LMFDB - Embedded newform 1008.2.v.e.323.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(323,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1008.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.v (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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.17
Character	$\chi$	$=$	1008.323
Dual form			1008.2.v.e.827.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13420 + 0.844744i) q^{2} +(0.572816 + 1.91622i) q^{4} +(-2.12043 - 2.12043i) q^{5} +1.00000 q^{7} +(-0.969023 + 2.65725i) q^{8} +O(q^{10})$	\(q+(1.13420 + 0.844744i) q^{2} +(0.572816 + 1.91622i) q^{4} +(-2.12043 - 2.12043i) q^{5} +1.00000 q^{7} +(-0.969023 + 2.65725i) q^{8} +(-0.613769 - 4.19620i) q^{10} +(-4.03827 + 4.03827i) q^{11} +(-4.91665 - 4.91665i) q^{13} +(1.13420 + 0.844744i) q^{14} +(-3.34376 + 2.19528i) q^{16} +4.76253i q^{17} +(-2.21762 + 2.21762i) q^{19} +(2.84858 - 5.27781i) q^{20} +(-7.99151 + 1.16890i) q^{22} +6.91384i q^{23} +3.99241i q^{25} +(-1.42315 - 9.72977i) q^{26} +(0.572816 + 1.91622i) q^{28} +(-2.61285 + 2.61285i) q^{29} +0.712246i q^{31} +(-5.64694 - 0.334739i) q^{32} +(-4.02312 + 5.40166i) q^{34} +(-2.12043 - 2.12043i) q^{35} +(5.73777 - 5.73777i) q^{37} +(-4.38854 + 0.641902i) q^{38} +(7.68925 - 3.57977i) q^{40} +3.59400 q^{41} +(3.36325 + 3.36325i) q^{43} +(-10.0514 - 5.42501i) q^{44} +(-5.84042 + 7.84167i) q^{46} -6.04590 q^{47} +1.00000 q^{49} +(-3.37256 + 4.52819i) q^{50} +(6.60502 - 12.2377i) q^{52} +(-4.53235 - 4.53235i) q^{53} +17.1257 q^{55} +(-0.969023 + 2.65725i) q^{56} +(-5.17067 + 0.756303i) q^{58} +(4.82118 - 4.82118i) q^{59} +(-6.72581 - 6.72581i) q^{61} +(-0.601665 + 0.807828i) q^{62} +(-6.12199 - 5.14988i) q^{64} +20.8508i q^{65} +(-3.87274 + 3.87274i) q^{67} +(-9.12604 + 2.72806i) q^{68} +(-0.613769 - 4.19620i) q^{70} -14.7448i q^{71} +4.61241i q^{73} +(11.3547 - 1.66083i) q^{74} +(-5.51972 - 2.97914i) q^{76} +(-4.03827 + 4.03827i) q^{77} +7.43429i q^{79} +(11.7451 + 2.43528i) q^{80} +(4.07631 + 3.03601i) q^{82} +(-2.44737 - 2.44737i) q^{83} +(10.0986 - 10.0986i) q^{85} +(0.973511 + 6.65568i) q^{86} +(-6.81753 - 14.6439i) q^{88} -4.23689 q^{89} +(-4.91665 - 4.91665i) q^{91} +(-13.2484 + 3.96036i) q^{92} +(-6.85725 - 5.10723i) q^{94} +9.40458 q^{95} -6.76292 q^{97} +(1.13420 + 0.844744i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{7}+O(q^{10}) $ 40 * q + 40 * q^7	$ 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70} - 24 q^{76} - 64 q^{82} + 64 q^{85} - 120 q^{88} - 24 q^{91} - 128 q^{94} + 64 q^{97}+O(q^{100}) $ 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.13420	+	0.844744i	0.802000	+	0.597324i
$2$	1.13420	+	0.844744i	0.802000	+	0.597324i
$3$		0			0
$3$		0			0
$4$	0.572816	+	1.91622i	0.286408	+	0.958108i
$5$	−2.12043	−	2.12043i	−0.948283	−	0.948283i	0.0504437	−	0.998727i	$-0.483936\pi$
$5$	−2.12043	−	2.12043i	−0.948283	−	0.948283i	−0.998727	+	0.0504437i	$0.983936\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−0.969023	+	2.65725i	−0.342601	+	0.939481i
$9$		0			0
$10$	−0.613769	−	4.19620i	−0.194091	−	1.32696i
$11$	−4.03827	+	4.03827i	−1.21759	+	1.21759i	−0.249110	+	0.968475i	$0.580138\pi$
$11$	−4.03827	+	4.03827i	−1.21759	+	1.21759i	−0.968475	+	0.249110i	$0.919862\pi$
$12$		0			0
$13$	−4.91665	−	4.91665i	−1.36363	−	1.36363i	−0.869237	−	0.494396i	$-0.835389\pi$
$13$	−4.91665	−	4.91665i	−1.36363	−	1.36363i	−0.494396	−	0.869237i	$-0.664611\pi$
$14$	1.13420	+	0.844744i	0.303128	+	0.225767i
$15$		0			0
$16$	−3.34376	+	2.19528i	−0.835941	+	0.548820i
$17$			4.76253i			1.15508i	0.816361	+	0.577542i	$0.195988\pi$
$17$			4.76253i			1.15508i	−0.816361	+	0.577542i	$0.804012\pi$
$18$		0			0
$19$	−2.21762	+	2.21762i	−0.508756	+	0.508756i	−0.914145	−	0.405388i	$-0.867136\pi$
$19$	−2.21762	+	2.21762i	−0.508756	+	0.508756i	0.405388	+	0.914145i	$0.367136\pi$
$20$	2.84858	−	5.27781i	0.636961	−	1.18015i
$21$		0			0
$22$	−7.99151	+	1.16890i	−1.70380	+	0.249211i
$23$			6.91384i			1.44164i	0.693125	+	0.720818i	$0.256233\pi$
$23$			6.91384i			1.44164i	−0.693125	+	0.720818i	$0.743767\pi$
$24$		0			0
$25$			3.99241i			0.798482i
$26$	−1.42315	−	9.72977i	−0.279103	−	1.90816i
$27$		0			0
$28$	0.572816	+	1.91622i	0.108252	+	0.362131i
$29$	−2.61285	+	2.61285i	−0.485193	+	0.485193i	−0.906786	−	0.421592i	$-0.861471\pi$
$29$	−2.61285	+	2.61285i	−0.485193	+	0.485193i	0.421592	+	0.906786i	$0.361471\pi$
$30$		0			0
$31$			0.712246i			0.127923i	0.997952	+	0.0639615i	$0.0203735\pi$
$31$			0.712246i			0.127923i	−0.997952	+	0.0639615i	$0.979627\pi$
$32$	−5.64694	−	0.334739i	−0.998248	−	0.0591741i
$33$		0			0
$34$	−4.02312	+	5.40166i	−0.689960	+	0.926378i
$35$	−2.12043	−	2.12043i	−0.358417	−	0.358417i
$36$		0			0
$37$	5.73777	−	5.73777i	0.943283	−	0.943283i	−0.0551925	−	0.998476i	$-0.517577\pi$
$37$	5.73777	−	5.73777i	0.943283	−	0.943283i	0.998476	+	0.0551925i	$0.0175773\pi$
$38$	−4.38854	+	0.641902i	−0.711915	+	0.104130i
$39$		0			0
$40$	7.68925	−	3.57977i	1.21578	−	0.566011i
$41$	3.59400			0.561288			0.280644	−	0.959812i	$-0.409452\pi$
$41$	3.59400			0.561288			0.280644	+	0.959812i	$0.409452\pi$
$42$		0			0
$43$	3.36325	+	3.36325i	0.512891	+	0.512891i	0.915411	−	0.402520i	$-0.131866\pi$
$43$	3.36325	+	3.36325i	0.512891	+	0.512891i	−0.402520	+	0.915411i	$0.631866\pi$
$44$	−10.0514	−	5.42501i	−1.51530	−	0.817851i
$45$		0			0
$46$	−5.84042	+	7.84167i	−0.861123	+	1.15619i
$47$	−6.04590			−0.881885			−0.440942	−	0.897535i	$-0.645356\pi$
$47$	−6.04590			−0.881885			−0.440942	+	0.897535i	$0.645356\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−3.37256	+	4.52819i	−0.476952	+	0.640383i
$51$		0			0
$52$	6.60502	−	12.2377i	0.915952	−	1.69706i
$53$	−4.53235	−	4.53235i	−0.622566	−	0.622566i	0.323621	−	0.946187i	$-0.395100\pi$
$53$	−4.53235	−	4.53235i	−0.622566	−	0.622566i	−0.946187	+	0.323621i	$0.895100\pi$
$54$		0			0
$55$	17.1257			2.30923
$56$	−0.969023	+	2.65725i	−0.129491	+	0.355090i
$57$		0			0
$58$	−5.17067	+	0.756303i	−0.678943	+	0.0993075i
$59$	4.82118	−	4.82118i	0.627664	−	0.627664i	−0.319815	−	0.947480i	$-0.603621\pi$
$59$	4.82118	−	4.82118i	0.627664	−	0.627664i	0.947480	+	0.319815i	$0.103621\pi$
$60$		0			0
$61$	−6.72581	−	6.72581i	−0.861151	−	0.861151i	0.130321	−	0.991472i	$-0.458399\pi$
$61$	−6.72581	−	6.72581i	−0.861151	−	0.861151i	−0.991472	+	0.130321i	$0.958399\pi$
$62$	−0.601665	+	0.807828i	−0.0764115	+	0.102594i
$63$		0			0
$64$	−6.12199	−	5.14988i	−0.765249	−	0.643735i
$65$			20.8508i			2.58622i
$66$		0			0
$67$	−3.87274	+	3.87274i	−0.473130	+	0.473130i	−0.902926	−	0.429796i	$-0.858586\pi$
$67$	−3.87274	+	3.87274i	−0.473130	+	0.473130i	0.429796	+	0.902926i	$0.358586\pi$
$68$	−9.12604	+	2.72806i	−1.10670	+	0.330826i
$69$		0			0
$70$	−0.613769	−	4.19620i	−0.0733594	−	0.501542i
$71$		−	14.7448i		−	1.74988i	−0.484229	−	0.874941i	$-0.660900\pi$
$71$		−	14.7448i		−	1.74988i	0.484229	−	0.874941i	$-0.339100\pi$
$72$		0			0
$73$			4.61241i			0.539842i	0.962882	+	0.269921i	$0.0869976\pi$
$73$			4.61241i			0.539842i	−0.962882	+	0.269921i	$0.913002\pi$
$74$	11.3547	−	1.66083i	1.31996	−	0.193067i
$75$		0			0
$76$	−5.51972	−	2.97914i	−0.633155	−	0.341731i
$77$	−4.03827	+	4.03827i	−0.460204	+	0.460204i
$78$		0			0
$79$			7.43429i			0.836423i	0.908350	+	0.418211i	$0.137343\pi$
$79$			7.43429i			0.836423i	−0.908350	+	0.418211i	$0.862657\pi$
$80$	11.7451	+	2.43528i	1.31315	+	0.272272i
$81$		0			0
$82$	4.07631	+	3.03601i	0.450153	+	0.335271i
$83$	−2.44737	−	2.44737i	−0.268633	−	0.268633i	0.559916	−	0.828549i	$-0.310833\pi$
$83$	−2.44737	−	2.44737i	−0.268633	−	0.268633i	−0.828549	+	0.559916i	$0.810833\pi$
$84$		0			0
$85$	10.0986	−	10.0986i	1.09535	−	1.09535i
$86$	0.973511	+	6.65568i	0.104976	+	0.717700i
$87$		0			0
$88$	−6.81753	−	14.6439i	−0.726752	−	1.56104i
$89$	−4.23689			−0.449109			−0.224555	−	0.974461i	$-0.572093\pi$
$89$	−4.23689			−0.449109			−0.224555	+	0.974461i	$0.572093\pi$
$90$		0			0
$91$	−4.91665	−	4.91665i	−0.515405	−	0.515405i
$92$	−13.2484	+	3.96036i	−1.38124	+	0.412896i
$93$		0			0
$94$	−6.85725	−	5.10723i	−0.707272	−	0.526771i
$95$	9.40458			0.964890
$96$		0			0
$97$	−6.76292			−0.686670			−0.343335	−	0.939213i	$-0.611557\pi$
$97$	−6.76292			−0.686670			−0.343335	+	0.939213i	$0.611557\pi$
$98$	1.13420	+	0.844744i	0.114571	+	0.0853320i
$99$		0			0
$100$	−7.65032	+	2.28692i	−0.765032	+	0.228692i
$101$	12.7637	+	12.7637i	1.27003	+	1.27003i	0.946070	+	0.323963i	$0.105015\pi$
$101$	12.7637	+	12.7637i	1.27003	+	1.27003i	0.323963	+	0.946070i	$0.394985\pi$
$102$		0			0
$103$	5.09658			0.502181			0.251091	−	0.967964i	$-0.419211\pi$
$103$	5.09658			0.502181			0.251091	+	0.967964i	$0.419211\pi$
$104$	17.8291	−	8.30043i	1.74829	−	0.813924i
$105$		0			0
$106$	−1.31191	−	8.96926i	−0.127424	−	0.871171i
$107$	3.45316	−	3.45316i	0.333829	−	0.333829i	−0.520209	−	0.854039i	$-0.674146\pi$
$107$	3.45316	−	3.45316i	0.333829	−	0.333829i	0.854039	+	0.520209i	$0.174146\pi$
$108$		0			0
$109$	12.6452	+	12.6452i	1.21119	+	1.21119i	0.970635	+	0.240558i	$0.0773304\pi$
$109$	12.6452	+	12.6452i	1.21119	+	1.21119i	0.240558	+	0.970635i	$0.422670\pi$
$110$	19.4240	+	14.4668i	1.85200	+	1.37936i
$111$		0			0
$112$	−3.34376	+	2.19528i	−0.315956	+	0.207434i
$113$		−	5.90657i		−	0.555644i	−0.960633	−	0.277822i	$-0.910388\pi$
$113$		−	5.90657i		−	0.555644i	0.960633	−	0.277822i	$-0.0896125\pi$
$114$		0			0
$115$	14.6603	−	14.6603i	1.36708	−	1.36708i
$116$	−6.50346	−	3.51010i	−0.603831	−	0.325904i
$117$		0			0
$118$	9.54084	−	1.39552i	0.878306	−	0.128468i
$119$			4.76253i			0.436581i
$120$		0			0
$121$		−	21.6153i		−	1.96503i
$122$	−1.94682	−	13.3100i	−0.176257	−	1.20503i
$123$		0			0
$124$	−1.36482	+	0.407986i	−0.122564	+	0.0366382i
$125$	−2.13652	+	2.13652i	−0.191096	+	0.191096i
$126$		0			0
$127$		−	3.07038i		−	0.272452i	−0.990678	−	0.136226i	$-0.956503\pi$
$127$		−	3.07038i		−	0.272452i	0.990678	−	0.136226i	$-0.0434974\pi$
$128$	−2.59323	−	11.0125i	−0.229211	−	0.973377i
$129$		0			0
$130$	−17.6136	+	23.6489i	−1.54481	+	2.07415i
$131$	6.95401	+	6.95401i	0.607575	+	0.607575i	0.942312	−	0.334737i	$-0.108647\pi$
$131$	6.95401	+	6.95401i	0.607575	+	0.607575i	−0.334737	+	0.942312i	$0.608647\pi$
$132$		0			0
$133$	−2.21762	+	2.21762i	−0.192292	+	0.192292i
$134$	−7.66393	+	1.12099i	−0.662063	+	0.0968384i
$135$		0			0
$136$	−12.6553	−	4.61501i	−1.08518	−	0.395734i
$137$	−11.5548			−0.987193			−0.493596	−	0.869691i	$-0.664318\pi$
$137$	−11.5548			−0.987193			−0.493596	+	0.869691i	$0.664318\pi$
$138$		0			0
$139$	6.19355	+	6.19355i	0.525330	+	0.525330i	0.919176	−	0.393846i	$-0.128856\pi$
$139$	6.19355	+	6.19355i	0.525330	+	0.525330i	−0.393846	+	0.919176i	$0.628856\pi$
$140$	2.84858	−	5.27781i	0.240749	−	0.446056i
$141$		0			0
$142$	12.4556	−	16.7235i	1.04525	−	1.40341i
$143$	39.7095			3.32068
$144$		0			0
$145$	11.0807			0.920201
$146$	−3.89631	+	5.23139i	−0.322461	+	0.432953i
$147$		0			0
$148$	14.2815	+	7.70811i	1.17393	+	0.633603i
$149$	−2.38965	−	2.38965i	−0.195767	−	0.195767i	0.602415	−	0.798183i	$-0.294205\pi$
$149$	−2.38965	−	2.38965i	−0.195767	−	0.195767i	−0.798183	+	0.602415i	$0.794205\pi$
$150$		0			0
$151$	12.2639			0.998018			0.499009	−	0.866597i	$-0.333697\pi$
$151$	12.2639			0.998018			0.499009	+	0.866597i	$0.333697\pi$
$152$	−3.74385	−	8.04169i	−0.303666	−	0.652267i
$153$		0			0
$154$	−7.99151	+	1.16890i	−0.643974	+	0.0941927i
$155$	1.51026	−	1.51026i	0.121307	−	0.121307i
$156$		0			0
$157$	−4.81144	−	4.81144i	−0.383995	−	0.383995i	0.488544	−	0.872539i	$-0.337528\pi$
$157$	−4.81144	−	4.81144i	−0.383995	−	0.383995i	−0.872539	+	0.488544i	$0.837528\pi$
$158$	−6.28007	+	8.43196i	−0.499615	+	0.670811i
$159$		0			0
$160$	11.2641	+	12.6837i	0.890508	+	1.00274i
$161$			6.91384i			0.544887i
$162$		0			0
$163$	−6.02781	+	6.02781i	−0.472134	+	0.472134i	−0.902605	−	0.430470i	$-0.858348\pi$
$163$	−6.02781	+	6.02781i	−0.472134	+	0.472134i	0.430470	+	0.902605i	$0.358348\pi$
$164$	2.05870	+	6.88687i	0.160757	+	0.537775i
$165$		0			0
$166$	−0.708404	−	4.84320i	−0.0549828	−	0.375905i
$167$			4.75117i			0.367656i	0.982958	+	0.183828i	$0.0588490\pi$
$167$			4.75117i			0.367656i	−0.982958	+	0.183828i	$0.941151\pi$
$168$		0			0
$169$			35.3469i			2.71899i
$170$	19.9846	−	2.92310i	1.53275	−	0.224191i
$171$		0			0
$172$	−4.51819	+	8.37123i	−0.344508	+	0.638301i
$173$	−13.6615	+	13.6615i	−1.03867	+	1.03867i	−0.0394449	+	0.999222i	$0.512559\pi$
$173$	−13.6615	+	13.6615i	−1.03867	+	1.03867i	−0.999222	+	0.0394449i	$0.987441\pi$
$174$		0			0
$175$			3.99241i			0.301798i
$176$	4.63789	−	22.3682i	0.349594	−	1.68606i
$177$		0			0
$178$	−4.80548	−	3.57909i	−0.360186	−	0.268264i
$179$	9.71026	+	9.71026i	0.725779	+	0.725779i	0.969776	−	0.243997i	$-0.0784588\pi$
$179$	9.71026	+	9.71026i	0.725779	+	0.725779i	−0.243997	+	0.969776i	$0.578459\pi$
$180$		0			0
$181$	−3.99969	+	3.99969i	−0.297295	+	0.297295i	−0.839953	−	0.542659i	$-0.817418\pi$
$181$	−3.99969	+	3.99969i	−0.297295	+	0.297295i	0.542659	+	0.839953i	$0.317418\pi$
$182$	−1.42315	−	9.72977i	−0.105491	−	0.721218i
$183$		0			0
$184$	−18.3718	−	6.69967i	−1.35439	−	0.493906i
$185$	−24.3330			−1.78900
$186$		0			0
$187$	−19.2324	−	19.2324i	−1.40641	−	1.40641i
$188$	−3.46319	−	11.5852i	−0.252579	−	0.844941i
$189$		0			0
$190$	10.6667	+	7.94446i	0.773842	+	0.576352i
$191$	−15.9802			−1.15629			−0.578143	−	0.815936i	$-0.696222\pi$
$191$	−15.9802			−1.15629			−0.578143	+	0.815936i	$0.696222\pi$
$192$		0			0
$193$	−3.55024			−0.255552			−0.127776	−	0.991803i	$-0.540784\pi$
$193$	−3.55024			−0.255552			−0.127776	+	0.991803i	$0.540784\pi$
$194$	−7.67050	−	5.71293i	−0.550710	−	0.410165i
$195$		0			0
$196$	0.572816	+	1.91622i	0.0409154	+	0.136873i
$197$	10.4049	+	10.4049i	0.741320	+	0.741320i	0.972832	−	0.231512i	$-0.0743671\pi$
$197$	10.4049	+	10.4049i	0.741320	+	0.741320i	−0.231512	+	0.972832i	$0.574367\pi$
$198$		0			0
$199$	20.0463			1.42104			0.710521	−	0.703676i	$-0.248459\pi$
$199$	20.0463			1.42104			0.710521	+	0.703676i	$0.248459\pi$
$200$	−10.6088	−	3.86874i	−0.750159	−	0.273561i
$201$		0			0
$202$	3.69452	+	25.2586i	0.259945	+	1.77719i
$203$	−2.61285	+	2.61285i	−0.183386	+	0.183386i
$204$		0			0
$205$	−7.62081	−	7.62081i	−0.532260	−	0.532260i
$206$	5.78054	+	4.30531i	0.402749	+	0.299965i
$207$		0			0
$208$	27.2335	+	5.64669i	1.88830	+	0.391528i
$209$		−	17.9107i		−	1.23891i
$210$		0			0
$211$	−14.2434	+	14.2434i	−0.980558	+	0.980558i	−0.999815	−	0.0192564i	$-0.993870\pi$
$211$	−14.2434	+	14.2434i	−0.980558	+	0.980558i	0.0192564	+	0.999815i	$0.493870\pi$
$212$	6.08875	−	11.2812i	0.418177	−	0.774793i
$213$		0			0
$214$	6.83360	−	0.999536i	0.467135	−	0.0683269i
$215$		−	14.2630i		−	0.972731i
$216$		0			0
$217$			0.712246i			0.0483504i
$218$	3.66023	+	25.0242i	0.247902	+	1.69485i
$219$		0			0
$220$	9.80989	+	32.8166i	0.661382	+	2.21249i
$221$	23.4157	−	23.4157i	1.57511	−	1.57511i
$222$		0			0
$223$			17.0811i			1.14384i	0.820311	+	0.571918i	$0.193801\pi$
$223$			17.0811i			1.14384i	−0.820311	+	0.571918i	$0.806199\pi$
$224$	−5.64694	−	0.334739i	−0.377302	−	0.0223657i
$225$		0			0
$226$	4.98954	−	6.69923i	0.331899	−	0.445626i
$227$	−15.8882	−	15.8882i	−1.05453	−	1.05453i	−0.998425	−	0.0561098i	$-0.982130\pi$
$227$	−15.8882	−	15.8882i	−1.05453	−	1.05453i	−0.0561098	−	0.998425i	$-0.517870\pi$
$228$		0			0
$229$	−17.2648	+	17.2648i	−1.14089	+	1.14089i	−0.152605	+	0.988287i	$0.548766\pi$
$229$	−17.2648	+	17.2648i	−1.14089	+	1.14089i	−0.988287	+	0.152605i	$0.951234\pi$
$230$	29.0119	−	4.24350i	1.91299	−	0.279808i
$231$		0			0
$232$	−4.41109	−	9.47490i	−0.289602	−	0.622058i
$233$	−8.37677			−0.548780			−0.274390	−	0.961618i	$-0.588476\pi$
$233$	−8.37677			−0.548780			−0.274390	+	0.961618i	$0.588476\pi$
$234$		0			0
$235$	12.8199	+	12.8199i	0.836276	+	0.836276i
$236$	12.0001	+	6.47677i	0.781138	+	0.421602i
$237$		0			0
$238$	−4.02312	+	5.40166i	−0.260780	+	0.350138i
$239$	−6.24270			−0.403807			−0.201903	−	0.979405i	$-0.564713\pi$
$239$	−6.24270			−0.403807			−0.201903	+	0.979405i	$0.564713\pi$
$240$		0			0
$241$	−2.39859			−0.154507			−0.0772535	−	0.997011i	$-0.524615\pi$
$241$	−2.39859			−0.154507			−0.0772535	+	0.997011i	$0.524615\pi$
$242$	18.2594	−	24.5161i	1.17376	−	1.57595i
$243$		0			0
$244$	9.03544	−	16.7407i	0.578435	−	1.07172i
$245$	−2.12043	−	2.12043i	−0.135469	−	0.135469i
$246$		0			0
$247$	21.8065			1.38751
$248$	−1.89262	−	0.690182i	−0.120181	−	0.0438266i
$249$		0			0
$250$	−4.22805	+	0.618428i	−0.267405	+	0.0391128i
$251$	10.5027	−	10.5027i	0.662927	−	0.662927i	−0.293142	−	0.956069i	$-0.594701\pi$
$251$	10.5027	−	10.5027i	0.662927	−	0.662927i	0.956069	+	0.293142i	$0.0947008\pi$
$252$		0			0
$253$	−27.9200	−	27.9200i	−1.75531	−	1.75531i
$254$	2.59368	−	3.48242i	0.162742	−	0.218507i
$255$		0			0
$256$	6.36150	−	14.6810i	0.397594	−	0.917561i
$257$		−	1.99198i		−	0.124256i	−0.998068	−	0.0621282i	$-0.980211\pi$
$257$		−	1.99198i		−	0.124256i	0.998068	−	0.0621282i	$-0.0197888\pi$
$258$		0			0
$259$	5.73777	−	5.73777i	0.356528	−	0.356528i
$260$	−39.9546	+	11.9437i	−2.47788	+	0.740714i
$261$		0			0
$262$	2.01288	+	13.7616i	0.124356	+	0.850194i
$263$			4.76661i			0.293922i	0.989142	+	0.146961i	$0.0469492\pi$
$263$			4.76661i			0.293922i	−0.989142	+	0.146961i	$0.953051\pi$
$264$		0			0
$265$			19.2210i			1.18074i
$266$	−4.38854	+	0.641902i	−0.269078	+	0.0393575i
$267$		0			0
$268$	−9.63937	−	5.20263i	−0.588818	−	0.317801i
$269$	−10.1764	+	10.1764i	−0.620468	+	0.620468i	−0.945651	−	0.325183i	$-0.894574\pi$
$269$	−10.1764	+	10.1764i	−0.620468	+	0.620468i	0.325183	+	0.945651i	$0.394574\pi$
$270$		0			0
$271$		−	29.8185i		−	1.81135i	−0.423977	−	0.905673i	$-0.639366\pi$
$271$		−	29.8185i		−	1.81135i	0.423977	−	0.905673i	$-0.360634\pi$
$272$	−10.4551	−	15.9248i	−0.633933	−	0.965582i
$273$		0			0
$274$	−13.1054	−	9.76084i	−0.791729	−	0.589674i
$275$	−16.1224	−	16.1224i	−0.972220	−	0.972220i
$276$		0			0
$277$	10.3689	−	10.3689i	0.623007	−	0.623007i	−0.323292	−	0.946299i	$-0.604790\pi$
$277$	10.3689	−	10.3689i	0.623007	−	0.623007i	0.946299	+	0.323292i	$0.104790\pi$
$278$	1.79276	+	12.2567i	0.107522	+	0.735107i
$279$		0			0
$280$	7.68925	−	3.57977i	0.459521	−	0.213932i
$281$	−10.1234			−0.603909			−0.301954	−	0.953322i	$-0.597639\pi$
$281$	−10.1234			−0.603909			−0.301954	+	0.953322i	$0.597639\pi$
$282$		0			0
$283$	13.7990	+	13.7990i	0.820266	+	0.820266i	0.986146	−	0.165880i	$-0.0530463\pi$
$283$	13.7990	+	13.7990i	0.820266	+	0.820266i	−0.165880	+	0.986146i	$0.553046\pi$
$284$	28.2542	−	8.44605i	1.67658	−	0.501181i
$285$		0			0
$286$	45.0385	+	33.5444i	2.66318	+	1.98352i
$287$	3.59400			0.212147
$288$		0			0
$289$	−5.68174			−0.334220
$290$	12.5677	+	9.36035i	0.738002	+	0.549658i
$291$		0			0
$292$	−8.83837	+	2.64206i	−0.517227	+	0.154615i
$293$	4.85735	+	4.85735i	0.283770	+	0.283770i	0.834610	−	0.550841i	$-0.185693\pi$
$293$	4.85735	+	4.85735i	0.283770	+	0.283770i	−0.550841	+	0.834610i	$0.685693\pi$
$294$		0			0
$295$	−20.4459			−1.19041
$296$	9.68667	+	20.8067i	0.563026	+	1.20937i
$297$		0			0
$298$	−0.691696	−	4.72897i	−0.0400689	−	0.273942i
$299$	33.9929	−	33.9929i	1.96586	−	1.96586i
$300$		0			0
$301$	3.36325	+	3.36325i	0.193854	+	0.193854i
$302$	13.9097	+	10.3598i	0.800411	+	0.596140i
$303$		0			0
$304$	2.54690	−	12.2835i	0.146075	−	0.704505i
$305$			28.5231i			1.63323i
$306$		0			0
$307$	−21.4100	+	21.4100i	−1.22193	+	1.22193i	−0.254989	+	0.966944i	$0.582072\pi$
$307$	−21.4100	+	21.4100i	−1.22193	+	1.22193i	−0.966944	+	0.254989i	$0.917928\pi$
$308$	−10.0514	−	5.42501i	−0.572731	−	0.309119i
$309$		0			0
$310$	2.98873	−	0.437154i	0.169748	−	0.0248287i
$311$			3.23033i			0.183175i	0.995797	+	0.0915876i	$0.0291941\pi$
$311$			3.23033i			0.183175i	−0.995797	+	0.0915876i	$0.970806\pi$
$312$		0			0
$313$		−	6.53030i		−	0.369114i	−0.982822	−	0.184557i	$-0.940915\pi$
$313$		−	6.53030i		−	0.369114i	0.982822	−	0.184557i	$-0.0590851\pi$
$314$	−1.39270	−	9.52157i	−0.0785945	−	0.537333i
$315$		0			0
$316$	−14.2457	+	4.25848i	−0.801383	+	0.239558i
$317$	12.7296	−	12.7296i	0.714965	−	0.714965i	−0.252605	−	0.967570i	$-0.581287\pi$
$317$	12.7296	−	12.7296i	0.714965	−	0.714965i	0.967570	+	0.252605i	$0.0812872\pi$
$318$		0			0
$319$		−	21.1028i		−	1.18153i
$320$	2.06129	+	23.9012i	0.115229	+	1.33612i
$321$		0			0
$322$	−5.84042	+	7.84167i	−0.325474	+	0.436999i
$323$	−10.5615	−	10.5615i	−0.587656	−	0.587656i
$324$		0			0
$325$	19.6293	−	19.6293i	1.08884	−	1.08884i
$326$	−11.9287	+	1.74478i	−0.660669	+	0.0966346i
$327$		0			0
$328$	−3.48267	+	9.55016i	−0.192298	+	0.527320i
$329$	−6.04590			−0.333321
$330$		0			0
$331$	7.98204	+	7.98204i	0.438732	+	0.438732i	0.891585	−	0.452853i	$-0.149594\pi$
$331$	7.98204	+	7.98204i	0.438732	+	0.438732i	−0.452853	+	0.891585i	$0.649594\pi$
$332$	3.28779	−	6.09157i	0.180441	−	0.334319i
$333$		0			0
$334$	−4.01352	+	5.38877i	−0.219610	+	0.294860i
$335$	16.4237			0.897323
$336$		0			0
$337$	−1.43831			−0.0783498			−0.0391749	−	0.999232i	$-0.512473\pi$
$337$	−1.43831			−0.0783498			−0.0391749	+	0.999232i	$0.512473\pi$
$338$	−29.8590	+	40.0904i	−1.62412	+	2.18063i
$339$		0			0
$340$	25.1357	+	13.5665i	1.36318	+	0.735744i
$341$	−2.87624	−	2.87624i	−0.155757	−	0.155757i
$342$		0			0
$343$	1.00000			0.0539949
$344$	−12.1961	+	5.67794i	−0.657568	+	0.306134i
$345$		0			0
$346$	−27.0354	+	3.95441i	−1.45343	+	0.212590i
$347$	13.3928	−	13.3928i	0.718966	−	0.718966i	−0.249428	−	0.968393i	$-0.580242\pi$
$347$	13.3928	−	13.3928i	0.718966	−	0.718966i	0.968393	+	0.249428i	$0.0802425\pi$
$348$		0			0
$349$	−2.01384	−	2.01384i	−0.107798	−	0.107798i	0.651150	−	0.758949i	$-0.274287\pi$
$349$	−2.01384	−	2.01384i	−0.107798	−	0.107798i	−0.758949	+	0.651150i	$0.774287\pi$
$350$	−3.37256	+	4.52819i	−0.180271	+	0.242042i
$351$		0			0
$352$	24.1557	−	21.4521i	1.28750	−	1.14340i
$353$		−	10.9746i		−	0.584119i	−0.956400	−	0.292060i	$-0.905659\pi$
$353$		−	10.9746i		−	0.584119i	0.956400	−	0.292060i	$-0.0943406\pi$
$354$		0			0
$355$	−31.2652	+	31.2652i	−1.65938	+	1.65938i
$356$	−2.42696	−	8.11879i	−0.128629	−	0.430295i
$357$		0			0
$358$	2.81069	+	19.2160i	0.148549	+	1.01560i
$359$			13.8112i			0.728926i	0.931218	+	0.364463i	$0.118747\pi$
$359$			13.8112i			0.728926i	−0.931218	+	0.364463i	$0.881253\pi$
$360$		0			0
$361$			9.16435i			0.482334i
$362$	−7.91516	+	1.15773i	−0.416012	+	0.0608491i
$363$		0			0
$364$	6.60502	−	12.2377i	0.346197	−	0.641429i
$365$	9.78028	−	9.78028i	0.511923	−	0.511923i
$366$		0			0
$367$		−	1.72353i		−	0.0899673i	−0.998988	−	0.0449837i	$-0.985676\pi$
$367$		−	1.72353i		−	0.0899673i	0.998988	−	0.0449837i	$-0.0143236\pi$
$368$	−15.1778	−	23.1182i	−0.791198	−	1.20512i
$369$		0			0
$370$	−27.5985	−	20.5552i	−1.43478	−	1.06861i
$371$	−4.53235	−	4.53235i	−0.235308	−	0.235308i
$372$		0			0
$373$	5.17122	−	5.17122i	0.267756	−	0.267756i	−0.560440	−	0.828195i	$-0.689368\pi$
$373$	5.17122	−	5.17122i	0.267756	−	0.267756i	0.828195	+	0.560440i	$0.189368\pi$
$374$	−5.56693	−	38.0599i	−0.287859	−	1.96803i
$375$		0			0
$376$	5.85861	−	16.0655i	0.302135	−	0.828514i
$377$	25.6929			1.32325
$378$		0			0
$379$	−4.73174	−	4.73174i	−0.243053	−	0.243053i	0.575059	−	0.818112i	$-0.304979\pi$
$379$	−4.73174	−	4.73174i	−0.243053	−	0.243053i	−0.818112	+	0.575059i	$0.804979\pi$
$380$	5.38710	+	18.0212i	0.276352	+	0.924468i
$381$		0			0
$382$	−18.1247	−	13.4992i	−0.927341	−	0.690677i
$383$	−11.9260			−0.609388			−0.304694	−	0.952450i	$-0.598554\pi$
$383$	−11.9260			−0.609388			−0.304694	+	0.952450i	$0.598554\pi$
$384$		0			0
$385$	17.1257			0.872807
$386$	−4.02668	−	2.99904i	−0.204952	−	0.152647i
$387$		0			0
$388$	−3.87391	−	12.9592i	−0.196668	−	0.657904i
$389$	21.5999	+	21.5999i	1.09516	+	1.09516i	0.994968	+	0.100189i	$0.0319448\pi$
$389$	21.5999	+	21.5999i	1.09516	+	1.09516i	0.100189	+	0.994968i	$0.468055\pi$
$390$		0			0
$391$	−32.9274			−1.66521
$392$	−0.969023	+	2.65725i	−0.0489431	+	0.134212i
$393$		0			0
$394$	3.01177	+	20.5908i	0.151731	+	1.03735i
$395$	15.7639	−	15.7639i	0.793165	−	0.793165i
$396$		0			0
$397$	−24.1706	−	24.1706i	−1.21309	−	1.21309i	−0.970005	−	0.243084i	$-0.921841\pi$
$397$	−24.1706	−	24.1706i	−1.21309	−	1.21309i	−0.243084	−	0.970005i	$-0.578159\pi$
$398$	22.7364	+	16.9339i	1.13968	+	0.848822i
$399$		0			0
$400$	−8.76445	−	13.3497i	−0.438223	−	0.667484i
$401$			32.3793i			1.61694i	0.588536	+	0.808471i	$0.299705\pi$
$401$			32.3793i			1.61694i	−0.588536	+	0.808471i	$0.700295\pi$
$402$		0			0
$403$	3.50186	−	3.50186i	0.174440	−	0.174440i
$404$	−17.1467	+	31.7692i	−0.853081	+	1.58058i
$405$		0			0
$406$	−5.17067	+	0.756303i	−0.256616	+	0.0375347i
$407$			46.3413i			2.29706i
$408$		0			0
$409$			15.5253i			0.767676i	0.923400	+	0.383838i	$0.125398\pi$
$409$			15.5253i			0.767676i	−0.923400	+	0.383838i	$0.874602\pi$
$410$	−2.20589	−	15.0811i	−0.108941	−	0.744804i
$411$		0			0
$412$	2.91941	+	9.76615i	0.143829	+	0.481144i
$413$	4.82118	−	4.82118i	0.237235	−	0.237235i
$414$		0			0
$415$			10.3789i			0.509481i
$416$	26.1182	+	29.4098i	1.28055	+	1.44194i
$417$		0			0
$418$	15.1299	−	20.3143i	0.740029	−	0.993604i
$419$	−24.1080	−	24.1080i	−1.17775	−	1.17775i	−0.980315	−	0.197438i	$-0.936738\pi$
$419$	−24.1080	−	24.1080i	−1.17775	−	1.17775i	−0.197438	−	0.980315i	$-0.563262\pi$
$420$		0			0
$421$	−21.4110	+	21.4110i	−1.04351	+	1.04351i	−0.0444969	+	0.999010i	$0.514168\pi$
$421$	−21.4110	+	21.4110i	−1.04351	+	1.04351i	−0.999010	+	0.0444969i	$0.985832\pi$
$422$	−28.1869	+	4.12284i	−1.37212	+	0.200697i
$423$		0			0
$424$	16.4355	−	7.65164i	0.798180	−	0.371597i
$425$	−19.0140			−0.922314
$426$		0			0
$427$	−6.72581	−	6.72581i	−0.325485	−	0.325485i
$428$	8.59502	+	4.63897i	0.415456	+	0.224233i
$429$		0			0
$430$	12.0486	−	16.1771i	0.581036	−	0.780130i
$431$	−18.7984			−0.905485			−0.452742	−	0.891641i	$-0.649554\pi$
$431$	−18.7984			−0.905485			−0.452742	+	0.891641i	$0.649554\pi$
$432$		0			0
$433$	26.4453			1.27088			0.635440	−	0.772150i	$-0.280819\pi$
$433$	26.4453			1.27088			0.635440	+	0.772150i	$0.280819\pi$
$434$	−0.601665	+	0.807828i	−0.0288808	+	0.0387770i
$435$		0			0
$436$	−16.9876	+	31.4744i	−0.813558	+	1.50735i
$437$	−15.3322	−	15.3322i	−0.733441	−	0.733441i
$438$		0			0
$439$	7.11296			0.339483			0.169742	−	0.985489i	$-0.445707\pi$
$439$	7.11296			0.339483			0.169742	+	0.985489i	$0.445707\pi$
$440$	−16.5952	+	45.5074i	−0.791146	+	2.16948i
$441$		0			0
$442$	46.3384	−	6.77781i	2.20409	−	0.322388i
$443$	−0.0108636	+	0.0108636i	−0.000516147	+	0.000516147i	−0.707365	−	0.706849i	$-0.750116\pi$
$443$	−0.0108636	+	0.0108636i	−0.000516147	+	0.000516147i	0.706849	+	0.707365i	$0.250116\pi$
$444$		0			0
$445$	8.98401	+	8.98401i	0.425883	+	0.425883i
$446$	−14.4292	+	19.3734i	−0.683241	+	0.917357i
$447$		0			0
$448$	−6.12199	−	5.14988i	−0.289237	−	0.243309i
$449$		−	32.7577i		−	1.54593i	−0.634448	−	0.772966i	$-0.718772\pi$
$449$		−	32.7577i		−	1.54593i	0.634448	−	0.772966i	$-0.281228\pi$
$450$		0			0
$451$	−14.5135	+	14.5135i	−0.683416	+	0.683416i
$452$	11.3183	−	3.38338i	0.532366	−	0.159141i
$453$		0			0
$454$	−4.59892	−	31.4418i	−0.215838	−	1.47564i
$455$			20.8508i			0.977499i
$456$		0			0
$457$		−	10.0528i		−	0.470252i	−0.971965	−	0.235126i	$-0.924450\pi$
$457$		−	10.0528i		−	0.470252i	0.971965	−	0.235126i	$-0.0755502\pi$
$458$	−34.1661	+	4.99740i	−1.59648	+	0.233513i
$459$		0			0
$460$	36.4899	+	19.6946i	1.70135	+	0.918266i
$461$	15.1351	−	15.1351i	0.704910	−	0.704910i	−0.260550	−	0.965460i	$-0.583904\pi$
$461$	15.1351	−	15.1351i	0.704910	−	0.704910i	0.965460	+	0.260550i	$0.0839039\pi$
$462$		0			0
$463$			10.6714i			0.495940i	0.968768	+	0.247970i	$0.0797635\pi$
$463$			10.6714i			0.495940i	−0.968768	+	0.247970i	$0.920236\pi$
$464$	3.00081	−	14.4727i	0.139309	−	0.671877i
$465$		0			0
$466$	−9.50093	−	7.07622i	−0.440122	−	0.327800i
$467$	3.67348	+	3.67348i	0.169989	+	0.169989i	0.786974	−	0.616986i	$-0.211646\pi$
$467$	3.67348	+	3.67348i	0.169989	+	0.169989i	−0.616986	+	0.786974i	$0.711646\pi$
$468$		0			0
$469$	−3.87274	+	3.87274i	−0.178826	+	0.178826i
$470$	3.71079	+	25.3698i	0.171166	+	1.17022i
$471$		0			0
$472$	8.13926	+	17.4829i	0.374640	+	0.804717i
$473$	−27.1634			−1.24898
$474$		0			0
$475$	−8.85363	−	8.85363i	−0.406233	−	0.406233i
$476$	−9.12604	+	2.72806i	−0.418291	+	0.125040i
$477$		0			0
$478$	−7.08047	−	5.27349i	−0.323853	−	0.241204i
$479$	−4.41155			−0.201569			−0.100784	−	0.994908i	$-0.532135\pi$
$479$	−4.41155			−0.201569			−0.100784	+	0.994908i	$0.532135\pi$
$480$		0			0
$481$	−56.4212			−2.57258
$482$	−2.72048	−	2.02620i	−0.123915	−	0.0922907i
$483$		0			0
$484$	41.4196	−	12.3816i	1.88271	−	0.562800i
$485$	14.3403	+	14.3403i	0.651158	+	0.651158i
$486$		0			0
$487$	9.97116			0.451837			0.225918	−	0.974146i	$-0.427462\pi$
$487$	9.97116			0.451837			0.225918	+	0.974146i	$0.427462\pi$
$488$	24.3896	−	11.3547i	1.10407	−	0.514003i
$489$		0			0
$490$	−0.613769	−	4.19620i	−0.0277273	−	0.189565i
$491$	−30.2732	+	30.2732i	−1.36621	+	1.36621i	−0.500440	+	0.865771i	$0.666828\pi$
$491$	−30.2732	+	30.2732i	−1.36621	+	1.36621i	−0.865771	+	0.500440i	$0.833172\pi$
$492$		0			0
$493$	−12.4438	−	12.4438i	−0.560439	−	0.560439i
$494$	24.7329	+	18.4209i	1.11279	+	0.828795i
$495$		0			0
$496$	−1.56358	−	2.38158i	−0.0702067	−	0.106936i
$497$		−	14.7448i		−	0.661394i
$498$		0			0
$499$	10.4161	−	10.4161i	0.466289	−	0.466289i	−0.434421	−	0.900710i	$-0.643047\pi$
$499$	10.4161	−	10.4161i	0.466289	−	0.466289i	0.900710	+	0.434421i	$0.143047\pi$
$500$	−5.31786	−	2.87020i	−0.237822	−	0.128359i
$501$		0			0
$502$	20.7843	−	3.04008i	0.927650	−	0.135685i
$503$			8.37172i			0.373277i	0.982429	+	0.186638i	$0.0597592\pi$
$503$			8.37172i			0.373277i	−0.982429	+	0.186638i	$0.940241\pi$
$504$		0			0
$505$		−	54.1288i		−	2.40870i
$506$	−8.08159	−	55.2520i	−0.359271	−	2.45625i
$507$		0			0
$508$	5.88351	−	1.75876i	0.261039	−	0.0780325i
$509$	17.0580	−	17.0580i	0.756083	−	0.756083i	−0.219524	−	0.975607i	$-0.570450\pi$
$509$	17.0580	−	17.0580i	0.756083	−	0.756083i	0.975607	+	0.219524i	$0.0704503\pi$
$510$		0			0
$511$			4.61241i			0.204041i
$512$	19.6169	−	11.2773i	0.866952	−	0.498392i
$513$		0			0
$514$	1.68271	−	2.25930i	0.0742213	−	0.0996537i
$515$	−10.8069	−	10.8069i	−0.476210	−	0.476210i
$516$		0			0
$517$	24.4150	−	24.4150i	1.07377	−	1.07377i
$518$	11.3547	−	1.66083i	0.498898	−	0.0729726i
$519$		0			0
$520$	−55.4058	−	20.2049i	−2.42970	−	0.886043i
$521$	12.2025			0.534601			0.267300	−	0.963613i	$-0.413868\pi$
$521$	12.2025			0.534601			0.267300	+	0.963613i	$0.413868\pi$
$522$		0			0
$523$	−8.77429	−	8.77429i	−0.383673	−	0.383673i	0.488751	−	0.872423i	$-0.337453\pi$
$523$	−8.77429	−	8.77429i	−0.383673	−	0.383673i	−0.872423	+	0.488751i	$0.837453\pi$
$524$	−9.34202	+	17.3088i	−0.408108	+	0.756137i
$525$		0			0
$526$	−4.02657	+	5.40629i	−0.175567	+	0.235725i
$527$	−3.39209			−0.147762
$528$		0			0
$529$	−24.8012			−1.07831
$530$	−16.2368	+	21.8005i	−0.705283	+	0.946951i
$531$		0			0
$532$	−5.51972	−	2.97914i	−0.239310	−	0.129162i
$533$	−17.6704	−	17.6704i	−0.765391	−	0.765391i
$534$		0			0
$535$	−14.6443			−0.633129
$536$	−6.53807	−	14.0436i	−0.282402	−	0.606592i
$537$		0			0
$538$	−20.1386	+	2.94563i	−0.868236	+	0.126995i
$539$	−4.03827	+	4.03827i	−0.173941	+	0.173941i
$540$		0			0
$541$	−23.2625	−	23.2625i	−1.00013	−	1.00013i	−1.00000		0.000132738i	$-0.999958\pi$
$541$	−23.2625	−	23.2625i	−1.00013	−	1.00013i	−0.000132738	−	1.00000i	$-0.500042\pi$
$542$	25.1890	−	33.8201i	1.08196	−	1.45270i
$543$		0			0
$544$	1.59421	−	26.8938i	0.0683511	−	1.15306i
$545$		−	53.6265i		−	2.29711i
$546$		0			0
$547$	24.7224	−	24.7224i	1.05705	−	1.05705i	0.0587833	−	0.998271i	$-0.481278\pi$
$547$	24.7224	−	24.7224i	1.05705	−	1.05705i	0.998271	−	0.0587833i	$-0.0187221\pi$
$548$	−6.61877	−	22.1415i	−0.282740	−	0.945837i
$549$		0			0
$550$	−4.66673	−	31.9054i	−0.198990	−	1.36045i
$551$		−	11.5886i		−	0.493690i
$552$		0			0
$553$			7.43429i			0.316138i
$554$	20.5195	−	3.00134i	0.871788	−	0.127515i
$555$		0			0
$556$	−8.32041	+	15.4159i	−0.352864	+	0.653782i
$557$	15.9473	−	15.9473i	0.675708	−	0.675708i	−0.283318	−	0.959026i	$-0.591435\pi$
$557$	15.9473	−	15.9473i	0.675708	−	0.675708i	0.959026	+	0.283318i	$0.0914352\pi$
$558$		0			0
$559$		−	33.0718i		−	1.39879i
$560$	11.7451	+	2.43528i	0.496322	+	0.102909i
$561$		0			0
$562$	−11.4819	−	8.55164i	−0.484335	−	0.360729i
$563$	8.75478	+	8.75478i	0.368970	+	0.368970i	0.867101	−	0.498132i	$-0.165980\pi$
$563$	8.75478	+	8.75478i	0.368970	+	0.368970i	−0.498132	+	0.867101i	$0.665980\pi$
$564$		0			0
$565$	−12.5244	+	12.5244i	−0.526908	+	0.526908i
$566$	3.99420	+	27.3075i	0.167889	+	1.14782i
$567$		0			0
$568$	39.1806	+	14.2880i	1.64398	+	0.599512i
$569$	−24.3805			−1.02209			−0.511043	−	0.859555i	$-0.670741\pi$
$569$	−24.3805			−1.02209			−0.511043	+	0.859555i	$0.670741\pi$
$570$		0			0
$571$	−9.52629	−	9.52629i	−0.398663	−	0.398663i	0.479098	−	0.877761i	$-0.340964\pi$
$571$	−9.52629	−	9.52629i	−0.398663	−	0.398663i	−0.877761	+	0.479098i	$0.840964\pi$
$572$	22.7463	+	76.0920i	0.951069	+	3.18157i
$573$		0			0
$574$	4.07631	+	3.03601i	0.170142	+	0.126720i
$575$	−27.6029			−1.15112
$576$		0			0
$577$	1.46394			0.0609448			0.0304724	−	0.999536i	$-0.490299\pi$
$577$	1.46394			0.0609448			0.0304724	+	0.999536i	$0.490299\pi$
$578$	−6.44422	−	4.79961i	−0.268044	−	0.199638i
$579$		0			0
$580$	6.34720	+	21.2330i	0.263553	+	0.881652i
$581$	−2.44737	−	2.44737i	−0.101534	−	0.101534i
$582$		0			0
$583$	36.6057			1.51605
$584$	−12.2563	−	4.46953i	−0.507171	−	0.184951i
$585$		0			0
$586$	1.40599	+	9.61242i	0.0580808	+	0.397086i
$587$	−7.13883	+	7.13883i	−0.294651	+	0.294651i	−0.838914	−	0.544263i	$-0.816809\pi$
$587$	−7.13883	+	7.13883i	−0.294651	+	0.294651i	0.544263	+	0.838914i	$0.316809\pi$
$588$		0			0
$589$	−1.57949	−	1.57949i	−0.0650816	−	0.0650816i
$590$	−23.1897	−	17.2716i	−0.954707	−	0.711059i
$591$		0			0
$592$	−6.58974	+	31.7817i	−0.270837	+	1.30622i
$593$			14.7385i			0.605237i	0.953112	+	0.302619i	$0.0978609\pi$
$593$			14.7385i			0.605237i	−0.953112	+	0.302619i	$0.902139\pi$
$594$		0			0
$595$	10.0986	−	10.0986i	0.414002	−	0.414002i
$596$	3.21025	−	5.94790i	0.131497	−	0.243636i
$597$		0			0
$598$	67.2700	−	9.83944i	2.75088	−	0.402365i
$599$		−	17.8924i		−	0.731062i	−0.930799	−	0.365531i	$-0.880887\pi$
$599$		−	17.8924i		−	0.731062i	0.930799	−	0.365531i	$-0.119113\pi$
$600$		0			0
$601$			6.69170i			0.272960i	0.990643	+	0.136480i	$0.0435790\pi$
$601$			6.69170i			0.272960i	−0.990643	+	0.136480i	$0.956421\pi$
$602$	0.973511	+	6.65568i	0.0396774	+	0.271265i
$603$		0			0
$604$	7.02493	+	23.5002i	0.285841	+	0.956209i
$605$	−45.8336	+	45.8336i	−1.86340	+	1.86340i
$606$		0			0
$607$			27.0776i			1.09904i	0.835479	+	0.549522i	$0.185190\pi$
$607$			27.0776i			1.09904i	−0.835479	+	0.549522i	$0.814810\pi$
$608$	13.2651	−	11.7804i	0.537970	−	0.477759i
$609$		0			0
$610$	−24.0947	+	32.3509i	−0.975568	+	1.30985i
$611$	29.7255	+	29.7255i	1.20257	+	1.20257i
$612$		0			0
$613$	22.9059	−	22.9059i	0.925159	−	0.925159i	−0.0722294	−	0.997388i	$-0.523011\pi$
$613$	22.9059	−	22.9059i	0.925159	−	0.925159i	0.997388	+	0.0722294i	$0.0230114\pi$
$614$	−42.3692	+	6.19724i	−1.70988	+	0.250100i
$615$		0			0
$616$	−6.81753	−	14.6439i	−0.274686	−	0.590019i
$617$	10.3945			0.418466			0.209233	−	0.977866i	$-0.432903\pi$
$617$	10.3945			0.418466			0.209233	+	0.977866i	$0.432903\pi$
$618$		0			0
$619$	−8.53232	−	8.53232i	−0.342943	−	0.342943i	0.514530	−	0.857473i	$-0.327967\pi$
$619$	−8.53232	−	8.53232i	−0.342943	−	0.342943i	−0.857473	+	0.514530i	$0.827967\pi$
$620$	3.75909	+	2.02889i	0.150969	+	0.0814821i
$621$		0			0
$622$	−2.72880	+	3.66384i	−0.109415	+	0.146906i
$623$	−4.23689			−0.169747
$624$		0			0
$625$	29.0227			1.16091
$626$	5.51643	−	7.40666i	0.220481	−	0.296030i
$627$		0			0
$628$	6.46369	−	11.9758i	0.257929	−	0.477888i
$629$	27.3263	+	27.3263i	1.08957	+	1.08957i
$630$		0			0
$631$	−3.74199			−0.148966			−0.0744831	−	0.997222i	$-0.523731\pi$
$631$	−3.74199			−0.148966			−0.0744831	+	0.997222i	$0.523731\pi$
$632$	−19.7548	−	7.20399i	−0.785803	−	0.286560i
$633$		0			0
$634$	25.1911	−	3.68465i	1.00047	−	0.146336i
$635$	−6.51051	+	6.51051i	−0.258362	+	0.258362i
$636$		0			0
$637$	−4.91665	−	4.91665i	−0.194805	−	0.194805i
$638$	17.8264	−	23.9348i	0.705755	−	0.947586i
$639$		0			0
$640$	−17.8524	+	28.8499i	−0.705680	+	1.14039i
$641$			15.1283i			0.597531i	0.954326	+	0.298766i	$0.0965749\pi$
$641$			15.1283i			0.597531i	−0.954326	+	0.298766i	$0.903425\pi$
$642$		0			0
$643$	−0.845317	+	0.845317i	−0.0333361	+	0.0333361i	−0.723578	−	0.690242i	$-0.757504\pi$
$643$	−0.845317	+	0.845317i	−0.0333361	+	0.0333361i	0.690242	+	0.723578i	$0.257504\pi$
$644$	−13.2484	+	3.96036i	−0.522060	+	0.156060i
$645$		0			0
$646$	−3.05708	−	20.9006i	−0.120279	−	0.822321i
$647$		−	23.9117i		−	0.940064i	−0.882649	−	0.470032i	$-0.844242\pi$
$647$		−	23.9117i		−	0.940064i	0.882649	−	0.470032i	$-0.155758\pi$
$648$		0			0
$649$			38.9385i			1.52847i
$650$	38.8452	−	5.68181i	1.52363	−	0.222859i
$651$		0			0
$652$	−15.0034	−	8.09775i	−0.587579	−	0.317132i
$653$	−19.8544	+	19.8544i	−0.776964	+	0.776964i	−0.979313	−	0.202350i	$-0.935142\pi$
$653$	−19.8544	+	19.8544i	−0.776964	+	0.776964i	0.202350	+	0.979313i	$0.435142\pi$
$654$		0			0
$655$		−	29.4909i		−	1.15231i
$656$	−12.0175	+	7.88983i	−0.469204	+	0.308046i
$657$		0			0
$658$	−6.85725	−	5.10723i	−0.267324	−	0.199101i
$659$	9.03903	+	9.03903i	0.352111	+	0.352111i	0.860894	−	0.508784i	$-0.169905\pi$
$659$	9.03903	+	9.03903i	0.352111	+	0.352111i	−0.508784	+	0.860894i	$0.669905\pi$
$660$		0			0
$661$	−31.4210	+	31.4210i	−1.22213	+	1.22213i	−0.255261	+	0.966872i	$0.582161\pi$
$661$	−31.4210	+	31.4210i	−1.22213	+	1.22213i	−0.966872	+	0.255261i	$0.917839\pi$
$662$	2.31045	+	15.7960i	0.0897980	+	0.613929i
$663$		0			0
$664$	8.87483	−	4.13172i	0.344410	−	0.160342i
$665$	9.40458			0.364694
$666$		0			0
$667$	−18.0648	−	18.0648i	−0.699472	−	0.699472i
$668$	−9.10426	+	2.72155i	−0.352254	+	0.105300i
$669$		0			0
$670$	18.6278	+	13.8738i	0.719653	+	0.535993i
$671$	54.3213			2.09705
$672$		0			0
$673$	16.8543			0.649684			0.324842	−	0.945768i	$-0.394689\pi$
$673$	16.8543			0.649684			0.324842	+	0.945768i	$0.394689\pi$
$674$	−1.63133	−	1.21500i	−0.0628366	−	0.0468002i
$675$		0			0
$676$	−67.7322	+	20.2473i	−2.60508	+	0.778741i
$677$	−20.8816	−	20.8816i	−0.802545	−	0.802545i	0.180948	−	0.983493i	$-0.442084\pi$
$677$	−20.8816	−	20.8816i	−0.802545	−	0.802545i	−0.983493	+	0.180948i	$0.942084\pi$
$678$		0			0
$679$	−6.76292			−0.259537
$680$	17.0488	+	36.6203i	0.653790	+	1.40433i
$681$		0			0
$682$	−0.832544	−	5.69192i	−0.0318798	−	0.217955i
$683$	−18.9351	+	18.9351i	−0.724533	+	0.724533i	−0.969525	−	0.244992i	$-0.921215\pi$
$683$	−18.9351	+	18.9351i	−0.724533	+	0.724533i	0.244992	+	0.969525i	$0.421215\pi$
$684$		0			0
$685$	24.5011	+	24.5011i	0.936138	+	0.936138i
$686$	1.13420	+	0.844744i	0.0433039	+	0.0322525i
$687$		0			0
$688$	−18.6292	−	3.86264i	−0.710231	−	0.147262i
$689$			44.5679i			1.69790i
$690$		0			0
$691$	−2.24775	+	2.24775i	−0.0855083	+	0.0855083i	−0.748567	−	0.663059i	$-0.769258\pi$
$691$	−2.24775	+	2.24775i	−0.0855083	+	0.0855083i	0.663059	+	0.748567i	$0.269258\pi$
$692$	−34.0040	−	18.3529i	−1.29264	−	0.697672i
$693$		0			0
$694$	26.5037	−	3.87664i	1.00607	−	0.147155i
$695$		−	26.2659i		−	0.996323i
$696$		0			0
$697$			17.1165i			0.648335i
$698$	−0.582916	−	3.98527i	−0.0220637	−	0.150845i
$699$		0			0
$700$	−7.65032	+	2.28692i	−0.289155	+	0.0864374i
$701$	8.17318	−	8.17318i	0.308697	−	0.308697i	−0.535707	−	0.844404i	$-0.679955\pi$
$701$	8.17318	−	8.17318i	0.308697	−	0.308697i	0.844404	+	0.535707i	$0.179955\pi$
$702$		0			0
$703$			25.4483i			0.959802i
$704$	45.5189	−	3.92564i	1.71556	−	0.147953i
$705$		0			0
$706$	9.27073	−	12.4474i	0.348908	−	0.468464i
$707$	12.7637	+	12.7637i	0.480027	+	0.480027i
$708$		0			0
$709$	−11.4595	+	11.4595i	−0.430372	+	0.430372i	−0.888755	−	0.458383i	$-0.848429\pi$
$709$	−11.4595	+	11.4595i	−0.430372	+	0.430372i	0.458383	+	0.888755i	$0.348429\pi$
$710$	−61.8720	+	9.04989i	−2.32202	+	0.339636i
$711$		0			0
$712$	4.10564	−	11.2585i	0.153866	−	0.421930i
$713$	−4.92435			−0.184418
$714$		0			0
$715$	−84.2011	−	84.2011i	−3.14894	−	3.14894i
$716$	−13.0447	+	24.1691i	−0.487505	+	0.903243i
$717$		0			0
$718$	−11.6669	+	15.6646i	−0.435405	+	0.584599i
$719$	−23.6156			−0.880714			−0.440357	−	0.897823i	$-0.645148\pi$
$719$	−23.6156			−0.880714			−0.440357	+	0.897823i	$0.645148\pi$
$720$		0			0
$721$	5.09658			0.189807
$722$	−7.74153	+	10.3942i	−0.288110	+	0.386832i
$723$		0			0
$724$	−9.95536	−	5.37318i	−0.369988	−	0.199693i
$725$	−10.4316	−	10.4316i	−0.387418	−	0.387418i
$726$		0			0
$727$	−11.2623			−0.417695			−0.208848	−	0.977948i	$-0.566971\pi$
$727$	−11.2623			−0.417695			−0.208848	+	0.977948i	$0.566971\pi$
$728$	17.8291	−	8.30043i	0.660791	−	0.307635i
$729$		0			0
$730$	19.3546	−	2.83096i	0.716346	−	0.104778i
$731$	−16.0176	+	16.0176i	−0.592432	+	0.592432i
$732$		0			0
$733$	8.10898	+	8.10898i	0.299512	+	0.299512i	0.840823	−	0.541311i	$-0.182072\pi$
$733$	8.10898	+	8.10898i	0.299512	+	0.299512i	−0.541311	+	0.840823i	$0.682072\pi$
$734$	1.45594	−	1.95482i	0.0537396	−	0.0721538i
$735$		0			0
$736$	2.31433	−	39.0420i	0.0853075	−	1.43911i
$737$		−	31.2783i		−	1.15215i
$738$		0			0
$739$	−35.7952	+	35.7952i	−1.31675	+	1.31675i	−0.400410	+	0.916336i	$0.631132\pi$
$739$	−35.7952	+	35.7952i	−1.31675	+	1.31675i	−0.916336	+	0.400410i	$0.868868\pi$
$740$	−13.9383	−	46.6273i	−0.512384	−	1.71405i
$741$		0			0
$742$	−1.31191	−	8.96926i	−0.0481619	−	0.329272i
$743$			24.0620i			0.882748i	0.897323	+	0.441374i	$0.145509\pi$
$743$			24.0620i			0.882748i	−0.897323	+	0.441374i	$0.854491\pi$
$744$		0			0
$745$			10.1341i			0.371286i
$746$	10.2336	−	1.49684i	0.374677	−	0.0548032i
$747$		0			0
$748$	25.8368	−	47.8701i	0.944687	−	1.75030i
$749$	3.45316	−	3.45316i	0.126176	−	0.126176i
$750$		0			0
$751$			39.8810i			1.45528i	0.685961	+	0.727639i	$0.259382\pi$
$751$			39.8810i			1.45528i	−0.685961	+	0.727639i	$0.740618\pi$
$752$	20.2160	−	13.2724i	0.737203	−	0.483996i
$753$		0			0
$754$	29.1409	+	21.7039i	1.06125	+	0.790410i
$755$	−26.0046	−	26.0046i	−0.946404	−	0.946404i
$756$		0			0
$757$	−11.5955	+	11.5955i	−0.421446	+	0.421446i	−0.885701	−	0.464255i	$-0.846322\pi$
$757$	−11.5955	+	11.5955i	−0.421446	+	0.421446i	0.464255	+	0.885701i	$0.346322\pi$
$758$	−1.36963	−	9.36384i	−0.0497472	−	0.340110i
$759$		0			0
$760$	−9.11326	+	24.9904i	−0.330573	+	0.906495i
$761$	17.8050			0.645430			0.322715	−	0.946496i	$-0.395404\pi$
$761$	17.8050			0.645430			0.322715	+	0.946496i	$0.395404\pi$
$762$		0			0
$763$	12.6452	+	12.6452i	0.457788	+	0.457788i
$764$	−9.15371	−	30.6215i	−0.331170	−	1.10785i
$765$		0			0
$766$	−13.5264	−	10.0744i	−0.488729	−	0.364002i
$767$	−47.4081			−1.71181
$768$		0			0
$769$	−6.78949			−0.244835			−0.122418	−	0.992479i	$-0.539065\pi$
$769$	−6.78949			−0.244835			−0.122418	+	0.992479i	$0.539065\pi$
$770$	19.4240	+	14.4668i	0.699991	+	0.521349i
$771$		0			0
$772$	−2.03363	−	6.80302i	−0.0731921	−	0.244846i
$773$	20.3304	+	20.3304i	0.731235	+	0.731235i	0.970864	−	0.239629i	$-0.0770259\pi$
$773$	20.3304	+	20.3304i	0.731235	+	0.731235i	−0.239629	+	0.970864i	$0.577026\pi$
$774$		0			0
$775$	−2.84358			−0.102144
$776$	6.55342	−	17.9708i	0.235254	−	0.645113i
$777$		0			0
$778$	6.25221	+	42.7449i	0.224153	+	1.53248i
$779$	−7.97011	+	7.97011i	−0.285559	+	0.285559i
$780$		0			0
$781$	59.5434	+	59.5434i	2.13063	+	2.13063i
$782$	−37.3462	−	27.8152i	−1.33550	−	0.994670i
$783$		0			0
$784$	−3.34376	+	2.19528i	−0.119420	+	0.0784028i
$785$			20.4046i			0.728272i
$786$		0			0
$787$	−11.8828	+	11.8828i	−0.423577	+	0.423577i	−0.886433	−	0.462856i	$-0.846825\pi$
$787$	−11.8828	+	11.8828i	−0.423577	+	0.423577i	0.462856	+	0.886433i	$0.346825\pi$
$788$	−13.9780	+	25.8982i	−0.497945	+	0.922585i
$789$		0			0
$790$	31.1958	−	4.56294i	1.10990	−	0.162342i
$791$		−	5.90657i		−	0.210014i
$792$		0			0
$793$			66.1368i			2.34859i
$794$	−6.99632	−	47.8323i	−0.248290	−	1.69750i
$795$		0			0
$796$	11.4828	+	38.4129i	0.406998	+	1.36151i
$797$	−4.57631	+	4.57631i	−0.162101	+	0.162101i	−0.783497	−	0.621396i	$-0.786566\pi$
$797$	−4.57631	+	4.57631i	−0.162101	+	0.162101i	0.621396	+	0.783497i	$0.286566\pi$
$798$		0			0
$799$		−	28.7938i		−	1.01865i
$800$	1.33642	−	22.5449i	0.0472495	−	0.797083i
$801$		0			0
$802$	−27.3522	+	36.7245i	−0.965839	+	1.29679i
$803$	−18.6262	−	18.6262i	−0.657303	−	0.657303i
$804$		0			0
$805$	14.6603	−	14.6603i	0.516707	−	0.516707i
$806$	6.92998	−	1.01363i	0.244098	−	0.0357037i
$807$		0			0
$808$	−46.2846	+	21.5480i	−1.62829	+	0.758057i
$809$	25.1471			0.884123			0.442062	−	0.896985i	$-0.354247\pi$
$809$	25.1471			0.884123			0.442062	+	0.896985i	$0.354247\pi$
$810$		0			0
$811$	24.5249	+	24.5249i	0.861187	+	0.861187i	0.991476	−	0.130289i	$-0.0415906\pi$
$811$	24.5249	+	24.5249i	0.861187	+	0.861187i	−0.130289	+	0.991476i	$0.541591\pi$
$812$	−6.50346	−	3.51010i	−0.228227	−	0.123180i
$813$		0			0
$814$	−39.1466	+	52.5603i	−1.37209	+	1.84224i
$815$	25.5630			0.895434
$816$		0			0
$817$	−14.9168			−0.521873
$818$	−13.1149	+	17.6088i	−0.458551	+	0.615676i
$819$		0			0
$820$	10.2378	−	18.9684i	0.357519	−	0.662406i
$821$	−24.4111	−	24.4111i	−0.851955	−	0.851955i	0.138419	−	0.990374i	$-0.455798\pi$
$821$	−24.4111	−	24.4111i	−0.851955	−	0.851955i	−0.990374	+	0.138419i	$0.955798\pi$
$822$		0			0
$823$	15.7338			0.548445			0.274223	−	0.961666i	$-0.411579\pi$
$823$	15.7338			0.548445			0.274223	+	0.961666i	$0.411579\pi$
$824$	−4.93871	+	13.5429i	−0.172048	+	0.471790i
$825$		0			0
$826$	9.54084	−	1.39552i	0.331968	−	0.0485563i
$827$	25.0353	−	25.0353i	0.870564	−	0.870564i	−0.121970	−	0.992534i	$-0.538921\pi$
$827$	25.0353	−	25.0353i	0.870564	−	0.870564i	0.992534	+	0.121970i	$0.0389212\pi$
$828$		0			0
$829$	−21.0067	−	21.0067i	−0.729592	−	0.729592i	0.240947	−	0.970538i	$-0.422542\pi$
$829$	−21.0067	−	21.0067i	−0.729592	−	0.729592i	−0.970538	+	0.240947i	$0.922542\pi$
$830$	−8.76753	+	11.7718i	−0.304325	+	0.408604i
$831$		0			0
$832$	4.77952	+	55.4198i	0.165700	+	1.92134i
$833$			4.76253i			0.165012i
$834$		0			0
$835$	10.0745	−	10.0745i	0.348642	−	0.348642i
$836$	34.3207	−	10.2595i	1.18701	−	0.354833i
$837$		0			0
$838$	−6.97820	−	47.7084i	−0.241058	−	1.64806i
$839$		−	7.34682i		−	0.253640i	−0.991926	−	0.126820i	$-0.959523\pi$
$839$		−	7.34682i		−	0.253640i	0.991926	−	0.126820i	$-0.0404771\pi$
$840$		0			0
$841$			15.3461i			0.529175i
$842$	−42.3711	+	6.19752i	−1.46020	+	0.213581i
$843$		0			0
$844$	−35.4523	−	19.1346i	−1.22032	−	0.658641i
$845$	74.9504	−	74.9504i	2.57837	−	2.57837i
$846$		0			0
$847$		−	21.6153i		−	0.742710i
$848$	25.1049	+	5.20533i	0.862104	+	0.178752i
$849$		0			0
$850$	−21.5657	−	16.0620i	−0.739696	−	0.550920i
$851$	39.6700	+	39.6700i	1.35987	+	1.35987i
$852$		0			0
$853$	27.5322	−	27.5322i	0.942685	−	0.942685i	−0.0557594	−	0.998444i	$-0.517758\pi$
$853$	27.5322	−	27.5322i	0.942685	−	0.942685i	0.998444	+	0.0557594i	$0.0177580\pi$
$854$	−1.94682	−	13.3100i	−0.0666189	−	0.455458i
$855$		0			0
$856$	5.82972	+	12.5221i	0.199256	+	0.427997i
$857$	−14.8983			−0.508915			−0.254457	−	0.967084i	$-0.581897\pi$
$857$	−14.8983			−0.508915			−0.254457	+	0.967084i	$0.581897\pi$
$858$		0			0
$859$	13.6121	+	13.6121i	0.464439	+	0.464439i	0.900107	−	0.435668i	$-0.143488\pi$
$859$	13.6121	+	13.6121i	0.464439	+	0.464439i	−0.435668	+	0.900107i	$0.643488\pi$
$860$	27.3311	−	8.17010i	0.931981	−	0.278598i
$861$		0			0
$862$	−21.3211	−	15.8798i	−0.726199	−	0.540868i
$863$	43.8205			1.49167			0.745834	−	0.666132i	$-0.232051\pi$
$863$	43.8205			1.49167			0.745834	+	0.666132i	$0.232051\pi$
$864$		0			0
$865$	57.9365			1.96990
$866$	29.9942	+	22.3395i	1.01925	+	0.759127i
$867$		0			0
$868$	−1.36482	+	0.407986i	−0.0463249	+	0.0138479i
$869$	−30.0217	−	30.0217i	−1.01842	−	1.01842i
$870$		0			0
$871$	38.0818			1.29035
$872$	−45.8551	+	21.3480i	−1.55285	+	0.722936i
$873$		0			0
$874$	−4.43800	−	30.3416i	−0.150118	−	1.02632i
$875$	−2.13652	+	2.13652i	−0.0722275	+	0.0722275i
$876$		0			0
$877$	15.3765	+	15.3765i	0.519229	+	0.519229i	0.917338	−	0.398109i	$-0.130333\pi$
$877$	15.3765	+	15.3765i	0.519229	+	0.519229i	−0.398109	+	0.917338i	$0.630333\pi$
$878$	8.06751	+	6.00863i	0.272265	+	0.202781i
$879$		0			0
$880$	−57.2643	+	37.5957i	−1.93038	+	1.26735i
$881$		−	19.9612i		−	0.672509i	−0.941771	−	0.336254i	$-0.890840\pi$
$881$		−	19.9612i		−	0.672509i	0.941771	−	0.336254i	$-0.109160\pi$
$882$		0			0
$883$	−16.8680	+	16.8680i	−0.567654	+	0.567654i	−0.931471	−	0.363816i	$-0.881474\pi$
$883$	−16.8680	+	16.8680i	−0.567654	+	0.567654i	0.363816	+	0.931471i	$0.381474\pi$
$884$	58.2824	+	31.4566i	1.96025	+	1.05800i
$885$		0			0
$886$	−0.0214985	+	0.00314454i	−0.000722257	+	0.000105643i
$887$		−	25.0819i		−	0.842167i	−0.907022	−	0.421084i	$-0.861650\pi$
$887$		−	25.0819i		−	0.842167i	0.907022	−	0.421084i	$-0.138350\pi$
$888$		0			0
$889$		−	3.07038i		−	0.102977i
$890$	2.60047	+	17.7788i	0.0871680	+	0.595948i
$891$		0			0
$892$	−32.7311	+	9.78435i	−1.09592	+	0.327604i
$893$	13.4075	−	13.4075i	0.448664	−	0.448664i
$894$		0			0
$895$		−	41.1797i		−	1.37649i
$896$	−2.59323	−	11.0125i	−0.0866336	−	0.367902i
$897$		0			0
$898$	27.6719	−	37.1538i	0.923422	−	1.23984i
$899$	−1.86099	−	1.86099i	−0.0620674	−	0.0620674i
$900$		0			0
$901$	21.5855	−	21.5855i	0.719116	−	0.719116i
$902$	−28.7215	+	4.20103i	−0.956321	+	0.139879i
$903$		0			0
$904$	15.6953	+	5.72361i	0.522017	+	0.190364i
$905$	16.9621			0.563839
$906$		0			0
$907$	−6.00255	−	6.00255i	−0.199311	−	0.199311i	0.600393	−	0.799705i	$-0.295011\pi$
$907$	−6.00255	−	6.00255i	−0.199311	−	0.199311i	−0.799705	+	0.600393i	$0.795011\pi$
$908$	21.3441	−	39.5461i	0.708330	−	1.31238i
$909$		0			0
$910$	−17.6136	+	23.6489i	−0.583884	+	0.783955i
$911$	14.6496			0.485363			0.242682	−	0.970106i	$-0.421973\pi$
$911$	14.6496			0.485363			0.242682	+	0.970106i	$0.421973\pi$
$912$		0			0
$913$	19.7663			0.654168
$914$	8.49207	−	11.4019i	0.280893	−	0.377142i
$915$		0			0
$916$	−42.9727	−	23.1936i	−1.41986	−	0.766337i
$917$	6.95401	+	6.95401i	0.229642	+	0.229642i
$918$		0			0
$919$	4.17227			0.137631			0.0688153	−	0.997629i	$-0.478078\pi$
$919$	4.17227			0.137631			0.0688153	+	0.997629i	$0.478078\pi$
$920$	24.7499	+	53.1622i	0.815981	+	1.75271i
$921$		0			0
$922$	29.9514	−	4.38093i	0.986398	−	0.144278i
$923$	−72.4949	+	72.4949i	−2.38620	+	2.38620i
$924$		0			0
$925$	22.9075	+	22.9075i	0.753195	+	0.753195i
$926$	−9.01457	+	12.1035i	−0.296237	+	0.397744i
$927$		0			0
$928$	15.6292	−	13.8800i	0.513054	−	0.455632i
$929$		−	38.1876i		−	1.25290i	−0.779463	−	0.626448i	$-0.784508\pi$
$929$		−	38.1876i		−	1.25290i	0.779463	−	0.626448i	$-0.215492\pi$
$930$		0			0
$931$	−2.21762	+	2.21762i	−0.0726794	+	0.0726794i
$932$	−4.79835	−	16.0517i	−0.157175	−	0.525791i
$933$		0			0
$934$	1.06331	+	7.26961i	0.0347926	+	0.237869i
$935$			81.5618i			2.66736i
$936$		0			0
$937$			45.0796i			1.47269i	0.676609	+	0.736343i	$0.263449\pi$
$937$			45.0796i			1.47269i	−0.676609	+	0.736343i	$0.736551\pi$
$938$	−7.66393	+	1.12099i	−0.250236	+	0.0366015i
$939$		0			0
$940$	−17.2222	+	31.9091i	−0.561727	+	1.04076i
$941$	3.09966	−	3.09966i	0.101046	−	0.101046i	−0.654777	−	0.755822i	$-0.727237\pi$
$941$	3.09966	−	3.09966i	0.101046	−	0.101046i	0.755822	+	0.654777i	$0.227237\pi$
$942$		0			0
$943$			24.8483i			0.809173i
$944$	−5.53705	+	26.7047i	−0.180216	+	0.869165i
$945$		0			0
$946$	−30.8087	−	22.9461i	−1.00168	−	0.746043i
$947$	16.6180	+	16.6180i	0.540012	+	0.540012i	0.923532	−	0.383520i	$-0.125288\pi$
$947$	16.6180	+	16.6180i	0.540012	+	0.540012i	−0.383520	+	0.923532i	$0.625288\pi$
$948$		0			0
$949$	22.6776	−	22.6776i	0.736146	−	0.736146i
$950$	−2.56273	−	17.5208i	−0.0831461	−	0.568451i
$951$		0			0
$952$	−12.6553	−	4.61501i	−0.410159	−	0.149573i
$953$	57.9097			1.87588			0.937939	−	0.346801i	$-0.112732\pi$
$953$	57.9097			1.87588			0.937939	+	0.346801i	$0.112732\pi$
$954$		0			0
$955$	33.8848	+	33.8848i	1.09649	+	1.09649i
$956$	−3.57592	−	11.9624i	−0.115654	−	0.386891i
$957$		0			0
$958$	−5.00358	−	3.72663i	−0.161658	−	0.120402i
$959$	−11.5548			−0.373124
$960$		0			0
$961$	30.4927			0.983636
$962$	−63.9929	−	47.6614i	−2.06321	−	1.53667i
$963$		0			0
$964$	−1.37395	−	4.59622i	−0.0442521	−	0.148034i
$965$	7.52801	+	7.52801i	0.242335	+	0.242335i
$966$		0			0
$967$	37.9630			1.22081			0.610404	−	0.792090i	$-0.291007\pi$
$967$	37.9630			1.22081			0.610404	+	0.792090i	$0.291007\pi$
$968$	57.4373	+	20.9457i	1.84611	+	0.673221i
$969$		0			0
$970$	4.15087	+	28.3786i	0.133276	+	0.911181i
$971$	−1.00112	+	1.00112i	−0.0321273	+	0.0321273i	−0.722988	−	0.690861i	$-0.757232\pi$
$971$	−1.00112	+	1.00112i	−0.0321273	+	0.0321273i	0.690861	+	0.722988i	$0.257232\pi$
$972$		0			0
$973$	6.19355	+	6.19355i	0.198556	+	0.198556i
$974$	11.3093	+	8.42308i	0.362373	+	0.269893i
$975$		0			0
$976$	37.2545	+	7.72448i	1.19249	+	0.247255i
$977$		−	24.6595i		−	0.788928i	−0.918911	−	0.394464i	$-0.870930\pi$
$977$		−	24.6595i		−	0.788928i	0.918911	−	0.394464i	$-0.129070\pi$
$978$		0			0
$979$	17.1097	−	17.1097i	0.546829	−	0.546829i
$980$	2.84858	−	5.27781i	0.0909945	−	0.168593i
$981$		0			0
$982$	−59.9090	+	8.76275i	−1.91177	+	0.279631i
$983$			20.2723i			0.646586i	0.946299	+	0.323293i	$0.104790\pi$
$983$			20.2723i			0.646586i	−0.946299	+	0.323293i	$0.895210\pi$
$984$		0			0
$985$		−	44.1258i		−	1.40596i
$986$	−3.60192	−	24.6255i	−0.114709	−	0.784236i
$987$		0			0
$988$	12.4911	+	41.7859i	0.397395	+	1.32939i
$989$	−23.2530	+	23.2530i	−0.739401	+	0.739401i
$990$		0			0
$991$		−	50.4804i		−	1.60356i	−0.597618	−	0.801781i	$-0.703886\pi$
$991$		−	50.4804i		−	1.60356i	0.597618	−	0.801781i	$-0.296114\pi$
$992$	0.238417	−	4.02201i	0.00756973	−	0.127699i
$993$		0			0
$994$	12.4556	−	16.7235i	0.395066	−	0.530438i
$995$	−42.5066	−	42.5066i	−1.34755	−	1.34755i
$996$		0			0
$997$	28.1175	−	28.1175i	0.890492	−	0.890492i	−0.104077	−	0.994569i	$-0.533189\pi$
$997$	28.1175	−	28.1175i	0.890492	−	0.890492i	0.994569	+	0.104077i	$0.0331890\pi$
$998$	20.6129	−	3.01500i	0.652489	−	0.0954382i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.v.e.323.17	yes	40
3.2	odd	2	inner	1008.2.v.e.323.4	✓	40
4.3	odd	2		4032.2.v.e.1583.4		40
12.11	even	2		4032.2.v.e.1583.17		40
16.5	even	4		4032.2.v.e.3599.17		40
16.11	odd	4	inner	1008.2.v.e.827.4	yes	40
48.5	odd	4		4032.2.v.e.3599.4		40
48.11	even	4	inner	1008.2.v.e.827.17	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.v.e.323.4	✓	40	3.2	odd	2	inner
1008.2.v.e.323.17	yes	40	1.1	even	1	trivial
1008.2.v.e.827.4	yes	40	16.11	odd	4	inner
1008.2.v.e.827.17	yes	40	48.11	even	4	inner
4032.2.v.e.1583.4		40	4.3	odd	2
4032.2.v.e.1583.17		40	12.11	even	2
4032.2.v.e.3599.4		40	48.5	odd	4
4032.2.v.e.3599.17		40	16.5	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13420 + 0.844744i) q^{2} +(0.572816 + 1.91622i) q^{4} +(-2.12043 - 2.12043i) q^{5} +1.00000 q^{7} +(-0.969023 + 2.65725i) q^{8} +O(q^{10})\)	\(q+(1.13420 + 0.844744i) q^{2} +(0.572816 + 1.91622i) q^{4} +(-2.12043 - 2.12043i) q^{5} +1.00000 q^{7} +(-0.969023 + 2.65725i) q^{8} +(-0.613769 - 4.19620i) q^{10} +(-4.03827 + 4.03827i) q^{11} +(-4.91665 - 4.91665i) q^{13} +(1.13420 + 0.844744i) q^{14} +(-3.34376 + 2.19528i) q^{16} +4.76253i q^{17} +(-2.21762 + 2.21762i) q^{19} +(2.84858 - 5.27781i) q^{20} +(-7.99151 + 1.16890i) q^{22} +6.91384i q^{23} +3.99241i q^{25} +(-1.42315 - 9.72977i) q^{26} +(0.572816 + 1.91622i) q^{28} +(-2.61285 + 2.61285i) q^{29} +0.712246i q^{31} +(-5.64694 - 0.334739i) q^{32} +(-4.02312 + 5.40166i) q^{34} +(-2.12043 - 2.12043i) q^{35} +(5.73777 - 5.73777i) q^{37} +(-4.38854 + 0.641902i) q^{38} +(7.68925 - 3.57977i) q^{40} +3.59400 q^{41} +(3.36325 + 3.36325i) q^{43} +(-10.0514 - 5.42501i) q^{44} +(-5.84042 + 7.84167i) q^{46} -6.04590 q^{47} +1.00000 q^{49} +(-3.37256 + 4.52819i) q^{50} +(6.60502 - 12.2377i) q^{52} +(-4.53235 - 4.53235i) q^{53} +17.1257 q^{55} +(-0.969023 + 2.65725i) q^{56} +(-5.17067 + 0.756303i) q^{58} +(4.82118 - 4.82118i) q^{59} +(-6.72581 - 6.72581i) q^{61} +(-0.601665 + 0.807828i) q^{62} +(-6.12199 - 5.14988i) q^{64} +20.8508i q^{65} +(-3.87274 + 3.87274i) q^{67} +(-9.12604 + 2.72806i) q^{68} +(-0.613769 - 4.19620i) q^{70} -14.7448i q^{71} +4.61241i q^{73} +(11.3547 - 1.66083i) q^{74} +(-5.51972 - 2.97914i) q^{76} +(-4.03827 + 4.03827i) q^{77} +7.43429i q^{79} +(11.7451 + 2.43528i) q^{80} +(4.07631 + 3.03601i) q^{82} +(-2.44737 - 2.44737i) q^{83} +(10.0986 - 10.0986i) q^{85} +(0.973511 + 6.65568i) q^{86} +(-6.81753 - 14.6439i) q^{88} -4.23689 q^{89} +(-4.91665 - 4.91665i) q^{91} +(-13.2484 + 3.96036i) q^{92} +(-6.85725 - 5.10723i) q^{94} +9.40458 q^{95} -6.76292 q^{97} +(1.13420 + 0.844744i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{7}+O(q^{10}) \) 40 * q + 40 * q^7	\( 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70} - 24 q^{76} - 64 q^{82} + 64 q^{85} - 120 q^{88} - 24 q^{91} - 128 q^{94} + 64 q^{97}+O(q^{100}) \) 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

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