LMFDB - Embedded newform 725.2.j.b.307.3

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:	$16$
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			307.3
Root			$2.34301i$ of defining polynomial
Character	$\chi$	$=$	725.307
Dual form			725.2.j.b.418.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.34301 q^{2} -0.842805i q^{3} -0.196335 q^{4} +1.13189i q^{6} +(-0.720606 - 0.720606i) q^{7} +2.94969 q^{8} +2.28968 q^{9} +(-3.92923 + 3.92923i) q^{11} +0.165472i q^{12} +(-1.70489 - 1.70489i) q^{13} +(0.967779 + 0.967779i) q^{14} -3.56878 q^{16} -5.73391 q^{17} -3.07505 q^{18} +(2.92923 + 2.92923i) q^{19} +(-0.607331 + 0.607331i) q^{21} +(5.27698 - 5.27698i) q^{22} +(4.87499 - 4.87499i) q^{23} -2.48601i q^{24} +(2.28968 + 2.28968i) q^{26} -4.45817i q^{27} +(0.141480 + 0.141480i) q^{28} +(-4.06112 + 3.53656i) q^{29} +(-1.73290 + 1.73290i) q^{31} -1.10648 q^{32} +(3.31158 + 3.31158i) q^{33} +7.70068 q^{34} -0.449543 q^{36} +10.1921i q^{37} +(-3.93398 - 3.93398i) q^{38} +(-1.43689 + 1.43689i) q^{39} +(4.09335 + 4.09335i) q^{41} +(0.815649 - 0.815649i) q^{42} +4.30057i q^{43} +(0.771444 - 0.771444i) q^{44} +(-6.54714 + 6.54714i) q^{46} +9.82103i q^{47} +3.00779i q^{48} -5.96145i q^{49} +4.83257i q^{51} +(0.334729 + 0.334729i) q^{52} +(-3.18621 + 3.18621i) q^{53} +5.98735i q^{54} +(-2.12557 - 2.12557i) q^{56} +(2.46877 - 2.46877i) q^{57} +(5.45411 - 4.74962i) q^{58} +13.0837i q^{59} +(2.32823 - 2.32823i) q^{61} +(2.32729 - 2.32729i) q^{62} +(-1.64996 - 1.64996i) q^{63} +8.62358 q^{64} +(-4.44747 - 4.44747i) q^{66} +(0.260514 - 0.260514i) q^{67} +1.12577 q^{68} +(-4.10866 - 4.10866i) q^{69} +3.55346i q^{71} +6.75385 q^{72} -3.04002 q^{73} -13.6880i q^{74} +(-0.575110 - 0.575110i) q^{76} +5.66286 q^{77} +(1.92975 - 1.92975i) q^{78} +(-2.65013 - 2.65013i) q^{79} +3.11167 q^{81} +(-5.49739 - 5.49739i) q^{82} +(-8.47107 + 8.47107i) q^{83} +(0.119240 - 0.119240i) q^{84} -5.77569i q^{86} +(2.98063 + 3.42274i) q^{87} +(-11.5900 + 11.5900i) q^{88} +(7.42157 + 7.42157i) q^{89} +2.45711i q^{91} +(-0.957129 + 0.957129i) q^{92} +(1.46049 + 1.46049i) q^{93} -13.1897i q^{94} +0.932550i q^{96} +1.36383i q^{97} +8.00627i q^{98} +(-8.99668 + 8.99668i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.34301			−0.949649			−0.474824	−	0.880081i	$-0.657488\pi$
$2$	−1.34301			−0.949649			−0.474824	+	0.880081i	$0.657488\pi$
$3$		−	0.842805i		−	0.486594i	−0.969952	−	0.243297i	$-0.921771\pi$
$3$		−	0.842805i		−	0.486594i	0.969952	−	0.243297i	$-0.0782289\pi$
$4$	−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	$0.811689\pi$
$8$	2.94969			1.04287
$9$	2.28968			0.763227
$10$		0			0
$11$	−3.92923	+	3.92923i	−1.18471	+	1.18471i	−0.206197	+	0.978510i	$0.566109\pi$
$11$	−3.92923	+	3.92923i	−1.18471	+	1.18471i	−0.978510	+	0.206197i	$0.933891\pi$
$12$			0.165472i			0.0477676i
$13$	−1.70489	−	1.70489i	−0.472852	−	0.472852i	0.429984	−	0.902836i	$-0.358519\pi$
$13$	−1.70489	−	1.70489i	−0.472852	−	0.472852i	−0.902836	+	0.429984i	$0.858519\pi$
$14$	0.967779	+	0.967779i	0.258650	+	0.258650i
$15$		0			0
$16$	−3.56878			−0.892196
$17$	−5.73391			−1.39068			−0.695339	−	0.718682i	$-0.744746\pi$
$17$	−5.73391			−1.39068			−0.695339	+	0.718682i	$0.744746\pi$
$18$	−3.07505			−0.724797
$19$	2.92923	+	2.92923i	0.672012	+	0.672012i	0.958180	−	0.286168i	$-0.0923815\pi$
$19$	2.92923	+	2.92923i	0.672012	+	0.672012i	−0.286168	+	0.958180i	$0.592381\pi$
$20$		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
$27$		−	4.45817i		−	0.857975i
$28$	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	−0.845389	−	0.534151i	$-0.820631\pi$
$31$	−1.73290	+	1.73290i	−0.311237	+	0.311237i	0.534151	+	0.845389i	$0.320631\pi$
$32$	−1.10648			−0.195601
$33$	3.31158	+	3.31158i	0.576471	+	0.576471i
$34$	7.70068			1.32065
$35$		0			0
$36$	−0.449543			−0.0749239
$37$			10.1921i			1.67557i	0.546002	+	0.837784i	$0.316149\pi$
$37$			10.1921i			1.67557i	−0.546002	+	0.837784i	$0.683851\pi$
$38$	−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	0.950376	−	0.311103i	$-0.100698\pi$
$41$	4.09335	+	4.09335i	0.639273	+	0.639273i	−0.311103	+	0.950376i	$0.600698\pi$
$42$	0.815649	−	0.815649i	0.125857	−	0.125857i
$43$			4.30057i			0.655831i	0.944707	+	0.327916i	$0.106346\pi$
$43$			4.30057i			0.655831i	−0.944707	+	0.327916i	$0.893654\pi$
$44$	0.771444	−	0.771444i	0.116300	−	0.116300i
$45$		0			0
$46$	−6.54714	+	6.54714i	−0.965323	+	0.965323i
$47$			9.82103i			1.43254i	0.697821	+	0.716272i	$0.254153\pi$
$47$			9.82103i			1.43254i	−0.697821	+	0.716272i	$0.745847\pi$
$48$			3.00779i			0.434137i
$49$		−	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
$58$	5.45411	−	4.74962i	0.716160	−	0.623656i
$59$			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	−0.542170	−	0.840269i	$-0.682397\pi$
$61$	2.32823	−	2.32823i	0.298099	−	0.298099i	0.840269	+	0.542170i	$0.182397\pi$
$62$	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	−0.691014	−	0.722841i	$-0.742836\pi$
$67$	0.260514	−	0.260514i	0.0318269	−	0.0318269i	0.722841	+	0.691014i	$0.242836\pi$
$68$	1.12577			0.136519
$69$	−4.10866	−	4.10866i	−0.494625	−	0.494625i
$70$		0			0
$71$			3.55346i			0.421719i	0.977516	+	0.210859i	$0.0676262\pi$
$71$			3.55346i			0.421719i	−0.977516	+	0.210859i	$0.932374\pi$
$72$	6.75385			0.795949
$73$	−3.04002			−0.355808			−0.177904	−	0.984048i	$-0.556932\pi$
$73$	−3.04002			−0.355808			−0.177904	+	0.984048i	$0.556932\pi$
$74$		−	13.6880i		−	1.59120i
$75$		0			0
$76$	−0.575110	−	0.575110i	−0.0659696	−	0.0659696i
$77$	5.66286			0.645343
$78$	1.92975	−	1.92975i	0.218502	−	0.218502i
$79$	−2.65013	−	2.65013i	−0.298163	−	0.298163i	0.542131	−	0.840294i	$-0.317618\pi$
$79$	−2.65013	−	2.65013i	−0.298163	−	0.298163i	−0.840294	+	0.542131i	$0.817618\pi$
$80$		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
$87$	2.98063	+	3.42274i	0.319557	+	0.366956i
$88$	−11.5900	+	11.5900i	−1.23550	+	1.23550i
$89$	7.42157	+	7.42157i	0.786685	+	0.786685i	0.980949	−	0.194264i	$-0.0622319\pi$
$89$	7.42157	+	7.42157i	0.786685	+	0.786685i	−0.194264	+	0.980949i	$0.562232\pi$
$90$		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
$97$			1.36383i			0.138476i	0.997600	+	0.0692382i	$0.0220568\pi$
$97$			1.36383i			0.138476i	−0.997600	+	0.0692382i	$0.977943\pi$
$98$			8.00627i			0.808755i
$99$	−8.99668	+	8.99668i	−0.904201	+	0.904201i
$100$		0			0
$101$	6.31858	−	6.31858i	0.628722	−	0.628722i	−0.319024	−	0.947747i	$-0.603355\pi$
$101$	6.31858	−	6.31858i	0.628722	−	0.628722i	0.947747	+	0.319024i	$0.103355\pi$
$102$		−	6.49017i		−	0.642622i
$103$	−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	$0.646820\pi$
$108$			0.875293i			0.0842251i
$109$	−9.88169			−0.946494			−0.473247	−	0.880930i	$-0.656918\pi$
$109$	−9.88169			−0.946494			−0.473247	+	0.880930i	$0.656918\pi$
$110$		0			0
$111$	8.58994			0.815321
$112$	2.57169	+	2.57169i	0.243002	+	0.243002i
$113$	15.8164			1.48788			0.743940	−	0.668247i	$-0.232955\pi$
$113$	15.8164			1.48788			0.743940	+	0.668247i	$0.232955\pi$
$114$	−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
$118$		−	17.5715i		−	1.61759i
$119$	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
$127$	−2.61496			−0.232040			−0.116020	−	0.993247i	$-0.537014\pi$
$127$	−2.61496			−0.232040			−0.116020	+	0.993247i	$0.537014\pi$
$128$	−9.36855			−0.828071
$129$	3.62454			0.319123
$130$		0			0
$131$	−3.31623	−	3.31623i	−0.289740	−	0.289740i	0.547237	−	0.836977i	$-0.315679\pi$
$131$	−3.31623	−	3.31623i	−0.289740	−	0.289740i	−0.836977	+	0.547237i	$0.815679\pi$
$132$	−0.650177	−	0.650177i	−0.0565907	−	0.0565907i
$133$		−	4.22165i		−	0.366063i
$134$	−0.349872	+	0.349872i	−0.0302244	+	0.0302244i
$135$		0			0
$136$	−16.9133			−1.45030
$137$	−19.7299			−1.68564			−0.842819	−	0.538197i	$-0.819106\pi$
$137$	−19.7299			−1.68564			−0.842819	+	0.538197i	$0.819106\pi$
$138$	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
$142$		−	4.77232i		−	0.400485i
$143$	13.3978			1.12038
$144$	−8.17137			−0.680948
$145$		0			0
$146$	4.08277			0.337892
$147$	−5.02434			−0.414401
$148$		−	2.00106i		−	0.164486i
$149$	−10.9316			−0.895551			−0.447775	−	0.894146i	$-0.647784\pi$
$149$	−10.9316			−0.895551			−0.447775	+	0.894146i	$0.647784\pi$
$150$		0			0
$151$		−	4.56878i		−	0.371802i	−0.982568	−	0.185901i	$-0.940480\pi$
$151$		−	4.56878i		−	0.371802i	0.982568	−	0.185901i	$-0.0595204\pi$
$152$	8.64033	+	8.64033i	0.700823	+	0.700823i
$153$	−13.1288			−1.06140
$154$	−7.60525			−0.612849
$155$		0			0
$156$	0.282111	−	0.282111i	0.0225870	−	0.0225870i
$157$		−	11.3102i		−	0.902654i	−0.892359	−	0.451327i	$-0.850951\pi$
$157$		−	11.3102i		−	0.902654i	0.892359	−	0.451327i	$-0.149049\pi$
$158$	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
$162$	−4.17899			−0.328333
$163$	8.22196			0.643994			0.321997	−	0.946741i	$-0.395646\pi$
$163$	8.22196			0.643994			0.321997	+	0.946741i	$0.395646\pi$
$164$	−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	$0.702952\pi$
$167$	−18.0764	+	18.0764i	−1.39879	+	1.39879i	−0.803531	+	0.595263i	$0.797048\pi$
$168$	−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
$172$		−	0.844351i		−	0.0643812i
$173$	−3.03649	−	3.03649i	−0.230860	−	0.230860i	0.582192	−	0.813052i	$-0.302195\pi$
$173$	−3.03649	−	3.03649i	−0.230860	−	0.230860i	−0.813052	+	0.582192i	$0.802195\pi$
$174$	−4.00301	−	4.59675i	−0.303467	−	0.348479i
$175$		0			0
$176$	14.0226	−	14.0226i	1.05699	−	1.05699i
$177$	11.0270			0.828841
$178$	−9.96722	−	9.96722i	−0.747074	−	0.747074i
$179$	9.50623			0.710529			0.355265	−	0.934766i	$-0.384391\pi$
$179$	9.50623			0.710529			0.355265	+	0.934766i	$0.384391\pi$
$180$		0			0
$181$	−2.41590			−0.179572			−0.0897861	−	0.995961i	$-0.528618\pi$
$181$	−2.41590			−0.179572			−0.0897861	+	0.995961i	$0.528618\pi$
$182$		−	3.29992i		−	0.244606i
$183$	−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
$188$		−	1.92821i		−	0.140629i
$189$	−3.21259	+	3.21259i	−0.233681	+	0.233681i
$190$		0			0
$191$	6.82624	−	6.82624i	0.493930	−	0.493930i	−0.415612	−	0.909542i	$-0.636433\pi$
$191$	6.82624	−	6.82624i	0.493930	−	0.493930i	0.909542	+	0.415612i	$0.136433\pi$
$192$		−	7.26800i		−	0.524523i
$193$		−	26.4787i		−	1.90598i	−0.303009	−	0.952988i	$-0.597991\pi$
$193$		−	26.4787i		−	1.90598i	0.303009	−	0.952988i	$-0.402009\pi$
$194$		−	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
$203$	5.47494	+	0.378002i	0.384266	+	0.0265306i
$204$		−	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	0.998971	−	0.0453507i	$-0.0144405\pi$
$211$	13.8521	+	13.8521i	0.953620	+	0.953620i	−0.0453507	+	0.998971i	$0.514441\pi$
$212$	0.625564	−	0.625564i	0.0429639	−	0.0429639i
$213$	2.99488			0.205206
$214$	−6.25746	−	6.25746i	−0.427751	−	0.427751i
$215$		0			0
$216$		−	13.1502i		−	0.894759i
$217$	2.49747			0.169540
$218$	13.2712			0.898837
$219$			2.56215i			0.173134i
$220$		0			0
$221$	9.77569	+	9.77569i	0.657584	+	0.657584i
$222$	−11.5363			−0.774268
$223$	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	$-0.920402\pi$
$229$	−10.9172	+	10.9172i	−0.721431	+	0.721431i	0.247466	+	0.968897i	$0.420402\pi$
$230$		0			0
$231$		−	4.77269i		−	0.314020i
$232$	−11.9791	+	10.4318i	−0.786464	+	0.684879i
$233$	−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	$-0.879103\pi$
$241$		−	11.5109i		−	0.741485i	0.928736	−	0.370743i	$-0.120897\pi$
$242$			26.6959i			1.71608i
$243$		−	15.9970i		−	1.02621i
$244$	−0.457112	+	0.457112i	−0.0292636	+	0.0292636i
$245$		0			0
$246$	−4.63323	+	4.63323i	−0.295404	+	0.295404i
$247$		−	9.98804i		−	0.635524i
$248$	−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	−0.0129347	+	0.999916i	$0.504117\pi$
$251$	−16.0466	+	16.0466i	−1.01285	+	1.01285i	−0.999916	+	0.0129347i	$0.995883\pi$
$252$	0.323944	+	0.323944i	0.0204065	+	0.0204065i
$253$			38.3099i			2.40852i
$254$	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	$0.795434\pi$
$258$	−4.86778			−0.303055
$259$	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
$263$			1.63737i			0.100965i	0.998725	+	0.0504824i	$0.0160759\pi$
$263$			1.63737i			0.100965i	−0.998725	+	0.0504824i	$0.983924\pi$
$264$	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	−0.209737	+	0.977758i	$0.567261\pi$
$269$	−19.4764	+	19.4764i	−1.18750	+	1.18750i	−0.977758	+	0.209737i	$0.932739\pi$
$270$		0			0
$271$	−10.5808	−	10.5808i	−0.642737	−	0.642737i	0.308491	−	0.951227i	$-0.400176\pi$
$271$	−10.5808	−	10.5808i	−0.642737	−	0.642737i	−0.951227	+	0.308491i	$0.900176\pi$
$272$	20.4631			1.24076
$273$	2.07087			0.125335
$274$	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	$0.872687\pi$
$278$			7.00332i			0.420031i
$279$	−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	$0.366740\pi$
$282$	−11.1163			−0.661969
$283$	0.976410	+	0.976410i	0.0580416	+	0.0580416i	0.735532	−	0.677490i	$-0.236932\pi$
$283$	0.976410	+	0.976410i	0.0580416	+	0.0580416i	−0.677490	+	0.735532i	$0.736932\pi$
$284$		−	0.697668i		−	0.0413990i
$285$		0			0
$286$	−17.9934			−1.06397
$287$		−	5.89938i		−	0.348229i
$288$	−2.53349			−0.149288
$289$	15.8777			0.933984
$290$		0			0
$291$	1.14945			0.0673817
$292$	0.596862			0.0349287
$293$		−	16.5338i		−	0.965916i	−0.875644	−	0.482958i	$-0.839562\pi$
$293$		−	16.5338i		−	0.965916i	0.875644	−	0.482958i	$-0.160438\pi$
$294$	6.74772			0.393535
$295$		0			0
$296$			30.0635i			1.74740i
$297$	17.5172	+	17.5172i	1.01645	+	1.01645i
$298$	14.6812			0.850458
$299$	−16.6226			−0.961313
$300$		0			0
$301$	3.09902	−	3.09902i	0.178625	−	0.178625i
$302$			6.13590i			0.353082i
$303$	−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
$307$	−20.7862			−1.18633			−0.593164	−	0.805082i	$-0.702121\pi$
$307$	−20.7862			−1.18633			−0.593164	+	0.805082i	$0.702121\pi$
$308$	−1.11182			−0.0633516
$309$	4.30801	+	4.30801i	0.245074	+	0.245074i
$310$		0			0
$311$	−16.5356	+	16.5356i	−0.937648	+	0.937648i	−0.998167	−	0.0605192i	$-0.980724\pi$
$311$	−16.5356	+	16.5356i	−0.937648	+	0.937648i	0.0605192	+	0.998167i	$0.480724\pi$
$312$	−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
$317$		−	23.7769i		−	1.33544i	−0.744411	−	0.667722i	$-0.767270\pi$
$317$		−	23.7769i		−	1.33544i	0.744411	−	0.667722i	$-0.232730\pi$
$318$	−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
$322$	9.43582			0.525838
$323$	−16.7959	−	16.7959i	−0.934552	−	0.934552i
$324$	−0.610929			−0.0339405
$325$		0			0
$326$	−11.0421			−0.611568
$327$			8.32834i			0.460558i
$328$	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	0.859961	−	0.510359i	$-0.170488\pi$
$331$	6.36045	+	6.36045i	0.349602	+	0.349602i	−0.510359	+	0.859961i	$0.670488\pi$
$332$	1.66316	−	1.66316i	0.0912780	−	0.0912780i
$333$			23.3366i			1.27884i
$334$	24.2767	−	24.2767i	1.32836	−	1.32836i
$335$		0			0
$336$	2.16743	−	2.16743i	0.118243	−	0.118243i
$337$			7.39775i			0.402981i	0.979490	+	0.201490i	$0.0645785\pi$
$337$			7.39775i			0.402981i	−0.979490	+	0.201490i	$0.935422\pi$
$338$			9.65177i			0.524987i
$339$		−	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	−0.850999	−	0.525168i	$-0.824003\pi$
$347$	−6.06956	+	6.06956i	−0.325831	+	0.325831i	0.525168	+	0.850999i	$0.324003\pi$
$348$	−0.585201	−	0.672002i	−0.0313701	−	0.0360231i
$349$		−	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	0.957755	−	0.287585i	$-0.0928525\pi$
$353$	12.5913	+	12.5913i	0.670170	+	0.670170i	−0.287585	+	0.957755i	$0.592852\pi$
$354$	−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
$358$	−12.7669			−0.674753
$359$	17.2438	+	17.2438i	0.910095	+	0.910095i	0.996279	−	0.0861840i	$-0.0274673\pi$
$359$	17.2438	+	17.2438i	0.910095	+	0.910095i	−0.0861840	+	0.996279i	$0.527467\pi$
$360$		0			0
$361$		−	1.83920i		−	0.0968003i
$362$	3.24456			0.170531
$363$	−16.7530			−0.879307
$364$		−	0.482416i		−	0.0252855i
$365$		0			0
$366$	2.63530	+	2.63530i	0.137749	+	0.137749i
$367$	31.1348			1.62522			0.812611	−	0.582806i	$-0.198045\pi$
$367$	31.1348			1.62522			0.812611	+	0.582806i	$0.198045\pi$
$368$	−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
$377$	12.9532	+	0.894321i	0.667125	+	0.0460599i
$378$	4.31452	−	4.31452i	0.221915	−	0.221915i
$379$	26.9196	+	26.9196i	1.38277	+	1.38277i	0.839671	+	0.543095i	$0.182748\pi$
$379$	26.9196	+	26.9196i	1.38277	+	1.38277i	0.543095	+	0.839671i	$0.317252\pi$
$380$		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	0.321377	−	0.946951i	$-0.395854\pi$
$383$	−12.2427	−	12.2427i	−0.625575	−	0.625575i	−0.946951	+	0.321377i	$0.895854\pi$
$384$			7.89587i			0.402934i
$385$		0			0
$386$			35.5610i			1.81001i
$387$			9.84693i			0.500548i
$388$		−	0.267768i		−	0.0135938i
$389$	10.8199	−	10.8199i	0.548592	−	0.548592i	−0.377442	−	0.926033i	$-0.623196\pi$
$389$	10.8199	−	10.8199i	0.548592	−	0.548592i	0.926033	+	0.377442i	$0.123196\pi$
$390$		0			0
$391$	−27.9527	+	27.9527i	−1.41363	+	1.41363i
$392$		−	17.5844i		−	0.888148i
$393$	−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	$0.393756\pi$
$398$			5.68618i			0.285022i
$399$	−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
$403$	5.90880			0.294338
$404$	−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
$408$			14.2546i			0.705707i
$409$	−2.60826	−	2.60826i	−0.128970	−	0.128970i	0.639675	−	0.768645i	$-0.279069\pi$
$409$	−2.60826	−	2.60826i	−0.128970	−	0.128970i	−0.768645	+	0.639675i	$0.779069\pi$
$410$		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
$417$	−4.39494			−0.215221
$418$	30.9150			1.51210
$419$	23.6950			1.15758			0.578788	−	0.815478i	$-0.303526\pi$
$419$	23.6950			1.15758			0.578788	+	0.815478i	$0.303526\pi$
$420$		0			0
$421$	−24.2906	−	24.2906i	−1.18385	−	1.18385i	−0.978738	−	0.205114i	$-0.934244\pi$
$421$	−24.2906	−	24.2906i	−1.18385	−	1.18385i	−0.205114	−	0.978738i	$-0.565756\pi$
$422$	−18.6035	−	18.6035i	−0.905604	−	0.905604i
$423$			22.4870i			1.09336i
$424$	−9.39834	+	9.39834i	−0.456424	+	0.456424i
$425$		0			0
$426$	−4.02214			−0.194873
$427$	−3.35547			−0.162383
$428$	−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	$0.424392\pi$
$432$			15.9102i			0.765482i
$433$	−25.1499			−1.20863			−0.604314	−	0.796747i	$-0.706553\pi$
$433$	−25.1499			−1.20863			−0.604314	+	0.796747i	$0.706553\pi$
$434$	−3.35412			−0.161003
$435$		0			0
$436$	1.94012			0.0929148
$437$	28.5599			1.36621
$438$		−	3.44098i		−	0.164416i
$439$	24.6379			1.17590			0.587952	−	0.808896i	$-0.299934\pi$
$439$	24.6379			1.17590			0.587952	+	0.808896i	$0.299934\pi$
$440$		0			0
$441$		−	13.6498i		−	0.649991i
$442$	−13.1288	−	13.1288i	−0.624474	−	0.624474i
$443$	36.1431			1.71721			0.858606	−	0.512636i	$-0.171331\pi$
$443$	36.1431			1.71721			0.858606	+	0.512636i	$0.171331\pi$
$444$	−1.68650			−0.0800378
$445$		0			0
$446$	−3.45854	+	3.45854i	−0.163766	+	0.163766i
$447$			9.21320i			0.435769i
$448$	−6.21421	−	6.21421i	−0.293594	−	0.293594i
$449$	−15.3830	−	15.3830i	−0.725970	−	0.725970i	0.243845	−	0.969814i	$-0.421591\pi$
$449$	−15.3830	−	15.3830i	−0.725970	−	0.725970i	−0.969814	+	0.243845i	$0.921591\pi$
$450$		0			0
$451$	−32.1674			−1.51470
$452$	−3.10530			−0.146061
$453$	−3.85059			−0.180917
$454$	−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	−0.877846	−	0.478944i	$-0.841020\pi$
$457$	−8.52755	+	8.52755i	−0.398902	+	0.398902i	0.478944	+	0.877846i	$0.341020\pi$
$458$	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	0.982956	−	0.183839i	$-0.0588524\pi$
$461$	17.1578	+	17.1578i	0.799118	+	0.799118i	−0.183839	+	0.982956i	$0.558852\pi$
$462$			6.40975i			0.298208i
$463$	−15.1460	−	15.1460i	−0.703894	−	0.703894i	0.261350	−	0.965244i	$-0.415832\pi$
$463$	−15.1460	−	15.1460i	−0.703894	−	0.703894i	−0.965244	+	0.261350i	$0.915832\pi$
$464$	14.4933	−	12.6212i	0.672833	−	0.585926i
$465$		0			0
$466$	7.77569	−	7.77569i	0.360202	−	0.360202i
$467$	−17.6567			−0.817057			−0.408528	−	0.912746i	$-0.633958\pi$
$467$	−17.6567			−0.817057			−0.408528	+	0.912746i	$0.633958\pi$
$468$	0.766423	+	0.766423i	0.0354279	+	0.0354279i
$469$	−0.375457			−0.0173370
$470$		0			0
$471$	−9.53231			−0.439226
$472$			38.5929i			1.77638i
$473$	−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
$478$			2.14062i			0.0979099i
$479$	19.8578	−	19.8578i	0.907327	−	0.907327i	−0.0887292	−	0.996056i	$-0.528281\pi$
$479$	19.8578	−	19.8578i	0.907327	−	0.907327i	0.996056	+	0.0887292i	$0.0282806\pi$
$480$		0			0
$481$	17.3764	−	17.3764i	0.792295	−	0.792295i
$482$			15.4593i			0.704151i
$483$			5.92146i			0.269436i
$484$			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	0.633958	−	0.773367i	$-0.281429\pi$
$491$	−3.08910	−	3.08910i	−0.139409	−	0.139409i	−0.773367	+	0.633958i	$0.781429\pi$
$492$	−0.677333	+	0.677333i	−0.0305365	+	0.0305365i
$493$	23.2861	−	20.2783i	1.04875	−	0.913290i
$494$			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	$-0.733809\pi$
$499$	−29.9441			−1.34048			−0.670240	+	0.742144i	$0.733809\pi$
$500$		0			0
$501$	15.2349	+	15.2349i	0.680644	+	0.680644i
$502$	21.5507	−	21.5507i	0.961853	−	0.961853i
$503$	34.4190			1.53467			0.767333	−	0.641249i	$-0.221584\pi$
$503$	34.4190			1.53467			0.767333	+	0.641249i	$0.221584\pi$
$504$	−4.86687	−	4.86687i	−0.216787	−	0.216787i
$505$		0			0
$506$		−	51.4504i		−	2.28725i
$507$	−6.05698			−0.269000
$508$	0.513408			0.0227788
$509$		−	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
$512$	25.0024			1.10496
$513$	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	$0.0349003\pi$
$521$			4.99526i			0.218846i	−0.993995	+	0.109423i	$0.965100\pi$
$522$	12.4882	−	10.8751i	0.546593	−	0.475991i
$523$	−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
$532$			0.828855i			0.0359354i
$533$		−	13.9574i		−	0.604563i
$534$	−8.40042	+	8.40042i	−0.363522	+	0.363522i
$535$		0			0
$536$	0.768437	−	0.768437i	0.0331914	−	0.0331914i
$537$		−	8.01190i		−	0.345739i
$538$	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	0.0290356	−	0.999578i	$-0.490756\pi$
$541$	23.9250	−	23.9250i	1.02861	−	1.02861i	0.999578	−	0.0290356i	$-0.00924362\pi$
$542$	14.2101	+	14.2101i	0.610374	+	0.610374i
$543$			2.03613i			0.0873787i
$544$	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	$0.876865\pi$
$548$	3.87366			0.165475
$549$	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
$553$			3.81940i			0.162417i
$554$	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	−0.503752	−	0.863849i	$-0.668047\pi$
$557$	8.49859	−	8.49859i	0.360097	−	0.360097i	0.863849	+	0.503752i	$0.168047\pi$
$558$	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
$562$	−18.3042			−0.772115
$563$	−12.1685			−0.512842			−0.256421	−	0.966565i	$-0.582543\pi$
$563$	−12.1685			−0.512842			−0.256421	+	0.966565i	$0.582543\pi$
$564$	−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
$568$			10.4816i			0.439799i
$569$	−24.9932	+	24.9932i	−1.04777	+	1.04777i	−0.0489683	+	0.998800i	$0.515593\pi$
$569$	−24.9932	+	24.9932i	−1.04777	+	1.04777i	−0.998800	+	0.0489683i	$0.984407\pi$
$570$		0			0
$571$	−21.0943			−0.882768			−0.441384	−	0.897318i	$-0.645512\pi$
$571$	−21.0943			−0.882768			−0.441384	+	0.897318i	$0.645512\pi$
$572$	−2.63046			−0.109985
$573$	−5.75319	−	5.75319i	−0.240343	−	0.240343i
$574$			7.92291i			0.330696i
$575$		0			0
$576$	19.7452			0.822718
$577$			40.5782i			1.68929i	0.535325	+	0.844646i	$0.320189\pi$
$577$			40.5782i			1.68929i	−0.535325	+	0.844646i	$0.679811\pi$
$578$	−21.3239			−0.886956
$579$	−22.3163			−0.927436
$580$		0			0
$581$	12.2086			0.506499
$582$	−1.54371			−0.0639890
$583$		−	25.0387i		−	1.03700i
$584$	−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	$0.785550\pi$
$588$	0.986452			0.0406806
$589$	−10.1521			−0.418311
$590$		0			0
$591$	−9.90492	+	9.90492i	−0.407434	+	0.407434i
$592$		−	36.3733i		−	1.49493i
$593$	−24.9702	−	24.9702i	−1.02540	−	1.02540i	−0.999669	−	0.0257336i	$-0.991808\pi$
$593$	−24.9702	−	24.9702i	−1.02540	−	1.02540i	−0.0257336	−	0.999669i	$-0.508192\pi$
$594$	−23.5257	−	23.5257i	−0.965270	−	0.965270i
$595$		0			0
$596$	2.14625			0.0879138
$597$	−3.56837			−0.146044
$598$	22.3243			0.912909
$599$	3.13220	+	3.13220i	0.127978	+	0.127978i	0.768195	−	0.640216i	$-0.221155\pi$
$599$	3.13220	+	3.13220i	0.127978	+	0.127978i	−0.640216	+	0.768195i	$0.721155\pi$
$600$		0			0
$601$	12.8277	−	12.8277i	0.523251	−	0.523251i	−0.395300	−	0.918552i	$-0.629360\pi$
$601$	12.8277	−	12.8277i	0.523251	−	0.523251i	0.918552	+	0.395300i	$0.129360\pi$
$602$	−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
$607$			10.6408i			0.431895i	0.976405	+	0.215948i	$0.0692841\pi$
$607$			10.6408i			0.431895i	−0.976405	+	0.215948i	$0.930716\pi$
$608$	−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
$612$	2.57764			0.104195
$613$	19.6421	+	19.6421i	0.793335	+	0.793335i	0.982035	−	0.188700i	$-0.0604273\pi$
$613$	19.6421	+	19.6421i	0.793335	+	0.793335i	−0.188700	+	0.982035i	$0.560427\pi$
$614$	27.9159			1.12660
$615$		0			0
$616$	16.7037			0.673011
$617$			5.28522i			0.212775i	0.994325	+	0.106388i	$0.0339284\pi$
$617$			5.28522i			0.212775i	−0.994325	+	0.106388i	$0.966072\pi$
$618$	−5.78568	−	5.78568i	−0.232734	−	0.232734i
$619$	−12.2093	+	12.2093i	−0.490732	+	0.490732i	−0.908537	−	0.417805i	$-0.862800\pi$
$619$	−12.2093	+	12.2093i	−0.490732	+	0.490732i	0.417805	+	0.908537i	$0.362800\pi$
$620$		0			0
$621$	−21.7335	−	21.7335i	−0.872136	−	0.872136i
$622$	22.2074	−	22.2074i	0.890436	−	0.890436i
$623$		−	10.6961i		−	0.428529i
$624$	5.12795	−	5.12795i	0.205282	−	0.205282i
$625$		0			0
$626$	20.6419	−	20.6419i	0.825017	−	0.825017i
$627$			19.4007i			0.774791i
$628$			2.22059i			0.0886111i
$629$		−	58.4405i		−	2.33017i
$630$		0			0
$631$		−	25.5814i		−	1.01838i	−0.860654	−	0.509190i	$-0.829945\pi$
$631$		−	25.5814i		−	1.01838i	0.860654	−	0.509190i	$-0.170055\pi$
$632$	−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
$638$	−2.76810	+	40.0929i	−0.109590	+	1.58729i
$639$			8.13629i			0.321867i
$640$		0			0
$641$	9.93460	−	9.93460i	0.392393	−	0.392393i	−0.483147	−	0.875539i	$-0.660506\pi$
$641$	9.93460	−	9.93460i	0.392393	−	0.392393i	0.875539	+	0.483147i	$0.160506\pi$
$642$	−5.27382	+	5.27382i	−0.208141	+	0.208141i
$643$	24.2029	+	24.2029i	0.954469	+	0.954469i	0.999008	−	0.0445391i	$-0.0141819\pi$
$643$	24.2029	+	24.2029i	0.954469	+	0.954469i	−0.0445391	+	0.999008i	$0.514182\pi$
$644$	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	−0.0966543	−	0.995318i	$-0.530814\pi$
$647$	22.8586	−	22.8586i	0.898664	−	0.898664i	0.995318	+	0.0966543i	$0.0308141\pi$
$648$	9.17847			0.360564
$649$	−51.4089	−	51.4089i	−2.01798	−	2.01798i
$650$		0			0
$651$		−	2.10488i		−	0.0824969i
$652$	−1.61426			−0.0632191
$653$	3.15622			0.123512			0.0617562	−	0.998091i	$-0.480330\pi$
$653$	3.15622			0.123512			0.0617562	+	0.998091i	$0.480330\pi$
$654$		−	11.1850i		−	0.437369i
$655$		0			0
$656$	−14.6083	−	14.6083i	−0.570357	−	0.570357i
$657$	−6.96068			−0.271562
$658$	−9.50458	+	9.50458i	−0.370527	+	0.370527i
$659$	2.95246	+	2.95246i	0.115011	+	0.115011i	0.762270	−	0.647259i	$-0.224085\pi$
$659$	2.95246	+	2.95246i	0.115011	+	0.115011i	−0.647259	+	0.762270i	$0.724085\pi$
$660$		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
$667$	−2.55723	+	37.0386i	−0.0990164	+	1.43414i
$668$	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	0.903670	−	0.428229i	$-0.140862\pi$
$673$	12.3340	+	12.3340i	0.475441	+	0.475441i	−0.428229	+	0.903670i	$0.640862\pi$
$674$		−	9.93522i		−	0.382690i
$675$		0			0
$676$			1.41100i			0.0542691i
$677$			20.9567i			0.805430i	0.915325	+	0.402715i	$0.131933\pi$
$677$			20.9567i			0.805430i	−0.915325	+	0.402715i	$0.868067\pi$
$678$			17.9024i			0.687539i
$679$	0.982787	−	0.982787i	0.0377159	−	0.0377159i
$680$		0			0
$681$	15.1604	−	15.1604i	0.580949	−	0.580949i
$682$			18.2889i			0.700319i
$683$	−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
$688$		−	15.3478i		−	0.585130i
$689$	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
$693$	12.9661			0.492543
$694$	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
$698$			14.4215i			0.545864i
$699$	4.87965	+	4.87965i	0.184565	+	0.184565i
$700$		0			0
$701$		−	22.9182i		−	0.865607i	−0.901488	−	0.432804i	$-0.857524\pi$
$701$		−	22.9182i		−	0.865607i	0.901488	−	0.432804i	$-0.142476\pi$
$702$	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
$707$	−9.10642			−0.342482
$708$	−2.16498			−0.0813651
$709$	53.2031			1.99808			0.999042	−	0.0437582i	$-0.0139331\pi$
$709$	53.2031			1.99808			0.999042	+	0.0437582i	$0.0139331\pi$
$710$		0			0
$711$	−6.06794	−	6.06794i	−0.227566	−	0.227566i
$712$	21.8913	+	21.8913i	0.820413	+	0.820413i
$713$			16.8957i			0.632749i
$714$	−4.67686	+	4.67686i	−0.175027	+	0.175027i
$715$		0			0
$716$	−1.86640			−0.0697508
$717$	−1.34335			−0.0501684
$718$	−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
$722$			2.47006i			0.0919262i
$723$	−9.70148			−0.360802
$724$	0.474324			0.0176281
$725$		0			0
$726$	22.4994			0.835033
$727$	−27.5262			−1.02089			−0.510446	−	0.859910i	$-0.670520\pi$
$727$	−27.5262			−1.02089			−0.510446	+	0.859910i	$0.670520\pi$
$728$			7.24772i			0.268618i
$729$	−4.14737			−0.153606
$730$		0			0
$731$		−	24.6591i		−	0.912049i
$732$	0.385256	+	0.385256i	0.0142395	+	0.0142395i
$733$	15.6923			0.579608			0.289804	−	0.957086i	$-0.406410\pi$
$733$	15.6923			0.579608			0.289804	+	0.957086i	$0.406410\pi$
$734$	−41.8142			−1.54339
$735$		0			0
$736$	−5.39409	+	5.39409i	−0.198829	+	0.198829i
$737$			2.04724i			0.0754111i
$738$	−12.5873	−	12.5873i	−0.463343	−	0.463343i
$739$	−3.42222	−	3.42222i	−0.125889	−	0.125889i	0.641355	−	0.767244i	$-0.278372\pi$
$739$	−3.42222	−	3.42222i	−0.125889	−	0.125889i	−0.767244	+	0.641355i	$0.778372\pi$
$740$		0			0
$741$	−8.41797			−0.309242
$742$	−6.16710			−0.226401
$743$	−34.1903			−1.25432			−0.627160	−	0.778890i	$-0.715783\pi$
$743$	−34.1903			−1.25432			−0.627160	+	0.778890i	$0.715783\pi$
$744$	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	0.527055	−	0.849831i	$-0.323296\pi$
$751$	−8.84550	−	8.84550i	−0.322777	−	0.322777i	−0.849831	+	0.527055i	$0.823296\pi$
$752$		−	35.0491i		−	1.27811i
$753$	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
$757$	23.6888			0.860984			0.430492	−	0.902594i	$-0.358340\pi$
$757$	23.6888			0.860984			0.430492	+	0.902594i	$0.358340\pi$
$758$	−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	$0.759151\pi$
$762$		−	2.95985i		−	0.107224i
$763$	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
$768$			3.93180i			0.141877i
$769$	−13.2917	+	13.2917i	−0.479312	+	0.479312i	−0.904912	−	0.425600i	$-0.860063\pi$
$769$	−13.2917	+	13.2917i	−0.479312	+	0.479312i	0.425600	+	0.904912i	$0.360063\pi$
$770$		0			0
$771$	−2.71807	+	2.71807i	−0.0978889	+	0.0978889i
$772$			5.19868i			0.187105i
$773$		−	8.06617i		−	0.290120i	−0.989423	−	0.145060i	$-0.953663\pi$
$773$		−	8.06617i		−	0.290120i	0.989423	−	0.145060i	$-0.0463375\pi$
$774$		−	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
$783$	15.7666	+	18.1052i	0.563452	+	0.647026i
$784$			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	−0.266320	−	0.963885i	$-0.585808\pi$
$787$	19.5691	−	19.5691i	0.697564	−	0.697564i	0.963885	+	0.266320i	$0.0858079\pi$
$788$	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
$793$	−7.93875			−0.281913
$794$	−34.0491	−	34.0491i	−1.20836	−	1.20836i
$795$		0			0
$796$			0.831265i			0.0294634i
$797$	4.45791			0.157907			0.0789537	−	0.996878i	$-0.474842\pi$
$797$	4.45791			0.157907			0.0789537	+	0.996878i	$0.474842\pi$
$798$	4.77845			0.169155
$799$		−	56.3129i		−	1.99221i
$800$		0			0
$801$	16.9930	+	16.9930i	0.600419	+	0.600419i
$802$	6.82744			0.241085
$803$	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	$-0.895419\pi$
$809$	−17.7438	+	17.7438i	−0.623838	+	0.623838i	0.322672	+	0.946511i	$0.395419\pi$
$810$		0			0
$811$			12.4871i			0.438482i	0.975671	+	0.219241i	$0.0703582\pi$
$811$			12.4871i			0.438482i	−0.975671	+	0.219241i	$0.929642\pi$
$812$	−1.07492	−	0.0742150i	−0.0377223	−	0.00260443i
$813$	−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	$-0.850632\pi$
$821$		−	25.9150i		−	0.904439i	0.891907	−	0.452219i	$-0.149368\pi$
$822$		−	22.3321i		−	0.778922i
$823$			22.1888i			0.773453i	0.922194	+	0.386726i	$0.126394\pi$
$823$			22.1888i			0.773453i	−0.922194	+	0.386726i	$0.873606\pi$
$824$	−15.0774	+	15.0774i	−0.525245	+	0.525245i
$825$		0			0
$826$	−12.6621	+	12.6621i	−0.440572	+	0.440572i
$827$		−	10.6389i		−	0.369951i	−0.982743	−	0.184976i	$-0.940779\pi$
$827$		−	10.6389i		−	0.369951i	0.982743	−	0.184976i	$-0.0592206\pi$
$828$	−2.19152	+	2.19152i	−0.0761605	+	0.0761605i
$829$	2.76134	+	2.76134i	0.0959052	+	0.0959052i	0.753432	−	0.657526i	$-0.228397\pi$
$829$	2.76134	+	2.76134i	0.0959052	+	0.0959052i	−0.657526	+	0.753432i	$0.728397\pi$
$830$		0			0
$831$	−7.45804	+	7.45804i	−0.258717	+	0.258717i
$832$	−14.7023	−	14.7023i	−0.509710	−	0.509710i
$833$			34.1824i			1.18435i
$834$	5.90244			0.204385
$835$		0			0
$836$	4.51948			0.156309
$837$	7.72555	+	7.72555i	0.267034	+	0.267034i
$838$	−31.8225			−1.09929
$839$	−11.8281	+	11.8281i	−0.408353	+	0.408353i	−0.881164	−	0.472811i	$-0.843239\pi$
$839$	−11.8281	+	11.8281i	−0.408353	+	0.408353i	0.472811	+	0.881164i	$0.343239\pi$
$840$		0			0
$841$	3.98545	−	28.7248i	0.137429	−	0.990512i
$842$	32.6224	+	32.6224i	1.12424	+	1.12424i
$843$		−	11.4868i		−	0.395627i
$844$	−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
$852$	−0.587998			−0.0201445
$853$	−23.4895			−0.804264			−0.402132	−	0.915582i	$-0.631731\pi$
$853$	−23.4895			−0.804264			−0.402132	+	0.915582i	$0.631731\pi$
$854$	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	$0.639741\pi$
$858$			15.1649i			0.517721i
$859$	4.09759	−	4.09759i	0.139808	−	0.139808i	−0.633739	−	0.773547i	$-0.718481\pi$
$859$	4.09759	−	4.09759i	0.139808	−	0.139808i	0.773547	+	0.633739i	$0.218481\pi$
$860$		0			0
$861$	−4.97203			−0.169446
$862$	−13.1212			−0.446910
$863$	11.6689	+	11.6689i	0.397215	+	0.397215i	0.877250	−	0.480034i	$-0.159376\pi$
$863$	11.6689	+	11.6689i	0.397215	+	0.397215i	−0.480034	+	0.877250i	$0.659376\pi$
$864$			4.93289i			0.167820i
$865$		0			0
$866$	33.7765			1.14777
$867$		−	13.3818i		−	0.454471i
$868$	−0.490341			−0.0166432
$869$	20.8259			0.706471
$870$		0			0
$871$	−0.888297			−0.0300988
$872$	−29.1479			−0.987074
$873$			3.12274i			0.105689i
$874$	−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	$0.483516\pi$
$878$	−33.0889			−1.11670
$879$	−13.9348			−0.470009
$880$		0			0
$881$	−34.2685	+	34.2685i	−1.15453	+	1.15453i	−0.168902	+	0.985633i	$0.554022\pi$
$881$	−34.2685	+	34.2685i	−1.15453	+	1.15453i	−0.985633	+	0.168902i	$0.945978\pi$
$882$			18.3318i			0.617263i
$883$	16.7707	+	16.7707i	0.564378	+	0.564378i	0.930548	−	0.366170i	$-0.119331\pi$
$883$	16.7707	+	16.7707i	0.564378	+	0.564378i	−0.366170	+	0.930548i	$0.619331\pi$
$884$	−1.91931	−	1.91931i	−0.0645533	−	0.0645533i
$885$		0			0
$886$	−48.5404			−1.63075
$887$	20.0504			0.673226			0.336613	−	0.941643i	$-0.390719\pi$
$887$	20.0504			0.673226			0.336613	+	0.941643i	$0.390719\pi$
$888$	25.3377			0.850276
$889$	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
$897$			14.0097i			0.467769i
$898$	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
$902$	43.2010			1.43844
$903$	−2.61187	−	2.61187i	−0.0869176	−	0.0869176i
$904$	46.6534			1.55167
$905$		0			0
$906$	5.17137			0.171807
$907$		−	11.5003i		−	0.381861i	−0.981604	−	0.190931i	$-0.938849\pi$
$907$		−	11.5003i		−	0.381861i	0.981604	−	0.190931i	$-0.0611506\pi$
$908$	−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	0.999978	+	0.00670420i	$0.00213403\pi$
$911$	30.3844	+	30.3844i	1.00668	+	1.00668i	0.00670420	+	0.999978i	$0.497866\pi$
$912$	−8.81051	+	8.81051i	−0.291745	+	0.291745i
$913$		−	66.5696i		−	2.20313i
$914$	11.4526	−	11.4526i	0.378817	−	0.378817i
$915$		0			0
$916$	2.14343	−	2.14343i	0.0708209	−	0.0708209i
$917$			4.77939i			0.157829i
$918$		−	34.3309i		−	1.13309i
$919$		−	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
$928$	4.49357	−	3.91315i	0.147509	−	0.128455i
$929$			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	−0.175811	−	0.984424i	$-0.556255\pi$
$937$	24.7520	−	24.7520i	0.808612	−	0.808612i	0.984424	+	0.175811i	$0.0562549\pi$
$938$	0.504240			0.0164640
$939$	12.9539	+	12.9539i	0.422733	+	0.422733i
$940$		0			0
$941$		−	30.2385i		−	0.985746i	−0.870101	−	0.492873i	$-0.835947\pi$
$941$		−	30.2385i		−	0.985746i	0.870101	−	0.492873i	$-0.164053\pi$
$942$	12.8020			0.417110
$943$	39.9100			1.29965
$944$		−	46.6929i		−	1.51972i
$945$		0			0
$946$	22.6940	+	22.6940i	0.737847	+	0.737847i
$947$	−0.446886			−0.0145218			−0.00726092	−	0.999974i	$-0.502311\pi$
$947$	−0.446886			−0.0145218			−0.00726092	+	0.999974i	$0.502311\pi$
$948$	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
$957$	−25.1603	−	1.73713i	−0.813318	−	0.0561533i
$958$	−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
$967$			22.6100i			0.727090i	0.931577	+	0.363545i	$0.118434\pi$
$967$			22.6100i			0.727090i	−0.931577	+	0.363545i	$0.881566\pi$
$968$		−	58.6331i		−	1.88454i
$969$	−14.1557	+	14.1557i	−0.454747	+	0.454747i
$970$		0			0
$971$	−26.2469	+	26.2469i	−0.842302	+	0.842302i	−0.989158	−	0.146856i	$-0.953085\pi$
$971$	−26.2469	+	26.2469i	−0.842302	+	0.842302i	0.146856	+	0.989158i	$0.453085\pi$
$972$			3.14077i			0.100740i
$973$	−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	$-0.585953\pi$
$978$			9.30638i			0.297585i
$979$	−58.3221			−1.86398
$980$		0			0
$981$	−22.6259			−0.722390
$982$	4.14867	+	4.14867i	0.132390	+	0.132390i
$983$	11.6191			0.370591			0.185296	−	0.982683i	$-0.440676\pi$
$983$	11.6191			0.370591			0.185296	+	0.982683i	$0.440676\pi$
$984$	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
$988$			1.96100i			0.0623877i
$989$	20.9652	+	20.9652i	0.666656	+	0.666656i
$990$		0			0
$991$		−	38.3726i		−	1.21895i	−0.792807	−	0.609473i	$-0.791381\pi$
$991$		−	38.3726i		−	1.21895i	0.792807	−	0.609473i	$-0.208619\pi$
$992$	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
$997$	4.59110			0.145402			0.0727008	−	0.997354i	$-0.476838\pi$
$997$	4.59110			0.145402			0.0727008	+	0.997354i	$0.476838\pi$
$998$	40.2151			1.27299
$999$	45.4380			1.43759

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.e.b.157.3	✓	16	29.12	odd	4
725.2.e.b.157.6	yes	16	145.99	odd	4
725.2.e.b.568.3	yes	16	5.2	odd	4
725.2.e.b.568.6	yes	16	5.3	odd	4
725.2.j.b.307.3	yes	16	1.1	even	1	trivial
725.2.j.b.307.6	yes	16	5.4	even	2	inner
725.2.j.b.418.3	yes	16	145.128	even	4	inner
725.2.j.b.418.6	yes	16	145.12	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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