LMFDB - Embedded newform 200.4.f.c.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,4,Mod(149,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not 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:	$11.8003820011$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 7x^{10} - 12x^{9} + 21x^{8} - 68x^{6} + 336x^{4} - 768x^{3} + 1792x^{2} - 4096x + 4096 $ x^12 - 4x^11 + 7x^10 - 12x^9 + 21x^8 - 68x^6 + 336x^4 - 768x^3 + 1792x^2 - 4096*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.2
Root			$-0.428316 + 1.95360i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.4.f.c.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.38191 + 1.52528i) q^{2} +1.51777 q^{3} +(3.34703 - 7.26618i) q^{4} +(-3.61520 + 2.31503i) q^{6} +5.13620i q^{7} +(3.11063 + 22.4126i) q^{8} -24.6964 q^{9} -31.3403i q^{11} +(5.08003 - 11.0284i) q^{12} +4.75340 q^{13} +(-7.83414 - 12.2340i) q^{14} +(-41.5948 - 48.6403i) q^{16} +108.154i q^{17} +(58.8246 - 37.6689i) q^{18} +89.8913i q^{19} +7.79558i q^{21} +(47.8028 + 74.6499i) q^{22} +68.5157i q^{23} +(4.72123 + 34.0172i) q^{24} +(-11.3222 + 7.25027i) q^{26} -78.4633 q^{27} +(37.3205 + 17.1910i) q^{28} -16.5719i q^{29} -300.523 q^{31} +(173.265 + 52.4132i) q^{32} -47.5675i q^{33} +(-164.966 - 257.614i) q^{34} +(-82.6595 + 179.448i) q^{36} -327.879 q^{37} +(-137.109 - 214.113i) q^{38} +7.21458 q^{39} -73.4968 q^{41} +(-11.8904 - 18.5684i) q^{42} -0.836008 q^{43} +(-227.724 - 104.897i) q^{44} +(-104.506 - 163.198i) q^{46} +228.335i q^{47} +(-63.1314 - 73.8249i) q^{48} +316.619 q^{49} +164.153i q^{51} +(15.9098 - 34.5391i) q^{52} -647.393 q^{53} +(186.893 - 119.679i) q^{54} +(-115.115 + 15.9768i) q^{56} +136.434i q^{57} +(25.2768 + 39.4728i) q^{58} +753.676i q^{59} -290.838i q^{61} +(715.821 - 458.383i) q^{62} -126.845i q^{63} +(-492.648 + 139.435i) q^{64} +(72.5538 + 113.302i) q^{66} -801.801 q^{67} +(785.868 + 361.995i) q^{68} +103.991i q^{69} +767.674 q^{71} +(-76.8213 - 553.509i) q^{72} +48.3194i q^{73} +(780.980 - 500.108i) q^{74} +(653.166 + 300.869i) q^{76} +160.970 q^{77} +(-17.1845 + 11.0043i) q^{78} -451.701 q^{79} +547.712 q^{81} +(175.063 - 112.103i) q^{82} +976.099 q^{83} +(56.6441 + 26.0920i) q^{84} +(1.99130 - 1.27515i) q^{86} -25.1524i q^{87} +(702.417 - 97.4881i) q^{88} +1204.25 q^{89} +24.4144i q^{91} +(497.847 + 229.324i) q^{92} -456.126 q^{93} +(-348.275 - 543.873i) q^{94} +(262.977 + 79.5513i) q^{96} -559.147i q^{97} +(-754.161 + 482.934i) q^{98} +773.992i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 12 q^{3} - 16 q^{4} - 36 q^{6} - 24 q^{8} + 108 q^{9} - 164 q^{12} - 68 q^{14} - 56 q^{16} + 450 q^{18} + 492 q^{22} - 360 q^{24} - 308 q^{26} + 432 q^{27} + 628 q^{28} - 264 q^{31} + 856 q^{32}+ \cdots + 638 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 + 12 * q^3 - 16 * q^4 - 36 * q^6 - 24 * q^8 + 108 * q^9 - 164 * q^12 - 68 * q^14 - 56 * q^16 + 450 * q^18 + 492 * q^22 - 360 * q^24 - 308 * q^26 + 432 * q^27 + 628 * q^28 - 264 * q^31 + 856 * q^32 + 180 * q^34 + 440 * q^36 + 136 * q^37 - 1388 * q^38 - 600 * q^39 + 40 * q^41 - 2332 * q^42 - 1204 * q^43 + 472 * q^44 - 1268 * q^46 - 2536 * q^48 - 1308 * q^49 - 1272 * q^52 + 1056 * q^53 + 1512 * q^54 - 728 * q^56 + 1528 * q^58 + 2104 * q^62 + 2048 * q^64 + 2928 * q^66 - 2412 * q^67 + 960 * q^68 - 1592 * q^71 + 744 * q^72 + 420 * q^74 + 2256 * q^76 + 824 * q^77 - 160 * q^78 - 2016 * q^79 + 2508 * q^81 + 352 * q^82 + 3556 * q^83 - 1048 * q^84 - 244 * q^86 + 1008 * q^88 + 424 * q^89 + 1068 * q^92 + 2784 * q^93 - 292 * q^94 - 5920 * q^96 + 638 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−2.38191	+	1.52528i	−0.842134	+	0.539269i
$2$	−2.38191	+	1.52528i	−0.842134	+	0.539269i
$3$	1.51777			0.292095			0.146048	−	0.989278i	$-0.453345\pi$
$3$	1.51777			0.292095			0.146048	+	0.989278i	$0.453345\pi$
$4$	3.34703	−	7.26618i	0.418379	−	0.908273i
$5$		0			0
$5$		0			0
$6$	−3.61520	+	2.31503i	−0.245983	+	0.157518i
$7$			5.13620i			0.277328i	0.990339	+	0.138664i	$0.0442809\pi$
$7$			5.13620i			0.277328i	−0.990339	+	0.138664i	$0.955719\pi$
$8$	3.11063	+	22.4126i	0.137472	+	0.990506i
$9$	−24.6964			−0.914680
$10$		0			0
$11$		−	31.3403i		−	0.859042i	−0.903057	−	0.429521i	$-0.858682\pi$
$11$		−	31.3403i		−	0.859042i	0.903057	−	0.429521i	$-0.141318\pi$
$12$	5.08003	−	11.0284i	0.122207	−	0.265302i
$13$	4.75340			0.101412			0.0507060	−	0.998714i	$-0.483853\pi$
$13$	4.75340			0.101412			0.0507060	+	0.998714i	$0.483853\pi$
$14$	−7.83414	−	12.2340i	−0.149555	−	0.233548i
$15$		0			0
$16$	−41.5948	−	48.6403i	−0.649918	−	0.760004i
$17$			108.154i			1.54301i	0.636221	+	0.771507i	$0.280497\pi$
$17$			108.154i			1.54301i	−0.636221	+	0.771507i	$0.719503\pi$
$18$	58.8246	−	37.6689i	0.770283	−	0.493258i
$19$			89.8913i			1.08539i	0.839929	+	0.542697i	$0.182597\pi$
$19$			89.8913i			1.08539i	−0.839929	+	0.542697i	$0.817403\pi$
$20$		0			0
$21$			7.79558i			0.0810064i
$22$	47.8028	+	74.6499i	0.463254	+	0.723428i
$23$			68.5157i			0.621152i	0.950548	+	0.310576i	$0.100522\pi$
$23$			68.5157i			0.621152i	−0.950548	+	0.310576i	$0.899478\pi$
$24$	4.72123	+	34.0172i	0.0401549	+	0.289322i
$25$		0			0
$26$	−11.3222	+	7.25027i	−0.0854025	+	0.0546883i
$27$	−78.4633			−0.559269
$28$	37.3205	+	17.1910i	0.251890	+	0.116028i
$29$		−	16.5719i		−	0.106115i	−0.998591	−	0.0530573i	$-0.983103\pi$
$29$		−	16.5719i		−	0.106115i	0.998591	−	0.0530573i	$-0.0168966\pi$
$30$		0			0
$31$	−300.523			−1.74115			−0.870574	−	0.492037i	$-0.836252\pi$
$31$	−300.523			−1.74115			−0.870574	+	0.492037i	$0.836252\pi$
$32$	173.265	+	52.4132i	0.957164	+	0.289545i
$33$		−	47.5675i		−	0.250922i
$34$	−164.966	−	257.614i	−0.832099	−	1.29942i
$35$		0			0
$36$	−82.6595	+	179.448i	−0.382683	+	0.830779i
$37$	−327.879			−1.45684			−0.728419	−	0.685132i	$-0.759744\pi$
$37$	−327.879			−1.45684			−0.728419	+	0.685132i	$0.759744\pi$
$38$	−137.109	−	214.113i	−0.585318	−	0.914046i
$39$	7.21458			0.0296220
$40$		0			0
$41$	−73.4968			−0.279958			−0.139979	−	0.990154i	$-0.544703\pi$
$41$	−73.4968			−0.279958			−0.139979	+	0.990154i	$0.544703\pi$
$42$	−11.8904	−	18.5684i	−0.0436842	−	0.0682182i
$43$	−0.836008			−0.00296489			−0.00148244	−	0.999999i	$-0.500472\pi$
$43$	−0.836008			−0.00296489			−0.00148244	+	0.999999i	$0.500472\pi$
$44$	−227.724	−	104.897i	−0.780244	−	0.359405i
$45$		0			0
$46$	−104.506	−	163.198i	−0.334968	−	0.523093i
$47$			228.335i			0.708639i	0.935124	+	0.354319i	$0.115287\pi$
$47$			228.335i			0.708639i	−0.935124	+	0.354319i	$0.884713\pi$
$48$	−63.1314	−	73.8249i	−0.189838	−	0.221994i
$49$	316.619			0.923089
$50$		0			0
$51$			164.153i			0.450707i
$52$	15.9098	−	34.5391i	0.0424286	−	0.0921097i
$53$	−647.393			−1.67785			−0.838927	−	0.544244i	$-0.816817\pi$
$53$	−647.393			−1.67785			−0.838927	+	0.544244i	$0.816817\pi$
$54$	186.893	−	119.679i	0.470980	−	0.301596i
$55$		0			0
$56$	−115.115	+	15.9768i	−0.274695	+	0.0381248i
$57$			136.434i			0.317038i
$58$	25.2768	+	39.4728i	0.0572243	+	0.0893627i
$59$			753.676i			1.66305i	0.555484	+	0.831527i	$0.312533\pi$
$59$			753.676i			1.66305i	−0.555484	+	0.831527i	$0.687467\pi$
$60$		0			0
$61$		−	290.838i		−	0.610459i	−0.952279	−	0.305229i	$-0.901267\pi$
$61$		−	290.838i		−	0.610459i	0.952279	−	0.305229i	$-0.0987331\pi$
$62$	715.821	−	458.383i	1.46628	−	0.938946i
$63$		−	126.845i		−	0.253667i
$64$	−492.648	+	139.435i	−0.962203	+	0.272333i
$65$		0			0
$66$	72.5538	+	113.302i	0.135314	+	0.211310i
$67$	−801.801			−1.46202			−0.731012	−	0.682364i	$-0.760952\pi$
$67$	−801.801			−1.46202			−0.731012	+	0.682364i	$0.760952\pi$
$68$	785.868	+	361.995i	1.40148	+	0.645565i
$69$			103.991i			0.181436i
$70$		0			0
$71$	767.674			1.28318			0.641592	−	0.767046i	$-0.278274\pi$
$71$	767.674			1.28318			0.641592	+	0.767046i	$0.278274\pi$
$72$	−76.8213	−	553.509i	−0.125743	−	0.905996i
$73$			48.3194i			0.0774707i	0.999250	+	0.0387353i	$0.0123329\pi$
$73$			48.3194i			0.0774707i	−0.999250	+	0.0387353i	$0.987667\pi$
$74$	780.980	−	500.108i	1.22685	−	0.785627i
$75$		0			0
$76$	653.166	+	300.869i	0.985833	+	0.454106i
$77$	160.970			0.238237
$78$	−17.1845	+	11.0043i	−0.0249457	+	0.0159742i
$79$	−451.701			−0.643296			−0.321648	−	0.946859i	$-0.604237\pi$
$79$	−451.701			−0.643296			−0.321648	+	0.946859i	$0.604237\pi$
$80$		0			0
$81$	547.712			0.751320
$82$	175.063	−	112.103i	0.235762	−	0.150973i
$83$	976.099			1.29085			0.645427	−	0.763822i	$-0.276680\pi$
$83$	976.099			1.29085			0.645427	+	0.763822i	$0.276680\pi$
$84$	56.6441	+	26.0920i	0.0735759	+	0.0338914i
$85$		0			0
$86$	1.99130	−	1.27515i	0.00249683	−	0.00159887i
$87$		−	25.1524i		−	0.0309956i
$88$	702.417	−	97.4881i	0.850886	−	0.118094i
$89$	1204.25			1.43428			0.717139	−	0.696930i	$-0.245451\pi$
$89$	1204.25			1.43428			0.717139	+	0.696930i	$0.245451\pi$
$90$		0			0
$91$			24.4144i			0.0281244i
$92$	497.847	+	229.324i	0.564176	+	0.259877i
$93$	−456.126			−0.508581
$94$	−348.275	−	543.873i	−0.382147	−	0.596769i
$95$		0			0
$96$	262.977	+	79.5513i	0.279583	+	0.0845747i
$97$		−	559.147i		−	0.585287i	−0.956222	−	0.292643i	$-0.905465\pi$
$97$		−	559.147i		−	0.585287i	0.956222	−	0.292643i	$-0.0945348\pi$
$98$	−754.161	+	482.934i	−0.777364	+	0.497793i
$99$			773.992i			0.785749i
$100$		0			0
$101$		−	542.070i		−	0.534039i	−0.963691	−	0.267020i	$-0.913961\pi$
$101$		−	542.070i		−	0.534039i	0.963691	−	0.267020i	$-0.0860389\pi$
$102$	−250.380	−	390.999i	−0.243052	−	0.379556i
$103$			1764.97i			1.68842i	0.536009	+	0.844212i	$0.319931\pi$
$103$			1764.97i			1.68842i	−0.536009	+	0.844212i	$0.680069\pi$
$104$	14.7861	+	106.536i	0.0139413	+	0.100449i
$105$		0			0
$106$	1542.03	−	987.457i	1.41298	−	0.904814i
$107$	442.840			0.400103			0.200051	−	0.979785i	$-0.435889\pi$
$107$	442.840			0.400103			0.200051	+	0.979785i	$0.435889\pi$
$108$	−262.619	+	570.129i	−0.233986	+	0.507969i
$109$		−	1547.20i		−	1.35959i	−0.733403	−	0.679795i	$-0.762069\pi$
$109$		−	1547.20i		−	1.35959i	0.733403	−	0.679795i	$-0.237931\pi$
$110$		0			0
$111$	−497.646			−0.425536
$112$	249.826	−	213.639i	0.210771	−	0.180241i
$113$		−	788.524i		−	0.656444i	−0.944601	−	0.328222i	$-0.893551\pi$
$113$		−	788.524i		−	0.656444i	0.944601	−	0.328222i	$-0.106449\pi$
$114$	−208.101	−	324.975i	−0.170969	−	0.266989i
$115$		0			0
$116$	−120.414	−	55.4667i	−0.0963810	−	0.0443961i
$117$	−117.392			−0.0927596
$118$	−1149.57	−	1795.19i	−0.896833	−	1.40051i
$119$	−555.501			−0.427922
$120$		0			0
$121$	348.785			0.262047
$122$	443.610	+	692.751i	0.329201	+	0.514088i
$123$	−111.551			−0.0817744
$124$	−1005.86	+	2183.66i	−0.728460	+	1.58144i
$125$		0			0
$126$	193.475	+	302.135i	0.136795	+	0.213621i
$127$		−	1543.92i		−	1.07875i	−0.842066	−	0.539374i	$-0.818661\pi$
$127$		−	1543.92i		−	1.07875i	0.842066	−	0.539374i	$-0.181339\pi$
$128$	960.768	−	1083.55i	0.663443	−	0.748227i
$129$	−1.26887			−0.000866029
$130$		0			0
$131$			1933.26i			1.28938i	0.764442	+	0.644692i	$0.223014\pi$
$131$			1933.26i			1.28938i	−0.764442	+	0.644692i	$0.776986\pi$
$132$	−345.634	−	159.210i	−0.227906	−	0.104981i
$133$	−461.699			−0.301010
$134$	1909.82	−	1222.97i	1.23122	−	0.788424i
$135$		0			0
$136$	−2424.02	+	336.428i	−1.52836	+	0.212121i
$137$			478.247i			0.298244i	0.988819	+	0.149122i	$0.0476447\pi$
$137$			478.247i			0.298244i	−0.988819	+	0.149122i	$0.952355\pi$
$138$	−158.616	−	247.698i	−0.0978426	−	0.152793i
$139$			2057.45i			1.25547i	0.778427	+	0.627735i	$0.216018\pi$
$139$			2057.45i			1.25547i	−0.778427	+	0.627735i	$0.783982\pi$
$140$		0			0
$141$			346.560i			0.206990i
$142$	−1828.53	+	1170.92i	−1.08061	+	0.691981i
$143$		−	148.973i		−	0.0871172i
$144$	1027.24	+	1201.24i	0.594467	+	0.695161i
$145$		0			0
$146$	−73.7007	−	115.093i	−0.0417775	−	0.0652407i
$147$	480.556			0.269630
$148$	−1097.42	+	2382.43i	−0.609510	+	1.32321i
$149$		−	2838.89i		−	1.56088i	−0.625231	−	0.780440i	$-0.714995\pi$
$149$		−	2838.89i		−	1.56088i	0.625231	−	0.780440i	$-0.285005\pi$
$150$		0			0
$151$	−2187.09			−1.17869			−0.589346	−	0.807881i	$-0.700615\pi$
$151$	−2187.09			−1.17869			−0.589346	+	0.807881i	$0.700615\pi$
$152$	−2014.70	+	279.619i	−1.07509	+	0.149211i
$153$		−	2671.02i		−	1.41136i
$154$	−383.417	+	245.525i	−0.200627	+	0.128474i
$155$		0			0
$156$	24.1474	−	52.4224i	0.0123932	−	0.0269048i
$157$	936.231			0.475920			0.237960	−	0.971275i	$-0.423521\pi$
$157$	936.231			0.475920			0.237960	+	0.971275i	$0.423521\pi$
$158$	1075.91	−	688.972i	0.541741	−	0.346909i
$159$	−982.595			−0.490093
$160$		0			0
$161$	−351.910			−0.172263
$162$	−1304.60	+	835.416i	−0.632712	+	0.405163i
$163$	2329.68			1.11948			0.559738	−	0.828670i	$-0.310902\pi$
$163$	2329.68			1.11948			0.559738	+	0.828670i	$0.310902\pi$
$164$	−245.996	+	534.041i	−0.117128	+	0.254278i
$165$		0			0
$166$	−2324.98	+	1488.83i	−1.08707	+	0.696117i
$167$			2020.42i			0.936195i	0.883677	+	0.468097i	$0.155060\pi$
$167$			2020.42i			0.936195i	−0.883677	+	0.468097i	$0.844940\pi$
$168$	−174.719	+	24.2492i	−0.0802373	+	0.0111361i
$169$	−2174.41			−0.989716
$170$		0			0
$171$		−	2219.99i		−	0.992788i
$172$	−2.79815	+	6.07459i	−0.00124045	+	0.00269292i
$173$	−912.153			−0.400866			−0.200433	−	0.979707i	$-0.564235\pi$
$173$	−912.153			−0.400866			−0.200433	+	0.979707i	$0.564235\pi$
$174$	38.3645	+	59.9108i	0.0167150	+	0.0261024i
$175$		0			0
$176$	−1524.40	+	1303.59i	−0.652875	+	0.558307i
$177$			1143.91i			0.485771i
$178$	−2868.43	+	1836.83i	−1.20785	+	0.773461i
$179$		−	3226.95i		−	1.34745i	−0.738982	−	0.673726i	$-0.764693\pi$
$179$		−	3226.95i		−	1.34745i	0.738982	−	0.673726i	$-0.235307\pi$
$180$		0			0
$181$		−	1003.43i		−	0.412068i	−0.978545	−	0.206034i	$-0.933944\pi$
$181$		−	1003.43i		−	0.412068i	0.978545	−	0.206034i	$-0.0660557\pi$
$182$	−37.2388	−	58.1530i	−0.0151666	−	0.0236845i
$183$		−	441.426i		−	0.178312i
$184$	−1535.61	+	213.127i	−0.615255	+	0.0853909i
$185$		0			0
$186$	1086.45	−	695.721i	0.428294	−	0.274262i
$187$	3389.59			1.32551
$188$	1659.12	+	764.243i	0.643637	+	0.296480i
$189$		−	403.003i		−	0.155101i
$190$		0			0
$191$	1272.08			0.481907			0.240953	−	0.970537i	$-0.422540\pi$
$191$	1272.08			0.481907			0.240953	+	0.970537i	$0.422540\pi$
$192$	−747.727	+	211.630i	−0.281055	+	0.0795473i
$193$			730.914i			0.272603i	0.990667	+	0.136301i	$0.0435216\pi$
$193$			730.914i			0.272603i	−0.990667	+	0.136301i	$0.956478\pi$
$194$	852.857	+	1331.84i	0.315627	+	0.492890i
$195$		0			0
$196$	1059.74	−	2300.61i	0.386201	−	0.838416i
$197$	3582.02			1.29547			0.647737	−	0.761864i	$-0.275716\pi$
$197$	3582.02			1.29547			0.647737	+	0.761864i	$0.275716\pi$
$198$	−1180.56	−	1843.58i	−0.423729	−	0.661705i
$199$	−2007.64			−0.715166			−0.357583	−	0.933881i	$-0.616399\pi$
$199$	−2007.64			−0.715166			−0.357583	+	0.933881i	$0.616399\pi$
$200$		0			0
$201$	−1216.95			−0.427051
$202$	826.809	+	1291.16i	0.287991	+	0.449733i
$203$	85.1165			0.0294286
$204$	1192.77	+	549.427i	0.409365	+	0.188567i
$205$		0			0
$206$	−2692.08	−	4204.01i	−0.910514	−	1.42188i
$207$		−	1692.09i		−	0.568156i
$208$	−197.717	−	231.207i	−0.0659095	−	0.0770736i
$209$	2817.22			0.932398
$210$		0			0
$211$			1414.79i			0.461603i	0.973001	+	0.230802i	$0.0741349\pi$
$211$			1414.79i			0.461603i	−0.973001	+	0.230802i	$0.925865\pi$
$212$	−2166.84	+	4704.07i	−0.701979	+	1.52395i
$213$	1165.15			0.374812
$214$	−1054.81	+	675.456i	−0.336940	+	0.215763i
$215$		0			0
$216$	−244.070	−	1758.57i	−0.0768837	−	0.553959i
$217$		−	1543.55i		−	0.482870i
$218$	2359.92	+	3685.31i	0.733184	+	1.14496i
$219$			73.3379i			0.0226288i
$220$		0			0
$221$			514.100i			0.156480i
$222$	1185.35	−	759.050i	0.358358	−	0.229478i
$223$		−	1.69909i		−	0.000510221i	−1.00000		0.000255111i	$-0.999919\pi$
$223$		−	1.69909i		−	0.000510221i	1.00000		0.000255111i	$-8.12042e-5\pi$
$224$	−269.205	+	889.924i	−0.0802990	+	0.265449i
$225$		0			0
$226$	1202.72	+	1878.20i	0.353999	+	0.552813i
$227$	−3374.87			−0.986775			−0.493387	−	0.869810i	$-0.664241\pi$
$227$	−3374.87			−0.986775			−0.493387	+	0.869810i	$0.664241\pi$
$228$	991.358	+	456.650i	0.287957	+	0.132642i
$229$		−	1330.69i		−	0.383994i	−0.981396	−	0.191997i	$-0.938504\pi$
$229$		−	1330.69i		−	0.383994i	0.981396	−	0.191997i	$-0.0614964\pi$
$230$		0			0
$231$	244.316			0.0695879
$232$	371.419	−	51.5491i	0.105107	−	0.0145878i
$233$			4373.02i			1.22955i	0.788701	+	0.614776i	$0.210754\pi$
$233$			4373.02i			1.22955i	−0.788701	+	0.614776i	$0.789246\pi$
$234$	279.617	−	179.055i	0.0781160	−	0.0500223i
$235$		0			0
$236$	5476.34	+	2522.58i	1.51051	+	0.695787i
$237$	−685.580			−0.187904
$238$	1323.16	−	847.296i	0.360367	−	0.230765i
$239$	−794.613			−0.215060			−0.107530	−	0.994202i	$-0.534294\pi$
$239$	−794.613			−0.215060			−0.107530	+	0.994202i	$0.534294\pi$
$240$		0			0
$241$	617.471			0.165041			0.0825204	−	0.996589i	$-0.473703\pi$
$241$	617.471			0.165041			0.0825204	+	0.996589i	$0.473703\pi$
$242$	−830.776	+	531.995i	−0.220679	+	0.141314i
$243$	2949.81			0.778727
$244$	−2113.28	−	973.444i	−0.554463	−	0.255403i
$245$		0			0
$246$	265.706	−	170.147i	0.0688650	−	0.0440984i
$247$			427.289i			0.110072i
$248$	−934.817	−	6735.51i	−0.239359	−	1.72462i
$249$	1481.50			0.377052
$250$		0			0
$251$			907.026i			0.228092i	0.993475	+	0.114046i	$0.0363811\pi$
$251$			907.026i			0.228092i	−0.993475	+	0.114046i	$0.963619\pi$
$252$	−921.681	−	424.555i	−0.230399	−	0.106129i
$253$	2147.30			0.533596
$254$	2354.92	+	3677.49i	0.581735	+	0.908450i
$255$		0			0
$256$	−635.751	+	4046.36i	−0.155213	+	0.987881i
$257$		−	4350.70i		−	1.05599i	−0.849248	−	0.527994i	$-0.822944\pi$
$257$		−	4350.70i		−	1.05599i	0.849248	−	0.527994i	$-0.177056\pi$
$258$	3.02234	−	1.93538i	0.000729313	−	0.000467022i
$259$		−	1684.05i		−	0.404022i
$260$		0			0
$261$			409.266i			0.0970610i
$262$	−2948.76	−	4604.85i	−0.695324	−	1.08583i
$263$		−	3606.18i		−	0.845499i	−0.906246	−	0.422750i	$-0.861065\pi$
$263$		−	3606.18i		−	0.845499i	0.906246	−	0.422750i	$-0.138935\pi$
$264$	1066.11	−	147.965i	0.248540	−	0.0344947i
$265$		0			0
$266$	1099.73	−	704.221i	0.253491	−	0.162325i
$267$	1827.78			0.418946
$268$	−2683.65	+	5826.03i	−0.611680	+	1.32792i
$269$			6501.85i			1.47370i	0.676057	+	0.736849i	$0.263687\pi$
$269$			6501.85i			1.47370i	−0.676057	+	0.736849i	$0.736313\pi$
$270$		0			0
$271$	1011.82			0.226803			0.113401	−	0.993549i	$-0.463825\pi$
$271$	1011.82			0.226803			0.113401	+	0.993549i	$0.463825\pi$
$272$	5260.65	−	4498.65i	1.17270	−	1.00283i
$273$			37.0555i			0.00821502i
$274$	−729.461	−	1139.14i	−0.160833	−	0.251161i
$275$		0			0
$276$	755.619	+	348.062i	0.164793	+	0.0759089i
$277$	−2618.50			−0.567979			−0.283990	−	0.958827i	$-0.591658\pi$
$277$	−2618.50			−0.567979			−0.283990	+	0.958827i	$0.591658\pi$
$278$	−3138.19	−	4900.66i	−0.677036	−	1.05727i
$279$	7421.84			1.59259
$280$		0			0
$281$	2302.29			0.488766			0.244383	−	0.969679i	$-0.421415\pi$
$281$	2302.29			0.488766			0.244383	+	0.969679i	$0.421415\pi$
$282$	−528.602	−	825.476i	−0.111623	−	0.174313i
$283$	−6591.42			−1.38452			−0.692260	−	0.721648i	$-0.743385\pi$
$283$	−6591.42			−1.38452			−0.692260	+	0.721648i	$0.743385\pi$
$284$	2569.43	−	5578.06i	0.536857	−	1.16548i
$285$		0			0
$286$	227.226	+	354.841i	0.0469795	+	0.0733643i
$287$		−	377.494i		−	0.0776403i
$288$	−4279.02	−	1294.42i	−0.875499	−	0.264841i
$289$	−6784.33			−1.38089
$290$		0			0
$291$		−	848.658i		−	0.170960i
$292$	351.098	+	161.727i	0.0703645	+	0.0324121i
$293$	−4765.54			−0.950190			−0.475095	−	0.879934i	$-0.657586\pi$
$293$	−4765.54			−0.950190			−0.475095	+	0.879934i	$0.657586\pi$
$294$	−1144.64	+	732.984i	−0.227065	+	0.145403i
$295$		0			0
$296$	−1019.91	−	7348.62i	−0.200274	−	1.44301i
$297$			2459.06i			0.480436i
$298$	4330.11	+	6762.00i	0.841733	+	1.31447i
$299$			325.682i			0.0629923i
$300$		0			0
$301$		−	4.29390i		−	0.000822247i
$302$	5209.45	−	3335.92i	0.992617	−	0.635632i
$303$		−	822.739i		−	0.155990i
$304$	4372.34	−	3739.01i	0.824903	−	0.705417i
$305$		0			0
$306$	4074.05	+	6362.13i	0.761105	+	1.18856i
$307$	117.958			0.0219290			0.0109645	−	0.999940i	$-0.496510\pi$
$307$	117.958			0.0219290			0.0109645	+	0.999940i	$0.496510\pi$
$308$	538.771	−	1169.64i	0.0996732	−	0.216384i
$309$			2678.82i			0.493181i
$310$		0			0
$311$	4085.06			0.744832			0.372416	−	0.928066i	$-0.378530\pi$
$311$	4085.06			0.744832			0.372416	+	0.928066i	$0.378530\pi$
$312$	22.4419	+	161.697i	0.00407219	+	0.0293407i
$313$		−	904.680i		−	0.163372i	−0.996658	−	0.0816861i	$-0.973969\pi$
$313$		−	904.680i		−	0.163372i	0.996658	−	0.0816861i	$-0.0260305\pi$
$314$	−2230.02	+	1428.02i	−0.400788	+	0.256648i
$315$		0			0
$316$	−1511.86	+	3282.14i	−0.269141	+	0.584288i
$317$	−5437.26			−0.963366			−0.481683	−	0.876346i	$-0.659974\pi$
$317$	−5437.26			−0.963366			−0.481683	+	0.876346i	$0.659974\pi$
$318$	2340.46	−	1498.73i	0.412724	−	0.264292i
$319$	−519.369			−0.0911569
$320$		0			0
$321$	672.131			0.116868
$322$	838.219	−	536.762i	0.145069	−	0.0928961i
$323$	−9722.12			−1.67478
$324$	1833.21	−	3979.78i	0.314337	−	0.682404i
$325$		0			0
$326$	−5549.10	+	3553.42i	−0.942749	+	0.603698i
$327$		−	2348.30i		−	0.397130i
$328$	−228.621	−	1647.25i	−0.0384863	−	0.277300i
$329$	−1172.77			−0.196526
$330$		0			0
$331$		−	5944.03i		−	0.987049i	−0.869732	−	0.493525i	$-0.835708\pi$
$331$		−	5944.03i		−	0.987049i	0.869732	−	0.493525i	$-0.164292\pi$
$332$	3267.03	−	7092.51i	0.540066	−	1.17245i
$333$	8097.42			1.33254
$334$	−3081.71	−	4812.46i	−0.504860	−	0.788401i
$335$		0			0
$336$	379.179	−	324.255i	0.0615652	−	0.0526475i
$337$			5636.91i			0.911164i	0.890194	+	0.455582i	$0.150569\pi$
$337$			5636.91i			0.911164i	−0.890194	+	0.455582i	$0.849431\pi$
$338$	5179.25	−	3316.58i	0.833473	−	0.533722i
$339$		−	1196.80i		−	0.191744i
$340$		0			0
$341$			9418.50i			1.49572i
$342$	3386.11	+	5287.82i	0.535379	+	0.836060i
$343$			3387.93i			0.533327i
$344$	−2.60051	−	18.7371i	−0.000407588	−	0.00293674i
$345$		0			0
$346$	2172.67	−	1391.29i	0.337582	−	0.216174i
$347$	−7761.12			−1.20069			−0.600344	−	0.799742i	$-0.704970\pi$
$347$	−7761.12			−1.20069			−0.600344	+	0.799742i	$0.704970\pi$
$348$	−182.762	−	84.1858i	−0.0281525	−	0.0129679i
$349$			8709.62i			1.33586i	0.744224	+	0.667930i	$0.232819\pi$
$349$			8709.62i			1.33586i	−0.744224	+	0.667930i	$0.767181\pi$
$350$		0			0
$351$	−372.968			−0.0567166
$352$	1642.65	−	5430.19i	0.248731	−	0.822244i
$353$			986.323i			0.148716i	0.997232	+	0.0743579i	$0.0236907\pi$
$353$			986.323i			0.148716i	−0.997232	+	0.0743579i	$0.976309\pi$
$354$	−1744.78	−	2724.69i	−0.261961	−	0.409084i
$355$		0			0
$356$	4030.68	−	8750.33i	0.600072	−	1.30272i
$357$	−843.124			−0.124994
$358$	4922.01	+	7686.32i	0.726638	+	1.13473i
$359$	11470.1			1.68626			0.843131	−	0.537708i	$-0.180710\pi$
$359$	11470.1			1.68626			0.843131	+	0.537708i	$0.180710\pi$
$360$		0			0
$361$	−1221.44			−0.178078
$362$	1530.51	+	2390.08i	0.222215	+	0.347016i
$363$	529.376			0.0765428
$364$	177.399	+	81.7157i	0.0255447	+	0.0117667i
$365$		0			0
$366$	673.299	+	1051.44i	0.0961582	+	0.150163i
$367$			3330.42i			0.473697i	0.971547	+	0.236848i	$0.0761145\pi$
$367$			3330.42i			0.473697i	−0.971547	+	0.236848i	$0.923886\pi$
$368$	3332.62	−	2849.89i	0.472078	−	0.403698i
$369$	1815.10			0.256072
$370$		0			0
$371$		−	3325.14i		−	0.465317i
$372$	−1526.67	+	3314.29i	−0.212780	+	0.461931i
$373$	9398.88			1.30471			0.652354	−	0.757915i	$-0.273782\pi$
$373$	9398.88			1.30471			0.652354	+	0.757915i	$0.273782\pi$
$374$	−8073.70	+	5170.07i	−1.11626	+	0.714808i
$375$		0			0
$376$	−5117.57	+	710.265i	−0.701911	+	0.0974178i
$377$		−	78.7729i		−	0.0107613i
$378$	614.693	+	959.918i	0.0836413	+	0.130616i
$379$		−	3840.58i		−	0.520521i	−0.965538	−	0.260260i	$-0.916192\pi$
$379$		−	3840.58i		−	0.520521i	0.965538	−	0.260260i	$-0.0838084\pi$
$380$		0			0
$381$		−	2343.32i		−	0.315097i
$382$	−3029.98	+	1940.27i	−0.405830	+	0.259877i
$383$			2969.97i			0.396236i	0.980178	+	0.198118i	$0.0634830\pi$
$383$			2969.97i			0.396236i	−0.980178	+	0.198118i	$0.936517\pi$
$384$	1458.23	−	1644.58i	0.193789	−	0.218554i
$385$		0			0
$386$	−1114.85	−	1740.98i	−0.147006	−	0.229568i
$387$	20.6464			0.00271192
$388$	−4062.86	−	1871.48i	−0.531600	−	0.244872i
$389$			8349.10i			1.08822i	0.839015	+	0.544108i	$0.183132\pi$
$389$			8349.10i			1.08822i	−0.839015	+	0.544108i	$0.816868\pi$
$390$		0			0
$391$	−7410.26			−0.958447
$392$	984.886	+	7096.26i	0.126899	+	0.914325i
$393$			2934.24i			0.376623i
$394$	−8532.06	+	5463.59i	−1.09096	+	0.698608i
$395$		0			0
$396$	5623.96	+	2590.57i	0.713674	+	0.328741i
$397$	−4506.27			−0.569680			−0.284840	−	0.958575i	$-0.591940\pi$
$397$	−4506.27			−0.569680			−0.284840	+	0.958575i	$0.591940\pi$
$398$	4782.03	−	3062.22i	0.602265	−	0.385666i
$399$	−700.754			−0.0879238
$400$		0			0
$401$	−7654.44			−0.953228			−0.476614	−	0.879113i	$-0.658136\pi$
$401$	−7654.44			−0.953228			−0.476614	+	0.879113i	$0.658136\pi$
$402$	2898.68	−	1856.19i	0.359634	−	0.230295i
$403$	−1428.51			−0.176573
$404$	−3938.78	−	1814.32i	−0.485053	−	0.223431i
$405$		0			0
$406$	−202.740	+	129.827i	−0.0247828	+	0.0158699i
$407$			10275.8i			1.25148i
$408$	−3679.10	+	510.621i	−0.446428	+	0.0619596i
$409$	−2603.53			−0.314758			−0.157379	−	0.987538i	$-0.550304\pi$
$409$	−2603.53			−0.314758			−0.157379	+	0.987538i	$0.550304\pi$
$410$		0			0
$411$			725.870i			0.0871156i
$412$	12824.6	+	5907.41i	1.53355	+	0.706401i
$413$	−3871.03			−0.461212
$414$	2580.91	+	4030.41i	0.306389	+	0.478463i
$415$		0			0
$416$	823.599	+	249.141i	0.0970680	+	0.0293633i
$417$			3122.74i			0.366717i
$418$	−6710.38	+	4297.05i	−0.785204	+	0.502813i
$419$		−	525.993i		−	0.0613280i	−0.999530	−	0.0306640i	$-0.990238\pi$
$419$		−	525.993i		−	0.0613280i	0.999530	−	0.0306640i	$-0.00976219\pi$
$420$		0			0
$421$		−	15126.1i		−	1.75107i	−0.483157	−	0.875534i	$-0.660510\pi$
$421$		−	15126.1i		−	1.75107i	0.483157	−	0.875534i	$-0.339490\pi$
$422$	−2157.96	−	3369.91i	−0.248928	−	0.388732i
$423$		−	5639.03i		−	0.648178i
$424$	−2013.80	−	14509.7i	−0.230658	−	1.66192i
$425$		0			0
$426$	−2775.30	+	1777.19i	−0.315642	+	0.202125i
$427$	1493.80			0.169298
$428$	1482.20	−	3217.76i	0.167394	−	0.363402i
$429$		−	226.107i		−	0.0254465i
$430$		0			0
$431$	4887.92			0.546271			0.273135	−	0.961976i	$-0.411939\pi$
$431$	4887.92			0.546271			0.273135	+	0.961976i	$0.411939\pi$
$432$	3263.66	+	3816.48i	0.363479	+	0.425047i
$433$			6944.15i			0.770704i	0.922770	+	0.385352i	$0.125920\pi$
$433$			6944.15i			0.770704i	−0.922770	+	0.385352i	$0.874080\pi$
$434$	2354.34	+	3676.60i	0.260397	+	0.406641i
$435$		0			0
$436$	−11242.3	−	5178.54i	−1.23488	−	0.568823i
$437$	−6158.96			−0.674195
$438$	−111.861	−	174.684i	−0.0122030	−	0.0190565i
$439$	−577.528			−0.0627879			−0.0313940	−	0.999507i	$-0.509995\pi$
$439$	−577.528			−0.0627879			−0.0313940	+	0.999507i	$0.509995\pi$
$440$		0			0
$441$	−7819.35			−0.844331
$442$	−784.148	−	1224.54i	−0.0843848	−	0.131777i
$443$	−7039.42			−0.754973			−0.377486	−	0.926015i	$-0.623211\pi$
$443$	−7039.42			−0.754973			−0.377486	+	0.926015i	$0.623211\pi$
$444$	−1665.64	+	3615.98i	−0.178035	+	0.386502i
$445$		0			0
$446$	2.59159	+	4.04708i	0.000275146	+	0.000429674i
$447$		−	4308.79i		−	0.455926i
$448$	−716.163	−	2530.34i	−0.0755257	−	0.266846i
$449$	−6396.99			−0.672366			−0.336183	−	0.941797i	$-0.609136\pi$
$449$	−6396.99			−0.672366			−0.336183	+	0.941797i	$0.609136\pi$
$450$		0			0
$451$			2303.41i			0.240496i
$452$	−5729.56	−	2639.22i	−0.596230	−	0.274642i
$453$	−3319.50			−0.344291
$454$	8038.65	−	5147.62i	0.830996	−	0.532136i
$455$		0			0
$456$	−3057.85	+	424.397i	−0.314028	+	0.0435838i
$457$		−	7015.85i		−	0.718135i	−0.933312	−	0.359068i	$-0.883095\pi$
$457$		−	7015.85i		−	0.718135i	0.933312	−	0.359068i	$-0.116905\pi$
$458$	2029.68	+	3169.60i	0.207076	+	0.323374i
$459$		−	8486.14i		−	0.862961i
$460$		0			0
$461$			13374.1i			1.35118i	0.737279	+	0.675588i	$0.236110\pi$
$461$			13374.1i			1.35118i	−0.737279	+	0.675588i	$0.763890\pi$
$462$	−581.939	+	372.650i	−0.0586023	+	0.0375265i
$463$		−	15414.3i		−	1.54722i	−0.633661	−	0.773611i	$-0.718449\pi$
$463$		−	15414.3i		−	1.54722i	0.633661	−	0.773611i	$-0.281551\pi$
$464$	−806.062	+	689.304i	−0.0806476	+	0.0689658i
$465$		0			0
$466$	−6670.08	−	10416.1i	−0.663059	−	1.03545i
$467$	−1796.43			−0.178006			−0.0890032	−	0.996031i	$-0.528368\pi$
$467$	−1796.43			−0.178006			−0.0890032	+	0.996031i	$0.528368\pi$
$468$	−392.914	+	852.989i	−0.0388086	+	0.0842510i
$469$		−	4118.21i		−	0.405461i
$470$		0			0
$471$	1420.99			0.139014
$472$	−16891.8	+	2344.41i	−1.64727	+	0.228623i
$473$			26.2008i			0.00254696i
$474$	1632.99	−	1045.70i	0.158240	−	0.101331i
$475$		0			0
$476$	−1859.28	+	4036.37i	−0.179033	+	0.388670i
$477$	15988.3			1.53470
$478$	1892.70	−	1212.01i	0.181109	−	0.115975i
$479$	−11789.0			−1.12454			−0.562270	−	0.826954i	$-0.690072\pi$
$479$	−11789.0			−1.12454			−0.562270	+	0.826954i	$0.690072\pi$
$480$		0			0
$481$	−1558.54			−0.147741
$482$	−1470.76	+	941.818i	−0.138986	+	0.0890013i
$483$	−534.119			−0.0503173
$484$	1167.39	−	2534.33i	0.109635	−	0.238010i
$485$		0			0
$486$	−7026.20	+	4499.29i	−0.655792	+	0.419943i
$487$			18083.0i			1.68258i	0.540582	+	0.841291i	$0.318204\pi$
$487$			18083.0i			1.68258i	−0.540582	+	0.841291i	$0.681796\pi$
$488$	6518.43	−	904.690i	0.604663	−	0.0839208i
$489$	3535.92			0.326994
$490$		0			0
$491$			11259.2i			1.03487i	0.855722	+	0.517435i	$0.173113\pi$
$491$			11259.2i			1.03487i	−0.855722	+	0.517435i	$0.826887\pi$
$492$	−373.366	+	810.553i	−0.0342127	+	0.0742735i
$493$	1792.32			0.163736
$494$	−651.736	−	1017.77i	−0.0593583	−	0.0926953i
$495$		0			0
$496$	12500.2	+	14617.5i	1.13160	+	1.32328i
$497$			3942.92i			0.355864i
$498$	−3528.80	+	2259.70i	−0.317529	+	0.203332i
$499$			4589.82i			0.411761i	0.978577	+	0.205880i	$0.0660058\pi$
$499$			4589.82i			0.411761i	−0.978577	+	0.205880i	$0.933994\pi$
$500$		0			0
$501$			3066.53i			0.273458i
$502$	−1383.47	−	2160.46i	−0.123003	−	0.192084i
$503$			5257.43i			0.466038i	0.972472	+	0.233019i	$0.0748604\pi$
$503$			5257.43i			0.466038i	−0.972472	+	0.233019i	$0.925140\pi$
$504$	2842.93	−	394.569i	0.251258	−	0.0348720i
$505$		0			0
$506$	−5114.69	+	3275.24i	−0.449359	+	0.287751i
$507$	−3300.25			−0.289091
$508$	−11218.4	−	5167.56i	−0.979797	−	0.451325i
$509$		−	2451.99i		−	0.213522i	−0.994285	−	0.106761i	$-0.965952\pi$
$509$		−	2451.99i		−	0.213522i	0.994285	−	0.106761i	$-0.0340479\pi$
$510$		0			0
$511$	−248.178			−0.0214848
$512$	−4657.54	−	10607.8i	−0.402023	−	0.915629i
$513$		−	7053.17i		−	0.607027i
$514$	6636.04	+	10363.0i	0.569461	+	0.889283i
$515$		0			0
$516$	−4.24695	+	9.21984i	−0.000362328	+	0.000786591i
$517$	7156.08			0.608750
$518$	2568.65	+	4011.26i	0.217877	+	0.340241i
$519$	−1384.44			−0.117091
$520$		0			0
$521$	10677.6			0.897878			0.448939	−	0.893562i	$-0.351802\pi$
$521$	10677.6			0.897878			0.448939	+	0.893562i	$0.351802\pi$
$522$	−624.246	−	974.836i	−0.0523419	−	0.0817383i
$523$	19565.8			1.63585			0.817927	−	0.575323i	$-0.195124\pi$
$523$	19565.8			1.63585			0.817927	+	0.575323i	$0.195124\pi$
$524$	14047.4	+	6470.67i	1.17111	+	0.539451i
$525$		0			0
$526$	5500.43	+	8589.60i	0.455951	+	0.712024i
$527$		−	32502.9i		−	2.68662i
$528$	−2313.69	+	1978.56i	−0.190702	+	0.163079i
$529$	7472.60			0.614170
$530$		0			0
$531$		−	18613.1i		−	1.52116i
$532$	−1545.32	+	3354.79i	−0.125936	+	0.273400i
$533$	−349.360			−0.0283911
$534$	−4353.63	+	2787.89i	−0.352809	+	0.225924i
$535$		0			0
$536$	−2494.11	−	17970.4i	−0.200987	−	1.44814i
$537$		−	4897.78i		−	0.393584i
$538$	−9917.16	−	15486.9i	−0.794719	−	1.24105i
$539$		−	9922.95i		−	0.792972i
$540$		0			0
$541$		−	3313.01i		−	0.263286i	−0.991297	−	0.131643i	$-0.957975\pi$
$541$		−	3313.01i		−	0.263286i	0.991297	−	0.131643i	$-0.0420252\pi$
$542$	−2410.07	+	1543.31i	−0.190998	+	0.122308i
$543$		−	1522.98i		−	0.120363i
$544$	−5668.71	+	18739.4i	−0.446772	+	1.47692i
$545$		0			0
$546$	−56.5201	−	88.2630i	−0.00443010	−	0.00691815i
$547$	25040.9			1.95735			0.978675	−	0.205414i	$-0.0658542\pi$
$547$	25040.9			1.95735			0.978675	+	0.205414i	$0.0658542\pi$
$548$	3475.03	+	1600.71i	0.270887	+	0.124779i
$549$			7182.64i			0.558375i
$550$		0			0
$551$	1489.67			0.115176
$552$	−2330.71	+	323.478i	−0.179713	+	0.0249423i
$553$		−	2320.03i		−	0.178404i
$554$	6237.04	−	3993.95i	0.478315	−	0.306293i
$555$		0			0
$556$	14949.8	+	6886.34i	1.14031	+	0.525263i
$557$	2708.11			0.206008			0.103004	−	0.994681i	$-0.467155\pi$
$557$	2708.11			0.206008			0.103004	+	0.994681i	$0.467155\pi$
$558$	−17678.2	+	11320.4i	−1.34118	+	0.858836i
$559$	−3.97388			−0.000300675
$560$		0			0
$561$	5144.62			0.387177
$562$	−5483.86	+	3511.64i	−0.411606	+	0.263576i
$563$	−9374.67			−0.701768			−0.350884	−	0.936419i	$-0.614119\pi$
$563$	−9374.67			−0.701768			−0.350884	+	0.936419i	$0.614119\pi$
$564$	2518.17	+	1159.95i	0.188003	+	0.0866003i
$565$		0			0
$566$	15700.2	−	10053.8i	1.16595	−	0.746628i
$567$			2813.16i			0.208363i
$568$	2387.95	+	17205.6i	0.176402	+	1.27100i
$569$	−12092.5			−0.890938			−0.445469	−	0.895297i	$-0.646963\pi$
$569$	−12092.5			−0.890938			−0.445469	+	0.895297i	$0.646963\pi$
$570$		0			0
$571$			10847.4i			0.795008i	0.917601	+	0.397504i	$0.130123\pi$
$571$			10847.4i			0.795008i	−0.917601	+	0.397504i	$0.869877\pi$
$572$	−1082.47	−	498.617i	−0.0791261	−	0.0364480i
$573$	1930.72			0.140763
$574$	575.785	+	899.158i	0.0418690	+	0.0653835i
$575$		0			0
$576$	12166.6	−	3443.53i	0.880108	−	0.249098i
$577$		−	22325.8i		−	1.61080i	−0.592729	−	0.805402i	$-0.701949\pi$
$577$		−	22325.8i		−	1.61080i	0.592729	−	0.805402i	$-0.298051\pi$
$578$	16159.7	−	10348.0i	1.16290	−	0.744673i
$579$			1109.36i			0.0796261i
$580$		0			0
$581$			5013.44i			0.357990i
$582$	1294.44	+	2021.43i	0.0921931	+	0.143971i
$583$			20289.5i			1.44135i
$584$	−1082.96	+	150.304i	−0.0767351	+	0.0106500i
$585$		0			0
$586$	11351.1	−	7268.79i	0.800187	−	0.512408i
$587$	281.244			0.0197754			0.00988770	−	0.999951i	$-0.496853\pi$
$587$	281.244			0.0197754			0.00988770	+	0.999951i	$0.496853\pi$
$588$	1608.44	−	3491.81i	0.112808	−	0.244898i
$589$		−	27014.4i		−	1.88983i
$590$		0			0
$591$	5436.69			0.378402
$592$	13638.1	+	15948.1i	0.946825	+	1.10720i
$593$			934.658i			0.0647248i	0.999476	+	0.0323624i	$0.0103031\pi$
$593$			934.658i			0.0647248i	−0.999476	+	0.0323624i	$0.989697\pi$
$594$	−3750.77	−	5857.28i	−0.259084	−	0.404591i
$595$		0			0
$596$	−20627.9	−	9501.86i	−1.41770	−	0.653039i
$597$	−3047.14			−0.208897
$598$	−496.757	−	775.748i	−0.0339698	−	0.0530480i
$599$	15278.2			1.04215			0.521077	−	0.853510i	$-0.325530\pi$
$599$	15278.2			1.04215			0.521077	+	0.853510i	$0.325530\pi$
$600$		0			0
$601$	10958.6			0.743780			0.371890	−	0.928277i	$-0.378710\pi$
$601$	10958.6			0.743780			0.371890	+	0.928277i	$0.378710\pi$
$602$	6.54941	+	10.2277i	0.000443412	+	0.000692442i
$603$	19801.6			1.33728
$604$	−7320.24	+	15891.8i	−0.493140	+	1.07057i
$605$		0			0
$606$	1254.91	+	1959.69i	0.0841207	+	0.131365i
$607$		−	24850.2i		−	1.66167i	−0.556515	−	0.830837i	$-0.687862\pi$
$607$		−	24850.2i		−	1.66167i	0.556515	−	0.830837i	$-0.312138\pi$
$608$	−4711.49	+	15575.0i	−0.314270	+	1.03890i
$609$	129.187			0.00859596
$610$		0			0
$611$			1085.37i			0.0718645i
$612$	−19408.1	−	8939.97i	−1.28190	−	0.590485i
$613$	−3961.58			−0.261022			−0.130511	−	0.991447i	$-0.541662\pi$
$613$	−3961.58			−0.261022			−0.130511	+	0.991447i	$0.541662\pi$
$614$	−280.965	+	179.919i	−0.0184671	+	0.0118256i
$615$		0			0
$616$	500.718	+	3607.75i	0.0327508	+	0.235975i
$617$			20732.3i			1.35275i	0.736555	+	0.676377i	$0.236451\pi$
$617$			20732.3i			1.35275i	−0.736555	+	0.676377i	$0.763549\pi$
$618$	−4085.96	−	6380.73i	−0.265957	−	0.415324i
$619$			7801.96i			0.506603i	0.967387	+	0.253301i	$0.0815164\pi$
$619$			7801.96i			0.506603i	−0.967387	+	0.253301i	$0.918484\pi$
$620$		0			0
$621$		−	5375.97i		−	0.347391i
$622$	−9730.27	+	6230.87i	−0.627248	+	0.401664i
$623$			6185.29i			0.397766i
$624$	−300.089	−	350.919i	−0.0192519	−	0.0225128i
$625$		0			0
$626$	1379.89	+	2154.87i	0.0881015	+	0.137581i
$627$	4275.90			0.272349
$628$	3133.59	−	6802.82i	0.199115	−	0.432265i
$629$		−	35461.5i		−	2.24792i
$630$		0			0
$631$	−9359.85			−0.590507			−0.295253	−	0.955419i	$-0.595404\pi$
$631$	−9359.85			−0.590507			−0.295253	+	0.955419i	$0.595404\pi$
$632$	−1405.08	−	10123.8i	−0.0884350	−	0.637188i
$633$			2147.33i			0.134832i
$634$	12951.1	−	8293.36i	0.811283	−	0.519513i
$635$		0			0
$636$	−3288.78	+	7139.71i	−0.205045	+	0.445138i
$637$	1505.02			0.0936123
$638$	1237.09	−	792.183i	0.0767663	−	0.0491581i
$639$	−18958.8			−1.17370
$640$		0			0
$641$	19129.1			1.17871			0.589356	−	0.807873i	$-0.299381\pi$
$641$	19129.1			1.17871			0.589356	+	0.807873i	$0.299381\pi$
$642$	−1600.96	+	1025.19i	−0.0984186	+	0.0630233i
$643$	11243.5			0.689582			0.344791	−	0.938680i	$-0.387950\pi$
$643$	11243.5			0.689582			0.344791	+	0.938680i	$0.387950\pi$
$644$	−1177.85	+	2557.04i	−0.0720713	+	0.156462i
$645$		0			0
$646$	23157.3	−	14829.0i	1.41039	−	0.903155i
$647$			11887.6i			0.722331i	0.932502	+	0.361166i	$0.117621\pi$
$647$			11887.6i			0.722331i	−0.932502	+	0.361166i	$0.882379\pi$
$648$	1703.73	+	12275.7i	0.103285	+	0.744187i
$649$	23620.4			1.42863
$650$		0			0
$651$		−	2342.75i		−	0.141044i
$652$	7797.51	−	16927.9i	0.468365	−	1.01679i
$653$	−5327.46			−0.319264			−0.159632	−	0.987177i	$-0.551031\pi$
$653$	−5327.46			−0.319264			−0.159632	+	0.987177i	$0.551031\pi$
$654$	3581.82	+	5593.46i	0.214160	+	0.334436i
$655$		0			0
$656$	3057.08	+	3574.91i	0.181950	+	0.212769i
$657$		−	1193.31i		−	0.0708609i
$658$	2793.44	−	1788.81i	0.165501	−	0.105980i
$659$			26016.2i			1.53786i	0.639334	+	0.768929i	$0.279210\pi$
$659$			26016.2i			1.53786i	−0.639334	+	0.768929i	$0.720790\pi$
$660$		0			0
$661$		−	5961.64i		−	0.350803i	−0.984497	−	0.175401i	$-0.943878\pi$
$661$		−	5961.64i		−	0.350803i	0.984497	−	0.175401i	$-0.0561224\pi$
$662$	9066.32	+	14158.2i	0.532285	+	0.831228i
$663$			780.287i			0.0457071i
$664$	3036.28	+	21876.9i	0.177456	+	1.27860i
$665$		0			0
$666$	−19287.4	+	12350.8i	−1.12218	+	0.718597i
$667$	1135.43			0.0659134
$668$	14680.7	+	6762.40i	0.850320	+	0.391684i
$669$		−	2.57883i		−	0.000149033i
$670$		0			0
$671$	−9114.95			−0.524410
$672$	−408.591	+	1350.70i	−0.0234550	+	0.0775364i
$673$		−	17544.1i		−	1.00487i	−0.864615	−	0.502435i	$-0.832438\pi$
$673$		−	17544.1i		−	1.00487i	0.864615	−	0.502435i	$-0.167562\pi$
$674$	−8597.88	−	13426.6i	−0.491362	−	0.767322i
$675$		0			0
$676$	−7277.80	+	15799.6i	−0.414076	+	0.898932i
$677$	17000.0			0.965088			0.482544	−	0.875872i	$-0.339713\pi$
$677$	17000.0			0.965088			0.482544	+	0.875872i	$0.339713\pi$
$678$	1825.46	+	2850.68i	0.103402	+	0.161474i
$679$	2871.89			0.162317
$680$		0			0
$681$	−5122.28			−0.288232
$682$	−14365.9	−	22434.1i	−0.806594	−	1.25960i
$683$	−5386.68			−0.301780			−0.150890	−	0.988551i	$-0.548214\pi$
$683$	−5386.68			−0.301780			−0.150890	+	0.988551i	$0.548214\pi$
$684$	−16130.8	−	7430.37i	−0.901722	−	0.415361i
$685$		0			0
$686$	−5167.55	−	8069.77i	−0.287607	−	0.449133i
$687$		−	2019.69i		−	0.112163i
$688$	34.7736	+	40.6637i	0.00192693	+	0.00225333i
$689$	−3077.32			−0.170155
$690$		0			0
$691$			18049.0i			0.993658i	0.867849	+	0.496829i	$0.165502\pi$
$691$			18049.0i			0.993658i	−0.867849	+	0.496829i	$0.834498\pi$
$692$	−3053.01	+	6627.87i	−0.167714	+	0.364095i
$693$	−3975.37			−0.217910
$694$	18486.3	−	11837.9i	1.01114	−	0.647493i
$695$		0			0
$696$	563.730	−	78.2397i	0.0307013	−	0.00426102i
$697$		−	7948.99i		−	0.431979i
$698$	−13284.6	−	20745.6i	−0.720387	−	1.12497i
$699$			6637.24i			0.359147i
$700$		0			0
$701$		−	7991.13i		−	0.430558i	−0.976553	−	0.215279i	$-0.930934\pi$
$701$		−	7991.13i		−	0.430558i	0.976553	−	0.215279i	$-0.0690660\pi$
$702$	888.377	−	568.881i	0.0477630	−	0.0305855i
$703$		−	29473.5i		−	1.58124i
$704$	4369.92	+	15439.7i	0.233946	+	0.826573i
$705$		0			0
$706$	−1504.42	−	2349.34i	−0.0801977	−	0.125239i
$707$	2784.18			0.148104
$708$	8311.84	+	3828.70i	0.441212	+	0.203236i
$709$			11306.8i			0.598920i	0.954109	+	0.299460i	$0.0968065\pi$
$709$			11306.8i			0.598920i	−0.954109	+	0.299460i	$0.903194\pi$
$710$		0			0
$711$	11155.4			0.588410
$712$	3745.99	+	26990.5i	0.197173	+	1.42066i
$713$		−	20590.6i		−	1.08152i
$714$	2008.25	−	1286.00i	0.105262	−	0.0674053i
$715$		0			0
$716$	−23447.6	−	10800.7i	−1.22385	−	0.563745i
$717$	−1206.04			−0.0628180
$718$	−27320.8	+	17495.1i	−1.42006	+	0.909348i
$719$	−30968.9			−1.60632			−0.803160	−	0.595763i	$-0.796850\pi$
$719$	−30968.9			−1.60632			−0.803160	+	0.595763i	$0.796850\pi$
$720$		0			0
$721$	−9065.23			−0.468248
$722$	2909.36	−	1863.04i	0.149966	−	0.0960320i
$723$	937.181			0.0482076
$724$	−7291.09	−	3358.51i	−0.374270	−	0.172400i
$725$		0			0
$726$	−1260.93	+	807.448i	−0.0644593	+	0.0412771i
$727$			26520.2i			1.35293i	0.736474	+	0.676466i	$0.236489\pi$
$727$			26520.2i			1.35293i	−0.736474	+	0.676466i	$0.763511\pi$
$728$	−547.190	+	75.9442i	−0.0278574	+	0.00386632i
$729$	−10311.1			−0.523858
$730$		0			0
$731$		−	90.4178i		−	0.00457486i
$732$	−3207.48	−	1477.47i	−0.161956	−	0.0746021i
$733$	−15980.8			−0.805270			−0.402635	−	0.915361i	$-0.631906\pi$
$733$	−15980.8			−0.805270			−0.402635	+	0.915361i	$0.631906\pi$
$734$	−5079.83	−	7932.78i	−0.255450	−	0.398916i
$735$		0			0
$736$	−3591.13	+	11871.4i	−0.179851	+	0.594545i
$737$			25128.7i			1.25594i
$738$	−4323.42	+	2768.55i	−0.215647	+	0.138092i
$739$			10163.8i			0.505927i	0.967476	+	0.252964i	$0.0814053\pi$
$739$			10163.8i			0.505927i	−0.967476	+	0.252964i	$0.918595\pi$
$740$		0			0
$741$			648.528i			0.0321515i
$742$	5071.77	+	7920.19i	0.250931	+	0.391859i
$743$			37765.7i			1.86472i	0.361530	+	0.932360i	$0.382254\pi$
$743$			37765.7i			1.86472i	−0.361530	+	0.932360i	$0.617746\pi$
$744$	−1418.84	−	10223.0i	−0.0699156	−	0.503753i
$745$		0			0
$746$	−22387.3	+	14335.9i	−1.09874	+	0.703588i
$747$	−24106.1			−1.18072
$748$	11345.1	−	24629.3i	0.554567	−	1.20393i
$749$			2274.51i			0.110960i
$750$		0			0
$751$	−20234.4			−0.983175			−0.491587	−	0.870828i	$-0.663583\pi$
$751$	−20234.4			−0.983175			−0.491587	+	0.870828i	$0.663583\pi$
$752$	11106.3	−	9497.52i	0.538568	−	0.460557i
$753$			1376.66i			0.0666245i
$754$	120.151	+	187.630i	0.00580323	+	0.00906245i
$755$		0			0
$756$	−2928.29	−	1348.86i	−0.140874	−	0.0648911i
$757$	−27066.9			−1.29956			−0.649778	−	0.760124i	$-0.725138\pi$
$757$	−27066.9			−1.29956			−0.649778	+	0.760124i	$0.725138\pi$
$758$	5857.97	+	9147.94i	0.280701	+	0.438348i
$759$	3259.12			0.155861
$760$		0			0
$761$	−30797.4			−1.46702			−0.733512	−	0.679677i	$-0.762120\pi$
$761$	−30797.4			−1.46702			−0.733512	+	0.679677i	$0.762120\pi$
$762$	3574.23	+	5581.59i	0.169922	+	0.265354i
$763$	7946.74			0.377053
$764$	4257.68	−	9243.13i	0.201620	−	0.437703i
$765$		0			0
$766$	−4530.05	−	7074.22i	−0.213678	−	0.333684i
$767$			3582.52i			0.168654i
$768$	−964.926	+	6141.45i	−0.0453369	+	0.288556i
$769$	35490.2			1.66425			0.832125	−	0.554588i	$-0.187124\pi$
$769$	35490.2			1.66425			0.832125	+	0.554588i	$0.187124\pi$
$770$		0			0
$771$		−	6603.37i		−	0.308449i
$772$	5310.96	+	2446.39i	0.247598	+	0.114051i
$773$	−37364.0			−1.73854			−0.869269	−	0.494339i	$-0.835410\pi$
$773$	−37364.0			−1.73854			−0.869269	+	0.494339i	$0.835410\pi$
$774$	−49.1779	+	31.4915i	−0.00228380	+	0.00146245i
$775$		0			0
$776$	12531.9	−	1739.30i	0.579730	−	0.0804604i
$777$		−	2556.01i		−	0.118013i
$778$	−12734.7	−	19886.8i	−0.586841	−	0.916424i
$779$		−	6606.72i		−	0.303864i
$780$		0			0
$781$		−	24059.1i		−	1.10231i
$782$	17650.6	−	11302.7i	0.807141	−	0.516860i
$783$			1300.29i			0.0593467i
$784$	−13169.7	−	15400.5i	−0.599932	−	0.701551i
$785$		0			0
$786$	−4475.55	−	6989.11i	−0.203101	−	0.317167i
$787$	−28529.7			−1.29222			−0.646108	−	0.763246i	$-0.723605\pi$
$787$	−28529.7			−1.29222			−0.646108	+	0.763246i	$0.723605\pi$
$788$	11989.1	−	26027.6i	0.541999	−	1.17664i
$789$		−	5473.35i		−	0.246967i
$790$		0			0
$791$	4050.01			0.182051
$792$	−17347.2	+	2407.60i	−0.778288	+	0.108018i
$793$		−	1382.47i		−	0.0619078i
$794$	10733.5	−	6873.33i	0.479747	−	0.307211i
$795$		0			0
$796$	−6719.64	+	14587.9i	−0.299210	+	0.649565i
$797$	−7130.44			−0.316905			−0.158452	−	0.987367i	$-0.550650\pi$
$797$	−7130.44			−0.316905			−0.158452	+	0.987367i	$0.550650\pi$
$798$	1669.14	−	1068.85i	0.0740436	−	0.0474145i
$799$	−24695.3			−1.09344
$800$		0			0
$801$	−29740.7			−1.31191
$802$	18232.2	−	11675.2i	0.802745	−	0.514046i
$803$	1514.35			0.0665505
$804$	−4073.18	+	8842.59i	−0.178669	+	0.387878i
$805$		0			0
$806$	3402.58	−	2178.88i	0.148698	−	0.0952204i
$807$			9868.33i			0.430461i
$808$	12149.2	−	1686.18i	0.528969	−	0.0734153i
$809$	11060.3			0.480665			0.240333	−	0.970691i	$-0.422743\pi$
$809$	11060.3			0.480665			0.240333	+	0.970691i	$0.422743\pi$
$810$		0			0
$811$			27381.5i			1.18557i	0.805361	+	0.592784i	$0.201971\pi$
$811$			27381.5i			1.18557i	−0.805361	+	0.592784i	$0.798029\pi$
$812$	284.888	−	618.472i	0.0123123	−	0.0267292i
$813$	1535.71			0.0662481
$814$	−15673.5	−	24476.1i	−0.674886	−	1.05392i
$815$		0			0
$816$	7984.47	−	6827.92i	0.342540	−	0.292923i
$817$		−	75.1498i		−	0.00321807i
$818$	6201.38	−	3971.11i	0.265069	−	0.169739i
$819$		−	602.947i		−	0.0257249i
$820$		0			0
$821$			30033.9i			1.27672i	0.769736	+	0.638362i	$0.220388\pi$
$821$			30033.9i			1.27672i	−0.769736	+	0.638362i	$0.779612\pi$
$822$	−1107.16	−	1728.96i	−0.0469787	−	0.0733630i
$823$		−	3186.93i		−	0.134981i	−0.997720	−	0.0674906i	$-0.978501\pi$
$823$		−	3186.93i		−	0.134981i	0.997720	−	0.0674906i	$-0.0214993\pi$
$824$	−39557.5	+	5490.17i	−1.67239	+	0.232111i
$825$		0			0
$826$	9220.45	−	5904.40i	0.388403	−	0.248717i
$827$	−18326.0			−0.770563			−0.385282	−	0.922799i	$-0.625896\pi$
$827$	−18326.0			−0.770563			−0.385282	+	0.922799i	$0.625896\pi$
$828$	−12295.0	−	5663.47i	−0.516040	−	0.237704i
$829$			4370.27i			0.183095i	0.995801	+	0.0915475i	$0.0291813\pi$
$829$			4370.27i			0.183095i	−0.995801	+	0.0915475i	$0.970819\pi$
$830$		0			0
$831$	−3974.28			−0.165904
$832$	−2341.75	+	662.788i	−0.0975789	+	0.0276179i
$833$			34243.7i			1.42434i
$834$	−4763.05	−	7438.09i	−0.197759	−	0.308825i
$835$		0			0
$836$	9429.32	−	20470.4i	0.390096	−	0.846872i
$837$	23580.1			0.973771
$838$	802.288	+	1252.87i	0.0330723	+	0.0516464i
$839$	29789.0			1.22578			0.612890	−	0.790168i	$-0.290007\pi$
$839$	29789.0			1.22578			0.612890	+	0.790168i	$0.290007\pi$
$840$		0			0
$841$	24114.4			0.988740
$842$	23071.5	+	36029.0i	0.944296	+	1.47463i
$843$	3494.35			0.142766
$844$	10280.1	+	4735.35i	0.419262	+	0.193125i
$845$		0			0
$846$	8601.12	+	13431.7i	0.349542	+	0.545853i
$847$			1791.43i			0.0726732i
$848$	26928.2	+	31489.4i	1.09047	+	1.27518i
$849$	−10004.3			−0.404412
$850$		0			0
$851$		−	22464.9i		−	0.904918i
$852$	3899.81	−	8466.22i	0.156814	−	0.340432i
$853$	39023.7			1.56641			0.783205	−	0.621764i	$-0.213584\pi$
$853$	39023.7			1.56641			0.783205	+	0.621764i	$0.213584\pi$
$854$	−3558.10	+	2278.47i	−0.142571	+	0.0912969i
$855$		0			0
$856$	1377.51	+	9925.19i	0.0550028	+	0.396304i
$857$		−	2749.52i		−	0.109594i	−0.998498	−	0.0547969i	$-0.982549\pi$
$857$		−	2749.52i		−	0.109594i	0.998498	−	0.0547969i	$-0.0174512\pi$
$858$	344.877	+	538.568i	0.0137225	+	0.0214294i
$859$			48225.6i			1.91553i	0.287559	+	0.957763i	$0.407156\pi$
$859$			48225.6i			1.91553i	−0.287559	+	0.957763i	$0.592844\pi$
$860$		0			0
$861$		−	572.950i		−	0.0226784i
$862$	−11642.6	+	7455.45i	−0.460033	+	0.294587i
$863$			12421.1i			0.489942i	0.969530	+	0.244971i	$0.0787784\pi$
$863$			12421.1i			0.489942i	−0.969530	+	0.244971i	$0.921222\pi$
$864$	−13595.0	−	4112.51i	−0.535313	−	0.161934i
$865$		0			0
$866$	−10591.8	−	16540.4i	−0.415616	−	0.649036i
$867$	−10297.1			−0.403353
$868$	−11215.7	−	5166.30i	−0.438578	−	0.202023i
$869$			14156.5i			0.552618i
$870$		0			0
$871$	−3811.28			−0.148267
$872$	34676.8	−	4812.78i	1.34668	−	0.186905i
$873$			13808.9i			0.535350i
$874$	14670.1	−	9394.15i	0.567762	−	0.363572i
$875$		0			0
$876$	532.886	+	245.464i	0.0205531	+	0.00946742i
$877$	−38301.8			−1.47475			−0.737377	−	0.675482i	$-0.763936\pi$
$877$	−38301.8			−1.47475			−0.737377	+	0.675482i	$0.763936\pi$
$878$	1375.62	−	880.892i	0.0528758	−	0.0338595i
$879$	−7233.00			−0.277546
$880$		0			0
$881$	14792.0			0.565671			0.282836	−	0.959168i	$-0.408725\pi$
$881$	14792.0			0.565671			0.282836	+	0.959168i	$0.408725\pi$
$882$	18625.0	−	11926.7i	0.711040	−	0.455321i
$883$	2064.99			0.0787002			0.0393501	−	0.999225i	$-0.487471\pi$
$883$	2064.99			0.0787002			0.0393501	+	0.999225i	$0.487471\pi$
$884$	3735.55	+	1720.71i	0.142127	+	0.0654680i
$885$		0			0
$886$	16767.3	−	10737.1i	0.635788	−	0.407133i
$887$			19268.8i			0.729406i	0.931124	+	0.364703i	$0.118829\pi$
$887$			19268.8i			0.729406i	−0.931124	+	0.364703i	$0.881171\pi$
$888$	−1547.99	−	11153.5i	−0.0584991	−	0.421495i
$889$	7929.89			0.299167
$890$		0			0
$891$		−	17165.5i		−	0.645415i
$892$	−12.3459	−	5.68690i	−0.000463420	−	0.000213466i
$893$	−20525.3			−0.769152
$894$	6572.12	+	10263.2i	0.245866	+	0.383951i
$895$		0			0
$896$	5565.31	+	4934.69i	0.207505	+	0.183992i
$897$			494.312i			0.0183998i
$898$	15237.1	−	9757.21i	0.566223	−	0.362586i
$899$			4980.24i			0.184761i
$900$		0			0
$901$		−	70018.3i		−	2.58895i
$902$	−3513.35	−	5486.53i	−0.129692	−	0.202529i
$903$		−	6.51717i		−	0.000240175i
$904$	17672.9	−	2452.81i	0.650211	−	0.0902425i
$905$		0			0
$906$	7906.76	−	5063.17i	0.289939	−	0.185665i
$907$	46355.6			1.69704			0.848519	−	0.529165i	$-0.177495\pi$
$907$	46355.6			1.69704			0.848519	+	0.529165i	$0.177495\pi$
$908$	−11295.8	+	24522.4i	−0.412846	+	0.896260i
$909$			13387.2i			0.488475i
$910$		0			0
$911$	23365.5			0.849761			0.424881	−	0.905249i	$-0.360316\pi$
$911$	23365.5			0.849761			0.424881	+	0.905249i	$0.360316\pi$
$912$	6636.21	−	5674.96i	0.240950	−	0.206049i
$913$		−	30591.3i		−	1.10890i
$914$	10701.2	+	16711.2i	0.387268	+	0.604766i
$915$		0			0
$916$	−9669.05	−	4453.87i	−0.348771	−	0.160655i
$917$	−9929.58			−0.357583
$918$	12943.8	+	20213.3i	0.465368	+	0.726728i
$919$	36178.5			1.29860			0.649302	−	0.760530i	$-0.275061\pi$
$919$	36178.5			1.29860			0.649302	+	0.760530i	$0.275061\pi$
$920$		0			0
$921$	179.033			0.00640535
$922$	−20399.2	−	31855.9i	−0.728647	−	1.13787i
$923$	3649.06			0.130130
$924$	817.732	−	1775.24i	0.0291141	−	0.0632047i
$925$		0			0
$926$	23511.2	+	36715.5i	0.834368	+	1.30297i
$927$		−	43588.4i		−	1.54437i
$928$	868.587	−	2871.33i	0.0307249	−	0.101569i
$929$	−17014.6			−0.600895			−0.300447	−	0.953798i	$-0.597136\pi$
$929$	−17014.6			−0.600895			−0.300447	+	0.953798i	$0.597136\pi$
$930$		0			0
$931$			28461.3i			1.00191i
$932$	31775.1	+	14636.6i	1.11677	+	0.514419i
$933$	6200.20			0.217562
$934$	4278.95	−	2740.07i	0.149905	−	0.0959933i
$935$		0			0
$936$	−365.162	−	2631.05i	−0.0127518	−	0.0918789i
$937$			16898.8i			0.589179i	0.955624	+	0.294589i	$0.0951829\pi$
$937$			16898.8i			0.589179i	−0.955624	+	0.294589i	$0.904817\pi$
$938$	6281.43	+	9809.22i	0.218652	+	0.341452i
$939$		−	1373.10i		−	0.0477203i
$940$		0			0
$941$			43995.9i			1.52415i	0.647489	+	0.762074i	$0.275819\pi$
$941$			43995.9i			1.52415i	−0.647489	+	0.762074i	$0.724181\pi$
$942$	−3384.67	+	2167.40i	−0.117068	+	0.0749658i
$943$		−	5035.68i		−	0.173897i
$944$	36659.0	−	31349.0i	1.26393	−	1.08085i
$945$		0			0
$946$	−39.9635	−	62.4080i	−0.00137350	−	0.00214488i
$947$	2588.13			0.0888099			0.0444050	−	0.999014i	$-0.485861\pi$
$947$	2588.13			0.0888099			0.0444050	+	0.999014i	$0.485861\pi$
$948$	−2294.66	+	4981.54i	−0.0786149	+	0.170668i
$949$			229.681i			0.00785646i
$950$		0			0
$951$	−8252.52			−0.281395
$952$	−1727.96	−	12450.2i	−0.0588272	−	0.423859i
$953$		−	7309.24i		−	0.248447i	−0.992254	−	0.124223i	$-0.960356\pi$
$953$		−	7309.24i		−	0.248447i	0.992254	−	0.124223i	$-0.0396439\pi$
$954$	−38082.7	+	24386.6i	−1.29242	+	0.827615i
$955$		0			0
$956$	−2659.60	+	5773.80i	−0.0899764	+	0.195333i
$957$	−788.283			−0.0266265
$958$	28080.5	−	17981.6i	0.947013	−	0.606429i
$959$	−2456.37			−0.0827115
$960$		0			0
$961$	60523.3			2.03160
$962$	3712.31	−	2377.21i	0.124418	−	0.0796720i
$963$	−10936.5			−0.365966
$964$	2066.70	−	4486.66i	0.0690496	−	0.149902i
$965$		0			0
$966$	1272.23	−	814.682i	0.0423739	−	0.0271345i
$967$			27600.6i			0.917866i	0.888471	+	0.458933i	$0.151768\pi$
$967$			27600.6i			0.917866i	−0.888471	+	0.458933i	$0.848232\pi$
$968$	1084.94	+	7817.17i	0.0360241	+	0.259559i
$969$	−14756.0			−0.489195
$970$		0			0
$971$		−	22638.5i		−	0.748201i	−0.927388	−	0.374100i	$-0.877952\pi$
$971$		−	22638.5i		−	0.748201i	0.927388	−	0.374100i	$-0.122048\pi$
$972$	9873.11	−	21433.9i	0.325803	−	0.707296i
$973$	−10567.5			−0.348178
$974$	−27581.6	−	43072.1i	−0.907364	−	1.41696i
$975$		0			0
$976$	−14146.4	+	12097.3i	−0.463951	+	0.396748i
$977$		−	18390.3i		−	0.602208i	−0.953591	−	0.301104i	$-0.902645\pi$
$977$		−	18390.3i		−	0.602208i	0.953591	−	0.301104i	$-0.0973551\pi$
$978$	−8422.27	+	5393.28i	−0.275373	+	0.176337i
$979$		−	37741.7i		−	1.23210i
$980$		0			0
$981$			38210.3i			1.24359i
$982$	−17173.5	−	26818.5i	−0.558073	−	0.871499i
$983$		−	11139.1i		−	0.361425i	−0.983536	−	0.180712i	$-0.942160\pi$
$983$		−	11139.1i		−	0.361425i	0.983536	−	0.180712i	$-0.0578404\pi$
$984$	−346.995	−	2500.16i	−0.0112417	−	0.0809980i
$985$		0			0
$986$	−4269.15	+	2733.79i	−0.137888	+	0.0882979i
$987$	−1780.00			−0.0574043
$988$	3104.76	+	1430.15i	0.0999753	+	0.0460518i
$989$		−	57.2797i		−	0.00184165i
$990$		0			0
$991$	30232.3			0.969083			0.484542	−	0.874768i	$-0.338986\pi$
$991$	30232.3			0.969083			0.484542	+	0.874768i	$0.338986\pi$
$992$	−52070.3	−	15751.4i	−1.66657	−	0.504141i
$993$		−	9021.68i		−	0.288313i
$994$	−6014.07	−	9391.70i	−0.191906	−	0.299685i
$995$		0			0
$996$	4958.62	−	10764.8i	0.157751	−	0.342466i
$997$	−9623.78			−0.305705			−0.152853	−	0.988249i	$-0.548846\pi$
$997$	−9623.78			−0.305705			−0.152853	+	0.988249i	$0.548846\pi$
$998$	−7000.77	−	10932.6i	−0.222050	−	0.346758i
$999$	25726.5			0.814764

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.4.f.c.149.2		12
4.3	odd	2		800.4.f.b.49.5		12
5.2	odd	4		200.4.d.b.101.5		12
5.3	odd	4		40.4.d.a.21.8	yes	12
5.4	even	2		200.4.f.b.149.11		12
8.3	odd	2		800.4.f.c.49.7		12
8.5	even	2		200.4.f.b.149.12		12
15.8	even	4		360.4.k.c.181.5		12
20.3	even	4		160.4.d.a.81.5		12
20.7	even	4		800.4.d.d.401.8		12
20.19	odd	2		800.4.f.c.49.8		12
40.3	even	4		160.4.d.a.81.8		12
40.13	odd	4		40.4.d.a.21.7	✓	12
40.19	odd	2		800.4.f.b.49.6		12
40.27	even	4		800.4.d.d.401.5		12
40.29	even	2	inner	200.4.f.c.149.1		12
40.37	odd	4		200.4.d.b.101.6		12
60.23	odd	4		1440.4.k.c.721.4		12
80.3	even	4		1280.4.a.bd.1.4		6
80.13	odd	4		1280.4.a.bb.1.3		6
80.43	even	4		1280.4.a.ba.1.3		6
80.53	odd	4		1280.4.a.bc.1.4		6
120.53	even	4		360.4.k.c.181.6		12
120.83	odd	4		1440.4.k.c.721.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.d.a.21.7	✓	12	40.13	odd	4
40.4.d.a.21.8	yes	12	5.3	odd	4
160.4.d.a.81.5		12	20.3	even	4
160.4.d.a.81.8		12	40.3	even	4
200.4.d.b.101.5		12	5.2	odd	4
200.4.d.b.101.6		12	40.37	odd	4
200.4.f.b.149.11		12	5.4	even	2
200.4.f.b.149.12		12	8.5	even	2
200.4.f.c.149.1		12	40.29	even	2	inner
200.4.f.c.149.2		12	1.1	even	1	trivial
360.4.k.c.181.5		12	15.8	even	4
360.4.k.c.181.6		12	120.53	even	4
800.4.d.d.401.5		12	40.27	even	4
800.4.d.d.401.8		12	20.7	even	4
800.4.f.b.49.5		12	4.3	odd	2
800.4.f.b.49.6		12	40.19	odd	2
800.4.f.c.49.7		12	8.3	odd	2
800.4.f.c.49.8		12	20.19	odd	2
1280.4.a.ba.1.3		6	80.43	even	4
1280.4.a.bb.1.3		6	80.13	odd	4
1280.4.a.bc.1.4		6	80.53	odd	4
1280.4.a.bd.1.4		6	80.3	even	4
1440.4.k.c.721.4		12	60.23	odd	4
1440.4.k.c.721.10		12	120.83	odd	4

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.38191 + 1.52528i) q^{2} +1.51777 q^{3} +(3.34703 - 7.26618i) q^{4} +(-3.61520 + 2.31503i) q^{6} +5.13620i q^{7} +(3.11063 + 22.4126i) q^{8} -24.6964 q^{9} -31.3403i q^{11} +(5.08003 - 11.0284i) q^{12} +4.75340 q^{13} +(-7.83414 - 12.2340i) q^{14} +(-41.5948 - 48.6403i) q^{16} +108.154i q^{17} +(58.8246 - 37.6689i) q^{18} +89.8913i q^{19} +7.79558i q^{21} +(47.8028 + 74.6499i) q^{22} +68.5157i q^{23} +(4.72123 + 34.0172i) q^{24} +(-11.3222 + 7.25027i) q^{26} -78.4633 q^{27} +(37.3205 + 17.1910i) q^{28} -16.5719i q^{29} -300.523 q^{31} +(173.265 + 52.4132i) q^{32} -47.5675i q^{33} +(-164.966 - 257.614i) q^{34} +(-82.6595 + 179.448i) q^{36} -327.879 q^{37} +(-137.109 - 214.113i) q^{38} +7.21458 q^{39} -73.4968 q^{41} +(-11.8904 - 18.5684i) q^{42} -0.836008 q^{43} +(-227.724 - 104.897i) q^{44} +(-104.506 - 163.198i) q^{46} +228.335i q^{47} +(-63.1314 - 73.8249i) q^{48} +316.619 q^{49} +164.153i q^{51} +(15.9098 - 34.5391i) q^{52} -647.393 q^{53} +(186.893 - 119.679i) q^{54} +(-115.115 + 15.9768i) q^{56} +136.434i q^{57} +(25.2768 + 39.4728i) q^{58} +753.676i q^{59} -290.838i q^{61} +(715.821 - 458.383i) q^{62} -126.845i q^{63} +(-492.648 + 139.435i) q^{64} +(72.5538 + 113.302i) q^{66} -801.801 q^{67} +(785.868 + 361.995i) q^{68} +103.991i q^{69} +767.674 q^{71} +(-76.8213 - 553.509i) q^{72} +48.3194i q^{73} +(780.980 - 500.108i) q^{74} +(653.166 + 300.869i) q^{76} +160.970 q^{77} +(-17.1845 + 11.0043i) q^{78} -451.701 q^{79} +547.712 q^{81} +(175.063 - 112.103i) q^{82} +976.099 q^{83} +(56.6441 + 26.0920i) q^{84} +(1.99130 - 1.27515i) q^{86} -25.1524i q^{87} +(702.417 - 97.4881i) q^{88} +1204.25 q^{89} +24.4144i q^{91} +(497.847 + 229.324i) q^{92} -456.126 q^{93} +(-348.275 - 543.873i) q^{94} +(262.977 + 79.5513i) q^{96} -559.147i q^{97} +(-754.161 + 482.934i) q^{98} +773.992i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 12 q^{3} - 16 q^{4} - 36 q^{6} - 24 q^{8} + 108 q^{9} - 164 q^{12} - 68 q^{14} - 56 q^{16} + 450 q^{18} + 492 q^{22} - 360 q^{24} - 308 q^{26} + 432 q^{27} + 628 q^{28} - 264 q^{31} + 856 q^{32}+ \cdots + 638 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 + 12 * q^3 - 16 * q^4 - 36 * q^6 - 24 * q^8 + 108 * q^9 - 164 * q^12 - 68 * q^14 - 56 * q^16 + 450 * q^18 + 492 * q^22 - 360 * q^24 - 308 * q^26 + 432 * q^27 + 628 * q^28 - 264 * q^31 + 856 * q^32 + 180 * q^34 + 440 * q^36 + 136 * q^37 - 1388 * q^38 - 600 * q^39 + 40 * q^41 - 2332 * q^42 - 1204 * q^43 + 472 * q^44 - 1268 * q^46 - 2536 * q^48 - 1308 * q^49 - 1272 * q^52 + 1056 * q^53 + 1512 * q^54 - 728 * q^56 + 1528 * q^58 + 2104 * q^62 + 2048 * q^64 + 2928 * q^66 - 2412 * q^67 + 960 * q^68 - 1592 * q^71 + 744 * q^72 + 420 * q^74 + 2256 * q^76 + 824 * q^77 - 160 * q^78 - 2016 * q^79 + 2508 * q^81 + 352 * q^82 + 3556 * q^83 - 1048 * q^84 - 244 * q^86 + 1008 * q^88 + 424 * q^89 + 1068 * q^92 + 2784 * q^93 - 292 * q^94 - 5920 * q^96 + 638 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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