LMFDB - Embedded newform 896.2.u.c.113.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(113,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("896.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.u (of order $8$, degree $4$, not 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			113.5
Character	$\chi$	$=$	896.113
Dual form			896.2.u.c.785.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.424336 - 1.02444i) q^{3} +(3.70330 + 1.53396i) q^{5} +(0.707107 + 0.707107i) q^{7} +(1.25191 - 1.25191i) q^{9} +O(q^{10})$	\(q+(-0.424336 - 1.02444i) q^{3} +(3.70330 + 1.53396i) q^{5} +(0.707107 + 0.707107i) q^{7} +(1.25191 - 1.25191i) q^{9} +(1.32694 - 3.20352i) q^{11} +(-1.88338 + 0.780120i) q^{13} -4.44471i q^{15} -3.99616i q^{17} +(2.05694 - 0.852011i) q^{19} +(0.424336 - 1.02444i) q^{21} +(-5.08811 + 5.08811i) q^{23} +(7.82588 + 7.82588i) q^{25} +(-4.88704 - 2.02428i) q^{27} +(2.71380 + 6.55170i) q^{29} +8.51005 q^{31} -3.84487 q^{33} +(1.53396 + 3.70330i) q^{35} +(-6.76303 - 2.80134i) q^{37} +(1.59837 + 1.59837i) q^{39} +(-1.33578 + 1.33578i) q^{41} +(1.30662 - 3.15446i) q^{43} +(6.55658 - 2.71582i) q^{45} +3.16999i q^{47} +1.00000i q^{49} +(-4.09381 + 1.69571i) q^{51} +(4.79044 - 11.5651i) q^{53} +(9.82812 - 9.82812i) q^{55} +(-1.74566 - 1.74566i) q^{57} +(-2.39858 - 0.993524i) q^{59} +(-3.85768 - 9.31326i) q^{61} +1.77047 q^{63} -8.17138 q^{65} +(0.315504 + 0.761694i) q^{67} +(7.37152 + 3.05338i) q^{69} +(6.21830 + 6.21830i) q^{71} +(-2.09089 + 2.09089i) q^{73} +(4.69632 - 11.3379i) q^{75} +(3.20352 - 1.32694i) q^{77} +9.23644i q^{79} +0.554037i q^{81} +(-4.95210 + 2.05123i) q^{83} +(6.12994 - 14.7990i) q^{85} +(5.56024 - 5.56024i) q^{87} +(9.12026 + 9.12026i) q^{89} +(-1.88338 - 0.780120i) q^{91} +(-3.61112 - 8.71801i) q^{93} +8.92440 q^{95} -9.76692 q^{97} +(-2.34931 - 5.67173i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q+O(q^{10}) $ 52 * q	$ 52 q + 20 q^{23} + 24 q^{27} - 48 q^{33} + 24 q^{39} + 44 q^{43} + 40 q^{45} - 16 q^{51} - 36 q^{53} - 32 q^{55} - 32 q^{61} - 68 q^{63} + 80 q^{65} - 28 q^{67} - 32 q^{69} - 32 q^{75} - 12 q^{77} + 64 q^{85} + 56 q^{87} + 64 q^{95} - 72 q^{97} + 64 q^{99}+O(q^{100}) $ 52 * q + 20 * q^23 + 24 * q^27 - 48 * q^33 + 24 * q^39 + 44 * q^43 + 40 * q^45 - 16 * q^51 - 36 * q^53 - 32 * q^55 - 32 * q^61 - 68 * q^63 + 80 * q^65 - 28 * q^67 - 32 * q^69 - 32 * q^75 - 12 * q^77 + 64 * q^85 + 56 * q^87 + 64 * q^95 - 72 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{8}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.424336	−	1.02444i	−0.244990	−	0.591459i	0.752775	−	0.658278i	$-0.228715\pi$
$3$	−0.424336	−	1.02444i	−0.244990	−	0.591459i	−0.997765	+	0.0668192i	$0.978715\pi$
$4$		0			0
$5$	3.70330	+	1.53396i	1.65617	+	0.686007i	0.997775	−	0.0666689i	$-0.0212371\pi$
$5$	3.70330	+	1.53396i	1.65617	+	0.686007i	0.658392	+	0.752676i	$0.271237\pi$
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		0			0
$9$	1.25191	−	1.25191i	0.417303	−	0.417303i
$10$		0			0
$11$	1.32694	−	3.20352i	0.400088	−	0.965897i	−0.587557	−	0.809183i	$-0.699910\pi$
$11$	1.32694	−	3.20352i	0.400088	−	0.965897i	0.987644	−	0.156714i	$-0.0500900\pi$
$12$		0			0
$13$	−1.88338	+	0.780120i	−0.522354	+	0.216366i	−0.628251	−	0.778011i	$-0.716229\pi$
$13$	−1.88338	+	0.780120i	−0.522354	+	0.216366i	0.105896	+	0.994377i	$0.466229\pi$
$14$		0			0
$15$		−	4.44471i		−	1.14762i
$16$		0			0
$17$		−	3.99616i		−	0.969210i	−0.874733	−	0.484605i	$-0.838963\pi$
$17$		−	3.99616i		−	0.969210i	0.874733	−	0.484605i	$-0.161037\pi$
$18$		0			0
$19$	2.05694	−	0.852011i	0.471893	−	0.195465i	−0.134047	−	0.990975i	$-0.542797\pi$
$19$	2.05694	−	0.852011i	0.471893	−	0.195465i	0.605940	+	0.795510i	$0.292797\pi$
$20$		0			0
$21$	0.424336	−	1.02444i	0.0925976	−	0.223550i
$22$		0			0
$23$	−5.08811	+	5.08811i	−1.06094	+	1.06094i	−0.0629268	+	0.998018i	$0.520043\pi$
$23$	−5.08811	+	5.08811i	−1.06094	+	1.06094i	−0.998018	+	0.0629268i	$0.979957\pi$
$24$		0			0
$25$	7.82588	+	7.82588i	1.56518	+	1.56518i
$26$		0			0
$27$	−4.88704	−	2.02428i	−0.940512	−	0.389573i
$28$		0			0
$29$	2.71380	+	6.55170i	0.503941	+	1.21662i	0.947321	+	0.320287i	$0.103779\pi$
$29$	2.71380	+	6.55170i	0.503941	+	1.21662i	−0.443380	+	0.896334i	$0.646221\pi$
$30$		0			0
$31$	8.51005			1.52845			0.764225	−	0.644950i	$-0.223122\pi$
$31$	8.51005			1.52845			0.764225	+	0.644950i	$0.223122\pi$
$32$		0			0
$33$	−3.84487			−0.669306
$34$		0			0
$35$	1.53396	+	3.70330i	0.259286	+	0.625972i
$36$		0			0
$37$	−6.76303	−	2.80134i	−1.11184	−	0.460537i	−0.250266	−	0.968177i	$-0.580518\pi$
$37$	−6.76303	−	2.80134i	−1.11184	−	0.460537i	−0.861570	+	0.507640i	$0.830518\pi$
$38$		0			0
$39$	1.59837	+	1.59837i	0.255944	+	0.255944i
$40$		0			0
$41$	−1.33578	+	1.33578i	−0.208614	+	0.208614i	−0.803678	−	0.595064i	$-0.797127\pi$
$41$	−1.33578	+	1.33578i	−0.208614	+	0.208614i	0.595064	+	0.803678i	$0.297127\pi$
$42$		0			0
$43$	1.30662	−	3.15446i	0.199258	−	0.481051i	−0.792392	−	0.610012i	$-0.791164\pi$
$43$	1.30662	−	3.15446i	0.199258	−	0.481051i	0.991650	+	0.128962i	$0.0411644\pi$
$44$		0			0
$45$	6.55658	−	2.71582i	0.977397	−	0.404851i
$46$		0			0
$47$			3.16999i			0.462390i	0.972907	+	0.231195i	$0.0742636\pi$
$47$			3.16999i			0.462390i	−0.972907	+	0.231195i	$0.925736\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−4.09381	+	1.69571i	−0.573248	+	0.237447i
$52$		0			0
$53$	4.79044	−	11.5651i	0.658017	−	1.58859i	−0.142845	−	0.989745i	$-0.545625\pi$
$53$	4.79044	−	11.5651i	0.658017	−	1.58859i	0.800862	−	0.598849i	$-0.204375\pi$
$54$		0			0
$55$	9.82812	−	9.82812i	1.32522	−	1.32522i
$56$		0			0
$57$	−1.74566	−	1.74566i	−0.231219	−	0.231219i
$58$		0			0
$59$	−2.39858	−	0.993524i	−0.312268	−	0.129346i	0.221045	−	0.975264i	$-0.429053\pi$
$59$	−2.39858	−	0.993524i	−0.312268	−	0.129346i	−0.533313	+	0.845918i	$0.679053\pi$
$60$		0			0
$61$	−3.85768	−	9.31326i	−0.493925	−	1.19244i	−0.952707	−	0.303891i	$-0.901714\pi$
$61$	−3.85768	−	9.31326i	−0.493925	−	1.19244i	0.458782	−	0.888549i	$-0.348286\pi$
$62$		0			0
$63$	1.77047			0.223058
$64$		0			0
$65$	−8.17138			−1.01353
$66$		0			0
$67$	0.315504	+	0.761694i	0.0385449	+	0.0930557i	0.941980	−	0.335670i	$-0.108963\pi$
$67$	0.315504	+	0.761694i	0.0385449	+	0.0930557i	−0.903435	+	0.428726i	$0.858963\pi$
$68$		0			0
$69$	7.37152	+	3.05338i	0.887427	+	0.367584i
$70$		0			0
$71$	6.21830	+	6.21830i	0.737977	+	0.737977i	0.972186	−	0.234210i	$-0.0752502\pi$
$71$	6.21830	+	6.21830i	0.737977	+	0.737977i	−0.234210	+	0.972186i	$0.575250\pi$
$72$		0			0
$73$	−2.09089	+	2.09089i	−0.244720	+	0.244720i	−0.818800	−	0.574079i	$-0.805360\pi$
$73$	−2.09089	+	2.09089i	−0.244720	+	0.244720i	0.574079	+	0.818800i	$0.305360\pi$
$74$		0			0
$75$	4.69632	−	11.3379i	0.542284	−	1.30919i
$76$		0			0
$77$	3.20352	−	1.32694i	0.365075	−	0.151219i
$78$		0			0
$79$			9.23644i			1.03918i	0.854416	+	0.519590i	$0.173915\pi$
$79$			9.23644i			1.03918i	−0.854416	+	0.519590i	$0.826085\pi$
$80$		0			0
$81$			0.554037i			0.0615596i
$82$		0			0
$83$	−4.95210	+	2.05123i	−0.543563	+	0.225151i	−0.637532	−	0.770424i	$-0.720045\pi$
$83$	−4.95210	+	2.05123i	−0.543563	+	0.225151i	0.0939688	+	0.995575i	$0.470045\pi$
$84$		0			0
$85$	6.12994	−	14.7990i	0.664885	−	1.60517i
$86$		0			0
$87$	5.56024	−	5.56024i	0.596121	−	0.596121i
$88$		0			0
$89$	9.12026	+	9.12026i	0.966745	+	0.966745i	0.999465	−	0.0327193i	$-0.0104167\pi$
$89$	9.12026	+	9.12026i	0.966745	+	0.966745i	−0.0327193	+	0.999465i	$0.510417\pi$
$90$		0			0
$91$	−1.88338	−	0.780120i	−0.197431	−	0.0817788i
$92$		0			0
$93$	−3.61112	−	8.71801i	−0.374455	−	0.904015i
$94$		0			0
$95$	8.92440			0.915624
$96$		0			0
$97$	−9.76692			−0.991681			−0.495840	−	0.868414i	$-0.665140\pi$
$97$	−9.76692			−0.991681			−0.495840	+	0.868414i	$0.665140\pi$
$98$		0			0
$99$	−2.34931	−	5.67173i	−0.236114	−	0.570030i
$100$		0			0
$101$	−10.9249	−	4.52526i	−1.08707	−	0.450280i	−0.234088	−	0.972216i	$-0.575210\pi$
$101$	−10.9249	−	4.52526i	−1.08707	−	0.450280i	−0.852985	+	0.521935i	$0.825210\pi$
$102$		0			0
$103$	−0.574490	−	0.574490i	−0.0566061	−	0.0566061i	0.678237	−	0.734843i	$-0.262744\pi$
$103$	−0.574490	−	0.574490i	−0.0566061	−	0.0566061i	−0.734843	+	0.678237i	$0.762744\pi$
$104$		0			0
$105$	3.14289	−	3.14289i	0.306714	−	0.306714i
$106$		0			0
$107$	0.927686	−	2.23963i	0.0896828	−	0.216513i	−0.872674	−	0.488304i	$-0.837616\pi$
$107$	0.927686	−	2.23963i	0.0896828	−	0.216513i	0.962356	+	0.271790i	$0.0876158\pi$
$108$		0			0
$109$	4.13881	−	1.71435i	0.396426	−	0.164205i	−0.175560	−	0.984469i	$-0.556173\pi$
$109$	4.13881	−	1.71435i	0.396426	−	0.164205i	0.571985	+	0.820264i	$0.306173\pi$
$110$		0			0
$111$			8.11701i			0.770432i
$112$		0			0
$113$			0.128309i			0.0120703i	0.999982	+	0.00603513i	$0.00192105\pi$
$113$			0.128309i			0.0120703i	−0.999982	+	0.00603513i	$0.998079\pi$
$114$		0			0
$115$	−26.6478	+	11.0379i	−2.48492	+	1.02929i
$116$		0			0
$117$	−1.38118	+	3.33446i	−0.127690	+	0.308271i
$118$		0			0
$119$	2.82571	−	2.82571i	0.259032	−	0.259032i
$120$		0			0
$121$	−0.723576	−	0.723576i	−0.0657796	−	0.0657796i
$122$		0			0
$123$	1.93524	+	0.801605i	0.174495	+	0.0722782i
$124$		0			0
$125$	9.30724	+	22.4697i	0.832465	+	2.00975i
$126$		0			0
$127$	6.89025			0.611411			0.305705	−	0.952126i	$-0.401108\pi$
$127$	6.89025			0.611411			0.305705	+	0.952126i	$0.401108\pi$
$128$		0			0
$129$	−3.78599			−0.333338
$130$		0			0
$131$	−0.879601	−	2.12354i	−0.0768511	−	0.185535i	0.880785	−	0.473517i	$-0.157016\pi$
$131$	−0.879601	−	2.12354i	−0.0768511	−	0.185535i	−0.957636	+	0.287982i	$0.907016\pi$
$132$		0			0
$133$	2.05694	+	0.852011i	0.178359	+	0.0738787i
$134$		0			0
$135$	−14.9930	−	14.9930i	−1.29040	−	1.29040i
$136$		0			0
$137$	1.06584	−	1.06584i	0.0910611	−	0.0910611i	−0.660109	−	0.751170i	$-0.729490\pi$
$137$	1.06584	−	1.06584i	0.0910611	−	0.0910611i	0.751170	+	0.660109i	$0.229490\pi$
$138$		0			0
$139$	−1.68081	+	4.05783i	−0.142564	+	0.344181i	−0.978993	−	0.203895i	$-0.934640\pi$
$139$	−1.68081	+	4.05783i	−0.142564	+	0.344181i	0.836428	+	0.548076i	$0.184640\pi$
$140$		0			0
$141$	3.24745	−	1.34514i	0.273485	−	0.113281i
$142$		0			0
$143$			7.06860i			0.591106i
$144$		0			0
$145$			28.4258i			2.36063i
$146$		0			0
$147$	1.02444	−	0.424336i	0.0844941	−	0.0349986i
$148$		0			0
$149$	1.61740	−	3.90476i	0.132503	−	0.319890i	−0.843678	−	0.536850i	$-0.819614\pi$
$149$	1.61740	−	3.90476i	0.132503	−	0.319890i	0.976181	+	0.216960i	$0.0696140\pi$
$150$		0			0
$151$	−14.4036	+	14.4036i	−1.17214	+	1.17214i	−0.190448	+	0.981697i	$0.560994\pi$
$151$	−14.4036	+	14.4036i	−1.17214	+	1.17214i	−0.981697	+	0.190448i	$0.939006\pi$
$152$		0			0
$153$	−5.00283	−	5.00283i	−0.404455	−	0.404455i
$154$		0			0
$155$	31.5153	+	13.0541i	2.53137	+	1.04853i
$156$		0			0
$157$	3.52753	+	8.51620i	0.281527	+	0.679667i	0.999872	−	0.0160208i	$-0.00509978\pi$
$157$	3.52753	+	8.51620i	0.281527	+	0.679667i	−0.718344	+	0.695688i	$0.755100\pi$
$158$		0			0
$159$	−13.8805			−1.10080
$160$		0			0
$161$	−7.19568			−0.567099
$162$		0			0
$163$	3.75784	+	9.07224i	0.294337	+	0.710593i	0.999998	+	0.00204276i	$0.000650232\pi$
$163$	3.75784	+	9.07224i	0.294337	+	0.710593i	−0.705661	+	0.708550i	$0.749350\pi$
$164$		0			0
$165$	−14.2387	−	5.89787i	−1.10848	−	0.459148i
$166$		0			0
$167$	−5.75159	−	5.75159i	−0.445071	−	0.445071i	0.448641	−	0.893712i	$-0.351908\pi$
$167$	−5.75159	−	5.75159i	−0.445071	−	0.445071i	−0.893712	+	0.448641i	$0.851908\pi$
$168$		0			0
$169$	−6.25387	+	6.25387i	−0.481067	+	0.481067i
$170$		0			0
$171$	1.50846	−	3.64174i	0.115355	−	0.278491i
$172$		0			0
$173$	−16.1234	+	6.67853i	−1.22584	+	0.507759i	−0.899262	−	0.437411i	$-0.855895\pi$
$173$	−16.1234	+	6.67853i	−1.22584	+	0.507759i	−0.326578	+	0.945170i	$0.605895\pi$
$174$		0			0
$175$			11.0675i			0.836622i
$176$		0			0
$177$			2.87878i			0.216382i
$178$		0			0
$179$	14.3176	−	5.93053i	1.07014	−	0.443269i	0.223103	−	0.974795i	$-0.428381\pi$
$179$	14.3176	−	5.93053i	1.07014	−	0.443269i	0.847042	+	0.531526i	$0.178381\pi$
$180$		0			0
$181$	−8.21076	+	19.8225i	−0.610301	+	1.47340i	0.252370	+	0.967631i	$0.418790\pi$
$181$	−8.21076	+	19.8225i	−0.610301	+	1.47340i	−0.862671	+	0.505766i	$0.831210\pi$
$182$		0			0
$183$	−7.90389	+	7.90389i	−0.584273	+	0.584273i
$184$		0			0
$185$	−20.7484	−	20.7484i	−1.52545	−	1.52545i
$186$		0			0
$187$	−12.8018	−	5.30266i	−0.936157	−	0.387769i
$188$		0			0
$189$	−2.02428	−	4.88704i	−0.147245	−	0.355480i
$190$		0			0
$191$	−10.2155			−0.739164			−0.369582	−	0.929198i	$-0.620499\pi$
$191$	−10.2155			−0.739164			−0.369582	+	0.929198i	$0.620499\pi$
$192$		0			0
$193$	1.33660			0.0962108			0.0481054	−	0.998842i	$-0.484682\pi$
$193$	1.33660			0.0962108			0.0481054	+	0.998842i	$0.484682\pi$
$194$		0			0
$195$	3.46741	+	8.37106i	0.248306	+	0.599464i
$196$		0			0
$197$	−4.81759	−	1.99551i	−0.343239	−	0.142174i	0.204403	−	0.978887i	$-0.434475\pi$
$197$	−4.81759	−	1.99551i	−0.343239	−	0.142174i	−0.547642	+	0.836712i	$0.684475\pi$
$198$		0			0
$199$	−14.6883	−	14.6883i	−1.04123	−	1.04123i	−0.999113	−	0.0421136i	$-0.986591\pi$
$199$	−14.6883	−	14.6883i	−1.04123	−	1.04123i	−0.0421136	−	0.999113i	$-0.513409\pi$
$200$		0			0
$201$	0.646428	−	0.646428i	0.0455955	−	0.0455955i
$202$		0			0
$203$	−2.71380	+	6.55170i	−0.190472	+	0.459840i
$204$		0			0
$205$	−6.99584	+	2.89777i	−0.488610	+	0.202389i
$206$		0			0
$207$			12.7397i			0.885472i
$208$		0			0
$209$		−	7.71999i		−	0.534003i
$210$		0			0
$211$	−21.1265	+	8.75089i	−1.45441	+	0.602436i	−0.963243	−	0.268631i	$-0.913429\pi$
$211$	−21.1265	+	8.75089i	−1.45441	+	0.602436i	−0.491165	+	0.871066i	$0.663429\pi$
$212$		0			0
$213$	3.73161	−	9.00890i	0.255686	−	0.617280i
$214$		0			0
$215$	9.67762	−	9.67762i	0.660008	−	0.660008i
$216$		0			0
$217$	6.01751	+	6.01751i	0.408495	+	0.408495i
$218$		0			0
$219$	3.02923	+	1.25475i	0.204696	+	0.0847879i
$220$		0			0
$221$	3.11748	+	7.52627i	0.209704	+	0.506271i
$222$		0			0
$223$	23.8764			1.59888			0.799442	−	0.600743i	$-0.205129\pi$
$223$	23.8764			1.59888			0.799442	+	0.600743i	$0.205129\pi$
$224$		0			0
$225$	19.5946			1.30631
$226$		0			0
$227$	−7.83210	−	18.9084i	−0.519835	−	1.25499i	−0.938004	−	0.346624i	$-0.887328\pi$
$227$	−7.83210	−	18.9084i	−0.519835	−	1.25499i	0.418169	−	0.908369i	$-0.362672\pi$
$228$		0			0
$229$	1.72921	+	0.716263i	0.114270	+	0.0473320i	0.439086	−	0.898445i	$-0.355302\pi$
$229$	1.72921	+	0.716263i	0.114270	+	0.0473320i	−0.324816	+	0.945777i	$0.605302\pi$
$230$		0			0
$231$	−2.71873	−	2.71873i	−0.178879	−	0.178879i
$232$		0			0
$233$	5.83290	−	5.83290i	0.382126	−	0.382126i	−0.489742	−	0.871868i	$-0.662909\pi$
$233$	5.83290	−	5.83290i	0.382126	−	0.382126i	0.871868	+	0.489742i	$0.162909\pi$
$234$		0			0
$235$	−4.86263	+	11.7394i	−0.317203	+	0.765795i
$236$		0			0
$237$	9.46214	−	3.91935i	0.614632	−	0.254589i
$238$		0			0
$239$		−	24.2326i		−	1.56748i	−0.621092	−	0.783738i	$-0.713311\pi$
$239$		−	24.2326i		−	1.56748i	0.621092	−	0.783738i	$-0.286689\pi$
$240$		0			0
$241$			2.18918i			0.141017i	0.997511	+	0.0705087i	$0.0224622\pi$
$241$			2.18918i			0.141017i	−0.997511	+	0.0705087i	$0.977538\pi$
$242$		0			0
$243$	−14.0936	+	5.83774i	−0.904102	+	0.374491i
$244$		0			0
$245$	−1.53396	+	3.70330i	−0.0980010	+	0.236595i
$246$		0			0
$247$	−3.20931	+	3.20931i	−0.204204	+	0.204204i
$248$		0			0
$249$	4.20270	+	4.20270i	0.266335	+	0.266335i
$250$		0			0
$251$	−10.0634	−	4.16841i	−0.635199	−	0.263108i	0.0417613	−	0.999128i	$-0.486703\pi$
$251$	−10.0634	−	4.16841i	−0.635199	−	0.263108i	−0.676960	+	0.736020i	$0.736703\pi$
$252$		0			0
$253$	9.54823	+	23.0515i	0.600292	+	1.44923i
$254$		0			0
$255$	−17.7618			−1.11228
$256$		0			0
$257$	−24.7180			−1.54187			−0.770934	−	0.636915i	$-0.780210\pi$
$257$	−24.7180			−1.54187			−0.770934	+	0.636915i	$0.780210\pi$
$258$		0			0
$259$	−2.80134	−	6.76303i	−0.174067	−	0.420234i
$260$		0			0
$261$	11.5996	+	4.80471i	0.717996	+	0.297404i
$262$		0			0
$263$	3.13019	+	3.13019i	0.193016	+	0.193016i	0.796998	−	0.603982i	$-0.206420\pi$
$263$	3.13019	+	3.13019i	0.193016	+	0.193016i	−0.603982	+	0.796998i	$0.706420\pi$
$264$		0			0
$265$	35.4809	−	35.4809i	2.17957	−	2.17957i
$266$		0			0
$267$	5.47308	−	13.2132i	0.334947	−	0.808633i
$268$		0			0
$269$	−19.0188	+	7.87784i	−1.15960	+	0.480320i	−0.877740	−	0.479137i	$-0.840950\pi$
$269$	−19.0188	+	7.87784i	−1.15960	+	0.480320i	−0.281855	+	0.959457i	$0.590950\pi$
$270$		0			0
$271$		−	6.36191i		−	0.386458i	−0.981154	−	0.193229i	$-0.938104\pi$
$271$		−	6.36191i		−	0.386458i	0.981154	−	0.193229i	$-0.0618961\pi$
$272$		0			0
$273$			2.26043i			0.136808i
$274$		0			0
$275$	35.4548	−	14.6859i	2.13801	−	0.885591i
$276$		0			0
$277$	−0.769977	+	1.85889i	−0.0462635	+	0.111690i	−0.945322	−	0.326139i	$-0.894252\pi$
$277$	−0.769977	+	1.85889i	−0.0462635	+	0.111690i	0.899058	+	0.437829i	$0.144252\pi$
$278$		0			0
$279$	10.6538	−	10.6538i	0.637827	−	0.637827i
$280$		0			0
$281$	16.6647	+	16.6647i	0.994135	+	0.994135i	0.999983	−	0.00584778i	$-0.00186142\pi$
$281$	16.6647	+	16.6647i	0.994135	+	0.994135i	−0.00584778	+	0.999983i	$0.501861\pi$
$282$		0			0
$283$	−5.33995	−	2.21188i	−0.317427	−	0.131483i	0.218281	−	0.975886i	$-0.429955\pi$
$283$	−5.33995	−	2.21188i	−0.317427	−	0.131483i	−0.535708	+	0.844403i	$0.679955\pi$
$284$		0			0
$285$	−3.78694	−	9.14248i	−0.224319	−	0.541554i
$286$		0			0
$287$	−1.88908			−0.111509
$288$		0			0
$289$	1.03073			0.0606311
$290$		0			0
$291$	4.14445	+	10.0056i	0.242952	+	0.586538i
$292$		0			0
$293$	12.1989	+	5.05294i	0.712666	+	0.295196i	0.709407	−	0.704799i	$-0.248963\pi$
$293$	12.1989	+	5.05294i	0.712666	+	0.295196i	0.00325849	+	0.999995i	$0.498963\pi$
$294$		0			0
$295$	−7.35863	−	7.35863i	−0.428436	−	0.428436i
$296$		0			0
$297$	−12.9696	+	12.9696i	−0.752574	+	0.752574i
$298$		0			0
$299$	5.61349	−	13.5522i	0.324637	−	0.783742i
$300$		0			0
$301$	3.15446	−	1.30662i	0.181820	−	0.0753123i
$302$		0			0
$303$			13.1121i			0.753273i
$304$		0			0
$305$		−	40.4073i		−	2.31372i
$306$		0			0
$307$	−8.01235	+	3.31882i	−0.457289	+	0.189415i	−0.599423	−	0.800432i	$-0.704603\pi$
$307$	−8.01235	+	3.31882i	−0.457289	+	0.189415i	0.142135	+	0.989847i	$0.454603\pi$
$308$		0			0
$309$	−0.344752	+	0.832305i	−0.0196123	+	0.0473482i
$310$		0			0
$311$	−21.3528	+	21.3528i	−1.21081	+	1.21081i	−0.240043	+	0.970762i	$0.577162\pi$
$311$	−21.3528	+	21.3528i	−1.21081	+	1.21081i	−0.970762	+	0.240043i	$0.922838\pi$
$312$		0			0
$313$	−6.73094	−	6.73094i	−0.380455	−	0.380455i	0.490811	−	0.871266i	$-0.336701\pi$
$313$	−6.73094	−	6.73094i	−0.380455	−	0.380455i	−0.871266	+	0.490811i	$0.836701\pi$
$314$		0			0
$315$	6.55658	+	2.71582i	0.369421	+	0.153019i
$316$		0			0
$317$	0.0760844	+	0.183684i	0.00427333	+	0.0103167i	0.926002	−	0.377519i	$-0.123223\pi$
$317$	0.0760844	+	0.183684i	0.00427333	+	0.0103167i	−0.921728	+	0.387836i	$0.873223\pi$
$318$		0			0
$319$	24.5896			1.37675
$320$		0			0
$321$	−2.68801			−0.150030
$322$		0			0
$323$	−3.40477	−	8.21984i	−0.189446	−	0.457364i
$324$		0			0
$325$	−20.8442	−	8.63395i	−1.15623	−	0.478925i
$326$		0			0
$327$	−3.51249	−	3.51249i	−0.194241	−	0.194241i
$328$		0			0
$329$	−2.24152	+	2.24152i	−0.123579	+	0.123579i
$330$		0			0
$331$	3.22280	−	7.78053i	0.177141	−	0.427657i	−0.810223	−	0.586121i	$-0.800654\pi$
$331$	3.22280	−	7.78053i	0.177141	−	0.427657i	0.987365	+	0.158464i	$0.0506543\pi$
$332$		0			0
$333$	−11.9737	+	4.95968i	−0.656157	+	0.271789i
$334$		0			0
$335$			3.30475i			0.180558i
$336$		0			0
$337$			23.3157i			1.27009i	0.772476	+	0.635044i	$0.219018\pi$
$337$			23.3157i			1.27009i	−0.772476	+	0.635044i	$0.780982\pi$
$338$		0			0
$339$	0.131444	−	0.0544459i	0.00713906	−	0.00295709i
$340$		0			0
$341$	11.2923	−	27.2621i	0.611514	−	1.47632i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$	22.6152	+	22.6152i	1.21756	+	1.21756i
$346$		0			0
$347$	−20.3270	−	8.41971i	−1.09121	−	0.451994i	−0.236781	−	0.971563i	$-0.576092\pi$
$347$	−20.3270	−	8.41971i	−1.09121	−	0.451994i	−0.854428	+	0.519569i	$0.826092\pi$
$348$		0			0
$349$	−8.67368	−	20.9401i	−0.464292	−	1.12090i	−0.966618	−	0.256221i	$-0.917522\pi$
$349$	−8.67368	−	20.9401i	−0.464292	−	1.12090i	0.502327	−	0.864678i	$-0.332478\pi$
$350$		0			0
$351$	10.7833			0.575571
$352$		0			0
$353$	−11.8631			−0.631409			−0.315704	−	0.948858i	$-0.602241\pi$
$353$	−11.8631			−0.631409			−0.315704	+	0.948858i	$0.602241\pi$
$354$		0			0
$355$	13.4896	+	32.5669i	0.715955	+	1.72847i
$356$		0			0
$357$	−4.09381	−	1.69571i	−0.216667	−	0.0897466i
$358$		0			0
$359$	0.519581	+	0.519581i	0.0274225	+	0.0274225i	0.720685	−	0.693263i	$-0.243827\pi$
$359$	0.519581	+	0.519581i	0.0274225	+	0.0274225i	−0.693263	+	0.720685i	$0.743827\pi$
$360$		0			0
$361$	−9.92997	+	9.92997i	−0.522630	+	0.522630i
$362$		0			0
$363$	−0.434219	+	1.04830i	−0.0227906	+	0.0550213i
$364$		0			0
$365$	−10.9505	+	4.53586i	−0.573177	+	0.237418i
$366$		0			0
$367$		−	20.8905i		−	1.09048i	−0.838281	−	0.545239i	$-0.816439\pi$
$367$		−	20.8905i		−	1.09048i	0.838281	−	0.545239i	$-0.183561\pi$
$368$		0			0
$369$			3.34456i			0.174111i
$370$		0			0
$371$	11.5651	−	4.79044i	0.600432	−	0.248707i
$372$		0			0
$373$	−0.402626	+	0.972025i	−0.0208472	+	0.0503296i	−0.933960	−	0.357377i	$-0.883671\pi$
$373$	−0.402626	+	0.972025i	−0.0208472	+	0.0503296i	0.913113	+	0.407706i	$0.133671\pi$
$374$		0			0
$375$	19.0694	−	19.0694i	0.984737	−	0.984737i
$376$		0			0
$377$	−10.2222	−	10.2222i	−0.526472	−	0.526472i
$378$		0			0
$379$	20.1406	+	8.34251i	1.03455	+	0.428526i	0.834354	−	0.551230i	$-0.185841\pi$
$379$	20.1406	+	8.34251i	1.03455	+	0.428526i	0.200199	+	0.979755i	$0.435841\pi$
$380$		0			0
$381$	−2.92378	−	7.05862i	−0.149790	−	0.361624i
$382$		0			0
$383$	−2.87465			−0.146888			−0.0734438	−	0.997299i	$-0.523399\pi$
$383$	−2.87465			−0.146888			−0.0734438	+	0.997299i	$0.523399\pi$
$384$		0			0
$385$	13.8991			0.708362
$386$		0			0
$387$	−2.31333	−	5.58487i	−0.117593	−	0.283895i
$388$		0			0
$389$	34.3165	+	14.2143i	1.73991	+	0.720696i	0.998782	+	0.0493368i	$0.0157108\pi$
$389$	34.3165	+	14.2143i	1.73991	+	0.720696i	0.741132	+	0.671359i	$0.234289\pi$
$390$		0			0
$391$	20.3329	+	20.3329i	1.02828	+	1.02828i
$392$		0			0
$393$	−1.80219	+	1.80219i	−0.0909085	+	0.0909085i
$394$		0			0
$395$	−14.1683	+	34.2053i	−0.712885	+	1.72106i
$396$		0			0
$397$	−30.2593	+	12.5338i	−1.51867	+	0.629054i	−0.977325	−	0.211745i	$-0.932085\pi$
$397$	−30.2593	+	12.5338i	−1.51867	+	0.629054i	−0.541347	+	0.840799i	$0.682085\pi$
$398$		0			0
$399$		−	2.46874i		−	0.123592i
$400$		0			0
$401$		−	36.1292i		−	1.80421i	−0.431522	−	0.902103i	$-0.642023\pi$
$401$		−	36.1292i		−	1.80421i	0.431522	−	0.902103i	$-0.357977\pi$
$402$		0			0
$403$	−16.0276	+	6.63886i	−0.798393	+	0.330705i
$404$		0			0
$405$	−0.849869	+	2.05176i	−0.0422303	+	0.101953i
$406$		0			0
$407$	−17.9483	+	17.9483i	−0.889663	+	0.889663i
$408$		0			0
$409$	12.5036	+	12.5036i	0.618265	+	0.618265i	0.945086	−	0.326821i	$-0.105978\pi$
$409$	12.5036	+	12.5036i	0.618265	+	0.618265i	−0.326821	+	0.945086i	$0.605978\pi$
$410$		0			0
$411$	−1.54416	−	0.639613i	−0.0761679	−	0.0315498i
$412$		0			0
$413$	−0.993524	−	2.39858i	−0.0488881	−	0.118026i
$414$		0			0
$415$	−21.4856			−1.05469
$416$		0			0
$417$	4.87022			0.238496
$418$		0			0
$419$	5.45653	+	13.1732i	0.266569	+	0.643554i	0.999317	−	0.0369456i	$-0.0117628\pi$
$419$	5.45653	+	13.1732i	0.266569	+	0.643554i	−0.732749	+	0.680500i	$0.761763\pi$
$420$		0			0
$421$	−0.496953	−	0.205845i	−0.0242200	−	0.0100323i	0.370541	−	0.928816i	$-0.379172\pi$
$421$	−0.496953	−	0.205845i	−0.0242200	−	0.0100323i	−0.394761	+	0.918784i	$0.629172\pi$
$422$		0			0
$423$	3.96854	+	3.96854i	0.192957	+	0.192957i
$424$		0			0
$425$	31.2735	−	31.2735i	1.51699	−	1.51699i
$426$		0			0
$427$	3.85768	−	9.31326i	0.186686	−	0.450700i
$428$		0			0
$429$	7.24133	−	2.99946i	0.349615	−	0.144815i
$430$		0			0
$431$		−	26.8787i		−	1.29470i	−0.762193	−	0.647350i	$-0.775877\pi$
$431$		−	26.8787i		−	1.29470i	0.762193	−	0.647350i	$-0.224123\pi$
$432$		0			0
$433$			1.35555i			0.0651438i	0.999469	+	0.0325719i	$0.0103698\pi$
$433$			1.35555i			0.0651438i	−0.999469	+	0.0325719i	$0.989630\pi$
$434$		0			0
$435$	29.1204	−	12.0621i	1.39622	−	0.578332i
$436$		0			0
$437$	−6.13079	+	14.8010i	−0.293276	+	0.708030i
$438$		0			0
$439$	−21.2655	+	21.2655i	−1.01495	+	1.01495i	−0.0150600	+	0.999887i	$0.504794\pi$
$439$	−21.2655	+	21.2655i	−1.01495	+	1.01495i	−0.999887	+	0.0150600i	$0.995206\pi$
$440$		0			0
$441$	1.25191	+	1.25191i	0.0596148	+	0.0596148i
$442$		0			0
$443$	2.39845	+	0.993471i	0.113954	+	0.0472012i	0.438932	−	0.898520i	$-0.355357\pi$
$443$	2.39845	+	0.993471i	0.113954	+	0.0472012i	−0.324978	+	0.945722i	$0.605357\pi$
$444$		0			0
$445$	19.7850	+	47.7651i	0.937898	+	2.26429i
$446$		0			0
$447$	−4.68650			−0.221664
$448$		0			0
$449$	32.1967			1.51945			0.759727	−	0.650242i	$-0.225332\pi$
$449$	32.1967			1.51945			0.759727	+	0.650242i	$0.225332\pi$
$450$		0			0
$451$	2.50670	+	6.05170i	0.118036	+	0.284964i
$452$		0			0
$453$	20.8675	+	8.64359i	0.980440	+	0.406111i
$454$		0			0
$455$	−5.77804	−	5.77804i	−0.270879	−	0.270879i
$456$		0			0
$457$	−15.6589	+	15.6589i	−0.732492	+	0.732492i	−0.971113	−	0.238621i	$-0.923305\pi$
$457$	−15.6589	+	15.6589i	−0.732492	+	0.732492i	0.238621	+	0.971113i	$0.423305\pi$
$458$		0			0
$459$	−8.08934	+	19.5294i	−0.377578	+	0.911554i
$460$		0			0
$461$	−11.9675	+	4.95708i	−0.557380	+	0.230874i	−0.643547	−	0.765406i	$-0.722538\pi$
$461$	−11.9675	+	4.95708i	−0.557380	+	0.230874i	0.0861675	+	0.996281i	$0.472538\pi$
$462$		0			0
$463$			30.8800i			1.43512i	0.696499	+	0.717558i	$0.254740\pi$
$463$			30.8800i			1.43512i	−0.696499	+	0.717558i	$0.745260\pi$
$464$		0			0
$465$		−	37.8247i		−	1.75408i
$466$		0			0
$467$	25.2521	−	10.4598i	1.16853	−	0.484020i	0.287823	−	0.957684i	$-0.407069\pi$
$467$	25.2521	−	10.4598i	1.16853	−	0.484020i	0.880706	+	0.473663i	$0.157069\pi$
$468$		0			0
$469$	−0.315504	+	0.761694i	−0.0145686	+	0.0351718i
$470$		0			0
$471$	7.22746	−	7.22746i	0.333024	−	0.333024i
$472$		0			0
$473$	−8.37156	−	8.37156i	−0.384925	−	0.384925i
$474$		0			0
$475$	22.7651	+	9.42960i	1.04453	+	0.432660i
$476$		0			0
$477$	−8.48132	−	20.4757i	−0.388333	−	0.937519i
$478$		0			0
$479$	17.3650			0.793426			0.396713	−	0.917943i	$-0.370151\pi$
$479$	17.3650			0.793426			0.396713	+	0.917943i	$0.370151\pi$
$480$		0			0
$481$	14.9227			0.680417
$482$		0			0
$483$	3.05338	+	7.37152i	0.138934	+	0.335416i
$484$		0			0
$485$	−36.1699	−	14.9820i	−1.64239	−	0.680300i
$486$		0			0
$487$	−5.96219	−	5.96219i	−0.270173	−	0.270173i	0.558997	−	0.829170i	$-0.311186\pi$
$487$	−5.96219	−	5.96219i	−0.270173	−	0.270173i	−0.829170	+	0.558997i	$0.811186\pi$
$488$		0			0
$489$	7.69935	−	7.69935i	0.348177	−	0.348177i
$490$		0			0
$491$	11.0080	−	26.5757i	0.496785	−	1.19934i	−0.454421	−	0.890787i	$-0.650154\pi$
$491$	11.0080	−	26.5757i	0.496785	−	1.19934i	0.951206	−	0.308557i	$-0.0998462\pi$
$492$		0			0
$493$	26.1816	−	10.8448i	1.17916	−	0.488425i
$494$		0			0
$495$		−	24.6078i		−	1.10604i
$496$		0			0
$497$			8.79401i			0.394465i
$498$		0			0
$499$	12.3497	−	5.11543i	0.552850	−	0.228998i	−0.0887276	−	0.996056i	$-0.528280\pi$
$499$	12.3497	−	5.11543i	0.552850	−	0.228998i	0.641578	+	0.767058i	$0.278280\pi$
$500$		0			0
$501$	−3.45154	+	8.33274i	−0.154203	+	0.372279i
$502$		0			0
$503$	16.4206	−	16.4206i	0.732158	−	0.732158i	−0.238889	−	0.971047i	$-0.576783\pi$
$503$	16.4206	−	16.4206i	0.732158	−	0.732158i	0.971047	+	0.238889i	$0.0767833\pi$
$504$		0			0
$505$	−33.5168	−	33.5168i	−1.49148	−	1.49148i
$506$		0			0
$507$	9.06044	+	3.75296i	0.402388	+	0.166675i
$508$		0			0
$509$	−1.21719	−	2.93855i	−0.0539509	−	0.130249i	0.894606	−	0.446856i	$-0.147456\pi$
$509$	−1.21719	−	2.93855i	−0.0539509	−	0.130249i	−0.948557	+	0.316607i	$0.897456\pi$
$510$		0			0
$511$	−2.95697			−0.130809
$512$		0			0
$513$	−11.7770			−0.519969
$514$		0			0
$515$	−1.24627	−	3.00875i	−0.0549170	−	0.132581i
$516$		0			0
$517$	10.1551	+	4.20638i	0.446621	+	0.184997i
$518$		0			0
$519$	13.6835	+	13.6835i	0.600637	+	0.600637i
$520$		0			0
$521$	2.47792	−	2.47792i	0.108560	−	0.108560i	−0.650741	−	0.759300i	$-0.725541\pi$
$521$	2.47792	−	2.47792i	0.108560	−	0.108560i	0.759300	+	0.650741i	$0.225541\pi$
$522$		0			0
$523$	6.15101	−	14.8499i	0.268965	−	0.649339i	−0.730470	−	0.682945i	$-0.760699\pi$
$523$	6.15101	−	14.8499i	0.268965	−	0.649339i	0.999435	+	0.0336055i	$0.0106990\pi$
$524$		0			0
$525$	11.3379	−	4.69632i	0.494827	−	0.204964i
$526$		0			0
$527$		−	34.0075i		−	1.48139i
$528$		0			0
$529$		−	28.7778i		−	1.25121i
$530$		0			0
$531$	−4.24661	+	1.75900i	−0.184287	+	0.0763342i
$532$		0			0
$533$	1.47371	−	3.55785i	0.0638335	−	0.154108i
$534$		0			0
$535$	6.87100	−	6.87100i	0.297059	−	0.297059i
$536$		0			0
$537$	−12.1509	−	12.1509i	−0.524350	−	0.524350i
$538$		0			0
$539$	3.20352	+	1.32694i	0.137985	+	0.0571554i
$540$		0			0
$541$	−0.620742	−	1.49860i	−0.0266878	−	0.0644300i	0.909974	−	0.414666i	$-0.136101\pi$
$541$	−0.620742	−	1.49860i	−0.0266878	−	0.0644300i	−0.936662	+	0.350236i	$0.886101\pi$
$542$		0			0
$543$	23.7910			1.02097
$544$		0			0
$545$	17.9570			0.769193
$546$		0			0
$547$	13.7263	+	33.1383i	0.586896	+	1.41689i	0.886455	+	0.462815i	$0.153160\pi$
$547$	13.7263	+	33.1383i	0.586896	+	1.41689i	−0.299559	+	0.954078i	$0.596840\pi$
$548$		0			0
$549$	−16.4888	−	6.82990i	−0.703726	−	0.291493i
$550$		0			0
$551$	11.1642	+	11.1642i	0.475613	+	0.475613i
$552$		0			0
$553$	−6.53115	+	6.53115i	−0.277733	+	0.277733i
$554$		0			0
$555$	−12.4511	+	30.0597i	−0.528522	+	1.27596i
$556$		0			0
$557$	15.8664	−	6.57207i	0.672280	−	0.278468i	−0.0203155	−	0.999794i	$-0.506467\pi$
$557$	15.8664	−	6.57207i	0.672280	−	0.278468i	0.692596	+	0.721326i	$0.256467\pi$
$558$		0			0
$559$			6.96035i			0.294392i
$560$		0			0
$561$			15.3647i			0.648698i
$562$		0			0
$563$	31.6643	−	13.1158i	1.33449	−	0.552765i	0.402559	−	0.915394i	$-0.368121\pi$
$563$	31.6643	−	13.1158i	1.33449	−	0.552765i	0.931934	+	0.362629i	$0.118121\pi$
$564$		0			0
$565$	−0.196820	+	0.475165i	−0.00828027	+	0.0199903i
$566$		0			0
$567$	−0.391763	+	0.391763i	−0.0164525	+	0.0164525i
$568$		0			0
$569$	−2.50103	−	2.50103i	−0.104849	−	0.104849i	0.652736	−	0.757585i	$-0.273621\pi$
$569$	−2.50103	−	2.50103i	−0.104849	−	0.104849i	−0.757585	+	0.652736i	$0.773621\pi$
$570$		0			0
$571$	10.0887	+	4.17887i	0.422198	+	0.174880i	0.583659	−	0.811999i	$-0.301621\pi$
$571$	10.0887	+	4.17887i	0.422198	+	0.174880i	−0.161461	+	0.986879i	$0.551621\pi$
$572$		0			0
$573$	4.33478	+	10.4651i	0.181088	+	0.437185i
$574$		0			0
$575$	−79.6379			−3.32113
$576$		0			0
$577$	6.21937			0.258916			0.129458	−	0.991585i	$-0.458676\pi$
$577$	6.21937			0.258916			0.129458	+	0.991585i	$0.458676\pi$
$578$		0			0
$579$	−0.567168	−	1.36927i	−0.0235707	−	0.0569047i
$580$		0			0
$581$	−4.95210	−	2.05123i	−0.205448	−	0.0850992i
$582$		0			0
$583$	−30.6925	−	30.6925i	−1.27115	−	1.27115i
$584$		0			0
$585$	−10.2298	+	10.2298i	−0.422952	+	0.422952i
$586$		0			0
$587$	3.46382	−	8.36239i	0.142967	−	0.345153i	−0.836135	−	0.548524i	$-0.815190\pi$
$587$	3.46382	−	8.36239i	0.142967	−	0.345153i	0.979102	+	0.203371i	$0.0651899\pi$
$588$		0			0
$589$	17.5046	−	7.25065i	0.721265	−	0.298758i
$590$		0			0
$591$			5.78208i			0.237843i
$592$		0			0
$593$			2.15762i			0.0886029i	0.999018	+	0.0443014i	$0.0141062\pi$
$593$			2.15762i			0.0886029i	−0.999018	+	0.0443014i	$0.985894\pi$
$594$		0			0
$595$	14.7990	−	6.12994i	0.606699	−	0.251303i
$596$		0			0
$597$	−8.81447	+	21.2800i	−0.360752	+	0.870933i
$598$		0			0
$599$	19.8845	−	19.8845i	0.812458	−	0.812458i	−0.172544	−	0.985002i	$-0.555199\pi$
$599$	19.8845	−	19.8845i	0.812458	−	0.812458i	0.985002	+	0.172544i	$0.0551985\pi$
$600$		0			0
$601$	−9.17640	−	9.17640i	−0.374313	−	0.374313i	0.494732	−	0.869045i	$-0.335266\pi$
$601$	−9.17640	−	9.17640i	−0.374313	−	0.374313i	−0.869045	+	0.494732i	$0.835266\pi$
$602$		0			0
$603$	1.34855	+	0.558590i	0.0549174	+	0.0227475i
$604$		0			0
$605$	−1.56969	−	3.78956i	−0.0638168	−	0.154067i
$606$		0			0
$607$	−33.4990			−1.35968			−0.679842	−	0.733359i	$-0.737952\pi$
$607$	−33.4990			−1.35968			−0.679842	+	0.733359i	$0.737952\pi$
$608$		0			0
$609$	7.86337			0.318640
$610$		0			0
$611$	−2.47297	−	5.97028i	−0.100046	−	0.241532i
$612$		0			0
$613$	16.4402	+	6.80976i	0.664014	+	0.275044i	0.689127	−	0.724641i	$-0.257994\pi$
$613$	16.4402	+	6.80976i	0.664014	+	0.275044i	−0.0251123	+	0.999685i	$0.507994\pi$
$614$		0			0
$615$	5.93717	+	5.93717i	0.239410	+	0.239410i
$616$		0			0
$617$	12.4869	−	12.4869i	0.502702	−	0.502702i	−0.409575	−	0.912277i	$-0.634323\pi$
$617$	12.4869	−	12.4869i	0.502702	−	0.502702i	0.912277	+	0.409575i	$0.134323\pi$
$618$		0			0
$619$	2.94179	−	7.10210i	0.118240	−	0.285458i	−0.853668	−	0.520818i	$-0.825627\pi$
$619$	2.94179	−	7.10210i	0.118240	−	0.285458i	0.971908	+	0.235360i	$0.0756270\pi$
$620$		0			0
$621$	35.1656	−	14.5661i	1.41115	−	0.584516i
$622$		0			0
$623$			12.8980i			0.516747i
$624$		0			0
$625$			42.1515i			1.68606i
$626$		0			0
$627$	−7.90865	+	3.27587i	−0.315841	+	0.130826i
$628$		0			0
$629$	−11.1946	+	27.0261i	−0.446358	+	1.07760i
$630$		0			0
$631$	11.1311	−	11.1311i	0.443121	−	0.443121i	−0.449938	−	0.893060i	$-0.648554\pi$
$631$	11.1311	−	11.1311i	0.443121	−	0.443121i	0.893060	+	0.449938i	$0.148554\pi$
$632$		0			0
$633$	17.9295	+	17.9295i	0.712632	+	0.712632i
$634$		0			0
$635$	25.5167	+	10.5693i	1.01260	+	0.419432i
$636$		0			0
$637$	−0.780120	−	1.88338i	−0.0309095	−	0.0746221i
$638$		0			0
$639$	15.5695			0.615920
$640$		0			0
$641$	14.5343			0.574072			0.287036	−	0.957920i	$-0.407330\pi$
$641$	14.5343			0.574072			0.287036	+	0.957920i	$0.407330\pi$
$642$		0			0
$643$	−17.7274	−	42.7978i	−0.699101	−	1.68778i	−0.725587	−	0.688130i	$-0.758432\pi$
$643$	−17.7274	−	42.7978i	−0.699101	−	1.68778i	0.0264860	−	0.999649i	$-0.491568\pi$
$644$		0			0
$645$	−14.0207	−	5.80755i	−0.552063	−	0.228672i
$646$		0			0
$647$	−1.39587	−	1.39587i	−0.0548772	−	0.0548772i	0.679136	−	0.734013i	$-0.262355\pi$
$647$	−1.39587	−	1.39587i	−0.0548772	−	0.0548772i	−0.734013	+	0.679136i	$0.762355\pi$
$648$		0			0
$649$	−6.36554	+	6.36554i	−0.249869	+	0.249869i
$650$		0			0
$651$	3.61112	−	8.71801i	0.141531	−	0.341686i
$652$		0			0
$653$	34.2784	−	14.1986i	1.34142	−	0.555633i	0.407527	−	0.913193i	$-0.366391\pi$
$653$	34.2784	−	14.1986i	1.34142	−	0.555633i	0.933890	+	0.357560i	$0.116391\pi$
$654$		0			0
$655$		−	9.21340i		−	0.359997i
$656$		0			0
$657$			5.23522i			0.204245i
$658$		0			0
$659$	−23.3595	+	9.67583i	−0.909958	+	0.376917i	−0.788040	−	0.615623i	$-0.788904\pi$
$659$	−23.3595	+	9.67583i	−0.909958	+	0.376917i	−0.121917	+	0.992540i	$0.538904\pi$
$660$		0			0
$661$	−6.63744	+	16.0242i	−0.258167	+	0.623269i	−0.998817	−	0.0486210i	$-0.984517\pi$
$661$	−6.63744	+	16.0242i	−0.258167	+	0.623269i	0.740651	+	0.671890i	$0.234517\pi$
$662$		0			0
$663$	6.38733	−	6.38733i	0.248063	−	0.248063i
$664$		0			0
$665$	6.31050	+	6.31050i	0.244711	+	0.244711i
$666$		0			0
$667$	−47.1440	−	19.5277i	−1.82542	−	0.756114i
$668$		0			0
$669$	−10.1316	−	24.4599i	−0.391711	−	0.945674i
$670$		0			0
$671$	−34.9541			−1.34939
$672$		0			0
$673$	−30.1958			−1.16396			−0.581980	−	0.813203i	$-0.697722\pi$
$673$	−30.1958			−1.16396			−0.581980	+	0.813203i	$0.697722\pi$
$674$		0			0
$675$	−22.4037	−	54.0872i	−0.862317	−	2.08182i
$676$		0			0
$677$	44.6271	+	18.4851i	1.71516	+	0.710442i	0.999933	+	0.0115465i	$0.00367546\pi$
$677$	44.6271	+	18.4851i	1.71516	+	0.710442i	0.715224	+	0.698895i	$0.246325\pi$
$678$		0			0
$679$	−6.90626	−	6.90626i	−0.265038	−	0.265038i
$680$		0			0
$681$	−16.0470	+	16.0470i	−0.614922	+	0.614922i
$682$		0			0
$683$	−9.95564	+	24.0350i	−0.380942	+	0.919675i	0.610842	+	0.791752i	$0.290831\pi$
$683$	−9.95564	+	24.0350i	−0.380942	+	0.919675i	−0.991784	+	0.127923i	$0.959169\pi$
$684$		0			0
$685$	5.58209	−	2.31218i	0.213281	−	0.0883438i
$686$		0			0
$687$		−	2.07540i		−	0.0791816i
$688$		0			0
$689$			25.5186i			0.972182i
$690$		0			0
$691$	−38.8924	+	16.1098i	−1.47954	+	0.612844i	−0.969011	−	0.247019i	$-0.920549\pi$
$691$	−38.8924	+	16.1098i	−1.47954	+	0.612844i	−0.510525	+	0.859863i	$0.670549\pi$
$692$		0			0
$693$	2.34931	−	5.67173i	0.0892427	−	0.215451i
$694$		0			0
$695$	−12.4491	+	12.4491i	−0.472221	+	0.472221i
$696$		0			0
$697$	5.33800	+	5.33800i	0.202191	+	0.202191i
$698$		0			0
$699$	−8.45054	−	3.50033i	−0.319629	−	0.132395i
$700$		0			0
$701$	−17.1972	−	41.5176i	−0.649528	−	1.56810i	−0.813456	−	0.581626i	$-0.802417\pi$
$701$	−17.1972	−	41.5176i	−0.649528	−	1.56810i	0.163929	−	0.986472i	$-0.447583\pi$
$702$		0			0
$703$	−16.2979			−0.614687
$704$		0			0
$705$	14.0897			0.530648
$706$		0			0
$707$	−4.52526	−	10.9249i	−0.170190	−	0.410875i
$708$		0			0
$709$	−32.3176	−	13.3864i	−1.21371	−	0.502736i	−0.318306	−	0.947988i	$-0.603114\pi$
$709$	−32.3176	−	13.3864i	−1.21371	−	0.502736i	−0.895405	+	0.445252i	$0.853114\pi$
$710$		0			0
$711$	11.5632	+	11.5632i	0.433653	+	0.433653i
$712$		0			0
$713$	−43.3001	+	43.3001i	−1.62160	+	1.62160i
$714$		0			0
$715$	−10.8429	+	26.1772i	−0.405503	+	0.978970i
$716$		0			0
$717$	−24.8247	+	10.2827i	−0.927097	+	0.384016i
$718$		0			0
$719$		−	8.83327i		−	0.329426i	−0.986342	−	0.164713i	$-0.947330\pi$
$719$		−	8.83327i		−	0.329426i	0.986342	−	0.164713i	$-0.0526697\pi$
$720$		0			0
$721$		−	0.812451i		−	0.0302573i
$722$		0			0
$723$	2.24267	−	0.928946i	0.0834059	−	0.0345479i
$724$		0			0
$725$	−30.0349	+	72.5108i	−1.11547	+	2.69298i
$726$		0			0
$727$	−10.6261	+	10.6261i	−0.394099	+	0.394099i	−0.876146	−	0.482046i	$-0.839894\pi$
$727$	−10.6261	+	10.6261i	−0.394099	+	0.394099i	0.482046	+	0.876146i	$0.339894\pi$
$728$		0			0
$729$	13.1361	+	13.1361i	0.486522	+	0.486522i
$730$		0			0
$731$	−12.6057	−	5.22146i	−0.466239	−	0.193123i
$732$		0			0
$733$	−6.91692	−	16.6989i	−0.255482	−	0.616789i	0.743147	−	0.669128i	$-0.233332\pi$
$733$	−6.91692	−	16.6989i	−0.255482	−	0.616789i	−0.998629	+	0.0523392i	$0.983332\pi$
$734$		0			0
$735$	4.44471			0.163946
$736$		0			0
$737$	2.85875			0.105304
$738$		0			0
$739$	−9.07991	−	21.9208i	−0.334010	−	0.806371i	−0.998266	−	0.0588659i	$-0.981252\pi$
$739$	−9.07991	−	21.9208i	−0.334010	−	0.806371i	0.664256	−	0.747505i	$-0.268748\pi$
$740$		0			0
$741$	4.64956	+	1.92591i	0.170806	+	0.0707502i
$742$		0			0
$743$	19.1248	+	19.1248i	0.701621	+	0.701621i	0.964758	−	0.263137i	$-0.0847572\pi$
$743$	19.1248	+	19.1248i	0.701621	+	0.701621i	−0.263137	+	0.964758i	$0.584757\pi$
$744$		0			0
$745$	11.9795	−	11.9795i	0.438894	−	0.438894i
$746$		0			0
$747$	−3.63163	+	8.76753i	−0.132874	+	0.320787i
$748$		0			0
$749$	2.23963	−	0.927686i	0.0818344	−	0.0338969i
$750$		0			0
$751$			25.3046i			0.923380i	0.887041	+	0.461690i	$0.152757\pi$
$751$			25.3046i			0.923380i	−0.887041	+	0.461690i	$0.847243\pi$
$752$		0			0
$753$			12.0782i			0.440153i
$754$		0			0
$755$	−75.4352	+	31.2463i	−2.74537	+	1.13717i
$756$		0			0
$757$	3.78355	−	9.13430i	0.137516	−	0.331992i	−0.840087	−	0.542452i	$-0.817496\pi$
$757$	3.78355	−	9.13430i	0.137516	−	0.331992i	0.977602	+	0.210460i	$0.0674961\pi$
$758$		0			0
$759$	19.5631	−	19.5631i	0.710097	−	0.710097i
$760$		0			0
$761$	−28.0212	−	28.0212i	−1.01577	−	1.01577i	−0.999874	−	0.0158923i	$-0.994941\pi$
$761$	−28.0212	−	28.0212i	−1.01577	−	1.01577i	−0.0158923	−	0.999874i	$-0.505059\pi$
$762$		0			0
$763$	4.13881	+	1.71435i	0.149835	+	0.0620636i
$764$		0			0
$765$	−10.8529	−	26.2011i	−0.392386	−	0.947303i
$766$		0			0
$767$	5.29249			0.191101
$768$		0			0
$769$	6.76588			0.243984			0.121992	−	0.992531i	$-0.461072\pi$
$769$	6.76588			0.243984			0.121992	+	0.992531i	$0.461072\pi$
$770$		0			0
$771$	10.4887	+	25.3221i	0.377743	+	0.911952i
$772$		0			0
$773$	28.0963	+	11.6379i	1.01055	+	0.418585i	0.825657	−	0.564173i	$-0.190805\pi$
$773$	28.0963	+	11.6379i	1.01055	+	0.418585i	0.184897	+	0.982758i	$0.440805\pi$
$774$		0			0
$775$	66.5986	+	66.5986i	2.39229	+	2.39229i
$776$		0			0
$777$	−5.73959	+	5.73959i	−0.205907	+	0.205907i
$778$		0			0
$779$	−1.60952	+	3.88572i	−0.0576669	+	0.139220i
$780$		0			0
$781$	28.1717	−	11.6691i	1.00806	−	0.417554i
$782$		0			0
$783$		−	37.5120i		−	1.34057i
$784$		0			0
$785$			36.9491i			1.31877i
$786$		0			0
$787$	13.6911	−	5.67103i	0.488034	−	0.202150i	−0.125077	−	0.992147i	$-0.539918\pi$
$787$	13.6911	−	5.67103i	0.488034	−	0.202150i	0.613111	+	0.789997i	$0.289918\pi$
$788$		0			0
$789$	1.87843	−	4.53493i	0.0668739	−	0.161448i
$790$		0			0
$791$	−0.0907278	+	0.0907278i	−0.00322591	+	0.00322591i
$792$		0			0
$793$	14.5309	+	14.5309i	0.516008	+	0.516008i
$794$		0			0
$795$	−51.4037	−	21.2921i	−1.82310	−	0.755153i
$796$		0			0
$797$	−0.393333	−	0.949589i	−0.0139326	−	0.0336362i	0.916760	−	0.399438i	$-0.130795\pi$
$797$	−0.393333	−	0.949589i	−0.0139326	−	0.0336362i	−0.930693	+	0.365802i	$0.880795\pi$
$798$		0			0
$799$	12.6678			0.448153
$800$		0			0
$801$	22.8355			0.806852
$802$		0			0
$803$	3.92372	+	9.47269i	0.138465	+	0.334284i
$804$		0			0
$805$	−26.6478	−	11.0379i	−0.939210	−	0.389034i
$806$		0			0
$807$	16.1407	+	16.1407i	0.568179	+	0.568179i
$808$		0			0
$809$	21.5861	−	21.5861i	0.758926	−	0.758926i	−0.217201	−	0.976127i	$-0.569693\pi$
$809$	21.5861	−	21.5861i	0.758926	−	0.758926i	0.976127	+	0.217201i	$0.0696927\pi$
$810$		0			0
$811$	0.128421	−	0.310037i	0.00450948	−	0.0108869i	−0.921609	−	0.388120i	$-0.873125\pi$
$811$	0.128421	−	0.310037i	0.00450948	−	0.0108869i	0.926118	+	0.377233i	$0.123125\pi$
$812$		0			0
$813$	−6.51737	+	2.69958i	−0.228574	+	0.0946786i
$814$		0			0
$815$			39.3616i			1.37878i
$816$		0			0
$817$		−	7.60177i		−	0.265952i
$818$		0			0
$819$	−3.33446	+	1.38118i	−0.116515	+	0.0482622i
$820$		0			0
$821$	11.6283	−	28.0731i	0.405829	−	0.979758i	−0.580394	−	0.814336i	$-0.697101\pi$
$821$	11.6283	−	28.0731i	0.405829	−	0.979758i	0.986223	−	0.165422i	$-0.0528986\pi$
$822$		0			0
$823$	−11.4890	+	11.4890i	−0.400482	+	0.400482i	−0.878403	−	0.477921i	$-0.841391\pi$
$823$	−11.4890	+	11.4890i	−0.400482	+	0.400482i	0.477921	+	0.878403i	$0.341391\pi$
$824$		0			0
$825$	−30.0895	−	30.0895i	−1.04758	−	1.04758i
$826$		0			0
$827$	−22.7523	−	9.42431i	−0.791175	−	0.327715i	−0.0497589	−	0.998761i	$-0.515845\pi$
$827$	−22.7523	−	9.42431i	−0.791175	−	0.327715i	−0.741416	+	0.671046i	$0.765845\pi$
$828$		0			0
$829$	13.0923	+	31.6076i	0.454714	+	1.09778i	0.970509	+	0.241065i	$0.0774966\pi$
$829$	13.0923	+	31.6076i	0.454714	+	1.09778i	−0.515795	+	0.856712i	$0.672503\pi$
$830$		0			0
$831$	2.23104			0.0773941
$832$		0			0
$833$	3.99616			0.138459
$834$		0			0
$835$	−12.4772	−	30.1226i	−0.431790	−	1.04243i
$836$		0			0
$837$	−41.5890	−	17.2267i	−1.43753	−	0.595443i
$838$		0			0
$839$	12.2520	+	12.2520i	0.422984	+	0.422984i	0.886230	−	0.463246i	$-0.153315\pi$
$839$	12.2520	+	12.2520i	0.422984	+	0.422984i	−0.463246	+	0.886230i	$0.653315\pi$
$840$		0			0
$841$	−15.0540	+	15.0540i	−0.519103	+	0.519103i
$842$		0			0
$843$	10.0005	−	24.1434i	0.344437	−	0.831544i
$844$		0			0
$845$	−32.7531	+	13.5668i	−1.12674	+	0.466712i
$846$		0			0
$847$		−	1.02329i		−	0.0351607i
$848$		0			0
$849$			6.40902i			0.219957i
$850$		0			0
$851$	48.6646	−	20.1575i	1.66820	−	0.690992i
$852$		0			0
$853$	8.77174	−	21.1769i	0.300339	−	0.725082i	−0.699606	−	0.714529i	$-0.746641\pi$
$853$	8.77174	−	21.1769i	0.300339	−	0.725082i	0.999944	−	0.0105525i	$-0.00335903\pi$
$854$		0			0
$855$	11.1725	−	11.1725i	0.382093	−	0.382093i
$856$		0			0
$857$	−13.5063	−	13.5063i	−0.461368	−	0.461368i	0.437736	−	0.899104i	$-0.355781\pi$
$857$	−13.5063	−	13.5063i	−0.461368	−	0.461368i	−0.899104	+	0.437736i	$0.855781\pi$
$858$		0			0
$859$	36.2180	+	15.0020i	1.23574	+	0.511861i	0.902381	−	0.430938i	$-0.141817\pi$
$859$	36.2180	+	15.0020i	1.23574	+	0.511861i	0.333361	+	0.942799i	$0.391817\pi$
$860$		0			0
$861$	0.801605	+	1.93524i	0.0273186	+	0.0659530i
$862$		0			0
$863$	21.7052			0.738852			0.369426	−	0.929260i	$-0.379554\pi$
$863$	21.7052			0.738852			0.369426	+	0.929260i	$0.379554\pi$
$864$		0			0
$865$	−69.9544			−2.37852
$866$		0			0
$867$	−0.437375	−	1.05592i	−0.0148540	−	0.0358608i
$868$		0			0
$869$	29.5891	+	12.2562i	1.00374	+	0.415763i
$870$		0			0
$871$	−1.18842	−	1.18842i	−0.0402682	−	0.0402682i
$872$		0			0
$873$	−12.2273	+	12.2273i	−0.413832	+	0.413832i
$874$		0			0
$875$	−9.30724	+	22.4697i	−0.314642	+	0.759613i
$876$		0			0
$877$	−6.12246	+	2.53600i	−0.206741	+	0.0856348i	−0.483651	−	0.875261i	$-0.660690\pi$
$877$	−6.12246	+	2.53600i	−0.206741	+	0.0856348i	0.276910	+	0.960896i	$0.410690\pi$
$878$		0			0
$879$		−	14.6411i		−	0.493833i
$880$		0			0
$881$		−	30.4993i		−	1.02755i	−0.857926	−	0.513773i	$-0.828247\pi$
$881$		−	30.4993i		−	1.02755i	0.857926	−	0.513773i	$-0.171753\pi$
$882$		0			0
$883$	31.8467	−	13.1913i	1.07173	−	0.443924i	0.224127	−	0.974560i	$-0.428047\pi$
$883$	31.8467	−	13.1913i	1.07173	−	0.443924i	0.847600	+	0.530636i	$0.178047\pi$
$884$		0			0
$885$	−4.41593	+	10.6610i	−0.148440	+	0.358365i
$886$		0			0
$887$	−17.0240	+	17.0240i	−0.571610	+	0.571610i	−0.932578	−	0.360968i	$-0.882446\pi$
$887$	−17.0240	+	17.0240i	−0.571610	+	0.571610i	0.360968	+	0.932578i	$0.382446\pi$
$888$		0			0
$889$	4.87214	+	4.87214i	0.163406	+	0.163406i
$890$		0			0
$891$	1.77487	+	0.735174i	0.0594603	+	0.0246292i
$892$		0			0
$893$	2.70086	+	6.52046i	0.0903809	+	0.218199i
$894$		0			0
$895$	62.1194			2.07642
$896$		0			0
$897$	−16.2653			−0.543084
$898$		0			0
$899$	23.0946	+	55.7553i	0.770248	+	1.85954i
$900$		0			0
$901$	−46.2161	−	19.1433i	−1.53968	−	0.637757i
$902$		0			0
$903$	−2.67710	−	2.67710i	−0.0890883	−	0.0890883i
$904$		0			0
$905$	−60.8138	+	60.8138i	−2.02152	+	2.02152i
$906$		0			0
$907$	−0.156780	+	0.378501i	−0.00520580	+	0.0125679i	−0.926461	−	0.376391i	$-0.877165\pi$
$907$	−0.156780	+	0.378501i	−0.00520580	+	0.0125679i	0.921255	+	0.388959i	$0.127165\pi$
$908$		0			0
$909$	−19.3423	+	8.01183i	−0.641543	+	0.265736i
$910$		0			0
$911$			48.2167i			1.59749i	0.601669	+	0.798745i	$0.294503\pi$
$911$			48.2167i			1.59749i	−0.601669	+	0.798745i	$0.705497\pi$
$912$		0			0
$913$			18.5860i			0.615106i
$914$		0			0
$915$	−41.3947	+	17.1463i	−1.36847	+	0.566838i
$916$		0			0
$917$	0.879601	−	2.12354i	0.0290470	−	0.0701256i
$918$		0			0
$919$	−20.5977	+	20.5977i	−0.679454	+	0.679454i	−0.959877	−	0.280423i	$-0.909525\pi$
$919$	−20.5977	+	20.5977i	−0.679454	+	0.679454i	0.280423	+	0.959877i	$0.409525\pi$
$920$		0			0
$921$	6.79985	+	6.79985i	0.224063	+	0.224063i
$922$		0			0
$923$	−16.5624	−	6.86038i	−0.545159	−	0.225812i
$924$		0			0
$925$	−31.0037	−	74.8497i	−1.01940	−	2.46104i
$926$		0			0
$927$	−1.43842			−0.0472439
$928$		0			0
$929$	47.7474			1.56654			0.783271	−	0.621681i	$-0.213550\pi$
$929$	47.7474			1.56654			0.783271	+	0.621681i	$0.213550\pi$
$930$		0			0
$931$	0.852011	+	2.05694i	0.0279235	+	0.0674133i
$932$		0			0
$933$	30.9353	+	12.8138i	1.01278	+	0.419506i
$934$		0			0
$935$	−39.2747	−	39.2747i	−1.28442	−	1.28442i
$936$		0			0
$937$	19.5686	−	19.5686i	0.639279	−	0.639279i	−0.311099	−	0.950378i	$-0.600697\pi$
$937$	19.5686	−	19.5686i	0.639279	−	0.639279i	0.950378	+	0.311099i	$0.100697\pi$
$938$		0			0
$939$	−4.03925	+	9.75160i	−0.131816	+	0.318231i
$940$		0			0
$941$	38.4802	−	15.9390i	1.25442	−	0.519598i	0.346227	−	0.938151i	$-0.387463\pi$
$941$	38.4802	−	15.9390i	1.25442	−	0.519598i	0.908192	+	0.418553i	$0.137463\pi$
$942$		0			0
$943$		−	13.5932i		−	0.442656i
$944$		0			0
$945$		−	21.2034i		−	0.689745i
$946$		0			0
$947$	−4.44575	+	1.84149i	−0.144467	+	0.0598404i	−0.453746	−	0.891131i	$-0.649913\pi$
$947$	−4.44575	+	1.84149i	−0.144467	+	0.0598404i	0.309278	+	0.950972i	$0.399913\pi$
$948$		0			0
$949$	2.30679	−	5.56908i	0.0748815	−	0.180780i
$950$		0			0
$951$	0.155887	−	0.155887i	0.00505500	−	0.00505500i
$952$		0			0
$953$	16.5975	+	16.5975i	0.537645	+	0.537645i	0.922837	−	0.385192i	$-0.125865\pi$
$953$	16.5975	+	16.5975i	0.537645	+	0.537645i	−0.385192	+	0.922837i	$0.625865\pi$
$954$		0			0
$955$	−37.8309	−	15.6701i	−1.22418	−	0.507072i
$956$		0			0
$957$	−10.4342	−	25.1904i	−0.337291	−	0.814291i
$958$		0			0
$959$	1.50733			0.0486742
$960$		0			0
$961$	41.4209			1.33616
$962$		0			0
$963$	−1.64244	−	3.96520i	−0.0529268	−	0.127777i
$964$		0			0
$965$	4.94984	+	2.05029i	0.159341	+	0.0660013i
$966$		0			0
$967$	−26.8258	−	26.8258i	−0.862659	−	0.862659i	0.128987	−	0.991646i	$-0.458827\pi$
$967$	−26.8258	−	26.8258i	−0.862659	−	0.862659i	−0.991646	+	0.128987i	$0.958827\pi$
$968$		0			0
$969$	−6.97594	+	6.97594i	−0.224099	+	0.224099i
$970$		0			0
$971$	−5.46841	+	13.2019i	−0.175490	+	0.423670i	−0.987011	−	0.160653i	$-0.948640\pi$
$971$	−5.46841	+	13.2019i	−0.175490	+	0.423670i	0.811521	+	0.584323i	$0.198640\pi$
$972$		0			0
$973$	−4.05783	+	1.68081i	−0.130088	+	0.0538843i
$974$		0			0
$975$			25.0173i			0.801194i
$976$		0			0
$977$		−	4.18523i		−	0.133897i	−0.997756	−	0.0669487i	$-0.978674\pi$
$977$		−	4.18523i		−	0.133897i	0.997756	−	0.0669487i	$-0.0213264\pi$
$978$		0			0
$979$	41.3189	−	17.1149i	1.32056	−	0.546993i
$980$		0			0
$981$	3.03520	−	7.32763i	0.0969065	−	0.233953i
$982$		0			0
$983$	17.4458	−	17.4458i	0.556435	−	0.556435i	−0.371856	−	0.928291i	$-0.621278\pi$
$983$	17.4458	−	17.4458i	0.556435	−	0.556435i	0.928291	+	0.371856i	$0.121278\pi$
$984$		0			0
$985$	−14.7800	−	14.7800i	−0.470929	−	0.470929i
$986$		0			0
$987$	3.24745	+	1.34514i	0.103368	+	0.0428162i
$988$		0			0
$989$	9.40202	+	22.6985i	0.298967	+	0.721770i
$990$		0			0
$991$	25.9523			0.824401			0.412201	−	0.911093i	$-0.364760\pi$
$991$	25.9523			0.824401			0.412201	+	0.911093i	$0.364760\pi$
$992$		0			0
$993$	−9.33822			−0.296339
$994$		0			0
$995$	−31.8640	−	76.9265i	−1.01016	−	2.43873i
$996$		0			0
$997$	21.1077	+	8.74308i	0.668486	+	0.276896i	0.691005	−	0.722850i	$-0.257168\pi$
$997$	21.1077	+	8.74308i	0.668486	+	0.276896i	−0.0225183	+	0.999746i	$0.507168\pi$
$998$		0			0
$999$	27.3805	+	27.3805i	0.866282	+	0.866282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.u.c.113.5		52
4.3	odd	2		224.2.u.c.197.1	yes	52
32.13	even	8	inner	896.2.u.c.785.5		52
32.19	odd	8		224.2.u.c.141.1	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.141.1	✓	52	32.19	odd	8
224.2.u.c.197.1	yes	52	4.3	odd	2
896.2.u.c.113.5		52	1.1	even	1	trivial
896.2.u.c.785.5		52	32.13	even	8	inner

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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.u (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.424336 - 1.02444i) q^{3} +(3.70330 + 1.53396i) q^{5} +(0.707107 + 0.707107i) q^{7} +(1.25191 - 1.25191i) q^{9} +O(q^{10})\)	\(q+(-0.424336 - 1.02444i) q^{3} +(3.70330 + 1.53396i) q^{5} +(0.707107 + 0.707107i) q^{7} +(1.25191 - 1.25191i) q^{9} +(1.32694 - 3.20352i) q^{11} +(-1.88338 + 0.780120i) q^{13} -4.44471i q^{15} -3.99616i q^{17} +(2.05694 - 0.852011i) q^{19} +(0.424336 - 1.02444i) q^{21} +(-5.08811 + 5.08811i) q^{23} +(7.82588 + 7.82588i) q^{25} +(-4.88704 - 2.02428i) q^{27} +(2.71380 + 6.55170i) q^{29} +8.51005 q^{31} -3.84487 q^{33} +(1.53396 + 3.70330i) q^{35} +(-6.76303 - 2.80134i) q^{37} +(1.59837 + 1.59837i) q^{39} +(-1.33578 + 1.33578i) q^{41} +(1.30662 - 3.15446i) q^{43} +(6.55658 - 2.71582i) q^{45} +3.16999i q^{47} +1.00000i q^{49} +(-4.09381 + 1.69571i) q^{51} +(4.79044 - 11.5651i) q^{53} +(9.82812 - 9.82812i) q^{55} +(-1.74566 - 1.74566i) q^{57} +(-2.39858 - 0.993524i) q^{59} +(-3.85768 - 9.31326i) q^{61} +1.77047 q^{63} -8.17138 q^{65} +(0.315504 + 0.761694i) q^{67} +(7.37152 + 3.05338i) q^{69} +(6.21830 + 6.21830i) q^{71} +(-2.09089 + 2.09089i) q^{73} +(4.69632 - 11.3379i) q^{75} +(3.20352 - 1.32694i) q^{77} +9.23644i q^{79} +0.554037i q^{81} +(-4.95210 + 2.05123i) q^{83} +(6.12994 - 14.7990i) q^{85} +(5.56024 - 5.56024i) q^{87} +(9.12026 + 9.12026i) q^{89} +(-1.88338 - 0.780120i) q^{91} +(-3.61112 - 8.71801i) q^{93} +8.92440 q^{95} -9.76692 q^{97} +(-2.34931 - 5.67173i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q+O(q^{10}) \) 52 * q	\( 52 q + 20 q^{23} + 24 q^{27} - 48 q^{33} + 24 q^{39} + 44 q^{43} + 40 q^{45} - 16 q^{51} - 36 q^{53} - 32 q^{55} - 32 q^{61} - 68 q^{63} + 80 q^{65} - 28 q^{67} - 32 q^{69} - 32 q^{75} - 12 q^{77} + 64 q^{85} + 56 q^{87} + 64 q^{95} - 72 q^{97} + 64 q^{99}+O(q^{100}) \) 52 * q + 20 * q^23 + 24 * q^27 - 48 * q^33 + 24 * q^39 + 44 * q^43 + 40 * q^45 - 16 * q^51 - 36 * q^53 - 32 * q^55 - 32 * q^61 - 68 * q^63 + 80 * q^65 - 28 * q^67 - 32 * q^69 - 32 * q^75 - 12 * q^77 + 64 * q^85 + 56 * q^87 + 64 * q^95 - 72 * q^97 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

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