LMFDB - Embedded newform 25.2.e.a.19.2

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			19.2
Root			$1.17421 - 0.0566033i$ of defining polynomial
Character	$\chi$	$=$	25.19
Dual form			25.2.e.a.4.2

$q$-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 $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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	−0.246777	−	0.969072i	$-0.579371\pi$
$2$	0.174207	−	0.0566033i	0.123183	−	0.0400246i	0.369960	+	0.929048i	$0.379371\pi$
$3$	−0.865190	−	1.19083i	−0.499518	−	0.687527i	0.482590	−	0.875846i	$-0.339696\pi$
$3$	−0.865190	−	1.19083i	−0.499518	−	0.687527i	−0.982108	+	0.188319i	$0.939696\pi$
$4$	−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	$-0.788654\pi$
$7$		−	3.26086i		−	1.23249i	0.787555	−	0.616244i	$-0.211346\pi$
$8$	−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	0.999969	−	0.00788181i	$-0.00250889\pi$
$11$	0.618034	+	1.90211i	0.186344	+	0.573509i	−0.813625	+	0.581390i	$0.802509\pi$
$12$	2.75284	+	0.894453i	0.794678	+	0.258206i
$13$	0.281873	+	0.0915860i	0.0781775	+	0.0254014i	0.347845	−	0.937552i	$-0.386914\pi$
$13$	0.281873	+	0.0915860i	0.0781775	+	0.0254014i	−0.269667	+	0.962954i	$0.586914\pi$
$14$	−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	0.262810	+	0.964847i	$0.415351\pi$
$17$	−3.03472	+	4.17693i	−0.736027	+	1.01305i	−0.998837	+	0.0482067i	$0.984649\pi$
$18$		−	0.152649i		−	0.0359798i
$19$	1.39991	+	1.01709i	0.321161	+	0.233337i	0.736671	−	0.676252i	$-0.236397\pi$
$19$	1.39991	+	1.01709i	0.321161	+	0.233337i	−0.415510	+	0.909589i	$0.636397\pi$
$20$	−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	−0.220540	−	0.975378i	$-0.570782\pi$
$23$	0.836161	−	0.271685i	0.174352	−	0.0566503i	0.394892	+	0.918728i	$0.370782\pi$
$24$	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	−0.0472171	−	0.998885i	$-0.515035\pi$
$29$	4.78304	−	3.47508i	0.888188	−	0.645306i	0.935405	+	0.353578i	$0.115035\pi$
$30$	0.330473	−	0.504244i	0.0603359	−	0.0920620i
$31$	−4.93462	−	3.58521i	−0.886285	−	0.643923i	0.0486220	−	0.998817i	$-0.484517\pi$
$31$	−4.93462	−	3.58521i	−0.886285	−	0.643923i	−0.934907	+	0.354894i	$0.884517\pi$
$32$		−	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	0.863125	−	0.504991i	$-0.168504\pi$
$37$	7.69215	+	2.49933i	1.26458	+	0.410887i	0.401457	+	0.915878i	$0.368504\pi$
$38$	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	−0.972559	−	0.232655i	$-0.925259\pi$
$41$	−0.313697	+	0.965461i	−0.0489913	+	0.150780i	0.923568	+	0.383434i	$0.125259\pi$
$42$	−0.516776	+	0.711281i	−0.0797403	+	0.109753i
$43$			3.24199i			0.494399i	0.968965	+	0.247200i	$0.0795103\pi$
$43$			3.24199i			0.494399i	−0.968965	+	0.247200i	$0.920490\pi$
$44$	−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	0.588844	−	0.808247i	$-0.299583\pi$
$47$	−2.48043	−	3.41402i	−0.361808	−	0.497986i	−0.950651	+	0.310261i	$0.899583\pi$
$48$	−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	0.345226	−	0.938520i	$-0.387802\pi$
$53$	−4.76148	−	6.55362i	−0.654040	−	0.900209i	−0.999266	+	0.0383106i	$0.987802\pi$
$54$	−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	0.757768	+	0.652524i	$0.226290\pi$
$59$	−1.83443	+	5.64581i	−0.238823	+	0.735021i	−0.996591	+	0.0824976i	$0.973710\pi$
$60$	−1.70135	+	6.24471i	−0.219643	+	0.806188i
$61$	0.282941	+	0.870802i	0.0362268	+	0.111495i	0.967535	−	0.252738i	$-0.0813312\pi$
$61$	0.282941	+	0.870802i	0.0362268	+	0.111495i	−0.931308	+	0.364233i	$0.881331\pi$
$62$	−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	−0.486606	−	0.873622i	$-0.661765\pi$
$67$	4.04870	−	5.57255i	0.494627	−	0.680796i	0.981233	+	0.192826i	$0.0617652\pi$
$68$		−	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	−0.263144	−	0.964757i	$-0.584759\pi$
$71$	4.82884	−	3.50836i	0.573078	−	0.416366i	0.836222	+	0.548391i	$0.184759\pi$
$72$	0.355890	+	0.489840i	0.0419420	+	0.0577282i
$73$	8.40107	−	2.72967i	0.983271	−	0.319484i	0.227110	−	0.973869i	$-0.427072\pi$
$73$	8.40107	−	2.72967i	0.983271	−	0.319484i	0.756161	+	0.654385i	$0.227072\pi$
$74$	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	−0.882006	−	0.471237i	$-0.843808\pi$
$79$	−6.27851	+	4.56161i	−0.706388	+	0.513221i	0.175618	+	0.984458i	$0.443808\pi$
$80$	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	0.0207694	+	0.999784i	$0.493388\pi$
$83$	−8.53192	+	11.7432i	−0.936500	+	1.28898i	−0.957269	+	0.289197i	$0.906612\pi$
$84$	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	−0.995380	−	0.0960092i	$-0.969392\pi$
$89$	−2.32579	−	7.15805i	−0.246534	−	0.758752i	0.748847	−	0.662743i	$-0.230608\pi$
$90$	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	0.961105	−	0.276184i	$-0.0890699\pi$
$97$	3.95373	+	5.44184i	0.401440	+	0.552535i	−0.559664	+	0.828719i	$0.689070\pi$
$98$	−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	0.847144	−	0.531363i	$-0.178320\pi$
$103$	0.811969	+	1.11758i	0.0800057	+	0.110118i	−0.767138	+	0.641482i	$0.778320\pi$
$104$	−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	$0.277311\pi$
$107$			15.8285i			1.53020i	−0.643911	+	0.765101i	$0.722689\pi$
$108$	6.52190	−	8.97663i	0.627570	−	0.863776i
$109$	0.619199	−	1.90570i	0.0593085	−	0.182533i	−0.917013	−	0.398857i	$-0.869407\pi$
$109$	0.619199	−	1.90570i	0.0593085	−	0.182533i	0.976322	+	0.216324i	$0.0694069\pi$
$110$	−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	0.735758	−	0.677244i	$-0.236826\pi$
$113$	9.91713	+	3.22227i	0.932925	+	0.303126i	0.197167	+	0.980370i	$0.436826\pi$
$114$	−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	−0.0515752	−	0.998669i	$-0.516424\pi$
$127$	5.56375	−	1.80777i	0.493703	−	0.160414i	0.545278	+	0.838255i	$0.316424\pi$
$128$	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	0.639422	−	0.768856i	$-0.279174\pi$
$131$	1.21081	+	0.879704i	0.105789	+	0.0768601i	−0.533633	+	0.845716i	$0.679174\pi$
$132$			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	−0.0277472	−	0.999615i	$-0.508833\pi$
$137$	−7.46472	−	2.42543i	−0.637754	−	0.207219i	−0.610007	+	0.792396i	$0.708833\pi$
$138$	−0.225446	−	0.0732518i	−0.0191912	−	0.00623560i
$139$	−1.66607	−	5.12764i	−0.141314	−	0.434921i	0.855204	−	0.518291i	$-0.173432\pi$
$139$	−1.66607	−	5.12764i	−0.141314	−	0.434921i	−0.996519	+	0.0833702i	$0.973432\pi$
$140$	−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	$0.0546808\pi$
$157$			4.28378i			0.341883i	−0.985281	+	0.170941i	$0.945319\pi$
$158$	−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	−0.342293	−	0.939593i	$-0.611204\pi$
$163$	−14.9566	−	4.85970i	−1.17149	−	0.380641i	−0.829200	+	0.558952i	$0.811204\pi$
$164$	−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	0.00816967	−	0.999967i	$-0.497399\pi$
$167$	12.3629	−	17.0161i	0.956670	−	1.31674i	0.948500	−	0.316777i	$-0.102601\pi$
$168$		−	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	−0.0382277	−	0.999269i	$-0.512171\pi$
$173$	6.81587	−	2.21461i	0.518201	−	0.168374i	0.556429	+	0.830895i	$0.312171\pi$
$174$	−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	−0.317565	−	0.948237i	$-0.602865\pi$
$179$	6.50396	−	4.72540i	0.486129	−	0.353193i	0.803694	+	0.595043i	$0.202865\pi$
$180$	−3.42649	+	1.29885i	−0.255395	+	0.0968108i
$181$	16.6796	+	12.1184i	1.23978	+	0.900756i	0.997584	−	0.0694707i	$-0.0221310\pi$
$181$	16.6796	+	12.1184i	1.23978	+	0.900756i	0.242200	+	0.970226i	$0.422131\pi$
$182$		−	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	−0.519277	−	0.854606i	$-0.673799\pi$
$191$	5.57167	−	17.1478i	0.403152	−	1.24077i	0.922429	−	0.386167i	$-0.126201\pi$
$192$	6.23453	−	8.58110i	0.449939	−	0.619288i
$193$		−	6.78859i		−	0.488653i	−0.969693	−	0.244327i	$-0.921433\pi$
$193$		−	6.78859i		−	0.488653i	0.969693	−	0.244327i	$-0.0785669\pi$
$194$	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	0.608092	−	0.793866i	$-0.291935\pi$
$197$	−4.69956	−	6.46839i	−0.334830	−	0.460854i	−0.942923	+	0.333012i	$0.891935\pi$
$198$	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	0.957055	+	0.289906i	$0.0936239\pi$
$211$	5.13029	+	15.7894i	0.353184	+	1.08699i	−0.603872	+	0.797082i	$0.706376\pi$
$212$	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	−0.0902485	−	0.995919i	$-0.528766\pi$
$223$	6.30368	−	2.04819i	0.422126	−	0.137157i	0.512374	+	0.858762i	$0.328766\pi$
$224$	−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	−0.699497	−	0.714636i	$-0.746593\pi$
$227$	−12.7365	+	4.13833i	−0.845350	+	0.274671i	−0.145853	+	0.989306i	$0.546593\pi$
$228$	2.94398	+	4.05205i	0.194970	+	0.268353i
$229$	8.16032	−	5.92882i	0.539249	−	0.391788i	−0.284557	−	0.958659i	$-0.591846\pi$
$229$	8.16032	−	5.92882i	0.539249	−	0.391788i	0.823806	+	0.566872i	$0.191846\pi$
$230$	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	0.137069	+	0.990562i	$0.456232\pi$
$233$	−12.9345	+	17.8028i	−0.847368	+	1.16630i	−0.984437	+	0.175740i	$0.943768\pi$
$234$	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	0.846627	−	0.532187i	$-0.178629\pi$
$239$	−2.33626	−	7.19026i	−0.151120	−	0.465099i	−0.997747	+	0.0670870i	$0.978629\pi$
$240$	−4.43299	−	11.6946i	−0.286148	−	0.754885i
$241$	−6.30226	+	19.3964i	−0.405964	+	1.24943i	0.514123	+	0.857716i	$0.328117\pi$
$241$	−6.30226	+	19.3964i	−0.405964	+	1.24943i	−0.920087	+	0.391713i	$0.871883\pi$
$242$	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	$-0.782150\pi$
$257$		−	20.2700i		−	1.26441i	0.774801	−	0.632205i	$-0.217850\pi$
$258$	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	0.978170	−	0.207806i	$-0.0666323\pi$
$263$	26.7160	+	8.68056i	1.64738	+	0.535267i	0.669211	+	0.743072i	$0.266632\pi$
$264$	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	0.962615	−	0.270873i	$-0.0873123\pi$
$269$	16.4416	+	11.9455i	1.00246	+	0.728333i	0.0398490	+	0.999206i	$0.487312\pi$
$270$	−1.44688	−	1.80214i	−0.0880541	−	0.109675i
$271$	−25.4409	+	18.4839i	−1.54543	+	1.12282i	−0.598610	+	0.801041i	$0.704280\pi$
$271$	−25.4409	+	18.4839i	−1.54543	+	1.12282i	−0.946816	+	0.321777i	$0.895720\pi$
$272$	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	−0.678672	−	0.734441i	$-0.737444\pi$
$277$	−13.2487	+	4.30475i	−0.796035	+	0.258648i	−0.117363	+	0.993089i	$0.537444\pi$
$278$	−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	−0.250748	−	0.968052i	$-0.580677\pi$
$281$	−20.9355	−	15.2105i	−1.24891	−	0.907383i	−0.998158	+	0.0606690i	$0.980677\pi$
$282$			1.13778i			0.0677541i
$283$	13.9491	−	19.1993i	0.829188	−	1.14128i	−0.158885	−	0.987297i	$-0.550790\pi$
$283$	13.9491	−	19.1993i	0.829188	−	1.14128i	0.988074	−	0.153983i	$-0.0492101\pi$
$284$	−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	$-0.882991\pi$
$293$		−	12.3029i		−	0.718742i	0.933195	−	0.359371i	$-0.117009\pi$
$294$	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	$-0.961003\pi$
$307$		−	4.28249i		−	0.244415i	0.992505	−	0.122207i	$-0.0389973\pi$
$308$	−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	0.877585	+	0.479421i	$0.159153\pi$
$311$	7.92526	+	24.3915i	0.449400	+	1.38311i	−0.428185	+	0.903691i	$0.640847\pi$
$312$	0.301444	+	0.0979452i	0.0170659	+	0.00554505i
$313$	−21.2573	−	6.90692i	−1.20153	−	0.390402i	−0.361209	−	0.932485i	$-0.617636\pi$
$313$	−21.2573	−	6.90692i	−1.20153	−	0.390402i	−0.840325	+	0.542083i	$0.817636\pi$
$314$	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	0.275645	+	0.961259i	$0.411108\pi$
$317$	−12.8859	+	17.7360i	−0.723746	+	0.996151i	−0.999391	+	0.0348911i	$0.988892\pi$
$318$			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	0.768955	−	0.639303i	$-0.220777\pi$
$331$	7.25121	+	5.26831i	0.398563	+	0.289573i	−0.370393	+	0.928875i	$0.620777\pi$
$332$		−	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	0.941976	−	0.335681i	$-0.108966\pi$
$337$	27.6601	+	8.98731i	1.50674	+	0.489570i	0.564766	+	0.825251i	$0.308966\pi$
$338$	−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	0.972641	−	0.232315i	$-0.0746302\pi$
$347$	8.40368	+	11.5667i	0.451133	+	0.620931i	−0.521508	+	0.853247i	$0.674630\pi$
$348$	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	0.778095	−	0.628147i	$-0.216186\pi$
$353$	−1.12265	−	1.54520i	−0.0597529	−	0.0822427i	−0.837848	+	0.545904i	$0.816186\pi$
$354$	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	0.589609	+	0.807689i	$0.299282\pi$
$359$	−6.86161	+	21.1179i	−0.362142	+	1.11456i	−0.951751	+	0.306870i	$0.900718\pi$
$360$	−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	−0.341435	−	0.939906i	$-0.610913\pi$
$367$	12.6050	−	17.3493i	0.657978	−	0.905629i	0.999412	+	0.0342768i	$0.0109128\pi$
$368$		−	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	−0.817178	−	0.576385i	$-0.804463\pi$
$373$	−22.0074	+	7.15063i	−1.13950	+	0.370245i	−0.322320	+	0.946631i	$0.604463\pi$
$374$	−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	−0.938390	−	0.345579i	$-0.887682\pi$
$379$	−17.5153	+	12.7256i	−0.899702	+	0.653672i	0.0386872	+	0.999251i	$0.487682\pi$
$380$	−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	−0.715610	−	0.698500i	$-0.753851\pi$
$383$	3.32381	−	4.57484i	0.169839	−	0.233763i	0.885449	+	0.464737i	$0.153851\pi$
$384$	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	0.994316	−	0.106468i	$-0.0339541\pi$
$389$	2.51109	+	7.72833i	0.127317	+	0.391842i	−0.866999	+	0.498310i	$0.833954\pi$
$390$	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	0.384111	−	0.923287i	$-0.374508\pi$
$397$	−12.2076	−	16.8024i	−0.612684	−	0.843287i	−0.996795	+	0.0799998i	$0.974508\pi$
$398$	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	−0.999294	−	0.0375613i	$-0.988041\pi$
$409$	−3.41317	+	10.5046i	−0.168770	+	0.519421i	0.830524	+	0.556983i	$0.188041\pi$
$410$	−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	−0.301179	−	0.953568i	$-0.597380\pi$
$419$	−26.6338	−	19.3506i	−1.30115	−	0.945337i	−0.999966	+	0.00823011i	$0.997380\pi$
$420$	20.3631	+	5.54786i	0.993617	+	0.270708i
$421$	16.3945	−	11.9113i	0.799019	−	0.580522i	−0.111607	−	0.993752i	$-0.535600\pi$
$421$	16.3945	−	11.9113i	0.799019	−	0.580522i	0.910626	+	0.413231i	$0.135600\pi$
$422$	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	0.439575	−	0.898206i	$-0.355129\pi$
$431$	−5.78873	−	4.20576i	−0.278833	−	0.202584i	−0.718408	+	0.695622i	$0.755129\pi$
$432$			21.4405i			1.03156i
$433$	−3.22262	+	4.43555i	−0.154869	+	0.213159i	−0.879400	−	0.476083i	$-0.842056\pi$
$433$	−3.22262	+	4.43555i	−0.154869	+	0.213159i	0.724531	+	0.689242i	$0.242056\pi$
$434$	−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	0.872761	+	0.488148i	$0.162327\pi$
$439$	9.50415	+	29.2508i	0.453609	+	1.39606i	−0.419153	+	0.907916i	$0.637673\pi$
$440$	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	$0.0869214\pi$
$443$			11.3527i			0.539381i	−0.962947	+	0.269691i	$0.913079\pi$
$444$	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	$0.0310735\pi$
$457$			4.16714i			0.194931i	−0.995239	+	0.0974653i	$0.968926\pi$
$458$	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	−0.961581	−	0.274521i	$-0.911481\pi$
$461$	−7.40758	−	22.7982i	−0.345005	−	1.06182i	0.616576	−	0.787296i	$-0.288519\pi$
$462$	−1.67232	−	0.543370i	−0.0778035	−	0.0252799i
$463$	39.3021	+	12.7700i	1.82652	+	0.593473i	0.999510	+	0.0312899i	$0.00996151\pi$
$463$	39.3021	+	12.7700i	1.82652	+	0.593473i	0.827013	+	0.562183i	$0.190038\pi$
$464$	−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	−0.643871	−	0.765134i	$-0.722673\pi$
$467$	6.11096	−	8.41102i	0.282782	−	0.389216i	0.926653	+	0.375918i	$0.122673\pi$
$468$			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	0.331314	−	0.943520i	$-0.392508\pi$
$479$	29.1312	−	21.1650i	1.33104	−	0.967055i	0.999723	−	0.0235349i	$-0.00749208\pi$
$480$	−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	0.0706809	−	0.997499i	$-0.477483\pi$
$487$	−10.1172	−	3.28726i	−0.458452	−	0.148960i	−0.529133	+	0.848539i	$0.677483\pi$
$488$	−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	0.748990	+	0.662581i	$0.230539\pi$
$491$	−5.46010	+	16.8045i	−0.246411	+	0.758375i	−0.995401	+	0.0957938i	$0.969461\pi$
$492$	−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	0.976961	−	0.213416i	$-0.0684590\pi$
$503$	10.5879	+	14.5730i	0.472093	+	0.649780i	−0.504869	+	0.863196i	$0.668459\pi$
$504$	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	−0.778961	−	0.627072i	$-0.784253\pi$
$509$	4.95926	−	15.2630i	0.219815	−	0.676522i	0.998777	−	0.0494500i	$-0.0157469\pi$
$510$	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	−0.548102	−	0.836412i	$-0.684649\pi$
$521$	1.78040	−	1.29354i	0.0780007	−	0.0566708i	0.626102	+	0.779741i	$0.284649\pi$
$522$	−0.530469	−	0.730127i	−0.0232180	−	0.0319568i
$523$	7.07194	−	2.29781i	0.309234	−	0.100476i	−0.150289	−	0.988642i	$-0.548020\pi$
$523$	7.07194	−	2.29781i	0.309234	−	0.100476i	0.459523	+	0.888166i	$0.348020\pi$
$524$	−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	−0.715085	−	0.699037i	$-0.753612\pi$
$541$	6.38040	−	19.6368i	0.274315	−	0.844254i	0.989400	−	0.145216i	$-0.0463878\pi$
$542$	−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	0.994288	+	0.106730i	$0.0340379\pi$
$547$	18.4424	+	25.3839i	0.788542	+	1.08534i	−0.205746	+	0.978605i	$0.565962\pi$
$548$	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	$0.157021\pi$
$557$			22.3515i			0.947064i	−0.880776	+	0.473532i	$0.842979\pi$
$558$	−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	−0.475639	−	0.879640i	$-0.657783\pi$
$563$	−32.6843	−	10.6198i	−1.37748	−	0.447570i	−0.901840	+	0.432070i	$0.857783\pi$
$564$	−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	0.979558	−	0.201162i	$-0.0644718\pi$
$569$	26.0230	+	18.9068i	1.09094	+	0.792615i	0.111383	+	0.993778i	$0.464472\pi$
$570$	0.975494	−	0.369773i	0.0408590	−	0.0154881i
$571$	21.9784	−	15.9683i	0.919768	−	0.668251i	−0.0236979	−	0.999719i	$-0.507544\pi$
$571$	21.9784	−	15.9683i	0.919768	−	0.668251i	0.943466	+	0.331468i	$0.107544\pi$
$572$	−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	−0.0217089	−	0.999764i	$-0.506911\pi$
$577$	13.1724	−	4.27998i	0.548375	−	0.178178i	0.570084	+	0.821586i	$0.306911\pi$
$578$	−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	−0.739185	−	0.673502i	$-0.764789\pi$
$587$	−41.9890	−	13.6431i	−1.73307	−	0.563110i	−0.993888	+	0.110392i	$0.964789\pi$
$588$	−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	$-0.891697\pi$
$593$		−	16.2531i		−	0.667437i	0.942673	−	0.333718i	$-0.108303\pi$
$594$	−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	$-0.946567\pi$
$607$		−	8.23276i		−	0.334157i	0.985944	−	0.167079i	$-0.0534334\pi$
$608$	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	0.399717	−	0.916638i	$-0.369108\pi$
$613$	4.56327	+	1.48270i	0.184309	+	0.0598856i	−0.215408	+	0.976524i	$0.569108\pi$
$614$	−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	−0.784300	−	0.620382i	$-0.786978\pi$
$617$	1.19428	−	1.64379i	0.0480800	−	0.0661765i	0.832380	+	0.554205i	$0.186978\pi$
$618$		−	0.372454i		−	0.0149823i
$619$	6.58621	+	4.78516i	0.264722	+	0.192332i	0.712226	−	0.701950i	$-0.247687\pi$
$619$	6.58621	+	4.78516i	0.264722	+	0.192332i	−0.447504	+	0.894282i	$0.647687\pi$
$620$	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	−0.0957154	−	0.995409i	$-0.530514\pi$
$631$	−26.9279	−	19.5643i	−1.07198	−	0.778841i	−0.976268	+	0.216567i	$0.930514\pi$
$632$		−	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	0.337590	+	0.941293i	$0.390388\pi$
$641$	−12.3755	+	38.0880i	−0.488804	+	1.50439i	−0.826394	+	0.563092i	$0.809612\pi$
$642$	2.50848	−	3.45263i	0.0990019	−	0.136264i
$643$		−	11.6870i		−	0.460890i	−0.973085	−	0.230445i	$-0.925982\pi$
$643$		−	11.6870i		−	0.460890i	0.973085	−	0.230445i	$-0.0740182\pi$
$644$	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	0.707231	−	0.706982i	$-0.249944\pi$
$647$	−4.67252	−	6.43117i	−0.183696	−	0.252835i	−0.890927	+	0.454147i	$0.849944\pi$
$648$	−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	0.768908	−	0.639360i	$-0.220801\pi$
$653$	−1.96165	−	2.69998i	−0.0767653	−	0.105658i	−0.845673	+	0.533702i	$0.820801\pi$
$654$	−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	−0.590259	−	0.807214i	$-0.700974\pi$
$659$	9.28621	−	28.5800i	0.361739	−	1.11332i	0.951998	−	0.306105i	$-0.0990257\pi$
$660$	−12.9296	+	0.623280i	−0.503285	+	0.0242611i
$661$	−2.03462	−	6.26192i	−0.0791375	−	0.243560i	0.903659	−	0.428253i	$-0.140871\pi$
$661$	−2.03462	−	6.26192i	−0.0791375	−	0.243560i	−0.982796	+	0.184693i	$0.940871\pi$
$662$	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	−0.429794	−	0.902927i	$-0.641414\pi$
$673$	−6.40194	+	2.08012i	−0.246777	+	0.0801826i	0.183017	+	0.983110i	$0.441414\pi$
$674$	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	−0.0487718	−	0.998810i	$-0.515531\pi$
$677$	12.9799	−	4.21741i	0.498857	−	0.162088i	0.547629	+	0.836722i	$0.315531\pi$
$678$	−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	−0.795632	−	0.605781i	$-0.792861\pi$
$683$	0.689001	−	0.948329i	0.0263639	−	0.0362868i	0.821995	+	0.569494i	$0.192861\pi$
$684$	−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	−0.852699	−	0.522403i	$-0.825036\pi$
$691$	3.79083	−	11.6670i	0.144210	−	0.443832i	0.996909	+	0.0785709i	$0.0250357\pi$
$692$	−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	−0.922309	−	0.386454i	$-0.873700\pi$
$709$	1.35816	−	4.17998i	0.0510067	−	0.156983i	0.973315	+	0.229471i	$0.0736998\pi$
$710$	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	0.410591	−	0.911819i	$-0.365322\pi$
$719$	−8.84119	−	6.42350i	−0.329721	−	0.239556i	−0.740312	+	0.672263i	$0.765322\pi$
$720$	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	−0.825122	−	0.564955i	$-0.808893\pi$
$727$	−31.2928	+	10.1677i	−1.16059	+	0.377097i	−0.335465	+	0.942053i	$0.608893\pi$
$728$	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	−0.931756	−	0.363086i	$-0.881723\pi$
$733$	−8.08190	+	11.1238i	−0.298512	+	0.410866i	0.633244	+	0.773952i	$0.281723\pi$
$734$	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	0.823177	+	0.567785i	$0.192200\pi$
$739$	13.3462	+	41.0754i	0.490949	+	1.51098i	−0.332228	+	0.943199i	$0.607800\pi$
$740$	−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	$-0.801411\pi$
$743$		−	31.8479i		−	1.16838i	0.811615	−	0.584192i	$-0.198589\pi$
$744$	−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	$-0.999431\pi$
$757$		−	0.0984401i		−	0.00357786i	0.999998	−	0.00178893i	$-0.000569435\pi$
$758$	−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	0.929243	−	0.369470i	$-0.120461\pi$
$761$	−1.09516	−	3.37056i	−0.0396996	−	0.122183i	−0.968942	+	0.247287i	$0.920461\pi$
$762$	−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

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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more