LMFDB - Embedded newform 276.2.o.a.35.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(35,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 20]))

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

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

chi := DirichletCharacter("276.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.o (of order $22$, degree $10$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$44$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.14
Character	$\chi$	$=$	276.35
Dual form			276.2.o.a.71.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.774443 + 1.18332i) q^{2} +(-1.59213 + 0.682004i) q^{3} +(-0.800475 - 1.83282i) q^{4} +(0.168792 + 0.574851i) q^{5} +(0.425987 - 2.41216i) q^{6} +(2.73269 - 2.36789i) q^{7} +(2.78873 + 0.472203i) q^{8} +(2.06974 - 2.17167i) q^{9} +O(q^{10})$	\(q+(-0.774443 + 1.18332i) q^{2} +(-1.59213 + 0.682004i) q^{3} +(-0.800475 - 1.83282i) q^{4} +(0.168792 + 0.574851i) q^{5} +(0.425987 - 2.41216i) q^{6} +(2.73269 - 2.36789i) q^{7} +(2.78873 + 0.472203i) q^{8} +(2.06974 - 2.17167i) q^{9} +(-0.810951 - 0.245456i) q^{10} +(2.81832 + 1.81123i) q^{11} +(2.52445 + 2.37216i) q^{12} +(-2.47007 + 2.85062i) q^{13} +(0.685649 + 5.06744i) q^{14} +(-0.660789 - 0.800120i) q^{15} +(-2.71848 + 2.93426i) q^{16} +(-1.55064 + 0.708152i) q^{17} +(0.966881 + 4.13100i) q^{18} +(0.386731 + 0.176614i) q^{19} +(0.918488 - 0.769519i) q^{20} +(-2.73589 + 5.63370i) q^{21} +(-4.32588 + 1.93227i) q^{22} +(3.51470 + 3.26296i) q^{23} +(-4.76206 + 1.15012i) q^{24} +(3.90430 - 2.50914i) q^{25} +(-1.46025 - 5.13052i) q^{26} +(-1.81420 + 4.86916i) q^{27} +(-6.52738 - 3.11311i) q^{28} +(-0.0545631 + 0.0249181i) q^{29} +(1.45854 - 0.162274i) q^{30} +(7.54204 - 1.08438i) q^{31} +(-1.36684 - 5.48924i) q^{32} +(-5.72239 - 0.961596i) q^{33} +(0.362913 - 2.38332i) q^{34} +(1.82244 + 1.17121i) q^{35} +(-5.63707 - 2.05510i) q^{36} +(9.04804 + 2.65674i) q^{37} +(-0.508491 + 0.320847i) q^{38} +(1.98854 - 6.22314i) q^{39} +(0.199268 + 1.68281i) q^{40} +(2.14166 + 7.29381i) q^{41} +(-4.54766 - 7.60040i) q^{42} +(-3.74007 - 0.537741i) q^{43} +(1.06366 - 6.61533i) q^{44} +(1.59775 + 0.823233i) q^{45} +(-6.58305 + 1.63203i) q^{46} -8.85011 q^{47} +(2.32699 - 6.52573i) q^{48} +(0.864497 - 6.01271i) q^{49} +(-0.0545521 + 6.56322i) q^{50} +(1.98585 - 2.18501i) q^{51} +(7.20191 + 2.24536i) q^{52} +(-2.10780 + 1.82642i) q^{53} +(-4.35675 - 5.91766i) q^{54} +(-0.565477 + 1.92584i) q^{55} +(8.73888 - 5.31303i) q^{56} +(-0.736176 - 0.0174402i) q^{57} +(0.0127700 - 0.0838631i) q^{58} +(3.59218 - 4.14560i) q^{59} +(-0.937534 + 1.85158i) q^{60} +(-1.40855 - 9.79667i) q^{61} +(-4.55772 + 9.76441i) q^{62} +(0.513676 - 10.8355i) q^{63} +(7.55405 + 2.63370i) q^{64} +(-2.05561 - 0.938765i) q^{65} +(5.56954 - 6.02670i) q^{66} +(4.30433 + 6.69767i) q^{67} +(2.53916 + 2.27519i) q^{68} +(-7.82120 - 2.79800i) q^{69} +(-2.79729 + 1.24949i) q^{70} +(11.2331 - 7.21909i) q^{71} +(6.79742 - 5.07888i) q^{72} +(-0.421746 + 0.923494i) q^{73} +(-10.1510 + 8.64919i) q^{74} +(-4.50490 + 6.65763i) q^{75} +(0.0141341 - 0.850184i) q^{76} +(11.9904 - 1.72396i) q^{77} +(5.82394 + 7.17254i) q^{78} +(-9.95979 - 8.63021i) q^{79} +(-2.14562 - 1.06744i) q^{80} +(-0.432343 - 8.98961i) q^{81} +(-10.2895 - 3.11439i) q^{82} +(-8.26280 - 2.42618i) q^{83} +(12.5156 + 0.504764i) q^{84} +(-0.668817 - 0.771856i) q^{85} +(3.53279 - 4.00923i) q^{86} +(0.0698772 - 0.0768851i) q^{87} +(7.00428 + 6.38184i) q^{88} +(-14.9047 - 2.14298i) q^{89} +(-2.21151 + 1.25309i) q^{90} +13.6387i q^{91} +(3.16699 - 9.05374i) q^{92} +(-11.2683 + 6.87017i) q^{93} +(6.85391 - 10.4725i) q^{94} +(-0.0362499 + 0.252124i) q^{95} +(5.91987 + 7.80738i) q^{96} +(6.21222 - 1.82407i) q^{97} +(6.44543 + 5.67948i) q^{98} +(9.76659 - 2.37171i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$-1$	$-1$

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 $

$2$	−0.774443	+	1.18332i	−0.547614	+	0.836731i
$2$	−0.774443	+	1.18332i	−0.547614	+	0.836731i
$3$	−1.59213	+	0.682004i	−0.919215	+	0.393755i
$3$	−1.59213	+	0.682004i	−0.919215	+	0.393755i
$4$	−0.800475	−	1.83282i	−0.400237	−	0.916412i
$5$	0.168792	+	0.574851i	0.0754859	+	0.257081i	0.988587	−	0.150652i	$-0.0481374\pi$
$5$	0.168792	+	0.574851i	0.0754859	+	0.257081i	−0.913101	+	0.407734i	$0.866319\pi$
$6$	0.425987	−	2.41216i	0.173908	−	0.984762i
$7$	2.73269	−	2.36789i	1.03286	−	0.894980i	0.0383142	−	0.999266i	$-0.487801\pi$
$7$	2.73269	−	2.36789i	1.03286	−	0.894980i	0.994547	+	0.104286i	$0.0332558\pi$
$8$	2.78873	+	0.472203i	0.985966	+	0.166949i
$9$	2.06974	−	2.17167i	0.689914	−	0.723892i
$10$	−0.810951	−	0.245456i	−0.256445	−	0.0776200i
$11$	2.81832	+	1.81123i	0.849756	+	0.546105i	0.891499	−	0.453023i	$-0.149655\pi$
$11$	2.81832	+	1.81123i	0.849756	+	0.546105i	−0.0417424	+	0.999128i	$0.513291\pi$
$12$	2.52445	+	2.37216i	0.728746	+	0.684784i
$13$	−2.47007	+	2.85062i	−0.685075	+	0.790619i	−0.986655	−	0.162822i	$-0.947940\pi$
$13$	−2.47007	+	2.85062i	−0.685075	+	0.790619i	0.301581	+	0.953441i	$0.402486\pi$
$14$	0.685649	+	5.06744i	0.183247	+	1.35433i
$15$	−0.660789	−	0.800120i	−0.170615	−	0.206590i
$16$	−2.71848	+	2.93426i	−0.679620	+	0.733564i
$17$	−1.55064	+	0.708152i	−0.376085	+	0.171752i	−0.594484	−	0.804107i	$-0.702644\pi$
$17$	−1.55064	+	0.708152i	−0.376085	+	0.171752i	0.218399	+	0.975859i	$0.429916\pi$
$18$	0.966881	+	4.13100i	0.227896	+	0.973685i
$19$	0.386731	+	0.176614i	0.0887221	+	0.0405180i	0.459282	−	0.888291i	$-0.348107\pi$
$19$	0.386731	+	0.176614i	0.0887221	+	0.0405180i	−0.370560	+	0.928809i	$0.620834\pi$
$20$	0.918488	−	0.769519i	0.205380	−	0.172070i
$21$	−2.73589	+	5.63370i	−0.597019	+	1.22937i
$22$	−4.32588	+	1.93227i	−0.922282	+	0.411962i
$23$	3.51470	+	3.26296i	0.732866	+	0.680374i
$23$	3.51470	+	3.26296i	0.732866	+	0.680374i
$24$	−4.76206	+	1.15012i	−0.972052	+	0.234767i
$25$	3.90430	−	2.50914i	0.780861	−	0.501829i
$26$	−1.46025	−	5.13052i	−0.286378	−	1.00618i
$27$	−1.81420	+	4.86916i	−0.349143	+	0.937069i
$28$	−6.52738	−	3.11311i	−1.23356	−	0.588322i
$29$	−0.0545631	+	0.0249181i	−0.0101321	+	0.00462718i	−0.420475	−	0.907304i	$-0.638136\pi$
$29$	−0.0545631	+	0.0249181i	−0.0101321	+	0.00462718i	0.410343	+	0.911931i	$0.365409\pi$
$30$	1.45854	−	0.162274i	0.266292	−	0.0296271i
$31$	7.54204	−	1.08438i	1.35459	−	0.194761i	0.573513	−	0.819196i	$-0.305580\pi$
$31$	7.54204	−	1.08438i	1.35459	−	0.194761i	0.781076	+	0.624435i	$0.214671\pi$
$32$	−1.36684	−	5.48924i	−0.241626	−	0.970369i
$33$	−5.72239	−	0.961596i	−0.996141	−	0.167392i
$34$	0.362913	−	2.38332i	0.0622390	−	0.408736i
$35$	1.82244	+	1.17121i	0.308049	+	0.197971i
$36$	−5.63707	−	2.05510i	−0.939512	−	0.342516i
$37$	9.04804	+	2.65674i	1.48749	+	0.436766i	0.921739	−	0.387811i	$-0.126769\pi$
$37$	9.04804	+	2.65674i	1.48749	+	0.436766i	0.565750	+	0.824577i	$0.308587\pi$
$38$	−0.508491	+	0.320847i	−0.0824882	+	0.0520483i
$39$	1.98854	−	6.22314i	0.318421	−	0.996501i
$40$	0.199268	+	1.68281i	0.0315070	+	0.266076i
$41$	2.14166	+	7.29381i	0.334471	+	1.13910i	0.939400	+	0.342823i	$0.111383\pi$
$41$	2.14166	+	7.29381i	0.334471	+	1.13910i	−0.604930	+	0.796279i	$0.706799\pi$
$42$	−4.54766	−	7.60040i	−0.701719	−	1.17277i
$43$	−3.74007	−	0.537741i	−0.570355	−	0.0820047i	−0.148897	−	0.988853i	$-0.547572\pi$
$43$	−3.74007	−	0.537741i	−0.570355	−	0.0820047i	−0.421458	+	0.906848i	$0.638481\pi$
$44$	1.06366	−	6.61533i	0.160353	−	0.997298i
$45$	1.59775	+	0.823233i	0.238178	+	0.122720i
$46$	−6.58305	+	1.63203i	−0.970617	+	0.240629i
$47$	−8.85011			−1.29092			−0.645461	−	0.763793i	$-0.723335\pi$
$47$	−8.85011			−1.29092			−0.645461	+	0.763793i	$0.723335\pi$
$48$	2.32699	−	6.52573i	0.335873	−	0.941907i
$49$	0.864497	−	6.01271i	0.123500	−	0.858959i
$50$	−0.0545521	+	6.56322i	−0.00771483	+	0.928179i
$51$	1.98585	−	2.18501i	0.278075	−	0.305963i
$52$	7.20191	+	2.24536i	0.998725	+	0.311375i
$53$	−2.10780	+	1.82642i	−0.289529	+	0.250878i	−0.787499	−	0.616316i	$-0.788624\pi$
$53$	−2.10780	+	1.82642i	−0.289529	+	0.250878i	0.497970	+	0.867194i	$0.334079\pi$
$54$	−4.35675	−	5.91766i	−0.592879	−	0.805291i
$55$	−0.565477	+	1.92584i	−0.0762489	+	0.259680i
$56$	8.73888	−	5.31303i	1.16778	−	0.709984i
$57$	−0.736176	−	0.0174402i	−0.0975089	−	0.00231000i
$58$	0.0127700	−	0.0838631i	0.00167678	−	0.0110118i
$59$	3.59218	−	4.14560i	0.467662	−	0.539711i	−0.472098	−	0.881546i	$-0.656503\pi$
$59$	3.59218	−	4.14560i	0.467662	−	0.539711i	0.939760	+	0.341835i	$0.111048\pi$
$60$	−0.937534	+	1.85158i	−0.121035	+	0.239039i
$61$	−1.40855	−	9.79667i	−0.180346	−	1.25434i	−0.855945	−	0.517066i	$-0.827024\pi$
$61$	−1.40855	−	9.79667i	−0.180346	−	1.25434i	0.675599	−	0.737269i	$-0.263885\pi$
$62$	−4.55772	+	9.76441i	−0.578830	+	1.24008i
$63$	0.513676	−	10.8355i	0.0647171	−	1.36514i
$64$	7.55405	+	2.63370i	0.944256	+	0.329212i
$65$	−2.05561	−	0.938765i	−0.254967	−	0.116439i
$66$	5.56954	−	6.02670i	0.685563	−	0.741835i
$67$	4.30433	+	6.69767i	0.525857	+	0.818250i	0.997996	−	0.0632741i	$-0.0201542\pi$
$67$	4.30433	+	6.69767i	0.525857	+	0.818250i	−0.472139	+	0.881524i	$0.656518\pi$
$68$	2.53916	+	2.27519i	0.307919	+	0.275907i
$69$	−7.82120	−	2.79800i	−0.941562	−	0.336840i
$70$	−2.79729	+	1.24949i	−0.334341	+	0.149342i
$71$	11.2331	−	7.21909i	1.33313	−	0.856749i	0.336733	−	0.941600i	$-0.390678\pi$
$71$	11.2331	−	7.21909i	1.33313	−	0.856749i	0.996394	+	0.0848515i	$0.0270416\pi$
$72$	6.79742	−	5.07888i	0.801084	−	0.598552i
$73$	−0.421746	+	0.923494i	−0.0493616	+	0.108087i	−0.932706	−	0.360638i	$-0.882559\pi$
$73$	−0.421746	+	0.923494i	−0.0493616	+	0.108087i	0.883344	+	0.468725i	$0.155286\pi$
$74$	−10.1510	+	8.64919i	−1.18003	+	1.00545i
$75$	−4.50490	+	6.65763i	−0.520182	+	0.768757i
$76$	0.0141341	−	0.850184i	0.00162129	−	0.0975228i
$77$	11.9904	−	1.72396i	1.36643	−	0.196463i
$78$	5.82394	+	7.17254i	0.659431	+	0.812131i
$79$	−9.95979	−	8.63021i	−1.12056	−	0.970974i	−0.120799	−	0.992677i	$-0.538546\pi$
$79$	−9.95979	−	8.63021i	−1.12056	−	0.970974i	−0.999764	+	0.0217029i	$0.993091\pi$
$80$	−2.14562	−	1.06744i	−0.239887	−	0.119344i
$81$	−0.432343	−	8.98961i	−0.0480381	−	0.998846i
$82$	−10.2895	−	3.11439i	−1.13628	−	0.343927i
$83$	−8.26280	−	2.42618i	−0.906961	−	0.266308i	−0.205200	−	0.978720i	$-0.565784\pi$
$83$	−8.26280	−	2.42618i	−0.906961	−	0.266308i	−0.701761	+	0.712412i	$0.747603\pi$
$84$	12.5156	+	0.504764i	1.36556	+	0.0550742i
$85$	−0.668817	−	0.771856i	−0.0725434	−	0.0837195i
$86$	3.53279	−	4.00923i	0.380950	−	0.432327i
$87$	0.0698772	−	0.0768851i	0.00749162	−	0.00824295i
$88$	7.00428	+	6.38184i	0.746659	+	0.680307i
$89$	−14.9047	−	2.14298i	−1.57990	−	0.227155i	−0.704195	−	0.710006i	$-0.748692\pi$
$89$	−14.9047	−	2.14298i	−1.57990	−	0.227155i	−0.875702	+	0.482851i	$0.839601\pi$
$90$	−2.21151	+	1.25309i	−0.233113	+	0.132087i
$91$			13.6387i			1.42973i
$92$	3.16699	−	9.05374i	0.330182	−	0.943917i
$93$	−11.2683	+	6.87017i	−1.16847	+	0.712404i
$94$	6.85391	−	10.4725i	0.706927	−	1.08015i
$95$	−0.0362499	+	0.252124i	−0.00371916	+	0.0258673i
$96$	5.91987	+	7.80738i	0.604194	+	0.796837i
$97$	6.21222	−	1.82407i	0.630755	−	0.185206i	0.0492990	−	0.998784i	$-0.484301\pi$
$97$	6.21222	−	1.82407i	0.630755	−	0.185206i	0.581456	+	0.813578i	$0.302483\pi$
$98$	6.44543	+	5.67948i	0.651087	+	0.573714i
$99$	9.76659	−	2.37171i	0.981579	−	0.238366i
$100$	−7.72411	−	5.14739i	−0.772411	−	0.514739i
$101$	0.0668407	−	0.227638i	0.00665090	−	0.0226509i	−0.956101	−	0.293038i	$-0.905334\pi$
$101$	0.0668407	−	0.227638i	0.00665090	−	0.0226509i	0.962752	+	0.270387i	$0.0871518\pi$
$102$	1.04763	+	4.04206i	0.103731	+	0.400223i
$103$	−4.94024	+	7.68716i	−0.486776	+	0.757439i	−0.994573	−	0.104038i	$-0.966824\pi$
$103$	−4.94024	+	7.68716i	−0.486776	+	0.757439i	0.507797	+	0.861477i	$0.330460\pi$
$104$	−8.23444	+	6.78323i	−0.807453	+	0.665150i
$105$	−3.70033	−	0.621807i	−0.361116	−	0.0606822i
$106$	−0.528860	−	3.90865i	−0.0513674	−	0.379642i
$107$	−0.0820034	−	0.570346i	−0.00792757	−	0.0551375i	0.985474	−	0.169828i	$-0.0543213\pi$
$107$	−0.0820034	−	0.570346i	−0.00792757	−	0.0551375i	−0.993401	+	0.114691i	$0.963412\pi$
$108$	10.3765	−	0.572525i	0.998481	−	0.0550913i
$109$	3.03415	+	6.64386i	0.290619	+	0.636366i	0.997477	−	0.0709887i	$-0.0226154\pi$
$109$	3.03415	+	6.64386i	0.290619	+	0.636366i	−0.706858	+	0.707355i	$0.749888\pi$
$110$	−1.84094	−	2.16059i	−0.175527	−	0.206004i
$111$	−16.2175	+	1.94092i	−1.53930	+	0.184224i
$112$	−0.480771	+	14.4555i	−0.0454286	+	1.36592i
$113$	−3.04806	−	4.74287i	−0.286737	−	0.446171i	0.667767	−	0.744371i	$-0.267250\pi$
$113$	−3.04806	−	4.74287i	−0.286737	−	0.446171i	−0.954504	+	0.298199i	$0.903614\pi$
$114$	0.590764	−	0.857623i	0.0553301	−	0.0803237i
$115$	−1.28246	+	2.57119i	−0.119590	+	0.239765i
$116$	0.0893469	+	0.0800582i	0.00829565	+	0.00743322i
$117$	1.07820	+	11.2642i	0.0996796	+	1.04138i
$118$	2.12361	+	7.46122i	0.195494	+	0.686861i
$119$	−2.56059	+	5.60691i	−0.234729	+	0.513985i
$120$	−1.46494	−	2.54335i	−0.133730	−	0.232175i
$121$	0.0928381	+	0.203287i	0.00843983	+	0.0184806i
$122$	12.6834	+	5.92021i	1.14830	+	0.535991i
$123$	−8.38420	−	10.1521i	−0.755978	−	0.915381i
$124$	−8.02469	−	12.9552i	−0.720638	−	1.16341i
$125$	4.36532	+	3.78257i	0.390446	+	0.338324i
$126$	12.4240	+	8.99929i	1.10681	+	0.801720i
$127$	−8.37991	+	13.0394i	−0.743597	+	1.15706i	0.238948	+	0.971032i	$0.423197\pi$
$127$	−8.37991	+	13.0394i	−0.743597	+	1.15706i	−0.982545	+	0.186026i	$0.940439\pi$
$128$	−8.96668	+	6.89918i	−0.792550	+	0.609807i
$129$	6.32141	−	1.69459i	0.556569	−	0.149200i
$130$	2.70281	−	1.70541i	0.237052	−	0.149575i
$131$	−8.68672	−	10.0250i	−0.758962	−	0.875889i	0.236443	−	0.971645i	$-0.424018\pi$
$131$	−8.68672	−	10.0250i	−0.758962	−	0.875889i	−0.995405	+	0.0957567i	$0.969473\pi$
$132$	2.81820	+	11.2579i	0.245292	+	0.979872i
$133$	1.47502	−	0.433105i	0.127900	−	0.0375550i
$134$	−11.2589	−	0.0935818i	−0.972622	−	0.00808424i
$135$	−3.10526	−	0.221024i	−0.267258	−	0.0190227i
$136$	−4.65870	+	1.24263i	−0.399481	+	0.106555i
$137$		−	18.0918i		−	1.54568i	−0.634599	−	0.772841i	$-0.718835\pi$
$137$		−	18.0918i		−	1.54568i	0.634599	−	0.772841i	$-0.281165\pi$
$138$	9.36800	−	7.08806i	0.797457	−	0.603375i
$139$		−	12.0588i		−	1.02281i	−0.859339	−	0.511406i	$-0.829125\pi$
$139$		−	12.0588i		−	1.02281i	0.859339	−	0.511406i	$-0.170875\pi$
$140$	0.687807	−	4.27774i	0.0581303	−	0.361535i
$141$	14.0905	−	6.03581i	1.18663	−	0.508307i
$142$	−0.156953	+	18.8831i	−0.0131712	+	1.58464i
$143$	−12.1246	+	3.56010i	−1.01391	+	0.297710i
$144$	0.745700	+	11.9768i	0.0621417	+	0.998067i
$145$	−0.0235340	−	0.0271597i	−0.00195439	−	0.00225549i
$146$	−0.766168	−	1.21425i	−0.0634085	−	0.100492i
$147$	2.72430	+	10.1626i	0.224697	+	0.838197i
$148$	−2.37338	−	18.7101i	−0.195091	−	1.53796i
$149$	−1.84514	+	2.87109i	−0.151160	+	0.235209i	−0.908572	−	0.417727i	$-0.862827\pi$
$149$	−1.84514	+	2.87109i	−0.151160	+	0.235209i	0.757413	+	0.652936i	$0.226463\pi$
$150$	−4.38929	−	10.4867i	−0.358384	−	0.856234i
$151$	10.1324	+	8.77976i	0.824562	+	0.714487i	0.961116	−	0.276146i	$-0.0890573\pi$
$151$	10.1324	+	8.77976i	0.824562	+	0.714487i	−0.136554	+	0.990633i	$0.543603\pi$
$152$	0.995090	+	0.675144i	0.0807125	+	0.0547614i
$153$	−1.67154	+	4.83317i	−0.135136	+	0.390739i
$154$	−7.24590	+	15.5236i	−0.583891	+	1.25092i
$155$	1.89639	+	4.15252i	0.152322	+	0.333538i
$156$	−12.9977	+	1.33683i	−1.04065	+	0.107032i
$157$	−5.46999	+	11.9776i	−0.436553	+	0.955917i	0.555666	+	0.831406i	$0.312463\pi$
$157$	−5.46999	+	11.9776i	−0.436553	+	0.955917i	−0.992218	+	0.124511i	$0.960264\pi$
$158$	17.9256	−	5.10197i	1.42608	−	0.405891i
$159$	2.11026	−	4.34542i	0.167355	−	0.344614i
$160$	2.92478	−	1.71227i	0.231225	−	0.135367i
$161$	17.3309	+	0.594231i	1.36587	+	0.0468319i
$162$	10.9724	+	6.45035i	0.862071	+	0.506787i
$163$	−0.0383352	−	0.0596507i	−0.00300265	−	0.00467221i	0.839749	−	0.542975i	$-0.182702\pi$
$163$	−0.0383352	−	0.0596507i	−0.00300265	−	0.00467221i	−0.842752	+	0.538303i	$0.819066\pi$
$164$	11.6539	−	9.76379i	0.910019	−	0.762424i
$165$	−0.413117	−	3.45184i	−0.0321611	−	0.268725i
$166$	9.27001	−	7.89857i	0.719492	−	0.613048i
$167$	7.85796	+	17.2065i	0.608067	+	1.33148i	0.923888	+	0.382663i	$0.124993\pi$
$167$	7.85796	+	17.2065i	0.608067	+	1.33148i	−0.315821	+	0.948819i	$0.602280\pi$
$168$	−10.2899	+	14.4190i	−0.793883	+	1.11245i
$169$	−0.174659	−	1.21478i	−0.0134353	−	0.0934445i
$170$	1.43131	−	0.193663i	0.109777	−	0.0148533i
$171$	1.18398	−	0.474308i	0.0905412	−	0.0362712i
$172$	2.00825	+	7.28533i	0.153127	+	0.555501i
$173$	6.36987	−	9.91171i	0.484292	−	0.753573i	−0.510010	−	0.860168i	$-0.670358\pi$
$173$	6.36987	−	9.91171i	0.484292	−	0.753573i	0.994303	+	0.106595i	$0.0339948\pi$
$174$	0.0368635	+	0.142230i	0.00279461	+	0.0107824i
$175$	4.72789	−	16.1017i	0.357395	−	1.21717i
$176$	−12.9762	+	3.34590i	−0.978115	+	0.252207i
$177$	−2.89190	+	9.05021i	−0.217368	+	0.680255i
$178$	14.0787	−	15.9774i	1.05524	−	1.19756i
$179$	−5.84903	+	1.71743i	−0.437177	+	0.128367i	−0.492913	−	0.870079i	$-0.664068\pi$
$179$	−5.84903	+	1.71743i	−0.437177	+	0.128367i	0.0557355	+	0.998446i	$0.482250\pi$
$180$	0.229886	−	3.58736i	0.0171347	−	0.267386i
$181$	2.23672	−	15.5567i	0.166254	−	1.15632i	−0.720288	−	0.693675i	$-0.755990\pi$
$181$	2.23672	−	15.5567i	0.166254	−	1.15632i	0.886542	−	0.462648i	$-0.153101\pi$
$182$	−16.1389	−	10.5624i	−1.19630	−	0.782939i
$183$	8.92396	+	14.6369i	0.659678	+	1.08199i
$184$	8.26078	+	10.7592i	0.608992	+	0.793176i
$185$			5.64971i			0.415375i
$186$	0.597101	−	18.6546i	0.0437816	−	1.36782i
$187$	−5.65282	−	0.812753i	−0.413375	−	0.0594344i
$188$	7.08429	+	16.2207i	0.516675	+	1.18302i
$189$	6.57198	+	17.6018i	0.478041	+	1.28034i
$190$	−0.270268	−	0.238151i	−0.0196073	−	0.0172773i
$191$	−5.05600	−	5.83494i	−0.365840	−	0.422201i	0.542748	−	0.839896i	$-0.317384\pi$
$191$	−5.05600	−	5.83494i	−0.365840	−	0.422201i	−0.908588	+	0.417694i	$0.862838\pi$
$192$	−13.8232	+	0.958710i	−0.997604	+	0.0691890i
$193$	−18.3695	−	5.39376i	−1.32226	−	0.388252i	−0.456954	−	0.889490i	$-0.651060\pi$
$193$	−18.3695	−	5.39376i	−1.32226	−	0.388252i	−0.865309	+	0.501239i	$0.832878\pi$
$194$	−2.65256	+	8.76366i	−0.190443	+	0.629194i
$195$	3.91303	+	0.0927005i	0.280218	+	0.00663842i
$196$	−11.7122	+	3.22855i	−0.836589	+	0.230611i
$197$	12.0613	+	10.4512i	0.859331	+	0.744614i	0.968395	−	0.249420i	$-0.0802401\pi$
$197$	12.0613	+	10.4512i	0.859331	+	0.744614i	−0.109065	+	0.994035i	$0.534786\pi$
$198$	−4.75719	+	13.3937i	−0.338079	+	0.951851i
$199$	−3.59602	+	0.517029i	−0.254915	+	0.0366512i	−0.268588	−	0.963255i	$-0.586557\pi$
$199$	−3.59602	+	0.517029i	−0.254915	+	0.0366512i	0.0136725	+	0.999907i	$0.495648\pi$
$200$	12.0729	−	5.15370i	0.853682	−	0.364422i
$201$	−11.4209	−	7.72797i	−0.805566	−	0.545089i
$202$	0.217604	+	0.255387i	0.0153106	+	0.0179690i
$203$	−0.0901008	+	0.197293i	−0.00632384	+	0.0138473i
$204$	−5.59436	−	1.89067i	−0.391684	−	0.132373i
$205$	−3.83136	+	2.46227i	−0.267594	+	0.171972i
$206$	−5.27041	−	11.7991i	−0.367207	−	0.822085i
$207$	14.3606	−	0.879308i	0.998131	−	0.0611162i
$208$	−1.64959	−	14.9972i	−0.114379	−	1.03987i
$209$	0.770044	+	1.19821i	0.0532650	+	0.0828820i
$210$	3.60149	−	3.89711i	0.248527	−	0.268926i
$211$	−8.60045	−	3.92769i	−0.592079	−	0.270394i	0.0967598	−	0.995308i	$-0.469152\pi$
$211$	−8.60045	−	3.92769i	−0.592079	−	0.270394i	−0.688839	+	0.724914i	$0.741879\pi$
$212$	5.03475	+	2.40122i	0.345788	+	0.164917i
$213$	−12.9611	+	19.1548i	−0.888081	+	1.31246i
$214$	0.738407	+	0.344665i	0.0504765	+	0.0235608i
$215$	−0.322171	−	2.24075i	−0.0219719	−	0.152818i
$216$	−7.35855	+	12.7221i	−0.500686	+	0.865629i
$217$	18.0424	−	20.8220i	1.22480	−	1.41349i
$218$	−10.2116	−	1.55494i	−0.691614	−	0.105314i
$219$	0.0416463	−	1.75795i	0.00281419	−	0.118791i
$220$	3.98237	−	0.505165i	0.268491	−	0.0340582i
$221$	1.81152	−	6.16946i	0.121856	−	0.415003i
$222$	10.2628	−	20.6936i	0.688797	−	1.38886i
$223$	6.09435	−	5.28078i	0.408108	−	0.353627i	−0.426485	−	0.904495i	$-0.640248\pi$
$223$	6.09435	−	5.28078i	0.408108	−	0.353627i	0.834593	+	0.550867i	$0.185703\pi$
$224$	−16.7331	−	11.7639i	−1.11803	−	0.786007i
$225$	2.63185	−	13.6722i	0.175457	−	0.911477i
$226$	7.97286	+	0.0662688i	0.530347	+	0.00440813i
$227$	3.59451	−	25.0004i	0.238576	−	1.65933i	−0.420527	−	0.907280i	$-0.638155\pi$
$227$	3.59451	−	25.0004i	0.238576	−	1.65933i	0.659103	−	0.752053i	$-0.270936\pi$
$228$	0.557325	+	1.36324i	0.0369098	+	0.0902828i
$229$	−14.8882			−0.983839			−0.491920	−	0.870641i	$-0.663705\pi$
$229$	−14.8882			−0.983839			−0.491920	+	0.870641i	$0.663705\pi$
$230$	−2.04934	−	3.50880i	−0.135129	−	0.231364i
$231$	−17.9145	+	10.9223i	−1.17869	+	0.718633i
$232$	−0.163928	+	0.0437251i	−0.0107624	+	0.00287069i
$233$	−17.4378	−	2.50718i	−1.14239	−	0.164251i	−0.454968	−	0.890508i	$-0.650349\pi$
$233$	−17.4378	−	2.50718i	−1.14239	−	0.164251i	−0.687423	+	0.726257i	$0.741258\pi$
$234$	−14.1642	−	7.44766i	−0.925940	−	0.486869i
$235$	−1.49382	−	5.08750i	−0.0974464	−	0.331872i
$236$	−10.4736	−	3.26539i	−0.681773	−	0.212559i
$237$	21.7431	+	6.94777i	1.41237	+	0.451306i
$238$	−4.65171	−	7.37222i	−0.301526	−	0.477870i
$239$	5.39705	+	1.58472i	0.349106	+	0.102507i	0.451584	−	0.892228i	$-0.350859\pi$
$239$	5.39705	+	1.58472i	0.349106	+	0.102507i	−0.102478	+	0.994735i	$0.532677\pi$
$240$	4.14410	+	0.236188i	0.267501	+	0.0152459i
$241$	25.3309	+	16.2792i	1.63171	+	1.04864i	0.947700	+	0.319162i	$0.103401\pi$
$241$	25.3309	+	16.2792i	1.63171	+	1.04864i	0.684009	+	0.729474i	$0.260235\pi$
$242$	−0.312451	−	0.0475775i	−0.0200851	−	0.00305840i
$243$	6.81929	+	14.0177i	0.437458	+	0.899239i
$244$	−16.8281	+	10.4236i	−1.07731	+	0.667303i
$245$	3.60234	−	0.517938i	0.230145	−	0.0330898i
$246$	18.5062	−	2.05896i	1.17991	−	0.131275i
$247$	−1.45871	+	0.666171i	−0.0928156	+	0.0423875i
$248$	21.5448	+	0.537326i	1.36809	+	0.0341202i
$249$	14.8101	−	1.77248i	0.938552	−	0.112326i
$250$	−7.85668	+	2.23617i	−0.496900	+	0.141428i
$251$	−16.3944	+	10.5360i	−1.03481	+	0.665029i	−0.943697	−	0.330812i	$-0.892677\pi$
$251$	−16.3944	+	10.5360i	−1.03481	+	0.665029i	−0.0911084	+	0.995841i	$0.529041\pi$
$252$	−20.2706	+	7.73203i	−1.27693	+	0.487072i
$253$	3.99561	+	15.5620i	0.251202	+	0.978373i
$254$	−8.93996	−	20.0144i	−0.560943	−	1.25581i
$255$	1.59125	+	0.772758i	0.0996480	+	0.0483920i
$256$	−1.21972	−	15.9534i	−0.0762328	−	0.997090i
$257$	−18.7173	−	8.54791i	−1.16755	−	0.533204i	−0.265198	−	0.964194i	$-0.585437\pi$
$257$	−18.7173	−	8.54791i	−1.16755	−	0.533204i	−0.902357	+	0.430990i	$0.858164\pi$
$258$	−2.89034	+	8.79259i	−0.179945	+	0.547403i
$259$	31.0164	−	14.1647i	1.92727	−	0.880153i
$260$	−0.0751276	+	4.51902i	−0.00465922	+	0.280258i
$261$	−0.0588174	+	0.170067i	−0.00364071	+	0.0105269i
$262$	18.5901	−	2.51533i	1.14850	−	0.155398i
$263$	11.2286	−	12.9585i	0.692385	−	0.799055i	−0.295317	−	0.955399i	$-0.595425\pi$
$263$	11.2286	−	12.9585i	0.692385	−	0.799055i	0.987703	+	0.156344i	$0.0499709\pi$
$264$	−15.5041	−	5.38377i	−0.954214	−	0.331348i
$265$	−1.40570	−	0.903388i	−0.0863514	−	0.0554947i
$266$	−0.629819	+	2.08083i	−0.0386167	+	0.127584i
$267$	25.1917	−	6.75319i	1.54171	−	0.413289i
$268$	8.83013	−	13.2504i	0.539386	−	0.809396i
$269$	−17.9579	+	15.5606i	−1.09491	+	0.948745i	−0.998912	−	0.0466360i	$-0.985150\pi$
$269$	−17.9579	+	15.5606i	−1.09491	+	0.948745i	−0.0959986	+	0.995381i	$0.530604\pi$
$270$	2.66639	−	3.50334i	0.162271	−	0.213206i
$271$	−2.45342	−	8.35559i	−0.149035	−	0.507566i	0.850805	−	0.525482i	$-0.176115\pi$
$271$	−2.45342	−	8.35559i	−0.149035	−	0.507566i	−0.999839	+	0.0179162i	$0.994297\pi$
$272$	2.13748	−	6.47507i	0.129604	−	0.392609i
$273$	−9.30167	−	21.7146i	−0.562963	−	1.31423i
$274$	21.4083	+	14.0110i	1.29332	+	0.846438i
$275$	15.5482			0.937593
$276$	1.13242	+	16.5746i	0.0681639	+	0.997674i
$277$	−25.8264			−1.55176			−0.775880	−	0.630881i	$-0.782694\pi$
$277$	−25.8264			−1.55176			−0.775880	+	0.630881i	$0.782694\pi$
$278$	14.2694	+	9.33884i	0.855819	+	0.560107i
$279$	13.2551	−	18.6232i	0.793565	−	1.11494i
$280$	4.52925	+	4.12676i	0.270675	+	0.246621i
$281$	−8.75598	−	29.8201i	−0.522338	−	1.77892i	−0.621012	−	0.783801i	$-0.713278\pi$
$281$	−8.75598	−	29.8201i	−0.522338	−	1.77892i	0.0986741	−	0.995120i	$-0.468540\pi$
$282$	−3.77003	+	21.3479i	−0.224502	+	1.27125i
$283$	15.5191	−	13.4474i	0.922513	−	0.799362i	−0.0574896	−	0.998346i	$-0.518310\pi$
$283$	15.5191	−	13.4474i	0.922513	−	0.799362i	0.980003	+	0.198984i	$0.0637641\pi$
$284$	−22.2232	−	14.8096i	−1.31870	−	0.878790i
$285$	−0.114235	−	0.426136i	−0.00676669	−	0.0252421i
$286$	5.17708	−	17.1043i	0.306127	−	1.01140i
$287$	23.1235	+	14.8605i	1.36493	+	0.877190i
$288$	−14.7499	−	8.39296i	−0.869143	−	0.494560i
$289$	−9.22964	+	10.6516i	−0.542920	+	0.626563i
$290$	0.0503643	−	0.00681453i	0.00295749	−	0.000400163i
$291$	−8.64662	+	7.14091i	−0.506874	+	0.418608i
$292$	2.03020	+	0.0337515i	0.118808	+	0.00197516i
$293$	−15.9216	+	7.27115i	−0.930149	+	0.424785i	−0.822089	−	0.569359i	$-0.807191\pi$
$293$	−15.9216	+	7.27115i	−0.930149	+	0.424785i	−0.108060	+	0.994144i	$0.534464\pi$
$294$	−14.1354	−	4.64664i	−0.824392	−	0.270998i
$295$	2.98943	+	1.36523i	0.174052	+	0.0794867i
$296$	23.9780	+	11.6815i	1.39369	+	0.678971i
$297$	−13.9321	+	10.4369i	−0.808425	+	0.605612i
$298$	−1.96845	−	4.40688i	−0.114029	−	0.255284i
$299$	−17.9830	+	1.95932i	−1.03998	+	0.113310i
$300$	15.8083	+	2.92743i	0.912694	+	0.169015i
$301$	−11.4938	+	7.38660i	−0.662490	+	0.425757i
$302$	−18.2362	+	5.19039i	−1.04937	+	0.298673i
$303$	0.0488314	+	0.408015i	0.00280529	+	0.0234399i
$304$	−1.56955	+	0.654645i	−0.0900199	+	0.0375465i
$305$	5.39388	−	2.46330i	0.308853	−	0.141048i
$306$	−4.42466	−	5.72098i	−0.252941	−	0.327047i
$307$	−8.89079	+	1.27830i	−0.507424	+	0.0729566i	−0.391272	−	0.920275i	$-0.627965\pi$
$307$	−8.89079	+	1.27830i	−0.507424	+	0.0729566i	−0.116152	+	0.993231i	$0.537056\pi$
$308$	−12.7577	−	20.5963i	−0.726939	−	1.17358i
$309$	2.62282	−	15.6082i	0.149207	−	0.887920i
$310$	−6.38239	−	0.971859i	−0.362495	−	0.0551979i
$311$	4.27612	+	2.74810i	0.242477	+	0.155830i	0.656235	−	0.754556i	$-0.272148\pi$
$311$	4.27612	+	2.74810i	0.242477	+	0.155830i	−0.413759	+	0.910387i	$0.635784\pi$
$312$	8.48409	−	16.4157i	0.480317	−	0.929355i
$313$	0.668165	+	0.196191i	0.0377669	+	0.0110894i	0.300561	−	0.953762i	$-0.402826\pi$
$313$	0.668165	+	0.196191i	0.0377669	+	0.0110894i	−0.262795	+	0.964852i	$0.584644\pi$
$314$	−9.93709	−	15.7487i	−0.560783	−	0.888751i
$315$	6.31548	−	1.53365i	0.355837	−	0.0864111i
$316$	−7.84508	+	25.1628i	−0.441320	+	1.41552i
$317$	1.96751	+	6.70072i	0.110506	+	0.376350i	0.996113	−	0.0880862i	$-0.0280751\pi$
$317$	1.96751	+	6.70072i	0.110506	+	0.376350i	−0.885606	+	0.464436i	$0.846257\pi$
$318$	3.50773	+	5.86239i	0.196704	+	0.328747i
$319$	−0.198909	−	0.0285988i	−0.0111368	−	0.00160122i
$320$	−0.238924	+	4.78700i	−0.0133563	+	0.267602i
$321$	0.519538	+	0.852137i	0.0289978	+	0.0475617i
$322$	−14.1250	+	20.0478i	−0.787155	+	1.11722i
$323$	−0.724749			−0.0403261
$324$	−16.1303	+	7.98836i	−0.896127	+	0.443798i
$325$	−2.49131	+	17.3274i	−0.138193	+	0.961153i
$326$	0.100274		0.000833458i	0.00555367		4.61610e-5i
$327$	−9.36189	−	8.50857i	−0.517714	−	0.470525i
$328$	2.52834	+	21.3518i	0.139604	+	1.17895i
$329$	−24.1847	+	20.9561i	−1.33334	+	1.15535i
$330$	4.40455	+	2.18440i	0.242462	+	0.120247i
$331$	2.26908	−	7.72776i	0.124720	−	0.424756i	−0.873334	−	0.487122i	$-0.838047\pi$
$331$	2.26908	−	7.72776i	0.124720	−	0.424756i	0.998053	+	0.0623663i	$0.0198647\pi$
$332$	2.16741	+	17.0864i	0.118952	+	0.937735i
$333$	24.4967	−	14.1506i	1.34241	−	0.775450i
$334$	−26.4463	−	4.02703i	−1.44708	−	0.220350i
$335$	−3.12363	+	3.60486i	−0.170662	+	0.196955i
$336$	−9.09326	−	23.3429i	−0.496078	−	1.27346i
$337$	2.37879	+	16.5448i	0.129581	+	0.901255i	0.946086	+	0.323917i	$0.105000\pi$
$337$	2.37879	+	16.5448i	0.129581	+	0.901255i	−0.816505	+	0.577339i	$0.804091\pi$
$338$	1.57273	+	0.734101i	0.0855453	+	0.0399298i
$339$	8.08755	+	5.47246i	0.439255	+	0.297223i
$340$	−0.879305	+	1.84367i	−0.0476870	+	0.0999873i
$341$	23.2200	+	10.6042i	1.25743	+	0.574250i
$342$	−0.355670	+	1.76835i	−0.0192324	+	0.0956213i
$343$	1.80917	+	2.81512i	0.0976860	+	0.152002i
$344$	−10.1761	−	3.26569i	−0.548660	−	0.176074i
$345$	0.288284	−	4.96831i	0.0155207	−	0.267485i
$346$	6.79558	+	15.2136i	0.365333	+	0.817890i
$347$	−15.0519	+	9.67324i	−0.808026	+	0.519287i	−0.878226	−	0.478246i	$-0.841273\pi$
$347$	−15.0519	+	9.67324i	−0.808026	+	0.519287i	0.0702000	+	0.997533i	$0.477636\pi$
$348$	−0.196852	−	0.0665279i	−0.0105524	−	0.00356627i
$349$	0.562820	−	1.23240i	0.0301271	−	0.0659691i	−0.893970	−	0.448126i	$-0.852091\pi$
$349$	0.562820	−	1.23240i	0.0301271	−	0.0659691i	0.924097	+	0.382157i	$0.124819\pi$
$350$	15.3919	+	18.0644i	0.822733	+	0.965585i
$351$	−9.39888	−	17.1988i	−0.501675	−	0.918002i
$352$	6.09004	−	17.9461i	0.324600	−	0.956531i
$353$	23.7738	−	3.41816i	1.26535	−	0.181930i	0.523229	−	0.852192i	$-0.324727\pi$
$353$	23.7738	−	3.41816i	1.26535	−	0.181930i	0.742125	+	0.670262i	$0.233818\pi$
$354$	−8.46965	−	10.4309i	−0.450157	−	0.554396i
$355$	6.04596	+	5.23886i	0.320886	+	0.278050i
$356$	8.00316	+	29.0331i	0.424167	+	1.53875i
$357$	0.252851	−	10.6732i	0.0133823	−	0.564888i
$358$	2.49748	−	8.25131i	0.131996	−	0.436095i
$359$	0.0674153	+	0.0197949i	0.00355804	+	0.00104474i	0.283511	−	0.958969i	$-0.408501\pi$
$359$	0.0674153	+	0.0197949i	0.00355804	+	0.00104474i	−0.279953	+	0.960014i	$0.590319\pi$
$360$	4.06695	+	3.05024i	0.214347	+	0.160762i
$361$	−12.3240	−	14.2226i	−0.648631	−	0.748560i
$362$	16.6763	+	14.6946i	0.876488	+	0.772329i
$363$	−0.286453	−	0.260343i	−0.0150349	−	0.0136645i
$364$	24.9974	−	10.9175i	1.31022	−	0.572230i
$365$	−0.602059	−	0.0865631i	−0.0315132	−	0.00453092i
$366$	−24.2312	−	0.775599i	−1.26659	−	0.0405412i
$367$			29.5553i			1.54277i	0.636366	+	0.771387i	$0.280437\pi$
$367$			29.5553i			1.54277i	−0.636366	+	0.771387i	$0.719563\pi$
$368$	−19.1290	+	1.44275i	−0.997168	+	0.0752083i
$369$	20.2725	+	10.4453i	1.05534	+	0.543762i
$370$	−6.68540	−	4.37538i	−0.347557	−	0.227465i
$371$	−1.43521	+	9.98210i	−0.0745123	+	0.518245i
$372$	21.6118	+	15.1535i	1.12052	+	0.785670i
$373$	3.31581	−	0.973610i	0.171686	−	0.0504116i	−0.194760	−	0.980851i	$-0.562393\pi$
$373$	3.31581	−	0.973610i	0.171686	−	0.0504116i	0.366446	+	0.930439i	$0.380575\pi$
$374$	5.33953	−	6.05964i	0.276101	−	0.313337i
$375$	−9.52988	−	3.04517i	−0.492121	−	0.157252i
$376$	−24.6806	−	4.17905i	−1.27280	−	0.215518i
$377$	0.0637428	−	0.217088i	0.00328292	−	0.0111806i
$378$	−25.9181	−	5.85483i	−1.33308	−	0.301140i
$379$	5.60208	−	8.71701i	0.287760	−	0.447763i	−0.667036	−	0.745025i	$-0.732437\pi$
$379$	5.60208	−	8.71701i	0.287760	−	0.447763i	0.954796	+	0.297263i	$0.0960737\pi$
$380$	0.491115	−	0.135379i	0.0251937	−	0.00694479i
$381$	4.44897	−	26.4755i	0.227927	−	1.35638i
$382$	10.8202	−	1.46402i	0.553608	−	0.0749058i
$383$	−0.253054	−	1.76003i	−0.0129305	−	0.0899334i	0.982334	−	0.187135i	$-0.0599201\pi$
$383$	−0.253054	−	1.76003i	−0.0129305	−	0.0899334i	−0.995265	+	0.0972012i	$0.969011\pi$
$384$	9.57083	−	17.0997i	0.488409	−	0.872615i
$385$	3.01490	+	6.60171i	0.153654	+	0.336454i
$386$	20.6086	−	17.5597i	1.04895	−	0.893767i
$387$	−8.90877	+	7.00923i	−0.452858	+	0.356299i
$388$	−8.31593	−	9.92578i	−0.422177	−	0.503905i
$389$	15.1683	+	23.6023i	0.769063	+	1.19669i	0.975880	+	0.218306i	$0.0700531\pi$
$389$	15.1683	+	23.6023i	0.769063	+	1.19669i	−0.206817	+	0.978380i	$0.566311\pi$
$390$	−3.14012	+	4.55856i	−0.159006	+	0.230832i
$391$	−7.76070	−	2.57072i	−0.392475	−	0.130007i
$392$	5.25007	−	16.3596i	0.265169	−	0.826285i
$393$	20.6675	+	10.0367i	1.04254	+	0.506285i
$394$	−21.7078	+	6.17848i	−1.09362	+	0.311267i
$395$	3.27996	−	7.18211i	0.165033	−	0.361371i
$396$	−12.1648	−	16.0019i	−0.611306	−	0.804128i
$397$	−1.11296	−	2.43705i	−0.0558580	−	0.122312i	0.879645	−	0.475631i	$-0.157780\pi$
$397$	−1.11296	−	2.43705i	−0.0558580	−	0.122312i	−0.935503	+	0.353319i	$0.885053\pi$
$398$	2.17310	−	4.65564i	0.108928	−	0.233366i
$399$	−2.05304	+	1.69553i	−0.102781	+	0.0848825i
$400$	−3.25130	+	18.2773i	−0.162565	+	0.913864i
$401$	26.8694	+	23.2825i	1.34179	+	1.16267i	0.972380	+	0.233405i	$0.0749868\pi$
$401$	26.8694	+	23.2825i	1.34179	+	1.16267i	0.369413	+	0.929265i	$0.379559\pi$
$402$	17.9895	−	7.52963i	0.897232	−	0.375544i
$403$	−15.5382	+	24.1780i	−0.774014	+	1.20439i
$404$	−0.470725	+	0.0597117i	−0.0234195	+	0.00297077i
$405$	5.09471	−	1.76590i	0.253158	−	0.0877485i
$406$	−0.163682	−	0.259410i	−0.00812342	−	0.0128743i
$407$	20.6883	+	23.8756i	1.02548	+	1.18347i
$408$	6.56977	−	5.15568i	0.325252	−	0.255244i
$409$	−3.00140	+	0.881289i	−0.148409	+	0.0435770i	−0.355094	−	0.934831i	$-0.615551\pi$
$409$	−3.00140	+	0.881289i	−0.148409	+	0.0435770i	0.206684	+	0.978408i	$0.433733\pi$
$410$	0.0535330	−	6.44060i	0.00264381	−	0.318079i
$411$	12.3386	+	28.8044i	0.608621	+	1.42082i
$412$	18.0437	+	2.90121i	0.888952	+	0.142932i
$413$		−	19.8346i		−	0.975995i
$414$	−10.0810	+	17.6741i	−0.495453	+	0.868635i
$415$		−	5.15940i		−	0.253265i
$416$	19.0239	+	9.66247i	0.932724	+	0.473742i
$417$	8.22414	+	19.1991i	0.402738	+	0.940185i
$418$	−2.01422	−	0.0167418i	−0.0985187	−	0.000818867i
$419$	27.0142	−	7.93210i	1.31973	−	0.387508i	0.455336	−	0.890320i	$-0.349519\pi$
$419$	27.0142	−	7.93210i	1.31973	−	0.387508i	0.864396	+	0.502812i	$0.167701\pi$
$420$	1.82236	+	7.27980i	0.0889221	+	0.355218i
$421$	−2.56922	−	2.96503i	−0.125216	−	0.144507i	0.689680	−	0.724114i	$-0.257751\pi$
$421$	−2.56922	−	2.96503i	−0.125216	−	0.144507i	−0.814896	+	0.579608i	$0.803206\pi$
$422$	11.3083	−	7.13527i	0.550478	−	0.347340i
$423$	−18.3174	+	19.2196i	−0.890625	+	0.934487i
$424$	−6.74053	+	4.09808i	−0.327349	+	0.199021i
$425$	−4.27730	+	6.65562i	−0.207480	+	0.322845i
$426$	−12.6285	−	30.1714i	−0.611852	−	1.46181i
$427$	−27.0466	−	23.4360i	−1.30888	−	1.13415i
$428$	−0.979702	+	0.606846i	−0.0473557	+	0.0293330i
$429$	16.8759	−	13.9371i	0.814775	−	0.672891i
$430$	2.90102	+	1.35410i	0.139900	+	0.0653007i
$431$	7.21986	+	15.8093i	0.347769	+	0.761507i	0.999994	+	0.00348181i	$0.00110830\pi$
$431$	7.21986	+	15.8093i	0.347769	+	0.761507i	−0.652225	+	0.758025i	$0.726164\pi$
$432$	−9.35548	−	18.5600i	−0.450116	−	0.892970i
$433$	1.26608	−	2.77233i	0.0608439	−	0.133230i	−0.876768	−	0.480914i	$-0.840305\pi$
$433$	1.26608	−	2.77233i	0.0608439	−	0.133230i	0.937611	+	0.347685i	$0.113032\pi$
$434$	10.6662	+	37.4753i	0.511995	+	1.79887i
$435$	0.0559922	+	0.0271914i	0.00268462	+	0.00130373i
$436$	9.74826	−	10.8793i	0.466857	−	0.521024i
$437$	0.782958	+	1.88263i	0.0374540	+	0.0900584i
$438$	2.04796	+	1.41072i	0.0978554	+	0.0674066i
$439$	−8.75428	−	13.6219i	−0.417819	−	0.650139i	0.567001	−	0.823717i	$-0.308104\pi$
$439$	−8.75428	−	13.6219i	−0.417819	−	0.650139i	−0.984820	+	0.173578i	$0.944467\pi$
$440$	−2.48635	+	5.10362i	−0.118532	+	0.243306i
$441$	−11.2684	−	14.3222i	−0.536589	−	0.682008i
$442$	5.89751	+	6.92150i	0.280516	+	0.329222i
$443$	−13.8651	−	30.3604i	−0.658752	−	1.44247i	−0.883681	−	0.468090i	$-0.844942\pi$
$443$	−13.8651	−	30.3604i	−0.658752	−	1.44247i	0.224929	−	0.974375i	$-0.427785\pi$
$444$	16.5391	+	28.1702i	0.784911	+	1.33690i
$445$	−1.28390	−	8.92972i	−0.0608627	−	0.423309i
$446$	1.52911	+	11.3012i	0.0724054	+	0.535128i
$447$	0.979600	−	5.82954i	0.0463335	−	0.275728i
$448$	26.8792	−	10.6901i	1.26992	−	0.505059i
$449$	11.8697	−	18.4697i	0.560168	−	0.871638i	−0.439478	−	0.898253i	$-0.644837\pi$
$449$	11.8697	−	18.4697i	0.560168	−	0.871638i	0.999646	+	0.0266153i	$0.00847292\pi$
$450$	14.1403	+	13.7026i	0.666578	+	0.645948i
$451$	−7.17486	+	24.4353i	−0.337851	+	1.15062i
$452$	−6.25294	+	9.38309i	−0.294114	+	0.441343i
$453$	−22.1199	−	7.06817i	−1.03928	−	0.332092i
$454$	26.7996	+	23.6148i	1.25777	+	1.10830i
$455$	−7.84025	+	2.30210i	−0.367556	+	0.107924i
$456$	−2.04476	−	0.396261i	−0.0957547	−	0.0185566i
$457$	2.45217	−	17.0552i	0.114708	−	0.797809i	−0.848528	−	0.529151i	$-0.822511\pi$
$457$	2.45217	−	17.0552i	0.114708	−	0.797809i	0.963236	−	0.268658i	$-0.0865803\pi$
$458$	11.5301	−	17.6174i	0.538764	−	0.823209i
$459$	−0.634935	−	8.83503i	−0.0296362	−	0.412384i
$460$	5.73912	+	0.292357i	0.267588	+	0.0136312i
$461$			24.6025i			1.14585i	0.819607	+	0.572927i	$0.194192\pi$
$461$			24.6025i			1.14585i	−0.819607	+	0.572927i	$0.805808\pi$
$462$	0.949277	−	29.6572i	0.0441644	−	1.37978i
$463$	−31.7070	−	4.55878i	−1.47355	−	0.211864i	−0.641738	−	0.766924i	$-0.721786\pi$
$463$	−31.7070	−	4.55878i	−1.47355	−	0.211864i	−0.831811	+	0.555060i	$0.812695\pi$
$464$	0.0752125	−	0.227842i	0.00349165	−	0.0105773i
$465$	−5.85133	−	5.31799i	−0.271349	−	0.246616i
$466$	16.4714	−	18.6928i	0.763024	−	0.865928i
$467$	−3.89243	−	4.49211i	−0.180120	−	0.207870i	0.658508	−	0.752573i	$-0.271188\pi$
$467$	−3.89243	−	4.49211i	−0.180120	−	0.207870i	−0.838629	+	0.544703i	$0.816642\pi$
$468$	19.7823	−	10.9929i	0.914436	−	0.508146i
$469$	27.6218	+	8.11049i	1.27546	+	0.374507i
$470$	7.17700	+	2.17231i	0.331051	+	0.100201i
$471$	0.540147	−	22.8004i	0.0248886	−	1.05059i
$472$	11.9752	−	9.86473i	0.551203	−	0.454061i
$473$	−9.56675	−	8.28964i	−0.439880	−	0.381158i
$474$	−25.0602	+	20.3483i	−1.15105	+	0.934628i
$475$	1.95306	−	0.280808i	0.0896127	−	0.0128844i
$476$	12.3262	+	0.204919i	0.564969	+	0.00939246i
$477$	−0.396212	+	8.35768i	−0.0181413	+	0.382672i
$478$	−6.05493	+	5.15914i	−0.276946	+	0.235974i
$479$	−1.59617	+	3.49513i	−0.0729309	+	0.159696i	−0.942586	−	0.333963i	$-0.891614\pi$
$479$	−1.59617	+	3.49513i	−0.0729309	+	0.159696i	0.869655	+	0.493660i	$0.164341\pi$
$480$	−3.48886	+	4.72087i	−0.159244	+	0.215477i
$481$	−29.9227	+	19.2301i	−1.36436	+	0.876819i
$482$	−38.8808	+	17.3672i	−1.77097	+	0.791054i
$483$	−27.9983	+	10.8737i	−1.27397	+	0.494769i
$484$	0.298275	−	0.332882i	0.0135579	−	0.0151310i
$485$	2.09714	+	3.26322i	0.0952263	+	0.148175i
$486$	−21.8686	−	2.78657i	−0.991979	−	0.126401i
$487$	7.49586	+	3.42325i	0.339670	+	0.155122i	0.577945	−	0.816076i	$-0.303855\pi$
$487$	7.49586	+	3.42325i	0.339670	+	0.155122i	−0.238275	+	0.971198i	$0.576582\pi$
$488$	0.697956	−	27.9854i	0.0315950	−	1.26684i
$489$	0.101717	+	0.0688268i	0.00459978	+	0.00311246i
$490$	−2.17692	+	4.66382i	−0.0983433	+	0.210690i
$491$	−0.190903	−	1.32776i	−0.00861534	−	0.0599210i	0.985060	−	0.172210i	$-0.0550908\pi$
$491$	−0.190903	−	1.32776i	−0.00861534	−	0.0599210i	−0.993676	+	0.112289i	$0.964182\pi$
$492$	−11.8956	+	23.4932i	−0.536295	+	1.05916i
$493$	0.0669618	−	0.0772780i	0.00301581	−	0.00348043i
$494$	0.341398	−	2.24203i	0.0153602	−	0.100874i
$495$	3.01190	+	5.21401i	0.135375	+	0.234353i
$496$	−17.3210	+	25.0781i	−0.777737	+	1.12604i
$497$	13.6027	−	46.3264i	0.610163	−	2.07802i
$498$	−9.37218	+	18.8977i	−0.419978	+	0.846827i
$499$	−3.85303	+	3.33867i	−0.172485	+	0.149459i	−0.736826	−	0.676083i	$-0.763676\pi$
$499$	−3.85303	+	3.33867i	−0.172485	+	0.149459i	0.564340	+	0.825542i	$0.309131\pi$
$500$	3.43846	−	11.0287i	0.153773	−	0.493219i
$501$	−24.2458	−	22.0358i	−1.08322	−	0.984489i
$502$	0.229067	−	27.5593i	0.0102238	−	1.23003i
$503$	3.63258	−	25.2651i	0.161969	−	1.12652i	−0.732949	−	0.680284i	$-0.761856\pi$
$503$	3.63258	−	25.2651i	0.161969	−	1.12652i	0.894917	−	0.446232i	$-0.147234\pi$
$504$	6.54904	−	29.9746i	0.291717	−	1.33518i
$505$	0.142140			0.00632517
$506$	−21.5091	−	7.32381i	−0.956197	−	0.325583i
$507$	1.10656	+	1.81497i	0.0491442	+	0.0806054i
$508$	30.6068	+	4.92119i	1.35796	+	0.218342i
$509$	15.4769	+	2.22524i	0.686001	+	0.0986320i	0.476497	−	0.879176i	$-0.341906\pi$
$509$	15.4769	+	2.22524i	0.686001	+	0.0986320i	0.209504	+	0.977808i	$0.432815\pi$
$510$	−2.14675	+	1.28450i	−0.0950597	+	0.0568785i
$511$	1.03423	+	3.52228i	0.0457518	+	0.155816i
$512$	19.8226	+	10.9117i	0.876042	+	0.482234i
$513$	−1.56157	+	1.56264i	−0.0689449	+	0.0689922i
$514$	24.6104	−	15.5286i	1.08552	−	0.684939i
$515$	−5.25285	−	1.54238i	−0.231468	−	0.0679652i
$516$	−8.16601	−	10.2295i	−0.359489	−	0.450331i
$517$	−24.9425	−	16.0296i	−1.09697	−	0.704979i
$518$	−7.25911	+	47.6720i	−0.318947	+	2.09459i
$519$	−3.38182	+	20.1250i	−0.148445	+	0.883389i
$520$	−5.28925	−	3.58863i	−0.231949	−	0.157372i
$521$	−35.4738	+	5.10037i	−1.55414	+	0.223451i	−0.865221	−	0.501391i	$-0.832822\pi$
$521$	−35.4738	+	5.10037i	−1.55414	+	0.223451i	−0.688915	+	0.724842i	$0.741913\pi$
$522$	−0.155693	−	0.201307i	−0.00681449	−	0.00881098i
$523$	−9.74343	+	4.44968i	−0.426051	+	0.194571i	−0.616888	−	0.787051i	$-0.711607\pi$
$523$	−9.74343	+	4.44968i	−0.426051	+	0.194571i	0.190838	+	0.981622i	$0.438880\pi$
$524$	−11.4206	+	23.9460i	−0.498910	+	1.04608i
$525$	3.45403	+	28.8604i	0.150746	+	1.25957i
$526$	6.63808	+	23.3226i	0.289434	+	1.01691i
$527$	−10.9271	+	7.02239i	−0.475990	+	0.305900i
$528$	18.3778	−	14.1769i	0.799790	−	0.616970i
$529$	1.70623	+	22.9366i	0.0741837	+	0.997245i
$530$	2.15763	−	0.963764i	0.0937214	−	0.0418632i
$531$	−1.56801	−	16.3814i	−0.0680457	−	0.710891i
$532$	−1.97452	−	2.35676i	−0.0856063	−	0.102179i
$533$	−26.0819	−	11.9112i	−1.12973	−	0.515932i
$534$	−11.5184	+	35.0398i	−0.498451	+	1.51632i
$535$	0.314023	−	0.143409i	0.0135764	−	0.00620013i
$536$	8.84096	+	20.7105i	0.381871	+	0.894558i
$537$	8.14111	−	6.72343i	0.351315	−	0.290138i
$538$	−4.50573	−	33.3006i	−0.194256	−	1.43569i
$539$	13.3268	−	15.3800i	0.574026	−	0.662462i
$540$	2.08059	+	5.86832i	0.0895342	+	0.252532i
$541$	7.39265	+	4.75097i	0.317835	+	0.204260i	0.689824	−	0.723977i	$-0.257688\pi$
$541$	7.39265	+	4.75097i	0.317835	+	0.204260i	−0.371989	+	0.928237i	$0.621324\pi$
$542$	11.7873	+	3.56776i	0.506309	+	0.153248i
$543$	7.04861	+	26.2938i	0.302485	+	1.12837i
$544$	6.00670	+	7.54389i	0.257535	+	0.323441i
$545$	−3.30709	+	2.86561i	−0.141660	+	0.122749i
$546$	32.8989	+	5.80992i	1.40794	+	0.248641i
$547$	1.99062	+	6.77942i	0.0851127	+	0.289867i	0.991040	−	0.133566i	$-0.0426429\pi$
$547$	1.99062	+	6.77942i	0.0851127	+	0.289867i	−0.905927	+	0.423433i	$0.860825\pi$
$548$	−33.1590	+	14.4820i	−1.41648	+	0.618640i
$549$	−24.1905	−	17.2177i	−1.03243	−	0.734832i
$550$	−12.0412	+	18.3985i	−0.513439	+	0.784513i
$551$	−0.0255021			−0.00108643
$552$	−20.4900	−	11.4961i	−0.872112	−	0.489306i
$553$	−47.6525			−2.02639
$554$	20.0011	−	30.5608i	0.849766	−	1.29841i
$555$	−3.85313	−	8.99507i	−0.163556	−	0.381819i
$556$	−22.1016	+	9.65275i	−0.937317	+	0.409368i
$557$	−5.56632	−	18.9571i	−0.235852	−	0.803240i	−0.989321	−	0.145755i	$-0.953439\pi$
$557$	−5.56632	−	18.9571i	−0.235852	−	0.803240i	0.753468	−	0.657484i	$-0.228379\pi$
$558$	11.7718	+	30.1077i	0.498341	+	1.27456i
$559$	10.7711	−	9.33324i	0.455570	−	0.394754i
$560$	−8.39092	+	2.16360i	−0.354581	+	0.0914286i
$561$	9.55431	−	2.56124i	0.403383	−	0.108136i
$562$	42.0677	+	12.7329i	1.77452	+	0.537106i
$563$	−4.15326	−	2.66914i	−0.175039	−	0.112491i	0.450188	−	0.892934i	$-0.351357\pi$
$563$	−4.15326	−	2.66914i	−0.175039	−	0.112491i	−0.625227	+	0.780443i	$0.714993\pi$
$564$	−22.3417	−	20.9939i	−0.940754	−	0.884002i
$565$	2.21196	−	2.55273i	0.0930577	−	0.107394i
$566$	3.89383	+	28.7782i	0.163670	+	1.20964i
$567$	−22.4679	−	23.5421i	−0.943563	−	0.988676i
$568$	34.7351	−	14.8278i	1.45745	−	0.622160i
$569$	1.79226	−	0.818499i	0.0751355	−	0.0343132i	−0.377493	−	0.926013i	$-0.623214\pi$
$569$	1.79226	−	0.818499i	0.0751355	−	0.0343132i	0.452628	+	0.891699i	$0.350486\pi$
$570$	0.592722	+	0.194842i	0.0248264	+	0.00816103i
$571$	8.05903	+	3.68044i	0.337260	+	0.154021i	0.576844	−	0.816854i	$-0.304284\pi$
$571$	8.05903	+	3.68044i	0.337260	+	0.154021i	−0.239584	+	0.970876i	$0.577011\pi$
$572$	16.2304	+	19.3724i	0.678629	+	0.810002i
$573$	12.0293	+	5.84175i	0.502529	+	0.244043i
$574$	−35.4925	+	15.8537i	−1.48143	+	0.661721i
$575$	21.9097	+	3.92069i	0.913697	+	0.163504i
$576$	21.3545	−	10.9539i	0.889769	−	0.456411i
$577$	22.7927	−	14.6480i	0.948872	−	0.609803i	0.0279748	−	0.999609i	$-0.491094\pi$
$577$	22.7927	−	14.6480i	0.948872	−	0.609803i	0.920897	+	0.389806i	$0.127458\pi$
$578$	−5.45634	−	19.1706i	−0.226954	−	0.797392i
$579$	32.9251	−	3.94049i	1.36832	−	0.163761i
$580$	−0.0309406	+	0.0648744i	−0.00128474	+	0.00269376i
$581$	−28.3247	+	12.9354i	−1.17510	+	0.536652i
$582$	−1.75364	−	15.7619i	−0.0726907	−	0.653353i
$583$	−9.24852	+	1.32974i	−0.383035	+	0.0550721i
$584$	−1.61221	+	2.37623i	−0.0667138	+	0.0983290i
$585$	−6.29327	+	2.52111i	−0.260195	+	0.104235i
$586$	3.72631	−	24.4714i	0.153932	−	1.01090i
$587$	−37.6386	−	24.1888i	−1.55351	−	0.998380i	−0.984365	−	0.176143i	$-0.943638\pi$
$587$	−37.6386	−	24.1888i	−1.55351	−	0.998380i	−0.569145	−	0.822237i	$-0.692726\pi$
$588$	16.4455	−	13.1281i	0.678201	−	0.541392i
$589$	3.10825	+	0.912666i	0.128073	+	0.0376057i
$590$	−3.93065	+	2.48015i	−0.161822	+	0.102106i
$591$	−26.3308	−	8.41374i	−1.08311	−	0.346095i
$592$	−32.3925	+	19.3270i	−1.33132	+	0.794333i
$593$	12.2300	+	41.6516i	0.502226	+	1.71042i	0.686129	+	0.727480i	$0.259309\pi$
$593$	12.2300	+	41.6516i	0.502226	+	1.71042i	−0.183903	+	0.982944i	$0.558873\pi$
$594$	−1.56052	−	24.5689i	−0.0640289	−	1.00808i
$595$	−3.65535	−	0.525559i	−0.149855	−	0.0215458i
$596$	6.73919	+	1.08358i	0.276048	+	0.0443850i
$597$	5.37271	−	3.27568i	0.219890	−	0.134064i
$598$	11.6083	−	22.7970i	0.474700	−	0.932237i
$599$	7.33899			0.299863			0.149931	−	0.988696i	$-0.452095\pi$
$599$	7.33899			0.299863			0.149931	+	0.988696i	$0.452095\pi$
$600$	−15.7067	+	16.4391i	−0.641224	+	0.671124i
$601$	0.405873	−	2.82291i	0.0165559	−	0.115149i	−0.979868	−	0.199648i	$-0.936020\pi$
$601$	0.405873	−	2.82291i	0.0165559	−	0.115149i	0.996424	+	0.0844994i	$0.0269291\pi$
$602$	0.160595	−	19.3213i	0.00654535	−	0.787477i
$603$	23.4540	+	4.51483i	0.955121	+	0.183858i
$604$	7.98103	−	25.5988i	0.324744	−	1.04160i
$605$	−0.101190	+	0.0876813i	−0.00411394	+	0.00356475i
$606$	−0.520628	−	0.258202i	−0.0211491	−	0.0104887i
$607$	−0.695016	+	2.36701i	−0.0282098	+	0.0960739i	−0.972395	−	0.233342i	$-0.925034\pi$
$607$	−0.695016	+	2.36701i	−0.0282098	+	0.0960739i	0.944185	+	0.329416i	$0.106852\pi$
$608$	0.440876	−	2.36426i	0.0178799	−	0.0958834i
$609$	0.00889721	−	0.375565i	0.000360533	−	0.0152187i
$610$	−1.26239	+	8.29035i	−0.0511126	+	0.335667i
$611$	21.8604	−	25.2283i	0.884378	−	1.02063i
$612$	10.1964	−	0.805192i	0.412164	−	0.0325480i
$613$	−5.00236	−	34.7922i	−0.202044	−	1.40524i	−0.798208	−	0.602382i	$-0.794219\pi$
$613$	−5.00236	−	34.7922i	−0.202044	−	1.40524i	0.596165	−	0.802862i	$-0.296691\pi$
$614$	5.37278	−	11.5106i	0.216828	−	0.464530i
$615$	4.42074	−	6.53325i	0.178262	−	0.263446i
$616$	34.2521	+	0.854246i	1.38006	+	0.0344186i
$617$	9.27982	+	4.23795i	0.373591	+	0.170613i	0.593357	−	0.804939i	$-0.297802\pi$
$617$	9.27982	+	4.23795i	0.373591	+	0.170613i	−0.219766	+	0.975553i	$0.570529\pi$
$618$	16.4382	+	15.1913i	0.661242	+	0.611084i
$619$	9.46240	+	14.7238i	0.380326	+	0.591799i	0.977660	−	0.210194i	$-0.0674096\pi$
$619$	9.46240	+	14.7238i	0.380326	+	0.591799i	−0.597334	+	0.801993i	$0.703773\pi$
$620$	6.09282	−	6.79973i	0.244693	−	0.273084i
$621$	−22.2642	+	11.1940i	−0.893432	+	0.449198i
$622$	−6.56348	+	2.93176i	−0.263172	+	0.117553i
$623$	−45.8044	+	29.4367i	−1.83511	+	1.17936i
$624$	12.8545	+	22.7524i	0.514592	+	0.910824i
$625$	8.20223	−	17.9604i	0.328089	−	0.718415i
$626$	−0.749612	+	0.638712i	−0.0299605	+	0.0255281i
$627$	−2.04319	−	1.38253i	−0.0815973	−	0.0552130i
$628$	26.3314	+	0.437753i	1.05074	+	0.0174682i
$629$	−15.9116	+	2.28774i	−0.634437	+	0.0912183i
$630$	−3.07619	+	8.66093i	−0.122558	+	0.345060i
$631$	23.1571	+	20.0657i	0.921870	+	0.798805i	0.979896	−	0.199510i	$-0.0639352\pi$
$631$	23.1571	+	20.0657i	0.921870	+	0.798805i	−0.0580261	+	0.998315i	$0.518481\pi$
$632$	−23.7000	−	28.7704i	−0.942734	−	1.14442i
$633$	16.3717	+	0.387849i	0.650717	+	0.0154156i
$634$	−9.45280	−	2.86115i	−0.375419	−	0.113631i
$635$	−8.91017	−	2.61626i	−0.353589	−	0.103823i
$636$	−9.65360	−	0.389338i	−0.382790	−	0.0154382i
$637$	15.0046	+	17.3162i	0.594502	+	0.686092i
$638$	0.187885	−	0.213224i	0.00743844	−	0.00844162i
$639$	7.57214	−	39.3363i	0.299549	−	1.55612i
$640$	−5.47950	−	3.98998i	−0.216596	−	0.157718i
$641$	3.88194	+	0.558138i	0.153327	+	0.0220451i	0.218551	−	0.975826i	$-0.429867\pi$
$641$	3.88194	+	0.558138i	0.153327	+	0.0220451i	−0.0652237	+	0.997871i	$0.520776\pi$
$642$	−1.41070	−	0.0451541i	−0.0556759	−	0.00178209i
$643$		−	42.3026i		−	1.66825i	−0.551575	−	0.834125i	$-0.685973\pi$
$643$		−	42.3026i		−	1.66825i	0.551575	−	0.834125i	$-0.314027\pi$
$644$	−12.7839	−	32.2402i	−0.503754	−	1.27044i
$645$	2.04114	+	3.34784i	0.0803697	+	0.131821i
$646$	0.561277	−	0.857607i	0.0220831	−	0.0337421i
$647$	−4.16570	+	28.9731i	−0.163771	+	1.13905i	0.727675	+	0.685922i	$0.240601\pi$
$647$	−4.16570	+	28.9731i	−0.163771	+	1.13905i	−0.891445	+	0.453128i	$0.850308\pi$
$648$	3.03923	−	25.2738i	0.119392	−	0.992847i
$649$	17.6325	−	5.17738i	0.692138	−	0.203230i
$650$	−18.5745	−	16.3671i	−0.728550	−	0.641972i
$651$	−14.5251	+	45.4563i	−0.569283	+	1.78157i
$652$	−0.0786429	+	0.118011i	−0.00307989	+	0.00462165i
$653$	3.37936	−	11.5090i	0.132245	−	0.450384i	−0.866570	−	0.499055i	$-0.833681\pi$
$653$	3.37936	−	11.5090i	0.132245	−	0.450384i	0.998815	+	0.0486714i	$0.0154987\pi$
$654$	17.3186	−	4.48867i	0.677210	−	0.175521i
$655$	4.29664	−	6.68571i	0.167884	−	0.261232i
$656$	−27.2240	−	13.5439i	−1.06292	−	0.528801i
$657$	1.13262	+	2.82729i	0.0441879	+	0.110303i
$658$	−6.06807	−	44.8474i	−0.236558	−	1.74833i
$659$	1.98147	+	13.7814i	0.0771869	+	0.536847i	0.991324	+	0.131442i	$0.0419606\pi$
$659$	1.98147	+	13.7814i	0.0771869	+	0.536847i	−0.914137	+	0.405405i	$0.867130\pi$
$660$	−5.99591	+	3.52028i	−0.233391	+	0.137027i
$661$	0.850184	+	1.86164i	0.0330683	+	0.0724095i	0.925445	−	0.378881i	$-0.123691\pi$
$661$	0.850184	+	1.86164i	0.0330683	+	0.0724095i	−0.892377	+	0.451291i	$0.850964\pi$
$662$	7.38712	+	8.66975i	0.287108	+	0.336959i
$663$	1.32343	+	11.0580i	0.0513978	+	0.429458i
$664$	−21.8971	−	10.6677i	−0.849772	−	0.413986i
$665$	0.497942	+	0.774813i	0.0193094	+	0.0300459i
$666$	−2.22663	+	39.9462i	−0.0862802	+	1.54788i
$667$	−0.273080	−	0.0904573i	−0.0105737	−	0.00350252i
$668$	25.2464	−	28.1756i	0.976814	−	1.09015i
$669$	−6.10147	+	12.5640i	−0.235896	+	0.485754i
$670$	−1.84661	−	6.48800i	−0.0713410	−	0.250653i
$671$	13.7742	−	30.1614i	0.531749	−	1.16437i
$672$	34.6642	+	7.31755i	1.33720	+	0.282280i
$673$	−12.6798	−	27.7649i	−0.488771	−	1.07026i	−0.979958	−	0.199205i	$-0.936164\pi$
$673$	−12.6798	−	27.7649i	−0.488771	−	1.07026i	0.491187	−	0.871054i	$-0.336563\pi$
$674$	−21.4200	−	9.99819i	−0.825069	−	0.385116i
$675$	5.13422	+	23.5628i	0.197616	+	0.906931i
$676$	−2.08666	+	1.29252i	−0.0802563	+	0.0497122i
$677$	−20.4310	−	17.7035i	−0.785226	−	0.680402i	0.166946	−	0.985966i	$-0.446609\pi$
$677$	−20.4310	−	17.7035i	−0.785226	−	0.680402i	−0.952171	+	0.305564i	$0.901155\pi$
$678$	−12.7390	+	5.33201i	−0.489238	+	0.204775i
$679$	12.6569	−	19.6945i	0.485727	−	0.755806i
$680$	−1.50068	−	2.46832i	−0.0575484	−	0.0946556i
$681$	11.3274	+	42.2552i	0.434068	+	1.61922i
$682$	−30.5307	+	19.2642i	−1.16908	+	0.737664i
$683$	−9.87008	−	11.3907i	−0.377668	−	0.435852i	0.534813	−	0.844970i	$-0.320382\pi$
$683$	−9.87008	−	11.3907i	−0.377668	−	0.435852i	−0.912481	+	0.409118i	$0.865836\pi$
$684$	−1.81707	−	1.79035i	−0.0694774	−	0.0684559i
$685$	10.4001	−	3.05374i	0.397366	−	0.116677i
$686$	−4.73228	−	0.0393338i	−0.180679	−	0.00150177i
$687$	23.7039	−	10.1538i	0.904360	−	0.387392i
$688$	11.7452	−	9.51248i	0.447781	−	0.362660i
$689$		−	10.5199i		−	0.400777i
$690$	5.65582	+	4.18880i	0.215313	+	0.159465i
$691$			5.33748i			0.203047i	0.994833	+	0.101524i	$0.0323717\pi$
$691$			5.33748i			0.203047i	−0.994833	+	0.101524i	$0.967628\pi$
$692$	−23.2653	−	3.74077i	−0.884415	−	0.142203i
$693$	21.0732	−	29.6074i	0.800503	−	1.12469i
$694$	0.210309	−	25.3025i	0.00798322	−	0.960469i
$695$	6.93201	−	2.03542i	0.262946	−	0.0772079i
$696$	0.231174	−	0.181416i	0.00876263	−	0.00687654i
$697$	−8.48606	−	9.79344i	−0.321433	−	0.370953i
$698$	1.02245	+	1.62042i	0.0387004	+	0.0613339i
$699$	29.4732	−	7.90092i	1.11478	−	0.298840i
$700$	−33.2961	+	4.22362i	−1.25848	+	0.159638i
$701$	24.7762	−	38.5525i	0.935783	−	1.45611i	0.0464120	−	0.998922i	$-0.485221\pi$
$701$	24.7762	−	38.5525i	0.935783	−	1.45611i	0.889372	−	0.457185i	$-0.151142\pi$
$702$	27.6305	+	2.19762i	1.04285	+	0.0829437i
$703$	3.02994	+	2.62545i	0.114276	+	0.0990209i
$704$	16.5195	+	21.1047i	0.622603	+	0.795413i
$705$	5.84805	+	7.08116i	0.220250	+	0.266692i
$706$	−14.3667	+	30.7791i	−0.540699	+	1.15839i
$707$	−0.356368	−	0.780338i	−0.0134026	−	0.0293476i
$708$	18.9023	−	1.94412i	0.710393	−	0.0730646i
$709$	6.57460	−	14.3964i	0.246914	−	0.540667i	−0.745076	−	0.666979i	$-0.767587\pi$
$709$	6.57460	−	14.3964i	0.246914	−	0.540667i	0.991990	+	0.126313i	$0.0403143\pi$
$710$	−10.8815	+	3.09709i	−0.408375	+	0.116232i
$711$	−39.3562	+	3.76713i	−1.47597	+	0.141278i
$712$	−40.5534	−	13.0142i	−1.51980	−	0.487729i
$713$	30.0463	+	20.7981i	1.12524	+	0.778894i
$714$	12.4340	+	8.56503i	0.465331	+	0.320538i
$715$	−4.09305	−	6.36891i	−0.153071	−	0.238184i
$716$	7.82975	+	9.34548i	0.292611	+	0.349257i
$717$	−9.67358	+	1.15774i	−0.361266	+	0.0432365i
$718$	−0.0756330	+	0.0644436i	−0.00282260	+	0.00240501i
$719$	6.68188	+	14.6313i	0.249192	+	0.545655i	0.992349	−	0.123462i	$-0.0393998\pi$
$719$	6.68188	+	14.6313i	0.249192	+	0.545655i	−0.743157	+	0.669117i	$0.766673\pi$
$720$	−6.75902	+	2.45025i	−0.251894	+	0.0913155i
$721$	4.70222	+	32.7046i	0.175120	+	1.21798i
$722$	26.3741	−	3.56854i	0.981543	−	0.132807i
$723$	−51.4326	−	8.64277i	−1.91280	−	0.321428i
$724$	−30.3032	+	8.35326i	−1.12621	+	0.310446i
$725$	−0.150508	+	0.234195i	−0.00558972	+	0.00869777i
$726$	0.529910	−	0.137343i	0.0196668	−	0.00509728i
$727$	1.21663	−	4.14347i	0.0451224	−	0.153673i	−0.933850	−	0.357664i	$-0.883573\pi$
$727$	1.21663	−	4.14347i	0.0451224	−	0.153673i	0.978973	+	0.203991i	$0.0653914\pi$
$728$	−6.44025	+	38.0348i	−0.238692	+	1.40966i
$729$	−20.4173	−	17.6673i	−0.756198	−	0.654343i
$730$	0.568692	−	0.645388i	0.0210482	−	0.0238869i
$731$	6.18029	−	1.81470i	0.228586	−	0.0671190i
$732$	19.6835	−	28.0725i	0.727522	−	1.03759i
$733$	−6.34214	+	44.1106i	−0.234252	+	1.62926i	0.445122	+	0.895470i	$0.353160\pi$
$733$	−6.34214	+	44.1106i	−0.234252	+	1.62926i	−0.679375	+	0.733792i	$0.737749\pi$
$734$	−34.9733	−	22.8889i	−1.29089	−	0.844845i
$735$	−5.38214	+	3.28143i	−0.198523	+	0.121037i
$736$	13.1071	−	23.7530i	0.483134	−	0.875546i
$737$			26.6723i			0.982487i
$738$	−28.0600	+	15.8994i	−1.03290	+	0.585266i
$739$	11.0292	+	1.58575i	0.405714	+	0.0583329i	0.342151	−	0.939645i	$-0.388845\pi$
$739$	11.0292	+	1.58575i	0.405714	+	0.0583329i	0.0635630	+	0.997978i	$0.479754\pi$
$740$	10.3549	−	4.52245i	0.380655	−	0.166249i
$741$	1.86812	−	2.05548i	0.0686272	−	0.0755098i
$742$	−10.7005	−	9.42888i	−0.392827	−	0.346145i
$743$	3.86230	+	4.45733i	0.141694	+	0.163524i	0.822161	−	0.569255i	$-0.192768\pi$
$743$	3.86230	+	4.45733i	0.141694	+	0.163524i	−0.680467	+	0.732779i	$0.738223\pi$
$744$	−34.6685	+	13.8381i	−1.27101	+	0.507330i
$745$	−1.96190	−	0.576064i	−0.0718783	−	0.0211054i
$746$	−1.41582	+	4.67766i	−0.0518368	+	0.171261i
$747$	−22.3707	+	12.9226i	−0.818502	+	0.472812i
$748$	3.03531	+	11.0112i	0.110982	+	0.402610i
$749$	−1.57461	−	1.36441i	−0.0575350	−	0.0498543i
$750$	10.9838	−	8.91855i	0.401070	−	0.325659i
$751$	7.06576	−	1.01590i	0.257833	−	0.0370708i	−0.0121859	−	0.999926i	$-0.503879\pi$
$751$	7.06576	−	1.01590i	0.257833	−	0.0370708i	0.270019	+	0.962855i	$0.412970\pi$
$752$	24.0589	−	25.9685i	0.877336	−	0.946974i
$753$	18.9164	−	27.9558i	0.689350	−	1.01876i
$754$	0.207519	+	0.243550i	0.00755738	+	0.00886958i
$755$	−3.33680	+	7.30657i	−0.121438	+	0.265913i
$756$	27.0002	−	26.1350i	0.981987	−	0.950522i
$757$	35.1466	−	22.5873i	1.27742	−	0.820951i	0.286857	−	0.957973i	$-0.407390\pi$
$757$	35.1466	−	22.5873i	1.27742	−	0.820951i	0.990568	+	0.137022i	$0.0437533\pi$
$758$	5.97648	+	13.3799i	0.217076	+	0.485978i
$759$	−16.9748	−	22.0516i	−0.616148	−	0.800424i
$760$	−0.220145	+	0.685988i	−0.00798549	+	0.0248834i
$761$	7.01580	+	10.9168i	0.254323	+	0.395734i	0.944814	−	0.327607i	$-0.106242\pi$
$761$	7.01580	+	10.9168i	0.254323	+	0.395734i	−0.690491	+	0.723341i	$0.742606\pi$
$762$	27.8834	+	25.7683i	1.01011	+	0.933488i
$763$	24.0234	+	10.9711i	0.869704	+	0.397181i
$764$	−6.64721	+	13.9375i	−0.240488	+	0.504240i
$765$	−3.06050	−	0.145089i	−0.110653	−	0.00524571i
$766$	2.27865	+	1.06360i	0.0823310	+	0.0384295i
$767$	2.94456	+	20.4799i	0.106322	+	0.739485i
$768$	12.8223	+	24.5681i	0.462684	+	0.886523i
$769$	8.92586	−	10.3010i	0.321875	−	0.371463i	−0.571634	−	0.820509i	$-0.693690\pi$
$769$	8.92586	−	10.3010i	0.321875	−	0.371463i	0.893509	+	0.449045i	$0.148236\pi$
$770$	−10.1468	−	1.54507i	−0.365665	−	0.0556805i
$771$	35.6301	+	0.844083i	1.28319	+	0.0303989i
$772$	4.81848	+	37.9856i	0.173421	+	1.36713i
$773$	7.53798	−	25.6720i	0.271122	−	0.923358i	−0.705557	−	0.708653i	$-0.749303\pi$
$773$	7.53798	−	25.6720i	0.271122	−	0.923358i	0.976679	−	0.214704i	$-0.0688788\pi$
$774$	−1.39479	−	15.9701i	−0.0501348	−	0.574035i
$775$	26.7255	−	23.1578i	0.960010	−	0.831853i
$776$	18.1855	−	2.15342i	0.652823	−	0.0773032i
$777$	−39.7217	+	43.7054i	−1.42501	+	1.56792i
$778$	−39.6760	−	0.329779i	−1.42245	−	0.0118231i
$779$	−0.459945	+	3.19899i	−0.0164792	+	0.114616i
$780$	−2.96238	−	7.24610i	−0.106070	−	0.259452i
$781$	44.7340			1.60071
$782$	9.05220	−	7.19248i	0.323706	−	0.257203i
$783$	−0.0223418	−	0.310883i	−0.000798431	−	0.0111100i
$784$	15.2927	+	18.8821i	0.546168	+	0.674361i
$785$	−7.80863	−	1.12271i	−0.278702	−	0.0400713i
$786$	−27.8824	+	16.6833i	−0.994531	+	0.595072i
$787$	14.0505	+	47.8517i	0.500847	+	1.70573i	0.690026	+	0.723785i	$0.257599\pi$
$787$	14.0505	+	47.8517i	0.500847	+	1.70573i	−0.189179	+	0.981943i	$0.560583\pi$
$788$	9.50038	−	30.4721i	0.338437	−	1.08552i
$789$	−9.03962	+	28.2895i	−0.321819	+	1.00713i
$790$	5.95856	+	9.44336i	0.211996	+	0.335980i
$791$	−19.5600	−	5.74334i	−0.695474	−	0.204210i
$792$	28.3563	−	2.00225i	1.00760	−	0.0711469i
$793$	31.4058	+	20.1833i	1.11525	+	0.716729i
$794$	3.74573	+	0.570370i	0.132931	+	0.0202417i
$795$	2.85417	+	0.479617i	0.101227	+	0.0170103i
$796$	3.82615	+	6.17700i	0.135614	+	0.218938i
$797$	35.1694	−	5.05659i	1.24576	−	0.179114i	0.512278	−	0.858820i	$-0.328802\pi$
$797$	35.1694	−	5.05659i	1.24576	−	0.179114i	0.733485	+	0.679706i	$0.237893\pi$
$798$	−0.416381	−	3.74249i	−0.0147397	−	0.132483i
$799$	13.7233	−	6.26723i	0.485496	−	0.221719i
$800$	−19.1099	−	18.0020i	−0.675636	−	0.636468i
$801$	−35.5028	+	27.9328i	−1.25443	+	0.986957i
$802$	−48.3593	+	13.7640i	−1.70763	+	0.486025i
$803$	−2.86127	+	1.83883i	−0.100972	+	0.0648908i
$804$	−5.02188	+	27.1185i	−0.177108	+	0.956395i
$805$	2.58372	+	10.0630i	0.0910642	+	0.354675i
$806$	−16.5767	−	37.1111i	−0.583889	−	1.30718i
$807$	17.9788	−	37.0218i	0.632885	−	1.30323i
$808$	0.293892	−	0.603260i	0.0103391	−	0.0212226i
$809$	10.5789	+	4.83121i	0.371933	+	0.169856i	0.592607	−	0.805491i	$-0.298099\pi$
$809$	10.5789	+	4.83121i	0.371933	+	0.169856i	−0.220674	+	0.975348i	$0.570826\pi$
$810$	−1.85595	+	7.39625i	−0.0652113	+	0.259878i
$811$	−13.9175	+	6.35593i	−0.488711	+	0.223187i	−0.644501	−	0.764603i	$-0.722935\pi$
$811$	−13.9175	+	6.35593i	−0.488711	+	0.223187i	0.155790	+	0.987790i	$0.450208\pi$
$812$	0.433727	+	0.00721060i	0.0152208	+	0.000253042i
$813$	9.60470	+	11.6299i	0.336852	+	0.407879i
$814$	−44.2743	+	5.99053i	−1.55181	+	0.209968i
$815$	0.0278197	−	0.0321056i	0.000974480	−	0.00112461i
$816$	1.01288	+	11.7669i	0.0354581	+	0.411924i
$817$	−1.35143	−	0.868509i	−0.0472804	−	0.0303853i
$818$	1.28157	−	4.23411i	0.0448090	−	0.148042i
$819$	29.6189	+	28.2286i	1.03497	+	0.986389i
$820$	7.57981	+	5.05123i	0.264699	+	0.176397i
$821$	−24.3408	+	21.0914i	−0.849500	+	0.736096i	−0.966399	−	0.257048i	$-0.917250\pi$
$821$	−24.3408	+	21.0914i	−0.849500	+	0.736096i	0.116899	+	0.993144i	$0.462705\pi$
$822$	−43.6403	−	7.70684i	−1.52213	−	0.268807i
$823$	7.80947	+	26.5966i	0.272221	+	0.927099i	0.976199	+	0.216877i	$0.0695872\pi$
$823$	7.80947	+	26.5966i	0.272221	+	0.927099i	−0.703978	+	0.710222i	$0.748595\pi$
$824$	−17.4069	+	19.1046i	−0.606398	+	0.665542i
$825$	−24.7547	+	10.6039i	−0.861850	+	0.369182i
$826$	23.4706	+	15.3608i	0.816645	+	0.534469i
$827$	−45.3313			−1.57632			−0.788161	−	0.615469i	$-0.788967\pi$
$827$	−45.3313			−1.57632			−0.788161	+	0.615469i	$0.788967\pi$
$828$	−13.1069	−	25.6166i	−0.455497	−	0.890237i
$829$	−0.873420			−0.0303351			−0.0151676	−	0.999885i	$-0.504828\pi$
$829$	−0.873420			−0.0303351			−0.0151676	+	0.999885i	$0.504828\pi$
$830$	6.10521	+	3.99567i	0.211915	+	0.138692i
$831$	41.1190	−	17.6137i	1.42640	−	0.611013i
$832$	−26.1667	+	15.0283i	−0.907167	+	0.521011i
$833$	2.91739	+	9.93573i	0.101082	+	0.344253i
$834$	−29.0878	−	5.13688i	−1.00723	−	0.177876i
$835$	−8.56484	+	7.42148i	−0.296399	+	0.256831i
$836$	1.57971	−	2.37049i	0.0546354	−	0.0819852i
$837$	−8.40275	+	38.6906i	−0.290442	+	1.33734i
$838$	−11.5348	+	38.1093i	−0.398464	+	1.31647i
$839$	14.6609	+	9.42201i	0.506151	+	0.325284i	0.768673	−	0.639642i	$-0.220918\pi$
$839$	14.6609	+	9.42201i	0.506151	+	0.325284i	−0.262521	+	0.964926i	$0.584554\pi$
$840$	−10.0256	−	3.48136i	−0.345917	−	0.120118i
$841$	−18.9886	+	21.9140i	−0.654779	+	0.755656i
$842$	5.49828	−	0.743944i	0.189483	−	0.0256380i
$843$	34.2781	+	41.5059i	1.18060	+	1.42954i
$844$	−0.314326	+	18.9071i	−0.0108195	+	0.650810i
$845$	0.668836	−	0.305447i	0.0230087	−	0.0105077i
$846$	−8.55700	−	36.5598i	−0.294196	−	1.25695i
$847$	0.735060	+	0.335691i	0.0252570	+	0.0115345i
$848$	0.370831	−	11.1499i	0.0127344	−	0.382890i
$849$	−15.5372	+	31.9940i	−0.533235	+	1.09803i
$850$	−4.56317	−	10.2158i	−0.156515	−	0.350399i
$851$	23.1323	+	38.8610i	0.792965	+	1.33214i
$852$	45.4823	+	8.42255i	1.55820	+	0.288552i
$853$	−16.2563	+	10.4473i	−0.556604	+	0.357708i	−0.788502	−	0.615033i	$-0.789143\pi$
$853$	−16.2563	+	10.4473i	−0.556604	+	0.357708i	0.231898	+	0.972740i	$0.425507\pi$
$854$	48.6783	−	13.8548i	1.66574	−	0.474102i
$855$	0.472503	+	0.600554i	0.0161592	+	0.0205385i
$856$	0.0406338	−	1.62927i	0.00138884	−	0.0556871i
$857$	−6.54509	+	2.98904i	−0.223576	+	0.102104i	−0.524054	−	0.851685i	$-0.675581\pi$
$857$	−6.54509	+	2.98904i	−0.223576	+	0.102104i	0.300478	+	0.953789i	$0.402854\pi$
$858$	3.42263	+	30.7630i	0.116847	+	1.05023i
$859$	−41.0783	+	5.90617i	−1.40157	+	0.201516i	−0.801292	−	0.598273i	$-0.795854\pi$
$859$	−41.0783	+	5.90617i	−1.40157	+	0.201516i	−0.600281	+	0.799789i	$0.704945\pi$
$860$	−3.84901	+	2.38415i	−0.131250	+	0.0812987i
$861$	−46.9505	−	7.88959i	−1.60007	−	0.268877i
$862$	−24.2988	−	3.70002i	−0.827619	−	0.126023i
$863$	21.4685	+	13.7970i	0.730797	+	0.469655i	0.852378	−	0.522927i	$-0.175160\pi$
$863$	21.4685	+	13.7970i	0.730797	+	0.469655i	−0.121580	+	0.992582i	$0.538796\pi$
$864$	29.2077	+	3.30321i	0.993666	+	0.112377i
$865$	6.77294	+	1.98871i	0.230287	+	0.0676183i
$866$	2.30003	+	3.64518i	0.0781583	+	0.123868i
$867$	7.43035	−	23.2533i	0.252348	−	0.789724i
$868$	−52.6056	−	16.4010i	−1.78555	−	0.556686i
$869$	−12.4386	−	42.3621i	−0.421952	−	1.43704i
$870$	−0.0755388	+	0.0451982i	−0.00256101	+	0.00153236i
$871$	−29.7245	−	4.27373i	−1.00718	−	0.144810i
$872$	5.32418	+	19.9607i	0.180299	+	0.675954i
$873$	8.89640	−	17.2663i	0.301097	−	0.584375i
$874$	−2.83410	−	0.531504i	−0.0958650	−	0.0179784i
$875$	20.8858			0.706070
$876$	−3.25535	+	1.33087i	−0.109988	+	0.0449658i
$877$	3.07148	−	21.3626i	0.103716	−	0.721364i	−0.869909	−	0.493212i	$-0.835823\pi$
$877$	3.07148	−	21.3626i	0.103716	−	0.721364i	0.973626	−	0.228152i	$-0.0732682\pi$
$878$	22.8988	+	0.190330i	0.772795	+	0.00642332i
$879$	20.3903	−	22.4352i	0.687746	−	0.756720i
$880$	−4.11366	−	6.89460i	−0.138672	−	0.232417i
$881$	13.0312	−	11.2916i	0.439032	−	0.380424i	−0.407111	−	0.913378i	$-0.633464\pi$
$881$	13.0312	−	11.2916i	0.439032	−	0.380424i	0.846144	+	0.532955i	$0.178918\pi$
$882$	25.6744	−	2.24234i	0.864501	−	0.0755034i
$883$	5.77409	−	19.6647i	0.194313	−	0.661771i	−0.803477	−	0.595335i	$-0.797019\pi$
$883$	5.77409	−	19.6647i	0.194313	−	0.661771i	0.997791	−	0.0664355i	$-0.0211626\pi$
$884$	−12.7576	+	1.61831i	−0.429085	+	0.0544295i
$885$	−5.69065	−	0.134813i	−0.191289	−	0.00453168i
$886$	46.6637	+	7.10557i	1.56770	+	0.238716i
$887$	−3.46255	+	3.99600i	−0.116261	+	0.134173i	−0.810897	−	0.585189i	$-0.801020\pi$
$887$	−3.46255	+	3.99600i	−0.116261	+	0.134173i	0.694636	+	0.719362i	$0.255566\pi$
$888$	−46.1429	−	2.24526i	−1.54845	−	0.0753461i
$889$	7.97616	+	55.4754i	0.267512	+	1.86059i
$890$	11.5610	+	5.39630i	0.387525	+	0.180885i
$891$	15.0637	−	26.1187i	0.504654	−	0.875009i
$892$	−14.5571	−	6.94273i	−0.487408	−	0.232460i
$893$	−3.42261	−	1.56305i	−0.114533	−	0.0523056i
$894$	6.13954	+	5.67382i	0.205337	+	0.189761i
$895$	−1.97454	−	3.07244i	−0.0660014	−	0.102700i
$896$	−8.16667	+	40.0855i	−0.272829	+	1.33916i
$897$	27.2950	−	15.3840i	0.911353	−	0.513656i
$898$	12.6630	+	28.3494i	0.422571	+	0.946031i
$899$	−0.384496	+	0.247101i	−0.0128237	+	0.00824127i
$900$	−27.1654	+	6.12049i	−0.905513	+	0.204016i
$901$	1.97505	−	4.32476i	0.0657985	−	0.144079i
$902$	−23.3582	−	27.4139i	−0.777743	−	0.912784i
$903$	13.2619	−	19.5992i	0.441327	−	0.652221i
$904$	−6.26061	−	14.6659i	−0.208225	−	0.487780i
$905$	9.32035	−	1.34006i	0.309819	−	0.0445453i
$906$	25.4945	−	20.7009i	0.846997	−	0.687742i
$907$	9.11640	+	7.89940i	0.302705	+	0.262295i	0.792946	−	0.609291i	$-0.208546\pi$
$907$	9.11640	+	7.89940i	0.302705	+	0.262295i	−0.490242	+	0.871587i	$0.663091\pi$
$908$	−48.6986	+	13.4241i	−1.61612	+	0.445493i
$909$	−0.356014	−	0.616309i	−0.0118082	−	0.0204417i
$910$	3.34771	−	11.0603i	0.110976	−	0.366647i
$911$	8.28222	+	2.43188i	0.274402	+	0.0805717i	0.416038	−	0.909347i	$-0.363418\pi$
$911$	8.28222	+	2.43188i	0.274402	+	0.0805717i	−0.141636	+	0.989919i	$0.545236\pi$
$912$	2.05245	−	2.11272i	0.0679635	−	0.0699591i
$913$	−18.8929	−	21.8036i	−0.625263	−	0.721592i
$914$	18.2826	+	16.1100i	0.604736	+	0.532871i
$915$	−6.90776	+	7.60054i	−0.228364	+	0.251266i
$916$	11.9176	+	27.2874i	0.393769	+	0.901602i
$917$	−47.4763	−	6.82606i	−1.56780	−	0.225416i
$918$	10.9464	+	6.09090i	0.361283	+	0.201030i
$919$		−	50.5053i		−	1.66602i	−0.553261	−	0.833008i	$-0.686617\pi$
$919$		−	50.5053i		−	1.66602i	0.553261	−	0.833008i	$-0.313383\pi$
$920$	−4.79057	+	6.56477i	−0.157940	+	0.216434i
$921$	13.2835	−	8.09877i	0.437705	−	0.266864i
$922$	−29.1126	−	19.0533i	−0.958771	−	0.627486i
$923$	−7.16778	+	49.8530i	−0.235930	+	1.64093i
$924$	34.3587	+	24.0911i	1.13032	+	0.792540i
$925$	41.9924	−	12.3301i	1.38070	−	0.405411i
$926$	29.9497	−	33.9889i	0.984210	−	1.11694i
$927$	6.46900	+	26.6390i	0.212470	+	0.874941i
$928$	0.211361	+	0.265451i	0.00693826	+	0.00871385i
$929$	13.5234	−	46.0564i	0.443688	−	1.51106i	−0.369595	−	0.929193i	$-0.620503\pi$
$929$	13.5234	−	46.0564i	0.443688	−	1.51106i	0.813283	−	0.581869i	$-0.197678\pi$
$930$	10.8244	−	2.80549i	0.354946	−	0.0919956i
$931$	1.39626	−	2.17262i	0.0457604	−	0.0712046i
$932$	9.36333	+	33.9674i	0.306706	+	1.11264i
$933$	−8.68234	−	1.45899i	−0.284247	−	0.0477651i
$934$	8.33005	−	1.12710i	0.272568	−	0.0368797i
$935$	−0.486937	−	3.38672i	−0.0159245	−	0.110758i
$936$	−2.31220	+	31.9220i	−0.0755765	+	1.04340i
$937$	−6.18981	−	13.5538i	−0.202212	−	0.442783i	0.781173	−	0.624315i	$-0.214622\pi$
$937$	−6.18981	−	13.5538i	−0.202212	−	0.442783i	−0.983385	+	0.181532i	$0.941895\pi$
$938$	−30.9888	+	26.4042i	−1.01182	+	0.862127i
$939$	−1.19761	+	0.143330i	−0.0390824	+	0.00467740i
$940$	−8.12872	+	6.81033i	−0.265130	+	0.222129i
$941$	−3.35864	−	5.22614i	−0.109488	−	0.170367i	0.782185	−	0.623046i	$-0.214105\pi$
$941$	−3.35864	−	5.22614i	−0.109488	−	0.170367i	−0.891674	+	0.452678i	$0.850469\pi$
$942$	26.5618	+	18.2968i	0.865430	+	0.596142i
$943$	−16.2721	+	32.6237i	−0.529893	+	1.06237i
$944$	2.39897	+	21.8101i	0.0780800	+	0.709859i
$945$	−9.00910	+	6.74894i	−0.293066	+	0.219543i
$946$	17.2182	−	4.90064i	0.559811	−	0.159333i
$947$	12.5055	−	27.3832i	0.406374	−	0.889835i	−0.590210	−	0.807250i	$-0.700955\pi$
$947$	12.5055	−	27.3832i	0.406374	−	0.889835i	0.996584	−	0.0825852i	$-0.0263176\pi$
$948$	−4.67075	−	45.4128i	−0.151699	−	1.47494i
$949$	−1.59079	−	3.48333i	−0.0516391	−	0.113074i
$950$	−1.18025	+	2.52856i	−0.0382924	+	0.0820374i
$951$	−7.70245	−	9.32656i	−0.249769	−	0.302434i
$952$	−9.78840	+	14.4270i	−0.317244	+	0.467583i
$953$	−4.21778	−	3.65472i	−0.136627	−	0.118388i	0.583866	−	0.811850i	$-0.301539\pi$
$953$	−4.21778	−	3.65472i	−0.136627	−	0.118388i	−0.720493	+	0.693462i	$0.756085\pi$
$954$	−9.58293	−	6.94139i	−0.310259	−	0.224736i
$955$	2.50081	−	3.89134i	0.0809244	−	0.125921i
$956$	−1.41570	−	11.1604i	−0.0457869	−	0.360952i
$957$	0.336193	−	0.0901237i	0.0108676	−	0.00291329i
$958$	−2.89969	−	4.59555i	−0.0936849	−	0.148476i
$959$	−42.8393	−	49.4392i	−1.38335	−	1.59648i
$960$	−2.88436	−	7.78446i	−0.0930922	−	0.251243i
$961$	25.9622	−	7.62318i	0.837489	−	0.245909i
$962$	0.418089	−	50.3006i	0.0134797	−	1.62176i
$963$	−1.40833	−	1.00238i	−0.0453829	−	0.0323014i
$964$	9.56013	−	59.4582i	0.307911	−	1.91502i
$965$		−	11.4701i		−	0.369237i
$966$	8.81613	−	41.5519i	0.283654	−	1.33691i
$967$		−	28.8249i		−	0.926946i	−0.886111	−	0.463473i	$-0.846603\pi$
$967$		−	28.8249i		−	0.926946i	0.886111	−	0.463473i	$-0.153397\pi$
$968$	0.162908	+	0.610752i	0.00523605	+	0.0196303i
$969$	1.15389	−	0.494281i	0.0370684	−	0.0158786i
$970$	−5.48553	−	0.0455946i	−0.176130	−	0.00146396i
$971$	−24.2241	+	7.11285i	−0.777390	+	0.228262i	−0.646275	−	0.763105i	$-0.723674\pi$
$971$	−24.2241	+	7.11285i	−0.777390	+	0.228262i	−0.131115	+	0.991367i	$0.541856\pi$
$972$	20.2334	−	23.7194i	0.648986	−	0.760800i
$973$	−28.5539	−	32.9530i	−0.915396	−	1.05642i
$974$	−9.85591	+	6.21887i	−0.315804	+	0.199265i
$975$	−7.85090	−	29.2866i	−0.251430	−	0.937921i
$976$	32.5751	+	22.4990i	1.04270	+	0.720176i
$977$	−17.6536	+	27.4696i	−0.564790	+	0.878830i	−0.999766	−	0.0216116i	$-0.993120\pi$
$977$	−17.6536	+	27.4696i	−0.564790	+	0.878830i	0.434977	+	0.900442i	$0.356757\pi$
$978$	−0.160218	+	0.0670604i	−0.00512320	+	0.00214435i
$979$	−38.1249	−	33.0354i	−1.21848	−	1.05582i
$980$	−3.83287	−	6.18785i	−0.122436	−	0.197664i
$981$	20.7082	+	7.16189i	0.661162	+	0.228661i
$982$	1.71900	+	0.802376i	0.0548556	+	0.0256049i
$983$	−3.37257	−	7.38489i	−0.107568	−	0.235541i	0.848192	−	0.529689i	$-0.177691\pi$
$983$	−3.37257	−	7.38489i	−0.107568	−	0.235541i	−0.955760	+	0.294148i	$0.904964\pi$
$984$	−18.5874	−	32.2704i	−0.592546	−	1.02874i
$985$	−3.97202	+	8.69751i	−0.126559	+	0.277126i
$986$	0.0395862	+	0.139084i	0.00126068	+	0.00442935i
$987$	24.2129	−	49.8589i	0.770705	−	1.58702i
$988$	2.38864	+	2.14031i	0.0759926	+	0.0680922i
$989$	−11.3906	−	14.0937i	−0.362200	−	0.448153i
$990$	−8.50238	−	0.473929i	−0.270223	−	0.0150624i
$991$	26.7983	+	41.6990i	0.851276	+	1.32461i	0.944346	+	0.328952i	$0.106696\pi$
$991$	26.7983	+	41.6990i	0.851276	+	1.32461i	−0.0930700	+	0.995660i	$0.529668\pi$
$992$	−16.2612	−	39.9179i	−0.516294	−	1.26739i
$993$	1.65771	+	13.8511i	0.0526057	+	0.439551i
$994$	44.2843	+	51.9734i	1.40461	+	1.64850i
$995$	−0.904193	−	1.97991i	−0.0286648	−	0.0627673i
$996$	−15.1038	−	25.7255i	−0.478581	−	0.815143i
$997$	−3.87504	−	26.9515i	−0.122724	−	0.853563i	−0.954449	−	0.298375i	$-0.903555\pi$
$997$	−3.87504	−	26.9515i	−0.122724	−	0.853563i	0.831725	−	0.555188i	$-0.187354\pi$
$998$	−0.966749	−	7.14497i	−0.0306019	−	0.226170i
$999$	−29.3511	+	39.2364i	−0.928627	+	1.24139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.o.a.35.14	yes	440
3.2	odd	2	inner	276.2.o.a.35.31	yes	440
4.3	odd	2	inner	276.2.o.a.35.42	yes	440
12.11	even	2	inner	276.2.o.a.35.3	✓	440
23.2	even	11	inner	276.2.o.a.71.3	yes	440
69.2	odd	22	inner	276.2.o.a.71.42	yes	440
92.71	odd	22	inner	276.2.o.a.71.31	yes	440
276.71	even	22	inner	276.2.o.a.71.14	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.o.a.35.3	✓	440	12.11	even	2	inner
276.2.o.a.35.14	yes	440	1.1	even	1	trivial
276.2.o.a.35.31	yes	440	3.2	odd	2	inner
276.2.o.a.35.42	yes	440	4.3	odd	2	inner
276.2.o.a.71.3	yes	440	23.2	even	11	inner
276.2.o.a.71.14	yes	440	276.71	even	22	inner
276.2.o.a.71.31	yes	440	92.71	odd	22	inner
276.2.o.a.71.42	yes	440	69.2	odd	22	inner

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.774443 + 1.18332i) q^{2} +(-1.59213 + 0.682004i) q^{3} +(-0.800475 - 1.83282i) q^{4} +(0.168792 + 0.574851i) q^{5} +(0.425987 - 2.41216i) q^{6} +(2.73269 - 2.36789i) q^{7} +(2.78873 + 0.472203i) q^{8} +(2.06974 - 2.17167i) q^{9} +O(q^{10})\)	\(q+(-0.774443 + 1.18332i) q^{2} +(-1.59213 + 0.682004i) q^{3} +(-0.800475 - 1.83282i) q^{4} +(0.168792 + 0.574851i) q^{5} +(0.425987 - 2.41216i) q^{6} +(2.73269 - 2.36789i) q^{7} +(2.78873 + 0.472203i) q^{8} +(2.06974 - 2.17167i) q^{9} +(-0.810951 - 0.245456i) q^{10} +(2.81832 + 1.81123i) q^{11} +(2.52445 + 2.37216i) q^{12} +(-2.47007 + 2.85062i) q^{13} +(0.685649 + 5.06744i) q^{14} +(-0.660789 - 0.800120i) q^{15} +(-2.71848 + 2.93426i) q^{16} +(-1.55064 + 0.708152i) q^{17} +(0.966881 + 4.13100i) q^{18} +(0.386731 + 0.176614i) q^{19} +(0.918488 - 0.769519i) q^{20} +(-2.73589 + 5.63370i) q^{21} +(-4.32588 + 1.93227i) q^{22} +(3.51470 + 3.26296i) q^{23} +(-4.76206 + 1.15012i) q^{24} +(3.90430 - 2.50914i) q^{25} +(-1.46025 - 5.13052i) q^{26} +(-1.81420 + 4.86916i) q^{27} +(-6.52738 - 3.11311i) q^{28} +(-0.0545631 + 0.0249181i) q^{29} +(1.45854 - 0.162274i) q^{30} +(7.54204 - 1.08438i) q^{31} +(-1.36684 - 5.48924i) q^{32} +(-5.72239 - 0.961596i) q^{33} +(0.362913 - 2.38332i) q^{34} +(1.82244 + 1.17121i) q^{35} +(-5.63707 - 2.05510i) q^{36} +(9.04804 + 2.65674i) q^{37} +(-0.508491 + 0.320847i) q^{38} +(1.98854 - 6.22314i) q^{39} +(0.199268 + 1.68281i) q^{40} +(2.14166 + 7.29381i) q^{41} +(-4.54766 - 7.60040i) q^{42} +(-3.74007 - 0.537741i) q^{43} +(1.06366 - 6.61533i) q^{44} +(1.59775 + 0.823233i) q^{45} +(-6.58305 + 1.63203i) q^{46} -8.85011 q^{47} +(2.32699 - 6.52573i) q^{48} +(0.864497 - 6.01271i) q^{49} +(-0.0545521 + 6.56322i) q^{50} +(1.98585 - 2.18501i) q^{51} +(7.20191 + 2.24536i) q^{52} +(-2.10780 + 1.82642i) q^{53} +(-4.35675 - 5.91766i) q^{54} +(-0.565477 + 1.92584i) q^{55} +(8.73888 - 5.31303i) q^{56} +(-0.736176 - 0.0174402i) q^{57} +(0.0127700 - 0.0838631i) q^{58} +(3.59218 - 4.14560i) q^{59} +(-0.937534 + 1.85158i) q^{60} +(-1.40855 - 9.79667i) q^{61} +(-4.55772 + 9.76441i) q^{62} +(0.513676 - 10.8355i) q^{63} +(7.55405 + 2.63370i) q^{64} +(-2.05561 - 0.938765i) q^{65} +(5.56954 - 6.02670i) q^{66} +(4.30433 + 6.69767i) q^{67} +(2.53916 + 2.27519i) q^{68} +(-7.82120 - 2.79800i) q^{69} +(-2.79729 + 1.24949i) q^{70} +(11.2331 - 7.21909i) q^{71} +(6.79742 - 5.07888i) q^{72} +(-0.421746 + 0.923494i) q^{73} +(-10.1510 + 8.64919i) q^{74} +(-4.50490 + 6.65763i) q^{75} +(0.0141341 - 0.850184i) q^{76} +(11.9904 - 1.72396i) q^{77} +(5.82394 + 7.17254i) q^{78} +(-9.95979 - 8.63021i) q^{79} +(-2.14562 - 1.06744i) q^{80} +(-0.432343 - 8.98961i) q^{81} +(-10.2895 - 3.11439i) q^{82} +(-8.26280 - 2.42618i) q^{83} +(12.5156 + 0.504764i) q^{84} +(-0.668817 - 0.771856i) q^{85} +(3.53279 - 4.00923i) q^{86} +(0.0698772 - 0.0768851i) q^{87} +(7.00428 + 6.38184i) q^{88} +(-14.9047 - 2.14298i) q^{89} +(-2.21151 + 1.25309i) q^{90} +13.6387i q^{91} +(3.16699 - 9.05374i) q^{92} +(-11.2683 + 6.87017i) q^{93} +(6.85391 - 10.4725i) q^{94} +(-0.0362499 + 0.252124i) q^{95} +(5.91987 + 7.80738i) q^{96} +(6.21222 - 1.82407i) q^{97} +(6.44543 + 5.67948i) q^{98} +(9.76659 - 2.37171i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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