LMFDB - Embedded newform 308.4.i.a.221.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,4,Mod(177,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("308.177");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	308.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$18.1725882818$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 194 x^{18} - 432 x^{17} + 24205 x^{16} - 47156 x^{15} + 1632616 x^{14} + \cdots + 7996651776 $ x^20 - 4x^19 + 194x^18 - 432x^17 + 24205x^16 - 47156x^15 + 1632616x^14 - 1838210x^13 + 75876043x^12 - 82333872x^11 + 1801672853x^10 - 471307576x^9 + 27041915377x^8 - 14255551602x^7 + 176709560868x^6 - 669217680x^5 + 678547482048x^4 - 436737562560x^3 + 226025971776x^2 - 48231013248*x + 7996651776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.10
Root			$5.05636 + 8.75787i$ of defining polynomial
Character	$\chi$	$=$	308.221
Dual form			308.4.i.a.177.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.55636 - 7.89185i) q^{3} +(-4.96059 - 8.59200i) q^{5} +(-7.98145 + 16.7122i) q^{7} +(-28.0208 - 48.5335i) q^{9} +(-5.50000 + 9.52628i) q^{11} -15.7278 q^{13} -90.4090 q^{15} +(-37.3293 + 64.6563i) q^{17} +(-62.3286 - 107.956i) q^{19} +(95.5235 + 139.135i) q^{21} +(-62.6087 - 108.441i) q^{23} +(13.2850 - 23.0104i) q^{25} -264.649 q^{27} -79.6577 q^{29} +(-112.549 + 194.941i) q^{31} +(50.1200 + 86.8103i) q^{33} +(183.184 - 14.3257i) q^{35} +(68.3380 + 118.365i) q^{37} +(-71.6613 + 124.121i) q^{39} +229.968 q^{41} +481.487 q^{43} +(-278.000 + 481.510i) q^{45} +(-76.5479 - 132.585i) q^{47} +(-215.593 - 266.775i) q^{49} +(340.172 + 589.194i) q^{51} +(-151.797 + 262.920i) q^{53} +109.133 q^{55} -1135.97 q^{57} +(-199.782 + 346.032i) q^{59} +(-279.508 - 484.123i) q^{61} +(1034.75 - 80.9213i) q^{63} +(78.0190 + 135.133i) q^{65} +(456.175 - 790.118i) q^{67} -1141.07 q^{69} -544.084 q^{71} +(399.846 - 692.554i) q^{73} +(-121.063 - 209.687i) q^{75} +(-115.307 - 167.950i) q^{77} +(-28.5350 - 49.4242i) q^{79} +(-449.272 + 778.162i) q^{81} -448.212 q^{83} +740.702 q^{85} +(-362.949 + 628.647i) q^{87} +(-618.816 - 1071.82i) q^{89} +(125.530 - 262.845i) q^{91} +(1025.63 + 1776.44i) q^{93} +(-618.373 + 1071.05i) q^{95} -1506.36 q^{97} +616.458 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} - 10 q^{5} - 20 q^{7} - 104 q^{9} - 110 q^{11} + 16 q^{13} + 108 q^{15} - 166 q^{17} - 342 q^{19} - 42 q^{21} + 54 q^{23} - 198 q^{25} + 612 q^{27} - 160 q^{29} - 492 q^{31} - 66 q^{33} + 310 q^{35}+ \cdots + 2288 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 - 10 * q^5 - 20 * q^7 - 104 * q^9 - 110 * q^11 + 16 * q^13 + 108 * q^15 - 166 * q^17 - 342 * q^19 - 42 * q^21 + 54 * q^23 - 198 * q^25 + 612 * q^27 - 160 * q^29 - 492 * q^31 - 66 * q^33 + 310 * q^35 - 258 * q^37 + 418 * q^39 + 1268 * q^41 - 548 * q^43 - 138 * q^45 - 312 * q^47 + 572 * q^49 + 196 * q^51 - 656 * q^53 + 220 * q^55 - 1476 * q^57 - 934 * q^59 + 228 * q^61 - 1270 * q^63 - 524 * q^65 - 478 * q^67 + 3144 * q^69 + 276 * q^71 + 364 * q^73 - 234 * q^75 - 154 * q^77 + 616 * q^79 - 4082 * q^81 - 264 * q^83 - 992 * q^85 + 2120 * q^87 - 1906 * q^89 - 94 * q^91 + 2984 * q^93 - 2322 * q^95 + 2700 * q^97 + 2288 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	4.55636	−	7.89185i	0.876872	−	1.51879i	0.0221168	−	0.999755i	$-0.492959\pi$
$3$	4.55636	−	7.89185i	0.876872	−	1.51879i	0.854755	−	0.519031i	$-0.173707\pi$
$4$		0			0
$5$	−4.96059	−	8.59200i	−0.443689	−	0.768492i	0.554271	−	0.832336i	$-0.312997\pi$
$5$	−4.96059	−	8.59200i	−0.443689	−	0.768492i	−0.997960	+	0.0638446i	$0.979664\pi$
$6$		0			0
$7$	−7.98145	+	16.7122i	−0.430958	+	0.902372i
$7$	−7.98145	+	16.7122i	−0.430958	+	0.902372i
$8$		0			0
$9$	−28.0208	−	48.5335i	−1.03781	−	1.79754i
$10$		0			0
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$12$		0			0
$13$	−15.7278			−0.335546			−0.167773	−	0.985826i	$-0.553658\pi$
$13$	−15.7278			−0.335546			−0.167773	+	0.985826i	$0.553658\pi$
$14$		0			0
$15$	−90.4090			−1.55623
$16$		0			0
$17$	−37.3293	+	64.6563i	−0.532570	+	0.922438i	0.466707	+	0.884412i	$0.345440\pi$
$17$	−37.3293	+	64.6563i	−0.532570	+	0.922438i	−0.999277	+	0.0380260i	$0.987893\pi$
$18$		0			0
$19$	−62.3286	−	107.956i	−0.752587	−	1.30352i	−0.946565	−	0.322513i	$-0.895472\pi$
$19$	−62.3286	−	107.956i	−0.752587	−	1.30352i	0.193978	−	0.981006i	$-0.437861\pi$
$20$		0			0
$21$	95.5235	+	139.135i	0.992616	+	1.44580i
$22$		0			0
$23$	−62.6087	−	108.441i	−0.567601	−	0.983113i	−0.996803	−	0.0799047i	$-0.974538\pi$
$23$	−62.6087	−	108.441i	−0.567601	−	0.983113i	0.429202	−	0.903209i	$-0.358795\pi$
$24$		0			0
$25$	13.2850	−	23.0104i	0.106280	−	0.184083i
$26$		0			0
$27$	−264.649			−1.88636
$28$		0			0
$29$	−79.6577			−0.510071			−0.255036	−	0.966932i	$-0.582087\pi$
$29$	−79.6577			−0.510071			−0.255036	+	0.966932i	$0.582087\pi$
$30$		0			0
$31$	−112.549	+	194.941i	−0.652079	+	1.12943i	0.330539	+	0.943792i	$0.392769\pi$
$31$	−112.549	+	194.941i	−0.652079	+	1.12943i	−0.982618	+	0.185641i	$0.940564\pi$
$32$		0			0
$33$	50.1200	+	86.8103i	0.264387	+	0.457931i
$34$		0			0
$35$	183.184	−	14.3257i	0.884677	−	0.0691852i
$36$		0			0
$37$	68.3380	+	118.365i	0.303640	+	0.525921i	0.976958	−	0.213433i	$-0.0684645\pi$
$37$	68.3380	+	118.365i	0.303640	+	0.525921i	−0.673317	+	0.739354i	$0.735131\pi$
$38$		0			0
$39$	−71.6613	+	124.121i	−0.294231	+	0.509623i
$40$		0			0
$41$	229.968			0.875973			0.437986	−	0.898982i	$-0.355692\pi$
$41$	229.968			0.875973			0.437986	+	0.898982i	$0.355692\pi$
$42$		0			0
$43$	481.487			1.70758			0.853792	−	0.520615i	$-0.174297\pi$
$43$	481.487			1.70758			0.853792	+	0.520615i	$0.174297\pi$
$44$		0			0
$45$	−278.000	+	481.510i	−0.920928	+	1.59509i
$46$		0			0
$47$	−76.5479	−	132.585i	−0.237567	−	0.411479i	0.722448	−	0.691425i	$-0.243017\pi$
$47$	−76.5479	−	132.585i	−0.237567	−	0.411479i	−0.960016	+	0.279946i	$0.909683\pi$
$48$		0			0
$49$	−215.593	−	266.775i	−0.628551	−	0.777768i
$50$		0			0
$51$	340.172	+	589.194i	0.933991	+	1.61772i
$52$		0			0
$53$	−151.797	+	262.920i	−0.393414	+	0.681413i	−0.992897	−	0.118974i	$-0.962039\pi$
$53$	−151.797	+	262.920i	−0.393414	+	0.681413i	0.599483	+	0.800387i	$0.295373\pi$
$54$		0			0
$55$	109.133			0.267554
$56$		0			0
$57$	−1135.97			−2.63969
$58$		0			0
$59$	−199.782	+	346.032i	−0.440837	+	0.763551i	−0.997752	−	0.0670179i	$-0.978652\pi$
$59$	−199.782	+	346.032i	−0.440837	+	0.763551i	0.556915	+	0.830569i	$0.311985\pi$
$60$		0			0
$61$	−279.508	−	484.123i	−0.586678	−	1.01616i	−0.994664	−	0.103168i	$-0.967102\pi$
$61$	−279.508	−	484.123i	−0.586678	−	1.01616i	0.407985	−	0.912988i	$-0.366231\pi$
$62$		0			0
$63$	1034.75	−	80.9213i	2.06930	−	0.161827i
$64$		0			0
$65$	78.0190	+	135.133i	0.148878	+	0.257864i
$66$		0			0
$67$	456.175	−	790.118i	0.831801	−	1.44072i	−0.0648080	−	0.997898i	$-0.520643\pi$
$67$	456.175	−	790.118i	0.831801	−	1.44072i	0.896609	−	0.442823i	$-0.146023\pi$
$68$		0			0
$69$	−1141.07			−1.99085
$70$		0			0
$71$	−544.084			−0.909449			−0.454724	−	0.890632i	$-0.650262\pi$
$71$	−544.084			−0.909449			−0.454724	+	0.890632i	$0.650262\pi$
$72$		0			0
$73$	399.846	−	692.554i	0.641075	−	1.11037i	−0.344119	−	0.938926i	$-0.611822\pi$
$73$	399.846	−	692.554i	0.641075	−	1.11037i	0.985193	−	0.171448i	$-0.0548445\pi$
$74$		0			0
$75$	−121.063	−	209.687i	−0.186388	−	0.322834i
$76$		0			0
$77$	−115.307	−	167.950i	−0.170655	−	0.248568i
$78$		0			0
$79$	−28.5350	−	49.4242i	−0.0406385	−	0.0703880i	0.844991	−	0.534781i	$-0.179606\pi$
$79$	−28.5350	−	49.4242i	−0.0406385	−	0.0703880i	−0.885629	+	0.464393i	$0.846273\pi$
$80$		0			0
$81$	−449.272	+	778.162i	−0.616285	+	1.06744i
$82$		0			0
$83$	−448.212			−0.592743			−0.296372	−	0.955073i	$-0.595777\pi$
$83$	−448.212			−0.592743			−0.296372	+	0.955073i	$0.595777\pi$
$84$		0			0
$85$	740.702			0.945181
$86$		0			0
$87$	−362.949	+	628.647i	−0.447267	+	0.774690i
$88$		0			0
$89$	−618.816	−	1071.82i	−0.737016	−	1.27655i	−0.953833	−	0.300337i	$-0.902901\pi$
$89$	−618.816	−	1071.82i	−0.737016	−	1.27655i	0.216817	−	0.976212i	$-0.430432\pi$
$90$		0			0
$91$	125.530	−	262.845i	0.144606	−	0.302787i
$92$		0			0
$93$	1025.63	+	1776.44i	1.14358	+	1.98074i
$94$		0			0
$95$	−618.373	+	1071.05i	−0.667829	+	1.15671i
$96$		0			0
$97$	−1506.36			−1.57678			−0.788389	−	0.615177i	$-0.789085\pi$
$97$	−1506.36			−1.57678			−0.788389	+	0.615177i	$0.789085\pi$
$98$		0			0
$99$	616.458			0.625822
$100$		0			0
$101$	451.249	−	781.587i	0.444564	−	0.770008i	−0.553458	−	0.832877i	$-0.686692\pi$
$101$	451.249	−	781.587i	0.444564	−	0.770008i	0.998022	+	0.0628696i	$0.0200252\pi$
$102$		0			0
$103$	−301.466	−	522.154i	−0.288392	−	0.499509i	0.685034	−	0.728511i	$-0.259787\pi$
$103$	−301.466	−	522.154i	−0.288392	−	0.499509i	−0.973426	+	0.229002i	$0.926454\pi$
$104$		0			0
$105$	721.594	−	1510.93i	0.670671	−	1.40430i
$106$		0			0
$107$	237.118	+	410.701i	0.214234	+	0.371065i	0.953035	−	0.302859i	$-0.0979410\pi$
$107$	237.118	+	410.701i	0.214234	+	0.371065i	−0.738801	+	0.673924i	$0.764608\pi$
$108$		0			0
$109$	−62.3166	+	107.936i	−0.0547601	+	0.0948473i	−0.892106	−	0.451826i	$-0.850773\pi$
$109$	−62.3166	+	107.936i	−0.0547601	+	0.0948473i	0.837346	+	0.546673i	$0.184106\pi$
$110$		0			0
$111$	1245.49			1.06501
$112$		0			0
$113$	−72.0601			−0.0599898			−0.0299949	−	0.999550i	$-0.509549\pi$
$113$	−72.0601			−0.0599898			−0.0299949	+	0.999550i	$0.509549\pi$
$114$		0			0
$115$	−621.153	+	1075.87i	−0.503676	+	0.872393i
$116$		0			0
$117$	440.705	+	763.324i	0.348232	+	0.603156i
$118$		0			0
$119$	−782.604	−	1139.90i	−0.602867	−	0.878108i
$120$		0			0
$121$	−60.5000	−	104.789i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	1047.81	−	1814.87i	0.768116	−	1.33042i
$124$		0			0
$125$	−1503.75			−1.07600
$126$		0			0
$127$	2417.76			1.68930			0.844651	−	0.535317i	$-0.179808\pi$
$127$	2417.76			1.68930			0.844651	+	0.535317i	$0.179808\pi$
$128$		0			0
$129$	2193.83	−	3799.82i	1.49733	−	2.59346i
$130$		0			0
$131$	−417.009	−	722.280i	−0.278124	−	0.481724i	0.692795	−	0.721135i	$-0.256379\pi$
$131$	−417.009	−	722.280i	−0.278124	−	0.481724i	−0.970918	+	0.239410i	$0.923046\pi$
$132$		0			0
$133$	2301.66	−	179.999i	1.50059	−	0.117352i
$134$		0			0
$135$	1312.81	+	2273.86i	0.836956	+	1.44965i
$136$		0			0
$137$	1501.61	−	2600.86i	0.936432	−	1.62195i	0.164371	−	0.986399i	$-0.447441\pi$
$137$	1501.61	−	2600.86i	0.936432	−	1.62195i	0.772061	−	0.635548i	$-0.219226\pi$
$138$		0			0
$139$	−1328.93			−0.810924			−0.405462	−	0.914112i	$-0.632889\pi$
$139$	−1328.93			−0.810924			−0.405462	+	0.914112i	$0.632889\pi$
$140$		0			0
$141$	−1395.12			−0.833264
$142$		0			0
$143$	86.5027	−	149.827i	0.0505854	−	0.0876166i
$144$		0			0
$145$	395.150	+	684.419i	0.226313	+	0.391986i
$146$		0			0
$147$	−3087.66	+	485.907i	−1.73242	+	0.272632i
$148$		0			0
$149$	550.274	+	953.102i	0.302552	+	0.524035i	0.976713	−	0.214549i	$-0.0688282\pi$
$149$	550.274	+	953.102i	0.302552	+	0.524035i	−0.674162	+	0.738584i	$0.735495\pi$
$150$		0			0
$151$	247.834	−	429.261i	0.133566	−	0.231343i	−0.791483	−	0.611191i	$-0.790691\pi$
$151$	247.834	−	429.261i	0.133566	−	0.231343i	0.925049	+	0.379849i	$0.124024\pi$
$152$		0			0
$153$	4183.99			2.21082
$154$		0			0
$155$	2233.24			1.15728
$156$		0			0
$157$	−132.962	+	230.296i	−0.0675891	+	0.117068i	−0.897840	−	0.440323i	$-0.854864\pi$
$157$	−132.962	+	230.296i	−0.0675891	+	0.117068i	0.830250	+	0.557391i	$0.188197\pi$
$158$		0			0
$159$	1383.28	+	2395.92i	0.689947	+	1.19502i
$160$		0			0
$161$	2312.00	−	180.808i	1.13175	−	0.0885070i
$162$		0			0
$163$	1537.41	+	2662.87i	0.738768	+	1.27958i	0.953050	+	0.302813i	$0.0979256\pi$
$163$	1537.41	+	2662.87i	0.738768	+	1.27958i	−0.214282	+	0.976772i	$0.568741\pi$
$164$		0			0
$165$	497.249	−	861.261i	0.234611	−	0.406358i
$166$		0			0
$167$	2668.18			1.23635			0.618173	−	0.786042i	$-0.287873\pi$
$167$	2668.18			1.23635			0.618173	+	0.786042i	$0.287873\pi$
$168$		0			0
$169$	−1949.64			−0.887409
$170$		0			0
$171$	−3493.00	+	6050.05i	−1.56208	+	2.70561i
$172$		0			0
$173$	−559.386	−	968.885i	−0.245834	−	0.425798i	0.716531	−	0.697555i	$-0.245729\pi$
$173$	−559.386	−	968.885i	−0.245834	−	0.425798i	−0.962366	+	0.271757i	$0.912395\pi$
$174$		0			0
$175$	278.519	+	405.678i	0.120309	+	0.175236i
$176$		0			0
$177$	1820.55	+	3153.29i	0.773115	+	1.33907i
$178$		0			0
$179$	−431.108	+	746.701i	−0.180014	+	0.311793i	−0.941885	−	0.335935i	$-0.890948\pi$
$179$	−431.108	+	746.701i	−0.180014	+	0.311793i	0.761871	+	0.647729i	$0.224281\pi$
$180$		0			0
$181$	3606.28			1.48095			0.740477	−	0.672081i	$-0.234600\pi$
$181$	3606.28			1.48095			0.740477	+	0.672081i	$0.234600\pi$
$182$		0			0
$183$	−5094.16			−2.05777
$184$		0			0
$185$	677.994	−	1174.32i	0.269444	−	0.466690i
$186$		0			0
$187$	−410.622	−	711.219i	−0.160576	−	0.278126i
$188$		0			0
$189$	2112.28	−	4422.85i	0.812940	−	1.70220i
$190$		0			0
$191$	−1334.98	−	2312.25i	−0.505736	−	0.875960i	−0.999978	−	0.00663603i	$-0.997888\pi$
$191$	−1334.98	−	2312.25i	−0.505736	−	0.875960i	0.494242	−	0.869324i	$-0.335446\pi$
$192$		0			0
$193$	1073.01	−	1858.50i	0.400190	−	0.693149i	−0.593559	−	0.804791i	$-0.702277\pi$
$193$	1073.01	−	1858.50i	0.400190	−	0.693149i	0.993749	+	0.111641i	$0.0356108\pi$
$194$		0			0
$195$	1421.93			0.522188
$196$		0			0
$197$	−5098.87			−1.84406			−0.922029	−	0.387121i	$-0.873470\pi$
$197$	−5098.87			−1.84406			−0.922029	+	0.387121i	$0.873470\pi$
$198$		0			0
$199$	−191.062	+	330.930i	−0.0680606	+	0.117884i	−0.898048	−	0.439898i	$-0.855014\pi$
$199$	−191.062	+	330.930i	−0.0680606	+	0.117884i	0.829987	+	0.557783i	$0.188348\pi$
$200$		0			0
$201$	−4157.00	−	7200.13i	−1.45877	−	2.52666i
$202$		0			0
$203$	635.784	−	1331.25i	0.219819	−	0.460274i
$204$		0			0
$205$	−1140.78	−	1975.88i	−0.388659	−	0.673178i
$206$		0			0
$207$	−3508.70	+	6077.24i	−1.17812	+	2.04057i
$208$		0			0
$209$	1371.23			0.453827
$210$		0			0
$211$	150.503			0.0491046			0.0245523	−	0.999699i	$-0.492184\pi$
$211$	150.503			0.0491046			0.0245523	+	0.999699i	$0.492184\pi$
$212$		0			0
$213$	−2479.04	+	4293.83i	−0.797470	+	1.38126i
$214$		0			0
$215$	−2388.46	−	4136.94i	−0.757636	−	1.31226i
$216$		0			0
$217$	−2359.58	−	3436.85i	−0.738151	−	1.07516i
$218$		0			0
$219$	−3643.69	−	6311.05i	−1.12428	−	1.94731i
$220$		0			0
$221$	587.107	−	1016.90i	0.178702	−	0.309520i
$222$		0			0
$223$	1883.27			0.565530			0.282765	−	0.959189i	$-0.408748\pi$
$223$	1883.27			0.565530			0.282765	+	0.959189i	$0.408748\pi$
$224$		0			0
$225$	−1489.03			−0.441195
$226$		0			0
$227$	−2975.34	+	5153.44i	−0.869957	+	1.50681i	−0.00791828	+	0.999969i	$0.502520\pi$
$227$	−2975.34	+	5153.44i	−0.869957	+	1.50681i	−0.862039	+	0.506842i	$0.830813\pi$
$228$		0			0
$229$	2664.47	+	4615.00i	0.768878	+	1.33174i	0.938172	+	0.346170i	$0.112518\pi$
$229$	2664.47	+	4615.00i	0.768878	+	1.33174i	−0.169293	+	0.985566i	$0.554149\pi$
$230$		0			0
$231$	−1850.82	+	144.741i	−0.527164	+	0.0412263i
$232$		0			0
$233$	−2417.76	−	4187.68i	−0.679797	−	1.17744i	−0.975042	−	0.222021i	$-0.928735\pi$
$233$	−2417.76	−	4187.68i	−0.679797	−	1.17744i	0.295245	−	0.955421i	$-0.404599\pi$
$234$		0			0
$235$	−759.446	+	1315.40i	−0.210812	+	0.365137i
$236$		0			0
$237$	−520.064			−0.142539
$238$		0			0
$239$	5051.71			1.36723			0.683615	−	0.729843i	$-0.260407\pi$
$239$	5051.71			1.36723			0.683615	+	0.729843i	$0.260407\pi$
$240$		0			0
$241$	−1320.30	+	2286.83i	−0.352896	+	0.611235i	−0.986756	−	0.162214i	$-0.948137\pi$
$241$	−1320.30	+	2286.83i	−0.352896	+	0.611235i	0.633859	+	0.773448i	$0.281470\pi$
$242$		0			0
$243$	521.334	+	902.977i	0.137628	+	0.238379i
$244$		0			0
$245$	−1222.66	+	3175.73i	−0.318827	+	0.828123i
$246$		0			0
$247$	980.289	+	1697.91i	0.252527	+	0.437390i
$248$		0			0
$249$	−2042.22	+	3537.22i	−0.519760	+	0.900250i
$250$		0			0
$251$	−1714.05			−0.431037			−0.215518	−	0.976500i	$-0.569144\pi$
$251$	−1714.05			−0.431037			−0.215518	+	0.976500i	$0.569144\pi$
$252$		0			0
$253$	1377.39			0.342276
$254$		0			0
$255$	3374.91	−	5845.51i	0.828803	−	1.43553i
$256$		0			0
$257$	−2437.85	−	4222.49i	−0.591709	−	1.02487i	−0.994002	−	0.109359i	$-0.965120\pi$
$257$	−2437.85	−	4222.49i	−0.591709	−	1.02487i	0.402293	−	0.915511i	$-0.368213\pi$
$258$		0			0
$259$	−2523.57	+	197.353i	−0.605432	+	0.0473472i
$260$		0			0
$261$	2232.08	+	3866.07i	0.529356	+	0.916872i
$262$		0			0
$263$	−2669.25	+	4623.28i	−0.625829	+	1.08397i	0.362550	+	0.931964i	$0.381906\pi$
$263$	−2669.25	+	4623.28i	−0.625829	+	1.08397i	−0.988380	+	0.152004i	$0.951427\pi$
$264$		0			0
$265$	3012.01			0.698214
$266$		0			0
$267$	−11278.2			−2.58507
$268$		0			0
$269$	1533.09	−	2655.38i	0.347487	−	0.601865i	−0.638316	−	0.769775i	$-0.720369\pi$
$269$	1533.09	−	2655.38i	0.347487	−	0.601865i	0.985802	+	0.167910i	$0.0537019\pi$
$270$		0			0
$271$	1969.71	+	3411.64i	0.441518	+	0.764731i	0.997802	−	0.0662606i	$-0.0211069\pi$
$271$	1969.71	+	3411.64i	0.441518	+	0.764731i	−0.556285	+	0.830992i	$0.687774\pi$
$272$		0			0
$273$	−1502.37	−	2188.28i	−0.333068	−	0.485131i
$274$		0			0
$275$	146.135	+	253.114i	0.0320447	+	0.0555031i
$276$		0			0
$277$	−2255.90	+	3907.34i	−0.489329	+	0.847543i	−0.999925	−	0.0122782i	$-0.996092\pi$
$277$	−2255.90	+	3907.34i	−0.489329	+	0.847543i	0.510596	+	0.859821i	$0.329425\pi$
$278$		0			0
$279$	12614.9			2.70693
$280$		0			0
$281$	3887.05			0.825203			0.412601	−	0.910912i	$-0.364620\pi$
$281$	3887.05			0.825203			0.412601	+	0.910912i	$0.364620\pi$
$282$		0			0
$283$	1079.42	−	1869.60i	0.226730	−	0.392708i	−0.730107	−	0.683333i	$-0.760530\pi$
$283$	1079.42	−	1869.60i	0.226730	−	0.392708i	0.956837	+	0.290625i	$0.0938631\pi$
$284$		0			0
$285$	5635.06	+	9760.22i	1.17120	+	2.02858i
$286$		0			0
$287$	−1835.47	+	3843.26i	−0.377507	+	0.790454i
$288$		0			0
$289$	−330.455	−	572.365i	−0.0672613	−	0.116500i
$290$		0			0
$291$	−6863.51	+	11888.0i	−1.38263	+	2.39479i
$292$		0			0
$293$	1115.27			0.222371			0.111186	−	0.993800i	$-0.464535\pi$
$293$	1115.27			0.222371			0.111186	+	0.993800i	$0.464535\pi$
$294$		0			0
$295$	3964.14			0.782377
$296$		0			0
$297$	1455.57	−	2521.12i	0.284379	−	0.492559i
$298$		0			0
$299$	984.695	+	1705.54i	0.190456	+	0.329880i
$300$		0			0
$301$	−3842.96	+	8046.69i	−0.735896	+	1.54088i
$302$		0			0
$303$	−4112.11	−	7122.38i	−0.779652	−	1.35040i
$304$		0			0
$305$	−2773.05	+	4803.07i	−0.520605	+	0.901715i
$306$		0			0
$307$	4618.19			0.858547			0.429273	−	0.903175i	$-0.358770\pi$
$307$	4618.19			0.858547			0.429273	+	0.903175i	$0.358770\pi$
$308$		0			0
$309$	−5494.35			−1.01153
$310$		0			0
$311$	2372.45	−	4109.20i	0.432570	−	0.749233i	−0.564524	−	0.825417i	$-0.690940\pi$
$311$	2372.45	−	4109.20i	0.432570	−	0.749233i	0.997094	+	0.0761840i	$0.0242736\pi$
$312$		0			0
$313$	−5034.28	−	8719.63i	−0.909120	−	1.57464i	−0.815290	−	0.579053i	$-0.803422\pi$
$313$	−5034.28	−	8719.63i	−0.909120	−	1.57464i	−0.0938302	−	0.995588i	$-0.529911\pi$
$314$		0			0
$315$	−5828.23	−	8489.13i	−1.04249	−	1.51844i
$316$		0			0
$317$	−1467.39	−	2541.60i	−0.259990	−	0.450317i	0.706249	−	0.707964i	$-0.250386\pi$
$317$	−1467.39	−	2541.60i	−0.259990	−	0.450317i	−0.966239	+	0.257647i	$0.917053\pi$
$318$		0			0
$319$	438.117	−	758.842i	0.0768961	−	0.133188i
$320$		0			0
$321$	4321.58			0.751425
$322$		0			0
$323$	9306.73			1.60322
$324$		0			0
$325$	−208.944	+	361.902i	−0.0356619	+	0.0617683i
$326$		0			0
$327$	567.874	+	983.587i	0.0960352	+	0.166338i
$328$		0			0
$329$	2826.74	−	221.063i	0.473688	−	0.0370443i
$330$		0			0
$331$	3474.25	+	6017.58i	0.576924	+	0.999262i	0.995830	+	0.0912325i	$0.0290806\pi$
$331$	3474.25	+	6017.58i	0.576924	+	0.999262i	−0.418905	+	0.908030i	$0.637586\pi$
$332$		0			0
$333$	3829.77	−	6633.36i	0.630241	−	1.09161i
$334$		0			0
$335$	−9051.59			−1.47624
$336$		0			0
$337$	−6196.25			−1.00158			−0.500788	−	0.865570i	$-0.666956\pi$
$337$	−6196.25			−1.00158			−0.500788	+	0.865570i	$0.666956\pi$
$338$		0			0
$339$	−328.332	+	568.688i	−0.0526034	+	0.0911117i
$340$		0			0
$341$	−1238.04	−	2144.35i	−0.196609	−	0.340537i
$342$		0			0
$343$	6179.12	−	1473.78i	0.972715	−	0.232002i
$344$		0			0
$345$	5660.39	+	9804.08i	0.883319	+	1.52995i
$346$		0			0
$347$	581.902	−	1007.88i	0.0900234	−	0.155925i	−0.817497	−	0.575932i	$-0.804639\pi$
$347$	581.902	−	1007.88i	0.0900234	−	0.155925i	0.907521	+	0.420007i	$0.137972\pi$
$348$		0			0
$349$	1043.63			0.160069			0.0800345	−	0.996792i	$-0.474497\pi$
$349$	1043.63			0.160069			0.0800345	+	0.996792i	$0.474497\pi$
$350$		0			0
$351$	4162.33			0.632960
$352$		0			0
$353$	−2851.93	+	4939.68i	−0.430008	+	0.744795i	−0.996873	−	0.0790152i	$-0.974822\pi$
$353$	−2851.93	+	4939.68i	−0.430008	+	0.744795i	0.566866	+	0.823810i	$0.308156\pi$
$354$		0			0
$355$	2698.98	+	4674.77i	0.403512	+	0.698904i
$356$		0			0
$357$	−12561.8	+	982.381i	−1.86230	+	0.145639i
$358$		0			0
$359$	1375.80	+	2382.95i	0.202262	+	0.350327i	0.949257	−	0.314502i	$-0.101838\pi$
$359$	1375.80	+	2382.95i	0.202262	+	0.350327i	−0.746995	+	0.664829i	$0.768504\pi$
$360$		0			0
$361$	−4340.20	+	7517.45i	−0.632775	+	1.09600i
$362$		0			0
$363$	−1102.64			−0.159431
$364$		0			0
$365$	−7933.90			−1.13775
$366$		0			0
$367$	1067.83	−	1849.53i	0.151881	−	0.263065i	−0.780038	−	0.625732i	$-0.784800\pi$
$367$	1067.83	−	1849.53i	0.151881	−	0.263065i	0.931919	+	0.362667i	$0.118134\pi$
$368$		0			0
$369$	−6443.88	−	11161.1i	−0.909092	−	1.57459i
$370$		0			0
$371$	−3182.41	−	4635.34i	−0.445343	−	0.648666i
$372$		0			0
$373$	4640.56	+	8037.68i	0.644179	+	1.11575i	0.984490	+	0.175438i	$0.0561343\pi$
$373$	4640.56	+	8037.68i	0.644179	+	1.11575i	−0.340311	+	0.940313i	$0.610532\pi$
$374$		0			0
$375$	−6851.65	+	11867.4i	−0.943514	+	1.63421i
$376$		0			0
$377$	1252.84			0.171152
$378$		0			0
$379$	14282.6			1.93574			0.967872	−	0.251443i	$-0.0809053\pi$
$379$	14282.6			1.93574			0.967872	+	0.251443i	$0.0809053\pi$
$380$		0			0
$381$	11016.2	−	19080.6i	1.48130	−	2.56569i
$382$		0			0
$383$	4819.64	+	8347.86i	0.643008	+	1.11372i	0.984758	+	0.173932i	$0.0556472\pi$
$383$	4819.64	+	8347.86i	0.643008	+	1.11372i	−0.341750	+	0.939791i	$0.611020\pi$
$384$		0			0
$385$	−871.039	+	1823.85i	−0.115305	+	0.241434i
$386$		0			0
$387$	−13491.7	−	23368.3i	−1.77215	−	3.06945i
$388$		0			0
$389$	−695.552	+	1204.73i	−0.0906579	+	0.157024i	−0.907788	−	0.419429i	$-0.862230\pi$
$389$	−695.552	+	1204.73i	−0.0906579	+	0.157024i	0.817130	+	0.576453i	$0.195564\pi$
$390$		0			0
$391$	9348.56			1.20915
$392$		0			0
$393$	−7600.16			−0.975515
$394$		0			0
$395$	−283.102	+	490.346i	−0.0360617	+	0.0624607i
$396$		0			0
$397$	−6577.06	−	11391.8i	−0.831468	−	1.44015i	−0.896874	−	0.442287i	$-0.854167\pi$
$397$	−6577.06	−	11391.8i	−0.831468	−	1.44015i	0.0654053	−	0.997859i	$-0.479166\pi$
$398$		0			0
$399$	9066.65	−	18984.4i	1.13759	−	2.38198i
$400$		0			0
$401$	−3777.51	−	6542.84i	−0.470424	−	0.814798i	0.529004	−	0.848619i	$-0.322566\pi$
$401$	−3777.51	−	6542.84i	−0.470424	−	0.814798i	−0.999428	+	0.0338213i	$0.989232\pi$
$402$		0			0
$403$	1770.15	−	3065.99i	0.218802	−	0.378977i
$404$		0			0
$405$	8914.62			1.09376
$406$		0			0
$407$	−1503.44			−0.183102
$408$		0			0
$409$	4638.54	−	8034.19i	0.560785	−	0.971309i	−0.436643	−	0.899635i	$-0.643833\pi$
$409$	4638.54	−	8034.19i	0.560785	−	0.971309i	0.997428	−	0.0716736i	$-0.0228340\pi$
$410$		0			0
$411$	−13683.7	−	23700.9i	−1.64226	−	2.84448i
$412$		0			0
$413$	−4188.40	−	6100.62i	−0.499026	−	0.726857i
$414$		0			0
$415$	2223.40	+	3851.04i	0.262994	+	0.455518i
$416$		0			0
$417$	−6055.09	+	10487.7i	−0.711077	+	1.23162i
$418$		0			0
$419$	15266.0			1.77993			0.889967	−	0.456025i	$-0.150727\pi$
$419$	15266.0			1.77993			0.889967	+	0.456025i	$0.150727\pi$
$420$		0			0
$421$	7092.61			0.821075			0.410538	−	0.911844i	$-0.365341\pi$
$421$	7092.61			0.821075			0.410538	+	0.911844i	$0.365341\pi$
$422$		0			0
$423$	−4289.87	+	7430.28i	−0.493099	+	0.854072i
$424$		0			0
$425$	991.843	+	1717.92i	0.113203	+	0.196074i
$426$		0			0
$427$	10321.6	−	807.192i	1.16979	−	0.0914818i
$428$		0			0
$429$	−788.275	−	1365.33i	−0.0887139	−	0.153657i
$430$		0			0
$431$	−6044.06	+	10468.6i	−0.675481	+	1.16997i	0.300847	+	0.953672i	$0.402731\pi$
$431$	−6044.06	+	10468.6i	−0.675481	+	1.16997i	−0.976328	+	0.216295i	$0.930603\pi$
$432$		0			0
$433$	8256.16			0.916318			0.458159	−	0.888870i	$-0.348509\pi$
$433$	8256.16			0.916318			0.458159	+	0.888870i	$0.348509\pi$
$434$		0			0
$435$	7201.77			0.793790
$436$		0			0
$437$	−7804.62	+	13518.0i	−0.854338	+	1.47976i
$438$		0			0
$439$	2467.17	+	4273.27i	0.268227	+	0.464583i	0.968404	−	0.249386i	$-0.0802289\pi$
$439$	2467.17	+	4273.27i	0.268227	+	0.464583i	−0.700177	+	0.713969i	$0.746896\pi$
$440$		0			0
$441$	−6906.41	+	17938.7i	−0.745752	+	1.93702i
$442$		0			0
$443$	−7042.35	−	12197.7i	−0.755287	−	1.30820i	−0.945232	−	0.326400i	$-0.894164\pi$
$443$	−7042.35	−	12197.7i	−0.755287	−	1.30820i	0.189945	−	0.981795i	$-0.439169\pi$
$444$		0			0
$445$	−6139.39	+	10633.7i	−0.654012	+	1.13278i
$446$		0			0
$447$	10029.0			1.06120
$448$		0			0
$449$	5036.63			0.529383			0.264692	−	0.964333i	$-0.414730\pi$
$449$	5036.63			0.529383			0.264692	+	0.964333i	$0.414730\pi$
$450$		0			0
$451$	−1264.82	+	2190.73i	−0.132058	+	0.228731i
$452$		0			0
$453$	−2258.44	−	3911.73i	−0.234240	−	0.405716i
$454$		0			0
$455$	−2881.07	+	225.311i	−0.296850	+	0.0232148i
$456$		0			0
$457$	5766.79	+	9988.38i	0.590283	+	1.02240i	0.994194	+	0.107602i	$0.0343171\pi$
$457$	5766.79	+	9988.38i	0.590283	+	1.02240i	−0.403911	+	0.914798i	$0.632350\pi$
$458$		0			0
$459$	9879.15	−	17111.2i	1.00462	−	1.74005i
$460$		0			0
$461$	−13844.8			−1.39874			−0.699369	−	0.714761i	$-0.746535\pi$
$461$	−13844.8			−1.39874			−0.699369	+	0.714761i	$0.746535\pi$
$462$		0			0
$463$	−11794.2			−1.18385			−0.591926	−	0.805992i	$-0.701632\pi$
$463$	−11794.2			−1.18385			−0.591926	+	0.805992i	$0.701632\pi$
$464$		0			0
$465$	10175.5	−	17624.4i	1.01479	−	1.75766i
$466$		0			0
$467$	8061.53	+	13963.0i	0.798807	+	1.38358i	0.920393	+	0.390994i	$0.127869\pi$
$467$	8061.53	+	13963.0i	0.798807	+	1.38358i	−0.121586	+	0.992581i	$0.538798\pi$
$468$		0			0
$469$	9563.65	+	13930.0i	0.941596	+	1.37148i
$470$		0			0
$471$	1211.64	+	2098.63i	0.118534	+	0.205307i
$472$		0			0
$473$	−2648.18	+	4586.78i	−0.257428	+	0.445878i
$474$		0			0
$475$	−3312.15			−0.319941
$476$		0			0
$477$	17013.9			1.63315
$478$		0			0
$479$	−6877.31	+	11911.9i	−0.656017	+	1.13626i	0.325620	+	0.945501i	$0.394427\pi$
$479$	−6877.31	+	11911.9i	−0.656017	+	1.13626i	−0.981638	+	0.190755i	$0.938906\pi$
$480$		0			0
$481$	−1074.80	−	1861.61i	−0.101885	−	0.176470i
$482$		0			0
$483$	9107.40	−	19069.8i	0.857973	−	1.79649i
$484$		0			0
$485$	7472.43	+	12942.6i	0.699599	+	1.21174i
$486$		0			0
$487$	3508.26	−	6076.49i	0.326437	−	0.565405i	−0.655365	−	0.755312i	$-0.727485\pi$
$487$	3508.26	−	6076.49i	0.326437	−	0.565405i	0.981802	+	0.189907i	$0.0608187\pi$
$488$		0			0
$489$	28020.0			2.59122
$490$		0			0
$491$	288.797			0.0265442			0.0132721	−	0.999912i	$-0.495775\pi$
$491$	288.797			0.0265442			0.0132721	+	0.999912i	$0.495775\pi$
$492$		0			0
$493$	2973.57	−	5150.37i	0.271649	−	0.470509i
$494$		0			0
$495$	−3058.00	−	5296.61i	−0.277670	−	0.480939i
$496$		0			0
$497$	4342.57	−	9092.82i	0.391934	−	0.820661i
$498$		0			0
$499$	−394.015	−	682.453i	−0.0353477	−	0.0612241i	0.847810	−	0.530300i	$-0.177921\pi$
$499$	−394.015	−	682.453i	−0.0353477	−	0.0612241i	−0.883158	+	0.469076i	$0.844587\pi$
$500$		0			0
$501$	12157.2	−	21056.8i	1.08412	−	1.87775i
$502$		0			0
$503$	−17569.9			−1.55746			−0.778731	−	0.627358i	$-0.784136\pi$
$503$	−17569.9			−1.55746			−0.778731	+	0.627358i	$0.784136\pi$
$504$		0			0
$505$	−8953.86			−0.788993
$506$		0			0
$507$	−8883.25	+	15386.2i	−0.778144	+	1.34778i
$508$		0			0
$509$	−2061.77	−	3571.09i	−0.179541	−	0.310974i	0.762182	−	0.647362i	$-0.224128\pi$
$509$	−2061.77	−	3571.09i	−0.179541	−	0.310974i	−0.941723	+	0.336388i	$0.890795\pi$
$510$		0			0
$511$	8382.72	+	12209.9i	0.725695	+	1.05701i
$512$		0			0
$513$	16495.2	+	28570.5i	1.41965	+	2.45890i
$514$		0			0
$515$	−2990.90	+	5180.39i	−0.255912	+	0.443253i
$516$		0			0
$517$	1684.05			0.143258
$518$		0			0
$519$	−10195.1			−0.862261
$520$		0			0
$521$	2962.28	−	5130.83i	0.249098	−	0.431450i	−0.714178	−	0.699964i	$-0.753199\pi$
$521$	2962.28	−	5130.83i	0.249098	−	0.431450i	0.963276	+	0.268514i	$0.0865326\pi$
$522$		0			0
$523$	4191.79	+	7260.40i	0.350467	+	0.607027i	0.986331	−	0.164774i	$-0.0526894\pi$
$523$	4191.79	+	7260.40i	0.350467	+	0.607027i	−0.635864	+	0.771801i	$0.719356\pi$
$524$		0			0
$525$	4470.58	−	349.617i	0.371642	−	0.0290639i
$526$		0			0
$527$	−8402.77	−	14554.0i	−0.694555	−	1.20300i
$528$		0			0
$529$	−1756.20	+	3041.83i	−0.144341	+	0.250006i
$530$		0			0
$531$	22392.2			1.83002
$532$		0			0
$533$	−3616.87			−0.293929
$534$		0			0
$535$	2352.49	−	4074.64i	0.190107	−	0.329275i
$536$		0			0
$537$	3928.57	+	6804.47i	0.315698	+	0.546806i
$538$		0			0
$539$	3727.13	−	586.540i	0.297846	−	0.0468721i
$540$		0			0
$541$	476.917	+	826.045i	0.0379007	+	0.0656459i	0.884354	−	0.466818i	$-0.154600\pi$
$541$	476.917	+	826.045i	0.0379007	+	0.0656459i	−0.846453	+	0.532464i	$0.821266\pi$
$542$		0			0
$543$	16431.5	−	28460.2i	1.29861	−	2.24925i
$544$		0			0
$545$	1236.51			0.0971858
$546$		0			0
$547$	−6400.37			−0.500292			−0.250146	−	0.968208i	$-0.580479\pi$
$547$	−6400.37			−0.500292			−0.250146	+	0.968208i	$0.580479\pi$
$548$		0			0
$549$	−15664.1	+	27131.1i	−1.21772	+	2.10915i
$550$		0			0
$551$	4964.95	+	8599.55i	0.383873	+	0.664888i
$552$		0			0
$553$	1053.74	−	82.4063i	0.0810297	−	0.00633684i
$554$		0			0
$555$	−6178.37	−	10701.2i	−0.472535	−	0.818455i
$556$		0			0
$557$	7663.38	−	13273.4i	0.582958	−	1.00971i	−0.412168	−	0.911108i	$-0.635228\pi$
$557$	7663.38	−	13273.4i	0.582958	−	1.00971i	0.995127	−	0.0986057i	$-0.0314382\pi$
$558$		0			0
$559$	−7572.71			−0.572973
$560$		0			0
$561$	−7483.77			−0.563218
$562$		0			0
$563$	8791.19	−	15226.8i	0.658090	−	1.13984i	−0.323020	−	0.946392i	$-0.604698\pi$
$563$	8791.19	−	15226.8i	0.658090	−	1.13984i	0.981110	−	0.193453i	$-0.0619686\pi$
$564$		0			0
$565$	357.461	+	619.140i	0.0266168	+	0.0461017i
$566$		0			0
$567$	−9418.93	−	13719.2i	−0.697633	−	1.01614i
$568$		0			0
$569$	−5687.27	−	9850.65i	−0.419021	−	0.725766i	0.576820	−	0.816871i	$-0.304293\pi$
$569$	−5687.27	−	9850.65i	−0.419021	−	0.725766i	−0.995841	+	0.0911054i	$0.970960\pi$
$570$		0			0
$571$	−142.660	+	247.094i	−0.0104556	+	0.0181096i	−0.871206	−	0.490918i	$-0.836662\pi$
$571$	−142.660	+	247.094i	−0.0104556	+	0.0181096i	0.860750	+	0.509027i	$0.169995\pi$
$572$		0			0
$573$	−24330.6			−1.77386
$574$		0			0
$575$	−3327.04			−0.241299
$576$		0			0
$577$	−5121.71	+	8871.07i	−0.369532	+	0.640048i	−0.989492	−	0.144585i	$-0.953815\pi$
$577$	−5121.71	+	8871.07i	−0.369532	+	0.640048i	0.619961	+	0.784633i	$0.287149\pi$
$578$		0			0
$579$	−9778.01	−	16936.0i	−0.701831	−	1.21561i
$580$		0			0
$581$	3577.38	−	7490.60i	0.255447	−	0.534875i
$582$		0			0
$583$	−1669.77	−	2892.12i	−0.118619	−	0.205454i
$584$		0			0
$585$	4372.32	−	7573.07i	0.309014	−	0.535228i
$586$		0			0
$587$	−26130.4			−1.83734			−0.918669	−	0.395029i	$-0.870735\pi$
$587$	−26130.4			−1.83734			−0.918669	+	0.395029i	$0.870735\pi$
$588$		0			0
$589$	28060.1			1.96298
$590$		0			0
$591$	−23232.3	+	40239.5i	−1.61700	+	2.80073i
$592$		0			0
$593$	4418.25	+	7652.64i	0.305963	+	0.529943i	0.977475	−	0.211050i	$-0.0676883\pi$
$593$	4418.25	+	7652.64i	0.305963	+	0.529943i	−0.671512	+	0.740993i	$0.734355\pi$
$594$		0			0
$595$	−5911.87	+	12378.7i	−0.407333	+	0.852905i
$596$		0			0
$597$	1741.10	+	3015.67i	0.119361	+	0.206739i
$598$		0			0
$599$	−1277.12	+	2212.03i	−0.0871145	+	0.150887i	−0.906290	−	0.422656i	$-0.861098\pi$
$599$	−1277.12	+	2212.03i	−0.0871145	+	0.150887i	0.819176	+	0.573543i	$0.194431\pi$
$600$		0			0
$601$	−630.033			−0.0427614			−0.0213807	−	0.999771i	$-0.506806\pi$
$601$	−630.033			−0.0427614			−0.0213807	+	0.999771i	$0.506806\pi$
$602$		0			0
$603$	−51129.6			−3.45300
$604$		0			0
$605$	−600.232	+	1039.63i	−0.0403354	+	0.0698629i
$606$		0			0
$607$	−1738.23	−	3010.70i	−0.116232	−	0.201319i	0.802040	−	0.597271i	$-0.203748\pi$
$607$	−1738.23	−	3010.70i	−0.116232	−	0.201319i	−0.918271	+	0.395952i	$0.870415\pi$
$608$		0			0
$609$	−7609.19	−	11083.2i	−0.506305	−	0.737460i
$610$		0			0
$611$	1203.93	+	2085.26i	0.0797147	+	0.138070i
$612$		0			0
$613$	−12192.9	+	21118.7i	−0.803372	+	1.39148i	0.114013	+	0.993479i	$0.463630\pi$
$613$	−12192.9	+	21118.7i	−0.803372	+	1.39148i	−0.917385	+	0.398002i	$0.869704\pi$
$614$		0			0
$615$	−20791.1			−1.36322
$616$		0			0
$617$	−15661.2			−1.02187			−0.510937	−	0.859618i	$-0.670701\pi$
$617$	−15661.2			−1.02187			−0.510937	+	0.859618i	$0.670701\pi$
$618$		0			0
$619$	−3923.58	+	6795.85i	−0.254769	+	0.441273i	−0.964833	−	0.262864i	$-0.915333\pi$
$619$	−3923.58	+	6795.85i	−0.254769	+	0.441273i	0.710064	+	0.704138i	$0.248666\pi$
$620$		0			0
$621$	16569.3	+	28698.9i	1.07070	+	1.85450i
$622$		0			0
$623$	22851.5	−	1787.08i	1.46954	−	0.114924i
$624$		0			0
$625$	5798.88	+	10044.0i	0.371129	+	0.642814i
$626$		0			0
$627$	6247.81	−	10821.5i	0.397948	−	0.689267i
$628$		0			0
$629$	−10204.0			−0.646839
$630$		0			0
$631$	13758.6			0.868022			0.434011	−	0.900908i	$-0.357098\pi$
$631$	13758.6			0.868022			0.434011	+	0.900908i	$0.357098\pi$
$632$		0			0
$633$	685.747	−	1187.75i	0.0430585	−	0.0745795i
$634$		0			0
$635$	−11993.5	−	20773.4i	−0.749525	−	1.29821i
$636$		0			0
$637$	3390.80	+	4195.77i	0.210908	+	0.260977i
$638$		0			0
$639$	15245.7	+	26406.3i	0.943834	+	1.63477i
$640$		0			0
$641$	8687.52	−	15047.2i	0.535314	−	0.927191i	−0.463834	−	0.885922i	$-0.653527\pi$
$641$	8687.52	−	15047.2i	0.535314	−	0.927191i	0.999148	−	0.0412689i	$-0.0131400\pi$
$642$		0			0
$643$	2616.82			0.160493			0.0802467	−	0.996775i	$-0.474429\pi$
$643$	2616.82			0.160493			0.0802467	+	0.996775i	$0.474429\pi$
$644$		0			0
$645$	−43530.8			−2.65740
$646$		0			0
$647$	1465.35	−	2538.06i	0.0890401	−	0.154222i	−0.818066	−	0.575125i	$-0.804953\pi$
$647$	1465.35	−	2538.06i	0.0890401	−	0.154222i	0.907106	+	0.420903i	$0.138287\pi$
$648$		0			0
$649$	−2197.60	−	3806.35i	−0.132917	−	0.230219i
$650$		0			0
$651$	−37874.2	+	2961.91i	−2.28020	+	0.178320i
$652$		0			0
$653$	8268.38	+	14321.3i	0.495508	+	0.858245i	0.999987	−	0.00517928i	$-0.00164862\pi$
$653$	8268.38	+	14321.3i	0.495508	+	0.858245i	−0.504479	+	0.863424i	$0.668315\pi$
$654$		0			0
$655$	−4137.22	+	7165.87i	−0.246801	+	0.427471i
$656$		0			0
$657$	−44816.1			−2.66125
$658$		0			0
$659$	11308.7			0.668473			0.334237	−	0.942489i	$-0.391521\pi$
$659$	11308.7			0.668473			0.334237	+	0.942489i	$0.391521\pi$
$660$		0			0
$661$	13423.5	−	23250.2i	0.789885	−	1.36812i	−0.136152	−	0.990688i	$-0.543474\pi$
$661$	13423.5	−	23250.2i	0.789885	−	1.36812i	0.926037	−	0.377433i	$-0.123193\pi$
$662$		0			0
$663$	−5350.14	−	9266.71i	−0.313397	−	0.542819i
$664$		0			0
$665$	−12964.1	−	18882.9i	−0.755980	−	1.10113i
$666$		0			0
$667$	4987.27	+	8638.20i	0.289517	+	0.501458i
$668$		0			0
$669$	8580.86	−	14862.5i	0.495897	−	0.858919i
$670$		0			0
$671$	6149.19			0.353780
$672$		0			0
$673$	−4676.83			−0.267873			−0.133936	−	0.990990i	$-0.542762\pi$
$673$	−4676.83			−0.267873			−0.133936	+	0.990990i	$0.542762\pi$
$674$		0			0
$675$	−3515.87	+	6089.66i	−0.200483	+	0.347246i
$676$		0			0
$677$	−16419.0	−	28438.6i	−0.932103	−	1.61445i	−0.779719	−	0.626129i	$-0.784638\pi$
$677$	−16419.0	−	28438.6i	−0.932103	−	1.61445i	−0.152384	−	0.988321i	$-0.548695\pi$
$678$		0			0
$679$	12022.9	−	25174.5i	0.679525	−	1.42284i
$680$		0			0
$681$	27113.5	+	46961.9i	1.52568	+	2.64256i
$682$		0			0
$683$	−10540.6	+	18256.9i	−0.590521	+	1.02281i	0.403641	+	0.914917i	$0.367744\pi$
$683$	−10540.6	+	18256.9i	−0.590521	+	1.02281i	−0.994162	+	0.107895i	$0.965589\pi$
$684$		0			0
$685$	−29795.5			−1.66194
$686$		0			0
$687$	48561.1			2.69683
$688$		0			0
$689$	2387.43	−	4135.15i	0.132008	−	0.228645i
$690$		0			0
$691$	−4033.46	−	6986.16i	−0.222055	−	0.384611i	0.733377	−	0.679823i	$-0.237943\pi$
$691$	−4033.46	−	6986.16i	−0.222055	−	0.384611i	−0.955432	+	0.295212i	$0.904610\pi$
$692$		0			0
$693$	−4920.23	+	10302.4i	−0.269703	+	0.564725i
$694$		0			0
$695$	6592.29	+	11418.2i	0.359798	+	0.623189i
$696$		0			0
$697$	−8584.53	+	14868.8i	−0.466517	+	0.808031i
$698$		0			0
$699$	−44064.7			−2.38438
$700$		0			0
$701$	9129.93			0.491915			0.245958	−	0.969281i	$-0.420898\pi$
$701$	9129.93			0.491915			0.245958	+	0.969281i	$0.420898\pi$
$702$		0			0
$703$	8518.82	−	14755.0i	0.457032	−	0.791602i
$704$		0			0
$705$	6920.62	+	11986.9i	0.369710	+	0.640357i
$706$		0			0
$707$	9460.39	+	13779.5i	0.503245	+	0.733003i
$708$		0			0
$709$	−14180.4	−	24561.1i	−0.751135	−	1.30100i	−0.947273	−	0.320428i	$-0.896173\pi$
$709$	−14180.4	−	24561.1i	−0.751135	−	1.30100i	0.196138	−	0.980576i	$-0.437160\pi$
$710$		0			0
$711$	−1599.15	+	2769.81i	−0.0843500	+	0.146099i
$712$		0			0
$713$	28186.2			1.48048
$714$		0			0
$715$	−1716.42			−0.0897768
$716$		0			0
$717$	23017.4	−	39867.3i	1.19889	−	2.07653i
$718$		0			0
$719$	1708.38	+	2959.00i	0.0886118	+	0.153480i	0.906925	−	0.421293i	$-0.138424\pi$
$719$	1708.38	+	2959.00i	0.0886118	+	0.153480i	−0.818313	+	0.574773i	$0.805090\pi$
$720$		0			0
$721$	11132.5	−	870.603i	0.575027	−	0.0449694i
$722$		0			0
$723$	12031.5	+	20839.2i	0.618890	+	1.07195i
$724$		0			0
$725$	−1058.26	+	1832.95i	−0.0542106	+	0.0938954i
$726$		0			0
$727$	953.823			0.0486593			0.0243297	−	0.999704i	$-0.492255\pi$
$727$	953.823			0.0486593			0.0243297	+	0.999704i	$0.492255\pi$
$728$		0			0
$729$	−14759.2			−0.749843
$730$		0			0
$731$	−17973.6	+	31131.2i	−0.909408	+	1.57514i
$732$		0			0
$733$	8405.36	+	14558.5i	0.423546	+	0.733603i	0.996283	−	0.0861358i	$-0.0274519\pi$
$733$	8405.36	+	14558.5i	0.423546	+	0.733603i	−0.572738	+	0.819739i	$0.694119\pi$
$734$		0			0
$735$	19491.5	+	24118.8i	0.978172	+	1.21039i
$736$		0			0
$737$	5017.93	+	8691.30i	0.250797	+	0.434394i
$738$		0			0
$739$	17264.6	−	29903.2i	0.859392	−	1.48851i	−0.0131187	−	0.999914i	$-0.504176\pi$
$739$	17264.6	−	29903.2i	0.859392	−	1.48851i	0.872510	−	0.488596i	$-0.162491\pi$
$740$		0			0
$741$	17866.2			0.885737
$742$		0			0
$743$	16824.5			0.830727			0.415364	−	0.909655i	$-0.363654\pi$
$743$	16824.5			0.830727			0.415364	+	0.909655i	$0.363654\pi$
$744$		0			0
$745$	5459.37	−	9455.91i	0.268478	−	0.465017i
$746$		0			0
$747$	12559.3	+	21753.3i	0.615154	+	1.06548i
$748$		0			0
$749$	−8756.25	+	684.773i	−0.427165	+	0.0334060i
$750$		0			0
$751$	8124.74	+	14072.5i	0.394775	+	0.683770i	0.993072	−	0.117504i	$-0.0374893\pi$
$751$	8124.74	+	14072.5i	0.394775	+	0.683770i	−0.598298	+	0.801274i	$0.704156\pi$
$752$		0			0
$753$	−7809.85	+	13527.1i	−0.377964	+	0.654653i
$754$		0			0
$755$	−4917.61			−0.237046
$756$		0			0
$757$	20023.1			0.961365			0.480682	−	0.876895i	$-0.340389\pi$
$757$	20023.1			0.961365			0.480682	+	0.876895i	$0.340389\pi$
$758$		0			0
$759$	6275.89	−	10870.2i	0.300132	−	0.519844i
$760$		0			0
$761$	−4106.85	−	7113.27i	−0.195628	−	0.338838i	0.751478	−	0.659758i	$-0.229341\pi$
$761$	−4106.85	−	7113.27i	−0.195628	−	0.338838i	−0.947106	+	0.320920i	$0.896008\pi$
$762$		0			0
$763$	−1306.46	−	1902.93i	−0.0619883	−	0.0902891i
$764$		0			0
$765$	−20755.1	−	35948.9i	−0.980918	−	1.69900i
$766$		0			0
$767$	3142.12	−	5442.31i	0.147921	−	0.256207i
$768$		0			0
$769$	1053.56			0.0494046			0.0247023	−	0.999695i	$-0.492136\pi$
$769$	1053.56			0.0494046			0.0247023	+	0.999695i	$0.492136\pi$
$770$		0			0
$771$	−44431.0			−2.07541
$772$		0			0
$773$	5586.56	−	9676.21i	0.259941	−	0.450232i	−0.706285	−	0.707928i	$-0.749630\pi$
$773$	5586.56	−	9676.21i	0.259941	−	0.450232i	0.966226	+	0.257696i	$0.0829634\pi$
$774$		0			0
$775$	2990.44	+	5179.60i	0.138606	+	0.240073i
$776$		0			0
$777$	−9940.81	+	20814.8i	−0.458976	+	0.961040i
$778$		0			0
$779$	−14333.5	−	24826.4i	−0.659246	−	1.14185i
$780$		0			0
$781$	2992.46	−	5183.09i	0.137105	−	0.237472i
$782$		0			0
$783$	21081.3			0.962177
$784$		0			0
$785$	2638.27			0.119954
$786$		0			0
$787$	−7061.85	+	12231.5i	−0.319857	+	0.554009i	−0.980458	−	0.196728i	$-0.936968\pi$
$787$	−7061.85	+	12231.5i	−0.319857	+	0.554009i	0.660601	+	0.750737i	$0.270302\pi$
$788$		0			0
$789$	24324.1	+	42130.7i	1.09754	+	1.90100i
$790$		0			0
$791$	575.144	−	1204.28i	0.0258531	−	0.0541331i
$792$		0			0
$793$	4396.04	+	7614.17i	0.196858	+	0.340967i
$794$		0			0
$795$	13723.8	−	23770.4i	0.612244	−	1.06044i
$796$		0			0
$797$	−5265.14			−0.234003			−0.117002	−	0.993132i	$-0.537328\pi$
$797$	−5265.14			−0.234003			−0.117002	+	0.993132i	$0.537328\pi$
$798$		0			0
$799$	11429.9			0.506085
$800$		0			0
$801$	−34679.5	+	60066.7i	−1.52976	+	2.64963i
$802$		0			0
$803$	4398.31	+	7618.09i	0.193291	+	0.334790i
$804$		0			0
$805$	−13022.4	−	18967.8i	−0.570160	−	0.830468i
$806$		0			0
$807$	−13970.6	−	24197.8i	−0.609403	−	1.05552i
$808$		0			0
$809$	−19746.4	+	34201.7i	−0.858152	+	1.48636i	0.0155368	+	0.999879i	$0.495054\pi$
$809$	−19746.4	+	34201.7i	−0.858152	+	1.48636i	−0.873689	+	0.486484i	$0.838279\pi$
$810$		0			0
$811$	25162.9			1.08950			0.544752	−	0.838597i	$-0.316624\pi$
$811$	25162.9			1.08950			0.544752	+	0.838597i	$0.316624\pi$
$812$		0			0
$813$	35898.8			1.54862
$814$		0			0
$815$	15252.9	−	26418.9i	0.655567	−	1.13547i
$816$		0			0
$817$	−30010.4	−	51979.5i	−1.28511	−	2.22587i
$818$		0			0
$819$	−16274.3	+	1272.71i	−0.694345	+	0.0543005i
$820$		0			0
$821$	11563.6	+	20028.7i	0.491560	+	0.851407i	0.999953	−	0.00971819i	$-0.00309344\pi$
$821$	11563.6	+	20028.7i	0.491560	+	0.851407i	−0.508393	+	0.861125i	$0.669760\pi$
$822$		0			0
$823$	8296.81	−	14370.5i	0.351408	−	0.608656i	−0.635089	−	0.772439i	$-0.719036\pi$
$823$	8296.81	−	14370.5i	0.351408	−	0.608656i	0.986496	+	0.163783i	$0.0523698\pi$
$824$		0			0
$825$	2663.38			0.112396
$826$		0			0
$827$	31971.5			1.34433			0.672164	−	0.740402i	$-0.265365\pi$
$827$	31971.5			1.34433			0.672164	+	0.740402i	$0.265365\pi$
$828$		0			0
$829$	−11365.4	+	19685.5i	−0.476161	+	0.824734i	−0.999627	−	0.0273119i	$-0.991305\pi$
$829$	−11365.4	+	19685.5i	−0.476161	+	0.824734i	0.523466	+	0.852046i	$0.324639\pi$
$830$		0			0
$831$	20557.4	+	35606.5i	0.858158	+	1.48637i
$832$		0			0
$833$	25296.6	−	3980.93i	1.05219	−	0.165584i
$834$		0			0
$835$	−13235.7	−	22925.0i	−0.548553	−	0.950121i
$836$		0			0
$837$	29786.0	−	51590.9i	1.23005	−	2.13052i
$838$		0			0
$839$	−25162.2			−1.03539			−0.517697	−	0.855564i	$-0.673211\pi$
$839$	−25162.2			−1.03539			−0.517697	+	0.855564i	$0.673211\pi$
$840$		0			0
$841$	−18043.6			−0.739827
$842$		0			0
$843$	17710.8	−	30676.0i	0.723597	−	1.25331i
$844$		0			0
$845$	9671.36	+	16751.3i	0.393733	+	0.681966i
$846$		0			0
$847$	2234.13	−	174.718i	0.0906324	−	0.00708781i
$848$		0			0
$849$	−9836.42	−	17037.2i	−0.397627	−	0.688710i
$850$		0			0
$851$	8557.11	−	14821.3i	0.344693	−	0.597026i
$852$		0			0
$853$	−38703.4			−1.55355			−0.776775	−	0.629778i	$-0.783146\pi$
$853$	−38703.4			−1.55355			−0.776775	+	0.629778i	$0.783146\pi$
$854$		0			0
$855$	69309.4			2.77232
$856$		0			0
$857$	−3772.40	+	6533.99i	−0.150365	+	0.260440i	−0.931362	−	0.364095i	$-0.881378\pi$
$857$	−3772.40	+	6533.99i	−0.150365	+	0.260440i	0.780997	+	0.624535i	$0.214712\pi$
$858$		0			0
$859$	−22883.5	−	39635.4i	−0.908935	−	1.57432i	−0.815547	−	0.578691i	$-0.803564\pi$
$859$	−22883.5	−	39635.4i	−0.908935	−	1.57432i	−0.0933882	−	0.995630i	$-0.529770\pi$
$860$		0			0
$861$	21967.3	+	31996.5i	0.869505	+	1.26648i
$862$		0			0
$863$	−18553.6	−	32135.7i	−0.731832	−	1.26757i	−0.956099	−	0.293042i	$-0.905332\pi$
$863$	−18553.6	−	32135.7i	−0.731832	−	1.26757i	0.224268	−	0.974528i	$-0.428001\pi$
$864$		0			0
$865$	−5549.77	+	9612.49i	−0.218148	+	0.377843i
$866$		0			0
$867$	−6022.69			−0.235918
$868$		0			0
$869$	627.771			0.0245060
$870$		0			0
$871$	−7174.61	+	12426.8i	−0.279107	+	0.483428i
$872$		0			0
$873$	42209.4	+	73108.9i	1.63639	+	2.83432i
$874$		0			0
$875$	12002.1	−	25131.0i	0.463710	−	0.970952i
$876$		0			0
$877$	−23680.6	−	41016.0i	−0.911786	−	1.57926i	−0.811540	−	0.584297i	$-0.801370\pi$
$877$	−23680.6	−	41016.0i	−0.911786	−	1.57926i	−0.100246	−	0.994963i	$-0.531963\pi$
$878$		0			0
$879$	5081.57	−	8801.53i	0.194991	−	0.337734i
$880$		0			0
$881$	16214.3			0.620062			0.310031	−	0.950727i	$-0.399661\pi$
$881$	16214.3			0.620062			0.310031	+	0.950727i	$0.399661\pi$
$882$		0			0
$883$	−34094.7			−1.29941			−0.649705	−	0.760186i	$-0.725108\pi$
$883$	−34094.7			−1.29941			−0.649705	+	0.760186i	$0.725108\pi$
$884$		0			0
$885$	18062.1	−	31284.4i	0.686045	−	1.18826i
$886$		0			0
$887$	−22393.2	−	38786.1i	−0.847677	−	1.46822i	−0.883276	−	0.468853i	$-0.844667\pi$
$887$	−22393.2	−	38786.1i	−0.847677	−	1.46822i	0.0355995	−	0.999366i	$-0.488666\pi$
$888$		0			0
$889$	−19297.2	+	40406.0i	−0.728018	+	1.52438i
$890$		0			0
$891$	−4941.99	−	8559.78i	−0.185817	−	0.321845i
$892$		0			0
$893$	−9542.25	+	16527.7i	−0.357580	+	0.619347i
$894$		0			0
$895$	8554.20			0.319481
$896$		0			0
$897$	17946.5			0.668022
$898$		0			0
$899$	8965.42	−	15528.6i	0.332607	−	0.576092i
$900$		0			0
$901$	−11333.0	−	19629.3i	−0.419041	−	0.725800i
$902$		0			0
$903$	45993.4	+	66991.7i	1.69498	+	2.46882i
$904$		0			0
$905$	−17889.3	−	30985.2i	−0.657083	−	1.13810i
$906$		0			0
$907$	13310.4	−	23054.3i	0.487282	−	0.843998i	−0.512611	−	0.858621i	$-0.671322\pi$
$907$	13310.4	−	23054.3i	0.487282	−	0.843998i	0.999893	+	0.0146235i	$0.00465497\pi$
$908$		0			0
$909$	−50577.5			−1.84549
$910$		0			0
$911$	20283.3			0.737667			0.368833	−	0.929495i	$-0.379757\pi$
$911$	20283.3			0.737667			0.368833	+	0.929495i	$0.379757\pi$
$912$		0			0
$913$	2465.17	−	4269.79i	0.0893594	−	0.154775i
$914$		0			0
$915$	25270.1	+	43769.1i	0.913009	+	1.58138i
$916$		0			0
$917$	15399.2	−	1204.28i	0.554554	−	0.0433683i
$918$		0			0
$919$	−46.1317	−	79.9025i	−0.00165587	−	0.00286805i	0.865196	−	0.501433i	$-0.167194\pi$
$919$	−46.1317	−	79.9025i	−0.00165587	−	0.00286805i	−0.866852	+	0.498565i	$0.833860\pi$
$920$		0			0
$921$	21042.1	−	36446.0i	0.752835	−	1.30395i
$922$		0			0
$923$	8557.22			0.305162
$924$		0			0
$925$	3631.49			0.129084
$926$		0			0
$927$	−16894.7	+	29262.4i	−0.598591	+	1.03679i
$928$		0			0
$929$	−9683.70	−	16772.7i	−0.341994	−	0.592350i	0.642809	−	0.766026i	$-0.277769\pi$
$929$	−9683.70	−	16772.7i	−0.341994	−	0.592350i	−0.984803	+	0.173676i	$0.944435\pi$
$930$		0			0
$931$	−15362.4	+	39902.3i	−0.540796	+	1.40467i
$932$		0			0
$933$	−21619.5	−	37446.0i	−0.758616	−	1.31396i
$934$		0			0
$935$	−4073.86	+	7056.13i	−0.142491	+	0.246802i
$936$		0			0
$937$	14299.1			0.498540			0.249270	−	0.968434i	$-0.419809\pi$
$937$	14299.1			0.498540			0.249270	+	0.968434i	$0.419809\pi$
$938$		0			0
$939$	−91752.0			−3.18873
$940$		0			0
$941$	8937.95	−	15481.0i	0.309637	−	0.536308i	−0.668646	−	0.743581i	$-0.733126\pi$
$941$	8937.95	−	15481.0i	0.309637	−	0.536308i	0.978283	+	0.207274i	$0.0664590\pi$
$942$		0			0
$943$	−14398.0	−	24938.0i	−0.497203	−	0.861181i
$944$		0			0
$945$	−48479.3	+	3791.27i	−1.66882	+	0.130508i
$946$		0			0
$947$	23712.9	+	41072.0i	0.813692	+	1.40936i	0.910263	+	0.414030i	$0.135879\pi$
$947$	23712.9	+	41072.0i	0.813692	+	1.40936i	−0.0965710	+	0.995326i	$0.530787\pi$
$948$		0			0
$949$	−6288.68	+	10892.3i	−0.215110	+	0.372581i
$950$		0			0
$951$	−26743.9			−0.911913
$952$		0			0
$953$	−22421.7			−0.762132			−0.381066	−	0.924548i	$-0.624443\pi$
$953$	−22421.7			−0.762132			−0.381066	+	0.924548i	$0.624443\pi$
$954$		0			0
$955$	−13244.6	+	22940.2i	−0.448779	+	0.777308i
$956$		0			0
$957$	−3992.44	−	6915.11i	−0.134856	−	0.233578i
$958$		0			0
$959$	31481.0	+	45853.8i	1.06004	+	1.54400i
$960$		0			0
$961$	−10439.2	−	18081.2i	−0.350413	−	0.606933i
$962$		0			0
$963$	13288.5	−	23016.4i	0.444669	−	0.770189i
$964$		0			0
$965$	−21291.0			−0.710240
$966$		0			0
$967$	44665.0			1.48535			0.742674	−	0.669653i	$-0.233557\pi$
$967$	44665.0			1.48535			0.742674	+	0.669653i	$0.233557\pi$
$968$		0			0
$969$	42404.8	−	73447.3i	1.40582	−	2.43495i
$970$		0			0
$971$	−2530.86	−	4383.57i	−0.0836447	−	0.144877i	0.821168	−	0.570686i	$-0.193323\pi$
$971$	−2530.86	−	4383.57i	−0.0836447	−	0.144877i	−0.904813	+	0.425809i	$0.859989\pi$
$972$		0			0
$973$	10606.8	−	22209.3i	0.349474	−	0.731755i
$974$		0			0
$975$	1904.05	+	3297.91i	0.0625419	+	0.108326i
$976$		0			0
$977$	−2787.18	+	4827.54i	−0.0912691	+	0.158083i	−0.908045	−	0.418872i	$-0.862426\pi$
$977$	−2787.18	+	4827.54i	−0.0912691	+	0.158083i	0.816776	+	0.576955i	$0.195759\pi$
$978$		0			0
$979$	13614.0			0.444437
$980$		0			0
$981$	6984.66			0.227322
$982$		0			0
$983$	27493.5	−	47620.1i	0.892072	−	1.54511i	0.0546840	−	0.998504i	$-0.482585\pi$
$983$	27493.5	−	47620.1i	0.892072	−	1.54511i	0.837388	−	0.546610i	$-0.184082\pi$
$984$		0			0
$985$	25293.4	+	43809.5i	0.818188	+	1.41714i
$986$		0			0
$987$	11135.1	−	23315.5i	0.359102	−	0.751915i
$988$		0			0
$989$	−30145.3	−	52213.2i	−0.969226	−	1.67875i
$990$		0			0
$991$	−1970.81	+	3413.53i	−0.0631733	+	0.109419i	−0.895882	−	0.444292i	$-0.853455\pi$
$991$	−1970.81	+	3413.53i	−0.0631733	+	0.109419i	0.832709	+	0.553711i	$0.186789\pi$
$992$		0			0
$993$	63319.7			2.02356
$994$		0			0
$995$	3791.13			0.120791
$996$		0			0
$997$	29680.0	−	51407.4i	0.942805	−	1.63299i	0.182717	−	0.983165i	$-0.441511\pi$
$997$	29680.0	−	51407.4i	0.942805	−	1.63299i	0.760088	−	0.649821i	$-0.225156\pi$
$998$		0			0
$999$	−18085.6	−	31325.1i	−0.572774	−	0.992074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.4.i.a.221.10	yes	20
7.2	even	3	inner	308.4.i.a.177.10	✓	20
7.3	odd	6		2156.4.a.j.1.10		10
7.4	even	3		2156.4.a.m.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.4.i.a.177.10	✓	20	7.2	even	3	inner
308.4.i.a.221.10	yes	20	1.1	even	1	trivial
2156.4.a.j.1.10		10	7.3	odd	6
2156.4.a.m.1.1		10	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	308.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.55636 - 7.89185i) q^{3} +(-4.96059 - 8.59200i) q^{5} +(-7.98145 + 16.7122i) q^{7} +(-28.0208 - 48.5335i) q^{9} +(-5.50000 + 9.52628i) q^{11} -15.7278 q^{13} -90.4090 q^{15} +(-37.3293 + 64.6563i) q^{17} +(-62.3286 - 107.956i) q^{19} +(95.5235 + 139.135i) q^{21} +(-62.6087 - 108.441i) q^{23} +(13.2850 - 23.0104i) q^{25} -264.649 q^{27} -79.6577 q^{29} +(-112.549 + 194.941i) q^{31} +(50.1200 + 86.8103i) q^{33} +(183.184 - 14.3257i) q^{35} +(68.3380 + 118.365i) q^{37} +(-71.6613 + 124.121i) q^{39} +229.968 q^{41} +481.487 q^{43} +(-278.000 + 481.510i) q^{45} +(-76.5479 - 132.585i) q^{47} +(-215.593 - 266.775i) q^{49} +(340.172 + 589.194i) q^{51} +(-151.797 + 262.920i) q^{53} +109.133 q^{55} -1135.97 q^{57} +(-199.782 + 346.032i) q^{59} +(-279.508 - 484.123i) q^{61} +(1034.75 - 80.9213i) q^{63} +(78.0190 + 135.133i) q^{65} +(456.175 - 790.118i) q^{67} -1141.07 q^{69} -544.084 q^{71} +(399.846 - 692.554i) q^{73} +(-121.063 - 209.687i) q^{75} +(-115.307 - 167.950i) q^{77} +(-28.5350 - 49.4242i) q^{79} +(-449.272 + 778.162i) q^{81} -448.212 q^{83} +740.702 q^{85} +(-362.949 + 628.647i) q^{87} +(-618.816 - 1071.82i) q^{89} +(125.530 - 262.845i) q^{91} +(1025.63 + 1776.44i) q^{93} +(-618.373 + 1071.05i) q^{95} -1506.36 q^{97} +616.458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} - 10 q^{5} - 20 q^{7} - 104 q^{9} - 110 q^{11} + 16 q^{13} + 108 q^{15} - 166 q^{17} - 342 q^{19} - 42 q^{21} + 54 q^{23} - 198 q^{25} + 612 q^{27} - 160 q^{29} - 492 q^{31} - 66 q^{33} + 310 q^{35}+ \cdots + 2288 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 - 10 * q^5 - 20 * q^7 - 104 * q^9 - 110 * q^11 + 16 * q^13 + 108 * q^15 - 166 * q^17 - 342 * q^19 - 42 * q^21 + 54 * q^23 - 198 * q^25 + 612 * q^27 - 160 * q^29 - 492 * q^31 - 66 * q^33 + 310 * q^35 - 258 * q^37 + 418 * q^39 + 1268 * q^41 - 548 * q^43 - 138 * q^45 - 312 * q^47 + 572 * q^49 + 196 * q^51 - 656 * q^53 + 220 * q^55 - 1476 * q^57 - 934 * q^59 + 228 * q^61 - 1270 * q^63 - 524 * q^65 - 478 * q^67 + 3144 * q^69 + 276 * q^71 + 364 * q^73 - 234 * q^75 - 154 * q^77 + 616 * q^79 - 4082 * q^81 - 264 * q^83 - 992 * q^85 + 2120 * q^87 - 1906 * q^89 - 94 * q^91 + 2984 * q^93 - 2322 * q^95 + 2700 * q^97 + 2288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more