LMFDB - Embedded newform 725.2.j.a.418.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("725.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			418.2
Root			$0.618034i$ of defining polynomial
Character	$\chi$	$=$	725.418
Dual form			725.2.j.a.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.23607 q^{2} +3.00000 q^{4} +(-2.23607 + 2.23607i) q^{7} +2.23607 q^{8} +3.00000 q^{9} +(4.00000 + 4.00000i) q^{11} +(4.47214 - 4.47214i) q^{13} +(-5.00000 + 5.00000i) q^{14} -1.00000 q^{16} -4.47214 q^{17} +6.70820 q^{18} +(2.00000 - 2.00000i) q^{19} +(8.94427 + 8.94427i) q^{22} +(2.23607 + 2.23607i) q^{23} +(10.0000 - 10.0000i) q^{26} +(-6.70820 + 6.70820i) q^{28} +(-2.00000 + 5.00000i) q^{29} +(-4.00000 - 4.00000i) q^{31} -6.70820 q^{32} -10.0000 q^{34} +9.00000 q^{36} -4.47214i q^{37} +(4.47214 - 4.47214i) q^{38} +(1.00000 - 1.00000i) q^{41} -4.47214i q^{43} +(12.0000 + 12.0000i) q^{44} +(5.00000 + 5.00000i) q^{46} +4.47214i q^{47} -3.00000i q^{49} +(13.4164 - 13.4164i) q^{52} +(-8.94427 - 8.94427i) q^{53} +(-5.00000 + 5.00000i) q^{56} +(-4.47214 + 11.1803i) q^{58} +(-9.00000 - 9.00000i) q^{61} +(-8.94427 - 8.94427i) q^{62} +(-6.70820 + 6.70820i) q^{63} -13.0000 q^{64} +(-2.23607 - 2.23607i) q^{67} -13.4164 q^{68} +12.0000i q^{71} +6.70820 q^{72} -4.47214 q^{73} -10.0000i q^{74} +(6.00000 - 6.00000i) q^{76} -17.8885 q^{77} +(2.00000 - 2.00000i) q^{79} +9.00000 q^{81} +(2.23607 - 2.23607i) q^{82} +(-6.70820 - 6.70820i) q^{83} -10.0000i q^{86} +(8.94427 + 8.94427i) q^{88} +(7.00000 - 7.00000i) q^{89} +20.0000i q^{91} +(6.70820 + 6.70820i) q^{92} +10.0000i q^{94} +4.47214i q^{97} -6.70820i q^{98} +(12.0000 + 12.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{4} + 12 q^{9} + 16 q^{11} - 20 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 8 q^{29} - 16 q^{31} - 40 q^{34} + 36 q^{36} + 4 q^{41} + 48 q^{44} + 20 q^{46} - 20 q^{56} - 36 q^{61} - 52 q^{64}+ \cdots + 48 q^{99}+O(q^{100}) $ 4 * q + 12 * q^4 + 12 * q^9 + 16 * q^11 - 20 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 8 * q^29 - 16 * q^31 - 40 * q^34 + 36 * q^36 + 4 * q^41 + 48 * q^44 + 20 * q^46 - 20 * q^56 - 36 * q^61 - 52 * q^64 + 24 * q^76 + 8 * q^79 + 36 * q^81 + 28 * q^89 + 48 * q^99

Character values

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

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

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 $

$2$	2.23607			1.58114			0.790569	−	0.612372i	$-0.209785\pi$
$2$	2.23607			1.58114			0.790569	+	0.612372i	$0.209785\pi$
$3$		0			0		1.00000			$0$
$3$		0			0		−1.00000			$\pi$
$4$	3.00000			1.50000
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.23607	+	2.23607i	−0.845154	+	0.845154i	−0.989524	−	0.144370i	$-0.953885\pi$
$7$	−2.23607	+	2.23607i	−0.845154	+	0.845154i	0.144370	+	0.989524i	$0.453885\pi$
$8$	2.23607			0.790569
$9$	3.00000			1.00000
$10$		0			0
$11$	4.00000	+	4.00000i	1.20605	+	1.20605i	0.972297	+	0.233748i	$0.0750991\pi$
$11$	4.00000	+	4.00000i	1.20605	+	1.20605i	0.233748	+	0.972297i	$0.424901\pi$
$12$		0			0
$13$	4.47214	−	4.47214i	1.24035	−	1.24035i	0.280491	−	0.959857i	$-0.409503\pi$
$13$	4.47214	−	4.47214i	1.24035	−	1.24035i	0.959857	−	0.280491i	$-0.0904971\pi$
$14$	−5.00000	+	5.00000i	−1.33631	+	1.33631i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−4.47214			−1.08465			−0.542326	−	0.840168i	$-0.682456\pi$
$17$	−4.47214			−1.08465			−0.542326	+	0.840168i	$0.682456\pi$
$18$	6.70820			1.58114
$19$	2.00000	−	2.00000i	0.458831	−	0.458831i	−0.439440	−	0.898272i	$-0.644823\pi$
$19$	2.00000	−	2.00000i	0.458831	−	0.458831i	0.898272	+	0.439440i	$0.144823\pi$
$20$		0			0
$21$		0			0
$22$	8.94427	+	8.94427i	1.90693	+	1.90693i
$23$	2.23607	+	2.23607i	0.466252	+	0.466252i	0.900698	−	0.434446i	$-0.143056\pi$
$23$	2.23607	+	2.23607i	0.466252	+	0.466252i	−0.434446	+	0.900698i	$0.643056\pi$
$24$		0			0
$25$		0			0
$26$	10.0000	−	10.0000i	1.96116	−	1.96116i
$27$		0			0
$28$	−6.70820	+	6.70820i	−1.26773	+	1.26773i
$29$	−2.00000	+	5.00000i	−0.371391	+	0.928477i
$29$	−2.00000	+	5.00000i	−0.371391	+	0.928477i
$30$		0			0
$31$	−4.00000	−	4.00000i	−0.718421	−	0.718421i	0.249861	−	0.968282i	$-0.419615\pi$
$31$	−4.00000	−	4.00000i	−0.718421	−	0.718421i	−0.968282	+	0.249861i	$0.919615\pi$
$32$	−6.70820			−1.18585
$33$		0			0
$34$	−10.0000			−1.71499
$35$		0			0
$36$	9.00000			1.50000
$37$		−	4.47214i		−	0.735215i	−0.929981	−	0.367607i	$-0.880177\pi$
$37$		−	4.47214i		−	0.735215i	0.929981	−	0.367607i	$-0.119823\pi$
$38$	4.47214	−	4.47214i	0.725476	−	0.725476i
$39$		0			0
$40$		0			0
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	1.00000	−	1.00000i	0.156174	−	0.156174i	0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$		−	4.47214i		−	0.681994i	−0.940064	−	0.340997i	$-0.889235\pi$
$43$		−	4.47214i		−	0.681994i	0.940064	−	0.340997i	$-0.110765\pi$
$44$	12.0000	+	12.0000i	1.80907	+	1.80907i
$45$		0			0
$46$	5.00000	+	5.00000i	0.737210	+	0.737210i
$47$			4.47214i			0.652328i	0.945313	+	0.326164i	$0.105756\pi$
$47$			4.47214i			0.652328i	−0.945313	+	0.326164i	$0.894244\pi$
$48$		0			0
$49$		−	3.00000i		−	0.428571i
$50$		0			0
$51$		0			0
$52$	13.4164	−	13.4164i	1.86052	−	1.86052i
$53$	−8.94427	−	8.94427i	−1.22859	−	1.22859i	−0.964497	−	0.264093i	$-0.914927\pi$
$53$	−8.94427	−	8.94427i	−1.22859	−	1.22859i	−0.264093	−	0.964497i	$-0.585073\pi$
$54$		0			0
$55$		0			0
$56$	−5.00000	+	5.00000i	−0.668153	+	0.668153i
$57$		0			0
$58$	−4.47214	+	11.1803i	−0.587220	+	1.46805i
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$		0			0
$61$	−9.00000	−	9.00000i	−1.15233	−	1.15233i	−0.986084	−	0.166248i	$-0.946835\pi$
$61$	−9.00000	−	9.00000i	−1.15233	−	1.15233i	−0.166248	−	0.986084i	$-0.553165\pi$
$62$	−8.94427	−	8.94427i	−1.13592	−	1.13592i
$63$	−6.70820	+	6.70820i	−0.845154	+	0.845154i
$64$	−13.0000			−1.62500
$65$		0			0
$66$		0			0
$67$	−2.23607	−	2.23607i	−0.273179	−	0.273179i	0.557199	−	0.830379i	$-0.311876\pi$
$67$	−2.23607	−	2.23607i	−0.273179	−	0.273179i	−0.830379	+	0.557199i	$0.811876\pi$
$68$	−13.4164			−1.62698
$69$		0			0
$70$		0			0
$71$			12.0000i			1.42414i	0.702109	+	0.712069i	$0.252242\pi$
$71$			12.0000i			1.42414i	−0.702109	+	0.712069i	$0.747758\pi$
$72$	6.70820			0.790569
$73$	−4.47214			−0.523424			−0.261712	−	0.965146i	$-0.584287\pi$
$73$	−4.47214			−0.523424			−0.261712	+	0.965146i	$0.584287\pi$
$74$		−	10.0000i		−	1.16248i
$75$		0			0
$76$	6.00000	−	6.00000i	0.688247	−	0.688247i
$77$	−17.8885			−2.03859
$78$		0			0
$79$	2.00000	−	2.00000i	0.225018	−	0.225018i	−0.585590	−	0.810607i	$-0.699137\pi$
$79$	2.00000	−	2.00000i	0.225018	−	0.225018i	0.810607	+	0.585590i	$0.199137\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$	2.23607	−	2.23607i	0.246932	−	0.246932i
$83$	−6.70820	−	6.70820i	−0.736321	−	0.736321i	0.235543	−	0.971864i	$-0.424313\pi$
$83$	−6.70820	−	6.70820i	−0.736321	−	0.736321i	−0.971864	+	0.235543i	$0.924313\pi$
$84$		0			0
$85$		0			0
$86$		−	10.0000i		−	1.07833i
$87$		0			0
$88$	8.94427	+	8.94427i	0.953463	+	0.953463i
$89$	7.00000	−	7.00000i	0.741999	−	0.741999i	−0.230964	−	0.972962i	$-0.574188\pi$
$89$	7.00000	−	7.00000i	0.741999	−	0.741999i	0.972962	+	0.230964i	$0.0741879\pi$
$90$		0			0
$91$			20.0000i			2.09657i
$92$	6.70820	+	6.70820i	0.699379	+	0.699379i
$93$		0			0
$94$			10.0000i			1.03142i
$95$		0			0
$96$		0			0
$97$			4.47214i			0.454077i	0.973886	+	0.227038i	$0.0729043\pi$
$97$			4.47214i			0.454077i	−0.973886	+	0.227038i	$0.927096\pi$
$98$		−	6.70820i		−	0.677631i
$99$	12.0000	+	12.0000i	1.20605	+	1.20605i
$100$		0			0
$101$	−1.00000	−	1.00000i	−0.0995037	−	0.0995037i	0.655602	−	0.755106i	$-0.272415\pi$
$101$	−1.00000	−	1.00000i	−0.0995037	−	0.0995037i	−0.755106	+	0.655602i	$0.772415\pi$
$102$		0			0
$103$	6.70820	+	6.70820i	0.660979	+	0.660979i	0.955611	−	0.294632i	$-0.0951970\pi$
$103$	6.70820	+	6.70820i	0.660979	+	0.660979i	−0.294632	+	0.955611i	$0.595197\pi$
$104$	10.0000	−	10.0000i	0.980581	−	0.980581i
$105$		0			0
$106$	−20.0000	−	20.0000i	−1.94257	−	1.94257i
$107$	−6.70820	+	6.70820i	−0.648507	+	0.648507i	−0.952632	−	0.304125i	$-0.901636\pi$
$107$	−6.70820	+	6.70820i	−0.648507	+	0.648507i	0.304125	+	0.952632i	$0.401636\pi$
$108$		0			0
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$		0			0
$111$		0			0
$112$	2.23607	−	2.23607i	0.211289	−	0.211289i
$113$	−4.47214			−0.420703			−0.210352	−	0.977626i	$-0.567461\pi$
$113$	−4.47214			−0.420703			−0.210352	+	0.977626i	$0.567461\pi$
$114$		0			0
$115$		0			0
$116$	−6.00000	+	15.0000i	−0.557086	+	1.39272i
$117$	13.4164	−	13.4164i	1.24035	−	1.24035i
$118$		0			0
$119$	10.0000	−	10.0000i	0.916698	−	0.916698i
$120$		0			0
$121$			21.0000i			1.90909i
$122$	−20.1246	−	20.1246i	−1.82200	−	1.82200i
$123$		0			0
$124$	−12.0000	−	12.0000i	−1.07763	−	1.07763i
$125$		0			0
$126$	−15.0000	+	15.0000i	−1.33631	+	1.33631i
$127$	−4.47214			−0.396838			−0.198419	−	0.980117i	$-0.563581\pi$
$127$	−4.47214			−0.396838			−0.198419	+	0.980117i	$0.563581\pi$
$128$	−15.6525			−1.38350
$129$		0			0
$130$		0			0
$131$	14.0000	−	14.0000i	1.22319	−	1.22319i	0.256693	−	0.966493i	$-0.417367\pi$
$131$	14.0000	−	14.0000i	1.22319	−	1.22319i	0.966493	−	0.256693i	$-0.0826328\pi$
$132$		0			0
$133$			8.94427i			0.775567i
$134$	−5.00000	−	5.00000i	−0.431934	−	0.431934i
$135$		0			0
$136$	−10.0000			−0.857493
$137$	13.4164			1.14624			0.573121	−	0.819471i	$-0.305733\pi$
$137$	13.4164			1.14624			0.573121	+	0.819471i	$0.305733\pi$
$138$		0			0
$139$			4.00000i			0.339276i	0.985506	+	0.169638i	$0.0542598\pi$
$139$			4.00000i			0.339276i	−0.985506	+	0.169638i	$0.945740\pi$
$140$		0			0
$141$		0			0
$142$			26.8328i			2.25176i
$143$	35.7771			2.99183
$144$	−3.00000			−0.250000
$145$		0			0
$146$	−10.0000			−0.827606
$147$		0			0
$148$		−	13.4164i		−	1.10282i
$149$	−20.0000			−1.63846			−0.819232	−	0.573462i	$-0.805600\pi$
$149$	−20.0000			−1.63846			−0.819232	+	0.573462i	$0.805600\pi$
$150$		0			0
$151$		−	12.0000i		−	0.976546i	−0.872691	−	0.488273i	$-0.837627\pi$
$151$		−	12.0000i		−	0.976546i	0.872691	−	0.488273i	$-0.162373\pi$
$152$	4.47214	−	4.47214i	0.362738	−	0.362738i
$153$	−13.4164			−1.08465
$154$	−40.0000			−3.22329
$155$		0			0
$156$		0			0
$157$			13.4164i			1.07075i	0.844616	+	0.535373i	$0.179829\pi$
$157$			13.4164i			1.07075i	−0.844616	+	0.535373i	$0.820171\pi$
$158$	4.47214	−	4.47214i	0.355784	−	0.355784i
$159$		0			0
$160$		0			0
$161$	−10.0000			−0.788110
$162$	20.1246			1.58114
$163$		0			0			−	1.00000i	$-0.5\pi$
$163$		0			0				1.00000i	$0.5\pi$
$164$	3.00000	−	3.00000i	0.234261	−	0.234261i
$165$		0			0
$166$	−15.0000	−	15.0000i	−1.16423	−	1.16423i
$167$	6.70820	+	6.70820i	0.519096	+	0.519096i	0.917298	−	0.398202i	$-0.130366\pi$
$167$	6.70820	+	6.70820i	0.519096	+	0.519096i	−0.398202	+	0.917298i	$0.630366\pi$
$168$		0			0
$169$		−	27.0000i		−	2.07692i
$170$		0			0
$171$	6.00000	−	6.00000i	0.458831	−	0.458831i
$172$		−	13.4164i		−	1.02299i
$173$	13.4164	−	13.4164i	1.02003	−	1.02003i	0.0202354	−	0.999795i	$-0.493558\pi$
$173$	13.4164	−	13.4164i	1.02003	−	1.02003i	0.999795	−	0.0202354i	$-0.00644155\pi$
$174$		0			0
$175$		0			0
$176$	−4.00000	−	4.00000i	−0.301511	−	0.301511i
$177$		0			0
$178$	15.6525	−	15.6525i	1.17320	−	1.17320i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	−20.0000			−1.48659			−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000			−1.48659			−0.743294	+	0.668965i	$0.766738\pi$
$182$			44.7214i			3.31497i
$183$		0			0
$184$	5.00000	+	5.00000i	0.368605	+	0.368605i
$185$		0			0
$186$		0			0
$187$	−17.8885	−	17.8885i	−1.30814	−	1.30814i
$188$			13.4164i			0.978492i
$189$		0			0
$190$		0			0
$191$	6.00000	+	6.00000i	0.434145	+	0.434145i	0.890036	−	0.455891i	$-0.150679\pi$
$191$	6.00000	+	6.00000i	0.434145	+	0.434145i	−0.455891	+	0.890036i	$0.650679\pi$
$192$		0			0
$193$			4.47214i			0.321911i	0.986962	+	0.160956i	$0.0514576\pi$
$193$			4.47214i			0.321911i	−0.986962	+	0.160956i	$0.948542\pi$
$194$			10.0000i			0.717958i
$195$		0			0
$196$		−	9.00000i		−	0.642857i
$197$	−13.4164	+	13.4164i	−0.955879	+	0.955879i	−0.999067	−	0.0431875i	$-0.986249\pi$
$197$	−13.4164	+	13.4164i	−0.955879	+	0.955879i	0.0431875	+	0.999067i	$0.486249\pi$
$198$	26.8328	+	26.8328i	1.90693	+	1.90693i
$199$			20.0000i			1.41776i	0.705328	+	0.708881i	$0.250800\pi$
$199$			20.0000i			1.41776i	−0.705328	+	0.708881i	$0.749200\pi$
$200$		0			0
$201$		0			0
$202$	−2.23607	−	2.23607i	−0.157329	−	0.157329i
$203$	−6.70820	−	15.6525i	−0.470824	−	1.09859i
$204$		0			0
$205$		0			0
$206$	15.0000	+	15.0000i	1.04510	+	1.04510i
$207$	6.70820	+	6.70820i	0.466252	+	0.466252i
$208$	−4.47214	+	4.47214i	−0.310087	+	0.310087i
$209$	16.0000			1.10674
$210$		0			0
$211$	16.0000	−	16.0000i	1.10149	−	1.10149i	0.107254	−	0.994232i	$-0.465794\pi$
$211$	16.0000	−	16.0000i	1.10149	−	1.10149i	0.994232	−	0.107254i	$-0.0342057\pi$
$212$	−26.8328	−	26.8328i	−1.84289	−	1.84289i
$213$		0			0
$214$	−15.0000	+	15.0000i	−1.02538	+	1.02538i
$215$		0			0
$216$		0			0
$217$	17.8885			1.21435
$218$	22.3607			1.51446
$219$		0			0
$220$		0			0
$221$	−20.0000	+	20.0000i	−1.34535	+	1.34535i
$222$		0			0
$223$	−11.1803	−	11.1803i	−0.748691	−	0.748691i	0.225542	−	0.974233i	$-0.427585\pi$
$223$	−11.1803	−	11.1803i	−0.748691	−	0.748691i	−0.974233	+	0.225542i	$0.927585\pi$
$224$	15.0000	−	15.0000i	1.00223	−	1.00223i
$225$		0			0
$226$	−10.0000			−0.665190
$227$	6.70820	−	6.70820i	0.445239	−	0.445239i	−0.448529	−	0.893768i	$-0.648052\pi$
$227$	6.70820	−	6.70820i	0.445239	−	0.445239i	0.893768	+	0.448529i	$0.148052\pi$
$228$		0			0
$229$	3.00000	+	3.00000i	0.198246	+	0.198246i	0.799248	−	0.601002i	$-0.205232\pi$
$229$	3.00000	+	3.00000i	0.198246	+	0.198246i	−0.601002	+	0.799248i	$0.705232\pi$
$230$		0			0
$231$		0			0
$232$	−4.47214	+	11.1803i	−0.293610	+	0.734025i
$233$	8.94427	+	8.94427i	0.585959	+	0.585959i	0.936534	−	0.350576i	$-0.114014\pi$
$233$	8.94427	+	8.94427i	0.585959	+	0.585959i	−0.350576	+	0.936534i	$0.614014\pi$
$234$	30.0000	−	30.0000i	1.96116	−	1.96116i
$235$		0			0
$236$		0			0
$237$		0			0
$238$	22.3607	−	22.3607i	1.44943	−	1.44943i
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$			8.00000i			0.515325i	0.966235	+	0.257663i	$0.0829523\pi$
$241$			8.00000i			0.515325i	−0.966235	+	0.257663i	$0.917048\pi$
$242$			46.9574i			3.01854i
$243$		0			0
$244$	−27.0000	−	27.0000i	−1.72850	−	1.72850i
$245$		0			0
$246$		0			0
$247$		−	17.8885i		−	1.13822i
$248$	−8.94427	−	8.94427i	−0.567962	−	0.567962i
$249$		0			0
$250$		0			0
$251$	4.00000	+	4.00000i	0.252478	+	0.252478i	0.821986	−	0.569508i	$-0.192866\pi$
$251$	4.00000	+	4.00000i	0.252478	+	0.252478i	−0.569508	+	0.821986i	$0.692866\pi$
$252$	−20.1246	+	20.1246i	−1.26773	+	1.26773i
$253$			17.8885i			1.12464i
$254$	−10.0000			−0.627456
$255$		0			0
$256$	−9.00000			−0.562500
$257$	4.47214	−	4.47214i	0.278964	−	0.278964i	−0.553731	−	0.832695i	$-0.686797\pi$
$257$	4.47214	−	4.47214i	0.278964	−	0.278964i	0.832695	+	0.553731i	$0.186797\pi$
$258$		0			0
$259$	10.0000	+	10.0000i	0.621370	+	0.621370i
$260$		0			0
$261$	−6.00000	+	15.0000i	−0.371391	+	0.928477i
$262$	31.3050	−	31.3050i	1.93403	−	1.93403i
$263$			8.94427i			0.551527i	0.961225	+	0.275764i	$0.0889307\pi$
$263$			8.94427i			0.551527i	−0.961225	+	0.275764i	$0.911069\pi$
$264$		0			0
$265$		0			0
$266$			20.0000i			1.22628i
$267$		0			0
$268$	−6.70820	−	6.70820i	−0.409769	−	0.409769i
$269$	7.00000	+	7.00000i	0.426798	+	0.426798i	0.887536	−	0.460738i	$-0.152415\pi$
$269$	7.00000	+	7.00000i	0.426798	+	0.426798i	−0.460738	+	0.887536i	$0.652415\pi$
$270$		0			0
$271$	14.0000	−	14.0000i	0.850439	−	0.850439i	−0.139748	−	0.990187i	$-0.544629\pi$
$271$	14.0000	−	14.0000i	0.850439	−	0.850439i	0.990187	+	0.139748i	$0.0446292\pi$
$272$	4.47214			0.271163
$273$		0			0
$274$	30.0000			1.81237
$275$		0			0
$276$		0			0
$277$	8.94427	−	8.94427i	0.537409	−	0.537409i	−0.385358	−	0.922767i	$-0.625922\pi$
$277$	8.94427	−	8.94427i	0.537409	−	0.537409i	0.922767	+	0.385358i	$0.125922\pi$
$278$			8.94427i			0.536442i
$279$	−12.0000	−	12.0000i	−0.718421	−	0.718421i
$280$		0			0
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$		0			0
$283$	−11.1803	+	11.1803i	−0.664602	+	0.664602i	−0.956461	−	0.291859i	$-0.905726\pi$
$283$	−11.1803	+	11.1803i	−0.664602	+	0.664602i	0.291859	+	0.956461i	$0.405726\pi$
$284$			36.0000i			2.13621i
$285$		0			0
$286$	80.0000			4.73050
$287$			4.47214i			0.263982i
$288$	−20.1246			−1.18585
$289$	3.00000			0.176471
$290$		0			0
$291$		0			0
$292$	−13.4164			−0.785136
$293$			4.47214i			0.261265i	0.991431	+	0.130632i	$0.0417008\pi$
$293$			4.47214i			0.261265i	−0.991431	+	0.130632i	$0.958299\pi$
$294$		0			0
$295$		0			0
$296$		−	10.0000i		−	0.581238i
$297$		0			0
$298$	−44.7214			−2.59064
$299$	20.0000			1.15663
$300$		0			0
$301$	10.0000	+	10.0000i	0.576390	+	0.576390i
$302$		−	26.8328i		−	1.54406i
$303$		0			0
$304$	−2.00000	+	2.00000i	−0.114708	+	0.114708i
$305$		0			0
$306$	−30.0000			−1.71499
$307$	31.3050			1.78667			0.893334	−	0.449393i	$-0.148360\pi$
$307$	31.3050			1.78667			0.893334	+	0.449393i	$0.148360\pi$
$308$	−53.6656			−3.05788
$309$		0			0
$310$		0			0
$311$	−4.00000	−	4.00000i	−0.226819	−	0.226819i	0.584543	−	0.811363i	$-0.301274\pi$
$311$	−4.00000	−	4.00000i	−0.226819	−	0.226819i	−0.811363	+	0.584543i	$0.801274\pi$
$312$		0			0
$313$	22.3607	+	22.3607i	1.26390	+	1.26390i	0.949187	+	0.314714i	$0.101909\pi$
$313$	22.3607	+	22.3607i	1.26390	+	1.26390i	0.314714	+	0.949187i	$0.398091\pi$
$314$			30.0000i			1.69300i
$315$		0			0
$316$	6.00000	−	6.00000i	0.337526	−	0.337526i
$317$		−	31.3050i		−	1.75826i	−0.476581	−	0.879131i	$-0.658124\pi$
$317$		−	31.3050i		−	1.75826i	0.476581	−	0.879131i	$-0.341876\pi$
$318$		0			0
$319$	−28.0000	+	12.0000i	−1.56770	+	0.671871i
$320$		0			0
$321$		0			0
$322$	−22.3607			−1.24611
$323$	−8.94427	+	8.94427i	−0.497673	+	0.497673i
$324$	27.0000			1.50000
$325$		0			0
$326$		0			0
$327$		0			0
$328$	2.23607	−	2.23607i	0.123466	−	0.123466i
$329$	−10.0000	−	10.0000i	−0.551318	−	0.551318i
$330$		0			0
$331$	−6.00000	+	6.00000i	−0.329790	+	0.329790i	−0.852506	−	0.522717i	$-0.824919\pi$
$331$	−6.00000	+	6.00000i	−0.329790	+	0.329790i	0.522717	+	0.852506i	$0.324919\pi$
$332$	−20.1246	−	20.1246i	−1.10448	−	1.10448i
$333$		−	13.4164i		−	0.735215i
$334$	15.0000	+	15.0000i	0.820763	+	0.820763i
$335$		0			0
$336$		0			0
$337$			13.4164i			0.730838i	0.930843	+	0.365419i	$0.119074\pi$
$337$			13.4164i			0.730838i	−0.930843	+	0.365419i	$0.880926\pi$
$338$		−	60.3738i		−	3.28390i
$339$		0			0
$340$		0			0
$341$		−	32.0000i		−	1.73290i
$342$	13.4164	−	13.4164i	0.725476	−	0.725476i
$343$	−8.94427	−	8.94427i	−0.482945	−	0.482945i
$344$		−	10.0000i		−	0.539164i
$345$		0			0
$346$	30.0000	−	30.0000i	1.61281	−	1.61281i
$347$	15.6525	+	15.6525i	0.840269	+	0.840269i	0.988894	−	0.148625i	$-0.0474846\pi$
$347$	15.6525	+	15.6525i	0.840269	+	0.840269i	−0.148625	+	0.988894i	$0.547485\pi$
$348$		0			0
$349$		−	30.0000i		−	1.60586i	−0.596071	−	0.802932i	$-0.703272\pi$
$349$		−	30.0000i		−	1.60586i	0.596071	−	0.802932i	$-0.296728\pi$
$350$		0			0
$351$		0			0
$352$	−26.8328	−	26.8328i	−1.43019	−	1.43019i
$353$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$353$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$354$		0			0
$355$		0			0
$356$	21.0000	−	21.0000i	1.11300	−	1.11300i
$357$		0			0
$358$		0			0
$359$	−12.0000	+	12.0000i	−0.633336	+	0.633336i	−0.948903	−	0.315567i	$-0.897805\pi$
$359$	−12.0000	+	12.0000i	−0.633336	+	0.633336i	0.315567	+	0.948903i	$0.397805\pi$
$360$		0			0
$361$			11.0000i			0.578947i
$362$	−44.7214			−2.35050
$363$		0			0
$364$			60.0000i			3.14485i
$365$		0			0
$366$		0			0
$367$	−26.8328			−1.40066			−0.700331	−	0.713818i	$-0.746964\pi$
$367$	−26.8328			−1.40066			−0.700331	+	0.713818i	$0.746964\pi$
$368$	−2.23607	−	2.23607i	−0.116563	−	0.116563i
$369$	3.00000	−	3.00000i	0.156174	−	0.156174i
$370$		0			0
$371$	40.0000			2.07670
$372$		0			0
$373$	13.4164	+	13.4164i	0.694675	+	0.694675i	0.963257	−	0.268582i	$-0.0865549\pi$
$373$	13.4164	+	13.4164i	0.694675	+	0.694675i	−0.268582	+	0.963257i	$0.586555\pi$
$374$	−40.0000	−	40.0000i	−2.06835	−	2.06835i
$375$		0			0
$376$			10.0000i			0.515711i
$377$	13.4164	+	31.3050i	0.690980	+	1.61229i
$378$		0			0
$379$	−12.0000	+	12.0000i	−0.616399	+	0.616399i	−0.944606	−	0.328207i	$-0.893556\pi$
$379$	−12.0000	+	12.0000i	−0.616399	+	0.616399i	0.328207	+	0.944606i	$0.393556\pi$
$380$		0			0
$381$		0			0
$382$	13.4164	+	13.4164i	0.686443	+	0.686443i
$383$	−11.1803	+	11.1803i	−0.571289	+	0.571289i	−0.932488	−	0.361200i	$-0.882367\pi$
$383$	−11.1803	+	11.1803i	−0.571289	+	0.571289i	0.361200	+	0.932488i	$0.382367\pi$
$384$		0			0
$385$		0			0
$386$			10.0000i			0.508987i
$387$		−	13.4164i		−	0.681994i
$388$			13.4164i			0.681115i
$389$	−7.00000	−	7.00000i	−0.354914	−	0.354914i	0.507020	−	0.861934i	$-0.330747\pi$
$389$	−7.00000	−	7.00000i	−0.354914	−	0.354914i	−0.861934	+	0.507020i	$0.830747\pi$
$390$		0			0
$391$	−10.0000	−	10.0000i	−0.505722	−	0.505722i
$392$		−	6.70820i		−	0.338815i
$393$		0			0
$394$	−30.0000	+	30.0000i	−1.51138	+	1.51138i
$395$		0			0
$396$	36.0000	+	36.0000i	1.80907	+	1.80907i
$397$	−13.4164	+	13.4164i	−0.673350	+	0.673350i	−0.958487	−	0.285137i	$-0.907961\pi$
$397$	−13.4164	+	13.4164i	−0.673350	+	0.673350i	0.285137	+	0.958487i	$0.407961\pi$
$398$			44.7214i			2.24168i
$399$		0			0
$400$		0			0
$401$	−20.0000			−0.998752			−0.499376	−	0.866385i	$-0.666437\pi$
$401$	−20.0000			−0.998752			−0.499376	+	0.866385i	$0.666437\pi$
$402$		0			0
$403$	−35.7771			−1.78218
$404$	−3.00000	−	3.00000i	−0.149256	−	0.149256i
$405$		0			0
$406$	−15.0000	−	35.0000i	−0.744438	−	1.73702i
$407$	17.8885	−	17.8885i	0.886702	−	0.886702i
$408$		0			0
$409$	−3.00000	+	3.00000i	−0.148340	+	0.148340i	−0.777376	−	0.629036i	$-0.783450\pi$
$409$	−3.00000	+	3.00000i	−0.148340	+	0.148340i	0.629036	+	0.777376i	$0.283450\pi$
$410$		0			0
$411$		0			0
$412$	20.1246	+	20.1246i	0.991468	+	0.991468i
$413$		0			0
$414$	15.0000	+	15.0000i	0.737210	+	0.737210i
$415$		0			0
$416$	−30.0000	+	30.0000i	−1.47087	+	1.47087i
$417$		0			0
$418$	35.7771			1.74991
$419$	24.0000			1.17248			0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	9.00000	−	9.00000i	0.438633	−	0.438633i	−0.452919	−	0.891552i	$-0.649617\pi$
$421$	9.00000	−	9.00000i	0.438633	−	0.438633i	0.891552	+	0.452919i	$0.149617\pi$
$422$	35.7771	−	35.7771i	1.74160	−	1.74160i
$423$			13.4164i			0.652328i
$424$	−20.0000	−	20.0000i	−0.971286	−	0.971286i
$425$		0			0
$426$		0			0
$427$	40.2492			1.94780
$428$	−20.1246	+	20.1246i	−0.972760	+	0.972760i
$429$		0			0
$430$		0			0
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$		0			0
$433$	−22.3607			−1.07459			−0.537293	−	0.843396i	$-0.680553\pi$
$433$	−22.3607			−1.07459			−0.537293	+	0.843396i	$0.680553\pi$
$434$	40.0000			1.92006
$435$		0			0
$436$	30.0000			1.43674
$437$	8.94427			0.427863
$438$		0			0
$439$	−16.0000			−0.763638			−0.381819	−	0.924237i	$-0.624702\pi$
$439$	−16.0000			−0.763638			−0.381819	+	0.924237i	$0.624702\pi$
$440$		0			0
$441$		−	9.00000i		−	0.428571i
$442$	−44.7214	+	44.7214i	−2.12718	+	2.12718i
$443$	31.3050			1.48734			0.743672	−	0.668545i	$-0.233083\pi$
$443$	31.3050			1.48734			0.743672	+	0.668545i	$0.233083\pi$
$444$		0			0
$445$		0			0
$446$	−25.0000	−	25.0000i	−1.18378	−	1.18378i
$447$		0			0
$448$	29.0689	−	29.0689i	1.37338	−	1.37338i
$449$	−13.0000	+	13.0000i	−0.613508	+	0.613508i	−0.943858	−	0.330350i	$-0.892833\pi$
$449$	−13.0000	+	13.0000i	−0.613508	+	0.613508i	0.330350	+	0.943858i	$0.392833\pi$
$450$		0			0
$451$	8.00000			0.376705
$452$	−13.4164			−0.631055
$453$		0			0
$454$	15.0000	−	15.0000i	0.703985	−	0.703985i
$455$		0			0
$456$		0			0
$457$	17.8885	+	17.8885i	0.836791	+	0.836791i	0.988435	−	0.151644i	$-0.0484568\pi$
$457$	17.8885	+	17.8885i	0.836791	+	0.836791i	−0.151644	+	0.988435i	$0.548457\pi$
$458$	6.70820	+	6.70820i	0.313454	+	0.313454i
$459$		0			0
$460$		0			0
$461$	−9.00000	+	9.00000i	−0.419172	+	0.419172i	−0.884918	−	0.465746i	$-0.845786\pi$
$461$	−9.00000	+	9.00000i	−0.419172	+	0.419172i	0.465746	+	0.884918i	$0.345786\pi$
$462$		0			0
$463$	−2.23607	+	2.23607i	−0.103919	+	0.103919i	−0.757155	−	0.653236i	$-0.773411\pi$
$463$	−2.23607	+	2.23607i	−0.103919	+	0.103919i	0.653236	+	0.757155i	$0.273411\pi$
$464$	2.00000	−	5.00000i	0.0928477	−	0.232119i
$465$		0			0
$466$	20.0000	+	20.0000i	0.926482	+	0.926482i
$467$	−13.4164			−0.620837			−0.310419	−	0.950600i	$-0.600469\pi$
$467$	−13.4164			−0.620837			−0.310419	+	0.950600i	$0.600469\pi$
$468$	40.2492	−	40.2492i	1.86052	−	1.86052i
$469$	10.0000			0.461757
$470$		0			0
$471$		0			0
$472$		0			0
$473$	17.8885	−	17.8885i	0.822516	−	0.822516i
$474$		0			0
$475$		0			0
$476$	30.0000	−	30.0000i	1.37505	−	1.37505i
$477$	−26.8328	−	26.8328i	−1.22859	−	1.22859i
$478$		0			0
$479$	18.0000	+	18.0000i	0.822441	+	0.822441i	0.986458	−	0.164017i	$-0.0524451\pi$
$479$	18.0000	+	18.0000i	0.822441	+	0.822441i	−0.164017	+	0.986458i	$0.552445\pi$
$480$		0			0
$481$	−20.0000	−	20.0000i	−0.911922	−	0.911922i
$482$			17.8885i			0.814801i
$483$		0			0
$484$			63.0000i			2.86364i
$485$		0			0
$486$		0			0
$487$	20.1246	−	20.1246i	0.911933	−	0.911933i	−0.0844910	−	0.996424i	$-0.526926\pi$
$487$	20.1246	−	20.1246i	0.911933	−	0.911933i	0.996424	+	0.0844910i	$0.0269264\pi$
$488$	−20.1246	−	20.1246i	−0.910998	−	0.910998i
$489$		0			0
$490$		0			0
$491$	−6.00000	+	6.00000i	−0.270776	+	0.270776i	−0.829413	−	0.558636i	$-0.811325\pi$
$491$	−6.00000	+	6.00000i	−0.270776	+	0.270776i	0.558636	+	0.829413i	$0.311325\pi$
$492$		0			0
$493$	8.94427	−	22.3607i	0.402830	−	1.00707i
$494$		−	40.0000i		−	1.79969i
$495$		0			0
$496$	4.00000	+	4.00000i	0.179605	+	0.179605i
$497$	−26.8328	−	26.8328i	−1.20362	−	1.20362i
$498$		0			0
$499$	−20.0000			−0.895323			−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000			−0.895323			−0.447661	+	0.894203i	$0.647743\pi$
$500$		0			0
$501$		0			0
$502$	8.94427	+	8.94427i	0.399202	+	0.399202i
$503$	−22.3607			−0.997013			−0.498507	−	0.866886i	$-0.666118\pi$
$503$	−22.3607			−0.997013			−0.498507	+	0.866886i	$0.666118\pi$
$504$	−15.0000	+	15.0000i	−0.668153	+	0.668153i
$505$		0			0
$506$			40.0000i			1.77822i
$507$		0			0
$508$	−13.4164			−0.595257
$509$			24.0000i			1.06378i	0.846813	+	0.531891i	$0.178518\pi$
$509$			24.0000i			1.06378i	−0.846813	+	0.531891i	$0.821482\pi$
$510$		0			0
$511$	10.0000	−	10.0000i	0.442374	−	0.442374i
$512$	11.1803			0.494106
$513$		0			0
$514$	10.0000	−	10.0000i	0.441081	−	0.441081i
$515$		0			0
$516$		0			0
$517$	−17.8885	+	17.8885i	−0.786737	+	0.786737i
$518$	22.3607	+	22.3607i	0.982472	+	0.982472i
$519$		0			0
$520$		0			0
$521$		−	10.0000i		−	0.438108i	−0.975713	−	0.219054i	$-0.929703\pi$
$521$		−	10.0000i		−	0.438108i	0.975713	−	0.219054i	$-0.0702971\pi$
$522$	−13.4164	+	33.5410i	−0.587220	+	1.46805i
$523$	15.6525	+	15.6525i	0.684435	+	0.684435i	0.960996	−	0.276561i	$-0.0891949\pi$
$523$	15.6525	+	15.6525i	0.684435	+	0.684435i	−0.276561	+	0.960996i	$0.589195\pi$
$524$	42.0000	−	42.0000i	1.83478	−	1.83478i
$525$		0			0
$526$			20.0000i			0.872041i
$527$	17.8885	+	17.8885i	0.779237	+	0.779237i
$528$		0			0
$529$		−	13.0000i		−	0.565217i
$530$		0			0
$531$		0			0
$532$			26.8328i			1.16335i
$533$		−	8.94427i		−	0.387419i
$534$		0			0
$535$		0			0
$536$	−5.00000	−	5.00000i	−0.215967	−	0.215967i
$537$		0			0
$538$	15.6525	+	15.6525i	0.674826	+	0.674826i
$539$	12.0000	−	12.0000i	0.516877	−	0.516877i
$540$		0			0
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$	31.3050	−	31.3050i	1.34466	−	1.34466i
$543$		0			0
$544$	30.0000			1.28624
$545$		0			0
$546$		0			0
$547$	−15.6525	+	15.6525i	−0.669252	+	0.669252i	−0.957543	−	0.288291i	$-0.906913\pi$
$547$	−15.6525	+	15.6525i	−0.669252	+	0.669252i	0.288291	+	0.957543i	$0.406913\pi$
$548$	40.2492			1.71936
$549$	−27.0000	−	27.0000i	−1.15233	−	1.15233i
$550$		0			0
$551$	6.00000	+	14.0000i	0.255609	+	0.596420i
$552$		0			0
$553$			8.94427i			0.380349i
$554$	20.0000	−	20.0000i	0.849719	−	0.849719i
$555$		0			0
$556$			12.0000i			0.508913i
$557$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$557$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$558$	−26.8328	−	26.8328i	−1.13592	−	1.13592i
$559$	−20.0000	−	20.0000i	−0.845910	−	0.845910i
$560$		0			0
$561$		0			0
$562$	−26.8328			−1.13187
$563$	35.7771			1.50782			0.753912	−	0.656975i	$-0.228164\pi$
$563$	35.7771			1.50782			0.753912	+	0.656975i	$0.228164\pi$
$564$		0			0
$565$		0			0
$566$	−25.0000	+	25.0000i	−1.05083	+	1.05083i
$567$	−20.1246	+	20.1246i	−0.845154	+	0.845154i
$568$			26.8328i			1.12588i
$569$	7.00000	+	7.00000i	0.293455	+	0.293455i	0.838444	−	0.544988i	$-0.183466\pi$
$569$	7.00000	+	7.00000i	0.293455	+	0.293455i	−0.544988	+	0.838444i	$0.683466\pi$
$570$		0			0
$571$	−12.0000			−0.502184			−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000			−0.502184			−0.251092	+	0.967963i	$0.580790\pi$
$572$	107.331			4.48775
$573$		0			0
$574$			10.0000i			0.417392i
$575$		0			0
$576$	−39.0000			−1.62500
$577$		−	40.2492i		−	1.67560i	−0.545979	−	0.837799i	$-0.683842\pi$
$577$		−	40.2492i		−	1.67560i	0.545979	−	0.837799i	$-0.316158\pi$
$578$	6.70820			0.279024
$579$		0			0
$580$		0			0
$581$	30.0000			1.24461
$582$		0			0
$583$		−	71.5542i		−	2.96347i
$584$	−10.0000			−0.413803
$585$		0			0
$586$			10.0000i			0.413096i
$587$	−20.1246	+	20.1246i	−0.830632	+	0.830632i	−0.987603	−	0.156972i	$-0.949827\pi$
$587$	−20.1246	+	20.1246i	−0.830632	+	0.830632i	0.156972	+	0.987603i	$0.449827\pi$
$588$		0			0
$589$	−16.0000			−0.659269
$590$		0			0
$591$		0			0
$592$			4.47214i			0.183804i
$593$	8.94427	−	8.94427i	0.367297	−	0.367297i	−0.499193	−	0.866491i	$-0.666370\pi$
$593$	8.94427	−	8.94427i	0.367297	−	0.367297i	0.866491	+	0.499193i	$0.166370\pi$
$594$		0			0
$595$		0			0
$596$	−60.0000			−2.45770
$597$		0			0
$598$	44.7214			1.82879
$599$	−22.0000	+	22.0000i	−0.898896	+	0.898896i	−0.995339	−	0.0964429i	$-0.969253\pi$
$599$	−22.0000	+	22.0000i	−0.898896	+	0.898896i	0.0964429	+	0.995339i	$0.469253\pi$
$600$		0			0
$601$	−21.0000	−	21.0000i	−0.856608	−	0.856608i	0.134329	−	0.990937i	$-0.457112\pi$
$601$	−21.0000	−	21.0000i	−0.856608	−	0.856608i	−0.990937	+	0.134329i	$0.957112\pi$
$602$	22.3607	+	22.3607i	0.911353	+	0.911353i
$603$	−6.70820	−	6.70820i	−0.273179	−	0.273179i
$604$		−	36.0000i		−	1.46482i
$605$		0			0
$606$		0			0
$607$			13.4164i			0.544555i	0.962219	+	0.272278i	$0.0877769\pi$
$607$			13.4164i			0.544555i	−0.962219	+	0.272278i	$0.912223\pi$
$608$	−13.4164	+	13.4164i	−0.544107	+	0.544107i
$609$		0			0
$610$		0			0
$611$	20.0000	+	20.0000i	0.809113	+	0.809113i
$612$	−40.2492			−1.62698
$613$	−8.94427	+	8.94427i	−0.361256	+	0.361256i	−0.864275	−	0.503019i	$-0.832222\pi$
$613$	−8.94427	+	8.94427i	−0.361256	+	0.361256i	0.503019	+	0.864275i	$0.332222\pi$
$614$	70.0000			2.82497
$615$		0			0
$616$	−40.0000			−1.61165
$617$			40.2492i			1.62037i	0.586172	+	0.810186i	$0.300634\pi$
$617$			40.2492i			1.62037i	−0.586172	+	0.810186i	$0.699366\pi$
$618$		0			0
$619$	12.0000	+	12.0000i	0.482321	+	0.482321i	0.905872	−	0.423551i	$-0.139217\pi$
$619$	12.0000	+	12.0000i	0.482321	+	0.482321i	−0.423551	+	0.905872i	$0.639217\pi$
$620$		0			0
$621$		0			0
$622$	−8.94427	−	8.94427i	−0.358633	−	0.358633i
$623$			31.3050i			1.25421i
$624$		0			0
$625$		0			0
$626$	50.0000	+	50.0000i	1.99840	+	1.99840i
$627$		0			0
$628$			40.2492i			1.60612i
$629$			20.0000i			0.797452i
$630$		0			0
$631$			40.0000i			1.59237i	0.605050	+	0.796187i	$0.293153\pi$
$631$			40.0000i			1.59237i	−0.605050	+	0.796187i	$0.706847\pi$
$632$	4.47214	−	4.47214i	0.177892	−	0.177892i
$633$		0			0
$634$		−	70.0000i		−	2.78006i
$635$		0			0
$636$		0			0
$637$	−13.4164	−	13.4164i	−0.531577	−	0.531577i
$638$	−62.6099	+	26.8328i	−2.47875	+	1.06232i
$639$			36.0000i			1.42414i
$640$		0			0
$641$	1.00000	+	1.00000i	0.0394976	+	0.0394976i	0.726580	−	0.687082i	$-0.241109\pi$
$641$	1.00000	+	1.00000i	0.0394976	+	0.0394976i	−0.687082	+	0.726580i	$0.741109\pi$
$642$		0			0
$643$	29.0689	−	29.0689i	1.14636	−	1.14636i	0.159103	−	0.987262i	$-0.449140\pi$
$643$	29.0689	−	29.0689i	1.14636	−	1.14636i	0.987262	−	0.159103i	$-0.0508601\pi$
$644$	−30.0000			−1.18217
$645$		0			0
$646$	−20.0000	+	20.0000i	−0.786889	+	0.786889i
$647$	−6.70820	−	6.70820i	−0.263727	−	0.263727i	0.562839	−	0.826566i	$-0.309709\pi$
$647$	−6.70820	−	6.70820i	−0.263727	−	0.263727i	−0.826566	+	0.562839i	$0.809709\pi$
$648$	20.1246			0.790569
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	31.3050			1.22506			0.612529	−	0.790448i	$-0.290152\pi$
$653$	31.3050			1.22506			0.612529	+	0.790448i	$0.290152\pi$
$654$		0			0
$655$		0			0
$656$	−1.00000	+	1.00000i	−0.0390434	+	0.0390434i
$657$	−13.4164			−0.523424
$658$	−22.3607	−	22.3607i	−0.871710	−	0.871710i
$659$	−2.00000	+	2.00000i	−0.0779089	+	0.0779089i	−0.744987	−	0.667078i	$-0.767545\pi$
$659$	−2.00000	+	2.00000i	−0.0779089	+	0.0779089i	0.667078	+	0.744987i	$0.267545\pi$
$660$		0			0
$661$	−40.0000			−1.55582			−0.777910	−	0.628376i	$-0.783720\pi$
$661$	−40.0000			−1.55582			−0.777910	+	0.628376i	$0.783720\pi$
$662$	−13.4164	+	13.4164i	−0.521443	+	0.521443i
$663$		0			0
$664$	−15.0000	−	15.0000i	−0.582113	−	0.582113i
$665$		0			0
$666$		−	30.0000i		−	1.16248i
$667$	−15.6525	+	6.70820i	−0.606066	+	0.259743i
$668$	20.1246	+	20.1246i	0.778645	+	0.778645i
$669$		0			0
$670$		0			0
$671$		−	72.0000i		−	2.77953i
$672$		0			0
$673$	−4.47214	+	4.47214i	−0.172388	+	0.172388i	−0.788028	−	0.615640i	$-0.788898\pi$
$673$	−4.47214	+	4.47214i	−0.172388	+	0.172388i	0.615640	+	0.788028i	$0.288898\pi$
$674$			30.0000i			1.15556i
$675$		0			0
$676$		−	81.0000i		−	3.11538i
$677$			4.47214i			0.171878i	0.996300	+	0.0859391i	$0.0273890\pi$
$677$			4.47214i			0.171878i	−0.996300	+	0.0859391i	$0.972611\pi$
$678$		0			0
$679$	−10.0000	−	10.0000i	−0.383765	−	0.383765i
$680$		0			0
$681$		0			0
$682$		−	71.5542i		−	2.73995i
$683$	33.5410	+	33.5410i	1.28341	+	1.28341i	0.938714	+	0.344698i	$0.112019\pi$
$683$	33.5410	+	33.5410i	1.28341	+	1.28341i	0.344698	+	0.938714i	$0.387981\pi$
$684$	18.0000	−	18.0000i	0.688247	−	0.688247i
$685$		0			0
$686$	−20.0000	−	20.0000i	−0.763604	−	0.763604i
$687$		0			0
$688$			4.47214i			0.170499i
$689$	−80.0000			−3.04776
$690$		0			0
$691$	−20.0000			−0.760836			−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000			−0.760836			−0.380418	+	0.924815i	$0.624220\pi$
$692$	40.2492	−	40.2492i	1.53005	−	1.53005i
$693$	−53.6656			−2.03859
$694$	35.0000	+	35.0000i	1.32858	+	1.32858i
$695$		0			0
$696$		0			0
$697$	−4.47214	+	4.47214i	−0.169394	+	0.169394i
$698$		−	67.0820i		−	2.53909i
$699$		0			0
$700$		0			0
$701$		−	18.0000i		−	0.679851i	−0.940452	−	0.339925i	$-0.889598\pi$
$701$		−	18.0000i		−	0.679851i	0.940452	−	0.339925i	$-0.110402\pi$
$702$		0			0
$703$	−8.94427	−	8.94427i	−0.337340	−	0.337340i
$704$	−52.0000	−	52.0000i	−1.95982	−	1.95982i
$705$		0			0
$706$		0			0
$707$	4.47214			0.168192
$708$		0			0
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$		0			0
$711$	6.00000	−	6.00000i	0.225018	−	0.225018i
$712$	15.6525	−	15.6525i	0.586601	−	0.586601i
$713$		−	17.8885i		−	0.669931i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	−26.8328	+	26.8328i	−1.00139	+	1.00139i
$719$		−	20.0000i		−	0.745874i	−0.927857	−	0.372937i	$-0.878351\pi$
$719$		−	20.0000i		−	0.745874i	0.927857	−	0.372937i	$-0.121649\pi$
$720$		0			0
$721$	−30.0000			−1.11726
$722$			24.5967i			0.915396i
$723$		0			0
$724$	−60.0000			−2.22988
$725$		0			0
$726$		0			0
$727$	−44.7214			−1.65862			−0.829312	−	0.558786i	$-0.811267\pi$
$727$	−44.7214			−1.65862			−0.829312	+	0.558786i	$0.811267\pi$
$728$			44.7214i			1.65748i
$729$	27.0000			1.00000
$730$		0			0
$731$			20.0000i			0.739727i
$732$		0			0
$733$	−4.47214			−0.165182			−0.0825911	−	0.996584i	$-0.526320\pi$
$733$	−4.47214			−0.165182			−0.0825911	+	0.996584i	$0.526320\pi$
$734$	−60.0000			−2.21464
$735$		0			0
$736$	−15.0000	−	15.0000i	−0.552907	−	0.552907i
$737$		−	17.8885i		−	0.658933i
$738$	6.70820	−	6.70820i	0.246932	−	0.246932i
$739$	18.0000	−	18.0000i	0.662141	−	0.662141i	−0.293744	−	0.955884i	$-0.594901\pi$
$739$	18.0000	−	18.0000i	0.662141	−	0.662141i	0.955884	+	0.293744i	$0.0949012\pi$
$740$		0			0
$741$		0			0
$742$	89.4427			3.28355
$743$	−22.3607			−0.820334			−0.410167	−	0.912010i	$-0.634530\pi$
$743$	−22.3607			−0.820334			−0.410167	+	0.912010i	$0.634530\pi$
$744$		0			0
$745$		0			0
$746$	30.0000	+	30.0000i	1.09838	+	1.09838i
$747$	−20.1246	−	20.1246i	−0.736321	−	0.736321i
$748$	−53.6656	−	53.6656i	−1.96221	−	1.96221i
$749$		−	30.0000i		−	1.09618i
$750$		0			0
$751$	24.0000	−	24.0000i	0.875772	−	0.875772i	−0.117322	−	0.993094i	$-0.537431\pi$
$751$	24.0000	−	24.0000i	0.875772	−	0.875772i	0.993094	+	0.117322i	$0.0374308\pi$
$752$		−	4.47214i		−	0.163082i
$753$		0			0
$754$	30.0000	+	70.0000i	1.09254	+	2.54925i
$755$		0			0
$756$		0			0
$757$	40.2492			1.46288			0.731441	−	0.681904i	$-0.238848\pi$
$757$	40.2492			1.46288			0.731441	+	0.681904i	$0.238848\pi$
$758$	−26.8328	+	26.8328i	−0.974612	+	0.974612i
$759$		0			0
$760$		0			0
$761$	10.0000			0.362500			0.181250	−	0.983437i	$-0.441986\pi$
$761$	10.0000			0.362500			0.181250	+	0.983437i	$0.441986\pi$
$762$		0			0
$763$	−22.3607	+	22.3607i	−0.809511	+	0.809511i
$764$	18.0000	+	18.0000i	0.651217	+	0.651217i
$765$		0			0
$766$	−25.0000	+	25.0000i	−0.903287	+	0.903287i
$767$		0			0
$768$		0			0
$769$	−27.0000	−	27.0000i	−0.973645	−	0.973645i	0.0260166	−	0.999662i	$-0.491718\pi$
$769$	−27.0000	−	27.0000i	−0.973645	−	0.973645i	−0.999662	+	0.0260166i	$0.991718\pi$
$770$		0			0
$771$		0			0
$772$			13.4164i			0.482867i
$773$		−	13.4164i		−	0.482555i	−0.970456	−	0.241277i	$-0.922434\pi$
$773$		−	13.4164i		−	0.482555i	0.970456	−	0.241277i	$-0.0775663\pi$
$774$		−	30.0000i		−	1.07833i
$775$		0			0
$776$			10.0000i			0.358979i
$777$		0			0
$778$	−15.6525	−	15.6525i	−0.561168	−	0.561168i
$779$		−	4.00000i		−	0.143315i
$780$		0			0
$781$	−48.0000	+	48.0000i	−1.71758	+	1.71758i
$782$	−22.3607	−	22.3607i	−0.799616	−	0.799616i
$783$		0			0
$784$			3.00000i			0.107143i
$785$		0			0
$786$		0			0
$787$	−33.5410	−	33.5410i	−1.19561	−	1.19561i	−0.975468	−	0.220140i	$-0.929349\pi$
$787$	−33.5410	−	33.5410i	−1.19561	−	1.19561i	−0.220140	−	0.975468i	$-0.570651\pi$
$788$	−40.2492	+	40.2492i	−1.43382	+	1.43382i
$789$		0			0
$790$		0			0
$791$	10.0000	−	10.0000i	0.355559	−	0.355559i
$792$	26.8328	+	26.8328i	0.953463	+	0.953463i
$793$	−80.4984			−2.85858
$794$	−30.0000	+	30.0000i	−1.06466	+	1.06466i
$795$		0			0
$796$			60.0000i			2.12664i
$797$	4.47214			0.158411			0.0792056	−	0.996858i	$-0.474762\pi$
$797$	4.47214			0.158411			0.0792056	+	0.996858i	$0.474762\pi$
$798$		0			0
$799$		−	20.0000i		−	0.707549i
$800$		0			0
$801$	21.0000	−	21.0000i	0.741999	−	0.741999i
$802$	−44.7214			−1.57917
$803$	−17.8885	−	17.8885i	−0.631273	−	0.631273i
$804$		0			0
$805$		0			0
$806$	−80.0000			−2.81788
$807$		0			0
$808$	−2.23607	−	2.23607i	−0.0786646	−	0.0786646i
$809$	7.00000	+	7.00000i	0.246107	+	0.246107i	0.819371	−	0.573264i	$-0.194323\pi$
$809$	7.00000	+	7.00000i	0.246107	+	0.246107i	−0.573264	+	0.819371i	$0.694323\pi$
$810$		0			0
$811$			20.0000i			0.702295i	0.936320	+	0.351147i	$0.114208\pi$
$811$			20.0000i			0.702295i	−0.936320	+	0.351147i	$0.885792\pi$
$812$	−20.1246	−	46.9574i	−0.706235	−	1.64788i
$813$		0			0
$814$	40.0000	−	40.0000i	1.40200	−	1.40200i
$815$		0			0
$816$		0			0
$817$	−8.94427	−	8.94427i	−0.312920	−	0.312920i
$818$	−6.70820	+	6.70820i	−0.234547	+	0.234547i
$819$			60.0000i			2.09657i
$820$		0			0
$821$		−	20.0000i		−	0.698005i	−0.937122	−	0.349002i	$-0.886521\pi$
$821$		−	20.0000i		−	0.698005i	0.937122	−	0.349002i	$-0.113479\pi$
$822$		0			0
$823$		−	44.7214i		−	1.55889i	−0.626472	−	0.779444i	$-0.715502\pi$
$823$		−	44.7214i		−	1.55889i	0.626472	−	0.779444i	$-0.284498\pi$
$824$	15.0000	+	15.0000i	0.522550	+	0.522550i
$825$		0			0
$826$		0			0
$827$			22.3607i			0.777557i	0.921331	+	0.388779i	$0.127103\pi$
$827$			22.3607i			0.777557i	−0.921331	+	0.388779i	$0.872897\pi$
$828$	20.1246	+	20.1246i	0.699379	+	0.699379i
$829$	27.0000	−	27.0000i	0.937749	−	0.937749i	−0.0604240	−	0.998173i	$-0.519245\pi$
$829$	27.0000	−	27.0000i	0.937749	−	0.937749i	0.998173	+	0.0604240i	$0.0192453\pi$
$830$		0			0
$831$		0			0
$832$	−58.1378	+	58.1378i	−2.01556	+	2.01556i
$833$			13.4164i			0.464851i
$834$		0			0
$835$		0			0
$836$	48.0000			1.66011
$837$		0			0
$838$	53.6656			1.85385
$839$	−2.00000	−	2.00000i	−0.0690477	−	0.0690477i	0.671740	−	0.740787i	$-0.265547\pi$
$839$	−2.00000	−	2.00000i	−0.0690477	−	0.0690477i	−0.740787	+	0.671740i	$0.765547\pi$
$840$		0			0
$841$	−21.0000	−	20.0000i	−0.724138	−	0.689655i
$842$	20.1246	−	20.1246i	0.693540	−	0.693540i
$843$		0			0
$844$	48.0000	−	48.0000i	1.65223	−	1.65223i
$845$		0			0
$846$			30.0000i			1.03142i
$847$	−46.9574	−	46.9574i	−1.61348	−	1.61348i
$848$	8.94427	+	8.94427i	0.307148	+	0.307148i
$849$		0			0
$850$		0			0
$851$	10.0000	−	10.0000i	0.342796	−	0.342796i
$852$		0			0
$853$	−22.3607			−0.765615			−0.382808	−	0.923828i	$-0.625043\pi$
$853$	−22.3607			−0.765615			−0.382808	+	0.923828i	$0.625043\pi$
$854$	90.0000			3.07974
$855$		0			0
$856$	−15.0000	+	15.0000i	−0.512689	+	0.512689i
$857$	13.4164	−	13.4164i	0.458296	−	0.458296i	−0.439800	−	0.898096i	$-0.644951\pi$
$857$	13.4164	−	13.4164i	0.458296	−	0.458296i	0.898096	+	0.439800i	$0.144951\pi$
$858$		0			0
$859$	−12.0000	−	12.0000i	−0.409435	−	0.409435i	0.472107	−	0.881541i	$-0.343494\pi$
$859$	−12.0000	−	12.0000i	−0.409435	−	0.409435i	−0.881541	+	0.472107i	$0.843494\pi$
$860$		0			0
$861$		0			0
$862$	26.8328			0.913929
$863$	33.5410	−	33.5410i	1.14175	−	1.14175i	0.153620	−	0.988130i	$-0.450907\pi$
$863$	33.5410	−	33.5410i	1.14175	−	1.14175i	0.988130	−	0.153620i	$-0.0490930\pi$
$864$		0			0
$865$		0			0
$866$	−50.0000			−1.69907
$867$		0			0
$868$	53.6656			1.82153
$869$	16.0000			0.542763
$870$		0			0
$871$	−20.0000			−0.677674
$872$	22.3607			0.757228
$873$			13.4164i			0.454077i
$874$	20.0000			0.676510
$875$		0			0
$876$		0			0
$877$	8.94427	−	8.94427i	0.302027	−	0.302027i	−0.539780	−	0.841806i	$-0.681492\pi$
$877$	8.94427	−	8.94427i	0.302027	−	0.302027i	0.841806	+	0.539780i	$0.181492\pi$
$878$	−35.7771			−1.20742
$879$		0			0
$880$		0			0
$881$	11.0000	+	11.0000i	0.370599	+	0.370599i	0.867696	−	0.497096i	$-0.165600\pi$
$881$	11.0000	+	11.0000i	0.370599	+	0.370599i	−0.497096	+	0.867696i	$0.665600\pi$
$882$		−	20.1246i		−	0.677631i
$883$	−20.1246	+	20.1246i	−0.677247	+	0.677247i	−0.959376	−	0.282129i	$-0.908959\pi$
$883$	−20.1246	+	20.1246i	−0.677247	+	0.677247i	0.282129	+	0.959376i	$0.408959\pi$
$884$	−60.0000	+	60.0000i	−2.01802	+	2.01802i
$885$		0			0
$886$	70.0000			2.35170
$887$	31.3050			1.05112			0.525559	−	0.850757i	$-0.323856\pi$
$887$	31.3050			1.05112			0.525559	+	0.850757i	$0.323856\pi$
$888$		0			0
$889$	10.0000	−	10.0000i	0.335389	−	0.335389i
$890$		0			0
$891$	36.0000	+	36.0000i	1.20605	+	1.20605i
$892$	−33.5410	−	33.5410i	−1.12304	−	1.12304i
$893$	8.94427	+	8.94427i	0.299309	+	0.299309i
$894$		0			0
$895$		0			0
$896$	35.0000	−	35.0000i	1.16927	−	1.16927i
$897$		0			0
$898$	−29.0689	+	29.0689i	−0.970041	+	0.970041i
$899$	28.0000	−	12.0000i	0.933852	−	0.400222i
$900$		0			0
$901$	40.0000	+	40.0000i	1.33259	+	1.33259i
$902$	17.8885			0.595623
$903$		0			0
$904$	−10.0000			−0.332595
$905$		0			0
$906$		0			0
$907$			40.2492i			1.33645i	0.743958	+	0.668227i	$0.232946\pi$
$907$			40.2492i			1.33645i	−0.743958	+	0.668227i	$0.767054\pi$
$908$	20.1246	−	20.1246i	0.667859	−	0.667859i
$909$	−3.00000	−	3.00000i	−0.0995037	−	0.0995037i
$910$		0			0
$911$	16.0000	−	16.0000i	0.530104	−	0.530104i	−0.390499	−	0.920603i	$-0.627698\pi$
$911$	16.0000	−	16.0000i	0.530104	−	0.530104i	0.920603	+	0.390499i	$0.127698\pi$
$912$		0			0
$913$		−	53.6656i		−	1.77607i
$914$	40.0000	+	40.0000i	1.32308	+	1.32308i
$915$		0			0
$916$	9.00000	+	9.00000i	0.297368	+	0.297368i
$917$			62.6099i			2.06756i
$918$		0			0
$919$			20.0000i			0.659739i	0.944027	+	0.329870i	$0.107005\pi$
$919$			20.0000i			0.659739i	−0.944027	+	0.329870i	$0.892995\pi$
$920$		0			0
$921$		0			0
$922$	−20.1246	+	20.1246i	−0.662769	+	0.662769i
$923$	53.6656	+	53.6656i	1.76643	+	1.76643i
$924$		0			0
$925$		0			0
$926$	−5.00000	+	5.00000i	−0.164310	+	0.164310i
$927$	20.1246	+	20.1246i	0.660979	+	0.660979i
$928$	13.4164	−	33.5410i	0.440415	−	1.10104i
$929$			14.0000i			0.459325i	0.973270	+	0.229663i	$0.0737623\pi$
$929$			14.0000i			0.459325i	−0.973270	+	0.229663i	$0.926238\pi$
$930$		0			0
$931$	−6.00000	−	6.00000i	−0.196642	−	0.196642i
$932$	26.8328	+	26.8328i	0.878938	+	0.878938i
$933$		0			0
$934$	−30.0000			−0.981630
$935$		0			0
$936$	30.0000	−	30.0000i	0.980581	−	0.980581i
$937$	−8.94427	−	8.94427i	−0.292197	−	0.292197i	0.545751	−	0.837947i	$-0.316245\pi$
$937$	−8.94427	−	8.94427i	−0.292197	−	0.292197i	−0.837947	+	0.545751i	$0.816245\pi$
$938$	22.3607			0.730102
$939$		0			0
$940$		0			0
$941$		−	40.0000i		−	1.30396i	−0.758235	−	0.651981i	$-0.773938\pi$
$941$		−	40.0000i		−	1.30396i	0.758235	−	0.651981i	$-0.226062\pi$
$942$		0			0
$943$	4.47214			0.145633
$944$		0			0
$945$		0			0
$946$	40.0000	−	40.0000i	1.30051	−	1.30051i
$947$	31.3050			1.01727			0.508637	−	0.860981i	$-0.330149\pi$
$947$	31.3050			1.01727			0.508637	+	0.860981i	$0.330149\pi$
$948$		0			0
$949$	−20.0000	+	20.0000i	−0.649227	+	0.649227i
$950$		0			0
$951$		0			0
$952$	22.3607	−	22.3607i	0.724714	−	0.724714i
$953$	8.94427	+	8.94427i	0.289733	+	0.289733i	0.836975	−	0.547241i	$-0.184322\pi$
$953$	8.94427	+	8.94427i	0.289733	+	0.289733i	−0.547241	+	0.836975i	$0.684322\pi$
$954$	−60.0000	−	60.0000i	−1.94257	−	1.94257i
$955$		0			0
$956$		0			0
$957$		0			0
$958$	40.2492	+	40.2492i	1.30039	+	1.30039i
$959$	−30.0000	+	30.0000i	−0.968751	+	0.968751i
$960$		0			0
$961$			1.00000i			0.0322581i
$962$	−44.7214	−	44.7214i	−1.44187	−	1.44187i
$963$	−20.1246	+	20.1246i	−0.648507	+	0.648507i
$964$			24.0000i			0.772988i
$965$		0			0
$966$		0			0
$967$			8.94427i			0.287628i	0.989605	+	0.143814i	$0.0459368\pi$
$967$			8.94427i			0.287628i	−0.989605	+	0.143814i	$0.954063\pi$
$968$			46.9574i			1.50927i
$969$		0			0
$970$		0			0
$971$	−14.0000	−	14.0000i	−0.449281	−	0.449281i	0.445834	−	0.895116i	$-0.352907\pi$
$971$	−14.0000	−	14.0000i	−0.449281	−	0.449281i	−0.895116	+	0.445834i	$0.852907\pi$
$972$		0			0
$973$	−8.94427	−	8.94427i	−0.286740	−	0.286740i
$974$	45.0000	−	45.0000i	1.44189	−	1.44189i
$975$		0			0
$976$	9.00000	+	9.00000i	0.288083	+	0.288083i
$977$	−4.47214	+	4.47214i	−0.143076	+	0.143076i	−0.775017	−	0.631941i	$-0.782259\pi$
$977$	−4.47214	+	4.47214i	−0.143076	+	0.143076i	0.631941	+	0.775017i	$0.282259\pi$
$978$		0			0
$979$	56.0000			1.78977
$980$		0			0
$981$	30.0000			0.957826
$982$	−13.4164	+	13.4164i	−0.428135	+	0.428135i
$983$	−13.4164			−0.427917			−0.213958	−	0.976843i	$-0.568636\pi$
$983$	−13.4164			−0.427917			−0.213958	+	0.976843i	$0.568636\pi$
$984$		0			0
$985$		0			0
$986$	20.0000	−	50.0000i	0.636930	−	1.59232i
$987$		0			0
$988$		−	53.6656i		−	1.70733i
$989$	10.0000	−	10.0000i	0.317982	−	0.317982i
$990$		0			0
$991$		−	32.0000i		−	1.01651i	−0.861206	−	0.508257i	$-0.830290\pi$
$991$		−	32.0000i		−	1.01651i	0.861206	−	0.508257i	$-0.169710\pi$
$992$	26.8328	+	26.8328i	0.851943	+	0.851943i
$993$		0			0
$994$	−60.0000	−	60.0000i	−1.90308	−	1.90308i
$995$		0			0
$996$		0			0
$997$	−13.4164			−0.424902			−0.212451	−	0.977172i	$-0.568145\pi$
$997$	−13.4164			−0.424902			−0.212451	+	0.977172i	$0.568145\pi$
$998$	−44.7214			−1.41563
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.j.a.418.2	yes	4
5.2	odd	4		725.2.e.a.157.2	yes	4
5.3	odd	4		725.2.e.a.157.1	✓	4
5.4	even	2	inner	725.2.j.a.418.1	yes	4
29.17	odd	4		725.2.e.a.568.1	yes	4
145.17	even	4	inner	725.2.j.a.307.2	yes	4
145.104	odd	4		725.2.e.a.568.2	yes	4
145.133	even	4	inner	725.2.j.a.307.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.e.a.157.1	✓	4	5.3	odd	4
725.2.e.a.157.2	yes	4	5.2	odd	4
725.2.e.a.568.1	yes	4	29.17	odd	4
725.2.e.a.568.2	yes	4	145.104	odd	4
725.2.j.a.307.1	yes	4	145.133	even	4	inner
725.2.j.a.307.2	yes	4	145.17	even	4	inner
725.2.j.a.418.1	yes	4	5.4	even	2	inner
725.2.j.a.418.2	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.23607 q^{2} +3.00000 q^{4} +(-2.23607 + 2.23607i) q^{7} +2.23607 q^{8} +3.00000 q^{9} +(4.00000 + 4.00000i) q^{11} +(4.47214 - 4.47214i) q^{13} +(-5.00000 + 5.00000i) q^{14} -1.00000 q^{16} -4.47214 q^{17} +6.70820 q^{18} +(2.00000 - 2.00000i) q^{19} +(8.94427 + 8.94427i) q^{22} +(2.23607 + 2.23607i) q^{23} +(10.0000 - 10.0000i) q^{26} +(-6.70820 + 6.70820i) q^{28} +(-2.00000 + 5.00000i) q^{29} +(-4.00000 - 4.00000i) q^{31} -6.70820 q^{32} -10.0000 q^{34} +9.00000 q^{36} -4.47214i q^{37} +(4.47214 - 4.47214i) q^{38} +(1.00000 - 1.00000i) q^{41} -4.47214i q^{43} +(12.0000 + 12.0000i) q^{44} +(5.00000 + 5.00000i) q^{46} +4.47214i q^{47} -3.00000i q^{49} +(13.4164 - 13.4164i) q^{52} +(-8.94427 - 8.94427i) q^{53} +(-5.00000 + 5.00000i) q^{56} +(-4.47214 + 11.1803i) q^{58} +(-9.00000 - 9.00000i) q^{61} +(-8.94427 - 8.94427i) q^{62} +(-6.70820 + 6.70820i) q^{63} -13.0000 q^{64} +(-2.23607 - 2.23607i) q^{67} -13.4164 q^{68} +12.0000i q^{71} +6.70820 q^{72} -4.47214 q^{73} -10.0000i q^{74} +(6.00000 - 6.00000i) q^{76} -17.8885 q^{77} +(2.00000 - 2.00000i) q^{79} +9.00000 q^{81} +(2.23607 - 2.23607i) q^{82} +(-6.70820 - 6.70820i) q^{83} -10.0000i q^{86} +(8.94427 + 8.94427i) q^{88} +(7.00000 - 7.00000i) q^{89} +20.0000i q^{91} +(6.70820 + 6.70820i) q^{92} +10.0000i q^{94} +4.47214i q^{97} -6.70820i q^{98} +(12.0000 + 12.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{4} + 12 q^{9} + 16 q^{11} - 20 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 8 q^{29} - 16 q^{31} - 40 q^{34} + 36 q^{36} + 4 q^{41} + 48 q^{44} + 20 q^{46} - 20 q^{56} - 36 q^{61} - 52 q^{64}+ \cdots + 48 q^{99}+O(q^{100}) \) 4 * q + 12 * q^4 + 12 * q^9 + 16 * q^11 - 20 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 8 * q^29 - 16 * q^31 - 40 * q^34 + 36 * q^36 + 4 * q^41 + 48 * q^44 + 20 * q^46 - 20 * q^56 - 36 * q^61 - 52 * q^64 + 24 * q^76 + 8 * q^79 + 36 * q^81 + 28 * q^89 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more