LMFDB - Embedded newform 350.3.p.c.207.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,3,Mod(93,350)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 4])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("350.93"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	350.p (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,4,0,0,-16,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.53680925261$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.3317760000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			207.1
Root			$0.578737 + 2.15988i$ of defining polynomial
Character	$\chi$	$=$	350.207
Dual form			350.3.p.c.93.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.366025 - 1.36603i) q^{2} +(-1.36843 - 5.10704i) q^{3} +(-1.73205 - 1.00000i) q^{4} -7.47723 q^{6} +(2.80041 + 6.41543i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-16.4150 + 9.47723i) q^{9} +(-1.73861 + 3.01137i) q^{11} +(-2.73685 + 10.2141i) q^{12} +(-10.9545 + 10.9545i) q^{13} +(9.78866 - 1.47723i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-9.49996 + 2.54551i) q^{17} +(6.93781 + 25.8923i) q^{18} +(-15.9623 + 9.21584i) q^{19} +(28.9317 - 23.0809i) q^{21} +(3.47723 + 3.47723i) q^{22} +(-17.3390 - 4.64598i) q^{23} +(12.9509 + 7.47723i) q^{24} +(10.9545 + 18.9737i) q^{26} +(37.2158 + 37.2158i) q^{27} +(1.56497 - 13.9123i) q^{28} -49.8634i q^{29} +(-8.00000 + 13.8564i) q^{31} +(5.46410 - 1.46410i) q^{32} +(17.7583 + 4.75833i) q^{33} +13.9089i q^{34} +37.9089 q^{36} +(9.16731 - 34.2129i) q^{37} +(6.74646 + 25.1781i) q^{38} +(70.9352 + 40.9545i) q^{39} -6.04555 q^{41} +(-20.9393 - 47.9696i) q^{42} +(9.64752 - 9.64752i) q^{43} +(6.02273 - 3.47723i) q^{44} +(-12.6931 + 21.9850i) q^{46} +(-5.44036 + 20.3037i) q^{47} +(14.9545 - 14.9545i) q^{48} +(-33.3154 + 35.9317i) q^{49} +(26.0000 + 45.0333i) q^{51} +(29.9281 - 8.01921i) q^{52} +(2.94488 + 10.9904i) q^{53} +(64.4597 - 37.2158i) q^{54} +(-18.4317 - 7.23003i) q^{56} +(68.9089 + 68.9089i) q^{57} +(-68.1146 - 18.2513i) q^{58} +(-65.3652 - 37.7386i) q^{59} +(-51.4545 - 89.1217i) q^{61} +(16.0000 + 16.0000i) q^{62} +(-106.769 - 78.7693i) q^{63} -8.00000i q^{64} +(13.0000 - 22.5167i) q^{66} +(-31.1237 + 8.33958i) q^{67} +(18.9999 + 5.09101i) q^{68} +94.9089i q^{69} +40.3406 q^{71} +(13.8756 - 51.7845i) q^{72} +(22.9762 + 85.7485i) q^{73} +(-43.3802 - 25.0455i) q^{74} +36.8634 q^{76} +(-24.1880 - 2.72088i) q^{77} +(81.9089 - 81.9089i) q^{78} +(-87.6452 + 50.6020i) q^{79} +(53.8406 - 93.2546i) q^{81} +(-2.21282 + 8.25837i) q^{82} +(-51.1247 + 51.1247i) q^{83} +(-73.1920 + 11.0455i) q^{84} +(-9.64752 - 16.7100i) q^{86} +(-254.654 + 68.2344i) q^{87} +(-2.54551 - 9.49996i) q^{88} +(71.6434 - 41.3634i) q^{89} +(-100.954 - 39.6005i) q^{91} +(25.3861 + 25.3861i) q^{92} +(81.7126 + 21.8948i) q^{93} +(25.7441 + 14.8634i) q^{94} +(-14.9545 - 25.9019i) q^{96} +(-45.7723 - 45.7723i) q^{97} +(36.8893 + 58.6616i) q^{98} -65.9089i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 4 q^{3} - 16 q^{6} + 4 q^{7} - 16 q^{8} + 8 q^{11} + 8 q^{12} + 16 q^{16} + 16 q^{17} - 32 q^{18} + 100 q^{21} - 16 q^{22} + 4 q^{23} + 232 q^{27} + 40 q^{28} - 64 q^{31} + 16 q^{32} + 52 q^{33}+ \cdots + 132 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 4 * q^3 - 16 * q^6 + 4 * q^7 - 16 * q^8 + 8 * q^11 + 8 * q^12 + 16 * q^16 + 16 * q^17 - 32 * q^18 + 100 * q^21 - 16 * q^22 + 4 * q^23 + 232 * q^27 + 40 * q^28 - 64 * q^31 + 16 * q^32 + 52 * q^33 + 128 * q^36 - 144 * q^37 - 8 * q^38 - 136 * q^41 - 188 * q^42 - 120 * q^43 + 8 * q^46 - 72 * q^47 + 32 * q^48 + 208 * q^51 - 76 * q^53 - 16 * q^56 + 376 * q^57 - 68 * q^58 - 324 * q^61 + 128 * q^62 - 112 * q^63 + 104 * q^66 - 124 * q^67 - 32 * q^68 + 16 * q^71 - 64 * q^72 - 32 * q^73 + 32 * q^76 - 20 * q^77 + 480 * q^78 + 124 * q^81 + 68 * q^82 - 168 * q^83 + 120 * q^86 - 428 * q^87 - 16 * q^88 - 720 * q^91 - 16 * q^92 + 64 * q^93 - 32 * q^96 + 72 * q^97 + 132 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$2$	0.366025	−	1.36603i	0.183013	−	0.683013i
$3$	−1.36843	−	5.10704i	−0.456142	−	1.70235i	−0.684707	−	0.728818i	$-0.740070\pi$
$3$	−1.36843	−	5.10704i	−0.456142	−	1.70235i	0.228565	−	0.973529i	$-0.426597\pi$
$4$	−1.73205	−	1.00000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	−7.47723			−1.24620
$7$	2.80041	+	6.41543i	0.400059	+	0.916489i
$7$	2.80041	+	6.41543i	0.400059	+	0.916489i
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$	−16.4150	+	9.47723i	−1.82389	+	1.05303i
$10$		0			0
$11$	−1.73861	+	3.01137i	−0.158056	+	0.273761i	−0.934167	−	0.356835i	$-0.883856\pi$
$11$	−1.73861	+	3.01137i	−0.158056	+	0.273761i	0.776112	+	0.630595i	$0.217189\pi$
$12$	−2.73685	+	10.2141i	−0.228071	+	0.851173i
$13$	−10.9545	+	10.9545i	−0.842650	+	0.842650i	−0.989203	−	0.146553i	$-0.953182\pi$
$13$	−10.9545	+	10.9545i	−0.842650	+	0.842650i	0.146553	+	0.989203i	$0.453182\pi$
$14$	9.78866	−	1.47723i	0.699190	−	0.105516i
$15$		0			0
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	−9.49996	+	2.54551i	−0.558821	+	0.149736i	−0.527165	−	0.849763i	$-0.676745\pi$
$17$	−9.49996	+	2.54551i	−0.558821	+	0.149736i	−0.0316564	+	0.999499i	$0.510078\pi$
$18$	6.93781	+	25.8923i	0.385434	+	1.43846i
$19$	−15.9623	+	9.21584i	−0.840121	+	0.485044i	−0.857305	−	0.514808i	$-0.827863\pi$
$19$	−15.9623	+	9.21584i	−0.840121	+	0.485044i	0.0171843	+	0.999852i	$0.494530\pi$
$20$		0			0
$21$	28.9317	−	23.0809i	1.37770	−	1.09909i
$22$	3.47723	+	3.47723i	0.158056	+	0.158056i
$23$	−17.3390	−	4.64598i	−0.753872	−	0.201999i	−0.138637	−	0.990343i	$-0.544272\pi$
$23$	−17.3390	−	4.64598i	−0.753872	−	0.201999i	−0.615235	+	0.788344i	$0.710939\pi$
$24$	12.9509	+	7.47723i	0.539622	+	0.311551i
$25$		0			0
$26$	10.9545	+	18.9737i	0.421325	+	0.729756i
$27$	37.2158	+	37.2158i	1.37836	+	1.37836i
$28$	1.56497	−	13.9123i	0.0558918	−	0.496866i
$29$		−	49.8634i		−	1.71943i	−0.510777	−	0.859713i	$-0.670642\pi$
$29$		−	49.8634i		−	1.71943i	0.510777	−	0.859713i	$-0.329358\pi$
$30$		0			0
$31$	−8.00000	+	13.8564i	−0.258065	+	0.446981i	−0.965723	−	0.259573i	$-0.916418\pi$
$31$	−8.00000	+	13.8564i	−0.258065	+	0.446981i	0.707659	+	0.706554i	$0.249751\pi$
$32$	5.46410	−	1.46410i	0.170753	−	0.0457532i
$33$	17.7583	+	4.75833i	0.538131	+	0.144192i
$34$			13.9089i			0.409085i
$35$		0			0
$36$	37.9089			1.05303
$37$	9.16731	−	34.2129i	0.247765	−	0.924672i	−0.724208	−	0.689581i	$-0.757795\pi$
$37$	9.16731	−	34.2129i	0.247765	−	0.924672i	0.971973	−	0.235091i	$-0.0755387\pi$
$38$	6.74646	+	25.1781i	0.177538	+	0.662583i
$39$	70.9352	+	40.9545i	1.81885	+	1.05011i
$40$		0			0
$41$	−6.04555			−0.147452			−0.0737262	−	0.997279i	$-0.523489\pi$
$41$	−6.04555			−0.147452			−0.0737262	+	0.997279i	$0.523489\pi$
$42$	−20.9393	−	47.9696i	−0.498555	−	1.14213i
$43$	9.64752	−	9.64752i	0.224361	−	0.224361i	−0.585971	−	0.810332i	$-0.699287\pi$
$43$	9.64752	−	9.64752i	0.224361	−	0.224361i	0.810332	+	0.585971i	$0.199287\pi$
$44$	6.02273	−	3.47723i	0.136880	−	0.0790279i
$45$		0			0
$46$	−12.6931	+	21.9850i	−0.275936	+	0.477935i
$47$	−5.44036	+	20.3037i	−0.115752	+	0.431994i	−0.999342	−	0.0362680i	$-0.988453\pi$
$47$	−5.44036	+	20.3037i	−0.115752	+	0.431994i	0.883590	+	0.468262i	$0.155120\pi$
$48$	14.9545	−	14.9545i	0.311551	−	0.311551i
$49$	−33.3154	+	35.9317i	−0.679906	+	0.733300i
$50$		0			0
$51$	26.0000	+	45.0333i	0.509804	+	0.883006i
$52$	29.9281	−	8.01921i	0.575541	−	0.154216i
$53$	2.94488	+	10.9904i	0.0555637	+	0.207366i	0.988127	−	0.153640i	$-0.0490997\pi$
$53$	2.94488	+	10.9904i	0.0555637	+	0.207366i	−0.932563	+	0.361007i	$0.882433\pi$
$54$	64.4597	−	37.2158i	1.19370	−	0.689182i
$55$		0			0
$56$	−18.4317	−	7.23003i	−0.329137	−	0.129108i
$57$	68.9089	+	68.9089i	1.20893	+	1.20893i
$58$	−68.1146	−	18.2513i	−1.17439	−	0.314677i
$59$	−65.3652	−	37.7386i	−1.10788	−	0.639638i	−0.169604	−	0.985512i	$-0.554249\pi$
$59$	−65.3652	−	37.7386i	−1.10788	−	0.639638i	−0.938281	+	0.345875i	$0.887582\pi$
$60$		0			0
$61$	−51.4545	−	89.1217i	−0.843516	−	1.46101i	−0.886904	−	0.461954i	$-0.847149\pi$
$61$	−51.4545	−	89.1217i	−0.843516	−	1.46101i	0.0433885	−	0.999058i	$-0.486185\pi$
$62$	16.0000	+	16.0000i	0.258065	+	0.258065i
$63$	−106.769	−	78.7693i	−1.69475	−	1.25031i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	13.0000	−	22.5167i	0.196970	−	0.341162i
$67$	−31.1237	+	8.33958i	−0.464533	+	0.124471i	−0.483492	−	0.875349i	$-0.660632\pi$
$67$	−31.1237	+	8.33958i	−0.464533	+	0.124471i	0.0189583	+	0.999820i	$0.493965\pi$
$68$	18.9999	+	5.09101i	0.279410	+	0.0748678i
$69$			94.9089i			1.37549i
$70$		0			0
$71$	40.3406			0.568177			0.284089	−	0.958798i	$-0.408309\pi$
$71$	40.3406			0.568177			0.284089	+	0.958798i	$0.408309\pi$
$72$	13.8756	−	51.7845i	0.192717	−	0.719229i
$73$	22.9762	+	85.7485i	0.314743	+	1.17464i	0.924229	+	0.381840i	$0.124709\pi$
$73$	22.9762	+	85.7485i	0.314743	+	1.17464i	−0.609486	+	0.792797i	$0.708624\pi$
$74$	−43.3802	−	25.0455i	−0.586218	−	0.338453i
$75$		0			0
$76$	36.8634			0.485044
$77$	−24.1880	−	2.72088i	−0.314130	−	0.0353361i
$78$	81.9089	−	81.9089i	1.05011	−	1.05011i
$79$	−87.6452	+	50.6020i	−1.10943	+	0.640531i	−0.938682	−	0.344783i	$-0.887952\pi$
$79$	−87.6452	+	50.6020i	−1.10943	+	0.640531i	−0.170750	+	0.985314i	$0.554619\pi$
$80$		0			0
$81$	53.8406	−	93.2546i	0.664699	−	1.15129i
$82$	−2.21282	+	8.25837i	−0.0269857	+	0.100712i
$83$	−51.1247	+	51.1247i	−0.615961	+	0.615961i	−0.944493	−	0.328532i	$-0.893446\pi$
$83$	−51.1247	+	51.1247i	−0.615961	+	0.615961i	0.328532	+	0.944493i	$0.393446\pi$
$84$	−73.1920	+	11.0455i	−0.871333	+	0.131495i
$85$		0			0
$86$	−9.64752	−	16.7100i	−0.112180	−	0.194302i
$87$	−254.654	+	68.2344i	−2.92706	+	0.784303i
$88$	−2.54551	−	9.49996i	−0.0289262	−	0.107954i
$89$	71.6434	−	41.3634i	0.804982	−	0.464757i	−0.0402280	−	0.999191i	$-0.512808\pi$
$89$	71.6434	−	41.3634i	0.804982	−	0.464757i	0.845210	+	0.534434i	$0.179475\pi$
$90$		0			0
$91$	−100.954	−	39.6005i	−1.10939	−	0.435170i
$92$	25.3861	+	25.3861i	0.275936	+	0.275936i
$93$	81.7126	+	21.8948i	0.878631	+	0.235428i
$94$	25.7441	+	14.8634i	0.273873	+	0.158121i
$95$		0			0
$96$	−14.9545	−	25.9019i	−0.155776	−	0.269811i
$97$	−45.7723	−	45.7723i	−0.471879	−	0.471879i	0.430643	−	0.902522i	$-0.358287\pi$
$97$	−45.7723	−	45.7723i	−0.471879	−	0.471879i	−0.902522	+	0.430643i	$0.858287\pi$
$98$	36.8893	+	58.6616i	0.376422	+	0.598587i
$99$		−	65.9089i		−	0.665746i
$100$		0			0
$101$	−71.7495	+	124.274i	−0.710391	+	1.23043i	0.254320	+	0.967120i	$0.418148\pi$
$101$	−71.7495	+	124.274i	−0.710391	+	1.23043i	−0.964710	+	0.263313i	$0.915185\pi$
$102$	71.0333	−	19.0333i	0.696405	−	0.186601i
$103$	54.2840	+	14.5453i	0.527029	+	0.141217i	0.512516	−	0.858678i	$-0.328714\pi$
$103$	54.2840	+	14.5453i	0.527029	+	0.141217i	0.0145128	+	0.999895i	$0.495380\pi$
$104$		−	43.8178i		−	0.421325i
$105$		0			0
$106$	16.0911			0.151803
$107$	15.5267	−	57.9465i	0.145109	−	0.541556i	−0.854641	−	0.519219i	$-0.826223\pi$
$107$	15.5267	−	57.9465i	0.145109	−	0.541556i	0.999751	−	0.0223366i	$-0.00711055\pi$
$108$	−27.2439	−	101.676i	−0.252258	−	0.941440i
$109$	32.2796	+	18.6366i	0.296143	+	0.170978i	0.640709	−	0.767784i	$-0.278640\pi$
$109$	32.2796	+	18.6366i	0.296143	+	0.170978i	−0.344566	+	0.938762i	$0.611974\pi$
$110$		0			0
$111$	−187.271			−1.68713
$112$	−16.6229	+	22.5318i	−0.148418	+	0.201176i
$113$	118.636	−	118.636i	1.04987	−	1.04987i	0.0511834	−	0.998689i	$-0.483701\pi$
$113$	118.636	−	118.636i	1.04987	−	1.04987i	0.998689	−	0.0511834i	$-0.0162993\pi$
$114$	119.354	−	68.9089i	1.04696	−	0.604464i
$115$		0			0
$116$	−49.8634	+	86.3659i	−0.429856	+	0.744533i
$117$	75.9999	−	283.636i	0.649572	−	2.42424i
$118$	−75.4772	+	75.4772i	−0.639638	+	0.639638i
$119$	−42.9343	−	53.8178i	−0.360792	−	0.452250i
$120$		0			0
$121$	54.4545	+	94.3179i	0.450037	+	0.779487i
$122$	−140.576	+	37.6673i	−1.15226	+	0.308748i
$123$	8.27289	+	30.8749i	0.0672593	+	0.251015i
$124$	27.7128	−	16.0000i	0.223490	−	0.129032i
$125$		0			0
$126$	−146.681	+	117.018i	−1.16414	+	0.928714i
$127$	−24.9545	−	24.9545i	−0.196492	−	0.196492i	0.602002	−	0.798494i	$-0.294370\pi$
$127$	−24.9545	−	24.9545i	−0.196492	−	0.196492i	−0.798494	+	0.602002i	$0.794370\pi$
$128$	−10.9282	−	2.92820i	−0.0853766	−	0.0228766i
$129$	−62.4722	−	36.0683i	−0.484280	−	0.279599i
$130$		0			0
$131$	35.0455	+	60.7007i	0.267523	+	0.463364i	0.968222	−	0.250094i	$-0.0804614\pi$
$131$	35.0455	+	60.7007i	0.267523	+	0.463364i	−0.700698	+	0.713458i	$0.747128\pi$
$132$	−26.0000	−	26.0000i	−0.196970	−	0.196970i
$133$	−103.825	−	76.5968i	−0.780636	−	0.575916i
$134$			45.5683i			0.340062i
$135$		0			0
$136$	13.9089	−	24.0909i	0.102271	−	0.177139i
$137$	−9.25107	+	2.47882i	−0.0675261	+	0.0180936i	−0.292424	−	0.956289i	$-0.594462\pi$
$137$	−9.25107	+	2.47882i	−0.0675261	+	0.0180936i	0.224898	+	0.974382i	$0.427795\pi$
$138$	129.648	+	34.7391i	0.939478	+	0.251732i
$139$		−	53.0217i		−	0.381451i	−0.981643	−	0.190726i	$-0.938916\pi$
$139$		−	53.0217i		−	0.381451i	0.981643	−	0.190726i	$-0.0610841\pi$
$140$		0			0
$141$	111.137			0.788203
$142$	14.7657	−	55.1063i	0.103984	−	0.388072i
$143$	−13.9423	−	52.0334i	−0.0974987	−	0.363870i
$144$	−65.6601	−	37.9089i	−0.455973	−	0.263256i
$145$		0			0
$146$	125.545			0.859894
$147$	229.094	+	120.973i	1.55846	+	0.822946i
$148$	−50.0911	+	50.0911i	−0.338453	+	0.338453i
$149$	181.078	−	104.546i	1.21529	−	0.701648i	0.251383	−	0.967888i	$-0.419115\pi$
$149$	181.078	−	104.546i	1.21529	−	0.701648i	0.963907	+	0.266240i	$0.0857813\pi$
$150$		0			0
$151$	−81.0455	+	140.375i	−0.536725	+	0.929636i	0.462352	+	0.886696i	$0.347006\pi$
$151$	−81.0455	+	140.375i	−0.536725	+	0.929636i	−0.999078	+	0.0429394i	$0.986328\pi$
$152$	13.4929	−	50.3563i	0.0887692	−	0.331291i
$153$	131.818	−	131.818i	0.861554	−	0.861554i
$154$	−12.5702	+	32.0455i	−0.0816248	+	0.208088i
$155$		0			0
$156$	−81.9089	−	141.870i	−0.525057	−	0.909426i
$157$	133.062	−	35.6538i	0.847526	−	0.227094i	0.191181	−	0.981555i	$-0.438768\pi$
$157$	133.062	−	35.6538i	0.847526	−	0.227094i	0.656345	+	0.754461i	$0.272102\pi$
$158$	37.0432	+	138.247i	0.234451	+	0.874982i
$159$	52.0987	−	30.0792i	0.327665	−	0.189177i
$160$		0			0
$161$	−18.7505	−	124.248i	−0.116463	−	0.771727i
$162$	−107.681	−	107.681i	−0.664699	−	0.664699i
$163$	91.8348	+	24.6071i	0.563404	+	0.150964i	0.529270	−	0.848454i	$-0.322466\pi$
$163$	91.8348	+	24.6071i	0.563404	+	0.150964i	0.0341341	+	0.999417i	$0.489133\pi$
$164$	10.4712	+	6.04555i	0.0638488	+	0.0368631i
$165$		0			0
$166$	51.1247	+	88.5506i	0.307980	+	0.533438i
$167$	−133.988	−	133.988i	−0.802324	−	0.802324i	0.181134	−	0.983458i	$-0.442023\pi$
$167$	−133.988	−	133.988i	−0.802324	−	0.802324i	−0.983458	+	0.181134i	$0.942023\pi$
$168$	−11.7016	+	104.025i	−0.0696526	+	0.619197i
$169$		−	71.0000i		−	0.420118i
$170$		0			0
$171$	174.681	−	302.557i	1.02153	−	1.76934i
$172$	−26.3575	+	7.06247i	−0.153241	+	0.0410609i
$173$	−0.248884	−	0.0666881i	−0.00143863	−	0.000385481i	0.258100	−	0.966118i	$-0.416904\pi$
$173$	−0.248884	−	0.0666881i	−0.00143863	−	0.000385481i	−0.259538	+	0.965733i	$0.583570\pi$
$174$			372.840i			2.14276i
$175$		0			0
$176$	−13.9089			−0.0790279
$177$	−103.285	+	385.465i	−0.583532	+	2.17777i
$178$	−30.2801	−	113.007i	−0.170113	−	0.634870i
$179$	37.7895	+	21.8178i	0.211115	+	0.121887i	0.601829	−	0.798625i	$-0.294439\pi$
$179$	37.7895	+	21.8178i	0.211115	+	0.121887i	−0.390715	+	0.920512i	$0.627772\pi$
$180$		0			0
$181$	3.68116			0.0203379			0.0101689	−	0.999948i	$-0.496763\pi$
$181$	3.68116			0.0203379			0.0101689	+	0.999948i	$0.496763\pi$
$182$	−91.0472	+	123.412i	−0.500259	+	0.678085i
$183$	−384.737	+	384.737i	−2.10239	+	2.10239i
$184$	43.9701	−	25.3861i	0.238968	−	0.137968i
$185$		0			0
$186$	59.8178	−	103.607i	0.321601	−	0.557029i
$187$	8.85130	−	33.0335i	0.0473331	−	0.176650i
$188$	29.7267	−	29.7267i	0.158121	−	0.158121i
$189$	−134.536	+	342.975i	−0.711829	+	1.81468i
$190$		0			0
$191$	−8.96636	−	15.5302i	−0.0469443	−	0.0813099i	0.841598	−	0.540104i	$-0.181615\pi$
$191$	−8.96636	−	15.5302i	−0.0469443	−	0.0813099i	−0.888543	+	0.458794i	$0.848282\pi$
$192$	−40.8563	+	10.9474i	−0.212793	+	0.0570178i
$193$	−55.0364	−	205.399i	−0.285163	−	1.06424i	−0.948720	−	0.316117i	$-0.897621\pi$
$193$	−55.0364	−	205.399i	−0.285163	−	1.06424i	0.663557	−	0.748125i	$-0.269046\pi$
$194$	−79.2799	+	45.7723i	−0.408659	+	0.235939i
$195$		0			0
$196$	93.6356	−	28.9201i	0.477733	−	0.147552i
$197$	−41.0911	−	41.0911i	−0.208584	−	0.208584i	0.595081	−	0.803666i	$-0.297120\pi$
$197$	−41.0911	−	41.0911i	−0.208584	−	0.208584i	−0.803666	+	0.595081i	$0.797120\pi$
$198$	−90.0332	−	24.1243i	−0.454713	−	0.121840i
$199$	−261.145	−	150.772i	−1.31229	−	0.757650i	−0.329813	−	0.944046i	$-0.606986\pi$
$199$	−261.145	−	150.772i	−1.31229	−	0.757650i	−0.982475	+	0.186397i	$0.940319\pi$
$200$		0			0
$201$	85.1812	+	147.538i	0.423787	+	0.734020i
$202$	143.499	+	143.499i	0.710391	+	0.710391i
$203$	319.895	−	139.638i	1.57584	−	0.687872i
$204$		−	104.000i		−	0.509804i
$205$		0			0
$206$	39.7386	−	68.8293i	0.192906	−	0.334123i
$207$	328.652	−	88.0621i	1.58769	−	0.425421i
$208$	−59.8562	−	16.0384i	−0.287770	−	0.0771078i
$209$		−	64.0911i		−	0.306656i
$210$		0			0
$211$	−177.703			−0.842194			−0.421097	−	0.907016i	$-0.638355\pi$
$211$	−177.703			−0.842194			−0.421097	+	0.907016i	$0.638355\pi$
$212$	5.88975	−	21.9808i	0.0277818	−	0.103683i
$213$	−55.2031	−	206.021i	−0.259170	−	0.967235i
$214$	−73.4732	−	42.4198i	−0.343333	−	0.198223i
$215$		0			0
$216$	−148.863			−0.689182
$217$	−111.298	−	12.5198i	−0.512894	−	0.0576947i
$218$	37.2733	−	37.2733i	0.170978	−	0.170978i
$219$	406.480	−	234.681i	1.85607	−	1.07160i
$220$		0			0
$221$	76.1822	−	131.951i	0.344716	−	0.597065i
$222$	−68.5460	+	255.817i	−0.308766	+	1.15233i
$223$	−249.113	+	249.113i	−1.11710	+	1.11710i	−0.124933	+	0.992165i	$0.539871\pi$
$223$	−249.113	+	249.113i	−1.11710	+	1.11710i	−0.992165	+	0.124933i	$0.960129\pi$
$224$	24.6946	+	30.9545i	0.110244	+	0.138190i
$225$		0			0
$226$	−118.636	−	205.483i	−0.524936	−	0.909216i
$227$	−40.0503	+	10.7314i	−0.176433	+	0.0472751i	−0.345954	−	0.938252i	$-0.612445\pi$
$227$	−40.0503	+	10.7314i	−0.176433	+	0.0472751i	0.169521	+	0.985527i	$0.445778\pi$
$228$	−50.4448	−	188.263i	−0.221249	−	0.825713i
$229$	−272.875	+	157.545i	−1.19159	+	0.687967i	−0.958668	−	0.284527i	$-0.908163\pi$
$229$	−272.875	+	157.545i	−1.19159	+	0.687967i	−0.232926	+	0.972494i	$0.574830\pi$
$230$		0			0
$231$	19.2039	+	127.253i	0.0831339	+	0.550877i
$232$	99.7267	+	99.7267i	0.429856	+	0.429856i
$233$	111.143	+	29.7807i	0.477009	+	0.127814i	0.489309	−	0.872110i	$-0.337249\pi$
$233$	111.143	+	29.7807i	0.477009	+	0.127814i	−0.0123008	+	0.999924i	$0.503916\pi$
$234$	−359.635	−	207.636i	−1.53690	−	0.887332i
$235$		0			0
$236$	75.4772	+	130.730i	0.319819	+	0.553942i
$237$	378.362	+	378.362i	1.59647	+	1.59647i
$238$	−89.2315	+	38.9507i	−0.374922	+	0.163658i
$239$			438.725i			1.83567i	0.396965	+	0.917834i	$0.370064\pi$
$239$			438.725i			1.83567i	−0.396965	+	0.917834i	$0.629936\pi$
$240$		0			0
$241$	78.0911	−	135.258i	0.324029	−	0.561235i	−0.657286	−	0.753641i	$-0.728296\pi$
$241$	78.0911	−	135.258i	0.324029	−	0.561235i	0.981315	+	0.192406i	$0.0616290\pi$
$242$	148.772	−	39.8634i	0.614762	−	0.164725i
$243$	−92.3920	−	24.7564i	−0.380214	−	0.101878i
$244$			205.818i			0.843516i
$245$		0			0
$246$	45.2039			0.183756
$247$	73.9038	−	275.813i	0.299206	−	1.11665i
$248$	−11.7128	−	43.7128i	−0.0472291	−	0.176261i
$249$	331.057	+	191.136i	1.32954	+	0.767613i
$250$		0			0
$251$	185.727			0.739947			0.369974	−	0.929042i	$-0.379367\pi$
$251$	185.727			0.739947			0.369974	+	0.929042i	$0.379367\pi$
$252$	106.161	+	243.202i	0.421272	+	0.965086i
$253$	44.1366	−	44.1366i	0.174453	−	0.174453i
$254$	−43.2224	+	24.9545i	−0.170167	+	0.0982459i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−61.7416	+	230.423i	−0.240240	+	0.896587i	0.735477	+	0.677550i	$0.236958\pi$
$257$	−61.7416	+	230.423i	−0.240240	+	0.896587i	−0.975717	+	0.219037i	$0.929709\pi$
$258$	−72.1366	+	72.1366i	−0.279599	+	0.279599i
$259$	245.162	−	36.9979i	0.946573	−	0.142849i
$260$		0			0
$261$	472.566	+	818.509i	1.81060	+	3.13605i
$262$	95.7462	−	25.6551i	0.365444	−	0.0979203i
$263$	85.0136	+	317.275i	0.323246	+	1.20637i	0.916064	+	0.401032i	$0.131349\pi$
$263$	85.0136	+	317.275i	0.323246	+	1.20637i	−0.592818	+	0.805336i	$0.701985\pi$
$264$	−45.0333	+	26.0000i	−0.170581	+	0.0984848i
$265$		0			0
$266$	−142.636	+	113.791i	−0.536224	+	0.427784i
$267$	−309.283	−	309.283i	−1.15836	−	1.15836i
$268$	62.2475	+	16.6792i	0.232267	+	0.0622357i
$269$	247.839	+	143.090i	0.921336	+	0.531933i	0.884061	−	0.467372i	$-0.154799\pi$
$269$	247.839	+	143.090i	0.921336	+	0.531933i	0.0372746	+	0.999305i	$0.488132\pi$
$270$		0			0
$271$	−204.760	−	354.655i	−0.755573	−	1.30869i	−0.945089	−	0.326814i	$-0.894025\pi$
$271$	−204.760	−	354.655i	−0.755573	−	1.30869i	0.189516	−	0.981878i	$-0.439308\pi$
$272$	−27.8178	−	27.8178i	−0.102271	−	0.102271i
$273$	−64.0925	+	569.769i	−0.234771	+	2.08707i
$274$			13.5445i			0.0494325i
$275$		0			0
$276$	94.9089	−	164.387i	0.343873	−	0.595605i
$277$	−15.7107	+	4.20967i	−0.0567174	+	0.0151974i	−0.287066	−	0.957911i	$-0.592680\pi$
$277$	−15.7107	+	4.20967i	−0.0567174	+	0.0151974i	0.230349	+	0.973108i	$0.426013\pi$
$278$	−72.4290	−	19.4073i	−0.260536	−	0.0698104i
$279$		−	303.271i		−	1.08699i
$280$		0			0
$281$	302.542			1.07666			0.538332	−	0.842733i	$-0.319055\pi$
$281$	302.542			1.07666			0.538332	+	0.842733i	$0.319055\pi$
$282$	40.6788	−	151.815i	0.144251	−	0.538353i
$283$	−41.0108	−	153.054i	−0.144914	−	0.540828i	−0.999759	−	0.0219440i	$-0.993014\pi$
$283$	−41.0108	−	153.054i	−0.144914	−	0.540828i	0.854845	−	0.518884i	$-0.173652\pi$
$284$	−69.8719	−	40.3406i	−0.246028	−	0.142044i
$285$		0			0
$286$	−76.1822			−0.266371
$287$	−16.9300	−	38.7848i	−0.0589897	−	0.135139i
$288$	−75.8178	+	75.8178i	−0.263256	+	0.263256i
$289$	−166.512	+	96.1356i	−0.576165	+	0.332649i
$290$		0			0
$291$	−171.125	+	296.397i	−0.588058	+	1.01855i
$292$	45.9525	−	171.497i	0.157372	−	0.587318i
$293$	100.182	−	100.182i	0.341919	−	0.341919i	−0.515170	−	0.857088i	$-0.672271\pi$
$293$	100.182	−	100.182i	0.341919	−	0.341919i	0.857088	+	0.515170i	$0.172271\pi$
$294$	249.107	−	268.669i	0.847301	−	0.913841i
$295$		0			0
$296$	50.0911	+	86.7603i	0.169227	+	0.293109i
$297$	−176.774	+	47.3666i	−0.595200	+	0.159483i
$298$	−76.5327	−	285.624i	−0.256821	−	0.958469i
$299$	240.834	−	139.046i	0.805465	−	0.465035i
$300$		0			0
$301$	88.9099	+	34.8759i	0.295382	+	0.115867i
$302$	162.091	+	162.091i	0.536725	+	0.536725i
$303$	732.855	+	196.368i	2.41866	+	0.648079i
$304$	−63.8492	−	36.8634i	−0.210030	−	0.121261i
$305$		0			0
$306$	−131.818	−	228.315i	−0.430777	−	0.746128i
$307$	242.602	+	242.602i	0.790234	+	0.790234i	0.981532	−	0.191298i	$-0.0612696\pi$
$307$	242.602	+	242.602i	0.790234	+	0.790234i	−0.191298	+	0.981532i	$0.561270\pi$
$308$	39.1740	+	28.9007i	0.127188	+	0.0938335i
$309$		−	297.135i		−	0.961601i
$310$		0			0
$311$	−3.73861	+	6.47547i	−0.0120213	+	0.0208214i	−0.871973	−	0.489553i	$-0.837160\pi$
$311$	−3.73861	+	6.47547i	−0.0120213	+	0.0208214i	0.859952	+	0.510375i	$0.170493\pi$
$312$	−223.779	+	59.9615i	−0.717241	+	0.192184i
$313$	−577.950	−	154.861i	−1.84649	−	0.494765i	−0.847156	−	0.531344i	$-0.821687\pi$
$313$	−577.950	−	154.861i	−1.84649	−	0.494765i	−0.999331	+	0.0365796i	$0.988354\pi$
$314$		−	194.816i		−	0.620432i
$315$		0			0
$316$	202.408			0.640531
$317$	105.415	−	393.415i	0.332540	−	1.24106i	−0.573971	−	0.818876i	$-0.694598\pi$
$317$	105.415	−	393.415i	0.332540	−	1.24106i	0.906511	−	0.422182i	$-0.138736\pi$
$318$	−22.0195	−	82.1779i	−0.0692437	−	0.258421i
$319$	150.157	+	86.6931i	0.470711	+	0.271765i
$320$		0			0
$321$	−317.182			−0.988107
$322$	−176.589	−	19.8643i	−0.548414	−	0.0616902i
$323$	128.182	−	128.182i	0.396849	−	0.396849i
$324$	−186.509	+	107.681i	−0.575646	+	0.332349i
$325$		0			0
$326$	67.2277	−	116.442i	0.206220	−	0.357184i
$327$	51.0058	−	190.356i	0.155981	−	0.582129i
$328$	12.0911	−	12.0911i	0.0368631	−	0.0368631i
$329$	−145.492	+	21.9565i	−0.442226	+	0.0667372i
$330$		0			0
$331$	−118.317	−	204.931i	−0.357452	−	0.619126i	0.630082	−	0.776529i	$-0.283021\pi$
$331$	−118.317	−	204.931i	−0.357452	−	0.619126i	−0.987534	+	0.157403i	$0.949688\pi$
$332$	139.675	−	37.4259i	0.420709	−	0.112729i
$333$	173.761	+	648.486i	0.521806	+	1.94741i
$334$	−232.074	+	133.988i	−0.694833	+	0.401162i
$335$		0			0
$336$	137.818	+	54.0605i	0.410172	+	0.160894i
$337$	−316.271	−	316.271i	−0.938490	−	0.938490i	0.0597246	−	0.998215i	$-0.480978\pi$
$337$	−316.271	−	316.271i	−0.938490	−	0.938490i	−0.998215	+	0.0597246i	$0.980978\pi$
$338$	−96.9878	−	25.9878i	−0.286946	−	0.0768870i
$339$	−768.221	−	443.533i	−2.26614	−	1.30836i
$340$		0			0
$341$	−27.8178	−	48.1819i	−0.0815771	−	0.141296i
$342$	−349.362	−	349.362i	−1.02153	−	1.02153i
$343$	−323.814	−	113.109i	−0.944064	−	0.329763i
$344$			38.5901i			0.112180i
$345$		0			0
$346$	−0.182195	+	0.315572i	−0.000526576	+	0.000912057i
$347$	−137.052	+	36.7228i	−0.394961	+	0.105830i	−0.450833	−	0.892608i	$-0.648873\pi$
$347$	−137.052	+	36.7228i	−0.394961	+	0.105830i	0.0558716	+	0.998438i	$0.482206\pi$
$348$	509.308	+	136.469i	1.46353	+	0.392152i
$349$			298.861i			0.856336i	0.903699	+	0.428168i	$0.140841\pi$
$349$			298.861i			0.856336i	−0.903699	+	0.428168i	$0.859159\pi$
$350$		0			0
$351$	−815.358			−2.32296
$352$	−5.09101	+	18.9999i	−0.0144631	+	0.0539770i
$353$	8.91723	+	33.2795i	0.0252613	+	0.0942763i	0.977406	−	0.211373i	$-0.0677933\pi$
$353$	8.91723	+	33.2795i	0.0252613	+	0.0942763i	−0.952144	+	0.305649i	$0.901127\pi$
$354$	488.750	+	282.180i	1.38065	+	0.797119i
$355$		0			0
$356$	−165.453			−0.464757
$357$	−216.097	+	292.913i	−0.605314	+	0.820484i
$358$	43.6356	−	43.6356i	0.121887	−	0.121887i
$359$	426.160	−	246.043i	1.18707	−	0.685358i	0.229434	−	0.973324i	$-0.426312\pi$
$359$	426.160	−	246.043i	1.18707	−	0.685358i	0.957641	+	0.287966i	$0.0929791\pi$
$360$		0			0
$361$	−10.6366	+	18.4232i	−0.0294644	+	0.0510338i
$362$	1.34740	−	5.02856i	0.00372209	−	0.0138910i
$363$	407.168	−	407.168i	1.12168	−	1.12168i
$364$	135.258	+	169.545i	0.371587	+	0.465782i
$365$		0			0
$366$	384.737	+	666.383i	1.05119	+	1.82072i
$367$	−70.3355	+	18.8463i	−0.191650	+	0.0513524i	−0.353367	−	0.935485i	$-0.614963\pi$
$367$	−70.3355	+	18.8463i	−0.191650	+	0.0513524i	0.161717	+	0.986837i	$0.448297\pi$
$368$	−18.5839	−	69.3562i	−0.0504998	−	0.188468i
$369$	99.2379	−	57.2950i	0.268937	−	0.155271i
$370$		0			0
$371$	−62.2614	+	49.6703i	−0.167820	+	0.133882i
$372$	−119.636	−	119.636i	−0.321601	−	0.321601i
$373$	−332.315	−	89.0434i	−0.890924	−	0.238722i	−0.215810	−	0.976435i	$-0.569239\pi$
$373$	−332.315	−	89.0434i	−0.890924	−	0.238722i	−0.675114	+	0.737713i	$0.735906\pi$
$374$	−41.8848	−	24.1822i	−0.111991	−	0.0646583i
$375$		0			0
$376$	−29.7267	−	51.4882i	−0.0790604	−	0.136937i
$377$	546.226	+	546.226i	1.44887	+	1.44887i
$378$	419.269	+	309.317i	1.10918	+	0.818299i
$379$		−	33.5683i		−	0.0885708i	−0.999019	−	0.0442854i	$-0.985899\pi$
$379$		−	33.5683i		−	0.0885708i	0.999019	−	0.0442854i	$-0.0141011\pi$
$380$		0			0
$381$	−93.2950	+	161.592i	−0.244869	+	0.424125i
$382$	−24.4965	+	6.56383i	−0.0641271	+	0.0171828i
$383$	−694.888	−	186.195i	−1.81433	−	0.486148i	−0.818269	−	0.574836i	$-0.805066\pi$
$383$	−694.888	−	186.195i	−1.81433	−	0.486148i	−0.996059	+	0.0886883i	$0.971733\pi$
$384$			59.8178i			0.155776i
$385$		0			0
$386$	−300.725			−0.779079
$387$	−66.9326	+	249.796i	−0.172953	+	0.645468i
$388$	33.5076	+	125.052i	0.0863598	+	0.322299i
$389$	−459.937	−	265.545i	−1.18236	−	0.682634i	−0.225798	−	0.974174i	$-0.572499\pi$
$389$	−459.937	−	265.545i	−1.18236	−	0.682634i	−0.956558	+	0.291540i	$0.905832\pi$
$390$		0			0
$391$	176.547			0.451526
$392$	−5.23259	−	138.494i	−0.0133484	−	0.353301i
$393$	262.043	−	262.043i	0.666777	−	0.666777i
$394$	−71.1719	+	41.0911i	−0.180639	+	0.104292i
$395$		0			0
$396$	−65.9089	+	114.158i	−0.166437	+	0.288277i
$397$	−69.5948	+	259.731i	−0.175302	+	0.654235i	0.821198	+	0.570643i	$0.193306\pi$
$397$	−69.5948	+	259.731i	−0.175302	+	0.654235i	−0.996500	+	0.0835924i	$0.973361\pi$
$398$	−301.545	+	301.545i	−0.757650	+	0.757650i
$399$	−249.107	+	635.053i	−0.624327	+	1.59161i
$400$		0			0
$401$	−276.270	−	478.514i	−0.688953	−	1.19330i	−0.972177	−	0.234248i	$-0.924737\pi$
$401$	−276.270	−	478.514i	−0.688953	−	1.19330i	0.283224	−	0.959054i	$-0.408596\pi$
$402$	232.719	−	62.3569i	0.578904	−	0.155117i
$403$	−64.1537	−	239.425i	−0.159190	−	0.594107i
$404$	248.547	−	143.499i	0.615217	−	0.355195i
$405$		0			0
$406$	−73.6594	−	488.095i	−0.181427	−	1.20221i
$407$	87.0890	+	87.0890i	0.213978	+	0.213978i
$408$	−142.067	−	38.0666i	−0.348203	−	0.0933006i
$409$	−108.528	−	62.6584i	−0.265348	−	0.153199i	0.361423	−	0.932402i	$-0.382291\pi$
$409$	−108.528	−	62.6584i	−0.265348	−	0.153199i	−0.626772	+	0.779203i	$0.715624\pi$
$410$		0			0
$411$	25.3188	+	43.8535i	0.0616030	+	0.106700i
$412$	−79.4772	−	79.4772i	−0.192906	−	0.192906i
$413$	59.0598	−	525.029i	0.143002	−	1.27126i
$414$		−	481.180i		−	1.16227i
$415$		0			0
$416$	−43.8178	+	75.8947i	−0.105331	+	0.182439i
$417$	−270.784	+	72.5564i	−0.649362	+	0.173996i
$418$	−87.5501	−	23.4590i	−0.209450	−	0.0561219i
$419$			116.269i			0.277492i	0.990328	+	0.138746i	$0.0443072\pi$
$419$			116.269i			0.277492i	−0.990328	+	0.138746i	$0.955693\pi$
$420$		0			0
$421$	534.449			1.26948			0.634738	−	0.772728i	$-0.281108\pi$
$421$	534.449			1.26948			0.634738	+	0.772728i	$0.281108\pi$
$422$	−65.0438	+	242.747i	−0.154132	+	0.575229i
$423$	−103.119	−	384.846i	−0.243780	−	0.909801i
$424$	−27.8706	−	16.0911i	−0.0657325	−	0.0379507i
$425$		0			0
$426$	−301.636			−0.708065
$427$	427.660	−	579.680i	1.00155	−	1.35756i
$428$	−84.8395	+	84.8395i	−0.198223	+	0.198223i
$429$	−246.658	+	142.408i	−0.574960	+	0.331953i
$430$		0			0
$431$	238.737	−	413.504i	0.553913	−	0.959406i	−0.444074	−	0.895990i	$-0.646467\pi$
$431$	238.737	−	413.504i	0.553913	−	0.959406i	0.997987	−	0.0634155i	$-0.0201994\pi$
$432$	−54.4878	+	203.351i	−0.126129	+	0.470720i
$433$	542.271	−	542.271i	1.25236	−	1.25236i	0.297699	−	0.954660i	$-0.403781\pi$
$433$	542.271	−	542.271i	1.25236	−	1.25236i	0.954660	−	0.297699i	$-0.0962190\pi$
$434$	−57.8402	+	147.453i	−0.133272	+	0.339754i
$435$		0			0
$436$	−37.2733	−	64.5592i	−0.0854892	−	0.148072i
$437$	319.588	−	85.6333i	0.731322	−	0.195957i
$438$	−171.799	−	641.161i	−0.392234	−	1.46384i
$439$	−232.568	+	134.273i	−0.529768	+	0.305862i	−0.740922	−	0.671591i	$-0.765611\pi$
$439$	−232.568	+	134.273i	−0.529768	+	0.305862i	0.211154	+	0.977453i	$0.432278\pi$
$440$		0			0
$441$	206.341	−	905.557i	0.467892	−	2.05342i
$442$	−152.364	−	152.364i	−0.344716	−	0.344716i
$443$	85.1751	+	22.8226i	0.192269	+	0.0515183i	0.353668	−	0.935371i	$-0.384934\pi$
$443$	85.1751	+	22.8226i	0.192269	+	0.0515183i	−0.161400	+	0.986889i	$0.551601\pi$
$444$	324.363	+	187.271i	0.730548	+	0.421782i
$445$		0			0
$446$	249.113	+	431.476i	0.558549	+	0.967435i
$447$	−781.711	−	781.711i	−1.74879	−	1.74879i
$448$	51.3234	−	22.4033i	0.114561	−	0.0500074i
$449$			100.410i			0.223630i	0.993729	+	0.111815i	$0.0356664\pi$
$449$			100.410i			0.223630i	−0.993729	+	0.111815i	$0.964334\pi$
$450$		0			0
$451$	10.5109	−	18.2054i	0.0233057	−	0.0403666i
$452$	−324.119	+	86.8473i	−0.717076	+	0.192140i
$453$	827.806	+	221.810i	1.82739	+	0.489647i
$454$			58.6377i			0.129158i
$455$		0			0
$456$	−275.636			−0.604464
$457$	180.050	−	671.954i	0.393982	−	1.47036i	−0.429526	−	0.903055i	$-0.641319\pi$
$457$	180.050	−	671.954i	0.393982	−	1.47036i	0.823508	−	0.567305i	$-0.192014\pi$
$458$	115.331	+	430.420i	0.251814	+	0.939781i
$459$	−448.282	−	258.816i	−0.976649	−	0.563869i
$460$		0			0
$461$	−191.636			−0.415695			−0.207848	−	0.978161i	$-0.566646\pi$
$461$	−191.636			−0.415695			−0.207848	+	0.978161i	$0.566646\pi$
$462$	180.859	+	20.3446i	0.391470	+	0.0440359i
$463$	−268.079	+	268.079i	−0.579005	+	0.579005i	−0.934629	−	0.355624i	$-0.884268\pi$
$463$	−268.079	+	268.079i	−0.579005	+	0.579005i	0.355624	+	0.934629i	$0.384268\pi$
$464$	172.732	−	99.7267i	0.372267	−	0.214928i
$465$		0			0
$466$	81.3623	−	140.924i	0.174597	−	0.302411i
$467$	−49.9577	+	186.445i	−0.106976	+	0.399239i	−0.998562	−	0.0536121i	$-0.982927\pi$
$467$	−49.9577	+	186.445i	−0.106976	+	0.399239i	0.891586	+	0.452851i	$0.149593\pi$
$468$	−415.271	+	415.271i	−0.887332	+	0.887332i
$469$	−140.661	−	176.318i	−0.299917	−	0.375944i
$470$		0			0
$471$	−364.170	−	630.761i	−0.773185	−	1.33920i
$472$	206.208	−	55.2532i	0.436881	−	0.117062i
$473$	12.2789	+	45.8255i	0.0259596	+	0.0968826i
$474$	655.343	−	378.362i	1.38258	−	0.798233i
$475$		0			0
$476$	20.5466	+	136.149i	0.0431651	+	0.286028i
$477$	−152.499	−	152.499i	−0.319704	−	0.319704i
$478$	599.309	+	160.584i	1.25378	+	0.335951i
$479$	642.196	+	370.772i	1.34070	+	0.774055i	0.986910	−	0.161269i	$-0.0515588\pi$
$479$	642.196	+	370.772i	1.34070	+	0.774055i	0.353792	+	0.935324i	$0.384892\pi$
$480$		0			0
$481$	274.360	+	475.206i	0.570396	+	0.987954i
$482$	−156.182	−	156.182i	−0.324029	−	0.324029i
$483$	−608.881	+	265.784i	−1.26062	+	0.550278i
$484$		−	217.818i		−	0.450037i
$485$		0			0
$486$	−67.6356	+	117.148i	−0.139168	+	0.241046i
$487$	−761.430	+	204.025i	−1.56351	+	0.418942i	−0.933773	−	0.357865i	$-0.883505\pi$
$487$	−761.430	+	204.025i	−1.56351	+	0.418942i	−0.629739	+	0.776807i	$0.716838\pi$
$488$	281.152	+	75.3345i	0.576132	+	0.154374i
$489$		−	502.677i		−	1.02797i
$490$		0			0
$491$	−232.000			−0.472505			−0.236253	−	0.971692i	$-0.575919\pi$
$491$	−232.000			−0.472505			−0.236253	+	0.971692i	$0.575919\pi$
$492$	16.5458	−	61.7497i	0.0336296	−	0.125508i
$493$	126.927	+	473.700i	0.257459	+	0.960851i
$494$	−349.716	−	201.909i	−0.707928	−	0.408722i
$495$		0			0
$496$	−64.0000			−0.129032
$497$	112.970	+	258.802i	0.227304	+	0.520728i
$498$	382.271	−	382.271i	0.767613	−	0.767613i
$499$	570.335	−	329.283i	1.14296	−	0.659886i	0.195795	−	0.980645i	$-0.437271\pi$
$499$	570.335	−	329.283i	1.14296	−	0.659886i	0.947161	+	0.320759i	$0.103938\pi$
$500$		0			0
$501$	−500.930	+	867.636i	−0.999859	+	1.73181i
$502$	67.9807	−	253.707i	0.135420	−	0.505393i
$503$	−230.055	+	230.055i	−0.457367	+	0.457367i	−0.897790	−	0.440424i	$-0.854828\pi$
$503$	−230.055	+	230.055i	−0.457367	+	0.457367i	0.440424	+	0.897790i	$0.354828\pi$
$504$	371.077	−	56.0000i	0.736264	−	0.111111i
$505$		0			0
$506$	−44.1366	−	76.4469i	−0.0872266	−	0.151081i
$507$	−362.600	+	97.1583i	−0.715187	+	0.191634i
$508$	18.2679	+	68.1768i	0.0359605	+	0.134206i
$509$	−105.300	+	60.7950i	−0.206876	+	0.119440i	−0.599859	−	0.800106i	$-0.704777\pi$
$509$	−105.300	+	60.7950i	−0.206876	+	0.119440i	0.392983	+	0.919546i	$0.371443\pi$
$510$		0			0
$511$	−485.770	+	387.534i	−0.950627	+	0.758383i
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−937.026	−	251.075i	−1.82656	−	0.489425i
$514$	292.164	+	168.681i	0.568413	+	0.328173i
$515$		0			0
$516$	72.1366	+	124.944i	0.139800	+	0.242140i
$517$	−51.6832	−	51.6832i	−0.0999676	−	0.0999676i
$518$	39.1955	−	348.440i	0.0756670	−	0.672664i
$519$			1.36232i			0.00262489i
$520$		0			0
$521$	244.135	−	422.853i	0.468588	−	0.811619i	−0.530767	−	0.847518i	$-0.678096\pi$
$521$	244.135	−	422.853i	0.468588	−	0.811619i	0.999355	+	0.0358988i	$0.0114294\pi$
$522$	1291.08	−	345.943i	2.47332	−	0.662725i
$523$	631.039	+	169.086i	1.20657	+	0.323301i	0.805417	−	0.592708i	$-0.201941\pi$
$523$	631.039	+	169.086i	1.20657	+	0.323301i	0.401158	+	0.916009i	$0.368608\pi$
$524$		−	140.182i		−	0.267523i
$525$		0			0
$526$	464.523			0.883123
$527$	40.7281	−	151.999i	0.0772829	−	0.288424i
$528$	19.0333	+	71.0333i	0.0360480	+	0.134533i
$529$	−179.070	−	103.386i	−0.338507	−	0.195437i
$530$		0			0
$531$	1430.63			2.69422
$532$	103.233	+	236.494i	0.194046	+	0.444538i
$533$	66.2257	−	66.2257i	0.124251	−	0.124251i
$534$	−535.694	+	309.283i	−1.00317	+	0.579182i
$535$		0			0
$536$	45.5683	−	78.9267i	0.0850155	−	0.147251i
$537$	59.7122	−	222.849i	0.111196	−	0.414988i
$538$	286.180	−	286.180i	0.531933	−	0.531933i
$539$	−50.2809	−	162.796i	−0.0932855	−	0.302034i
$540$		0			0
$541$	−221.793	−	384.157i	−0.409968	−	0.710086i	0.584917	−	0.811093i	$-0.301127\pi$
$541$	−221.793	−	384.157i	−0.409968	−	0.710086i	−0.994886	+	0.101007i	$0.967794\pi$
$542$	−559.416	+	149.895i	−1.03213	+	0.276559i
$543$	−5.03740	−	18.7998i	−0.00927697	−	0.0346221i
$544$	−48.1819	+	27.8178i	−0.0885696	+	0.0511357i
$545$		0			0
$546$	754.859	+	296.102i	1.38253	+	0.542311i
$547$	686.507	+	686.507i	1.25504	+	1.25504i	0.953432	+	0.301608i	$0.0975232\pi$
$547$	686.507	+	686.507i	1.25504	+	1.25504i	0.301608	+	0.953432i	$0.402477\pi$
$548$	18.5021	+	4.95764i	0.0337630	+	0.00904678i
$549$	1689.25	+	975.291i	3.07696	+	1.77649i
$550$		0			0
$551$	459.533	+	795.934i	0.833997	+	1.44453i
$552$	−189.818	−	189.818i	−0.343873	−	0.343873i
$553$	−570.076	−	420.575i	−1.03088	−	0.760533i
$554$			23.0021i			0.0415200i
$555$		0			0
$556$	−53.0217	+	91.8363i	−0.0953628	+	0.165173i
$557$	44.0239	−	11.7962i	0.0790376	−	0.0211780i	−0.219084	−	0.975706i	$-0.570307\pi$
$557$	44.0239	−	11.7962i	0.0790376	−	0.0211780i	0.298121	+	0.954528i	$0.403640\pi$
$558$	−414.276	−	111.005i	−0.742430	−	0.198934i
$559$			211.366i			0.378115i
$560$		0			0
$561$	−180.816			−0.322310
$562$	110.738	−	413.281i	0.197043	−	0.735375i
$563$	185.429	+	692.031i	0.329359	+	1.22919i	0.909857	+	0.414923i	$0.136191\pi$
$563$	185.429	+	692.031i	0.329359	+	1.22919i	−0.580497	+	0.814262i	$0.697142\pi$
$564$	−192.494	−	111.137i	−0.341302	−	0.197051i
$565$		0			0
$566$	−224.087			−0.395913
$567$	749.044	+	84.2589i	1.32107	+	0.148605i
$568$	−80.6812	+	80.6812i	−0.142044	+	0.142044i
$569$	−724.073	+	418.043i	−1.27254	+	0.734699i	−0.975464	−	0.220157i	$-0.929343\pi$
$569$	−724.073	+	418.043i	−1.27254	+	0.734699i	−0.297071	+	0.954855i	$0.596010\pi$
$570$		0			0
$571$	−517.327	+	896.036i	−0.906001	+	1.56924i	−0.0864332	+	0.996258i	$0.527547\pi$
$571$	−517.327	+	896.036i	−0.906001	+	1.56924i	−0.819568	+	0.572982i	$0.805786\pi$
$572$	−27.8846	+	104.067i	−0.0487493	+	0.181935i
$573$	−67.0435	+	67.0435i	−0.117004	+	0.117004i
$574$	−59.1778	+	8.93064i	−0.103097	+	0.0155586i
$575$		0			0
$576$	75.8178	+	131.320i	0.131628	+	0.227987i
$577$	115.431	−	30.9295i	0.200053	−	0.0536040i	−0.157401	−	0.987535i	$-0.550312\pi$
$577$	115.431	−	30.9295i	0.200053	−	0.0536040i	0.357454	+	0.933931i	$0.383645\pi$
$578$	70.3762	+	262.647i	0.121758	+	0.454407i
$579$	−973.666	+	562.146i	−1.68163	+	0.970892i
$580$		0			0
$581$	−471.157	−	184.817i	−0.810942	−	0.318101i
$582$	342.249	+	342.249i	0.588058	+	0.588058i
$583$	−38.2162	−	10.2400i	−0.0655509	−	0.0175643i
$584$	−217.449	−	125.545i	−0.372345	−	0.214973i
$585$		0			0
$586$	−100.182	−	173.521i	−0.170959	−	0.296110i
$587$	808.313	+	808.313i	1.37702	+	1.37702i	0.849607	+	0.527416i	$0.176839\pi$
$587$	808.313	+	808.313i	1.37702	+	1.37702i	0.527416	+	0.849607i	$0.323161\pi$
$588$	−275.830	−	438.626i	−0.469098	−	0.745962i
$589$		−	294.907i		−	0.500691i
$590$		0			0
$591$	−153.624	+	266.084i	−0.259939	+	0.450227i
$592$	136.851	−	36.6692i	0.231168	−	0.0619413i
$593$	−86.3085	−	23.1263i	−0.145546	−	0.0389988i	0.185311	−	0.982680i	$-0.440671\pi$
$593$	−86.3085	−	23.1263i	−0.145546	−	0.0389988i	−0.330856	+	0.943681i	$0.607338\pi$
$594$			258.816i			0.435717i
$595$		0			0
$596$	−418.182			−0.701648
$597$	−412.642	+	1540.00i	−0.691192	+	2.57956i
$598$	−101.788	−	379.880i	−0.170215	−	0.635250i
$599$	337.198	+	194.681i	0.562934	+	0.325010i	0.754322	−	0.656504i	$-0.227966\pi$
$599$	337.198	+	194.681i	0.562934	+	0.325010i	−0.191388	+	0.981514i	$0.561299\pi$
$600$		0			0
$601$	478.638			0.796402			0.398201	−	0.917298i	$-0.369635\pi$
$601$	478.638			0.796402			0.398201	+	0.917298i	$0.369635\pi$
$602$	80.1847	−	108.688i	0.133197	−	0.180544i
$603$	431.861	−	431.861i	0.716188	−	0.716188i
$604$	280.750	−	162.091i	0.464818	−	0.268363i
$605$		0			0
$606$	536.487	−	929.223i	0.885292	−	1.53337i
$607$	−165.729	+	618.509i	−0.273030	+	1.01896i	0.684121	+	0.729369i	$0.260186\pi$
$607$	−165.729	+	618.509i	−0.273030	+	1.01896i	−0.957150	+	0.289592i	$0.906481\pi$
$608$	−73.7267	+	73.7267i	−0.121261	+	0.121261i
$609$	−1150.89	−	1442.63i	−1.88980	−	2.36885i
$610$		0			0
$611$	−162.820	−	282.012i	−0.266481	−	0.461559i
$612$	−360.133	+	96.4973i	−0.588453	+	0.157675i
$613$	295.398	+	1102.44i	0.481889	+	1.79843i	0.593681	+	0.804701i	$0.297674\pi$
$613$	295.398	+	1102.44i	0.481889	+	1.79843i	−0.111792	+	0.993732i	$0.535659\pi$
$614$	420.199	−	242.602i	0.684363	−	0.395117i
$615$		0			0
$616$	53.8178	−	42.9343i	0.0873666	−	0.0696985i
$617$	−15.0890	−	15.0890i	−0.0244555	−	0.0244555i	0.694773	−	0.719229i	$-0.255505\pi$
$617$	−15.0890	−	15.0890i	−0.0244555	−	0.0244555i	−0.719229	+	0.694773i	$0.755505\pi$
$618$	−405.893	−	108.759i	−0.656785	−	0.175985i
$619$	−124.687	−	71.9881i	−0.201433	−	0.116297i	0.395891	−	0.918298i	$-0.370436\pi$
$619$	−124.687	−	71.9881i	−0.201433	−	0.116297i	−0.597324	+	0.802000i	$0.703769\pi$
$620$		0			0
$621$	−472.383	−	818.191i	−0.760681	−	1.31754i
$622$	7.47723	+	7.47723i	0.0120213	+	0.0120213i
$623$	465.995	+	343.789i	0.747985	+	0.551828i
$624$			327.636i			0.525057i
$625$		0			0
$626$	−423.089	+	732.812i	−0.675861	+	1.17063i
$627$	−327.316	+	87.7040i	−0.522035	+	0.139879i
$628$	−266.123	−	71.3075i	−0.423763	−	0.113547i
$629$			348.356i			0.553825i
$630$		0			0
$631$	395.200			0.626307			0.313154	−	0.949703i	$-0.398615\pi$
$631$	395.200			0.626307			0.313154	+	0.949703i	$0.398615\pi$
$632$	74.0864	−	276.494i	0.117225	−	0.437491i
$633$	243.173	+	907.536i	0.384160	+	1.43371i
$634$	−498.831	−	288.000i	−0.786799	−	0.454259i
$635$		0			0
$636$	−120.317			−0.189177
$637$	−28.6601	−	758.564i	−0.0449923	−	1.19084i
$638$	173.386	−	173.386i	0.271765	−	0.271765i
$639$	−662.192	+	382.317i	−1.03629	+	0.598305i
$640$		0			0
$641$	50.3416	−	87.1942i	0.0785361	−	0.136028i	−0.824082	−	0.566470i	$-0.808309\pi$
$641$	50.3416	−	87.1942i	0.0785361	−	0.136028i	0.902619	+	0.430441i	$0.141642\pi$
$642$	−116.097	+	433.279i	−0.180836	+	0.674889i
$643$	−301.770	+	301.770i	−0.469316	+	0.469316i	−0.901693	−	0.432377i	$-0.857675\pi$
$643$	−301.770	+	301.770i	−0.469316	+	0.469316i	0.432377	+	0.901693i	$0.357675\pi$
$644$	−91.7712	+	233.954i	−0.142502	+	0.363283i
$645$		0			0
$646$	−128.182	−	222.018i	−0.198424	−	0.343681i
$647$	−517.894	+	138.769i	−0.800454	+	0.214481i	−0.635784	−	0.771867i	$-0.719323\pi$
$647$	−517.894	+	138.769i	−0.800454	+	0.214481i	−0.164671	+	0.986349i	$0.552656\pi$
$648$	78.8281	+	294.190i	0.121648	+	0.453998i
$649$	227.290	−	131.226i	0.350215	−	0.202197i
$650$		0			0
$651$	88.3644	+	585.536i	0.135736	+	0.899441i
$652$	−134.455	−	134.455i	−0.206220	−	0.206220i
$653$	−938.581	−	251.492i	−1.43734	−	0.385133i	−0.545737	−	0.837957i	$-0.683750\pi$
$653$	−938.581	−	251.492i	−1.43734	−	0.385133i	−0.891600	+	0.452823i	$0.850417\pi$
$654$	−241.362	−	139.350i	−0.369055	−	0.213074i
$655$		0			0
$656$	−12.0911	−	20.9424i	−0.0184316	−	0.0319244i
$657$	−1189.81	−	1189.81i	−1.81098	−	1.81098i
$658$	−23.2607	+	206.783i	−0.0353506	+	0.314260i
$659$			735.842i			1.11660i	0.829638	+	0.558302i	$0.188547\pi$
$659$			735.842i			1.11660i	−0.829638	+	0.558302i	$0.811453\pi$
$660$		0			0
$661$	−23.0901	+	39.9932i	−0.0349320	+	0.0605040i	−0.882963	−	0.469443i	$-0.844455\pi$
$661$	−23.0901	+	39.9932i	−0.0349320	+	0.0605040i	0.848031	+	0.529947i	$0.177788\pi$
$662$	−323.247	+	86.6139i	−0.488289	+	0.130837i
$663$	−778.131	−	208.500i	−1.17365	−	0.314479i
$664$		−	204.499i		−	0.307980i
$665$		0			0
$666$	949.449			1.42560
$667$	−231.664	+	864.583i	−0.347323	+	1.29623i
$668$	98.0861	+	366.062i	0.146835	+	0.547997i
$669$	1613.12	+	931.336i	2.41124	+	1.39213i
$670$		0			0
$671$	357.837			0.533290
$672$	124.293	−	168.475i	0.184960	−	0.250707i
$673$	122.772	−	122.772i	0.182425	−	0.182425i	−0.609986	−	0.792412i	$-0.708825\pi$
$673$	122.772	−	122.772i	0.182425	−	0.182425i	0.792412	+	0.609986i	$0.208825\pi$
$674$	−547.798	+	316.271i	−0.812756	+	0.469245i
$675$		0			0
$676$	−71.0000	+	122.976i	−0.105030	+	0.181917i
$677$	89.4436	−	333.808i	0.132118	−	0.493069i	−0.867876	−	0.496782i	$-0.834515\pi$
$677$	89.4436	−	333.808i	0.132118	−	0.493069i	0.999993	+	0.00371227i	$0.00118165\pi$
$678$	−887.065	+	887.065i	−1.30836	+	1.30836i
$679$	165.467	−	421.830i	0.243693	−	0.621251i
$680$		0			0
$681$	109.612	+	189.853i	0.160957	+	0.278786i
$682$	−75.9997	+	20.3640i	−0.111436	+	0.0298593i
$683$	−183.607	−	685.231i	−0.268824	−	1.00327i	−0.959868	−	0.280453i	$-0.909515\pi$
$683$	−183.607	−	685.231i	−0.268824	−	1.00327i	0.691043	−	0.722813i	$-0.257151\pi$
$684$	−605.113	+	349.362i	−0.884669	+	0.510764i
$685$		0			0
$686$	−273.034	+	400.937i	−0.398008	+	0.584457i
$687$	1178.00	+	1178.00i	1.71470	+	1.71470i
$688$	52.7150	+	14.1249i	0.0766206	+	0.0205304i
$689$	−152.654	−	88.1346i	−0.221558	−	0.127917i
$690$		0			0
$691$	−572.329	−	991.302i	−0.828261	−	1.43459i	−0.899401	−	0.437125i	$-0.855997\pi$
$691$	−572.329	−	991.302i	−0.828261	−	1.43459i	0.0711395	−	0.997466i	$-0.477336\pi$
$692$	0.364391	+	0.364391i	0.000526576	+	0.000526576i
$693$	422.834	−	184.572i	0.610150	−	0.266338i
$694$			200.657i			0.289132i
$695$		0			0
$696$	372.840	−	645.777i	0.535689	−	0.927841i
$697$	57.4325	−	15.3890i	0.0823995	−	0.0220789i
$698$	408.252	+	109.391i	0.584888	+	0.156720i
$699$		−	608.364i		−	0.870335i
$700$		0			0
$701$	496.362			0.708077			0.354039	−	0.935231i	$-0.384808\pi$
$701$	496.362			0.708077			0.354039	+	0.935231i	$0.384808\pi$
$702$	−298.442	+	1113.80i	−0.425131	+	1.58661i
$703$	168.969	+	630.600i	0.240354	+	0.897013i
$704$	24.0909	+	13.9089i	0.0342201	+	0.0197570i
$705$		0			0
$706$	48.7246			0.0690151
$707$	−998.197	−	112.286i	−1.41188	−	0.158820i
$708$	564.360	−	564.360i	0.797119	−	0.797119i
$709$	282.281	−	162.975i	0.398140	−	0.229866i	−0.287541	−	0.957768i	$-0.592838\pi$
$709$	282.281	−	162.975i	0.398140	−	0.229866i	0.685681	+	0.727902i	$0.259504\pi$
$710$		0			0
$711$	959.132	−	1661.27i	1.34899	−	2.33652i
$712$	−60.5602	+	226.014i	−0.0850564	+	0.317435i
$713$	203.089	−	203.089i	0.284837	−	0.284837i
$714$	321.029	+	402.408i	0.449621	+	0.563596i
$715$		0			0
$716$	−43.6356	−	75.5791i	−0.0609436	−	0.105557i
$717$	2240.58	−	600.363i	3.12494	−	0.837326i
$718$	−180.116	−	672.203i	−0.250858	−	0.936216i
$719$	−543.130	+	313.576i	−0.755396	+	0.436128i	−0.827640	−	0.561259i	$-0.810317\pi$
$719$	−543.130	+	313.576i	−0.755396	+	0.436128i	0.0722443	+	0.997387i	$0.476984\pi$
$720$		0			0
$721$	58.7029	+	388.988i	0.0814187	+	0.539511i
$722$	21.2733	+	21.2733i	0.0294644	+	0.0294644i
$723$	−797.629	−	213.724i	−1.10322	−	0.295607i
$724$	−6.37595	−	3.68116i	−0.00880656	−	0.00508447i
$725$		0			0
$726$	−407.168	−	705.236i	−0.560838	−	0.971399i
$727$	9.62370	+	9.62370i	0.0132376	+	0.0132376i	0.713695	−	0.700457i	$-0.247020\pi$
$727$	9.62370	+	9.62370i	0.0132376	+	0.0132376i	−0.700457	+	0.713695i	$0.747020\pi$
$728$	281.110	−	122.708i	0.386140	−	0.168555i
$729$		−	463.404i		−	0.635670i
$730$		0			0
$731$	−67.0932	+	116.209i	−0.0917827	+	0.158972i
$732$	1051.12	−	281.647i	1.43596	−	0.384763i
$733$	211.301	+	56.6180i	0.288269	+	0.0772415i	0.400056	−	0.916491i	$-0.368991\pi$
$733$	211.301	+	56.6180i	0.288269	+	0.0772415i	−0.111787	+	0.993732i	$0.535657\pi$
$734$			102.978i			0.140297i
$735$		0			0
$736$	−101.545			−0.137968
$737$	28.9986	−	108.224i	0.0393468	−	0.146844i
$738$	−41.9429	−	156.533i	−0.0568332	−	0.212104i
$739$	−467.750	−	270.055i	−0.632949	−	0.365434i	0.148944	−	0.988846i	$-0.452413\pi$
$739$	−467.750	−	270.055i	−0.632949	−	0.365434i	−0.781893	+	0.623412i	$0.785746\pi$
$740$		0			0
$741$	−1509.72			−2.03741
$742$	45.0617	+	103.231i	0.0607301	+	0.139126i
$743$	−142.376	+	142.376i	−0.191624	+	0.191624i	−0.796397	−	0.604774i	$-0.793264\pi$
$743$	−142.376	+	142.376i	−0.191624	+	0.191624i	0.604774	+	0.796397i	$0.293264\pi$
$744$	−207.215	+	119.636i	−0.278515	+	0.160801i
$745$		0			0
$746$	−243.271	+	421.358i	−0.326101	+	0.564823i
$747$	354.694	−	1323.74i	0.474824	−	1.77207i
$748$	−48.3644	+	48.3644i	−0.0646583	+	0.0646583i
$749$	415.233	−	62.6636i	0.554383	−	0.0836630i
$750$		0			0
$751$	602.043	+	1042.77i	0.801656	+	1.38851i	0.918526	+	0.395361i	$0.129381\pi$
$751$	602.043	+	1042.77i	0.801656	+	1.38851i	−0.116870	+	0.993147i	$0.537286\pi$
$752$	−81.2149	+	21.7615i	−0.107999	+	0.0289381i
$753$	−254.153	−	948.514i	−0.337521	−	1.25965i
$754$	946.091	−	546.226i	1.25476	−	0.724437i
$755$		0			0
$756$	575.998	−	459.515i	0.761902	−	0.607824i
$757$	297.410	+	297.410i	0.392880	+	0.392880i	0.875713	−	0.482833i	$-0.160392\pi$
$757$	297.410	+	297.410i	0.392880	+	0.392880i	−0.482833	+	0.875713i	$0.660392\pi$
$758$	−45.8552	−	12.2869i	−0.0604950	−	0.0162096i
$759$	−285.805	−	165.010i	−0.376555	−	0.217404i
$760$		0			0
$761$	368.271	+	637.864i	0.483931	+	0.838192i	0.999830	−	0.0184569i	$-0.00587536\pi$
$761$	368.271	+	637.864i	0.483931	+	0.838192i	−0.515899	+	0.856649i	$0.672542\pi$
$762$	186.590	+	186.590i	0.244869	+	0.244869i
$763$	−29.1658	+	259.278i	−0.0382251	+	0.339814i
$764$			35.8654i			0.0469443i
$765$		0			0
$766$	−508.693	+	881.082i	−0.664090	+	1.15024i
$767$	1129.45	−	302.634i	1.47255	−	0.394569i
$768$	81.7126	+	21.8948i	0.106397	+	0.0285089i
$769$			1006.45i			1.30877i	0.756160	+	0.654387i	$0.227073\pi$
$769$			1006.45i			1.30877i	−0.756160	+	0.654387i	$0.772927\pi$
$770$		0			0
$771$	1261.27			1.63588
$772$	−110.073	+	410.797i	−0.142581	+	0.532121i
$773$	−208.117	−	776.703i	−0.269233	−	1.00479i	−0.959608	−	0.281339i	$-0.909221\pi$
$773$	−208.117	−	776.703i	−0.269233	−	1.00479i	0.690376	−	0.723451i	$-0.257445\pi$
$774$	316.729	+	182.863i	0.409210	+	0.236258i
$775$		0			0
$776$	183.089			0.235939
$777$	−524.437	−	1201.42i	−0.674951	−	1.54624i
$778$	−531.089	+	531.089i	−0.682634	+	0.682634i
$779$	96.5009	−	55.7148i	0.123878	−	0.0715209i
$780$		0			0
$781$	−70.1366	+	121.480i	−0.0898036	+	0.155544i
$782$	64.6205	−	241.167i	0.0826350	−	0.308398i
$783$	1855.71	−	1855.71i	2.37000	−	2.37000i
$784$	−191.102	−	43.5445i	−0.243752	−	0.0555415i
$785$		0			0
$786$	−262.043	−	453.873i	−0.333389	−	0.577446i
$787$	−643.687	+	172.475i	−0.817900	+	0.219156i	−0.643428	−	0.765507i	$-0.722488\pi$
$787$	−643.687	+	172.475i	−0.817900	+	0.219156i	−0.174472	+	0.984662i	$0.555822\pi$
$788$	30.0808	+	112.263i	0.0381736	+	0.142466i
$789$	1504.00	−	868.335i	1.90621	−	1.10055i
$790$		0			0
$791$	1093.33	+	428.869i	1.38221	+	0.542186i
$792$	131.818	+	131.818i	0.166437	+	0.166437i
$793$	1539.93	+	412.624i	1.94191	+	0.520333i
$794$	329.326	+	190.137i	0.414769	+	0.239467i
$795$		0			0
$796$	301.545	+	522.290i	0.378825	+	0.656144i
$797$	−202.408	−	202.408i	−0.253962	−	0.253962i	0.568631	−	0.822593i	$-0.307473\pi$
$797$	−202.408	−	202.408i	−0.253962	−	0.253962i	−0.822593	+	0.568631i	$0.807473\pi$
$798$	776.320	+	572.732i	0.972832	+	0.717709i
$799$		−	206.733i		−	0.258740i
$800$		0			0
$801$	−784.020	+	1357.96i	−0.978801	+	1.69533i
$802$	−754.784	+	202.244i	−0.941127	+	0.252174i
$803$	−298.167	−	79.8936i	−0.371316	−	0.0994939i
$804$		−	340.725i		−	0.423787i
$805$		0			0
$806$	−350.542			−0.434916
$807$	391.617	−	1461.53i	0.485275	−	1.81107i
$808$	−105.049	−	392.046i	−0.130011	−	0.485206i
$809$	138.014	+	79.6822i	0.170598	+	0.0984947i	0.582868	−	0.812567i	$-0.301931\pi$
$809$	138.014	+	79.6822i	0.170598	+	0.0984947i	−0.412270	+	0.911062i	$0.635264\pi$
$810$		0			0
$811$	741.545			0.914358			0.457179	−	0.889375i	$-0.348860\pi$
$811$	741.545			0.914358			0.457179	+	0.889375i	$0.348860\pi$
$812$	−693.712	−	78.0346i	−0.854325	−	0.0961018i
$813$	−1531.04	+	1531.04i	−1.88320	+	1.88320i
$814$	150.843	−	87.0890i	0.185310	−	0.106989i
$815$		0			0
$816$	−104.000	+	180.133i	−0.127451	+	0.220752i
$817$	−65.0866	+	242.906i	−0.0796654	+	0.297315i
$818$	−125.317	+	125.317i	−0.153199	+	0.153199i
$819$	2032.47	−	306.725i	2.48165	−	0.374511i
$820$		0			0
$821$	−788.950	−	1366.50i	−0.960963	−	1.66444i	−0.720092	−	0.693879i	$-0.755900\pi$
$821$	−788.950	−	1366.50i	−0.960963	−	1.66444i	−0.240871	−	0.970557i	$-0.577433\pi$
$822$	69.1724	−	18.5347i	0.0841513	−	0.0225483i
$823$	157.478	+	587.715i	0.191346	+	0.714114i	0.993182	+	0.116570i	$0.0371899\pi$
$823$	157.478	+	587.715i	0.191346	+	0.714114i	−0.801836	+	0.597544i	$0.796143\pi$
$824$	−137.659	+	79.4772i	−0.167061	+	0.0964529i
$825$		0			0
$826$	−695.586	−	272.851i	−0.842114	−	0.330328i
$827$	−1014.44	−	1014.44i	−1.22665	−	1.22665i	−0.965223	−	0.261426i	$-0.915807\pi$
$827$	−1014.44	−	1014.44i	−1.22665	−	1.22665i	−0.261426	−	0.965223i	$-0.584193\pi$
$828$	−657.304	−	176.124i	−0.793846	−	0.212710i
$829$	344.517	+	198.907i	0.415581	+	0.239936i	0.693185	−	0.720760i	$-0.256207\pi$
$829$	344.517	+	198.907i	0.415581	+	0.239936i	−0.277604	+	0.960696i	$0.589540\pi$
$830$		0			0
$831$	42.9979	+	74.4746i	0.0517424	+	0.0896204i
$832$	87.6356	+	87.6356i	0.105331	+	0.105331i
$833$	225.030	−	426.154i	0.270145	−	0.511589i
$834$			396.455i			0.475366i
$835$		0			0
$836$	−64.0911	+	111.009i	−0.0766640	+	0.132786i
$837$	−813.404	+	217.951i	−0.971809	+	0.260396i
$838$	158.827	+	42.5575i	0.189531	+	0.0507846i
$839$		−	1475.70i		−	1.75888i	−0.476011	−	0.879439i	$-0.657918\pi$
$839$		−	1475.70i		−	1.75888i	0.476011	−	0.879439i	$-0.342082\pi$
$840$		0			0
$841$	−1645.35			−1.95643
$842$	195.622	−	730.071i	0.232330	−	0.867068i
$843$	−414.007	−	1545.10i	−0.491112	−	1.83285i
$844$	307.790	+	177.703i	0.364681	+	0.210548i
$845$		0			0
$846$	−563.453			−0.666021
$847$	−452.594	+	613.477i	−0.534350	+	0.724295i
$848$	−32.1822	+	32.1822i	−0.0379507	+	0.0379507i
$849$	−725.534	+	418.887i	−0.854575	+	0.493389i
$850$		0			0
$851$	−317.905	+	550.627i	−0.373566	+	0.647035i
$852$	−110.406	+	412.042i	−0.129585	+	0.483617i
$853$	−307.404	+	307.404i	−0.360380	+	0.360380i	−0.863953	−	0.503573i	$-0.832018\pi$
$853$	−307.404	+	307.404i	−0.360380	+	0.360380i	0.503573	+	0.863953i	$0.332018\pi$
$854$	−635.323	−	796.372i	−0.743938	−	0.932520i
$855$		0			0
$856$	84.8395	+	146.946i	0.0991116	+	0.171666i
$857$	1162.11	−	311.386i	1.35602	−	0.363344i	0.493666	−	0.869651i	$-0.335656\pi$
$857$	1162.11	−	311.386i	1.35602	−	0.363344i	0.862353	+	0.506307i	$0.168990\pi$
$858$	104.250	+	389.066i	0.121503	+	0.453456i
$859$	−795.008	+	458.998i	−0.925504	+	0.534340i	−0.885387	−	0.464855i	$-0.846106\pi$
$859$	−795.008	+	458.998i	−0.925504	+	0.534340i	−0.0401170	+	0.999195i	$0.512773\pi$
$860$		0			0
$861$	−174.908	+	139.536i	−0.203145	+	0.162063i
$862$	−477.473	−	477.473i	−0.553913	−	0.553913i
$863$	1226.45	+	328.625i	1.42114	+	0.380794i	0.885889	−	0.463897i	$-0.153549\pi$
$863$	1226.45	+	328.625i	1.42114	+	0.380794i	0.535254	+	0.844691i	$0.320216\pi$
$864$	257.839	+	148.863i	0.298425	+	0.172296i
$865$		0			0
$866$	−542.271	−	939.241i	−0.626179	−	1.08457i
$867$	718.828	+	718.828i	0.829098	+	0.829098i
$868$	180.254	+	132.983i	0.207666	+	0.153206i
$869$		−	351.909i		−	0.404958i
$870$		0			0
$871$	249.588	−	432.299i	0.286553	−	0.496325i
$872$	−101.833	+	27.2859i	−0.116780	+	0.0312912i
$873$	1185.15	+	317.559i	1.35756	+	0.363756i
$874$		−	467.909i		−	0.535365i
$875$		0			0
$876$	−938.725			−1.07160
$877$	−104.335	+	389.382i	−0.118968	+	0.443993i	−0.999553	−	0.0298940i	$-0.990483\pi$
$877$	−104.335	+	389.382i	−0.118968	+	0.443993i	0.880585	+	0.473888i	$0.157150\pi$
$878$	98.2949	+	366.841i	0.111953	+	0.417815i
$879$	−648.727	−	374.542i	−0.738028	−	0.426101i
$880$		0			0
$881$	338.402			0.384111			0.192055	−	0.981384i	$-0.438485\pi$
$881$	338.402			0.384111			0.192055	+	0.981384i	$0.438485\pi$
$882$	−1161.49	−	613.323i	−1.31688	−	0.695378i
$883$	455.410	−	455.410i	0.515753	−	0.515753i	−0.400530	−	0.916283i	$-0.631174\pi$
$883$	455.410	−	455.410i	0.515753	−	0.515753i	0.916283	+	0.400530i	$0.131174\pi$
$884$	−263.903	+	152.364i	−0.298533	+	0.172358i
$885$		0			0
$886$	62.3525	−	107.998i	0.0703753	−	0.121894i
$887$	−104.463	+	389.861i	−0.117771	+	0.439528i	−0.999479	−	0.0322675i	$-0.989727\pi$
$887$	−104.463	+	389.861i	−0.117771	+	0.439528i	0.881708	+	0.471795i	$0.156394\pi$
$888$	374.542	−	374.542i	0.421782	−	0.421782i
$889$	90.2107	−	229.976i	0.101474	−	0.258691i
$890$		0			0
$891$	187.216	+	324.267i	0.210119	+	0.363936i
$892$	680.589	−	182.363i	0.762992	−	0.204443i
$893$	−100.275	−	374.232i	−0.112290	−	0.419072i
$894$	−1353.96	+	781.711i	−1.51450	+	0.874397i
$895$		0			0
$896$	−11.8178	−	78.3093i	−0.0131895	−	0.0873987i
$897$	−1039.67	−	1039.67i	−1.15906	−	1.15906i
$898$	137.163	+	36.7526i	0.152742	+	0.0409272i
$899$	690.927	+	398.907i	0.768550	+	0.443723i
$900$		0			0
$901$	−55.9524	−	96.9124i	−0.0621003	−	0.107561i
$902$	−21.0217	−	21.0217i	−0.0233057	−	0.0233057i
$903$	56.4458	−	501.792i	0.0625092	−	0.555694i
$904$			474.542i			0.524936i
$905$		0			0
$906$	605.996	−	1049.62i	0.668870	−	1.15852i
$907$	−589.236	+	157.885i	−0.649653	+	0.174074i	−0.568572	−	0.822633i	$-0.692504\pi$
$907$	−589.236	+	157.885i	−0.649653	+	0.174074i	−0.0810812	+	0.996707i	$0.525837\pi$
$908$	80.1006	+	21.4629i	0.0882165	+	0.0236375i
$909$		−	2719.94i		−	2.99224i
$910$		0			0
$911$	−716.063			−0.786019			−0.393009	−	0.919534i	$-0.628566\pi$
$911$	−716.063			−0.786019			−0.393009	+	0.919534i	$0.628566\pi$
$912$	−100.890	+	376.525i	−0.110625	+	0.412857i
$913$	−65.0692	−	242.841i	−0.0712696	−	0.265982i
$914$	−852.004	−	491.905i	−0.932171	−	0.538189i
$915$		0			0
$916$	630.178			0.687967
$917$	−291.279	+	394.819i	−0.317643	+	0.430555i
$918$	−517.631	+	517.631i	−0.563869	+	0.563869i
$919$	−222.629	+	128.535i	−0.242251	+	0.139864i	−0.616211	−	0.787581i	$-0.711333\pi$
$919$	−222.629	+	128.535i	−0.242251	+	0.139864i	0.373960	+	0.927445i	$0.378000\pi$
$920$		0			0
$921$	906.995	−	1570.96i	0.984793	−	1.70571i
$922$	−70.1435	+	261.779i	−0.0760776	+	0.283925i
$923$	−441.909	+	441.909i	−0.478775	+	0.478775i
$924$	93.9904	−	239.612i	0.101721	−	0.259320i
$925$		0			0
$926$	268.079	+	464.327i	0.289502	+	0.501433i
$927$	−1028.92	+	275.699i	−1.10995	+	0.297410i
$928$	−73.0050	−	272.458i	−0.0786692	−	0.293597i
$929$	−1104.77	+	637.841i	−1.18921	+	0.686588i	−0.958126	−	0.286346i	$-0.907559\pi$
$929$	−1104.77	+	637.841i	−1.18921	+	0.686588i	−0.231080	+	0.972935i	$0.574226\pi$
$930$		0			0
$931$	200.650	−	880.581i	0.215521	−	0.945845i
$932$	−162.725	−	162.725i	−0.174597	−	0.174597i
$933$	38.1865	+	10.2320i	0.0409287	+	0.0109668i
$934$	236.403	+	136.487i	0.253108	+	0.146132i
$935$		0			0
$936$	415.271	+	719.271i	0.443666	+	0.768452i
$937$	589.180	+	589.180i	0.628794	+	0.628794i	0.947765	−	0.318970i	$-0.103337\pi$
$937$	589.180	+	589.180i	0.628794	+	0.628794i	−0.318970	+	0.947765i	$0.603337\pi$
$938$	−292.340	+	127.610i	−0.311663	+	0.136045i
$939$			3163.53i			3.36904i
$940$		0			0
$941$	−98.6377	+	170.845i	−0.104822	+	0.181557i	−0.913666	−	0.406467i	$-0.866761\pi$
$941$	−98.6377	+	170.845i	−0.104822	+	0.181557i	0.808843	+	0.588024i	$0.200094\pi$
$942$	−994.932	+	266.591i	−1.05619	+	0.283005i
$943$	104.824	+	28.0875i	0.111160	+	0.0297853i
$944$		−	301.909i		−	0.319819i
$945$		0			0
$946$	67.0932			0.0709230
$947$	400.951	−	1496.37i	0.423390	−	1.58011i	−0.344023	−	0.938961i	$-0.611790\pi$
$947$	400.951	−	1496.37i	0.423390	−	1.58011i	0.767413	−	0.641153i	$-0.221544\pi$
$948$	−276.980	−	1033.71i	−0.292173	−	1.09041i
$949$	−1191.02	−	687.636i	−1.25503	−	0.724590i
$950$		0			0
$951$	−2153.44			−2.26440
$952$	193.504	+	21.7670i	0.203261	+	0.0228645i
$953$	−1139.41	+	1139.41i	−1.19560	+	1.19560i	−0.220128	+	0.975471i	$0.570647\pi$
$953$	−1139.41	+	1139.41i	−1.19560	+	1.19560i	−0.975471	+	0.220128i	$0.929353\pi$
$954$	−264.136	+	152.499i	−0.276872	+	0.159852i
$955$		0			0
$956$	438.725	−	759.893i	0.458917	−	0.794868i
$957$	237.266	−	885.490i	0.247927	−	0.925277i
$958$	741.545	−	741.545i	0.774055	−	0.774055i
$959$	−41.8095	−	52.4079i	−0.0435970	−	0.0546485i
$960$		0			0
$961$	352.500	+	610.548i	0.366805	+	0.635326i
$962$	749.566	−	200.846i	0.779175	−	0.208779i
$963$	294.300	+	1098.34i	0.305608	+	1.14054i
$964$	−270.515	+	156.182i	−0.280618	+	0.162015i
$965$		0			0
$966$	140.202	+	929.031i	0.145136	+	0.961729i
$967$	184.424	+	184.424i	0.190718	+	0.190718i	0.796006	−	0.605289i	$-0.206942\pi$
$967$	184.424	+	184.424i	0.190718	+	0.190718i	−0.605289	+	0.796006i	$0.706942\pi$
$968$	−297.545	−	79.7268i	−0.307381	−	0.0823624i
$969$	−830.040	−	479.224i	−0.856594	−	0.494555i
$970$		0			0
$971$	−745.089	−	1290.53i	−0.767342	−	1.32908i	−0.938999	−	0.343919i	$-0.888246\pi$
$971$	−745.089	−	1290.53i	−0.767342	−	1.32908i	0.171658	−	0.985157i	$-0.445088\pi$
$972$	135.271	+	135.271i	0.139168	+	0.139168i
$973$	340.157	−	148.483i	0.349596	−	0.152603i
$974$			1114.81i			1.14457i
$975$		0			0
$976$	205.818	−	356.487i	0.210879	−	0.365253i
$977$	−1016.44	+	272.355i	−1.04037	+	0.278767i	−0.738268	−	0.674507i	$-0.764356\pi$
$977$	−1016.44	+	272.355i	−1.04037	+	0.278767i	−0.302105	+	0.953275i	$0.597689\pi$
$978$	−686.670	−	183.993i	−0.702116	−	0.188131i
$979$			287.659i			0.293830i
$980$		0			0
$981$	−706.495			−0.720178
$982$	−84.9179	+	316.918i	−0.0864744	+	0.322727i
$983$	−185.170	−	691.062i	−0.188372	−	0.703014i	−0.993884	−	0.110434i	$-0.964776\pi$
$983$	−185.170	−	691.062i	−0.188372	−	0.703014i	0.805512	−	0.592580i	$-0.201891\pi$
$984$	−78.2955	−	45.2039i	−0.0795686	−	0.0459390i
$985$		0			0
$986$	693.545			0.703392
$987$	311.228	+	712.989i	0.315328	+	0.722380i
$988$	−403.818	+	403.818i	−0.408722	+	0.408722i
$989$	−212.101	+	122.457i	−0.214460	+	0.123819i
$990$		0			0
$991$	−646.768	+	1120.24i	−0.652642	+	1.13041i	0.329838	+	0.944038i	$0.393006\pi$
$991$	−646.768	+	1120.24i	−0.652642	+	1.13041i	−0.982479	+	0.186371i	$0.940327\pi$
$992$	−23.4256	+	87.4256i	−0.0236145	+	0.0881307i
$993$	−884.681	+	884.681i	−0.890918	+	0.890918i
$994$	394.880	−	59.5921i	0.397264	−	0.0599518i
$995$		0			0
$996$	−382.271	−	662.113i	−0.383806	−	0.664772i
$997$	175.157	−	46.9331i	0.175684	−	0.0470743i	−0.169905	−	0.985460i	$-0.554346\pi$
$997$	175.157	−	46.9331i	0.175684	−	0.0470743i	0.345588	+	0.938386i	$0.387679\pi$
$998$	−241.052	−	899.618i	−0.241535	−	0.901421i
$999$	1614.43	−	932.091i	1.61605	−	0.933024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.3.p.c.207.1		8
5.2	odd	4		70.3.l.a.53.1	yes	8
5.3	odd	4	inner	350.3.p.c.193.2		8
5.4	even	2		70.3.l.a.67.2	yes	8
7.2	even	3	inner	350.3.p.c.107.2		8
35.2	odd	12		70.3.l.a.23.2	✓	8
35.4	even	6		490.3.f.l.197.2		4
35.9	even	6		70.3.l.a.37.1	yes	8
35.17	even	12		490.3.f.e.393.1		4
35.23	odd	12	inner	350.3.p.c.93.1		8
35.24	odd	6		490.3.f.e.197.1		4
35.32	odd	12		490.3.f.l.393.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.a.23.2	✓	8	35.2	odd	12
70.3.l.a.37.1	yes	8	35.9	even	6
70.3.l.a.53.1	yes	8	5.2	odd	4
70.3.l.a.67.2	yes	8	5.4	even	2
350.3.p.c.93.1		8	35.23	odd	12	inner
350.3.p.c.107.2		8	7.2	even	3	inner
350.3.p.c.193.2		8	5.3	odd	4	inner
350.3.p.c.207.1		8	1.1	even	1	trivial
490.3.f.e.197.1		4	35.24	odd	6
490.3.f.e.393.1		4	35.17	even	12
490.3.f.l.197.2		4	35.4	even	6
490.3.f.l.393.2		4	35.32	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	350.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(-1.36843 - 5.10704i) q^{3} +(-1.73205 - 1.00000i) q^{4} -7.47723 q^{6} +(2.80041 + 6.41543i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-16.4150 + 9.47723i) q^{9} +(-1.73861 + 3.01137i) q^{11} +(-2.73685 + 10.2141i) q^{12} +(-10.9545 + 10.9545i) q^{13} +(9.78866 - 1.47723i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-9.49996 + 2.54551i) q^{17} +(6.93781 + 25.8923i) q^{18} +(-15.9623 + 9.21584i) q^{19} +(28.9317 - 23.0809i) q^{21} +(3.47723 + 3.47723i) q^{22} +(-17.3390 - 4.64598i) q^{23} +(12.9509 + 7.47723i) q^{24} +(10.9545 + 18.9737i) q^{26} +(37.2158 + 37.2158i) q^{27} +(1.56497 - 13.9123i) q^{28} -49.8634i q^{29} +(-8.00000 + 13.8564i) q^{31} +(5.46410 - 1.46410i) q^{32} +(17.7583 + 4.75833i) q^{33} +13.9089i q^{34} +37.9089 q^{36} +(9.16731 - 34.2129i) q^{37} +(6.74646 + 25.1781i) q^{38} +(70.9352 + 40.9545i) q^{39} -6.04555 q^{41} +(-20.9393 - 47.9696i) q^{42} +(9.64752 - 9.64752i) q^{43} +(6.02273 - 3.47723i) q^{44} +(-12.6931 + 21.9850i) q^{46} +(-5.44036 + 20.3037i) q^{47} +(14.9545 - 14.9545i) q^{48} +(-33.3154 + 35.9317i) q^{49} +(26.0000 + 45.0333i) q^{51} +(29.9281 - 8.01921i) q^{52} +(2.94488 + 10.9904i) q^{53} +(64.4597 - 37.2158i) q^{54} +(-18.4317 - 7.23003i) q^{56} +(68.9089 + 68.9089i) q^{57} +(-68.1146 - 18.2513i) q^{58} +(-65.3652 - 37.7386i) q^{59} +(-51.4545 - 89.1217i) q^{61} +(16.0000 + 16.0000i) q^{62} +(-106.769 - 78.7693i) q^{63} -8.00000i q^{64} +(13.0000 - 22.5167i) q^{66} +(-31.1237 + 8.33958i) q^{67} +(18.9999 + 5.09101i) q^{68} +94.9089i q^{69} +40.3406 q^{71} +(13.8756 - 51.7845i) q^{72} +(22.9762 + 85.7485i) q^{73} +(-43.3802 - 25.0455i) q^{74} +36.8634 q^{76} +(-24.1880 - 2.72088i) q^{77} +(81.9089 - 81.9089i) q^{78} +(-87.6452 + 50.6020i) q^{79} +(53.8406 - 93.2546i) q^{81} +(-2.21282 + 8.25837i) q^{82} +(-51.1247 + 51.1247i) q^{83} +(-73.1920 + 11.0455i) q^{84} +(-9.64752 - 16.7100i) q^{86} +(-254.654 + 68.2344i) q^{87} +(-2.54551 - 9.49996i) q^{88} +(71.6434 - 41.3634i) q^{89} +(-100.954 - 39.6005i) q^{91} +(25.3861 + 25.3861i) q^{92} +(81.7126 + 21.8948i) q^{93} +(25.7441 + 14.8634i) q^{94} +(-14.9545 - 25.9019i) q^{96} +(-45.7723 - 45.7723i) q^{97} +(36.8893 + 58.6616i) q^{98} -65.9089i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{3} - 16 q^{6} + 4 q^{7} - 16 q^{8} + 8 q^{11} + 8 q^{12} + 16 q^{16} + 16 q^{17} - 32 q^{18} + 100 q^{21} - 16 q^{22} + 4 q^{23} + 232 q^{27} + 40 q^{28} - 64 q^{31} + 16 q^{32} + 52 q^{33}+ \cdots + 132 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 4 * q^3 - 16 * q^6 + 4 * q^7 - 16 * q^8 + 8 * q^11 + 8 * q^12 + 16 * q^16 + 16 * q^17 - 32 * q^18 + 100 * q^21 - 16 * q^22 + 4 * q^23 + 232 * q^27 + 40 * q^28 - 64 * q^31 + 16 * q^32 + 52 * q^33 + 128 * q^36 - 144 * q^37 - 8 * q^38 - 136 * q^41 - 188 * q^42 - 120 * q^43 + 8 * q^46 - 72 * q^47 + 32 * q^48 + 208 * q^51 - 76 * q^53 - 16 * q^56 + 376 * q^57 - 68 * q^58 - 324 * q^61 + 128 * q^62 - 112 * q^63 + 104 * q^66 - 124 * q^67 - 32 * q^68 + 16 * q^71 - 64 * q^72 - 32 * q^73 + 32 * q^76 - 20 * q^77 + 480 * q^78 + 124 * q^81 + 68 * q^82 - 168 * q^83 + 120 * q^86 - 428 * q^87 - 16 * q^88 - 720 * q^91 - 16 * q^92 + 64 * q^93 - 32 * q^96 + 72 * q^97 + 132 * q^98

Introduction

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