	0.821995	−	0.569494i	$-0.192861\pi$
$683$	0.689001	+	0.948329i	0.0263639	+	0.0362868i	−0.795632	+	0.605781i	$0.792861\pi$
$684$	−0.876278	−	2.69691i	−0.0335053	−	0.103119i
$685$	4.61345	+	16.9334i	0.176271	+	0.646992i
$686$	−0.621431	+	1.91257i	−0.0237264	+	0.0730222i
$687$	−14.1205	+	4.58802i	−0.538729	+	0.175044i
$688$	11.7160	−	3.80677i	0.446669	−	0.145132i
$689$	−0.741913	+	2.28337i	−0.0282646	+	0.0869896i
$690$	0.139333	+	0.511414i	0.00530432	+	0.0194692i
$691$	3.79083	+	11.6670i	0.144210	+	0.443832i	0.996909	−	0.0785709i	$-0.0250357\pi$
$691$	3.79083	+	11.6670i	0.144210	+	0.443832i	−0.852699	+	0.522403i	$0.825036\pi$
$692$	−8.28354	−	11.4013i	−0.314893	−	0.433413i
$693$			5.43497i			0.206457i
$694$	2.11869	−	1.53932i	0.0804244	−	0.0584317i
$695$	11.2731	+	4.27320i	0.427612	+	0.162092i
$696$	5.11514	+	3.71637i	0.193889	+	0.140869i
$697$	−3.08068	+	4.24019i	−0.116689	+	0.160609i
$698$	−0.979709	−	0.318327i	−0.0370825	−	0.0120488i
$699$	32.3910			1.22514
$700$	−21.2528	+	24.0054i	−0.803282	+	0.907317i
$701$	−20.0271			−0.756415			−0.378207	−	0.925721i	$-0.623459\pi$
$701$	−20.0271			−0.756415			−0.378207	+	0.925721i	$0.623459\pi$
$702$	−0.291330	−	0.0946589i	−0.0109956	−	0.00357267i
$703$	8.22624	−	11.3225i	0.310259	−	0.427034i
$704$	−11.6595	−	8.47113i	−0.439434	−	0.319268i
$705$	−13.4010	+	3.65106i	−0.504711	+	0.137507i
$706$	−0.283038	+	0.205639i	−0.0106523	+	0.00773932i
$707$		−	39.7677i		−	1.49562i
$708$	−10.0998	−	13.9012i	−0.379574	−	0.522439i
$709$	1.35816	+	4.17998i	0.0510067	+	0.156983i	0.973315	−	0.229471i	$-0.0736998\pi$
$709$	1.35816	+	4.17998i	0.0510067	+	0.156983i	−0.922309	+	0.386454i	$0.873700\pi$
$710$	2.04472	−	1.34007i	0.0767369	−	0.0502921i
$711$	1.99856	−	6.15094i	0.0749519	−	0.230678i
$712$	5.20063	−	1.68979i	0.194902	−	0.0633275i
$713$	−5.10019	+	1.65715i	−0.191004	+	0.0620608i
$714$	−1.40270	+	4.31707i	−0.0524948	+	0.161562i
$715$	−1.32391	−	0.0638197i	−0.0495114	−	0.00238672i
$716$	−4.88523	−	15.0352i	−0.182570	−	0.561892i
$717$	−6.54109	−	9.00303i	−0.244281	−	0.336224i
$718$		−	4.06727i		−	0.151789i
$719$	−8.84119	+	6.42350i	−0.329721	+	0.239556i	−0.740312	−	0.672263i	$-0.765322\pi$
$719$	−8.84119	+	6.42350i	−0.329721	+	0.239556i	0.410591	+	0.911819i	$0.365322\pi$
$720$	3.88134	+	5.92225i	0.144649	+	0.220709i
$721$	3.64427	+	2.64772i	0.135720	+	0.0986061i
$722$	−1.72328	+	2.37189i	−0.0641337	+	0.0882725i
$723$	28.5505	+	9.27661i	1.06180	+	0.345001i
$724$	−40.5425			−1.50675
$725$	−22.1330	−	19.5952i	−0.821999	−	0.727747i
$726$	−1.88734			−0.0700458
$727$	−31.2928	−	10.1677i	−1.16059	−	0.377097i	−0.335465	−	0.942053i	$-0.608893\pi$
$727$	−31.2928	−	10.1677i	−1.16059	−	0.377097i	−0.825122	+	0.564955i	$0.808893\pi$
$728$	0.412723	−	0.568064i	0.0152965	−	0.0210538i
$729$	24.0719	+	17.4893i	0.891553	+	0.647751i
$730$	2.26510	−	2.82126i	0.0838350	−	0.104420i
$731$	−13.5416	+	9.83853i	−0.500853	+	0.363891i
$732$		−	2.65026i		−	0.0979564i
$733$	−8.08190	−	11.1238i	−0.298512	−	0.410866i	0.633244	−	0.773952i	$-0.281723\pi$
$733$	−8.08190	−	11.1238i	−0.298512	−	0.410866i	−0.931756	+	0.363086i	$0.881723\pi$
$734$	1.21386	+	3.73586i	0.0448042	+	0.137893i
$735$	−9.32470	−	7.48650i	−0.343947	−	0.276144i
$736$	−0.583880	+	1.79700i	−0.0215221	+	0.0662382i
$737$	13.1019	−	4.25705i	0.482613	−	0.156811i
$738$	0.147377	−	0.0478857i	0.00542502	−	0.00176270i
$739$	13.3462	−	41.0754i	0.490949	−	1.51098i	−0.332228	−	0.943199i	$-0.607800\pi$
$739$	13.3462	−	41.0754i	0.490949	−	1.51098i	0.823177	−	0.567785i	$-0.192200\pi$
$740$	−12.6057	+	33.2548i	−0.463393	+	1.22247i
$741$	0.233273	+	0.717939i	0.00856948	+	0.0263741i
$742$	−2.84402	−	3.91446i	−0.104407	−	0.143704i
$743$			31.8479i			1.16838i	0.811615	+	0.584192i	$0.198589\pi$
$743$			31.8479i			1.16838i	−0.811615	+	0.584192i	$0.801411\pi$
$744$	−5.27725	+	3.83415i	−0.193473	+	0.140567i
$745$	−2.02658	+	42.0404i	−0.0742482	+	1.54024i
$746$	−3.42909	−	2.49138i	−0.125548	−	0.0912158i
$747$	7.11021	−	9.78637i	0.260149	−	0.358064i
$748$	19.3116	+	6.27472i	0.706102	+	0.229426i
$749$	51.6145			1.88595
$750$	−1.40219	−	2.66847i	−0.0512009	−	0.0974387i
$751$	−29.5952			−1.07995			−0.539973	−	0.841682i	$-0.681565\pi$
$751$	−29.5952			−1.07995			−0.539973	+	0.841682i	$0.681565\pi$
$752$	−15.2502	−	4.95510i	−0.556119	−	0.180694i
$753$	−9.14650	+	12.5891i	−0.333317	+	0.458771i
$754$	0.259663	+	0.188656i	0.00945637	+	0.00687045i
$755$	−0.418601	+	8.68368i	−0.0152345	+	0.316031i
$756$	−29.2715	+	21.2670i	−1.06459	+	0.773473i
$757$			0.0984401i			0.00357786i	0.999998	+	0.00178893i	$0.000569435\pi$
$757$			0.0984401i			0.00357786i	−0.999998	+	0.00178893i	$0.999431\pi$
$758$	−2.33098	−	3.20832i	−0.0846651	−	0.116531i
$759$	0.799814	+	2.46157i	0.0290314	+	0.0893495i
$760$	−0.996425	+	2.62866i	−0.0361441	+	0.0953514i
$761$	−1.09516	+	3.37056i	−0.0396996	+	0.122183i	−0.968942	−	0.247287i	$-0.920461\pi$
$761$	−1.09516	+	3.37056i	−0.0396996	+	0.122183i	0.929243	+	0.369470i	$0.120461\pi$
$762$	−1.50010	+	0.487411i	−0.0543428	+	0.0176570i
$763$	−6.21421	+	2.01912i	−0.224969	+	0.0730970i
$764$	10.9564	−	33.7203i	0.396388	−	1.21996i
$765$	−7.50223	−	6.02330i	−0.271244	−	0.217773i
$766$	0.320081	+	0.985108i	0.0115650	+	0.0355934i
$767$	−1.03415	−	1.42339i	−0.0373411	−	0.0513957i
$768$		−	19.6989i		−	0.710822i
$769$	1.15494	−	0.839116i	0.0416484	−	0.0302593i	−0.566766	−	0.823879i	$-0.691806\pi$
$769$	1.15494	−	0.839116i	0.0416484	−	0.0302593i	0.608415	+	0.793619i	$0.291806\pi$
$770$	1.67232	−	2.08294i	0.0602663	−	0.0750639i
$771$	−24.1382	−	17.5374i	−0.869316	−	0.631595i
$772$	7.84659	−	10.7999i	0.282405	−	0.388697i
$773$	32.1274	+	10.4388i	1.15554	+	0.375458i	0.823228	−	0.567711i	$-0.192171\pi$
$773$	32.1274	+	10.4388i	1.15554	+	0.375458i	0.332313	+	0.943169i	$0.392171\pi$
$774$	0.494888			0.0177884
$775$	26.2830	−	15.4697i	0.944113	−	0.555688i
$776$	−4.88708			−0.175436
$777$	−36.9209	−	11.9963i	−1.32453	−	0.430366i
$778$	0.874898	−	1.20419i	0.0313666	−	0.0431725i
$779$	−1.42111	−	1.03250i	−0.0509165	−	0.0369930i
$780$	−1.05149	−	1.60439i	−0.0376495	−	0.0574465i
$781$	9.65769	−	7.01672i	0.345579	−	0.251078i
$782$		−	0.831462i		−	0.0297330i
$783$	−19.6082	−	26.9884i	−0.700740	−	0.964486i
$784$	−4.26610	−	13.1297i	−0.152361	−	0.468919i
$785$	−9.56771	−	0.461216i	−0.341486	−	0.0164615i
$786$	−0.124696	+	0.383775i	−0.00444776	+	0.0136888i
$787$	2.07358	−	0.673749i	0.0739153	−	0.0240165i	−0.271826	−	0.962346i	$-0.587627\pi$
$787$	2.07358	−	0.673749i	0.0739153	−	0.0240165i	0.345741	+	0.938330i	$0.387627\pi$
$788$	14.9530	−	4.85852i	0.532678	−	0.173077i
$789$	−12.7773	+	39.3246i	−0.454886	+	1.39999i
$790$	−2.65857	+	1.74238i	−0.0945875	+	0.0619911i
$791$	10.5074	+	32.3383i	0.373599	+	1.14982i
$792$	−0.711779	−	0.979680i	−0.0252920	−	0.0348114i
$793$		−	0.271369i		−	0.00963659i
$794$	−3.07773	+	2.23610i	−0.109224	+	0.0793562i
$795$	−25.7249	+	7.00866i	−0.912368	+	0.248572i
$796$	−8.28034	−	6.01602i	−0.293489	−	0.213232i
$797$	−13.8082	+	19.0053i	−0.489110	+	0.673203i	−0.980224	−	0.197893i	$-0.936590\pi$
$797$	−13.8082	+	19.0053i	−0.489110	+	0.673203i	0.491113	+	0.871096i	$0.336590\pi$
$798$	−1.44688	−	0.470119i	−0.0512189	−	0.0166420i
$799$	21.7875			0.770787
$800$	1.03359	−	10.6957i	0.0365428	−	0.378150i
$801$	−6.27226			−0.221620
$802$	5.24703	+	1.70486i	0.185279	+	0.0602009i
$803$	10.3843	−	14.2928i	0.366454	−	0.504380i
$804$	16.1298	+	11.7190i	0.568855	+	0.413297i
$805$	5.99441	+	2.27226i	0.211275	+	0.0800865i
$806$	−0.267892	+	0.194635i	−0.00943610	+	0.00685573i
$807$			29.9144i			1.05304i
$808$	5.20809	+	7.16833i	0.183220	+	0.252181i
$809$	11.7893	+	36.2837i	0.414489	+	1.27567i	0.912707	+	0.408615i	$0.133988\pi$
$809$	11.7893	+	36.2837i	0.414489	+	1.27567i	−0.498217	+	0.867052i	$0.666012\pi$
$810$	−0.625044	−	2.29419i	−0.0219618	−	0.0806095i
$811$	14.8040	−	45.5622i	0.519840	−	1.59990i	−0.254458	−	0.967084i	$-0.581897\pi$
$811$	14.8040	−	45.5622i	0.519840	−	1.59990i	0.774298	−	0.632821i	$-0.218103\pi$
$812$	36.0551	−	11.7150i	1.26529	−	0.411116i
$813$	44.0224	−	14.3038i	1.54393	−	0.501655i
$814$	0.915615	−	2.81797i	0.0320923	−	0.0987699i
$815$	9.24370	+	33.9285i	0.323793	+	1.18846i
$816$	8.92354	+	27.4638i	0.312386	+	0.961426i
$817$	−3.29740	−	4.53849i	−0.115362	−	0.158782i
$818$		−	2.02318i		−	0.0707388i
$819$	−0.651586	+	0.473405i	−0.0227683	+	0.0165421i
$820$	4.17390	+	1.58217i	0.145759	+	0.0552517i
$821$	−15.3558	−	11.1566i	−0.535920	−	0.389369i	0.286647	−	0.958036i	$-0.407459\pi$
$821$	−15.3558	−	11.1566i	−0.535920	−	0.389369i	−0.822568	+	0.568667i	$0.807459\pi$
$822$	1.24388	−	1.71205i	0.0433852	−	0.0597147i
$823$	−21.0831	−	6.85033i	−0.734912	−	0.238787i	−0.0824356	−	0.996596i	$-0.526270\pi$
$823$	−21.0831	−	6.85033i	−0.734912	−	0.238787i	−0.652476	+	0.757809i	$0.726270\pi$
$824$	−1.00365			−0.0349638
$825$	−7.46635	−	12.6853i	−0.259945	−	0.441646i
$826$	3.54577			0.123373
$827$	4.49790	+	1.46146i	0.156407	+	0.0508199i	0.386174	−	0.922426i	$-0.373796\pi$
$827$	4.49790	+	1.46146i	0.156407	+	0.0508199i	−0.229767	+	0.973246i	$0.573796\pi$
$828$	0.846877	−	1.16563i	0.0294310	−	0.0405083i
$829$	13.3003	+	9.66320i	0.461937	+	0.335617i	0.794291	−	0.607538i	$-0.207843\pi$
$829$	13.3003	+	9.66320i	0.461937	+	0.335617i	−0.332354	+	0.943155i	$0.607843\pi$
$830$	−5.73620	+	1.56281i	−0.199106	+	0.0542459i
$831$	16.5889	−	12.0525i	0.575461	−	0.418097i
$832$		−	2.13570i		−	0.0740419i
$833$	11.0257	+	15.1755i	0.382017	+	0.525801i
$834$	−0.449206	−	1.38251i	−0.0155547	−	0.0478726i
$835$	39.3360	−	25.7802i	1.36128	−	0.892160i
$836$	−2.10299	+	6.47232i	−0.0727333	+	0.223850i
$837$	32.7322	−	10.6354i	1.13139	−	0.367611i
$838$	−5.73510	+	1.86345i	−0.198116	+	0.0643717i
$839$	1.73075	−	5.32671i	0.0597522	−	0.183898i	−0.916725	−	0.399519i	$-0.869177\pi$
$839$	1.73075	−	5.32671i	0.0597522	−	0.183898i	0.976477	+	0.215620i	$0.0691773\pi$
$840$	7.78873	+	0.375460i	0.268737	+	0.0129546i
$841$	1.83977	+	5.66224i	0.0634405	+	0.195250i
$842$	2.18182	+	3.00302i	0.0751904	+	0.103491i
$843$		−	38.0906i		−	1.31191i
$844$	−26.4119	+	19.1894i	−0.909135	+	0.660525i
$845$	15.8264	+	24.1484i	0.544446	+	0.830729i
$846$	−0.521147	−	0.378636i	−0.0179174	−	0.0130178i
$847$	−13.4168	+	18.4666i	−0.461006	+	0.634520i
$848$	−29.2747	−	9.51192i	−1.00530	−	0.326641i
$849$	−34.9318			−1.19886
$850$	1.02186	+	4.61682i	0.0350496	+	0.158356i
$851$	7.11091			0.243759
$852$	16.4311	+	5.33879i	0.562921	+	0.182904i
$853$	−10.5158	+	14.4737i	−0.360053	+	0.495571i	−0.950164	−	0.311752i	$-0.899084\pi$
$853$	−10.5158	+	14.4737i	−0.360053	+	0.495571i	0.590110	+	0.807323i	$0.299084\pi$
$854$	0.442447	+	0.321457i	0.0151402	+	0.0110000i
$855$	2.01872	−	2.51439i	0.0690388	−	0.0859903i
$856$	−9.30377	+	6.75959i	−0.317996	+	0.231038i
$857$		−	3.19536i		−	0.109151i	−0.998510	−	0.0545757i	$-0.982619\pi$
$857$		−	3.19536i		−	0.109151i	0.998510	−	0.0545757i	$-0.0173806\pi$
$858$	0.0939394	+	0.129296i	0.00320704	+	0.00441411i
$859$	−13.4174	−	41.2945i	−0.457795	−	1.40895i	−0.867822	−	0.496875i	$-0.834481\pi$
$859$	−13.4174	−	41.2945i	−0.457795	−	1.40895i	0.410027	−	0.912073i	$-0.365519\pi$
$860$	11.1160	+	8.92470i	0.379054	+	0.304330i
$861$	−1.50569	+	4.63403i	−0.0513137	+	0.157927i
$862$	−1.24650	+	0.405011i	−0.0424558	+	0.0137947i
$863$	−41.1545	+	13.3719i	−1.40091	+	0.455185i	−0.909486	−	0.415734i	$-0.863525\pi$
$863$	−41.1545	+	13.3719i	−1.40091	+	0.455185i	−0.491428	+	0.870918i	$0.663525\pi$
$864$	3.74725	−	11.5329i	0.127484	−	0.392356i
$865$	5.68011	−	14.9846i	0.193130	−	0.509493i
$866$	−0.310336	−	0.955115i	−0.0105456	−	0.0324561i
$867$	−8.35449	−	11.4990i	−0.283733	−	0.390525i
$868$			39.1120i			1.32755i
$869$	−12.5570	+	9.12322i	−0.425968	+	0.309484i
$870$	−0.171623	+	3.56024i	−0.00581857	+	0.120703i
$871$	1.65159	+	1.19995i	0.0559619	+	0.0406587i
$872$	0.855712	−	1.17779i	0.0289781	−	0.0398849i
$873$	5.33126	+	1.73223i	0.180436	+	0.0586272i
$874$	0.278666			0.00942603
$875$	−36.0775	−	5.24996i	−1.21964	−	0.177481i
$876$	25.5684			0.863876
$877$	−32.5584	−	10.5789i	−1.09942	−	0.357223i	−0.297540	−	0.954709i	$-0.596166\pi$
$877$	−32.5584	−	10.5789i	−1.09942	−	0.357223i	−0.801879	+	0.597487i	$0.796166\pi$
$878$	3.31138	−	4.55772i	0.111754	−	0.153816i
$879$	−14.6507	−	10.6443i	−0.494154	−	0.359024i
$880$	0.818220	−	16.9736i	0.0275822	−	0.572179i
$881$	−22.3507	+	16.2388i	−0.753016	+	0.547098i	−0.896760	−	0.442517i	$-0.854086\pi$
$881$	−22.3507	+	16.2388i	−0.753016	+	0.547098i	0.143744	+	0.989615i	$0.454086\pi$
$882$		−	0.554602i		−	0.0186744i
$883$	−15.2231	−	20.9527i	−0.512297	−	0.705116i	0.472008	−	0.881594i	$-0.343529\pi$
$883$	−15.2231	−	20.9527i	−0.512297	−	0.705116i	−0.984305	+	0.176478i	$0.943529\pi$
$884$	0.929846	+	2.86177i	0.0312741	+	0.0962518i
$885$	6.92555	−	18.2702i	0.232800	−	0.614146i
$886$	0.642598	−	1.97771i	0.0215885	−	0.0664425i
$887$	16.4009	−	5.32897i	0.550688	−	0.178929i	−0.0204392	−	0.999791i	$-0.506506\pi$
$887$	16.4009	−	5.32897i	0.550688	−	0.178929i	0.571127	+	0.820862i	$0.306506\pi$
$888$	8.22624	−	2.67287i	0.276055	−	0.0896956i
$889$	−5.89488	+	18.1426i	−0.197708	+	0.608482i
$890$	2.40383	+	1.92995i	0.0805765	+	0.0646922i
$891$	−3.58794	−	11.0425i	−0.120200	−	0.369939i
$892$	−7.66106	−	10.5445i	−0.256511	−	0.353058i
$893$			7.30213i			0.244356i
$894$	4.10578	−	2.98302i	0.137318	−	0.0997673i
$895$	11.2543	−	14.0177i	0.376191	−	0.468559i
$896$	14.8212	+	10.7682i	0.495140	+	0.359740i
$897$	−0.225446	+	0.310299i	−0.00752741	+	0.0103606i
$898$	2.74657	+	0.892415i	0.0916543	+	0.0297803i
$899$	−36.0614			−1.20271
$900$	−3.26987	+	7.51313i	−0.108996	+	0.250438i
$901$	41.8238			1.39335
$902$	−0.353691	−	0.114921i	−0.0117766	−	0.00382645i
$903$	−9.14650	+	12.5891i	−0.304376	+	0.418938i
$904$	−6.12912	−	4.45307i	−0.203852	−	0.148107i
$905$	−25.2704	−	38.5582i	−0.840016	−	1.28172i
$906$	0.848071	−	0.616160i	0.0281753	−	0.0204705i
$907$			57.0465i			1.89420i	0.320940	+	0.947099i	$0.396001\pi$
$907$			57.0465i			1.89420i	−0.320940	+	0.947099i	$0.603999\pi$
$908$	15.4790	+	21.3051i	0.513690	+	0.707034i
$909$	−3.14063	−	9.66587i	−0.104168	−	0.320597i
$910$	0.395384	+	0.0190597i	0.0131068	+	0.000631822i
$911$	6.13965	−	18.8959i	0.203416	−	0.626049i	−0.796359	−	0.604824i	$-0.793243\pi$
$911$	6.13965	−	18.8959i	0.203416	−	0.626049i	0.999775	−	0.0212248i	$-0.00675656\pi$
$912$	−9.20456	+	2.99074i	−0.304793	+	0.0990334i
$913$	−27.6099	+	8.97099i	−0.913754	+	0.296897i
$914$	0.235874	−	0.725945i	0.00780201	−	0.0240121i
$915$	2.52055	−	1.65192i	0.0833267	−	0.0546109i
$916$	−6.12935	−	18.8642i	−0.202519	−	0.623291i
$917$	2.86859	+	3.94827i	0.0947291	+	0.130383i
$918$			5.33620i			0.176121i
$919$	22.6350	−	16.4453i	0.746661	−	0.542481i	−0.148129	−	0.988968i	$-0.547325\pi$
$919$	22.6350	−	16.4453i	0.746661	−	0.542481i	0.894790	+	0.446487i	$0.147325\pi$
$920$	−1.37810	+	0.375460i	−0.0454347	+	0.0123785i
$921$	−5.09972	−	3.70517i	−0.168042	−	0.122089i
$922$	−2.58090	+	3.55231i	−0.0849975	+	0.116989i
$923$	1.68244	+	0.546657i	0.0553781	+	0.0179934i
$924$	18.8772			0.621013
$925$	−39.4844	+	8.73926i	−1.29824	+	0.287345i
$926$	7.56952			0.248750
$927$	1.09487	+	0.355745i	0.0359603	+	0.0116842i
$928$	−7.46831	+	10.2792i	−0.245159	+	0.337433i
$929$	−11.4273	−	8.30242i	−0.374918	−	0.272394i	0.384329	−	0.923196i	$-0.374433\pi$
$929$	−11.4273	−	8.30242i	−0.374918	−	0.272394i	−0.759247	+	0.650802i	$0.774433\pi$
$930$	−3.43858	−	1.30344i	−0.112756	−	0.0427414i
$931$	−5.08611	+	3.69528i	−0.166691	+	0.121108i
$932$			43.2727i			1.41744i
$933$	22.1893	+	30.5409i	0.726444	+	0.999864i
$934$	0.588481	+	1.81116i	0.0192557	+	0.0592629i
$935$	6.06943	+	22.2775i	0.198492	+	0.728552i
$936$	0.0554531	−	0.170667i	0.00181254	−	0.00557843i
$937$	34.1949	−	11.1106i	1.11710	−	0.362967i	0.308438	−	0.951244i	$-0.400194\pi$
$937$	34.1949	−	11.1106i	1.11710	−	0.362967i	0.808659	+	0.588277i	$0.200194\pi$
$938$	−3.91286	+	1.27136i	−0.127759	+	0.0415115i
$939$	10.1666	−	31.2897i	0.331776	−	1.02110i
$940$	−4.87763	−	17.9031i	−0.159091	−	0.583934i
$941$	8.25011	+	25.3912i	0.268946	+	0.827730i	0.990758	+	0.135641i	$0.0433094\pi$
$941$	8.25011	+	25.3912i	0.268946	+	0.827730i	−0.721812	+	0.692089i	$0.756691\pi$
$942$	0.678887	+	0.934408i	0.0221193	+	0.0304447i
$943$		−	0.892508i		−	0.0290640i
$944$	18.2490	−	13.2587i	0.593955	−	0.431534i
$945$	−38.4712	−	14.5830i	−1.25147	−	0.474385i
$946$	−0.960857	−	0.698104i	−0.0312402	−	0.0226973i
$947$	−10.1747	+	14.0042i	−0.330633	+	0.455077i	−0.941676	−	0.336520i	$-0.890750\pi$
$947$	−10.1747	+	14.0042i	−0.330633	+	0.455077i	0.611044	+	0.791597i	$0.290750\pi$
$948$	−21.3639	−	6.94156i	−0.693868	−	0.225451i
$949$	2.61803			0.0849850
$950$	−1.54734	+	0.342479i	−0.0502023	+	0.0111115i
$951$	32.2693			1.04640
$952$	−11.6332	−	3.77985i	−0.377034	−	0.122506i
$953$	14.2610	−	19.6286i	0.461959	−	0.635831i	−0.512955	−	0.858416i	$-0.671449\pi$
$953$	14.2610	−	19.6286i	0.461959	−	0.635831i	0.974913	+	0.222584i	$0.0714492\pi$
$954$	−1.00041	−	0.726837i	−0.0323893	−	0.0235322i
$955$	38.8991	−	10.5979i	1.25875	−	0.342941i
$956$	12.0276	−	8.73855i	0.389000	−	0.282625i
$957$			17.4048i			0.562617i
$958$	3.87684	+	5.33602i	0.125255	+	0.172399i
$959$	−7.90899	−	24.3414i	−0.255395	−	0.786024i
$960$	19.8369	−	13.0008i	0.640234	−	0.419598i
$961$	1.91722	−	5.90061i	0.0618460	−	0.190342i
$962$	0.417594	−	0.135684i	0.0134638	−	0.00437464i
$963$	12.5453	−	4.07623i	0.404268	−	0.131355i
$964$	−12.3931	+	38.1419i	−0.399154	+	1.22847i
$965$	15.1621	+	0.730899i	0.488087	+	0.0235285i
$966$	−0.238863	−	0.735146i	−0.00768531	−	0.0236529i
$967$	−18.2885	−	25.1720i	−0.588120	−	0.809477i	0.406437	−	0.913679i	$-0.366771\pi$
$967$	−18.2885	−	25.1720i	−0.588120	−	0.809477i	−0.994556	+	0.104202i	$0.966771\pi$
$968$		−	5.08580i		−	0.163464i
$969$	10.6388	−	7.72952i	0.341767	−	0.248308i
$970$	−1.51019	−	2.30429i	−0.0484893	−	0.0739862i
$971$	14.0543	+	10.2111i	0.451025	+	0.327689i	0.790000	−	0.613106i	$-0.210080\pi$
$971$	14.0543	+	10.2111i	0.451025	+	0.327689i	−0.338975	+	0.940795i	$0.610080\pi$
$972$	−9.68867	+	13.3353i	−0.310764	+	0.427730i
$973$	−16.7205	−	5.43282i	−0.536034	−	0.174168i
$974$	−1.94855			−0.0624356
$975$	0.870467	−	2.00006i	0.0278773	−	0.0640531i
$976$	3.47917			0.111365
$977$	40.7936	+	13.2546i	1.30510	+	0.424054i	0.877354	−	0.479844i	$-0.159307\pi$
$977$	40.7936	+	13.2546i	1.30510	+	0.424054i	0.427749	+	0.903898i	$0.359307\pi$
$978$	2.49229	−	3.43034i	0.0796945	−	0.109690i
$979$	12.1780	+	8.84784i	0.389211	+	0.282778i
$980$	10.0016	−	12.4573i	0.319489	−	0.397935i
$981$	−1.35096	+	0.981527i	−0.0431327	+	0.0313377i
$982$		−	3.23651i		−	0.103281i
$983$	22.0145	+	30.3003i	0.702153	+	0.966431i	0.999930	+	0.0117954i	$0.00375468\pi$
$983$	22.0145	+	30.3003i	0.702153	+	0.966431i	−0.297777	+	0.954635i	$0.596245\pi$
$984$	−0.335478	−	1.03250i	−0.0106947	−	0.0329148i
$985$	13.9410	+	11.1928i	0.444198	+	0.356632i
$986$	1.72778	−	5.31755i	0.0550236	−	0.169345i
$987$	19.2637	−	6.25914i	0.613169	−	0.199231i
$988$	−0.959129	+	0.311640i	−0.0305140	+	0.00991459i
$989$	0.880801	−	2.71083i	0.0280078	−	0.0861993i
$990$	0.241973	−	0.638346i	0.00769041	−	0.0202880i
$991$	5.17987	+	15.9420i	0.164544	+	0.506415i	0.999002	−	0.0446564i	$-0.0142193\pi$
$991$	5.17987	+	15.9420i	0.164544	+	0.506415i	−0.834458	+	0.551071i	$0.814219\pi$
$992$	−7.70500	−	10.6050i	−0.244634	−	0.336710i
$993$			13.1931i			0.418669i
$994$	−2.88426	+	2.09554i	−0.0914831	+	0.0664663i
$995$	0.560384	−	11.6249i	0.0177654	−	0.368534i
$996$	−33.9908	−	24.6957i	−1.07704	−	0.782515i
$997$	35.1845	−	48.4273i	1.11430	−	1.53371i	0.299388	−	0.954132i	$-0.403218\pi$
$997$	35.1845	−	48.4273i	1.11430	−	1.53371i	0.814917	−	0.579577i	$-0.196782\pi$
$998$	1.64057	+	0.533052i	0.0519312	+	0.0168735i
$999$	−45.6367			−1.44388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.2.e.a.4.2	✓	8
3.2	odd	2		225.2.m.a.154.1		8
4.3	odd	2		400.2.y.c.129.2		8
5.2	odd	4		125.2.d.b.101.2		16
5.3	odd	4		125.2.d.b.101.3		16
5.4	even	2		125.2.e.b.24.1		8
25.2	odd	20		625.2.d.o.376.3		16
25.3	odd	20		625.2.d.o.251.2		16
25.4	even	10		625.2.e.a.374.2		8
25.6	even	5		125.2.e.b.99.1		8
25.8	odd	20		125.2.d.b.26.3		16
25.9	even	10		625.2.b.c.624.4		8
25.11	even	5		625.2.e.a.249.2		8
25.12	odd	20		625.2.a.f.1.4		8
25.13	odd	20		625.2.a.f.1.5		8
25.14	even	10		625.2.e.i.249.1		8
25.16	even	5		625.2.b.c.624.5		8
25.17	odd	20		125.2.d.b.26.2		16
25.19	even	10	inner	25.2.e.a.19.2	yes	8
25.21	even	5		625.2.e.i.374.1		8
25.22	odd	20		625.2.d.o.251.3		16
25.23	odd	20		625.2.d.o.376.2		16
75.38	even	20		5625.2.a.x.1.4		8
75.44	odd	10		225.2.m.a.19.1		8
75.62	even	20		5625.2.a.x.1.5		8
100.19	odd	10		400.2.y.c.369.2		8
100.63	even	20		10000.2.a.bj.1.3		8
100.87	even	20		10000.2.a.bj.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.4.2	✓	8	1.1	even	1	trivial
25.2.e.a.19.2	yes	8	25.19	even	10	inner
125.2.d.b.26.2		16	25.17	odd	20
125.2.d.b.26.3		16	25.8	odd	20
125.2.d.b.101.2		16	5.2	odd	4
125.2.d.b.101.3		16	5.3	odd	4
125.2.e.b.24.1		8	5.4	even	2
125.2.e.b.99.1		8	25.6	even	5
225.2.m.a.19.1		8	75.44	odd	10
225.2.m.a.154.1		8	3.2	odd	2
400.2.y.c.129.2		8	4.3	odd	2
400.2.y.c.369.2		8	100.19	odd	10
625.2.a.f.1.4		8	25.12	odd	20
625.2.a.f.1.5		8	25.13	odd	20
625.2.b.c.624.4		8	25.9	even	10
625.2.b.c.624.5		8	25.16	even	5
625.2.d.o.251.2		16	25.3	odd	20
625.2.d.o.251.3		16	25.22	odd	20
625.2.d.o.376.2		16	25.23	odd	20
625.2.d.o.376.3		16	25.2	odd	20
625.2.e.a.249.2		8	25.11	even	5
625.2.e.a.374.2		8	25.4	even	10
625.2.e.i.249.1		8	25.14	even	10
625.2.e.i.374.1		8	25.21	even	5
5625.2.a.x.1.4		8	75.38	even	20
5625.2.a.x.1.5		8	75.62	even	20
10000.2.a.bj.1.3		8	100.63	even	20
10000.2.a.bj.1.6		8	100.87	even	20

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	25.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.174207 + 0.0566033i) q^{2} +(-0.865190 + 1.19083i) q^{3} +(-1.59089 - 1.15585i) q^{4} +(0.107666 - 2.23347i) q^{5} +(-0.218127 + 0.158479i) q^{6} +3.26086i q^{7} +(-0.427051 - 0.587785i) q^{8} +(0.257524 + 0.792578i) q^{9} +O(q^{10})\)	\(q+(0.174207 + 0.0566033i) q^{2} +(-0.865190 + 1.19083i) q^{3} +(-1.59089 - 1.15585i) q^{4} +(0.107666 - 2.23347i) q^{5} +(-0.218127 + 0.158479i) q^{6} +3.26086i q^{7} +(-0.427051 - 0.587785i) q^{8} +(0.257524 + 0.792578i) q^{9} +(0.145178 - 0.382993i) q^{10} +(0.618034 - 1.90211i) q^{11} +(2.75284 - 0.894453i) q^{12} +(0.281873 - 0.0915860i) q^{13} +(-0.184575 + 0.568064i) q^{14} +(2.56654 + 2.06059i) q^{15} +(1.17421 + 3.61384i) q^{16} +(-3.03472 - 4.17693i) q^{17} +0.152649i q^{18} +(1.39991 - 1.01709i) q^{19} +(-2.75284 + 3.42877i) q^{20} +(-3.88313 - 2.82126i) q^{21} +(0.215332 - 0.296379i) q^{22} +(0.836161 + 0.271685i) q^{23} +1.06943 q^{24} +(-4.97682 - 0.480938i) q^{25} +0.0542883 q^{26} +(-5.36635 - 1.74363i) q^{27} +(3.76906 - 5.18766i) q^{28} +(4.78304 + 3.47508i) q^{29} +(0.330473 + 0.504244i) q^{30} +(-4.93462 + 3.58521i) q^{31} +2.14910i q^{32} +(1.73038 + 2.38166i) q^{33} +(-0.292241 - 0.899425i) q^{34} +(7.28304 + 0.351083i) q^{35} +(0.506408 - 1.55856i) q^{36} +(7.69215 - 2.49933i) q^{37} +(0.301444 - 0.0979452i) q^{38} +(-0.134810 + 0.414902i) q^{39} +(-1.35878 + 0.890523i) q^{40} +(-0.313697 - 0.965461i) q^{41} +(-0.516776 - 0.711281i) q^{42} -3.24199i q^{43} +(-3.18178 + 2.31170i) q^{44} +(1.79793 - 0.489840i) q^{45} +(0.130287 + 0.0946589i) q^{46} +(-2.48043 + 3.41402i) q^{47} +(-5.31939 - 1.72837i) q^{48} -3.63318 q^{49} +(-0.839774 - 0.365487i) q^{50} +7.59963 q^{51} +(-0.554288 - 0.180099i) q^{52} +(-4.76148 + 6.55362i) q^{53} +(-0.836161 - 0.607507i) q^{54} +(-4.18178 - 1.58516i) q^{55} +(1.91668 - 1.39255i) q^{56} +2.54703i q^{57} +(0.636538 + 0.876119i) q^{58} +(-1.83443 - 5.64581i) q^{59} +(-1.70135 - 6.24471i) q^{60} +(0.282941 - 0.870802i) q^{61} +(-1.06258 + 0.345253i) q^{62} +(-2.58448 + 0.839749i) q^{63} +(2.22677 - 6.85329i) q^{64} +(-0.174207 - 0.639416i) q^{65} +(0.166634 + 0.512848i) q^{66} +(4.04870 + 5.57255i) q^{67} +10.1527i q^{68} +(-1.04697 + 0.760668i) q^{69} +(1.24888 + 0.473405i) q^{70} +(4.82884 + 3.50836i) q^{71} +(0.355890 - 0.489840i) q^{72} +(8.40107 + 2.72967i) q^{73} +1.48150 q^{74} +(4.87861 - 5.51045i) q^{75} -3.40270 q^{76} +(6.20252 + 2.01532i) q^{77} +(-0.0469697 + 0.0646482i) q^{78} +(-6.27851 - 4.56161i) q^{79} +(8.19784 - 2.23347i) q^{80} +(4.69667 - 3.41233i) q^{81} -0.185946i q^{82} +(-8.53192 - 11.7432i) q^{83} +(2.91668 + 8.97663i) q^{84} +(-9.65580 + 6.32825i) q^{85} +(0.183507 - 0.564778i) q^{86} +(-8.27647 + 2.68919i) q^{87} +(-1.38197 + 0.449028i) q^{88} +(-2.32579 + 7.15805i) q^{89} +(0.340938 + 0.0164351i) q^{90} +(0.298649 + 0.919147i) q^{91} +(-1.01621 - 1.39870i) q^{92} -8.97820i q^{93} +(-0.625353 + 0.454345i) q^{94} +(-2.12093 - 3.23616i) q^{95} +(-2.55922 - 1.85938i) q^{96} +(3.95373 - 5.44184i) q^{97} +(-0.632925 - 0.205650i) q^{98} +1.66673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} - 5 q^{3} - q^{4} - 9 q^{6} + 10 q^{8} + q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 - 5 * q^3 - q^4 - 9 * q^6 + 10 * q^8 + q^9	\( 8 q - 5 q^{2} - 5 q^{3} - q^{4} - 9 q^{6} + 10 q^{8} + q^{9} - 5 q^{10} - 4 q^{11} + 15 q^{12} - 5 q^{13} + 13 q^{14} + 15 q^{15} + 3 q^{16} - 10 q^{17} - 5 q^{19} - 15 q^{20} - 4 q^{21} + 5 q^{23} - 20 q^{24} - 10 q^{25} + 6 q^{26} - 5 q^{27} - 15 q^{28} - 5 q^{29} + 15 q^{30} - 9 q^{31} + 10 q^{33} + 13 q^{34} + 15 q^{35} + 23 q^{36} + 30 q^{37} + 15 q^{38} - 3 q^{39} + 10 q^{40} - 4 q^{41} - 15 q^{42} - 2 q^{44} - 15 q^{45} - 19 q^{46} - 30 q^{48} + 14 q^{49} - 15 q^{50} - 4 q^{51} - 10 q^{52} - 10 q^{53} - 5 q^{54} - 10 q^{55} + 10 q^{56} + 20 q^{58} - 10 q^{60} - 9 q^{61} - 30 q^{62} + 10 q^{63} + 4 q^{64} + 5 q^{65} + 12 q^{66} + 20 q^{67} + 17 q^{69} + 30 q^{70} + 6 q^{71} + 5 q^{72} + 15 q^{73} - 12 q^{74} - 10 q^{75} - 20 q^{76} + 10 q^{77} + 25 q^{78} + 15 q^{79} + 20 q^{80} + 28 q^{81} - 45 q^{83} + 18 q^{84} - 15 q^{85} - 9 q^{86} - 20 q^{87} - 20 q^{88} - 25 q^{89} - 25 q^{90} + 6 q^{91} + 30 q^{92} - 27 q^{94} + 15 q^{95} + 16 q^{96} - 60 q^{97} - 10 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 - 5 * q^3 - q^4 - 9 * q^6 + 10 * q^8 + q^9 - 5 * q^10 - 4 * q^11 + 15 * q^12 - 5 * q^13 + 13 * q^14 + 15 * q^15 + 3 * q^16 - 10 * q^17 - 5 * q^19 - 15 * q^20 - 4 * q^21 + 5 * q^23 - 20 * q^24 - 10 * q^25 + 6 * q^26 - 5 * q^27 - 15 * q^28 - 5 * q^29 + 15 * q^30 - 9 * q^31 + 10 * q^33 + 13 * q^34 + 15 * q^35 + 23 * q^36 + 30 * q^37 + 15 * q^38 - 3 * q^39 + 10 * q^40 - 4 * q^41 - 15 * q^42 - 2 * q^44 - 15 * q^45 - 19 * q^46 - 30 * q^48 + 14 * q^49 - 15 * q^50 - 4 * q^51 - 10 * q^52 - 10 * q^53 - 5 * q^54 - 10 * q^55 + 10 * q^56 + 20 * q^58 - 10 * q^60 - 9 * q^61 - 30 * q^62 + 10 * q^63 + 4 * q^64 + 5 * q^65 + 12 * q^66 + 20 * q^67 + 17 * q^69 + 30 * q^70 + 6 * q^71 + 5 * q^72 + 15 * q^73 - 12 * q^74 - 10 * q^75 - 20 * q^76 + 10 * q^77 + 25 * q^78 + 15 * q^79 + 20 * q^80 + 28 * q^81 - 45 * q^83 + 18 * q^84 - 15 * q^85 - 9 * q^86 - 20 * q^87 - 20 * q^88 - 25 * q^89 - 25 * q^90 + 6 * q^91 + 30 * q^92 - 27 * q^94 + 15 * q^95 + 16 * q^96 - 60 * q^97 - 10 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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