LMFDB - Embedded newform 1008.2.v.e.827.4

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			827.4
Character	$\chi$	$=$	1008.827
Dual form			1008.2.v.e.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13420 + 0.844744i) q^{2} +(0.572816 - 1.91622i) q^{4} +(2.12043 - 2.12043i) q^{5} +1.00000 q^{7} +(0.969023 + 2.65725i) q^{8} +O(q^{10})$	\(q+(-1.13420 + 0.844744i) q^{2} +(0.572816 - 1.91622i) q^{4} +(2.12043 - 2.12043i) q^{5} +1.00000 q^{7} +(0.969023 + 2.65725i) q^{8} +(-0.613769 + 4.19620i) q^{10} +(4.03827 + 4.03827i) q^{11} +(-4.91665 + 4.91665i) q^{13} +(-1.13420 + 0.844744i) q^{14} +(-3.34376 - 2.19528i) q^{16} +4.76253i q^{17} +(-2.21762 - 2.21762i) q^{19} +(-2.84858 - 5.27781i) q^{20} +(-7.99151 - 1.16890i) q^{22} +6.91384i q^{23} -3.99241i q^{25} +(1.42315 - 9.72977i) q^{26} +(0.572816 - 1.91622i) q^{28} +(2.61285 + 2.61285i) q^{29} -0.712246i q^{31} +(5.64694 - 0.334739i) q^{32} +(-4.02312 - 5.40166i) q^{34} +(2.12043 - 2.12043i) q^{35} +(5.73777 + 5.73777i) q^{37} +(4.38854 + 0.641902i) q^{38} +(7.68925 + 3.57977i) q^{40} -3.59400 q^{41} +(3.36325 - 3.36325i) q^{43} +(10.0514 - 5.42501i) q^{44} +(-5.84042 - 7.84167i) q^{46} +6.04590 q^{47} +1.00000 q^{49} +(3.37256 + 4.52819i) q^{50} +(6.60502 + 12.2377i) q^{52} +(4.53235 - 4.53235i) q^{53} +17.1257 q^{55} +(0.969023 + 2.65725i) q^{56} +(-5.17067 - 0.756303i) q^{58} +(-4.82118 - 4.82118i) q^{59} +(-6.72581 + 6.72581i) q^{61} +(0.601665 + 0.807828i) q^{62} +(-6.12199 + 5.14988i) q^{64} +20.8508i q^{65} +(-3.87274 - 3.87274i) q^{67} +(9.12604 + 2.72806i) q^{68} +(-0.613769 + 4.19620i) q^{70} -14.7448i q^{71} -4.61241i q^{73} +(-11.3547 - 1.66083i) q^{74} +(-5.51972 + 2.97914i) q^{76} +(4.03827 + 4.03827i) q^{77} -7.43429i q^{79} +(-11.7451 + 2.43528i) q^{80} +(4.07631 - 3.03601i) q^{82} +(2.44737 - 2.44737i) q^{83} +(10.0986 + 10.0986i) q^{85} +(-0.973511 + 6.65568i) q^{86} +(-6.81753 + 14.6439i) q^{88} +4.23689 q^{89} +(-4.91665 + 4.91665i) q^{91} +(13.2484 + 3.96036i) q^{92} +(-6.85725 + 5.10723i) q^{94} -9.40458 q^{95} -6.76292 q^{97} +(-1.13420 + 0.844744i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

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

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	$-0.516064\pi$
$5$	2.12043	−	2.12043i	0.948283	−	0.948283i	0.998727	+	0.0504437i	$0.0160635\pi$
$6$		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	0.968475	+	0.249110i	$0.0801380\pi$
$11$	4.03827	+	4.03827i	1.21759	+	1.21759i	0.249110	+	0.968475i	$0.419862\pi$
$12$		0			0
$13$	−4.91665	+	4.91665i	−1.36363	+	1.36363i	−0.494396	+	0.869237i	$0.664611\pi$
$13$	−4.91665	+	4.91665i	−1.36363	+	1.36363i	−0.869237	+	0.494396i	$0.835389\pi$
$14$	−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	0.405388	−	0.914145i	$-0.367136\pi$
$19$	−2.21762	−	2.21762i	−0.508756	−	0.508756i	−0.914145	+	0.405388i	$0.867136\pi$
$20$	−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	$-0.138529\pi$
$29$	2.61285	+	2.61285i	0.485193	+	0.485193i	−0.421592	+	0.906786i	$0.638529\pi$
$30$		0			0
$31$		−	0.712246i		−	0.127923i	−0.997952	−	0.0639615i	$-0.979627\pi$
$31$		−	0.712246i		−	0.127923i	0.997952	−	0.0639615i	$-0.0203735\pi$
$32$	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	0.998476	−	0.0551925i	$-0.0175773\pi$
$37$	5.73777	+	5.73777i	0.943283	+	0.943283i	−0.0551925	+	0.998476i	$0.517577\pi$
$38$	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	$-0.590548\pi$
$41$	−3.59400			−0.561288			−0.280644	+	0.959812i	$0.590548\pi$
$42$		0			0
$43$	3.36325	−	3.36325i	0.512891	−	0.512891i	−0.402520	−	0.915411i	$-0.631866\pi$
$43$	3.36325	−	3.36325i	0.512891	−	0.512891i	0.915411	+	0.402520i	$0.131866\pi$
$44$	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	$-0.354644\pi$
$47$	6.04590			0.881885			0.440942	+	0.897535i	$0.354644\pi$
$48$		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	$-0.604900\pi$
$53$	4.53235	−	4.53235i	0.622566	−	0.622566i	0.946187	+	0.323621i	$0.104900\pi$
$54$		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	$-0.396379\pi$
$59$	−4.82118	−	4.82118i	−0.627664	−	0.627664i	−0.947480	+	0.319815i	$0.896379\pi$
$60$		0			0
$61$	−6.72581	+	6.72581i	−0.861151	+	0.861151i	−0.991472	−	0.130321i	$-0.958399\pi$
$61$	−6.72581	+	6.72581i	−0.861151	+	0.861151i	0.130321	+	0.991472i	$0.458399\pi$
$62$	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	0.429796	−	0.902926i	$-0.358586\pi$
$67$	−3.87274	−	3.87274i	−0.473130	−	0.473130i	−0.902926	+	0.429796i	$0.858586\pi$
$68$	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	$-0.913002\pi$
$73$		−	4.61241i		−	0.539842i	0.962882	−	0.269921i	$-0.0869976\pi$
$74$	−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	$-0.862657\pi$
$79$		−	7.43429i		−	0.836423i	0.908350	−	0.418211i	$-0.137343\pi$
$80$	−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	$-0.689167\pi$
$83$	2.44737	−	2.44737i	0.268633	−	0.268633i	0.828549	+	0.559916i	$0.189167\pi$
$84$		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	$-0.427907\pi$
$89$	4.23689			0.449109			0.224555	+	0.974461i	$0.427907\pi$
$90$		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	−0.323963	+	0.946070i	$0.605015\pi$
$101$	−12.7637	+	12.7637i	−1.27003	+	1.27003i	−0.946070	+	0.323963i	$0.894985\pi$
$102$		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	$-0.325854\pi$
$107$	−3.45316	−	3.45316i	−0.333829	−	0.333829i	−0.854039	+	0.520209i	$0.825854\pi$
$108$		0			0
$109$	12.6452	−	12.6452i	1.21119	−	1.21119i	0.240558	−	0.970635i	$-0.422670\pi$
$109$	12.6452	−	12.6452i	1.21119	−	1.21119i	0.970635	−	0.240558i	$-0.0773304\pi$
$110$	−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	$0.0434974\pi$
$127$			3.07038i			0.272452i	−0.990678	+	0.136226i	$0.956503\pi$
$128$	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	$-0.891353\pi$
$131$	−6.95401	+	6.95401i	−0.607575	+	0.607575i	0.334737	+	0.942312i	$0.391353\pi$
$132$		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	$-0.335682\pi$
$137$	11.5548			0.987193			0.493596	+	0.869691i	$0.335682\pi$
$138$		0			0
$139$	6.19355	−	6.19355i	0.525330	−	0.525330i	−0.393846	−	0.919176i	$-0.628856\pi$
$139$	6.19355	−	6.19355i	0.525330	−	0.525330i	0.919176	+	0.393846i	$0.128856\pi$
$140$	−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	$-0.705795\pi$
$149$	2.38965	−	2.38965i	0.195767	−	0.195767i	0.798183	+	0.602415i	$0.205795\pi$
$150$		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	−0.872539	−	0.488544i	$-0.837528\pi$
$157$	−4.81144	+	4.81144i	−0.383995	+	0.383995i	0.488544	+	0.872539i	$0.337528\pi$
$158$	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	0.430470	−	0.902605i	$-0.358348\pi$
$163$	−6.02781	−	6.02781i	−0.472134	−	0.472134i	−0.902605	+	0.430470i	$0.858348\pi$
$164$	−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	0.999222	+	0.0394449i	$0.0125590\pi$
$173$	13.6615	+	13.6615i	1.03867	+	1.03867i	0.0394449	+	0.999222i	$0.487441\pi$
$174$		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	$-0.921541\pi$
$179$	−9.71026	+	9.71026i	−0.725779	+	0.725779i	0.243997	+	0.969776i	$0.421541\pi$
$180$		0			0
$181$	−3.99969	−	3.99969i	−0.297295	−	0.297295i	0.542659	−	0.839953i	$-0.317418\pi$
$181$	−3.99969	−	3.99969i	−0.297295	−	0.297295i	−0.839953	+	0.542659i	$0.817418\pi$
$182$	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	$-0.303778\pi$
$191$	15.9802			1.15629			0.578143	+	0.815936i	$0.303778\pi$
$192$		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	$-0.925633\pi$
$197$	−10.4049	+	10.4049i	−0.741320	+	0.741320i	0.231512	+	0.972832i	$0.425633\pi$
$198$		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	0.0192564	−	0.999815i	$-0.493870\pi$
$211$	−14.2434	−	14.2434i	−0.980558	−	0.980558i	−0.999815	+	0.0192564i	$0.993870\pi$
$212$	−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	$-0.806199\pi$
$223$		−	17.0811i		−	1.14384i	0.820311	−	0.571918i	$-0.193801\pi$
$224$	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	0.0561098	−	0.998425i	$-0.482130\pi$
$227$	15.8882	−	15.8882i	1.05453	−	1.05453i	0.998425	−	0.0561098i	$-0.0178697\pi$
$228$		0			0
$229$	−17.2648	−	17.2648i	−1.14089	−	1.14089i	−0.988287	−	0.152605i	$-0.951234\pi$
$229$	−17.2648	−	17.2648i	−1.14089	−	1.14089i	−0.152605	−	0.988287i	$-0.548766\pi$
$230$	−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	$-0.411524\pi$
$233$	8.37677			0.548780			0.274390	+	0.961618i	$0.411524\pi$
$234$		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	$-0.435287\pi$
$239$	6.24270			0.403807			0.201903	+	0.979405i	$0.435287\pi$
$240$		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	$-0.405299\pi$
$251$	−10.5027	−	10.5027i	−0.662927	−	0.662927i	−0.956069	+	0.293142i	$0.905299\pi$
$252$		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	$-0.105426\pi$
$269$	10.1764	+	10.1764i	0.620468	+	0.620468i	−0.325183	+	0.945651i	$0.605426\pi$
$270$		0			0
$271$			29.8185i			1.81135i	0.423977	+	0.905673i	$0.360634\pi$
$271$			29.8185i			1.81135i	−0.423977	+	0.905673i	$0.639366\pi$
$272$	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	0.946299	−	0.323292i	$-0.104790\pi$
$277$	10.3689	+	10.3689i	0.623007	+	0.623007i	−0.323292	+	0.946299i	$0.604790\pi$
$278$	−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	$-0.402361\pi$
$281$	10.1234			0.603909			0.301954	+	0.953322i	$0.402361\pi$
$282$		0			0
$283$	13.7990	−	13.7990i	0.820266	−	0.820266i	−0.165880	−	0.986146i	$-0.553046\pi$
$283$	13.7990	−	13.7990i	0.820266	−	0.820266i	0.986146	+	0.165880i	$0.0530463\pi$
$284$	−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	$-0.814307\pi$
$293$	−4.85735	+	4.85735i	−0.283770	+	0.283770i	0.550841	+	0.834610i	$0.314307\pi$
$294$		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	−0.966944	−	0.254989i	$-0.917928\pi$
$307$	−21.4100	−	21.4100i	−1.22193	−	1.22193i	−0.254989	−	0.966944i	$-0.582072\pi$
$308$	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	$0.0590851\pi$
$313$			6.53030i			0.369114i	−0.982822	+	0.184557i	$0.940915\pi$
$314$	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	$-0.418713\pi$
$317$	−12.7296	−	12.7296i	−0.714965	−	0.714965i	−0.967570	+	0.252605i	$0.918713\pi$
$318$		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	−0.452853	−	0.891585i	$-0.649594\pi$
$331$	7.98204	−	7.98204i	0.438732	−	0.438732i	0.891585	+	0.452853i	$0.149594\pi$
$332$	−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	$-0.419758\pi$
$347$	−13.3928	−	13.3928i	−0.718966	−	0.718966i	−0.968393	+	0.249428i	$0.919758\pi$
$348$		0			0
$349$	−2.01384	+	2.01384i	−0.107798	+	0.107798i	−0.758949	−	0.651150i	$-0.774287\pi$
$349$	−2.01384	+	2.01384i	−0.107798	+	0.107798i	0.651150	+	0.758949i	$0.274287\pi$
$350$	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	$0.0143236\pi$
$367$			1.72353i			0.0899673i	−0.998988	+	0.0449837i	$0.985676\pi$
$368$	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	0.828195	−	0.560440i	$-0.189368\pi$
$373$	5.17122	+	5.17122i	0.267756	+	0.267756i	−0.560440	+	0.828195i	$0.689368\pi$
$374$	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	−0.818112	−	0.575059i	$-0.804979\pi$
$379$	−4.73174	+	4.73174i	−0.243053	+	0.243053i	0.575059	+	0.818112i	$0.304979\pi$
$380$	−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	$-0.401446\pi$
$383$	11.9260			0.609388			0.304694	+	0.952450i	$0.401446\pi$
$384$		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	−0.100189	+	0.994968i	$0.531945\pi$
$389$	−21.5999	+	21.5999i	−1.09516	+	1.09516i	−0.994968	+	0.100189i	$0.968055\pi$
$390$		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	−0.243084	+	0.970005i	$0.578159\pi$
$397$	−24.1706	+	24.1706i	−1.21309	+	1.21309i	−0.970005	+	0.243084i	$0.921841\pi$
$398$	−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	$-0.874602\pi$
$409$		−	15.5253i		−	0.767676i	0.923400	−	0.383838i	$-0.125398\pi$
$410$	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	0.197438	−	0.980315i	$-0.436738\pi$
$419$	24.1080	−	24.1080i	1.17775	−	1.17775i	0.980315	−	0.197438i	$-0.0632622\pi$
$420$		0			0
$421$	−21.4110	−	21.4110i	−1.04351	−	1.04351i	−0.999010	−	0.0444969i	$-0.985832\pi$
$421$	−21.4110	−	21.4110i	−1.04351	−	1.04351i	−0.0444969	−	0.999010i	$-0.514168\pi$
$422$	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	$-0.350446\pi$
$431$	18.7984			0.905485			0.452742	+	0.891641i	$0.350446\pi$
$432$		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	$-0.249884\pi$
$443$	0.0108636	+	0.0108636i	0.000516147	+	0.000516147i	−0.706849	+	0.707365i	$0.749884\pi$
$444$		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	$0.0755502\pi$
$457$			10.0528i			0.470252i	−0.971965	+	0.235126i	$0.924450\pi$
$458$	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	$-0.416096\pi$
$461$	−15.1351	−	15.1351i	−0.704910	−	0.704910i	−0.965460	+	0.260550i	$0.916096\pi$
$462$		0			0
$463$		−	10.6714i		−	0.495940i	−0.968768	−	0.247970i	$-0.920236\pi$
$463$		−	10.6714i		−	0.495940i	0.968768	−	0.247970i	$-0.0797635\pi$
$464$	−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	$-0.788354\pi$
$467$	−3.67348	+	3.67348i	−0.169989	+	0.169989i	0.616986	+	0.786974i	$0.288354\pi$
$468$		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	$-0.467865\pi$
$479$	4.41155			0.201569			0.100784	+	0.994908i	$0.467865\pi$
$480$		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	0.865771	+	0.500440i	$0.166828\pi$
$491$	30.2732	+	30.2732i	1.36621	+	1.36621i	0.500440	+	0.865771i	$0.333172\pi$
$492$		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	0.900710	−	0.434421i	$-0.143047\pi$
$499$	10.4161	+	10.4161i	0.466289	+	0.466289i	−0.434421	+	0.900710i	$0.643047\pi$
$500$	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	$-0.429550\pi$
$509$	−17.0580	−	17.0580i	−0.756083	−	0.756083i	−0.975607	+	0.219524i	$0.929550\pi$
$510$		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	$-0.586132\pi$
$521$	−12.2025			−0.534601			−0.267300	+	0.963613i	$0.586132\pi$
$522$		0			0
$523$	−8.77429	+	8.77429i	−0.383673	+	0.383673i	−0.872423	−	0.488751i	$-0.837453\pi$
$523$	−8.77429	+	8.77429i	−0.383673	+	0.383673i	0.488751	+	0.872423i	$0.337453\pi$
$524$	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	−0.000132738		1.00000i	$0.500042\pi$
$541$	−23.2625	+	23.2625i	−1.00013	+	1.00013i	−1.00000		0.000132738i	$0.999958\pi$
$542$	−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	0.998271	+	0.0587833i	$0.0187221\pi$
$547$	24.7224	+	24.7224i	1.05705	+	1.05705i	0.0587833	+	0.998271i	$0.481278\pi$
$548$	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	$-0.408565\pi$
$557$	−15.9473	−	15.9473i	−0.675708	−	0.675708i	−0.959026	+	0.283318i	$0.908565\pi$
$558$		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	$-0.834020\pi$
$563$	−8.75478	+	8.75478i	−0.368970	+	0.368970i	0.498132	+	0.867101i	$0.334020\pi$
$564$		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	$-0.329259\pi$
$569$	24.3805			1.02209			0.511043	+	0.859555i	$0.329259\pi$
$570$		0			0
$571$	−9.52629	+	9.52629i	−0.398663	+	0.398663i	−0.877761	−	0.479098i	$-0.840964\pi$
$571$	−9.52629	+	9.52629i	−0.398663	+	0.398663i	0.479098	+	0.877761i	$0.340964\pi$
$572$	−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	$-0.183191\pi$
$587$	7.13883	+	7.13883i	0.294651	+	0.294651i	−0.544263	+	0.838914i	$0.683191\pi$
$588$		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	$-0.956421\pi$
$601$		−	6.69170i		−	0.272960i	0.990643	−	0.136480i	$-0.0435790\pi$
$602$	−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	$-0.814810\pi$
$607$		−	27.0776i		−	1.09904i	0.835479	−	0.549522i	$-0.185190\pi$
$608$	−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	0.997388	−	0.0722294i	$-0.0230114\pi$
$613$	22.9059	+	22.9059i	0.925159	+	0.925159i	−0.0722294	+	0.997388i	$0.523011\pi$
$614$	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	$-0.567097\pi$
$617$	−10.3945			−0.418466			−0.209233	+	0.977866i	$0.567097\pi$
$618$		0			0
$619$	−8.53232	+	8.53232i	−0.342943	+	0.342943i	−0.857473	−	0.514530i	$-0.827967\pi$
$619$	−8.53232	+	8.53232i	−0.342943	+	0.342943i	0.514530	+	0.857473i	$0.327967\pi$
$620$	−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	0.690242	−	0.723578i	$-0.257504\pi$
$643$	−0.845317	−	0.845317i	−0.0333361	−	0.0333361i	−0.723578	+	0.690242i	$0.757504\pi$
$644$	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	$-0.0648578\pi$
$653$	19.8544	+	19.8544i	0.776964	+	0.776964i	−0.202350	+	0.979313i	$0.564858\pi$
$654$		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	$-0.830095\pi$
$659$	−9.03903	+	9.03903i	−0.352111	+	0.352111i	0.508784	+	0.860894i	$0.330095\pi$
$660$		0			0
$661$	−31.4210	−	31.4210i	−1.22213	−	1.22213i	−0.966872	−	0.255261i	$-0.917839\pi$
$661$	−31.4210	−	31.4210i	−1.22213	−	1.22213i	−0.255261	−	0.966872i	$-0.582161\pi$
$662$	−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	$-0.557916\pi$
$677$	20.8816	−	20.8816i	0.802545	−	0.802545i	0.983493	+	0.180948i	$0.0579165\pi$
$678$		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	$-0.0787854\pi$
$683$	18.9351	+	18.9351i	0.724533	+	0.724533i	−0.244992	+	0.969525i	$0.578785\pi$
$684$		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	0.663059	−	0.748567i	$-0.269258\pi$
$691$	−2.24775	−	2.24775i	−0.0855083	−	0.0855083i	−0.748567	+	0.663059i	$0.769258\pi$
$692$	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	$-0.320045\pi$
$701$	−8.17318	−	8.17318i	−0.308697	−	0.308697i	−0.844404	+	0.535707i	$0.820045\pi$
$702$		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	0.458383	−	0.888755i	$-0.348429\pi$
$709$	−11.4595	−	11.4595i	−0.430372	−	0.430372i	−0.888755	+	0.458383i	$0.848429\pi$
$710$	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	$-0.354852\pi$
$719$	23.6156			0.880714			0.440357	+	0.897823i	$0.354852\pi$
$720$		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	−0.541311	−	0.840823i	$-0.682072\pi$
$733$	8.10898	−	8.10898i	0.299512	−	0.299512i	0.840823	+	0.541311i	$0.182072\pi$
$734$	−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	−0.916336	−	0.400410i	$-0.868868\pi$
$739$	−35.7952	−	35.7952i	−1.31675	−	1.31675i	−0.400410	−	0.916336i	$-0.631132\pi$
$740$	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	$-0.740618\pi$
$751$		−	39.8810i		−	1.45528i	0.685961	−	0.727639i	$-0.259382\pi$
$752$	−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	0.464255	−	0.885701i	$-0.346322\pi$
$757$	−11.5955	−	11.5955i	−0.421446	−	0.421446i	−0.885701	+	0.464255i	$0.846322\pi$
$758$	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	$-0.604596\pi$
$761$	−17.8050			−0.645430			−0.322715	+	0.946496i	$0.604596\pi$
$762$		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	$-0.922974\pi$
$773$	−20.3304	+	20.3304i	−0.731235	+	0.731235i	0.239629	+	0.970864i	$0.422974\pi$
$774$		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	0.462856	−	0.886433i	$-0.346825\pi$
$787$	−11.8828	−	11.8828i	−0.423577	−	0.423577i	−0.886433	+	0.462856i	$0.846825\pi$
$788$	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	$-0.213434\pi$
$797$	4.57631	+	4.57631i	0.162101	+	0.162101i	−0.621396	+	0.783497i	$0.713434\pi$
$798$		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	$-0.645753\pi$
$809$	−25.1471			−0.884123			−0.442062	+	0.896985i	$0.645753\pi$
$810$		0			0
$811$	24.5249	−	24.5249i	0.861187	−	0.861187i	−0.130289	−	0.991476i	$-0.541591\pi$
$811$	24.5249	−	24.5249i	0.861187	−	0.861187i	0.991476	+	0.130289i	$0.0415906\pi$
$812$	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	$-0.544202\pi$
$821$	24.4111	−	24.4111i	0.851955	−	0.851955i	0.990374	+	0.138419i	$0.0442021\pi$
$822$		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	$-0.461079\pi$
$827$	−25.0353	−	25.0353i	−0.870564	−	0.870564i	−0.992534	+	0.121970i	$0.961079\pi$
$828$		0			0
$829$	−21.0067	+	21.0067i	−0.729592	+	0.729592i	−0.970538	−	0.240947i	$-0.922542\pi$
$829$	−21.0067	+	21.0067i	−0.729592	+	0.729592i	0.240947	+	0.970538i	$0.422542\pi$
$830$	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	0.998444	−	0.0557594i	$-0.0177580\pi$
$853$	27.5322	+	27.5322i	0.942685	+	0.942685i	−0.0557594	+	0.998444i	$0.517758\pi$
$854$	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	$-0.418103\pi$
$857$	14.8983			0.508915			0.254457	+	0.967084i	$0.418103\pi$
$858$		0			0
$859$	13.6121	−	13.6121i	0.464439	−	0.464439i	−0.435668	−	0.900107i	$-0.643488\pi$
$859$	13.6121	−	13.6121i	0.464439	−	0.464439i	0.900107	+	0.435668i	$0.143488\pi$
$860$	−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	$-0.767949\pi$
$863$	−43.8205			−1.49167			−0.745834	+	0.666132i	$0.767949\pi$
$864$		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	−0.398109	−	0.917338i	$-0.630333\pi$
$877$	15.3765	−	15.3765i	0.519229	−	0.519229i	0.917338	+	0.398109i	$0.130333\pi$
$878$	−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	0.363816	−	0.931471i	$-0.381474\pi$
$883$	−16.8680	−	16.8680i	−0.567654	−	0.567654i	−0.931471	+	0.363816i	$0.881474\pi$
$884$	−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	−0.799705	−	0.600393i	$-0.795011\pi$
$907$	−6.00255	+	6.00255i	−0.199311	+	0.199311i	0.600393	+	0.799705i	$0.295011\pi$
$908$	−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	$-0.578027\pi$
$911$	−14.6496			−0.485363			−0.242682	+	0.970106i	$0.578027\pi$
$912$		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	$-0.736551\pi$
$937$		−	45.0796i		−	1.47269i	0.676609	−	0.736343i	$-0.263449\pi$
$938$	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	$-0.272763\pi$
$941$	−3.09966	−	3.09966i	−0.101046	−	0.101046i	−0.755822	+	0.654777i	$0.772763\pi$
$942$		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	$-0.874712\pi$
$947$	−16.6180	+	16.6180i	−0.540012	+	0.540012i	0.383520	+	0.923532i	$0.374712\pi$
$948$		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	$-0.887268\pi$
$953$	−57.9097			−1.87588			−0.937939	+	0.346801i	$0.887268\pi$
$954$		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	$-0.242768\pi$
$971$	1.00112	+	1.00112i	0.0321273	+	0.0321273i	−0.690861	+	0.722988i	$0.742768\pi$
$972$		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	$0.296114\pi$
$991$			50.4804i			1.60356i	−0.597618	+	0.801781i	$0.703886\pi$
$992$	−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	0.994569	−	0.104077i	$-0.0331890\pi$
$997$	28.1175	+	28.1175i	0.890492	+	0.890492i	−0.104077	+	0.994569i	$0.533189\pi$
$998$	−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.827.4	yes	40
3.2	odd	2	inner	1008.2.v.e.827.17	yes	40
4.3	odd	2		4032.2.v.e.3599.17		40
12.11	even	2		4032.2.v.e.3599.4		40
16.3	odd	4	inner	1008.2.v.e.323.17	yes	40
16.13	even	4		4032.2.v.e.1583.4		40
48.29	odd	4		4032.2.v.e.1583.17		40
48.35	even	4	inner	1008.2.v.e.323.4	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.v.e.323.4	✓	40	48.35	even	4	inner
1008.2.v.e.323.17	yes	40	16.3	odd	4	inner
1008.2.v.e.827.4	yes	40	1.1	even	1	trivial
1008.2.v.e.827.17	yes	40	3.2	odd	2	inner
4032.2.v.e.1583.4		40	16.13	even	4
4032.2.v.e.1583.17		40	48.29	odd	4
4032.2.v.e.3599.4		40	12.11	even	2
4032.2.v.e.3599.17		40	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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