LMFDB - Embedded newform 252.2.bj.b.103.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(103,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 5]))

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

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

chi := DirichletCharacter("252.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bj (of order $6$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.15
Character	$\chi$	$=$	252.103
Dual form			252.2.bj.b.115.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.412858 - 1.35261i) q^{2} +(1.24372 + 1.20547i) q^{3} +(-1.65910 + 1.11687i) q^{4} +(0.514884 - 0.297269i) q^{5} +(1.11705 - 2.17995i) q^{6} +(1.74201 - 1.99133i) q^{7} +(2.19566 + 1.78300i) q^{8} +(0.0936760 + 2.99854i) q^{9} +O(q^{10})$	\(q+(-0.412858 - 1.35261i) q^{2} +(1.24372 + 1.20547i) q^{3} +(-1.65910 + 1.11687i) q^{4} +(0.514884 - 0.297269i) q^{5} +(1.11705 - 2.17995i) q^{6} +(1.74201 - 1.99133i) q^{7} +(2.19566 + 1.78300i) q^{8} +(0.0936760 + 2.99854i) q^{9} +(-0.614662 - 0.573707i) q^{10} +(-2.63566 - 1.52170i) q^{11} +(-3.40981 - 0.610922i) q^{12} +(6.21148 + 3.58620i) q^{13} +(-3.41269 - 1.53413i) q^{14} +(0.998720 + 0.250960i) q^{15} +(1.50521 - 3.70599i) q^{16} +(2.28182 - 1.31741i) q^{17} +(4.01717 - 1.36468i) q^{18} +(1.15636 - 2.00287i) q^{19} +(-0.522233 + 1.06826i) q^{20} +(4.56707 - 0.376706i) q^{21} +(-0.970111 + 4.19326i) q^{22} +(1.34481 - 0.776425i) q^{23} +(0.581426 + 4.86435i) q^{24} +(-2.32326 + 4.02401i) q^{25} +(2.28627 - 9.88229i) q^{26} +(-3.49814 + 3.84226i) q^{27} +(-0.666115 + 5.24941i) q^{28} +(-3.50068 - 6.06335i) q^{29} +(-0.0728793 - 1.45449i) q^{30} -5.91792 q^{31} +(-5.63419 - 0.505907i) q^{32} +(-1.44366 - 5.06978i) q^{33} +(-2.72401 - 2.54251i) q^{34} +(0.304976 - 1.54315i) q^{35} +(-3.50439 - 4.87024i) q^{36} +(-2.74961 + 4.76246i) q^{37} +(-3.18651 - 0.737199i) q^{38} +(3.40228 + 11.9480i) q^{39} +(1.66054 + 0.265339i) q^{40} +(-3.27676 - 1.89184i) q^{41} +(-2.39508 - 6.02192i) q^{42} +(2.52490 - 1.45775i) q^{43} +(6.07236 - 0.419042i) q^{44} +(0.939603 + 1.51605i) q^{45} +(-1.60541 - 1.49844i) q^{46} -9.67847 q^{47} +(6.33952 - 2.79473i) q^{48} +(-0.930778 - 6.93784i) q^{49} +(6.40208 + 1.48112i) q^{50} +(4.42605 + 1.11218i) q^{51} +(-14.3108 + 0.987559i) q^{52} +(4.10505 + 7.11016i) q^{53} +(6.64131 + 3.14531i) q^{54} -1.80941 q^{55} +(7.37540 - 1.26627i) q^{56} +(3.85259 - 1.09705i) q^{57} +(-6.75605 + 7.23834i) q^{58} -3.77001 q^{59} +(-1.93726 + 0.699074i) q^{60} +2.67699i q^{61} +(2.44326 + 8.00462i) q^{62} +(6.13426 + 5.03695i) q^{63} +(1.64182 + 7.82971i) q^{64} +4.26426 q^{65} +(-6.26141 + 4.04580i) q^{66} -8.92572i q^{67} +(-2.31439 + 4.73421i) q^{68} +(2.60852 + 0.655472i) q^{69} +(-2.21319 + 0.224588i) q^{70} +8.75743i q^{71} +(-5.14071 + 6.75078i) q^{72} +(-1.30083 + 0.751036i) q^{73} +(7.57694 + 1.75292i) q^{74} +(-7.74032 + 2.20411i) q^{75} +(0.318435 + 4.61446i) q^{76} +(-7.62156 + 2.59765i) q^{77} +(14.7563 - 9.53477i) q^{78} +6.73276i q^{79} +(-0.326667 - 2.35561i) q^{80} +(-8.98245 + 0.561782i) q^{81} +(-1.20608 + 5.21323i) q^{82} +(-4.99378 - 8.64947i) q^{83} +(-7.15647 + 5.72581i) q^{84} +(0.783250 - 1.35663i) q^{85} +(-3.01419 - 2.81336i) q^{86} +(2.95534 - 11.7611i) q^{87} +(-3.07382 - 8.04052i) q^{88} +(-13.7577 - 7.94299i) q^{89} +(1.66270 - 1.89683i) q^{90} +(17.9618 - 6.12189i) q^{91} +(-1.36400 + 2.79014i) q^{92} +(-7.36023 - 7.13388i) q^{93} +(3.99583 + 13.0912i) q^{94} -1.37500i q^{95} +(-6.39749 - 7.42106i) q^{96} +(1.20110 - 0.693454i) q^{97} +(-8.99990 + 4.12332i) q^{98} +(4.31598 - 8.04568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9}+O(q^{10}) $ 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9	$ 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 11 q^{30} - 18 q^{32} - 18 q^{33} - 24 q^{34} - 38 q^{36} + 2 q^{37} + 33 q^{38} + 6 q^{40} + 6 q^{41} - 38 q^{42} - 13 q^{44} - 54 q^{45} + 10 q^{46} + 9 q^{48} - 28 q^{49} - 17 q^{50} - 27 q^{52} - 2 q^{53} - 39 q^{54} + 58 q^{56} + 6 q^{57} - 13 q^{58} - 31 q^{60} - 8 q^{64} - 100 q^{65} + 30 q^{66} - 18 q^{68} - 18 q^{69} - 19 q^{70} + 26 q^{72} + 30 q^{73} - 23 q^{74} - 2 q^{77} + 15 q^{78} + 3 q^{80} - 32 q^{81} - 18 q^{82} + 23 q^{84} - 50 q^{85} - 9 q^{86} + q^{88} - 102 q^{89} - 39 q^{90} + 28 q^{92} - 36 q^{93} + 63 q^{96} + 6 q^{97} + 21 q^{98}+O(q^{100}) $ 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9 - 18 * q^10 - 6 * q^12 + 18 * q^13 + 14 * q^14 + 14 * q^16 + 6 * q^17 - 10 * q^18 - 24 * q^20 + 4 * q^21 + 6 * q^22 - 6 * q^24 + 16 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 11 * q^30 - 18 * q^32 - 18 * q^33 - 24 * q^34 - 38 * q^36 + 2 * q^37 + 33 * q^38 + 6 * q^40 + 6 * q^41 - 38 * q^42 - 13 * q^44 - 54 * q^45 + 10 * q^46 + 9 * q^48 - 28 * q^49 - 17 * q^50 - 27 * q^52 - 2 * q^53 - 39 * q^54 + 58 * q^56 + 6 * q^57 - 13 * q^58 - 31 * q^60 - 8 * q^64 - 100 * q^65 + 30 * q^66 - 18 * q^68 - 18 * q^69 - 19 * q^70 + 26 * q^72 + 30 * q^73 - 23 * q^74 - 2 * q^77 + 15 * q^78 + 3 * q^80 - 32 * q^81 - 18 * q^82 + 23 * q^84 - 50 * q^85 - 9 * q^86 + q^88 - 102 * q^89 - 39 * q^90 + 28 * q^92 - 36 * q^93 + 63 * q^96 + 6 * q^97 + 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.412858	−	1.35261i	−0.291935	−	0.956438i
$2$	−0.412858	−	1.35261i	−0.291935	−	0.956438i
$3$	1.24372	+	1.20547i	0.718062	+	0.695979i
$3$	1.24372	+	1.20547i	0.718062	+	0.695979i
$4$	−1.65910	+	1.11687i	−0.829548	+	0.558435i
$5$	0.514884	−	0.297269i	0.230263	−	0.132943i	−0.380430	−	0.924810i	$-0.624224\pi$
$5$	0.514884	−	0.297269i	0.230263	−	0.132943i	0.610693	+	0.791867i	$0.290891\pi$
$6$	1.11705	−	2.17995i	0.456034	−	0.889962i
$7$	1.74201	−	1.99133i	0.658419	−	0.752651i
$7$	1.74201	−	1.99133i	0.658419	−	0.752651i
$8$	2.19566	+	1.78300i	0.776282	+	0.630386i
$9$	0.0936760	+	2.99854i	0.0312253	+	0.999512i
$10$	−0.614662	−	0.573707i	−0.194373	−	0.181422i
$11$	−2.63566	−	1.52170i	−0.794682	−	0.458810i	0.0469262	−	0.998898i	$-0.485057\pi$
$11$	−2.63566	−	1.52170i	−0.794682	−	0.458810i	−0.841608	+	0.540088i	$0.818391\pi$
$12$	−3.40981	−	0.610922i	−0.984326	−	0.176358i
$13$	6.21148	+	3.58620i	1.72275	+	0.994633i	0.913110	+	0.407712i	$0.133673\pi$
$13$	6.21148	+	3.58620i	1.72275	+	0.994633i	0.809644	+	0.586921i	$0.199660\pi$
$14$	−3.41269	−	1.53413i	−0.912080	−	0.410012i
$15$	0.998720	+	0.250960i	0.257868	+	0.0647975i
$16$	1.50521	−	3.70599i	0.376301	−	0.926497i
$17$	2.28182	−	1.31741i	0.553423	−	0.319519i	−0.197078	−	0.980388i	$-0.563145\pi$
$17$	2.28182	−	1.31741i	0.553423	−	0.319519i	0.750502	+	0.660869i	$0.229812\pi$
$18$	4.01717	−	1.36468i	0.946856	−	0.321657i
$19$	1.15636	−	2.00287i	0.265287	−	0.459490i	−0.702352	−	0.711830i	$-0.747867\pi$
$19$	1.15636	−	2.00287i	0.265287	−	0.459490i	0.967639	+	0.252340i	$0.0812000\pi$
$20$	−0.522233	+	1.06826i	−0.116775	+	0.238869i
$21$	4.56707	−	0.376706i	0.996616	−	0.0822040i
$22$	−0.970111	+	4.19326i	−0.206828	+	0.894007i
$23$	1.34481	−	0.776425i	0.280412	−	0.161896i	−0.353198	−	0.935549i	$-0.614906\pi$
$23$	1.34481	−	0.776425i	0.280412	−	0.161896i	0.633610	+	0.773653i	$0.281573\pi$
$24$	0.581426	+	4.86435i	0.118683	+	0.992932i
$25$	−2.32326	+	4.02401i	−0.464653	+	0.804802i
$26$	2.28627	−	9.88229i	0.448374	−	1.93808i
$27$	−3.49814	+	3.84226i	−0.673218	+	0.739444i
$28$	−0.666115	+	5.24941i	−0.125884	+	0.992045i
$29$	−3.50068	−	6.06335i	−0.650059	−	1.12594i	−0.983108	−	0.183026i	$-0.941411\pi$
$29$	−3.50068	−	6.06335i	−0.650059	−	1.12594i	0.333049	−	0.942910i	$-0.391923\pi$
$30$	−0.0728793	−	1.45449i	−0.0133059	−	0.265552i
$31$	−5.91792			−1.06289			−0.531445	−	0.847093i	$-0.678351\pi$
$31$	−5.91792			−1.06289			−0.531445	+	0.847093i	$0.678351\pi$
$32$	−5.63419	−	0.505907i	−0.995993	−	0.0894325i
$33$	−1.44366	−	5.06978i	−0.251309	−	0.882536i
$34$	−2.72401	−	2.54251i	−0.467164	−	0.436037i
$35$	0.304976	−	1.54315i	0.0515503	−	0.260840i
$36$	−3.50439	−	4.87024i	−0.584065	−	0.811707i
$37$	−2.74961	+	4.76246i	−0.452033	+	0.782944i	−0.998512	−	0.0545287i	$-0.982634\pi$
$37$	−2.74961	+	4.76246i	−0.452033	+	0.782944i	0.546479	+	0.837473i	$0.315968\pi$
$38$	−3.18651	−	0.737199i	−0.516921	−	0.119589i
$39$	3.40228	+	11.9480i	0.544800	+	1.91321i
$40$	1.66054	+	0.265339i	0.262554	+	0.0419537i
$41$	−3.27676	−	1.89184i	−0.511744	−	0.295456i	0.221806	−	0.975091i	$-0.428805\pi$
$41$	−3.27676	−	1.89184i	−0.511744	−	0.295456i	−0.733550	+	0.679635i	$0.762138\pi$
$42$	−2.39508	−	6.02192i	−0.369570	−	0.929203i
$43$	2.52490	−	1.45775i	0.385044	−	0.222305i	−0.294967	−	0.955508i	$-0.595309\pi$
$43$	2.52490	−	1.45775i	0.385044	−	0.222305i	0.680011	+	0.733202i	$0.261975\pi$
$44$	6.07236	−	0.419042i	0.915443	−	0.0631730i
$45$	0.939603	+	1.51605i	0.140068	+	0.226000i
$46$	−1.60541	−	1.49844i	−0.236705	−	0.220934i
$47$	−9.67847			−1.41175			−0.705875	−	0.708336i	$-0.749446\pi$
$47$	−9.67847			−1.41175			−0.705875	+	0.708336i	$0.749446\pi$
$48$	6.33952	−	2.79473i	0.915031	−	0.403384i
$49$	−0.930778	−	6.93784i	−0.132968	−	0.991120i
$50$	6.40208	+	1.48112i	0.905391	+	0.209462i
$51$	4.42605	+	1.11218i	0.619771	+	0.155737i
$52$	−14.3108	+	0.987559i	−1.98455	+	0.136950i
$53$	4.10505	+	7.11016i	0.563872	+	0.976655i	0.997154	+	0.0753965i	$0.0240223\pi$
$53$	4.10505	+	7.11016i	0.563872	+	0.976655i	−0.433282	+	0.901259i	$0.642644\pi$
$54$	6.64131	+	3.14531i	0.903768	+	0.428023i
$55$	−1.80941			−0.243981
$56$	7.37540	−	1.26627i	0.985580	−	0.169212i
$57$	3.85259	−	1.09705i	0.510288	−	0.145308i
$58$	−6.75605	+	7.23834i	−0.887113	+	0.950441i
$59$	−3.77001			−0.490814			−0.245407	−	0.969420i	$-0.578922\pi$
$59$	−3.77001			−0.490814			−0.245407	+	0.969420i	$0.578922\pi$
$60$	−1.93726	+	0.699074i	−0.250100	+	0.0902500i
$61$			2.67699i			0.342754i	0.985206	+	0.171377i	$0.0548216\pi$
$61$			2.67699i			0.342754i	−0.985206	+	0.171377i	$0.945178\pi$
$62$	2.44326	+	8.00462i	0.310294	+	1.01659i
$63$	6.13426	+	5.03695i	0.772844	+	0.634596i
$64$	1.64182	+	7.82971i	0.205228	+	0.978714i
$65$	4.26426			0.528916
$66$	−6.26141	+	4.04580i	−0.770726	+	0.498004i
$67$		−	8.92572i		−	1.09045i	−0.838290	−	0.545225i	$-0.816444\pi$
$67$		−	8.92572i		−	1.09045i	0.838290	−	0.545225i	$-0.183556\pi$
$68$	−2.31439	+	4.73421i	−0.280661	+	0.574107i
$69$	2.60852	+	0.655472i	0.314029	+	0.0789096i
$70$	−2.21319	+	0.224588i	−0.264527	+	0.0268434i
$71$			8.75743i			1.03932i	0.854374	+	0.519658i	$0.173941\pi$
$71$			8.75743i			1.03932i	−0.854374	+	0.519658i	$0.826059\pi$
$72$	−5.14071	+	6.75078i	−0.605839	+	0.795588i
$73$	−1.30083	+	0.751036i	−0.152251	+	0.0879022i	−0.574190	−	0.818722i	$-0.694683\pi$
$73$	−1.30083	+	0.751036i	−0.152251	+	0.0879022i	0.421939	+	0.906624i	$0.361350\pi$
$74$	7.57694	+	1.75292i	0.880802	+	0.203773i
$75$	−7.74032	+	2.20411i	−0.893775	+	0.254509i
$76$	0.318435	+	4.61446i	0.0365270	+	0.529315i
$77$	−7.62156	+	2.59765i	−0.868558	+	0.296029i
$78$	14.7563	−	9.53477i	1.67082	−	1.07960i
$79$			6.73276i			0.757495i	0.925500	+	0.378747i	$0.123645\pi$
$79$			6.73276i			0.757495i	−0.925500	+	0.378747i	$0.876355\pi$
$80$	−0.326667	−	2.35561i	−0.0365225	−	0.263365i
$81$	−8.98245	+	0.561782i	−0.998050	+	0.0624202i
$82$	−1.20608	+	5.21323i	−0.133189	+	0.575705i
$83$	−4.99378	−	8.64947i	−0.548138	−	0.949403i	−0.998402	−	0.0565077i	$-0.982003\pi$
$83$	−4.99378	−	8.64947i	−0.548138	−	0.949403i	0.450264	−	0.892895i	$-0.351330\pi$
$84$	−7.15647	+	5.72581i	−0.780835	+	0.624737i
$85$	0.783250	−	1.35663i	0.0849554	−	0.147147i
$86$	−3.01419	−	2.81336i	−0.325029	−	0.303372i
$87$	2.95534	−	11.7611i	0.316845	−	1.26092i
$88$	−3.07382	−	8.04052i	−0.327670	−	0.857122i
$89$	−13.7577	−	7.94299i	−1.45831	−	0.841955i	−0.459381	−	0.888239i	$-0.651929\pi$
$89$	−13.7577	−	7.94299i	−1.45831	−	0.841955i	−0.998928	+	0.0462839i	$0.985262\pi$
$90$	1.66270	−	1.89683i	0.175264	−	0.199943i
$91$	17.9618	−	6.12189i	1.88291	−	0.641748i
$92$	−1.36400	+	2.79014i	−0.142207	+	0.290892i
$93$	−7.36023	−	7.13388i	−0.763220	−	0.739749i
$94$	3.99583	+	13.0912i	0.412139	+	1.35025i
$95$		−	1.37500i		−	0.141072i
$96$	−6.39749	−	7.42106i	−0.652941	−	0.757409i
$97$	1.20110	−	0.693454i	0.121953	−	0.0704096i	−0.437783	−	0.899081i	$-0.644236\pi$
$97$	1.20110	−	0.693454i	0.121953	−	0.0704096i	0.559736	+	0.828671i	$0.310903\pi$
$98$	−8.99990	+	4.12332i	−0.909127	+	0.416518i
$99$	4.31598	−	8.04568i	0.433772	−	0.808621i
$100$	−0.639774	−	9.27100i	−0.0639774	−	0.927100i
$101$	6.87010	+	3.96646i	0.683601	+	0.394677i	0.801210	−	0.598383i	$-0.204190\pi$
$101$	6.87010	+	3.96646i	0.683601	+	0.394677i	−0.117610	+	0.993060i	$0.537523\pi$
$102$	−0.322981	−	6.44588i	−0.0319799	−	0.638238i
$103$	4.75698	+	8.23933i	0.468719	+	0.811846i	0.999361	−	0.0357508i	$-0.0113823\pi$
$103$	4.75698	+	8.23933i	0.468719	+	0.811846i	−0.530641	+	0.847596i	$0.678049\pi$
$104$	7.24409	+	18.9491i	0.710342	+	1.85812i
$105$	2.23953	−	1.55161i	0.218555	−	0.151421i
$106$	7.92245	−	8.48801i	0.769497	−	0.824428i
$107$	11.8104	+	6.81874i	1.14176	+	0.659193i	0.946865	−	0.321632i	$-0.104231\pi$
$107$	11.8104	+	6.81874i	1.14176	+	0.659193i	0.194891	+	0.980825i	$0.437565\pi$
$108$	1.51246	−	10.2817i	0.145536	−	0.989353i
$109$	−4.57329	−	7.92116i	−0.438041	−	0.758710i	0.559497	−	0.828832i	$-0.310994\pi$
$109$	−4.57329	−	7.92116i	−0.438041	−	0.758710i	−0.997538	+	0.0701225i	$0.977661\pi$
$110$	0.747031	+	2.44743i	0.0712266	+	0.233353i
$111$	−9.16075	+	2.60859i	−0.869500	+	0.247596i
$112$	−4.75775	−	9.45324i	−0.449565	−	0.893247i
$113$	3.57459	−	6.19136i	0.336269	−	0.582435i	−0.647459	−	0.762100i	$-0.724168\pi$
$113$	3.57459	−	6.19136i	0.336269	−	0.582435i	0.983728	+	0.179666i	$0.0575016\pi$
$114$	−3.07446	−	4.75812i	−0.287949	−	0.445639i
$115$	0.461613	−	0.799538i	0.0430457	−	0.0745573i
$116$	12.5799	+	6.14988i	1.16802	+	0.571002i
$117$	−10.1715	+	18.9613i	−0.940354	+	1.75297i
$118$	1.55648	+	5.09935i	0.143285	+	0.469433i
$119$	1.35157	−	6.83881i	0.123898	−	0.626912i
$120$	1.74539	+	2.33174i	0.159331	+	0.212858i
$121$	−0.868856	−	1.50490i	−0.0789869	−	0.136809i
$122$	3.62092	−	1.10522i	0.327823	−	0.100062i
$123$	−1.79481	−	6.30296i	−0.161833	−	0.568319i
$124$	9.81840	−	6.60954i	0.881718	−	0.593554i
$125$			5.73522i			0.512973i
$126$	4.28045	−	10.3768i	0.381332	−	0.924438i
$127$		−	11.0990i		−	0.984879i	−0.870347	−	0.492439i	$-0.836105\pi$
$127$		−	11.0990i		−	0.984879i	0.870347	−	0.492439i	$-0.163895\pi$
$128$	9.91269	−	5.45330i	0.876167	−	0.482008i
$129$	4.89755	+	1.23066i	0.431205	+	0.108354i
$130$	−1.76053	−	5.76787i	−0.154409	−	0.505876i
$131$	2.49572	+	4.32271i	0.218052	+	0.377677i	0.954212	−	0.299130i	$-0.0966965\pi$
$131$	2.49572	+	4.32271i	0.218052	+	0.377677i	−0.736160	+	0.676807i	$0.763363\pi$
$132$	8.05746	+	6.79889i	0.701312	+	0.591767i
$133$	−1.97398	−	5.79172i	−0.171166	−	0.502206i
$134$	−12.0730	+	3.68505i	−1.04295	+	0.318340i
$135$	−0.658956	+	3.01821i	−0.0567139	+	0.259766i
$136$	7.35905	+	1.17591i	0.631033	+	0.100833i
$137$	3.15468	−	5.46407i	0.269523	−	0.466827i	−0.699216	−	0.714911i	$-0.746467\pi$
$137$	3.15468	−	5.46407i	0.269523	−	0.466827i	0.968739	+	0.248084i	$0.0798007\pi$
$138$	−0.190351	−	3.79892i	−0.0162037	−	0.323386i
$139$	3.37429	−	5.84444i	0.286203	−	0.495719i	−0.686697	−	0.726944i	$-0.740940\pi$
$139$	3.37429	−	5.84444i	0.286203	−	0.495719i	0.972900	+	0.231225i	$0.0742733\pi$
$140$	1.21751	+	2.90085i	0.102899	+	0.245167i
$141$	−12.0373	−	11.6671i	−1.01372	−	0.982549i
$142$	11.8454	−	3.61557i	0.994042	−	0.303412i
$143$	−10.9142	−	18.9040i	−0.912695	−	1.58083i
$144$	11.2535	+	4.16625i	0.937796	+	0.347188i
$145$	−3.60489	−	2.08128i	−0.299369	−	0.172841i
$146$	1.55292	+	1.44945i	0.128520	+	0.119957i
$147$	7.20575	−	9.75076i	0.594320	−	0.804229i
$148$	−0.757180	−	10.9723i	−0.0622399	−	0.901921i
$149$	2.73106	+	4.73034i	0.223737	+	0.387525i	0.955940	−	0.293562i	$-0.0948408\pi$
$149$	2.73106	+	4.73034i	0.223737	+	0.387525i	−0.732202	+	0.681087i	$0.761508\pi$
$150$	6.17695	+	9.55963i	0.504346	+	0.780541i
$151$	−11.9298	−	6.88770i	−0.970837	−	0.560513i	−0.0713457	−	0.997452i	$-0.522729\pi$
$151$	−11.9298	−	6.88770i	−0.970837	−	0.560513i	−0.899491	+	0.436939i	$0.856063\pi$
$152$	6.11009	−	2.33583i	0.495594	−	0.189461i
$153$	4.16406	+	6.71872i	0.336644	+	0.543176i
$154$	6.66022	+	9.23653i	0.536696	+	0.744301i
$155$	−3.04704	+	1.75921i	−0.244744	+	0.141303i
$156$	−18.9891	−	16.0230i	−1.52034	−	1.28286i
$157$		−	11.7945i		−	0.941303i	−0.882319	−	0.470652i	$-0.844019\pi$
$157$		−	11.7945i		−	0.941303i	0.882319	−	0.470652i	$-0.155981\pi$
$158$	9.10678	−	2.77967i	0.724497	−	0.221139i
$159$	−3.46556	+	13.7916i	−0.274837	+	1.09374i
$160$	−3.05134	+	1.41438i	−0.241230	+	0.111817i
$161$	0.796555	−	4.03050i	0.0627774	−	0.317648i
$162$	4.46834	+	11.9178i	0.351066	+	0.936351i
$163$	−2.95281	−	1.70481i	−0.231282	−	0.133531i	0.379881	−	0.925035i	$-0.375965\pi$
$163$	−2.95281	−	1.70481i	−0.231282	−	0.133531i	−0.611163	+	0.791505i	$0.709298\pi$
$164$	7.54940	−	0.520970i	0.589509	−	0.0406809i
$165$	−2.25040	−	2.18120i	−0.175194	−	0.169806i
$166$	−9.63763	+	10.3256i	−0.748025	+	0.801424i
$167$	−6.47738	+	11.2191i	−0.501235	+	0.868164i	0.498764	+	0.866738i	$0.333787\pi$
$167$	−6.47738	+	11.2191i	−0.501235	+	0.868164i	−0.999999	+	0.00142608i	$0.999546\pi$
$168$	10.6994	+	7.31596i	0.825475	+	0.564439i
$169$	19.2217	+	33.2929i	1.47859	+	2.56099i
$170$	−2.15836	−	0.499335i	−0.165538	−	0.0382973i
$171$	6.11401	+	3.27976i	0.467550	+	0.250810i
$172$	−2.56094	+	5.23854i	−0.195270	+	0.399435i
$173$			1.24744i			0.0948408i	0.998875	+	0.0474204i	$0.0151000\pi$
$173$			1.24744i			0.0948408i	−0.998875	+	0.0474204i	$0.984900\pi$
$174$	−17.1282	+	0.858237i	−1.29849	+	0.0650628i
$175$	3.96597	+	11.6363i	0.299799	+	0.879618i
$176$	−9.60662	+	7.47726i	−0.724126	+	0.563620i
$177$	−4.68884	−	4.54464i	−0.352435	−	0.341596i
$178$	−5.06380	+	21.8881i	−0.379548	+	1.64058i
$179$	−0.0914691	+	0.0528097i	−0.00683672	+	0.00394718i	−0.503414	−	0.864045i	$-0.667923\pi$
$179$	−0.0914691	+	0.0528097i	−0.00683672	+	0.00394718i	0.496578	+	0.867992i	$0.334590\pi$
$180$	−3.25213	−	1.46586i	−0.242399	−	0.109259i
$181$		−	22.3860i		−	1.66394i	−0.554821	−	0.831970i	$-0.687213\pi$
$181$		−	22.3860i		−	1.66394i	0.554821	−	0.831970i	$-0.312787\pi$
$182$	−15.6962	−	21.7678i	−1.16348	−	1.61354i
$183$	−3.22704	+	3.32943i	−0.238550	+	0.246118i
$184$	4.33710	+	0.693028i	0.319735	+	0.0510907i
$185$			3.26949i			0.240378i
$186$	−6.61062	+	12.9008i	−0.484714	+	0.945931i
$187$	−8.01882			−0.586394
$188$	16.0575	−	10.8096i	1.17111	−	0.788370i
$189$	1.55739	+	13.6592i	0.113284	+	0.993563i
$190$	−1.85983	+	0.567678i	−0.134926	+	0.0411837i
$191$			21.6364i			1.56555i	0.622302	+	0.782777i	$0.286198\pi$
$191$			21.6364i			1.56555i	−0.622302	+	0.782777i	$0.713802\pi$
$192$	−7.39653	+	11.7171i	−0.533799	+	0.845612i
$193$	1.91328			0.137721			0.0688605	−	0.997626i	$-0.478064\pi$
$193$	1.91328			0.137721			0.0688605	+	0.997626i	$0.478064\pi$
$194$	−1.43385	−	1.33832i	−0.102945	−	0.0960856i
$195$	5.30354	+	5.14044i	0.379794	+	0.368115i
$196$	9.29291	+	10.4710i	0.663780	+	0.747928i
$197$	17.4136			1.24067			0.620334	−	0.784337i	$-0.286997\pi$
$197$	17.4136			1.24067			0.620334	+	0.784337i	$0.286997\pi$
$198$	−12.6645	−	2.51610i	−0.900029	−	0.178812i
$199$	1.77704	+	3.07792i	0.125971	+	0.218188i	0.922112	−	0.386923i	$-0.126462\pi$
$199$	1.77704	+	3.07792i	0.125971	+	0.218188i	−0.796141	+	0.605111i	$0.793129\pi$
$200$	−12.2759	+	4.69297i	−0.868037	+	0.331843i
$201$	10.7597	−	11.1011i	0.758931	−	0.783011i
$202$	2.52868	−	10.9301i	0.177918	−	0.769042i
$203$	−18.1723	−	3.59144i	−1.27545	−	0.252070i
$204$	−8.58541	+	3.09810i	−0.601099	+	0.216910i
$205$	−2.24954			−0.157114
$206$	9.18063	−	9.83600i	0.639645	−	0.685307i
$207$	2.45411	+	3.95972i	0.170573	+	0.275220i
$208$	22.6400	−	17.6217i	1.56980	−	1.22185i
$209$	−6.09554	+	3.51926i	−0.421638	+	0.243433i
$210$	−3.02332	−	2.38861i	−0.208629	−	0.164830i
$211$	2.88477	+	1.66552i	0.198596	+	0.114659i	0.596000	−	0.802984i	$-0.296756\pi$
$211$	2.88477	+	1.66552i	0.198596	+	0.114659i	−0.397405	+	0.917643i	$0.630089\pi$
$212$	−14.7518	−	7.21163i	−1.01316	−	0.495297i
$213$	−10.5568	+	10.8918i	−0.723342	+	0.746293i
$214$	4.34707	−	18.7900i	0.297159	−	1.28446i
$215$	0.866688	−	1.50115i	0.0591076	−	0.102377i
$216$	−14.5315	+	2.19910i	−0.988742	+	0.149630i
$217$	−10.3091	+	11.7845i	−0.699827	+	0.799985i
$218$	−8.82611	+	9.45618i	−0.597780	+	0.640453i
$219$	−2.52322	−	0.634039i	−0.170504	−	0.0428444i
$220$	3.00199	−	2.02088i	0.202394	−	0.136248i
$221$	18.8980			1.27122
$222$	7.31049	+	11.3139i	0.490648	+	0.759341i
$223$	6.52029	+	11.2935i	0.436631	+	0.756267i	0.997427	−	0.0716868i	$-0.0228382\pi$
$223$	6.52029	+	11.2935i	0.436631	+	0.756267i	−0.560796	+	0.827954i	$0.689505\pi$
$224$	−10.8223	+	10.3382i	−0.723092	+	0.690751i
$225$	−12.2838	−	6.58944i	−0.818918	−	0.439296i
$226$	−9.85028	−	2.27886i	−0.655231	−	0.151588i
$227$	4.72639	−	8.18636i	0.313702	−	0.543347i	−0.665459	−	0.746435i	$-0.731764\pi$
$227$	4.72639	−	8.18636i	0.313702	−	0.543347i	0.979161	+	0.203087i	$0.0650974\pi$
$228$	−5.16656	+	6.12296i	−0.342164	+	0.405503i
$229$	12.2899	−	7.09560i	0.812142	−	0.468890i	−0.0355574	−	0.999368i	$-0.511321\pi$
$229$	12.2899	−	7.09560i	0.812142	−	0.468890i	0.847699	+	0.530477i	$0.177987\pi$
$230$	−1.27204	−	0.294287i	−0.0838759	−	0.0194047i
$231$	−12.6105	−	5.95684i	−0.829709	−	0.391931i
$232$	3.12466	−	19.5547i	0.205144	−	1.28383i
$233$	−12.9100	+	22.3607i	−0.845761	+	1.46490i	0.0391981	+	0.999231i	$0.487520\pi$
$233$	−12.9100	+	22.3607i	−0.845761	+	1.46490i	−0.884959	+	0.465669i	$0.845814\pi$
$234$	29.8466	+	5.92972i	1.95113	+	0.387638i
$235$	−4.98329	+	2.87710i	−0.325074	+	0.187682i
$236$	6.25482	−	4.21061i	0.407154	−	0.274087i
$237$	−8.11615	+	8.37366i	−0.527201	+	0.543928i
$238$	−9.80823	+	0.995313i	−0.635773	+	0.0645165i
$239$	18.8003	+	10.8544i	1.21609	+	0.702110i	0.964079	−	0.265614i	$-0.0855746\pi$
$239$	18.8003	+	10.8544i	1.21609	+	0.702110i	0.252011	+	0.967724i	$0.418908\pi$
$240$	2.43333	−	3.32350i	0.157071	−	0.214531i
$241$	−3.26469	−	1.88487i	−0.210297	−	0.121415i	0.391152	−	0.920326i	$-0.372077\pi$
$241$	−3.26469	−	1.88487i	−0.210297	−	0.121415i	−0.601450	+	0.798911i	$0.705410\pi$
$242$	−1.67683	+	1.79653i	−0.107791	+	0.115485i
$243$	−11.8489	−	10.1294i	−0.760105	−	0.649801i
$244$	−2.98985	−	4.44139i	−0.191406	−	0.284331i
$245$	−2.54165	−	3.29549i	−0.162380	−	0.210541i
$246$	−7.78443	+	5.02990i	−0.496317	+	0.320695i
$247$	14.3654	−	8.29387i	0.914049	−	0.527726i
$248$	−12.9937	−	10.5516i	−0.825102	−	0.670030i
$249$	4.21584	−	16.7774i	0.267168	−	1.06322i
$250$	7.75750	−	2.36783i	0.490627	−	0.149755i
$251$	13.8993			0.877316			0.438658	−	0.898654i	$-0.355454\pi$
$251$	13.8993			0.877316			0.438658	+	0.898654i	$0.355454\pi$
$252$	−15.8029	−	1.50563i	−0.995492	−	0.0948457i
$253$	−4.72594			−0.297118
$254$	−15.0126	+	4.58232i	−0.941976	+	0.287520i
$255$	2.60952	−	0.743080i	0.163415	−	0.0465335i
$256$	−11.4687	−	11.1566i	−0.716795	−	0.697284i
$257$	3.71735	−	2.14621i	0.231882	−	0.133877i	−0.379558	−	0.925168i	$-0.623924\pi$
$257$	3.71735	−	2.14621i	0.231882	−	0.133877i	0.611440	+	0.791291i	$0.290591\pi$
$258$	−0.357387	−	7.13255i	−0.0222500	−	0.444053i
$259$	4.69377	+	13.7716i	0.291657	+	0.855728i
$260$	−7.07482	+	4.76262i	−0.438762	+	0.295365i
$261$	17.8532	−	11.0649i	1.10509	−	0.684900i
$262$	4.81656	−	5.16039i	0.297568	−	0.318810i
$263$	15.1754	+	8.76154i	0.935758	+	0.540260i	0.888628	−	0.458629i	$-0.151659\pi$
$263$	15.1754	+	8.76154i	0.935758	+	0.540260i	0.0471298	+	0.998889i	$0.484993\pi$
$264$	5.86965	−	13.7056i	0.361252	−	0.843518i
$265$	4.22725	+	2.44061i	0.259678	+	0.149925i
$266$	−7.01895	+	5.06118i	−0.430360	+	0.310321i
$267$	−7.53562	−	26.4633i	−0.461173	−	1.61953i
$268$	9.96886	+	14.8086i	0.608945	+	0.904581i
$269$	3.89531	−	2.24896i	0.237501	−	0.137122i	−0.376526	−	0.926406i	$-0.622882\pi$
$269$	3.89531	−	2.24896i	0.237501	−	0.137122i	0.614028	+	0.789284i	$0.289548\pi$
$270$	4.35451	−	0.354782i	0.265007	−	0.0215913i
$271$	−10.3784	+	17.9759i	−0.630442	+	1.09196i	0.357019	+	0.934097i	$0.383793\pi$
$271$	−10.3784	+	17.9759i	−0.630442	+	1.09196i	−0.987461	+	0.157861i	$0.949540\pi$
$272$	−1.44770	−	10.4394i	−0.0877796	−	0.632981i
$273$	29.7192	+	14.0385i	1.79869	+	0.849649i
$274$	−8.69318	−	2.01116i	−0.525174	−	0.121499i
$275$	12.2467	−	7.07062i	0.738502	−	0.426374i
$276$	−5.05987	+	1.82588i	−0.304568	+	0.109905i
$277$	6.85236	−	11.8686i	0.411718	−	0.713117i	−0.583359	−	0.812214i	$-0.698262\pi$
$277$	6.85236	−	11.8686i	0.411718	−	0.713117i	0.995078	+	0.0990971i	$0.0315954\pi$
$278$	−9.29834	−	2.15117i	−0.557677	−	0.129018i
$279$	−0.554367	−	17.7451i	−0.0331891	−	1.06237i
$280$	3.42106	−	2.84446i	0.204447	−	0.169989i
$281$	−1.27529	−	2.20886i	−0.0760773	−	0.131770i	0.825477	−	0.564436i	$-0.190906\pi$
$281$	−1.27529	−	2.20886i	−0.0760773	−	0.131770i	−0.901554	+	0.432666i	$0.857573\pi$
$282$	−10.8113	+	21.0986i	−0.643806	+	1.25640i
$283$	−8.59795			−0.511095			−0.255547	−	0.966797i	$-0.582256\pi$
$283$	−8.59795			−0.511095			−0.255547	+	0.966797i	$0.582256\pi$
$284$	−9.78091	−	14.5294i	−0.580390	−	0.862163i
$285$	1.65752	−	1.71011i	0.0981830	−	0.101298i
$286$	−21.0637	+	22.5674i	−1.24552	+	1.33444i
$287$	−9.47543	+	3.22950i	−0.559317	+	0.190631i
$288$	0.989192	−	16.9417i	0.0582887	−	0.998300i
$289$	−5.02886	+	8.71023i	−0.295815	+	0.512367i
$290$	−1.32685	+	5.73527i	−0.0779155	+	0.336787i
$291$	2.32977	+	0.585427i	0.136573	+	0.0343184i
$292$	1.31940	−	2.69890i	0.0772120	−	0.157941i
$293$	−17.2244	−	9.94449i	−1.00626	−	0.580963i	−0.0961641	−	0.995365i	$-0.530657\pi$
$293$	−17.2244	−	9.94449i	−1.00626	−	0.580963i	−0.910094	+	0.414402i	$0.863991\pi$
$294$	−16.1639	−	5.72087i	−0.942698	−	0.333648i
$295$	−1.94112	+	1.12071i	−0.113016	+	0.0652500i
$296$	−14.5287	+	5.55418i	−0.844462	+	0.322830i
$297$	15.0667	−	4.80378i	0.874259	−	0.278744i
$298$	5.27076	−	5.64702i	0.305327	−	0.327123i
$299$	11.1377			0.644107
$300$	10.3802	−	12.3018i	0.599303	−	0.710242i
$301$	1.49555	−	7.56733i	0.0862020	−	0.436174i
$302$	−4.39103	+	18.9800i	−0.252675	+	1.09218i
$303$	3.76303	+	13.2149i	0.216180	+	0.759175i
$304$	−5.68207	−	7.30019i	−0.325889	−	0.418695i
$305$	0.795786	+	1.37834i	0.0455665	+	0.0789236i
$306$	7.36863	−	8.40622i	0.421237	−	0.480551i
$307$	−26.7987			−1.52948			−0.764742	−	0.644337i	$-0.777133\pi$
$307$	−26.7987			−1.52948			−0.764742	+	0.644337i	$0.777133\pi$
$308$	9.74368	−	12.8220i	0.555198	−	0.730604i
$309$	−4.01593	+	15.9818i	−0.228458	+	0.909174i
$310$	3.63752	+	3.39515i	0.206597	+	0.192832i
$311$	−4.79353			−0.271816			−0.135908	−	0.990721i	$-0.543395\pi$
$311$	−4.79353			−0.271816			−0.135908	+	0.990721i	$0.543395\pi$
$312$	−13.8330	+	32.3000i	−0.783141	+	1.82862i
$313$			8.81253i			0.498113i	0.968489	+	0.249057i	$0.0801206\pi$
$313$			8.81253i			0.498113i	−0.968489	+	0.249057i	$0.919879\pi$
$314$	−15.9533	+	4.86945i	−0.900299	+	0.274799i
$315$	4.65576	+	0.769926i	0.262322	+	0.0433804i
$316$	−7.51961	−	11.1703i	−0.423011	−	0.628378i
$317$	18.1124			1.01729			0.508646	−	0.860976i	$-0.330146\pi$
$317$	18.1124			1.01729			0.508646	+	0.860976i	$0.330146\pi$
$318$	20.0854	−	1.00641i	1.12633	−	0.0564365i
$319$			21.3079i			1.19301i
$320$	3.17288	+	3.54333i	0.177369	+	0.198078i
$321$	6.46903	+	22.7177i	0.361066	+	1.26798i
$322$	−5.78054	+	0.586594i	−0.322137	+	0.0326896i
$323$		−	6.09360i		−	0.339057i
$324$	14.2753	−	10.9643i	0.793073	−	0.609126i
$325$	−28.8618	+	16.6634i	−1.60096	+	0.924318i
$326$	−1.08684	+	4.69784i	−0.0601947	+	0.260189i
$327$	3.86085	−	15.3647i	0.213506	−	0.849668i
$328$	−3.82150	−	9.99629i	−0.211007	−	0.551953i
$329$	−16.8600	+	19.2730i	−0.929523	+	1.06256i
$330$	−2.02121	+	3.94444i	−0.111264	+	0.217134i
$331$		−	7.76983i		−	0.427068i	−0.976936	−	0.213534i	$-0.931503\pi$
$331$		−	7.76983i		−	0.427068i	0.976936	−	0.213534i	$-0.0684975\pi$
$332$	17.9455	+	8.77292i	0.984887	+	0.481477i
$333$	−14.5380	−	7.79867i	−0.796677	−	0.427365i
$334$	17.8493	+	4.12944i	0.976673	+	0.225953i
$335$	−2.65334	−	4.59571i	−0.144967	−	0.251091i
$336$	5.47830	−	17.4925i	0.298866	−	0.954295i
$337$	3.96613	−	6.86954i	0.216049	−	0.374208i	−0.737548	−	0.675295i	$-0.764016\pi$
$337$	3.96613	−	6.86954i	0.216049	−	0.374208i	0.953597	+	0.301087i	$0.0973496\pi$
$338$	37.0964	−	39.7446i	2.01778	−	2.16182i
$339$	11.9093	−	3.39126i	0.646824	−	0.184188i
$340$	0.215689	+	3.12557i	0.0116974	+	0.169508i
$341$	15.5976	+	9.00530i	0.844659	+	0.487664i
$342$	1.91202	−	9.62394i	0.103390	−	0.520403i
$343$	−15.4370	−	10.2323i	−0.833517	−	0.552494i
$344$	8.14299	+	1.30117i	0.439041	+	0.0701546i
$345$	1.53794	−	0.437939i	0.0827998	−	0.0235778i
$346$	1.68729	−	0.515014i	0.0907094	−	0.0276873i
$347$		−	0.835385i		−	0.0448458i	−0.999749	−	0.0224229i	$-0.992862\pi$
$347$		−	0.835385i		−	0.0448458i	0.999749	−	0.0224229i	$-0.00713803\pi$
$348$	8.23239	+	22.8135i	0.441302	+	1.22293i
$349$	13.8892	−	8.01895i	0.743473	−	0.429244i	−0.0798577	−	0.996806i	$-0.525447\pi$
$349$	13.8892	−	8.01895i	0.743473	−	0.429244i	0.823331	+	0.567562i	$0.192113\pi$
$350$	14.1019	−	10.1685i	0.753779	−	0.543530i
$351$	−35.5078	+	11.3211i	−1.89527	+	0.604275i
$352$	14.0800	+	9.90694i	0.750465	+	0.528042i
$353$	−11.2880	−	6.51711i	−0.600798	−	0.346871i	0.168558	−	0.985692i	$-0.446089\pi$
$353$	−11.2880	−	6.51711i	−0.600798	−	0.346871i	−0.769355	+	0.638821i	$0.779422\pi$
$354$	−4.21130	+	8.21845i	−0.223828	+	0.436806i
$355$	2.60331	+	4.50906i	0.138169	+	0.239316i
$356$	31.6966	−	2.18732i	1.67992	−	0.115928i
$357$	9.92496	−	6.87628i	0.525285	−	0.363931i
$358$	0.109195	+	0.101919i	0.00577111	+	0.00538658i
$359$	−6.68926	−	3.86205i	−0.353046	−	0.203831i	0.312980	−	0.949760i	$-0.398673\pi$
$359$	−6.68926	−	3.86205i	−0.353046	−	0.203831i	−0.666026	+	0.745929i	$0.732006\pi$
$360$	−0.640075	+	5.00404i	−0.0337349	+	0.263736i
$361$	6.82567	+	11.8224i	0.359246	+	0.622232i
$362$	−30.2795	+	9.24224i	−1.59146	+	0.485761i
$363$	0.733504	−	2.91906i	0.0384990	−	0.153211i
$364$	−22.9630	+	30.2178i	−1.20359	+	1.58384i
$365$	−0.446519	+	0.773394i	−0.0233719	+	0.0404813i
$366$	5.83572	+	2.99034i	0.305038	+	0.156307i
$367$	−0.426271	+	0.738323i	−0.0222512	+	0.0385402i	−0.876937	−	0.480606i	$-0.840417\pi$
$367$	−0.426271	+	0.738323i	−0.0222512	+	0.0385402i	0.854685	+	0.519146i	$0.173750\pi$
$368$	−0.853211	−	6.15252i	−0.0444767	−	0.320722i
$369$	5.36579	−	10.0027i	0.279332	−	0.520720i
$370$	4.42234	−	1.34983i	0.229906	−	0.0701745i
$371$	21.3097	+	4.21148i	1.10635	+	0.218649i
$372$	20.1789	+	3.61539i	1.04623	+	0.187449i
$373$	1.16495	+	2.01776i	0.0603190	+	0.104476i	0.894608	−	0.446852i	$-0.147455\pi$
$373$	1.16495	+	2.01776i	0.0603190	+	0.104476i	−0.834289	+	0.551327i	$0.814122\pi$
$374$	3.31063	+	10.8463i	0.171189	+	0.560850i
$375$	−6.91364	+	7.13300i	−0.357019	+	0.368347i
$376$	−21.2506	−	17.2567i	−1.09592	−	0.889947i
$377$		−	50.2165i		−	2.58628i
$378$	17.8326	−	7.74586i	0.917210	−	0.398404i
$379$			28.9056i			1.48478i	0.669968	+	0.742390i	$0.266308\pi$
$379$			28.9056i			1.48478i	−0.669968	+	0.742390i	$0.733692\pi$
$380$	1.53569	+	2.28125i	0.0787793	+	0.117026i
$381$	13.3796	−	13.8041i	0.685455	−	0.707204i
$382$	29.2656	−	8.93275i	1.49736	−	0.457039i
$383$	8.89994	+	15.4151i	0.454766	+	0.787677i	0.998675	−	0.0514671i	$-0.0163897\pi$
$383$	8.89994	+	15.4151i	0.454766	+	0.787677i	−0.543909	+	0.839144i	$0.683056\pi$
$384$	18.9024	+	5.16709i	0.964610	+	0.263682i
$385$	−3.15202	+	3.60314i	−0.160642	+	0.183633i
$386$	−0.789913	−	2.58792i	−0.0402055	−	0.131722i
$387$	4.60765	+	7.43446i	0.234220	+	0.377915i
$388$	−1.21824	+	2.49198i	−0.0618468	+	0.126511i
$389$	−12.8152	+	22.1966i	−0.649757	+	1.12541i	0.333424	+	0.942777i	$0.391796\pi$
$389$	−12.8152	+	22.1966i	−0.649757	+	1.12541i	−0.983181	+	0.182635i	$0.941537\pi$
$390$	4.76340	−	9.29588i	0.241204	−	0.470715i
$391$	2.04574	−	3.54333i	0.103458	−	0.179194i
$392$	10.3265	−	16.8927i	0.521567	−	0.853210i
$393$	−2.10693	+	8.38476i	−0.106281	+	0.422955i
$394$	−7.18935	−	23.5538i	−0.362194	−	1.18662i
$395$	2.00144	+	3.46659i	0.100703	+	0.174423i
$396$	1.82535	+	18.1689i	0.0917272	+	0.913024i
$397$	5.33703	+	3.08134i	0.267858	+	0.154648i	0.627914	−	0.778283i	$-0.283909\pi$
$397$	5.33703	+	3.08134i	0.267858	+	0.154648i	−0.360056	+	0.932931i	$0.617242\pi$
$398$	3.42956	−	3.67438i	0.171908	−	0.184180i
$399$	4.52667	−	9.58286i	0.226617	−	0.479743i
$400$	11.4159	+	14.6669i	0.570797	+	0.733347i
$401$	−0.135983	−	0.235529i	−0.00679066	−	0.0117618i	0.862610	−	0.505869i	$-0.168828\pi$
$401$	−0.135983	−	0.235529i	−0.00679066	−	0.0117618i	−0.869401	+	0.494108i	$0.835495\pi$
$402$	−19.4577	−	9.97049i	−0.970460	−	0.497283i
$403$	−36.7590	−	21.2228i	−1.83110	−	1.05718i
$404$	−15.8282	+	1.09227i	−0.787481	+	0.0543426i
$405$	−4.45792	+	2.95945i	−0.221516	+	0.147056i
$406$	2.64478	+	26.0628i	0.131258	+	1.29348i
$407$	14.4941	−	8.36816i	0.718445	−	0.414794i
$408$	7.73507	+	10.3336i	0.382943	+	0.511590i
$409$		−	6.53526i		−	0.323148i	−0.986861	−	0.161574i	$-0.948343\pi$
$409$		−	6.53526i		−	0.323148i	0.986861	−	0.161574i	$-0.0516570\pi$
$410$	0.928738	+	3.04274i	0.0458671	+	0.150270i
$411$	10.5103	−	2.99289i	0.518436	−	0.147628i
$412$	−17.0946	−	8.35693i	−0.842188	−	0.411716i
$413$	−6.56741	+	7.50733i	−0.323161	+	0.369412i
$414$	4.34275	−	4.95426i	0.213435	−	0.243488i
$415$	−5.14243	−	2.96899i	−0.252432	−	0.145742i
$416$	−33.1824	−	23.3478i	−1.62690	−	1.14472i
$417$	11.2420	−	3.20123i	0.550522	−	0.156765i
$418$	7.27678	+	6.79193i	0.355919	+	0.332204i
$419$	18.6788	−	32.3526i	0.912519	−	1.58053i	0.102026	−	0.994782i	$-0.467468\pi$
$419$	18.6788	−	32.3526i	0.912519	−	1.58053i	0.810493	−	0.585748i	$-0.199199\pi$
$420$	−1.98265	+	5.07552i	−0.0967436	+	0.247660i
$421$	8.81289	+	15.2644i	0.429514	+	0.743940i	0.996830	−	0.0795601i	$-0.0253516\pi$
$421$	8.81289	+	15.2644i	0.429514	+	0.743940i	−0.567316	+	0.823500i	$0.692018\pi$
$422$	1.06180	−	4.58958i	0.0516875	−	0.223417i
$423$	−0.906641	−	29.0213i	−0.0440824	−	1.41106i
$424$	−3.66412	+	22.9308i	−0.177945	+	1.11362i
$425$			12.2428i			0.593862i
$426$	19.0908	+	9.78250i	0.924952	+	0.473964i
$427$	5.33077	+	4.66336i	0.257974	+	0.225676i
$428$	−27.2103	+	1.87773i	−1.31526	+	0.0907634i
$429$	9.21401	−	36.6681i	0.444857	−	1.77035i
$430$	−2.38828	−	0.552529i	−0.115173	−	0.0266453i
$431$	26.8406	−	15.4964i	1.29286	−	0.746436i	0.313703	−	0.949521i	$-0.398430\pi$
$431$	26.8406	−	15.4964i	1.29286	−	0.746436i	0.979161	+	0.203085i	$0.0650969\pi$
$432$	8.97396	+	18.7475i	0.431760	+	0.901989i
$433$		−	20.1669i		−	0.969161i	−0.874747	−	0.484581i	$-0.838972\pi$
$433$		−	20.1669i		−	0.969161i	0.874747	−	0.484581i	$-0.161028\pi$
$434$	20.1960	+	9.07883i	0.969440	+	0.435798i
$435$	−1.97454	−	6.93412i	−0.0946719	−	0.332465i
$436$	16.4344	+	8.03422i	0.787066	+	0.384769i
$437$		−	3.59130i		−	0.171795i
$438$	0.184127	+	3.67470i	0.00879791	+	0.175584i
$439$	1.31016			0.0625304			0.0312652	−	0.999511i	$-0.490046\pi$
$439$	1.31016			0.0625304			0.0312652	+	0.999511i	$0.490046\pi$
$440$	−3.97285	−	3.22619i	−0.189398	−	0.153802i
$441$	20.7162	−	3.44088i	0.986485	−	0.163852i
$442$	−7.80219	−	25.5616i	−0.371112	−	1.21584i
$443$		−	2.54555i		−	0.120943i	−0.998170	−	0.0604713i	$-0.980740\pi$
$443$		−	2.54555i		−	0.120943i	0.998170	−	0.0604713i	$-0.0192604\pi$
$444$	12.2851	−	14.5593i	0.583026	−	0.690952i
$445$	−9.44481			−0.447727
$446$	12.5837	−	13.4820i	0.595855	−	0.638391i
$447$	−2.30562	+	9.17544i	−0.109052	+	0.433983i
$448$	18.4516	+	10.3701i	0.871757	+	0.489939i
$449$	−30.0500			−1.41815			−0.709073	−	0.705135i	$-0.750886\pi$
$449$	−30.0500			−1.41815			−0.709073	+	0.705135i	$0.750886\pi$
$450$	−3.84147	+	19.3356i	−0.181089	+	0.911490i
$451$	5.75762	+	9.97249i	0.271116	+	0.469586i
$452$	0.984361	+	14.2644i	0.0463004	+	0.670942i
$453$	−6.53445	−	22.9475i	−0.307015	−	1.07817i
$454$	−13.0243	−	3.01316i	−0.611259	−	0.141415i
$455$	7.42839	−	8.49154i	0.348249	−	0.398089i
$456$	10.4150	+	4.46042i	0.487728	+	0.208878i
$457$	−38.3846			−1.79556			−0.897779	−	0.440447i	$-0.854820\pi$
$457$	−38.3846			−1.79556			−0.897779	+	0.440447i	$0.854820\pi$
$458$	−14.6716	−	13.6940i	−0.685557	−	0.639878i
$459$	−2.92031	+	13.3759i	−0.136308	+	0.624332i
$460$	0.127118	+	1.84207i	0.00592690	+	0.0858871i
$461$	−29.8694	+	17.2451i	−1.39116	+	0.803186i	−0.993444	−	0.114323i	$-0.963530\pi$
$461$	−29.8694	+	17.2451i	−1.39116	+	0.803186i	−0.397715	+	0.917509i	$0.630197\pi$
$462$	−2.85093	+	19.5164i	−0.132637	+	0.907983i
$463$	−23.3117	−	13.4590i	−1.08339	−	0.625493i	−0.151578	−	0.988445i	$-0.548435\pi$
$463$	−23.3117	−	13.4590i	−1.08339	−	0.625493i	−0.931808	+	0.362952i	$0.881769\pi$
$464$	−27.7399	+	3.84688i	−1.28779	+	0.178587i
$465$	−5.91034	−	1.48516i	−0.274086	−	0.0688726i
$466$	35.5753	+	8.23034i	1.64799	+	0.381263i
$467$	−10.1757	+	17.6248i	−0.470874	+	0.815577i	−0.999445	−	0.0333119i	$-0.989395\pi$
$467$	−10.1757	+	17.6248i	−0.470874	+	0.815577i	0.528571	+	0.848889i	$0.322728\pi$
$468$	−4.30181	−	42.8189i	−0.198851	−	1.97930i
$469$	−17.7740	−	15.5487i	−0.820729	−	0.717973i
$470$	5.94899	+	5.55260i	0.274406	+	0.256123i
$471$	14.2179	−	14.6690i	0.655128	−	0.675914i
$472$	−8.27766	−	6.72193i	−0.381010	−	0.309402i
$473$	−8.87305			−0.407983
$474$	14.6771	+	7.52084i	0.674142	+	0.345444i
$475$	5.37305	+	9.30640i	0.246533	+	0.427007i
$476$	5.39567	+	12.8558i	0.247310	+	0.589243i
$477$	−20.9355	+	12.9752i	−0.958572	+	0.594094i
$478$	6.91985	−	29.9108i	0.316506	−	1.36809i
$479$	1.09961	−	1.90458i	0.0502424	−	0.0870225i	−0.839810	−	0.542880i	$-0.817334\pi$
$479$	1.09961	−	1.90458i	0.0502424	−	0.0870225i	0.890053	+	0.455857i	$0.150667\pi$
$480$	−5.50001	−	1.91921i	−0.251040	−	0.0875997i
$481$	−34.1583	+	19.7213i	−1.55748	+	0.899214i
$482$	−1.20164	+	5.19403i	−0.0547331	+	0.236582i
$483$	5.84934	−	4.05258i	0.266154	−	0.184399i
$484$	3.12230	+	1.52638i	0.141923	+	0.0693809i
$485$	0.412284	−	0.714098i	0.0187209	−	0.0324255i
$486$	−8.80920	+	20.2089i	−0.399593	+	0.916692i
$487$	16.7601	−	9.67646i	0.759473	−	0.438482i	−0.0696332	−	0.997573i	$-0.522183\pi$
$487$	16.7601	−	9.67646i	0.759473	−	0.438482i	0.829107	+	0.559090i	$0.188850\pi$
$488$	−4.77308	+	5.87776i	−0.216067	+	0.266074i
$489$	−1.61737	−	5.67983i	−0.0731401	−	0.256851i
$490$	−3.40817	+	4.79842i	−0.153966	+	0.216771i
$491$	−20.0539	−	11.5781i	−0.905020	−	0.522514i	−0.0261947	−	0.999657i	$-0.508339\pi$
$491$	−20.0539	−	11.5781i	−0.905020	−	0.522514i	−0.878826	+	0.477143i	$0.841672\pi$
$492$	10.0173	+	8.45265i	0.451617	+	0.381075i
$493$	−15.9758	−	9.22366i	−0.719516	−	0.415413i
$494$	−17.1492	−	16.0066i	−0.771580	−	0.720170i
$495$	−0.169499	−	5.42560i	−0.00761840	−	0.243862i
$496$	−8.90768	+	21.9317i	−0.399967	+	0.984764i
$497$	17.4389	+	15.2556i	0.782243	+	0.684306i
$498$	−24.4338	+	1.22429i	−1.09490	+	0.0548618i
$499$	−4.60461	+	2.65847i	−0.206131	+	0.119010i	−0.599512	−	0.800366i	$-0.704639\pi$
$499$	−4.60461	+	2.65847i	−0.206131	+	0.119010i	0.393381	+	0.919375i	$0.371305\pi$
$500$	−6.40549	−	9.51528i	−0.286462	−	0.425536i
$501$	−21.5804	+	6.14518i	−0.964141	+	0.274546i
$502$	−5.73844	−	18.8003i	−0.256119	−	0.839099i
$503$	−1.45521			−0.0648844			−0.0324422	−	0.999474i	$-0.510328\pi$
$503$	−1.45521			−0.0648844			−0.0324422	+	0.999474i	$0.510328\pi$
$504$	4.48784	+	21.9968i	0.199904	+	0.979815i
$505$	4.71641			0.209877
$506$	1.95114	+	6.39235i	0.0867389	+	0.284175i
$507$	−16.2273	+	64.5782i	−0.720679	+	2.86802i
$508$	12.3962	+	18.4144i	0.549990	+	0.817005i
$509$	37.5080	−	21.6553i	1.66251	−	0.959853i	0.691006	−	0.722849i	$-0.257168\pi$
$509$	37.5080	−	21.6553i	1.66251	−	0.959853i	0.971508	−	0.237005i	$-0.0761657\pi$
$510$	−2.08246	−	3.22287i	−0.0922127	−	0.142711i
$511$	−0.770509	+	3.89870i	−0.0340853	+	0.172468i
$512$	−10.3555	+	20.1187i	−0.457652	+	0.889131i
$513$	3.65045	+	11.4494i	0.161171	+	0.505502i
$514$	−4.43772	−	4.14204i	−0.195740	−	0.182698i
$515$	4.89859	+	2.82820i	0.215858	+	0.124625i
$516$	−9.50000	+	3.42813i	−0.418214	+	0.150915i
$517$	25.5092	+	14.7277i	1.12189	+	0.647725i
$518$	16.6898	−	12.0346i	0.733307	−	0.528768i
$519$	−1.50375	+	1.55146i	−0.0660072	+	0.0681016i
$520$	9.36285	+	7.60317i	0.410588	+	0.333421i
$521$	28.2426	−	16.3059i	1.23733	−	0.714373i	0.268783	−	0.963201i	$-0.413378\pi$
$521$	28.2426	−	16.3059i	1.23733	−	0.714373i	0.968548	+	0.248827i	$0.0800451\pi$
$522$	−22.3373	−	19.5802i	−0.977678	−	0.857003i
$523$	13.1872	−	22.8409i	0.576637	−	0.998765i	−0.419224	−	0.907883i	$-0.637698\pi$
$523$	13.1872	−	22.8409i	0.576637	−	0.998765i	0.995862	−	0.0908822i	$-0.0289687\pi$
$524$	−8.96854	−	4.38440i	−0.391793	−	0.191534i
$525$	−9.09463	+	19.2531i	−0.396922	+	0.840274i
$526$	5.58564	−	24.1437i	0.243545	−	1.05272i
$527$	−13.5036	+	7.79633i	−0.588228	+	0.339613i
$528$	−20.9616	−	2.28089i	−0.912235	−	0.0992629i
$529$	−10.2943	+	17.8303i	−0.447580	+	0.775230i
$530$	1.55593	−	6.72544i	0.0675852	−	0.292134i
$531$	−0.353160	−	11.3045i	−0.0153258	−	0.490574i
$532$	9.74363	+	7.40434i	0.422440	+	0.321019i
$533$	−13.5690	−	23.5022i	−0.587740	−	1.01799i
$534$	−32.6834	+	21.1183i	−1.41435	+	0.913880i
$535$	8.10799			0.350539
$536$	15.9146	−	19.5978i	0.687404	−	0.846497i
$537$	−0.177423	−	0.0445830i	−0.00765635	−	0.00192390i
$538$	−4.65017	−	4.34033i	−0.200483	−	0.187125i
$539$	−8.10410	+	19.7022i	−0.349068	+	0.848633i
$540$	−2.27767	−	5.74347i	−0.0980155	−	0.247160i
$541$	12.4508	−	21.5653i	0.535300	−	0.927166i	−0.463849	−	0.885914i	$-0.653532\pi$
$541$	12.4508	−	21.5653i	0.535300	−	0.927166i	0.999149	−	0.0412520i	$-0.0131346\pi$
$542$	28.5991	+	6.61641i	1.22844	+	0.284199i
$543$	26.9857	−	27.8419i	1.15807	−	1.19481i
$544$	−13.5227	+	6.26815i	−0.579781	+	0.268745i
$545$	−4.70943	−	2.71899i	−0.201730	−	0.116469i
$546$	6.71881	−	45.9943i	0.287538	−	1.96838i
$547$	31.0502	−	17.9268i	1.32761	−	0.766496i	0.342680	−	0.939452i	$-0.388665\pi$
$547$	31.0502	−	17.9268i	1.32761	−	0.766496i	0.984929	+	0.172957i	$0.0553321\pi$
$548$	0.868729	+	12.5888i	0.0371102	+	0.537766i
$549$	−8.02706	+	0.250770i	−0.342587	+	0.0107026i
$550$	−14.6199	−	13.6458i	−0.623395	−	0.581858i
$551$	−16.1921			−0.689809
$552$	4.55871	+	6.09018i	0.194032	+	0.259215i
$553$	13.4071	+	11.7286i	0.570129	+	0.498749i
$554$	−18.8827	−	4.36850i	−0.802247	−	0.185600i
$555$	−3.94128	+	4.06633i	−0.167298	+	0.172606i
$556$	0.929203	+	13.4651i	0.0394070	+	0.571049i
$557$	3.14023	+	5.43904i	0.133056	+	0.230459i	0.924853	−	0.380325i	$-0.124188\pi$
$557$	3.14023	+	5.43904i	0.133056	+	0.230459i	−0.791797	+	0.610784i	$0.790854\pi$
$558$	−23.7733	+	8.07604i	−1.00640	+	0.341886i
$559$	20.9112			0.884448
$560$	−5.25984	−	3.45299i	−0.222269	−	0.145916i
$561$	−9.97316	−	9.66646i	−0.421067	−	0.408118i
$562$	−2.46121	+	2.63691i	−0.103820	+	0.111231i
$563$	−15.5747			−0.656397			−0.328198	−	0.944609i	$-0.606441\pi$
$563$	−15.5747			−0.656397			−0.328198	+	0.944609i	$0.606441\pi$
$564$	33.0017	+	5.91279i	1.38962	+	0.248973i
$565$		−	4.25045i		−	0.178818i
$566$	3.54973	+	11.6297i	0.149206	+	0.488831i
$567$	−14.5289	+	18.8656i	−0.610155	+	0.792282i
$568$	−15.6145	+	19.2283i	−0.655170	+	0.806802i
$569$	−3.13499			−0.131426			−0.0657128	−	0.997839i	$-0.520932\pi$
$569$	−3.13499			−0.131426			−0.0657128	+	0.997839i	$0.520932\pi$
$570$	−2.99743	−	1.53594i	−0.125548	−	0.0643335i
$571$			44.4748i			1.86121i	0.366022	+	0.930606i	$0.380720\pi$
$571$			44.4748i			1.86121i	−0.366022	+	0.930606i	$0.619280\pi$
$572$	39.2211	+	19.1738i	1.63992	+	0.801698i
$573$	−26.0821	+	26.9096i	−1.08959	+	1.12416i
$574$	8.28025	+	11.4832i	0.345611	+	0.479300i
$575$			7.21536i			0.300901i
$576$	−23.3239	+	5.65653i	−0.971829	+	0.235689i
$577$	30.5353	−	17.6296i	1.27120	−	0.733929i	0.295988	−	0.955192i	$-0.404351\pi$
$577$	30.5353	−	17.6296i	1.27120	−	0.733929i	0.975214	+	0.221263i	$0.0710179\pi$
$578$	13.8577	+	3.20598i	0.576406	+	0.133351i
$579$	2.37959	+	2.30641i	0.0988922	+	0.0958510i
$580$	8.30537	−	0.573138i	0.344862	−	0.0237983i
$581$	−25.9232	−	5.12325i	−1.07547	−	0.212548i
$582$	−0.170010	−	3.39296i	−0.00704712	−	0.140643i
$583$		−	24.9866i		−	1.03484i
$584$	−4.19528	−	0.670367i	−0.173602	−	0.0277400i
$585$	0.399459	+	12.7865i	0.0165156	+	0.528658i
$586$	−6.33979	+	27.4035i	−0.261894	+	1.13203i
$587$	19.6358	+	34.0102i	0.810455	+	1.40375i	0.912546	+	0.408974i	$0.134113\pi$
$587$	19.6358	+	34.0102i	0.810455	+	1.40375i	−0.102091	+	0.994775i	$0.532553\pi$
$588$	−1.06471	+	24.2253i	−0.0439079	+	0.999036i
$589$	−6.84324	+	11.8528i	−0.281971	+	0.488387i
$590$	2.31728	+	2.16288i	0.0954010	+	0.0890445i
$591$	21.6577	+	20.9916i	0.890877	+	0.863480i
$592$	13.5109	+	17.3585i	0.555295	+	0.713430i
$593$	−28.1689	−	16.2633i	−1.15676	−	0.667855i	−0.206234	−	0.978503i	$-0.566121\pi$
$593$	−28.1689	−	16.2633i	−1.15676	−	0.667855i	−0.950525	+	0.310648i	$0.899454\pi$
$594$	−12.7180	−	18.3961i	−0.521827	−	0.754800i
$595$	−1.33706	−	3.92297i	−0.0548142	−	0.160826i
$596$	−9.81427	−	4.79785i	−0.402008	−	0.196528i
$597$	−1.50021	+	5.97024i	−0.0613995	+	0.244346i
$598$	−4.59827	−	15.0649i	−0.188037	−	0.616049i
$599$		−	4.39397i		−	0.179533i	−0.995963	−	0.0897663i	$-0.971388\pi$
$599$		−	4.39397i		−	0.179533i	0.995963	−	0.0897663i	$-0.0286120\pi$
$600$	−20.9250	−	8.96151i	−0.854260	−	0.365852i
$601$	14.6174	−	8.43937i	0.596257	−	0.344249i	−0.171311	−	0.985217i	$-0.554800\pi$
$601$	14.6174	−	8.43937i	0.596257	−	0.344249i	0.767568	+	0.640968i	$0.221467\pi$
$602$	−10.8531	+	1.10134i	−0.442339	+	0.0448873i
$603$	26.7641	−	0.836126i	1.08992	−	0.0340497i
$604$	27.4854	−	1.89672i	1.11837	−	0.0771764i
$605$	−0.894720	−	0.516567i	−0.0363755	−	0.0210014i
$606$	16.3209	−	10.5458i	0.662993	−	0.428392i
$607$	−16.7306	−	28.9782i	−0.679072	−	1.17619i	−0.975261	−	0.221058i	$-0.929049\pi$
$607$	−16.7306	−	28.9782i	−0.679072	−	1.17619i	0.296188	−	0.955130i	$-0.404284\pi$
$608$	−7.52841	+	10.6995i	−0.305317	+	0.433924i
$609$	−18.2719	−	26.3730i	−0.740415	−	1.06869i
$610$	1.53581	−	1.64544i	0.0621831	−	0.0666221i
$611$	−60.1176	−	34.7089i	−2.43210	−	1.40417i
$612$	−14.4125	−	6.49630i	−0.582591	−	0.262597i
$613$	18.0048	+	31.1852i	0.727207	+	1.25956i	0.958059	+	0.286570i	$0.0925152\pi$
$613$	18.0048	+	31.1852i	0.727207	+	1.25956i	−0.230852	+	0.972989i	$0.574151\pi$
$614$	11.0641	+	36.2482i	0.446509	+	1.46286i
$615$	−2.79779	−	2.71175i	−0.112818	−	0.109348i
$616$	−21.3660	−	7.88570i	−0.860859	−	0.317724i
$617$	17.8922	−	30.9902i	0.720314	−	1.24762i	−0.240560	−	0.970634i	$-0.577331\pi$
$617$	17.8922	−	30.9902i	0.720314	−	1.24762i	0.960874	−	0.276986i	$-0.0893354\pi$
$618$	23.2752	−	1.16624i	0.936264	−	0.0469129i
$619$	−8.72404	+	15.1105i	−0.350649	+	0.607341i	−0.986363	−	0.164583i	$-0.947372\pi$
$619$	−8.72404	+	15.1105i	−0.350649	+	0.607341i	0.635715	+	0.771924i	$0.280706\pi$
$620$	3.09053	−	6.32185i	0.124119	−	0.253892i
$621$	−1.72110	+	7.88315i	−0.0690655	+	0.316340i
$622$	1.97905	+	6.48377i	0.0793526	+	0.259976i
$623$	−39.7831	+	13.5592i	−1.59388	+	0.543239i
$624$	49.4003	+	5.37538i	1.97759	+	0.215187i
$625$	−9.91141	−	17.1671i	−0.396457	−	0.686683i
$626$	11.9199	−	3.63832i	0.476415	−	0.145417i
$627$	−11.8235	−	2.97103i	−0.472186	−	0.118651i
$628$	13.1729	+	19.5682i	0.525656	+	0.780857i
$629$			14.4895i			0.577733i
$630$	−0.880759	−	6.61529i	−0.0350903	−	0.263559i
$631$			17.8634i			0.711133i	0.934651	+	0.355566i	$0.115712\pi$
$631$			17.8634i			0.711133i	−0.934651	+	0.355566i	$0.884288\pi$
$632$	−12.0045	+	14.7828i	−0.477514	+	0.588030i
$633$	1.58010	+	5.54894i	0.0628034	+	0.220551i
$634$	−7.47783	−	24.4989i	−0.296983	−	0.972977i
$635$	−3.29939	−	5.71471i	−0.130932	−	0.226781i
$636$	−9.65367	−	26.7521i	−0.382793	−	1.06079i
$637$	19.0990	−	46.4322i	0.756729	−	1.83971i
$638$	28.8213	−	8.79714i	1.14104	−	0.348282i
$639$	−26.2595	+	0.820361i	−1.03881	+	0.0324530i
$640$	3.48279	−	5.75455i	0.137670	−	0.227469i
$641$	23.5403	−	40.7730i	0.929786	−	1.61044i	0.146108	−	0.989269i	$-0.453325\pi$
$641$	23.5403	−	40.7730i	0.929786	−	1.61044i	0.783678	−	0.621168i	$-0.213341\pi$
$642$	28.0574	−	18.1293i	1.10734	−	0.715504i
$643$	11.4838	−	19.8904i	0.452875	−	0.784403i	−0.545688	−	0.837988i	$-0.683732\pi$
$643$	11.4838	−	19.8904i	0.452875	−	0.784403i	0.998563	+	0.0535856i	$0.0170650\pi$
$644$	3.17997	+	7.57663i	0.125309	+	0.298561i
$645$	2.88751	−	0.822239i	0.113696	−	0.0323756i
$646$	−8.24225	+	2.51579i	−0.324287	+	0.0989825i
$647$	17.5968	+	30.4785i	0.691800	+	1.19823i	0.971248	+	0.238072i	$0.0765153\pi$
$647$	17.5968	+	30.4785i	0.691800	+	1.19823i	−0.279448	+	0.960161i	$0.590151\pi$
$648$	−20.7240	−	14.7822i	−0.814117	−	0.580701i
$649$	9.93648	+	5.73683i	0.390041	+	0.225190i
$650$	34.4548	+	32.1591i	1.35143	+	1.26138i
$651$	−27.0275	+	2.22931i	−1.05929	+	0.0873737i
$652$	6.80304	−	0.469465i	0.266428	−	0.0183857i
$653$	18.4253	+	31.9135i	0.721036	+	1.24887i	0.960585	+	0.277987i	$0.0896672\pi$
$653$	18.4253	+	31.9135i	0.721036	+	1.24887i	−0.239549	+	0.970884i	$0.576999\pi$
$654$	−22.3764	+	1.12120i	−0.874985	+	0.0438425i
$655$	2.57001	+	1.48380i	0.100419	+	0.0579767i
$656$	−11.9433	+	9.29603i	−0.466309	+	0.362949i
$657$	−2.37387	−	3.83024i	−0.0926134	−	0.149432i
$658$	33.0296	+	14.8480i	1.28763	+	0.578835i
$659$	−6.21863	+	3.59033i	−0.242244	+	0.139859i	−0.616207	−	0.787584i	$-0.711332\pi$
$659$	−6.21863	+	3.59033i	−0.242244	+	0.139859i	0.373964	+	0.927443i	$0.377998\pi$
$660$	6.16975	+	1.10541i	0.240157	+	0.0430281i
$661$			2.24017i			0.0871324i	0.999051	+	0.0435662i	$0.0138719\pi$
$661$			2.24017i			0.0871324i	−0.999051	+	0.0435662i	$0.986128\pi$
$662$	−10.5095	+	3.20783i	−0.408464	+	0.124676i
$663$	23.5038	+	22.7810i	0.912812	+	0.884741i
$664$	4.45739	−	27.8952i	0.172980	−	1.08254i
$665$	−2.73807	−	2.39526i	−0.106178	−	0.0928843i
$666$	−4.54643	+	22.8839i	−0.176171	+	0.886735i
$667$	−9.41547	−	5.43602i	−0.364568	−	0.210484i
$668$	−1.78372	−	25.8480i	−0.0690144	−	1.00009i
$669$	−5.50455	+	21.9059i	−0.212818	+	0.846933i
$670$	−5.12075	+	5.48630i	−0.197832	+	0.211954i
$671$	4.07358	−	7.05565i	0.157259	−	0.272380i
$672$	−25.9223	−	0.188078i	−0.999974	−	0.00725525i
$673$	7.99088	+	13.8406i	0.308026	+	0.533516i	0.977930	−	0.208931i	$-0.0669984\pi$
$673$	7.99088	+	13.8406i	0.308026	+	0.533516i	−0.669905	+	0.742447i	$0.733665\pi$
$674$	−10.9292	−	2.52848i	−0.420979	−	0.0973933i
$675$	−7.33419	−	23.0032i	−0.282293	−	0.885392i
$676$	−69.0744	−	33.7681i	−2.65671	−	1.29877i
$677$			16.6132i			0.638498i	0.947671	+	0.319249i	$0.103431\pi$
$677$			16.6132i			0.638498i	−0.947671	+	0.319249i	$0.896569\pi$
$678$	−9.50389	−	14.7085i	−0.364995	−	0.564877i
$679$	0.711434	−	3.59979i	0.0273023	−	0.138147i
$680$	4.13862	−	1.58216i	0.158709	−	0.0606730i
$681$	15.7467	−	4.48399i	0.603416	−	0.171827i
$682$	5.74103	−	24.8154i	0.219836	−	0.950230i
$683$	−24.9863	+	14.4258i	−0.956073	+	0.551989i	−0.894962	−	0.446142i	$-0.852798\pi$
$683$	−24.9863	+	14.4258i	−0.956073	+	0.551989i	−0.0611106	+	0.998131i	$0.519464\pi$
$684$	−13.8068	+	1.38710i	−0.527916	+	0.0530373i
$685$		−	3.75115i		−	0.143324i
$686$	−7.46707	+	25.1046i	−0.285094	+	0.958500i
$687$	23.8388	+	5.99024i	0.909506	+	0.228542i
$688$	−1.60192	−	11.5515i	−0.0610726	−	0.440396i
$689$			58.8861i			2.24338i
$690$	−1.22731	−	1.89942i	−0.0467229	−	0.0723097i
$691$	31.5172			1.19897			0.599485	−	0.800386i	$-0.295372\pi$
$691$	31.5172			1.19897			0.599485	+	0.800386i	$0.295372\pi$
$692$	−1.39322	−	2.06962i	−0.0529624	−	0.0786750i
$693$	−8.50310	−	22.6102i	−0.323006	−	0.858891i
$694$	−1.12995	+	0.344895i	−0.0428922	+	0.0130920i
$695$		−	4.01228i		−	0.152194i
$696$	27.4589	−	20.5539i	1.04083	−	0.779094i
$697$	−9.96932			−0.377615
$698$	−16.5808	−	15.4760i	−0.627591	−	0.585775i
$699$	−43.0116	+	12.2479i	−1.62685	+	0.463257i
$700$	−19.5761	−	14.8762i	−0.739907	−	0.562268i
$701$	38.3817			1.44966			0.724829	−	0.688929i	$-0.241919\pi$
$701$	38.3817			1.44966			0.724829	+	0.688929i	$0.241919\pi$
$702$	29.9727	+	43.3541i	1.13125	+	1.63630i
$703$	6.35907	+	11.0142i	0.239837	+	0.415410i
$704$	7.58718	−	23.1348i	0.285953	−	0.871927i
$705$	−9.66608	−	2.42891i	−0.364046	−	0.0914779i
$706$	−4.15477	+	17.9588i	−0.156367	+	0.675890i
$707$	19.8663	−	6.77101i	0.747150	−	0.254650i
$708$	12.8550	+	2.30318i	0.483121	+	0.0865590i
$709$	−10.5603			−0.396602			−0.198301	−	0.980141i	$-0.563542\pi$
$709$	−10.5603			−0.396602			−0.198301	+	0.980141i	$0.563542\pi$
$710$	5.02420	−	5.38286i	0.188555	−	0.202015i
$711$	−20.1884	+	0.630698i	−0.757125	+	0.0236530i
$712$	−16.0448	−	41.9700i	−0.601303	−	1.57289i
$713$	−7.95846	+	4.59482i	−0.298047	+	0.172077i
$714$	−13.3985	−	10.5857i	−0.501427	−	0.396158i
$715$	−11.2391	−	6.48892i	−0.420320	−	0.242672i
$716$	0.0927746	−	0.189776i	0.00346715	−	0.00709224i
$717$	10.2977	+	36.1630i	0.384574	+	1.35053i
$718$	−2.46212	+	10.6424i	−0.0918856	+	0.397172i
$719$	17.7183	−	30.6890i	0.660782	−	1.14451i	−0.319629	−	0.947543i	$-0.603558\pi$
$719$	17.7183	−	30.6890i	0.660782	−	1.14451i	0.980411	−	0.196965i	$-0.0631084\pi$
$720$	7.03277	−	1.20019i	0.262096	−	0.0447284i
$721$	24.6939	+	4.88032i	0.919651	+	0.181752i
$722$	13.1730	−	14.1134i	0.490250	−	0.525247i
$723$	−1.78820	−	6.27974i	−0.0665039	−	0.233546i
$724$	25.0023	+	37.1406i	0.929201	+	1.38032i
$725$	32.5320			1.20821
$726$	−4.25117	+	0.213011i	−0.157776	+	0.00790560i
$727$	16.3858	+	28.3811i	0.607717	+	1.05260i	0.991616	+	0.129222i	$0.0412480\pi$
$727$	16.3858	+	28.3811i	0.607717	+	1.05260i	−0.383898	+	0.923375i	$0.625419\pi$
$728$	50.3533	+	18.5843i	1.86622	+	0.688779i
$729$	−2.52596	−	26.8816i	−0.0935542	−	0.995614i
$730$	1.23045	+	0.284664i	0.0455409	+	0.0105359i
$731$	3.84092	−	6.65267i	0.142062	−	0.246058i
$732$	1.63543	−	9.12802i	0.0604474	−	0.337381i
$733$	4.86739	−	2.81019i	0.179781	−	0.103797i	−0.407409	−	0.913246i	$-0.633568\pi$
$733$	4.86739	−	2.81019i	0.179781	−	0.103797i	0.587190	+	0.809449i	$0.300234\pi$
$734$	1.17465	+	0.271755i	0.0433572	+	0.0100307i
$735$	0.811532	−	7.16255i	0.0299338	−	0.264195i
$736$	−7.96969	+	3.69417i	−0.293767	+	0.136169i
$737$	−13.5823	+	23.5252i	−0.500309	+	0.866561i
$738$	−15.7451	−	3.12812i	−0.579583	−	0.115148i
$739$	37.9429	−	21.9063i	1.39575	−	0.805838i	0.401808	−	0.915724i	$-0.368382\pi$
$739$	37.9429	−	21.9063i	1.39575	−	0.805838i	0.993944	+	0.109886i	$0.0350487\pi$
$740$	−3.65159	−	5.42440i	−0.134235	−	0.199405i
$741$	27.8646	+	7.00184i	1.02363	+	0.257219i
$742$	−3.10139	−	30.5624i	−0.113856	−	1.12198i
$743$	9.43980	+	5.45007i	0.346313	+	0.199944i	0.663060	−	0.748566i	$-0.269257\pi$
$743$	9.43980	+	5.45007i	0.346313	+	0.199944i	−0.316747	+	0.948510i	$0.602591\pi$
$744$	−3.44083	−	28.7868i	−0.126147	−	1.05538i
$745$	2.81236	+	1.62372i	0.103037	+	0.0594885i
$746$	2.24827	−	2.40877i	0.0823152	−	0.0881914i
$747$	25.4680	−	15.7843i	0.931824	−	0.577516i
$748$	13.3040	−	8.95598i	0.486442	−	0.327463i
$749$	34.1522	−	11.6401i	1.24790	−	0.425319i
$750$	12.5025	+	6.40653i	0.456527	+	0.233934i
$751$	8.29441	−	4.78878i	0.302667	−	0.174745i	−0.340973	−	0.940073i	$-0.610757\pi$
$751$	8.29441	−	4.78878i	0.302667	−	0.174745i	0.643641	+	0.765328i	$0.277423\pi$
$752$	−14.5681	+	35.8683i	−0.531243	+	1.30798i
$753$	17.2868	+	16.7552i	0.629967	+	0.610594i
$754$	−67.9232	+	20.7323i	−2.47362	+	0.755025i
$755$	−8.18999			−0.298064
$756$	−17.8394	−	20.9226i	−0.648814	−	0.760947i
$757$	−1.91601			−0.0696384			−0.0348192	−	0.999394i	$-0.511086\pi$
$757$	−1.91601			−0.0696384			−0.0348192	+	0.999394i	$0.511086\pi$
$758$	39.0979	−	11.9339i	1.42010	−	0.433459i
$759$	−5.87775	−	5.69699i	−0.213349	−	0.206788i
$760$	2.45162	−	3.01902i	0.0889295	−	0.109511i
$761$	−0.552623	+	0.319057i	−0.0200326	+	0.0115658i	−0.509983	−	0.860185i	$-0.670348\pi$
$761$	−0.552623	+	0.319057i	−0.0200326	+	0.0115658i	0.489950	+	0.871750i	$0.337015\pi$
$762$	−24.1953	−	12.3982i	−0.876505	−	0.449139i
$763$	−23.7404	−	4.69186i	−0.859459	−	0.169857i
$764$	−24.1650	−	35.8969i	−0.874260	−	1.29870i
$765$	4.14127	+	2.22152i	0.149728	+	0.0803192i
$766$	17.1762	−	18.4024i	0.620603	−	0.664905i
$767$	−23.4174	−	13.5200i	−0.845552	−	0.488180i
$768$	−0.814954	−	27.7008i	−0.0294071	−	0.999568i
$769$	4.56501	+	2.63561i	0.164618	+	0.0950425i	0.580046	−	0.814584i	$-0.303035\pi$
$769$	4.56501	+	2.63561i	0.164618	+	0.0950425i	−0.415427	+	0.909626i	$0.636368\pi$
$770$	6.17497	+	2.77587i	0.222531	+	0.100035i
$771$	7.21054	+	1.81187i	0.259681	+	0.0652531i
$772$	−3.17432	+	2.13689i	−0.114246	+	0.0769082i
$773$	−34.2460	+	19.7719i	−1.23174	+	0.711147i	−0.967393	−	0.253280i	$-0.918491\pi$
$773$	−34.2460	+	19.7719i	−1.23174	+	0.711147i	−0.264350	+	0.964427i	$0.585157\pi$
$774$	8.15360	−	9.30171i	0.293075	−	0.334343i
$775$	13.7489	−	23.8138i	0.493874	−	0.855415i
$776$	3.87363	+	0.618970i	0.139055	+	0.0222197i
$777$	−10.7636	+	22.7863i	−0.386142	+	0.817453i
$778$	35.3142	+	8.16992i	1.26607	+	0.292906i
$779$	−7.57822	+	4.37529i	−0.271518	+	0.156761i
$780$	−14.5403	−	2.60513i	−0.520626	−	0.0932786i
$781$	13.3262	−	23.0816i	0.476848	−	0.825926i
$782$	−5.63733	−	1.30420i	−0.201591	−	0.0466379i
$783$	35.5428	+	7.75995i	1.27020	+	0.277318i
$784$	−27.1126	−	6.99342i	−0.968306	−	0.249765i
$785$	−3.50613	−	6.07280i	−0.125139	−	0.216748i
$786$	12.2112	−	0.611858i	0.435557	−	0.0218243i
$787$	2.01708			0.0719013			0.0359506	−	0.999354i	$-0.488554\pi$
$787$	2.01708			0.0719013			0.0359506	+	0.999354i	$0.488554\pi$
$788$	−28.8909	+	19.4487i	−1.02919	+	0.692832i
$789$	8.31220	+	29.1905i	0.295922	+	1.03921i
$790$	3.86263	−	4.13837i	0.137426	−	0.147237i
$791$	−6.10206	−	17.9036i	−0.216964	−	0.636579i
$792$	23.8218	−	9.97017i	0.846473	−	0.354275i
$793$	−9.60023	+	16.6281i	−0.340914	+	0.590481i
$794$	1.96441	−	8.49106i	0.0697141	−	0.301337i
$795$	2.31544	+	8.13126i	0.0821200	+	0.288386i
$796$	−6.38592	−	3.12185i	−0.226343	−	0.110651i
$797$	16.7785	+	9.68708i	0.594326	+	0.343134i	0.766806	−	0.641879i	$-0.221845\pi$
$797$	16.7785	+	9.68708i	0.594326	+	0.343134i	−0.172480	+	0.985013i	$0.555178\pi$
$798$	−14.8307	−	2.16646i	−0.525002	−	0.0766918i
$799$	−22.0846	+	12.7505i	−0.781295	+	0.451081i
$800$	15.1255	−	21.4967i	0.534766	−	0.760022i
$801$	22.5286	−	41.9969i	0.796009	−	1.48389i
$802$	−0.262437	+	0.281172i	−0.00926698	+	0.00992851i
$803$	4.57141			0.161322
$804$	−5.45292	+	30.4350i	−0.192310	+	1.07336i
$805$	−0.788006	−	2.31203i	−0.0277735	−	0.0814883i
$806$	−13.5299	+	58.4826i	−0.476571	+	2.05996i
$807$	7.55574	+	1.89861i	0.265975	+	0.0668344i
$808$	8.01220	+	20.9584i	0.281868	+	0.737313i
$809$	−9.30812	−	16.1221i	−0.327256	−	0.566824i	0.654710	−	0.755880i	$-0.272791\pi$
$809$	−9.30812	−	16.1221i	−0.327256	−	0.566824i	−0.981966	+	0.189056i	$0.939457\pi$
$810$	5.84347	+	4.80799i	0.205318	+	0.168935i
$811$	−1.07212			−0.0376471			−0.0188236	−	0.999823i	$-0.505992\pi$
$811$	−1.07212			−0.0376471			−0.0188236	+	0.999823i	$0.505992\pi$
$812$	34.1608	−	14.3376i	1.19881	−	0.503151i
$813$	−34.5772	+	9.84612i	−1.21268	+	0.345318i
$814$	−17.3028	−	16.1499i	−0.606464	−	0.566055i
$815$	−2.02714			−0.0710076
$816$	10.7839	−	14.7288i	0.377510	−	0.515612i
$817$		−	6.74274i		−	0.235899i
$818$	−8.83965	+	2.69813i	−0.309071	+	0.0943380i
$819$	20.0393	+	53.2856i	0.700230	+	1.86195i
$820$	3.73220	−	2.51244i	0.130334	−	0.0877381i
$821$	39.6372			1.38335			0.691674	−	0.722209i	$-0.256873\pi$
$821$	39.6372			1.38335			0.691674	+	0.722209i	$0.256873\pi$
$822$	−8.38747	−	12.9807i	−0.292547	−	0.452754i
$823$		−	21.9087i		−	0.763690i	−0.924226	−	0.381845i	$-0.875289\pi$
$823$		−	21.9087i		−	0.763690i	0.924226	−	0.381845i	$-0.124711\pi$
$824$	−4.24603	+	26.5724i	−0.147917	+	0.925695i
$825$	23.7549	+	5.96915i	0.827038	+	0.207819i
$826$	12.8659	+	5.78367i	0.447661	+	0.201240i
$827$			40.4761i			1.40749i	0.710451	+	0.703746i	$0.248491\pi$
$827$			40.4761i			1.40749i	−0.710451	+	0.703746i	$0.751509\pi$
$828$	−8.49411	−	3.82864i	−0.295191	−	0.133054i
$829$	4.10818	−	2.37186i	0.142683	−	0.0823780i	−0.426959	−	0.904271i	$-0.640415\pi$
$829$	4.10818	−	2.37186i	0.142683	−	0.0823780i	0.569642	+	0.821893i	$0.307082\pi$
$830$	−1.89278	+	8.18147i	−0.0656994	+	0.283983i
$831$	22.8297	−	6.50092i	0.791954	−	0.225515i
$832$	−17.8808	+	54.5220i	−0.619904	+	1.89021i
$833$	−11.2639	−	14.6047i	−0.390270	−	0.506023i
$834$	−8.97135	−	13.8843i	−0.310652	−	0.480775i
$835$			7.70208i			0.266542i
$836$	6.18254	−	12.6467i	0.213828	−	0.437396i
$837$	20.7017	−	22.7382i	0.715557	−	0.785947i
$838$	−51.4721	−	11.9081i	−1.77807	−	0.411357i
$839$	−28.2350	−	48.9045i	−0.974782	−	1.68837i	−0.680653	−	0.732606i	$-0.738304\pi$
$839$	−28.2350	−	48.9045i	−0.974782	−	1.68837i	−0.294128	−	0.955766i	$-0.595029\pi$
$840$	7.68375	+	0.586283i	0.265114	+	0.0202287i
$841$	−10.0095	+	17.3369i	−0.345154	+	0.597824i
$842$	17.0082	−	18.2224i	0.586143	−	0.627985i
$843$	1.07662	−	4.28453i	0.0370808	−	0.147567i
$844$	−6.64628	+	0.458647i	−0.228774	+	0.0157873i
$845$	19.7939	+	11.4280i	0.680930	+	0.393135i
$846$	−38.8801	+	13.2080i	−1.33672	+	0.454100i
$847$	−4.51031	−	0.891383i	−0.154976	−	0.0306283i
$848$	32.5291	−	4.51103i	1.11705	−	0.154909i
$849$	−10.6934	−	10.3646i	−0.366998	−	0.355712i
$850$	16.5597	−	5.05452i	0.567992	−	0.173369i
$851$			8.53946i			0.292729i
$852$	5.35011	−	29.8611i	0.183292	−	1.02303i
$853$	−8.07503	+	4.66212i	−0.276484	+	0.159628i	−0.631830	−	0.775107i	$-0.717696\pi$
$853$	−8.07503	+	4.66212i	−0.276484	+	0.159628i	0.355347	+	0.934735i	$0.384363\pi$
$854$	4.10684	−	9.13575i	0.140533	−	0.312619i
$855$	4.12298	−	0.128804i	0.141003	−	0.00440501i
$856$	13.7738	+	36.0296i	0.470779	+	1.23147i
$857$	−14.2780	−	8.24340i	−0.487727	−	0.281589i	0.235904	−	0.971776i	$-0.424195\pi$
$857$	−14.2780	−	8.24340i	−0.487727	−	0.281589i	−0.723631	+	0.690187i	$0.757528\pi$
$858$	−53.4017	+	2.67577i	−1.82310	+	0.0913493i
$859$	−14.2428	−	24.6693i	−0.485959	−	0.841706i	0.513910	−	0.857844i	$-0.328196\pi$
$859$	−14.2428	−	24.6693i	−0.485959	−	0.841706i	−0.999870	+	0.0161374i	$0.994863\pi$
$860$	0.238666	+	3.45853i	0.00813846	+	0.117935i
$861$	−15.6778	−	7.40578i	−0.534300	−	0.252388i
$862$	−32.0419	−	29.9070i	−1.09135	−	1.01863i
$863$	4.17974	+	2.41317i	0.142280	+	0.0821454i	0.569450	−	0.822026i	$-0.307156\pi$
$863$	4.17974	+	2.41317i	0.142280	+	0.0821454i	−0.427170	+	0.904171i	$0.640489\pi$
$864$	21.6530	−	19.8783i	0.736651	−	0.676273i
$865$	0.370823	+	0.642285i	0.0126084	+	0.0218383i
$866$	−27.2780	+	8.32608i	−0.926943	+	0.282932i
$867$	−16.7544	+	4.77094i	−0.569010	+	0.162030i
$868$	3.94202	−	31.0656i	0.133801	−	1.05443i
$869$	10.2452	−	17.7453i	0.347546	−	0.601967i
$870$	−8.56394	+	5.53358i	−0.290345	+	0.187606i
$871$	32.0094	−	55.4419i	1.08460	−	1.87858i
$872$	4.08206	−	25.5463i	0.138236	−	0.865108i
$873$	2.19186	+	3.53658i	0.0741833	+	0.119695i
$874$	−4.85762	+	1.48270i	−0.164312	+	0.0501530i
$875$	11.4207	+	9.99083i	0.386090	+	0.337752i
$876$	4.89441	−	1.76618i	0.165367	−	0.0596737i
$877$	−11.8885	−	20.5915i	−0.401447	−	0.695327i	0.592454	−	0.805604i	$-0.298159\pi$
$877$	−11.8885	−	20.5915i	−0.401447	−	0.695327i	−0.993901	+	0.110278i	$0.964826\pi$
$878$	−0.540908	−	1.77213i	−0.0182548	−	0.0598064i
$879$	−9.43447	−	33.1316i	−0.318217	−	1.11750i
$880$	−2.72354	+	6.70567i	−0.0918105	+	0.226048i
$881$			15.9241i			0.536495i	0.963350	+	0.268248i	$0.0864445\pi$
$881$			15.9241i			0.536495i	−0.963350	+	0.268248i	$0.913555\pi$
$882$	−13.2070	−	26.6003i	−0.444703	−	0.895678i
$883$			0.631703i			0.0212585i	0.999944	+	0.0106292i	$0.00338346\pi$
$883$			0.631703i			0.0212585i	−0.999944	+	0.0106292i	$0.996617\pi$
$884$	−31.3536	+	21.1066i	−1.05454	+	0.709892i
$885$	−3.76519	−	0.946121i	−0.126565	−	0.0318035i
$886$	−3.44313	+	1.05095i	−0.115674	+	0.0353073i
$887$	−7.53340	−	13.0482i	−0.252947	−	0.438117i	0.711389	−	0.702799i	$-0.248066\pi$
$887$	−7.53340	−	13.0482i	−0.252947	−	0.438117i	−0.964336	+	0.264682i	$0.914733\pi$
$888$	−24.7650	−	10.6061i	−0.831059	−	0.355916i
$889$	−22.1018	−	19.3346i	−0.741270	−	0.648463i
$890$	3.89936	+	12.7751i	0.130707	+	0.428223i
$891$	24.5296	+	12.1879i	0.821771	+	0.408311i
$892$	−23.4311	−	11.4547i	−0.784532	−	0.383530i
$893$	−11.1918	+	19.3847i	−0.374519	+	0.648686i
$894$	13.3627	−	0.669557i	0.446914	−	0.0223933i
$895$	−0.0313973	+	0.0543818i	−0.00104950	+	0.00181778i
$896$	6.40873	−	29.2392i	0.214101	−	0.976812i
$897$	13.8521	+	13.4261i	0.462509	+	0.448285i
$898$	12.4064	+	40.6459i	0.414006	+	1.35637i
$899$	20.7167	+	35.8824i	0.690941	+	1.19674i
$900$	27.7395	−	2.78686i	0.924650	−	0.0928953i
$901$	18.7340	+	10.8161i	0.624120	+	0.360336i
$902$	11.1118	−	11.9050i	0.369982	−	0.396394i
$903$	10.9822	−	7.60880i	0.365466	−	0.253205i
$904$	18.8878	−	7.22063i	0.628198	−	0.240155i
$905$	−6.65466	−	11.5262i	−0.221208	−	0.383144i
$906$	−28.3411	+	18.3126i	−0.941570	+	0.608395i
$907$	25.5312	+	14.7404i	0.847748	+	0.489448i	0.859890	−	0.510479i	$-0.170532\pi$
$907$	25.5312	+	14.7404i	0.847748	+	0.489448i	−0.0121421	+	0.999926i	$0.503865\pi$
$908$	1.30154	+	18.8607i	0.0431932	+	0.625915i
$909$	−11.2500	+	20.9718i	−0.373139	+	0.695591i
$910$	−14.5526	−	6.54191i	−0.482414	−	0.216862i
$911$	−14.4832	+	8.36189i	−0.479850	+	0.277042i	−0.720354	−	0.693606i	$-0.756021\pi$
$911$	−14.4832	+	8.36189i	−0.479850	+	0.277042i	0.240504	+	0.970648i	$0.422687\pi$
$912$	1.73327	−	15.9290i	0.0573945	−	0.527460i
$913$			30.3961i			1.00596i
$914$	15.8474	+	51.9194i	0.524185	+	1.71734i
$915$	−0.671817	+	2.67357i	−0.0222096	+	0.0883854i
$916$	−12.4653	+	25.4985i	−0.411866	+	0.842495i
$917$	12.9555	+	2.56043i	0.427829	+	0.0845527i
$918$	19.2980	−	1.57229i	0.636928	−	0.0518935i
$919$	0.945149	+	0.545682i	0.0311776	+	0.0180004i	0.515508	−	0.856885i	$-0.327603\pi$
$919$	0.945149	+	0.545682i	0.0311776	+	0.0180004i	−0.484330	+	0.874885i	$0.660937\pi$
$920$	2.43912	−	0.932455i	0.0804154	−	0.0307421i
$921$	−33.3301	−	32.3051i	−1.09826	−	1.06449i
$922$	35.6577	+	33.2819i	1.17433	+	1.09608i
$923$	−31.4059	+	54.3966i	−1.03374	+	1.79049i
$924$	27.5750	−	4.20129i	0.907151	−	0.138212i
$925$	−12.7761	−	22.1289i	−0.420076	−	0.727594i
$926$	−8.58035	+	37.0882i	−0.281968	+	1.21879i
$927$	−24.2603	+	15.0358i	−0.796814	+	0.493841i
$928$	16.6560	+	35.9330i	0.546759	+	1.17956i
$929$		−	17.1306i		−	0.562036i	−0.959703	−	0.281018i	$-0.909328\pi$
$929$		−	17.1306i		−	0.562036i	0.959703	−	0.281018i	$-0.0906720\pi$
$930$	0.431294	+	8.60754i	0.0141427	+	0.282252i
$931$	−14.9719	−	6.15841i	−0.490685	−	0.201834i
$932$	−3.55512	−	51.5174i	−0.116452	−	1.68751i
$933$	−5.96181	−	5.77847i	−0.195181	−	0.189179i
$934$	28.0405	+	6.48716i	0.917513	+	0.212266i
$935$	−4.12876	+	2.38374i	−0.135025	+	0.0779567i
$936$	−56.1411	+	23.4968i	−1.83503	+	0.768015i
$937$			17.6461i			0.576474i	0.957559	+	0.288237i	$0.0930692\pi$
$937$			17.6461i			0.576474i	−0.957559	+	0.288237i	$0.906931\pi$
$938$	−13.6932	+	30.4607i	−0.447098	+	0.994578i
$939$	−10.6233	+	10.9603i	−0.346677	+	0.357676i
$940$	5.05441	−	10.3391i	0.164857	−	0.337224i
$941$			14.3693i			0.468425i	0.972185	+	0.234212i	$0.0752511\pi$
$941$			14.3693i			0.468425i	−0.972185	+	0.234212i	$0.924749\pi$
$942$	−25.7115	−	13.1751i	−0.837724	−	0.429267i
$943$	−5.87548			−0.191332
$944$	−5.67464	+	13.9716i	−0.184694	+	0.454738i
$945$	4.86234	+	6.56996i	0.158172	+	0.213721i
$946$	3.66331	+	12.0018i	0.119104	+	0.390211i
$947$		−	9.85597i		−	0.320276i	−0.987095	−	0.160138i	$-0.948806\pi$
$947$		−	9.85597i		−	0.320276i	0.987095	−	0.160138i	$-0.0511939\pi$
$948$	4.11319	−	22.9574i	0.133590	−	0.745622i
$949$	−10.7735			−0.349722
$950$	10.3696	−	11.1099i	0.336434	−	0.360451i
$951$	22.5267	+	21.8339i	0.730478	+	0.708014i
$952$	15.1612	−	12.6058i	0.491376	−	0.408557i
$953$	9.71521			0.314707			0.157353	−	0.987542i	$-0.449704\pi$
$953$	9.71521			0.314707			0.157353	+	0.987542i	$0.449704\pi$
$954$	26.1938	+	22.9606i	0.848054	+	0.743378i
$955$	6.43182	+	11.1402i	0.208129	+	0.360490i
$956$	−43.3144	+	2.98905i	−1.40089	+	0.0966727i
$957$	−25.6861	+	26.5011i	−0.830313	+	0.856658i
$958$	−3.03013	−	0.701020i	−0.0978991	−	0.0226489i
$959$	−5.38526	−	15.8005i	−0.173899	−	0.510224i
$960$	−0.325219	+	8.23173i	−0.0104964	+	0.265678i
$961$	4.02174			0.129734
$962$	40.7777	+	38.0607i	1.31473	+	1.22713i
$963$	−19.3399	+	36.0527i	−0.623220	+	1.16178i
$964$	7.52159	−	0.519051i	0.242254	−	0.0167175i
$965$	0.985119	−	0.568759i	0.0317121	−	0.0183090i
$966$	−7.89650	−	6.23872i	−0.254066	−	0.200728i
$967$	19.5928	+	11.3119i	0.630061	+	0.363766i	0.780776	−	0.624812i	$-0.214824\pi$
$967$	19.5928	+	11.3119i	0.630061	+	0.363766i	−0.150715	+	0.988577i	$0.548158\pi$
$968$	0.775531	−	4.85342i	0.0249265	−	0.155995i
$969$	7.34566	−	7.57873i	0.235977	−	0.243464i
$970$	−1.13611	−	0.262839i	−0.0364783	−	0.00843924i
$971$	8.13371	−	14.0880i	0.261023	−	0.452105i	−0.705491	−	0.708719i	$-0.749273\pi$
$971$	8.13371	−	14.0880i	0.261023	−	0.452105i	0.966514	+	0.256614i	$0.0826068\pi$
$972$	30.9716	+	3.57201i	0.993415	+	0.114572i
$973$	−5.76014	−	16.9004i	−0.184662	−	0.541802i
$974$	−20.0080	−	18.6749i	−0.641098	−	0.598381i
$975$	−55.9832	−	14.0675i	−1.79290	−	0.450522i
$976$	9.92090	+	4.02942i	0.317560	+	0.128979i
$977$	−35.5330			−1.13680			−0.568400	−	0.822752i	$-0.692437\pi$
$977$	−35.5330			−1.13680			−0.568400	+	0.822752i	$0.692437\pi$
$978$	−7.01484	+	4.53263i	−0.224310	+	0.144938i
$979$	24.1737	+	41.8701i	0.772595	+	1.33817i
$980$	7.89747	+	2.62886i	0.252276	+	0.0839758i
$981$	23.3235	−	14.4552i	0.744662	−	0.461519i
$982$	−7.38126	+	31.9052i	−0.235545	+	1.01814i
$983$	−12.8397	+	22.2390i	−0.409523	+	0.709315i	−0.994836	−	0.101493i	$-0.967638\pi$
$983$	−12.8397	+	22.2390i	−0.409523	+	0.709315i	0.585313	+	0.810807i	$0.300972\pi$
$984$	7.29738	−	17.0393i	0.232632	−	0.543193i
$985$	8.96600	−	5.17652i	0.285680	−	0.164938i
$986$	−5.88024	+	25.4171i	−0.187265	+	0.809446i
$987$	−44.2022	+	3.64594i	−1.40697	+	0.116051i
$988$	−14.5704	+	29.8046i	−0.463547	+	0.948211i
$989$	2.26367	−	3.92079i	0.0719805	−	0.124674i
$990$	−7.26873	+	2.46927i	−0.231015	+	0.0784784i
$991$	20.2815	−	11.7096i	0.644264	−	0.371966i	−0.141991	−	0.989868i	$-0.545350\pi$
$991$	20.2815	−	11.7096i	0.644264	−	0.371966i	0.786255	+	0.617902i	$0.212017\pi$
$992$	33.3426	+	2.99391i	1.05863	+	0.0950569i
$993$	9.36631	−	9.66348i	0.297231	−	0.306661i
$994$	13.4350	−	29.8864i	0.426132	−	0.947939i
$995$	1.82994	+	1.05652i	0.0580130	+	0.0334938i
$996$	11.7437	+	32.5438i	0.372112	+	1.03119i
$997$	−1.36608	−	0.788707i	−0.0432642	−	0.0249786i	0.478212	−	0.878244i	$-0.341285\pi$
$997$	−1.36608	−	0.788707i	−0.0432642	−	0.0249786i	−0.521476	+	0.853266i	$0.674618\pi$
$998$	5.49692	+	5.13066i	0.174002	+	0.162408i
$999$	−8.68010	−	27.2245i	−0.274626	−	0.861345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bj.b.103.15	yes	84
3.2	odd	2		756.2.bj.b.523.28		84
4.3	odd	2	inner	252.2.bj.b.103.16	yes	84
7.3	odd	6		252.2.n.b.31.41	yes	84
9.2	odd	6		756.2.n.b.19.30		84
9.7	even	3		252.2.n.b.187.13	yes	84
12.11	even	2		756.2.bj.b.523.27		84
21.17	even	6		756.2.n.b.199.2		84
28.3	even	6		252.2.n.b.31.13	✓	84
36.7	odd	6		252.2.n.b.187.41	yes	84
36.11	even	6		756.2.n.b.19.2		84
63.38	even	6		756.2.bj.b.451.28		84
63.52	odd	6	inner	252.2.bj.b.115.15	yes	84
84.59	odd	6		756.2.n.b.199.30		84
252.115	even	6	inner	252.2.bj.b.115.16	yes	84
252.227	odd	6		756.2.bj.b.451.27		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.13	✓	84	28.3	even	6
252.2.n.b.31.41	yes	84	7.3	odd	6
252.2.n.b.187.13	yes	84	9.7	even	3
252.2.n.b.187.41	yes	84	36.7	odd	6
252.2.bj.b.103.15	yes	84	1.1	even	1	trivial
252.2.bj.b.103.16	yes	84	4.3	odd	2	inner
252.2.bj.b.115.15	yes	84	63.52	odd	6	inner
252.2.bj.b.115.16	yes	84	252.115	even	6	inner
756.2.n.b.19.2		84	36.11	even	6
756.2.n.b.19.30		84	9.2	odd	6
756.2.n.b.199.2		84	21.17	even	6
756.2.n.b.199.30		84	84.59	odd	6
756.2.bj.b.451.27		84	252.227	odd	6
756.2.bj.b.451.28		84	63.38	even	6
756.2.bj.b.523.27		84	12.11	even	2
756.2.bj.b.523.28		84	3.2	odd	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.412858 - 1.35261i) q^{2} +(1.24372 + 1.20547i) q^{3} +(-1.65910 + 1.11687i) q^{4} +(0.514884 - 0.297269i) q^{5} +(1.11705 - 2.17995i) q^{6} +(1.74201 - 1.99133i) q^{7} +(2.19566 + 1.78300i) q^{8} +(0.0936760 + 2.99854i) q^{9} +O(q^{10})\)	\(q+(-0.412858 - 1.35261i) q^{2} +(1.24372 + 1.20547i) q^{3} +(-1.65910 + 1.11687i) q^{4} +(0.514884 - 0.297269i) q^{5} +(1.11705 - 2.17995i) q^{6} +(1.74201 - 1.99133i) q^{7} +(2.19566 + 1.78300i) q^{8} +(0.0936760 + 2.99854i) q^{9} +(-0.614662 - 0.573707i) q^{10} +(-2.63566 - 1.52170i) q^{11} +(-3.40981 - 0.610922i) q^{12} +(6.21148 + 3.58620i) q^{13} +(-3.41269 - 1.53413i) q^{14} +(0.998720 + 0.250960i) q^{15} +(1.50521 - 3.70599i) q^{16} +(2.28182 - 1.31741i) q^{17} +(4.01717 - 1.36468i) q^{18} +(1.15636 - 2.00287i) q^{19} +(-0.522233 + 1.06826i) q^{20} +(4.56707 - 0.376706i) q^{21} +(-0.970111 + 4.19326i) q^{22} +(1.34481 - 0.776425i) q^{23} +(0.581426 + 4.86435i) q^{24} +(-2.32326 + 4.02401i) q^{25} +(2.28627 - 9.88229i) q^{26} +(-3.49814 + 3.84226i) q^{27} +(-0.666115 + 5.24941i) q^{28} +(-3.50068 - 6.06335i) q^{29} +(-0.0728793 - 1.45449i) q^{30} -5.91792 q^{31} +(-5.63419 - 0.505907i) q^{32} +(-1.44366 - 5.06978i) q^{33} +(-2.72401 - 2.54251i) q^{34} +(0.304976 - 1.54315i) q^{35} +(-3.50439 - 4.87024i) q^{36} +(-2.74961 + 4.76246i) q^{37} +(-3.18651 - 0.737199i) q^{38} +(3.40228 + 11.9480i) q^{39} +(1.66054 + 0.265339i) q^{40} +(-3.27676 - 1.89184i) q^{41} +(-2.39508 - 6.02192i) q^{42} +(2.52490 - 1.45775i) q^{43} +(6.07236 - 0.419042i) q^{44} +(0.939603 + 1.51605i) q^{45} +(-1.60541 - 1.49844i) q^{46} -9.67847 q^{47} +(6.33952 - 2.79473i) q^{48} +(-0.930778 - 6.93784i) q^{49} +(6.40208 + 1.48112i) q^{50} +(4.42605 + 1.11218i) q^{51} +(-14.3108 + 0.987559i) q^{52} +(4.10505 + 7.11016i) q^{53} +(6.64131 + 3.14531i) q^{54} -1.80941 q^{55} +(7.37540 - 1.26627i) q^{56} +(3.85259 - 1.09705i) q^{57} +(-6.75605 + 7.23834i) q^{58} -3.77001 q^{59} +(-1.93726 + 0.699074i) q^{60} +2.67699i q^{61} +(2.44326 + 8.00462i) q^{62} +(6.13426 + 5.03695i) q^{63} +(1.64182 + 7.82971i) q^{64} +4.26426 q^{65} +(-6.26141 + 4.04580i) q^{66} -8.92572i q^{67} +(-2.31439 + 4.73421i) q^{68} +(2.60852 + 0.655472i) q^{69} +(-2.21319 + 0.224588i) q^{70} +8.75743i q^{71} +(-5.14071 + 6.75078i) q^{72} +(-1.30083 + 0.751036i) q^{73} +(7.57694 + 1.75292i) q^{74} +(-7.74032 + 2.20411i) q^{75} +(0.318435 + 4.61446i) q^{76} +(-7.62156 + 2.59765i) q^{77} +(14.7563 - 9.53477i) q^{78} +6.73276i q^{79} +(-0.326667 - 2.35561i) q^{80} +(-8.98245 + 0.561782i) q^{81} +(-1.20608 + 5.21323i) q^{82} +(-4.99378 - 8.64947i) q^{83} +(-7.15647 + 5.72581i) q^{84} +(0.783250 - 1.35663i) q^{85} +(-3.01419 - 2.81336i) q^{86} +(2.95534 - 11.7611i) q^{87} +(-3.07382 - 8.04052i) q^{88} +(-13.7577 - 7.94299i) q^{89} +(1.66270 - 1.89683i) q^{90} +(17.9618 - 6.12189i) q^{91} +(-1.36400 + 2.79014i) q^{92} +(-7.36023 - 7.13388i) q^{93} +(3.99583 + 13.0912i) q^{94} -1.37500i q^{95} +(-6.39749 - 7.42106i) q^{96} +(1.20110 - 0.693454i) q^{97} +(-8.99990 + 4.12332i) q^{98} +(4.31598 - 8.04568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9}+O(q^{10}) \) 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9	\( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 11 q^{30} - 18 q^{32} - 18 q^{33} - 24 q^{34} - 38 q^{36} + 2 q^{37} + 33 q^{38} + 6 q^{40} + 6 q^{41} - 38 q^{42} - 13 q^{44} - 54 q^{45} + 10 q^{46} + 9 q^{48} - 28 q^{49} - 17 q^{50} - 27 q^{52} - 2 q^{53} - 39 q^{54} + 58 q^{56} + 6 q^{57} - 13 q^{58} - 31 q^{60} - 8 q^{64} - 100 q^{65} + 30 q^{66} - 18 q^{68} - 18 q^{69} - 19 q^{70} + 26 q^{72} + 30 q^{73} - 23 q^{74} - 2 q^{77} + 15 q^{78} + 3 q^{80} - 32 q^{81} - 18 q^{82} + 23 q^{84} - 50 q^{85} - 9 q^{86} + q^{88} - 102 q^{89} - 39 q^{90} + 28 q^{92} - 36 q^{93} + 63 q^{96} + 6 q^{97} + 21 q^{98}+O(q^{100}) \) 84 * q + 2 * q^2 - 2 * q^4 + 6 * q^5 - 16 * q^8 + 4 * q^9 - 18 * q^10 - 6 * q^12 + 18 * q^13 + 14 * q^14 + 14 * q^16 + 6 * q^17 - 10 * q^18 - 24 * q^20 + 4 * q^21 + 6 * q^22 - 6 * q^24 + 16 * q^25 - 30 * q^26 - 4 * q^28 + 10 * q^29 + 11 * q^30 - 18 * q^32 - 18 * q^33 - 24 * q^34 - 38 * q^36 + 2 * q^37 + 33 * q^38 + 6 * q^40 + 6 * q^41 - 38 * q^42 - 13 * q^44 - 54 * q^45 + 10 * q^46 + 9 * q^48 - 28 * q^49 - 17 * q^50 - 27 * q^52 - 2 * q^53 - 39 * q^54 + 58 * q^56 + 6 * q^57 - 13 * q^58 - 31 * q^60 - 8 * q^64 - 100 * q^65 + 30 * q^66 - 18 * q^68 - 18 * q^69 - 19 * q^70 + 26 * q^72 + 30 * q^73 - 23 * q^74 - 2 * q^77 + 15 * q^78 + 3 * q^80 - 32 * q^81 - 18 * q^82 + 23 * q^84 - 50 * q^85 - 9 * q^86 + q^88 - 102 * q^89 - 39 * q^90 + 28 * q^92 - 36 * q^93 + 63 * q^96 + 6 * q^97 + 21 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more