LMFDB - Embedded newform 315.3.o.b.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,3,Mod(127,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("315.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	315.o (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.58312832735$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.3
Character	$\chi$	$=$	315.127
Dual form			315.3.o.b.253.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24469 - 2.24469i) q^{2} +6.07726i q^{4} +(3.05058 - 3.96156i) q^{5} +(1.87083 + 1.87083i) q^{7} +(4.66280 - 4.66280i) q^{8} +O(q^{10})$	\(q+(-2.24469 - 2.24469i) q^{2} +6.07726i q^{4} +(3.05058 - 3.96156i) q^{5} +(1.87083 + 1.87083i) q^{7} +(4.66280 - 4.66280i) q^{8} +(-15.7401 + 2.04487i) q^{10} -3.94671 q^{11} +(8.57045 - 8.57045i) q^{13} -8.39886i q^{14} +3.37595 q^{16} +(17.2039 + 17.2039i) q^{17} -24.3758i q^{19} +(24.0754 + 18.5392i) q^{20} +(8.85913 + 8.85913i) q^{22} +(19.6705 - 19.6705i) q^{23} +(-6.38793 - 24.1701i) q^{25} -38.4760 q^{26} +(-11.3695 + 11.3695i) q^{28} -17.5580i q^{29} -43.8736 q^{31} +(-26.2292 - 26.2292i) q^{32} -77.2348i q^{34} +(13.1185 - 1.70429i) q^{35} +(32.9598 + 32.9598i) q^{37} +(-54.7160 + 54.7160i) q^{38} +(-4.24773 - 32.6962i) q^{40} -22.4582 q^{41} +(14.3533 - 14.3533i) q^{43} -23.9852i q^{44} -88.3085 q^{46} +(-38.7355 - 38.7355i) q^{47} +7.00000i q^{49} +(-39.9155 + 68.5933i) q^{50} +(52.0849 + 52.0849i) q^{52} +(-9.01352 + 9.01352i) q^{53} +(-12.0397 + 15.6351i) q^{55} +17.4466 q^{56} +(-39.4121 + 39.4121i) q^{58} -58.0335i q^{59} -89.2995 q^{61} +(98.4827 + 98.4827i) q^{62} +104.249i q^{64} +(-7.80752 - 60.0972i) q^{65} +(-21.2058 - 21.2058i) q^{67} +(-104.552 + 104.552i) q^{68} +(-33.2726 - 25.6214i) q^{70} +78.8147 q^{71} +(-18.2694 + 18.2694i) q^{73} -147.969i q^{74} +148.138 q^{76} +(-7.38362 - 7.38362i) q^{77} -112.267i q^{79} +(10.2986 - 13.3740i) q^{80} +(50.4118 + 50.4118i) q^{82} +(12.9380 - 12.9380i) q^{83} +(120.636 - 15.6724i) q^{85} -64.4373 q^{86} +(-18.4027 + 18.4027i) q^{88} -22.2193i q^{89} +32.0677 q^{91} +(119.543 + 119.543i) q^{92} +173.898i q^{94} +(-96.5661 - 74.3602i) q^{95} +(90.6427 + 90.6427i) q^{97} +(15.7128 - 15.7128i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8}+O(q^{10}) $ 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8	$ 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8} - 40 q^{10} + 64 q^{13} - 184 q^{16} - 24 q^{17} - 72 q^{20} + 8 q^{22} - 8 q^{23} - 136 q^{25} + 80 q^{26} + 96 q^{31} - 56 q^{32} + 8 q^{37} - 56 q^{38} + 232 q^{40} - 320 q^{41} - 112 q^{43} + 320 q^{46} - 64 q^{47} + 256 q^{50} + 96 q^{52} + 72 q^{53} - 80 q^{55} + 336 q^{56} - 512 q^{58} - 496 q^{61} + 776 q^{62} - 312 q^{65} - 192 q^{67} - 568 q^{68} + 112 q^{70} + 144 q^{71} + 224 q^{73} + 416 q^{76} - 112 q^{77} + 528 q^{80} + 352 q^{82} + 32 q^{83} + 24 q^{85} - 240 q^{86} + 216 q^{88} - 1304 q^{92} - 376 q^{95} - 816 q^{97} + 56 q^{98}+O(q^{100}) $ 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8 - 40 * q^10 + 64 * q^13 - 184 * q^16 - 24 * q^17 - 72 * q^20 + 8 * q^22 - 8 * q^23 - 136 * q^25 + 80 * q^26 + 96 * q^31 - 56 * q^32 + 8 * q^37 - 56 * q^38 + 232 * q^40 - 320 * q^41 - 112 * q^43 + 320 * q^46 - 64 * q^47 + 256 * q^50 + 96 * q^52 + 72 * q^53 - 80 * q^55 + 336 * q^56 - 512 * q^58 - 496 * q^61 + 776 * q^62 - 312 * q^65 - 192 * q^67 - 568 * q^68 + 112 * q^70 + 144 * q^71 + 224 * q^73 + 416 * q^76 - 112 * q^77 + 528 * q^80 + 352 * q^82 + 32 * q^83 + 24 * q^85 - 240 * q^86 + 216 * q^88 - 1304 * q^92 - 376 * q^95 - 816 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−2.24469	−	2.24469i	−1.12234	−	1.12234i	−0.991388	−	0.130957i	$-0.958195\pi$
$2$	−2.24469	−	2.24469i	−1.12234	−	1.12234i	−0.130957	−	0.991388i	$-0.541805\pi$
$3$		0			0
$3$		0			0
$4$			6.07726i			1.51932i
$5$	3.05058	−	3.96156i	0.610116	−	0.792312i
$5$	3.05058	−	3.96156i	0.610116	−	0.792312i
$6$		0			0
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$8$	4.66280	−	4.66280i	0.582850	−	0.582850i
$9$		0			0
$10$	−15.7401	+	2.04487i	−1.57401	+	0.204487i
$11$	−3.94671			−0.358792			−0.179396	−	0.983777i	$-0.557414\pi$
$11$	−3.94671			−0.358792			−0.179396	+	0.983777i	$0.557414\pi$
$12$		0			0
$13$	8.57045	−	8.57045i	0.659265	−	0.659265i	−0.295941	−	0.955206i	$-0.595633\pi$
$13$	8.57045	−	8.57045i	0.659265	−	0.659265i	0.955206	+	0.295941i	$0.0956331\pi$
$14$		−	8.39886i		−	0.599918i
$15$		0			0
$16$	3.37595			0.210997
$17$	17.2039	+	17.2039i	1.01199	+	1.01199i	0.999927	+	0.0120660i	$0.00384082\pi$
$17$	17.2039	+	17.2039i	1.01199	+	1.01199i	0.0120660	+	0.999927i	$0.496159\pi$
$18$		0			0
$19$		−	24.3758i		−	1.28294i	−0.767150	−	0.641468i	$-0.778326\pi$
$19$		−	24.3758i		−	1.28294i	0.767150	−	0.641468i	$-0.221674\pi$
$20$	24.0754	+	18.5392i	1.20377	+	0.926958i
$21$		0			0
$22$	8.85913	+	8.85913i	0.402688	+	0.402688i
$23$	19.6705	−	19.6705i	0.855240	−	0.855240i	−0.135533	−	0.990773i	$-0.543275\pi$
$23$	19.6705	−	19.6705i	0.855240	−	0.855240i	0.990773	+	0.135533i	$0.0432745\pi$
$24$		0			0
$25$	−6.38793	−	24.1701i	−0.255517	−	0.966804i
$26$	−38.4760			−1.47985
$27$		0			0
$28$	−11.3695	+	11.3695i	−0.406054	+	0.406054i
$29$		−	17.5580i		−	0.605447i	−0.953078	−	0.302723i	$-0.902104\pi$
$29$		−	17.5580i		−	0.605447i	0.953078	−	0.302723i	$-0.0978958\pi$
$30$		0			0
$31$	−43.8736			−1.41528			−0.707639	−	0.706574i	$-0.750240\pi$
$31$	−43.8736			−1.41528			−0.707639	+	0.706574i	$0.750240\pi$
$32$	−26.2292	−	26.2292i	−0.819662	−	0.819662i
$33$		0			0
$34$		−	77.2348i		−	2.27161i
$35$	13.1185	−	1.70429i	0.374815	−	0.0486940i
$36$		0			0
$37$	32.9598	+	32.9598i	0.890805	+	0.890805i	0.994599	−	0.103794i	$-0.0330981\pi$
$37$	32.9598	+	32.9598i	0.890805	+	0.890805i	−0.103794	+	0.994599i	$0.533098\pi$
$38$	−54.7160	+	54.7160i	−1.43990	+	1.43990i
$39$		0			0
$40$	−4.24773	−	32.6962i	−0.106193	−	0.817406i
$41$	−22.4582			−0.547762			−0.273881	−	0.961764i	$-0.588307\pi$
$41$	−22.4582			−0.547762			−0.273881	+	0.961764i	$0.588307\pi$
$42$		0			0
$43$	14.3533	−	14.3533i	0.333797	−	0.333797i	−0.520230	−	0.854026i	$-0.674154\pi$
$43$	14.3533	−	14.3533i	0.333797	−	0.333797i	0.854026	+	0.520230i	$0.174154\pi$
$44$		−	23.9852i		−	0.545118i
$45$		0			0
$46$	−88.3085			−1.91975
$47$	−38.7355	−	38.7355i	−0.824159	−	0.824159i	0.162542	−	0.986702i	$-0.448031\pi$
$47$	−38.7355	−	38.7355i	−0.824159	−	0.824159i	−0.986702	+	0.162542i	$0.948031\pi$
$48$		0			0
$49$			7.00000i			0.142857i
$50$	−39.9155	+	68.5933i	−0.798309	+	1.37187i
$51$		0			0
$52$	52.0849	+	52.0849i	1.00163	+	1.00163i
$53$	−9.01352	+	9.01352i	−0.170067	+	0.170067i	−0.787009	−	0.616942i	$-0.788371\pi$
$53$	−9.01352	+	9.01352i	−0.170067	+	0.170067i	0.616942	+	0.787009i	$0.288371\pi$
$54$		0			0
$55$	−12.0397	+	15.6351i	−0.218905	+	0.284275i
$56$	17.4466			0.311547
$57$		0			0
$58$	−39.4121	+	39.4121i	−0.679520	+	0.679520i
$59$		−	58.0335i		−	0.983618i	−0.870703	−	0.491809i	$-0.836336\pi$
$59$		−	58.0335i		−	0.983618i	0.870703	−	0.491809i	$-0.163664\pi$
$60$		0			0
$61$	−89.2995			−1.46393			−0.731963	−	0.681344i	$-0.761396\pi$
$61$	−89.2995			−1.46393			−0.731963	+	0.681344i	$0.761396\pi$
$62$	98.4827	+	98.4827i	1.58843	+	1.58843i
$63$		0			0
$64$			104.249i			1.62889i
$65$	−7.80752	−	60.0972i	−0.120116	−	0.924572i
$66$		0			0
$67$	−21.2058	−	21.2058i	−0.316505	−	0.316505i	0.530918	−	0.847423i	$-0.321847\pi$
$67$	−21.2058	−	21.2058i	−0.316505	−	0.316505i	−0.847423	+	0.530918i	$0.821847\pi$
$68$	−104.552	+	104.552i	−1.53754	+	1.53754i
$69$		0			0
$70$	−33.2726	−	25.6214i	−0.475323	−	0.366020i
$71$	78.8147			1.11007			0.555033	−	0.831828i	$-0.312706\pi$
$71$	78.8147			1.11007			0.555033	+	0.831828i	$0.312706\pi$
$72$		0			0
$73$	−18.2694	+	18.2694i	−0.250266	+	0.250266i	−0.821080	−	0.570814i	$-0.806628\pi$
$73$	−18.2694	+	18.2694i	−0.250266	+	0.250266i	0.570814	+	0.821080i	$0.306628\pi$
$74$		−	147.969i		−	1.99958i
$75$		0			0
$76$	148.138			1.94918
$77$	−7.38362	−	7.38362i	−0.0958911	−	0.0958911i
$78$		0			0
$79$		−	112.267i		−	1.42110i	−0.703646	−	0.710551i	$-0.748446\pi$
$79$		−	112.267i		−	1.42110i	0.703646	−	0.710551i	$-0.251554\pi$
$80$	10.2986	−	13.3740i	0.128732	−	0.167175i
$81$		0			0
$82$	50.4118	+	50.4118i	0.614777	+	0.614777i
$83$	12.9380	−	12.9380i	0.155879	−	0.155879i	−0.624859	−	0.780738i	$-0.714843\pi$
$83$	12.9380	−	12.9380i	0.155879	−	0.155879i	0.780738	+	0.624859i	$0.214843\pi$
$84$		0			0
$85$	120.636	−	15.6724i	1.41925	−	0.184382i
$86$	−64.4373			−0.749270
$87$		0			0
$88$	−18.4027	+	18.4027i	−0.209122	+	0.209122i
$89$		−	22.2193i		−	0.249655i	−0.992178	−	0.124827i	$-0.960162\pi$
$89$		−	22.2193i		−	0.249655i	0.992178	−	0.124827i	$-0.0398377\pi$
$90$		0			0
$91$	32.0677			0.352392
$92$	119.543	+	119.543i	1.29938	+	1.29938i
$93$		0			0
$94$			173.898i			1.84998i
$95$	−96.5661	−	74.3602i	−1.01649	−	0.782739i
$96$		0			0
$97$	90.6427	+	90.6427i	0.934461	+	0.934461i	0.997981	−	0.0635195i	$-0.0202325\pi$
$97$	90.6427	+	90.6427i	0.934461	+	0.934461i	−0.0635195	+	0.997981i	$0.520233\pi$
$98$	15.7128	−	15.7128i	0.160335	−	0.160335i
$99$		0			0
$100$	146.888	−	38.8211i	1.46888	−	0.388211i
$101$	180.124			1.78341			0.891703	−	0.452621i	$-0.149511\pi$
$101$	180.124			1.78341			0.891703	+	0.452621i	$0.149511\pi$
$102$		0			0
$103$	137.374	−	137.374i	1.33373	−	1.33373i	0.431729	−	0.902003i	$-0.357904\pi$
$103$	137.374	−	137.374i	1.33373	−	1.33373i	0.902003	−	0.431729i	$-0.142096\pi$
$104$		−	79.9247i		−	0.768506i
$105$		0			0
$106$	40.4651			0.381746
$107$	102.254	+	102.254i	0.955648	+	0.955648i	0.999057	−	0.0434091i	$-0.0138219\pi$
$107$	102.254	+	102.254i	0.955648	+	0.955648i	−0.0434091	+	0.999057i	$0.513822\pi$
$108$		0			0
$109$			58.4672i			0.536396i	0.963364	+	0.268198i	$0.0864282\pi$
$109$			58.4672i			0.536396i	−0.963364	+	0.268198i	$0.913572\pi$
$110$	62.1215	−	8.07051i	0.564741	−	0.0733683i
$111$		0			0
$112$	6.31582	+	6.31582i	0.0563913	+	0.0563913i
$113$	−39.8190	+	39.8190i	−0.352381	+	0.352381i	−0.860995	−	0.508614i	$-0.830158\pi$
$113$	−39.8190	+	39.8190i	−0.352381	+	0.352381i	0.508614	+	0.860995i	$0.330158\pi$
$114$		0			0
$115$	−17.9195	−	137.933i	−0.155822	−	1.19941i
$116$	106.704			0.919864
$117$		0			0
$118$	−130.267	+	130.267i	−1.10396	+	1.10396i
$119$			64.3710i			0.540933i
$120$		0			0
$121$	−105.423			−0.871269
$122$	200.450	+	200.450i	1.64303	+	1.64303i
$123$		0			0
$124$		−	266.631i		−	2.15025i
$125$	−115.238	−	48.4267i	−0.921906	−	0.387413i
$126$		0			0
$127$	28.1517	+	28.1517i	0.221667	+	0.221667i	0.809200	−	0.587533i	$-0.199901\pi$
$127$	28.1517	+	28.1517i	0.221667	+	0.221667i	−0.587533	+	0.809200i	$0.699901\pi$
$128$	129.090	−	129.090i	1.00851	−	1.00851i
$129$		0			0
$130$	−117.374	+	152.425i	−0.902877	+	1.17250i
$131$	32.5463			0.248445			0.124223	−	0.992254i	$-0.460356\pi$
$131$	32.5463			0.248445			0.124223	+	0.992254i	$0.460356\pi$
$132$		0			0
$133$	45.6029	−	45.6029i	0.342879	−	0.342879i
$134$			95.2009i			0.710454i
$135$		0			0
$136$	160.437			1.17968
$137$	−184.159	−	184.159i	−1.34423	−	1.34423i	−0.891804	−	0.452422i	$-0.850560\pi$
$137$	−184.159	−	184.159i	−1.34423	−	1.34423i	−0.452422	−	0.891804i	$-0.649440\pi$
$138$		0			0
$139$		−	76.2552i		−	0.548599i	−0.961644	−	0.274299i	$-0.911554\pi$
$139$		−	76.2552i		−	0.548599i	0.961644	−	0.274299i	$-0.0884459\pi$
$140$	10.3574	+	79.7246i	0.0739816	+	0.569462i
$141$		0			0
$142$	−176.914	−	176.914i	−1.24588	−	1.24588i
$143$	−33.8251	+	33.8251i	−0.236539	+	0.236539i
$144$		0			0
$145$	−69.5569	−	53.5619i	−0.479703	−	0.369393i
$146$	82.0184			0.561770
$147$		0			0
$148$	−200.305	+	200.305i	−1.35341	+	1.35341i
$149$			232.403i			1.55975i	0.625933	+	0.779877i	$0.284718\pi$
$149$			232.403i			1.55975i	−0.625933	+	0.779877i	$0.715282\pi$
$150$		0			0
$151$	170.930			1.13199			0.565994	−	0.824409i	$-0.308492\pi$
$151$	170.930			1.13199			0.565994	+	0.824409i	$0.308492\pi$
$152$	−113.659	−	113.659i	−0.747760	−	0.747760i
$153$		0			0
$154$			33.1478i			0.215246i
$155$	−133.840	+	173.808i	−0.863484	+	1.12134i
$156$		0			0
$157$	199.875	+	199.875i	1.27309	+	1.27309i	0.944457	+	0.328635i	$0.106589\pi$
$157$	199.875	+	199.875i	1.27309	+	1.27309i	0.328635	+	0.944457i	$0.393411\pi$
$158$	−252.005	+	252.005i	−1.59497	+	1.59497i
$159$		0			0
$160$	−183.923	+	23.8943i	−1.14952	+	0.149339i
$161$	73.6004			0.457145
$162$		0			0
$163$	−147.090	+	147.090i	−0.902392	+	0.902392i	−0.995643	−	0.0932506i	$-0.970274\pi$
$163$	−147.090	+	147.090i	−0.902392	+	0.902392i	0.0932506	+	0.995643i	$0.470274\pi$
$164$		−	136.485i		−	0.832223i
$165$		0			0
$166$	−58.0834			−0.349900
$167$	−43.6355	−	43.6355i	−0.261290	−	0.261290i	0.564288	−	0.825578i	$-0.309151\pi$
$167$	−43.6355	−	43.6355i	−0.261290	−	0.261290i	−0.825578	+	0.564288i	$0.809151\pi$
$168$		0			0
$169$			22.0948i			0.130738i
$170$	−305.970	−	235.611i	−1.79982	−	1.38595i
$171$		0			0
$172$	87.2285	+	87.2285i	0.507143	+	0.507143i
$173$	79.6322	−	79.6322i	0.460302	−	0.460302i	−0.438453	−	0.898754i	$-0.644473\pi$
$173$	79.6322	−	79.6322i	0.460302	−	0.460302i	0.898754	+	0.438453i	$0.144473\pi$
$174$		0			0
$175$	33.2674	−	57.1689i	0.190099	−	0.326679i
$176$	−13.3239			−0.0757039
$177$		0			0
$178$	−49.8754	+	49.8754i	−0.280199	+	0.280199i
$179$			189.993i			1.06141i	0.847555	+	0.530707i	$0.178074\pi$
$179$			189.993i			1.06141i	−0.847555	+	0.530707i	$0.821926\pi$
$180$		0			0
$181$	193.279			1.06784			0.533920	−	0.845535i	$-0.320718\pi$
$181$	193.279			1.06784			0.533920	+	0.845535i	$0.320718\pi$
$182$	−71.9820	−	71.9820i	−0.395505	−	0.395505i
$183$		0			0
$184$		−	183.440i		−	0.996955i
$185$	231.119	−	30.0258i	1.24929	−	0.162302i
$186$		0			0
$187$	−67.8987	−	67.8987i	−0.363095	−	0.363095i
$188$	235.406	−	235.406i	1.25216	−	1.25216i
$189$		0			0
$190$	49.8453	+	383.677i	0.262344	+	2.01935i
$191$	−236.062			−1.23593			−0.617963	−	0.786207i	$-0.712042\pi$
$191$	−236.062			−1.23593			−0.617963	+	0.786207i	$0.712042\pi$
$192$		0			0
$193$	126.994	−	126.994i	0.658001	−	0.658001i	−0.296906	−	0.954907i	$-0.595955\pi$
$193$	126.994	−	126.994i	0.658001	−	0.658001i	0.954907	+	0.296906i	$0.0959548\pi$
$194$		−	406.930i		−	2.09757i
$195$		0			0
$196$	−42.5408			−0.217045
$197$	−123.086	−	123.086i	−0.624804	−	0.624804i	0.321952	−	0.946756i	$-0.395661\pi$
$197$	−123.086	−	123.086i	−0.624804	−	0.624804i	−0.946756	+	0.321952i	$0.895661\pi$
$198$		0			0
$199$		−	27.6913i		−	0.139152i	−0.997577	−	0.0695761i	$-0.977835\pi$
$199$		−	27.6913i		−	0.139152i	0.997577	−	0.0695761i	$-0.0221647\pi$
$200$	−142.486	−	82.9148i	−0.712431	−	0.414574i
$201$		0			0
$202$	−404.322	−	404.322i	−2.00160	−	2.00160i
$203$	32.8479	−	32.8479i	0.161812	−	0.161812i
$204$		0			0
$205$	−68.5106	+	88.9697i	−0.334198	+	0.433998i
$206$	−616.726			−2.99381
$207$		0			0
$208$	28.9334	−	28.9334i	0.139103	−	0.139103i
$209$			96.2041i			0.460307i
$210$		0			0
$211$	−171.536			−0.812965			−0.406483	−	0.913658i	$-0.633245\pi$
$211$	−171.536			−0.812965			−0.406483	+	0.913658i	$0.633245\pi$
$212$	−54.7775	−	54.7775i	−0.258385	−	0.258385i
$213$		0			0
$214$		−	459.059i		−	2.14513i
$215$	−13.0756	−	100.647i	−0.0608166	−	0.468126i
$216$		0			0
$217$	−82.0801	−	82.0801i	−0.378249	−	0.378249i
$218$	131.241	−	131.241i	0.602021	−	0.602021i
$219$		0			0
$220$	−95.0187	−	73.1687i	−0.431903	−	0.332585i
$221$	294.890			1.33434
$222$		0			0
$223$	6.27227	−	6.27227i	0.0281268	−	0.0281268i	−0.692904	−	0.721030i	$-0.743669\pi$
$223$	6.27227	−	6.27227i	0.0281268	−	0.0281268i	0.721030	+	0.692904i	$0.243669\pi$
$224$		−	98.1406i		−	0.438128i
$225$		0			0
$226$	178.763			0.790985
$227$	155.382	+	155.382i	0.684501	+	0.684501i	0.961011	−	0.276510i	$-0.0891779\pi$
$227$	155.382	+	155.382i	0.684501	+	0.684501i	−0.276510	+	0.961011i	$0.589178\pi$
$228$		0			0
$229$			283.171i			1.23656i	0.785960	+	0.618278i	$0.212169\pi$
$229$			283.171i			1.23656i	−0.785960	+	0.618278i	$0.787831\pi$
$230$	−269.392	+	349.839i	−1.17127	+	1.52104i
$231$		0			0
$232$	−81.8693	−	81.8693i	−0.352885	−	0.352885i
$233$	−18.5950	+	18.5950i	−0.0798069	+	0.0798069i	−0.745883	−	0.666077i	$-0.767972\pi$
$233$	−18.5950	+	18.5950i	−0.0798069	+	0.0798069i	0.666077	+	0.745883i	$0.267972\pi$
$234$		0			0
$235$	−271.619	+	35.2873i	−1.15582	+	0.150159i
$236$	352.684			1.49443
$237$		0			0
$238$	144.493	−	144.493i	0.607113	−	0.607113i
$239$			265.031i			1.10892i	0.832211	+	0.554459i	$0.187075\pi$
$239$			265.031i			1.10892i	−0.832211	+	0.554459i	$0.812925\pi$
$240$		0			0
$241$	127.492			0.529011			0.264506	−	0.964384i	$-0.414791\pi$
$241$	127.492			0.529011			0.264506	+	0.964384i	$0.414791\pi$
$242$	236.643	+	236.643i	0.977864	+	0.977864i
$243$		0			0
$244$		−	542.696i		−	2.22417i
$245$	27.7309	+	21.3541i	0.113187	+	0.0871594i
$246$		0			0
$247$	−208.911	−	208.911i	−0.845795	−	0.845795i
$248$	−204.574	+	204.574i	−0.824896	+	0.824896i
$249$		0			0
$250$	149.971	+	367.377i	0.599885	+	1.46951i
$251$	−31.9519			−0.127298			−0.0636492	−	0.997972i	$-0.520274\pi$
$251$	−31.9519			−0.127298			−0.0636492	+	0.997972i	$0.520274\pi$
$252$		0			0
$253$	−77.6338	+	77.6338i	−0.306853	+	0.306853i
$254$		−	126.383i		−	0.497573i
$255$		0			0
$256$	−162.537			−0.634910
$257$	138.387	+	138.387i	0.538470	+	0.538470i	0.923079	−	0.384610i	$-0.125664\pi$
$257$	138.387	+	138.387i	0.538470	+	0.538470i	−0.384610	+	0.923079i	$0.625664\pi$
$258$		0			0
$259$			123.324i			0.476155i
$260$	365.226	−	47.4484i	1.40472	−	0.182494i
$261$		0			0
$262$	−73.0564	−	73.0564i	−0.278841	−	0.278841i
$263$	230.486	−	230.486i	0.876373	−	0.876373i	−0.116785	−	0.993157i	$-0.537259\pi$
$263$	230.486	−	230.486i	0.876373	−	0.876373i	0.993157	+	0.116785i	$0.0372587\pi$
$264$		0			0
$265$	8.21116	+	63.2041i	0.0309855	+	0.238506i
$266$	−204.729			−0.769657
$267$		0			0
$268$	128.873	−	128.873i	0.480870	−	0.480870i
$269$		−	332.673i		−	1.23670i	−0.785901	−	0.618352i	$-0.787801\pi$
$269$		−	332.673i		−	1.23670i	0.785901	−	0.618352i	$-0.212199\pi$
$270$		0			0
$271$	−253.724			−0.936251			−0.468126	−	0.883662i	$-0.655071\pi$
$271$	−253.724			−0.936251			−0.468126	+	0.883662i	$0.655071\pi$
$272$	58.0794	+	58.0794i	0.213527	+	0.213527i
$273$		0			0
$274$			826.759i			3.01737i
$275$	25.2113	+	95.3924i	0.0916775	+	0.346881i
$276$		0			0
$277$	252.491	+	252.491i	0.911521	+	0.911521i	0.996392	−	0.0848711i	$-0.0270479\pi$
$277$	252.491	+	252.491i	0.911521	+	0.911521i	−0.0848711	+	0.996392i	$0.527048\pi$
$278$	−171.169	+	171.169i	−0.615717	+	0.615717i
$279$		0			0
$280$	53.2223	−	69.1158i	0.190080	−	0.246842i
$281$	3.26524			0.0116201			0.00581004	−	0.999983i	$-0.498151\pi$
$281$	3.26524			0.0116201			0.00581004	+	0.999983i	$0.498151\pi$
$282$		0			0
$283$	61.6256	−	61.6256i	0.217758	−	0.217758i	−0.589795	−	0.807553i	$-0.700791\pi$
$283$	61.6256	−	61.6256i	0.217758	−	0.217758i	0.807553	+	0.589795i	$0.200791\pi$
$284$			478.977i			1.68654i
$285$		0			0
$286$	151.854			0.530956
$287$	−42.0155	−	42.0155i	−0.146395	−	0.146395i
$288$		0			0
$289$			302.947i			1.04826i
$290$	35.9038	+	276.364i	0.123806	+	0.952978i
$291$		0			0
$292$	−111.028	−	111.028i	−0.380233	−	0.380233i
$293$	−150.796	+	150.796i	−0.514663	+	0.514663i	−0.915952	−	0.401289i	$-0.868562\pi$
$293$	−150.796	+	150.796i	−0.514663	+	0.514663i	0.401289	+	0.915952i	$0.368562\pi$
$294$		0			0
$295$	−229.903	−	177.036i	−0.779332	−	0.600121i
$296$	307.370			1.03841
$297$		0			0
$298$	521.673	−	521.673i	1.75058	−	1.75058i
$299$		−	337.171i		−	1.12766i
$300$		0			0
$301$	53.7050			0.178422
$302$	−383.685	−	383.685i	−1.27048	−	1.27048i
$303$		0			0
$304$		−	82.2914i		−	0.270695i
$305$	−272.415	+	353.766i	−0.893165	+	1.15989i
$306$		0			0
$307$	37.6731	+	37.6731i	0.122714	+	0.122714i	0.765797	−	0.643083i	$-0.222345\pi$
$307$	37.6731	+	37.6731i	0.122714	+	0.122714i	−0.643083	+	0.765797i	$0.722345\pi$
$308$	44.8722	−	44.8722i	0.145689	−	0.145689i
$309$		0			0
$310$	690.574	−	89.7159i	2.22766	−	0.289406i
$311$	−208.646			−0.670888			−0.335444	−	0.942060i	$-0.608886\pi$
$311$	−208.646			−0.670888			−0.335444	+	0.942060i	$0.608886\pi$
$312$		0			0
$313$	−25.0439	+	25.0439i	−0.0800125	+	0.0800125i	−0.745980	−	0.665968i	$-0.768019\pi$
$313$	−25.0439	+	25.0439i	−0.0800125	+	0.0800125i	0.665968	+	0.745980i	$0.268019\pi$
$314$		−	897.316i		−	2.85770i
$315$		0			0
$316$	682.276			2.15910
$317$	164.900	+	164.900i	0.520188	+	0.520188i	0.917628	−	0.397440i	$-0.130101\pi$
$317$	164.900	+	164.900i	0.520188	+	0.520188i	−0.397440	+	0.917628i	$0.630101\pi$
$318$		0			0
$319$			69.2961i			0.217229i
$320$	412.988	+	318.019i	1.29059	+	0.993811i
$321$		0			0
$322$	−165.210	−	165.210i	−0.513074	−	0.513074i
$323$	419.358	−	419.358i	1.29832	−	1.29832i
$324$		0			0
$325$	−261.896	−	152.401i	−0.805834	−	0.468927i
$326$	660.342			2.02559
$327$		0			0
$328$	−104.718	+	104.718i	−0.319263	+	0.319263i
$329$		−	144.935i		−	0.440532i
$330$		0			0
$331$	−324.395			−0.980045			−0.490023	−	0.871710i	$-0.663011\pi$
$331$	−324.395			−0.980045			−0.490023	+	0.871710i	$0.663011\pi$
$332$	78.6273	+	78.6273i	0.236829	+	0.236829i
$333$		0			0
$334$			195.896i			0.586516i
$335$	−148.698	+	19.3181i	−0.443875	+	0.0576660i
$336$		0			0
$337$	−27.1490	−	27.1490i	−0.0805607	−	0.0805607i	0.665678	−	0.746239i	$-0.268142\pi$
$337$	−27.1490	−	27.1490i	−0.0805607	−	0.0805607i	−0.746239	+	0.665678i	$0.768142\pi$
$338$	49.5959	−	49.5959i	0.146734	−	0.146734i
$339$		0			0
$340$	95.2454	+	733.137i	0.280134	+	2.15628i
$341$	173.156			0.507790
$342$		0			0
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$		−	133.853i		−	0.389107i
$345$		0			0
$346$	−357.499			−1.03323
$347$	0.188420	+	0.188420i	0.000542997	+	0.000542997i	0.707378	−	0.706835i	$-0.249878\pi$
$347$	0.188420	+	0.188420i	0.000542997	+	0.000542997i	−0.706835	+	0.707378i	$0.749878\pi$
$348$		0			0
$349$			222.903i			0.638690i	0.947638	+	0.319345i	$0.103463\pi$
$349$			222.903i			0.638690i	−0.947638	+	0.319345i	$0.896537\pi$
$350$	−203.001	+	53.6513i	−0.580004	+	0.153290i
$351$		0			0
$352$	103.519	+	103.519i	0.294088	+	0.294088i
$353$	−10.0036	+	10.0036i	−0.0283387	+	0.0283387i	−0.721134	−	0.692795i	$-0.756379\pi$
$353$	−10.0036	+	10.0036i	−0.0283387	+	0.0283387i	0.692795	+	0.721134i	$0.256379\pi$
$354$		0			0
$355$	240.430	−	312.229i	0.677269	−	0.879519i
$356$	135.032			0.379304
$357$		0			0
$358$	426.476	−	426.476i	1.19127	−	1.19127i
$359$			605.191i			1.68577i	0.538096	+	0.842884i	$0.319144\pi$
$359$			605.191i			1.68577i	−0.538096	+	0.842884i	$0.680856\pi$
$360$		0			0
$361$	−233.179			−0.645924
$362$	−433.851	−	433.851i	−1.19848	−	1.19848i
$363$		0			0
$364$			194.884i			0.535395i
$365$	16.6431	+	128.108i	0.0455976	+	0.350980i
$366$		0			0
$367$	259.533	+	259.533i	0.707174	+	0.707174i	0.965940	−	0.258766i	$-0.0833157\pi$
$367$	259.533	+	259.533i	0.707174	+	0.707174i	−0.258766	+	0.965940i	$0.583316\pi$
$368$	66.4067	−	66.4067i	0.180453	−	0.180453i
$369$		0			0
$370$	−586.188	−	451.391i	−1.58429	−	1.21998i
$371$	−33.7255			−0.0909044
$372$		0			0
$373$	446.882	−	446.882i	1.19807	−	1.19807i	0.223332	−	0.974742i	$-0.428307\pi$
$373$	446.882	−	446.882i	1.19807	−	1.19807i	0.974742	−	0.223332i	$-0.0716934\pi$
$374$			304.823i			0.815035i
$375$		0			0
$376$	−361.232			−0.960724
$377$	−150.480	−	150.480i	−0.399150	−	0.399150i
$378$		0			0
$379$		−	51.1198i		−	0.134881i	−0.997723	−	0.0674404i	$-0.978517\pi$
$379$		−	51.1198i		−	0.134881i	0.997723	−	0.0674404i	$-0.0214832\pi$
$380$	451.907	−	586.858i	1.18923	−	1.54436i
$381$		0			0
$382$	529.886	+	529.886i	1.38714	+	1.38714i
$383$	−405.345	+	405.345i	−1.05834	+	1.05834i	−0.0601525	+	0.998189i	$0.519159\pi$
$383$	−405.345	+	405.345i	−1.05834	+	1.05834i	−0.998189	+	0.0601525i	$0.980841\pi$
$384$		0			0
$385$	−51.7750	+	6.72634i	−0.134480	+	0.0174710i
$386$	−570.125			−1.47701
$387$		0			0
$388$	−550.859	+	550.859i	−1.41974	+	1.41974i
$389$			47.3061i			0.121609i	0.998150	+	0.0608047i	$0.0193667\pi$
$389$			47.3061i			0.121609i	−0.998150	+	0.0608047i	$0.980633\pi$
$390$		0			0
$391$	676.819			1.73099
$392$	32.6396	+	32.6396i	0.0832644	+	0.0832644i
$393$		0			0
$394$			552.581i			1.40249i
$395$	−444.753	−	342.480i	−1.12596	−	0.867037i
$396$		0			0
$397$	−338.755	−	338.755i	−0.853287	−	0.853287i	0.137249	−	0.990537i	$-0.456174\pi$
$397$	−338.755	−	338.755i	−0.853287	−	0.853287i	−0.990537	+	0.137249i	$0.956174\pi$
$398$	−62.1583	+	62.1583i	−0.156177	+	0.156177i
$399$		0			0
$400$	−21.5653	−	81.5971i	−0.0539133	−	0.203993i
$401$	−351.967			−0.877723			−0.438861	−	0.898555i	$-0.644618\pi$
$401$	−351.967			−0.877723			−0.438861	+	0.898555i	$0.644618\pi$
$402$		0			0
$403$	−376.017	+	376.017i	−0.933044	+	0.933044i
$404$			1094.66i			2.70955i
$405$		0			0
$406$	−147.467			−0.363219
$407$	−130.083	−	130.083i	−0.319614	−	0.319614i
$408$		0			0
$409$			34.7110i			0.0848681i	0.999099	+	0.0424340i	$0.0135112\pi$
$409$			34.7110i			0.0848681i	−0.999099	+	0.0424340i	$0.986489\pi$
$410$	353.494	−	45.9242i	0.862181	−	0.112010i
$411$		0			0
$412$	834.860	+	834.860i	2.02636	+	2.02636i
$413$	108.571	−	108.571i	0.262883	−	0.262883i
$414$		0			0
$415$	−11.7862	−	90.7228i	−0.0284006	−	0.218609i
$416$	−449.592			−1.08075
$417$		0			0
$418$	215.948	−	215.948i	0.516623	−	0.516623i
$419$		−	522.337i		−	1.24663i	−0.781972	−	0.623313i	$-0.785786\pi$
$419$		−	522.337i		−	1.24663i	0.781972	−	0.623313i	$-0.214214\pi$
$420$		0			0
$421$	150.337			0.357096			0.178548	−	0.983931i	$-0.442860\pi$
$421$	150.337			0.357096			0.178548	+	0.983931i	$0.442860\pi$
$422$	385.044	+	385.044i	0.912427	+	0.912427i
$423$		0			0
$424$			84.0566i			0.198247i
$425$	305.923	−	525.717i	0.719818	−	1.23698i
$426$		0			0
$427$	−167.064	−	167.064i	−0.391251	−	0.391251i
$428$	−621.426	+	621.426i	−1.45193	+	1.45193i
$429$		0			0
$430$	−196.571	+	255.272i	−0.457142	+	0.593656i
$431$	165.122			0.383113			0.191557	−	0.981482i	$-0.438646\pi$
$431$	165.122			0.383113			0.191557	+	0.981482i	$0.438646\pi$
$432$		0			0
$433$	−173.796	+	173.796i	−0.401377	+	0.401377i	−0.878718	−	0.477341i	$-0.841601\pi$
$433$	−173.796	+	173.796i	−0.401377	+	0.401377i	0.477341	+	0.878718i	$0.341601\pi$
$434$			368.488i			0.849052i
$435$		0			0
$436$	−355.320			−0.814955
$437$	−479.484	−	479.484i	−1.09722	−	1.09722i
$438$		0			0
$439$			140.286i			0.319558i	0.987153	+	0.159779i	$0.0510782\pi$
$439$			140.286i			0.319558i	−0.987153	+	0.159779i	$0.948922\pi$
$440$	16.7646	+	129.043i	0.0381013	+	0.293278i
$441$		0			0
$442$	−661.937	−	661.937i	−1.49759	−	1.49759i
$443$	−548.196	+	548.196i	−1.23746	+	1.23746i	−0.276429	+	0.961034i	$0.589151\pi$
$443$	−548.196	+	548.196i	−1.23746	+	1.23746i	−0.961034	+	0.276429i	$0.910849\pi$
$444$		0			0
$445$	−88.0230	−	67.7817i	−0.197805	−	0.152318i
$446$	−28.1586			−0.0631359
$447$		0			0
$448$	−195.032	+	195.032i	−0.435339	+	0.435339i
$449$			693.773i			1.54515i	0.634923	+	0.772576i	$0.281032\pi$
$449$			693.773i			1.54515i	−0.634923	+	0.772576i	$0.718968\pi$
$450$		0			0
$451$	88.6361			0.196532
$452$	−241.990	−	241.990i	−0.535377	−	0.535377i
$453$		0			0
$454$		−	697.568i		−	1.53649i
$455$	97.8250	−	127.038i	0.215000	−	0.279205i
$456$		0			0
$457$	327.671	+	327.671i	0.717004	+	0.717004i	0.967990	−	0.250987i	$-0.0807551\pi$
$457$	327.671	+	327.671i	0.717004	+	0.717004i	−0.250987	+	0.967990i	$0.580755\pi$
$458$	635.632	−	635.632i	1.38784	−	1.38784i
$459$		0			0
$460$	838.252	−	108.901i	1.82229	−	0.236742i
$461$	−93.1493			−0.202059			−0.101030	−	0.994883i	$-0.532214\pi$
$461$	−93.1493			−0.202059			−0.101030	+	0.994883i	$0.532214\pi$
$462$		0			0
$463$	−498.598	+	498.598i	−1.07689	+	1.07689i	−0.0800990	+	0.996787i	$0.525524\pi$
$463$	−498.598	+	498.598i	−1.07689	+	1.07689i	−0.996787	+	0.0800990i	$0.974476\pi$
$464$		−	59.2747i		−	0.127747i
$465$		0			0
$466$	83.4800			0.179142
$467$	308.256	+	308.256i	0.660078	+	0.660078i	0.955398	−	0.295320i	$-0.0954264\pi$
$467$	308.256	+	308.256i	0.660078	+	0.660078i	−0.295320	+	0.955398i	$0.595426\pi$
$468$		0			0
$469$		−	79.3449i		−	0.169179i
$470$	688.909	+	530.491i	1.46576	+	1.12870i
$471$		0			0
$472$	−270.599	−	270.599i	−0.573302	−	0.573302i
$473$	−56.6482	+	56.6482i	−0.119764	+	0.119764i
$474$		0			0
$475$	−589.165	+	155.711i	−1.24035	+	0.327812i
$476$	−391.200			−0.821848
$477$		0			0
$478$	594.913	−	594.913i	1.24459	−	1.24459i
$479$		−	178.073i		−	0.371760i	−0.982572	−	0.185880i	$-0.940486\pi$
$479$		−	178.073i		−	0.371760i	0.982572	−	0.185880i	$-0.0595136\pi$
$480$		0			0
$481$	564.961			1.17455
$482$	−286.179	−	286.179i	−0.593733	−	0.593733i
$483$		0			0
$484$		−	640.686i		−	1.32373i
$485$	635.600	−	82.5739i	1.31051	−	0.170255i
$486$		0			0
$487$	−330.361	−	330.361i	−0.678359	−	0.678359i	0.281270	−	0.959629i	$-0.409244\pi$
$487$	−330.361	−	330.361i	−0.678359	−	0.678359i	−0.959629	+	0.281270i	$0.909244\pi$
$488$	−416.386	+	416.386i	−0.853250	+	0.853250i
$489$		0			0
$490$	−14.3141	−	110.181i	−0.0292124	−	0.224858i
$491$	729.372			1.48548			0.742741	−	0.669578i	$-0.233525\pi$
$491$	729.372			1.48548			0.742741	+	0.669578i	$0.233525\pi$
$492$		0			0
$493$	302.065	−	302.065i	0.612708	−	0.612708i
$494$			937.882i			1.89855i
$495$		0			0
$496$	−148.115			−0.298619
$497$	147.449	+	147.449i	0.296678	+	0.296678i
$498$		0			0
$499$			385.715i			0.772976i	0.922294	+	0.386488i	$0.126312\pi$
$499$			385.715i			0.772976i	−0.922294	+	0.386488i	$0.873688\pi$
$500$	294.301	−	700.333i	0.588603	−	1.40067i
$501$		0			0
$502$	71.7220	+	71.7220i	0.142873	+	0.142873i
$503$	139.070	−	139.070i	0.276482	−	0.276482i	−0.555221	−	0.831703i	$-0.687366\pi$
$503$	139.070	−	139.070i	0.276482	−	0.276482i	0.831703	+	0.555221i	$0.187366\pi$
$504$		0			0
$505$	549.482	−	713.572i	1.08808	−	1.41301i
$506$	348.528			0.688790
$507$		0			0
$508$	−171.085	+	171.085i	−0.336781	+	0.336781i
$509$			337.164i			0.662404i	0.943560	+	0.331202i	$0.107454\pi$
$509$			337.164i			0.662404i	−0.943560	+	0.331202i	$0.892546\pi$
$510$		0			0
$511$	−68.3579			−0.133773
$512$	−151.514	−	151.514i	−0.295926	−	0.295926i
$513$		0			0
$514$		−	621.270i		−	1.20870i
$515$	−125.146	−	963.289i	−0.243001	−	1.87046i
$516$		0			0
$517$	152.878	+	152.878i	0.295702	+	0.295702i
$518$	276.825	−	276.825i	0.534411	−	0.534411i
$519$		0			0
$520$	−316.626	−	243.816i	−0.608897	−	0.468878i
$521$	346.121			0.664340			0.332170	−	0.943220i	$-0.392219\pi$
$521$	346.121			0.664340			0.332170	+	0.943220i	$0.392219\pi$
$522$		0			0
$523$	−295.339	+	295.339i	−0.564702	+	0.564702i	−0.930639	−	0.365938i	$-0.880748\pi$
$523$	−295.339	+	295.339i	−0.564702	+	0.564702i	0.365938	+	0.930639i	$0.380748\pi$
$524$			197.793i			0.377467i
$525$		0			0
$526$	−1034.74			−1.96718
$527$	−754.797	−	754.797i	−1.43225	−	1.43225i
$528$		0			0
$529$		−	244.859i		−	0.462872i
$530$	123.442	−	160.305i	0.232910	−	0.302462i
$531$		0			0
$532$	277.141	+	277.141i	0.520941	+	0.520941i
$533$	−192.477	+	192.477i	−0.361120	+	0.361120i
$534$		0			0
$535$	717.022	−	93.1519i	1.34023	−	0.174116i
$536$	−197.757			−0.368950
$537$		0			0
$538$	−746.748	+	746.748i	−1.38801	+	1.38801i
$539$		−	27.6270i		−	0.0512560i
$540$		0			0
$541$	−734.168			−1.35706			−0.678529	−	0.734574i	$-0.737382\pi$
$541$	−734.168			−1.35706			−0.678529	+	0.734574i	$0.737382\pi$
$542$	569.532	+	569.532i	1.05080	+	1.05080i
$543$		0			0
$544$		−	902.487i		−	1.65898i
$545$	231.621	+	178.359i	0.424993	+	0.327264i
$546$		0			0
$547$	124.027	+	124.027i	0.226740	+	0.226740i	0.811329	−	0.584589i	$-0.198744\pi$
$547$	124.027	+	124.027i	0.226740	+	0.226740i	−0.584589	+	0.811329i	$0.698744\pi$
$548$	1119.18	−	1119.18i	2.04230	−	2.04230i
$549$		0			0
$550$	157.535	−	270.718i	0.286427	−	0.492214i
$551$	−427.989			−0.776749
$552$		0			0
$553$	210.032	−	210.032i	0.379805	−	0.379805i
$554$		−	1133.53i		−	2.04608i
$555$		0			0
$556$	463.423			0.833494
$557$	436.412	+	436.412i	0.783504	+	0.783504i	0.980420	−	0.196916i	$-0.0630926\pi$
$557$	436.412	+	436.412i	0.783504	+	0.783504i	−0.196916	+	0.980420i	$0.563093\pi$
$558$		0			0
$559$		−	246.028i		−	0.440121i
$560$	44.2874	−	5.75360i	0.0790847	−	0.0102743i
$561$		0			0
$562$	−7.32946	−	7.32946i	−0.0130417	−	0.0130417i
$563$	259.609	−	259.609i	0.461117	−	0.461117i	−0.437905	−	0.899021i	$-0.644279\pi$
$563$	259.609	−	259.609i	0.461117	−	0.461117i	0.899021	+	0.437905i	$0.144279\pi$
$564$		0			0
$565$	36.2744	+	279.216i	0.0642025	+	0.494188i
$566$	−276.661			−0.488800
$567$		0			0
$568$	367.497	−	367.497i	0.647002	−	0.647002i
$569$		−	151.092i		−	0.265539i	−0.991147	−	0.132770i	$-0.957613\pi$
$569$		−	151.092i		−	0.265539i	0.991147	−	0.132770i	$-0.0423870\pi$
$570$		0			0
$571$	−502.406			−0.879871			−0.439935	−	0.898029i	$-0.644999\pi$
$571$	−502.406			−0.879871			−0.439935	+	0.898029i	$0.644999\pi$
$572$	−205.564	−	205.564i	−0.359377	−	0.359377i
$573$		0			0
$574$			188.624i			0.328612i
$575$	−601.093	−	349.785i	−1.04538	−	0.608321i
$576$		0			0
$577$	81.3805	+	81.3805i	0.141041	+	0.141041i	0.774102	−	0.633061i	$-0.218202\pi$
$577$	81.3805	+	81.3805i	0.141041	+	0.141041i	−0.633061	+	0.774102i	$0.718202\pi$
$578$	680.023	−	680.023i	1.17651	−	1.17651i
$579$		0			0
$580$	325.510	−	422.715i	0.561224	−	0.728820i
$581$	48.4094			0.0833208
$582$		0			0
$583$	35.5738	−	35.5738i	0.0610185	−	0.0610185i
$584$			170.374i			0.291736i
$585$		0			0
$586$	676.981			1.15526
$587$	283.065	+	283.065i	0.482224	+	0.482224i	0.905841	−	0.423617i	$-0.139240\pi$
$587$	283.065	+	283.065i	0.482224	+	0.482224i	−0.423617	+	0.905841i	$0.639240\pi$
$588$		0			0
$589$			1069.45i			1.81571i
$590$	118.671	+	913.451i	0.201137	+	1.54822i
$591$		0			0
$592$	111.271	+	111.271i	0.187957	+	0.187957i
$593$	−5.75309	+	5.75309i	−0.00970167	+	0.00970167i	−0.711941	−	0.702239i	$-0.752184\pi$
$593$	−5.75309	+	5.75309i	−0.00970167	+	0.00970167i	0.702239	+	0.711941i	$0.252184\pi$
$594$		0			0
$595$	255.010	+	196.369i	0.428588	+	0.330032i
$596$	−1412.38			−2.36976
$597$		0			0
$598$	−756.843	+	756.843i	−1.26562	+	1.26562i
$599$		−	619.287i		−	1.03387i	−0.856025	−	0.516934i	$-0.827073\pi$
$599$		−	619.287i		−	1.03387i	0.856025	−	0.516934i	$-0.172927\pi$
$600$		0			0
$601$	457.367			0.761011			0.380505	−	0.924779i	$-0.375750\pi$
$601$	457.367			0.761011			0.380505	+	0.924779i	$0.375750\pi$
$602$	−120.551	−	120.551i	−0.200251	−	0.200251i
$603$		0			0
$604$			1038.79i			1.71985i
$605$	−321.603	+	417.642i	−0.531575	+	0.690317i
$606$		0			0
$607$	−25.5979	−	25.5979i	−0.0421713	−	0.0421713i	0.685707	−	0.727878i	$-0.259493\pi$
$607$	−25.5979	−	25.5979i	−0.0421713	−	0.0421713i	−0.727878	+	0.685707i	$0.759493\pi$
$608$	−639.356	+	639.356i	−1.05157	+	1.05157i
$609$		0			0
$610$	1405.58	−	182.606i	2.30423	−	0.299354i
$611$	−663.961			−1.08668
$612$		0			0
$613$	−308.221	+	308.221i	−0.502808	+	0.502808i	−0.912309	−	0.409501i	$-0.865703\pi$
$613$	−308.221	+	308.221i	−0.502808	+	0.502808i	0.409501	+	0.912309i	$0.365703\pi$
$614$		−	169.129i		−	0.275454i
$615$		0			0
$616$	−68.8567			−0.111780
$617$	−21.2194	−	21.2194i	−0.0343913	−	0.0343913i	0.689702	−	0.724093i	$-0.257742\pi$
$617$	−21.2194	−	21.2194i	−0.0343913	−	0.0343913i	−0.724093	+	0.689702i	$0.757742\pi$
$618$		0			0
$619$		−	794.043i		−	1.28278i	−0.767213	−	0.641392i	$-0.778357\pi$
$619$		−	794.043i		−	1.28278i	0.767213	−	0.641392i	$-0.221643\pi$
$620$	−1056.28	−	813.380i	−1.70367	−	1.31190i
$621$		0			0
$622$	468.346	+	468.346i	0.752968	+	0.752968i
$623$	41.5685	−	41.5685i	0.0667230	−	0.0667230i
$624$		0			0
$625$	−543.389	+	308.794i	−0.869422	+	0.494071i
$626$	112.432			0.179603
$627$		0			0
$628$	−1214.69	+	1214.69i	−1.93423	+	1.93423i
$629$			1134.07i			1.80298i
$630$		0			0
$631$	−365.937			−0.579932			−0.289966	−	0.957037i	$-0.593644\pi$
$631$	−365.937			−0.579932			−0.289966	+	0.957037i	$0.593644\pi$
$632$	−523.479	−	523.479i	−0.828290	−	0.828290i
$633$		0			0
$634$		−	740.297i		−	1.16766i
$635$	197.403	−	25.6457i	0.310871	−	0.0403869i
$636$		0			0
$637$	59.9931	+	59.9931i	0.0941808	+	0.0941808i
$638$	155.548	−	155.548i	0.243806	−	0.243806i
$639$		0			0
$640$	−117.598	−	905.195i	−0.183747	−	1.41437i
$641$	−610.251			−0.952029			−0.476014	−	0.879437i	$-0.657919\pi$
$641$	−610.251			−0.952029			−0.476014	+	0.879437i	$0.657919\pi$
$642$		0			0
$643$	−18.4704	+	18.4704i	−0.0287253	+	0.0287253i	−0.721324	−	0.692598i	$-0.756466\pi$
$643$	−18.4704	+	18.4704i	−0.0287253	+	0.0287253i	0.692598	+	0.721324i	$0.256466\pi$
$644$			447.289i			0.694548i
$645$		0			0
$646$	−1882.66			−2.91433
$647$	633.369	+	633.369i	0.978931	+	0.978931i	0.999783	−	0.0208512i	$-0.00663764\pi$
$647$	633.369	+	633.369i	0.978931	+	0.978931i	−0.0208512	+	0.999783i	$0.506638\pi$
$648$		0			0
$649$			229.041i			0.352914i
$650$	245.782	+	929.969i	0.378126	+	1.43072i
$651$		0			0
$652$	−893.904	−	893.904i	−1.37102	−	1.37102i
$653$	−345.393	+	345.393i	−0.528933	+	0.528933i	−0.920254	−	0.391321i	$-0.872018\pi$
$653$	−345.393	+	345.393i	−0.528933	+	0.528933i	0.391321	+	0.920254i	$0.372018\pi$
$654$		0			0
$655$	99.2852	−	128.934i	0.151580	−	0.196846i
$656$	−75.8178			−0.115576
$657$		0			0
$658$	−325.334	+	325.334i	−0.494428	+	0.494428i
$659$		−	347.238i		−	0.526917i	−0.964671	−	0.263458i	$-0.915137\pi$
$659$		−	347.238i		−	0.526917i	0.964671	−	0.263458i	$-0.0848632\pi$
$660$		0			0
$661$	−482.959			−0.730649			−0.365324	−	0.930880i	$-0.619042\pi$
$661$	−482.959			−0.730649			−0.365324	+	0.930880i	$0.619042\pi$
$662$	728.166	+	728.166i	1.09995	+	1.09995i
$663$		0			0
$664$		−	120.654i		−	0.181708i
$665$	−41.5434	−	319.774i	−0.0624713	−	0.480863i
$666$		0			0
$667$	−345.374	−	345.374i	−0.517802	−	0.517802i
$668$	265.184	−	265.184i	0.396982	−	0.396982i
$669$		0			0
$670$	377.144	+	290.418i	0.562902	+	0.433459i
$671$	352.439			0.525245
$672$		0			0
$673$	769.503	−	769.503i	1.14339	−	1.14339i	0.155566	−	0.987825i	$-0.450280\pi$
$673$	769.503	−	769.503i	1.14339	−	1.14339i	0.987825	−	0.155566i	$-0.0497202\pi$
$674$			121.882i			0.180834i
$675$		0			0
$676$	−134.276			−0.198633
$677$	−265.615	−	265.615i	−0.392341	−	0.392341i	0.483180	−	0.875521i	$-0.339482\pi$
$677$	−265.615	−	265.615i	−0.392341	−	0.392341i	−0.875521	+	0.483180i	$0.839482\pi$
$678$		0			0
$679$			339.154i			0.499490i
$680$	489.425	−	635.580i	0.719742	−	0.934676i
$681$		0			0
$682$	−388.682	−	388.682i	−0.569916	−	0.569916i
$683$	−346.533	+	346.533i	−0.507369	+	0.507369i	−0.913718	−	0.406349i	$-0.866802\pi$
$683$	−346.533	+	346.533i	−0.507369	+	0.507369i	0.406349	+	0.913718i	$0.366802\pi$
$684$		0			0
$685$	−1291.35	+	167.766i	−1.88518	+	0.244913i
$686$	58.7920			0.0857026
$687$		0			0
$688$	48.4559	−	48.4559i	0.0704301	−	0.0704301i
$689$			154.500i			0.224238i
$690$		0			0
$691$	−330.788			−0.478709			−0.239355	−	0.970932i	$-0.576936\pi$
$691$	−330.788			−0.478709			−0.239355	+	0.970932i	$0.576936\pi$
$692$	483.946	+	483.946i	0.699343	+	0.699343i
$693$		0			0
$694$		−	0.845888i		−	0.00121886i
$695$	−302.090	−	232.623i	−0.434661	−	0.334709i
$696$		0			0
$697$	−386.369	−	386.369i	−0.554331	−	0.554331i
$698$	500.348	−	500.348i	0.716830	−	0.716830i
$699$		0			0
$700$	347.430	+	202.175i	0.496329	+	0.288821i
$701$	595.747			0.849853			0.424926	−	0.905228i	$-0.360300\pi$
$701$	595.747			0.849853			0.424926	+	0.905228i	$0.360300\pi$
$702$		0			0
$703$	803.421	−	803.421i	1.14285	−	1.14285i
$704$		−	411.440i		−	0.584432i
$705$		0			0
$706$	44.9098			0.0636116
$707$	336.981	+	336.981i	0.476635	+	0.476635i
$708$		0			0
$709$			546.791i			0.771215i	0.922663	+	0.385608i	$0.126008\pi$
$709$			546.791i			0.771215i	−0.922663	+	0.385608i	$0.873992\pi$
$710$	−1240.55	+	161.166i	−1.74725	+	0.226994i
$711$		0			0
$712$	−103.604	−	103.604i	−0.145511	−	0.145511i
$713$	−863.018	+	863.018i	−1.21040	+	1.21040i
$714$		0			0
$715$	30.8140	+	237.186i	0.0430965	+	0.331729i
$716$	−1154.64			−1.61262
$717$		0			0
$718$	1358.46	−	1358.46i	1.89201	−	1.89201i
$719$			383.796i			0.533791i	0.963725	+	0.266896i	$0.0859979\pi$
$719$			383.796i			0.533791i	−0.963725	+	0.266896i	$0.914002\pi$
$720$		0			0
$721$	514.008			0.712910
$722$	523.413	+	523.413i	0.724949	+	0.724949i
$723$		0			0
$724$			1174.61i			1.62239i
$725$	−424.378	+	112.159i	−0.585349	+	0.154702i
$726$		0			0
$727$	−331.503	−	331.503i	−0.455988	−	0.455988i	0.441348	−	0.897336i	$-0.354500\pi$
$727$	−331.503	−	331.503i	−0.455988	−	0.455988i	−0.897336	+	0.441348i	$0.854500\pi$
$728$	149.525	−	149.525i	0.205392	−	0.205392i
$729$		0			0
$730$	250.204	−	324.921i	0.342745	−	0.445097i
$731$	493.864			0.675600
$732$		0			0
$733$	771.577	−	771.577i	1.05263	−	1.05263i	0.0540934	−	0.998536i	$-0.482773\pi$
$733$	771.577	−	771.577i	1.05263	−	1.05263i	0.998536	−	0.0540934i	$-0.0172269\pi$
$734$		−	1165.14i		−	1.58739i
$735$		0			0
$736$	−1031.88			−1.40202
$737$	83.6931	+	83.6931i	0.113559	+	0.113559i
$738$		0			0
$739$		−	644.895i		−	0.872658i	−0.899787	−	0.436329i	$-0.856278\pi$
$739$		−	644.895i		−	0.872658i	0.899787	−	0.436329i	$-0.143722\pi$
$740$	182.474	+	1404.57i	0.246587	+	1.89807i
$741$		0			0
$742$	75.7033	+	75.7033i	0.102026	+	0.102026i
$743$	−351.711	+	351.711i	−0.473366	+	0.473366i	−0.903002	−	0.429636i	$-0.858642\pi$
$743$	−351.711	+	351.711i	−0.473366	+	0.473366i	0.429636	+	0.903002i	$0.358642\pi$
$744$		0			0
$745$	920.680	+	708.965i	1.23581	+	0.951631i
$746$	−2006.22			−2.68930
$747$		0			0
$748$	412.638	−	412.638i	0.551655	−	0.551655i
$749$			382.601i			0.510815i
$750$		0			0
$751$	1346.30			1.79268			0.896339	−	0.443369i	$-0.146217\pi$
$751$	1346.30			1.79268			0.896339	+	0.443369i	$0.146217\pi$
$752$	−130.769	−	130.769i	−0.173895	−	0.173895i
$753$		0			0
$754$			675.560i			0.895968i
$755$	521.436	−	677.151i	0.690644	−	0.896888i
$756$		0			0
$757$	391.030	+	391.030i	0.516553	+	0.516553i	0.916527	−	0.399974i	$-0.130981\pi$
$757$	391.030	+	391.030i	0.516553	+	0.516553i	−0.399974	+	0.916527i	$0.630981\pi$
$758$	−114.748	+	114.748i	−0.151383	+	0.151383i
$759$		0			0
$760$	−796.996	+	103.542i	−1.04868	+	0.136239i
$761$	385.783			0.506943			0.253471	−	0.967343i	$-0.418428\pi$
$761$	385.783			0.506943			0.253471	+	0.967343i	$0.418428\pi$
$762$		0			0
$763$	−109.382	+	109.382i	−0.143358	+	0.143358i
$764$		−	1434.61i		−	1.87776i
$765$		0			0
$766$	1819.75			2.37565
$767$	−497.373	−	497.373i	−0.648465	−	0.648465i
$768$		0			0
$769$		−	1014.63i		−	1.31941i	−0.751525	−	0.659705i	$-0.770681\pi$
$769$		−	1014.63i		−	1.31941i	0.751525	−	0.659705i	$-0.229319\pi$
$770$	131.317	+	101.120i	0.170542	+	0.131325i
$771$		0			0
$772$	771.776	+	771.776i	0.999710	+	0.999710i
$773$	833.644	−	833.644i	1.07845	−	1.07845i	0.0818044	−	0.996648i	$-0.473932\pi$
$773$	833.644	−	833.644i	1.07845	−	1.07845i	0.996648	−	0.0818044i	$-0.0260683\pi$
$774$		0			0
$775$	280.262	+	1060.43i	0.361628	+	1.36830i
$776$	845.299			1.08930
$777$		0			0
$778$	106.187	−	106.187i	0.136488	−	0.136488i
$779$			547.437i			0.702743i
$780$		0			0
$781$	−311.058			−0.398282
$782$	−1519.25	−	1519.25i	−1.94277	−	1.94277i
$783$		0			0
$784$			23.6316i			0.0301424i
$785$	1401.55	−	182.083i	1.78542	−	0.231953i
$786$		0			0
$787$	−204.794	−	204.794i	−0.260221	−	0.260221i	0.564923	−	0.825144i	$-0.308906\pi$
$787$	−204.794	−	204.794i	−0.260221	−	0.260221i	−0.825144	+	0.564923i	$0.808906\pi$
$788$	748.028	−	748.028i	0.949274	−	0.949274i
$789$		0			0
$790$	229.572	+	1767.09i	0.290597	+	2.23683i
$791$	−148.989			−0.188355
$792$		0			0
$793$	−765.337	+	765.337i	−0.965116	+	0.965116i
$794$			1520.80i			1.91537i
$795$		0			0
$796$	168.287			0.211416
$797$	813.821	+	813.821i	1.02111	+	1.02111i	0.999772	+	0.0213333i	$0.00679110\pi$
$797$	813.821	+	813.821i	1.02111	+	1.02111i	0.0213333	+	0.999772i	$0.493209\pi$
$798$		0			0
$799$		−	1332.80i		−	1.66809i
$800$	−466.412	+	801.512i	−0.583015	+	1.00189i
$801$		0			0
$802$	790.056	+	790.056i	0.985108	+	0.985108i
$803$	72.1041	−	72.1041i	0.0897934	−	0.0897934i
$804$		0			0
$805$	224.524	−	291.572i	0.278912	−	0.362202i
$806$	1688.08			2.09439
$807$		0			0
$808$	839.883	−	839.883i	1.03946	−	1.03946i
$809$		−	288.800i		−	0.356984i	−0.983941	−	0.178492i	$-0.942878\pi$
$809$		−	288.800i		−	0.356984i	0.983941	−	0.178492i	$-0.0571219\pi$
$810$		0			0
$811$	929.694			1.14635			0.573177	−	0.819431i	$-0.305711\pi$
$811$	929.694			1.14635			0.573177	+	0.819431i	$0.305711\pi$
$812$	199.625	+	199.625i	0.245844	+	0.245844i
$813$		0			0
$814$			583.991i			0.717433i
$815$	133.996	+	1031.42i	0.164413	+	1.26554i
$816$		0			0
$817$	−349.872	−	349.872i	−0.428240	−	0.428240i
$818$	77.9155	−	77.9155i	0.0952512	−	0.0952512i
$819$		0			0
$820$	−540.692	−	416.357i	−0.659380	−	0.507752i
$821$	257.969			0.314214			0.157107	−	0.987582i	$-0.449783\pi$
$821$	257.969			0.314214			0.157107	+	0.987582i	$0.449783\pi$
$822$		0			0
$823$	−1099.78	+	1099.78i	−1.33631	+	1.33631i	−0.436703	+	0.899606i	$0.643854\pi$
$823$	−1099.78	+	1099.78i	−1.33631	+	1.33631i	−0.899606	+	0.436703i	$0.856146\pi$
$824$		−	1281.10i		−	1.55473i
$825$		0			0
$826$	−487.415			−0.590091
$827$	−145.623	−	145.623i	−0.176086	−	0.176086i	0.613561	−	0.789647i	$-0.289736\pi$
$827$	−145.623	−	145.623i	−0.176086	−	0.176086i	−0.789647	+	0.613561i	$0.789736\pi$
$828$		0			0
$829$			1281.05i			1.54530i	0.634835	+	0.772648i	$0.281068\pi$
$829$			1281.05i			1.54530i	−0.634835	+	0.772648i	$0.718932\pi$
$830$	−177.188	+	230.101i	−0.213479	+	0.277230i
$831$		0			0
$832$	893.460	+	893.460i	1.07387	+	1.07387i
$833$	−120.427	+	120.427i	−0.144570	+	0.144570i
$834$		0			0
$835$	−305.978	+	39.7511i	−0.366441	+	0.0476061i
$836$	−584.657			−0.699351
$837$		0			0
$838$	−1172.48	+	1172.48i	−1.39915	+	1.39915i
$839$		−	303.598i		−	0.361858i	−0.983496	−	0.180929i	$-0.942090\pi$
$839$		−	303.598i		−	0.361858i	0.983496	−	0.180929i	$-0.0579103\pi$
$840$		0			0
$841$	532.718			0.633434
$842$	−337.461	−	337.461i	−0.400785	−	0.400785i
$843$		0			0
$844$		−	1042.47i		−	1.23515i
$845$	87.5298	+	67.4019i	0.103586	+	0.0797656i
$846$		0			0
$847$	−197.229	−	197.229i	−0.232856	−	0.232856i
$848$	−30.4292	+	30.4292i	−0.0358835	+	0.0358835i
$849$		0			0
$850$	−1866.77	+	493.370i	−2.19620	+	0.580436i
$851$	1296.67			1.52371
$852$		0			0
$853$	39.5202	−	39.5202i	0.0463309	−	0.0463309i	−0.683562	−	0.729893i	$-0.739570\pi$
$853$	39.5202	−	39.5202i	0.0463309	−	0.0463309i	0.729893	+	0.683562i	$0.239570\pi$
$854$			750.014i			0.878237i
$855$		0			0
$856$	953.584			1.11400
$857$	−388.871	−	388.871i	−0.453758	−	0.453758i	0.442842	−	0.896600i	$-0.353970\pi$
$857$	−388.871	−	388.871i	−0.453758	−	0.453758i	−0.896600	+	0.442842i	$0.853970\pi$
$858$		0			0
$859$		−	375.068i		−	0.436633i	−0.975878	−	0.218317i	$-0.929943\pi$
$859$		−	375.068i		−	0.436633i	0.975878	−	0.218317i	$-0.0700565\pi$
$860$	611.659	−	79.4636i	0.711231	−	0.0923996i
$861$		0			0
$862$	−370.647	−	370.647i	−0.429985	−	0.429985i
$863$	374.656	−	374.656i	0.434132	−	0.434132i	−0.455899	−	0.890031i	$-0.650682\pi$
$863$	374.656	−	374.656i	0.434132	−	0.434132i	0.890031	+	0.455899i	$0.150682\pi$
$864$		0			0
$865$	−72.5435	−	558.392i	−0.0838653	−	0.645540i
$866$	780.236			0.900966
$867$		0			0
$868$	498.822	−	498.822i	0.574680	−	0.574680i
$869$			443.085i			0.509880i
$870$		0			0
$871$	−363.487			−0.417321
$872$	272.621	+	272.621i	0.312639	+	0.312639i
$873$		0			0
$874$			2152.59i			2.46291i
$875$	−124.993	−	306.189i	−0.142849	−	0.349930i
$876$		0			0
$877$	281.962	+	281.962i	0.321507	+	0.321507i	0.849345	−	0.527838i	$-0.176997\pi$
$877$	281.962	+	281.962i	0.321507	+	0.321507i	−0.527838	+	0.849345i	$0.676997\pi$
$878$	314.899	−	314.899i	0.358654	−	0.358654i
$879$		0			0
$880$	−40.6456	+	52.7834i	−0.0461881	+	0.0599811i
$881$	950.305			1.07867			0.539333	−	0.842092i	$-0.318676\pi$
$881$	950.305			1.07867			0.539333	+	0.842092i	$0.318676\pi$
$882$		0			0
$883$	−891.004	+	891.004i	−1.00907	+	1.00907i	−0.00910653	+	0.999959i	$0.502899\pi$
$883$	−891.004	+	891.004i	−1.00907	+	1.00907i	−0.999959	+	0.00910653i	$0.997101\pi$
$884$			1792.12i			2.02729i
$885$		0			0
$886$	2461.06			2.77772
$887$	−316.251	−	316.251i	−0.356540	−	0.356540i	0.505996	−	0.862536i	$-0.331125\pi$
$887$	−316.251	−	316.251i	−0.356540	−	0.356540i	−0.862536	+	0.505996i	$0.831125\pi$
$888$		0			0
$889$			105.334i			0.118486i
$890$	45.4356	+	349.733i	0.0510512	+	0.392959i
$891$		0			0
$892$	38.1182	+	38.1182i	0.0427334	+	0.0427334i
$893$	−944.208	+	944.208i	−1.05734	+	1.05734i
$894$		0			0
$895$	752.670	+	579.589i	0.840972	+	0.647586i
$896$	483.009			0.539073
$897$		0			0
$898$	1557.30	−	1557.30i	1.73419	−	1.73419i
$899$			770.331i			0.856876i
$900$		0			0
$901$	−310.135			−0.344212
$902$	−198.961	−	198.961i	−0.220577	−	0.220577i
$903$		0			0
$904$			371.336i			0.410770i
$905$	589.613	−	765.687i	0.651506	−	0.846063i
$906$		0			0
$907$	−407.150	−	407.150i	−0.448897	−	0.448897i	0.446091	−	0.894988i	$-0.352816\pi$
$907$	−407.150	−	407.150i	−0.448897	−	0.448897i	−0.894988	+	0.446091i	$0.852816\pi$
$908$	−944.295	+	944.295i	−1.03997	+	1.03997i
$909$		0			0
$910$	−504.748	+	65.5743i	−0.554668	+	0.0720597i
$911$	−637.398			−0.699668			−0.349834	−	0.936812i	$-0.613762\pi$
$911$	−637.398			−0.699668			−0.349834	+	0.936812i	$0.613762\pi$
$912$		0			0
$913$	−51.0623	+	51.0623i	−0.0559281	+	0.0559281i
$914$		−	1471.04i		−	1.60945i
$915$		0			0
$916$	−1720.91			−1.87872
$917$	60.8886	+	60.8886i	0.0663998	+	0.0663998i
$918$		0			0
$919$		−	1104.07i		−	1.20138i	−0.799483	−	0.600689i	$-0.794893\pi$
$919$		−	1104.07i		−	1.20138i	0.799483	−	0.600689i	$-0.205107\pi$
$920$	−726.707	−	559.597i	−0.789899	−	0.608258i
$921$		0			0
$922$	209.091	+	209.091i	0.226780	+	0.226780i
$923$	675.477	−	675.477i	0.731828	−	0.731828i
$924$		0			0
$925$	586.097	−	1007.19i	0.633618	−	1.08885i
$926$	2238.40			2.41727
$927$		0			0
$928$	−460.531	+	460.531i	−0.496261	+	0.496261i
$929$		−	1765.37i		−	1.90029i	−0.311814	−	0.950143i	$-0.600937\pi$
$929$		−	1765.37i		−	1.90029i	0.311814	−	0.950143i	$-0.399063\pi$
$930$		0			0
$931$	170.630			0.183277
$932$	−113.007	−	113.007i	−0.121252	−	0.121252i
$933$		0			0
$934$		−	1383.88i		−	1.48167i
$935$	−476.115	+	61.8545i	−0.509214	+	0.0661546i
$936$		0			0
$937$	867.153	+	867.153i	0.925457	+	0.925457i	0.997408	−	0.0719509i	$-0.0229225\pi$
$937$	867.153	+	867.153i	0.925457	+	0.925457i	−0.0719509	+	0.997408i	$0.522923\pi$
$938$	−178.105	+	178.105i	−0.189877	+	0.189877i
$939$		0			0
$940$	−214.450	−	1650.70i	−0.228139	−	1.75606i
$941$	1390.62			1.47781			0.738907	−	0.673807i	$-0.235342\pi$
$941$	1390.62			1.47781			0.738907	+	0.673807i	$0.235342\pi$
$942$		0			0
$943$	−441.765	+	441.765i	−0.468468	+	0.468468i
$944$		−	195.918i		−	0.207540i
$945$		0			0
$946$	254.315			0.268832
$947$	55.6539	+	55.6539i	0.0587686	+	0.0587686i	0.735880	−	0.677112i	$-0.236769\pi$
$947$	55.6539	+	55.6539i	0.0587686	+	0.0587686i	−0.677112	+	0.735880i	$0.736769\pi$
$948$		0			0
$949$			313.154i			0.329984i
$950$	1672.02	+	972.971i	1.76002	+	1.02418i
$951$		0			0
$952$	300.150	+	300.150i	0.315283	+	0.315283i
$953$	−222.327	+	222.327i	−0.233292	+	0.233292i	−0.814065	−	0.580773i	$-0.802750\pi$
$953$	−222.327	+	222.327i	−0.233292	+	0.233292i	0.580773	+	0.814065i	$0.302750\pi$
$954$		0			0
$955$	−720.126	+	935.174i	−0.754058	+	0.979240i
$956$	−1610.66			−1.68479
$957$		0			0
$958$	−399.719	+	399.719i	−0.417243	+	0.417243i
$959$		−	689.060i		−	0.718519i
$960$		0			0
$961$	963.896			1.00301
$962$	−1268.16	−	1268.16i	−1.31825	−	1.31825i
$963$		0			0
$964$			774.800i			0.803735i
$965$	−115.689	−	890.501i	−0.119885	−	0.922798i
$966$		0			0
$967$	807.256	+	807.256i	0.834805	+	0.834805i	0.988170	−	0.153365i	$-0.0490110\pi$
$967$	807.256	+	807.256i	0.834805	+	0.834805i	−0.153365	+	0.988170i	$0.549011\pi$
$968$	−491.569	+	491.569i	−0.507819	+	0.507819i
$969$		0			0
$970$	−1612.08	−	1241.37i	−1.66193	−	1.27976i
$971$	−458.168			−0.471852			−0.235926	−	0.971771i	$-0.575812\pi$
$971$	−458.168			−0.471852			−0.235926	+	0.971771i	$0.575812\pi$
$972$		0			0
$973$	142.660	−	142.660i	0.146619	−	0.146619i
$974$			1483.12i			1.52271i
$975$		0			0
$976$	−301.471			−0.308884
$977$	−921.703	−	921.703i	−0.943401	−	0.943401i	0.0550806	−	0.998482i	$-0.482458\pi$
$977$	−921.703	−	921.703i	−0.943401	−	0.943401i	−0.998482	+	0.0550806i	$0.982458\pi$
$978$		0			0
$979$			87.6930i			0.0895741i
$980$	−129.774	+	168.528i	−0.132423	+	0.171967i
$981$		0			0
$982$	−1637.21	−	1637.21i	−1.66722	−	1.66722i
$983$	−398.575	+	398.575i	−0.405468	+	0.405468i	−0.880155	−	0.474687i	$-0.842561\pi$
$983$	−398.575	+	398.575i	−0.405468	+	0.405468i	0.474687	+	0.880155i	$0.342561\pi$
$984$		0			0
$985$	−863.099	+	112.129i	−0.876243	+	0.113837i
$986$	−1356.08			−1.37534
$987$		0			0
$988$	1269.61	−	1269.61i	1.28503	−	1.28503i
$989$		−	564.673i		−	0.570953i
$990$		0			0
$991$	861.216			0.869037			0.434519	−	0.900663i	$-0.356918\pi$
$991$	861.216			0.869037			0.434519	+	0.900663i	$0.356918\pi$
$992$	1150.77	+	1150.77i	1.16005	+	1.16005i
$993$		0			0
$994$		−	661.953i		−	0.665949i
$995$	−109.701	−	84.4744i	−0.110252	−	0.0848989i
$996$		0			0
$997$	−1147.18	−	1147.18i	−1.15063	−	1.15063i	−0.986426	−	0.164209i	$-0.947493\pi$
$997$	−1147.18	−	1147.18i	−1.15063	−	1.15063i	−0.164209	−	0.986426i	$-0.552507\pi$
$998$	865.811	−	865.811i	0.867546	−	0.867546i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.3.o.b.127.3		24
3.2	odd	2		105.3.l.a.22.10	✓	24
5.3	odd	4	inner	315.3.o.b.253.3		24
15.2	even	4		525.3.l.e.43.3		24
15.8	even	4		105.3.l.a.43.10	yes	24
15.14	odd	2		525.3.l.e.232.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.10	✓	24	3.2	odd	2
105.3.l.a.43.10	yes	24	15.8	even	4
315.3.o.b.127.3		24	1.1	even	1	trivial
315.3.o.b.253.3		24	5.3	odd	4	inner
525.3.l.e.43.3		24	15.2	even	4
525.3.l.e.232.3		24	15.14	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.24469 - 2.24469i) q^{2} +6.07726i q^{4} +(3.05058 - 3.96156i) q^{5} +(1.87083 + 1.87083i) q^{7} +(4.66280 - 4.66280i) q^{8} +O(q^{10})\)	\(q+(-2.24469 - 2.24469i) q^{2} +6.07726i q^{4} +(3.05058 - 3.96156i) q^{5} +(1.87083 + 1.87083i) q^{7} +(4.66280 - 4.66280i) q^{8} +(-15.7401 + 2.04487i) q^{10} -3.94671 q^{11} +(8.57045 - 8.57045i) q^{13} -8.39886i q^{14} +3.37595 q^{16} +(17.2039 + 17.2039i) q^{17} -24.3758i q^{19} +(24.0754 + 18.5392i) q^{20} +(8.85913 + 8.85913i) q^{22} +(19.6705 - 19.6705i) q^{23} +(-6.38793 - 24.1701i) q^{25} -38.4760 q^{26} +(-11.3695 + 11.3695i) q^{28} -17.5580i q^{29} -43.8736 q^{31} +(-26.2292 - 26.2292i) q^{32} -77.2348i q^{34} +(13.1185 - 1.70429i) q^{35} +(32.9598 + 32.9598i) q^{37} +(-54.7160 + 54.7160i) q^{38} +(-4.24773 - 32.6962i) q^{40} -22.4582 q^{41} +(14.3533 - 14.3533i) q^{43} -23.9852i q^{44} -88.3085 q^{46} +(-38.7355 - 38.7355i) q^{47} +7.00000i q^{49} +(-39.9155 + 68.5933i) q^{50} +(52.0849 + 52.0849i) q^{52} +(-9.01352 + 9.01352i) q^{53} +(-12.0397 + 15.6351i) q^{55} +17.4466 q^{56} +(-39.4121 + 39.4121i) q^{58} -58.0335i q^{59} -89.2995 q^{61} +(98.4827 + 98.4827i) q^{62} +104.249i q^{64} +(-7.80752 - 60.0972i) q^{65} +(-21.2058 - 21.2058i) q^{67} +(-104.552 + 104.552i) q^{68} +(-33.2726 - 25.6214i) q^{70} +78.8147 q^{71} +(-18.2694 + 18.2694i) q^{73} -147.969i q^{74} +148.138 q^{76} +(-7.38362 - 7.38362i) q^{77} -112.267i q^{79} +(10.2986 - 13.3740i) q^{80} +(50.4118 + 50.4118i) q^{82} +(12.9380 - 12.9380i) q^{83} +(120.636 - 15.6724i) q^{85} -64.4373 q^{86} +(-18.4027 + 18.4027i) q^{88} -22.2193i q^{89} +32.0677 q^{91} +(119.543 + 119.543i) q^{92} +173.898i q^{94} +(-96.5661 - 74.3602i) q^{95} +(90.6427 + 90.6427i) q^{97} +(15.7128 - 15.7128i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8}+O(q^{10}) \) 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8	\( 24 q - 8 q^{2} - 16 q^{5} + 48 q^{8} - 40 q^{10} + 64 q^{13} - 184 q^{16} - 24 q^{17} - 72 q^{20} + 8 q^{22} - 8 q^{23} - 136 q^{25} + 80 q^{26} + 96 q^{31} - 56 q^{32} + 8 q^{37} - 56 q^{38} + 232 q^{40} - 320 q^{41} - 112 q^{43} + 320 q^{46} - 64 q^{47} + 256 q^{50} + 96 q^{52} + 72 q^{53} - 80 q^{55} + 336 q^{56} - 512 q^{58} - 496 q^{61} + 776 q^{62} - 312 q^{65} - 192 q^{67} - 568 q^{68} + 112 q^{70} + 144 q^{71} + 224 q^{73} + 416 q^{76} - 112 q^{77} + 528 q^{80} + 352 q^{82} + 32 q^{83} + 24 q^{85} - 240 q^{86} + 216 q^{88} - 1304 q^{92} - 376 q^{95} - 816 q^{97} + 56 q^{98}+O(q^{100}) \) 24 * q - 8 * q^2 - 16 * q^5 + 48 * q^8 - 40 * q^10 + 64 * q^13 - 184 * q^16 - 24 * q^17 - 72 * q^20 + 8 * q^22 - 8 * q^23 - 136 * q^25 + 80 * q^26 + 96 * q^31 - 56 * q^32 + 8 * q^37 - 56 * q^38 + 232 * q^40 - 320 * q^41 - 112 * q^43 + 320 * q^46 - 64 * q^47 + 256 * q^50 + 96 * q^52 + 72 * q^53 - 80 * q^55 + 336 * q^56 - 512 * q^58 - 496 * q^61 + 776 * q^62 - 312 * q^65 - 192 * q^67 - 568 * q^68 + 112 * q^70 + 144 * q^71 + 224 * q^73 + 416 * q^76 - 112 * q^77 + 528 * q^80 + 352 * q^82 + 32 * q^83 + 24 * q^85 - 240 * q^86 + 216 * q^88 - 1304 * q^92 - 376 * q^95 - 816 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more