LMFDB - Embedded newform 725.2.e.c.157.13

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			157.13
Character	$\chi$	$=$	725.157
Dual form			725.2.e.c.568.1

$q$-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 $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

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

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 $

$2$			2.73482i			1.93381i	0.255136	+	0.966905i	$0.417880\pi$
$2$			2.73482i			1.93381i	−0.255136	+	0.966905i	$0.582120\pi$
$3$	−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	0.478094	−	0.878309i	$-0.341328\pi$
$7$	−1.05887	−	1.05887i	−0.400215	−	0.400215i	−0.878309	+	0.478094i	$0.841328\pi$
$8$		−	9.51511i		−	3.36410i
$9$	−0.337028			−0.112343
$10$		0			0
$11$	1.15733	+	1.15733i	0.348948	+	0.348948i	0.859717	−	0.510770i	$-0.170640\pi$
$11$	1.15733	+	1.15733i	0.348948	+	0.348948i	−0.510770	+	0.859717i	$0.670640\pi$
$12$	8.94137			2.58115
$13$	1.53095	+	1.53095i	0.424608	+	0.424608i	0.886787	−	0.462179i	$-0.152932\pi$
$13$	1.53095	+	1.53095i	0.424608	+	0.424608i	−0.462179	+	0.886787i	$0.652932\pi$
$14$	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	$-0.664471\pi$
$17$		−	7.16970i		−	1.73891i	0.494015	−	0.869453i	$-0.335529\pi$
$18$		−	0.921711i		−	0.217249i
$19$	1.87609	−	1.87609i	0.430404	−	0.430404i	−0.458362	−	0.888766i	$-0.651564\pi$
$19$	1.87609	−	1.87609i	0.430404	−	0.430404i	0.888766	+	0.458362i	$0.151564\pi$
$20$		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
$27$	5.44557			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	0.660359	−	0.750950i	$-0.270404\pi$
$31$	−0.504388	−	0.504388i	−0.0905907	−	0.0905907i	−0.750950	+	0.660359i	$0.770404\pi$
$32$			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	−0.496125	−	0.868251i	$-0.665244\pi$
$41$	2.38277	−	2.38277i	0.372126	−	0.372126i	0.868251	+	0.496125i	$0.165244\pi$
$42$	−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	−0.231664	−	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
$58$	−14.4524	+	2.83326i	−1.89769	+	0.372026i
$59$			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	0.649370	−	0.760473i	$-0.275033\pi$
$61$	−0.867739	−	0.867739i	−0.111103	−	0.111103i	−0.760473	+	0.649370i	$0.775033\pi$
$62$	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	−0.125665	−	0.992073i	$-0.540106\pi$
$67$	7.09185	−	7.09185i	0.866408	−	0.866408i	0.992073	+	0.125665i	$0.0401065\pi$
$68$			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	$0.0628096\pi$
$71$			3.30380i			0.392089i	−0.980595	+	0.196044i	$0.937190\pi$
$72$			3.20686i			0.377932i
$73$		−	11.7385i		−	1.37389i	−0.726708	−	0.686946i	$-0.758951\pi$
$73$		−	11.7385i		−	1.37389i	0.726708	−	0.686946i	$-0.241049\pi$
$74$		−	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	−0.811424	−	0.584458i	$-0.801307\pi$
$79$	−2.01731	+	2.01731i	−0.226966	+	0.226966i	0.584458	+	0.811424i	$0.301307\pi$
$80$		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
$87$	−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	0.0808784	−	0.996724i	$-0.474227\pi$
$89$	10.1661	−	10.1661i	1.07760	−	1.07760i	0.996724	−	0.0808784i	$-0.0257725\pi$
$90$		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	0.866623	−	0.498964i	$-0.166286\pi$
$101$	3.69493	+	3.69493i	0.367659	+	0.367659i	−0.498964	+	0.866623i	$0.666286\pi$
$102$	−31.9973			−3.16820
$103$	−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	$0.555662\pi$
$108$	−29.8376			−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	$-0.997668\pi$
$113$		−	0.155786i		−	0.0146552i	0.999973	−	0.00732758i	$-0.00233246\pi$
$114$	−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	$0.307085\pi$
$127$			18.5247i			1.64380i	−0.569634	+	0.821899i	$0.692915\pi$
$128$		−	39.0610i		−	3.45253i
$129$	−13.1519			−1.15796
$130$		0			0
$131$	4.58794	−	4.58794i	0.400850	−	0.400850i	−0.477682	−	0.878533i	$-0.658523\pi$
$131$	4.58794	−	4.58794i	0.400850	−	0.400850i	0.878533	+	0.477682i	$0.158523\pi$
$132$	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	$0.0370230\pi$
$137$			2.71664i			0.232098i	−0.993243	+	0.116049i	$0.962977\pi$
$138$	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
$142$	−9.03529			−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	$-0.796842\pi$
$151$		−	14.6422i		−	1.19156i	0.803146	−	0.595782i	$-0.203158\pi$
$152$	−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	$0.0351262\pi$
$163$			2.81205i			0.220257i	−0.993917	+	0.110128i	$0.964874\pi$
$164$	−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	−0.485923	−	0.874001i	$-0.661517\pi$
$167$	5.01507	−	5.01507i	0.388078	−	0.388078i	0.874001	+	0.485923i	$0.161517\pi$
$168$	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	0.0929073	−	0.995675i	$-0.470384\pi$
$173$	−11.8741	−	11.8741i	−0.902767	−	0.902767i	−0.995675	+	0.0929073i	$0.970384\pi$
$174$	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	0.773285	−	0.634058i	$-0.218612\pi$
$191$	1.92415	+	1.92415i	0.139227	+	0.139227i	−0.634058	+	0.773285i	$0.718612\pi$
$192$	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	0.106324	−	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
$203$	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	−0.462520	−	0.886609i	$-0.653055\pi$
$211$	6.16024	−	6.16024i	0.424088	−	0.424088i	0.886609	+	0.462520i	$0.153055\pi$
$212$	−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	−0.976595	−	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	$-0.244879\pi$
$229$	0.344302	+	0.344302i	0.0227521	+	0.0227521i	−0.695639	+	0.718391i	$0.744879\pi$
$230$		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	−0.239625	−	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	$0.0118926\pi$
$241$			1.15975i			0.0747058i	−0.999302	+	0.0373529i	$0.988107\pi$
$242$	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	−0.993759	−	0.111547i	$-0.964420\pi$
$251$	−17.5113	−	17.5113i	−1.10531	−	1.10531i	−0.111547	−	0.993759i	$-0.535580\pi$
$252$	−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	0.193362	−	0.981127i	$-0.438061\pi$
$257$	−12.6288	−	12.6288i	−0.787765	−	0.787765i	−0.981127	+	0.193362i	$0.938061\pi$
$258$		−	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	0.958824	−	0.284000i	$-0.0916617\pi$
$269$	11.0679	+	11.0679i	0.674824	+	0.674824i	−0.284000	+	0.958824i	$0.591662\pi$
$270$		0			0
$271$	2.17997	−	2.17997i	0.132424	−	0.132424i	−0.637788	−	0.770212i	$-0.720150\pi$
$271$	2.17997	−	2.17997i	0.132424	−	0.132424i	0.770212	+	0.637788i	$0.220150\pi$
$272$		−	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	−0.991838	−	0.127503i	$-0.959304\pi$
$277$	−18.6295	−	18.6295i	−1.11934	−	1.11934i	−0.127503	−	0.991838i	$-0.540696\pi$
$278$	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	0.556403	−	0.830913i	$-0.312181\pi$
$283$	−4.61797	−	4.61797i	−0.274510	−	0.274510i	−0.830913	+	0.556403i	$0.812181\pi$
$284$		−	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	$-0.995566\pi$
$307$		−	0.488133i		−	0.0278592i	0.999903	−	0.0139296i	$-0.00443407\pi$
$308$			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	0.882585	−	0.470153i	$-0.155801\pi$
$311$	7.27332	+	7.27332i	0.412432	+	0.412432i	−0.470153	+	0.882585i	$0.655801\pi$
$312$	−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
$317$	2.65586			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	−0.976003	−	0.217756i	$-0.930126\pi$
$331$	−13.7951	+	13.7951i	−0.758248	+	0.758248i	0.217756	+	0.976003i	$0.430126\pi$
$332$	−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	−0.786815	−	0.617188i	$-0.788272\pi$
$347$	−3.15980	+	3.15980i	−0.169627	+	0.169627i	0.617188	+	0.786815i	$0.288272\pi$
$348$	9.26322	+	47.2513i	0.496561	+	2.53294i
$349$		−	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	0.914915	−	0.403647i	$-0.132258\pi$
$353$	9.60586	+	9.60586i	0.511268	+	0.511268i	−0.403647	+	0.914915i	$0.632258\pi$
$354$	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	−0.113618	−	0.993524i	$-0.536244\pi$
$359$	16.6718	−	16.6718i	0.879906	−	0.879906i	0.993524	+	0.113618i	$0.0362440\pi$
$360$		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	$0.0460840\pi$
$367$			5.52771i			0.288544i	−0.989538	+	0.144272i	$0.953916\pi$
$368$	−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
$377$	−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	−0.136859	+	0.990590i	$0.543701\pi$
$379$	−21.9491	+	21.9491i	−1.12745	+	1.12745i	−0.990590	+	0.136859i	$0.956299\pi$
$380$		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	0.884714	−	0.466134i	$-0.154353\pi$
$383$	8.19179	+	8.19179i	0.418581	+	0.418581i	−0.466134	+	0.884714i	$0.654353\pi$
$384$			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	0.681170	−	0.732125i	$-0.261472\pi$
$389$	−1.00500	−	1.00500i	−0.0509555	−	0.0509555i	−0.732125	+	0.681170i	$0.761472\pi$
$390$		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	0.900045	−	0.435797i	$-0.143533\pi$
$397$	9.25008	+	9.25008i	0.464248	+	0.464248i	−0.435797	+	0.900045i	$0.643533\pi$
$398$	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	−0.739160	−	0.673530i	$-0.764777\pi$
$409$	−1.32729	+	1.32729i	−0.0656305	+	0.0656305i	0.673530	+	0.739160i	$0.264777\pi$
$410$		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	−0.542741	−	0.839900i	$-0.682614\pi$
$421$	6.09719	−	6.09719i	0.297159	−	0.297159i	0.839900	+	0.542741i	$0.182614\pi$
$422$	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	$0.233890\pi$
$433$			27.9015i			1.34086i	−0.741973	+	0.670430i	$0.766110\pi$
$434$	−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	$-0.899104\pi$
$443$		−	13.1208i		−	0.623388i	0.950183	−	0.311694i	$-0.100896\pi$
$444$	−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	−0.957685	−	0.287819i	$-0.907070\pi$
$449$	−14.1942	+	14.1942i	−0.669865	+	0.669865i	0.287819	+	0.957685i	$0.407070\pi$
$450$		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	−0.0375345	−	0.999295i	$-0.511950\pi$
$457$	20.5601	−	20.5601i	0.961761	−	0.961761i	0.999295	+	0.0375345i	$0.0119504\pi$
$458$	−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	−0.403823	−	0.914837i	$-0.632319\pi$
$461$	10.9719	−	10.9719i	0.511014	−	0.511014i	0.914837	+	0.403823i	$0.132319\pi$
$462$	−10.9381			−0.508885
$463$	19.5635	+	19.5635i	0.909193	+	0.909193i	0.996207	−	0.0870140i	$-0.0277325\pi$
$463$	19.5635	+	19.5635i	0.909193	+	0.909193i	−0.0870140	+	0.996207i	$0.527732\pi$
$464$	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	$0.348390\pi$
$467$			38.4099i			1.77740i	−0.458491	+	0.888699i	$0.651610\pi$
$468$	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	0.961123	−	0.276121i	$-0.0890491\pi$
$479$	14.9920	+	14.9920i	0.685002	+	0.685002i	−0.276121	+	0.961123i	$0.589049\pi$
$480$		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	−0.944697	−	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	0.156764	−	0.987636i	$-0.449894\pi$
$491$	25.3582	−	25.3582i	1.14440	−	1.14440i	0.987636	−	0.156764i	$-0.0501062\pi$
$492$	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	$-0.711766\pi$
$503$		−	35.2896i		−	1.57348i	0.617282	−	0.786742i	$-0.288234\pi$
$504$	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	$-0.767257\pi$
$509$		−	30.1303i		−	1.33550i	0.744384	−	0.667752i	$-0.232743\pi$
$510$		0			0
$511$	−12.4296	+	12.4296i	−0.549852	+	0.549852i
$512$			47.2382i			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	$0.186841\pi$
$521$			25.2836i			1.10769i	−0.832619	+	0.553847i	$0.813159\pi$
$522$	4.87085	−	0.954889i	0.213191	−	0.0417943i
$523$	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
$532$	21.7694			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	0.603865	−	0.797087i	$-0.293627\pi$
$541$	−4.49423	−	4.49423i	−0.193222	−	0.193222i	−0.797087	+	0.603865i	$0.793627\pi$
$542$	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	0.580876	−	0.813992i	$-0.302710\pi$
$547$	−5.45211	−	5.45211i	−0.233115	−	0.233115i	−0.813992	+	0.580876i	$0.802710\pi$
$548$		−	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	0.489958	−	0.871746i	$-0.337012\pi$
$557$	32.1374	−	32.1374i	1.36170	−	1.36170i	0.871746	−	0.489958i	$-0.162988\pi$
$558$	−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	$0.0174527\pi$
$563$			2.60063i			0.109603i	−0.998497	+	0.0548017i	$0.982547\pi$
$564$	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	0.961338	−	0.275372i	$-0.0888012\pi$
$569$	16.3628	+	16.3628i	0.685965	+	0.685965i	−0.275372	+	0.961338i	$0.588801\pi$
$570$		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	0.996535	+	0.0831773i	$0.0265068\pi$
$587$	26.1594	+	26.1594i	1.07971	+	1.07971i	0.0831773	+	0.996535i	$0.473493\pi$
$588$		−	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	0.887533	−	0.460743i	$-0.152417\pi$
$593$	10.3930	+	10.3930i	0.426790	+	0.426790i	−0.460743	+	0.887533i	$0.652417\pi$
$594$	−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	−0.445427	−	0.895318i	$-0.646948\pi$
$599$	11.0108	−	11.0108i	0.449891	−	0.449891i	0.895318	+	0.445427i	$0.146948\pi$
$600$		0			0
$601$	4.22053	+	4.22053i	0.172159	+	0.172159i	0.787927	−	0.615768i	$-0.211154\pi$
$601$	4.22053	+	4.22053i	0.172159	+	0.172159i	−0.615768	+	0.787927i	$0.711154\pi$
$602$	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	0.364471	−	0.931215i	$-0.381250\pi$
$613$	−14.0319	−	14.0319i	−0.566744	−	0.566744i	−0.931215	+	0.364471i	$0.881250\pi$
$614$	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	0.874044	−	0.485846i	$-0.161488\pi$
$619$	9.65826	+	9.65826i	0.388198	+	0.388198i	−0.485846	+	0.874044i	$0.661488\pi$
$620$		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	$0.165604\pi$
$631$			24.9743i			0.994212i	−0.867690	+	0.497106i	$0.834396\pi$
$632$	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	0.967540	+	0.252716i	$0.0813239\pi$
$641$	30.8944	+	30.8944i	1.22026	+	1.22026i	0.252716	+	0.967540i	$0.418676\pi$
$642$	37.4286	−	37.4286i	1.47719	−	1.47719i
$643$	−6.59143	−	6.59143i	−0.259941	−	0.259941i	0.565089	−	0.825030i	$-0.308842\pi$
$643$	−6.59143	−	6.59143i	−0.259941	−	0.259941i	−0.825030	+	0.565089i	$0.808842\pi$
$644$	−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	$0.625420\pi$
$647$	−33.2521	+	33.2521i	−1.30728	+	1.30728i	−0.923373	+	0.383903i	$0.874580\pi$
$648$			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	$0.264038\pi$
$653$			37.6967i			1.47519i	−0.675245	+	0.737593i	$0.735962\pi$
$654$		−	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	−0.985898	−	0.167349i	$-0.946479\pi$
$659$	−21.0129	+	21.0129i	−0.818548	+	0.818548i	0.167349	+	0.985898i	$0.446479\pi$
$660$		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	0.687232	−	0.726438i	$-0.258826\pi$
$673$	−1.01710	−	1.01710i	−0.0392064	−	0.0392064i	−0.726438	+	0.687232i	$0.758826\pi$
$674$		−	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	0.147379	−	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
$688$	121.404			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	$0.00617568\pi$
$701$			1.02730i			0.0388005i	−0.999812	+	0.0194003i	$0.993824\pi$
$702$	−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	$0.192095\pi$
$719$			30.4349i			1.13503i	−0.823363	+	0.567515i	$0.807905\pi$
$720$		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	$0.00811900\pi$
$727$			1.37532i			0.0510077i	−0.999675	+	0.0255038i	$0.991881\pi$
$728$	−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	$0.0486203\pi$
$733$			8.23872i			0.304304i	−0.988357	+	0.152152i	$0.951380\pi$
$734$	−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	0.133918	−	0.990992i	$-0.457244\pi$
$739$	30.5802	−	30.5802i	1.12491	−	1.12491i	0.990992	−	0.133918i	$-0.0427558\pi$
$740$		0			0
$741$	−9.37403			−0.344364
$742$		−	31.2489i		−	1.14718i
$743$			33.4069i			1.22558i	0.790245	+	0.612791i	$0.209953\pi$
$743$			33.4069i			1.22558i	−0.790245	+	0.612791i	$0.790047\pi$
$744$	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	−0.573779	−	0.819010i	$-0.694523\pi$
$751$	6.72041	−	6.72041i	0.245231	−	0.245231i	0.819010	+	0.573779i	$0.194523\pi$
$752$	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	$-0.710655\pi$
$757$		−	43.4105i		−	1.57778i	0.614532	−	0.788892i	$-0.289345\pi$
$758$	−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	−0.944856	−	0.327487i	$-0.893798\pi$
$769$	−35.2831	−	35.2831i	−1.27234	−	1.27234i	−0.327487	−	0.944856i	$-0.606202\pi$
$770$		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	−0.441518	−	0.897253i	$-0.645560\pi$
$787$	12.7850	−	12.7850i	0.455735	−	0.455735i	0.897253	+	0.441518i	$0.145560\pi$
$788$	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	$0.0717241\pi$
$797$			12.6152i			0.446852i	−0.974721	+	0.223426i	$0.928276\pi$
$798$			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	0.998243	−	0.0592478i	$-0.0188702\pi$
$809$	26.7078	+	26.7078i	0.938996	+	0.938996i	−0.0592478	+	0.998243i	$0.518870\pi$
$810$		0			0
$811$			26.4437i			0.928564i	0.885687	+	0.464282i	$0.153688\pi$
$811$			26.4437i			0.928564i	−0.885687	+	0.464282i	$0.846312\pi$
$812$	−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	$0.201722\pi$
$821$			33.9341i			1.18431i	−0.805825	+	0.592154i	$0.798278\pi$
$822$	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	−0.979340	−	0.202221i	$-0.935184\pi$
$829$	−22.3751	+	22.3751i	−0.777119	+	0.777119i	0.202221	+	0.979340i	$0.435184\pi$
$830$		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	0.561437	−	0.827520i	$-0.310249\pi$
$839$	−7.70723	−	7.70723i	−0.266083	−	0.266083i	−0.827520	+	0.561437i	$0.810249\pi$
$840$		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	$-0.935259\pi$
$853$		−	11.7987i		−	0.403981i	0.979388	−	0.201990i	$-0.0647410\pi$
$854$	−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	$0.826413\pi$
$858$	15.8146			0.539902
$859$	−29.8718	−	29.8718i	−1.01921	−	1.01921i	−0.999812	−	0.0194004i	$-0.993824\pi$
$859$	−29.8718	−	29.8718i	−1.01921	−	1.01921i	−0.0194004	−	0.999812i	$-0.506176\pi$
$860$		0			0
$861$	8.23449			0.280631
$862$		−	21.8093i		−	0.742829i
$863$	13.8824	+	13.8824i	0.472561	+	0.472561i	0.902742	−	0.430181i	$-0.141550\pi$
$863$	13.8824	+	13.8824i	0.472561	+	0.472561i	−0.430181	+	0.902742i	$0.641550\pi$
$864$			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	0.318667	−	0.947867i	$-0.396765\pi$
$877$	−18.6332	−	18.6332i	−0.629200	−	0.629200i	−0.947867	+	0.318667i	$0.896765\pi$
$878$			63.1446i			2.13103i
$879$	−15.9994			−0.539648
$880$		0			0
$881$	33.3971	+	33.3971i	1.12518	+	1.12518i	0.990951	+	0.134226i	$0.0428547\pi$
$881$	33.3971	+	33.3971i	1.12518	+	1.12518i	0.134226	+	0.990951i	$0.457145\pi$
$882$	−4.38513			−0.147655
$883$	−12.9731	−	12.9731i	−0.436580	−	0.436580i	0.454279	−	0.890859i	$-0.349897\pi$
$883$	−12.9731	−	12.9731i	−0.436580	−	0.436580i	−0.890859	+	0.454279i	$0.849897\pi$
$884$	−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	$-0.936564\pi$
$887$		−	11.7923i		−	0.395948i	0.980207	−	0.197974i	$-0.0634362\pi$
$888$		−	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	0.274400	−	0.961616i	$-0.411521\pi$
$911$	37.3064	−	37.3064i	1.23602	−	1.23602i	0.961616	−	0.274400i	$-0.0884794\pi$
$912$	−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	$-0.779514\pi$
$919$		−	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
$928$	−117.139	+	22.9640i	−3.84526	+	0.753831i
$929$		−	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	−0.886517	−	0.462696i	$-0.846882\pi$
$937$	−12.9733	+	12.9733i	−0.423820	+	0.423820i	0.462696	+	0.886517i	$0.346882\pi$
$938$		−	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	$-0.896795\pi$
$941$		−	19.5452i		−	0.637155i	0.947897	−	0.318578i	$-0.103205\pi$
$942$			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	$-0.921850\pi$
$947$		−	14.9594i		−	0.486115i	0.970012	−	0.243058i	$-0.0781504\pi$
$948$	−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
$957$	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	0.922624	+	0.385701i	$0.126040\pi$
$971$	40.7685	+	40.7685i	1.30832	+	1.30832i	0.385701	+	0.922624i	$0.373960\pi$
$972$	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	0.743754	−	0.668453i	$-0.233043\pi$
$977$	2.35368	+	2.35368i	0.0753008	+	0.0753008i	−0.668453	+	0.743754i	$0.733043\pi$
$978$	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	$0.00465119\pi$
$983$			0.916231i			0.0292232i	−0.999893	+	0.0146116i	$0.995349\pi$
$984$	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	$-0.942634\pi$
$991$		−	11.2855i		−	0.358495i	0.983804	−	0.179248i	$-0.0573663\pi$
$992$	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	$0.252490\pi$
$997$			45.0022i			1.42523i	−0.701553	+	0.712617i	$0.747510\pi$
$998$			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.157.13		26
5.2	odd	4		145.2.j.a.128.1	yes	26
5.3	odd	4		725.2.j.c.418.13		26
5.4	even	2		145.2.e.a.12.1	✓	26
29.17	odd	4		725.2.j.c.307.13		26
145.17	even	4		145.2.e.a.133.13	yes	26
145.104	odd	4		145.2.j.a.17.1	yes	26
145.133	even	4	inner	725.2.e.c.568.1		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.e.a.12.1	✓	26	5.4	even	2
145.2.e.a.133.13	yes	26	145.17	even	4
145.2.j.a.17.1	yes	26	145.104	odd	4
145.2.j.a.128.1	yes	26	5.2	odd	4
725.2.e.c.157.13		26	1.1	even	1	trivial
725.2.e.c.568.1		26	145.133	even	4	inner
725.2.j.c.307.13		26	29.17	odd	4
725.2.j.c.418.13		26	5.3	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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