LMFDB - Embedded newform 200.4.d.e.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,4,Mod(101,200)]

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, 0]))

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

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

chi := DirichletCharacter("200.101");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	200.d (of order $2$, degree $1$, 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2x^{14} + 44x^{12} - 400x^{10} - 3200x^{8} - 25600x^{6} + 180224x^{4} + 524288x^{2} + 16777216 $ x^16 + 2x^14 + 44x^12 - 400x^10 - 3200x^8 - 25600x^6 + 180224x^4 + 524288*x^2 + 16777216
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.4
Root			$-1.92212 + 2.07496i$ of defining polynomial
Character	$\chi$	$=$	200.101
Dual form			200.4.d.e.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.92212 + 2.07496i) q^{2} -6.67494i q^{3} +(-0.610901 - 7.97664i) q^{4} +(13.8502 + 12.8300i) q^{6} +29.8250 q^{7} +(17.7254 + 14.0645i) q^{8} -17.5548 q^{9} +34.8520i q^{11} +(-53.2436 + 4.07773i) q^{12} -20.6159i q^{13} +(-57.3272 + 61.8856i) q^{14} +(-63.2536 + 9.74588i) q^{16} +89.9765 q^{17} +(33.7424 - 36.4254i) q^{18} +0.475810i q^{19} -199.080i q^{21} +(-72.3164 - 66.9897i) q^{22} +100.299 q^{23} +(93.8795 - 118.316i) q^{24} +(42.7771 + 39.6263i) q^{26} -63.0462i q^{27} +(-18.2201 - 237.903i) q^{28} -132.077i q^{29} -137.250 q^{31} +(101.359 - 149.981i) q^{32} +232.635 q^{33} +(-172.946 + 186.697i) q^{34} +(10.7242 + 140.028i) q^{36} +57.1057i q^{37} +(-0.987285 - 0.914564i) q^{38} -137.610 q^{39} +298.591 q^{41} +(413.082 + 382.656i) q^{42} -248.058i q^{43} +(278.002 - 21.2911i) q^{44} +(-192.787 + 208.117i) q^{46} -323.827 q^{47} +(65.0532 + 422.214i) q^{48} +546.530 q^{49} -600.588i q^{51} +(-164.446 + 12.5943i) q^{52} +55.4295i q^{53} +(130.818 + 121.182i) q^{54} +(528.660 + 419.473i) q^{56} +3.17600 q^{57} +(274.055 + 253.868i) q^{58} +167.879i q^{59} -164.687i q^{61} +(263.810 - 284.787i) q^{62} -523.571 q^{63} +(116.381 + 498.597i) q^{64} +(-447.152 + 482.707i) q^{66} -666.565i q^{67} +(-54.9668 - 717.710i) q^{68} -669.491i q^{69} +384.334 q^{71} +(-311.166 - 246.899i) q^{72} -749.119 q^{73} +(-118.492 - 109.764i) q^{74} +(3.79536 - 0.290673i) q^{76} +1039.46i q^{77} +(264.503 - 285.535i) q^{78} -582.564 q^{79} -894.809 q^{81} +(-573.928 + 619.564i) q^{82} +636.408i q^{83} +(-1587.99 + 121.618i) q^{84} +(514.710 + 476.798i) q^{86} -881.607 q^{87} +(-490.175 + 617.766i) q^{88} -759.913 q^{89} -614.869i q^{91} +(-61.2730 - 800.051i) q^{92} +916.133i q^{93} +(622.435 - 671.928i) q^{94} +(-1001.12 - 676.563i) q^{96} +1279.63 q^{97} +(-1050.50 + 1134.03i) q^{98} -611.819i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 12 q^{6} - 104 q^{9} - 28 q^{14} - 168 q^{16} + 112 q^{24} + 200 q^{26} - 112 q^{31} - 408 q^{34} - 84 q^{36} + 736 q^{39} + 232 q^{41} - 920 q^{44} + 212 q^{46} + 200 q^{49} + 2320 q^{54}+ \cdots + 3632 q^{96}+O(q^{100}) $ 16 * q - 4 * q^4 - 12 * q^6 - 104 * q^9 - 28 * q^14 - 168 * q^16 + 112 * q^24 + 200 * q^26 - 112 * q^31 - 408 * q^34 - 84 * q^36 + 736 * q^39 + 232 * q^41 - 920 * q^44 + 212 * q^46 + 200 * q^49 + 2320 * q^54 + 1120 * q^56 + 2912 * q^64 - 2488 * q^66 + 2096 * q^71 - 4224 * q^74 - 3000 * q^76 - 2992 * q^79 - 728 * q^81 - 7304 * q^84 + 3076 * q^86 + 208 * q^89 + 7036 * q^94 + 3632 * 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 $

$2$	−1.92212	+	2.07496i	−0.679572	+	0.733608i
$2$	−1.92212	+	2.07496i	−0.679572	+	0.733608i
$3$		−	6.67494i		−	1.28459i	−0.766457	−	0.642296i	$-0.777982\pi$
$3$		−	6.67494i		−	1.28459i	0.766457	−	0.642296i	$-0.222018\pi$
$4$	−0.610901	−	7.97664i	−0.0763627	−	0.997080i
$5$		0			0
$5$		0			0
$6$	13.8502	+	12.8300i	0.942388	+	0.872973i
$7$	29.8250			1.61040			0.805199	−	0.593005i	$-0.202059\pi$
$7$	29.8250			1.61040			0.805199	+	0.593005i	$0.202059\pi$
$8$	17.7254	+	14.0645i	0.783360	+	0.621568i
$9$	−17.5548			−0.650177
$10$		0			0
$11$			34.8520i			0.955297i	0.878551	+	0.477648i	$0.158511\pi$
$11$			34.8520i			0.955297i	−0.878551	+	0.477648i	$0.841489\pi$
$12$	−53.2436	+	4.07773i	−1.28084	+	0.0980949i
$13$		−	20.6159i		−	0.439833i	−0.975519	−	0.219916i	$-0.929422\pi$
$13$		−	20.6159i		−	0.439833i	0.975519	−	0.219916i	$-0.0705784\pi$
$14$	−57.3272	+	61.8856i	−1.09438	+	1.18140i
$15$		0			0
$16$	−63.2536	+	9.74588i	−0.988337	+	0.152279i
$17$	89.9765			1.28368			0.641839	−	0.766840i	$-0.278172\pi$
$17$	89.9765			1.28368			0.641839	+	0.766840i	$0.278172\pi$
$18$	33.7424	−	36.4254i	0.441842	−	0.476975i
$19$			0.475810i			0.00574517i	0.999996	+	0.00287259i	$0.000914374\pi$
$19$			0.475810i			0.00574517i	−0.999996	+	0.00287259i	$0.999086\pi$
$20$		0			0
$21$		−	199.080i		−	2.06870i
$22$	−72.3164	−	66.9897i	−0.700814	−	0.649193i
$23$	100.299			0.909298			0.454649	−	0.890671i	$-0.349765\pi$
$23$	100.299			0.909298			0.454649	+	0.890671i	$0.349765\pi$
$24$	93.8795	−	118.316i	0.798461	−	1.00630i
$25$		0			0
$26$	42.7771	+	39.6263i	0.322665	+	0.298898i
$27$		−	63.0462i		−	0.449380i
$28$	−18.2201	−	237.903i	−0.122974	−	1.60570i
$29$		−	132.077i		−	0.845729i	−0.906193	−	0.422864i	$-0.861025\pi$
$29$		−	132.077i		−	0.845729i	0.906193	−	0.422864i	$-0.138975\pi$
$30$		0			0
$31$	−137.250			−0.795186			−0.397593	−	0.917562i	$-0.630154\pi$
$31$	−137.250			−0.795186			−0.397593	+	0.917562i	$0.630154\pi$
$32$	101.359	−	149.981i	0.559933	−	0.828538i
$33$	232.635			1.22717
$34$	−172.946	+	186.697i	−0.872351	+	0.941716i
$35$		0			0
$36$	10.7242	+	140.028i	0.0496493	+	0.648279i
$37$			57.1057i			0.253733i	0.991920	+	0.126866i	$0.0404920\pi$
$37$			57.1057i			0.253733i	−0.991920	+	0.126866i	$0.959508\pi$
$38$	−0.987285	−	0.914564i	−0.00421471	−	0.00390426i
$39$	−137.610			−0.565005
$40$		0			0
$41$	298.591			1.13737			0.568684	−	0.822556i	$-0.307453\pi$
$41$	298.591			1.13737			0.568684	+	0.822556i	$0.307453\pi$
$42$	413.082	+	382.656i	1.51762	+	1.40583i
$43$		−	248.058i		−	0.879733i	−0.898063	−	0.439866i	$-0.855026\pi$
$43$		−	248.058i		−	0.879733i	0.898063	−	0.439866i	$-0.144974\pi$
$44$	278.002	−	21.2911i	0.952507	−	0.0729490i
$45$		0			0
$46$	−192.787	+	208.117i	−0.617934	+	0.667068i
$47$	−323.827			−1.00500			−0.502501	−	0.864577i	$-0.667587\pi$
$47$	−323.827			−1.00500			−0.502501	+	0.864577i	$0.667587\pi$
$48$	65.0532	+	422.214i	0.195617	+	1.26961i
$49$	546.530			1.59338
$50$		0			0
$51$		−	600.588i		−	1.64900i
$52$	−164.446	+	12.5943i	−0.438548	+	0.0335868i
$53$			55.4295i			0.143657i	0.997417	+	0.0718285i	$0.0228834\pi$
$53$			55.4295i			0.143657i	−0.997417	+	0.0718285i	$0.977117\pi$
$54$	130.818	+	121.182i	0.329669	+	0.305386i
$55$		0			0
$56$	528.660	+	419.473i	1.26152	+	1.00097i
$57$	3.17600			0.00738020
$58$	274.055	+	253.868i	0.620434	+	0.574734i
$59$			167.879i			0.370440i	0.982697	+	0.185220i	$0.0592998\pi$
$59$			167.879i			0.370440i	−0.982697	+	0.185220i	$0.940700\pi$
$60$		0			0
$61$		−	164.687i		−	0.345672i	−0.984951	−	0.172836i	$-0.944707\pi$
$61$		−	164.687i		−	0.345672i	0.984951	−	0.172836i	$-0.0552930\pi$
$62$	263.810	−	284.787i	0.540386	−	0.583355i
$63$	−523.571			−1.04704
$64$	116.381	+	498.597i	0.227307	+	0.973823i
$65$		0			0
$66$	−447.152	+	482.707i	−0.833949	+	0.900260i
$67$		−	666.565i		−	1.21543i	−0.794155	−	0.607715i	$-0.792086\pi$
$67$		−	666.565i		−	1.21543i	0.794155	−	0.607715i	$-0.207914\pi$
$68$	−54.9668	−	717.710i	−0.0980250	−	1.27993i
$69$		−	669.491i		−	1.16808i
$70$		0			0
$71$	384.334			0.642424			0.321212	−	0.947007i	$-0.395910\pi$
$71$	384.334			0.642424			0.321212	+	0.947007i	$0.395910\pi$
$72$	−311.166	−	246.899i	−0.509323	−	0.404129i
$73$	−749.119			−1.20107			−0.600533	−	0.799600i	$-0.705045\pi$
$73$	−749.119			−1.20107			−0.600533	+	0.799600i	$0.705045\pi$
$74$	−118.492	−	109.764i	−0.186141	−	0.172430i
$75$		0			0
$76$	3.79536	−	0.290673i	0.00572840	−	0.000438717i
$77$			1039.46i			1.53841i
$78$	264.503	−	285.535i	0.383962	−	0.414493i
$79$	−582.564			−0.829666			−0.414833	−	0.909898i	$-0.636160\pi$
$79$	−582.564			−0.829666			−0.414833	+	0.909898i	$0.636160\pi$
$80$		0			0
$81$	−894.809			−1.22745
$82$	−573.928	+	619.564i	−0.772924	+	0.834383i
$83$			636.408i			0.841625i	0.907148	+	0.420813i	$0.138255\pi$
$83$			636.408i			0.841625i	−0.907148	+	0.420813i	$0.861745\pi$
$84$	−1587.99	+	121.618i	−2.06266	+	0.157972i
$85$		0			0
$86$	514.710	+	476.798i	0.645379	+	0.597842i
$87$	−881.607			−1.08642
$88$	−490.175	+	617.766i	−0.593782	+	0.748341i
$89$	−759.913			−0.905064			−0.452532	−	0.891748i	$-0.649479\pi$
$89$	−759.913			−0.905064			−0.452532	+	0.891748i	$0.649479\pi$
$90$		0			0
$91$		−	614.869i		−	0.708305i
$92$	−61.2730	−	800.051i	−0.0694364	−	0.906643i
$93$			916.133i			1.02149i
$94$	622.435	−	671.928i	0.682971	−	0.737278i
$95$		0			0
$96$	−1001.12	−	676.563i	−1.06433	−	0.719286i
$97$	1279.63			1.33945			0.669723	−	0.742611i	$-0.266413\pi$
$97$	1279.63			1.33945			0.669723	+	0.742611i	$0.266413\pi$
$98$	−1050.50	+	1134.03i	−1.08282	+	1.16892i
$99$		−	611.819i		−	0.621112i
$100$		0			0
$101$		−	806.217i		−	0.794273i	−0.917760	−	0.397137i	$-0.870004\pi$
$101$		−	806.217i		−	0.794273i	0.917760	−	0.397137i	$-0.129996\pi$
$102$	1246.19	+	1154.40i	1.20972	+	1.12062i
$103$	−497.704			−0.476119			−0.238059	−	0.971251i	$-0.576511\pi$
$103$	−497.704			−0.476119			−0.238059	+	0.971251i	$0.576511\pi$
$104$	289.952	−	365.426i	0.273386	−	0.344547i
$105$		0			0
$106$	−115.014	−	106.542i	−0.105388	−	0.0976254i
$107$		−	111.714i		−	0.100933i	−0.998726	−	0.0504666i	$-0.983929\pi$
$107$		−	111.714i		−	0.100933i	0.998726	−	0.0504666i	$-0.0160708\pi$
$108$	−502.897	+	38.5150i	−0.448068	+	0.0343158i
$109$			1098.19i			0.965022i	0.875890	+	0.482511i	$0.160275\pi$
$109$			1098.19i			0.965022i	−0.875890	+	0.482511i	$0.839725\pi$
$110$		0			0
$111$	381.177			0.325943
$112$	−1886.54	+	290.671i	−1.59162	+	0.245230i
$113$	2118.96			1.76403			0.882015	−	0.471221i	$-0.156187\pi$
$113$	2118.96			1.76403			0.882015	+	0.471221i	$0.156187\pi$
$114$	−6.10466	+	6.59007i	−0.00501538	+	0.00541418i
$115$		0			0
$116$	−1053.53	+	80.6862i	−0.843259	+	0.0645821i
$117$			361.908i			0.285969i
$118$	−348.341	−	322.683i	−0.271758	−	0.251741i
$119$	2683.55			2.06723
$120$		0			0
$121$	116.341			0.0874084
$122$	341.718	+	316.548i	0.253588	+	0.234909i
$123$		−	1993.08i		−	1.46105i
$124$	83.8460	+	1094.79i	0.0607225	+	0.792864i
$125$		0			0
$126$	1006.37	−	1086.39i	0.711542	−	0.768120i
$127$	−567.970			−0.396844			−0.198422	−	0.980117i	$-0.563582\pi$
$127$	−567.970			−0.396844			−0.198422	+	0.980117i	$0.563582\pi$
$128$	−1258.27	−	716.879i	−0.868876	−	0.495029i
$129$	−1655.77			−1.13010
$130$		0			0
$131$			2238.84i			1.49319i	0.665278	+	0.746596i	$0.268313\pi$
$131$			2238.84i			1.49319i	−0.665278	+	0.746596i	$0.731687\pi$
$132$	−142.117	−	1855.64i	−0.0937097	−	1.22358i
$133$			14.1910i			0.00925201i
$134$	1383.09	+	1281.22i	0.891650	+	0.825973i
$135$		0			0
$136$	1594.87	+	1265.47i	1.00558	+	0.797892i
$137$	1428.64			0.890925			0.445462	−	0.895301i	$-0.353039\pi$
$137$	1428.64			0.890925			0.445462	+	0.895301i	$0.353039\pi$
$138$	1389.17	+	1286.84i	0.856911	+	0.793793i
$139$		−	1467.79i		−	0.895659i	−0.894119	−	0.447829i	$-0.852197\pi$
$139$		−	1467.79i		−	0.895659i	0.894119	−	0.447829i	$-0.147803\pi$
$140$		0			0
$141$			2161.53i			1.29102i
$142$	−738.737	+	797.478i	−0.436574	+	0.471288i
$143$	718.505			0.420171
$144$	1110.40	−	171.087i	0.642594	−	0.0990086i
$145$		0			0
$146$	1439.90	−	1554.39i	0.816211	−	0.881112i
$147$		−	3648.05i		−	2.04684i
$148$	455.512	−	34.8860i	0.252992	−	0.0193757i
$149$			2881.15i			1.58411i	0.610449	+	0.792056i	$0.290989\pi$
$149$			2881.15i			1.58411i	−0.610449	+	0.792056i	$0.709011\pi$
$150$		0			0
$151$	−949.291			−0.511604			−0.255802	−	0.966729i	$-0.582340\pi$
$151$	−949.291			−0.511604			−0.255802	+	0.966729i	$0.582340\pi$
$152$	−6.69202	+	8.43393i	−0.00357101	+	0.00450054i
$153$	−1579.52			−0.834617
$154$	−2156.83	−	1997.97i	−1.12859	−	1.04546i
$155$		0			0
$156$	84.0661	+	1097.66i	0.0431453	+	0.563356i
$157$			3159.30i			1.60599i	0.595988	+	0.802993i	$0.296761\pi$
$157$			3159.30i			1.60599i	−0.595988	+	0.802993i	$0.703239\pi$
$158$	1119.76	−	1208.80i	0.563818	−	0.608650i
$159$	369.988			0.184541
$160$		0			0
$161$	2991.42			1.46433
$162$	1719.93	−	1856.69i	0.834139	−	0.900465i
$163$			1361.75i			0.654360i	0.944962	+	0.327180i	$0.106098\pi$
$163$			1361.75i			0.654360i	−0.944962	+	0.327180i	$0.893902\pi$
$164$	−182.410	−	2381.75i	−0.0868525	−	1.13405i
$165$		0			0
$166$	−1320.52	−	1223.25i	−0.617423	−	0.571945i
$167$	−641.323			−0.297168			−0.148584	−	0.988900i	$-0.547472\pi$
$167$	−641.323			−0.297168			−0.148584	+	0.988900i	$0.547472\pi$
$168$	2799.95	−	3528.77i	1.28584	−	1.62054i
$169$	1771.98			0.806547
$170$		0			0
$171$		−	8.35274i		−	0.00373538i
$172$	−1978.67	+	151.539i	−0.877164	+	0.0671787i
$173$			57.9969i			0.0254880i	0.999919	+	0.0127440i	$0.00405665\pi$
$173$			57.9969i			0.0254880i	−0.999919	+	0.0127440i	$0.995943\pi$
$174$	1694.56	−	1829.30i	0.738299	−	0.797004i
$175$		0			0
$176$	−339.663	−	2204.51i	−0.145472	−	0.944155i
$177$	1120.58			0.475864
$178$	1460.65	−	1576.79i	0.615056	−	0.663962i
$179$			1608.75i			0.671753i	0.941906	+	0.335876i	$0.109032\pi$
$179$			1608.75i			0.671753i	−0.941906	+	0.335876i	$0.890968\pi$
$180$		0			0
$181$			2665.60i			1.09465i	0.836919	+	0.547327i	$0.184354\pi$
$181$			2665.60i			1.09465i	−0.836919	+	0.547327i	$0.815646\pi$
$182$	1275.83	+	1181.85i	0.519619	+	0.481345i
$183$	−1099.27			−0.444047
$184$	1777.85	+	1410.66i	0.712308	+	0.565190i
$185$		0			0
$186$	−1900.94	−	1760.92i	−0.749373	−	0.694176i
$187$			3135.86i			1.22629i
$188$	197.827	+	2583.05i	0.0767446	+	1.00207i
$189$		−	1880.35i		−	0.723680i
$190$		0			0
$191$	−2879.60			−1.09089			−0.545446	−	0.838146i	$-0.683640\pi$
$191$	−2879.60			−1.09089			−0.545446	+	0.838146i	$0.683640\pi$
$192$	3328.11	−	776.837i	1.25097	−	0.291997i
$193$	2401.35			0.895611			0.447805	−	0.894131i	$-0.352206\pi$
$193$	2401.35			0.895611			0.447805	+	0.894131i	$0.352206\pi$
$194$	−2459.60	+	2655.17i	−0.910251	+	0.982629i
$195$		0			0
$196$	−333.876	−	4359.47i	−0.121675	−	1.58873i
$197$		−	4454.03i		−	1.61085i	−0.592700	−	0.805423i	$-0.701938\pi$
$197$		−	4454.03i		−	1.61085i	0.592700	−	0.805423i	$-0.298062\pi$
$198$	1269.50	+	1175.99i	0.455653	+	0.422091i
$199$	−4903.81			−1.74684			−0.873422	−	0.486964i	$-0.838104\pi$
$199$	−4903.81			−1.74684			−0.873422	+	0.486964i	$0.838104\pi$
$200$		0			0
$201$	−4449.28			−1.56133
$202$	1672.87	+	1549.65i	0.582685	+	0.539766i
$203$		−	3939.20i		−	1.36196i
$204$	−4790.67	+	366.900i	−1.64419	+	0.125922i
$205$		0			0
$206$	956.647	−	1032.72i	0.323557	−	0.349285i
$207$	−1760.73			−0.591205
$208$	200.920	+	1304.03i	0.0669774	+	0.434703i
$209$	−16.5829			−0.00548834
$210$		0			0
$211$			1226.59i			0.400200i	0.979776	+	0.200100i	$0.0641266\pi$
$211$			1226.59i			0.400200i	−0.979776	+	0.200100i	$0.935873\pi$
$212$	442.141	−	33.8620i	0.143238	−	0.0109700i
$213$		−	2565.41i		−	0.825253i
$214$	231.803	+	214.729i	0.0740454	+	0.0685914i
$215$		0			0
$216$	886.712	−	1117.52i	0.279320	−	0.352026i
$217$	−4093.47			−1.28057
$218$	−2278.69	−	2110.85i	−0.707948	−	0.655802i
$219$			5000.32i			1.54288i
$220$		0			0
$221$		−	1854.95i		−	0.564603i
$222$	−732.668	+	790.926i	−0.221502	+	0.239115i
$223$	1542.77			0.463281			0.231641	−	0.972801i	$-0.425591\pi$
$223$	1542.77			0.463281			0.231641	+	0.972801i	$0.425591\pi$
$224$	3023.02	−	4473.19i	0.901716	−	1.33428i
$225$		0			0
$226$	−4072.91	+	4396.76i	−1.19879	+	1.29411i
$227$		−	3851.34i		−	1.12609i	−0.826426	−	0.563045i	$-0.809630\pi$
$227$		−	3851.34i		−	1.12609i	0.826426	−	0.563045i	$-0.190370\pi$
$228$	−1.94022	−	25.3338i	−0.000563572	−	0.00735865i
$229$		−	5232.61i		−	1.50996i	−0.655748	−	0.754980i	$-0.727647\pi$
$229$		−	5232.61i		−	1.50996i	0.655748	−	0.754980i	$-0.272353\pi$
$230$		0			0
$231$	6938.32			1.97623
$232$	1857.60	−	2341.13i	0.525678	−	0.662510i
$233$	181.419			0.0510094			0.0255047	−	0.999675i	$-0.491881\pi$
$233$	181.419			0.0510094			0.0255047	+	0.999675i	$0.491881\pi$
$234$	−750.943	−	695.630i	−0.209789	−	0.194337i
$235$		0			0
$236$	1339.11	−	102.557i	0.369358	−	0.0282878i
$237$			3888.58i			1.06578i
$238$	−5158.10	+	5568.25i	−1.40483	+	1.51654i
$239$	−2507.75			−0.678716			−0.339358	−	0.940657i	$-0.610210\pi$
$239$	−2507.75			−0.678716			−0.339358	+	0.940657i	$0.610210\pi$
$240$		0			0
$241$	−1089.46			−0.291196			−0.145598	−	0.989344i	$-0.546511\pi$
$241$	−1089.46			−0.291196			−0.145598	+	0.989344i	$0.546511\pi$
$242$	−223.621	+	241.402i	−0.0594003	+	0.0641235i
$243$			4270.54i			1.12739i
$244$	−1313.65	+	100.607i	−0.344662	+	0.0263964i
$245$		0			0
$246$	4135.55	+	3830.93i	1.07184	+	0.992892i
$247$	9.80925			0.00252691
$248$	−2432.81	−	1930.34i	−0.622917	−	0.494262i
$249$	4247.99			1.08115
$250$		0			0
$251$			5380.02i			1.35292i	0.736478	+	0.676461i	$0.236487\pi$
$251$			5380.02i			1.35292i	−0.736478	+	0.676461i	$0.763513\pi$
$252$	319.850	+	4176.34i	0.0799551	+	1.04399i
$253$			3495.63i			0.868649i
$254$	1091.71	−	1178.51i	0.269684	−	0.291128i
$255$		0			0
$256$	3906.04	−	1232.92i	0.953622	−	0.301007i
$257$	1377.98			0.334458			0.167229	−	0.985918i	$-0.446518\pi$
$257$	1377.98			0.334458			0.167229	+	0.985918i	$0.446518\pi$
$258$	3182.59	−	3435.66i	0.767983	−	0.829049i
$259$			1703.18i			0.408611i
$260$		0			0
$261$			2318.59i			0.549873i
$262$	−4645.49	−	4303.32i	−1.09542	−	1.01473i
$263$	411.340			0.0964422			0.0482211	−	0.998837i	$-0.484645\pi$
$263$	411.340			0.0964422			0.0482211	+	0.998837i	$0.484645\pi$
$264$	4123.55	+	3271.88i	0.961314	+	0.762767i
$265$		0			0
$266$	−29.4458	−	27.2769i	−0.00678735	−	0.00628741i
$267$			5072.37i			1.16264i
$268$	−5316.95	+	407.205i	−1.21188	+	0.0928135i
$269$			407.204i			0.0922961i	0.998935	+	0.0461481i	$0.0146946\pi$
$269$			407.204i			0.0922961i	−0.998935	+	0.0461481i	$0.985305\pi$
$270$		0			0
$271$	−1329.04			−0.297909			−0.148954	−	0.988844i	$-0.547591\pi$
$271$	−1329.04			−0.297909			−0.148954	+	0.988844i	$0.547591\pi$
$272$	−5691.34	+	876.900i	−1.26871	+	0.195478i
$273$	−4104.21			−0.909884
$274$	−2746.01	+	2964.36i	−0.605448	+	0.653590i
$275$		0			0
$276$	−5340.29	+	408.993i	−1.16467	+	0.0891975i
$277$		−	4411.34i		−	0.956866i	−0.878124	−	0.478433i	$-0.841205\pi$
$277$		−	4411.34i		−	0.956866i	0.878124	−	0.478433i	$-0.158795\pi$
$278$	3045.61	+	2821.28i	0.657063	+	0.608665i
$279$	2409.39			0.517012
$280$		0			0
$281$	5134.23			1.08997			0.544986	−	0.838445i	$-0.316535\pi$
$281$	5134.23			1.08997			0.544986	+	0.838445i	$0.316535\pi$
$282$	−4485.08	−	4154.72i	−0.947101	−	0.877340i
$283$			3093.54i			0.649794i	0.945749	+	0.324897i	$0.105330\pi$
$283$			3093.54i			0.649794i	−0.945749	+	0.324897i	$0.894670\pi$
$284$	−234.790	−	3065.70i	−0.0490572	−	0.640548i
$285$		0			0
$286$	−1381.05	+	1490.87i	−0.285536	+	0.308241i
$287$	8905.47			1.83161
$288$	−1779.33	+	2632.89i	−0.364056	+	0.538696i
$289$	3182.77			0.647827
$290$		0			0
$291$		−	8541.42i		−	1.72064i
$292$	457.638	+	5975.45i	0.0917166	+	1.19756i
$293$			671.319i			0.133853i	0.997758	+	0.0669264i	$0.0213193\pi$
$293$			671.319i			0.133853i	−0.997758	+	0.0669264i	$0.978681\pi$
$294$	7569.55	+	7011.99i	1.50158	+	1.39098i
$295$		0			0
$296$	−803.162	+	1012.22i	−0.157712	+	0.198764i
$297$	2197.28			0.429291
$298$	−5978.26	−	5537.91i	−1.16212	−	1.07652i
$299$		−	2067.76i		−	0.399939i
$300$		0			0
$301$		−	7398.33i		−	1.41672i
$302$	1824.65	−	1969.74i	0.347672	−	0.375317i
$303$	−5381.45			−1.02032
$304$	−4.63719	−	30.0967i	−0.000874871	−	0.00567817i
$305$		0			0
$306$	3036.02	−	3277.43i	0.567183	−	0.612282i
$307$			5810.78i			1.08026i	0.841583	+	0.540128i	$0.181624\pi$
$307$			5810.78i			1.08026i	−0.841583	+	0.540128i	$0.818376\pi$
$308$	8291.39	−	635.007i	1.53392	−	0.117477i
$309$			3322.14i			0.611619i
$310$		0			0
$311$	−7223.30			−1.31703			−0.658514	−	0.752568i	$-0.728815\pi$
$311$	−7223.30			−1.31703			−0.658514	+	0.752568i	$0.728815\pi$
$312$	−2439.19	−	1935.41i	−0.442603	−	0.351189i
$313$	−1804.40			−0.325849			−0.162925	−	0.986638i	$-0.552093\pi$
$313$	−1804.40			−0.325849			−0.162925	+	0.986638i	$0.552093\pi$
$314$	−6555.42	−	6072.56i	−1.17817	−	1.09138i
$315$		0			0
$316$	355.889	+	4646.91i	0.0633555	+	0.827244i
$317$			1593.07i			0.282259i	0.989991	+	0.141129i	$0.0450733\pi$
$317$			1593.07i			0.282259i	−0.989991	+	0.141129i	$0.954927\pi$
$318$	−711.162	+	767.710i	−0.125409	+	0.135381i
$319$	4603.15			0.807922
$320$		0			0
$321$	−745.687			−0.129658
$322$	−5749.88	+	6207.08i	−0.995119	+	1.07425i
$323$			42.8117i			0.00737495i
$324$	546.640	+	7137.57i	0.0937311	+	1.22386i
$325$		0			0
$326$	−2825.58	−	2617.45i	−0.480044	−	0.444685i
$327$	7330.34			1.23966
$328$	5292.65	+	4199.53i	0.890969	+	0.706951i
$329$	−9658.14			−1.61845
$330$		0			0
$331$		−	6213.17i		−	1.03174i	−0.856666	−	0.515871i	$-0.827468\pi$
$331$		−	6213.17i		−	1.03174i	0.856666	−	0.515871i	$-0.172532\pi$
$332$	5076.40	−	388.783i	0.839168	−	0.0642688i
$333$		−	1002.48i		−	0.164971i
$334$	1232.70	−	1330.72i	0.201947	−	0.218005i
$335$		0			0
$336$	1940.21	+	12592.5i	0.315021	+	2.04458i
$337$	−11379.1			−1.83935			−0.919673	−	0.392686i	$-0.871546\pi$
$337$	−11379.1			−1.83935			−0.919673	+	0.392686i	$0.871546\pi$
$338$	−3405.97	+	3676.79i	−0.548107	+	0.591690i
$339$		−	14144.0i		−	2.26606i
$340$		0			0
$341$		−	4783.42i		−	0.759638i
$342$	17.3316	+	16.0550i	0.00274031	+	0.00253846i
$343$	6070.27			0.955579
$344$	3488.81	−	4396.93i	0.546814	−	0.689148i
$345$		0			0
$346$	−120.341	−	111.477i	−0.0186982	−	0.0173209i
$347$			2528.79i			0.391217i	0.980682	+	0.195609i	$0.0626682\pi$
$347$			2528.79i			0.391217i	−0.980682	+	0.195609i	$0.937332\pi$
$348$	538.575	+	7032.27i	0.0829617	+	1.08324i
$349$			110.562i			0.0169577i	0.999964	+	0.00847885i	$0.00269893\pi$
$349$			110.562i			0.0169577i	−0.999964	+	0.00847885i	$0.997301\pi$
$350$		0			0
$351$	−1299.76			−0.197652
$352$	5227.14	+	3532.55i	0.791499	+	0.534903i
$353$	−7118.00			−1.07324			−0.536619	−	0.843825i	$-0.680299\pi$
$353$	−7118.00			−1.07324			−0.536619	+	0.843825i	$0.680299\pi$
$354$	−2153.89	+	2325.16i	−0.323384	+	0.349098i
$355$		0			0
$356$	464.232	+	6061.56i	0.0691131	+	0.902421i
$357$		−	17912.5i		−	2.65555i
$358$	−3338.09	−	3092.22i	−0.492804	−	0.456505i
$359$	3118.04			0.458396			0.229198	−	0.973380i	$-0.426390\pi$
$359$	3118.04			0.458396			0.229198	+	0.973380i	$0.426390\pi$
$360$		0			0
$361$	6858.77			0.999967
$362$	−5531.00	−	5123.60i	−0.803047	−	0.743896i
$363$		−	776.566i		−	0.112284i
$364$	−4904.59	+	375.624i	−0.706237	+	0.0540881i
$365$		0			0
$366$	2112.94	−	2280.95i	0.301762	−	0.325757i
$367$	−11007.8			−1.56567			−0.782835	−	0.622230i	$-0.786227\pi$
$367$	−11007.8			−1.56567			−0.782835	+	0.622230i	$0.786227\pi$
$368$	−6344.29	+	977.505i	−0.898693	+	0.138467i
$369$	−5241.70			−0.739491
$370$		0			0
$371$			1653.18i			0.231345i
$372$	7307.66	−	559.667i	1.01851	−	0.0780037i
$373$		−	12872.3i		−	1.78687i	−0.449190	−	0.893436i	$-0.648287\pi$
$373$		−	12872.3i		−	1.78687i	0.449190	−	0.893436i	$-0.351713\pi$
$374$	−6506.77	−	6027.50i	−0.899618	−	0.833354i
$375$		0			0
$376$	−5739.98	−	4554.46i	−0.787278	−	0.624677i
$377$	−2722.89			−0.371979
$378$	3901.65	+	3614.27i	0.530898	+	0.491793i
$379$		−	6010.29i		−	0.814586i	−0.913298	−	0.407293i	$-0.866473\pi$
$379$		−	6010.29i		−	0.814586i	0.913298	−	0.407293i	$-0.133527\pi$
$380$		0			0
$381$			3791.16i			0.509783i
$382$	5534.93	−	5975.04i	0.741340	−	0.800287i
$383$	4012.72			0.535354			0.267677	−	0.963509i	$-0.413744\pi$
$383$	4012.72			0.535354			0.267677	+	0.963509i	$0.413744\pi$
$384$	−4785.12	+	8398.86i	−0.635911	+	1.11615i
$385$		0			0
$386$	−4615.68	+	4982.70i	−0.608632	+	0.657028i
$387$			4354.61i			0.571982i
$388$	−781.725	−	10207.1i	−0.102284	−	1.33554i
$389$			9488.02i			1.23666i	0.785918	+	0.618331i	$0.212191\pi$
$389$			9488.02i			1.23666i	−0.785918	+	0.618331i	$0.787809\pi$
$390$		0			0
$391$	9024.58			1.16724
$392$	9687.47	+	7686.65i	1.24819	+	0.990394i
$393$	14944.1			1.91814
$394$	9241.93	+	8561.19i	1.18173	+	1.09469i
$395$		0			0
$396$	−4880.26	+	373.761i	−0.619298	+	0.0474298i
$397$			4950.44i			0.625832i	0.949781	+	0.312916i	$0.101306\pi$
$397$			4950.44i			0.625832i	−0.949781	+	0.312916i	$0.898694\pi$
$398$	9425.72	−	10175.2i	1.18711	−	1.28150i
$399$	94.7242			0.0118851
$400$		0			0
$401$	−8799.56			−1.09583			−0.547917	−	0.836533i	$-0.684579\pi$
$401$	−8799.56			−1.09583			−0.547917	+	0.836533i	$0.684579\pi$
$402$	8552.05	−	9232.06i	1.06104	−	1.14541i
$403$			2829.53i			0.349749i
$404$	−6430.90	+	492.519i	−0.791954	+	0.0606528i
$405$		0			0
$406$	8173.68	+	7571.62i	0.999145	+	0.925550i
$407$	−1990.25			−0.242390
$408$	8446.95	−	10645.7i	1.02497	−	1.29176i
$409$	−7179.75			−0.868009			−0.434005	−	0.900911i	$-0.642900\pi$
$409$	−7179.75			−0.868009			−0.434005	+	0.900911i	$0.642900\pi$
$410$		0			0
$411$		−	9536.06i		−	1.14447i
$412$	304.048	+	3970.01i	0.0363577	+	0.474729i
$413$			5006.98i			0.596556i
$414$	3384.34	−	3653.44i	0.401766	−	0.433713i
$415$		0			0
$416$	−3092.00	−	2089.60i	−0.364418	−	0.246277i
$417$	−9797.42			−1.15056
$418$	31.8744	−	34.4088i	0.00372973	−	0.00402629i
$419$			13557.2i			1.58070i	0.612657	+	0.790349i	$0.290101\pi$
$419$			13557.2i			1.58070i	−0.612657	+	0.790349i	$0.709899\pi$
$420$		0			0
$421$		−	7428.36i		−	0.859943i	−0.902843	−	0.429971i	$-0.858524\pi$
$421$		−	7428.36i		−	0.859943i	0.902843	−	0.429971i	$-0.141476\pi$
$422$	−2545.13	−	2357.66i	−0.293590	−	0.271965i
$423$	5684.72			0.653429
$424$	−779.587	+	982.511i	−0.0892926	+	0.112535i
$425$		0			0
$426$	5323.11	+	4931.02i	0.605412	+	0.560819i
$427$		−	4911.78i		−	0.556669i
$428$	−891.106	+	68.2465i	−0.100638	+	0.00770752i
$429$		−	4795.97i		−	0.539748i
$430$		0			0
$431$	−1591.77			−0.177895			−0.0889475	−	0.996036i	$-0.528350\pi$
$431$	−1591.77			−0.177895			−0.0889475	+	0.996036i	$0.528350\pi$
$432$	614.441	+	3987.90i	0.0684313	+	0.444139i
$433$	−10811.6			−1.19994			−0.599970	−	0.800023i	$-0.704821\pi$
$433$	−10811.6			−1.19994			−0.599970	+	0.800023i	$0.704821\pi$
$434$	7868.14	−	8493.77i	0.870237	−	0.939434i
$435$		0			0
$436$	8759.85	−	670.885i	0.962204	−	0.0736916i
$437$			47.7234i			0.00522407i
$438$	−10375.5	−	9611.23i	−1.13187	−	1.04850i
$439$	4891.74			0.531823			0.265911	−	0.963997i	$-0.414327\pi$
$439$	4891.74			0.531823			0.265911	+	0.963997i	$0.414327\pi$
$440$		0			0
$441$	−9594.21			−1.03598
$442$	3848.94	+	3565.43i	0.414197	+	0.383689i
$443$			2116.86i			0.227032i	0.993536	+	0.113516i	$0.0362113\pi$
$443$			2116.86i			0.227032i	−0.993536	+	0.113516i	$0.963789\pi$
$444$	−232.862	−	3040.51i	−0.0248899	−	0.324992i
$445$		0			0
$446$	−2965.40	+	3201.19i	−0.314833	+	0.339867i
$447$	19231.5			2.03494
$448$	3471.06	+	14870.7i	0.366054	+	1.56824i
$449$	13253.6			1.39305			0.696523	−	0.717535i	$-0.254730\pi$
$449$	13253.6			1.39305			0.696523	+	0.717535i	$0.254730\pi$
$450$		0			0
$451$			10406.5i			1.08652i
$452$	−1294.48	−	16902.2i	−0.134706	−	1.75888i
$453$			6336.46i			0.657202i
$454$	7991.37	+	7402.74i	0.826109	+	0.765260i
$455$		0			0
$456$	56.2960	+	44.6688i	0.00578136	+	0.00458730i
$457$	3969.19			0.406282			0.203141	−	0.979150i	$-0.434885\pi$
$457$	3969.19			0.406282			0.203141	+	0.979150i	$0.434885\pi$
$458$	10857.4	+	10057.7i	1.10772	+	1.02613i
$459$		−	5672.68i		−	0.576858i
$460$		0			0
$461$			7068.99i			0.714177i	0.934071	+	0.357089i	$0.116231\pi$
$461$			7068.99i			0.714177i	−0.934071	+	0.357089i	$0.883769\pi$
$462$	−13336.3	+	14396.7i	−1.34299	+	1.44978i
$463$	−178.581			−0.0179251			−0.00896257	−	0.999960i	$-0.502853\pi$
$463$	−178.581			−0.0179251			−0.00896257	+	0.999960i	$0.502853\pi$
$464$	1287.21	+	8354.36i	0.128787	+	0.835865i
$465$		0			0
$466$	−348.710	+	376.438i	−0.0346646	+	0.0374209i
$467$			11576.2i			1.14707i	0.819180	+	0.573536i	$0.194429\pi$
$467$			11576.2i			1.14707i	−0.819180	+	0.573536i	$0.805571\pi$
$468$	2886.81	−	221.090i	0.285134	−	0.0218374i
$469$		−	19880.3i		−	1.95733i
$470$		0			0
$471$	21088.2			2.06304
$472$	−2361.13	+	2975.72i	−0.230254	+	0.290188i
$473$	8645.31			0.840406
$474$	−8068.64	−	7474.32i	−0.781867	−	0.724276i
$475$		0			0
$476$	−1639.38	−	21405.7i	−0.157859	−	2.06119i
$477$		−	973.053i		−	0.0934025i
$478$	4820.20	−	5203.48i	0.461236	−	0.497911i
$479$	−12742.0			−1.21544			−0.607720	−	0.794152i	$-0.707916\pi$
$479$	−12742.0			−1.21544			−0.607720	+	0.794152i	$0.707916\pi$
$480$		0			0
$481$	1177.29			0.111600
$482$	2094.07	−	2260.58i	0.197889	−	0.213624i
$483$		−	19967.6i		−	1.88107i
$484$	−71.0726	−	928.007i	−0.00667474	−	0.0871532i
$485$		0			0
$486$	−8861.20	−	8208.50i	−0.827062	−	0.766142i
$487$	13309.0			1.23838			0.619188	−	0.785243i	$-0.287462\pi$
$487$	13309.0			1.23838			0.619188	+	0.785243i	$0.287462\pi$
$488$	2316.23	−	2919.14i	0.214858	−	0.270785i
$489$	9089.62			0.840586
$490$		0			0
$491$			216.689i			0.0199166i	0.999950	+	0.00995830i	$0.00316988\pi$
$491$			216.689i			0.0199166i	−0.999950	+	0.00995830i	$0.996830\pi$
$492$	−15898.1	+	1217.57i	−1.45679	+	0.111570i
$493$		−	11883.9i		−	1.08564i
$494$	−18.8546	+	20.3538i	−0.00171722	+	0.00185377i
$495$		0			0
$496$	8681.53	−	1337.62i	0.785912	−	0.121090i
$497$	11462.8			1.03456
$498$	−8165.14	+	8814.39i	−0.734716	+	0.793137i
$499$			10800.4i			0.968921i	0.874813	+	0.484460i	$0.160984\pi$
$499$			10800.4i			0.968921i	−0.874813	+	0.484460i	$0.839016\pi$
$500$		0			0
$501$			4280.79i			0.381740i
$502$	−11163.3	−	10341.0i	−0.992516	−	0.919409i
$503$	−16697.6			−1.48013			−0.740067	−	0.672533i	$-0.765206\pi$
$503$	−16697.6			−1.48013			−0.740067	+	0.672533i	$0.765206\pi$
$504$	−9280.52	−	7363.75i	−0.820213	−	0.650809i
$505$		0			0
$506$	−7253.28	−	6719.02i	−0.637248	−	0.590310i
$507$		−	11827.9i		−	1.03608i
$508$	346.974	+	4530.49i	0.0303041	+	0.395685i
$509$			13066.1i			1.13781i	0.822402	+	0.568906i	$0.192633\pi$
$509$			13066.1i			1.13781i	−0.822402	+	0.568906i	$0.807367\pi$
$510$		0			0
$511$	−22342.5			−1.93419
$512$	−4949.61	+	10474.7i	−0.427234	+	0.904141i
$513$	29.9980			0.00258176
$514$	−2648.64	+	2859.24i	−0.227289	+	0.245361i
$515$		0			0
$516$	1011.51	+	13207.5i	0.0862973	+	1.12680i
$517$		−	11286.0i		−	0.960075i
$518$	−3534.02	−	3273.71i	−0.299760	−	0.277681i
$519$	387.126			0.0327417
$520$		0			0
$521$	−269.920			−0.0226975			−0.0113488	−	0.999936i	$-0.503613\pi$
$521$	−269.920			−0.0226975			−0.0113488	+	0.999936i	$0.503613\pi$
$522$	−4810.97	−	4456.61i	−0.403392	−	0.373679i
$523$			19287.7i			1.61260i	0.591506	+	0.806300i	$0.298533\pi$
$523$			19287.7i			1.61260i	−0.591506	+	0.806300i	$0.701467\pi$
$524$	17858.4	−	1367.71i	1.48883	−	0.114024i
$525$		0			0
$526$	−790.645	+	853.513i	−0.0655395	+	0.0707508i
$527$	−12349.2			−1.02076
$528$	−14715.0	+	2267.23i	−1.21285	+	0.186872i
$529$	−2107.06			−0.173178
$530$		0			0
$531$		−	2947.08i		−	0.240852i
$532$	113.197	−	8.66931i	0.00922500	−	0.000706508i
$533$		−	6155.72i		−	0.500251i
$534$	−10525.0	−	9749.72i	−0.852921	−	0.790096i
$535$		0			0
$536$	9374.88	−	11815.1i	0.755472	−	0.952120i
$537$	10738.3			0.862928
$538$	−844.931	−	782.695i	−0.0677092	−	0.0627219i
$539$			19047.6i			1.52215i
$540$		0			0
$541$			8722.31i			0.693164i	0.938020	+	0.346582i	$0.112658\pi$
$541$			8722.31i			0.693164i	−0.938020	+	0.346582i	$0.887342\pi$
$542$	2554.57	−	2757.70i	0.202450	−	0.218548i
$543$	17792.7			1.40618
$544$	9119.91	−	13494.8i	0.718774	−	1.06357i
$545$		0			0
$546$	7888.79	−	8516.07i	0.618332	−	0.667498i
$547$			8718.86i			0.681520i	0.940150	+	0.340760i	$0.110684\pi$
$547$			8718.86i			0.681520i	−0.940150	+	0.340760i	$0.889316\pi$
$548$	−872.756	−	11395.7i	−0.0680334	−	0.888323i
$549$			2891.04i			0.224748i
$550$		0			0
$551$	62.8437			0.00485886
$552$	9416.04	−	11867.0i	0.726039	−	0.915025i
$553$	−17375.0			−1.33609
$554$	9153.35	+	8479.13i	0.701965	+	0.650260i
$555$		0			0
$556$	−11708.1	+	896.677i	−0.893043	+	0.0683949i
$557$			11758.7i			0.894489i	0.894412	+	0.447245i	$0.147595\pi$
$557$			11758.7i			0.894489i	−0.894412	+	0.447245i	$0.852405\pi$
$558$	−4631.13	+	4999.38i	−0.351347	+	0.379284i
$559$	−5113.94			−0.386935
$560$		0			0
$561$	20931.7			1.57529
$562$	−9868.60	+	10653.3i	−0.740715	+	0.799613i
$563$			5260.52i			0.393791i	0.980424	+	0.196896i	$0.0630860\pi$
$563$			5260.52i			0.393791i	−0.980424	+	0.196896i	$0.936914\pi$
$564$	17241.7	−	1320.48i	1.28725	−	0.0985855i
$565$		0			0
$566$	−6418.96	−	5946.16i	−0.476695	−	0.441582i
$567$	−26687.7			−1.97668
$568$	6812.49	+	5405.46i	0.503250	+	0.399310i
$569$	19030.4			1.40210			0.701050	−	0.713112i	$-0.252715\pi$
$569$	19030.4			1.40210			0.701050	+	0.713112i	$0.252715\pi$
$570$		0			0
$571$			23227.4i			1.70234i	0.524887	+	0.851172i	$0.324108\pi$
$571$			23227.4i			1.70234i	−0.524887	+	0.851172i	$0.675892\pi$
$572$	−438.936	−	5731.25i	−0.0320853	−	0.418944i
$573$			19221.1i			1.40135i
$574$	−17117.4	+	18478.5i	−1.24471	+	1.34369i
$575$		0			0
$576$	−2043.05	−	8752.77i	−0.147790	−	0.633158i
$577$	−526.632			−0.0379965			−0.0189983	−	0.999820i	$-0.506048\pi$
$577$	−526.632			−0.0379965			−0.0189983	+	0.999820i	$0.506048\pi$
$578$	−6117.67	+	6604.12i	−0.440245	+	0.475251i
$579$		−	16028.9i		−	1.15049i
$580$		0			0
$581$			18980.9i			1.35535i
$582$	17723.1	+	16417.6i	1.26228	+	1.16930i
$583$	−1931.83			−0.137235
$584$	−13278.5	−	10536.0i	−0.940867	−	0.746544i
$585$		0			0
$586$	−1392.96	−	1290.36i	−0.0981956	−	0.0909627i
$587$		−	14220.5i		−	0.999902i	−0.866054	−	0.499951i	$-0.833351\pi$
$587$		−	14220.5i		−	0.999902i	0.866054	−	0.499951i	$-0.166649\pi$
$588$	−29099.2	+	2228.60i	−2.04087	+	0.156303i
$589$		−	65.3047i		−	0.00456848i
$590$		0			0
$591$	−29730.4			−2.06928
$592$	−556.545	−	3612.14i	−0.0386383	−	0.250774i
$593$	10794.3			0.747500			0.373750	−	0.927529i	$-0.378072\pi$
$593$	10794.3			0.747500			0.373750	+	0.927529i	$0.378072\pi$
$594$	−4223.45	+	4559.27i	−0.291734	+	0.314931i
$595$		0			0
$596$	22981.9	−	1760.10i	1.57949	−	0.120967i
$597$			32732.6i			2.24398i
$598$	4290.52	+	3974.49i	0.293398	+	0.271787i
$599$	−10036.9			−0.684634			−0.342317	−	0.939584i	$-0.611212\pi$
$599$	−10036.9			−0.684634			−0.342317	+	0.939584i	$0.611212\pi$
$600$		0			0
$601$	8251.09			0.560015			0.280008	−	0.959998i	$-0.409663\pi$
$601$	8251.09			0.560015			0.280008	+	0.959998i	$0.409663\pi$
$602$	15351.2	+	14220.5i	1.03932	+	0.962764i
$603$			11701.4i			0.790245i
$604$	579.923	+	7572.15i	0.0390674	+	0.510110i
$605$		0			0
$606$	10343.8	−	11166.3i	0.693379	−	0.748513i
$607$	8119.05			0.542903			0.271451	−	0.962452i	$-0.412496\pi$
$607$	8119.05			0.542903			0.271451	+	0.962452i	$0.412496\pi$
$608$	71.3626	+	48.2275i	0.00476009	+	0.00321691i
$609$	−26293.9			−1.74956
$610$		0			0
$611$			6675.99i			0.442032i
$612$	964.930	+	12599.2i	0.0637336	+	0.832180i
$613$			20527.3i			1.35251i	0.736668	+	0.676255i	$0.236398\pi$
$613$			20527.3i			1.35251i	−0.736668	+	0.676255i	$0.763602\pi$
$614$	−12057.1	−	11169.0i	−0.792485	−	0.734112i
$615$		0			0
$616$	−14619.4	+	18424.9i	−0.956225	+	1.20513i
$617$	−27545.7			−1.79732			−0.898661	−	0.438643i	$-0.855459\pi$
$617$	−27545.7			−1.79732			−0.898661	+	0.438643i	$0.855459\pi$
$618$	−6893.31	−	6385.56i	−0.448689	−	0.415639i
$619$		−	1777.17i		−	0.115396i	−0.998334	−	0.0576982i	$-0.981624\pi$
$619$		−	1777.17i		−	0.115396i	0.998334	−	0.0576982i	$-0.0183761\pi$
$620$		0			0
$621$		−	6323.49i		−	0.408620i
$622$	13884.1	−	14988.1i	0.895016	−	0.966183i
$623$	−22664.4			−1.45751
$624$	8704.32	−	1341.13i	0.558416	−	0.0860387i
$625$		0			0
$626$	3468.28	−	3744.06i	0.221438	−	0.239046i
$627$			110.690i			0.00705028i
$628$	25200.6	−	1930.02i	1.60130	−	0.122637i
$629$			5138.17i			0.325711i
$630$		0			0
$631$	16484.4			1.03999			0.519995	−	0.854169i	$-0.325934\pi$
$631$	16484.4			1.03999			0.519995	+	0.854169i	$0.325934\pi$
$632$	−10326.2	−	8193.46i	−0.649927	−	0.515694i
$633$	8187.43			0.514093
$634$	−3305.56	−	3062.08i	−0.207067	−	0.191815i
$635$		0			0
$636$	−226.026	−	2951.26i	−0.0140920	−	0.184002i
$637$		−	11267.2i		−	0.700821i
$638$	−8847.82	+	9551.35i	−0.549041	+	0.592698i
$639$	−6746.91			−0.417689
$640$		0			0
$641$	−24.7805			−0.00152694			−0.000763470	−	1.00000i	$-0.500243\pi$
$641$	−24.7805			−0.00152694			−0.000763470		1.00000i	$0.500243\pi$
$642$	1433.30	−	1547.27i	0.0881119	−	0.0951181i
$643$		−	29107.1i		−	1.78518i	−0.450870	−	0.892590i	$-0.648886\pi$
$643$		−	29107.1i		−	1.78518i	0.450870	−	0.892590i	$-0.351114\pi$
$644$	−1827.47	−	23861.5i	−0.111820	−	1.46006i
$645$		0			0
$646$	−88.8325	−	82.2893i	−0.00541032	−	0.00501181i
$647$	−13419.6			−0.815421			−0.407711	−	0.913111i	$-0.633673\pi$
$647$	−13419.6			−0.815421			−0.407711	+	0.913111i	$0.633673\pi$
$648$	−15860.9	−	12585.0i	−0.961533	−	0.762941i
$649$	−5850.91			−0.353880
$650$		0			0
$651$			27323.6i			1.64500i
$652$	10862.2	−	831.897i	0.652450	−	0.0499687i
$653$			1926.26i			0.115437i	0.998333	+	0.0577186i	$0.0183826\pi$
$653$			1926.26i			0.115437i	−0.998333	+	0.0577186i	$0.981617\pi$
$654$	−14089.8	+	15210.1i	−0.842438	+	0.909425i
$655$		0			0
$656$	−18887.0	+	2910.03i	−1.12410	+	0.173198i
$657$	13150.6			0.780905
$658$	18564.1	−	20040.2i	1.09986	−	1.18731i
$659$			13158.1i			0.777797i	0.921281	+	0.388899i	$0.127144\pi$
$659$			13158.1i			0.777797i	−0.921281	+	0.388899i	$0.872856\pi$
$660$		0			0
$661$		−	27392.1i		−	1.61184i	−0.592023	−	0.805921i	$-0.701670\pi$
$661$		−	27392.1i		−	1.61184i	0.592023	−	0.805921i	$-0.298330\pi$
$662$	12892.1	+	11942.5i	0.756895	+	0.701143i
$663$	−12381.7			−0.725285
$664$	−8950.75	+	11280.6i	−0.523127	+	0.659296i
$665$		0			0
$666$	2080.10	+	1926.88i	0.121024	+	0.112110i
$667$		−	13247.3i		−	0.769019i
$668$	391.785	+	5115.61i	0.0226926	+	0.296301i
$669$		−	10297.9i		−	0.595128i
$670$		0			0
$671$	5739.65			0.330219
$672$	−29858.3	−	20178.5i	−1.71400	−	1.15834i
$673$	−5569.75			−0.319017			−0.159508	−	0.987197i	$-0.550991\pi$
$673$	−5569.75			−0.319017			−0.159508	+	0.987197i	$0.550991\pi$
$674$	21872.0	−	23611.2i	1.24997	−	1.34936i
$675$		0			0
$676$	−1082.51	−	14134.5i	−0.0615901	−	0.804192i
$677$		−	4130.23i		−	0.234472i	−0.993104	−	0.117236i	$-0.962597\pi$
$677$		−	4130.23i		−	0.234472i	0.993104	−	0.117236i	$-0.0374034\pi$
$678$	29348.1	+	27186.4i	1.66240	+	1.53995i
$679$	38164.8			2.15704
$680$		0			0
$681$	−25707.5			−1.44657
$682$	9925.39	+	9194.31i	0.557277	+	0.516229i
$683$		−	22875.3i		−	1.28155i	−0.767728	−	0.640776i	$-0.778613\pi$
$683$		−	22875.3i		−	1.28155i	0.767728	−	0.640776i	$-0.221387\pi$
$684$	−66.6268	+	5.10270i	−0.00372447	+	0.000285244i
$685$		0			0
$686$	−11667.8	+	12595.5i	−0.649385	+	0.701021i
$687$	−34927.3			−1.93968
$688$	2417.55	+	15690.6i	0.133965	+	0.869473i
$689$	1142.73			0.0631851
$690$		0			0
$691$		−	19910.4i		−	1.09613i	−0.836435	−	0.548066i	$-0.815364\pi$
$691$		−	19910.4i		−	1.09613i	0.836435	−	0.548066i	$-0.184636\pi$
$692$	462.620	−	35.4304i	0.0254136	−	0.00194633i
$693$		−	18247.5i		−	1.00024i
$694$	−5247.12	−	4860.63i	−0.287000	−	0.265860i
$695$		0			0
$696$	−15626.9	−	12399.3i	−0.851056	−	0.675282i
$697$	26866.2			1.46001
$698$	−229.411	−	212.513i	−0.0124403	−	0.0115240i
$699$		−	1210.96i		−	0.0655262i
$700$		0			0
$701$			3428.44i			0.184722i	0.995726	+	0.0923612i	$0.0294414\pi$
$701$			3428.44i			0.184722i	−0.995726	+	0.0923612i	$0.970559\pi$
$702$	2498.29	−	2696.94i	0.134319	−	0.144999i
$703$	−27.1715			−0.00145774
$704$	−17377.1	+	4056.11i	−0.930290	+	0.217145i
$705$		0			0
$706$	13681.7	−	14769.6i	0.729343	−	0.787337i
$707$		−	24045.4i		−	1.27910i
$708$	−684.564	−	8938.47i	−0.0363383	−	0.474475i
$709$			15608.3i			0.826771i	0.910556	+	0.413385i	$0.135654\pi$
$709$			15608.3i			0.826771i	−0.910556	+	0.413385i	$0.864346\pi$
$710$		0			0
$711$	10226.8			0.539430
$712$	−13469.8	−	10687.8i	−0.708991	−	0.562558i
$713$	−13766.0			−0.723061
$714$	37167.7	+	34430.0i	1.94813	+	1.80464i
$715$		0			0
$716$	12832.4	−	982.789i	0.669791	−	0.0512968i
$717$			16739.1i			0.871873i
$718$	−5993.26	+	6469.81i	−0.311513	+	0.336283i
$719$	−8282.41			−0.429599			−0.214800	−	0.976658i	$-0.568910\pi$
$719$	−8282.41			−0.429599			−0.214800	+	0.976658i	$0.568910\pi$
$720$		0			0
$721$	−14844.0			−0.766741
$722$	−13183.4	+	14231.7i	−0.679550	+	0.733584i
$723$			7272.08i			0.374068i
$724$	21262.5	−	1628.42i	1.09146	−	0.0835907i
$725$		0			0
$726$	1611.34	+	1492.65i	0.0823726	+	0.0763052i
$727$	20590.4			1.05042			0.525210	−	0.850973i	$-0.323987\pi$
$727$	20590.4			1.05042			0.525210	+	0.850973i	$0.323987\pi$
$728$	8647.81	−	10898.8i	0.440260	−	0.554858i
$729$	4345.77			0.220788
$730$		0			0
$731$		−	22319.4i		−	1.12929i
$732$	671.548	+	8768.51i	0.0339086	+	0.442751i
$733$		−	24257.3i		−	1.22232i	−0.791506	−	0.611162i	$-0.790703\pi$
$733$		−	24257.3i		−	1.22232i	0.791506	−	0.611162i	$-0.209297\pi$
$734$	21158.3	−	22840.6i	1.06399	−	1.14859i
$735$		0			0
$736$	10166.2	−	15043.0i	0.509146	−	0.753387i
$737$	23231.1			1.16110
$738$	10075.2	−	10876.3i	0.502537	−	0.542497i
$739$		−	25426.8i		−	1.26569i	−0.774280	−	0.632843i	$-0.781888\pi$
$739$		−	25426.8i		−	1.26569i	0.774280	−	0.632843i	$-0.218112\pi$
$740$		0			0
$741$		−	65.4761i		−	0.00324605i
$742$	−3430.29	−	3177.62i	−0.169717	−	0.157216i
$743$	22658.4			1.11878			0.559391	−	0.828904i	$-0.311035\pi$
$743$	22658.4			1.11878			0.559391	+	0.828904i	$0.311035\pi$
$744$	−12884.9	+	16238.8i	−0.634925	+	0.800194i
$745$		0			0
$746$	26709.5	+	24742.2i	1.31086	+	1.21431i
$747$		−	11172.0i		−	0.547205i
$748$	25013.6	−	1915.70i	1.22271	−	0.0936430i
$749$		−	3331.88i		−	0.162542i
$750$		0			0
$751$	−10999.0			−0.534431			−0.267215	−	0.963637i	$-0.586104\pi$
$751$	−10999.0			−0.534431			−0.267215	+	0.963637i	$0.586104\pi$
$752$	20483.2	−	3155.98i	0.993281	−	0.153041i
$753$	35911.3			1.73795
$754$	5233.73	−	5649.89i	0.252787	−	0.272887i
$755$		0			0
$756$	−14998.9	+	1148.71i	−0.721567	+	0.0552621i
$757$			30279.9i			1.45382i	0.686734	+	0.726909i	$0.259044\pi$
$757$			30279.9i			1.45382i	−0.686734	+	0.726909i	$0.740956\pi$
$758$	12471.1	+	11552.5i	0.597587	+	0.553570i
$759$	23333.1			1.11586
$760$		0			0
$761$	4374.09			0.208358			0.104179	−	0.994559i	$-0.466778\pi$
$761$	4374.09			0.208358			0.104179	+	0.994559i	$0.466778\pi$
$762$	−7866.50	−	7287.07i	−0.373981	−	0.346434i
$763$			32753.4i			1.55407i
$764$	1759.15	+	22969.5i	0.0833034	+	1.08771i
$765$		0			0
$766$	−7712.93	+	8326.23i	−0.363812	+	0.392740i
$767$	3460.97			0.162932
$768$	−8229.69	−	26072.5i	−0.386671	−	1.22502i
$769$	12982.1			0.608774			0.304387	−	0.952548i	$-0.401548\pi$
$769$	12982.1			0.608774			0.304387	+	0.952548i	$0.401548\pi$
$770$		0			0
$771$		−	9197.90i		−	0.429642i
$772$	−1466.99	−	19154.7i	−0.0683912	−	0.892996i
$773$			34056.3i			1.58463i	0.610112	+	0.792316i	$0.291125\pi$
$773$			34056.3i			1.58463i	−0.610112	+	0.792316i	$0.708875\pi$
$774$	−9035.63	−	8370.08i	−0.419611	−	0.388703i
$775$		0			0
$776$	22681.9	+	17997.3i	1.04927	+	0.832557i
$777$	11368.6			0.524898
$778$	−19687.2	−	18237.1i	−0.907226	−	0.840402i
$779$			142.073i			0.00653437i
$780$		0			0
$781$			13394.8i			0.613706i
$782$	−17346.3	+	18725.6i	−0.793227	+	0.856300i
$783$	−8326.97			−0.380053
$784$	−34570.0	+	5326.41i	−1.57480	+	0.242639i
$785$		0			0
$786$	−28724.4	+	31008.4i	−1.30352	+	1.40717i
$787$			11962.9i			0.541842i	0.962602	+	0.270921i	$0.0873282\pi$
$787$			11962.9i			0.541842i	−0.962602	+	0.270921i	$0.912672\pi$
$788$	−35528.2	+	2720.98i	−1.60614	+	0.123009i
$789$		−	2745.67i		−	0.123889i
$790$		0			0
$791$	63198.1			2.84079
$792$	8604.91	−	10844.7i	0.386063	−	0.486555i
$793$	−3395.17			−0.152038
$794$	−10272.0	−	9515.34i	−0.459116	−	0.425298i
$795$		0			0
$796$	2995.75	+	39116.0i	0.133394	+	1.74174i
$797$		−	17898.9i		−	0.795498i	−0.917494	−	0.397749i	$-0.869791\pi$
$797$		−	17898.9i		−	0.795498i	0.917494	−	0.397749i	$-0.130209\pi$
$798$	−182.071	+	196.549i	−0.00807676	+	0.00871898i
$799$	−29136.9			−1.29010
$800$		0			0
$801$	13340.1			0.588452
$802$	16913.8	−	18258.7i	0.744698	−	0.803913i
$803$		−	26108.3i		−	1.14737i
$804$	2718.07	+	35490.3i	0.119228	+	1.55677i
$805$		0			0
$806$	−5871.15	−	5438.69i	−0.256579	−	0.237680i
$807$	2718.06			0.118563
$808$	11339.0	−	14290.5i	0.493695	−	0.622202i
$809$	−27690.6			−1.20340			−0.601700	−	0.798722i	$-0.705510\pi$
$809$	−27690.6			−1.20340			−0.601700	+	0.798722i	$0.705510\pi$
$810$		0			0
$811$		−	44013.9i		−	1.90572i	−0.303412	−	0.952859i	$-0.598126\pi$
$811$		−	44013.9i		−	1.90572i	0.303412	−	0.952859i	$-0.401874\pi$
$812$	−31421.6	+	2406.46i	−1.35798	+	0.104003i
$813$			8871.24i			0.382691i
$814$	3825.49	−	4129.68i	0.164722	−	0.177820i
$815$		0			0
$816$	5853.26	+	37989.3i	0.251109	+	1.62977i
$817$	118.028			0.00505422
$818$	13800.3	−	14897.7i	0.589875	−	0.636779i
$819$			10793.9i			0.460524i
$820$		0			0
$821$			30978.8i			1.31689i	0.752628	+	0.658446i	$0.228786\pi$
$821$			30978.8i			1.31689i	−0.752628	+	0.658446i	$0.771214\pi$
$822$	19786.9	+	18329.5i	0.839596	+	0.777753i
$823$	41684.8			1.76554			0.882771	−	0.469804i	$-0.155675\pi$
$823$	41684.8			1.76554			0.882771	+	0.469804i	$0.155675\pi$
$824$	−8822.01	−	6999.95i	−0.372973	−	0.295940i
$825$		0			0
$826$	−10389.3	−	9624.03i	−0.437638	−	0.405403i
$827$			11988.7i			0.504096i	0.967715	+	0.252048i	$0.0811042\pi$
$827$			11988.7i			0.504096i	−0.967715	+	0.252048i	$0.918896\pi$
$828$	1075.63	+	14044.7i	0.0451460	+	0.589478i
$829$			2023.64i			0.0847814i	0.999101	+	0.0423907i	$0.0134974\pi$
$829$			2023.64i			0.0847814i	−0.999101	+	0.0423907i	$0.986503\pi$
$830$		0			0
$831$	−29445.4			−1.22918
$832$	10279.0	−	2399.30i	0.428319	−	0.0999770i
$833$	49174.8			2.04539
$834$	18831.8	−	20329.2i	0.781886	−	0.844058i
$835$		0			0
$836$	10.1305	+	132.276i	0.000419105	+	0.00547232i
$837$			8653.07i			0.357340i
$838$	−28130.6	−	26058.6i	−1.15961	−	1.07420i
$839$	10706.3			0.440553			0.220276	−	0.975438i	$-0.429304\pi$
$839$	10706.3			0.440553			0.220276	+	0.975438i	$0.429304\pi$
$840$		0			0
$841$	6944.60			0.284743
$842$	15413.5	+	14278.2i	0.630861	+	0.584393i
$843$		−	34270.6i		−	1.40017i
$844$	9784.09	−	749.327i	0.399031	−	0.0305603i
$845$		0			0
$846$	−10926.7	+	11795.6i	−0.444052	+	0.479361i
$847$	3469.86			0.140762
$848$	−540.209	−	3506.11i	−0.0218760	−	0.141982i
$849$	20649.2			0.834721
$850$		0			0
$851$			5727.66i			0.230719i
$852$	−20463.3	+	1567.21i	−0.822843	+	0.0630185i
$853$		−	29816.5i		−	1.19683i	−0.801186	−	0.598416i	$-0.795797\pi$
$853$		−	29816.5i		−	1.19683i	0.801186	−	0.598416i	$-0.204203\pi$
$854$	10191.7	+	9441.03i	0.408377	+	0.378297i
$855$		0			0
$856$	1571.21	−	1980.19i	0.0627368	−	0.0790670i
$857$	−6572.14			−0.261960			−0.130980	−	0.991385i	$-0.541812\pi$
$857$	−6572.14			−0.261960			−0.130980	+	0.991385i	$0.541812\pi$
$858$	9951.44	+	9218.44i	0.395964	+	0.366798i
$859$		−	45723.7i		−	1.81615i	−0.418809	−	0.908075i	$-0.637552\pi$
$859$		−	45723.7i		−	1.81615i	0.418809	−	0.908075i	$-0.362448\pi$
$860$		0			0
$861$		−	59443.5i		−	2.35288i
$862$	3059.57	−	3302.85i	0.120893	−	0.130505i
$863$	−13343.7			−0.526331			−0.263166	−	0.964751i	$-0.584767\pi$
$863$	−13343.7			−0.526331			−0.263166	+	0.964751i	$0.584767\pi$
$864$	−9455.76	−	6390.29i	−0.372328	−	0.251623i
$865$		0			0
$866$	20781.3	−	22433.7i	0.815446	−	0.880286i
$867$		−	21244.8i		−	0.832193i
$868$	2500.71	+	32652.1i	0.0977874	+	1.27683i
$869$		−	20303.5i		−	0.792577i
$870$		0			0
$871$	−13741.8			−0.534586
$872$	−15445.4	+	19465.9i	−0.599826	+	0.755960i
$873$	−22463.6			−0.870878
$874$	−99.0240	−	91.7301i	−0.00383242	−	0.00355013i
$875$		0			0
$876$	39885.8	−	3054.70i	1.53837	−	0.117818i
$877$		−	41636.8i		−	1.60317i	−0.597884	−	0.801583i	$-0.703992\pi$
$877$		−	41636.8i		−	1.60317i	0.597884	−	0.801583i	$-0.296008\pi$
$878$	−9402.52	+	10150.2i	−0.361412	+	0.390150i
$879$	4481.01			0.171946
$880$		0			0
$881$	−31220.6			−1.19392			−0.596962	−	0.802269i	$-0.703626\pi$
$881$	−31220.6			−1.19392			−0.596962	+	0.802269i	$0.703626\pi$
$882$	18441.2	−	19907.6i	0.704023	−	0.760003i
$883$			35199.4i			1.34151i	0.741679	+	0.670755i	$0.234030\pi$
$883$			35199.4i			1.34151i	−0.741679	+	0.670755i	$0.765970\pi$
$884$	−14796.2	+	1133.19i	−0.562954	+	0.0431146i
$885$		0			0
$886$	−4392.40	−	4068.86i	−0.166552	−	0.154284i
$887$	−12744.8			−0.482444			−0.241222	−	0.970470i	$-0.577548\pi$
$887$	−12744.8			−0.482444			−0.241222	+	0.970470i	$0.577548\pi$
$888$	6756.52	+	5361.05i	0.255331	+	0.202596i
$889$	−16939.7			−0.639076
$890$		0			0
$891$		−	31185.8i		−	1.17258i
$892$	−942.482	−	12306.1i	−0.0353774	−	0.461929i
$893$		−	154.080i		−	0.00577391i
$894$	−36965.2	+	39904.5i	−1.38289	+	1.49285i
$895$		0			0
$896$	−37527.8	−	21380.9i	−1.39924	−	0.797194i
$897$	−13802.2			−0.513758
$898$	−25475.1	+	27500.7i	−0.946675	+	1.02195i
$899$			18127.6i			0.672512i
$900$		0			0
$901$			4987.35i			0.184409i
$902$	−21593.0	−	20002.5i	−0.797083	−	0.738372i
$903$	−49383.4			−1.81991
$904$	37559.5	+	29802.1i	1.38187	+	1.09646i
$905$		0			0
$906$	−13147.9	−	12179.4i	−0.482129	−	0.446617i
$907$		−	16588.8i		−	0.607299i	−0.952784	−	0.303650i	$-0.901795\pi$
$907$		−	16588.8i		−	0.607299i	0.952784	−	0.303650i	$-0.0982052\pi$
$908$	−30720.8	+	2352.79i	−1.12280	+	0.0859912i
$909$			14153.0i			0.516418i
$910$		0			0
$911$	−46114.7			−1.67711			−0.838555	−	0.544816i	$-0.816599\pi$
$911$	−46114.7			−1.67711			−0.838555	+	0.544816i	$0.816599\pi$
$912$	−200.893	+	30.9529i	−0.00729413	+	0.00112385i
$913$	−22180.1			−0.804002
$914$	−7629.26	+	8235.90i	−0.276098	+	0.298052i
$915$		0			0
$916$	−41738.7	+	3196.61i	−1.50555	+	0.115305i
$917$			66773.3i			2.40463i
$918$	11770.6	+	10903.6i	0.423188	+	0.392017i
$919$	−47522.6			−1.70580			−0.852898	−	0.522077i	$-0.825157\pi$
$919$	−47522.6			−1.70580			−0.852898	+	0.522077i	$0.825157\pi$
$920$		0			0
$921$	38786.6			1.38769
$922$	−14667.9	−	13587.5i	−0.523926	−	0.485335i
$923$		−	7923.40i		−	0.282559i
$924$	−4238.63	−	55344.5i	−0.150910	−	1.97046i
$925$		0			0
$926$	343.253	−	370.547i	0.0121814	−	0.0131500i
$927$	8737.09			0.309562
$928$	−19809.1	−	13387.2i	−0.700718	−	0.473552i
$929$	−13494.3			−0.476570			−0.238285	−	0.971195i	$-0.576585\pi$
$929$	−13494.3			−0.476570			−0.238285	+	0.971195i	$0.576585\pi$
$930$		0			0
$931$			260.044i			0.00915425i
$932$	−110.829	−	1447.12i	−0.00389521	−	0.0508604i
$933$			48215.1i			1.69184i
$934$	−24020.1	−	22250.9i	−0.841502	−	0.779519i
$935$		0			0
$936$	−5090.04	+	6414.97i	−0.177749	+	0.224017i
$937$	−12453.1			−0.434179			−0.217089	−	0.976152i	$-0.569656\pi$
$937$	−12453.1			−0.434179			−0.217089	+	0.976152i	$0.569656\pi$
$938$	41250.7	+	38212.3i	1.43591	+	1.33014i
$939$			12044.3i			0.418584i
$940$		0			0
$941$		−	40466.5i		−	1.40188i	−0.713220	−	0.700940i	$-0.752764\pi$
$941$		−	40466.5i		−	1.40188i	0.713220	−	0.700940i	$-0.247236\pi$
$942$	−40534.0	+	43757.0i	−1.40198	+	1.51346i
$943$	29948.5			1.03421
$944$	−1636.13	−	10618.9i	−0.0564104	−	0.366120i
$945$		0			0
$946$	−16617.3	+	17938.7i	−0.571117	+	0.616529i
$947$			2645.96i			0.0907943i	0.998969	+	0.0453971i	$0.0144553\pi$
$947$			2645.96i			0.0907943i	−0.998969	+	0.0453971i	$0.985545\pi$
$948$	31017.8	−	2375.54i	1.06267	−	0.0813860i
$949$			15443.8i			0.528268i
$950$		0			0
$951$	10633.7			0.362587
$952$	47567.0	+	37742.7i	1.61939	+	1.28492i
$953$	−40045.8			−1.36119			−0.680593	−	0.732662i	$-0.738278\pi$
$953$	−40045.8			−1.36119			−0.680593	+	0.732662i	$0.738278\pi$
$954$	2019.04	+	1870.32i	0.0685209	+	0.0634738i
$955$		0			0
$956$	1531.99	+	20003.4i	0.0518285	+	0.676734i
$957$		−	30725.8i		−	1.03785i
$958$	24491.6	−	26439.1i	0.825979	−	0.891657i
$959$	42609.1			1.43474
$960$		0			0
$961$	−10953.5			−0.367679
$962$	−2262.89	+	2442.82i	−0.0758403	+	0.0818707i
$963$			1961.12i			0.0656244i
$964$	665.553	+	8690.23i	0.0222365	+	0.290346i
$965$		0			0
$966$	41431.9	+	38380.1i	1.37997	+	1.27832i
$967$	−11049.0			−0.367439			−0.183719	−	0.982979i	$-0.558814\pi$
$967$	−11049.0			−0.367439			−0.183719	+	0.982979i	$0.558814\pi$
$968$	2062.19	+	1636.27i	0.0684723	+	0.0543302i
$969$	285.765			0.00947380
$970$		0			0
$971$			26708.5i			0.882717i	0.897331	+	0.441358i	$0.145503\pi$
$971$			26708.5i			0.882717i	−0.897331	+	0.441358i	$0.854497\pi$
$972$	34064.6	−	2608.88i	1.12410	−	0.0860904i
$973$		−	43776.9i		−	1.44237i
$974$	−25581.5	+	27615.7i	−0.841566	+	0.908483i
$975$		0			0
$976$	1605.02	+	10417.0i	0.0526387	+	0.341640i
$977$	11102.6			0.363566			0.181783	−	0.983339i	$-0.441813\pi$
$977$	11102.6			0.363566			0.181783	+	0.983339i	$0.441813\pi$
$978$	−17471.3	+	18860.6i	−0.571239	+	0.616661i
$979$		−	26484.5i		−	0.864604i
$980$		0			0
$981$		−	19278.5i		−	0.627435i
$982$	−449.621	−	416.503i	−0.0146110	−	0.0135348i
$983$	−33544.2			−1.08840			−0.544198	−	0.838957i	$-0.683166\pi$
$983$	−33544.2			−1.08840			−0.544198	+	0.838957i	$0.683166\pi$
$984$	28031.6	−	35328.1i	0.908144	−	1.14453i
$985$		0			0
$986$	24658.5	+	22842.2i	0.796436	+	0.737773i
$987$			64467.5i			2.07905i
$988$	−5.99249	−	78.2449i	−0.000192962	−	0.00251954i
$989$		−	24880.0i		−	0.799939i
$990$		0			0
$991$	5538.20			0.177524			0.0887622	−	0.996053i	$-0.471709\pi$
$991$	5538.20			0.177524			0.0887622	+	0.996053i	$0.471709\pi$
$992$	−13911.5	+	20584.9i	−0.445251	+	0.658841i
$993$	−41472.5			−1.32537
$994$	−22032.8	+	23784.8i	−0.703057	+	0.758961i
$995$		0			0
$996$	−2595.10	−	33884.7i	−0.0825591	−	1.07799i
$997$		−	24192.6i		−	0.768492i	−0.923231	−	0.384246i	$-0.874461\pi$
$997$		−	24192.6i		−	0.768492i	0.923231	−	0.384246i	$-0.125539\pi$
$998$	−22410.3	−	20759.6i	−0.710808	−	0.658452i
$999$	3600.30			0.114022

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.4.d.e.101.4		16
4.3	odd	2		800.4.d.e.401.13		16
5.2	odd	4		40.4.f.a.29.5	✓	16
5.3	odd	4		40.4.f.a.29.12	yes	16
5.4	even	2	inner	200.4.d.e.101.13		16
8.3	odd	2		800.4.d.e.401.3		16
8.5	even	2	inner	200.4.d.e.101.3		16
15.2	even	4		360.4.d.d.109.12		16
15.8	even	4		360.4.d.d.109.5		16
20.3	even	4		160.4.f.a.49.3		16
20.7	even	4		160.4.f.a.49.13		16
20.19	odd	2		800.4.d.e.401.4		16
40.3	even	4		160.4.f.a.49.14		16
40.13	odd	4		40.4.f.a.29.6	yes	16
40.19	odd	2		800.4.d.e.401.14		16
40.27	even	4		160.4.f.a.49.4		16
40.29	even	2	inner	200.4.d.e.101.14		16
40.37	odd	4		40.4.f.a.29.11	yes	16
60.23	odd	4		1440.4.d.d.1009.16		16
60.47	odd	4		1440.4.d.d.1009.2		16
120.53	even	4		360.4.d.d.109.11		16
120.77	even	4		360.4.d.d.109.6		16
120.83	odd	4		1440.4.d.d.1009.1		16
120.107	odd	4		1440.4.d.d.1009.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.f.a.29.5	✓	16	5.2	odd	4
40.4.f.a.29.6	yes	16	40.13	odd	4
40.4.f.a.29.11	yes	16	40.37	odd	4
40.4.f.a.29.12	yes	16	5.3	odd	4
160.4.f.a.49.3		16	20.3	even	4
160.4.f.a.49.4		16	40.27	even	4
160.4.f.a.49.13		16	20.7	even	4
160.4.f.a.49.14		16	40.3	even	4
200.4.d.e.101.3		16	8.5	even	2	inner
200.4.d.e.101.4		16	1.1	even	1	trivial
200.4.d.e.101.13		16	5.4	even	2	inner
200.4.d.e.101.14		16	40.29	even	2	inner
360.4.d.d.109.5		16	15.8	even	4
360.4.d.d.109.6		16	120.77	even	4
360.4.d.d.109.11		16	120.53	even	4
360.4.d.d.109.12		16	15.2	even	4
800.4.d.e.401.3		16	8.3	odd	2
800.4.d.e.401.4		16	20.19	odd	2
800.4.d.e.401.13		16	4.3	odd	2
800.4.d.e.401.14		16	40.19	odd	2
1440.4.d.d.1009.1		16	120.83	odd	4
1440.4.d.d.1009.2		16	60.47	odd	4
1440.4.d.d.1009.15		16	120.107	odd	4
1440.4.d.d.1009.16		16	60.23	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.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.92212 + 2.07496i) q^{2} -6.67494i q^{3} +(-0.610901 - 7.97664i) q^{4} +(13.8502 + 12.8300i) q^{6} +29.8250 q^{7} +(17.7254 + 14.0645i) q^{8} -17.5548 q^{9} +34.8520i q^{11} +(-53.2436 + 4.07773i) q^{12} -20.6159i q^{13} +(-57.3272 + 61.8856i) q^{14} +(-63.2536 + 9.74588i) q^{16} +89.9765 q^{17} +(33.7424 - 36.4254i) q^{18} +0.475810i q^{19} -199.080i q^{21} +(-72.3164 - 66.9897i) q^{22} +100.299 q^{23} +(93.8795 - 118.316i) q^{24} +(42.7771 + 39.6263i) q^{26} -63.0462i q^{27} +(-18.2201 - 237.903i) q^{28} -132.077i q^{29} -137.250 q^{31} +(101.359 - 149.981i) q^{32} +232.635 q^{33} +(-172.946 + 186.697i) q^{34} +(10.7242 + 140.028i) q^{36} +57.1057i q^{37} +(-0.987285 - 0.914564i) q^{38} -137.610 q^{39} +298.591 q^{41} +(413.082 + 382.656i) q^{42} -248.058i q^{43} +(278.002 - 21.2911i) q^{44} +(-192.787 + 208.117i) q^{46} -323.827 q^{47} +(65.0532 + 422.214i) q^{48} +546.530 q^{49} -600.588i q^{51} +(-164.446 + 12.5943i) q^{52} +55.4295i q^{53} +(130.818 + 121.182i) q^{54} +(528.660 + 419.473i) q^{56} +3.17600 q^{57} +(274.055 + 253.868i) q^{58} +167.879i q^{59} -164.687i q^{61} +(263.810 - 284.787i) q^{62} -523.571 q^{63} +(116.381 + 498.597i) q^{64} +(-447.152 + 482.707i) q^{66} -666.565i q^{67} +(-54.9668 - 717.710i) q^{68} -669.491i q^{69} +384.334 q^{71} +(-311.166 - 246.899i) q^{72} -749.119 q^{73} +(-118.492 - 109.764i) q^{74} +(3.79536 - 0.290673i) q^{76} +1039.46i q^{77} +(264.503 - 285.535i) q^{78} -582.564 q^{79} -894.809 q^{81} +(-573.928 + 619.564i) q^{82} +636.408i q^{83} +(-1587.99 + 121.618i) q^{84} +(514.710 + 476.798i) q^{86} -881.607 q^{87} +(-490.175 + 617.766i) q^{88} -759.913 q^{89} -614.869i q^{91} +(-61.2730 - 800.051i) q^{92} +916.133i q^{93} +(622.435 - 671.928i) q^{94} +(-1001.12 - 676.563i) q^{96} +1279.63 q^{97} +(-1050.50 + 1134.03i) q^{98} -611.819i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 12 q^{6} - 104 q^{9} - 28 q^{14} - 168 q^{16} + 112 q^{24} + 200 q^{26} - 112 q^{31} - 408 q^{34} - 84 q^{36} + 736 q^{39} + 232 q^{41} - 920 q^{44} + 212 q^{46} + 200 q^{49} + 2320 q^{54}+ \cdots + 3632 q^{96}+O(q^{100}) \) 16 * q - 4 * q^4 - 12 * q^6 - 104 * q^9 - 28 * q^14 - 168 * q^16 + 112 * q^24 + 200 * q^26 - 112 * q^31 - 408 * q^34 - 84 * q^36 + 736 * q^39 + 232 * q^41 - 920 * q^44 + 212 * q^46 + 200 * q^49 + 2320 * q^54 + 1120 * q^56 + 2912 * q^64 - 2488 * q^66 + 2096 * q^71 - 4224 * q^74 - 3000 * q^76 - 2992 * q^79 - 728 * q^81 - 7304 * q^84 + 3076 * q^86 + 208 * q^89 + 7036 * q^94 + 3632 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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