LMFDB - Embedded newform 360.4.d.d.109.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,4,Mod(109,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("360.109");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	360.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:	$21.2406876021$
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:	$\Z[a_1, \ldots, a_{11}]$
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			109.6
Root			$2.07496 - 1.92212i$ of defining polynomial
Character	$\chi$	$=$	360.109
Dual form			360.4.d.d.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.07496 + 1.92212i) q^{2} +(0.610901 - 7.97664i) q^{4} +(11.1461 - 0.874848i) q^{5} +29.8250i q^{7} +(14.0645 + 17.7254i) q^{8} +(-21.4460 + 23.2393i) q^{10} +34.8520i q^{11} +20.6159 q^{13} +(-57.3272 - 61.8856i) q^{14} +(-63.2536 - 9.74588i) q^{16} -89.9765i q^{17} +0.475810i q^{19} +(-0.169205 - 89.4426i) q^{20} +(-66.9897 - 72.3164i) q^{22} +100.299i q^{23} +(123.469 - 19.5022i) q^{25} +(-42.7771 + 39.6263i) q^{26} +(237.903 + 18.2201i) q^{28} +132.077i q^{29} -137.250 q^{31} +(149.981 - 101.359i) q^{32} +(172.946 + 186.697i) q^{34} +(26.0923 + 332.431i) q^{35} +57.1057 q^{37} +(-0.914564 - 0.987285i) q^{38} +(172.271 + 185.264i) q^{40} -298.591 q^{41} +248.058 q^{43} +(278.002 + 21.2911i) q^{44} +(-192.787 - 208.117i) q^{46} +323.827i q^{47} -546.530 q^{49} +(-218.708 + 277.789i) q^{50} +(12.5943 - 164.446i) q^{52} +55.4295 q^{53} +(30.4902 + 388.462i) q^{55} +(-528.660 + 419.473i) q^{56} +(-253.868 - 274.055i) q^{58} -167.879i q^{59} +164.687i q^{61} +(284.787 - 263.810i) q^{62} +(-116.381 + 498.597i) q^{64} +(229.786 - 18.0358i) q^{65} -666.565 q^{67} +(-717.710 - 54.9668i) q^{68} +(-693.113 - 639.628i) q^{70} -384.334 q^{71} +749.119i q^{73} +(-118.492 + 109.764i) q^{74} +(3.79536 + 0.290673i) q^{76} -1039.46 q^{77} +582.564 q^{79} +(-713.555 - 53.2909i) q^{80} +(619.564 - 573.928i) q^{82} +636.408 q^{83} +(-78.7158 - 1002.88i) q^{85} +(-514.710 + 476.798i) q^{86} +(-617.766 + 490.175i) q^{88} -759.913 q^{89} +614.869i q^{91} +(800.051 + 61.2730i) q^{92} +(-622.435 - 671.928i) q^{94} +(0.416261 + 5.30340i) q^{95} +1279.63i q^{97} +(1134.03 - 1050.50i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} - 48 q^{10} - 28 q^{14} - 168 q^{16} + 196 q^{20} - 24 q^{25} - 200 q^{26} - 112 q^{31} + 408 q^{34} + 672 q^{40} - 232 q^{41} - 920 q^{44} + 212 q^{46} - 200 q^{49} + 648 q^{50} + 392 q^{55}+ \cdots + 1064 q^{95}+O(q^{100}) $ 16 * q + 4 * q^4 - 48 * q^10 - 28 * q^14 - 168 * q^16 + 196 * q^20 - 24 * q^25 - 200 * q^26 - 112 * q^31 + 408 * q^34 + 672 * q^40 - 232 * q^41 - 920 * q^44 + 212 * q^46 - 200 * q^49 + 648 * q^50 + 392 * q^55 - 1120 * q^56 - 2912 * q^64 + 600 * q^65 + 1532 * q^70 - 2096 * q^71 - 4224 * q^74 - 3000 * q^76 + 2992 * q^79 - 2280 * q^80 - 3076 * q^86 + 208 * q^89 - 7036 * q^94 + 1064 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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 $

$2$	−2.07496	+	1.92212i	−0.733608	+	0.679572i
$2$	−2.07496	+	1.92212i	−0.733608	+	0.679572i
$3$		0			0
$3$		0			0
$4$	0.610901	−	7.97664i	0.0763627	−	0.997080i
$5$	11.1461	−	0.874848i	0.996934	−	0.0782488i
$5$	11.1461	−	0.874848i	0.996934	−	0.0782488i
$6$		0			0
$7$			29.8250i			1.61040i	0.593005	+	0.805199i	$0.297941\pi$
$7$			29.8250i			1.61040i	−0.593005	+	0.805199i	$0.702059\pi$
$8$	14.0645	+	17.7254i	0.621568	+	0.783360i
$9$		0			0
$10$	−21.4460	+	23.2393i	−0.678183	+	0.734893i
$11$			34.8520i			0.955297i	0.878551	+	0.477648i	$0.158511\pi$
$11$			34.8520i			0.955297i	−0.878551	+	0.477648i	$0.841489\pi$
$12$		0			0
$13$	20.6159			0.439833			0.219916	−	0.975519i	$-0.429422\pi$
$13$	20.6159			0.439833			0.219916	+	0.975519i	$0.429422\pi$
$14$	−57.3272	−	61.8856i	−1.09438	−	1.18140i
$15$		0			0
$16$	−63.2536	−	9.74588i	−0.988337	−	0.152279i
$17$		−	89.9765i		−	1.28368i	−0.766840	−	0.641839i	$-0.778172\pi$
$17$		−	89.9765i		−	1.28368i	0.766840	−	0.641839i	$-0.221828\pi$
$18$		0			0
$19$			0.475810i			0.00574517i	0.999996	+	0.00287259i	$0.000914374\pi$
$19$			0.475810i			0.00574517i	−0.999996	+	0.00287259i	$0.999086\pi$
$20$	−0.169205	−	89.4426i	−0.00189177	−	0.999998i
$21$		0			0
$22$	−66.9897	−	72.3164i	−0.649193	−	0.700814i
$23$			100.299i			0.909298i	0.890671	+	0.454649i	$0.150235\pi$
$23$			100.299i			0.909298i	−0.890671	+	0.454649i	$0.849765\pi$
$24$		0			0
$25$	123.469	−	19.5022i	0.987754	−	0.156018i
$26$	−42.7771	+	39.6263i	−0.322665	+	0.298898i
$27$		0			0
$28$	237.903	+	18.2201i	1.60570	+	0.122974i
$29$			132.077i			0.845729i	0.906193	+	0.422864i	$0.138975\pi$
$29$			132.077i			0.845729i	−0.906193	+	0.422864i	$0.861025\pi$
$30$		0			0
$31$	−137.250			−0.795186			−0.397593	−	0.917562i	$-0.630154\pi$
$31$	−137.250			−0.795186			−0.397593	+	0.917562i	$0.630154\pi$
$32$	149.981	−	101.359i	0.828538	−	0.559933i
$33$		0			0
$34$	172.946	+	186.697i	0.872351	+	0.941716i
$35$	26.0923	+	332.431i	0.126012	+	1.60546i
$36$		0			0
$37$	57.1057			0.253733			0.126866	−	0.991920i	$-0.459508\pi$
$37$	57.1057			0.253733			0.126866	+	0.991920i	$0.459508\pi$
$38$	−0.914564	−	0.987285i	−0.00390426	−	0.00421471i
$39$		0			0
$40$	172.271	+	185.264i	0.680959	+	0.732322i
$41$	−298.591			−1.13737			−0.568684	−	0.822556i	$-0.692547\pi$
$41$	−298.591			−1.13737			−0.568684	+	0.822556i	$0.692547\pi$
$42$		0			0
$43$	248.058			0.879733			0.439866	−	0.898063i	$-0.355026\pi$
$43$	248.058			0.879733			0.439866	+	0.898063i	$0.355026\pi$
$44$	278.002	+	21.2911i	0.952507	+	0.0729490i
$45$		0			0
$46$	−192.787	−	208.117i	−0.617934	−	0.667068i
$47$			323.827i			1.00500i	0.864577	+	0.502501i	$0.167587\pi$
$47$			323.827i			1.00500i	−0.864577	+	0.502501i	$0.832413\pi$
$48$		0			0
$49$	−546.530			−1.59338
$50$	−218.708	+	277.789i	−0.618600	+	0.785706i
$51$		0			0
$52$	12.5943	−	164.446i	0.0335868	−	0.438548i
$53$	55.4295			0.143657			0.0718285	−	0.997417i	$-0.477117\pi$
$53$	55.4295			0.143657			0.0718285	+	0.997417i	$0.477117\pi$
$54$		0			0
$55$	30.4902	+	388.462i	0.0747508	+	0.952368i
$56$	−528.660	+	419.473i	−1.26152	+	1.00097i
$57$		0			0
$58$	−253.868	−	274.055i	−0.574734	−	0.620434i
$59$		−	167.879i		−	0.370440i	−0.982697	−	0.185220i	$-0.940700\pi$
$59$		−	167.879i		−	0.370440i	0.982697	−	0.185220i	$-0.0592998\pi$
$60$		0			0
$61$			164.687i			0.345672i	0.984951	+	0.172836i	$0.0552930\pi$
$61$			164.687i			0.345672i	−0.984951	+	0.172836i	$0.944707\pi$
$62$	284.787	−	263.810i	0.583355	−	0.540386i
$63$		0			0
$64$	−116.381	+	498.597i	−0.227307	+	0.973823i
$65$	229.786	−	18.0358i	0.438484	−	0.0344164i
$66$		0			0
$67$	−666.565			−1.21543			−0.607715	−	0.794155i	$-0.707914\pi$
$67$	−666.565			−1.21543			−0.607715	+	0.794155i	$0.707914\pi$
$68$	−717.710	−	54.9668i	−1.27993	−	0.0980250i
$69$		0			0
$70$	−693.113	−	639.628i	−1.18347	−	1.09214i
$71$	−384.334			−0.642424			−0.321212	−	0.947007i	$-0.604090\pi$
$71$	−384.334			−0.642424			−0.321212	+	0.947007i	$0.604090\pi$
$72$		0			0
$73$			749.119i			1.20107i	0.799600	+	0.600533i	$0.205045\pi$
$73$			749.119i			1.20107i	−0.799600	+	0.600533i	$0.794955\pi$
$74$	−118.492	+	109.764i	−0.186141	+	0.172430i
$75$		0			0
$76$	3.79536	+	0.290673i	0.00572840	+	0.000438717i
$77$	−1039.46			−1.53841
$78$		0			0
$79$	582.564			0.829666			0.414833	−	0.909898i	$-0.363840\pi$
$79$	582.564			0.829666			0.414833	+	0.909898i	$0.363840\pi$
$80$	−713.555	−	53.2909i	−0.997223	−	0.0744763i
$81$		0			0
$82$	619.564	−	573.928i	0.834383	−	0.772924i
$83$	636.408			0.841625			0.420813	−	0.907148i	$-0.361745\pi$
$83$	636.408			0.841625			0.420813	+	0.907148i	$0.361745\pi$
$84$		0			0
$85$	−78.7158	−	1002.88i	−0.100446	−	1.27974i
$86$	−514.710	+	476.798i	−0.645379	+	0.597842i
$87$		0			0
$88$	−617.766	+	490.175i	−0.748341	+	0.593782i
$89$	−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
$92$	800.051	+	61.2730i	0.906643	+	0.0694364i
$93$		0			0
$94$	−622.435	−	671.928i	−0.682971	−	0.737278i
$95$	0.416261	+	5.30340i	0.000449553	+	0.00572756i
$96$		0			0
$97$			1279.63i			1.33945i	0.742611	+	0.669723i	$0.233587\pi$
$97$			1279.63i			1.33945i	−0.742611	+	0.669723i	$0.766413\pi$
$98$	1134.03	−	1050.50i	1.16892	−	1.08282i
$99$		0			0
$100$	−80.1346	−	996.784i	−0.0801346	−	0.996784i
$101$		−	806.217i		−	0.794273i	−0.917760	−	0.397137i	$-0.870004\pi$
$101$		−	806.217i		−	0.794273i	0.917760	−	0.397137i	$-0.129996\pi$
$102$		0			0
$103$			497.704i			0.476119i	0.971251	+	0.238059i	$0.0765113\pi$
$103$			497.704i			0.476119i	−0.971251	+	0.238059i	$0.923489\pi$
$104$	289.952	+	365.426i	0.273386	+	0.344547i
$105$		0			0
$106$	−115.014	+	106.542i	−0.105388	+	0.0976254i
$107$	111.714			0.100933			0.0504666	−	0.998726i	$-0.483929\pi$
$107$	111.714			0.100933			0.0504666	+	0.998726i	$0.483929\pi$
$108$		0			0
$109$			1098.19i			0.965022i	0.875890	+	0.482511i	$0.160275\pi$
$109$			1098.19i			0.965022i	−0.875890	+	0.482511i	$0.839725\pi$
$110$	−809.937	−	747.437i	−0.702041	−	0.647866i
$111$		0			0
$112$	290.671	−	1886.54i	0.245230	−	1.59162i
$113$			2118.96i			1.76403i	0.471221	+	0.882015i	$0.343813\pi$
$113$			2118.96i			1.76403i	−0.471221	+	0.882015i	$0.656187\pi$
$114$		0			0
$115$	87.7466	+	1117.94i	0.0711514	+	0.906510i
$116$	1053.53	+	80.6862i	0.843259	+	0.0645821i
$117$		0			0
$118$	322.683	+	348.341i	0.251741	+	0.271758i
$119$	2683.55			2.06723
$120$		0			0
$121$	116.341			0.0874084
$122$	−316.548	−	341.718i	−0.234909	−	0.253588i
$123$		0			0
$124$	−83.8460	+	1094.79i	−0.0607225	+	0.792864i
$125$	1359.13	−	325.390i	0.972517	−	0.232830i
$126$		0			0
$127$		−	567.970i		−	0.396844i	−0.980117	−	0.198422i	$-0.936418\pi$
$127$		−	567.970i		−	0.396844i	0.980117	−	0.198422i	$-0.0635816\pi$
$128$	−716.879	−	1258.27i	−0.495029	−	0.868876i
$129$		0			0
$130$	−442.130	+	479.100i	−0.298287	+	0.323230i
$131$			2238.84i			1.49319i	0.665278	+	0.746596i	$0.268313\pi$
$131$			2238.84i			1.49319i	−0.665278	+	0.746596i	$0.731687\pi$
$132$		0			0
$133$	−14.1910			−0.00925201
$134$	1383.09	−	1281.22i	0.891650	−	0.825973i
$135$		0			0
$136$	1594.87	−	1265.47i	1.00558	−	0.797892i
$137$		−	1428.64i		−	0.890925i	−0.895301	−	0.445462i	$-0.853039\pi$
$137$		−	1428.64i		−	0.890925i	0.895301	−	0.445462i	$-0.146961\pi$
$138$		0			0
$139$		−	1467.79i		−	0.895659i	−0.894119	−	0.447829i	$-0.852197\pi$
$139$		−	1467.79i		−	0.895659i	0.894119	−	0.447829i	$-0.147803\pi$
$140$	2667.62	−	5.04655i	1.61039	−	0.00304651i
$141$		0			0
$142$	797.478	−	738.737i	0.471288	−	0.436574i
$143$			718.505i			0.420171i
$144$		0			0
$145$	115.548	+	1472.14i	0.0661772	+	0.843136i
$146$	−1439.90	−	1554.39i	−0.816211	−	0.881112i
$147$		0			0
$148$	34.8860	−	455.512i	0.0193757	−	0.252992i
$149$		−	2881.15i		−	1.58411i	−0.610449	−	0.792056i	$-0.709011\pi$
$149$		−	2881.15i		−	1.58411i	0.610449	−	0.792056i	$-0.290989\pi$
$150$		0			0
$151$	−949.291			−0.511604			−0.255802	−	0.966729i	$-0.582340\pi$
$151$	−949.291			−0.511604			−0.255802	+	0.966729i	$0.582340\pi$
$152$	−8.43393	+	6.69202i	−0.00450054	+	0.00357101i
$153$		0			0
$154$	2156.83	−	1997.97i	1.12859	−	1.04546i
$155$	−1529.79	+	120.073i	−0.792748	+	0.0622223i
$156$		0			0
$157$	3159.30			1.60599			0.802993	−	0.595988i	$-0.203239\pi$
$157$	3159.30			1.60599			0.802993	+	0.595988i	$0.203239\pi$
$158$	−1208.80	+	1119.76i	−0.608650	+	0.563818i
$159$		0			0
$160$	1583.03	−	1260.96i	0.782183	−	0.623049i
$161$	−2991.42			−1.46433
$162$		0			0
$163$	−1361.75			−0.654360			−0.327180	−	0.944962i	$-0.606098\pi$
$163$	−1361.75			−0.654360			−0.327180	+	0.944962i	$0.606098\pi$
$164$	−182.410	+	2381.75i	−0.0868525	+	1.13405i
$165$		0			0
$166$	−1320.52	+	1223.25i	−0.617423	+	0.571945i
$167$			641.323i			0.297168i	0.988900	+	0.148584i	$0.0474716\pi$
$167$			641.323i			0.297168i	−0.988900	+	0.148584i	$0.952528\pi$
$168$		0			0
$169$	−1771.98			−0.806547
$170$	2091.00	+	1929.64i	0.943365	+	0.870568i
$171$		0			0
$172$	151.539	−	1978.67i	0.0671787	−	0.877164i
$173$	57.9969			0.0254880			0.0127440	−	0.999919i	$-0.495943\pi$
$173$	57.9969			0.0254880			0.0127440	+	0.999919i	$0.495943\pi$
$174$		0			0
$175$	581.653	+	3682.47i	0.251251	+	1.59068i
$176$	339.663	−	2204.51i	0.145472	−	0.944155i
$177$		0			0
$178$	1576.79	−	1460.65i	0.663962	−	0.615056i
$179$		−	1608.75i		−	0.671753i	−0.941906	−	0.335876i	$-0.890968\pi$
$179$		−	1608.75i		−	0.671753i	0.941906	−	0.335876i	$-0.109032\pi$
$180$		0			0
$181$		−	2665.60i		−	1.09465i	−0.836919	−	0.547327i	$-0.815646\pi$
$181$		−	2665.60i		−	1.09465i	0.836919	−	0.547327i	$-0.184354\pi$
$182$	−1181.85	−	1275.83i	−0.481345	−	0.519619i
$183$		0			0
$184$	−1777.85	+	1410.66i	−0.712308	+	0.565190i
$185$	636.504	−	49.9588i	0.252955	−	0.0198543i
$186$		0			0
$187$	3135.86			1.22629
$188$	2583.05	+	197.827i	1.00207	+	0.0767446i
$189$		0			0
$190$	−11.0575	−	10.2042i	−0.00422209	−	0.00389628i
$191$	2879.60			1.09089			0.545446	−	0.838146i	$-0.316360\pi$
$191$	2879.60			1.09089			0.545446	+	0.838146i	$0.316360\pi$
$192$		0			0
$193$		−	2401.35i		−	0.895611i	−0.894131	−	0.447805i	$-0.852206\pi$
$193$		−	2401.35i		−	0.895611i	0.894131	−	0.447805i	$-0.147794\pi$
$194$	−2459.60	−	2655.17i	−0.910251	−	0.982629i
$195$		0			0
$196$	−333.876	+	4359.47i	−0.121675	+	1.58873i
$197$	4454.03			1.61085			0.805423	−	0.592700i	$-0.201938\pi$
$197$	4454.03			1.61085			0.805423	+	0.592700i	$0.201938\pi$
$198$		0			0
$199$	4903.81			1.74684			0.873422	−	0.486964i	$-0.161896\pi$
$199$	4903.81			1.74684			0.873422	+	0.486964i	$0.161896\pi$
$200$	2082.22	+	1914.26i	0.736174	+	0.676792i
$201$		0			0
$202$	1549.65	+	1672.87i	0.539766	+	0.582685i
$203$	−3939.20			−1.36196
$204$		0			0
$205$	−3328.11	+	261.222i	−1.13388	+	0.0889977i
$206$	−956.647	−	1032.72i	−0.323557	−	0.349285i
$207$		0			0
$208$	−1304.03	−	200.920i	−0.434703	−	0.0669774i
$209$	−16.5829			−0.00548834
$210$		0			0
$211$		−	1226.59i		−	0.400200i	−0.979776	−	0.200100i	$-0.935873\pi$
$211$		−	1226.59i		−	0.400200i	0.979776	−	0.200100i	$-0.0641266\pi$
$212$	33.8620	−	442.141i	0.0109700	−	0.143238i
$213$		0			0
$214$	−231.803	+	214.729i	−0.0740454	+	0.0685914i
$215$	2764.87	−	217.013i	0.877035	−	0.0688380i
$216$		0			0
$217$		−	4093.47i		−	1.28057i
$218$	−2110.85	−	2278.69i	−0.655802	−	0.707948i
$219$		0			0
$220$	3117.25	−	5.89714i	0.955295	−	0.00180721i
$221$		−	1854.95i		−	0.564603i
$222$		0			0
$223$		−	1542.77i		−	0.463281i	−0.972801	−	0.231641i	$-0.925591\pi$
$223$		−	1542.77i		−	0.463281i	0.972801	−	0.231641i	$-0.0744093\pi$
$224$	3023.02	+	4473.19i	0.901716	+	1.33428i
$225$		0			0
$226$	−4072.91	−	4396.76i	−1.19879	−	1.29411i
$227$	3851.34			1.12609			0.563045	−	0.826426i	$-0.309630\pi$
$227$	3851.34			1.12609			0.563045	+	0.826426i	$0.309630\pi$
$228$		0			0
$229$		−	5232.61i		−	1.50996i	−0.655748	−	0.754980i	$-0.727647\pi$
$229$		−	5232.61i		−	1.50996i	0.655748	−	0.754980i	$-0.272353\pi$
$230$	−2330.89	−	2151.02i	−0.668236	−	0.616671i
$231$		0			0
$232$	−2341.13	+	1857.60i	−0.662510	+	0.525678i
$233$			181.419i			0.0510094i	0.999675	+	0.0255047i	$0.00811927\pi$
$233$			181.419i			0.0510094i	−0.999675	+	0.0255047i	$0.991881\pi$
$234$		0			0
$235$	283.300	+	3609.40i	0.0786402	+	1.00192i
$236$	−1339.11	−	102.557i	−0.369358	−	0.0282878i
$237$		0			0
$238$	−5568.25	+	5158.10i	−1.51654	+	1.40483i
$239$	−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	$0.546511\pi$
$242$	−241.402	+	223.621i	−0.0641235	+	0.0594003i
$243$		0			0
$244$	1313.65	+	100.607i	0.344662	+	0.0263964i
$245$	−6091.65	+	478.130i	−1.58850	+	0.124680i
$246$		0			0
$247$			9.80925i			0.00252691i
$248$	−1930.34	−	2432.81i	−0.494262	−	0.622917i
$249$		0			0
$250$	−2194.71	+	3287.59i	−0.555222	+	0.831702i
$251$			5380.02i			1.35292i	0.736478	+	0.676461i	$0.236487\pi$
$251$			5380.02i			1.35292i	−0.736478	+	0.676461i	$0.763513\pi$
$252$		0			0
$253$	−3495.63			−0.868649
$254$	1091.71	+	1178.51i	0.269684	+	0.291128i
$255$		0			0
$256$	3906.04	+	1232.92i	0.953622	+	0.301007i
$257$		−	1377.98i		−	0.334458i	−0.985918	−	0.167229i	$-0.946518\pi$
$257$		−	1377.98i		−	0.334458i	0.985918	−	0.167229i	$-0.0534819\pi$
$258$		0			0
$259$			1703.18i			0.408611i
$260$	−3.48832	−	1843.94i	−0.000832064	−	0.439832i
$261$		0			0
$262$	−4303.32	−	4645.49i	−1.01473	−	1.09542i
$263$			411.340i			0.0964422i	0.998837	+	0.0482211i	$0.0153552\pi$
$263$			411.340i			0.0964422i	−0.998837	+	0.0482211i	$0.984645\pi$
$264$		0			0
$265$	617.820	−	48.4924i	0.143217	−	0.0112410i
$266$	29.4458	−	27.2769i	0.00678735	−	0.00628741i
$267$		0			0
$268$	−407.205	+	5316.95i	−0.0928135	+	1.21188i
$269$		−	407.204i		−	0.0922961i	−0.998935	−	0.0461481i	$-0.985305\pi$
$269$		−	407.204i		−	0.0922961i	0.998935	−	0.0461481i	$-0.0146946\pi$
$270$		0			0
$271$	−1329.04			−0.297909			−0.148954	−	0.988844i	$-0.547591\pi$
$271$	−1329.04			−0.297909			−0.148954	+	0.988844i	$0.547591\pi$
$272$	−876.900	+	5691.34i	−0.195478	+	1.26871i
$273$		0			0
$274$	2746.01	+	2964.36i	0.605448	+	0.653590i
$275$	679.691	+	4303.15i	0.149043	+	0.943598i
$276$		0			0
$277$	−4411.34			−0.956866			−0.478433	−	0.878124i	$-0.658795\pi$
$277$	−4411.34			−0.956866			−0.478433	+	0.878124i	$0.658795\pi$
$278$	2821.28	+	3045.61i	0.608665	+	0.657063i
$279$		0			0
$280$	−5525.51	+	5137.97i	−1.17933	+	1.09661i
$281$	−5134.23			−1.08997			−0.544986	−	0.838445i	$-0.683465\pi$
$281$	−5134.23			−1.08997			−0.544986	+	0.838445i	$0.683465\pi$
$282$		0			0
$283$	−3093.54			−0.649794			−0.324897	−	0.945749i	$-0.605330\pi$
$283$	−3093.54			−0.649794			−0.324897	+	0.945749i	$0.605330\pi$
$284$	−234.790	+	3065.70i	−0.0490572	+	0.640548i
$285$		0			0
$286$	−1381.05	−	1490.87i	−0.285536	−	0.308241i
$287$		−	8905.47i		−	1.83161i
$288$		0			0
$289$	−3182.77			−0.647827
$290$	−3069.39	−	2832.53i	−0.621520	−	0.573559i
$291$		0			0
$292$	5975.45	+	457.638i	1.19756	+	0.0917166i
$293$	671.319			0.133853			0.0669264	−	0.997758i	$-0.478681\pi$
$293$	671.319			0.133853			0.0669264	+	0.997758i	$0.478681\pi$
$294$		0			0
$295$	−146.868	−	1871.19i	−0.0289865	−	0.369304i
$296$	803.162	+	1012.22i	0.157712	+	0.198764i
$297$		0			0
$298$	5537.91	+	5978.26i	1.07652	+	1.16212i
$299$			2067.76i			0.399939i
$300$		0			0
$301$			7398.33i			1.41672i
$302$	1969.74	−	1824.65i	0.375317	−	0.347672i
$303$		0			0
$304$	4.63719	−	30.0967i	0.000874871	−	0.00567817i
$305$	144.076	+	1835.61i	0.0270484	+	0.344612i
$306$		0			0
$307$	5810.78			1.08026			0.540128	−	0.841583i	$-0.318376\pi$
$307$	5810.78			1.08026			0.540128	+	0.841583i	$0.318376\pi$
$308$	−635.007	+	8291.39i	−0.117477	+	1.53392i
$309$		0			0
$310$	2943.46	−	3189.59i	0.539282	−	0.584376i
$311$	7223.30			1.31703			0.658514	−	0.752568i	$-0.271185\pi$
$311$	7223.30			1.31703			0.658514	+	0.752568i	$0.271185\pi$
$312$		0			0
$313$			1804.40i			0.325849i	0.986638	+	0.162925i	$0.0520928\pi$
$313$			1804.40i			0.325849i	−0.986638	+	0.162925i	$0.947907\pi$
$314$	−6555.42	+	6072.56i	−1.17817	+	1.09138i
$315$		0			0
$316$	355.889	−	4646.91i	0.0633555	−	0.827244i
$317$	−1593.07			−0.282259			−0.141129	−	0.989991i	$-0.545073\pi$
$317$	−1593.07			−0.282259			−0.141129	+	0.989991i	$0.545073\pi$
$318$		0			0
$319$	−4603.15			−0.807922
$320$	−860.994	+	5659.21i	−0.150409	+	0.988624i
$321$		0			0
$322$	6207.08	−	5749.88i	1.07425	−	0.995119i
$323$	42.8117			0.00737495
$324$		0			0
$325$	2545.43	−	402.056i	0.434446	−	0.0686217i
$326$	2825.58	−	2617.45i	0.480044	−	0.444685i
$327$		0			0
$328$	−4199.53	−	5292.65i	−0.706951	−	0.890969i
$329$	−9658.14			−1.61845
$330$		0			0
$331$			6213.17i			1.03174i	0.856666	+	0.515871i	$0.172532\pi$
$331$			6213.17i			1.03174i	−0.856666	+	0.515871i	$0.827468\pi$
$332$	388.783	−	5076.40i	0.0642688	−	0.839168i
$333$		0			0
$334$	−1232.70	−	1330.72i	−0.201947	−	0.218005i
$335$	−7429.57	+	583.143i	−1.21170	+	0.0951059i
$336$		0			0
$337$		−	11379.1i		−	1.83935i	−0.392686	−	0.919673i	$-0.628454\pi$
$337$		−	11379.1i		−	1.83935i	0.392686	−	0.919673i	$-0.371546\pi$
$338$	3676.79	−	3405.97i	0.591690	−	0.548107i
$339$		0			0
$340$	−8047.73	+	15.2245i	−1.28367	+	0.00242843i
$341$		−	4783.42i		−	0.759638i
$342$		0			0
$343$		−	6070.27i		−	0.955579i
$344$	3488.81	+	4396.93i	0.546814	+	0.689148i
$345$		0			0
$346$	−120.341	+	111.477i	−0.0186982	+	0.0173209i
$347$	−2528.79			−0.391217			−0.195609	−	0.980682i	$-0.562668\pi$
$347$	−2528.79			−0.391217			−0.195609	+	0.980682i	$0.562668\pi$
$348$		0			0
$349$			110.562i			0.0169577i	0.999964	+	0.00847885i	$0.00269893\pi$
$349$			110.562i			0.0169577i	−0.999964	+	0.00847885i	$0.997301\pi$
$350$	−8285.06	−	6522.96i	−1.26530	−	0.996191i
$351$		0			0
$352$	3532.55	+	5227.14i	0.534903	+	0.791499i
$353$		−	7118.00i		−	1.07324i	−0.843825	−	0.536619i	$-0.819701\pi$
$353$		−	7118.00i		−	1.07324i	0.843825	−	0.536619i	$-0.180299\pi$
$354$		0			0
$355$	−4283.81	+	336.234i	−0.640454	+	0.0502689i
$356$	−464.232	+	6061.56i	−0.0691131	+	0.902421i
$357$		0			0
$358$	3092.22	+	3338.09i	0.456505	+	0.492804i
$359$	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
$362$	5123.60	+	5531.00i	0.743896	+	0.803047i
$363$		0			0
$364$	4904.59	+	375.624i	0.706237	+	0.0540881i
$365$	655.365	+	8349.73i	0.0939819	+	1.19738i
$366$		0			0
$367$		−	11007.8i		−	1.56567i	−0.622230	−	0.782835i	$-0.713773\pi$
$367$		−	11007.8i		−	1.56567i	0.622230	−	0.782835i	$-0.286227\pi$
$368$	977.505	−	6344.29i	0.138467	−	0.898693i
$369$		0			0
$370$	−1224.69	+	1327.10i	−0.172077	+	0.186466i
$371$			1653.18i			0.231345i
$372$		0			0
$373$	12872.3			1.78687			0.893436	−	0.449190i	$-0.148287\pi$
$373$	12872.3			1.78687			0.893436	+	0.449190i	$0.148287\pi$
$374$	−6506.77	+	6027.50i	−0.899618	+	0.833354i
$375$		0			0
$376$	−5739.98	+	4554.46i	−0.787278	+	0.624677i
$377$			2722.89i			0.371979i
$378$		0			0
$379$		−	6010.29i		−	0.814586i	−0.913298	−	0.407293i	$-0.866473\pi$
$379$		−	6010.29i		−	0.814586i	0.913298	−	0.407293i	$-0.133527\pi$
$380$	42.5577	−	0.0805096i	0.00574516	−	1.08686e-5i
$381$		0			0
$382$	−5975.04	+	5534.93i	−0.800287	+	0.741340i
$383$			4012.72i			0.535354i	0.963509	+	0.267677i	$0.0862559\pi$
$383$			4012.72i			0.535354i	−0.963509	+	0.267677i	$0.913744\pi$
$384$		0			0
$385$	−11585.9	+	909.369i	−1.53369	+	0.120379i
$386$	4615.68	+	4982.70i	0.608632	+	0.657028i
$387$		0			0
$388$	10207.1	+	781.725i	1.33554	+	0.102284i
$389$		−	9488.02i		−	1.23666i	−0.785918	−	0.618331i	$-0.787809\pi$
$389$		−	9488.02i		−	1.23666i	0.785918	−	0.618331i	$-0.212191\pi$
$390$		0			0
$391$	9024.58			1.16724
$392$	−7686.65	−	9687.47i	−0.990394	−	1.24819i
$393$		0			0
$394$	−9241.93	+	8561.19i	−1.18173	+	1.09469i
$395$	6493.30	−	509.655i	0.827122	−	0.0649204i
$396$		0			0
$397$	4950.44			0.625832			0.312916	−	0.949781i	$-0.398694\pi$
$397$	4950.44			0.625832			0.312916	+	0.949781i	$0.398694\pi$
$398$	−10175.2	+	9425.72i	−1.28150	+	1.18711i
$399$		0			0
$400$	−7999.94	+	30.2683i	−0.999993	+	0.00378354i
$401$	8799.56			1.09583			0.547917	−	0.836533i	$-0.315421\pi$
$401$	8799.56			1.09583			0.547917	+	0.836533i	$0.315421\pi$
$402$		0			0
$403$	−2829.53			−0.349749
$404$	−6430.90	−	492.519i	−0.791954	−	0.0606528i
$405$		0			0
$406$	8173.68	−	7571.62i	0.999145	−	0.925550i
$407$			1990.25i			0.242390i
$408$		0			0
$409$	7179.75			0.868009			0.434005	−	0.900911i	$-0.357100\pi$
$409$	7179.75			0.868009			0.434005	+	0.900911i	$0.357100\pi$
$410$	6403.60	−	6939.06i	0.771344	−	0.835843i
$411$		0			0
$412$	3970.01	+	304.048i	0.474729	+	0.0363577i
$413$	5006.98			0.596556
$414$		0			0
$415$	7093.45	−	556.761i	0.839045	−	0.0658562i
$416$	3092.00	−	2089.60i	0.364418	−	0.246277i
$417$		0			0
$418$	34.4088	−	31.8744i	0.00402629	−	0.00372973i
$419$		−	13557.2i		−	1.58070i	−0.612657	−	0.790349i	$-0.709899\pi$
$419$		−	13557.2i		−	1.58070i	0.612657	−	0.790349i	$-0.290101\pi$
$420$		0			0
$421$			7428.36i			0.859943i	0.902843	+	0.429971i	$0.141476\pi$
$421$			7428.36i			0.859943i	−0.902843	+	0.429971i	$0.858524\pi$
$422$	2357.66	+	2545.13i	0.271965	+	0.293590i
$423$		0			0
$424$	779.587	+	982.511i	0.0892926	+	0.112535i
$425$	−1754.74	−	11109.3i	−0.200276	−	1.26796i
$426$		0			0
$427$	−4911.78			−0.556669
$428$	68.2465	−	891.106i	0.00770752	−	0.100638i
$429$		0			0
$430$	−5319.86	+	5764.71i	−0.596620	+	0.646509i
$431$	1591.77			0.177895			0.0889475	−	0.996036i	$-0.471650\pi$
$431$	1591.77			0.177895			0.0889475	+	0.996036i	$0.471650\pi$
$432$		0			0
$433$			10811.6i			1.19994i	0.800023	+	0.599970i	$0.204821\pi$
$433$			10811.6i			1.19994i	−0.800023	+	0.599970i	$0.795179\pi$
$434$	7868.14	+	8493.77i	0.870237	+	0.939434i
$435$		0			0
$436$	8759.85	+	670.885i	0.962204	+	0.0736916i
$437$	−47.7234			−0.00522407
$438$		0			0
$439$	−4891.74			−0.531823			−0.265911	−	0.963997i	$-0.585673\pi$
$439$	−4891.74			−0.531823			−0.265911	+	0.963997i	$0.585673\pi$
$440$	−6456.83	+	6003.97i	−0.699584	+	0.650518i
$441$		0			0
$442$	3565.43	+	3848.94i	0.383689	+	0.414197i
$443$	2116.86			0.227032			0.113516	−	0.993536i	$-0.463789\pi$
$443$	2116.86			0.227032			0.113516	+	0.993536i	$0.463789\pi$
$444$		0			0
$445$	−8470.04	+	664.809i	−0.902289	+	0.0708201i
$446$	2965.40	+	3201.19i	0.314833	+	0.339867i
$447$		0			0
$448$	−14870.7	−	3471.06i	−1.56824	−	0.366054i
$449$	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
$452$	16902.2	+	1294.48i	1.75888	+	0.134706i
$453$		0			0
$454$	−7991.37	+	7402.74i	−0.826109	+	0.765260i
$455$	537.917	+	6853.37i	0.0554240	+	0.706134i
$456$		0			0
$457$			3969.19i			0.406282i	0.979150	+	0.203141i	$0.0651150\pi$
$457$			3969.19i			0.406282i	−0.979150	+	0.203141i	$0.934885\pi$
$458$	10057.7	+	10857.4i	1.02613	+	1.10772i
$459$		0			0
$460$	8971.02	−	16.9712i	0.909296	−	0.00172019i
$461$			7068.99i			0.714177i	0.934071	+	0.357089i	$0.116231\pi$
$461$			7068.99i			0.714177i	−0.934071	+	0.357089i	$0.883769\pi$
$462$		0			0
$463$			178.581i			0.0179251i	0.999960	+	0.00896257i	$0.00285291\pi$
$463$			178.581i			0.0179251i	−0.999960	+	0.00896257i	$0.997147\pi$
$464$	1287.21	−	8354.36i	0.128787	−	0.835865i
$465$		0			0
$466$	−348.710	−	376.438i	−0.0346646	−	0.0374209i
$467$	−11576.2			−1.14707			−0.573536	−	0.819180i	$-0.694429\pi$
$467$	−11576.2			−1.14707			−0.573536	+	0.819180i	$0.694429\pi$
$468$		0			0
$469$		−	19880.3i		−	1.95733i
$470$	−7525.54	−	6944.81i	−0.738568	−	0.681575i
$471$		0			0
$472$	2975.72	−	2361.13i	0.290188	−	0.230254i
$473$			8645.31i			0.840406i
$474$		0			0
$475$	9.27935	+	58.7479i	0.000896349	+	0.00567482i
$476$	1639.38	−	21405.7i	0.157859	−	2.06119i
$477$		0			0
$478$	5203.48	−	4820.20i	0.497911	−	0.461236i
$479$	−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
$482$	2260.58	−	2094.07i	0.213624	−	0.197889i
$483$		0			0
$484$	71.0726	−	928.007i	0.00667474	−	0.0871532i
$485$	1119.48	+	14262.8i	0.104810	+	1.33534i
$486$		0			0
$487$			13309.0i			1.23838i	0.785243	+	0.619188i	$0.212538\pi$
$487$			13309.0i			1.23838i	−0.785243	+	0.619188i	$0.787462\pi$
$488$	−2919.14	+	2316.23i	−0.270785	+	0.214858i
$489$		0			0
$490$	11720.9	−	12701.0i	1.08060	−	1.17096i
$491$			216.689i			0.0199166i	0.999950	+	0.00995830i	$0.00316988\pi$
$491$			216.689i			0.0199166i	−0.999950	+	0.00995830i	$0.996830\pi$
$492$		0			0
$493$	11883.9			1.08564
$494$	−18.8546	−	20.3538i	−0.00171722	−	0.00185377i
$495$		0			0
$496$	8681.53	+	1337.62i	0.785912	+	0.121090i
$497$		−	11462.8i		−	1.03456i
$498$		0			0
$499$			10800.4i			0.968921i	0.874813	+	0.484460i	$0.160984\pi$
$499$			10800.4i			0.968921i	−0.874813	+	0.484460i	$0.839016\pi$
$500$	−1765.22	−	11040.1i	−0.157886	−	0.987457i
$501$		0			0
$502$	−10341.0	−	11163.3i	−0.919409	−	0.992516i
$503$		−	16697.6i		−	1.48013i	−0.672533	−	0.740067i	$-0.734794\pi$
$503$		−	16697.6i		−	1.48013i	0.672533	−	0.740067i	$-0.265206\pi$
$504$		0			0
$505$	−705.317	−	8986.14i	−0.0621509	−	0.791838i
$506$	7253.28	−	6719.02i	0.637248	−	0.590310i
$507$		0			0
$508$	−4530.49	−	346.974i	−0.395685	−	0.0303041i
$509$		−	13066.1i		−	1.13781i	−0.822402	−	0.568906i	$-0.807367\pi$
$509$		−	13066.1i		−	1.13781i	0.822402	−	0.568906i	$-0.192633\pi$
$510$		0			0
$511$	−22342.5			−1.93419
$512$	−10474.7	+	4949.61i	−0.904141	+	0.427234i
$513$		0			0
$514$	2648.64	+	2859.24i	0.227289	+	0.245361i
$515$	435.415	+	5547.44i	0.0372557	+	0.474659i
$516$		0			0
$517$	−11286.0			−0.960075
$518$	−3273.71	−	3534.02i	−0.277681	−	0.299760i
$519$		0			0
$520$	3551.51	+	3819.39i	0.299508	+	0.322099i
$521$	269.920			0.0226975			0.0113488	−	0.999936i	$-0.496387\pi$
$521$	269.920			0.0226975			0.0113488	+	0.999936i	$0.496387\pi$
$522$		0			0
$523$	−19287.7			−1.61260			−0.806300	−	0.591506i	$-0.798533\pi$
$523$	−19287.7			−1.61260			−0.806300	+	0.591506i	$0.798533\pi$
$524$	17858.4	+	1367.71i	1.48883	+	0.114024i
$525$		0			0
$526$	−790.645	−	853.513i	−0.0655395	−	0.0707508i
$527$			12349.2i			1.02076i
$528$		0			0
$529$	2107.06			0.173178
$530$	−1188.74	+	1288.15i	−0.0974258	+	0.105573i
$531$		0			0
$532$	−8.66931	+	113.197i	−0.000706508	+	0.00922500i
$533$	−6155.72			−0.500251
$534$		0			0
$535$	1245.18	−	97.7332i	0.100624	−	0.00789790i
$536$	−9374.88	−	11815.1i	−0.755472	−	0.952120i
$537$		0			0
$538$	782.695	+	844.931i	0.0627219	+	0.0677092i
$539$		−	19047.6i		−	1.52215i
$540$		0			0
$541$		−	8722.31i		−	0.693164i	−0.938020	−	0.346582i	$-0.887342\pi$
$541$		−	8722.31i		−	0.693164i	0.938020	−	0.346582i	$-0.112658\pi$
$542$	2757.70	−	2554.57i	0.218548	−	0.202450i
$543$		0			0
$544$	−9119.91	−	13494.8i	−0.718774	−	1.06357i
$545$	960.748	+	12240.5i	0.0755118	+	0.962063i
$546$		0			0
$547$	8718.86			0.681520			0.340760	−	0.940150i	$-0.389316\pi$
$547$	8718.86			0.681520			0.340760	+	0.940150i	$0.389316\pi$
$548$	−11395.7	−	872.756i	−0.888323	−	0.0680334i
$549$		0			0
$550$	−9681.50	−	7622.40i	−0.750583	−	0.590946i
$551$	−62.8437			−0.00485886
$552$		0			0
$553$			17375.0i			1.33609i
$554$	9153.35	−	8479.13i	0.701965	−	0.650260i
$555$		0			0
$556$	−11708.1	−	896.677i	−0.893043	−	0.0683949i
$557$	−11758.7			−0.894489			−0.447245	−	0.894412i	$-0.647595\pi$
$557$	−11758.7			−0.894489			−0.447245	+	0.894412i	$0.647595\pi$
$558$		0			0
$559$	5113.94			0.386935
$560$	1589.40	−	21281.8i	0.119936	−	1.60593i
$561$		0			0
$562$	10653.3	−	9868.60i	0.799613	−	0.740715i
$563$	5260.52			0.393791			0.196896	−	0.980424i	$-0.436914\pi$
$563$	5260.52			0.393791			0.196896	+	0.980424i	$0.436914\pi$
$564$		0			0
$565$	1853.77	+	23618.1i	0.138033	+	1.75862i
$566$	6418.96	−	5946.16i	0.476695	−	0.441582i
$567$		0			0
$568$	−5405.46	−	6812.49i	−0.399310	−	0.503250i
$569$	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	$-0.675892\pi$
$571$		−	23227.4i		−	1.70234i	0.524887	−	0.851172i	$-0.324108\pi$
$572$	5731.25	+	438.936i	0.418944	+	0.0320853i
$573$		0			0
$574$	17117.4	+	18478.5i	1.24471	+	1.34369i
$575$	1956.06	+	12383.9i	0.141867	+	0.898163i
$576$		0			0
$577$		−	526.632i		−	0.0379965i	−0.999820	−	0.0189983i	$-0.993952\pi$
$577$		−	526.632i		−	0.0379965i	0.999820	−	0.0189983i	$-0.00604770\pi$
$578$	6604.12	−	6117.67i	0.475251	−	0.440245i
$579$		0			0
$580$	11813.3	−	22.3482i	0.845727	−	0.00159993i
$581$			18980.9i			1.35535i
$582$		0			0
$583$			1931.83i			0.137235i
$584$	−13278.5	+	10536.0i	−0.940867	+	0.746544i
$585$		0			0
$586$	−1392.96	+	1290.36i	−0.0981956	+	0.0909627i
$587$	14220.5			0.999902			0.499951	−	0.866054i	$-0.333351\pi$
$587$	14220.5			0.999902			0.499951	+	0.866054i	$0.333351\pi$
$588$		0			0
$589$		−	65.3047i		−	0.00456848i
$590$	3901.39	+	3600.34i	0.272234	+	0.251226i
$591$		0			0
$592$	−3612.14	−	556.545i	−0.250774	−	0.0386383i
$593$			10794.3i			0.747500i	0.927529	+	0.373750i	$0.121928\pi$
$593$			10794.3i			0.747500i	−0.927529	+	0.373750i	$0.878072\pi$
$594$		0			0
$595$	29911.0	−	2347.70i	2.06089	−	0.161758i
$596$	−22981.9	−	1760.10i	−1.57949	−	0.120967i
$597$		0			0
$598$	−3974.49	−	4290.52i	−0.271787	−	0.293398i
$599$	−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	$0.409663\pi$
$602$	−14220.5	−	15351.2i	−0.962764	−	1.03932i
$603$		0			0
$604$	−579.923	+	7572.15i	−0.0390674	+	0.510110i
$605$	1296.74	−	101.780i	0.0871404	−	0.00683960i
$606$		0			0
$607$			8119.05i			0.542903i	0.962452	+	0.271451i	$0.0875036\pi$
$607$			8119.05i			0.542903i	−0.962452	+	0.271451i	$0.912496\pi$
$608$	48.2275	+	71.3626i	0.00321691	+	0.00476009i
$609$		0			0
$610$	−3827.21	−	3531.88i	−0.254032	−	0.234429i
$611$			6675.99i			0.442032i
$612$		0			0
$613$	−20527.3			−1.35251			−0.676255	−	0.736668i	$-0.736398\pi$
$613$	−20527.3			−1.35251			−0.676255	+	0.736668i	$0.736398\pi$
$614$	−12057.1	+	11169.0i	−0.792485	+	0.734112i
$615$		0			0
$616$	−14619.4	−	18424.9i	−0.956225	−	1.20513i
$617$			27545.7i			1.79732i	0.438643	+	0.898661i	$0.355459\pi$
$617$			27545.7i			1.79732i	−0.438643	+	0.898661i	$0.644541\pi$
$618$		0			0
$619$		−	1777.17i		−	0.115396i	−0.998334	−	0.0576982i	$-0.981624\pi$
$619$		−	1777.17i		−	0.115396i	0.998334	−	0.0576982i	$-0.0183761\pi$
$620$	23.2234	+	12276.0i	0.00150431	+	0.795184i
$621$		0			0
$622$	−14988.1	+	13884.1i	−0.966183	+	0.895016i
$623$		−	22664.4i		−	1.45751i
$624$		0			0
$625$	14864.3	−	4815.85i	0.951317	−	0.308214i
$626$	−3468.28	−	3744.06i	−0.221438	−	0.239046i
$627$		0			0
$628$	1930.02	−	25200.6i	0.122637	−	1.60130i
$629$		−	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	$0.325934\pi$
$632$	8193.46	+	10326.2i	0.515694	+	0.649927i
$633$		0			0
$634$	3305.56	−	3062.08i	0.207067	−	0.191815i
$635$	−496.887	−	6330.63i	−0.0310526	−	0.395627i
$636$		0			0
$637$	−11267.2			−0.700821
$638$	9551.35	−	8847.82i	0.592698	−	0.549041i
$639$		0			0
$640$	−9091.17	−	13397.6i	−0.561500	−	0.827477i
$641$	24.7805			0.00152694			0.000763470	−	1.00000i	$-0.499757\pi$
$641$	24.7805			0.00152694			0.000763470		1.00000i	$0.499757\pi$
$642$		0			0
$643$	29107.1			1.78518			0.892590	−	0.450870i	$-0.148886\pi$
$643$	29107.1			1.78518			0.892590	+	0.450870i	$0.148886\pi$
$644$	−1827.47	+	23861.5i	−0.111820	+	1.46006i
$645$		0			0
$646$	−88.8325	+	82.2893i	−0.00541032	+	0.00501181i
$647$			13419.6i			0.815421i	0.913111	+	0.407711i	$0.133673\pi$
$647$			13419.6i			0.815421i	−0.913111	+	0.407711i	$0.866327\pi$
$648$		0			0
$649$	5850.91			0.353880
$650$	−4508.86	+	5726.88i	−0.272080	+	0.345579i
$651$		0			0
$652$	−831.897	+	10862.2i	−0.0499687	+	0.652450i
$653$	1926.26			0.115437			0.0577186	−	0.998333i	$-0.481617\pi$
$653$	1926.26			0.115437			0.0577186	+	0.998333i	$0.481617\pi$
$654$		0			0
$655$	1958.64	+	24954.2i	0.116840	+	1.48861i
$656$	18887.0	+	2910.03i	1.12410	+	0.173198i
$657$		0			0
$658$	20040.2	−	18564.1i	1.18731	−	1.09986i
$659$		−	13158.1i		−	0.777797i	−0.921281	−	0.388899i	$-0.872856\pi$
$659$		−	13158.1i		−	0.777797i	0.921281	−	0.388899i	$-0.127144\pi$
$660$		0			0
$661$			27392.1i			1.61184i	0.592023	+	0.805921i	$0.298330\pi$
$661$			27392.1i			1.61184i	−0.592023	+	0.805921i	$0.701670\pi$
$662$	−11942.5	−	12892.1i	−0.701143	−	0.756895i
$663$		0			0
$664$	8950.75	+	11280.6i	0.523127	+	0.659296i
$665$	−158.174	+	12.4150i	−0.00922364	+	0.000723959i
$666$		0			0
$667$	−13247.3			−0.769019
$668$	5115.61	+	391.785i	0.296301	+	0.0226926i
$669$		0			0
$670$	14295.2	−	15490.5i	0.824285	−	0.893211i
$671$	−5739.65			−0.330219
$672$		0			0
$673$			5569.75i			0.319017i	0.987197	+	0.159508i	$0.0509909\pi$
$673$			5569.75i			0.319017i	−0.987197	+	0.159508i	$0.949009\pi$
$674$	21872.0	+	23611.2i	1.24997	+	1.34936i
$675$		0			0
$676$	−1082.51	+	14134.5i	−0.0615901	+	0.804192i
$677$	4130.23			0.234472			0.117236	−	0.993104i	$-0.462597\pi$
$677$	4130.23			0.234472			0.117236	+	0.993104i	$0.462597\pi$
$678$		0			0
$679$	−38164.8			−2.15704
$680$	16669.4	−	15500.3i	0.940064	−	0.874131i
$681$		0			0
$682$	9194.31	+	9925.39i	0.516229	+	0.557277i
$683$	−22875.3			−1.28155			−0.640776	−	0.767728i	$-0.721387\pi$
$683$	−22875.3			−1.28155			−0.640776	+	0.767728i	$0.721387\pi$
$684$		0			0
$685$	−1249.84	−	15923.7i	−0.0697138	−	0.888193i
$686$	11667.8	+	12595.5i	0.649385	+	0.701021i
$687$		0			0
$688$	−15690.6	−	2417.55i	−0.869473	−	0.133965i
$689$	1142.73			0.0631851
$690$		0			0
$691$			19910.4i			1.09613i	0.836435	+	0.548066i	$0.184636\pi$
$691$			19910.4i			1.09613i	−0.836435	+	0.548066i	$0.815364\pi$
$692$	35.4304	−	462.620i	0.00194633	−	0.0254136i
$693$		0			0
$694$	5247.12	−	4860.63i	0.287000	−	0.265860i
$695$	−1284.10	−	16360.1i	−0.0700842	−	0.892912i
$696$		0			0
$697$			26866.2i			1.46001i
$698$	−212.513	−	229.411i	−0.0115240	−	0.0124403i
$699$		0			0
$700$	29729.1	−	2390.01i	1.60522	−	0.129049i
$701$			3428.44i			0.184722i	0.995726	+	0.0923612i	$0.0294414\pi$
$701$			3428.44i			0.184722i	−0.995726	+	0.0923612i	$0.970559\pi$
$702$		0			0
$703$			27.1715i			0.00145774i
$704$	−17377.1	−	4056.11i	−0.930290	−	0.217145i
$705$		0			0
$706$	13681.7	+	14769.6i	0.729343	+	0.787337i
$707$	24045.4			1.27910
$708$		0			0
$709$			15608.3i			0.826771i	0.910556	+	0.413385i	$0.135654\pi$
$709$			15608.3i			0.826771i	−0.910556	+	0.413385i	$0.864346\pi$
$710$	8242.45	−	8931.68i	0.435681	−	0.472113i
$711$		0			0
$712$	−10687.8	−	13469.8i	−0.562558	−	0.708991i
$713$		−	13766.0i		−	0.723061i
$714$		0			0
$715$	628.583	+	8008.50i	0.0328778	+	0.418882i
$716$	−12832.4	−	982.789i	−0.669791	−	0.0512968i
$717$		0			0
$718$	−6469.81	+	5993.26i	−0.336283	+	0.311513i
$719$	−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
$722$	−14231.7	+	13183.4i	−0.733584	+	0.679550i
$723$		0			0
$724$	−21262.5	−	1628.42i	−1.09146	−	0.0835907i
$725$	2575.80	+	16307.5i	0.131949	+	0.835372i
$726$		0			0
$727$			20590.4i			1.05042i	0.850973	+	0.525210i	$0.176013\pi$
$727$			20590.4i			1.05042i	−0.850973	+	0.525210i	$0.823987\pi$
$728$	−10898.8	+	8647.81i	−0.554858	+	0.440260i
$729$		0			0
$730$	−17409.0	−	16065.6i	−0.882654	−	0.814543i
$731$		−	22319.4i		−	1.12929i
$732$		0			0
$733$	24257.3			1.22232			0.611162	−	0.791506i	$-0.290703\pi$
$733$	24257.3			1.22232			0.611162	+	0.791506i	$0.290703\pi$
$734$	21158.3	+	22840.6i	1.06399	+	1.14859i
$735$		0			0
$736$	10166.2	+	15043.0i	0.509146	+	0.753387i
$737$		−	23231.1i		−	1.16110i
$738$		0			0
$739$		−	25426.8i		−	1.26569i	−0.774280	−	0.632843i	$-0.781888\pi$
$739$		−	25426.8i		−	1.26569i	0.774280	−	0.632843i	$-0.218112\pi$
$740$	−9.66259	−	5107.68i	−0.000480005	−	0.253732i
$741$		0			0
$742$	−3177.62	−	3430.29i	−0.157216	−	0.169717i
$743$			22658.4i			1.11878i	0.828904	+	0.559391i	$0.188965\pi$
$743$			22658.4i			1.11878i	−0.828904	+	0.559391i	$0.811035\pi$
$744$		0			0
$745$	−2520.56	−	32113.4i	−0.123955	−	1.57925i
$746$	−26709.5	+	24742.2i	−1.31086	+	1.21431i
$747$		0			0
$748$	1915.70	−	25013.6i	0.0936430	−	1.22271i
$749$			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	$0.586104\pi$
$752$	3155.98	−	20483.2i	0.153041	−	0.993281i
$753$		0			0
$754$	−5233.73	−	5649.89i	−0.252787	−	0.272887i
$755$	−10580.9	+	830.485i	−0.510035	+	0.0400324i
$756$		0			0
$757$	30279.9			1.45382			0.726909	−	0.686734i	$-0.240956\pi$
$757$	30279.9			1.45382			0.726909	+	0.686734i	$0.240956\pi$
$758$	11552.5	+	12471.1i	0.553570	+	0.597587i
$759$		0			0
$760$	−88.1506	+	81.9680i	−0.00420731	+	0.00391223i
$761$	−4374.09			−0.208358			−0.104179	−	0.994559i	$-0.533222\pi$
$761$	−4374.09			−0.208358			−0.104179	+	0.994559i	$0.533222\pi$
$762$		0			0
$763$	−32753.4			−1.55407
$764$	1759.15	−	22969.5i	0.0833034	−	1.08771i
$765$		0			0
$766$	−7712.93	−	8326.23i	−0.363812	−	0.392740i
$767$		−	3460.97i		−	0.162932i
$768$		0			0
$769$	−12982.1			−0.608774			−0.304387	−	0.952548i	$-0.598452\pi$
$769$	−12982.1			−0.608774			−0.304387	+	0.952548i	$0.598452\pi$
$770$	22292.3	−	24156.4i	1.04332	−	1.13056i
$771$		0			0
$772$	−19154.7	−	1466.99i	−0.892996	−	0.0683912i
$773$	34056.3			1.58463			0.792316	−	0.610112i	$-0.208875\pi$
$773$	34056.3			1.58463			0.792316	+	0.610112i	$0.208875\pi$
$774$		0			0
$775$	−16946.1	+	2676.67i	−0.785448	+	0.124063i
$776$	−22681.9	+	17997.3i	−1.04927	+	0.832557i
$777$		0			0
$778$	18237.1	+	19687.2i	0.840402	+	0.907226i
$779$		−	142.073i		−	0.00653437i
$780$		0			0
$781$		−	13394.8i		−	0.613706i
$782$	−18725.6	+	17346.3i	−0.856300	+	0.793227i
$783$		0			0
$784$	34570.0	+	5326.41i	1.57480	+	0.242639i
$785$	35213.8	−	2763.91i	1.60106	−	0.125667i
$786$		0			0
$787$	11962.9			0.541842			0.270921	−	0.962602i	$-0.412672\pi$
$787$	11962.9			0.541842			0.270921	+	0.962602i	$0.412672\pi$
$788$	2720.98	−	35528.2i	0.123009	−	1.60614i
$789$		0			0
$790$	−12493.7	+	13538.4i	−0.562666	+	0.609716i
$791$	−63198.1			−2.84079
$792$		0			0
$793$			3395.17i			0.152038i
$794$	−10272.0	+	9515.34i	−0.459116	+	0.425298i
$795$		0			0
$796$	2995.75	−	39116.0i	0.133394	−	1.74174i
$797$	17898.9			0.795498			0.397749	−	0.917494i	$-0.369791\pi$
$797$	17898.9			0.795498			0.397749	+	0.917494i	$0.369791\pi$
$798$		0			0
$799$	29136.9			1.29010
$800$	16541.4	−	15439.7i	0.731032	−	0.682343i
$801$		0			0
$802$	−18258.7	+	16913.8i	−0.803913	+	0.744698i
$803$	−26108.3			−1.14737
$804$		0			0
$805$	−33342.6	+	2617.04i	−1.45984	+	0.114582i
$806$	5871.15	−	5438.69i	0.256579	−	0.237680i
$807$		0			0
$808$	14290.5	−	11339.0i	0.622202	−	0.493695i
$809$	−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	$0.401874\pi$
$811$			44013.9i			1.90572i	−0.303412	+	0.952859i	$0.598126\pi$
$812$	−2406.46	+	31421.6i	−0.104003	+	1.35798i
$813$		0			0
$814$	−3825.49	−	4129.68i	−0.164722	−	0.177820i
$815$	−15178.2	+	1191.33i	−0.652354	+	0.0512029i
$816$		0			0
$817$			118.028i			0.00505422i
$818$	−14897.7	+	13800.3i	−0.636779	+	0.589875i
$819$		0			0
$820$	50.5232	+	26706.7i	0.00215164	+	1.13737i
$821$			30978.8i			1.31689i	0.752628	+	0.658446i	$0.228786\pi$
$821$			30978.8i			1.31689i	−0.752628	+	0.658446i	$0.771214\pi$
$822$		0			0
$823$		−	41684.8i		−	1.76554i	−0.469804	−	0.882771i	$-0.655675\pi$
$823$		−	41684.8i		−	1.76554i	0.469804	−	0.882771i	$-0.344325\pi$
$824$	−8822.01	+	6999.95i	−0.372973	+	0.295940i
$825$		0			0
$826$	−10389.3	+	9624.03i	−0.437638	+	0.405403i
$827$	−11988.7			−0.504096			−0.252048	−	0.967715i	$-0.581104\pi$
$827$	−11988.7			−0.504096			−0.252048	+	0.967715i	$0.581104\pi$
$828$		0			0
$829$			2023.64i			0.0847814i	0.999101	+	0.0423907i	$0.0134974\pi$
$829$			2023.64i			0.0847814i	−0.999101	+	0.0423907i	$0.986503\pi$
$830$	−13648.4	+	14789.7i	−0.570776	+	0.618504i
$831$		0			0
$832$	−2399.30	+	10279.0i	−0.0999770	+	0.428319i
$833$			49174.8i			2.04539i
$834$		0			0
$835$	561.061	+	7148.23i	0.0232531	+	0.296257i
$836$	−10.1305	+	132.276i	−0.000419105	+	0.00547232i
$837$		0			0
$838$	26058.6	+	28130.6i	1.07420	+	1.15961i
$839$	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
$842$	−14278.2	−	15413.5i	−0.584393	−	0.630861i
$843$		0			0
$844$	−9784.09	−	749.327i	−0.399031	−	0.0305603i
$845$	−19750.6	+	1550.22i	−0.804074	+	0.0631114i
$846$		0			0
$847$			3469.86i			0.140762i
$848$	−3506.11	−	540.209i	−0.141982	−	0.0218760i
$849$		0			0
$850$	24994.5	+	19678.6i	1.00859	+	0.794082i
$851$			5727.66i			0.230719i
$852$		0			0
$853$	29816.5			1.19683			0.598416	−	0.801186i	$-0.295797\pi$
$853$	29816.5			1.19683			0.598416	+	0.801186i	$0.295797\pi$
$854$	10191.7	−	9441.03i	0.408377	−	0.378297i
$855$		0			0
$856$	1571.21	+	1980.19i	0.0627368	+	0.0790670i
$857$			6572.14i			0.261960i	0.991385	+	0.130980i	$0.0418124\pi$
$857$			6572.14i			0.261960i	−0.991385	+	0.130980i	$0.958188\pi$
$858$		0			0
$859$		−	45723.7i		−	1.81615i	−0.418809	−	0.908075i	$-0.637552\pi$
$859$		−	45723.7i		−	1.81615i	0.418809	−	0.908075i	$-0.362448\pi$
$860$	−41.9728	−	22187.0i	−0.00166426	−	0.879731i
$861$		0			0
$862$	−3302.85	+	3059.57i	−0.130505	+	0.120893i
$863$		−	13343.7i		−	0.526331i	−0.964751	−	0.263166i	$-0.915233\pi$
$863$		−	13343.7i		−	0.526331i	0.964751	−	0.263166i	$-0.0847665\pi$
$864$		0			0
$865$	646.437	−	50.7385i	0.0254098	−	0.00199440i
$866$	−20781.3	−	22433.7i	−0.815446	−	0.880286i
$867$		0			0
$868$	−32652.1	−	2500.71i	−1.27683	−	0.0977874i
$869$			20303.5i			0.792577i
$870$		0			0
$871$	−13741.8			−0.534586
$872$	−19465.9	+	15445.4i	−0.755960	+	0.599826i
$873$		0			0
$874$	99.0240	−	91.7301i	0.00383242	−	0.00355013i
$875$	9704.74	+	40536.2i	0.374949	+	1.56614i
$876$		0			0
$877$	−41636.8			−1.60317			−0.801583	−	0.597884i	$-0.796008\pi$
$877$	−41636.8			−1.60317			−0.801583	+	0.597884i	$0.796008\pi$
$878$	10150.2	−	9402.52i	0.390150	−	0.361412i
$879$		0			0
$880$	1857.29	−	24868.8i	0.0711469	−	0.952644i
$881$	31220.6			1.19392			0.596962	−	0.802269i	$-0.296374\pi$
$881$	31220.6			1.19392			0.596962	+	0.802269i	$0.296374\pi$
$882$		0			0
$883$	−35199.4			−1.34151			−0.670755	−	0.741679i	$-0.734030\pi$
$883$	−35199.4			−1.34151			−0.670755	+	0.741679i	$0.734030\pi$
$884$	−14796.2	−	1133.19i	−0.562954	−	0.0431146i
$885$		0			0
$886$	−4392.40	+	4068.86i	−0.166552	+	0.154284i
$887$			12744.8i			0.482444i	0.970470	+	0.241222i	$0.0775482\pi$
$887$			12744.8i			0.482444i	−0.970470	+	0.241222i	$0.922452\pi$
$888$		0			0
$889$	16939.7			0.639076
$890$	16297.1	−	17659.9i	0.613799	−	0.665125i
$891$		0			0
$892$	−12306.1	−	942.482i	−0.461929	−	0.0353774i
$893$	−154.080			−0.00577391
$894$		0			0
$895$	−1407.41	−	17931.2i	−0.0525638	−	0.669693i
$896$	37527.8	−	21380.9i	1.39924	−	0.797194i
$897$		0			0
$898$	−27500.7	+	25475.1i	−1.02195	+	0.946675i
$899$		−	18127.6i		−	0.672512i
$900$		0			0
$901$		−	4987.35i		−	0.184409i
$902$	20002.5	+	21593.0i	0.738372	+	0.797083i
$903$		0			0
$904$	−37559.5	+	29802.1i	−1.38187	+	1.09646i
$905$	−2331.99	−	29710.9i	−0.0856553	−	1.09130i
$906$		0			0
$907$	−16588.8			−0.607299			−0.303650	−	0.952784i	$-0.598205\pi$
$907$	−16588.8			−0.607299			−0.303650	+	0.952784i	$0.598205\pi$
$908$	2352.79	−	30720.8i	0.0859912	−	1.12280i
$909$		0			0
$910$	−14289.2	−	13186.5i	−0.520528	−	0.480361i
$911$	46114.7			1.67711			0.838555	−	0.544816i	$-0.183401\pi$
$911$	46114.7			1.67711			0.838555	+	0.544816i	$0.183401\pi$
$912$		0			0
$913$			22180.1i			0.804002i
$914$	−7629.26	−	8235.90i	−0.276098	−	0.298052i
$915$		0			0
$916$	−41738.7	−	3196.61i	−1.50555	−	0.115305i
$917$	−66773.3			−2.40463
$918$		0			0
$919$	47522.6			1.70580			0.852898	−	0.522077i	$-0.174843\pi$
$919$	47522.6			1.70580			0.852898	+	0.522077i	$0.174843\pi$
$920$	−18581.9	+	17278.6i	−0.665898	+	0.619194i
$921$		0			0
$922$	−13587.5	−	14667.9i	−0.485335	−	0.523926i
$923$	−7923.40			−0.282559
$924$		0			0
$925$	7050.80	−	1113.69i	0.250626	−	0.0395868i
$926$	−343.253	−	370.547i	−0.0121814	−	0.0131500i
$927$		0			0
$928$	13387.2	+	19809.1i	0.473552	+	0.700718i
$929$	−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
$932$	1447.12	+	110.829i	0.0508604	+	0.00389521i
$933$		0			0
$934$	24020.1	−	22250.9i	0.841502	−	0.779519i
$935$	34952.5	−	2743.40i	1.22253	−	0.0959559i
$936$		0			0
$937$		−	12453.1i		−	0.434179i	−0.976152	−	0.217089i	$-0.930344\pi$
$937$		−	12453.1i		−	0.434179i	0.976152	−	0.217089i	$-0.0696563\pi$
$938$	38212.3	+	41250.7i	1.33014	+	1.43591i
$939$		0			0
$940$	28963.9	−	54.7933i	1.00500	−	0.00190124i
$941$		−	40466.5i		−	1.40188i	−0.713220	−	0.700940i	$-0.752764\pi$
$941$		−	40466.5i		−	1.40188i	0.713220	−	0.700940i	$-0.247236\pi$
$942$		0			0
$943$		−	29948.5i		−	1.03421i
$944$	−1636.13	+	10618.9i	−0.0564104	+	0.366120i
$945$		0			0
$946$	−16617.3	−	17938.7i	−0.571117	−	0.616529i
$947$	−2645.96			−0.0907943			−0.0453971	−	0.998969i	$-0.514455\pi$
$947$	−2645.96			−0.0907943			−0.0453971	+	0.998969i	$0.514455\pi$
$948$		0			0
$949$			15443.8i			0.528268i
$950$	−132.175	−	104.063i	−0.00451402	−	0.00355396i
$951$		0			0
$952$	37742.7	+	47567.0i	1.28492	+	1.61939i
$953$		−	40045.8i		−	1.36119i	−0.732662	−	0.680593i	$-0.761722\pi$
$953$		−	40045.8i		−	1.36119i	0.732662	−	0.680593i	$-0.238278\pi$
$954$		0			0
$955$	32096.1	−	2519.21i	1.08755	−	0.0853609i
$956$	−1531.99	+	20003.4i	−0.0518285	+	0.676734i
$957$		0			0
$958$	26439.1	−	24491.6i	0.891657	−	0.825979i
$959$	42609.1			1.43474
$960$		0			0
$961$	−10953.5			−0.367679
$962$	−2442.82	+	2262.89i	−0.0818707	+	0.0758403i
$963$		0			0
$964$	−665.553	+	8690.23i	−0.0222365	+	0.290346i
$965$	−2100.82	−	26765.6i	−0.0700805	−	0.892865i
$966$		0			0
$967$		−	11049.0i		−	0.367439i	−0.982979	−	0.183719i	$-0.941186\pi$
$967$		−	11049.0i		−	0.367439i	0.982979	−	0.183719i	$-0.0588137\pi$
$968$	1636.27	+	2062.19i	0.0543302	+	0.0684723i
$969$		0			0
$970$	−29737.7	−	27442.9i	−0.984350	−	0.908390i
$971$			26708.5i			0.882717i	0.897331	+	0.441358i	$0.145503\pi$
$971$			26708.5i			0.882717i	−0.897331	+	0.441358i	$0.854497\pi$
$972$		0			0
$973$	43776.9			1.44237
$974$	−25581.5	−	27615.7i	−0.841566	−	0.908483i
$975$		0			0
$976$	1605.02	−	10417.0i	0.0526387	−	0.341640i
$977$		−	11102.6i		−	0.363566i	−0.983339	−	0.181783i	$-0.941813\pi$
$977$		−	11102.6i		−	0.363566i	0.983339	−	0.181783i	$-0.0581869\pi$
$978$		0			0
$979$		−	26484.5i		−	0.864604i
$980$	92.4758	+	48883.0i	0.00301432	+	1.59338i
$981$		0			0
$982$	−416.503	−	449.621i	−0.0135348	−	0.0146110i
$983$		−	33544.2i		−	1.08840i	−0.838957	−	0.544198i	$-0.816834\pi$
$983$		−	33544.2i		−	1.08840i	0.838957	−	0.544198i	$-0.183166\pi$
$984$		0			0
$985$	49644.9	−	3896.60i	1.60591	−	0.126047i
$986$	−24658.5	+	22842.2i	−0.796436	+	0.737773i
$987$		0			0
$988$	78.2449	+	5.99249i	0.00251954	+	0.000192962i
$989$			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	$0.471709\pi$
$992$	−20584.9	+	13911.5i	−0.658841	+	0.445251i
$993$		0			0
$994$	22032.8	+	23784.8i	0.703057	+	0.758961i
$995$	54658.2	−	4290.09i	1.74149	−	0.136688i
$996$		0			0
$997$	−24192.6			−0.768492			−0.384246	−	0.923231i	$-0.625539\pi$
$997$	−24192.6			−0.768492			−0.384246	+	0.923231i	$0.625539\pi$
$998$	−20759.6	−	22410.3i	−0.658452	−	0.710808i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.f.a.29.5	✓	16	24.5	odd	2
40.4.f.a.29.6	yes	16	15.14	odd	2
40.4.f.a.29.11	yes	16	3.2	odd	2
40.4.f.a.29.12	yes	16	120.29	odd	2
160.4.f.a.49.3		16	120.59	even	2
160.4.f.a.49.4		16	12.11	even	2
160.4.f.a.49.13		16	24.11	even	2
160.4.f.a.49.14		16	60.59	even	2
200.4.d.e.101.3		16	15.8	even	4
200.4.d.e.101.4		16	120.53	even	4
200.4.d.e.101.13		16	120.77	even	4
200.4.d.e.101.14		16	15.2	even	4
360.4.d.d.109.5		16	40.29	even	2	inner
360.4.d.d.109.6		16	1.1	even	1	trivial
360.4.d.d.109.11		16	5.4	even	2	inner
360.4.d.d.109.12		16	8.5	even	2	inner
800.4.d.e.401.3		16	60.23	odd	4
800.4.d.e.401.4		16	120.107	odd	4
800.4.d.e.401.13		16	120.83	odd	4
800.4.d.e.401.14		16	60.47	odd	4
1440.4.d.d.1009.1		16	20.19	odd	2
1440.4.d.d.1009.2		16	8.3	odd	2
1440.4.d.d.1009.15		16	4.3	odd	2
1440.4.d.d.1009.16		16	40.19	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.07496 + 1.92212i) q^{2} +(0.610901 - 7.97664i) q^{4} +(11.1461 - 0.874848i) q^{5} +29.8250i q^{7} +(14.0645 + 17.7254i) q^{8} +(-21.4460 + 23.2393i) q^{10} +34.8520i q^{11} +20.6159 q^{13} +(-57.3272 - 61.8856i) q^{14} +(-63.2536 - 9.74588i) q^{16} -89.9765i q^{17} +0.475810i q^{19} +(-0.169205 - 89.4426i) q^{20} +(-66.9897 - 72.3164i) q^{22} +100.299i q^{23} +(123.469 - 19.5022i) q^{25} +(-42.7771 + 39.6263i) q^{26} +(237.903 + 18.2201i) q^{28} +132.077i q^{29} -137.250 q^{31} +(149.981 - 101.359i) q^{32} +(172.946 + 186.697i) q^{34} +(26.0923 + 332.431i) q^{35} +57.1057 q^{37} +(-0.914564 - 0.987285i) q^{38} +(172.271 + 185.264i) q^{40} -298.591 q^{41} +248.058 q^{43} +(278.002 + 21.2911i) q^{44} +(-192.787 - 208.117i) q^{46} +323.827i q^{47} -546.530 q^{49} +(-218.708 + 277.789i) q^{50} +(12.5943 - 164.446i) q^{52} +55.4295 q^{53} +(30.4902 + 388.462i) q^{55} +(-528.660 + 419.473i) q^{56} +(-253.868 - 274.055i) q^{58} -167.879i q^{59} +164.687i q^{61} +(284.787 - 263.810i) q^{62} +(-116.381 + 498.597i) q^{64} +(229.786 - 18.0358i) q^{65} -666.565 q^{67} +(-717.710 - 54.9668i) q^{68} +(-693.113 - 639.628i) q^{70} -384.334 q^{71} +749.119i q^{73} +(-118.492 + 109.764i) q^{74} +(3.79536 + 0.290673i) q^{76} -1039.46 q^{77} +582.564 q^{79} +(-713.555 - 53.2909i) q^{80} +(619.564 - 573.928i) q^{82} +636.408 q^{83} +(-78.7158 - 1002.88i) q^{85} +(-514.710 + 476.798i) q^{86} +(-617.766 + 490.175i) q^{88} -759.913 q^{89} +614.869i q^{91} +(800.051 + 61.2730i) q^{92} +(-622.435 - 671.928i) q^{94} +(0.416261 + 5.30340i) q^{95} +1279.63i q^{97} +(1134.03 - 1050.50i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} - 48 q^{10} - 28 q^{14} - 168 q^{16} + 196 q^{20} - 24 q^{25} - 200 q^{26} - 112 q^{31} + 408 q^{34} + 672 q^{40} - 232 q^{41} - 920 q^{44} + 212 q^{46} - 200 q^{49} + 648 q^{50} + 392 q^{55}+ \cdots + 1064 q^{95}+O(q^{100}) \) 16 * q + 4 * q^4 - 48 * q^10 - 28 * q^14 - 168 * q^16 + 196 * q^20 - 24 * q^25 - 200 * q^26 - 112 * q^31 + 408 * q^34 + 672 * q^40 - 232 * q^41 - 920 * q^44 + 212 * q^46 - 200 * q^49 + 648 * q^50 + 392 * q^55 - 1120 * q^56 - 2912 * q^64 + 600 * q^65 + 1532 * q^70 - 2096 * q^71 - 4224 * q^74 - 3000 * q^76 + 2992 * q^79 - 2280 * q^80 - 3076 * q^86 + 208 * q^89 - 7036 * q^94 + 1064 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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