LMFDB - Embedded newform 350.3.p.c.193.2

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			193.2
Root			$2.15988 - 0.578737i$ of defining polynomial
Character	$\chi$	$=$	350.193
Dual form			350.3.p.c.107.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36603 - 0.366025i) q^{2} +(5.10704 - 1.36843i) q^{3} +(1.73205 + 1.00000i) q^{4} -7.47723 q^{6} +(6.41543 - 2.80041i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(16.4150 - 9.47723i) q^{9} +(-1.73861 + 3.01137i) q^{11} +(10.2141 + 2.73685i) q^{12} +(-10.9545 - 10.9545i) q^{13} +(-9.78866 + 1.47723i) q^{14} +(2.00000 + 3.46410i) q^{16} +(2.54551 + 9.49996i) q^{17} +(-25.8923 + 6.93781i) q^{18} +(15.9623 - 9.21584i) q^{19} +(28.9317 - 23.0809i) q^{21} +(3.47723 - 3.47723i) q^{22} +(4.64598 - 17.3390i) q^{23} +(-12.9509 - 7.47723i) q^{24} +(10.9545 + 18.9737i) q^{26} +(37.2158 - 37.2158i) q^{27} +(13.9123 + 1.56497i) q^{28} +49.8634i q^{29} +(-8.00000 + 13.8564i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-4.75833 + 17.7583i) q^{33} -13.9089i q^{34} +37.9089 q^{36} +(-34.2129 - 9.16731i) q^{37} +(-25.1781 + 6.74646i) q^{38} +(-70.9352 - 40.9545i) q^{39} -6.04555 q^{41} +(-47.9696 + 20.9393i) q^{42} +(9.64752 + 9.64752i) q^{43} +(-6.02273 + 3.47723i) q^{44} +(-12.6931 + 21.9850i) q^{46} +(20.3037 + 5.44036i) q^{47} +(14.9545 + 14.9545i) q^{48} +(33.3154 - 35.9317i) q^{49} +(26.0000 + 45.0333i) q^{51} +(-8.01921 - 29.9281i) q^{52} +(-10.9904 + 2.94488i) q^{53} +(-64.4597 + 37.2158i) q^{54} +(-18.4317 - 7.23003i) q^{56} +(68.9089 - 68.9089i) q^{57} +(18.2513 - 68.1146i) q^{58} +(65.3652 + 37.7386i) q^{59} +(-51.4545 - 89.1217i) q^{61} +(16.0000 - 16.0000i) q^{62} +(78.7693 - 106.769i) q^{63} +8.00000i q^{64} +(13.0000 - 22.5167i) q^{66} +(8.33958 + 31.1237i) q^{67} +(-5.09101 + 18.9999i) q^{68} -94.9089i q^{69} +40.3406 q^{71} +(-51.7845 - 13.8756i) q^{72} +(-85.7485 + 22.9762i) q^{73} +(43.3802 + 25.0455i) q^{74} +36.8634 q^{76} +(-2.72088 + 24.1880i) q^{77} +(81.9089 + 81.9089i) q^{78} +(87.6452 - 50.6020i) q^{79} +(53.8406 - 93.2546i) q^{81} +(8.25837 + 2.21282i) q^{82} +(-51.1247 - 51.1247i) q^{83} +(73.1920 - 11.0455i) q^{84} +(-9.64752 - 16.7100i) q^{86} +(68.2344 + 254.654i) q^{87} +(9.49996 - 2.54551i) q^{88} +(-71.6434 + 41.3634i) q^{89} +(-100.954 - 39.6005i) q^{91} +(25.3861 - 25.3861i) q^{92} +(-21.8948 + 81.7126i) q^{93} +(-25.7441 - 14.8634i) q^{94} +(-14.9545 - 25.9019i) q^{96} +(-45.7723 + 45.7723i) q^{97} +(-58.6616 + 36.8893i) 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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$3$	5.10704	−	1.36843i	1.70235	−	0.456142i	0.728818	−	0.684707i	$-0.240070\pi$
$3$	5.10704	−	1.36843i	1.70235	−	0.456142i	0.973529	+	0.228565i	$0.0734034\pi$
$4$	1.73205	+	1.00000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−7.47723			−1.24620
$7$	6.41543	−	2.80041i	0.916489	−	0.400059i
$7$	6.41543	−	2.80041i	0.916489	−	0.400059i
$8$	−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	$0.217189\pi$
$12$	10.2141	+	2.73685i	0.851173	+	0.228071i
$13$	−10.9545	−	10.9545i	−0.842650	−	0.842650i	0.146553	−	0.989203i	$-0.453182\pi$
$13$	−10.9545	−	10.9545i	−0.842650	−	0.842650i	−0.989203	+	0.146553i	$0.953182\pi$
$14$	−9.78866	+	1.47723i	−0.699190	+	0.105516i
$15$		0			0
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	2.54551	+	9.49996i	0.149736	+	0.558821i	0.999499	+	0.0316564i	$0.0100782\pi$
$17$	2.54551	+	9.49996i	0.149736	+	0.558821i	−0.849763	+	0.527165i	$0.823255\pi$
$18$	−25.8923	+	6.93781i	−1.43846	+	0.385434i
$19$	15.9623	−	9.21584i	0.840121	−	0.485044i	−0.0171843	−	0.999852i	$-0.505470\pi$
$19$	15.9623	−	9.21584i	0.840121	−	0.485044i	0.857305	+	0.514808i	$0.172137\pi$
$20$		0			0
$21$	28.9317	−	23.0809i	1.37770	−	1.09909i
$22$	3.47723	−	3.47723i	0.158056	−	0.158056i
$23$	4.64598	−	17.3390i	0.201999	−	0.753872i	−0.788344	−	0.615235i	$-0.789061\pi$
$23$	4.64598	−	17.3390i	0.201999	−	0.753872i	0.990343	−	0.138637i	$-0.0442721\pi$
$24$	−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
$28$	13.9123	+	1.56497i	0.496866	+	0.0558918i
$29$			49.8634i			1.71943i	0.510777	+	0.859713i	$0.329358\pi$
$29$			49.8634i			1.71943i	−0.510777	+	0.859713i	$0.670642\pi$
$30$		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	$0.249751\pi$
$32$	−1.46410	−	5.46410i	−0.0457532	−	0.170753i
$33$	−4.75833	+	17.7583i	−0.144192	+	0.538131i
$34$		−	13.9089i		−	0.409085i
$35$		0			0
$36$	37.9089			1.05303
$37$	−34.2129	−	9.16731i	−0.924672	−	0.247765i	−0.235091	−	0.971973i	$-0.575539\pi$
$37$	−34.2129	−	9.16731i	−0.924672	−	0.247765i	−0.689581	+	0.724208i	$0.742205\pi$
$38$	−25.1781	+	6.74646i	−0.662583	+	0.177538i
$39$	−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	$0.523489\pi$
$42$	−47.9696	+	20.9393i	−1.14213	+	0.498555i
$43$	9.64752	+	9.64752i	0.224361	+	0.224361i	0.810332	−	0.585971i	$-0.199287\pi$
$43$	9.64752	+	9.64752i	0.224361	+	0.224361i	−0.585971	+	0.810332i	$0.699287\pi$
$44$	−6.02273	+	3.47723i	−0.136880	+	0.0790279i
$45$		0			0
$46$	−12.6931	+	21.9850i	−0.275936	+	0.477935i
$47$	20.3037	+	5.44036i	0.431994	+	0.115752i	0.468262	−	0.883590i	$-0.344880\pi$
$47$	20.3037	+	5.44036i	0.431994	+	0.115752i	−0.0362680	+	0.999342i	$0.511547\pi$
$48$	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
$52$	−8.01921	−	29.9281i	−0.154216	−	0.575541i
$53$	−10.9904	+	2.94488i	−0.207366	+	0.0555637i	−0.361007	−	0.932563i	$-0.617567\pi$
$53$	−10.9904	+	2.94488i	−0.207366	+	0.0555637i	0.153640	+	0.988127i	$0.450900\pi$
$54$	−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
$58$	18.2513	−	68.1146i	0.314677	−	1.17439i
$59$	65.3652	+	37.7386i	1.10788	+	0.639638i	0.938281	−	0.345875i	$-0.112418\pi$
$59$	65.3652	+	37.7386i	1.10788	+	0.639638i	0.169604	+	0.985512i	$0.445751\pi$
$60$		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
$63$	78.7693	−	106.769i	1.25031	−	1.69475i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	13.0000	−	22.5167i	0.196970	−	0.341162i
$67$	8.33958	+	31.1237i	0.124471	+	0.464533i	0.999820	−	0.0189583i	$-0.00603497\pi$
$67$	8.33958	+	31.1237i	0.124471	+	0.464533i	−0.875349	+	0.483492i	$0.839368\pi$
$68$	−5.09101	+	18.9999i	−0.0748678	+	0.279410i
$69$		−	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	$0.408309\pi$
$72$	−51.7845	−	13.8756i	−0.719229	−	0.192717i
$73$	−85.7485	+	22.9762i	−1.17464	+	0.314743i	−0.792797	−	0.609486i	$-0.791376\pi$
$73$	−85.7485	+	22.9762i	−1.17464	+	0.314743i	−0.381840	+	0.924229i	$0.624709\pi$
$74$	43.3802	+	25.0455i	0.586218	+	0.338453i
$75$		0			0
$76$	36.8634			0.485044
$77$	−2.72088	+	24.1880i	−0.0353361	+	0.314130i
$78$	81.9089	+	81.9089i	1.05011	+	1.05011i
$79$	87.6452	−	50.6020i	1.10943	−	0.640531i	0.170750	−	0.985314i	$-0.445381\pi$
$79$	87.6452	−	50.6020i	1.10943	−	0.640531i	0.938682	+	0.344783i	$0.112048\pi$
$80$		0			0
$81$	53.8406	−	93.2546i	0.664699	−	1.15129i
$82$	8.25837	+	2.21282i	0.100712	+	0.0269857i
$83$	−51.1247	−	51.1247i	−0.615961	−	0.615961i	0.328532	−	0.944493i	$-0.393446\pi$
$83$	−51.1247	−	51.1247i	−0.615961	−	0.615961i	−0.944493	+	0.328532i	$0.893446\pi$
$84$	73.1920	−	11.0455i	0.871333	−	0.131495i
$85$		0			0
$86$	−9.64752	−	16.7100i	−0.112180	−	0.194302i
$87$	68.2344	+	254.654i	0.784303	+	2.92706i
$88$	9.49996	−	2.54551i	0.107954	−	0.0289262i
$89$	−71.6434	+	41.3634i	−0.804982	+	0.464757i	−0.845210	−	0.534434i	$-0.820525\pi$
$89$	−71.6434	+	41.3634i	−0.804982	+	0.464757i	0.0402280	+	0.999191i	$0.487192\pi$
$90$		0			0
$91$	−100.954	−	39.6005i	−1.10939	−	0.435170i
$92$	25.3861	−	25.3861i	0.275936	−	0.275936i
$93$	−21.8948	+	81.7126i	−0.235428	+	0.878631i
$94$	−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	−0.902522	−	0.430643i	$-0.858287\pi$
$97$	−45.7723	+	45.7723i	−0.471879	+	0.471879i	0.430643	+	0.902522i	$0.358287\pi$
$98$	−58.6616	+	36.8893i	−0.598587	+	0.376422i
$99$			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	$0.915185\pi$
$102$	−19.0333	−	71.0333i	−0.186601	−	0.696405i
$103$	−14.5453	+	54.2840i	−0.141217	+	0.527029i	0.858678	+	0.512516i	$0.171286\pi$
$103$	−14.5453	+	54.2840i	−0.141217	+	0.527029i	−0.999895	+	0.0145128i	$0.995380\pi$
$104$			43.8178i			0.421325i
$105$		0			0
$106$	16.0911			0.151803
$107$	−57.9465	−	15.5267i	−0.541556	−	0.145109i	−0.0223366	−	0.999751i	$-0.507111\pi$
$107$	−57.9465	−	15.5267i	−0.541556	−	0.145109i	−0.519219	+	0.854641i	$0.673777\pi$
$108$	101.676	−	27.2439i	0.941440	−	0.252258i
$109$	−32.2796	−	18.6366i	−0.296143	−	0.170978i	0.344566	−	0.938762i	$-0.388026\pi$
$109$	−32.2796	−	18.6366i	−0.296143	−	0.170978i	−0.640709	+	0.767784i	$0.721360\pi$
$110$		0			0
$111$	−187.271			−1.68713
$112$	22.5318	+	16.6229i	0.201176	+	0.148418i
$113$	118.636	+	118.636i	1.04987	+	1.04987i	0.998689	+	0.0511834i	$0.0162993\pi$
$113$	118.636	+	118.636i	1.04987	+	1.04987i	0.0511834	+	0.998689i	$0.483701\pi$
$114$	−119.354	+	68.9089i	−1.04696	+	0.604464i
$115$		0			0
$116$	−49.8634	+	86.3659i	−0.429856	+	0.744533i
$117$	−283.636	−	75.9999i	−2.42424	−	0.649572i
$118$	−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
$122$	37.6673	+	140.576i	0.308748	+	1.15226i
$123$	−30.8749	+	8.27289i	−0.251015	+	0.0672593i
$124$	−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	−0.798494	−	0.602002i	$-0.794370\pi$
$127$	−24.9545	+	24.9545i	−0.196492	+	0.196492i	0.602002	+	0.798494i	$0.294370\pi$
$128$	2.92820	−	10.9282i	0.0228766	−	0.0853766i
$129$	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
$133$	76.5968	−	103.825i	0.575916	−	0.780636i
$134$		−	45.5683i		−	0.340062i
$135$		0			0
$136$	13.9089	−	24.0909i	0.102271	−	0.177139i
$137$	2.47882	+	9.25107i	0.0180936	+	0.0675261i	0.974382	−	0.224898i	$-0.0722048\pi$
$137$	2.47882	+	9.25107i	0.0180936	+	0.0675261i	−0.956289	+	0.292424i	$0.905538\pi$
$138$	−34.7391	+	129.648i	−0.251732	+	0.939478i
$139$			53.0217i			0.381451i	0.981643	+	0.190726i	$0.0610841\pi$
$139$			53.0217i			0.381451i	−0.981643	+	0.190726i	$0.938916\pi$
$140$		0			0
$141$	111.137			0.788203
$142$	−55.1063	−	14.7657i	−0.388072	−	0.103984i
$143$	52.0334	−	13.9423i	0.363870	−	0.0974987i
$144$	65.6601	+	37.9089i	0.455973	+	0.263256i
$145$		0			0
$146$	125.545			0.859894
$147$	120.973	−	229.094i	0.822946	−	1.55846i
$148$	−50.0911	−	50.0911i	−0.338453	−	0.338453i
$149$	−181.078	+	104.546i	−1.21529	+	0.701648i	−0.963907	−	0.266240i	$-0.914219\pi$
$149$	−181.078	+	104.546i	−1.21529	+	0.701648i	−0.251383	+	0.967888i	$0.580885\pi$
$150$		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	$0.986328\pi$
$152$	−50.3563	−	13.4929i	−0.331291	−	0.0887692i
$153$	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
$157$	−35.6538	−	133.062i	−0.227094	−	0.847526i	−0.981555	−	0.191181i	$-0.938768\pi$
$157$	−35.6538	−	133.062i	−0.227094	−	0.847526i	0.754461	−	0.656345i	$-0.227898\pi$
$158$	−138.247	+	37.0432i	−0.874982	+	0.234451i
$159$	−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
$163$	−24.6071	+	91.8348i	−0.150964	+	0.563404i	0.848454	+	0.529270i	$0.177534\pi$
$163$	−24.6071	+	91.8348i	−0.150964	+	0.563404i	−0.999417	+	0.0341341i	$0.989133\pi$
$164$	−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	−0.983458	−	0.181134i	$-0.942023\pi$
$167$	−133.988	+	133.988i	−0.802324	+	0.802324i	0.181134	+	0.983458i	$0.442023\pi$
$168$	−104.025	−	11.7016i	−0.619197	−	0.0696526i
$169$			71.0000i			0.420118i
$170$		0			0
$171$	174.681	−	302.557i	1.02153	−	1.76934i
$172$	7.06247	+	26.3575i	0.0410609	+	0.153241i
$173$	0.0666881	−	0.248884i	0.000385481	−	0.00143863i	−0.965733	−	0.259538i	$-0.916430\pi$
$173$	0.0666881	−	0.248884i	0.000385481	−	0.00143863i	0.966118	+	0.258100i	$0.0830963\pi$
$174$		−	372.840i		−	2.14276i
$175$		0			0
$176$	−13.9089			−0.0790279
$177$	385.465	+	103.285i	2.17777	+	0.583532i
$178$	113.007	−	30.2801i	0.634870	−	0.170113i
$179$	−37.7895	−	21.8178i	−0.211115	−	0.121887i	0.390715	−	0.920512i	$-0.372228\pi$
$179$	−37.7895	−	21.8178i	−0.211115	−	0.121887i	−0.601829	+	0.798625i	$0.705561\pi$
$180$		0			0
$181$	3.68116			0.0203379			0.0101689	−	0.999948i	$-0.496763\pi$
$181$	3.68116			0.0203379			0.0101689	+	0.999948i	$0.496763\pi$
$182$	123.412	+	91.0472i	0.678085	+	0.500259i
$183$	−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
$187$	−33.0335	−	8.85130i	−0.176650	−	0.0473331i
$188$	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	$0.848282\pi$
$192$	10.9474	+	40.8563i	0.0570178	+	0.212793i
$193$	205.399	−	55.0364i	1.06424	−	0.285163i	0.316117	−	0.948720i	$-0.397621\pi$
$193$	205.399	−	55.0364i	1.06424	−	0.285163i	0.748125	+	0.663557i	$0.230954\pi$
$194$	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	−0.803666	−	0.595081i	$-0.797120\pi$
$197$	−41.0911	+	41.0911i	−0.208584	+	0.208584i	0.595081	+	0.803666i	$0.297120\pi$
$198$	24.1243	−	90.0332i	0.121840	−	0.454713i
$199$	261.145	+	150.772i	1.31229	+	0.757650i	0.982475	−	0.186397i	$-0.0596810\pi$
$199$	261.145	+	150.772i	1.31229	+	0.757650i	0.329813	+	0.944046i	$0.393014\pi$
$200$		0			0
$201$	85.1812	+	147.538i	0.423787	+	0.734020i
$202$	143.499	−	143.499i	0.710391	−	0.710391i
$203$	139.638	+	319.895i	0.687872	+	1.57584i
$204$			104.000i			0.509804i
$205$		0			0
$206$	39.7386	−	68.8293i	0.192906	−	0.334123i
$207$	−88.0621	−	328.652i	−0.425421	−	1.58769i
$208$	16.0384	−	59.8562i	0.0771078	−	0.287770i
$209$			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	$0.638355\pi$
$212$	−21.9808	−	5.88975i	−0.103683	−	0.0277818i
$213$	206.021	−	55.2031i	0.967235	−	0.259170i
$214$	73.4732	+	42.4198i	0.343333	+	0.198223i
$215$		0			0
$216$	−148.863			−0.689182
$217$	−12.5198	+	111.298i	−0.0576947	+	0.512894i
$218$	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
$222$	255.817	+	68.5460i	1.15233	+	0.308766i
$223$	−249.113	−	249.113i	−1.11710	−	1.11710i	−0.992165	−	0.124933i	$-0.960129\pi$
$223$	−249.113	−	249.113i	−1.11710	−	1.11710i	−0.124933	−	0.992165i	$-0.539871\pi$
$224$	−24.6946	−	30.9545i	−0.110244	−	0.138190i
$225$		0			0
$226$	−118.636	−	205.483i	−0.524936	−	0.909216i
$227$	10.7314	+	40.0503i	0.0472751	+	0.176433i	0.985527	−	0.169521i	$-0.0542220\pi$
$227$	10.7314	+	40.0503i	0.0472751	+	0.176433i	−0.938252	+	0.345954i	$0.887555\pi$
$228$	188.263	−	50.4448i	0.825713	−	0.221249i
$229$	272.875	−	157.545i	1.19159	−	0.687967i	0.232926	−	0.972494i	$-0.425170\pi$
$229$	272.875	−	157.545i	1.19159	−	0.687967i	0.958668	+	0.284527i	$0.0918366\pi$
$230$		0			0
$231$	19.2039	+	127.253i	0.0831339	+	0.550877i
$232$	99.7267	−	99.7267i	0.429856	−	0.429856i
$233$	−29.7807	+	111.143i	−0.127814	+	0.477009i	−0.999924	−	0.0123008i	$-0.996084\pi$
$233$	−29.7807	+	111.143i	−0.127814	+	0.477009i	0.872110	+	0.489309i	$0.162751\pi$
$234$	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
$238$	−38.9507	−	89.2315i	−0.163658	−	0.374922i
$239$		−	438.725i		−	1.83567i	−0.396965	−	0.917834i	$-0.629936\pi$
$239$		−	438.725i		−	1.83567i	0.396965	−	0.917834i	$-0.370064\pi$
$240$		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	$0.0616290\pi$
$242$	−39.8634	−	148.772i	−0.164725	−	0.614762i
$243$	24.7564	−	92.3920i	0.101878	−	0.380214i
$244$		−	205.818i		−	0.843516i
$245$		0			0
$246$	45.2039			0.183756
$247$	−275.813	−	73.9038i	−1.11665	−	0.299206i
$248$	43.7128	−	11.7128i	0.176261	−	0.0472291i
$249$	−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	$0.379367\pi$
$252$	243.202	−	106.161i	0.965086	−	0.421272i
$253$	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
$257$	230.423	+	61.7416i	0.896587	+	0.240240i	0.677550	−	0.735477i	$-0.263042\pi$
$257$	230.423	+	61.7416i	0.896587	+	0.240240i	0.219037	+	0.975717i	$0.429709\pi$
$258$	−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
$262$	−25.6551	−	95.7462i	−0.0979203	−	0.365444i
$263$	−317.275	+	85.0136i	−1.20637	+	0.323246i	−0.805336	−	0.592818i	$-0.798015\pi$
$263$	−317.275	+	85.0136i	−1.20637	+	0.323246i	−0.401032	+	0.916064i	$0.631349\pi$
$264$	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
$268$	−16.6792	+	62.2475i	−0.0622357	+	0.232267i
$269$	−247.839	−	143.090i	−0.921336	−	0.531933i	−0.0372746	−	0.999305i	$-0.511868\pi$
$269$	−247.839	−	143.090i	−0.921336	−	0.531933i	−0.884061	+	0.467372i	$0.845201\pi$
$270$		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
$273$	−569.769	−	64.0925i	−2.08707	−	0.234771i
$274$		−	13.5445i		−	0.0494325i
$275$		0			0
$276$	94.9089	−	164.387i	0.343873	−	0.595605i
$277$	4.20967	+	15.7107i	0.0151974	+	0.0567174i	0.973108	−	0.230349i	$-0.0739867\pi$
$277$	4.20967	+	15.7107i	0.0151974	+	0.0567174i	−0.957911	+	0.287066i	$0.907320\pi$
$278$	19.4073	−	72.4290i	0.0698104	−	0.260536i
$279$			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	$0.319055\pi$
$282$	−151.815	−	40.6788i	−0.538353	−	0.144251i
$283$	153.054	−	41.0108i	0.540828	−	0.144914i	0.0219440	−	0.999759i	$-0.493014\pi$
$283$	153.054	−	41.0108i	0.540828	−	0.144914i	0.518884	+	0.854845i	$0.326348\pi$
$284$	69.8719	+	40.3406i	0.246028	+	0.142044i
$285$		0			0
$286$	−76.1822			−0.266371
$287$	−38.7848	+	16.9300i	−0.135139	+	0.0589897i
$288$	−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
$292$	−171.497	−	45.9525i	−0.587318	−	0.157372i
$293$	100.182	+	100.182i	0.341919	+	0.341919i	0.857088	−	0.515170i	$-0.172271\pi$
$293$	100.182	+	100.182i	0.341919	+	0.341919i	−0.515170	+	0.857088i	$0.672271\pi$
$294$	−249.107	+	268.669i	−0.847301	+	0.913841i
$295$		0			0
$296$	50.0911	+	86.7603i	0.169227	+	0.293109i
$297$	47.3666	+	176.774i	0.159483	+	0.595200i
$298$	285.624	−	76.5327i	0.958469	−	0.256821i
$299$	−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
$303$	−196.368	+	732.855i	−0.648079	+	2.41866i
$304$	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	−0.191298	−	0.981532i	$-0.561270\pi$
$307$	242.602	−	242.602i	0.790234	−	0.790234i	0.981532	+	0.191298i	$0.0612696\pi$
$308$	−28.9007	+	39.1740i	−0.0938335	+	0.127188i
$309$			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	$0.170493\pi$
$312$	59.9615	+	223.779i	0.192184	+	0.717241i
$313$	154.861	−	577.950i	0.494765	−	1.84649i	−0.0365796	−	0.999331i	$-0.511646\pi$
$313$	154.861	−	577.950i	0.494765	−	1.84649i	0.531344	−	0.847156i	$-0.321687\pi$
$314$			194.816i			0.620432i
$315$		0			0
$316$	202.408			0.640531
$317$	−393.415	−	105.415i	−1.24106	−	0.332540i	−0.422182	−	0.906511i	$-0.638736\pi$
$317$	−393.415	−	105.415i	−1.24106	−	0.332540i	−0.818876	+	0.573971i	$0.805402\pi$
$318$	82.1779	−	22.0195i	0.258421	−	0.0692437i
$319$	−150.157	−	86.6931i	−0.470711	−	0.271765i
$320$		0			0
$321$	−317.182			−0.988107
$322$	−19.8643	+	176.589i	−0.0616902	+	0.548414i
$323$	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
$327$	−190.356	−	51.0058i	−0.582129	−	0.155981i
$328$	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	$0.949688\pi$
$332$	−37.4259	−	139.675i	−0.112729	−	0.420709i
$333$	−648.486	+	173.761i	−1.94741	+	0.521806i
$334$	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	−0.998215	−	0.0597246i	$-0.980978\pi$
$337$	−316.271	+	316.271i	−0.938490	+	0.938490i	0.0597246	+	0.998215i	$0.480978\pi$
$338$	25.9878	−	96.9878i	0.0768870	−	0.286946i
$339$	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
$343$	113.109	−	323.814i	0.329763	−	0.944064i
$344$		−	38.5901i		−	0.112180i
$345$		0			0
$346$	−0.182195	+	0.315572i	−0.000526576	+	0.000912057i
$347$	36.7228	+	137.052i	0.105830	+	0.394961i	0.998438	−	0.0558716i	$-0.0177938\pi$
$347$	36.7228	+	137.052i	0.105830	+	0.394961i	−0.892608	+	0.450833i	$0.851127\pi$
$348$	−136.469	+	509.308i	−0.392152	+	1.46353i
$349$		−	298.861i		−	0.856336i	−0.903699	−	0.428168i	$-0.859159\pi$
$349$		−	298.861i		−	0.856336i	0.903699	−	0.428168i	$-0.140841\pi$
$350$		0			0
$351$	−815.358			−2.32296
$352$	18.9999	+	5.09101i	0.0539770	+	0.0144631i
$353$	−33.2795	+	8.91723i	−0.0942763	+	0.0252613i	−0.305649	−	0.952144i	$-0.598873\pi$
$353$	−33.2795	+	8.91723i	−0.0942763	+	0.0252613i	0.211373	+	0.977406i	$0.432207\pi$
$354$	−488.750	−	282.180i	−1.38065	−	0.797119i
$355$		0			0
$356$	−165.453			−0.464757
$357$	292.913	+	216.097i	0.820484	+	0.605314i
$358$	43.6356	+	43.6356i	0.121887	+	0.121887i
$359$	−426.160	+	246.043i	−1.18707	+	0.685358i	−0.957641	−	0.287966i	$-0.907021\pi$
$359$	−426.160	+	246.043i	−1.18707	+	0.685358i	−0.229434	+	0.973324i	$0.573688\pi$
$360$		0			0
$361$	−10.6366	+	18.4232i	−0.0294644	+	0.0510338i
$362$	−5.02856	−	1.34740i	−0.0138910	−	0.00372209i
$363$	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
$367$	18.8463	+	70.3355i	0.0513524	+	0.191650i	0.986837	−	0.161717i	$-0.0517033\pi$
$367$	18.8463	+	70.3355i	0.0513524	+	0.191650i	−0.935485	+	0.353367i	$0.885037\pi$
$368$	69.3562	−	18.5839i	0.188468	−	0.0504998i
$369$	−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
$373$	89.0434	−	332.315i	0.238722	−	0.890924i	−0.737713	−	0.675114i	$-0.764094\pi$
$373$	89.0434	−	332.315i	0.238722	−	0.890924i	0.976435	−	0.215810i	$-0.0692391\pi$
$374$	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
$378$	−309.317	+	419.269i	−0.818299	+	1.10918i
$379$			33.5683i			0.0885708i	0.999019	+	0.0442854i	$0.0141011\pi$
$379$			33.5683i			0.0885708i	−0.999019	+	0.0442854i	$0.985899\pi$
$380$		0			0
$381$	−93.2950	+	161.592i	−0.244869	+	0.424125i
$382$	6.56383	+	24.4965i	0.0171828	+	0.0641271i
$383$	186.195	−	694.888i	0.486148	−	1.81433i	−0.0886883	−	0.996059i	$-0.528267\pi$
$383$	186.195	−	694.888i	0.486148	−	1.81433i	0.574836	−	0.818269i	$-0.305066\pi$
$384$		−	59.8178i		−	0.155776i
$385$		0			0
$386$	−300.725			−0.779079
$387$	249.796	+	66.9326i	0.645468	+	0.172953i
$388$	−125.052	+	33.5076i	−0.322299	+	0.0863598i
$389$	459.937	+	265.545i	1.18236	+	0.682634i	0.956558	−	0.291540i	$-0.0941678\pi$
$389$	459.937	+	265.545i	1.18236	+	0.682634i	0.225798	+	0.974174i	$0.427501\pi$
$390$		0			0
$391$	176.547			0.451526
$392$	−138.494	+	5.23259i	−0.353301	+	0.0133484i
$393$	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
$397$	259.731	+	69.5948i	0.654235	+	0.175302i	0.570643	−	0.821198i	$-0.306694\pi$
$397$	259.731	+	69.5948i	0.654235	+	0.175302i	0.0835924	+	0.996500i	$0.473361\pi$
$398$	−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	$-0.408596\pi$
$402$	−62.3569	−	232.719i	−0.155117	−	0.578904i
$403$	239.425	−	64.1537i	0.594107	−	0.159190i
$404$	−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
$408$	38.0666	−	142.067i	0.0933006	−	0.348203i
$409$	108.528	+	62.6584i	0.265348	+	0.153199i	0.626772	−	0.779203i	$-0.284376\pi$
$409$	108.528	+	62.6584i	0.265348	+	0.153199i	−0.361423	+	0.932402i	$0.617709\pi$
$410$		0			0
$411$	25.3188	+	43.8535i	0.0616030	+	0.106700i
$412$	−79.4772	+	79.4772i	−0.192906	+	0.192906i
$413$	525.029	+	59.0598i	1.27126	+	0.143002i
$414$			481.180i			1.16227i
$415$		0			0
$416$	−43.8178	+	75.8947i	−0.105331	+	0.182439i
$417$	72.5564	+	270.784i	0.173996	+	0.649362i
$418$	23.4590	−	87.5501i	0.0561219	−	0.209450i
$419$		−	116.269i		−	0.277492i	−0.990328	−	0.138746i	$-0.955693\pi$
$419$		−	116.269i		−	0.277492i	0.990328	−	0.138746i	$-0.0443072\pi$
$420$		0			0
$421$	534.449			1.26948			0.634738	−	0.772728i	$-0.281108\pi$
$421$	534.449			1.26948			0.634738	+	0.772728i	$0.281108\pi$
$422$	242.747	+	65.0438i	0.575229	+	0.154132i
$423$	384.846	−	103.119i	0.909801	−	0.243780i
$424$	27.8706	+	16.0911i	0.0657325	+	0.0379507i
$425$		0			0
$426$	−301.636			−0.708065
$427$	−579.680	−	427.660i	−1.35756	−	1.00155i
$428$	−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	$-0.0201994\pi$
$432$	203.351	+	54.4878i	0.470720	+	0.126129i
$433$	542.271	+	542.271i	1.25236	+	1.25236i	0.954660	+	0.297699i	$0.0962190\pi$
$433$	542.271	+	542.271i	1.25236	+	1.25236i	0.297699	+	0.954660i	$0.403781\pi$
$434$	57.8402	−	147.453i	0.133272	−	0.339754i
$435$		0			0
$436$	−37.2733	−	64.5592i	−0.0854892	−	0.148072i
$437$	−85.6333	−	319.588i	−0.195957	−	0.731322i
$438$	641.161	−	171.799i	1.46384	−	0.392234i
$439$	232.568	−	134.273i	0.529768	−	0.305862i	−0.211154	−	0.977453i	$-0.567722\pi$
$439$	232.568	−	134.273i	0.529768	−	0.305862i	0.740922	+	0.671591i	$0.234389\pi$
$440$		0			0
$441$	206.341	−	905.557i	0.467892	−	2.05342i
$442$	−152.364	+	152.364i	−0.344716	+	0.344716i
$443$	−22.8226	+	85.1751i	−0.0515183	+	0.192269i	−0.986889	−	0.161400i	$-0.948399\pi$
$443$	−22.8226	+	85.1751i	−0.0515183	+	0.192269i	0.935371	+	0.353668i	$0.115066\pi$
$444$	−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
$448$	22.4033	+	51.3234i	0.0500074	+	0.114561i
$449$		−	100.410i		−	0.223630i	−0.993729	−	0.111815i	$-0.964334\pi$
$449$		−	100.410i		−	0.223630i	0.993729	−	0.111815i	$-0.0356664\pi$
$450$		0			0
$451$	10.5109	−	18.2054i	0.0233057	−	0.0403666i
$452$	86.8473	+	324.119i	0.192140	+	0.717076i
$453$	−221.810	+	827.806i	−0.489647	+	1.82739i
$454$		−	58.6377i		−	0.129158i
$455$		0			0
$456$	−275.636			−0.604464
$457$	−671.954	−	180.050i	−1.47036	−	0.393982i	−0.567305	−	0.823508i	$-0.692014\pi$
$457$	−671.954	−	180.050i	−1.47036	−	0.393982i	−0.903055	+	0.429526i	$0.858681\pi$
$458$	−430.420	+	115.331i	−0.939781	+	0.251814i
$459$	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	$0.566646\pi$
$462$	20.3446	−	180.859i	0.0440359	−	0.391470i
$463$	−268.079	−	268.079i	−0.579005	−	0.579005i	0.355624	−	0.934629i	$-0.384268\pi$
$463$	−268.079	−	268.079i	−0.579005	−	0.579005i	−0.934629	+	0.355624i	$0.884268\pi$
$464$	−172.732	+	99.7267i	−0.372267	+	0.214928i
$465$		0			0
$466$	81.3623	−	140.924i	0.174597	−	0.302411i
$467$	186.445	+	49.9577i	0.399239	+	0.106976i	0.452851	−	0.891586i	$-0.350407\pi$
$467$	186.445	+	49.9577i	0.399239	+	0.106976i	−0.0536121	+	0.998562i	$0.517073\pi$
$468$	−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
$472$	−55.2532	−	206.208i	−0.117062	−	0.436881i
$473$	−45.8255	+	12.2789i	−0.0968826	+	0.0259596i
$474$	−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
$478$	−160.584	+	599.309i	−0.335951	+	1.25378i
$479$	−642.196	−	370.772i	−1.34070	−	0.774055i	−0.353792	−	0.935324i	$-0.615108\pi$
$479$	−642.196	−	370.772i	−1.34070	−	0.774055i	−0.986910	+	0.161269i	$0.948441\pi$
$480$		0			0
$481$	274.360	+	475.206i	0.570396	+	0.987954i
$482$	−156.182	+	156.182i	−0.324029	+	0.324029i
$483$	−265.784	−	608.881i	−0.550278	−	1.26062i
$484$			217.818i			0.450037i
$485$		0			0
$486$	−67.6356	+	117.148i	−0.139168	+	0.241046i
$487$	204.025	+	761.430i	0.418942	+	1.56351i	0.776807	+	0.629739i	$0.216838\pi$
$487$	204.025	+	761.430i	0.418942	+	1.56351i	−0.357865	+	0.933773i	$0.616495\pi$
$488$	−75.3345	+	281.152i	−0.154374	+	0.576132i
$489$			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	$0.575919\pi$
$492$	−61.7497	−	16.5458i	−0.125508	−	0.0336296i
$493$	−473.700	+	126.927i	−0.960851	+	0.257459i
$494$	349.716	+	201.909i	0.707928	+	0.408722i
$495$		0			0
$496$	−64.0000			−0.129032
$497$	258.802	−	112.970i	0.520728	−	0.227304i
$498$	382.271	+	382.271i	0.767613	+	0.767613i
$499$	−570.335	+	329.283i	−1.14296	+	0.659886i	−0.947161	−	0.320759i	$-0.896062\pi$
$499$	−570.335	+	329.283i	−1.14296	+	0.659886i	−0.195795	+	0.980645i	$0.562729\pi$
$500$		0			0
$501$	−500.930	+	867.636i	−0.999859	+	1.73181i
$502$	−253.707	−	67.9807i	−0.505393	−	0.135420i
$503$	−230.055	−	230.055i	−0.457367	−	0.457367i	0.440424	−	0.897790i	$-0.354828\pi$
$503$	−230.055	−	230.055i	−0.457367	−	0.457367i	−0.897790	+	0.440424i	$0.854828\pi$
$504$	−371.077	+	56.0000i	−0.736264	+	0.111111i
$505$		0			0
$506$	−44.1366	−	76.4469i	−0.0872266	−	0.151081i
$507$	97.1583	+	362.600i	0.191634	+	0.715187i
$508$	−68.1768	+	18.2679i	−0.134206	+	0.0359605i
$509$	105.300	−	60.7950i	0.206876	−	0.119440i	−0.392983	−	0.919546i	$-0.628557\pi$
$509$	105.300	−	60.7950i	0.206876	−	0.119440i	0.599859	+	0.800106i	$0.295223\pi$
$510$		0			0
$511$	−485.770	+	387.534i	−0.950627	+	0.758383i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	251.075	−	937.026i	0.489425	−	1.82656i
$514$	−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
$518$	348.440	+	39.1955i	0.672664	+	0.0756670i
$519$		−	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	$0.0114294\pi$
$522$	−345.943	−	1291.08i	−0.662725	−	2.47332i
$523$	−169.086	+	631.039i	−0.323301	+	1.20657i	0.592708	+	0.805417i	$0.298059\pi$
$523$	−169.086	+	631.039i	−0.323301	+	1.20657i	−0.916009	+	0.401158i	$0.868608\pi$
$524$			140.182i			0.267523i
$525$		0			0
$526$	464.523			0.883123
$527$	−151.999	−	40.7281i	−0.288424	−	0.0772829i
$528$	−71.0333	+	19.0333i	−0.134533	+	0.0360480i
$529$	179.070	+	103.386i	0.338507	+	0.195437i
$530$		0			0
$531$	1430.63			2.69422
$532$	236.494	−	103.233i	0.444538	−	0.194046i
$533$	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
$537$	−222.849	−	59.7122i	−0.414988	−	0.111196i
$538$	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	$0.967794\pi$
$542$	149.895	+	559.416i	0.276559	+	1.03213i
$543$	18.7998	−	5.03740i	0.0346221	−	0.00927697i
$544$	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	0.301608	−	0.953432i	$-0.402477\pi$
$547$	686.507	−	686.507i	1.25504	−	1.25504i	0.953432	−	0.301608i	$-0.0975232\pi$
$548$	−4.95764	+	18.5021i	−0.00904678	+	0.0337630i
$549$	−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
$553$	420.575	−	570.076i	0.760533	−	1.03088i
$554$		−	23.0021i		−	0.0415200i
$555$		0			0
$556$	−53.0217	+	91.8363i	−0.0953628	+	0.165173i
$557$	−11.7962	−	44.0239i	−0.0211780	−	0.0790376i	0.954528	−	0.298121i	$-0.0963599\pi$
$557$	−11.7962	−	44.0239i	−0.0211780	−	0.0790376i	−0.975706	+	0.219084i	$0.929693\pi$
$558$	111.005	−	414.276i	0.198934	−	0.742430i
$559$		−	211.366i		−	0.378115i
$560$		0			0
$561$	−180.816			−0.322310
$562$	−413.281	−	110.738i	−0.735375	−	0.197043i
$563$	−692.031	+	185.429i	−1.22919	+	0.329359i	−0.814262	−	0.580497i	$-0.802858\pi$
$563$	−692.031	+	185.429i	−1.22919	+	0.329359i	−0.414923	+	0.909857i	$0.636191\pi$
$564$	192.494	+	111.137i	0.341302	+	0.197051i
$565$		0			0
$566$	−224.087			−0.395913
$567$	84.2589	−	749.044i	0.148605	−	1.32107i
$568$	−80.6812	−	80.6812i	−0.142044	−	0.142044i
$569$	724.073	−	418.043i	1.27254	−	0.734699i	0.297071	−	0.954855i	$-0.403990\pi$
$569$	724.073	−	418.043i	1.27254	−	0.734699i	0.975464	+	0.220157i	$0.0706569\pi$
$570$		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	$0.805786\pi$
$572$	104.067	+	27.8846i	0.181935	+	0.0487493i
$573$	−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
$577$	−30.9295	−	115.431i	−0.0536040	−	0.200053i	0.933931	−	0.357454i	$-0.116355\pi$
$577$	−30.9295	−	115.431i	−0.0536040	−	0.200053i	−0.987535	+	0.157401i	$0.949688\pi$
$578$	−262.647	+	70.3762i	−0.454407	+	0.121758i
$579$	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
$583$	10.2400	−	38.2162i	0.0175643	−	0.0655509i
$584$	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	0.527416	−	0.849607i	$-0.323161\pi$
$587$	808.313	−	808.313i	1.37702	−	1.37702i	0.849607	−	0.527416i	$-0.176839\pi$
$588$	438.626	−	275.830i	0.745962	−	0.469098i
$589$			294.907i			0.500691i
$590$		0			0
$591$	−153.624	+	266.084i	−0.259939	+	0.450227i
$592$	−36.6692	−	136.851i	−0.0619413	−	0.231168i
$593$	23.1263	−	86.3085i	0.0389988	−	0.145546i	−0.943681	−	0.330856i	$-0.892662\pi$
$593$	23.1263	−	86.3085i	0.0389988	−	0.145546i	0.982680	+	0.185311i	$0.0593292\pi$
$594$		−	258.816i		−	0.435717i
$595$		0			0
$596$	−418.182			−0.701648
$597$	1540.00	+	412.642i	2.57956	+	0.691192i
$598$	379.880	−	101.788i	0.635250	−	0.170215i
$599$	−337.198	−	194.681i	−0.562934	−	0.325010i	0.191388	−	0.981514i	$-0.438701\pi$
$599$	−337.198	−	194.681i	−0.562934	−	0.325010i	−0.754322	+	0.656504i	$0.772034\pi$
$600$		0			0
$601$	478.638			0.796402			0.398201	−	0.917298i	$-0.369635\pi$
$601$	478.638			0.796402			0.398201	+	0.917298i	$0.369635\pi$
$602$	−108.688	−	80.1847i	−0.180544	−	0.133197i
$603$	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
$607$	618.509	+	165.729i	1.01896	+	0.273030i	0.729369	−	0.684121i	$-0.239814\pi$
$607$	618.509	+	165.729i	1.01896	+	0.273030i	0.289592	+	0.957150i	$0.406481\pi$
$608$	−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
$612$	96.4973	+	360.133i	0.157675	+	0.588453i
$613$	−1102.44	+	295.398i	−1.79843	+	0.481889i	−0.993732	−	0.111792i	$-0.964341\pi$
$613$	−1102.44	+	295.398i	−1.79843	+	0.481889i	−0.804701	+	0.593681i	$0.797674\pi$
$614$	−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	−0.719229	−	0.694773i	$-0.755505\pi$
$617$	−15.0890	+	15.0890i	−0.0244555	+	0.0244555i	0.694773	+	0.719229i	$0.255505\pi$
$618$	108.759	−	405.893i	0.175985	−	0.656785i
$619$	124.687	+	71.9881i	0.201433	+	0.116297i	0.597324	−	0.802000i	$-0.296231\pi$
$619$	124.687	+	71.9881i	0.201433	+	0.116297i	−0.395891	+	0.918298i	$0.629564\pi$
$620$		0			0
$621$	−472.383	−	818.191i	−0.760681	−	1.31754i
$622$	7.47723	−	7.47723i	0.0120213	−	0.0120213i
$623$	−343.789	+	465.995i	−0.551828	+	0.747985i
$624$		−	327.636i		−	0.525057i
$625$		0			0
$626$	−423.089	+	732.812i	−0.675861	+	1.17063i
$627$	87.7040	+	327.316i	0.139879	+	0.522035i
$628$	71.3075	−	266.123i	0.113547	−	0.423763i
$629$		−	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	$0.398615\pi$
$632$	−276.494	−	74.0864i	−0.437491	−	0.117225i
$633$	−907.536	+	243.173i	−1.43371	+	0.384160i
$634$	498.831	+	288.000i	0.786799	+	0.454259i
$635$		0			0
$636$	−120.317			−0.189177
$637$	−758.564	+	28.6601i	−1.19084	+	0.0449923i
$638$	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	$0.141642\pi$
$642$	433.279	+	116.097i	0.674889	+	0.180836i
$643$	−301.770	−	301.770i	−0.469316	−	0.469316i	0.432377	−	0.901693i	$-0.357675\pi$
$643$	−301.770	−	301.770i	−0.469316	−	0.469316i	−0.901693	+	0.432377i	$0.857675\pi$
$644$	91.7712	−	233.954i	0.142502	−	0.363283i
$645$		0			0
$646$	−128.182	−	222.018i	−0.198424	−	0.343681i
$647$	138.769	+	517.894i	0.214481	+	0.800454i	0.986349	+	0.164671i	$0.0526562\pi$
$647$	138.769	+	517.894i	0.214481	+	0.800454i	−0.771867	+	0.635784i	$0.780677\pi$
$648$	−294.190	+	78.8281i	−0.453998	+	0.121648i
$649$	−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
$653$	251.492	−	938.581i	0.385133	−	1.43734i	−0.452823	−	0.891600i	$-0.649583\pi$
$653$	251.492	−	938.581i	0.385133	−	1.43734i	0.837957	−	0.545737i	$-0.183750\pi$
$654$	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
$658$	−206.783	−	23.2607i	−0.314260	−	0.0353506i
$659$		−	735.842i		−	1.11660i	−0.829638	−	0.558302i	$-0.811453\pi$
$659$		−	735.842i		−	1.11660i	0.829638	−	0.558302i	$-0.188547\pi$
$660$		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	$0.177788\pi$
$662$	86.6139	+	323.247i	0.130837	+	0.488289i
$663$	208.500	−	778.131i	0.314479	−	1.17365i
$664$			204.499i			0.307980i
$665$		0			0
$666$	949.449			1.42560
$667$	864.583	+	231.664i	1.29623	+	0.347323i
$668$	−366.062	+	98.0861i	−0.547997	+	0.146835i
$669$	−1613.12	−	931.336i	−2.41124	−	1.39213i
$670$		0			0
$671$	357.837			0.533290
$672$	−168.475	−	124.293i	−0.250707	−	0.184960i
$673$	122.772	+	122.772i	0.182425	+	0.182425i	0.792412	−	0.609986i	$-0.208825\pi$
$673$	122.772	+	122.772i	0.182425	+	0.182425i	−0.609986	+	0.792412i	$0.708825\pi$
$674$	547.798	−	316.271i	0.812756	−	0.469245i
$675$		0			0
$676$	−71.0000	+	122.976i	−0.105030	+	0.181917i
$677$	−333.808	−	89.4436i	−0.493069	−	0.132118i	0.00371227	−	0.999993i	$-0.498818\pi$
$677$	−333.808	−	89.4436i	−0.493069	−	0.132118i	−0.496782	+	0.867876i	$0.665485\pi$
$678$	−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
$682$	20.3640	+	75.9997i	0.0298593	+	0.111436i
$683$	685.231	−	183.607i	1.00327	−	0.268824i	0.280453	−	0.959868i	$-0.409515\pi$
$683$	685.231	−	183.607i	1.00327	−	0.268824i	0.722813	+	0.691043i	$0.242849\pi$
$684$	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
$688$	−14.1249	+	52.7150i	−0.0205304	+	0.0766206i
$689$	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
$693$	184.572	+	422.834i	0.266338	+	0.610150i
$694$		−	200.657i		−	0.289132i
$695$		0			0
$696$	372.840	−	645.777i	0.535689	−	0.927841i
$697$	−15.3890	−	57.4325i	−0.0220789	−	0.0823995i
$698$	−109.391	+	408.252i	−0.156720	+	0.584888i
$699$			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	$0.384808\pi$
$702$	1113.80	+	298.442i	1.58661	+	0.425131i
$703$	−630.600	+	168.969i	−0.897013	+	0.240354i
$704$	−24.0909	−	13.9089i	−0.0342201	−	0.0197570i
$705$		0			0
$706$	48.7246			0.0690151
$707$	−112.286	+	998.197i	−0.158820	+	1.41188i
$708$	564.360	+	564.360i	0.797119	+	0.797119i
$709$	−282.281	+	162.975i	−0.398140	+	0.229866i	−0.685681	−	0.727902i	$-0.740496\pi$
$709$	−282.281	+	162.975i	−0.398140	+	0.229866i	0.287541	+	0.957768i	$0.407162\pi$
$710$		0			0
$711$	959.132	−	1661.27i	1.34899	−	2.33652i
$712$	226.014	+	60.5602i	0.317435	+	0.0850564i
$713$	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
$717$	−600.363	−	2240.58i	−0.837326	−	3.12494i
$718$	672.203	−	180.116i	0.936216	−	0.250858i
$719$	543.130	−	313.576i	0.755396	−	0.436128i	−0.0722443	−	0.997387i	$-0.523016\pi$
$719$	543.130	−	313.576i	0.755396	−	0.436128i	0.827640	+	0.561259i	$0.189683\pi$
$720$		0			0
$721$	58.7029	+	388.988i	0.0814187	+	0.539511i
$722$	21.2733	−	21.2733i	0.0294644	−	0.0294644i
$723$	213.724	−	797.629i	0.295607	−	1.10322i
$724$	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	−0.700457	−	0.713695i	$-0.747020\pi$
$727$	9.62370	−	9.62370i	0.0132376	−	0.0132376i	0.713695	+	0.700457i	$0.247020\pi$
$728$	122.708	+	281.110i	0.168555	+	0.386140i
$729$			463.404i			0.635670i
$730$		0			0
$731$	−67.0932	+	116.209i	−0.0917827	+	0.158972i
$732$	−281.647	−	1051.12i	−0.384763	−	1.43596i
$733$	−56.6180	+	211.301i	−0.0772415	+	0.288269i	−0.993732	−	0.111787i	$-0.964343\pi$
$733$	−56.6180	+	211.301i	−0.0772415	+	0.288269i	0.916491	+	0.400056i	$0.131009\pi$
$734$		−	102.978i		−	0.140297i
$735$		0			0
$736$	−101.545			−0.137968
$737$	−108.224	−	28.9986i	−0.146844	−	0.0393468i
$738$	156.533	−	41.9429i	0.212104	−	0.0568332i
$739$	467.750	+	270.055i	0.632949	+	0.365434i	0.781893	−	0.623412i	$-0.214254\pi$
$739$	467.750	+	270.055i	0.632949	+	0.365434i	−0.148944	+	0.988846i	$0.547587\pi$
$740$		0			0
$741$	−1509.72			−2.03741
$742$	103.231	−	45.0617i	0.139126	−	0.0607301i
$743$	−142.376	−	142.376i	−0.191624	−	0.191624i	0.604774	−	0.796397i	$-0.293264\pi$
$743$	−142.376	−	142.376i	−0.191624	−	0.191624i	−0.796397	+	0.604774i	$0.793264\pi$
$744$	207.215	−	119.636i	0.278515	−	0.160801i
$745$		0			0
$746$	−243.271	+	421.358i	−0.326101	+	0.564823i
$747$	−1323.74	−	354.694i	−1.77207	−	0.474824i
$748$	−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	$0.537286\pi$
$752$	21.7615	+	81.2149i	0.0289381	+	0.107999i
$753$	948.514	−	254.153i	1.25965	−	0.337521i
$754$	−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	−0.482833	−	0.875713i	$-0.660392\pi$
$757$	297.410	−	297.410i	0.392880	−	0.392880i	0.875713	+	0.482833i	$0.160392\pi$
$758$	12.2869	−	45.8552i	0.0162096	−	0.0604950i
$759$	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
$763$	−259.278	−	29.1658i	−0.339814	−	0.0382251i
$764$		−	35.8654i		−	0.0469443i
$765$		0			0
$766$	−508.693	+	881.082i	−0.664090	+	1.15024i
$767$	−302.634	−	1129.45i	−0.394569	−	1.47255i
$768$	−21.8948	+	81.7126i	−0.0285089	+	0.106397i
$769$		−	1006.45i		−	1.30877i	−0.756160	−	0.654387i	$-0.772927\pi$
$769$		−	1006.45i		−	1.30877i	0.756160	−	0.654387i	$-0.227073\pi$
$770$		0			0
$771$	1261.27			1.63588
$772$	410.797	+	110.073i	0.532121	+	0.142581i
$773$	776.703	−	208.117i	1.00479	−	0.269233i	0.281339	−	0.959608i	$-0.409221\pi$
$773$	776.703	−	208.117i	1.00479	−	0.269233i	0.723451	+	0.690376i	$0.242555\pi$
$774$	−316.729	−	182.863i	−0.409210	−	0.236258i
$775$		0			0
$776$	183.089			0.235939
$777$	−1201.42	+	524.437i	−1.54624	+	0.674951i
$778$	−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
$782$	−241.167	−	64.6205i	−0.308398	−	0.0826350i
$783$	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
$787$	172.475	+	643.687i	0.219156	+	0.817900i	0.984662	+	0.174472i	$0.0558218\pi$
$787$	172.475	+	643.687i	0.219156	+	0.817900i	−0.765507	+	0.643428i	$0.777512\pi$
$788$	−112.263	+	30.0808i	−0.142466	+	0.0381736i
$789$	−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
$793$	−412.624	+	1539.93i	−0.520333	+	1.94191i
$794$	−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	−0.822593	−	0.568631i	$-0.807473\pi$
$797$	−202.408	+	202.408i	−0.253962	+	0.253962i	0.568631	+	0.822593i	$0.307473\pi$
$798$	−572.732	+	776.320i	−0.717709	+	0.972832i
$799$			206.733i			0.258740i
$800$		0			0
$801$	−784.020	+	1357.96i	−0.978801	+	1.69533i
$802$	202.244	+	754.784i	0.252174	+	0.941127i
$803$	79.8936	−	298.167i	0.0994939	−	0.371316i
$804$			340.725i			0.423787i
$805$		0			0
$806$	−350.542			−0.434916
$807$	−1461.53	−	391.617i	−1.81107	−	0.485275i
$808$	392.046	−	105.049i	0.485206	−	0.130011i
$809$	−138.014	−	79.6822i	−0.170598	−	0.0984947i	0.412270	−	0.911062i	$-0.364736\pi$
$809$	−138.014	−	79.6822i	−0.170598	−	0.0984947i	−0.582868	+	0.812567i	$0.698069\pi$
$810$		0			0
$811$	741.545			0.914358			0.457179	−	0.889375i	$-0.348860\pi$
$811$	741.545			0.914358			0.457179	+	0.889375i	$0.348860\pi$
$812$	−78.0346	+	693.712i	−0.0961018	+	0.854325i
$813$	−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
$817$	242.906	+	65.0866i	0.297315	+	0.0796654i
$818$	−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	$-0.577433\pi$
$822$	−18.5347	−	69.1724i	−0.0225483	−	0.0841513i
$823$	−587.715	+	157.478i	−0.714114	+	0.191346i	−0.597544	−	0.801836i	$-0.703857\pi$
$823$	−587.715	+	157.478i	−0.714114	+	0.191346i	−0.116570	+	0.993182i	$0.537190\pi$
$824$	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	−0.261426	+	0.965223i	$0.584193\pi$
$827$	−1014.44	+	1014.44i	−1.22665	+	1.22665i	−0.965223	+	0.261426i	$0.915807\pi$
$828$	176.124	−	657.304i	0.212710	−	0.793846i
$829$	−344.517	−	198.907i	−0.415581	−	0.239936i	0.277604	−	0.960696i	$-0.410460\pi$
$829$	−344.517	−	198.907i	−0.415581	−	0.239936i	−0.693185	+	0.720760i	$0.743793\pi$
$830$		0			0
$831$	42.9979	+	74.4746i	0.0517424	+	0.0896204i
$832$	87.6356	−	87.6356i	0.105331	−	0.105331i
$833$	426.154	+	225.030i	0.511589	+	0.270145i
$834$		−	396.455i		−	0.475366i
$835$		0			0
$836$	−64.0911	+	111.009i	−0.0766640	+	0.132786i
$837$	217.951	+	813.404i	0.260396	+	0.971809i
$838$	−42.5575	+	158.827i	−0.0507846	+	0.189531i
$839$			1475.70i			1.75888i	0.476011	+	0.879439i	$0.342082\pi$
$839$			1475.70i			1.75888i	−0.476011	+	0.879439i	$0.657918\pi$
$840$		0			0
$841$	−1645.35			−1.95643
$842$	−730.071	−	195.622i	−0.867068	−	0.232330i
$843$	1545.10	−	414.007i	1.83285	−	0.491112i
$844$	−307.790	−	177.703i	−0.364681	−	0.210548i
$845$		0			0
$846$	−563.453			−0.666021
$847$	613.477	+	452.594i	0.724295	+	0.534350i
$848$	−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
$852$	412.042	+	110.406i	0.483617	+	0.129585i
$853$	−307.404	−	307.404i	−0.360380	−	0.360380i	0.503573	−	0.863953i	$-0.332018\pi$
$853$	−307.404	−	307.404i	−0.360380	−	0.360380i	−0.863953	+	0.503573i	$0.832018\pi$
$854$	635.323	+	796.372i	0.743938	+	0.932520i
$855$		0			0
$856$	84.8395	+	146.946i	0.0991116	+	0.171666i
$857$	−311.386	−	1162.11i	−0.363344	−	1.35602i	−0.869651	−	0.493666i	$-0.835656\pi$
$857$	−311.386	−	1162.11i	−0.363344	−	1.35602i	0.506307	−	0.862353i	$-0.331010\pi$
$858$	−389.066	+	104.250i	−0.453456	+	0.121503i
$859$	795.008	−	458.998i	0.925504	−	0.534340i	0.0401170	−	0.999195i	$-0.487227\pi$
$859$	795.008	−	458.998i	0.925504	−	0.534340i	0.885387	+	0.464855i	$0.153894\pi$
$860$		0			0
$861$	−174.908	+	139.536i	−0.203145	+	0.162063i
$862$	−477.473	+	477.473i	−0.553913	+	0.553913i
$863$	−328.625	+	1226.45i	−0.380794	+	1.42114i	0.463897	+	0.885889i	$0.346451\pi$
$863$	−328.625	+	1226.45i	−0.380794	+	1.42114i	−0.844691	+	0.535254i	$0.820216\pi$
$864$	−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
$868$	−132.983	+	180.254i	−0.153206	+	0.207666i
$869$			351.909i			0.404958i
$870$		0			0
$871$	249.588	−	432.299i	0.286553	−	0.496325i
$872$	27.2859	+	101.833i	0.0312912	+	0.116780i
$873$	−317.559	+	1185.15i	−0.363756	+	1.35756i
$874$			467.909i			0.535365i
$875$		0			0
$876$	−938.725			−1.07160
$877$	389.382	+	104.335i	0.443993	+	0.118968i	0.473888	−	0.880585i	$-0.342850\pi$
$877$	389.382	+	104.335i	0.443993	+	0.118968i	−0.0298940	+	0.999553i	$0.509517\pi$
$878$	−366.841	+	98.2949i	−0.417815	+	0.111953i
$879$	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	$0.438485\pi$
$882$	−613.323	+	1161.49i	−0.695378	+	1.31688i
$883$	455.410	+	455.410i	0.515753	+	0.515753i	0.916283	−	0.400530i	$-0.131174\pi$
$883$	455.410	+	455.410i	0.515753	+	0.515753i	−0.400530	+	0.916283i	$0.631174\pi$
$884$	263.903	−	152.364i	0.298533	−	0.172358i
$885$		0			0
$886$	62.3525	−	107.998i	0.0703753	−	0.121894i
$887$	389.861	+	104.463i	0.439528	+	0.117771i	0.471795	−	0.881708i	$-0.343606\pi$
$887$	389.861	+	104.463i	0.439528	+	0.117771i	−0.0322675	+	0.999479i	$0.510273\pi$
$888$	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
$892$	−182.363	−	680.589i	−0.204443	−	0.762992i
$893$	374.232	−	100.275i	0.419072	−	0.112290i
$894$	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
$898$	−36.7526	+	137.163i	−0.0409272	+	0.152742i
$899$	−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
$903$	501.792	+	56.4458i	0.555694	+	0.0625092i
$904$		−	474.542i		−	0.524936i
$905$		0			0
$906$	605.996	−	1049.62i	0.668870	−	1.15852i
$907$	157.885	+	589.236i	0.174074	+	0.649653i	0.996707	+	0.0810812i	$0.0258373\pi$
$907$	157.885	+	589.236i	0.174074	+	0.649653i	−0.822633	+	0.568572i	$0.807496\pi$
$908$	−21.4629	+	80.1006i	−0.0236375	+	0.0882165i
$909$			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	$0.628566\pi$
$912$	376.525	+	100.890i	0.412857	+	0.110625i
$913$	242.841	−	65.0692i	0.265982	−	0.0712696i
$914$	852.004	+	491.905i	0.932171	+	0.538189i
$915$		0			0
$916$	630.178			0.687967
$917$	394.819	+	291.279i	0.430555	+	0.317643i
$918$	−517.631	−	517.631i	−0.563869	−	0.563869i
$919$	222.629	−	128.535i	0.242251	−	0.139864i	−0.373960	−	0.927445i	$-0.622000\pi$
$919$	222.629	−	128.535i	0.242251	−	0.139864i	0.616211	+	0.787581i	$0.288667\pi$
$920$		0			0
$921$	906.995	−	1570.96i	0.984793	−	1.70571i
$922$	261.779	+	70.1435i	0.283925	+	0.0760776i
$923$	−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
$927$	275.699	+	1028.92i	0.297410	+	1.10995i
$928$	272.458	−	73.0050i	0.293597	−	0.0786692i
$929$	1104.77	−	637.841i	1.18921	−	0.686588i	0.231080	−	0.972935i	$-0.425774\pi$
$929$	1104.77	−	637.841i	1.18921	−	0.686588i	0.958126	+	0.286346i	$0.0924408\pi$
$930$		0			0
$931$	200.650	−	880.581i	0.215521	−	0.945845i
$932$	−162.725	+	162.725i	−0.174597	+	0.174597i
$933$	−10.2320	+	38.1865i	−0.0109668	+	0.0409287i
$934$	−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	−0.318970	−	0.947765i	$-0.603337\pi$
$937$	589.180	−	589.180i	0.628794	−	0.628794i	0.947765	+	0.318970i	$0.103337\pi$
$938$	−127.610	−	292.340i	−0.136045	−	0.311663i
$939$		−	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	$0.200094\pi$
$942$	266.591	+	994.932i	0.283005	+	1.05619i
$943$	−28.0875	+	104.824i	−0.0297853	+	0.111160i
$944$			301.909i			0.319819i
$945$		0			0
$946$	67.0932			0.0709230
$947$	−1496.37	−	400.951i	−1.58011	−	0.423390i	−0.641153	−	0.767413i	$-0.721544\pi$
$947$	−1496.37	−	400.951i	−1.58011	−	0.423390i	−0.938961	+	0.344023i	$0.888210\pi$
$948$	1033.71	−	276.980i	1.09041	−	0.292173i
$949$	1191.02	+	687.636i	1.25503	+	0.724590i
$950$		0			0
$951$	−2153.44			−2.26440
$952$	21.7670	−	193.504i	0.0228645	−	0.203261i
$953$	−1139.41	−	1139.41i	−1.19560	−	1.19560i	−0.975471	−	0.220128i	$-0.929353\pi$
$953$	−1139.41	−	1139.41i	−1.19560	−	1.19560i	−0.220128	−	0.975471i	$-0.570647\pi$
$954$	264.136	−	152.499i	0.276872	−	0.159852i
$955$		0			0
$956$	438.725	−	759.893i	0.458917	−	0.794868i
$957$	−885.490	−	237.266i	−0.925277	−	0.247927i
$958$	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
$962$	−200.846	−	749.566i	−0.208779	−	0.779175i
$963$	−1098.34	+	294.300i	−1.14054	+	0.305608i
$964$	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	−0.605289	−	0.796006i	$-0.706942\pi$
$967$	184.424	−	184.424i	0.190718	−	0.190718i	0.796006	+	0.605289i	$0.206942\pi$
$968$	79.7268	−	297.545i	0.0823624	−	0.307381i
$969$	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
$973$	148.483	+	340.157i	0.152603	+	0.349596i
$974$		−	1114.81i		−	1.14457i
$975$		0			0
$976$	205.818	−	356.487i	0.210879	−	0.365253i
$977$	272.355	+	1016.44i	0.278767	+	1.04037i	0.953275	+	0.302105i	$0.0976894\pi$
$977$	272.355	+	1016.44i	0.278767	+	1.04037i	−0.674507	+	0.738268i	$0.735644\pi$
$978$	183.993	−	686.670i	0.188131	−	0.702116i
$979$		−	287.659i		−	0.293830i
$980$		0			0
$981$	−706.495			−0.720178
$982$	316.918	+	84.9179i	0.322727	+	0.0864744i
$983$	691.062	−	185.170i	0.703014	−	0.188372i	0.110434	−	0.993884i	$-0.464776\pi$
$983$	691.062	−	185.170i	0.703014	−	0.188372i	0.592580	+	0.805512i	$0.298109\pi$
$984$	78.2955	+	45.2039i	0.0795686	+	0.0459390i
$985$		0			0
$986$	693.545			0.703392
$987$	712.989	−	311.228i	0.722380	−	0.315328i
$988$	−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	$0.940327\pi$
$992$	87.4256	+	23.4256i	0.0881307	+	0.0236145i
$993$	−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
$997$	−46.9331	−	175.157i	−0.0470743	−	0.175684i	0.938386	−	0.345588i	$-0.112321\pi$
$997$	−46.9331	−	175.157i	−0.0470743	−	0.175684i	−0.985460	+	0.169905i	$0.945654\pi$
$998$	899.618	−	241.052i	0.901421	−	0.241535i
$999$	−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.193.2		8
5.2	odd	4	inner	350.3.p.c.207.1		8
5.3	odd	4		70.3.l.a.67.2	yes	8
5.4	even	2		70.3.l.a.53.1	yes	8
7.2	even	3	inner	350.3.p.c.93.1		8
35.2	odd	12	inner	350.3.p.c.107.2		8
35.3	even	12		490.3.f.e.197.1		4
35.4	even	6		490.3.f.l.393.2		4
35.9	even	6		70.3.l.a.23.2	✓	8
35.18	odd	12		490.3.f.l.197.2		4
35.23	odd	12		70.3.l.a.37.1	yes	8
35.24	odd	6		490.3.f.e.393.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.l.a.23.2	✓	8	35.9	even	6
70.3.l.a.37.1	yes	8	35.23	odd	12
70.3.l.a.53.1	yes	8	5.4	even	2
70.3.l.a.67.2	yes	8	5.3	odd	4
350.3.p.c.93.1		8	7.2	even	3	inner
350.3.p.c.107.2		8	35.2	odd	12	inner
350.3.p.c.193.2		8	1.1	even	1	trivial
350.3.p.c.207.1		8	5.2	odd	4	inner
490.3.f.e.197.1		4	35.3	even	12
490.3.f.e.393.1		4	35.24	odd	6
490.3.f.l.197.2		4	35.18	odd	12
490.3.f.l.393.2		4	35.4	even	6

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

L-functions

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