LMFDB - Embedded newform 725.2.e.b.157.3

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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 288x^{12} + 1372x^{10} + 3184x^{8} + 3696x^{6} + 2076x^{4} + 504x^{2} + 36 $ x^16 + 28x^14 + 288x^12 + 1372x^10 + 3184x^8 + 3696x^6 + 2076x^4 + 504*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			157.3
Root			$-2.34301i$ of defining polynomial
Character	$\chi$	$=$	725.157
Dual form			725.2.e.b.568.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.34301i q^{2} +0.842805 q^{3} +0.196335 q^{4} -1.13189i q^{6} +(-0.720606 - 0.720606i) q^{7} -2.94969i q^{8} -2.28968 q^{9} +(-3.92923 - 3.92923i) q^{11} +0.165472 q^{12} +(1.70489 + 1.70489i) q^{13} +(-0.967779 + 0.967779i) q^{14} -3.56878 q^{16} -5.73391i q^{17} +3.07505i q^{18} +(-2.92923 + 2.92923i) q^{19} +(-0.607331 - 0.607331i) q^{21} +(-5.27698 + 5.27698i) q^{22} +(4.87499 - 4.87499i) q^{23} -2.48601i q^{24} +(2.28968 - 2.28968i) q^{26} -4.45817 q^{27} +(-0.141480 - 0.141480i) q^{28} +(4.06112 + 3.53656i) q^{29} +(-1.73290 - 1.73290i) q^{31} -1.10648i q^{32} +(-3.31158 - 3.31158i) q^{33} -7.70068 q^{34} -0.449543 q^{36} +10.1921 q^{37} +(3.93398 + 3.93398i) q^{38} +(1.43689 + 1.43689i) q^{39} +(4.09335 - 4.09335i) q^{41} +(-0.815649 + 0.815649i) q^{42} -4.30057 q^{43} +(-0.771444 - 0.771444i) q^{44} +(-6.54714 - 6.54714i) q^{46} +9.82103 q^{47} -3.00779 q^{48} -5.96145i q^{49} -4.83257i q^{51} +(0.334729 + 0.334729i) q^{52} +(-3.18621 + 3.18621i) q^{53} +5.98735i q^{54} +(-2.12557 + 2.12557i) q^{56} +(-2.46877 + 2.46877i) q^{57} +(4.74962 - 5.45411i) q^{58} +13.0837i q^{59} +(2.32823 + 2.32823i) q^{61} +(-2.32729 + 2.32729i) q^{62} +(1.64996 + 1.64996i) q^{63} -8.62358 q^{64} +(-4.44747 + 4.44747i) q^{66} +(-0.260514 + 0.260514i) q^{67} -1.12577i q^{68} +(4.10866 - 4.10866i) q^{69} -3.55346i q^{71} +6.75385i q^{72} +3.04002i q^{73} -13.6880i q^{74} +(-0.575110 + 0.575110i) q^{76} +5.66286i q^{77} +(1.92975 - 1.92975i) q^{78} +(2.65013 - 2.65013i) q^{79} +3.11167 q^{81} +(-5.49739 - 5.49739i) q^{82} +(-8.47107 + 8.47107i) q^{83} +(-0.119240 - 0.119240i) q^{84} +5.77569i q^{86} +(3.42274 + 2.98063i) q^{87} +(-11.5900 + 11.5900i) q^{88} +(-7.42157 + 7.42157i) q^{89} -2.45711i q^{91} +(0.957129 - 0.957129i) q^{92} +(-1.46049 - 1.46049i) q^{93} -13.1897i q^{94} -0.932550i q^{96} +1.36383 q^{97} -8.00627 q^{98} +(8.99668 + 8.99668i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} + 40 q^{9} - 4 q^{11} - 20 q^{14} - 16 q^{16} + 12 q^{19} - 32 q^{21} - 40 q^{26} + 4 q^{29} + 20 q^{31} - 80 q^{34} - 104 q^{36} - 16 q^{39} - 28 q^{44} + 44 q^{46} + 36 q^{56} + 24 q^{61}+ \cdots + 92 q^{99}+O(q^{100}) $ 16 * q - 8 * q^4 + 40 * q^9 - 4 * q^11 - 20 * q^14 - 16 * q^16 + 12 * q^19 - 32 * q^21 - 40 * q^26 + 4 * q^29 + 20 * q^31 - 80 * q^34 - 104 * q^36 - 16 * q^39 - 28 * q^44 + 44 * q^46 + 36 * q^56 + 24 * q^61 + 32 * q^64 + 80 * q^66 + 40 * q^69 - 36 * q^76 - 52 * q^79 + 40 * q^81 + 136 * q^84 - 40 * q^89 + 92 * q^99

Character values

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

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

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 $

$2$		−	1.34301i		−	0.949649i	−0.880081	−	0.474824i	$-0.842512\pi$
$2$		−	1.34301i		−	0.949649i	0.880081	−	0.474824i	$-0.157488\pi$
$3$	0.842805			0.486594			0.243297	−	0.969952i	$-0.421771\pi$
$3$	0.842805			0.486594			0.243297	+	0.969952i	$0.421771\pi$
$4$	0.196335			0.0981673
$5$		0			0
$5$		0			0
$6$		−	1.13189i		−	0.462093i
$7$	−0.720606	−	0.720606i	−0.272364	−	0.272364i	0.557687	−	0.830051i	$-0.311689\pi$
$7$	−0.720606	−	0.720606i	−0.272364	−	0.272364i	−0.830051	+	0.557687i	$0.811689\pi$
$8$		−	2.94969i		−	1.04287i
$9$	−2.28968			−0.763227
$10$		0			0
$11$	−3.92923	−	3.92923i	−1.18471	−	1.18471i	−0.978510	−	0.206197i	$-0.933891\pi$
$11$	−3.92923	−	3.92923i	−1.18471	−	1.18471i	−0.206197	−	0.978510i	$-0.566109\pi$
$12$	0.165472			0.0477676
$13$	1.70489	+	1.70489i	0.472852	+	0.472852i	0.902836	−	0.429984i	$-0.141481\pi$
$13$	1.70489	+	1.70489i	0.472852	+	0.472852i	−0.429984	+	0.902836i	$0.641481\pi$
$14$	−0.967779	+	0.967779i	−0.258650	+	0.258650i
$15$		0			0
$16$	−3.56878			−0.892196
$17$		−	5.73391i		−	1.39068i	−0.718682	−	0.695339i	$-0.755254\pi$
$17$		−	5.73391i		−	1.39068i	0.718682	−	0.695339i	$-0.244746\pi$
$18$			3.07505i			0.724797i
$19$	−2.92923	+	2.92923i	−0.672012	+	0.672012i	−0.958180	−	0.286168i	$-0.907619\pi$
$19$	−2.92923	+	2.92923i	−0.672012	+	0.672012i	0.286168	+	0.958180i	$0.407619\pi$
$20$		0			0
$21$	−0.607331	−	0.607331i	−0.132530	−	0.132530i
$22$	−5.27698	+	5.27698i	−1.12506	+	1.12506i
$23$	4.87499	−	4.87499i	1.01651	−	1.01651i	0.0166437	−	0.999861i	$-0.494702\pi$
$23$	4.87499	−	4.87499i	1.01651	−	1.01651i	0.999861	−	0.0166437i	$-0.00529810\pi$
$24$		−	2.48601i		−	0.507456i
$25$		0			0
$26$	2.28968	−	2.28968i	0.449043	−	0.449043i
$27$	−4.45817			−0.857975
$28$	−0.141480	−	0.141480i	−0.0267372	−	0.0267372i
$29$	4.06112	+	3.53656i	0.754132	+	0.656723i
$29$	4.06112	+	3.53656i	0.754132	+	0.656723i
$30$		0			0
$31$	−1.73290	−	1.73290i	−0.311237	−	0.311237i	0.534151	−	0.845389i	$-0.320631\pi$
$31$	−1.73290	−	1.73290i	−0.311237	−	0.311237i	−0.845389	+	0.534151i	$0.820631\pi$
$32$		−	1.10648i		−	0.195601i
$33$	−3.31158	−	3.31158i	−0.576471	−	0.576471i
$34$	−7.70068			−1.32065
$35$		0			0
$36$	−0.449543			−0.0749239
$37$	10.1921			1.67557			0.837784	−	0.546002i	$-0.183851\pi$
$37$	10.1921			1.67557			0.837784	+	0.546002i	$0.183851\pi$
$38$	3.93398	+	3.93398i	0.638175	+	0.638175i
$39$	1.43689	+	1.43689i	0.230087	+	0.230087i
$40$		0			0
$41$	4.09335	−	4.09335i	0.639273	−	0.639273i	−0.311103	−	0.950376i	$-0.600698\pi$
$41$	4.09335	−	4.09335i	0.639273	−	0.639273i	0.950376	+	0.311103i	$0.100698\pi$
$42$	−0.815649	+	0.815649i	−0.125857	+	0.125857i
$43$	−4.30057			−0.655831			−0.327916	−	0.944707i	$-0.606346\pi$
$43$	−4.30057			−0.655831			−0.327916	+	0.944707i	$0.606346\pi$
$44$	−0.771444	−	0.771444i	−0.116300	−	0.116300i
$45$		0			0
$46$	−6.54714	−	6.54714i	−0.965323	−	0.965323i
$47$	9.82103			1.43254			0.716272	−	0.697821i	$-0.245847\pi$
$47$	9.82103			1.43254			0.716272	+	0.697821i	$0.245847\pi$
$48$	−3.00779			−0.434137
$49$		−	5.96145i		−	0.851636i
$50$		0			0
$51$		−	4.83257i		−	0.676695i
$52$	0.334729	+	0.334729i	0.0464186	+	0.0464186i
$53$	−3.18621	+	3.18621i	−0.437660	+	0.437660i	−0.891224	−	0.453564i	$-0.850152\pi$
$53$	−3.18621	+	3.18621i	−0.437660	+	0.437660i	0.453564	+	0.891224i	$0.350152\pi$
$54$			5.98735i			0.814775i
$55$		0			0
$56$	−2.12557	+	2.12557i	−0.284041	+	0.284041i
$57$	−2.46877	+	2.46877i	−0.326997	+	0.326997i
$58$	4.74962	−	5.45411i	0.623656	−	0.716160i
$59$			13.0837i			1.70335i	0.524068	+	0.851676i	$0.324414\pi$
$59$			13.0837i			1.70335i	−0.524068	+	0.851676i	$0.675586\pi$
$60$		0			0
$61$	2.32823	+	2.32823i	0.298099	+	0.298099i	0.840269	−	0.542170i	$-0.182397\pi$
$61$	2.32823	+	2.32823i	0.298099	+	0.298099i	−0.542170	+	0.840269i	$0.682397\pi$
$62$	−2.32729	+	2.32729i	−0.295566	+	0.295566i
$63$	1.64996	+	1.64996i	0.207875	+	0.207875i
$64$	−8.62358			−1.07795
$65$		0			0
$66$	−4.44747	+	4.44747i	−0.547445	+	0.547445i
$67$	−0.260514	+	0.260514i	−0.0318269	+	0.0318269i	−0.722841	−	0.691014i	$-0.757164\pi$
$67$	−0.260514	+	0.260514i	−0.0318269	+	0.0318269i	0.691014	+	0.722841i	$0.257164\pi$
$68$		−	1.12577i		−	0.136519i
$69$	4.10866	−	4.10866i	0.494625	−	0.494625i
$70$		0			0
$71$		−	3.55346i		−	0.421719i	−0.977516	−	0.210859i	$-0.932374\pi$
$71$		−	3.55346i		−	0.421719i	0.977516	−	0.210859i	$-0.0676262\pi$
$72$			6.75385i			0.795949i
$73$			3.04002i			0.355808i	0.984048	+	0.177904i	$0.0569316\pi$
$73$			3.04002i			0.355808i	−0.984048	+	0.177904i	$0.943068\pi$
$74$		−	13.6880i		−	1.59120i
$75$		0			0
$76$	−0.575110	+	0.575110i	−0.0659696	+	0.0659696i
$77$			5.66286i			0.645343i
$78$	1.92975	−	1.92975i	0.218502	−	0.218502i
$79$	2.65013	−	2.65013i	0.298163	−	0.298163i	−0.542131	−	0.840294i	$-0.682382\pi$
$79$	2.65013	−	2.65013i	0.298163	−	0.298163i	0.840294	+	0.542131i	$0.182382\pi$
$80$		0			0
$81$	3.11167			0.345741
$82$	−5.49739	−	5.49739i	−0.607085	−	0.607085i
$83$	−8.47107	+	8.47107i	−0.929821	+	0.929821i	−0.997694	−	0.0678732i	$-0.978379\pi$
$83$	−8.47107	+	8.47107i	−0.929821	+	0.929821i	0.0678732	+	0.997694i	$0.478379\pi$
$84$	−0.119240	−	0.119240i	−0.0130102	−	0.0130102i
$85$		0			0
$86$			5.77569i			0.622809i
$87$	3.42274	+	2.98063i	0.366956	+	0.319557i
$88$	−11.5900	+	11.5900i	−1.23550	+	1.23550i
$89$	−7.42157	+	7.42157i	−0.786685	+	0.786685i	−0.980949	−	0.194264i	$-0.937768\pi$
$89$	−7.42157	+	7.42157i	−0.786685	+	0.786685i	0.194264	+	0.980949i	$0.437768\pi$
$90$		0			0
$91$		−	2.45711i		−	0.257575i
$92$	0.957129	−	0.957129i	0.0997876	−	0.0997876i
$93$	−1.46049	−	1.46049i	−0.151446	−	0.151446i
$94$		−	13.1897i		−	1.36041i
$95$		0			0
$96$		−	0.932550i		−	0.0951780i
$97$	1.36383			0.138476			0.0692382	−	0.997600i	$-0.477943\pi$
$97$	1.36383			0.138476			0.0692382	+	0.997600i	$0.477943\pi$
$98$	−8.00627			−0.808755
$99$	8.99668	+	8.99668i	0.904201	+	0.904201i
$100$		0			0
$101$	6.31858	+	6.31858i	0.628722	+	0.628722i	0.947747	−	0.319024i	$-0.103355\pi$
$101$	6.31858	+	6.31858i	0.628722	+	0.628722i	−0.319024	+	0.947747i	$0.603355\pi$
$102$	−6.49017			−0.642622
$103$	−5.11151	+	5.11151i	−0.503652	+	0.503652i	−0.912571	−	0.408919i	$-0.865906\pi$
$103$	−5.11151	+	5.11151i	−0.503652	+	0.503652i	0.408919	+	0.912571i	$0.365906\pi$
$104$	5.02890	−	5.02890i	0.493124	−	0.493124i
$105$		0			0
$106$	4.27910	+	4.27910i	0.415623	+	0.415623i
$107$	4.65929	+	4.65929i	0.450431	+	0.450431i	0.895497	−	0.445067i	$-0.146820\pi$
$107$	4.65929	+	4.65929i	0.450431	+	0.450431i	−0.445067	+	0.895497i	$0.646820\pi$
$108$	−0.875293			−0.0842251
$109$	9.88169			0.946494			0.473247	−	0.880930i	$-0.343082\pi$
$109$	9.88169			0.946494			0.473247	+	0.880930i	$0.343082\pi$
$110$		0			0
$111$	8.58994			0.815321
$112$	2.57169	+	2.57169i	0.243002	+	0.243002i
$113$		−	15.8164i		−	1.48788i	−0.668247	−	0.743940i	$-0.732955\pi$
$113$		−	15.8164i		−	1.48788i	0.668247	−	0.743940i	$-0.267045\pi$
$114$	3.31557	+	3.31557i	0.310532	+	0.310532i
$115$		0			0
$116$	0.797339	+	0.694350i	0.0740311	+	0.0644687i
$117$	−3.90366	−	3.90366i	−0.360893	−	0.360893i
$118$	17.5715			1.61759
$119$	−4.13189	+	4.13189i	−0.378770	+	0.378770i
$120$		0			0
$121$			19.8777i			1.80707i
$122$	3.12682	−	3.12682i	0.283089	−	0.283089i
$123$	3.44989	−	3.44989i	0.311066	−	0.311066i
$124$	−0.340228	−	0.340228i	−0.0305533	−	0.0305533i
$125$		0			0
$126$	2.21590	−	2.21590i	0.197408	−	0.197408i
$127$		−	2.61496i		−	0.232040i	−0.993247	−	0.116020i	$-0.962986\pi$
$127$		−	2.61496i		−	0.232040i	0.993247	−	0.116020i	$-0.0370137\pi$
$128$			9.36855i			0.828071i
$129$	−3.62454			−0.319123
$130$		0			0
$131$	−3.31623	+	3.31623i	−0.289740	+	0.289740i	−0.836977	−	0.547237i	$-0.815679\pi$
$131$	−3.31623	+	3.31623i	−0.289740	+	0.289740i	0.547237	+	0.836977i	$0.315679\pi$
$132$	−0.650177	−	0.650177i	−0.0565907	−	0.0565907i
$133$	4.22165			0.366063
$134$	0.349872	+	0.349872i	0.0302244	+	0.0302244i
$135$		0			0
$136$	−16.9133			−1.45030
$137$		−	19.7299i		−	1.68564i	−0.538197	−	0.842819i	$-0.680894\pi$
$137$		−	19.7299i		−	1.68564i	0.538197	−	0.842819i	$-0.319106\pi$
$138$	−5.51796	−	5.51796i	−0.469720	−	0.469720i
$139$		−	5.21466i		−	0.442302i	−0.975240	−	0.221151i	$-0.929019\pi$
$139$		−	5.21466i		−	0.442302i	0.975240	−	0.221151i	$-0.0709813\pi$
$140$		0			0
$141$	8.27721			0.697067
$142$	−4.77232			−0.400485
$143$		−	13.3978i		−	1.12038i
$144$	8.17137			0.680948
$145$		0			0
$146$	4.08277			0.337892
$147$		−	5.02434i		−	0.414401i
$148$	2.00106			0.164486
$149$	10.9316			0.895551			0.447775	−	0.894146i	$-0.352216\pi$
$149$	10.9316			0.895551			0.447775	+	0.894146i	$0.352216\pi$
$150$		0			0
$151$			4.56878i			0.371802i	0.982568	+	0.185901i	$0.0595204\pi$
$151$			4.56878i			0.371802i	−0.982568	+	0.185901i	$0.940480\pi$
$152$	8.64033	+	8.64033i	0.700823	+	0.700823i
$153$			13.1288i			1.06140i
$154$	7.60525			0.612849
$155$		0			0
$156$	0.282111	+	0.282111i	0.0225870	+	0.0225870i
$157$	−11.3102			−0.902654			−0.451327	−	0.892359i	$-0.649049\pi$
$157$	−11.3102			−0.902654			−0.451327	+	0.892359i	$0.649049\pi$
$158$	−3.55914	−	3.55914i	−0.283150	−	0.283150i
$159$	−2.68536	+	2.68536i	−0.212963	+	0.212963i
$160$		0			0
$161$	−7.02590			−0.553718
$162$		−	4.17899i		−	0.328333i
$163$		−	8.22196i		−	0.643994i	−0.946741	−	0.321997i	$-0.895646\pi$
$163$		−	8.22196i		−	0.643994i	0.946741	−	0.321997i	$-0.104354\pi$
$164$	0.803665	−	0.803665i	0.0627557	−	0.0627557i
$165$		0			0
$166$	11.3767	+	11.3767i	0.883003	+	0.883003i
$167$	18.0764	−	18.0764i	1.39879	−	1.39879i	0.595263	−	0.803531i	$-0.297048\pi$
$167$	18.0764	−	18.0764i	1.39879	−	1.39879i	0.803531	−	0.595263i	$-0.202952\pi$
$168$	−1.79144	+	1.79144i	−0.138212	+	0.138212i
$169$		−	7.18669i		−	0.552822i
$170$		0			0
$171$	6.70700	−	6.70700i	0.512897	−	0.512897i
$172$	−0.844351			−0.0643812
$173$	3.03649	+	3.03649i	0.230860	+	0.230860i	0.813052	−	0.582192i	$-0.197805\pi$
$173$	3.03649	+	3.03649i	0.230860	+	0.230860i	−0.582192	+	0.813052i	$0.697805\pi$
$174$	4.00301	−	4.59675i	0.303467	−	0.348479i
$175$		0			0
$176$	14.0226	+	14.0226i	1.05699	+	1.05699i
$177$			11.0270i			0.828841i
$178$	9.96722	+	9.96722i	0.747074	+	0.747074i
$179$	−9.50623			−0.710529			−0.355265	−	0.934766i	$-0.615609\pi$
$179$	−9.50623			−0.710529			−0.355265	+	0.934766i	$0.615609\pi$
$180$		0			0
$181$	−2.41590			−0.179572			−0.0897861	−	0.995961i	$-0.528618\pi$
$181$	−2.41590			−0.179572			−0.0897861	+	0.995961i	$0.528618\pi$
$182$	−3.29992			−0.244606
$183$	1.96224	+	1.96224i	0.145053	+	0.145053i
$184$	−14.3797	−	14.3797i	−1.06009	−	1.06009i
$185$		0			0
$186$	−1.96145	+	1.96145i	−0.143821	+	0.143821i
$187$	−22.5299	+	22.5299i	−1.64755	+	1.64755i
$188$	1.92821			0.140629
$189$	3.21259	+	3.21259i	0.233681	+	0.233681i
$190$		0			0
$191$	6.82624	+	6.82624i	0.493930	+	0.493930i	0.909542	−	0.415612i	$-0.136433\pi$
$191$	6.82624	+	6.82624i	0.493930	+	0.493930i	−0.415612	+	0.909542i	$0.636433\pi$
$192$	−7.26800			−0.524523
$193$	26.4787			1.90598			0.952988	−	0.303009i	$-0.0979911\pi$
$193$	26.4787			1.90598			0.952988	+	0.303009i	$0.0979911\pi$
$194$		−	1.83164i		−	0.131504i
$195$		0			0
$196$		−	1.17044i		−	0.0836028i
$197$	−11.7523	−	11.7523i	−0.837319	−	0.837319i	0.151187	−	0.988505i	$-0.451691\pi$
$197$	−11.7523	−	11.7523i	−0.837319	−	0.837319i	−0.988505	+	0.151187i	$0.951691\pi$
$198$	12.0826	−	12.0826i	0.858673	−	0.858673i
$199$		−	4.23392i		−	0.300135i	−0.988676	−	0.150067i	$-0.952051\pi$
$199$		−	4.23392i		−	0.300135i	0.988676	−	0.150067i	$-0.0479490\pi$
$200$		0			0
$201$	−0.219563	+	0.219563i	−0.0154868	+	0.0154868i
$202$	8.48589	−	8.48589i	0.597065	−	0.597065i
$203$	−0.378002	−	5.47494i	−0.0265306	−	0.384266i
$204$		−	0.948800i		−	0.0664293i
$205$		0			0
$206$	6.86479	+	6.86479i	0.478293	+	0.478293i
$207$	−11.1622	+	11.1622i	−0.775824	+	0.775824i
$208$	−6.08439	−	6.08439i	−0.421876	−	0.421876i
$209$	23.0193			1.59228
$210$		0			0
$211$	13.8521	−	13.8521i	0.953620	−	0.953620i	−0.0453507	−	0.998971i	$-0.514441\pi$
$211$	13.8521	−	13.8521i	0.953620	−	0.953620i	0.998971	+	0.0453507i	$0.0144405\pi$
$212$	−0.625564	+	0.625564i	−0.0429639	+	0.0429639i
$213$		−	2.99488i		−	0.205206i
$214$	6.25746	−	6.25746i	0.427751	−	0.427751i
$215$		0			0
$216$			13.1502i			0.894759i
$217$			2.49747i			0.169540i
$218$		−	13.2712i		−	0.898837i
$219$			2.56215i			0.173134i
$220$		0			0
$221$	9.77569	−	9.77569i	0.657584	−	0.657584i
$222$		−	11.5363i		−	0.774268i
$223$	2.57522	−	2.57522i	0.172450	−	0.172450i	−0.615605	−	0.788055i	$-0.711088\pi$
$223$	2.57522	−	2.57522i	0.172450	−	0.172450i	0.788055	+	0.615605i	$0.211088\pi$
$224$	−0.797339	+	0.797339i	−0.0532745	+	0.0532745i
$225$		0			0
$226$	−21.2415			−1.41296
$227$	17.9881	+	17.9881i	1.19391	+	1.19391i	0.975960	+	0.217949i	$0.0699366\pi$
$227$	17.9881	+	17.9881i	1.19391	+	1.19391i	0.217949	+	0.975960i	$0.430063\pi$
$228$	−0.484705	+	0.484705i	−0.0321004	+	0.0321004i
$229$	10.9172	+	10.9172i	0.721431	+	0.721431i	0.968897	−	0.247466i	$-0.0795978\pi$
$229$	10.9172	+	10.9172i	0.721431	+	0.721431i	−0.247466	+	0.968897i	$0.579598\pi$
$230$		0			0
$231$			4.77269i			0.314020i
$232$	10.4318	−	11.9791i	0.684879	−	0.786464i
$233$	−5.78977	+	5.78977i	−0.379300	+	0.379300i	−0.870850	−	0.491549i	$-0.836431\pi$
$233$	−5.78977	+	5.78977i	−0.379300	+	0.379300i	0.491549	+	0.870850i	$0.336431\pi$
$234$	−5.24263	+	5.24263i	−0.342722	+	0.342722i
$235$		0			0
$236$			2.56878i			0.167214i
$237$	2.23354	−	2.23354i	0.145084	−	0.145084i
$238$	5.54916	+	5.54916i	0.359698	+	0.359698i
$239$		−	1.59391i		−	0.103101i	−0.998670	−	0.0515506i	$-0.983584\pi$
$239$		−	1.59391i		−	0.103101i	0.998670	−	0.0515506i	$-0.0164163\pi$
$240$		0			0
$241$			11.5109i			0.741485i	0.928736	+	0.370743i	$0.120897\pi$
$241$			11.5109i			0.741485i	−0.928736	+	0.370743i	$0.879103\pi$
$242$	26.6959			1.71608
$243$	15.9970			1.02621
$244$	0.457112	+	0.457112i	0.0292636	+	0.0292636i
$245$		0			0
$246$	−4.63323	−	4.63323i	−0.295404	−	0.295404i
$247$	−9.98804			−0.635524
$248$	−5.11151	+	5.11151i	−0.324581	+	0.324581i
$249$	−7.13946	+	7.13946i	−0.452445	+	0.452445i
$250$		0			0
$251$	−16.0466	−	16.0466i	−1.01285	−	1.01285i	−0.999916	−	0.0129347i	$-0.995883\pi$
$251$	−16.0466	−	16.0466i	−1.01285	−	1.01285i	−0.0129347	−	0.999916i	$-0.504117\pi$
$252$	0.323944	+	0.323944i	0.0204065	+	0.0204065i
$253$	−38.3099			−2.40852
$254$	−3.51191			−0.220357
$255$		0			0
$256$	−4.66514			−0.291571
$257$	−3.22503	−	3.22503i	−0.201172	−	0.201172i	0.599330	−	0.800502i	$-0.295434\pi$
$257$	−3.22503	−	3.22503i	−0.201172	−	0.201172i	−0.800502	+	0.599330i	$0.795434\pi$
$258$			4.86778i			0.303055i
$259$	−7.34448	−	7.34448i	−0.456364	−	0.456364i
$260$		0			0
$261$	−9.29867	−	8.09759i	−0.575573	−	0.501229i
$262$	4.45371	+	4.45371i	0.275151	+	0.275151i
$263$	−1.63737			−0.100965			−0.0504824	−	0.998725i	$-0.516076\pi$
$263$	−1.63737			−0.100965			−0.0504824	+	0.998725i	$0.516076\pi$
$264$	−9.76813	+	9.76813i	−0.601187	+	0.601187i
$265$		0			0
$266$		−	5.66970i		−	0.347631i
$267$	−6.25494	+	6.25494i	−0.382796	+	0.382796i
$268$	−0.0511480	+	0.0511480i	−0.00312436	+	0.00312436i
$269$	19.4764	+	19.4764i	1.18750	+	1.18750i	0.977758	+	0.209737i	$0.0672609\pi$
$269$	19.4764	+	19.4764i	1.18750	+	1.18750i	0.209737	+	0.977758i	$0.432739\pi$
$270$		0			0
$271$	−10.5808	+	10.5808i	−0.642737	+	0.642737i	−0.951227	−	0.308491i	$-0.900176\pi$
$271$	−10.5808	+	10.5808i	−0.642737	+	0.642737i	0.308491	+	0.951227i	$0.400176\pi$
$272$			20.4631i			1.24076i
$273$		−	2.07087i		−	0.125335i
$274$	−26.4974			−1.60076
$275$		0			0
$276$	0.806673	−	0.806673i	0.0485560	−	0.0485560i
$277$	−8.84907	−	8.84907i	−0.531689	−	0.531689i	0.389386	−	0.921075i	$-0.372687\pi$
$277$	−8.84907	−	8.84907i	−0.531689	−	0.531689i	−0.921075	+	0.389386i	$0.872687\pi$
$278$	−7.00332			−0.420031
$279$	3.96778	+	3.96778i	0.237545	+	0.237545i
$280$		0			0
$281$	13.6293			0.813053			0.406527	−	0.913639i	$-0.366740\pi$
$281$	13.6293			0.813053			0.406527	+	0.913639i	$0.366740\pi$
$282$		−	11.1163i		−	0.661969i
$283$	−0.976410	−	0.976410i	−0.0580416	−	0.0580416i	0.677490	−	0.735532i	$-0.263068\pi$
$283$	−0.976410	−	0.976410i	−0.0580416	−	0.0580416i	−0.735532	+	0.677490i	$0.763068\pi$
$284$		−	0.697668i		−	0.0413990i
$285$		0			0
$286$	−17.9934			−1.06397
$287$	−5.89938			−0.348229
$288$			2.53349i			0.149288i
$289$	−15.8777			−0.933984
$290$		0			0
$291$	1.14945			0.0673817
$292$			0.596862i			0.0349287i
$293$	16.5338			0.965916			0.482958	−	0.875644i	$-0.339562\pi$
$293$	16.5338			0.965916			0.482958	+	0.875644i	$0.339562\pi$
$294$	−6.74772			−0.393535
$295$		0			0
$296$		−	30.0635i		−	1.74740i
$297$	17.5172	+	17.5172i	1.01645	+	1.01645i
$298$		−	14.6812i		−	0.850458i
$299$	16.6226			0.961313
$300$		0			0
$301$	3.09902	+	3.09902i	0.178625	+	0.178625i
$302$	6.13590			0.353082
$303$	5.32533	+	5.32533i	0.305932	+	0.305932i
$304$	10.4538	−	10.4538i	0.599566	−	0.599566i
$305$		0			0
$306$	17.6321			1.00796
$307$		−	20.7862i		−	1.18633i	−0.805082	−	0.593164i	$-0.797879\pi$
$307$		−	20.7862i		−	1.18633i	0.805082	−	0.593164i	$-0.202121\pi$
$308$			1.11182i			0.0633516i
$309$	−4.30801	+	4.30801i	−0.245074	+	0.245074i
$310$		0			0
$311$	−16.5356	−	16.5356i	−0.937648	−	0.937648i	0.0605192	−	0.998167i	$-0.480724\pi$
$311$	−16.5356	−	16.5356i	−0.937648	−	0.937648i	−0.998167	+	0.0605192i	$0.980724\pi$
$312$	4.23838	−	4.23838i	0.239951	−	0.239951i
$313$	−15.3699	+	15.3699i	−0.868760	+	0.868760i	−0.992335	−	0.123575i	$-0.960564\pi$
$313$	−15.3699	+	15.3699i	−0.868760	+	0.868760i	0.123575	+	0.992335i	$0.460564\pi$
$314$			15.1897i			0.857204i
$315$		0			0
$316$	0.520312	−	0.520312i	0.0292698	−	0.0292698i
$317$	−23.7769			−1.33544			−0.667722	−	0.744411i	$-0.732730\pi$
$317$	−23.7769			−1.33544			−0.667722	+	0.744411i	$0.732730\pi$
$318$	3.60645	+	3.60645i	0.202240	+	0.202240i
$319$	−2.06112	−	29.8531i	−0.115401	−	1.67145i
$320$		0			0
$321$	3.92688	+	3.92688i	0.219177	+	0.219177i
$322$			9.43582i			0.525838i
$323$	16.7959	+	16.7959i	0.934552	+	0.934552i
$324$	0.610929			0.0339405
$325$		0			0
$326$	−11.0421			−0.611568
$327$	8.32834			0.460558
$328$	−12.0741	−	12.0741i	−0.666681	−	0.666681i
$329$	−7.07709	−	7.07709i	−0.390173	−	0.390173i
$330$		0			0
$331$	6.36045	−	6.36045i	0.349602	−	0.349602i	−0.510359	−	0.859961i	$-0.670488\pi$
$331$	6.36045	−	6.36045i	0.349602	−	0.349602i	0.859961	+	0.510359i	$0.170488\pi$
$332$	−1.66316	+	1.66316i	−0.0912780	+	0.0912780i
$333$	−23.3366			−1.27884
$334$	−24.2767	−	24.2767i	−1.32836	−	1.32836i
$335$		0			0
$336$	2.16743	+	2.16743i	0.118243	+	0.118243i
$337$	7.39775			0.402981			0.201490	−	0.979490i	$-0.435422\pi$
$337$	7.39775			0.402981			0.201490	+	0.979490i	$0.435422\pi$
$338$	−9.65177			−0.524987
$339$		−	13.3301i		−	0.723993i
$340$		0			0
$341$			13.6179i			0.737451i
$342$	−9.00754	−	9.00754i	−0.487072	−	0.487072i
$343$	−9.34011	+	9.34011i	−0.504318	+	0.504318i
$344$			12.6854i			0.683949i
$345$		0			0
$346$	4.07803	−	4.07803i	0.219236	−	0.219236i
$347$	6.06956	−	6.06956i	0.325831	−	0.325831i	−0.525168	−	0.850999i	$-0.675997\pi$
$347$	6.06956	−	6.06956i	0.325831	−	0.325831i	0.850999	+	0.525168i	$0.175997\pi$
$348$	0.672002	+	0.585201i	0.0360231	+	0.0313701i
$349$		−	10.7383i		−	0.574806i	−0.957810	−	0.287403i	$-0.907208\pi$
$349$		−	10.7383i		−	0.574806i	0.957810	−	0.287403i	$-0.0927919\pi$
$350$		0			0
$351$	−7.60069	−	7.60069i	−0.405695	−	0.405695i
$352$	−4.34763	+	4.34763i	−0.231729	+	0.231729i
$353$	−12.5913	−	12.5913i	−0.670170	−	0.670170i	0.287585	−	0.957755i	$-0.407148\pi$
$353$	−12.5913	−	12.5913i	−0.670170	−	0.670170i	−0.957755	+	0.287585i	$0.907148\pi$
$354$	14.8093			0.787108
$355$		0			0
$356$	−1.45711	+	1.45711i	−0.0772268	+	0.0772268i
$357$	−3.48238	+	3.48238i	−0.184307	+	0.184307i
$358$			12.7669i			0.674753i
$359$	−17.2438	+	17.2438i	−0.910095	+	0.910095i	−0.996279	−	0.0861840i	$-0.972533\pi$
$359$	−17.2438	+	17.2438i	−0.910095	+	0.910095i	0.0861840	+	0.996279i	$0.472533\pi$
$360$		0			0
$361$			1.83920i			0.0968003i
$362$			3.24456i			0.170531i
$363$			16.7530i			0.879307i
$364$		−	0.482416i		−	0.0252855i
$365$		0			0
$366$	2.63530	−	2.63530i	0.137749	−	0.137749i
$367$			31.1348i			1.62522i	0.582806	+	0.812611i	$0.301955\pi$
$367$			31.1348i			1.62522i	−0.582806	+	0.812611i	$0.698045\pi$
$368$	−17.3978	+	17.3978i	−0.906922	+	0.906922i
$369$	−9.37245	+	9.37245i	−0.487910	+	0.487910i
$370$		0			0
$371$	4.59201			0.238405
$372$	−0.286746	−	0.286746i	−0.0148671	−	0.0148671i
$373$	4.56778	−	4.56778i	0.236511	−	0.236511i	−0.578893	−	0.815404i	$-0.696515\pi$
$373$	4.56778	−	4.56778i	0.236511	−	0.236511i	0.815404	+	0.578893i	$0.196515\pi$
$374$	30.2577	+	30.2577i	1.56459	+	1.56459i
$375$		0			0
$376$		−	28.9690i		−	1.49396i
$377$	0.894321	+	12.9532i	0.0460599	+	0.667125i
$378$	4.31452	−	4.31452i	0.221915	−	0.221915i
$379$	−26.9196	+	26.9196i	−1.38277	+	1.38277i	−0.543095	+	0.839671i	$0.682748\pi$
$379$	−26.9196	+	26.9196i	−1.38277	+	1.38277i	−0.839671	+	0.543095i	$0.817252\pi$
$380$		0			0
$381$		−	2.20390i		−	0.112909i
$382$	9.16768	−	9.16768i	0.469060	−	0.469060i
$383$	12.2427	+	12.2427i	0.625575	+	0.625575i	0.946951	−	0.321377i	$-0.104146\pi$
$383$	12.2427	+	12.2427i	0.625575	+	0.625575i	−0.321377	+	0.946951i	$0.604146\pi$
$384$			7.89587i			0.402934i
$385$		0			0
$386$		−	35.5610i		−	1.81001i
$387$	9.84693			0.500548
$388$	0.267768			0.0135938
$389$	−10.8199	−	10.8199i	−0.548592	−	0.548592i	0.377442	−	0.926033i	$-0.376804\pi$
$389$	−10.8199	−	10.8199i	−0.548592	−	0.548592i	−0.926033	+	0.377442i	$0.876804\pi$
$390$		0			0
$391$	−27.9527	−	27.9527i	−1.41363	−	1.41363i
$392$	−17.5844			−0.888148
$393$	−2.79493	+	2.79493i	−0.140986	+	0.140986i
$394$	−15.7834	+	15.7834i	−0.795158	+	0.795158i
$395$		0			0
$396$	1.76636	+	1.76636i	0.0887629	+	0.0887629i
$397$	25.3529	+	25.3529i	1.27243	+	1.27243i	0.944812	+	0.327613i	$0.106244\pi$
$397$	25.3529	+	25.3529i	1.27243	+	1.27243i	0.327613	+	0.944812i	$0.393756\pi$
$398$	−5.68618			−0.285022
$399$	3.55802			0.178124
$400$		0			0
$401$	−5.08370			−0.253868			−0.126934	−	0.991911i	$-0.540514\pi$
$401$	−5.08370			−0.253868			−0.126934	+	0.991911i	$0.540514\pi$
$402$	0.294874	+	0.294874i	0.0147070	+	0.0147070i
$403$		−	5.90880i		−	0.294338i
$404$	1.24056	+	1.24056i	0.0617200	+	0.0617200i
$405$		0			0
$406$	−7.35288	+	0.507660i	−0.364917	+	0.0251947i
$407$	−40.0470	−	40.0470i	−1.98506	−	1.98506i
$408$	−14.2546			−0.705707
$409$	2.60826	−	2.60826i	0.128970	−	0.128970i	−0.639675	−	0.768645i	$-0.720931\pi$
$409$	2.60826	−	2.60826i	0.128970	−	0.128970i	0.768645	+	0.639675i	$0.220931\pi$
$410$		0			0
$411$		−	16.6285i		−	0.820221i
$412$	−1.00357	+	1.00357i	−0.0494422	+	0.0494422i
$413$	9.42820	−	9.42820i	0.463931	−	0.463931i
$414$	14.9908	+	14.9908i	0.736760	+	0.736760i
$415$		0			0
$416$	1.88643	−	1.88643i	0.0924901	−	0.0924901i
$417$		−	4.39494i		−	0.215221i
$418$		−	30.9150i		−	1.51210i
$419$	−23.6950			−1.15758			−0.578788	−	0.815478i	$-0.696474\pi$
$419$	−23.6950			−1.15758			−0.578788	+	0.815478i	$0.696474\pi$
$420$		0			0
$421$	−24.2906	+	24.2906i	−1.18385	+	1.18385i	−0.205114	+	0.978738i	$0.565756\pi$
$421$	−24.2906	+	24.2906i	−1.18385	+	1.18385i	−0.978738	+	0.205114i	$0.934244\pi$
$422$	−18.6035	−	18.6035i	−0.905604	−	0.905604i
$423$	−22.4870			−1.09336
$424$	9.39834	+	9.39834i	0.456424	+	0.456424i
$425$		0			0
$426$	−4.02214			−0.194873
$427$		−	3.35547i		−	0.162383i
$428$	0.914780	+	0.914780i	0.0442176	+	0.0442176i
$429$		−	11.2918i		−	0.545171i
$430$		0			0
$431$	9.77002			0.470605			0.235303	−	0.971922i	$-0.424392\pi$
$431$	9.77002			0.470605			0.235303	+	0.971922i	$0.424392\pi$
$432$	15.9102			0.765482
$433$			25.1499i			1.20863i	0.796747	+	0.604314i	$0.206553\pi$
$433$			25.1499i			1.20863i	−0.796747	+	0.604314i	$0.793447\pi$
$434$	3.35412			0.161003
$435$		0			0
$436$	1.94012			0.0929148
$437$			28.5599i			1.36621i
$438$	3.44098			0.164416
$439$	−24.6379			−1.17590			−0.587952	−	0.808896i	$-0.700066\pi$
$439$	−24.6379			−1.17590			−0.587952	+	0.808896i	$0.700066\pi$
$440$		0			0
$441$			13.6498i			0.649991i
$442$	−13.1288	−	13.1288i	−0.624474	−	0.624474i
$443$		−	36.1431i		−	1.71721i	−0.512636	−	0.858606i	$-0.671331\pi$
$443$		−	36.1431i		−	1.71721i	0.512636	−	0.858606i	$-0.328669\pi$
$444$	1.68650			0.0800378
$445$		0			0
$446$	−3.45854	−	3.45854i	−0.163766	−	0.163766i
$447$	9.21320			0.435769
$448$	6.21421	+	6.21421i	0.293594	+	0.293594i
$449$	15.3830	−	15.3830i	0.725970	−	0.725970i	−0.243845	−	0.969814i	$-0.578409\pi$
$449$	15.3830	−	15.3830i	0.725970	−	0.725970i	0.969814	+	0.243845i	$0.0784087\pi$
$450$		0			0
$451$	−32.1674			−1.51470
$452$		−	3.10530i		−	0.146061i
$453$			3.85059i			0.180917i
$454$	24.1581	−	24.1581i	1.13379	−	1.13379i
$455$		0			0
$456$	7.28211	+	7.28211i	0.341016	+	0.341016i
$457$	8.52755	−	8.52755i	0.398902	−	0.398902i	−0.478944	−	0.877846i	$-0.658980\pi$
$457$	8.52755	−	8.52755i	0.398902	−	0.398902i	0.877846	+	0.478944i	$0.158980\pi$
$458$	14.6619	−	14.6619i	0.685106	−	0.685106i
$459$			25.5627i			1.19317i
$460$		0			0
$461$	17.1578	−	17.1578i	0.799118	−	0.799118i	−0.183839	−	0.982956i	$-0.558852\pi$
$461$	17.1578	−	17.1578i	0.799118	−	0.799118i	0.982956	+	0.183839i	$0.0588524\pi$
$462$	6.40975			0.298208
$463$	15.1460	+	15.1460i	0.703894	+	0.703894i	0.965244	−	0.261350i	$-0.0841677\pi$
$463$	15.1460	+	15.1460i	0.703894	+	0.703894i	−0.261350	+	0.965244i	$0.584168\pi$
$464$	−14.4933	−	12.6212i	−0.672833	−	0.585926i
$465$		0			0
$466$	7.77569	+	7.77569i	0.360202	+	0.360202i
$467$		−	17.6567i		−	0.817057i	−0.912746	−	0.408528i	$-0.866042\pi$
$467$		−	17.6567i		−	0.817057i	0.912746	−	0.408528i	$-0.133958\pi$
$468$	−0.766423	−	0.766423i	−0.0354279	−	0.0354279i
$469$	0.375457			0.0173370
$470$		0			0
$471$	−9.53231			−0.439226
$472$	38.5929			1.77638
$473$	16.8979	+	16.8979i	0.776968	+	0.776968i
$474$	−2.99966	−	2.99966i	−0.137779	−	0.137779i
$475$		0			0
$476$	−0.811234	+	0.811234i	−0.0371828	+	0.0371828i
$477$	7.29541	−	7.29541i	0.334034	−	0.334034i
$478$	−2.14062			−0.0979099
$479$	−19.8578	−	19.8578i	−0.907327	−	0.907327i	0.0887292	−	0.996056i	$-0.471719\pi$
$479$	−19.8578	−	19.8578i	−0.907327	−	0.907327i	−0.996056	+	0.0887292i	$0.971719\pi$
$480$		0			0
$481$	17.3764	+	17.3764i	0.792295	+	0.792295i
$482$	15.4593			0.704151
$483$	−5.92146			−0.269436
$484$			3.90269i			0.177395i
$485$		0			0
$486$		−	21.4841i		−	0.974540i
$487$	13.4023	+	13.4023i	0.607315	+	0.607315i	0.942244	−	0.334928i	$-0.108712\pi$
$487$	13.4023	+	13.4023i	0.607315	+	0.607315i	−0.334928	+	0.942244i	$0.608712\pi$
$488$	6.86755	−	6.86755i	0.310879	−	0.310879i
$489$		−	6.92951i		−	0.313363i
$490$		0			0
$491$	−3.08910	+	3.08910i	−0.139409	+	0.139409i	−0.773367	−	0.633958i	$-0.781429\pi$
$491$	−3.08910	+	3.08910i	−0.139409	+	0.139409i	0.633958	+	0.773367i	$0.281429\pi$
$492$	0.677333	−	0.677333i	0.0305365	−	0.0305365i
$493$	20.2783	−	23.2861i	0.913290	−	1.04875i
$494$			13.4140i			0.603525i
$495$		0			0
$496$	6.18433	+	6.18433i	0.277685	+	0.277685i
$497$	−2.56065	+	2.56065i	−0.114861	+	0.114861i
$498$	9.58834	+	9.58834i	0.429664	+	0.429664i
$499$	29.9441			1.34048			0.670240	−	0.742144i	$-0.266191\pi$
$499$	29.9441			1.34048			0.670240	+	0.742144i	$0.266191\pi$
$500$		0			0
$501$	15.2349	−	15.2349i	0.680644	−	0.680644i
$502$	−21.5507	+	21.5507i	−0.961853	+	0.961853i
$503$		−	34.4190i		−	1.53467i	−0.641249	−	0.767333i	$-0.721584\pi$
$503$		−	34.4190i		−	1.53467i	0.641249	−	0.767333i	$-0.278416\pi$
$504$	4.86687	−	4.86687i	0.216787	−	0.216787i
$505$		0			0
$506$			51.4504i			2.28725i
$507$		−	6.05698i		−	0.269000i
$508$		−	0.513408i		−	0.0227788i
$509$		−	17.7806i		−	0.788111i	−0.919087	−	0.394056i	$-0.871072\pi$
$509$		−	17.7806i		−	0.788111i	0.919087	−	0.394056i	$-0.128928\pi$
$510$		0			0
$511$	2.19066	−	2.19066i	0.0969091	−	0.0969091i
$512$			25.0024i			1.10496i
$513$	13.0590	−	13.0590i	0.576569	−	0.576569i
$514$	−4.33123	+	4.33123i	−0.191043	+	0.191043i
$515$		0			0
$516$	−0.711623			−0.0313275
$517$	−38.5891	−	38.5891i	−1.69715	−	1.69715i
$518$	−9.86368	+	9.86368i	−0.433385	+	0.433385i
$519$	2.55917	+	2.55917i	0.112335	+	0.112335i
$520$		0			0
$521$		−	4.99526i		−	0.218846i	−0.993995	−	0.109423i	$-0.965100\pi$
$521$		−	4.99526i		−	0.218846i	0.993995	−	0.109423i	$-0.0349003\pi$
$522$	−10.8751	+	12.4882i	−0.475991	+	0.546593i
$523$	−12.7767	+	12.7767i	−0.558687	+	0.558687i	−0.928934	−	0.370247i	$-0.879273\pi$
$523$	−12.7767	+	12.7767i	−0.558687	+	0.558687i	0.370247	+	0.928934i	$0.379273\pi$
$524$	−0.651090	+	0.651090i	−0.0284430	+	0.0284430i
$525$		0			0
$526$			2.19900i			0.0958810i
$527$	−9.93627	+	9.93627i	−0.432831	+	0.432831i
$528$	11.8183	+	11.8183i	0.514325	+	0.514325i
$529$		−	24.5310i		−	1.06657i
$530$		0			0
$531$		−	29.9575i		−	1.30004i
$532$	0.828855			0.0359354
$533$	13.9574			0.604563
$534$	8.40042	+	8.40042i	0.363522	+	0.363522i
$535$		0			0
$536$	0.768437	+	0.768437i	0.0331914	+	0.0331914i
$537$	−8.01190			−0.345739
$538$	26.1569	−	26.1569i	1.12770	−	1.12770i
$539$	−23.4239	+	23.4239i	−1.00894	+	1.00894i
$540$		0			0
$541$	23.9250	+	23.9250i	1.02861	+	1.02861i	0.999578	+	0.0290356i	$0.00924362\pi$
$541$	23.9250	+	23.9250i	1.02861	+	1.02861i	0.0290356	+	0.999578i	$0.490756\pi$
$542$	14.2101	+	14.2101i	0.610374	+	0.610374i
$543$	−2.03613			−0.0873787
$544$	−6.34448			−0.272017
$545$		0			0
$546$	−2.78119			−0.119024
$547$	−12.8364	−	12.8364i	−0.548843	−	0.548843i	0.377263	−	0.926106i	$-0.376865\pi$
$547$	−12.8364	−	12.8364i	−0.548843	−	0.548843i	−0.926106	+	0.377263i	$0.876865\pi$
$548$		−	3.87366i		−	0.165475i
$549$	−5.33089	−	5.33089i	−0.227517	−	0.227517i
$550$		0			0
$551$	−22.2554	+	1.53656i	−0.948111	+	0.0654598i
$552$	−12.1193	−	12.1193i	−0.515831	−	0.515831i
$553$	−3.81940			−0.162417
$554$	−11.8844	+	11.8844i	−0.504918	+	0.504918i
$555$		0			0
$556$		−	1.02382i		−	0.0434196i
$557$	−8.49859	+	8.49859i	−0.360097	+	0.360097i	−0.863849	−	0.503752i	$-0.831953\pi$
$557$	−8.49859	+	8.49859i	−0.360097	+	0.360097i	0.503752	+	0.863849i	$0.331953\pi$
$558$	5.32875	−	5.32875i	0.225584	−	0.225584i
$559$	−7.33201	−	7.33201i	−0.310111	−	0.310111i
$560$		0			0
$561$	−18.9883	+	18.9883i	−0.801686	+	0.801686i
$562$		−	18.3042i		−	0.772115i
$563$			12.1685i			0.512842i	0.966565	+	0.256421i	$0.0825434\pi$
$563$			12.1685i			0.512842i	−0.966565	+	0.256421i	$0.917457\pi$
$564$	1.62510			0.0684292
$565$		0			0
$566$	−1.31132	+	1.31132i	−0.0551191	+	0.0551191i
$567$	−2.24229	−	2.24229i	−0.0941674	−	0.0941674i
$568$	−10.4816			−0.439799
$569$	24.9932	+	24.9932i	1.04777	+	1.04777i	0.998800	+	0.0489683i	$0.0155933\pi$
$569$	24.9932	+	24.9932i	1.04777	+	1.04777i	0.0489683	+	0.998800i	$0.484407\pi$
$570$		0			0
$571$	−21.0943			−0.882768			−0.441384	−	0.897318i	$-0.645512\pi$
$571$	−21.0943			−0.882768			−0.441384	+	0.897318i	$0.645512\pi$
$572$		−	2.63046i		−	0.109985i
$573$	5.75319	+	5.75319i	0.240343	+	0.240343i
$574$			7.92291i			0.330696i
$575$		0			0
$576$	19.7452			0.822718
$577$	40.5782			1.68929			0.844646	−	0.535325i	$-0.179811\pi$
$577$	40.5782			1.68929			0.844646	+	0.535325i	$0.179811\pi$
$578$			21.3239i			0.886956i
$579$	22.3163			0.927436
$580$		0			0
$581$	12.2086			0.506499
$582$		−	1.54371i		−	0.0639890i
$583$	25.0387			1.03700
$584$	8.96713			0.371062
$585$		0			0
$586$		−	22.2050i		−	0.917281i
$587$	−3.81873	−	3.81873i	−0.157616	−	0.157616i	0.623894	−	0.781509i	$-0.285550\pi$
$587$	−3.81873	−	3.81873i	−0.157616	−	0.157616i	−0.781509	+	0.623894i	$0.785550\pi$
$588$		−	0.986452i		−	0.0406806i
$589$	10.1521			0.418311
$590$		0			0
$591$	−9.90492	−	9.90492i	−0.407434	−	0.407434i
$592$	−36.3733			−1.49493
$593$	24.9702	+	24.9702i	1.02540	+	1.02540i	0.999669	+	0.0257336i	$0.00819217\pi$
$593$	24.9702	+	24.9702i	1.02540	+	1.02540i	0.0257336	+	0.999669i	$0.491808\pi$
$594$	23.5257	−	23.5257i	0.965270	−	0.965270i
$595$		0			0
$596$	2.14625			0.0879138
$597$		−	3.56837i		−	0.146044i
$598$		−	22.3243i		−	0.912909i
$599$	−3.13220	+	3.13220i	−0.127978	+	0.127978i	−0.768195	−	0.640216i	$-0.778845\pi$
$599$	−3.13220	+	3.13220i	−0.127978	+	0.127978i	0.640216	+	0.768195i	$0.278845\pi$
$600$		0			0
$601$	12.8277	+	12.8277i	0.523251	+	0.523251i	0.918552	−	0.395300i	$-0.129360\pi$
$601$	12.8277	+	12.8277i	0.523251	+	0.523251i	−0.395300	+	0.918552i	$0.629360\pi$
$602$	4.16200	−	4.16200i	0.169631	−	0.169631i
$603$	0.596494	−	0.596494i	0.0242911	−	0.0242911i
$604$			0.897010i			0.0364988i
$605$		0			0
$606$	7.15195	−	7.15195i	0.290528	−	0.290528i
$607$	10.6408			0.431895			0.215948	−	0.976405i	$-0.430716\pi$
$607$	10.6408			0.431895			0.215948	+	0.976405i	$0.430716\pi$
$608$	3.24115	+	3.24115i	0.131446	+	0.131446i
$609$	−0.318582	−	4.61431i	−0.0129096	−	0.186981i
$610$		0			0
$611$	16.7438	+	16.7438i	0.677381	+	0.677381i
$612$			2.57764i			0.104195i
$613$	−19.6421	−	19.6421i	−0.793335	−	0.793335i	0.188700	−	0.982035i	$-0.439573\pi$
$613$	−19.6421	−	19.6421i	−0.793335	−	0.793335i	−0.982035	+	0.188700i	$0.939573\pi$
$614$	−27.9159			−1.12660
$615$		0			0
$616$	16.7037			0.673011
$617$	5.28522			0.212775			0.106388	−	0.994325i	$-0.466072\pi$
$617$	5.28522			0.212775			0.106388	+	0.994325i	$0.466072\pi$
$618$	5.78568	+	5.78568i	0.232734	+	0.232734i
$619$	12.2093	+	12.2093i	0.490732	+	0.490732i	0.908537	−	0.417805i	$-0.137200\pi$
$619$	12.2093	+	12.2093i	0.490732	+	0.490732i	−0.417805	+	0.908537i	$0.637200\pi$
$620$		0			0
$621$	−21.7335	+	21.7335i	−0.872136	+	0.872136i
$622$	−22.2074	+	22.2074i	−0.890436	+	0.890436i
$623$	10.6961			0.428529
$624$	−5.12795	−	5.12795i	−0.205282	−	0.205282i
$625$		0			0
$626$	20.6419	+	20.6419i	0.825017	+	0.825017i
$627$	19.4007			0.774791
$628$	−2.22059			−0.0886111
$629$		−	58.4405i		−	2.33017i
$630$		0			0
$631$			25.5814i			1.01838i	0.860654	+	0.509190i	$0.170055\pi$
$631$			25.5814i			1.01838i	−0.860654	+	0.509190i	$0.829945\pi$
$632$	−7.81706	−	7.81706i	−0.310946	−	0.310946i
$633$	11.6747	−	11.6747i	0.464026	−	0.464026i
$634$			31.9325i			1.26820i
$635$		0			0
$636$	−0.527228	+	0.527228i	−0.0209060	+	0.0209060i
$637$	10.1636	−	10.1636i	0.402698	−	0.402698i
$638$	−40.0929	+	2.76810i	−1.58729	+	0.109590i
$639$			8.13629i			0.321867i
$640$		0			0
$641$	9.93460	+	9.93460i	0.392393	+	0.392393i	0.875539	−	0.483147i	$-0.160506\pi$
$641$	9.93460	+	9.93460i	0.392393	+	0.392393i	−0.483147	+	0.875539i	$0.660506\pi$
$642$	5.27382	−	5.27382i	0.208141	−	0.208141i
$643$	−24.2029	−	24.2029i	−0.954469	−	0.954469i	0.0445391	−	0.999008i	$-0.485818\pi$
$643$	−24.2029	−	24.2029i	−0.954469	−	0.954469i	−0.999008	+	0.0445391i	$0.985818\pi$
$644$	−1.37943			−0.0543570
$645$		0			0
$646$	22.5571	−	22.5571i	0.887496	−	0.887496i
$647$	−22.8586	+	22.8586i	−0.898664	+	0.898664i	−0.995318	−	0.0966543i	$-0.969186\pi$
$647$	−22.8586	+	22.8586i	−0.898664	+	0.898664i	0.0966543	+	0.995318i	$0.469186\pi$
$648$		−	9.17847i		−	0.360564i
$649$	51.4089	−	51.4089i	2.01798	−	2.01798i
$650$		0			0
$651$			2.10488i			0.0824969i
$652$		−	1.61426i		−	0.0632191i
$653$		−	3.15622i		−	0.123512i	−0.998091	−	0.0617562i	$-0.980330\pi$
$653$		−	3.15622i		−	0.123512i	0.998091	−	0.0617562i	$-0.0196701\pi$
$654$		−	11.1850i		−	0.437369i
$655$		0			0
$656$	−14.6083	+	14.6083i	−0.570357	+	0.570357i
$657$		−	6.96068i		−	0.271562i
$658$	−9.50458	+	9.50458i	−0.370527	+	0.370527i
$659$	−2.95246	+	2.95246i	−0.115011	+	0.115011i	−0.762270	−	0.647259i	$-0.775915\pi$
$659$	−2.95246	+	2.95246i	−0.115011	+	0.115011i	0.647259	+	0.762270i	$0.275915\pi$
$660$		0			0
$661$	17.3475			0.674739			0.337369	−	0.941372i	$-0.390463\pi$
$661$	17.3475			0.674739			0.337369	+	0.941372i	$0.390463\pi$
$662$	−8.54212	−	8.54212i	−0.331999	−	0.331999i
$663$	8.23900	−	8.23900i	0.319976	−	0.319976i
$664$	24.9870	+	24.9870i	0.969685	+	0.969685i
$665$		0			0
$666$			31.3412i			1.21445i
$667$	37.0386	−	2.55723i	1.43414	−	0.0990164i
$668$	3.54902	−	3.54902i	0.137316	−	0.137316i
$669$	2.17041	−	2.17041i	0.0839128	−	0.0839128i
$670$		0			0
$671$		−	18.2963i		−	0.706320i
$672$	−0.672002	+	0.672002i	−0.0259230	+	0.0259230i
$673$	−12.3340	−	12.3340i	−0.475441	−	0.475441i	0.428229	−	0.903670i	$-0.359138\pi$
$673$	−12.3340	−	12.3340i	−0.475441	−	0.475441i	−0.903670	+	0.428229i	$0.859138\pi$
$674$		−	9.93522i		−	0.382690i
$675$		0			0
$676$		−	1.41100i		−	0.0542691i
$677$	20.9567			0.805430			0.402715	−	0.915325i	$-0.368067\pi$
$677$	20.9567			0.805430			0.402715	+	0.915325i	$0.368067\pi$
$678$	−17.9024			−0.687539
$679$	−0.982787	−	0.982787i	−0.0377159	−	0.0377159i
$680$		0			0
$681$	15.1604	+	15.1604i	0.580949	+	0.580949i
$682$	18.2889			0.700319
$683$	−22.5870	+	22.5870i	−0.864269	+	0.864269i	−0.991831	−	0.127562i	$-0.959285\pi$
$683$	−22.5870	+	22.5870i	−0.864269	+	0.864269i	0.127562	+	0.991831i	$0.459285\pi$
$684$	1.31682	−	1.31682i	0.0503497	−	0.0503497i
$685$		0			0
$686$	12.5438	+	12.5438i	0.478925	+	0.478925i
$687$	9.20110	+	9.20110i	0.351044	+	0.351044i
$688$	15.3478			0.585130
$689$	−10.8643			−0.413897
$690$		0			0
$691$	18.3742			0.698986			0.349493	−	0.936939i	$-0.386354\pi$
$691$	18.3742			0.698986			0.349493	+	0.936939i	$0.386354\pi$
$692$	0.596168	+	0.596168i	0.0226629	+	0.0226629i
$693$		−	12.9661i		−	0.492543i
$694$	−8.15146	−	8.15146i	−0.309425	−	0.309425i
$695$		0			0
$696$	8.79194	−	10.0960i	0.333258	−	0.382688i
$697$	−23.4709	−	23.4709i	−0.889023	−	0.889023i
$698$	−14.4215			−0.545864
$699$	−4.87965	+	4.87965i	−0.184565	+	0.184565i
$700$		0			0
$701$			22.9182i			0.865607i	0.901488	+	0.432804i	$0.142476\pi$
$701$			22.9182i			0.865607i	−0.901488	+	0.432804i	$0.857524\pi$
$702$	−10.2078	+	10.2078i	−0.385268	+	0.385268i
$703$	−29.8550	+	29.8550i	−1.12600	+	1.12600i
$704$	33.8840	+	33.8840i	1.27705	+	1.27705i
$705$		0			0
$706$	−16.9103	+	16.9103i	−0.636426	+	0.636426i
$707$		−	9.10642i		−	0.342482i
$708$			2.16498i			0.0813651i
$709$	−53.2031			−1.99808			−0.999042	−	0.0437582i	$-0.986067\pi$
$709$	−53.2031			−1.99808			−0.999042	+	0.0437582i	$0.986067\pi$
$710$		0			0
$711$	−6.06794	+	6.06794i	−0.227566	+	0.227566i
$712$	21.8913	+	21.8913i	0.820413	+	0.820413i
$713$	−16.8957			−0.632749
$714$	4.67686	+	4.67686i	0.175027	+	0.175027i
$715$		0			0
$716$	−1.86640			−0.0697508
$717$		−	1.34335i		−	0.0501684i
$718$	23.1586	+	23.1586i	0.864271	+	0.864271i
$719$		−	46.4822i		−	1.73349i	−0.498748	−	0.866747i	$-0.666207\pi$
$719$		−	46.4822i		−	1.73349i	0.498748	−	0.866747i	$-0.333793\pi$
$720$		0			0
$721$	7.36677			0.274353
$722$	2.47006			0.0919262
$723$			9.70148i			0.360802i
$724$	−0.474324			−0.0176281
$725$		0			0
$726$	22.4994			0.835033
$727$		−	27.5262i		−	1.02089i	−0.859910	−	0.510446i	$-0.829480\pi$
$727$		−	27.5262i		−	1.02089i	0.859910	−	0.510446i	$-0.170520\pi$
$728$	−7.24772			−0.268618
$729$	4.14737			0.153606
$730$		0			0
$731$			24.6591i			0.912049i
$732$	0.385256	+	0.385256i	0.0142395	+	0.0142395i
$733$		−	15.6923i		−	0.579608i	−0.957086	−	0.289804i	$-0.906410\pi$
$733$		−	15.6923i		−	0.579608i	0.957086	−	0.289804i	$-0.0935902\pi$
$734$	41.8142			1.54339
$735$		0			0
$736$	−5.39409	−	5.39409i	−0.198829	−	0.198829i
$737$	2.04724			0.0754111
$738$	12.5873	+	12.5873i	0.463343	+	0.463343i
$739$	3.42222	−	3.42222i	0.125889	−	0.125889i	−0.641355	−	0.767244i	$-0.721628\pi$
$739$	3.42222	−	3.42222i	0.125889	−	0.125889i	0.767244	+	0.641355i	$0.221628\pi$
$740$		0			0
$741$	−8.41797			−0.309242
$742$		−	6.16710i		−	0.226401i
$743$			34.1903i			1.25432i	0.778890	+	0.627160i	$0.215783\pi$
$743$			34.1903i			1.25432i	−0.778890	+	0.627160i	$0.784217\pi$
$744$	−4.30801	+	4.30801i	−0.157939	+	0.157939i
$745$		0			0
$746$	−6.13456	−	6.13456i	−0.224602	−	0.224602i
$747$	19.3960	−	19.3960i	0.709664	−	0.709664i
$748$	−4.42339	+	4.42339i	−0.161735	+	0.161735i
$749$		−	6.71503i		−	0.245362i
$750$		0			0
$751$	−8.84550	+	8.84550i	−0.322777	+	0.322777i	−0.849831	−	0.527055i	$-0.823296\pi$
$751$	−8.84550	+	8.84550i	−0.322777	+	0.322777i	0.527055	+	0.849831i	$0.323296\pi$
$752$	−35.0491			−1.27811
$753$	−13.5241	−	13.5241i	−0.492847	−	0.492847i
$754$	17.3963	−	1.20108i	0.633535	−	0.0437407i
$755$		0			0
$756$	0.630742	+	0.630742i	0.0229399	+	0.0229399i
$757$			23.6888i			0.860984i	0.902594	+	0.430492i	$0.141660\pi$
$757$			23.6888i			0.860984i	−0.902594	+	0.430492i	$0.858340\pi$
$758$	36.1532	+	36.1532i	1.31314	+	1.31314i
$759$	−32.2878			−1.17197
$760$		0			0
$761$	−40.1181			−1.45428			−0.727140	−	0.686489i	$-0.759151\pi$
$761$	−40.1181			−1.45428			−0.727140	+	0.686489i	$0.759151\pi$
$762$	−2.95985			−0.107224
$763$	−7.12081	−	7.12081i	−0.257791	−	0.257791i
$764$	1.34023	+	1.34023i	0.0484877	+	0.0484877i
$765$		0			0
$766$	16.4421	−	16.4421i	0.594076	−	0.594076i
$767$	−22.3063	+	22.3063i	−0.805433	+	0.805433i
$768$	−3.93180			−0.141877
$769$	13.2917	+	13.2917i	0.479312	+	0.479312i	0.904912	−	0.425600i	$-0.139937\pi$
$769$	13.2917	+	13.2917i	0.479312	+	0.479312i	−0.425600	+	0.904912i	$0.639937\pi$
$770$		0			0
$771$	−2.71807	−	2.71807i	−0.0978889	−	0.0978889i
$772$	5.19868			0.187105
$773$	8.06617			0.290120			0.145060	−	0.989423i	$-0.453663\pi$
$773$	8.06617			0.290120			0.145060	+	0.989423i	$0.453663\pi$
$774$		−	13.2245i		−	0.475344i
$775$		0			0
$776$		−	4.02289i		−	0.144413i
$777$	−6.18996	−	6.18996i	−0.222064	−	0.222064i
$778$	−14.5312	+	14.5312i	−0.520969	+	0.520969i
$779$			23.9807i			0.859198i
$780$		0			0
$781$	−13.9624	+	13.9624i	−0.499613	+	0.499613i
$782$	−37.5407	+	37.5407i	−1.34245	+	1.34245i
$783$	−18.1052	−	15.7666i	−0.647026	−	0.563452i
$784$			21.2751i			0.759826i
$785$		0			0
$786$	3.75361	+	3.75361i	0.133887	+	0.133887i
$787$	−19.5691	+	19.5691i	−0.697564	+	0.697564i	−0.963885	−	0.266320i	$-0.914192\pi$
$787$	−19.5691	+	19.5691i	−0.697564	+	0.697564i	0.266320	+	0.963885i	$0.414192\pi$
$788$	−2.30739	−	2.30739i	−0.0821973	−	0.0821973i
$789$	−1.37999			−0.0491288
$790$		0			0
$791$	−11.3974	+	11.3974i	−0.405244	+	0.405244i
$792$	26.5374	−	26.5374i	0.942966	−	0.942966i
$793$			7.93875i			0.281913i
$794$	34.0491	−	34.0491i	1.20836	−	1.20836i
$795$		0			0
$796$		−	0.831265i		−	0.0294634i
$797$			4.45791i			0.157907i	0.996878	+	0.0789537i	$0.0251579\pi$
$797$			4.45791i			0.157907i	−0.996878	+	0.0789537i	$0.974842\pi$
$798$		−	4.77845i		−	0.169155i
$799$		−	56.3129i		−	1.99221i
$800$		0			0
$801$	16.9930	−	16.9930i	0.600419	−	0.600419i
$802$			6.82744i			0.241085i
$803$	11.9450	−	11.9450i	0.421528	−	0.421528i
$804$	−0.0431078	+	0.0431078i	−0.00152029	+	0.00152029i
$805$		0			0
$806$	−7.93556			−0.279518
$807$	16.4148	+	16.4148i	0.577828	+	0.577828i
$808$	18.6379	−	18.6379i	0.655678	−	0.655678i
$809$	17.7438	+	17.7438i	0.623838	+	0.623838i	0.946511	−	0.322672i	$-0.104581\pi$
$809$	17.7438	+	17.7438i	0.623838	+	0.623838i	−0.322672	+	0.946511i	$0.604581\pi$
$810$		0			0
$811$		−	12.4871i		−	0.438482i	−0.975671	−	0.219241i	$-0.929642\pi$
$811$		−	12.4871i		−	0.438482i	0.975671	−	0.219241i	$-0.0703582\pi$
$812$	−0.0742150	−	1.07492i	−0.00260443	−	0.0377223i
$813$	−8.91754	+	8.91754i	−0.312752	+	0.312752i
$814$	−53.7834	+	53.7834i	−1.88511	+	1.88511i
$815$		0			0
$816$			17.2464i			0.603744i
$817$	12.5974	−	12.5974i	0.440726	−	0.440726i
$818$	−3.50291	−	3.50291i	−0.122476	−	0.122476i
$819$			5.62600i			0.196588i
$820$		0			0
$821$			25.9150i			0.904439i	0.891907	+	0.452219i	$0.149368\pi$
$821$			25.9150i			0.904439i	−0.891907	+	0.452219i	$0.850632\pi$
$822$	−22.3321			−0.778922
$823$	−22.1888			−0.773453			−0.386726	−	0.922194i	$-0.626394\pi$
$823$	−22.1888			−0.773453			−0.386726	+	0.922194i	$0.626394\pi$
$824$	15.0774	+	15.0774i	0.525245	+	0.525245i
$825$		0			0
$826$	−12.6621	−	12.6621i	−0.440572	−	0.440572i
$827$	−10.6389			−0.369951			−0.184976	−	0.982743i	$-0.559221\pi$
$827$	−10.6389			−0.369951			−0.184976	+	0.982743i	$0.559221\pi$
$828$	−2.19152	+	2.19152i	−0.0761605	+	0.0761605i
$829$	−2.76134	+	2.76134i	−0.0959052	+	0.0959052i	−0.753432	−	0.657526i	$-0.771603\pi$
$829$	−2.76134	+	2.76134i	−0.0959052	+	0.0959052i	0.657526	+	0.753432i	$0.271603\pi$
$830$		0			0
$831$	−7.45804	−	7.45804i	−0.258717	−	0.258717i
$832$	−14.7023	−	14.7023i	−0.509710	−	0.509710i
$833$	−34.1824			−1.18435
$834$	−5.90244			−0.204385
$835$		0			0
$836$	4.51948			0.156309
$837$	7.72555	+	7.72555i	0.267034	+	0.267034i
$838$			31.8225i			1.09929i
$839$	11.8281	+	11.8281i	0.408353	+	0.408353i	0.881164	−	0.472811i	$-0.156761\pi$
$839$	11.8281	+	11.8281i	0.408353	+	0.408353i	−0.472811	+	0.881164i	$0.656761\pi$
$840$		0			0
$841$	3.98545	+	28.7248i	0.137429	+	0.990512i
$842$	32.6224	+	32.6224i	1.12424	+	1.12424i
$843$	11.4868			0.395627
$844$	2.71965	−	2.71965i	0.0936144	−	0.0936144i
$845$		0			0
$846$			30.2002i			1.03830i
$847$	14.3240	−	14.3240i	0.492179	−	0.492179i
$848$	11.3709	−	11.3709i	0.390478	−	0.390478i
$849$	−0.822924	−	0.822924i	−0.0282427	−	0.0282427i
$850$		0			0
$851$	49.6863	−	49.6863i	1.70322	−	1.70322i
$852$		−	0.587998i		−	0.0201445i
$853$			23.4895i			0.804264i	0.915582	+	0.402132i	$0.131731\pi$
$853$			23.4895i			0.804264i	−0.915582	+	0.402132i	$0.868269\pi$
$854$	−4.50642			−0.154206
$855$		0			0
$856$	13.7435	−	13.7435i	0.469742	−	0.469742i
$857$	14.0556	+	14.0556i	0.480131	+	0.480131i	0.905173	−	0.425042i	$-0.139741\pi$
$857$	14.0556	+	14.0556i	0.480131	+	0.480131i	−0.425042	+	0.905173i	$0.639741\pi$
$858$	−15.1649			−0.517721
$859$	−4.09759	−	4.09759i	−0.139808	−	0.139808i	0.633739	−	0.773547i	$-0.281519\pi$
$859$	−4.09759	−	4.09759i	−0.139808	−	0.139808i	−0.773547	+	0.633739i	$0.781519\pi$
$860$		0			0
$861$	−4.97203			−0.169446
$862$		−	13.1212i		−	0.446910i
$863$	−11.6689	−	11.6689i	−0.397215	−	0.397215i	0.480034	−	0.877250i	$-0.340624\pi$
$863$	−11.6689	−	11.6689i	−0.397215	−	0.397215i	−0.877250	+	0.480034i	$0.840624\pi$
$864$			4.93289i			0.167820i
$865$		0			0
$866$	33.7765			1.14777
$867$	−13.3818			−0.454471
$868$			0.490341i			0.0166432i
$869$	−20.8259			−0.706471
$870$		0			0
$871$	−0.888297			−0.0300988
$872$		−	29.1479i		−	0.987074i
$873$	−3.12274			−0.105689
$874$	38.3562			1.29742
$875$		0			0
$876$			0.503038i			0.0169961i
$877$	31.1074	+	31.1074i	1.05042	+	1.05042i	0.998659	+	0.0517621i	$0.0164837\pi$
$877$	31.1074	+	31.1074i	1.05042	+	1.05042i	0.0517621	+	0.998659i	$0.483516\pi$
$878$			33.0889i			1.11670i
$879$	13.9348			0.470009
$880$		0			0
$881$	−34.2685	−	34.2685i	−1.15453	−	1.15453i	−0.985633	−	0.168902i	$-0.945978\pi$
$881$	−34.2685	−	34.2685i	−1.15453	−	1.15453i	−0.168902	−	0.985633i	$-0.554022\pi$
$882$	18.3318			0.617263
$883$	−16.7707	−	16.7707i	−0.564378	−	0.564378i	0.366170	−	0.930548i	$-0.380669\pi$
$883$	−16.7707	−	16.7707i	−0.564378	−	0.564378i	−0.930548	+	0.366170i	$0.880669\pi$
$884$	1.91931	−	1.91931i	0.0645533	−	0.0645533i
$885$		0			0
$886$	−48.5404			−1.63075
$887$			20.0504i			0.673226i	0.941643	+	0.336613i	$0.109281\pi$
$887$			20.0504i			0.673226i	−0.941643	+	0.336613i	$0.890719\pi$
$888$		−	25.3377i		−	0.850276i
$889$	−1.88436	+	1.88436i	−0.0631993	+	0.0631993i
$890$		0			0
$891$	−12.2265	−	12.2265i	−0.409602	−	0.409602i
$892$	0.505605	−	0.505605i	0.0169289	−	0.0169289i
$893$	−28.7681	+	28.7681i	−0.962686	+	0.962686i
$894$		−	12.3734i		−	0.413828i
$895$		0			0
$896$	6.75104	−	6.75104i	0.225536	−	0.225536i
$897$	14.0097			0.467769
$898$	−20.6595	−	20.6595i	−0.689416	−	0.689416i
$899$	−0.909011	−	13.1660i	−0.0303172	−	0.439111i
$900$		0			0
$901$	18.2695	+	18.2695i	0.608644	+	0.608644i
$902$			43.2010i			1.43844i
$903$	2.61187	+	2.61187i	0.0869176	+	0.0869176i
$904$	−46.6534			−1.55167
$905$		0			0
$906$	5.17137			0.171807
$907$	−11.5003			−0.381861			−0.190931	−	0.981604i	$-0.561151\pi$
$907$	−11.5003			−0.381861			−0.190931	+	0.981604i	$0.561151\pi$
$908$	3.53168	+	3.53168i	0.117203	+	0.117203i
$909$	−14.4675	−	14.4675i	−0.479858	−	0.479858i
$910$		0			0
$911$	30.3844	−	30.3844i	1.00668	−	1.00668i	0.00670420	−	0.999978i	$-0.497866\pi$
$911$	30.3844	−	30.3844i	1.00668	−	1.00668i	0.999978	−	0.00670420i	$-0.00213403\pi$
$912$	8.81051	−	8.81051i	0.291745	−	0.291745i
$913$	66.5696			2.20313
$914$	−11.4526	−	11.4526i	−0.378817	−	0.378817i
$915$		0			0
$916$	2.14343	+	2.14343i	0.0708209	+	0.0708209i
$917$	4.77939			0.157829
$918$	34.3309			1.13309
$919$		−	17.4379i		−	0.575222i	−0.957747	−	0.287611i	$-0.907139\pi$
$919$		−	17.4379i		−	0.575222i	0.957747	−	0.287611i	$-0.0928610\pi$
$920$		0			0
$921$		−	17.5187i		−	0.577260i
$922$	−23.0430	−	23.0430i	−0.758881	−	0.758881i
$923$	6.05827	−	6.05827i	0.199410	−	0.199410i
$924$			0.937044i			0.0308265i
$925$		0			0
$926$	20.3412	−	20.3412i	0.668452	−	0.668452i
$927$	11.7037	−	11.7037i	0.384401	−	0.384401i
$928$	3.91315	−	4.49357i	0.128455	−	0.147509i
$929$			25.1262i			0.824364i	0.911101	+	0.412182i	$0.135233\pi$
$929$			25.1262i			0.824364i	−0.911101	+	0.412182i	$0.864767\pi$
$930$		0			0
$931$	17.4625	+	17.4625i	0.572310	+	0.572310i
$932$	−1.13673	+	1.13673i	−0.0372349	+	0.0372349i
$933$	−13.9363	−	13.9363i	−0.456254	−	0.456254i
$934$	−23.7131			−0.775917
$935$		0			0
$936$	−11.5146	+	11.5146i	−0.376366	+	0.376366i
$937$	−24.7520	+	24.7520i	−0.808612	+	0.808612i	−0.984424	−	0.175811i	$-0.943745\pi$
$937$	−24.7520	+	24.7520i	−0.808612	+	0.808612i	0.175811	+	0.984424i	$0.443745\pi$
$938$		−	0.504240i		−	0.0164640i
$939$	−12.9539	+	12.9539i	−0.422733	+	0.422733i
$940$		0			0
$941$			30.2385i			0.985746i	0.870101	+	0.492873i	$0.164053\pi$
$941$			30.2385i			0.985746i	−0.870101	+	0.492873i	$0.835947\pi$
$942$			12.8020i			0.417110i
$943$		−	39.9100i		−	1.29965i
$944$		−	46.6929i		−	1.51972i
$945$		0			0
$946$	22.6940	−	22.6940i	0.737847	−	0.737847i
$947$		−	0.446886i		−	0.0145218i	−0.999974	−	0.00726092i	$-0.997689\pi$
$947$		−	0.446886i		−	0.0145218i	0.999974	−	0.00726092i	$-0.00231124\pi$
$948$	0.438521	−	0.438521i	0.0142425	−	0.0142425i
$949$	−5.18291	+	5.18291i	−0.168244	+	0.168244i
$950$		0			0
$951$	−20.0393			−0.649818
$952$	12.1878	+	12.1878i	0.395009	+	0.395009i
$953$	17.2854	−	17.2854i	0.559930	−	0.559930i	−0.369357	−	0.929287i	$-0.620422\pi$
$953$	17.2854	−	17.2854i	0.559930	−	0.559930i	0.929287	+	0.369357i	$0.120422\pi$
$954$	−9.79778	−	9.79778i	−0.317215	−	0.317215i
$955$		0			0
$956$		−	0.312939i		−	0.0101212i
$957$	−1.73713	−	25.1603i	−0.0561533	−	0.813318i
$958$	−26.6692	+	26.6692i	−0.861642	+	0.861642i
$959$	−14.2175	+	14.2175i	−0.459107	+	0.459107i
$960$		0			0
$961$		−	24.9941i		−	0.806262i
$962$	23.3366	−	23.3366i	0.752402	−	0.752402i
$963$	−10.6683	−	10.6683i	−0.343781	−	0.343781i
$964$			2.26000i			0.0727896i
$965$		0			0
$966$			7.95256i			0.255869i
$967$	22.6100			0.727090			0.363545	−	0.931577i	$-0.381566\pi$
$967$	22.6100			0.727090			0.363545	+	0.931577i	$0.381566\pi$
$968$	58.6331			1.88454
$969$	14.1557	+	14.1557i	0.454747	+	0.454747i
$970$		0			0
$971$	−26.2469	−	26.2469i	−0.842302	−	0.842302i	0.146856	−	0.989158i	$-0.453085\pi$
$971$	−26.2469	−	26.2469i	−0.842302	−	0.842302i	−0.989158	+	0.146856i	$0.953085\pi$
$972$	3.14077			0.100740
$973$	−3.75772	+	3.75772i	−0.120467	+	0.120467i
$974$	17.9993	−	17.9993i	0.576736	−	0.576736i
$975$		0			0
$976$	−8.30894	−	8.30894i	−0.265963	−	0.265963i
$977$	−38.4624	−	38.4624i	−1.23052	−	1.23052i	−0.963763	−	0.266759i	$-0.914047\pi$
$977$	−38.4624	−	38.4624i	−1.23052	−	1.23052i	−0.266759	−	0.963763i	$-0.585953\pi$
$978$	−9.30638			−0.297585
$979$	58.3221			1.86398
$980$		0			0
$981$	−22.6259			−0.722390
$982$	4.14867	+	4.14867i	0.132390	+	0.132390i
$983$		−	11.6191i		−	0.370591i	−0.982683	−	0.185296i	$-0.940676\pi$
$983$		−	11.6191i		−	0.370591i	0.982683	−	0.185296i	$-0.0593243\pi$
$984$	−10.1761	−	10.1761i	−0.324403	−	0.324403i
$985$		0			0
$986$	−31.2734	−	27.2339i	−0.995948	−	0.867305i
$987$	−5.96461	−	5.96461i	−0.189856	−	0.189856i
$988$	−1.96100			−0.0623877
$989$	−20.9652	+	20.9652i	−0.666656	+	0.666656i
$990$		0			0
$991$			38.3726i			1.21895i	0.792807	+	0.609473i	$0.208619\pi$
$991$			38.3726i			1.21895i	−0.792807	+	0.609473i	$0.791381\pi$
$992$	−1.91742	+	1.91742i	−0.0608782	+	0.0608782i
$993$	5.36062	−	5.36062i	0.170114	−	0.170114i
$994$	3.43897	+	3.43897i	0.109077	+	0.109077i
$995$		0			0
$996$	−1.40172	+	1.40172i	−0.0444153	+	0.0444153i
$997$			4.59110i			0.145402i	0.997354	+	0.0727008i	$0.0231618\pi$
$997$			4.59110i			0.145402i	−0.997354	+	0.0727008i	$0.976838\pi$
$998$		−	40.2151i		−	1.27299i
$999$	−45.4380			−1.43759

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.e.b.157.3	✓	16
5.2	odd	4		725.2.j.b.418.6	yes	16
5.3	odd	4		725.2.j.b.418.3	yes	16
5.4	even	2	inner	725.2.e.b.157.6	yes	16
29.17	odd	4		725.2.j.b.307.3	yes	16
145.17	even	4	inner	725.2.e.b.568.3	yes	16
145.104	odd	4		725.2.j.b.307.6	yes	16
145.133	even	4	inner	725.2.e.b.568.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.e.b.157.3	✓	16	1.1	even	1	trivial
725.2.e.b.157.6	yes	16	5.4	even	2	inner
725.2.e.b.568.3	yes	16	145.17	even	4	inner
725.2.e.b.568.6	yes	16	145.133	even	4	inner
725.2.j.b.307.3	yes	16	29.17	odd	4
725.2.j.b.307.6	yes	16	145.104	odd	4
725.2.j.b.418.3	yes	16	5.3	odd	4
725.2.j.b.418.6	yes	16	5.2	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)

\(f(q)\)	\(=\)	\(q-1.34301i q^{2} +0.842805 q^{3} +0.196335 q^{4} -1.13189i q^{6} +(-0.720606 - 0.720606i) q^{7} -2.94969i q^{8} -2.28968 q^{9} +(-3.92923 - 3.92923i) q^{11} +0.165472 q^{12} +(1.70489 + 1.70489i) q^{13} +(-0.967779 + 0.967779i) q^{14} -3.56878 q^{16} -5.73391i q^{17} +3.07505i q^{18} +(-2.92923 + 2.92923i) q^{19} +(-0.607331 - 0.607331i) q^{21} +(-5.27698 + 5.27698i) q^{22} +(4.87499 - 4.87499i) q^{23} -2.48601i q^{24} +(2.28968 - 2.28968i) q^{26} -4.45817 q^{27} +(-0.141480 - 0.141480i) q^{28} +(4.06112 + 3.53656i) q^{29} +(-1.73290 - 1.73290i) q^{31} -1.10648i q^{32} +(-3.31158 - 3.31158i) q^{33} -7.70068 q^{34} -0.449543 q^{36} +10.1921 q^{37} +(3.93398 + 3.93398i) q^{38} +(1.43689 + 1.43689i) q^{39} +(4.09335 - 4.09335i) q^{41} +(-0.815649 + 0.815649i) q^{42} -4.30057 q^{43} +(-0.771444 - 0.771444i) q^{44} +(-6.54714 - 6.54714i) q^{46} +9.82103 q^{47} -3.00779 q^{48} -5.96145i q^{49} -4.83257i q^{51} +(0.334729 + 0.334729i) q^{52} +(-3.18621 + 3.18621i) q^{53} +5.98735i q^{54} +(-2.12557 + 2.12557i) q^{56} +(-2.46877 + 2.46877i) q^{57} +(4.74962 - 5.45411i) q^{58} +13.0837i q^{59} +(2.32823 + 2.32823i) q^{61} +(-2.32729 + 2.32729i) q^{62} +(1.64996 + 1.64996i) q^{63} -8.62358 q^{64} +(-4.44747 + 4.44747i) q^{66} +(-0.260514 + 0.260514i) q^{67} -1.12577i q^{68} +(4.10866 - 4.10866i) q^{69} -3.55346i q^{71} +6.75385i q^{72} +3.04002i q^{73} -13.6880i q^{74} +(-0.575110 + 0.575110i) q^{76} +5.66286i q^{77} +(1.92975 - 1.92975i) q^{78} +(2.65013 - 2.65013i) q^{79} +3.11167 q^{81} +(-5.49739 - 5.49739i) q^{82} +(-8.47107 + 8.47107i) q^{83} +(-0.119240 - 0.119240i) q^{84} +5.77569i q^{86} +(3.42274 + 2.98063i) q^{87} +(-11.5900 + 11.5900i) q^{88} +(-7.42157 + 7.42157i) q^{89} -2.45711i q^{91} +(0.957129 - 0.957129i) q^{92} +(-1.46049 - 1.46049i) q^{93} -13.1897i q^{94} -0.932550i q^{96} +1.36383 q^{97} -8.00627 q^{98} +(8.99668 + 8.99668i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} + 40 q^{9} - 4 q^{11} - 20 q^{14} - 16 q^{16} + 12 q^{19} - 32 q^{21} - 40 q^{26} + 4 q^{29} + 20 q^{31} - 80 q^{34} - 104 q^{36} - 16 q^{39} - 28 q^{44} + 44 q^{46} + 36 q^{56} + 24 q^{61}+ \cdots + 92 q^{99}+O(q^{100}) \) 16 * q - 8 * q^4 + 40 * q^9 - 4 * q^11 - 20 * q^14 - 16 * q^16 + 12 * q^19 - 32 * q^21 - 40 * q^26 + 4 * q^29 + 20 * q^31 - 80 * q^34 - 104 * q^36 - 16 * q^39 - 28 * q^44 + 44 * q^46 + 36 * q^56 + 24 * q^61 + 32 * q^64 + 80 * q^66 + 40 * q^69 - 36 * q^76 - 52 * q^79 + 40 * q^81 + 136 * q^84 - 40 * q^89 + 92 * q^99

Introduction

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