LMFDB - Embedded newform 725.2.e.c.568.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(157,725)]

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, 1]))

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

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

chi := DirichletCharacter("725.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.e (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			568.1
Character	$\chi$	$=$	725.568
Dual form			725.2.e.c.157.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	2.73482i		−	1.93381i	−0.255136	−	0.966905i	$-0.582120\pi$
$2$		−	2.73482i		−	1.93381i	0.255136	−	0.966905i	$-0.417880\pi$
$3$	−1.63186			−0.942156			−0.471078	−	0.882092i	$-0.656135\pi$
$3$	−1.63186			−0.942156			−0.471078	+	0.882092i	$0.656135\pi$
$4$	−5.47925			−2.73962
$5$		0			0
$5$		0			0
$6$			4.46285i			1.82195i
$7$	−1.05887	+	1.05887i	−0.400215	+	0.400215i	−0.878309	−	0.478094i	$-0.841328\pi$
$7$	−1.05887	+	1.05887i	−0.400215	+	0.400215i	0.478094	+	0.878309i	$0.341328\pi$
$8$			9.51511i			3.36410i
$9$	−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	$0.170640\pi$
$12$	8.94137			2.58115
$13$	1.53095	−	1.53095i	0.424608	−	0.424608i	−0.462179	−	0.886787i	$-0.652932\pi$
$13$	1.53095	−	1.53095i	0.424608	−	0.424608i	0.886787	+	0.462179i	$0.152932\pi$
$14$	2.89582	+	2.89582i	0.773939	+	0.773939i
$15$		0			0
$16$	15.0636			3.76591
$17$			7.16970i			1.73891i	0.494015	+	0.869453i	$0.335529\pi$
$17$			7.16970i			1.73891i	−0.494015	+	0.869453i	$0.664471\pi$
$18$			0.921711i			0.217249i
$19$	1.87609	+	1.87609i	0.430404	+	0.430404i	0.888766	−	0.458362i	$-0.151564\pi$
$19$	1.87609	+	1.87609i	0.430404	+	0.430404i	−0.458362	+	0.888766i	$0.651564\pi$
$20$		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	0.122924	−	0.992416i	$-0.460773\pi$
$23$	−4.16994	−	4.16994i	−0.869492	−	0.869492i	−0.992416	+	0.122924i	$0.960773\pi$
$24$		−	15.5273i		−	3.16951i
$25$		0			0
$26$	−4.18686	−	4.18686i	−0.821111	−	0.821111i
$27$	5.44557			1.04800
$28$	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	$0.270404\pi$
$32$		−	22.1661i		−	3.91846i
$33$	−1.88860	+	1.88860i	−0.328763	+	0.328763i
$34$	19.6078			3.36272
$35$		0			0
$36$	1.84666			0.307777
$37$	−4.74574			−0.780194			−0.390097	−	0.920774i	$-0.627559\pi$
$37$	−4.74574			−0.780194			−0.390097	+	0.920774i	$0.627559\pi$
$38$	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
$43$	8.05942			1.22905			0.614525	−	0.788897i	$-0.289348\pi$
$43$	8.05942			1.22905			0.614525	+	0.788897i	$0.289348\pi$
$44$	−6.34129	+	6.34129i	−0.955985	+	0.955985i
$45$		0			0
$46$	−11.4040	+	11.4040i	−1.68143	+	1.68143i
$47$	1.86671			0.272287			0.136144	−	0.990689i	$-0.456529\pi$
$47$	1.86671			0.272287			0.136144	+	0.990689i	$0.456529\pi$
$48$	−24.5818			−3.54807
$49$			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	0.972796	−	0.231664i	$-0.0744169\pi$
$53$	5.39552	+	5.39552i	0.741132	+	0.741132i	−0.231664	+	0.972796i	$0.574417\pi$
$54$		−	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
$58$	−14.4524	−	2.83326i	−1.89769	−	0.372026i
$59$		−	3.57926i		−	0.465979i	−0.972479	−	0.232990i	$-0.925149\pi$
$59$		−	3.57926i		−	0.465979i	0.972479	−	0.232990i	$-0.0748509\pi$
$60$		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	$-0.0401065\pi$
$67$	7.09185	+	7.09185i	0.866408	+	0.866408i	−0.125665	+	0.992073i	$0.540106\pi$
$68$		−	39.2845i		−	4.76395i
$69$	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	$-0.0628096\pi$
$72$		−	3.20686i		−	0.377932i
$73$			11.7385i			1.37389i	0.726708	+	0.686946i	$0.241049\pi$
$73$			11.7385i			1.37389i	−0.726708	+	0.686946i	$0.758951\pi$
$74$			12.9787i			1.50875i
$75$		0			0
$76$	−10.2795	−	10.2795i	−1.17914	−	1.17914i
$77$			2.45092i			0.279308i
$78$	6.83238	+	6.83238i	0.773615	+	0.773615i
$79$	−2.01731	−	2.01731i	−0.226966	−	0.226966i	0.584458	−	0.811424i	$-0.301307\pi$
$79$	−2.01731	−	2.01731i	−0.226966	−	0.226966i	−0.811424	+	0.584458i	$0.801307\pi$
$80$		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	0.934834	−	0.355085i	$-0.115548\pi$
$83$	5.28177	+	5.28177i	0.579749	+	0.579749i	−0.355085	+	0.934834i	$0.615548\pi$
$84$	−9.46773	+	9.46773i	−1.03301	+	1.03301i
$85$		0			0
$86$		−	22.0411i		−	2.37675i
$87$	−1.69060	+	8.62369i	−0.181251	+	0.924557i
$88$	11.0121	+	11.0121i	1.17390	+	1.17390i
$89$	10.1661	+	10.1661i	1.07760	+	1.07760i	0.996724	+	0.0808784i	$0.0257725\pi$
$89$	10.1661	+	10.1661i	1.07760	+	1.07760i	0.0808784	+	0.996724i	$0.474227\pi$
$90$		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
$97$	6.05786			0.615082			0.307541	−	0.951535i	$-0.400494\pi$
$97$	6.05786			0.615082			0.307541	+	0.951535i	$0.400494\pi$
$98$	13.0112			1.31433
$99$	−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	$0.166286\pi$
$102$	−31.9973			−3.16820
$103$	−0.333704	−	0.333704i	−0.0328808	−	0.0328808i	0.690475	−	0.723356i	$-0.257401\pi$
$103$	−0.333704	−	0.333704i	−0.0328808	−	0.0328808i	−0.723356	+	0.690475i	$0.757401\pi$
$104$	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	−0.173976	−	0.984750i	$-0.555662\pi$
$107$	8.38671	−	8.38671i	0.810774	−	0.810774i	0.984750	+	0.173976i	$0.0556615\pi$
$108$	−29.8376			−2.87112
$109$	1.22995			0.117808			0.0589040	−	0.998264i	$-0.481239\pi$
$109$	1.22995			0.117808			0.0589040	+	0.998264i	$0.481239\pi$
$110$		0			0
$111$	7.74438			0.735064
$112$	−15.9504	+	15.9504i	−1.50717	+	1.50717i
$113$			0.155786i			0.0146552i	0.999973	+	0.00732758i	$0.00233246\pi$
$113$			0.155786i			0.0146552i	−0.999973	+	0.00732758i	$0.997668\pi$
$114$	−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
$118$	−9.78863			−0.901116
$119$	−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
$127$		−	18.5247i		−	1.64380i	−0.569634	−	0.821899i	$-0.692915\pi$
$127$		−	18.5247i		−	1.64380i	0.569634	−	0.821899i	$-0.307085\pi$
$128$			39.0610i			3.45253i
$129$	−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
$133$	−3.97306			−0.344508
$134$	19.3949	−	19.3949i	1.67547	−	1.67547i
$135$		0			0
$136$	−68.2205			−5.84986
$137$		−	2.71664i		−	0.232098i	−0.993243	−	0.116049i	$-0.962977\pi$
$137$		−	2.71664i		−	0.232098i	0.993243	−	0.116049i	$-0.0370230\pi$
$138$	18.6098	−	18.6098i	1.58417	−	1.58417i
$139$			12.0322i			1.02056i	0.860009	+	0.510279i	$0.170458\pi$
$139$			12.0322i			1.02056i	−0.860009	+	0.510279i	$0.829542\pi$
$140$		0			0
$141$	−3.04621			−0.256537
$142$	−9.03529			−0.758225
$143$		−	3.54362i		−	0.296332i
$144$	−5.07687			−0.423072
$145$		0			0
$146$	32.1028			2.65685
$147$		−	7.76374i		−	0.640342i
$148$	26.0031			2.13744
$149$	9.07657			0.743581			0.371791	−	0.928317i	$-0.378744\pi$
$149$	9.07657			0.743581			0.371791	+	0.928317i	$0.378744\pi$
$150$		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
$153$		−	2.41639i		−	0.195353i
$154$	6.70282			0.540129
$155$		0			0
$156$	13.6888	−	13.6888i	1.09598	−	1.09598i
$157$	−1.37029			−0.109361			−0.0546805	−	0.998504i	$-0.517414\pi$
$157$	−1.37029			−0.109361			−0.0546805	+	0.998504i	$0.517414\pi$
$158$	−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
$162$			21.5376i			1.69215i
$163$		−	2.81205i		−	0.220257i	−0.993917	−	0.110128i	$-0.964874\pi$
$163$		−	2.81205i		−	0.220257i	0.993917	−	0.110128i	$-0.0351262\pi$
$164$	−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	$-0.161517\pi$
$167$	5.01507	+	5.01507i	0.388078	+	0.388078i	−0.485923	+	0.874001i	$0.661517\pi$
$168$	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
$172$	−44.1595			−3.36713
$173$	−11.8741	+	11.8741i	−0.902767	+	0.902767i	−0.995675	−	0.0929073i	$-0.970384\pi$
$173$	−11.8741	+	11.8741i	−0.902767	+	0.902767i	0.0929073	+	0.995675i	$0.470384\pi$
$174$	23.5843	+	4.62349i	1.78792	+	0.350506i
$175$		0			0
$176$	17.4336	−	17.4336i	1.31411	−	1.31411i
$177$			5.84085i			0.439025i
$178$	27.8024	−	27.8024i	2.08388	−	2.08388i
$179$	0.831099			0.0621193			0.0310596	−	0.999518i	$-0.490112\pi$
$179$	0.831099			0.0621193			0.0310596	+	0.999518i	$0.490112\pi$
$180$		0			0
$181$	−16.5277			−1.22849			−0.614245	−	0.789115i	$-0.710540\pi$
$181$	−16.5277			−1.22849			−0.614245	+	0.789115i	$0.710540\pi$
$182$	8.86667			0.657242
$183$	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
$188$	−10.2282			−0.745965
$189$	−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	$0.218612\pi$
$192$	49.7606			3.59116
$193$	−5.17863			−0.372766			−0.186383	−	0.982477i	$-0.559677\pi$
$193$	−5.17863			−0.372766			−0.186383	+	0.982477i	$0.559677\pi$
$194$		−	16.5672i		−	1.18945i
$195$		0			0
$196$		−	26.0680i		−	1.86200i
$197$	−12.4638	+	12.4638i	−0.888007	+	0.888007i	−0.994332	−	0.106324i	$-0.966092\pi$
$197$	−12.4638	+	12.4638i	−0.888007	+	0.888007i	0.106324	+	0.994332i	$0.466092\pi$
$198$	1.06672	+	1.06672i	0.0758087	+	0.0758087i
$199$			8.92943i			0.632990i	0.948594	+	0.316495i	$0.102506\pi$
$199$			8.92943i			0.632990i	−0.948594	+	0.316495i	$0.897494\pi$
$200$		0			0
$201$	−11.5729	−	11.5729i	−0.816291	−	0.816291i
$202$	−10.1050	−	10.1050i	−0.710983	−	0.710983i
$203$	4.49868	+	6.69265i	0.315746	+	0.469732i
$204$			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
$213$			5.39134i			0.369409i
$214$	−22.9362	−	22.9362i	−1.56788	−	1.56788i
$215$		0			0
$216$			51.8152i			3.52558i
$217$		−	1.06816i		−	0.0725115i
$218$		−	3.36370i		−	0.227819i
$219$		−	19.1557i		−	1.29442i
$220$		0			0
$221$	10.9764	+	10.9764i	0.738354	+	0.738354i
$222$		−	21.1795i		−	1.42148i
$223$	−11.3717	−	11.3717i	−0.761509	−	0.761509i	0.215086	−	0.976595i	$-0.430997\pi$
$223$	−11.3717	−	11.3717i	−0.761509	−	0.761509i	−0.976595	+	0.215086i	$0.930997\pi$
$224$	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	0.413497	−	0.910506i	$-0.364307\pi$
$227$	19.9481	−	19.9481i	1.32400	−	1.32400i	0.910506	−	0.413497i	$-0.135693\pi$
$228$	16.7748	+	16.7748i	1.11094	+	1.11094i
$229$	0.344302	−	0.344302i	0.0227521	−	0.0227521i	−0.695639	−	0.718391i	$-0.744879\pi$
$229$	0.344302	−	0.344302i	0.0227521	−	0.0227521i	0.718391	+	0.695639i	$0.244879\pi$
$230$		0			0
$231$		−	3.99956i		−	0.263152i
$232$	50.2833	+	9.85762i	3.30126	+	0.647184i
$233$	11.1619	+	11.1619i	0.731241	+	0.731241i	0.970866	−	0.239625i	$-0.0770244\pi$
$233$	11.1619	+	11.1619i	0.731241	+	0.731241i	−0.239625	+	0.970866i	$0.577024\pi$
$234$	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	$-0.868310\pi$
$239$		−	12.4300i		−	0.804031i	0.915633	−	0.402016i	$-0.131690\pi$
$240$		0			0
$241$		−	1.15975i		−	0.0747058i	−0.999302	−	0.0373529i	$-0.988107\pi$
$241$		−	1.15975i		−	0.0747058i	0.999302	−	0.0373529i	$-0.0118926\pi$
$242$	22.7569			1.46287
$243$	−3.48526			−0.223579
$244$	4.75455	−	4.75455i	0.304379	−	0.304379i
$245$		0			0
$246$	−10.6339	+	10.6339i	−0.677995	+	0.677995i
$247$	5.74438			0.365506
$248$	−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
$253$	−9.65198			−0.606815
$254$	−50.6616			−3.17879
$255$		0			0
$256$	45.8385			2.86491
$257$	−12.6288	+	12.6288i	−0.787765	+	0.787765i	−0.981127	−	0.193362i	$-0.938061\pi$
$257$	−12.6288	+	12.6288i	−0.787765	+	0.787765i	0.193362	+	0.981127i	$0.438061\pi$
$258$			35.9680i			2.23927i
$259$	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
$263$	−28.1945			−1.73855			−0.869275	−	0.494329i	$-0.835414\pi$
$263$	−28.1945			−1.73855			−0.869275	+	0.494329i	$0.835414\pi$
$264$	−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	−0.284000	−	0.958824i	$-0.591662\pi$
$269$	11.0679	−	11.0679i	0.674824	−	0.674824i	0.958824	+	0.284000i	$0.0916617\pi$
$270$		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	$0.720150\pi$
$272$			108.002i			6.54857i
$273$		−	5.29072i		−	0.320209i
$274$	−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	−0.127503	+	0.991838i	$0.540696\pi$
$277$	−18.6295	+	18.6295i	−1.11934	+	1.11934i	−0.991838	+	0.127503i	$0.959304\pi$
$278$	32.9059			1.97357
$279$	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	$0.276494\pi$
$282$			8.33084i			0.496094i
$283$	−4.61797	+	4.61797i	−0.274510	+	0.274510i	−0.830913	−	0.556403i	$-0.812181\pi$
$283$	−4.61797	+	4.61797i	−0.274510	+	0.274510i	0.556403	+	0.830913i	$0.312181\pi$
$284$			18.1023i			1.07417i
$285$		0			0
$286$	−9.69115			−0.573050
$287$	−5.04607			−0.297860
$288$			7.47061i			0.440210i
$289$	−34.4045			−2.02380
$290$		0			0
$291$	−9.88558			−0.579503
$292$		−	64.3183i		−	3.76395i
$293$	9.80441			0.572780			0.286390	−	0.958113i	$-0.407545\pi$
$293$	9.80441			0.572780			0.286390	+	0.958113i	$0.407545\pi$
$294$	−21.2324			−1.23830
$295$		0			0
$296$		−	45.1562i		−	2.62465i
$297$	6.30231	−	6.30231i	0.365697	−	0.365697i
$298$		−	24.8228i		−	1.43795i
$299$	−12.7679			−0.738387
$300$		0			0
$301$	−8.53386	+	8.53386i	−0.491884	+	0.491884i
$302$	40.0438			2.30426
$303$	−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
$307$			0.488133i			0.0278592i	0.999903	+	0.0139296i	$0.00443407\pi$
$307$			0.488133i			0.0278592i	−0.999903	+	0.0139296i	$0.995566\pi$
$308$		−	13.4292i		−	0.765198i
$309$	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	0.995452	+	0.0952605i	$0.0303684\pi$
$313$	19.2967	+	19.2967i	1.09071	+	1.09071i	0.0952605	+	0.995452i	$0.469632\pi$
$314$			3.74750i			0.211483i
$315$		0			0
$316$	11.0534	+	11.0534i	0.621800	+	0.621800i
$317$	2.65586			0.149168			0.0745839	−	0.997215i	$-0.476237\pi$
$317$	2.65586			0.149168			0.0745839	+	0.997215i	$0.476237\pi$
$318$	−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
$322$		−	24.1507i		−	1.34587i
$323$	−13.4510	+	13.4510i	−0.748433	+	0.748433i
$324$	43.1509			2.39727
$325$		0			0
$326$	−7.69045			−0.425935
$327$	−2.00711			−0.110994
$328$	−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
$333$	1.59945			0.0876491
$334$	13.7153	−	13.7153i	0.750469	−	0.750469i
$335$		0			0
$336$	26.0289	−	26.0289i	1.41999	−	1.41999i
$337$	−16.3087			−0.888389			−0.444195	−	0.895930i	$-0.646510\pi$
$337$	−16.3087			−0.888389			−0.444195	+	0.895930i	$0.646510\pi$
$338$	22.7329			1.23651
$339$		−	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	$-0.288272\pi$
$347$	−3.15980	−	3.15980i	−0.169627	−	0.169627i	−0.786815	+	0.617188i	$0.788272\pi$
$348$	9.26322	−	47.2513i	0.496561	−	2.53294i
$349$			17.3855i			0.930627i	0.885146	+	0.465313i	$0.154058\pi$
$349$			17.3855i			0.930627i	−0.885146	+	0.465313i	$0.845942\pi$
$350$		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	$-0.632258\pi$
$353$	9.60586	−	9.60586i	0.511268	−	0.511268i	0.914915	+	0.403647i	$0.132258\pi$
$354$	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
$358$		−	2.27291i		−	0.120127i
$359$	16.6718	+	16.6718i	0.879906	+	0.879906i	0.993524	−	0.113618i	$-0.0362440\pi$
$359$	16.6718	+	16.6718i	0.879906	+	0.879906i	−0.113618	+	0.993524i	$0.536244\pi$
$360$		0			0
$361$		−	11.9606i		−	0.629505i
$362$			45.2002i			2.37567i
$363$		−	13.5790i		−	0.712713i
$364$		−	17.7645i		−	0.931112i
$365$		0			0
$366$	−3.87259	−	3.87259i	−0.202423	−	0.202423i
$367$		−	5.52771i		−	0.288544i	−0.989538	−	0.144272i	$-0.953916\pi$
$367$		−	5.52771i		−	0.288544i	0.989538	−	0.144272i	$-0.0460840\pi$
$368$	−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	0.720076	−	0.693895i	$-0.244107\pi$
$373$	0.505639	+	0.505639i	0.0261810	+	0.0261810i	−0.693895	+	0.720076i	$0.744107\pi$
$374$	22.6927	−	22.6927i	1.17341	−	1.17341i
$375$		0			0
$376$			17.7619i			0.916003i
$377$	−6.50434	−	9.67645i	−0.334991	−	0.498363i
$378$	15.7694	+	15.7694i	0.811088	+	0.811088i
$379$	−21.9491	−	21.9491i	−1.12745	−	1.12745i	−0.990590	−	0.136859i	$-0.956299\pi$
$379$	−21.9491	−	21.9491i	−1.12745	−	1.12745i	−0.136859	−	0.990590i	$-0.543701\pi$
$380$		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	$-0.654353\pi$
$383$	8.19179	−	8.19179i	0.418581	−	0.418581i	0.884714	+	0.466134i	$0.154353\pi$
$384$		−	63.7421i		−	3.25282i
$385$		0			0
$386$			14.1626i			0.720859i
$387$	−2.71625			−0.138075
$388$	−33.1925			−1.68509
$389$	−1.00500	+	1.00500i	−0.0509555	+	0.0509555i	−0.732125	−	0.681170i	$-0.761472\pi$
$389$	−1.00500	+	1.00500i	−0.0509555	+	0.0509555i	0.681170	+	0.732125i	$0.261472\pi$
$390$		0			0
$391$	29.8972	−	29.8972i	1.51197	−	1.51197i
$392$	−45.2691			−2.28643
$393$	−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	−0.435797	−	0.900045i	$-0.643533\pi$
$397$	9.25008	−	9.25008i	0.464248	−	0.464248i	0.900045	+	0.435797i	$0.143533\pi$
$398$	24.4204			1.22408
$399$	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
$403$			1.54438i			0.0769311i
$404$	−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
$408$	111.326			5.51148
$409$	−1.32729	−	1.32729i	−0.0656305	−	0.0656305i	0.673530	−	0.739160i	$-0.264777\pi$
$409$	−1.32729	−	1.32729i	−0.0656305	−	0.0656305i	−0.739160	+	0.673530i	$0.764777\pi$
$410$		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
$417$		−	19.6349i		−	0.961525i
$418$		−	11.8760i		−	0.580872i
$419$	−13.3122			−0.650345			−0.325172	−	0.945655i	$-0.605422\pi$
$419$	−13.3122			−0.650345			−0.325172	+	0.945655i	$0.605422\pi$
$420$		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
$423$	−0.629133			−0.0305895
$424$	−51.3390	+	51.3390i	−2.49324	+	2.49324i
$425$		0			0
$426$	14.7443			0.714366
$427$		−	1.83764i		−	0.0889297i
$428$	−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	$0.561518\pi$
$432$	82.0301			3.94667
$433$		−	27.9015i		−	1.34086i	−0.741973	−	0.670430i	$-0.766110\pi$
$433$		−	27.9015i		−	1.34086i	0.741973	−	0.670430i	$-0.233890\pi$
$434$	−2.92123			−0.140223
$435$		0			0
$436$	−6.73921			−0.322750
$437$		−	15.6463i		−	0.748466i
$438$	−52.3873			−2.50316
$439$	23.0891			1.10198			0.550991	−	0.834511i	$-0.314250\pi$
$439$	23.0891			1.10198			0.550991	+	0.834511i	$0.314250\pi$
$440$		0			0
$441$		−	1.60344i		−	0.0763544i
$442$	30.0185	−	30.0185i	1.42784	−	1.42784i
$443$			13.1208i			0.623388i	0.950183	+	0.311694i	$0.100896\pi$
$443$			13.1208i			0.623388i	−0.950183	+	0.311694i	$0.899104\pi$
$444$	−42.4334			−2.01380
$445$		0			0
$446$	−31.0997	+	31.0997i	−1.47261	+	1.47261i
$447$	−14.8117			−0.700569
$448$	32.2882	−	32.2882i	1.52547	−	1.52547i
$449$	−14.1942	−	14.1942i	−0.669865	−	0.669865i	0.287819	−	0.957685i	$-0.407070\pi$
$449$	−14.1942	−	14.1942i	−0.669865	−	0.669865i	−0.957685	+	0.287819i	$0.907070\pi$
$450$		0			0
$451$	5.51529			0.259705
$452$		−	0.853592i		−	0.0401496i
$453$		−	23.8940i		−	1.12264i
$454$	−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	$-0.0119504\pi$
$457$	20.5601	+	20.5601i	0.961761	+	0.961761i	−0.0375345	+	0.999295i	$0.511950\pi$
$458$	−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	$0.632319\pi$
$462$	−10.9381			−0.508885
$463$	19.5635	−	19.5635i	0.909193	−	0.909193i	−0.0870140	−	0.996207i	$-0.527732\pi$
$463$	19.5635	−	19.5635i	0.909193	−	0.909193i	0.996207	+	0.0870140i	$0.0277325\pi$
$464$	15.6059	−	79.6049i	0.724484	−	3.69557i
$465$		0			0
$466$	30.5258	−	30.5258i	1.41408	−	1.41408i
$467$		−	38.4099i		−	1.77740i	−0.458491	−	0.888699i	$-0.651610\pi$
$467$		−	38.4099i		−	1.77740i	0.458491	−	0.888699i	$-0.348390\pi$
$468$	2.82714	−	2.82714i	0.130684	−	0.130684i
$469$	−15.0187			−0.693498
$470$		0			0
$471$	2.23612			0.103035
$472$	34.0570			1.56760
$473$	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
$478$	−33.9939			−1.55484
$479$	14.9920	−	14.9920i	0.685002	−	0.685002i	−0.276121	−	0.961123i	$-0.589049\pi$
$479$	14.9920	−	14.9920i	0.685002	−	0.685002i	0.961123	+	0.276121i	$0.0890491\pi$
$480$		0			0
$481$	−7.26547	+	7.26547i	−0.331277	+	0.331277i
$482$	−3.17170			−0.144467
$483$	−14.4107			−0.655709
$484$		−	45.5938i		−	2.07245i
$485$		0			0
$486$			9.53156i			0.432360i
$487$	−28.0848	+	28.0848i	−1.27264	+	1.27264i	−0.327945	+	0.944697i	$0.606356\pi$
$487$	−28.0848	+	28.0848i	−1.27264	+	1.27264i	−0.944697	+	0.327945i	$0.893644\pi$
$488$	−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
$493$	37.8888	+	7.42777i	1.70643	+	0.334530i
$494$		−	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	$-0.465744\pi$
$499$	4.79875			0.214821			0.107411	+	0.994215i	$0.465744\pi$
$500$		0			0
$501$	−8.18390	−	8.18390i	−0.365630	−	0.365630i
$502$	47.8904	+	47.8904i	2.13745	+	2.13745i
$503$			35.2896i			1.57348i	0.617282	+	0.786742i	$0.288234\pi$
$503$			35.2896i			1.57348i	−0.617282	+	0.786742i	$0.711766\pi$
$504$	3.39564	+	3.39564i	0.151254	+	0.151254i
$505$		0			0
$506$			26.3964i			1.17346i
$507$		−	13.5647i		−	0.602429i
$508$			101.501i			4.50339i
$509$			30.1303i			1.33550i	0.744384	+	0.667752i	$0.232743\pi$
$509$			30.1303i			1.33550i	−0.744384	+	0.667752i	$0.767257\pi$
$510$		0			0
$511$	−12.4296	−	12.4296i	−0.549852	−	0.549852i
$512$		−	47.2382i		−	2.08765i
$513$	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	$-0.186841\pi$
$522$	4.87085	+	0.954889i	0.213191	+	0.0417943i
$523$	3.79891	+	3.79891i	0.166115	+	0.166115i	0.785269	−	0.619155i	$-0.212525\pi$
$523$	3.79891	+	3.79891i	0.166115	+	0.166115i	−0.619155	+	0.785269i	$0.712525\pi$
$524$	−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
$532$	21.7694			0.943822
$533$	7.29578			0.316015
$534$	−45.3697	+	45.3697i	−1.96334	+	1.96334i
$535$		0			0
$536$	−67.4798	+	67.4798i	−2.91468	+	2.91468i
$537$	−1.35624			−0.0585260
$538$	−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
$543$	26.9708			1.15743
$544$	158.924			6.81383
$545$		0			0
$546$	−14.4692			−0.619224
$547$	−5.45211	+	5.45211i	−0.233115	+	0.233115i	−0.813992	−	0.580876i	$-0.802710\pi$
$547$	−5.45211	+	5.45211i	−0.233115	+	0.233115i	0.580876	+	0.813992i	$0.302710\pi$
$548$			14.8851i			0.635862i
$549$	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
$553$	4.27214			0.181670
$554$	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	0.871746	+	0.489958i	$0.162988\pi$
$557$	32.1374	+	32.1374i	1.36170	+	1.36170i	0.489958	+	0.871746i	$0.337012\pi$
$558$	−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
$562$		−	59.2186i		−	2.49798i
$563$		−	2.60063i		−	0.109603i	−0.998497	−	0.0548017i	$-0.982547\pi$
$563$		−	2.60063i		−	0.109603i	0.998497	−	0.0548017i	$-0.0174527\pi$
$564$	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
$568$	31.4360			1.31903
$569$	16.3628	−	16.3628i	0.685965	−	0.685965i	−0.275372	−	0.961338i	$-0.588801\pi$
$569$	16.3628	−	16.3628i	0.685965	−	0.685965i	0.961338	+	0.275372i	$0.0888012\pi$
$570$		0			0
$571$	−10.3466			−0.432992			−0.216496	−	0.976284i	$-0.569463\pi$
$571$	−10.3466			−0.432992			−0.216496	+	0.976284i	$0.569463\pi$
$572$			19.4163i			0.811838i
$573$	−3.13995	+	3.13995i	−0.131173	+	0.131173i
$574$			13.8001i			0.576005i
$575$		0			0
$576$	10.2770			0.428210
$577$	−23.3309			−0.971278			−0.485639	−	0.874159i	$-0.661413\pi$
$577$	−23.3309			−0.971278			−0.485639	+	0.874159i	$0.661413\pi$
$578$			94.0903i			3.91364i
$579$	8.45081			0.351204
$580$		0			0
$581$	−11.1854			−0.464048
$582$			27.0353i			1.12065i
$583$	12.4888			0.517233
$584$	−111.694			−4.62191
$585$		0			0
$586$		−	26.8133i		−	1.10765i
$587$	26.1594	−	26.1594i	1.07971	−	1.07971i	0.0831773	−	0.996535i	$-0.473493\pi$
$587$	26.1594	−	26.1594i	1.07971	−	1.07971i	0.996535	−	0.0831773i	$-0.0265068\pi$
$588$			42.5394i			1.75430i
$589$	−1.89255			−0.0779812
$590$		0			0
$591$	20.3392	−	20.3392i	0.836641	−	0.836641i
$592$	−71.4881			−2.93814
$593$	10.3930	−	10.3930i	0.426790	−	0.426790i	−0.460743	−	0.887533i	$-0.652417\pi$
$593$	10.3930	−	10.3930i	0.426790	−	0.426790i	0.887533	+	0.460743i	$0.152417\pi$
$594$	−17.2357	−	17.2357i	−0.707189	−	0.707189i
$595$		0			0
$596$	−49.7327			−2.03713
$597$		−	14.5716i		−	0.596375i
$598$			34.9179i			1.42790i
$599$	11.0108	+	11.0108i	0.449891	+	0.449891i	0.895318	−	0.445427i	$-0.146948\pi$
$599$	11.0108	+	11.0108i	0.449891	+	0.449891i	−0.445427	+	0.895318i	$0.646948\pi$
$600$		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
$607$	48.6467			1.97451			0.987254	−	0.159154i	$-0.0508767\pi$
$607$	48.6467			1.97451			0.987254	+	0.159154i	$0.0508767\pi$
$608$	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
$612$			13.2400i			0.535195i
$613$	−14.0319	+	14.0319i	−0.566744	+	0.566744i	−0.931215	−	0.364471i	$-0.881250\pi$
$613$	−14.0319	+	14.0319i	−0.566744	+	0.566744i	0.364471	+	0.931215i	$0.381250\pi$
$614$	1.33496			0.0538744
$615$		0			0
$616$	−23.3208			−0.939620
$617$	−35.2664			−1.41977			−0.709885	−	0.704318i	$-0.751253\pi$
$617$	−35.2664			−1.41977			−0.709885	+	0.704318i	$0.751253\pi$
$618$	1.48927	−	1.48927i	0.0599072	−	0.0599072i
$619$	9.65826	−	9.65826i	0.388198	−	0.388198i	−0.485846	−	0.874044i	$-0.661488\pi$
$619$	9.65826	−	9.65826i	0.388198	−	0.388198i	0.874044	+	0.485846i	$0.161488\pi$
$620$		0			0
$621$	−22.7077	−	22.7077i	−0.911228	−	0.911228i
$622$	−19.8912	−	19.8912i	−0.797566	−	0.797566i
$623$	−21.5291			−0.862544
$624$	−37.6334	+	37.6334i	−1.50654	+	1.50654i
$625$		0			0
$626$	52.7730	−	52.7730i	2.10923	−	2.10923i
$627$	−7.08636			−0.283002
$628$	7.50815			0.299608
$629$		−	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
$638$	−20.0051	+	13.4471i	−0.792011	+	0.532376i
$639$			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	$-0.808842\pi$
$643$	−6.59143	+	6.59143i	−0.259941	+	0.259941i	0.565089	+	0.825030i	$0.308842\pi$
$644$	−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	−0.923373	−	0.383903i	$-0.874580\pi$
$647$	−33.2521	−	33.2521i	−1.30728	−	1.30728i	−0.383903	−	0.923373i	$-0.625420\pi$
$648$		−	74.9346i		−	2.94371i
$649$	−4.14238	−	4.14238i	−0.162602	−	0.162602i
$650$		0			0
$651$			1.74309i			0.0683171i
$652$			15.4079i			0.603420i
$653$		−	37.6967i		−	1.47519i	−0.675245	−	0.737593i	$-0.735962\pi$
$653$		−	37.6967i		−	1.47519i	0.675245	−	0.737593i	$-0.264038\pi$
$654$			5.48909i			0.214641i
$655$		0			0
$656$	35.8931	+	35.8931i	1.40139	+	1.40139i
$657$		−	3.95622i		−	0.154347i
$658$	5.40564	+	5.40564i	0.210734	+	0.210734i
$659$	−21.0129	−	21.0129i	−0.818548	−	0.818548i	0.167349	−	0.985898i	$-0.446479\pi$
$659$	−21.0129	−	21.0129i	−0.818548	−	0.818548i	−0.985898	+	0.167349i	$0.946479\pi$
$660$		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
$667$	−26.3564	+	17.7163i	−1.02052	+	0.685978i
$668$	−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	$-0.758826\pi$
$673$	−1.01710	+	1.01710i	−0.0392064	+	0.0392064i	0.687232	+	0.726438i	$0.258826\pi$
$674$			44.6013i			1.71798i
$675$		0			0
$676$		−	45.5457i		−	1.75176i
$677$	19.8563			0.763140			0.381570	−	0.924340i	$-0.375383\pi$
$677$	19.8563			0.763140			0.381570	+	0.924340i	$0.375383\pi$
$678$	−0.695252			−0.0267010
$679$	−6.41447	+	6.41447i	−0.246165	+	0.246165i
$680$		0			0
$681$	−32.5525	+	32.5525i	−1.24742	+	1.24742i
$682$	3.19286			0.122261
$683$	29.7005	+	29.7005i	1.13646	+	1.13646i	0.989080	+	0.147379i	$0.0470838\pi$
$683$	29.7005	+	29.7005i	1.13646	+	1.13646i	0.147379	+	0.989080i	$0.452916\pi$
$684$	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
$688$	121.404			4.62849
$689$	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
$693$		−	0.826028i		−	0.0313782i
$694$	−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
$698$	47.5463			1.79966
$699$	−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
$707$			7.82489i			0.294285i
$708$		−	32.0035i		−	1.20276i
$709$	32.8376			1.23324			0.616621	−	0.787260i	$-0.288501\pi$
$709$	32.8376			1.23324			0.616621	+	0.787260i	$0.288501\pi$
$710$		0			0
$711$	0.679891	+	0.679891i	0.0254979	+	0.0254979i
$712$	−96.7314	+	96.7314i	−3.62516	+	3.62516i
$713$	4.20653			0.157536
$714$	33.8809	−	33.8809i	1.26796	−	1.26796i
$715$		0			0
$716$	−4.55380			−0.170183
$717$			20.2841i			0.757523i
$718$	45.5945	−	45.5945i	1.70157	−	1.70157i
$719$		−	30.4349i		−	1.13503i	−0.823363	−	0.567515i	$-0.807905\pi$
$719$		−	30.4349i		−	1.13503i	0.823363	−	0.567515i	$-0.192095\pi$
$720$		0			0
$721$	0.706697			0.0263188
$722$	−32.7101			−1.21734
$723$			1.89255i			0.0703845i
$724$	90.5591			3.36560
$725$		0			0
$726$	−37.1362			−1.37825
$727$		−	1.37532i		−	0.0510077i	−0.999675	−	0.0255038i	$-0.991881\pi$
$727$		−	1.37532i		−	0.0510077i	0.999675	−	0.0255038i	$-0.00811900\pi$
$728$	−30.8493			−1.14335
$729$	29.3134			1.08568
$730$		0			0
$731$			57.7836i			2.13720i
$732$	−7.75877	+	7.75877i	−0.286772	+	0.286772i
$733$		−	8.23872i		−	0.304304i	−0.988357	−	0.152152i	$-0.951380\pi$
$733$		−	8.23872i		−	0.304304i	0.988357	−	0.152152i	$-0.0486203\pi$
$734$	−15.1173			−0.557990
$735$		0			0
$736$	−92.4314	+	92.4314i	−3.40707	+	3.40707i
$737$	16.4152			0.604662
$738$	−2.19622	+	2.19622i	−0.0808441	+	0.0808441i
$739$	30.5802	+	30.5802i	1.12491	+	1.12491i	0.990992	+	0.133918i	$0.0427558\pi$
$739$	30.5802	+	30.5802i	1.12491	+	1.12491i	0.133918	+	0.990992i	$0.457244\pi$
$740$		0			0
$741$	−9.37403			−0.344364
$742$			31.2489i			1.14718i
$743$		−	33.4069i		−	1.22558i	−0.790245	−	0.612791i	$-0.790047\pi$
$743$		−	33.4069i		−	1.22558i	0.790245	−	0.612791i	$-0.209953\pi$
$744$	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	$0.694523\pi$
$752$	28.1194			1.02541
$753$	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
$757$			43.4105i			1.57778i	0.614532	+	0.788892i	$0.289345\pi$
$757$			43.4105i			1.57778i	−0.614532	+	0.788892i	$0.710655\pi$
$758$	−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	$0.191780\pi$
$762$	82.6728			2.99492
$763$	−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
$768$	−74.8021			−2.69919
$769$	−35.2831	+	35.2831i	−1.27234	+	1.27234i	−0.327487	+	0.944856i	$0.606202\pi$
$769$	−35.2831	+	35.2831i	−1.27234	+	1.27234i	−0.944856	+	0.327487i	$0.893798\pi$
$770$		0			0
$771$	20.6085	−	20.6085i	0.742198	−	0.742198i
$772$	28.3750			1.02124
$773$	−30.5826			−1.09998			−0.549990	−	0.835171i	$-0.685368\pi$
$773$	−30.5826			−1.09998			−0.549990	+	0.835171i	$0.685368\pi$
$774$			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
$783$	5.64158	−	28.7775i	0.201614	−	1.02842i
$784$			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	$-0.145560\pi$
$787$	12.7850	+	12.7850i	0.455735	+	0.455735i	−0.441518	+	0.897253i	$0.645560\pi$
$788$	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
$793$			2.65692i			0.0943501i
$794$	−25.2973	−	25.2973i	−0.897768	−	0.897768i
$795$		0			0
$796$		−	48.9265i		−	1.73415i
$797$		−	12.6152i		−	0.446852i	−0.974721	−	0.223426i	$-0.928276\pi$
$797$		−	12.6152i		−	0.446852i	0.974721	−	0.223426i	$-0.0717241\pi$
$798$		−	17.7312i		−	0.627677i
$799$			13.3837i			0.473483i
$800$		0			0
$801$	−3.42625	−	3.42625i	−0.121061	−	0.121061i
$802$			27.1388i			0.958304i
$803$	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	−0.0592478	−	0.998243i	$-0.518870\pi$
$809$	26.7078	−	26.7078i	0.938996	−	0.938996i	0.998243	+	0.0592478i	$0.0188702\pi$
$810$		0			0
$811$		−	26.4437i		−	0.928564i	−0.885687	−	0.464282i	$-0.846312\pi$
$811$		−	26.4437i		−	0.928564i	0.885687	−	0.464282i	$-0.153688\pi$
$812$	−24.6494	−	36.6707i	−0.865024	−	1.28689i
$813$	−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	$-0.201722\pi$
$822$	12.1240			0.422872
$823$	−6.03790			−0.210468			−0.105234	−	0.994447i	$-0.533559\pi$
$823$	−6.03790			−0.210468			−0.105234	+	0.994447i	$0.533559\pi$
$824$	3.17523	−	3.17523i	0.110614	−	0.110614i
$825$		0			0
$826$	10.3649	−	10.3649i	0.360640	−	0.360640i
$827$	34.3817			1.19557			0.597784	−	0.801657i	$-0.296048\pi$
$827$	34.3817			1.19557			0.597784	+	0.801657i	$0.296048\pi$
$828$	−7.70046	−	7.70046i	−0.267609	−	0.267609i
$829$	−22.3751	−	22.3751i	−0.777119	−	0.777119i	0.202221	−	0.979340i	$-0.435184\pi$
$829$	−22.3751	−	22.3751i	−0.777119	−	0.777119i	−0.979340	+	0.202221i	$0.935184\pi$
$830$		0			0
$831$	30.4008	−	30.4008i	1.05459	−	1.05459i
$832$	−46.6833	+	46.6833i	−1.61845	+	1.61845i
$833$	−34.1105			−1.18186
$834$	−53.6979			−1.85941
$835$		0			0
$836$	−23.7936			−0.822920
$837$	−2.74668	+	2.74668i	−0.0949391	+	0.0949391i
$838$			36.4065i			1.25764i
$839$	−7.70723	+	7.70723i	−0.266083	+	0.266083i	−0.827520	−	0.561437i	$-0.810249\pi$
$839$	−7.70723	+	7.70723i	−0.266083	+	0.266083i	0.561437	+	0.827520i	$0.310249\pi$
$840$		0			0
$841$	−26.8534	−	10.9496i	−0.925980	−	0.377572i
$842$	16.6747	−	16.6747i	0.574649	−	0.574649i
$843$	−35.3356			−1.21702
$844$	−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
$852$		−	29.5405i		−	1.01204i
$853$			11.7987i			0.403981i	0.979388	+	0.201990i	$0.0647410\pi$
$853$			11.7987i			0.403981i	−0.979388	+	0.201990i	$0.935259\pi$
$854$	−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	−0.854951	−	0.518708i	$-0.826413\pi$
$857$	−9.84337	+	9.84337i	−0.336243	+	0.336243i	0.518708	+	0.854951i	$0.326413\pi$
$858$	15.8146			0.539902
$859$	−29.8718	+	29.8718i	−1.01921	+	1.01921i	−0.0194004	+	0.999812i	$0.506176\pi$
$859$	−29.8718	+	29.8718i	−1.01921	+	1.01921i	−0.999812	+	0.0194004i	$0.993824\pi$
$860$		0			0
$861$	8.23449			0.280631
$862$			21.8093i			0.742829i
$863$	13.8824	−	13.8824i	0.472561	−	0.472561i	−0.430181	−	0.902742i	$-0.641550\pi$
$863$	13.8824	−	13.8824i	0.472561	−	0.472561i	0.902742	+	0.430181i	$0.141550\pi$
$864$		−	120.707i		−	4.10654i
$865$		0			0
$866$	−76.3055			−2.59297
$867$	56.1435			1.90673
$868$			5.85271i			0.198654i
$869$	−4.66939			−0.158398
$870$		0			0
$871$	21.7145			0.735767
$872$			11.7031i			0.396318i
$873$	−2.04167			−0.0691000
$874$	−42.7899			−1.44739
$875$		0			0
$876$			104.959i			3.54622i
$877$	−18.6332	+	18.6332i	−0.629200	+	0.629200i	−0.947867	−	0.318667i	$-0.896765\pi$
$877$	−18.6332	+	18.6332i	−0.629200	+	0.629200i	0.318667	+	0.947867i	$0.396765\pi$
$878$		−	63.1446i		−	2.13103i
$879$	−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	$-0.0428547\pi$
$882$	−4.38513			−0.147655
$883$	−12.9731	+	12.9731i	−0.436580	+	0.436580i	−0.890859	−	0.454279i	$-0.849897\pi$
$883$	−12.9731	+	12.9731i	−0.436580	+	0.436580i	0.454279	+	0.890859i	$0.349897\pi$
$884$	−60.1425	−	60.1425i	−2.02281	−	2.02281i
$885$		0			0
$886$	35.8830			1.20551
$887$			11.7923i			0.395948i	0.980207	+	0.197974i	$0.0634362\pi$
$887$			11.7923i			0.395948i	−0.980207	+	0.197974i	$0.936564\pi$
$888$			73.6887i			2.47283i
$889$	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
$897$	20.8354			0.695675
$898$	−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
$902$		−	15.0833i		−	0.502220i
$903$	13.9261	−	13.9261i	0.463431	−	0.463431i
$904$	−1.48233			−0.0493014
$905$		0			0
$906$	−65.3459			−2.17097
$907$	−37.1013			−1.23193			−0.615964	−	0.787775i	$-0.711233\pi$
$907$	−37.1013			−1.23193			−0.615964	+	0.787775i	$0.711233\pi$
$908$	−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
$913$	12.2255			0.404604
$914$	56.2282	−	56.2282i	1.85986	−	1.85986i
$915$		0			0
$916$	−1.88651	+	1.88651i	−0.0623322	+	0.0623322i
$917$	−9.71605			−0.320852
$918$	106.776			3.52413
$919$			38.7184i			1.27720i	0.769538	+	0.638601i	$0.220486\pi$
$919$			38.7184i			1.27720i	−0.769538	+	0.638601i	$0.779514\pi$
$920$		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
$928$	−117.139	−	22.9640i	−3.84526	−	0.753831i
$929$			25.0417i			0.821591i	0.911728	+	0.410795i	$0.134749\pi$
$929$			25.0417i			0.821591i	−0.911728	+	0.410795i	$0.865251\pi$
$930$		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	$-0.346882\pi$
$937$	−12.9733	−	12.9733i	−0.423820	−	0.423820i	−0.886517	+	0.462696i	$0.846882\pi$
$938$			41.0734i			1.34109i
$939$	−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	$0.896795\pi$
$942$		−	6.11540i		−	0.199250i
$943$		−	19.8720i		−	0.647121i
$944$		−	53.9166i		−	1.75484i
$945$		0			0
$946$	−25.5088	−	25.5088i	−0.829361	−	0.829361i
$947$			14.9594i			0.486115i	0.970012	+	0.243058i	$0.0781504\pi$
$947$			14.9594i			0.486115i	−0.970012	+	0.243058i	$0.921850\pi$
$948$	−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	0.901514	−	0.432749i	$-0.142456\pi$
$953$	14.4711	+	14.4711i	0.468765	+	0.468765i	−0.432749	+	0.901514i	$0.642456\pi$
$954$	−4.97311	+	4.97311i	−0.161011	+	0.161011i
$955$		0			0
$956$			68.1071i			2.20274i
$957$	8.02386	+	11.9370i	0.259375	+	0.385869i
$958$	−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
$967$	−49.4414			−1.58993			−0.794963	−	0.606657i	$-0.792510\pi$
$967$	−49.4414			−1.58993			−0.794963	+	0.606657i	$0.792510\pi$
$968$	−79.1770			−2.54484
$969$	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	$-0.126040\pi$
$972$	19.0966			0.612523
$973$	−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	−0.668453	−	0.743754i	$-0.733043\pi$
$977$	2.35368	−	2.35368i	0.0753008	−	0.0753008i	0.743754	+	0.668453i	$0.233043\pi$
$978$	12.5498			0.401297
$979$	23.5310			0.752054
$980$		0			0
$981$	−0.414528			−0.0132349
$982$	69.3502	−	69.3502i	2.21305	−	2.21305i
$983$		−	0.916231i		−	0.0292232i	−0.999893	−	0.0146116i	$-0.995349\pi$
$983$		−	0.916231i		−	0.0292232i	0.999893	−	0.0146116i	$-0.00465119\pi$
$984$	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
$988$	−31.4749			−1.00135
$989$	−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
$997$		−	45.0022i		−	1.42523i	−0.701553	−	0.712617i	$-0.747510\pi$
$997$		−	45.0022i		−	1.42523i	0.701553	−	0.712617i	$-0.252490\pi$
$998$		−	13.1237i		−	0.415424i
$999$	−25.8432			−0.817644

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.e (of order \(4\), degree \(2\), minimal)

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

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