LMFDB - Embedded newform 200.4.f.d.149.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,4,Mod(149,200)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [24,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$11.8003820011$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.3
Character	$\chi$	$=$	200.149
Dual form			200.4.f.d.149.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.79756 - 0.416712i) q^{2} +2.73090 q^{3} +(7.65270 + 2.33156i) q^{4} +(-7.63987 - 1.13800i) q^{6} +31.2997i q^{7} +(-20.4373 - 9.71165i) q^{8} -19.5422 q^{9} -34.7644i q^{11} +(20.8988 + 6.36726i) q^{12} -73.2979 q^{13} +(13.0430 - 87.5628i) q^{14} +(53.1277 + 35.6854i) q^{16} +16.6889i q^{17} +(54.6704 + 8.14346i) q^{18} -68.5157i q^{19} +85.4764i q^{21} +(-14.4867 + 97.2555i) q^{22} -82.5447i q^{23} +(-55.8123 - 26.5216i) q^{24} +(205.055 + 30.5441i) q^{26} -127.102 q^{27} +(-72.9770 + 239.527i) q^{28} -84.8247i q^{29} -34.9084 q^{31} +(-133.757 - 121.971i) q^{32} -94.9381i q^{33} +(6.95448 - 46.6883i) q^{34} +(-149.550 - 45.5637i) q^{36} -19.5402 q^{37} +(-28.5513 + 191.677i) q^{38} -200.169 q^{39} -299.703 q^{41} +(35.6191 - 239.126i) q^{42} -513.714 q^{43} +(81.0551 - 266.041i) q^{44} +(-34.3974 + 230.924i) q^{46} +355.157i q^{47} +(145.087 + 97.4534i) q^{48} -636.671 q^{49} +45.5758i q^{51} +(-560.927 - 170.898i) q^{52} +488.561 q^{53} +(355.576 + 52.9650i) q^{54} +(303.972 - 639.682i) q^{56} -187.110i q^{57} +(-35.3475 + 237.302i) q^{58} +540.267i q^{59} +666.853i q^{61} +(97.6585 + 14.5468i) q^{62} -611.664i q^{63} +(323.368 + 396.960i) q^{64} +(-39.5619 + 265.595i) q^{66} +84.8076 q^{67} +(-38.9111 + 127.715i) q^{68} -225.422i q^{69} -620.051 q^{71} +(399.390 + 189.787i) q^{72} -1120.50i q^{73} +(54.6649 + 8.14264i) q^{74} +(159.748 - 524.330i) q^{76} +1088.11 q^{77} +(559.986 + 83.4131i) q^{78} +155.358 q^{79} +180.535 q^{81} +(838.438 + 124.890i) q^{82} +73.5452 q^{83} +(-199.293 + 654.126i) q^{84} +(1437.15 + 214.071i) q^{86} -231.648i q^{87} +(-337.619 + 710.491i) q^{88} +1111.63 q^{89} -2294.20i q^{91} +(192.458 - 631.690i) q^{92} -95.3315 q^{93} +(147.998 - 993.574i) q^{94} +(-365.278 - 333.091i) q^{96} +1081.77i q^{97} +(1781.13 + 265.309i) q^{98} +679.371i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{4} + 18 q^{6} + 216 q^{9} + 224 q^{14} + 338 q^{16} + 570 q^{24} - 376 q^{26} - 528 q^{31} - 930 q^{34} - 1400 q^{36} + 600 q^{39} - 40 q^{41} - 766 q^{44} + 824 q^{46} - 456 q^{49} + 1674 q^{54}+ \cdots + 5470 q^{96}+O(q^{100}) $ 24 * q - 2 * q^4 + 18 * q^6 + 216 * q^9 + 224 * q^14 + 338 * q^16 + 570 * q^24 - 376 * q^26 - 528 * q^31 - 930 * q^34 - 1400 * q^36 + 600 * q^39 - 40 * q^41 - 766 * q^44 + 824 * q^46 - 456 * q^49 + 1674 * q^54 + 1304 * q^56 + 1486 * q^64 - 1794 * q^66 + 1256 * q^71 - 2160 * q^74 - 1938 * q^76 - 2232 * q^79 + 2256 * q^81 - 5096 * q^84 + 5452 * q^86 + 848 * q^89 + 3736 * q^94 + 5470 * q^96

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 $

$2$	−2.79756	−	0.416712i	−0.989087	−	0.147330i
$2$	−2.79756	−	0.416712i	−0.989087	−	0.147330i
$3$	2.73090			0.525562			0.262781	−	0.964855i	$-0.415360\pi$
$3$	2.73090			0.525562			0.262781	+	0.964855i	$0.415360\pi$
$4$	7.65270	+	2.33156i	0.956588	+	0.291445i
$5$		0			0
$5$		0			0
$6$	−7.63987	−	1.13800i	−0.519827	−	0.0774312i
$7$			31.2997i			1.69002i	0.534747	+	0.845012i	$0.320407\pi$
$7$			31.2997i			1.69002i	−0.534747	+	0.845012i	$0.679593\pi$
$8$	−20.4373	−	9.71165i	−0.903210	−	0.429198i
$9$	−19.5422			−0.723784
$10$		0			0
$11$		−	34.7644i		−	0.952896i	−0.879203	−	0.476448i	$-0.841924\pi$
$11$		−	34.7644i		−	0.952896i	0.879203	−	0.476448i	$-0.158076\pi$
$12$	20.8988	+	6.36726i	0.502747	+	0.153172i
$13$	−73.2979			−1.56378			−0.781891	−	0.623415i	$-0.785745\pi$
$13$	−73.2979			−1.56378			−0.781891	+	0.623415i	$0.785745\pi$
$14$	13.0430	−	87.5628i	0.248991	−	1.67158i
$15$		0			0
$16$	53.1277	+	35.6854i	0.830120	+	0.557585i
$17$			16.6889i			0.238097i	0.992888	+	0.119049i	$0.0379845\pi$
$17$			16.6889i			0.238097i	−0.992888	+	0.119049i	$0.962016\pi$
$18$	54.6704	+	8.14346i	0.715886	+	0.106635i
$19$		−	68.5157i		−	0.827294i	−0.910437	−	0.413647i	$-0.864255\pi$
$19$		−	68.5157i		−	0.827294i	0.910437	−	0.413647i	$-0.135745\pi$
$20$		0			0
$21$			85.4764i			0.888214i
$22$	−14.4867	+	97.2555i	−0.140390	+	0.942497i
$23$		−	82.5447i		−	0.748338i	−0.927361	−	0.374169i	$-0.877928\pi$
$23$		−	82.5447i		−	0.748338i	0.927361	−	0.374169i	$-0.122072\pi$
$24$	−55.8123	−	26.5216i	−0.474693	−	0.225571i
$25$		0			0
$26$	205.055	+	30.5441i	1.54672	+	0.230392i
$27$	−127.102			−0.905956
$28$	−72.9770	+	239.527i	−0.492549	+	1.61666i
$29$		−	84.8247i		−	0.543157i	−0.962416	−	0.271578i	$-0.912454\pi$
$29$		−	84.8247i		−	0.543157i	0.962416	−	0.271578i	$-0.0875456\pi$
$30$		0			0
$31$	−34.9084			−0.202250			−0.101125	−	0.994874i	$-0.532244\pi$
$31$	−34.9084			−0.202250			−0.101125	+	0.994874i	$0.532244\pi$
$32$	−133.757	−	121.971i	−0.738912	−	0.673802i
$33$		−	94.9381i		−	0.500806i
$34$	6.95448	−	46.6883i	0.0350789	−	0.235499i
$35$		0			0
$36$	−149.550	−	45.5637i	−0.692363	−	0.210943i
$37$	−19.5402			−0.0868213			−0.0434106	−	0.999057i	$-0.513822\pi$
$37$	−19.5402			−0.0868213			−0.0434106	+	0.999057i	$0.513822\pi$
$38$	−28.5513	+	191.677i	−0.121885	+	0.818266i
$39$	−200.169			−0.821865
$40$		0			0
$41$	−299.703			−1.14160			−0.570802	−	0.821088i	$-0.693368\pi$
$41$	−299.703			−1.14160			−0.570802	+	0.821088i	$0.693368\pi$
$42$	35.6191	−	239.126i	0.130861	−	0.878521i
$43$	−513.714			−1.82188			−0.910938	−	0.412544i	$-0.864640\pi$
$43$	−513.714			−1.82188			−0.910938	+	0.412544i	$0.864640\pi$
$44$	81.0551	−	266.041i	0.277716	−	0.911528i
$45$		0			0
$46$	−34.3974	+	230.924i	−0.110253	+	0.740171i
$47$			355.157i			1.10223i	0.834428	+	0.551117i	$0.185798\pi$
$47$			355.157i			1.10223i	−0.834428	+	0.551117i	$0.814202\pi$
$48$	145.087	+	97.4534i	0.436280	+	0.293046i
$49$	−636.671			−1.85618
$50$		0			0
$51$			45.5758i			0.125135i
$52$	−560.927	−	170.898i	−1.49590	−	0.455756i
$53$	488.561			1.26621			0.633104	−	0.774067i	$-0.281781\pi$
$53$	488.561			1.26621			0.633104	+	0.774067i	$0.281781\pi$
$54$	355.576	+	52.9650i	0.896070	+	0.133475i
$55$		0			0
$56$	303.972	−	639.682i	0.725356	−	1.52645i
$57$		−	187.110i		−	0.434794i
$58$	−35.3475	+	237.302i	−0.0800233	+	0.537229i
$59$			540.267i			1.19215i	0.802929	+	0.596074i	$0.203274\pi$
$59$			540.267i			1.19215i	−0.802929	+	0.596074i	$0.796726\pi$
$60$		0			0
$61$			666.853i			1.39970i	0.714290	+	0.699850i	$0.246750\pi$
$61$			666.853i			1.39970i	−0.714290	+	0.699850i	$0.753250\pi$
$62$	97.6585	+	14.5468i	0.200043	+	0.0297975i
$63$		−	611.664i		−	1.22321i
$64$	323.368	+	396.960i	0.631578	+	0.775313i
$65$		0			0
$66$	−39.5619	+	265.595i	−0.0737838	+	0.495341i
$67$	84.8076			0.154640			0.0773201	−	0.997006i	$-0.475364\pi$
$67$	84.8076			0.154640			0.0773201	+	0.997006i	$0.475364\pi$
$68$	−38.9111	+	127.715i	−0.0693922	+	0.227761i
$69$		−	225.422i		−	0.393298i
$70$		0			0
$71$	−620.051			−1.03643			−0.518215	−	0.855250i	$-0.673403\pi$
$71$	−620.051			−1.03643			−0.518215	+	0.855250i	$0.673403\pi$
$72$	399.390	+	189.787i	0.653729	+	0.310647i
$73$		−	1120.50i		−	1.79650i	−0.439489	−	0.898248i	$-0.644840\pi$
$73$		−	1120.50i		−	1.79650i	0.439489	−	0.898248i	$-0.355160\pi$
$74$	54.6649	+	8.14264i	0.0858738	+	0.0127914i
$75$		0			0
$76$	159.748	−	524.330i	0.241110	−	0.791379i
$77$	1088.11			1.61042
$78$	559.986	+	83.4131i	0.812897	+	0.121085i
$79$	155.358			0.221255			0.110627	−	0.993862i	$-0.464714\pi$
$79$	155.358			0.221255			0.110627	+	0.993862i	$0.464714\pi$
$80$		0			0
$81$	180.535			0.247648
$82$	838.438	+	124.890i	1.12915	+	0.168193i
$83$	73.5452			0.0972606			0.0486303	−	0.998817i	$-0.484514\pi$
$83$	73.5452			0.0972606			0.0486303	+	0.998817i	$0.484514\pi$
$84$	−199.293	+	654.126i	−0.258865	+	0.849654i
$85$		0			0
$86$	1437.15	+	214.071i	1.80199	+	0.268417i
$87$		−	231.648i		−	0.285463i
$88$	−337.619	+	710.491i	−0.408981	+	0.860665i
$89$	1111.63			1.32396			0.661981	−	0.749521i	$-0.269716\pi$
$89$	1111.63			1.32396			0.661981	+	0.749521i	$0.269716\pi$
$90$		0			0
$91$		−	2294.20i		−	2.64283i
$92$	192.458	−	631.690i	0.218099	−	0.715851i
$93$	−95.3315			−0.106295
$94$	147.998	−	993.574i	0.162392	−	1.09021i
$95$		0			0
$96$	−365.278	−	333.091i	−0.388345	−	0.354125i
$97$			1081.77i			1.13235i	0.824286	+	0.566173i	$0.191577\pi$
$97$			1081.77i			1.13235i	−0.824286	+	0.566173i	$0.808423\pi$
$98$	1781.13	+	265.309i	1.83593	+	0.273472i
$99$			679.371i			0.689691i
$100$		0			0
$101$			1309.04i			1.28965i	0.764332	+	0.644823i	$0.223069\pi$
$101$			1309.04i			1.28965i	−0.764332	+	0.644823i	$0.776931\pi$
$102$	18.9920	−	127.501i	0.0184362	−	0.123770i
$103$		−	51.0520i		−	0.0488379i	−0.999702	−	0.0244189i	$-0.992226\pi$
$103$		−	51.0520i		−	0.0488379i	0.999702	−	0.0244189i	$-0.00777356\pi$
$104$	1498.01	+	711.843i	1.41242	+	0.671173i
$105$		0			0
$106$	−1366.78	−	203.589i	−1.25239	−	0.186550i
$107$	−1389.17			−1.25510			−0.627550	−	0.778576i	$-0.715942\pi$
$107$	−1389.17			−1.25510			−0.627550	+	0.778576i	$0.715942\pi$
$108$	−972.675	−	296.346i	−0.866627	−	0.264036i
$109$			1023.87i			0.899720i	0.893099	+	0.449860i	$0.148526\pi$
$109$			1023.87i			0.899720i	−0.893099	+	0.449860i	$0.851474\pi$
$110$		0			0
$111$	−53.3624			−0.0456300
$112$	−1116.94	+	1662.88i	−0.942332	+	1.40292i
$113$			1005.40i			0.836994i	0.908218	+	0.418497i	$0.137443\pi$
$113$			1005.40i			0.836994i	−0.908218	+	0.418497i	$0.862557\pi$
$114$	−77.9709	+	523.451i	−0.0640583	+	0.430050i
$115$		0			0
$116$	197.774	−	649.138i	0.158300	−	0.519577i
$117$	1432.40			1.13184
$118$	225.136	−	1511.43i	0.175639	−	1.17914i
$119$	−522.358			−0.402390
$120$		0			0
$121$	122.438			0.0919895
$122$	277.886	−	1865.56i	0.206218	−	1.38443i
$123$	−818.460			−0.599984
$124$	−267.144	−	81.3910i	−0.193470	−	0.0589446i
$125$		0			0
$126$	−254.888	+	1711.17i	−0.180216	+	1.20986i
$127$		−	168.986i		−	0.118071i	−0.998256	−	0.0590356i	$-0.981197\pi$
$127$		−	168.986i		−	0.118071i	0.998256	−	0.0590356i	$-0.0188025\pi$
$128$	−739.223	−	1245.27i	−0.510459	−	0.859902i
$129$	−1402.90			−0.957509
$130$		0			0
$131$		−	1221.13i		−	0.814434i	−0.913331	−	0.407217i	$-0.866499\pi$
$131$		−	1221.13i		−	0.814434i	0.913331	−	0.407217i	$-0.133501\pi$
$132$	221.354	−	726.533i	0.145957	−	0.479065i
$133$	2144.52			1.39815
$134$	−237.255	−	35.3404i	−0.152953	−	0.0227832i
$135$		0			0
$136$	162.077	−	341.077i	0.102191	−	0.215052i
$137$		−	2091.31i		−	1.30418i	−0.758143	−	0.652089i	$-0.773893\pi$
$137$		−	2091.31i		−	1.30418i	0.758143	−	0.652089i	$-0.226107\pi$
$138$	−93.9360	+	630.631i	−0.0579447	+	0.389006i
$139$			158.107i			0.0964781i	0.998836	+	0.0482390i	$0.0153609\pi$
$139$			158.107i			0.0964781i	−0.998836	+	0.0482390i	$0.984639\pi$
$140$		0			0
$141$			969.900i			0.579293i
$142$	1734.63	+	258.383i	1.02512	+	0.152697i
$143$			2548.16i			1.49012i
$144$	−1038.23	−	697.371i	−0.600828	−	0.403571i
$145$		0			0
$146$	−466.925	+	3134.66i	−0.264678	+	1.77689i
$147$	−1738.69			−0.975540
$148$	−149.535	−	45.5591i	−0.0830522	−	0.0253036i
$149$		−	3129.78i		−	1.72081i	−0.509607	−	0.860407i	$-0.670209\pi$
$149$		−	3129.78i		−	1.72081i	0.509607	−	0.860407i	$-0.329791\pi$
$150$		0			0
$151$	−609.263			−0.328352			−0.164176	−	0.986431i	$-0.552496\pi$
$151$	−609.263			−0.328352			−0.164176	+	0.986431i	$0.552496\pi$
$152$	−665.400	+	1400.28i	−0.355073	+	0.747220i
$153$		−	326.138i		−	0.172331i
$154$	−3044.07	−	453.431i	−1.59284	−	0.237263i
$155$		0			0
$156$	−1531.84	−	466.706i	−0.786186	−	0.239528i
$157$	−1856.37			−0.943657			−0.471829	−	0.881690i	$-0.656406\pi$
$157$	−1856.37			−0.943657			−0.471829	+	0.881690i	$0.656406\pi$
$158$	−434.623	−	64.7396i	−0.218840	−	0.0325975i
$159$	1334.21			0.665471
$160$		0			0
$161$	2583.63			1.26471
$162$	−505.058	−	75.2312i	−0.244945	−	0.0364859i
$163$	−3339.59			−1.60477			−0.802383	−	0.596810i	$-0.796435\pi$
$163$	−3339.59			−1.60477			−0.802383	+	0.596810i	$0.796435\pi$
$164$	−2293.54	−	698.775i	−1.09204	−	0.332714i
$165$		0			0
$166$	−205.747	−	30.6472i	−0.0961993	−	0.0143294i
$167$		−	1591.60i		−	0.737496i	−0.929529	−	0.368748i	$-0.879786\pi$
$167$		−	1591.60i		−	0.737496i	0.929529	−	0.368748i	$-0.120214\pi$
$168$	830.117	−	1746.91i	0.381220	−	0.802244i
$169$	3175.58			1.44542
$170$		0			0
$171$			1338.95i			0.598782i
$172$	−3931.30	−	1197.75i	−1.74278	−	0.530976i
$173$	1688.21			0.741919			0.370960	−	0.928649i	$-0.379029\pi$
$173$	1688.21			0.741919			0.370960	+	0.928649i	$0.379029\pi$
$174$	−96.5306	+	648.049i	−0.0420573	+	0.282348i
$175$		0			0
$176$	1240.58	−	1846.95i	0.531320	−	0.791018i
$177$			1475.42i			0.626548i
$178$	−3109.85	−	463.230i	−1.30951	−	0.195059i
$179$			66.8624i			0.0279192i	0.999903	+	0.0139596i	$0.00444362\pi$
$179$			66.8624i			0.0279192i	−0.999903	+	0.0139596i	$0.995556\pi$
$180$		0			0
$181$			1646.17i			0.676014i	0.941144	+	0.338007i	$0.109753\pi$
$181$			1646.17i			0.676014i	−0.941144	+	0.338007i	$0.890247\pi$
$182$	−956.022	+	6418.17i	−0.389369	+	2.61399i
$183$			1821.11i			0.735630i
$184$	−801.646	+	1686.99i	−0.321185	+	0.675906i
$185$		0			0
$186$	266.696	+	39.7258i	0.105135	+	0.0156604i
$187$	580.180			0.226882
$188$	−828.069	+	2717.91i	−0.321240	+	1.05438i
$189$		−	3978.26i		−	1.53109i
$190$		0			0
$191$	3408.02			1.29108			0.645538	−	0.763729i	$-0.276633\pi$
$191$	3408.02			1.29108			0.645538	+	0.763729i	$0.276633\pi$
$192$	883.086	+	1084.06i	0.331933	+	0.407475i
$193$			4312.88i			1.60854i	0.594265	+	0.804270i	$0.297443\pi$
$193$			4312.88i			1.60854i	−0.594265	+	0.804270i	$0.702557\pi$
$194$	450.789	−	3026.33i	0.166829	−	1.11999i
$195$		0			0
$196$	−4872.25	−	1484.43i	−1.77560	−	0.540975i
$197$	1425.64			0.515597			0.257799	−	0.966199i	$-0.417003\pi$
$197$	1425.64			0.515597			0.257799	+	0.966199i	$0.417003\pi$
$198$	283.102	−	1900.58i	0.101612	−	0.682165i
$199$	922.125			0.328481			0.164240	−	0.986420i	$-0.447483\pi$
$199$	922.125			0.328481			0.164240	+	0.986420i	$0.447483\pi$
$200$		0			0
$201$	231.601			0.0812731
$202$	545.492	−	3662.11i	0.190004	−	1.27557i
$203$	2654.99			0.917948
$204$	−106.263	+	348.778i	−0.0364699	+	0.119703i
$205$		0			0
$206$	−21.2740	+	142.821i	−0.00719529	+	0.0483049i
$207$			1613.10i			0.541635i
$208$	−3894.15	−	2615.67i	−1.29813	−	0.871941i
$209$	−2381.91			−0.788325
$210$		0			0
$211$		−	4106.85i		−	1.33994i	−0.742389	−	0.669970i	$-0.766307\pi$
$211$		−	4106.85i		−	1.33994i	0.742389	−	0.669970i	$-0.233693\pi$
$212$	3738.81	+	1139.11i	1.21124	+	0.369029i
$213$	−1693.30			−0.544709
$214$	3886.28	+	578.882i	1.24140	+	0.184914i
$215$		0			0
$216$	2597.63	+	1234.37i	0.818269	+	0.388835i
$217$		−	1092.62i		−	0.341807i
$218$	426.661	−	2864.35i	0.132556	−	0.889901i
$219$		−	3059.97i		−	0.944171i
$220$		0			0
$221$		−	1223.26i		−	0.372333i
$222$	149.285	+	22.2368i	0.0451321	+	0.00672267i
$223$			296.498i			0.0890359i	0.999009	+	0.0445179i	$0.0141752\pi$
$223$			296.498i			0.0890359i	−0.999009	+	0.0445179i	$0.985825\pi$
$224$	3817.66	−	4186.57i	1.13874	−	1.24878i
$225$		0			0
$226$	418.964	−	2812.68i	0.123314	−	0.827860i
$227$	−712.060			−0.208199			−0.104099	−	0.994567i	$-0.533196\pi$
$227$	−712.060			−0.208199			−0.104099	+	0.994567i	$0.533196\pi$
$228$	436.257	−	1431.89i	0.126719	−	0.415919i
$229$			5245.53i			1.51369i	0.653595	+	0.756844i	$0.273260\pi$
$229$			5245.53i			1.51369i	−0.653595	+	0.756844i	$0.726740\pi$
$230$		0			0
$231$	2971.53			0.846375
$232$	−823.787	+	1733.59i	−0.233122	+	0.490585i
$233$			1527.84i			0.429581i	0.976660	+	0.214790i	$0.0689068\pi$
$233$			1527.84i			0.429581i	−0.976660	+	0.214790i	$0.931093\pi$
$234$	−4007.23	−	596.899i	−1.11949	−	0.166754i
$235$		0			0
$236$	−1259.66	+	4134.50i	−0.347445	+	1.14039i
$237$	424.267			0.116283
$238$	1461.33	+	217.673i	0.397999	+	0.0592842i
$239$	1111.38			0.300792			0.150396	−	0.988626i	$-0.451945\pi$
$239$	1111.38			0.300792			0.150396	+	0.988626i	$0.451945\pi$
$240$		0			0
$241$	−1006.39			−0.268992			−0.134496	−	0.990914i	$-0.542942\pi$
$241$	−1006.39			−0.268992			−0.134496	+	0.990914i	$0.542942\pi$
$242$	−342.528	−	51.0215i	−0.0909857	−	0.0135528i
$243$	3924.78			1.03611
$244$	−1554.80	+	5103.22i	−0.407935	+	1.33894i
$245$		0			0
$246$	2289.69	+	341.062i	0.593437	+	0.0883957i
$247$			5022.06i			1.29371i
$248$	713.435	+	339.018i	0.182674	+	0.0868052i
$249$	200.845			0.0511165
$250$		0			0
$251$			3073.70i			0.772950i	0.922300	+	0.386475i	$0.126307\pi$
$251$			3073.70i			0.772950i	−0.922300	+	0.386475i	$0.873693\pi$
$252$	1426.13	−	4680.88i	0.356499	−	1.17011i
$253$	−2869.62			−0.713088
$254$	−70.4184	+	472.747i	−0.0173954	+	0.116783i
$255$		0			0
$256$	1549.10	+	3791.77i	0.378199	+	0.925724i
$257$		−	5320.81i		−	1.29145i	−0.763570	−	0.645725i	$-0.776555\pi$
$257$		−	5320.81i		−	1.29145i	0.763570	−	0.645725i	$-0.223445\pi$
$258$	3924.71	+	584.607i	0.947060	+	0.141070i
$259$		−	611.602i		−	0.146730i
$260$		0			0
$261$			1657.66i			0.393128i
$262$	−508.861	+	3416.20i	−0.119991	+	0.805547i
$263$		−	5684.45i		−	1.33277i	−0.745608	−	0.666385i	$-0.767841\pi$
$263$		−	5684.45i		−	1.33277i	0.745608	−	0.666385i	$-0.232159\pi$
$264$	−922.006	+	1940.28i	−0.214945	+	0.452333i
$265$		0			0
$266$	−5999.43	−	893.648i	−1.38289	−	0.205989i
$267$	3035.75			0.695824
$268$	649.007	+	197.734i	0.147927	+	0.0450691i
$269$			6128.17i			1.38900i	0.719493	+	0.694500i	$0.244374\pi$
$269$			6128.17i			1.38900i	−0.719493	+	0.694500i	$0.755626\pi$
$270$		0			0
$271$	−4758.45			−1.06662			−0.533312	−	0.845918i	$-0.679053\pi$
$271$	−4758.45			−1.06662			−0.533312	+	0.845918i	$0.679053\pi$
$272$	−595.551	+	886.643i	−0.132759	+	0.197649i
$273$		−	6265.24i		−	1.38897i
$274$	−871.473	+	5850.56i	−0.192145	+	1.28995i
$275$		0			0
$276$	525.583	−	1725.08i	0.114625	−	0.376224i
$277$	−780.996			−0.169406			−0.0847031	−	0.996406i	$-0.526994\pi$
$277$	−780.996			−0.169406			−0.0847031	+	0.996406i	$0.526994\pi$
$278$	65.8851	−	442.314i	0.0142141	−	0.0954253i
$279$	682.187			0.146385
$280$		0			0
$281$	−3327.18			−0.706344			−0.353172	−	0.935558i	$-0.614897\pi$
$281$	−3327.18			−0.706344			−0.353172	+	0.935558i	$0.614897\pi$
$282$	404.169	−	2713.36i	0.0853473	−	0.572971i
$283$	−236.405			−0.0496566			−0.0248283	−	0.999692i	$-0.507904\pi$
$283$	−236.405			−0.0496566			−0.0248283	+	0.999692i	$0.507904\pi$
$284$	−4745.07	−	1445.69i	−0.991437	−	0.302062i
$285$		0			0
$286$	1061.85	−	7128.62i	0.219540	−	1.47386i
$287$		−	9380.61i		−	1.92934i
$288$	2613.91	+	2383.58i	0.534813	+	0.487687i
$289$	4634.48			0.943310
$290$		0			0
$291$			2954.22i			0.595119i
$292$	2612.50	−	8574.83i	0.523579	−	1.71851i
$293$	−123.056			−0.0245359			−0.0122680	−	0.999925i	$-0.503905\pi$
$293$	−123.056			−0.0245359			−0.0122680	+	0.999925i	$0.503905\pi$
$294$	4864.08	+	724.532i	0.964895	+	0.143726i
$295$		0			0
$296$	399.349	+	189.768i	0.0784179	+	0.0372636i
$297$			4418.63i			0.863282i
$298$	−1304.22	+	8755.75i	−0.253528	+	1.70204i
$299$			6050.35i			1.17024i
$300$		0			0
$301$		−	16079.1i		−	3.07901i
$302$	1704.45	+	253.887i	0.324769	+	0.0483761i
$303$			3574.86i			0.677789i
$304$	2445.01	−	3640.08i	0.461286	−	0.686753i
$305$		0			0
$306$	−135.906	+	912.390i	−0.0253896	+	0.170451i
$307$	1706.98			0.317337			0.158669	−	0.987332i	$-0.449280\pi$
$307$	1706.98			0.317337			0.158669	+	0.987332i	$0.449280\pi$
$308$	8327.01	+	2537.00i	1.54051	+	0.469347i
$309$		−	139.418i		−	0.0256674i
$310$		0			0
$311$	−7441.46			−1.35681			−0.678403	−	0.734690i	$-0.737328\pi$
$311$	−7441.46			−1.35681			−0.678403	+	0.734690i	$0.737328\pi$
$312$	4090.92	+	1943.97i	0.742317	+	0.352743i
$313$		−	70.7973i		−	0.0127850i	−0.999980	−	0.00639249i	$-0.997965\pi$
$313$		−	70.7973i		−	0.0127850i	0.999980	−	0.00639249i	$-0.00203481\pi$
$314$	5193.30	+	773.571i	0.933360	+	0.139029i
$315$		0			0
$316$	1188.91	+	362.226i	0.211650	+	0.0644835i
$317$	−7516.28			−1.33172			−0.665862	−	0.746075i	$-0.731936\pi$
$317$	−7516.28			−1.33172			−0.665862	+	0.746075i	$0.731936\pi$
$318$	−3732.54	−	555.983i	−0.658209	−	0.0980439i
$319$	−2948.88			−0.517572
$320$		0			0
$321$	−3793.67			−0.659633
$322$	−7227.85	−	1076.63i	−1.25091	−	0.186330i
$323$	1143.45			0.196976
$324$	1381.58	+	420.928i	0.236897	+	0.0721755i
$325$		0			0
$326$	9342.71	+	1391.65i	1.58725	+	0.236430i
$327$			2796.10i			0.472859i
$328$	6125.13	+	2910.61i	1.03111	+	0.489974i
$329$	−11116.3			−1.86280
$330$		0			0
$331$			7290.44i			1.21063i	0.795986	+	0.605316i	$0.206953\pi$
$331$			7290.44i			1.21063i	−0.795986	+	0.605316i	$0.793047\pi$
$332$	562.819	+	171.475i	0.0930383	+	0.0283461i
$333$	381.858			0.0628399
$334$	−663.240	+	4452.61i	−0.108655	+	0.729448i
$335$		0			0
$336$	−3050.26	+	4541.16i	−0.495254	+	0.737324i
$337$			4645.79i			0.750957i	0.926831	+	0.375478i	$0.122522\pi$
$337$			4645.79i			0.750957i	−0.926831	+	0.375478i	$0.877478\pi$
$338$	−8883.88	−	1323.30i	−1.42964	−	0.212953i
$339$			2745.66i			0.439893i
$340$		0			0
$341$			1213.57i			0.192723i
$342$	557.955	−	3745.78i	0.0882186	−	0.592248i
$343$		−	9191.81i		−	1.44697i
$344$	10498.9	+	4989.01i	1.64554	+	0.781946i
$345$		0			0
$346$	−4722.86	−	703.497i	−0.733823	−	0.109307i
$347$	9363.62			1.44860			0.724302	−	0.689483i	$-0.242162\pi$
$347$	9363.62			1.44860			0.724302	+	0.689483i	$0.242162\pi$
$348$	540.100	−	1772.73i	0.0831966	−	0.273070i
$349$		−	1050.35i		−	0.161101i	−0.996751	−	0.0805504i	$-0.974332\pi$
$349$		−	1050.35i		−	0.161101i	0.996751	−	0.0805504i	$-0.0256678\pi$
$350$		0			0
$351$	9316.32			1.41672
$352$	−4240.25	+	4649.99i	−0.642063	+	0.704106i
$353$		−	4294.72i		−	0.647550i	−0.946134	−	0.323775i	$-0.895048\pi$
$353$		−	4294.72i		−	0.647550i	0.946134	−	0.323775i	$-0.104952\pi$
$354$	614.824	−	4127.57i	0.0923094	−	0.619711i
$355$		0			0
$356$	8506.97	+	2591.83i	1.26648	+	0.385861i
$357$	−1426.51			−0.211481
$358$	27.8624	−	187.052i	0.00411333	−	0.0276145i
$359$	−11047.3			−1.62411			−0.812054	−	0.583583i	$-0.801650\pi$
$359$	−11047.3			−1.62411			−0.812054	+	0.583583i	$0.801650\pi$
$360$		0			0
$361$	2164.60			0.315585
$362$	685.977	−	4605.25i	0.0995972	−	0.668637i
$363$	334.366			0.0483463
$364$	5349.06	−	17556.8i	0.770239	−	2.52810i
$365$		0			0
$366$	758.879	−	5094.67i	0.108380	−	0.727602i
$367$			4347.92i			0.618419i	0.950994	+	0.309209i	$0.100064\pi$
$367$			4347.92i			0.618419i	−0.950994	+	0.309209i	$0.899936\pi$
$368$	2945.64	−	4385.41i	0.417262	−	0.621210i
$369$	5856.85			0.826275
$370$		0			0
$371$			15291.8i			2.13992i
$372$	−729.544	−	222.271i	−0.101680	−	0.0309791i
$373$	−5431.84			−0.754022			−0.377011	−	0.926209i	$-0.623048\pi$
$373$	−5431.84			−0.754022			−0.377011	+	0.926209i	$0.623048\pi$
$374$	−1623.09	−	241.768i	−0.224406	−	0.0334265i
$375$		0			0
$376$	3449.16	−	7258.46i	0.473077	−	0.995549i
$377$			6217.47i			0.849379i
$378$	−1657.79	+	11129.4i	−0.225575	+	1.51438i
$379$		−	9385.95i		−	1.27209i	−0.771650	−	0.636047i	$-0.780568\pi$
$379$		−	9385.95i		−	1.27209i	0.771650	−	0.636047i	$-0.219432\pi$
$380$		0			0
$381$		−	461.483i		−	0.0620538i
$382$	−9534.13	−	1420.16i	−1.27699	−	0.190214i
$383$		−	2666.15i		−	0.355702i	−0.984057	−	0.177851i	$-0.943086\pi$
$383$		−	2666.15i		−	0.355702i	0.984057	−	0.177851i	$-0.0569144\pi$
$384$	−2018.75	−	3400.72i	−0.268278	−	0.451932i
$385$		0			0
$386$	1797.23	−	12065.6i	0.236986	−	1.59099i
$387$	10039.1			1.31864
$388$	−2522.22	+	8278.50i	−0.330016	+	1.08319i
$389$		−	3089.22i		−	0.402647i	−0.979525	−	0.201324i	$-0.935476\pi$
$389$		−	3089.22i		−	0.402647i	0.979525	−	0.201324i	$-0.0645243\pi$
$390$		0			0
$391$	1377.58			0.178177
$392$	13011.8	+	6183.12i	1.67652	+	0.796671i
$393$		−	3334.80i		−	0.428036i
$394$	−3988.32	−	594.082i	−0.509971	−	0.0759630i
$395$		0			0
$396$	−1583.99	+	5199.03i	−0.201007	+	0.659750i
$397$	2663.69			0.336743			0.168371	−	0.985724i	$-0.446149\pi$
$397$	2663.69			0.336743			0.168371	+	0.985724i	$0.446149\pi$
$398$	−2579.70	−	384.261i	−0.324896	−	0.0483951i
$399$	5856.48			0.734813
$400$		0			0
$401$	−7804.95			−0.971971			−0.485986	−	0.873967i	$-0.661539\pi$
$401$	−7804.95			−0.971971			−0.485986	+	0.873967i	$0.661539\pi$
$402$	−647.919	−	96.5111i	−0.0803862	−	0.0119740i
$403$	2558.71			0.316275
$404$	−3052.10	+	10017.7i	−0.375860	+	1.23366i
$405$		0			0
$406$	−7427.49	−	1106.37i	−0.907931	−	0.135241i
$407$			679.303i			0.0827317i
$408$	442.616	−	931.447i	0.0537078	−	0.113023i
$409$	−4203.14			−0.508146			−0.254073	−	0.967185i	$-0.581770\pi$
$409$	−4203.14			−0.508146			−0.254073	+	0.967185i	$0.581770\pi$
$410$		0			0
$411$		−	5711.15i		−	0.685427i
$412$	119.031	−	390.686i	0.0142335	−	0.0467177i
$413$	−16910.2			−2.01476
$414$	672.200	−	4512.76i	0.0797991	−	0.535724i
$415$		0			0
$416$	9804.13	+	8940.22i	1.15550	+	1.05368i
$417$			431.775i			0.0507053i
$418$	6663.53	+	992.569i	0.779722	+	0.116144i
$419$		−	14112.6i		−	1.64546i	−0.568435	−	0.822728i	$-0.692451\pi$
$419$		−	14112.6i		−	1.64546i	0.568435	−	0.822728i	$-0.307549\pi$
$420$		0			0
$421$		−	8042.17i		−	0.931001i	−0.885048	−	0.465501i	$-0.845874\pi$
$421$		−	8042.17i		−	0.931001i	0.885048	−	0.465501i	$-0.154126\pi$
$422$	−1711.37	+	11489.2i	−0.197413	+	1.32532i
$423$		−	6940.54i		−	0.797780i
$424$	−9984.87	−	4744.73i	−1.14365	−	0.543454i
$425$		0			0
$426$	4737.11	+	705.619i	0.538765	+	0.0802520i
$427$	−20872.3			−2.36553
$428$	−10630.9	−	3238.92i	−1.20061	−	0.365792i
$429$			6958.76i			0.783152i
$430$		0			0
$431$	−14634.6			−1.63555			−0.817775	−	0.575539i	$-0.804792\pi$
$431$	−14634.6			−1.63555			−0.817775	+	0.575539i	$0.804792\pi$
$432$	−6752.64	−	4535.69i	−0.752052	−	0.505147i
$433$		−	7212.59i		−	0.800496i	−0.916407	−	0.400248i	$-0.868924\pi$
$433$		−	7212.59i		−	0.800496i	0.916407	−	0.400248i	$-0.131076\pi$
$434$	−455.310	+	3056.68i	−0.0503584	+	0.338077i
$435$		0			0
$436$	−2387.22	+	7835.41i	−0.262218	+	0.860661i
$437$	−5655.61			−0.619095
$438$	−1275.13	+	8560.45i	−0.139105	+	0.933868i
$439$	−3676.98			−0.399756			−0.199878	−	0.979821i	$-0.564055\pi$
$439$	−3676.98			−0.399756			−0.199878	+	0.979821i	$0.564055\pi$
$440$		0			0
$441$	12441.9			1.34348
$442$	−509.748	+	3422.15i	−0.0548558	+	0.368269i
$443$	5290.59			0.567412			0.283706	−	0.958911i	$-0.408436\pi$
$443$	5290.59			0.567412			0.283706	+	0.958911i	$0.408436\pi$
$444$	−408.366	−	124.417i	−0.0436491	−	0.0132986i
$445$		0			0
$446$	123.555	−	829.472i	0.0131177	−	0.0880643i
$447$		−	8547.12i		−	0.904396i
$448$	−12424.7	+	10121.3i	−1.31030	+	1.06738i
$449$	6726.44			0.706994			0.353497	−	0.935436i	$-0.384992\pi$
$449$	6726.44			0.706994			0.353497	+	0.935436i	$0.384992\pi$
$450$		0			0
$451$			10419.0i			1.08783i
$452$	−2344.15	+	7694.05i	−0.243937	+	0.800658i
$453$	−1663.84			−0.172569
$454$	1992.03	+	296.724i	0.205927	+	0.0306739i
$455$		0			0
$456$	−1817.14	+	3824.02i	−0.186613	+	0.392711i
$457$			5266.91i			0.539115i	0.962984	+	0.269557i	$0.0868774\pi$
$457$			5266.91i			0.539115i	−0.962984	+	0.269557i	$0.913123\pi$
$458$	2185.88	−	14674.7i	0.223012	−	1.49717i
$459$		−	2121.20i		−	0.215706i
$460$		0			0
$461$			8102.90i			0.818633i	0.912393	+	0.409316i	$0.134233\pi$
$461$			8102.90i			0.818633i	−0.912393	+	0.409316i	$0.865767\pi$
$462$	−8313.05	−	1238.28i	−0.837139	−	0.124696i
$463$			19671.2i			1.97451i	0.159147	+	0.987255i	$0.449126\pi$
$463$			19671.2i			1.97451i	−0.159147	+	0.987255i	$0.550874\pi$
$464$	3027.00	−	4506.54i	0.302856	−	0.450885i
$465$		0			0
$466$	636.671	−	4274.23i	0.0632902	−	0.424893i
$467$	3143.78			0.311514			0.155757	−	0.987795i	$-0.450218\pi$
$467$	3143.78			0.311514			0.155757	+	0.987795i	$0.450218\pi$
$468$	10961.7	+	3339.72i	1.08271	+	0.329869i
$469$			2654.45i			0.261346i
$470$		0			0
$471$	−5069.56			−0.495951
$472$	5246.88	−	11041.6i	0.511668	−	1.07676i
$473$			17858.9i			1.73606i
$474$	−1186.91	−	176.797i	−0.115014	−	0.0171320i
$475$		0			0
$476$	−3997.45	−	1217.91i	−0.384922	−	0.117275i
$477$	−9547.54			−0.916461
$478$	−3109.16	−	463.126i	−0.297510	−	0.0443157i
$479$	−7050.53			−0.672541			−0.336270	−	0.941765i	$-0.609166\pi$
$479$	−7050.53			−0.672541			−0.336270	+	0.941765i	$0.609166\pi$
$480$		0			0
$481$	1432.25			0.135770
$482$	2815.43	+	419.374i	0.266056	+	0.0396306i
$483$	7055.63			0.664684
$484$	936.982	+	285.471i	0.0879961	+	0.0268099i
$485$		0			0
$486$	−10979.8	−	1635.50i	−1.02480	−	0.152650i
$487$			2412.03i			0.224434i	0.993684	+	0.112217i	$0.0357952\pi$
$487$			2412.03i			0.224434i	−0.993684	+	0.112217i	$0.964205\pi$
$488$	6476.24	−	13628.7i	0.600749	−	1.26422i
$489$	−9120.09			−0.843405
$490$		0			0
$491$		−	8009.43i		−	0.736172i	−0.929792	−	0.368086i	$-0.880013\pi$
$491$		−	8009.43i		−	0.736172i	0.929792	−	0.368086i	$-0.119987\pi$
$492$	−6263.43	−	1908.29i	−0.573937	−	0.174862i
$493$	1415.63			0.129324
$494$	2092.75	−	14049.5i	0.190602	−	1.27959i
$495$		0			0
$496$	−1854.60	−	1245.72i	−0.167891	−	0.112771i
$497$		−	19407.4i		−	1.75159i
$498$	−561.876	−	83.6945i	−0.0505587	−	0.00753100i
$499$			4017.44i			0.360411i	0.983629	+	0.180206i	$0.0576763\pi$
$499$			4017.44i			0.360411i	−0.983629	+	0.180206i	$0.942324\pi$
$500$		0			0
$501$		−	4346.51i		−	0.387600i
$502$	1280.85	−	8598.87i	0.113879	−	0.764515i
$503$			685.739i			0.0607865i	0.999538	+	0.0303932i	$0.00967596\pi$
$503$			685.739i			0.0607865i	−0.999538	+	0.0303932i	$0.990324\pi$
$504$	−5940.27	+	12500.8i	−0.525001	+	1.10482i
$505$		0			0
$506$	8027.93	+	1195.80i	0.705306	+	0.105059i
$507$	8672.20			0.759657
$508$	393.999	−	1293.20i	0.0344112	−	0.112945i
$509$		−	888.059i		−	0.0773330i	−0.999252	−	0.0386665i	$-0.987689\pi$
$509$		−	888.059i		−	0.0773330i	0.999252	−	0.0386665i	$-0.0123110\pi$
$510$		0			0
$511$	35071.2			3.03612
$512$	−2753.63	−	11253.2i	−0.237684	−	0.971342i
$513$			8708.49i			0.749492i
$514$	−2217.25	+	14885.3i	−0.190270	+	1.27736i
$515$		0			0
$516$	−10736.0	−	3270.95i	−0.915942	−	0.279061i
$517$	12346.8			1.05031
$518$	−254.862	+	1710.99i	−0.0216178	+	0.145129i
$519$	4610.33			0.389925
$520$		0			0
$521$	−12190.8			−1.02512			−0.512562	−	0.858650i	$-0.671304\pi$
$521$	−12190.8			−1.02512			−0.512562	+	0.858650i	$0.671304\pi$
$522$	690.767	−	4637.40i	0.0579196	−	0.388838i
$523$	−9047.07			−0.756406			−0.378203	−	0.925723i	$-0.623458\pi$
$523$	−9047.07			−0.756406			−0.378203	+	0.925723i	$0.623458\pi$
$524$	2847.14	−	9344.97i	0.237363	−	0.779078i
$525$		0			0
$526$	−2368.78	+	15902.6i	−0.196357	+	1.31823i
$527$		−	582.584i		−	0.0481551i
$528$	3387.91	−	5043.84i	0.279242	−	0.415729i
$529$	5353.36			0.439991
$530$		0			0
$531$		−	10558.0i		−	0.862858i
$532$	16411.4	+	5000.07i	1.33745	+	0.407482i
$533$	21967.6			1.78522
$534$	−8492.71	−	1265.04i	−0.688231	−	0.102516i
$535$		0			0
$536$	−1733.24	−	823.622i	−0.139673	−	0.0663714i
$537$			182.595i			0.0146733i
$538$	2553.68	−	17143.9i	0.204642	−	1.37384i
$539$			22133.5i			1.76875i
$540$		0			0
$541$		−	7504.70i		−	0.596400i	−0.954503	−	0.298200i	$-0.903614\pi$
$541$		−	7504.70i		−	0.596400i	0.954503	−	0.298200i	$-0.0963862\pi$
$542$	13312.1	+	1982.90i	1.05498	+	0.157146i
$543$			4495.52i			0.355287i
$544$	2035.57	−	2232.27i	0.160430	−	0.175933i
$545$		0			0
$546$	−2610.80	+	17527.4i	−0.204637	+	1.37382i
$547$	−5218.06			−0.407876			−0.203938	−	0.978984i	$-0.565374\pi$
$547$	−5218.06			−0.407876			−0.203938	+	0.978984i	$0.565374\pi$
$548$	4876.00	−	16004.1i	0.380095	−	1.24756i
$549$		−	13031.7i		−	1.01308i
$550$		0			0
$551$	−5811.82			−0.449350
$552$	−2189.22	+	4607.01i	−0.168803	+	0.355231i
$553$			4862.65i			0.373926i
$554$	2184.89	+	325.451i	0.167558	+	0.0249586i
$555$		0			0
$556$	−368.635	+	1209.95i	−0.0281180	+	0.0922898i
$557$	−10013.9			−0.761765			−0.380882	−	0.924623i	$-0.624380\pi$
$557$	−10013.9			−0.761765			−0.380882	+	0.924623i	$0.624380\pi$
$558$	−1908.46	−	284.276i	−0.144788	−	0.0215669i
$559$	37654.1			2.84902
$560$		0			0
$561$	1584.41			0.119241
$562$	9307.98	+	1386.48i	0.698636	+	0.104066i
$563$	−8043.73			−0.602136			−0.301068	−	0.953603i	$-0.597343\pi$
$563$	−8043.73			−0.602136			−0.301068	+	0.953603i	$0.597343\pi$
$564$	−2261.38	+	7422.36i	−0.168832	+	0.554145i
$565$		0			0
$566$	661.357	+	98.5128i	0.0491147	+	0.00731590i
$567$			5650.69i			0.418530i
$568$	12672.2	+	6021.72i	0.936115	+	0.444834i
$569$	8205.39			0.604548			0.302274	−	0.953221i	$-0.402254\pi$
$569$	8205.39			0.604548			0.302274	+	0.953221i	$0.402254\pi$
$570$		0			0
$571$			3471.92i			0.254458i	0.991873	+	0.127229i	$0.0406083\pi$
$571$			3471.92i			0.254458i	−0.991873	+	0.127229i	$0.959392\pi$
$572$	−5941.17	+	19500.3i	−0.434288	+	1.42543i
$573$	9306.96			0.678541
$574$	−3909.02	+	26242.8i	−0.284250	+	1.90828i
$575$		0			0
$576$	−6319.31	−	7757.46i	−0.457126	−	0.561159i
$577$		−	3311.45i		−	0.238921i	−0.992839	−	0.119460i	$-0.961884\pi$
$577$		−	3311.45i		−	0.238921i	0.992839	−	0.119460i	$-0.0381165\pi$
$578$	−12965.2	−	1931.25i	−0.933016	−	0.138978i
$579$			11778.1i			0.845388i
$580$		0			0
$581$			2301.94i			0.164373i
$582$	1231.06	−	8264.62i	0.0876789	−	0.588624i
$583$		−	16984.5i		−	1.20656i
$584$	−10881.9	+	22899.9i	−0.771053	+	1.62261i
$585$		0			0
$586$	344.257	+	51.2790i	0.0242682	+	0.00361488i
$587$	6777.87			0.476581			0.238290	−	0.971194i	$-0.423413\pi$
$587$	6777.87			0.476581			0.238290	+	0.971194i	$0.423413\pi$
$588$	−13305.6	−	4053.85i	−0.933190	−	0.284316i
$589$			2391.78i			0.167320i
$590$		0			0
$591$	3893.28			0.270979
$592$	−1038.13	−	697.300i	−0.0720721	−	0.0484102i
$593$		−	421.958i		−	0.0292205i	−0.999893	−	0.0146102i	$-0.995349\pi$
$593$		−	421.958i		−	0.0292205i	0.999893	−	0.0146102i	$-0.00465075\pi$
$594$	1841.30	−	12361.4i	0.127187	−	0.853861i
$595$		0			0
$596$	7297.26	−	23951.3i	0.501522	−	1.64611i
$597$	2518.23			0.172637
$598$	2521.26	−	16926.2i	0.172411	−	1.15747i
$599$	−4175.09			−0.284790			−0.142395	−	0.989810i	$-0.545480\pi$
$599$	−4175.09			−0.284790			−0.142395	+	0.989810i	$0.545480\pi$
$600$		0			0
$601$	9149.52			0.620993			0.310496	−	0.950575i	$-0.399505\pi$
$601$	9149.52			0.620993			0.310496	+	0.950575i	$0.399505\pi$
$602$	−6700.35	+	44982.2i	−0.453631	+	3.04541i
$603$	−1657.32			−0.111926
$604$	−4662.51	−	1420.53i	−0.314097	−	0.0956963i
$605$		0			0
$606$	1489.69	−	10000.9i	0.0998587	−	0.670393i
$607$			128.094i			0.00856535i	0.999991	+	0.00428268i	$0.00136322\pi$
$607$			128.094i			0.00856535i	−0.999991	+	0.00428268i	$0.998637\pi$
$608$	−8356.94	+	9164.48i	−0.557432	+	0.611297i
$609$	7250.51			0.482439
$610$		0			0
$611$		−	26032.3i		−	1.72366i
$612$	760.408	−	2495.83i	0.0502250	−	0.164850i
$613$	17342.6			1.14268			0.571338	−	0.820715i	$-0.306425\pi$
$613$	17342.6			1.14268			0.571338	+	0.820715i	$0.306425\pi$
$614$	−4775.38	−	711.320i	−0.313874	−	0.0467533i
$615$		0			0
$616$	−22238.1	−	10567.4i	−1.45455	−	0.691188i
$617$		−	18906.1i		−	1.23360i	−0.787120	−	0.616800i	$-0.788429\pi$
$617$		−	18906.1i		−	1.23360i	0.787120	−	0.616800i	$-0.211571\pi$
$618$	−58.0972	+	390.030i	−0.00378157	+	0.0253873i
$619$		−	20922.5i		−	1.35856i	−0.733881	−	0.679279i	$-0.762293\pi$
$619$		−	20922.5i		−	1.35856i	0.733881	−	0.679279i	$-0.237707\pi$
$620$		0			0
$621$			10491.6i			0.677961i
$622$	20818.0	+	3100.95i	1.34200	+	0.199898i
$623$			34793.7i			2.23753i
$624$	−10634.5	−	7143.13i	−0.682247	−	0.458260i
$625$		0			0
$626$	−29.5021	+	198.060i	−0.00188361	+	0.0126455i
$627$	−6504.75			−0.414314
$628$	−14206.2	−	4328.23i	−0.902691	−	0.275024i
$629$		−	326.105i		−	0.0206719i
$630$		0			0
$631$	−21508.0			−1.35693			−0.678463	−	0.734635i	$-0.737354\pi$
$631$	−21508.0			−1.35693			−0.678463	+	0.734635i	$0.737354\pi$
$632$	−3175.10	−	1508.78i	−0.199840	−	0.0949622i
$633$		−	11215.4i		−	0.704222i
$634$	21027.3	+	3132.13i	1.31719	+	0.196203i
$635$		0			0
$636$	10210.3	+	3110.79i	0.636581	+	0.193948i
$637$	46666.6			2.90267
$638$	8249.66	+	1228.83i	0.511924	+	0.0762539i
$639$	12117.1			0.750152
$640$		0			0
$641$	21724.6			1.33864			0.669320	−	0.742974i	$-0.266585\pi$
$641$	21724.6			1.33864			0.669320	+	0.742974i	$0.266585\pi$
$642$	10613.0	+	1580.87i	0.652435	+	0.0971838i
$643$	−4224.08			−0.259069			−0.129535	−	0.991575i	$-0.541348\pi$
$643$	−4224.08			−0.259069			−0.129535	+	0.991575i	$0.541348\pi$
$644$	19771.7	+	6023.87i	1.20981	+	0.368593i
$645$		0			0
$646$	−3198.88	−	476.491i	−0.194827	−	0.0290206i
$647$		−	14990.5i		−	0.910877i	−0.890267	−	0.455439i	$-0.849482\pi$
$647$		−	14990.5i		−	0.910877i	0.890267	−	0.455439i	$-0.150518\pi$
$648$	−3689.65	−	1753.29i	−0.223678	−	0.106290i
$649$	18782.0			1.13599
$650$		0			0
$651$		−	2983.85i		−	0.179641i
$652$	−25556.9	−	7786.44i	−1.53510	−	0.467700i
$653$	−258.080			−0.0154662			−0.00773311	−	0.999970i	$-0.502462\pi$
$653$	−258.080			−0.0154662			−0.00773311	+	0.999970i	$0.502462\pi$
$654$	1165.17	−	7822.27i	0.0696663	−	0.467699i
$655$		0			0
$656$	−15922.5	−	10695.0i	−0.947668	−	0.636541i
$657$			21896.9i			1.30028i
$658$	31098.6	+	4632.31i	1.84248	+	0.274447i
$659$			7828.25i			0.462739i	0.972866	+	0.231370i	$0.0743207\pi$
$659$			7828.25i			0.462739i	−0.972866	+	0.231370i	$0.925679\pi$
$660$		0			0
$661$			26579.2i			1.56401i	0.623271	+	0.782006i	$0.285803\pi$
$661$			26579.2i			1.56401i	−0.623271	+	0.782006i	$0.714197\pi$
$662$	3038.02	−	20395.5i	0.178362	−	1.19742i
$663$		−	3340.61i		−	0.195684i
$664$	−1503.07	−	714.245i	−0.0878468	−	0.0417441i
$665$		0			0
$666$	−1068.27	−	159.125i	−0.0621541	−	0.00925820i
$667$	−7001.83			−0.406465
$668$	3710.91	−	12180.1i	0.214939	−	0.705480i
$669$			809.708i			0.0467939i
$670$		0			0
$671$	23182.7			1.33377
$672$	10425.7	−	11433.1i	0.598480	−	0.656312i
$673$			11616.5i			0.665355i	0.943041	+	0.332677i	$0.107952\pi$
$673$			11616.5i			0.665355i	−0.943041	+	0.332677i	$0.892048\pi$
$674$	1935.96	−	12996.9i	0.110639	−	0.742762i
$675$		0			0
$676$	24301.8	+	7404.04i	1.38267	+	0.421259i
$677$	−6063.77			−0.344239			−0.172119	−	0.985076i	$-0.555061\pi$
$677$	−6063.77			−0.344239			−0.172119	+	0.985076i	$0.555061\pi$
$678$	1144.15	−	7681.15i	0.0648094	−	0.435092i
$679$	−33859.2			−1.91369
$680$		0			0
$681$	−1944.57			−0.109421
$682$	505.710	−	3395.04i	0.0283939	−	0.190620i
$683$	15228.2			0.853136			0.426568	−	0.904455i	$-0.359722\pi$
$683$	15228.2			0.853136			0.426568	+	0.904455i	$0.359722\pi$
$684$	−3121.83	+	10246.5i	−0.174512	+	0.572787i
$685$		0			0
$686$	−3830.34	+	25714.6i	−0.213182	+	1.43118i
$687$			14325.0i			0.795538i
$688$	−27292.4	−	18332.1i	−1.51238	−	1.01585i
$689$	−35810.5			−1.98007
$690$		0			0
$691$		−	18344.1i		−	1.00990i	−0.863148	−	0.504951i	$-0.831511\pi$
$691$		−	18344.1i		−	1.00990i	0.863148	−	0.504951i	$-0.168489\pi$
$692$	12919.3	+	3936.15i	0.709711	+	0.216228i
$693$	−21264.1			−1.16559
$694$	−26195.3	−	3901.93i	−1.43280	−	0.213423i
$695$		0			0
$696$	−2249.68	+	4734.26i	−0.122520	+	0.257833i
$697$		−	5001.72i		−	0.271813i
$698$	−437.695	+	2938.43i	−0.0237350	+	0.159343i
$699$			4172.39i			0.225772i
$700$		0			0
$701$			23884.3i			1.28687i	0.765499	+	0.643437i	$0.222492\pi$
$701$			23884.3i			1.28687i	−0.765499	+	0.643437i	$0.777508\pi$
$702$	−26063.0	−	3882.22i	−1.40126	−	0.208725i
$703$			1338.81i			0.0718267i
$704$	13800.1	−	11241.7i	0.738792	−	0.601828i
$705$		0			0
$706$	−1789.66	+	12014.8i	−0.0954036	+	0.640484i
$707$	−40972.5			−2.17953
$708$	−3440.02	+	11290.9i	−0.182604	+	0.599349i
$709$			13849.0i			0.733582i	0.930303	+	0.366791i	$0.119544\pi$
$709$			13849.0i			0.733582i	−0.930303	+	0.366791i	$0.880456\pi$
$710$		0			0
$711$	−3036.03			−0.160141
$712$	−22718.7	−	10795.8i	−1.19582	−	0.568242i
$713$			2881.51i			0.151351i
$714$	3990.75	+	594.444i	0.209174	+	0.0311576i
$715$		0			0
$716$	−155.893	+	511.678i	−0.00813689	+	0.0267071i
$717$	3035.08			0.158085
$718$	30905.5	+	4603.55i	1.60638	+	0.239280i
$719$	3172.16			0.164536			0.0822682	−	0.996610i	$-0.473784\pi$
$719$	3172.16			0.164536			0.0822682	+	0.996610i	$0.473784\pi$
$720$		0			0
$721$	1597.91			0.0825372
$722$	−6055.60	−	902.015i	−0.312141	−	0.0464952i
$723$	−2748.34			−0.141372
$724$	−3838.13	+	12597.6i	−0.197021	+	0.646666i
$725$		0			0
$726$	−935.411	−	139.335i	−0.0478187	−	0.00712286i
$727$			15403.4i			0.785805i	0.919580	+	0.392902i	$0.128529\pi$
$727$			15403.4i			0.785805i	−0.919580	+	0.392902i	$0.871471\pi$
$728$	−22280.5	+	46887.3i	−1.13430	+	2.38703i
$729$	5843.75			0.296893
$730$		0			0
$731$		−	8573.33i		−	0.433784i
$732$	−4246.02	+	13936.4i	−0.214395	+	0.703695i
$733$	35460.6			1.78686			0.893430	−	0.449203i	$-0.148292\pi$
$733$	35460.6			1.78686			0.893430	+	0.449203i	$0.148292\pi$
$734$	1811.83	−	12163.6i	0.0911117	−	0.611670i
$735$		0			0
$736$	−10068.1	+	11041.0i	−0.504231	+	0.552956i
$737$		−	2948.28i		−	0.147356i
$738$	−16384.9	−	2440.62i	−0.817258	−	0.121735i
$739$		−	26202.9i		−	1.30432i	−0.758083	−	0.652158i	$-0.773864\pi$
$739$		−	26202.9i		−	1.30432i	0.758083	−	0.652158i	$-0.226136\pi$
$740$		0			0
$741$			13714.7i			0.679924i
$742$	6372.28	−	42779.8i	0.315275	−	2.11657i
$743$		−	22682.3i		−	1.11996i	−0.828506	−	0.559981i	$-0.810809\pi$
$743$		−	22682.3i		−	1.11996i	0.828506	−	0.559981i	$-0.189191\pi$
$744$	1948.32	+	925.826i	0.0960066	+	0.0456216i
$745$		0			0
$746$	15195.9	+	2263.52i	0.745793	+	0.111090i
$747$	−1437.23			−0.0703957
$748$	4439.94	+	1352.72i	0.217033	+	0.0661235i
$749$		−	43480.4i		−	2.12115i
$750$		0			0
$751$	−16294.9			−0.791756			−0.395878	−	0.918303i	$-0.629560\pi$
$751$	−16294.9			−0.791756			−0.395878	+	0.918303i	$0.629560\pi$
$752$	−12673.9	+	18868.7i	−0.614589	+	0.914987i
$753$			8393.98i			0.406233i
$754$	2590.90	−	17393.8i	0.125139	−	0.840110i
$755$		0			0
$756$	9275.54	−	30444.4i	0.446227	−	1.46462i
$757$	−6340.22			−0.304411			−0.152206	−	0.988349i	$-0.548638\pi$
$757$	−6340.22			−0.304411			−0.152206	+	0.988349i	$0.548638\pi$
$758$	−3911.24	+	26257.8i	−0.187418	+	1.25821i
$759$	−7836.64			−0.374772
$760$		0			0
$761$	−21014.7			−1.00103			−0.500514	−	0.865729i	$-0.666855\pi$
$761$	−21014.7			−1.00103			−0.500514	+	0.865729i	$0.666855\pi$
$762$	−192.306	+	1291.03i	−0.00914239	+	0.0613766i
$763$	−32047.0			−1.52055
$764$	26080.5	+	7945.98i	1.23503	+	0.376277i
$765$		0			0
$766$	−1111.02	+	7458.71i	−0.0524055	+	0.351820i
$767$		−	39600.4i		−	1.86426i
$768$	4230.45	+	10354.9i	0.198767	+	0.486526i
$769$	−20861.6			−0.978267			−0.489133	−	0.872209i	$-0.662687\pi$
$769$	−20861.6			−0.978267			−0.489133	+	0.872209i	$0.662687\pi$
$770$		0			0
$771$		−	14530.6i		−	0.678738i
$772$	−10055.7	+	33005.2i	−0.468800	+	1.53871i
$773$	−31160.2			−1.44988			−0.724939	−	0.688813i	$-0.758132\pi$
$773$	−31160.2			−1.44988			−0.724939	+	0.688813i	$0.758132\pi$
$774$	−28085.0	−	4183.41i	−1.30425	−	0.194276i
$775$		0			0
$776$	10505.8	−	22108.6i	0.486001	−	1.02275i
$777$		−	1670.23i		−	0.0771158i
$778$	−1287.32	+	8642.29i	−0.0593220	+	0.398253i
$779$			20534.4i			0.944441i
$780$		0			0
$781$			21555.7i			0.987610i
$782$	−3853.87	−	574.055i	−0.176233	−	0.0262509i
$783$			10781.4i			0.492076i
$784$	−33824.8	−	22719.9i	−1.54085	−	1.03498i
$785$		0			0
$786$	−1389.65	+	9329.30i	−0.0630626	+	0.423365i
$787$	8330.18			0.377305			0.188652	−	0.982044i	$-0.439588\pi$
$787$	8330.18			0.377305			0.188652	+	0.982044i	$0.439588\pi$
$788$	10910.0	+	3323.96i	0.493214	+	0.150268i
$789$		−	15523.7i		−	0.700454i
$790$		0			0
$791$	−31468.8			−1.41454
$792$	6597.82	−	13884.5i	0.296014	−	0.622936i
$793$		−	48878.9i		−	2.18883i
$794$	−7451.84	−	1109.99i	−0.333068	−	0.0496123i
$795$		0			0
$796$	7056.75	+	2149.99i	0.314221	+	0.0957340i
$797$	−12575.3			−0.558898			−0.279449	−	0.960161i	$-0.590152\pi$
$797$	−12575.3			−0.558898			−0.279449	+	0.960161i	$0.590152\pi$
$798$	−16383.9	−	2440.47i	−0.726795	−	0.108260i
$799$	−5927.19			−0.262439
$800$		0			0
$801$	−21723.7			−0.958262
$802$	21834.8	+	3252.42i	0.961365	+	0.143201i
$803$	−38953.4			−1.71187
$804$	1772.38	+	539.992i	0.0777449	+	0.0236866i
$805$		0			0
$806$	−7158.16	−	1066.25i	−0.312823	−	0.0465967i
$807$			16735.4i			0.730006i
$808$	12712.9	−	26753.2i	0.553514	−	1.16482i
$809$	11092.0			0.482046			0.241023	−	0.970519i	$-0.422517\pi$
$809$	11092.0			0.482046			0.241023	+	0.970519i	$0.422517\pi$
$810$		0			0
$811$			15824.3i			0.685162i	0.939488	+	0.342581i	$0.111301\pi$
$811$			15824.3i			0.685162i	−0.939488	+	0.342581i	$0.888699\pi$
$812$	20317.8	+	6190.25i	0.878098	+	0.267531i
$813$	−12994.9			−0.560578
$814$	283.074	−	1900.39i	0.0121889	−	0.0818288i
$815$		0			0
$816$	−1626.39	+	2421.34i	−0.0697734	+	0.103877i
$817$			35197.5i			1.50723i
$818$	11758.5	+	1751.50i	0.502601	+	0.0748652i
$819$			44833.7i			1.91284i
$820$		0			0
$821$		−	20277.4i		−	0.861979i	−0.902357	−	0.430990i	$-0.858165\pi$
$821$		−	20277.4i		−	0.861979i	0.902357	−	0.430990i	$-0.141835\pi$
$822$	−2379.91	+	15977.3i	−0.100984	+	0.677947i
$823$		−	32147.3i		−	1.36158i	−0.732477	−	0.680792i	$-0.761636\pi$
$823$		−	32147.3i		−	1.36158i	0.732477	−	0.680792i	$-0.238364\pi$
$824$	−495.799	+	1043.37i	−0.0209611	+	0.0441109i
$825$		0			0
$826$	47307.3	+	7046.68i	1.99277	+	0.296835i
$827$	−20611.4			−0.866661			−0.433330	−	0.901235i	$-0.642662\pi$
$827$	−20611.4			−0.866661			−0.433330	+	0.901235i	$0.642662\pi$
$828$	−3761.04	+	12344.6i	−0.157857	+	0.518121i
$829$			14373.9i			0.602204i	0.953592	+	0.301102i	$0.0973544\pi$
$829$			14373.9i			0.602204i	−0.953592	+	0.301102i	$0.902646\pi$
$830$		0			0
$831$	−2132.82			−0.0890335
$832$	−23702.2	−	29096.3i	−0.987650	−	1.21242i
$833$		−	10625.3i		−	0.441952i
$834$	179.926	−	1207.92i	0.00747041	−	0.0501519i
$835$		0			0
$836$	−18228.0	−	5553.55i	−0.754102	−	0.229753i
$837$	4436.94			0.183229
$838$	−5880.90	+	39480.9i	−0.242425	+	1.62750i
$839$	−17880.7			−0.735768			−0.367884	−	0.929872i	$-0.619918\pi$
$839$	−17880.7			−0.735768			−0.367884	+	0.929872i	$0.619918\pi$
$840$		0			0
$841$	17193.8			0.704981
$842$	−3351.27	+	22498.5i	−0.137164	+	0.920842i
$843$	−9086.20			−0.371228
$844$	9575.35	−	31428.5i	0.390518	−	1.28177i
$845$		0			0
$846$	−2892.21	+	19416.6i	−0.117537	+	0.789074i
$847$			3832.27i			0.155465i
$848$	25956.1	+	17434.5i	1.05110	+	0.706018i
$849$	−645.598			−0.0260976
$850$		0			0
$851$			1612.94i			0.0649717i
$852$	−12958.3	−	3948.03i	−0.521062	−	0.158752i
$853$	32787.6			1.31609			0.658045	−	0.752978i	$-0.271384\pi$
$853$	32787.6			1.31609			0.658045	+	0.752978i	$0.271384\pi$
$854$	58391.5	+	8697.74i	2.33971	+	0.348513i
$855$		0			0
$856$	28390.8	+	13491.1i	1.13362	+	0.538687i
$857$			18652.5i			0.743472i	0.928338	+	0.371736i	$0.121237\pi$
$857$			18652.5i			0.743472i	−0.928338	+	0.371736i	$0.878763\pi$
$858$	2899.80	−	19467.6i	0.115382	−	0.774606i
$859$		−	25357.7i		−	1.00721i	−0.863934	−	0.503605i	$-0.832007\pi$
$859$		−	25357.7i		−	1.00721i	0.863934	−	0.503605i	$-0.167993\pi$
$860$		0			0
$861$		−	25617.5i		−	1.01399i
$862$	40941.1	+	6098.40i	1.61770	+	0.240966i
$863$			29233.8i			1.15311i	0.817059	+	0.576554i	$0.195603\pi$
$863$			29233.8i			1.15311i	−0.817059	+	0.576554i	$0.804397\pi$
$864$	17000.9	+	15502.8i	0.669422	+	0.610435i
$865$		0			0
$866$	−3005.58	+	20177.7i	−0.117937	+	0.791761i
$867$	12656.3			0.495768
$868$	2547.51	−	8361.52i	0.0996178	−	0.326968i
$869$		−	5400.92i		−	0.210833i
$870$		0			0
$871$	−6216.22			−0.241824
$872$	9943.51	−	20925.3i	0.386158	−	0.812636i
$873$		−	21140.2i		−	0.819574i
$874$	15821.9	+	2356.76i	0.612339	+	0.0912113i
$875$		0			0
$876$	7134.49	−	23417.0i	0.275174	−	0.903182i
$877$	5427.91			0.208994			0.104497	−	0.994525i	$-0.466677\pi$
$877$	5427.91			0.208994			0.104497	+	0.994525i	$0.466677\pi$
$878$	10286.6	+	1532.24i	0.395393	+	0.0588960i
$879$	−336.054			−0.0128951
$880$		0			0
$881$	23309.0			0.891375			0.445688	−	0.895189i	$-0.352959\pi$
$881$	23309.0			0.891375			0.445688	+	0.895189i	$0.352959\pi$
$882$	−34807.1	−	5184.71i	−1.32882	−	0.197934i
$883$	−12533.3			−0.477665			−0.238833	−	0.971061i	$-0.576765\pi$
$883$	−12533.3			−0.477665			−0.238833	+	0.971061i	$0.576765\pi$
$884$	2852.10	−	9361.26i	0.108514	−	0.356169i
$885$		0			0
$886$	−14800.7	−	2204.65i	−0.561220	−	0.0835968i
$887$			29703.3i			1.12439i	0.827003	+	0.562197i	$0.190044\pi$
$887$			29703.3i			1.12439i	−0.827003	+	0.562197i	$0.809956\pi$
$888$	1090.58	+	518.237i	0.0412135	+	0.0195843i
$889$	5289.19			0.199543
$890$		0			0
$891$		−	6276.19i		−	0.235982i
$892$	−691.303	+	2269.01i	−0.0259490	+	0.0851706i
$893$	24333.8			0.911871
$894$	−3561.69	+	23911.1i	−0.133245	+	0.894526i
$895$		0			0
$896$	38976.6	−	23137.5i	1.45326	−	0.862687i
$897$			16522.9i			0.615033i
$898$	−18817.6	−	2802.99i	−0.699279	−	0.104161i
$899$			2961.10i			0.109853i
$900$		0			0
$901$			8153.55i			0.301481i
$902$	4341.72	−	29147.8i	0.160270	−	1.07596i
$903$		−	43910.4i		−	1.61821i
$904$	9764.12	−	20547.7i	0.359237	−	0.755982i
$905$		0			0
$906$	4654.69	+	693.342i	0.170686	+	0.0254246i
$907$	25888.3			0.947749			0.473875	−	0.880592i	$-0.342855\pi$
$907$	25888.3			0.947749			0.473875	+	0.880592i	$0.342855\pi$
$908$	−5449.18	−	1660.21i	−0.199160	−	0.0606784i
$909$		−	25581.4i		−	0.933425i
$910$		0			0
$911$	23119.5			0.840816			0.420408	−	0.907335i	$-0.361887\pi$
$911$	23119.5			0.840816			0.420408	+	0.907335i	$0.361887\pi$
$912$	6677.09	−	9940.70i	0.242435	−	0.360932i
$913$		−	2556.75i		−	0.0926793i
$914$	2194.79	−	14734.5i	0.0794278	−	0.533232i
$915$		0			0
$916$	−12230.3	+	40142.5i	−0.441156	+	1.44798i
$917$	38221.1			1.37641
$918$	−883.929	+	5934.18i	−0.0317800	+	0.213352i
$919$	−24277.7			−0.871434			−0.435717	−	0.900084i	$-0.643505\pi$
$919$	−24277.7			−0.871434			−0.435717	+	0.900084i	$0.643505\pi$
$920$		0			0
$921$	4661.60			0.166780
$922$	3376.58	−	22668.4i	0.120609	−	0.809699i
$923$	45448.4			1.62075
$924$	22740.3	+	6928.30i	0.809632	+	0.246671i
$925$		0			0
$926$	8197.23	−	55031.4i	0.290905	−	1.95296i
$927$			997.667i			0.0353481i
$928$	−10346.2	+	11345.9i	−0.365980	+	0.401345i
$929$	−43087.8			−1.52171			−0.760853	−	0.648924i	$-0.775219\pi$
$929$	−43087.8			−1.52171			−0.760853	+	0.648924i	$0.775219\pi$
$930$		0			0
$931$			43621.9i			1.53561i
$932$	−3562.25	+	11692.1i	−0.125199	+	0.410932i
$933$	−20321.9			−0.713086
$934$	−8794.93	−	1310.05i	−0.308114	−	0.0458953i
$935$		0			0
$936$	−29274.4	−	13911.0i	−1.02229	−	0.485784i
$937$		−	45230.7i		−	1.57697i	−0.615053	−	0.788486i	$-0.710865\pi$
$937$		−	45230.7i		−	1.57697i	0.615053	−	0.788486i	$-0.289135\pi$
$938$	1106.14	−	7425.99i	0.0385041	−	0.258494i
$939$		−	193.341i		−	0.00671931i
$940$		0			0
$941$			3631.17i			0.125795i	0.998020	+	0.0628973i	$0.0200341\pi$
$941$			3631.17i			0.125795i	−0.998020	+	0.0628973i	$0.979966\pi$
$942$	14182.4	+	2112.55i	0.490539	+	0.0730685i
$943$			24738.9i			0.854305i
$944$	−19279.6	+	28703.1i	−0.664724	+	0.989626i
$945$		0			0
$946$	7442.04	−	49961.5i	0.255773	−	1.71711i
$947$	38493.1			1.32086			0.660432	−	0.750886i	$-0.270373\pi$
$947$	38493.1			1.32086			0.660432	+	0.750886i	$0.270373\pi$
$948$	3246.79	+	989.203i	0.111235	+	0.0338901i
$949$			82130.0i			2.80933i
$950$		0			0
$951$	−20526.2			−0.699904
$952$	10675.6	+	5072.96i	0.363443	+	0.172705i
$953$			15541.2i			0.528258i	0.964487	+	0.264129i	$0.0850844\pi$
$953$			15541.2i			0.528258i	−0.964487	+	0.264129i	$0.914916\pi$
$954$	26709.8	+	3978.58i	0.906460	+	0.135022i
$955$		0			0
$956$	8505.07	+	2591.25i	0.287734	+	0.0876642i
$957$	−8053.10			−0.272016
$958$	19724.3	+	2938.04i	0.665202	+	0.0990855i
$959$	65457.2			2.20409
$960$		0			0
$961$	−28572.4			−0.959095
$962$	−4006.82	−	596.838i	−0.134288	−	0.0200030i
$963$	27147.3			0.908421
$964$	−7701.57	−	2346.45i	−0.257314	−	0.0783962i
$965$		0			0
$966$	−19738.6	−	2940.17i	−0.657430	−	0.0979279i
$967$			7995.61i			0.265896i	0.991123	+	0.132948i	$0.0424443\pi$
$967$			7995.61i			0.265896i	−0.991123	+	0.132948i	$0.957556\pi$
$968$	−2502.31	−	1189.08i	−0.0830859	−	0.0394818i
$969$	3122.66			0.103523
$970$		0			0
$971$		−	34412.7i		−	1.13734i	−0.822567	−	0.568669i	$-0.807459\pi$
$971$		−	34412.7i		−	1.13734i	0.822567	−	0.568669i	$-0.192541\pi$
$972$	30035.2	+	9150.85i	0.991131	+	0.301969i
$973$	−4948.70			−0.163050
$974$	1005.12	−	6747.79i	0.0330659	−	0.221985i
$975$		0			0
$976$	−23796.9	+	35428.3i	−0.780452	+	1.16192i
$977$		−	23300.8i		−	0.763007i	−0.924367	−	0.381503i	$-0.875407\pi$
$977$		−	23300.8i		−	0.763007i	0.924367	−	0.381503i	$-0.124593\pi$
$978$	25514.0	+	3800.46i	0.834201	+	0.124259i
$979$		−	38645.1i		−	1.26160i
$980$		0			0
$981$		−	20008.7i		−	0.651203i
$982$	−3337.63	+	22406.9i	−0.108460	+	0.728139i
$983$		−	47674.2i		−	1.54687i	−0.633877	−	0.773434i	$-0.718537\pi$
$983$		−	47674.2i		−	1.54687i	0.633877	−	0.773434i	$-0.281463\pi$
$984$	16727.1	+	7948.59i	0.541912	+	0.257512i
$985$		0			0
$986$	−3960.32	−	589.911i	−0.127913	−	0.0190533i
$987$	−30357.6			−0.979019
$988$	−11709.2	+	38432.3i	−0.377044	+	1.23754i
$989$			42404.4i			1.36338i
$990$		0			0
$991$	43640.7			1.39888			0.699441	−	0.714691i	$-0.253433\pi$
$991$	43640.7			1.39888			0.699441	+	0.714691i	$0.253433\pi$
$992$	4669.26	+	4257.82i	0.149445	+	0.136276i
$993$			19909.5i			0.636262i
$994$	−8087.31	+	54293.4i	−0.258062	+	1.73248i
$995$		0			0
$996$	1537.00	+	468.281i	0.0488975	+	0.0148976i
$997$	−25244.6			−0.801909			−0.400955	−	0.916098i	$-0.631321\pi$
$997$	−25244.6			−0.801909			−0.400955	+	0.916098i	$0.631321\pi$
$998$	1674.12	−	11239.0i	0.0530994	−	0.356478i
$999$	2483.60			0.0786563

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.4.f.d.149.3		24
4.3	odd	2		800.4.f.d.49.10		24
5.2	odd	4		200.4.d.d.101.7	yes	12
5.3	odd	4		200.4.d.c.101.6	yes	12
5.4	even	2	inner	200.4.f.d.149.22		24
8.3	odd	2		800.4.f.d.49.16		24
8.5	even	2	inner	200.4.f.d.149.21		24
20.3	even	4		800.4.d.b.401.5		12
20.7	even	4		800.4.d.c.401.8		12
20.19	odd	2		800.4.f.d.49.15		24
40.3	even	4		800.4.d.b.401.8		12
40.13	odd	4		200.4.d.c.101.5	✓	12
40.19	odd	2		800.4.f.d.49.9		24
40.27	even	4		800.4.d.c.401.5		12
40.29	even	2	inner	200.4.f.d.149.4		24
40.37	odd	4		200.4.d.d.101.8	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.4.d.c.101.5	✓	12	40.13	odd	4
200.4.d.c.101.6	yes	12	5.3	odd	4
200.4.d.d.101.7	yes	12	5.2	odd	4
200.4.d.d.101.8	yes	12	40.37	odd	4
200.4.f.d.149.3		24	1.1	even	1	trivial
200.4.f.d.149.4		24	40.29	even	2	inner
200.4.f.d.149.21		24	8.5	even	2	inner
200.4.f.d.149.22		24	5.4	even	2	inner
800.4.d.b.401.5		12	20.3	even	4
800.4.d.b.401.8		12	40.3	even	4
800.4.d.c.401.5		12	40.27	even	4
800.4.d.c.401.8		12	20.7	even	4
800.4.f.d.49.9		24	40.19	odd	2
800.4.f.d.49.10		24	4.3	odd	2
800.4.f.d.49.15		24	20.19	odd	2
800.4.f.d.49.16		24	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.79756 - 0.416712i) q^{2} +2.73090 q^{3} +(7.65270 + 2.33156i) q^{4} +(-7.63987 - 1.13800i) q^{6} +31.2997i q^{7} +(-20.4373 - 9.71165i) q^{8} -19.5422 q^{9} -34.7644i q^{11} +(20.8988 + 6.36726i) q^{12} -73.2979 q^{13} +(13.0430 - 87.5628i) q^{14} +(53.1277 + 35.6854i) q^{16} +16.6889i q^{17} +(54.6704 + 8.14346i) q^{18} -68.5157i q^{19} +85.4764i q^{21} +(-14.4867 + 97.2555i) q^{22} -82.5447i q^{23} +(-55.8123 - 26.5216i) q^{24} +(205.055 + 30.5441i) q^{26} -127.102 q^{27} +(-72.9770 + 239.527i) q^{28} -84.8247i q^{29} -34.9084 q^{31} +(-133.757 - 121.971i) q^{32} -94.9381i q^{33} +(6.95448 - 46.6883i) q^{34} +(-149.550 - 45.5637i) q^{36} -19.5402 q^{37} +(-28.5513 + 191.677i) q^{38} -200.169 q^{39} -299.703 q^{41} +(35.6191 - 239.126i) q^{42} -513.714 q^{43} +(81.0551 - 266.041i) q^{44} +(-34.3974 + 230.924i) q^{46} +355.157i q^{47} +(145.087 + 97.4534i) q^{48} -636.671 q^{49} +45.5758i q^{51} +(-560.927 - 170.898i) q^{52} +488.561 q^{53} +(355.576 + 52.9650i) q^{54} +(303.972 - 639.682i) q^{56} -187.110i q^{57} +(-35.3475 + 237.302i) q^{58} +540.267i q^{59} +666.853i q^{61} +(97.6585 + 14.5468i) q^{62} -611.664i q^{63} +(323.368 + 396.960i) q^{64} +(-39.5619 + 265.595i) q^{66} +84.8076 q^{67} +(-38.9111 + 127.715i) q^{68} -225.422i q^{69} -620.051 q^{71} +(399.390 + 189.787i) q^{72} -1120.50i q^{73} +(54.6649 + 8.14264i) q^{74} +(159.748 - 524.330i) q^{76} +1088.11 q^{77} +(559.986 + 83.4131i) q^{78} +155.358 q^{79} +180.535 q^{81} +(838.438 + 124.890i) q^{82} +73.5452 q^{83} +(-199.293 + 654.126i) q^{84} +(1437.15 + 214.071i) q^{86} -231.648i q^{87} +(-337.619 + 710.491i) q^{88} +1111.63 q^{89} -2294.20i q^{91} +(192.458 - 631.690i) q^{92} -95.3315 q^{93} +(147.998 - 993.574i) q^{94} +(-365.278 - 333.091i) q^{96} +1081.77i q^{97} +(1781.13 + 265.309i) q^{98} +679.371i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{4} + 18 q^{6} + 216 q^{9} + 224 q^{14} + 338 q^{16} + 570 q^{24} - 376 q^{26} - 528 q^{31} - 930 q^{34} - 1400 q^{36} + 600 q^{39} - 40 q^{41} - 766 q^{44} + 824 q^{46} - 456 q^{49} + 1674 q^{54}+ \cdots + 5470 q^{96}+O(q^{100}) \) 24 * q - 2 * q^4 + 18 * q^6 + 216 * q^9 + 224 * q^14 + 338 * q^16 + 570 * q^24 - 376 * q^26 - 528 * q^31 - 930 * q^34 - 1400 * q^36 + 600 * q^39 - 40 * q^41 - 766 * q^44 + 824 * q^46 - 456 * q^49 + 1674 * q^54 + 1304 * q^56 + 1486 * q^64 - 1794 * q^66 + 1256 * q^71 - 2160 * q^74 - 1938 * q^76 - 2232 * q^79 + 2256 * q^81 - 5096 * q^84 + 5452 * q^86 + 848 * q^89 + 3736 * q^94 + 5470 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more