LMFDB - Embedded newform 725.2.j.c.307.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(307,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("725.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.j (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:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.13
Character	$\chi$	$=$	725.307
Dual form			725.2.j.c.418.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.73482 q^{2} +1.63186i q^{3} +5.47925 q^{4} +4.46285i q^{6} +(-1.05887 - 1.05887i) q^{7} +9.51511 q^{8} +0.337028 q^{9} +O(q^{10})$	\(q+2.73482 q^{2} +1.63186i q^{3} +5.47925 q^{4} +4.46285i q^{6} +(-1.05887 - 1.05887i) q^{7} +9.51511 q^{8} +0.337028 q^{9} +(1.15733 - 1.15733i) q^{11} +8.94137i q^{12} +(-1.53095 - 1.53095i) q^{13} +(-2.89582 - 2.89582i) q^{14} +15.0636 q^{16} -7.16970 q^{17} +0.921711 q^{18} +(-1.87609 - 1.87609i) q^{19} +(1.72793 - 1.72793i) q^{21} +(3.16509 - 3.16509i) q^{22} +(-4.16994 + 4.16994i) q^{23} +15.5273i q^{24} +(-4.18686 - 4.18686i) q^{26} +5.44557i q^{27} +(-5.80180 - 5.80180i) q^{28} +(-1.03600 + 5.28457i) q^{29} +(-0.504388 + 0.504388i) q^{31} +22.1661 q^{32} +(1.88860 + 1.88860i) q^{33} -19.6078 q^{34} +1.84666 q^{36} -4.74574i q^{37} +(-5.13076 - 5.13076i) q^{38} +(2.49829 - 2.49829i) q^{39} +(2.38277 + 2.38277i) q^{41} +(4.72557 - 4.72557i) q^{42} -8.05942i q^{43} +(6.34129 - 6.34129i) q^{44} +(-11.4040 + 11.4040i) q^{46} +1.86671i q^{47} +24.5818i q^{48} -4.75760i q^{49} -11.7000i q^{51} +(-8.38843 - 8.38843i) q^{52} +(5.39552 - 5.39552i) q^{53} +14.8927i q^{54} +(-10.0753 - 10.0753i) q^{56} +(3.06152 - 3.06152i) q^{57} +(-2.83326 + 14.4524i) q^{58} +3.57926i q^{59} +(-0.867739 + 0.867739i) q^{61} +(-1.37941 + 1.37941i) q^{62} +(-0.356868 - 0.356868i) q^{63} +30.4931 q^{64} +(5.16498 + 5.16498i) q^{66} +(-7.09185 + 7.09185i) q^{67} -39.2845 q^{68} +(-6.80476 - 6.80476i) q^{69} -3.30380i q^{71} +3.20686 q^{72} +11.7385 q^{73} -12.9787i q^{74} +(-10.2795 - 10.2795i) q^{76} -2.45092 q^{77} +(6.83238 - 6.83238i) q^{78} +(2.01731 + 2.01731i) q^{79} -7.87533 q^{81} +(6.51644 + 6.51644i) q^{82} +(5.28177 - 5.28177i) q^{83} +(9.46773 - 9.46773i) q^{84} -22.0411i q^{86} +(-8.62369 - 1.69060i) q^{87} +(11.0121 - 11.0121i) q^{88} +(-10.1661 - 10.1661i) q^{89} +3.24214i q^{91} +(-22.8481 + 22.8481i) q^{92} +(-0.823091 - 0.823091i) q^{93} +5.10511i q^{94} +36.1721i q^{96} +6.05786i q^{97} -13.0112i q^{98} +(0.390052 - 0.390052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 6 q^{2} + 22 q^{4} + 4 q^{7} + 18 q^{8} - 10 q^{9}+O(q^{10}) $ 26 * q + 6 * q^2 + 22 * q^4 + 4 * q^7 + 18 * q^8 - 10 * q^9	$ 26 q + 6 q^{2} + 22 q^{4} + 4 q^{7} + 18 q^{8} - 10 q^{9} - 8 q^{11} - 14 q^{13} - 4 q^{14} + 6 q^{16} - 20 q^{17} + 18 q^{18} + 16 q^{21} + 8 q^{22} + 4 q^{23} + 6 q^{26} + 8 q^{28} + 8 q^{31} + 42 q^{32} - 32 q^{34} - 22 q^{36} + 8 q^{38} - 16 q^{39} - 6 q^{41} + 4 q^{42} - 32 q^{46} - 26 q^{52} - 14 q^{53} - 32 q^{56} + 12 q^{57} - 28 q^{58} + 18 q^{61} - 28 q^{62} - 60 q^{63} + 30 q^{64} + 20 q^{66} - 32 q^{67} - 72 q^{68} + 12 q^{69} - 10 q^{72} + 4 q^{73} + 20 q^{76} + 12 q^{77} - 56 q^{78} + 4 q^{79} - 86 q^{81} + 58 q^{82} + 60 q^{83} + 76 q^{84} - 60 q^{87} + 68 q^{88} - 46 q^{89} + 28 q^{92} + 8 q^{93} + 36 q^{99}+O(q^{100}) $ 26 * q + 6 * q^2 + 22 * q^4 + 4 * q^7 + 18 * q^8 - 10 * q^9 - 8 * q^11 - 14 * q^13 - 4 * q^14 + 6 * q^16 - 20 * q^17 + 18 * q^18 + 16 * q^21 + 8 * q^22 + 4 * q^23 + 6 * q^26 + 8 * q^28 + 8 * q^31 + 42 * q^32 - 32 * q^34 - 22 * q^36 + 8 * q^38 - 16 * q^39 - 6 * q^41 + 4 * q^42 - 32 * q^46 - 26 * q^52 - 14 * q^53 - 32 * q^56 + 12 * q^57 - 28 * q^58 + 18 * q^61 - 28 * q^62 - 60 * q^63 + 30 * q^64 + 20 * q^66 - 32 * q^67 - 72 * q^68 + 12 * q^69 - 10 * q^72 + 4 * q^73 + 20 * q^76 + 12 * q^77 - 56 * q^78 + 4 * q^79 - 86 * q^81 + 58 * q^82 + 60 * q^83 + 76 * q^84 - 60 * q^87 + 68 * q^88 - 46 * q^89 + 28 * q^92 + 8 * q^93 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.73482			1.93381			0.966905	−	0.255136i	$-0.0821202\pi$
$2$	2.73482			1.93381			0.966905	+	0.255136i	$0.0821202\pi$
$3$			1.63186i			0.942156i	0.882092	+	0.471078i	$0.156135\pi$
$3$			1.63186i			0.942156i	−0.882092	+	0.471078i	$0.843865\pi$
$4$	5.47925			2.73962
$5$		0			0
$5$		0			0
$6$			4.46285i			1.82195i
$7$	−1.05887	−	1.05887i	−0.400215	−	0.400215i	0.478094	−	0.878309i	$-0.341328\pi$
$7$	−1.05887	−	1.05887i	−0.400215	−	0.400215i	−0.878309	+	0.478094i	$0.841328\pi$
$8$	9.51511			3.36410
$9$	0.337028			0.112343
$10$		0			0
$11$	1.15733	−	1.15733i	0.348948	−	0.348948i	−0.510770	−	0.859717i	$-0.670640\pi$
$11$	1.15733	−	1.15733i	0.348948	−	0.348948i	0.859717	+	0.510770i	$0.170640\pi$
$12$			8.94137i			2.58115i
$13$	−1.53095	−	1.53095i	−0.424608	−	0.424608i	0.462179	−	0.886787i	$-0.347068\pi$
$13$	−1.53095	−	1.53095i	−0.424608	−	0.424608i	−0.886787	+	0.462179i	$0.847068\pi$
$14$	−2.89582	−	2.89582i	−0.773939	−	0.773939i
$15$		0			0
$16$	15.0636			3.76591
$17$	−7.16970			−1.73891			−0.869453	−	0.494015i	$-0.835529\pi$
$17$	−7.16970			−1.73891			−0.869453	+	0.494015i	$0.835529\pi$
$18$	0.921711			0.217249
$19$	−1.87609	−	1.87609i	−0.430404	−	0.430404i	0.458362	−	0.888766i	$-0.348436\pi$
$19$	−1.87609	−	1.87609i	−0.430404	−	0.430404i	−0.888766	+	0.458362i	$0.848436\pi$
$20$		0			0
$21$	1.72793	−	1.72793i	0.377064	−	0.377064i
$22$	3.16509	−	3.16509i	0.674799	−	0.674799i
$23$	−4.16994	+	4.16994i	−0.869492	+	0.869492i	−0.992416	−	0.122924i	$-0.960773\pi$
$23$	−4.16994	+	4.16994i	−0.869492	+	0.869492i	0.122924	+	0.992416i	$0.460773\pi$
$24$			15.5273i			3.16951i
$25$		0			0
$26$	−4.18686	−	4.18686i	−0.821111	−	0.821111i
$27$			5.44557i			1.04800i
$28$	−5.80180	−	5.80180i	−1.09644	−	1.09644i
$29$	−1.03600	+	5.28457i	−0.192380	+	0.981321i
$29$	−1.03600	+	5.28457i	−0.192380	+	0.981321i
$30$		0			0
$31$	−0.504388	+	0.504388i	−0.0905907	+	0.0905907i	−0.750950	−	0.660359i	$-0.770404\pi$
$31$	−0.504388	+	0.504388i	−0.0905907	+	0.0905907i	0.660359	+	0.750950i	$0.270404\pi$
$32$	22.1661			3.91846
$33$	1.88860	+	1.88860i	0.328763	+	0.328763i
$34$	−19.6078			−3.36272
$35$		0			0
$36$	1.84666			0.307777
$37$		−	4.74574i		−	0.780194i	−0.920774	−	0.390097i	$-0.872441\pi$
$37$		−	4.74574i		−	0.780194i	0.920774	−	0.390097i	$-0.127559\pi$
$38$	−5.13076	−	5.13076i	−0.832320	−	0.832320i
$39$	2.49829	−	2.49829i	0.400047	−	0.400047i
$40$		0			0
$41$	2.38277	+	2.38277i	0.372126	+	0.372126i	0.868251	−	0.496125i	$-0.165244\pi$
$41$	2.38277	+	2.38277i	0.372126	+	0.372126i	−0.496125	+	0.868251i	$0.665244\pi$
$42$	4.72557	−	4.72557i	0.729171	−	0.729171i
$43$		−	8.05942i		−	1.22905i	−0.788897	−	0.614525i	$-0.789348\pi$
$43$		−	8.05942i		−	1.22905i	0.788897	−	0.614525i	$-0.210652\pi$
$44$	6.34129	−	6.34129i	0.955985	−	0.955985i
$45$		0			0
$46$	−11.4040	+	11.4040i	−1.68143	+	1.68143i
$47$			1.86671i			0.272287i	0.990689	+	0.136144i	$0.0434709\pi$
$47$			1.86671i			0.272287i	−0.990689	+	0.136144i	$0.956529\pi$
$48$			24.5818i			3.54807i
$49$		−	4.75760i		−	0.679657i
$50$		0			0
$51$		−	11.7000i		−	1.63832i
$52$	−8.38843	−	8.38843i	−1.16327	−	1.16327i
$53$	5.39552	−	5.39552i	0.741132	−	0.741132i	−0.231664	−	0.972796i	$-0.574417\pi$
$53$	5.39552	−	5.39552i	0.741132	−	0.741132i	0.972796	+	0.231664i	$0.0744169\pi$
$54$			14.8927i			2.02663i
$55$		0			0
$56$	−10.0753	−	10.0753i	−1.34636	−	1.34636i
$57$	3.06152	−	3.06152i	0.405508	−	0.405508i
$58$	−2.83326	+	14.4524i	−0.372026	+	1.89769i
$59$			3.57926i			0.465979i	0.972479	+	0.232990i	$0.0748509\pi$
$59$			3.57926i			0.465979i	−0.972479	+	0.232990i	$0.925149\pi$
$60$		0			0
$61$	−0.867739	+	0.867739i	−0.111103	+	0.111103i	−0.760473	−	0.649370i	$-0.775033\pi$
$61$	−0.867739	+	0.867739i	−0.111103	+	0.111103i	0.649370	+	0.760473i	$0.275033\pi$
$62$	−1.37941	+	1.37941i	−0.175185	+	0.175185i
$63$	−0.356868	−	0.356868i	−0.0449612	−	0.0449612i
$64$	30.4931			3.81164
$65$		0			0
$66$	5.16498	+	5.16498i	0.635765	+	0.635765i
$67$	−7.09185	+	7.09185i	−0.866408	+	0.866408i	−0.992073	−	0.125665i	$-0.959894\pi$
$67$	−7.09185	+	7.09185i	−0.866408	+	0.866408i	0.125665	+	0.992073i	$0.459894\pi$
$68$	−39.2845			−4.76395
$69$	−6.80476	−	6.80476i	−0.819197	−	0.819197i
$70$		0			0
$71$		−	3.30380i		−	0.392089i	−0.980595	−	0.196044i	$-0.937190\pi$
$71$		−	3.30380i		−	0.392089i	0.980595	−	0.196044i	$-0.0628096\pi$
$72$	3.20686			0.377932
$73$	11.7385			1.37389			0.686946	−	0.726708i	$-0.258951\pi$
$73$	11.7385			1.37389			0.686946	+	0.726708i	$0.258951\pi$
$74$		−	12.9787i		−	1.50875i
$75$		0			0
$76$	−10.2795	−	10.2795i	−1.17914	−	1.17914i
$77$	−2.45092			−0.279308
$78$	6.83238	−	6.83238i	0.773615	−	0.773615i
$79$	2.01731	+	2.01731i	0.226966	+	0.226966i	0.811424	−	0.584458i	$-0.198693\pi$
$79$	2.01731	+	2.01731i	0.226966	+	0.226966i	−0.584458	+	0.811424i	$0.698693\pi$
$80$		0			0
$81$	−7.87533			−0.875036
$82$	6.51644	+	6.51644i	0.719621	+	0.719621i
$83$	5.28177	−	5.28177i	0.579749	−	0.579749i	−0.355085	−	0.934834i	$-0.615548\pi$
$83$	5.28177	−	5.28177i	0.579749	−	0.579749i	0.934834	+	0.355085i	$0.115548\pi$
$84$	9.46773	−	9.46773i	1.03301	−	1.03301i
$85$		0			0
$86$		−	22.0411i		−	2.37675i
$87$	−8.62369	−	1.69060i	−0.924557	−	0.181251i
$88$	11.0121	−	11.0121i	1.17390	−	1.17390i
$89$	−10.1661	−	10.1661i	−1.07760	−	1.07760i	−0.996724	−	0.0808784i	$-0.974227\pi$
$89$	−10.1661	−	10.1661i	−1.07760	−	1.07760i	−0.0808784	−	0.996724i	$-0.525773\pi$
$90$		0			0
$91$			3.24214i			0.339869i
$92$	−22.8481	+	22.8481i	−2.38208	+	2.38208i
$93$	−0.823091	−	0.823091i	−0.0853506	−	0.0853506i
$94$			5.10511i			0.526552i
$95$		0			0
$96$			36.1721i			3.69180i
$97$			6.05786i			0.615082i	0.951535	+	0.307541i	$0.0995062\pi$
$97$			6.05786i			0.615082i	−0.951535	+	0.307541i	$0.900494\pi$
$98$		−	13.0112i		−	1.31433i
$99$	0.390052	−	0.390052i	0.0392017	−	0.0392017i
$100$		0			0
$101$	3.69493	−	3.69493i	0.367659	−	0.367659i	−0.498964	−	0.866623i	$-0.666286\pi$
$101$	3.69493	−	3.69493i	0.367659	−	0.367659i	0.866623	+	0.498964i	$0.166286\pi$
$102$		−	31.9973i		−	3.16820i
$103$	−0.333704	+	0.333704i	−0.0328808	+	0.0328808i	−0.723356	−	0.690475i	$-0.757401\pi$
$103$	−0.333704	+	0.333704i	−0.0328808	+	0.0328808i	0.690475	+	0.723356i	$0.257401\pi$
$104$	−14.5671	−	14.5671i	−1.42842	−	1.42842i
$105$		0			0
$106$	14.7558	−	14.7558i	1.43321	−	1.43321i
$107$	8.38671	+	8.38671i	0.810774	+	0.810774i	0.984750	−	0.173976i	$-0.0556615\pi$
$107$	8.38671	+	8.38671i	0.810774	+	0.810774i	−0.173976	+	0.984750i	$0.555662\pi$
$108$			29.8376i			2.87112i
$109$	−1.22995			−0.117808			−0.0589040	−	0.998264i	$-0.518761\pi$
$109$	−1.22995			−0.117808			−0.0589040	+	0.998264i	$0.518761\pi$
$110$		0			0
$111$	7.74438			0.735064
$112$	−15.9504	−	15.9504i	−1.50717	−	1.50717i
$113$	0.155786			0.0146552			0.00732758	−	0.999973i	$-0.497668\pi$
$113$	0.155786			0.0146552			0.00732758	+	0.999973i	$0.497668\pi$
$114$	8.37270	−	8.37270i	0.784175	−	0.784175i
$115$		0			0
$116$	−5.67647	+	28.9555i	−0.527047	+	2.68845i
$117$	−0.515972	−	0.515972i	−0.0477016	−	0.0477016i
$118$			9.78863i			0.901116i
$119$	7.59176	+	7.59176i	0.695936	+	0.695936i
$120$		0			0
$121$			8.32118i			0.756471i
$122$	−2.37311	+	2.37311i	−0.214851	+	0.214851i
$123$	−3.88835	+	3.88835i	−0.350600	+	0.350600i
$124$	−2.76366	+	2.76366i	−0.248184	+	0.248184i
$125$		0			0
$126$	−0.975971	−	0.975971i	−0.0869464	−	0.0869464i
$127$	18.5247			1.64380			0.821899	−	0.569634i	$-0.192915\pi$
$127$	18.5247			1.64380			0.821899	+	0.569634i	$0.192915\pi$
$128$	39.0610			3.45253
$129$	13.1519			1.15796
$130$		0			0
$131$	4.58794	+	4.58794i	0.400850	+	0.400850i	0.878533	−	0.477682i	$-0.158523\pi$
$131$	4.58794	+	4.58794i	0.400850	+	0.400850i	−0.477682	+	0.878533i	$0.658523\pi$
$132$	10.3481	+	10.3481i	0.900687	+	0.900687i
$133$			3.97306i			0.344508i
$134$	−19.3949	+	19.3949i	−1.67547	+	1.67547i
$135$		0			0
$136$	−68.2205			−5.84986
$137$	2.71664			0.232098			0.116049	−	0.993243i	$-0.462977\pi$
$137$	2.71664			0.232098			0.116049	+	0.993243i	$0.462977\pi$
$138$	−18.6098	−	18.6098i	−1.58417	−	1.58417i
$139$		−	12.0322i		−	1.02056i	−0.860009	−	0.510279i	$-0.829542\pi$
$139$		−	12.0322i		−	1.02056i	0.860009	−	0.510279i	$-0.170458\pi$
$140$		0			0
$141$	−3.04621			−0.256537
$142$		−	9.03529i		−	0.758225i
$143$	−3.54362			−0.296332
$144$	5.07687			0.423072
$145$		0			0
$146$	32.1028			2.65685
$147$	7.76374			0.640342
$148$		−	26.0031i		−	2.13744i
$149$	−9.07657			−0.743581			−0.371791	−	0.928317i	$-0.621256\pi$
$149$	−9.07657			−0.743581			−0.371791	+	0.928317i	$0.621256\pi$
$150$		0			0
$151$			14.6422i			1.19156i	0.803146	+	0.595782i	$0.203158\pi$
$151$			14.6422i			1.19156i	−0.803146	+	0.595782i	$0.796842\pi$
$152$	−17.8512	−	17.8512i	−1.44792	−	1.44792i
$153$	−2.41639			−0.195353
$154$	−6.70282			−0.540129
$155$		0			0
$156$	13.6888	−	13.6888i	1.09598	−	1.09598i
$157$		−	1.37029i		−	0.109361i	−0.998504	−	0.0546805i	$-0.982586\pi$
$157$		−	1.37029i		−	0.109361i	0.998504	−	0.0546805i	$-0.0174140\pi$
$158$	5.51699	+	5.51699i	0.438908	+	0.438908i
$159$	8.80475	+	8.80475i	0.698262	+	0.698262i
$160$		0			0
$161$	8.83083			0.695967
$162$	−21.5376			−1.69215
$163$	−2.81205			−0.220257			−0.110128	−	0.993917i	$-0.535126\pi$
$163$	−2.81205			−0.220257			−0.110128	+	0.993917i	$0.535126\pi$
$164$	13.0558	+	13.0558i	1.01948	+	1.01948i
$165$		0			0
$166$	14.4447	−	14.4447i	1.12113	−	1.12113i
$167$	−5.01507	+	5.01507i	−0.388078	+	0.388078i	−0.874001	−	0.485923i	$-0.838483\pi$
$167$	−5.01507	+	5.01507i	−0.388078	+	0.388078i	0.485923	+	0.874001i	$0.338483\pi$
$168$	16.4414	−	16.4414i	1.26848	−	1.26848i
$169$		−	8.31241i		−	0.639416i
$170$		0			0
$171$	−0.632294	−	0.632294i	−0.0483527	−	0.0483527i
$172$		−	44.1595i		−	3.36713i
$173$	11.8741	+	11.8741i	0.902767	+	0.902767i	0.995675	−	0.0929073i	$-0.0296160\pi$
$173$	11.8741	+	11.8741i	0.902767	+	0.902767i	−0.0929073	+	0.995675i	$0.529616\pi$
$174$	−23.5843	−	4.62349i	−1.78792	−	0.350506i
$175$		0			0
$176$	17.4336	−	17.4336i	1.31411	−	1.31411i
$177$	−5.84085			−0.439025
$178$	−27.8024	−	27.8024i	−2.08388	−	2.08388i
$179$	−0.831099			−0.0621193			−0.0310596	−	0.999518i	$-0.509888\pi$
$179$	−0.831099			−0.0621193			−0.0310596	+	0.999518i	$0.509888\pi$
$180$		0			0
$181$	−16.5277			−1.22849			−0.614245	−	0.789115i	$-0.710540\pi$
$181$	−16.5277			−1.22849			−0.614245	+	0.789115i	$0.710540\pi$
$182$			8.86667i			0.657242i
$183$	−1.41603	−	1.41603i	−0.104676	−	0.104676i
$184$	−39.6774	+	39.6774i	−2.92506	+	2.92506i
$185$		0			0
$186$	−2.25101	−	2.25101i	−0.165052	−	0.165052i
$187$	−8.29769	+	8.29769i	−0.606787	+	0.606787i
$188$			10.2282i			0.745965i
$189$	5.76614	−	5.76614i	0.419425	−	0.419425i
$190$		0			0
$191$	1.92415	−	1.92415i	0.139227	−	0.139227i	−0.634058	−	0.773285i	$-0.718612\pi$
$191$	1.92415	−	1.92415i	0.139227	−	0.139227i	0.773285	+	0.634058i	$0.218612\pi$
$192$			49.7606i			3.59116i
$193$			5.17863i			0.372766i	0.982477	+	0.186383i	$0.0596765\pi$
$193$			5.17863i			0.372766i	−0.982477	+	0.186383i	$0.940323\pi$
$194$			16.5672i			1.18945i
$195$		0			0
$196$		−	26.0680i		−	1.86200i
$197$	−12.4638	−	12.4638i	−0.888007	−	0.888007i	0.106324	−	0.994332i	$-0.466092\pi$
$197$	−12.4638	−	12.4638i	−0.888007	−	0.888007i	−0.994332	+	0.106324i	$0.966092\pi$
$198$	1.06672	−	1.06672i	0.0758087	−	0.0758087i
$199$		−	8.92943i		−	0.632990i	−0.948594	−	0.316495i	$-0.897494\pi$
$199$		−	8.92943i		−	0.632990i	0.948594	−	0.316495i	$-0.102506\pi$
$200$		0			0
$201$	−11.5729	−	11.5729i	−0.816291	−	0.816291i
$202$	10.1050	−	10.1050i	0.710983	−	0.710983i
$203$	6.69265	−	4.49868i	0.469732	−	0.315746i
$204$		−	64.1069i		−	4.48838i
$205$		0			0
$206$	−0.912621	+	0.912621i	−0.0635853	+	0.0635853i
$207$	−1.40539	+	1.40539i	−0.0976811	+	0.0976811i
$208$	−23.0616	−	23.0616i	−1.59904	−	1.59904i
$209$	−4.34250			−0.300377
$210$		0			0
$211$	6.16024	+	6.16024i	0.424088	+	0.424088i	0.886609	−	0.462520i	$-0.153055\pi$
$211$	6.16024	+	6.16024i	0.424088	+	0.424088i	−0.462520	+	0.886609i	$0.653055\pi$
$212$	29.5634	−	29.5634i	2.03042	−	2.03042i
$213$	5.39134			0.369409
$214$	22.9362	+	22.9362i	1.56788	+	1.56788i
$215$		0			0
$216$			51.8152i			3.52558i
$217$	1.06816			0.0725115
$218$	−3.36370			−0.227819
$219$			19.1557i			1.29442i
$220$		0			0
$221$	10.9764	+	10.9764i	0.738354	+	0.738354i
$222$	21.1795			1.42148
$223$	−11.3717	+	11.3717i	−0.761509	+	0.761509i	−0.976595	−	0.215086i	$-0.930997\pi$
$223$	−11.3717	+	11.3717i	−0.761509	+	0.761509i	0.215086	+	0.976595i	$0.430997\pi$
$224$	−23.4710	−	23.4710i	−1.56822	−	1.56822i
$225$		0			0
$226$	0.426048			0.0283403
$227$	19.9481	+	19.9481i	1.32400	+	1.32400i	0.910506	+	0.413497i	$0.135693\pi$
$227$	19.9481	+	19.9481i	1.32400	+	1.32400i	0.413497	+	0.910506i	$0.364307\pi$
$228$	16.7748	−	16.7748i	1.11094	−	1.11094i
$229$	−0.344302	+	0.344302i	−0.0227521	+	0.0227521i	−0.718391	−	0.695639i	$-0.755121\pi$
$229$	−0.344302	+	0.344302i	−0.0227521	+	0.0227521i	0.695639	+	0.718391i	$0.255121\pi$
$230$		0			0
$231$		−	3.99956i		−	0.263152i
$232$	−9.85762	+	50.2833i	−0.647184	+	3.30126i
$233$	11.1619	−	11.1619i	0.731241	−	0.731241i	−0.239625	−	0.970866i	$-0.577024\pi$
$233$	11.1619	−	11.1619i	0.731241	−	0.731241i	0.970866	+	0.239625i	$0.0770244\pi$
$234$	−1.41109	−	1.41109i	−0.0922459	−	0.0922459i
$235$		0			0
$236$			19.6116i			1.27661i
$237$	−3.29198	+	3.29198i	−0.213837	+	0.213837i
$238$	20.7621	+	20.7621i	1.34581	+	1.34581i
$239$			12.4300i			0.804031i	0.915633	+	0.402016i	$0.131690\pi$
$239$			12.4300i			0.804031i	−0.915633	+	0.402016i	$0.868310\pi$
$240$		0			0
$241$		−	1.15975i		−	0.0747058i	−0.999302	−	0.0373529i	$-0.988107\pi$
$241$		−	1.15975i		−	0.0747058i	0.999302	−	0.0373529i	$-0.0118926\pi$
$242$			22.7569i			1.46287i
$243$			3.48526i			0.223579i
$244$	−4.75455	+	4.75455i	−0.304379	+	0.304379i
$245$		0			0
$246$	−10.6339	+	10.6339i	−0.677995	+	0.677995i
$247$			5.74438i			0.365506i
$248$	−4.79931	+	4.79931i	−0.304756	+	0.304756i
$249$	8.61911	+	8.61911i	0.546214	+	0.546214i
$250$		0			0
$251$	−17.5113	+	17.5113i	−1.10531	+	1.10531i	−0.111547	+	0.993759i	$0.535580\pi$
$251$	−17.5113	+	17.5113i	−1.10531	+	1.10531i	−0.993759	+	0.111547i	$0.964420\pi$
$252$	−1.95537	−	1.95537i	−0.123177	−	0.123177i
$253$			9.65198i			0.606815i
$254$	50.6616			3.17879
$255$		0			0
$256$	45.8385			2.86491
$257$	−12.6288	−	12.6288i	−0.787765	−	0.787765i	0.193362	−	0.981127i	$-0.438061\pi$
$257$	−12.6288	−	12.6288i	−0.787765	−	0.787765i	−0.981127	+	0.193362i	$0.938061\pi$
$258$	35.9680			2.23927
$259$	−5.02511	+	5.02511i	−0.312245	+	0.312245i
$260$		0			0
$261$	−0.349160	+	1.78105i	−0.0216124	+	0.110244i
$262$	12.5472	+	12.5472i	0.775168	+	0.775168i
$263$			28.1945i			1.73855i	0.494329	+	0.869275i	$0.335414\pi$
$263$			28.1945i			1.73855i	−0.494329	+	0.869275i	$0.664586\pi$
$264$	17.9702	+	17.9702i	1.10599	+	1.10599i
$265$		0			0
$266$			10.8656i			0.666213i
$267$	16.5896	−	16.5896i	1.01527	−	1.01527i
$268$	−38.8580	+	38.8580i	−2.37363	+	2.37363i
$269$	−11.0679	+	11.0679i	−0.674824	+	0.674824i	−0.958824	−	0.284000i	$-0.908338\pi$
$269$	−11.0679	+	11.0679i	−0.674824	+	0.674824i	0.284000	+	0.958824i	$0.408338\pi$
$270$		0			0
$271$	2.17997	+	2.17997i	0.132424	+	0.132424i	0.770212	−	0.637788i	$-0.220150\pi$
$271$	2.17997	+	2.17997i	0.132424	+	0.132424i	−0.637788	+	0.770212i	$0.720150\pi$
$272$	−108.002			−6.54857
$273$	−5.29072			−0.320209
$274$	7.42953			0.448834
$275$		0			0
$276$	−37.2850	−	37.2850i	−2.24429	−	2.24429i
$277$	−18.6295	−	18.6295i	−1.11934	−	1.11934i	−0.991838	−	0.127503i	$-0.959304\pi$
$277$	−18.6295	−	18.6295i	−1.11934	−	1.11934i	−0.127503	−	0.991838i	$-0.540696\pi$
$278$		−	32.9059i		−	1.97357i
$279$	−0.169993	+	0.169993i	−0.0101772	+	0.0101772i
$280$		0			0
$281$	21.6535			1.29174			0.645871	−	0.763447i	$-0.276494\pi$
$281$	21.6535			1.29174			0.645871	+	0.763447i	$0.276494\pi$
$282$	−8.33084			−0.496094
$283$	4.61797	+	4.61797i	0.274510	+	0.274510i	0.830913	−	0.556403i	$-0.187819\pi$
$283$	4.61797	+	4.61797i	0.274510	+	0.274510i	−0.556403	+	0.830913i	$0.687819\pi$
$284$		−	18.1023i		−	1.07417i
$285$		0			0
$286$	−9.69115			−0.573050
$287$		−	5.04607i		−	0.297860i
$288$	7.47061			0.440210
$289$	34.4045			2.02380
$290$		0			0
$291$	−9.88558			−0.579503
$292$	64.3183			3.76395
$293$		−	9.80441i		−	0.572780i	−0.958113	−	0.286390i	$-0.907545\pi$
$293$		−	9.80441i		−	0.572780i	0.958113	−	0.286390i	$-0.0924553\pi$
$294$	21.2324			1.23830
$295$		0			0
$296$		−	45.1562i		−	2.62465i
$297$	6.30231	+	6.30231i	0.365697	+	0.365697i
$298$	−24.8228			−1.43795
$299$	12.7679			0.738387
$300$		0			0
$301$	−8.53386	+	8.53386i	−0.491884	+	0.491884i
$302$			40.0438i			2.30426i
$303$	6.02961	+	6.02961i	0.346392	+	0.346392i
$304$	−28.2607	−	28.2607i	−1.62086	−	1.62086i
$305$		0			0
$306$	−6.60839			−0.377777
$307$	−0.488133			−0.0278592			−0.0139296	−	0.999903i	$-0.504434\pi$
$307$	−0.488133			−0.0278592			−0.0139296	+	0.999903i	$0.504434\pi$
$308$	−13.4292			−0.765198
$309$	−0.544559	−	0.544559i	−0.0309789	−	0.0309789i
$310$		0			0
$311$	7.27332	−	7.27332i	0.412432	−	0.412432i	−0.470153	−	0.882585i	$-0.655801\pi$
$311$	7.27332	−	7.27332i	0.412432	−	0.412432i	0.882585	+	0.470153i	$0.155801\pi$
$312$	23.7715	−	23.7715i	1.34580	−	1.34580i
$313$	19.2967	−	19.2967i	1.09071	−	1.09071i	0.0952605	−	0.995452i	$-0.469632\pi$
$313$	19.2967	−	19.2967i	1.09071	−	1.09071i	0.995452	−	0.0952605i	$-0.0303684\pi$
$314$		−	3.74750i		−	0.211483i
$315$		0			0
$316$	11.0534	+	11.0534i	0.621800	+	0.621800i
$317$			2.65586i			0.149168i	0.997215	+	0.0745839i	$0.0237629\pi$
$317$			2.65586i			0.149168i	−0.997215	+	0.0745839i	$0.976237\pi$
$318$	24.0794	+	24.0794i	1.35031	+	1.35031i
$319$	4.91700	+	7.31497i	0.275299	+	0.409560i
$320$		0			0
$321$	−13.6860	+	13.6860i	−0.763875	+	0.763875i
$322$	24.1507			1.34587
$323$	13.4510	+	13.4510i	0.748433	+	0.748433i
$324$	−43.1509			−2.39727
$325$		0			0
$326$	−7.69045			−0.425935
$327$		−	2.00711i		−	0.110994i
$328$	22.6723	+	22.6723i	1.25187	+	1.25187i
$329$	1.97660	−	1.97660i	0.108973	−	0.108973i
$330$		0			0
$331$	−13.7951	−	13.7951i	−0.758248	−	0.758248i	0.217756	−	0.976003i	$-0.430126\pi$
$331$	−13.7951	−	13.7951i	−0.758248	−	0.758248i	−0.976003	+	0.217756i	$0.930126\pi$
$332$	28.9401	−	28.9401i	1.58829	−	1.58829i
$333$		−	1.59945i		−	0.0876491i
$334$	−13.7153	+	13.7153i	−0.750469	+	0.750469i
$335$		0			0
$336$	26.0289	−	26.0289i	1.41999	−	1.41999i
$337$		−	16.3087i		−	0.888389i	−0.895930	−	0.444195i	$-0.853490\pi$
$337$		−	16.3087i		−	0.888389i	0.895930	−	0.444195i	$-0.146510\pi$
$338$		−	22.7329i		−	1.23651i
$339$			0.254222i			0.0138074i
$340$		0			0
$341$			1.16748i			0.0632228i
$342$	−1.72921	−	1.72921i	−0.0935051	−	0.0935051i
$343$	−12.4497	+	12.4497i	−0.672223	+	0.672223i
$344$		−	76.6863i		−	4.13465i
$345$		0			0
$346$	32.4734	+	32.4734i	1.74578	+	1.74578i
$347$	3.15980	−	3.15980i	0.169627	−	0.169627i	−0.617188	−	0.786815i	$-0.711728\pi$
$347$	3.15980	−	3.15980i	0.169627	−	0.169627i	0.786815	+	0.617188i	$0.211728\pi$
$348$	−47.2513	−	9.26322i	−2.53294	−	0.496561i
$349$		−	17.3855i		−	0.930627i	−0.885146	−	0.465313i	$-0.845942\pi$
$349$		−	17.3855i		−	0.930627i	0.885146	−	0.465313i	$-0.154058\pi$
$350$		0			0
$351$	8.33687	−	8.33687i	0.444989	−	0.444989i
$352$	25.6535	−	25.6535i	1.36734	−	1.36734i
$353$	−9.60586	−	9.60586i	−0.511268	−	0.511268i	0.403647	−	0.914915i	$-0.367742\pi$
$353$	−9.60586	−	9.60586i	−0.511268	−	0.511268i	−0.914915	+	0.403647i	$0.867742\pi$
$354$	−15.9737			−0.848992
$355$		0			0
$356$	−55.7024	−	55.7024i	−2.95222	−	2.95222i
$357$	−12.3887	+	12.3887i	−0.655680	+	0.655680i
$358$	−2.27291			−0.120127
$359$	−16.6718	−	16.6718i	−0.879906	−	0.879906i	0.113618	−	0.993524i	$-0.463756\pi$
$359$	−16.6718	−	16.6718i	−0.879906	−	0.879906i	−0.993524	+	0.113618i	$0.963756\pi$
$360$		0			0
$361$		−	11.9606i		−	0.629505i
$362$	−45.2002			−2.37567
$363$	−13.5790			−0.712713
$364$			17.7645i			0.931112i
$365$		0			0
$366$	−3.87259	−	3.87259i	−0.202423	−	0.202423i
$367$	5.52771			0.288544			0.144272	−	0.989538i	$-0.453916\pi$
$367$	5.52771			0.288544			0.144272	+	0.989538i	$0.453916\pi$
$368$	−62.8145	+	62.8145i	−3.27443	+	3.27443i
$369$	0.803059	+	0.803059i	0.0418056	+	0.0418056i
$370$		0			0
$371$	−11.4263			−0.593224
$372$	−4.50992	−	4.50992i	−0.233828	−	0.233828i
$373$	0.505639	−	0.505639i	0.0261810	−	0.0261810i	−0.693895	−	0.720076i	$-0.744107\pi$
$373$	0.505639	−	0.505639i	0.0261810	−	0.0261810i	0.720076	+	0.693895i	$0.244107\pi$
$374$	−22.6927	+	22.6927i	−1.17341	+	1.17341i
$375$		0			0
$376$			17.7619i			0.916003i
$377$	9.67645	−	6.50434i	0.498363	−	0.334991i
$378$	15.7694	−	15.7694i	0.811088	−	0.811088i
$379$	21.9491	+	21.9491i	1.12745	+	1.12745i	0.990590	+	0.136859i	$0.0437009\pi$
$379$	21.9491	+	21.9491i	1.12745	+	1.12745i	0.136859	+	0.990590i	$0.456299\pi$
$380$		0			0
$381$			30.2297i			1.54871i
$382$	5.26221	−	5.26221i	0.269238	−	0.269238i
$383$	−8.19179	−	8.19179i	−0.418581	−	0.418581i	0.466134	−	0.884714i	$-0.345647\pi$
$383$	−8.19179	−	8.19179i	−0.418581	−	0.418581i	−0.884714	+	0.466134i	$0.845647\pi$
$384$			63.7421i			3.25282i
$385$		0			0
$386$			14.1626i			0.720859i
$387$		−	2.71625i		−	0.138075i
$388$			33.1925i			1.68509i
$389$	1.00500	−	1.00500i	0.0509555	−	0.0509555i	−0.681170	−	0.732125i	$-0.738528\pi$
$389$	1.00500	−	1.00500i	0.0509555	−	0.0509555i	0.732125	+	0.681170i	$0.238528\pi$
$390$		0			0
$391$	29.8972	−	29.8972i	1.51197	−	1.51197i
$392$		−	45.2691i		−	2.28643i
$393$	−7.48688	+	7.48688i	−0.377663	+	0.377663i
$394$	−34.0862	−	34.0862i	−1.71724	−	1.71724i
$395$		0			0
$396$	2.13719	−	2.13719i	0.107398	−	0.107398i
$397$	9.25008	+	9.25008i	0.464248	+	0.464248i	0.900045	−	0.435797i	$-0.143533\pi$
$397$	9.25008	+	9.25008i	0.464248	+	0.464248i	−0.435797	+	0.900045i	$0.643533\pi$
$398$		−	24.4204i		−	1.22408i
$399$	−6.48348			−0.324580
$400$		0			0
$401$	−9.92342			−0.495552			−0.247776	−	0.968817i	$-0.579700\pi$
$401$	−9.92342			−0.495552			−0.247776	+	0.968817i	$0.579700\pi$
$402$	−31.6499	−	31.6499i	−1.57855	−	1.57855i
$403$	1.54438			0.0769311
$404$	20.2454	−	20.2454i	1.00725	−	1.00725i
$405$		0			0
$406$	18.3032	−	12.3031i	0.908373	−	0.610592i
$407$	−5.49238	−	5.49238i	−0.272247	−	0.272247i
$408$		−	111.326i		−	5.51148i
$409$	1.32729	+	1.32729i	0.0656305	+	0.0656305i	0.739160	−	0.673530i	$-0.235223\pi$
$409$	1.32729	+	1.32729i	0.0656305	+	0.0656305i	−0.673530	+	0.739160i	$0.735223\pi$
$410$		0			0
$411$			4.43318i			0.218673i
$412$	−1.82845	+	1.82845i	−0.0900811	+	0.0900811i
$413$	3.78996	−	3.78996i	0.186492	−	0.186492i
$414$	−3.84348	+	3.84348i	−0.188897	+	0.188897i
$415$		0			0
$416$	−33.9352	−	33.9352i	−1.66381	−	1.66381i
$417$	19.6349			0.961525
$418$	−11.8760			−0.580872
$419$	13.3122			0.650345			0.325172	−	0.945655i	$-0.394578\pi$
$419$	13.3122			0.650345			0.325172	+	0.945655i	$0.394578\pi$
$420$		0			0
$421$	6.09719	+	6.09719i	0.297159	+	0.297159i	0.839900	−	0.542741i	$-0.182614\pi$
$421$	6.09719	+	6.09719i	0.297159	+	0.297159i	−0.542741	+	0.839900i	$0.682614\pi$
$422$	16.8471	+	16.8471i	0.820106	+	0.820106i
$423$			0.629133i			0.0305895i
$424$	51.3390	−	51.3390i	2.49324	−	2.49324i
$425$		0			0
$426$	14.7443			0.714366
$427$	1.83764			0.0889297
$428$	45.9528	+	45.9528i	2.22121	+	2.22121i
$429$		−	5.78269i		−	0.279191i
$430$		0			0
$431$	−7.97468			−0.384127			−0.192063	−	0.981383i	$-0.561518\pi$
$431$	−7.97468			−0.384127			−0.192063	+	0.981383i	$0.561518\pi$
$432$			82.0301i			3.94667i
$433$	−27.9015			−1.34086			−0.670430	−	0.741973i	$-0.733890\pi$
$433$	−27.9015			−1.34086			−0.670430	+	0.741973i	$0.733890\pi$
$434$	2.92123			0.140223
$435$		0			0
$436$	−6.73921			−0.322750
$437$	15.6463			0.748466
$438$			52.3873i			2.50316i
$439$	−23.0891			−1.10198			−0.550991	−	0.834511i	$-0.685750\pi$
$439$	−23.0891			−1.10198			−0.550991	+	0.834511i	$0.685750\pi$
$440$		0			0
$441$		−	1.60344i		−	0.0763544i
$442$	30.0185	+	30.0185i	1.42784	+	1.42784i
$443$	13.1208			0.623388			0.311694	−	0.950183i	$-0.399104\pi$
$443$	13.1208			0.623388			0.311694	+	0.950183i	$0.399104\pi$
$444$	42.4334			2.01380
$445$		0			0
$446$	−31.0997	+	31.0997i	−1.47261	+	1.47261i
$447$		−	14.8117i		−	0.700569i
$448$	−32.2882	−	32.2882i	−1.52547	−	1.52547i
$449$	14.1942	+	14.1942i	0.669865	+	0.669865i	0.957685	−	0.287819i	$-0.0929302\pi$
$449$	14.1942	+	14.1942i	0.669865	+	0.669865i	−0.287819	+	0.957685i	$0.592930\pi$
$450$		0			0
$451$	5.51529			0.259705
$452$	0.853592			0.0401496
$453$	−23.8940			−1.12264
$454$	54.5545	+	54.5545i	2.56037	+	2.56037i
$455$		0			0
$456$	29.1307	−	29.1307i	1.36417	−	1.36417i
$457$	−20.5601	+	20.5601i	−0.961761	+	0.961761i	−0.999295	−	0.0375345i	$-0.988050\pi$
$457$	−20.5601	+	20.5601i	−0.961761	+	0.961761i	0.0375345	+	0.999295i	$0.488050\pi$
$458$	−0.941604	+	0.941604i	−0.0439983	+	0.0439983i
$459$		−	39.0431i		−	1.82237i
$460$		0			0
$461$	10.9719	+	10.9719i	0.511014	+	0.511014i	0.914837	−	0.403823i	$-0.132319\pi$
$461$	10.9719	+	10.9719i	0.511014	+	0.511014i	−0.403823	+	0.914837i	$0.632319\pi$
$462$		−	10.9381i		−	0.508885i
$463$	−19.5635	−	19.5635i	−0.909193	−	0.909193i	0.0870140	−	0.996207i	$-0.472268\pi$
$463$	−19.5635	−	19.5635i	−0.909193	−	0.909193i	−0.996207	+	0.0870140i	$0.972268\pi$
$464$	−15.6059	+	79.6049i	−0.724484	+	3.69557i
$465$		0			0
$466$	30.5258	−	30.5258i	1.41408	−	1.41408i
$467$	38.4099			1.77740			0.888699	−	0.458491i	$-0.151610\pi$
$467$	38.4099			1.77740			0.888699	+	0.458491i	$0.151610\pi$
$468$	−2.82714	−	2.82714i	−0.130684	−	0.130684i
$469$	15.0187			0.693498
$470$		0			0
$471$	2.23612			0.103035
$472$			34.0570i			1.56760i
$473$	−9.32739	−	9.32739i	−0.428874	−	0.428874i
$474$	−9.00297	+	9.00297i	−0.413520	+	0.413520i
$475$		0			0
$476$	41.5971	+	41.5971i	1.90660	+	1.90660i
$477$	1.81844	−	1.81844i	0.0832608	−	0.0832608i
$478$			33.9939i			1.55484i
$479$	−14.9920	+	14.9920i	−0.685002	+	0.685002i	−0.961123	−	0.276121i	$-0.910951\pi$
$479$	−14.9920	+	14.9920i	−0.685002	+	0.685002i	0.276121	+	0.961123i	$0.410951\pi$
$480$		0			0
$481$	−7.26547	+	7.26547i	−0.331277	+	0.331277i
$482$		−	3.17170i		−	0.144467i
$483$			14.4107i			0.655709i
$484$			45.5938i			2.07245i
$485$		0			0
$486$			9.53156i			0.432360i
$487$	−28.0848	−	28.0848i	−1.27264	−	1.27264i	−0.944697	−	0.327945i	$-0.893644\pi$
$487$	−28.0848	−	28.0848i	−1.27264	−	1.27264i	−0.327945	−	0.944697i	$-0.606356\pi$
$488$	−8.25663	+	8.25663i	−0.373760	+	0.373760i
$489$		−	4.58888i		−	0.207516i
$490$		0			0
$491$	25.3582	+	25.3582i	1.14440	+	1.14440i	0.987636	+	0.156764i	$0.0501062\pi$
$491$	25.3582	+	25.3582i	1.14440	+	1.14440i	0.156764	+	0.987636i	$0.449894\pi$
$492$	−21.3052	+	21.3052i	−0.960513	+	0.960513i
$493$	7.42777	−	37.8888i	0.334530	−	1.70643i
$494$			15.7098i			0.706820i
$495$		0			0
$496$	−7.59792	+	7.59792i	−0.341156	+	0.341156i
$497$	−3.49829	+	3.49829i	−0.156920	+	0.156920i
$498$	23.5717	+	23.5717i	1.05627	+	1.05627i
$499$	−4.79875			−0.214821			−0.107411	−	0.994215i	$-0.534256\pi$
$499$	−4.79875			−0.214821			−0.107411	+	0.994215i	$0.534256\pi$
$500$		0			0
$501$	−8.18390	−	8.18390i	−0.365630	−	0.365630i
$502$	−47.8904	+	47.8904i	−2.13745	+	2.13745i
$503$	35.2896			1.57348			0.786742	−	0.617282i	$-0.211766\pi$
$503$	35.2896			1.57348			0.786742	+	0.617282i	$0.211766\pi$
$504$	−3.39564	−	3.39564i	−0.151254	−	0.151254i
$505$		0			0
$506$			26.3964i			1.17346i
$507$	13.5647			0.602429
$508$	101.501			4.50339
$509$		−	30.1303i		−	1.33550i	−0.744384	−	0.667752i	$-0.767257\pi$
$509$		−	30.1303i		−	1.33550i	0.744384	−	0.667752i	$-0.232743\pi$
$510$		0			0
$511$	−12.4296	−	12.4296i	−0.549852	−	0.549852i
$512$	47.2382			2.08765
$513$	10.2164	−	10.2164i	0.451063	−	0.451063i
$514$	−34.5376	−	34.5376i	−1.52339	−	1.52339i
$515$		0			0
$516$	72.0622			3.17236
$517$	2.16040	+	2.16040i	0.0950141	+	0.0950141i
$518$	−13.7428	+	13.7428i	−0.603823	+	0.603823i
$519$	−19.3768	+	19.3768i	−0.850548	+	0.850548i
$520$		0			0
$521$		−	25.2836i		−	1.10769i	−0.832619	−	0.553847i	$-0.813159\pi$
$521$		−	25.2836i		−	1.10769i	0.832619	−	0.553847i	$-0.186841\pi$
$522$	−0.954889	+	4.87085i	−0.0417943	+	0.213191i
$523$	3.79891	−	3.79891i	0.166115	−	0.166115i	−0.619155	−	0.785269i	$-0.712525\pi$
$523$	3.79891	−	3.79891i	0.166115	−	0.166115i	0.785269	+	0.619155i	$0.212525\pi$
$524$	25.1384	+	25.1384i	1.09818	+	1.09818i
$525$		0			0
$526$			77.1070i			3.36203i
$527$	3.61631	−	3.61631i	0.157529	−	0.157529i
$528$	28.4492	+	28.4492i	1.23809	+	1.23809i
$529$		−	11.7768i		−	0.512033i
$530$		0			0
$531$			1.20631i			0.0523494i
$532$			21.7694i			0.943822i
$533$		−	7.29578i		−	0.316015i
$534$	45.3697	−	45.3697i	1.96334	−	1.96334i
$535$		0			0
$536$	−67.4798	+	67.4798i	−2.91468	+	2.91468i
$537$		−	1.35624i		−	0.0585260i
$538$	−30.2688	+	30.2688i	−1.30498	+	1.30498i
$539$	−5.50610	−	5.50610i	−0.237165	−	0.237165i
$540$		0			0
$541$	−4.49423	+	4.49423i	−0.193222	+	0.193222i	−0.797087	−	0.603865i	$-0.793627\pi$
$541$	−4.49423	+	4.49423i	−0.193222	+	0.193222i	0.603865	+	0.797087i	$0.293627\pi$
$542$	5.96182	+	5.96182i	0.256082	+	0.256082i
$543$		−	26.9708i		−	1.15743i
$544$	−158.924			−6.81383
$545$		0			0
$546$	−14.4692			−0.619224
$547$	−5.45211	−	5.45211i	−0.233115	−	0.233115i	0.580876	−	0.813992i	$-0.302710\pi$
$547$	−5.45211	−	5.45211i	−0.233115	−	0.233115i	−0.813992	+	0.580876i	$0.802710\pi$
$548$	14.8851			0.635862
$549$	−0.292452	+	0.292452i	−0.0124816	+	0.0124816i
$550$		0			0
$551$	11.8579	−	7.97071i	0.505165	−	0.339563i
$552$	−64.7481	−	64.7481i	−2.75586	−	2.75586i
$553$		−	4.27214i		−	0.181670i
$554$	−50.9485	−	50.9485i	−2.16459	−	2.16459i
$555$		0			0
$556$		−	65.9274i		−	2.79595i
$557$	−32.1374	+	32.1374i	−1.36170	+	1.36170i	−0.489958	+	0.871746i	$0.662988\pi$
$557$	−32.1374	+	32.1374i	−1.36170	+	1.36170i	−0.871746	+	0.489958i	$0.837012\pi$
$558$	−0.464900	+	0.464900i	−0.0196808	+	0.0196808i
$559$	−12.3385	+	12.3385i	−0.521864	+	0.521864i
$560$		0			0
$561$	−13.5407	−	13.5407i	−0.571688	−	0.571688i
$562$	59.2186			2.49798
$563$	−2.60063			−0.109603			−0.0548017	−	0.998497i	$-0.517453\pi$
$563$	−2.60063			−0.109603			−0.0548017	+	0.998497i	$0.517453\pi$
$564$	−16.6909			−0.702815
$565$		0			0
$566$	12.6293	+	12.6293i	0.530850	+	0.530850i
$567$	8.33894	+	8.33894i	0.350202	+	0.350202i
$568$		−	31.4360i		−	1.31903i
$569$	−16.3628	+	16.3628i	−0.685965	+	0.685965i	−0.961338	−	0.275372i	$-0.911199\pi$
$569$	−16.3628	+	16.3628i	−0.685965	+	0.685965i	0.275372	+	0.961338i	$0.411199\pi$
$570$		0			0
$571$	−10.3466			−0.432992			−0.216496	−	0.976284i	$-0.569463\pi$
$571$	−10.3466			−0.432992			−0.216496	+	0.976284i	$0.569463\pi$
$572$	−19.4163			−0.811838
$573$	3.13995	+	3.13995i	0.131173	+	0.131173i
$574$		−	13.8001i		−	0.576005i
$575$		0			0
$576$	10.2770			0.428210
$577$		−	23.3309i		−	0.971278i	−0.874159	−	0.485639i	$-0.838587\pi$
$577$		−	23.3309i		−	0.971278i	0.874159	−	0.485639i	$-0.161413\pi$
$578$	94.0903			3.91364
$579$	−8.45081			−0.351204
$580$		0			0
$581$	−11.1854			−0.464048
$582$	−27.0353			−1.12065
$583$		−	12.4888i		−	0.517233i
$584$	111.694			4.62191
$585$		0			0
$586$		−	26.8133i		−	1.10765i
$587$	26.1594	+	26.1594i	1.07971	+	1.07971i	0.996535	+	0.0831773i	$0.0265068\pi$
$587$	26.1594	+	26.1594i	1.07971	+	1.07971i	0.0831773	+	0.996535i	$0.473493\pi$
$588$	42.5394			1.75430
$589$	1.89255			0.0779812
$590$		0			0
$591$	20.3392	−	20.3392i	0.836641	−	0.836641i
$592$		−	71.4881i		−	2.93814i
$593$	−10.3930	−	10.3930i	−0.426790	−	0.426790i	0.460743	−	0.887533i	$-0.347583\pi$
$593$	−10.3930	−	10.3930i	−0.426790	−	0.426790i	−0.887533	+	0.460743i	$0.847583\pi$
$594$	17.2357	+	17.2357i	0.707189	+	0.707189i
$595$		0			0
$596$	−49.7327			−2.03713
$597$	14.5716			0.596375
$598$	34.9179			1.42790
$599$	−11.0108	−	11.0108i	−0.449891	−	0.449891i	0.445427	−	0.895318i	$-0.353052\pi$
$599$	−11.0108	−	11.0108i	−0.449891	−	0.449891i	−0.895318	+	0.445427i	$0.853052\pi$
$600$		0			0
$601$	4.22053	−	4.22053i	0.172159	−	0.172159i	−0.615768	−	0.787927i	$-0.711154\pi$
$601$	4.22053	−	4.22053i	0.172159	−	0.172159i	0.787927	+	0.615768i	$0.211154\pi$
$602$	−23.3386	+	23.3386i	−0.951210	+	0.951210i
$603$	−2.39015	+	2.39015i	−0.0973345	+	0.0973345i
$604$			80.2282i			3.26444i
$605$		0			0
$606$	16.4899	+	16.4899i	0.669857	+	0.669857i
$607$			48.6467i			1.97451i	0.159154	+	0.987254i	$0.449123\pi$
$607$			48.6467i			1.97451i	−0.159154	+	0.987254i	$0.550877\pi$
$608$	−41.5856	−	41.5856i	−1.68652	−	1.68652i
$609$	7.34123	+	10.9215i	0.297482	+	0.442561i
$610$		0			0
$611$	2.85783	−	2.85783i	0.115615	−	0.115615i
$612$	−13.2400			−0.535195
$613$	14.0319	+	14.0319i	0.566744	+	0.566744i	0.931215	−	0.364471i	$-0.118750\pi$
$613$	14.0319	+	14.0319i	0.566744	+	0.566744i	−0.364471	+	0.931215i	$0.618750\pi$
$614$	−1.33496			−0.0538744
$615$		0			0
$616$	−23.3208			−0.939620
$617$		−	35.2664i		−	1.41977i	−0.704318	−	0.709885i	$-0.748747\pi$
$617$		−	35.2664i		−	1.41977i	0.704318	−	0.709885i	$-0.251253\pi$
$618$	−1.48927	−	1.48927i	−0.0599072	−	0.0599072i
$619$	−9.65826	+	9.65826i	−0.388198	+	0.388198i	−0.874044	−	0.485846i	$-0.838512\pi$
$619$	−9.65826	+	9.65826i	−0.388198	+	0.388198i	0.485846	+	0.874044i	$0.338512\pi$
$620$		0			0
$621$	−22.7077	−	22.7077i	−0.911228	−	0.911228i
$622$	19.8912	−	19.8912i	0.797566	−	0.797566i
$623$			21.5291i			0.862544i
$624$	37.6334	−	37.6334i	1.50654	−	1.50654i
$625$		0			0
$626$	52.7730	−	52.7730i	2.10923	−	2.10923i
$627$		−	7.08636i		−	0.283002i
$628$		−	7.50815i		−	0.299608i
$629$			34.0255i			1.35669i
$630$		0			0
$631$		−	24.9743i		−	0.994212i	−0.867690	−	0.497106i	$-0.834396\pi$
$631$		−	24.9743i		−	0.994212i	0.867690	−	0.497106i	$-0.165604\pi$
$632$	19.1950	+	19.1950i	0.763535	+	0.763535i
$633$	−10.0527	+	10.0527i	−0.399557	+	0.399557i
$634$			7.26329i			0.288462i
$635$		0			0
$636$	48.2434	+	48.2434i	1.91297	+	1.91297i
$637$	−7.28362	+	7.28362i	−0.288588	+	0.288588i
$638$	13.4471	+	20.0051i	0.532376	+	0.792011i
$639$		−	1.11347i		−	0.0440483i
$640$		0			0
$641$	30.8944	−	30.8944i	1.22026	−	1.22026i	0.252716	−	0.967540i	$-0.418676\pi$
$641$	30.8944	−	30.8944i	1.22026	−	1.22026i	0.967540	−	0.252716i	$-0.0813239\pi$
$642$	−37.4286	+	37.4286i	−1.47719	+	1.47719i
$643$	6.59143	+	6.59143i	0.259941	+	0.259941i	0.825030	−	0.565089i	$-0.191158\pi$
$643$	6.59143	+	6.59143i	0.259941	+	0.259941i	−0.565089	+	0.825030i	$0.691158\pi$
$644$	48.3863			1.90669
$645$		0			0
$646$	36.7860	+	36.7860i	1.44733	+	1.44733i
$647$	33.2521	−	33.2521i	1.30728	−	1.30728i	0.383903	−	0.923373i	$-0.374580\pi$
$647$	33.2521	−	33.2521i	1.30728	−	1.30728i	0.923373	−	0.383903i	$-0.125420\pi$
$648$	−74.9346			−2.94371
$649$	4.14238	+	4.14238i	0.162602	+	0.162602i
$650$		0			0
$651$			1.74309i			0.0683171i
$652$	−15.4079			−0.603420
$653$	−37.6967			−1.47519			−0.737593	−	0.675245i	$-0.764038\pi$
$653$	−37.6967			−1.47519			−0.737593	+	0.675245i	$0.764038\pi$
$654$		−	5.48909i		−	0.214641i
$655$		0			0
$656$	35.8931	+	35.8931i	1.40139	+	1.40139i
$657$	3.95622			0.154347
$658$	5.40564	−	5.40564i	0.210734	−	0.210734i
$659$	21.0129	+	21.0129i	0.818548	+	0.818548i	0.985898	−	0.167349i	$-0.0535208\pi$
$659$	21.0129	+	21.0129i	0.818548	+	0.818548i	−0.167349	+	0.985898i	$0.553521\pi$
$660$		0			0
$661$	−27.4749			−1.06865			−0.534325	−	0.845279i	$-0.679434\pi$
$661$	−27.4749			−1.06865			−0.534325	+	0.845279i	$0.679434\pi$
$662$	−37.7271	−	37.7271i	−1.46631	−	1.46631i
$663$	−17.9120	+	17.9120i	−0.695644	+	0.695644i
$664$	50.2566	−	50.2566i	1.95034	−	1.95034i
$665$		0			0
$666$		−	4.37420i		−	0.169497i
$667$	−17.7163	−	26.3564i	−0.685978	−	1.02052i
$668$	−27.4788	+	27.4788i	−1.06319	+	1.06319i
$669$	−18.5571	−	18.5571i	−0.717460	−	0.717460i
$670$		0			0
$671$			2.00852i			0.0775379i
$672$	38.3014	−	38.3014i	1.47751	−	1.47751i
$673$	1.01710	+	1.01710i	0.0392064	+	0.0392064i	0.726438	−	0.687232i	$-0.241174\pi$
$673$	1.01710	+	1.01710i	0.0392064	+	0.0392064i	−0.687232	+	0.726438i	$0.741174\pi$
$674$		−	44.6013i		−	1.71798i
$675$		0			0
$676$		−	45.5457i		−	1.75176i
$677$			19.8563i			0.763140i	0.924340	+	0.381570i	$0.124617\pi$
$677$			19.8563i			0.763140i	−0.924340	+	0.381570i	$0.875383\pi$
$678$			0.695252i			0.0267010i
$679$	6.41447	−	6.41447i	0.246165	−	0.246165i
$680$		0			0
$681$	−32.5525	+	32.5525i	−1.24742	+	1.24742i
$682$			3.19286i			0.122261i
$683$	29.7005	−	29.7005i	1.13646	−	1.13646i	0.147379	−	0.989080i	$-0.452916\pi$
$683$	29.7005	−	29.7005i	1.13646	−	1.13646i	0.989080	−	0.147379i	$-0.0470838\pi$
$684$	−3.46450	−	3.46450i	−0.132468	−	0.132468i
$685$		0			0
$686$	−34.0478	+	34.0478i	−1.29995	+	1.29995i
$687$	−0.561853	−	0.561853i	−0.0214360	−	0.0214360i
$688$		−	121.404i		−	4.62849i
$689$	−16.5205			−0.629381
$690$		0			0
$691$	−26.7508			−1.01765			−0.508824	−	0.860871i	$-0.669920\pi$
$691$	−26.7508			−1.01765			−0.508824	+	0.860871i	$0.669920\pi$
$692$	65.0608	+	65.0608i	2.47324	+	2.47324i
$693$	−0.826028			−0.0313782
$694$	8.64148	−	8.64148i	0.328026	−	0.328026i
$695$		0			0
$696$	−82.0554	−	16.0863i	−3.11030	−	0.609748i
$697$	−17.0837	−	17.0837i	−0.647092	−	0.647092i
$698$		−	47.5463i		−	1.79966i
$699$	18.2147	+	18.2147i	0.688943	+	0.688943i
$700$		0			0
$701$		−	1.02730i		−	0.0388005i	−0.999812	−	0.0194003i	$-0.993824\pi$
$701$		−	1.02730i		−	0.0388005i	0.999812	−	0.0194003i	$-0.00617568\pi$
$702$	22.7998	−	22.7998i	0.860525	−	0.860525i
$703$	−8.90342	+	8.90342i	−0.335799	+	0.335799i
$704$	35.2906	−	35.2906i	1.33006	−	1.33006i
$705$		0			0
$706$	−26.2703	−	26.2703i	−0.988696	−	0.988696i
$707$	−7.82489			−0.294285
$708$	−32.0035			−1.20276
$709$	−32.8376			−1.23324			−0.616621	−	0.787260i	$-0.711499\pi$
$709$	−32.8376			−1.23324			−0.616621	+	0.787260i	$0.711499\pi$
$710$		0			0
$711$	0.679891	+	0.679891i	0.0254979	+	0.0254979i
$712$	−96.7314	−	96.7314i	−3.62516	−	3.62516i
$713$		−	4.20653i		−	0.157536i
$714$	−33.8809	+	33.8809i	−1.26796	+	1.26796i
$715$		0			0
$716$	−4.55380			−0.170183
$717$	−20.2841			−0.757523
$718$	−45.5945	−	45.5945i	−1.70157	−	1.70157i
$719$			30.4349i			1.13503i	0.823363	+	0.567515i	$0.192095\pi$
$719$			30.4349i			1.13503i	−0.823363	+	0.567515i	$0.807905\pi$
$720$		0			0
$721$	0.706697			0.0263188
$722$		−	32.7101i		−	1.21734i
$723$	1.89255			0.0703845
$724$	−90.5591			−3.36560
$725$		0			0
$726$	−37.1362			−1.37825
$727$	1.37532			0.0510077			0.0255038	−	0.999675i	$-0.491881\pi$
$727$	1.37532			0.0510077			0.0255038	+	0.999675i	$0.491881\pi$
$728$			30.8493i			1.14335i
$729$	−29.3134			−1.08568
$730$		0			0
$731$			57.7836i			2.13720i
$732$	−7.75877	−	7.75877i	−0.286772	−	0.286772i
$733$	−8.23872			−0.304304			−0.152152	−	0.988357i	$-0.548620\pi$
$733$	−8.23872			−0.304304			−0.152152	+	0.988357i	$0.548620\pi$
$734$	15.1173			0.557990
$735$		0			0
$736$	−92.4314	+	92.4314i	−3.40707	+	3.40707i
$737$			16.4152i			0.604662i
$738$	2.19622	+	2.19622i	0.0808441	+	0.0808441i
$739$	−30.5802	−	30.5802i	−1.12491	−	1.12491i	−0.990992	−	0.133918i	$-0.957244\pi$
$739$	−30.5802	−	30.5802i	−1.12491	−	1.12491i	−0.133918	−	0.990992i	$-0.542756\pi$
$740$		0			0
$741$	−9.37403			−0.344364
$742$	−31.2489			−1.14718
$743$	−33.4069			−1.22558			−0.612791	−	0.790245i	$-0.709953\pi$
$743$	−33.4069			−1.22558			−0.612791	+	0.790245i	$0.709953\pi$
$744$	−7.83180	−	7.83180i	−0.287128	−	0.287128i
$745$		0			0
$746$	1.38283	−	1.38283i	0.0506291	−	0.0506291i
$747$	1.78010	−	1.78010i	0.0651306	−	0.0651306i
$748$	−45.4651	+	45.4651i	−1.66237	+	1.66237i
$749$		−	17.7608i		−	0.648967i
$750$		0			0
$751$	6.72041	+	6.72041i	0.245231	+	0.245231i	0.819010	−	0.573779i	$-0.194523\pi$
$751$	6.72041	+	6.72041i	0.245231	+	0.245231i	−0.573779	+	0.819010i	$0.694523\pi$
$752$			28.1194i			1.02541i
$753$	−28.5761	−	28.5761i	−1.04137	−	1.04137i
$754$	26.4634	−	17.7882i	0.963739	−	0.647809i
$755$		0			0
$756$	31.5941	−	31.5941i	1.14907	−	1.14907i
$757$	−43.4105			−1.57778			−0.788892	−	0.614532i	$-0.789345\pi$
$757$	−43.4105			−1.57778			−0.788892	+	0.614532i	$0.789345\pi$
$758$	60.0269	+	60.0269i	2.18027	+	2.18027i
$759$	−15.7507			−0.571714
$760$		0			0
$761$	45.4580			1.64785			0.823925	−	0.566699i	$-0.191780\pi$
$761$	45.4580			1.64785			0.823925	+	0.566699i	$0.191780\pi$
$762$			82.6728i			2.99492i
$763$	1.30236	+	1.30236i	0.0471485	+	0.0471485i
$764$	10.5429	−	10.5429i	0.381429	−	0.381429i
$765$		0			0
$766$	−22.4031	−	22.4031i	−0.809456	−	0.809456i
$767$	5.47965	−	5.47965i	0.197859	−	0.197859i
$768$			74.8021i			2.69919i
$769$	35.2831	−	35.2831i	1.27234	−	1.27234i	0.327487	−	0.944856i	$-0.393798\pi$
$769$	35.2831	−	35.2831i	1.27234	−	1.27234i	0.944856	−	0.327487i	$-0.106202\pi$
$770$		0			0
$771$	20.6085	−	20.6085i	0.742198	−	0.742198i
$772$			28.3750i			1.02124i
$773$			30.5826i			1.09998i	0.835171	+	0.549990i	$0.185368\pi$
$773$			30.5826i			1.09998i	−0.835171	+	0.549990i	$0.814632\pi$
$774$		−	7.42846i		−	0.267010i
$775$		0			0
$776$			57.6412i			2.06920i
$777$	−8.20028	−	8.20028i	−0.294184	−	0.294184i
$778$	2.74850	−	2.74850i	0.0985384	−	0.0985384i
$779$		−	8.94056i		−	0.320329i
$780$		0			0
$781$	−3.82358	−	3.82358i	−0.136818	−	0.136818i
$782$	81.7635	−	81.7635i	2.92386	−	2.92386i
$783$	−28.7775	−	5.64158i	−1.02842	−	0.201614i
$784$		−	71.6667i		−	2.55953i
$785$		0			0
$786$	−20.4753	+	20.4753i	−0.730329	+	0.730329i
$787$	−12.7850	+	12.7850i	−0.455735	+	0.455735i	−0.897253	−	0.441518i	$-0.854440\pi$
$787$	−12.7850	+	12.7850i	−0.455735	+	0.455735i	0.441518	+	0.897253i	$0.354440\pi$
$788$	−68.2921	−	68.2921i	−2.43281	−	2.43281i
$789$	−46.0096			−1.63798
$790$		0			0
$791$	−0.164957	−	0.164957i	−0.00586521	−	0.00586521i
$792$	3.71139	−	3.71139i	0.131879	−	0.131879i
$793$	2.65692			0.0943501
$794$	25.2973	+	25.2973i	0.897768	+	0.897768i
$795$		0			0
$796$		−	48.9265i		−	1.73415i
$797$	12.6152			0.446852			0.223426	−	0.974721i	$-0.428276\pi$
$797$	12.6152			0.446852			0.223426	+	0.974721i	$0.428276\pi$
$798$	−17.7312			−0.627677
$799$		−	13.3837i		−	0.473483i
$800$		0			0
$801$	−3.42625	−	3.42625i	−0.121061	−	0.121061i
$802$	−27.1388			−0.958304
$803$	13.5853	−	13.5853i	0.479417	−	0.479417i
$804$	−63.4109	−	63.4109i	−2.23633	−	2.23633i
$805$		0			0
$806$	4.22361			0.148770
$807$	−18.0613	−	18.0613i	−0.635789	−	0.635789i
$808$	35.1577	−	35.1577i	1.23684	−	1.23684i
$809$	−26.7078	+	26.7078i	−0.938996	+	0.938996i	−0.998243	−	0.0592478i	$-0.981130\pi$
$809$	−26.7078	+	26.7078i	−0.938996	+	0.938996i	0.0592478	+	0.998243i	$0.481130\pi$
$810$		0			0
$811$		−	26.4437i		−	0.928564i	−0.885687	−	0.464282i	$-0.846312\pi$
$811$		−	26.4437i		−	0.928564i	0.885687	−	0.464282i	$-0.153688\pi$
$812$	36.6707	−	24.6494i	1.28689	−	0.865024i
$813$	−3.55741	+	3.55741i	−0.124764	+	0.124764i
$814$	−15.0207	−	15.0207i	−0.526474	−	0.526474i
$815$		0			0
$816$		−	176.244i		−	6.16977i
$817$	−15.1202	+	15.1202i	−0.528988	+	0.528988i
$818$	3.62991	+	3.62991i	0.126917	+	0.126917i
$819$			1.09269i			0.0381818i
$820$		0			0
$821$		−	33.9341i		−	1.18431i	−0.805825	−	0.592154i	$-0.798278\pi$
$821$		−	33.9341i		−	1.18431i	0.805825	−	0.592154i	$-0.201722\pi$
$822$			12.1240i			0.422872i
$823$			6.03790i			0.210468i	0.994447	+	0.105234i	$0.0335591\pi$
$823$			6.03790i			0.210468i	−0.994447	+	0.105234i	$0.966441\pi$
$824$	−3.17523	+	3.17523i	−0.110614	+	0.110614i
$825$		0			0
$826$	10.3649	−	10.3649i	0.360640	−	0.360640i
$827$			34.3817i			1.19557i	0.801657	+	0.597784i	$0.203952\pi$
$827$			34.3817i			1.19557i	−0.801657	+	0.597784i	$0.796048\pi$
$828$	−7.70046	+	7.70046i	−0.267609	+	0.267609i
$829$	22.3751	+	22.3751i	0.777119	+	0.777119i	0.979340	−	0.202221i	$-0.0648159\pi$
$829$	22.3751	+	22.3751i	0.777119	+	0.777119i	−0.202221	+	0.979340i	$0.564816\pi$
$830$		0			0
$831$	30.4008	−	30.4008i	1.05459	−	1.05459i
$832$	−46.6833	−	46.6833i	−1.61845	−	1.61845i
$833$			34.1105i			1.18186i
$834$	53.6979			1.85941
$835$		0			0
$836$	−23.7936			−0.822920
$837$	−2.74668	−	2.74668i	−0.0949391	−	0.0949391i
$838$	36.4065			1.25764
$839$	7.70723	−	7.70723i	0.266083	−	0.266083i	−0.561437	−	0.827520i	$-0.689751\pi$
$839$	7.70723	−	7.70723i	0.266083	−	0.266083i	0.827520	+	0.561437i	$0.189751\pi$
$840$		0			0
$841$	−26.8534	−	10.9496i	−0.925980	−	0.377572i
$842$	16.6747	+	16.6747i	0.574649	+	0.574649i
$843$			35.3356i			1.21702i
$844$	33.7534	+	33.7534i	1.16184	+	1.16184i
$845$		0			0
$846$			1.72057i			0.0591543i
$847$	8.81104	−	8.81104i	0.302751	−	0.302751i
$848$	81.2762	−	81.2762i	2.79104	−	2.79104i
$849$	−7.53588	+	7.53588i	−0.258631	+	0.258631i
$850$		0			0
$851$	19.7894	+	19.7894i	0.678373	+	0.678373i
$852$	29.5405			1.01204
$853$	11.7987			0.403981			0.201990	−	0.979388i	$-0.435259\pi$
$853$	11.7987			0.403981			0.201990	+	0.979388i	$0.435259\pi$
$854$	5.02562			0.171973
$855$		0			0
$856$	79.8005	+	79.8005i	2.72753	+	2.72753i
$857$	−9.84337	−	9.84337i	−0.336243	−	0.336243i	0.518708	−	0.854951i	$-0.326413\pi$
$857$	−9.84337	−	9.84337i	−0.336243	−	0.336243i	−0.854951	+	0.518708i	$0.826413\pi$
$858$		−	15.8146i		−	0.539902i
$859$	29.8718	−	29.8718i	1.01921	−	1.01921i	0.0194004	−	0.999812i	$-0.493824\pi$
$859$	29.8718	−	29.8718i	1.01921	−	1.01921i	0.999812	−	0.0194004i	$-0.00617572\pi$
$860$		0			0
$861$	8.23449			0.280631
$862$	−21.8093			−0.742829
$863$	−13.8824	−	13.8824i	−0.472561	−	0.472561i	0.430181	−	0.902742i	$-0.358450\pi$
$863$	−13.8824	−	13.8824i	−0.472561	−	0.472561i	−0.902742	+	0.430181i	$0.858450\pi$
$864$			120.707i			4.10654i
$865$		0			0
$866$	−76.3055			−2.59297
$867$			56.1435i			1.90673i
$868$	5.85271			0.198654
$869$	4.66939			0.158398
$870$		0			0
$871$	21.7145			0.735767
$872$	−11.7031			−0.396318
$873$			2.04167i			0.0691000i
$874$	42.7899			1.44739
$875$		0			0
$876$			104.959i			3.54622i
$877$	−18.6332	−	18.6332i	−0.629200	−	0.629200i	0.318667	−	0.947867i	$-0.396765\pi$
$877$	−18.6332	−	18.6332i	−0.629200	−	0.629200i	−0.947867	+	0.318667i	$0.896765\pi$
$878$	−63.1446			−2.13103
$879$	15.9994			0.539648
$880$		0			0
$881$	33.3971	−	33.3971i	1.12518	−	1.12518i	0.134226	−	0.990951i	$-0.457145\pi$
$881$	33.3971	−	33.3971i	1.12518	−	1.12518i	0.990951	−	0.134226i	$-0.0428547\pi$
$882$		−	4.38513i		−	0.147655i
$883$	12.9731	+	12.9731i	0.436580	+	0.436580i	0.890859	−	0.454279i	$-0.150103\pi$
$883$	12.9731	+	12.9731i	0.436580	+	0.436580i	−0.454279	+	0.890859i	$0.650103\pi$
$884$	60.1425	+	60.1425i	2.02281	+	2.02281i
$885$		0			0
$886$	35.8830			1.20551
$887$	−11.7923			−0.395948			−0.197974	−	0.980207i	$-0.563436\pi$
$887$	−11.7923			−0.395948			−0.197974	+	0.980207i	$0.563436\pi$
$888$	73.6887			2.47283
$889$	−19.6152	−	19.6152i	−0.657872	−	0.657872i
$890$		0			0
$891$	−9.11434	+	9.11434i	−0.305342	+	0.305342i
$892$	−62.3086	+	62.3086i	−2.08625	+	2.08625i
$893$	3.50211	−	3.50211i	0.117194	−	0.117194i
$894$		−	40.5074i		−	1.35477i
$895$		0			0
$896$	−41.3604	−	41.3604i	−1.38175	−	1.38175i
$897$			20.8354i			0.695675i
$898$	38.8186	+	38.8186i	1.29539	+	1.29539i
$899$	−2.14293	−	3.18802i	−0.0714707	−	0.106326i
$900$		0			0
$901$	−38.6843	+	38.6843i	−1.28876	+	1.28876i
$902$	15.0833			0.502220
$903$	−13.9261	−	13.9261i	−0.463431	−	0.463431i
$904$	1.48233			0.0493014
$905$		0			0
$906$	−65.3459			−2.17097
$907$		−	37.1013i		−	1.23193i	−0.787775	−	0.615964i	$-0.788767\pi$
$907$		−	37.1013i		−	1.23193i	0.787775	−	0.615964i	$-0.211233\pi$
$908$	109.301	+	109.301i	3.62727	+	3.62727i
$909$	1.24529	−	1.24529i	0.0413038	−	0.0413038i
$910$		0			0
$911$	37.3064	+	37.3064i	1.23602	+	1.23602i	0.961616	+	0.274400i	$0.0884794\pi$
$911$	37.3064	+	37.3064i	1.23602	+	1.23602i	0.274400	+	0.961616i	$0.411521\pi$
$912$	46.1176	−	46.1176i	1.52711	−	1.52711i
$913$		−	12.2255i		−	0.404604i
$914$	−56.2282	+	56.2282i	−1.85986	+	1.85986i
$915$		0			0
$916$	−1.88651	+	1.88651i	−0.0623322	+	0.0623322i
$917$		−	9.71605i		−	0.320852i
$918$		−	106.776i		−	3.52413i
$919$		−	38.7184i		−	1.27720i	−0.769538	−	0.638601i	$-0.779514\pi$
$919$		−	38.7184i		−	1.27720i	0.769538	−	0.638601i	$-0.220486\pi$
$920$		0			0
$921$		−	0.796565i		−	0.0262477i
$922$	30.0063	+	30.0063i	0.988204	+	0.988204i
$923$	−5.05794	+	5.05794i	−0.166484	+	0.166484i
$924$		−	21.9146i		−	0.720936i
$925$		0			0
$926$	−53.5027	−	53.5027i	−1.75821	−	1.75821i
$927$	−0.112468	+	0.112468i	−0.00369392	+	0.00369392i
$928$	−22.9640	+	117.139i	−0.753831	+	3.84526i
$929$		−	25.0417i		−	0.821591i	−0.911728	−	0.410795i	$-0.865251\pi$
$929$		−	25.0417i		−	0.821591i	0.911728	−	0.410795i	$-0.134749\pi$
$930$		0			0
$931$	−8.92567	+	8.92567i	−0.292527	+	0.292527i
$932$	61.1588	−	61.1588i	2.00332	−	2.00332i
$933$	11.8691	+	11.8691i	0.388575	+	0.388575i
$934$	105.044			3.43715
$935$		0			0
$936$	−4.90953	−	4.90953i	−0.160473	−	0.160473i
$937$	12.9733	−	12.9733i	0.423820	−	0.423820i	−0.462696	−	0.886517i	$-0.653118\pi$
$937$	12.9733	−	12.9733i	0.423820	−	0.423820i	0.886517	+	0.462696i	$0.153118\pi$
$938$	41.0734			1.34109
$939$	31.4895	+	31.4895i	1.02762	+	1.02762i
$940$		0			0
$941$			19.5452i			0.637155i	0.947897	+	0.318578i	$0.103205\pi$
$941$			19.5452i			0.637155i	−0.947897	+	0.318578i	$0.896795\pi$
$942$	6.11540			0.199250
$943$	−19.8720			−0.647121
$944$			53.9166i			1.75484i
$945$		0			0
$946$	−25.5088	−	25.5088i	−0.829361	−	0.829361i
$947$	−14.9594			−0.486115			−0.243058	−	0.970012i	$-0.578150\pi$
$947$	−14.9594			−0.486115			−0.243058	+	0.970012i	$0.578150\pi$
$948$	−18.0376	+	18.0376i	−0.585833	+	0.585833i
$949$	−17.9711	−	17.9711i	−0.583366	−	0.583366i
$950$		0			0
$951$	−4.33399			−0.140539
$952$	72.2365	+	72.2365i	2.34120	+	2.34120i
$953$	14.4711	−	14.4711i	0.468765	−	0.468765i	−0.432749	−	0.901514i	$-0.642456\pi$
$953$	14.4711	−	14.4711i	0.468765	−	0.468765i	0.901514	+	0.432749i	$0.142456\pi$
$954$	4.97311	−	4.97311i	0.161011	−	0.161011i
$955$		0			0
$956$			68.1071i			2.20274i
$957$	−11.9370	+	8.02386i	−0.385869	+	0.259375i
$958$	−41.0004	+	41.0004i	−1.32466	+	1.32466i
$959$	−2.87657	−	2.87657i	−0.0928892	−	0.0928892i
$960$		0			0
$961$			30.4912i			0.983587i
$962$	−19.8698	+	19.8698i	−0.640626	+	0.640626i
$963$	2.82656	+	2.82656i	0.0910845	+	0.0910845i
$964$		−	6.35454i		−	0.204666i
$965$		0			0
$966$			39.4107i			1.26802i
$967$		−	49.4414i		−	1.58993i	−0.606657	−	0.794963i	$-0.707490\pi$
$967$		−	49.4414i		−	1.58993i	0.606657	−	0.794963i	$-0.292510\pi$
$968$			79.1770i			2.54484i
$969$	−21.9501	+	21.9501i	−0.705140	+	0.705140i
$970$		0			0
$971$	40.7685	−	40.7685i	1.30832	−	1.30832i	0.385701	−	0.922624i	$-0.373960\pi$
$971$	40.7685	−	40.7685i	1.30832	−	1.30832i	0.922624	−	0.385701i	$-0.126040\pi$
$972$			19.0966i			0.612523i
$973$	−12.7405	+	12.7405i	−0.408443	+	0.408443i
$974$	−76.8068	−	76.8068i	−2.46105	−	2.46105i
$975$		0			0
$976$	−13.0713	+	13.0713i	−0.418402	+	0.418402i
$977$	2.35368	+	2.35368i	0.0753008	+	0.0753008i	0.743754	−	0.668453i	$-0.233043\pi$
$977$	2.35368	+	2.35368i	0.0753008	+	0.0753008i	−0.668453	+	0.743754i	$0.733043\pi$
$978$		−	12.5498i		−	0.401297i
$979$	−23.5310			−0.752054
$980$		0			0
$981$	−0.414528			−0.0132349
$982$	69.3502	+	69.3502i	2.21305	+	2.21305i
$983$	−0.916231			−0.0292232			−0.0146116	−	0.999893i	$-0.504651\pi$
$983$	−0.916231			−0.0292232			−0.0146116	+	0.999893i	$0.504651\pi$
$984$	−36.9980	+	36.9980i	−1.17945	+	1.17945i
$985$		0			0
$986$	20.3136	−	103.619i	0.646918	−	3.29990i
$987$	3.22554	+	3.22554i	0.102670	+	0.102670i
$988$			31.4749i			1.00135i
$989$	33.6073	+	33.6073i	1.06865	+	1.06865i
$990$		0			0
$991$			11.2855i			0.358495i	0.983804	+	0.179248i	$0.0573663\pi$
$991$			11.2855i			0.358495i	−0.983804	+	0.179248i	$0.942634\pi$
$992$	−11.1803	+	11.1803i	−0.354976	+	0.354976i
$993$	22.5117	−	22.5117i	0.714387	−	0.714387i
$994$	−9.56719	+	9.56719i	−0.303453	+	0.303453i
$995$		0			0
$996$	47.2262	+	47.2262i	1.49642	+	1.49642i
$997$	45.0022			1.42523			0.712617	−	0.701553i	$-0.247510\pi$
$997$	45.0022			1.42523			0.712617	+	0.701553i	$0.247510\pi$
$998$	−13.1237			−0.415424
$999$	25.8432			0.817644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.j.c.307.13		26
5.2	odd	4		145.2.e.a.133.13	yes	26
5.3	odd	4		725.2.e.c.568.1		26
5.4	even	2		145.2.j.a.17.1	yes	26
29.12	odd	4		725.2.e.c.157.13		26
145.12	even	4		145.2.j.a.128.1	yes	26
145.99	odd	4		145.2.e.a.12.1	✓	26
145.128	even	4	inner	725.2.j.c.418.13		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.e.a.12.1	✓	26	145.99	odd	4
145.2.e.a.133.13	yes	26	5.2	odd	4
145.2.j.a.17.1	yes	26	5.4	even	2
145.2.j.a.128.1	yes	26	145.12	even	4
725.2.e.c.157.13		26	29.12	odd	4
725.2.e.c.568.1		26	5.3	odd	4
725.2.j.c.307.13		26	1.1	even	1	trivial
725.2.j.c.418.13		26	145.128	even	4	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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.73482 q^{2} +1.63186i q^{3} +5.47925 q^{4} +4.46285i q^{6} +(-1.05887 - 1.05887i) q^{7} +9.51511 q^{8} +0.337028 q^{9} +O(q^{10})\)	\(q+2.73482 q^{2} +1.63186i q^{3} +5.47925 q^{4} +4.46285i q^{6} +(-1.05887 - 1.05887i) q^{7} +9.51511 q^{8} +0.337028 q^{9} +(1.15733 - 1.15733i) q^{11} +8.94137i q^{12} +(-1.53095 - 1.53095i) q^{13} +(-2.89582 - 2.89582i) q^{14} +15.0636 q^{16} -7.16970 q^{17} +0.921711 q^{18} +(-1.87609 - 1.87609i) q^{19} +(1.72793 - 1.72793i) q^{21} +(3.16509 - 3.16509i) q^{22} +(-4.16994 + 4.16994i) q^{23} +15.5273i q^{24} +(-4.18686 - 4.18686i) q^{26} +5.44557i q^{27} +(-5.80180 - 5.80180i) q^{28} +(-1.03600 + 5.28457i) q^{29} +(-0.504388 + 0.504388i) q^{31} +22.1661 q^{32} +(1.88860 + 1.88860i) q^{33} -19.6078 q^{34} +1.84666 q^{36} -4.74574i q^{37} +(-5.13076 - 5.13076i) q^{38} +(2.49829 - 2.49829i) q^{39} +(2.38277 + 2.38277i) q^{41} +(4.72557 - 4.72557i) q^{42} -8.05942i q^{43} +(6.34129 - 6.34129i) q^{44} +(-11.4040 + 11.4040i) q^{46} +1.86671i q^{47} +24.5818i q^{48} -4.75760i q^{49} -11.7000i q^{51} +(-8.38843 - 8.38843i) q^{52} +(5.39552 - 5.39552i) q^{53} +14.8927i q^{54} +(-10.0753 - 10.0753i) q^{56} +(3.06152 - 3.06152i) q^{57} +(-2.83326 + 14.4524i) q^{58} +3.57926i q^{59} +(-0.867739 + 0.867739i) q^{61} +(-1.37941 + 1.37941i) q^{62} +(-0.356868 - 0.356868i) q^{63} +30.4931 q^{64} +(5.16498 + 5.16498i) q^{66} +(-7.09185 + 7.09185i) q^{67} -39.2845 q^{68} +(-6.80476 - 6.80476i) q^{69} -3.30380i q^{71} +3.20686 q^{72} +11.7385 q^{73} -12.9787i q^{74} +(-10.2795 - 10.2795i) q^{76} -2.45092 q^{77} +(6.83238 - 6.83238i) q^{78} +(2.01731 + 2.01731i) q^{79} -7.87533 q^{81} +(6.51644 + 6.51644i) q^{82} +(5.28177 - 5.28177i) q^{83} +(9.46773 - 9.46773i) q^{84} -22.0411i q^{86} +(-8.62369 - 1.69060i) q^{87} +(11.0121 - 11.0121i) q^{88} +(-10.1661 - 10.1661i) q^{89} +3.24214i q^{91} +(-22.8481 + 22.8481i) q^{92} +(-0.823091 - 0.823091i) q^{93} +5.10511i q^{94} +36.1721i q^{96} +6.05786i q^{97} -13.0112i q^{98} +(0.390052 - 0.390052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 6 q^{2} + 22 q^{4} + 4 q^{7} + 18 q^{8} - 10 q^{9}+O(q^{10}) \) 26 * q + 6 * q^2 + 22 * q^4 + 4 * q^7 + 18 * q^8 - 10 * q^9	\( 26 q + 6 q^{2} + 22 q^{4} + 4 q^{7} + 18 q^{8} - 10 q^{9} - 8 q^{11} - 14 q^{13} - 4 q^{14} + 6 q^{16} - 20 q^{17} + 18 q^{18} + 16 q^{21} + 8 q^{22} + 4 q^{23} + 6 q^{26} + 8 q^{28} + 8 q^{31} + 42 q^{32} - 32 q^{34} - 22 q^{36} + 8 q^{38} - 16 q^{39} - 6 q^{41} + 4 q^{42} - 32 q^{46} - 26 q^{52} - 14 q^{53} - 32 q^{56} + 12 q^{57} - 28 q^{58} + 18 q^{61} - 28 q^{62} - 60 q^{63} + 30 q^{64} + 20 q^{66} - 32 q^{67} - 72 q^{68} + 12 q^{69} - 10 q^{72} + 4 q^{73} + 20 q^{76} + 12 q^{77} - 56 q^{78} + 4 q^{79} - 86 q^{81} + 58 q^{82} + 60 q^{83} + 76 q^{84} - 60 q^{87} + 68 q^{88} - 46 q^{89} + 28 q^{92} + 8 q^{93} + 36 q^{99}+O(q^{100}) \) 26 * q + 6 * q^2 + 22 * q^4 + 4 * q^7 + 18 * q^8 - 10 * q^9 - 8 * q^11 - 14 * q^13 - 4 * q^14 + 6 * q^16 - 20 * q^17 + 18 * q^18 + 16 * q^21 + 8 * q^22 + 4 * q^23 + 6 * q^26 + 8 * q^28 + 8 * q^31 + 42 * q^32 - 32 * q^34 - 22 * q^36 + 8 * q^38 - 16 * q^39 - 6 * q^41 + 4 * q^42 - 32 * q^46 - 26 * q^52 - 14 * q^53 - 32 * q^56 + 12 * q^57 - 28 * q^58 + 18 * q^61 - 28 * q^62 - 60 * q^63 + 30 * q^64 + 20 * q^66 - 32 * q^67 - 72 * q^68 + 12 * q^69 - 10 * q^72 + 4 * q^73 + 20 * q^76 + 12 * q^77 - 56 * q^78 + 4 * q^79 - 86 * q^81 + 58 * q^82 + 60 * q^83 + 76 * q^84 - 60 * q^87 + 68 * q^88 - 46 * q^89 + 28 * q^92 + 8 * q^93 + 36 * q^99

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