LMFDB - Embedded newform 644.2.y.a.261.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(9,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 22, 30]))

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

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

chi := DirichletCharacter("644.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.y (of order $33$, degree $20$, 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:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			261.9
Character	$\chi$	$=$	644.261
Dual form			644.2.y.a.417.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.289991 - 0.407235i) q^{3} +(1.84733 - 0.356043i) q^{5} +(-0.899818 + 2.48804i) q^{7} +(0.899458 + 2.59881i) q^{9} +O(q^{10})$	\(q+(0.289991 - 0.407235i) q^{3} +(1.84733 - 0.356043i) q^{5} +(-0.899818 + 2.48804i) q^{7} +(0.899458 + 2.59881i) q^{9} +(3.95170 - 3.10765i) q^{11} +(-2.25836 + 1.45136i) q^{13} +(0.390714 - 0.855544i) q^{15} +(3.04272 + 2.90123i) q^{17} +(-4.10939 + 3.91830i) q^{19} +(0.752277 + 1.08794i) q^{21} +(1.63253 - 4.50942i) q^{23} +(-1.35600 + 0.542859i) q^{25} +(2.75821 + 0.809885i) q^{27} +(0.995306 - 0.292248i) q^{29} +(8.64582 - 0.825576i) q^{31} +(-0.119588 - 2.51046i) q^{33} +(-0.776409 + 4.91659i) q^{35} +(3.20369 + 9.25645i) q^{37} +(-0.0638590 + 1.34057i) q^{39} +(-3.60663 - 4.16227i) q^{41} +(-4.06181 - 8.89412i) q^{43} +(2.58688 + 4.48061i) q^{45} +(4.67045 - 8.08946i) q^{47} +(-5.38065 - 4.47756i) q^{49} +(2.06384 - 0.397773i) q^{51} +(0.308741 - 6.48127i) q^{53} +(6.19361 - 7.14781i) q^{55} +(0.403982 + 2.80976i) q^{57} +(8.38685 + 4.32372i) q^{59} +(5.33003 + 7.48498i) q^{61} +(-7.27529 - 0.100575i) q^{63} +(-3.65518 + 3.48521i) q^{65} +(-6.04020 + 2.41813i) q^{67} +(-1.36297 - 1.97251i) q^{69} +(-1.39774 + 9.72149i) q^{71} +(-0.226000 - 0.931586i) q^{73} +(-0.172155 + 0.709633i) q^{75} +(4.17614 + 12.6283i) q^{77} +(-0.803880 - 16.8755i) q^{79} +(-5.35542 + 4.21155i) q^{81} +(-7.45299 + 8.60121i) q^{83} +(6.65385 + 4.27617i) q^{85} +(0.169616 - 0.490073i) q^{87} +(3.65370 + 0.348886i) q^{89} +(-1.57893 - 6.92485i) q^{91} +(2.17100 - 3.76029i) q^{93} +(-6.19630 + 8.70149i) q^{95} +(-5.84419 - 6.74456i) q^{97} +(11.6306 + 7.47452i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9	$ 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9} - 2 q^{11} - 16 q^{15} + 4 q^{17} - 50 q^{21} + 25 q^{23} + 44 q^{25} + 54 q^{27} + 12 q^{29} + 2 q^{31} - 12 q^{33} - 22 q^{35} - 44 q^{37} - 4 q^{39} + 12 q^{41} + 76 q^{43} - 114 q^{45} - 10 q^{47} - 74 q^{49} - 30 q^{51} - 20 q^{53} + 32 q^{55} + 52 q^{57} - 32 q^{59} + 74 q^{61} + 87 q^{63} - 75 q^{65} - 8 q^{67} + 10 q^{69} + 8 q^{73} + 118 q^{75} + 5 q^{77} - 40 q^{79} - 44 q^{81} - 52 q^{83} - 100 q^{85} + 84 q^{87} + 36 q^{89} + 30 q^{91} - 12 q^{93} - 25 q^{95} + 72 q^{97} + 2 q^{99}+O(q^{100}) $ 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9 - 2 * q^11 - 16 * q^15 + 4 * q^17 - 50 * q^21 + 25 * q^23 + 44 * q^25 + 54 * q^27 + 12 * q^29 + 2 * q^31 - 12 * q^33 - 22 * q^35 - 44 * q^37 - 4 * q^39 + 12 * q^41 + 76 * q^43 - 114 * q^45 - 10 * q^47 - 74 * q^49 - 30 * q^51 - 20 * q^53 + 32 * q^55 + 52 * q^57 - 32 * q^59 + 74 * q^61 + 87 * q^63 - 75 * q^65 - 8 * q^67 + 10 * q^69 + 8 * q^73 + 118 * q^75 + 5 * q^77 - 40 * q^79 - 44 * q^81 - 52 * q^83 - 100 * q^85 + 84 * q^87 + 36 * q^89 + 30 * q^91 - 12 * q^93 - 25 * q^95 + 72 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{11}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.289991	−	0.407235i	0.167426	−	0.235117i	−0.722335	−	0.691543i	$-0.756931\pi$
$3$	0.289991	−	0.407235i	0.167426	−	0.235117i	0.889761	+	0.456426i	$0.150871\pi$
$4$		0			0
$5$	1.84733	−	0.356043i	0.826149	−	0.159227i	0.241384	−	0.970430i	$-0.422399\pi$
$5$	1.84733	−	0.356043i	0.826149	−	0.159227i	0.584765	+	0.811203i	$0.301187\pi$
$6$		0			0
$7$	−0.899818	+	2.48804i	−0.340099	+	0.940390i
$7$	−0.899818	+	2.48804i	−0.340099	+	0.940390i
$8$		0			0
$9$	0.899458	+	2.59881i	0.299819	+	0.866271i
$10$		0			0
$11$	3.95170	−	3.10765i	1.19148	−	0.936991i	0.192464	−	0.981304i	$-0.438352\pi$
$11$	3.95170	−	3.10765i	1.19148	−	0.936991i	0.999018	+	0.0443126i	$0.0141098\pi$
$12$		0			0
$13$	−2.25836	+	1.45136i	−0.626357	+	0.402535i	−0.814959	−	0.579518i	$-0.803241\pi$
$13$	−2.25836	+	1.45136i	−0.626357	+	0.402535i	0.188602	+	0.982054i	$0.439604\pi$
$14$		0			0
$15$	0.390714	−	0.855544i	0.100882	−	0.220901i
$16$		0			0
$17$	3.04272	+	2.90123i	0.737967	+	0.703650i	0.962640	−	0.270784i	$-0.0872828\pi$
$17$	3.04272	+	2.90123i	0.737967	+	0.703650i	−0.224673	+	0.974434i	$0.572131\pi$
$18$		0			0
$19$	−4.10939	+	3.91830i	−0.942759	+	0.898919i	−0.995016	−	0.0997144i	$-0.968207\pi$
$19$	−4.10939	+	3.91830i	−0.942759	+	0.898919i	0.0522567	+	0.998634i	$0.483359\pi$
$20$		0			0
$21$	0.752277	+	1.08794i	0.164160	+	0.237409i
$22$		0			0
$23$	1.63253	−	4.50942i	0.340406	−	0.940279i
$23$	1.63253	−	4.50942i	0.340406	−	0.940279i
$24$		0			0
$25$	−1.35600	+	0.542859i	−0.271199	+	0.108572i
$26$		0			0
$27$	2.75821	+	0.809885i	0.530819	+	0.155862i
$28$		0			0
$29$	0.995306	−	0.292248i	0.184824	−	0.0542691i	−0.188011	−	0.982167i	$-0.560204\pi$
$29$	0.995306	−	0.292248i	0.184824	−	0.0542691i	0.372835	+	0.927898i	$0.378386\pi$
$30$		0			0
$31$	8.64582	−	0.825576i	1.55284	−	0.148278i	0.716928	−	0.697148i	$-0.245548\pi$
$31$	8.64582	−	0.825576i	1.55284	−	0.148278i	0.835908	+	0.548870i	$0.184942\pi$
$32$		0			0
$33$	−0.119588	−	2.51046i	−0.0208176	−	0.437015i
$34$		0			0
$35$	−0.776409	+	4.91659i	−0.131237	+	0.831055i
$36$		0			0
$37$	3.20369	+	9.25645i	0.526683	+	1.52175i	0.823783	+	0.566905i	$0.191859\pi$
$37$	3.20369	+	9.25645i	0.526683	+	1.52175i	−0.297100	+	0.954846i	$0.596020\pi$
$38$		0			0
$39$	−0.0638590	+	1.34057i	−0.0102256	+	0.214662i
$40$		0			0
$41$	−3.60663	−	4.16227i	−0.563261	−	0.650037i	0.400660	−	0.916227i	$-0.368781\pi$
$41$	−3.60663	−	4.16227i	−0.563261	−	0.650037i	−0.963921	+	0.266189i	$0.914235\pi$
$42$		0			0
$43$	−4.06181	−	8.89412i	−0.619420	−	1.35634i	−0.915940	−	0.401314i	$-0.868554\pi$
$43$	−4.06181	−	8.89412i	−0.619420	−	1.35634i	0.296520	−	0.955027i	$-0.404174\pi$
$44$		0			0
$45$	2.58688	+	4.48061i	0.385629	+	0.667930i
$46$		0			0
$47$	4.67045	−	8.08946i	0.681255	−	1.17997i	−0.293343	−	0.956007i	$-0.594768\pi$
$47$	4.67045	−	8.08946i	0.681255	−	1.17997i	0.974598	−	0.223962i	$-0.0718990\pi$
$48$		0			0
$49$	−5.38065	−	4.47756i	−0.768665	−	0.639652i
$50$		0			0
$51$	2.06384	−	0.397773i	0.288995	−	0.0556993i
$52$		0			0
$53$	0.308741	−	6.48127i	0.0424088	−	0.890271i	−0.872994	−	0.487731i	$-0.837825\pi$
$53$	0.308741	−	6.48127i	0.0424088	−	0.890271i	0.915403	−	0.402539i	$-0.131872\pi$
$54$		0			0
$55$	6.19361	−	7.14781i	0.835147	−	0.963811i
$56$		0			0
$57$	0.403982	+	2.80976i	0.0535088	+	0.372162i
$58$		0			0
$59$	8.38685	+	4.32372i	1.09188	+	0.562901i	0.907541	−	0.419963i	$-0.137957\pi$
$59$	8.38685	+	4.32372i	1.09188	+	0.562901i	0.184334	+	0.982864i	$0.440987\pi$
$60$		0			0
$61$	5.33003	+	7.48498i	0.682441	+	0.958354i	0.999949	+	0.0100984i	$0.00321447\pi$
$61$	5.33003	+	7.48498i	0.682441	+	0.958354i	−0.317508	+	0.948255i	$0.602846\pi$
$62$		0			0
$63$	−7.27529	−	0.100575i	−0.916601	−	0.0126713i
$64$		0			0
$65$	−3.65518	+	3.48521i	−0.453370	+	0.432287i
$66$		0			0
$67$	−6.04020	+	2.41813i	−0.737928	+	0.295422i	−0.710013	−	0.704188i	$-0.751311\pi$
$67$	−6.04020	+	2.41813i	−0.737928	+	0.295422i	−0.0279149	+	0.999610i	$0.508887\pi$
$68$		0			0
$69$	−1.36297	−	1.97251i	−0.164083	−	0.237463i
$70$		0			0
$71$	−1.39774	+	9.72149i	−0.165881	+	1.15373i	0.721407	+	0.692512i	$0.243496\pi$
$71$	−1.39774	+	9.72149i	−0.165881	+	1.15373i	−0.887288	+	0.461216i	$0.847413\pi$
$72$		0			0
$73$	−0.226000	−	0.931586i	−0.0264513	−	0.109034i	0.957056	−	0.289905i	$-0.0936236\pi$
$73$	−0.226000	−	0.931586i	−0.0264513	−	0.109034i	−0.983507	+	0.180871i	$0.942108\pi$
$74$		0			0
$75$	−0.172155	+	0.709633i	−0.0198788	+	0.0819413i
$76$		0			0
$77$	4.17614	+	12.6283i	0.475915	+	1.43913i
$78$		0			0
$79$	−0.803880	−	16.8755i	−0.0904436	−	1.89864i	−0.355903	−	0.934523i	$-0.615827\pi$
$79$	−0.803880	−	16.8755i	−0.0904436	−	1.89864i	0.265460	−	0.964122i	$-0.414476\pi$
$80$		0			0
$81$	−5.35542	+	4.21155i	−0.595047	+	0.467950i
$82$		0			0
$83$	−7.45299	+	8.60121i	−0.818072	+	0.944106i	−0.999226	−	0.0393490i	$-0.987472\pi$
$83$	−7.45299	+	8.60121i	−0.818072	+	0.944106i	0.181153	+	0.983455i	$0.442017\pi$
$84$		0			0
$85$	6.65385	+	4.27617i	0.721711	+	0.463816i
$86$		0			0
$87$	0.169616	−	0.490073i	0.0181847	−	0.0525413i
$88$		0			0
$89$	3.65370	+	0.348886i	0.387291	+	0.0369818i	0.286886	−	0.957965i	$-0.407380\pi$
$89$	3.65370	+	0.348886i	0.387291	+	0.0369818i	0.100405	+	0.994947i	$0.467986\pi$
$90$		0			0
$91$	−1.57893	−	6.92485i	−0.165516	−	0.725922i
$92$		0			0
$93$	2.17100	−	3.76029i	0.225123	−	0.389924i
$94$		0			0
$95$	−6.19630	+	8.70149i	−0.635727	+	0.892754i
$96$		0			0
$97$	−5.84419	−	6.74456i	−0.593388	−	0.684806i	0.377040	−	0.926197i	$-0.376942\pi$
$97$	−5.84419	−	6.74456i	−0.593388	−	0.684806i	−0.970428	+	0.241391i	$0.922396\pi$
$98$		0			0
$99$	11.6306	+	7.47452i	1.16892	+	0.751218i
$100$		0			0
$101$	−4.91764	−	0.947797i	−0.489323	−	0.0943093i	−0.0613791	−	0.998115i	$-0.519550\pi$
$101$	−4.91764	−	0.947797i	−0.489323	−	0.0943093i	−0.427944	+	0.903805i	$0.640762\pi$
$102$		0			0
$103$	−8.44649	−	3.38146i	−0.832257	−	0.333186i	−0.0838941	−	0.996475i	$-0.526736\pi$
$103$	−8.44649	−	3.38146i	−0.832257	−	0.333186i	−0.748363	+	0.663289i	$0.769160\pi$
$104$		0			0
$105$	1.77705	+	1.74195i	0.173423	+	0.169996i
$106$		0			0
$107$	−11.2484	−	15.7962i	−1.08743	−	1.52708i	−0.827513	−	0.561446i	$-0.810245\pi$
$107$	−11.2484	−	15.7962i	−1.08743	−	1.52708i	−0.259914	−	0.965632i	$-0.583694\pi$
$108$		0			0
$109$	8.07608	+	7.70053i	0.773548	+	0.737577i	0.970044	−	0.242928i	$-0.0781078\pi$
$109$	8.07608	+	7.70053i	0.773548	+	0.737577i	−0.196496	+	0.980505i	$0.562956\pi$
$110$		0			0
$111$	4.69859	+	1.37963i	0.445970	+	0.130949i
$112$		0			0
$113$	0.961312	−	6.68607i	0.0904327	−	0.628973i	−0.893317	−	0.449427i	$-0.851628\pi$
$113$	0.961312	−	6.68607i	0.0904327	−	0.628973i	0.983750	−	0.179546i	$-0.0574628\pi$
$114$		0			0
$115$	1.41027	−	8.91161i	0.131508	−	0.831012i
$116$		0			0
$117$	−5.80312	−	4.56363i	−0.536499	−	0.421907i
$118$		0			0
$119$	−9.95625	+	4.95982i	−0.912688	+	0.454666i
$120$		0			0
$121$	3.36508	−	13.8710i	0.305916	−	1.26100i
$122$		0			0
$123$	−2.74091	+	0.261725i	−0.247140	+	0.0235990i
$124$		0			0
$125$	−10.2250	+	6.57123i	−0.914555	+	0.587749i
$126$		0			0
$127$	−0.493738	−	3.43402i	−0.0438122	−	0.304720i	−0.999931	−	0.0117413i	$-0.996263\pi$
$127$	−0.493738	−	3.43402i	−0.0438122	−	0.304720i	0.956119	−	0.292979i	$-0.0946466\pi$
$128$		0			0
$129$	−4.79988	−	0.925102i	−0.422606	−	0.0814507i
$130$		0			0
$131$	−3.43794	+	1.77238i	−0.300374	+	0.154854i	−0.601825	−	0.798628i	$-0.705559\pi$
$131$	−3.43794	+	1.77238i	−0.300374	+	0.154854i	0.301451	+	0.953482i	$0.402529\pi$
$132$		0			0
$133$	−6.05116	−	13.7501i	−0.524702	−	1.19228i
$134$		0			0
$135$	5.38367	+	0.514078i	0.463353	+	0.0442448i
$136$		0			0
$137$	−7.90491	−	13.6917i	−0.675362	−	1.16976i	−0.976363	−	0.216138i	$-0.930654\pi$
$137$	−7.90491	−	13.6917i	−0.675362	−	1.16976i	0.301001	−	0.953624i	$-0.402679\pi$
$138$		0			0
$139$	−10.8108			−0.916963			−0.458482	−	0.888704i	$-0.651607\pi$
$139$	−10.8108			−0.916963			−0.458482	+	0.888704i	$0.651607\pi$
$140$		0			0
$141$	−1.93992	−	4.24784i	−0.163371	−	0.357733i
$142$		0			0
$143$	−4.41404	+	12.7535i	−0.369121	+	1.06650i
$144$		0			0
$145$	1.73460	−	0.894249i	0.144051	−	0.0742634i
$146$		0			0
$147$	−3.38376	+	0.892739i	−0.279088	+	0.0736319i
$148$		0			0
$149$	−4.47384	−	1.79105i	−0.366511	−	0.146729i	0.181094	−	0.983466i	$-0.442036\pi$
$149$	−4.47384	−	1.79105i	−0.366511	−	0.146729i	−0.547605	+	0.836737i	$0.684460\pi$
$150$		0			0
$151$	−9.81606	−	5.06053i	−0.798820	−	0.411820i	0.00994628	−	0.999951i	$-0.496834\pi$
$151$	−9.81606	−	5.06053i	−0.798820	−	0.411820i	−0.808766	+	0.588130i	$0.799864\pi$
$152$		0			0
$153$	−4.80295	+	10.5170i	−0.388295	+	0.850248i
$154$		0			0
$155$	15.6777	−	4.60339i	1.25926	−	0.369753i
$156$		0			0
$157$	4.16489	+	17.1679i	0.332394	+	1.37015i	0.855466	+	0.517860i	$0.173271\pi$
$157$	4.16489	+	17.1679i	0.332394	+	1.37015i	−0.523071	+	0.852289i	$0.675214\pi$
$158$		0			0
$159$	−2.54987	−	2.00524i	−0.202218	−	0.159026i
$160$		0			0
$161$	9.75062	+	8.11945i	0.768456	+	0.639902i
$162$		0			0
$163$	−5.48170	−	4.31086i	−0.429360	−	0.337652i	0.379978	−	0.924995i	$-0.375932\pi$
$163$	−5.48170	−	4.31086i	−0.429360	−	0.337652i	−0.809338	+	0.587343i	$0.800174\pi$
$164$		0			0
$165$	−1.11475	−	4.59505i	−0.0867830	−	0.357724i
$166$		0			0
$167$	−3.33671	+	0.979747i	−0.258202	+	0.0758151i	−0.408272	−	0.912860i	$-0.633868\pi$
$167$	−3.33671	+	0.979747i	−0.258202	+	0.0758151i	0.150069	+	0.988675i	$0.452050\pi$
$168$		0			0
$169$	−2.40664	+	5.26981i	−0.185126	+	0.405370i
$170$		0			0
$171$	−13.8792	−	7.15520i	−1.06137	−	0.547172i
$172$		0			0
$173$	−8.26557	−	3.30903i	−0.628420	−	0.251581i	0.0355183	−	0.999369i	$-0.488692\pi$
$173$	−8.26557	−	3.30903i	−0.628420	−	0.251581i	−0.663938	+	0.747788i	$0.731116\pi$
$174$		0			0
$175$	−0.130503	−	3.86224i	−0.00986510	−	0.291958i
$176$		0			0
$177$	4.19288	−	2.16158i	0.315156	−	0.162474i
$178$		0			0
$179$	6.65138	−	19.2179i	0.497148	−	1.43641i	−0.365596	−	0.930773i	$-0.619135\pi$
$179$	6.65138	−	19.2179i	0.497148	−	1.43641i	0.862744	−	0.505641i	$-0.168744\pi$
$180$		0			0
$181$	3.43918	+	7.53075i	0.255632	+	0.559756i	0.993321	−	0.115385i	$-0.0368101\pi$
$181$	3.43918	+	7.53075i	0.255632	+	0.559756i	−0.737689	+	0.675141i	$0.764083\pi$
$182$		0			0
$183$	4.59381			0.339584
$184$		0			0
$185$	9.21395	+	15.9590i	0.677423	+	1.17333i
$186$		0			0
$187$	21.0399	+	2.00907i	1.53859	+	0.146917i
$188$		0			0
$189$	−4.49691	+	6.13379i	−0.327102	+	0.446168i
$190$		0			0
$191$	8.51532	−	4.38995i	0.616147	−	0.317646i	−0.121748	−	0.992561i	$-0.538850\pi$
$191$	8.51532	−	4.38995i	0.616147	−	0.317646i	0.737895	+	0.674915i	$0.235820\pi$
$192$		0			0
$193$	−8.09147	−	1.55950i	−0.582437	−	0.112255i	−0.110482	−	0.993878i	$-0.535239\pi$
$193$	−8.09147	−	1.55950i	−0.582437	−	0.112255i	−0.471955	+	0.881623i	$0.656452\pi$
$194$		0			0
$195$	0.359330	+	2.49920i	0.0257322	+	0.178971i
$196$		0			0
$197$	−14.2054	+	9.12928i	−1.01210	+	0.650434i	−0.937935	−	0.346812i	$-0.887264\pi$
$197$	−14.2054	+	9.12928i	−1.01210	+	0.650434i	−0.0741608	+	0.997246i	$0.523628\pi$
$198$		0			0
$199$	25.0631	−	2.39323i	1.77667	−	0.169652i	0.845440	−	0.534071i	$-0.179339\pi$
$199$	25.0631	−	2.39323i	1.77667	−	0.169652i	0.931235	+	0.364419i	$0.118732\pi$
$200$		0			0
$201$	−0.766854	+	3.16102i	−0.0540897	+	0.222961i
$202$		0			0
$203$	−0.168470	+	2.73933i	−0.0118243	+	0.192263i
$204$		0			0
$205$	−8.14456	−	6.40495i	−0.568841	−	0.447341i
$206$		0			0
$207$	13.1875	+	0.186606i	0.916597	+	0.0129700i
$208$		0			0
$209$	−4.06238	+	28.2545i	−0.281001	+	1.95440i
$210$		0			0
$211$	−0.939486	−	0.275858i	−0.0646769	−	0.0189908i	0.249234	−	0.968443i	$-0.419821\pi$
$211$	−0.939486	−	0.275858i	−0.0646769	−	0.0189908i	−0.313911	+	0.949452i	$0.601639\pi$
$212$		0			0
$213$	3.55360	+	3.38835i	0.243488	+	0.232166i
$214$		0			0
$215$	−10.6702	−	14.9842i	−0.727699	−	1.02191i
$216$		0			0
$217$	−5.72561	+	22.2540i	−0.388679	+	1.51070i
$218$		0			0
$219$	−0.444912	−	0.178116i	−0.0300644	−	0.0120360i
$220$		0			0
$221$	−11.0823	−	2.13594i	−0.745475	−	0.143679i
$222$		0			0
$223$	−7.22216	−	4.64140i	−0.483632	−	0.310811i	0.276008	−	0.961155i	$-0.410988\pi$
$223$	−7.22216	−	4.64140i	−0.483632	−	0.310811i	−0.759640	+	0.650344i	$0.774625\pi$
$224$		0			0
$225$	−2.63045	−	3.03570i	−0.175363	−	0.202380i
$226$		0			0
$227$	−3.98619	+	5.59782i	−0.264573	+	0.371540i	−0.925396	−	0.379001i	$-0.876268\pi$
$227$	−3.98619	+	5.59782i	−0.264573	+	0.371540i	0.660824	+	0.750541i	$0.270207\pi$
$228$		0			0
$229$	13.6541	−	23.6496i	0.902288	−	1.56281i	0.0777718	−	0.996971i	$-0.475219\pi$
$229$	13.6541	−	23.6496i	0.902288	−	1.56281i	0.824517	−	0.565838i	$-0.191447\pi$
$230$		0			0
$231$	6.35372	+	1.96142i	0.418044	+	0.129052i
$232$		0			0
$233$	−1.48998	−	0.142275i	−0.0976116	−	0.00932078i	0.0461359	−	0.998935i	$-0.485309\pi$
$233$	−1.48998	−	0.142275i	−0.0976116	−	0.00932078i	−0.143748	+	0.989614i	$0.545915\pi$
$234$		0			0
$235$	5.74765	−	16.6067i	0.374935	−	1.08330i
$236$		0			0
$237$	−7.10542	−	4.56638i	−0.461547	−	0.296618i
$238$		0			0
$239$	9.65279	−	11.1399i	0.624387	−	0.720581i	−0.352147	−	0.935945i	$-0.614548\pi$
$239$	9.65279	−	11.1399i	0.624387	−	0.720581i	0.976534	+	0.215363i	$0.0690936\pi$
$240$		0			0
$241$	17.4751	−	13.7425i	1.12567	−	0.885235i	0.131313	−	0.991341i	$-0.458081\pi$
$241$	17.4751	−	13.7425i	1.12567	−	0.885235i	0.994355	+	0.106106i	$0.0338383\pi$
$242$		0			0
$243$	0.572413	+	12.0164i	0.0367203	+	0.770854i
$244$		0			0
$245$	−11.5340	−	6.35577i	−0.736882	−	0.406055i
$246$		0			0
$247$	3.59363	−	14.8132i	0.228657	−	0.942538i
$248$		0			0
$249$	1.34142	+	5.52939i	0.0850088	+	0.350411i
$250$		0			0
$251$	0.730864	−	5.08327i	0.0461317	−	0.320853i	−0.953668	−	0.300860i	$-0.902726\pi$
$251$	0.730864	−	5.08327i	0.0461317	−	0.320853i	0.999800	−	0.0199935i	$-0.00636454\pi$
$252$		0			0
$253$	−7.56243	−	22.8932i	−0.475446	−	1.43928i
$254$		0			0
$255$	3.67096	−	1.46963i	0.229884	−	0.0920318i
$256$		0			0
$257$	−4.92236	+	4.69346i	−0.307048	+	0.292770i	−0.827898	−	0.560878i	$-0.810464\pi$
$257$	−4.92236	+	4.69346i	−0.307048	+	0.292770i	0.520850	+	0.853648i	$0.325615\pi$
$258$		0			0
$259$	−25.9131	−	0.358228i	−1.61016	−	0.0222592i
$260$		0			0
$261$	1.65474	+	2.32375i	0.102426	+	0.143837i
$262$		0			0
$263$	27.2246	+	14.0353i	1.67874	+	0.865452i	0.990102	+	0.140350i	$0.0448227\pi$
$263$	27.2246	+	14.0353i	1.67874	+	0.865452i	0.688641	+	0.725102i	$0.258208\pi$
$264$		0			0
$265$	−1.73726	−	12.0829i	−0.106719	−	0.742249i
$266$		0			0
$267$	1.20162	−	1.38674i	0.0735377	−	0.0848670i
$268$		0			0
$269$	−0.937885	+	19.6886i	−0.0571839	+	1.20044i	0.769828	+	0.638252i	$0.220342\pi$
$269$	−0.937885	+	19.6886i	−0.0571839	+	1.20044i	−0.827012	+	0.562185i	$0.809961\pi$
$270$		0			0
$271$	−21.0512	+	4.05730i	−1.27877	+	0.246463i	−0.783018	−	0.621999i	$-0.786321\pi$
$271$	−21.0512	+	4.05730i	−1.27877	+	0.246463i	−0.495755	+	0.868463i	$0.665108\pi$
$272$		0			0
$273$	−3.27791	−	1.36515i	−0.198388	−	0.0826226i
$274$		0			0
$275$	−3.67147	+	6.35917i	−0.221398	+	0.383473i
$276$		0			0
$277$	−0.821745	−	1.42330i	−0.0493739	−	0.0855181i	0.840282	−	0.542149i	$-0.182389\pi$
$277$	−0.821745	−	1.42330i	−0.0493739	−	0.0855181i	−0.889656	+	0.456631i	$0.849056\pi$
$278$		0			0
$279$	9.92207	+	21.7263i	0.594019	+	1.30072i
$280$		0			0
$281$	3.26852	+	3.77208i	0.194984	+	0.225023i	0.844819	−	0.535051i	$-0.179708\pi$
$281$	3.26852	+	3.77208i	0.194984	+	0.225023i	−0.649836	+	0.760075i	$0.725162\pi$
$282$		0			0
$283$	−1.11162	+	23.3357i	−0.0660787	+	1.38716i	0.685766	+	0.727822i	$0.259467\pi$
$283$	−1.11162	+	23.3357i	−0.0660787	+	1.38716i	−0.751845	+	0.659340i	$0.770836\pi$
$284$		0			0
$285$	1.74668	+	5.04670i	0.103464	+	0.298941i
$286$		0			0
$287$	13.6012	−	5.22814i	0.802853	−	0.308607i
$288$		0			0
$289$	0.0321291	+	0.674472i	0.00188995	+	0.0396748i
$290$		0			0
$291$	−4.44138	+	0.424100i	−0.260358	+	0.0248612i
$292$		0			0
$293$	12.4161	−	3.64570i	0.725357	−	0.212984i	0.101848	−	0.994800i	$-0.467525\pi$
$293$	12.4161	−	3.64570i	0.725357	−	0.212984i	0.623509	+	0.781816i	$0.285706\pi$
$294$		0			0
$295$	17.0327	+	5.00124i	0.991681	+	0.291184i
$296$		0			0
$297$	13.4165	−	5.37114i	0.778502	−	0.311665i
$298$		0			0
$299$	2.85795	+	12.5533i	0.165280	+	0.725976i
$300$		0			0
$301$	25.7838	−	2.10284i	1.48615	−	0.121206i
$302$		0			0
$303$	−1.81204	+	1.72778i	−0.104099	+	0.0992584i
$304$		0			0
$305$	12.5113	+	11.9295i	0.716394	+	0.683080i
$306$		0			0
$307$	5.49680	−	12.0363i	0.313719	−	0.686949i	−0.685432	−	0.728136i	$-0.740387\pi$
$307$	5.49680	−	12.0363i	0.313719	−	0.686949i	0.999151	+	0.0411873i	$0.0131140\pi$
$308$		0			0
$309$	−3.82645	+	2.45911i	−0.217679	+	0.139894i
$310$		0			0
$311$	−8.88663	+	6.98853i	−0.503915	+	0.396283i	−0.837500	−	0.546437i	$-0.815984\pi$
$311$	−8.88663	+	6.98853i	−0.503915	+	0.396283i	0.333585	+	0.942720i	$0.391741\pi$
$312$		0			0
$313$	5.79412	+	16.7410i	0.327503	+	0.946258i	0.981783	+	0.190006i	$0.0608506\pi$
$313$	5.79412	+	16.7410i	0.327503	+	0.946258i	−0.654280	+	0.756253i	$0.727028\pi$
$314$		0			0
$315$	−13.4756	+	2.40452i	−0.759266	+	0.135479i
$316$		0			0
$317$	24.6027	−	4.74179i	1.38183	−	0.266326i	0.556438	−	0.830889i	$-0.312168\pi$
$317$	24.6027	−	4.74179i	1.38183	−	0.266326i	0.825390	+	0.564563i	$0.190955\pi$
$318$		0			0
$319$	3.02494	−	4.24794i	0.169364	−	0.237839i
$320$		0			0
$321$	−9.69471			−0.541106
$322$		0			0
$323$	−23.8716			−1.32825
$324$		0			0
$325$	2.27445	−	3.19401i	0.126164	−	0.177172i
$326$		0			0
$327$	5.47791	−	1.05578i	0.302929	−	0.0583848i
$328$		0			0
$329$	15.9243	+	18.8993i	0.877936	+	1.04195i
$330$		0			0
$331$	1.27831	+	3.69343i	0.0702622	+	0.203009i	0.974665	−	0.223671i	$-0.0718042\pi$
$331$	1.27831	+	3.69343i	0.0702622	+	0.203009i	−0.904403	+	0.426680i	$0.859683\pi$
$332$		0			0
$333$	−21.1742	+	16.6516i	−1.16034	+	0.912501i
$334$		0			0
$335$	−10.2973	+	6.61765i	−0.562599	+	0.361561i
$336$		0			0
$337$	12.7637	−	27.9486i	0.695284	−	1.52246i	−0.150314	−	0.988638i	$-0.548029\pi$
$337$	12.7637	−	27.9486i	0.695284	−	1.52246i	0.845598	−	0.533820i	$-0.179244\pi$
$338$		0			0
$339$	−2.44403	−	2.33038i	−0.132742	−	0.126569i
$340$		0			0
$341$	31.6001	−	30.1306i	1.71124	−	1.63166i
$342$		0			0
$343$	15.9819	−	9.35827i	0.862944	−	0.505299i
$344$		0			0
$345$	−3.22016	−	3.15859i	−0.173367	−	0.170053i
$346$		0			0
$347$	−13.9635	+	5.59015i	−0.749600	+	0.300095i	−0.714828	−	0.699301i	$-0.753495\pi$
$347$	−13.9635	+	5.59015i	−0.749600	+	0.300095i	−0.0347726	+	0.999395i	$0.511071\pi$
$348$		0			0
$349$	−19.9624	−	5.86149i	−1.06856	−	0.313758i	−0.300268	−	0.953855i	$-0.597076\pi$
$349$	−19.9624	−	5.86149i	−1.06856	−	0.313758i	−0.768295	+	0.640096i	$0.778894\pi$
$350$		0			0
$351$	−7.40448	+	2.17415i	−0.395222	+	0.116048i
$352$		0			0
$353$	7.13261	−	0.681082i	0.379631	−	0.0362503i	0.0965033	−	0.995333i	$-0.469234\pi$
$353$	7.13261	−	0.681082i	0.379631	−	0.0362503i	0.283127	+	0.959082i	$0.408628\pi$
$354$		0			0
$355$	0.879187	+	18.4564i	0.0466624	+	0.979564i
$356$		0			0
$357$	−0.867408	+	5.49283i	−0.0459081	+	0.290712i
$358$		0			0
$359$	0.933662	+	2.69764i	0.0492768	+	0.142376i	0.966954	−	0.254951i	$-0.0820592\pi$
$359$	0.933662	+	2.69764i	0.0492768	+	0.142376i	−0.917677	+	0.397327i	$0.869938\pi$
$360$		0			0
$361$	0.629993	−	13.2252i	0.0331575	−	0.696062i
$362$		0			0
$363$	−4.67293	−	5.39285i	−0.245265	−	0.283051i
$364$		0			0
$365$	−0.749181	−	1.64048i	−0.0392139	−	0.0858665i
$366$		0			0
$367$	12.0710	+	20.9076i	0.630101	+	1.09137i	0.987531	+	0.157427i	$0.0503200\pi$
$367$	12.0710	+	20.9076i	0.630101	+	1.09137i	−0.357429	+	0.933940i	$0.616347\pi$
$368$		0			0
$369$	7.57296	−	13.1167i	0.394232	−	0.682830i
$370$		0			0
$371$	15.8478	+	6.60012i	0.822778	+	0.342661i
$372$		0			0
$373$	−8.56739	+	1.65123i	−0.443602	+	0.0854974i	−0.406161	−	0.913801i	$-0.633133\pi$
$373$	−8.56739	+	1.65123i	−0.443602	+	0.0854974i	−0.0374413	+	0.999299i	$0.511921\pi$
$374$		0			0
$375$	−0.289130	+	6.06959i	−0.0149306	+	0.313432i
$376$		0			0
$377$	−1.82360	+	2.10455i	−0.0939204	+	0.108390i
$378$		0			0
$379$	1.68666	+	11.7310i	0.0866381	+	0.602581i	0.986171	+	0.165729i	$0.0529977\pi$
$379$	1.68666	+	11.7310i	0.0866381	+	0.602581i	−0.899533	+	0.436852i	$0.856093\pi$
$380$		0			0
$381$	−1.54163	−	0.794767i	−0.0789803	−	0.0407172i
$382$		0			0
$383$	12.1513	+	17.0641i	0.620904	+	0.871937i	0.998540	−	0.0540169i	$-0.0172025\pi$
$383$	12.1513	+	17.0641i	0.620904	+	0.871937i	−0.377636	+	0.925954i	$0.623263\pi$
$384$		0			0
$385$	12.2109	+	21.8417i	0.622325	+	1.11315i
$386$		0			0
$387$	19.4607	−	18.5558i	0.989245	−	0.943243i
$388$		0			0
$389$	30.5488	−	12.2299i	1.54889	−	0.620080i	0.569484	−	0.822003i	$-0.307143\pi$
$389$	30.5488	−	12.2299i	1.54889	−	0.620080i	0.979401	+	0.201923i	$0.0647189\pi$
$390$		0			0
$391$	18.0502	−	8.98455i	0.912836	−	0.454368i
$392$		0			0
$393$	−0.275195	+	1.91402i	−0.0138817	+	0.0965496i
$394$		0			0
$395$	−7.49344	−	30.8884i	−0.377036	−	1.55416i
$396$		0			0
$397$	0.412126	−	1.69880i	0.0206840	−	0.0852606i	−0.960534	−	0.278162i	$-0.910275\pi$
$397$	0.412126	−	1.69880i	0.0206840	−	0.0852606i	0.981218	+	0.192902i	$0.0617898\pi$
$398$		0			0
$399$	−7.35429	−	1.52315i	−0.368175	−	0.0762528i
$400$		0			0
$401$	0.403317	+	8.46666i	0.0201407	+	0.422805i	0.986311	+	0.164898i	$0.0527296\pi$
$401$	0.403317	+	8.46666i	0.0201407	+	0.422805i	−0.966170	+	0.257907i	$0.916967\pi$
$402$		0			0
$403$	−18.3272	+	14.4127i	−0.912943	+	0.717946i
$404$		0			0
$405$	−8.39371	+	9.68686i	−0.417087	+	0.481344i
$406$		0			0
$407$	41.4258	+	26.6227i	2.05340	+	1.31964i
$408$		0			0
$409$	7.19689	−	20.7940i	0.355863	−	1.02820i	−0.614992	−	0.788533i	$-0.710841\pi$
$409$	7.19689	−	20.7940i	0.355863	−	1.02820i	0.970855	−	0.239666i	$-0.0770380\pi$
$410$		0			0
$411$	−7.86809	−	0.751312i	−0.388104	−	0.0370595i
$412$		0			0
$413$	−18.3042	+	16.9762i	−0.900692	+	0.835346i
$414$		0			0
$415$	−10.7057	+	18.5428i	−0.525522	+	0.910231i
$416$		0			0
$417$	−3.13504	+	4.40255i	−0.153524	+	0.215594i
$418$		0			0
$419$	−22.9525	−	26.4885i	−1.12130	−	1.29405i	−0.951183	−	0.308626i	$-0.900131\pi$
$419$	−22.9525	−	26.4885i	−1.12130	−	1.29405i	−0.170118	−	0.985424i	$-0.554415\pi$
$420$		0			0
$421$	3.66484	+	2.35525i	0.178614	+	0.114788i	0.626893	−	0.779106i	$-0.284327\pi$
$421$	3.66484	+	2.35525i	0.178614	+	0.114788i	−0.448279	+	0.893894i	$0.647963\pi$
$422$		0			0
$423$	25.2239	+	4.86150i	1.22643	+	0.236374i
$424$		0			0
$425$	−5.70087	−	2.28228i	−0.276533	−	0.110707i
$426$		0			0
$427$	−23.4190	+	6.52619i	−1.13332	+	0.315825i
$428$		0			0
$429$	3.91366	+	5.49596i	0.188953	+	0.265347i
$430$		0			0
$431$	4.09654	+	3.90604i	0.197323	+	0.188147i	0.782298	−	0.622904i	$-0.214047\pi$
$431$	4.09654	+	3.90604i	0.197323	+	0.188147i	−0.584975	+	0.811051i	$0.698896\pi$
$432$		0			0
$433$	17.7556	+	5.21351i	0.853279	+	0.250545i	0.678989	−	0.734149i	$-0.262419\pi$
$433$	17.7556	+	5.21351i	0.853279	+	0.250545i	0.174291	+	0.984694i	$0.444237\pi$
$434$		0			0
$435$	0.138849	−	0.965714i	0.00665729	−	0.0463025i
$436$		0			0
$437$	10.9605	+	24.9277i	0.524314	+	1.19245i
$438$		0			0
$439$	−15.9653	−	12.5553i	−0.761983	−	0.599230i	0.159704	−	0.987165i	$-0.448946\pi$
$439$	−15.9653	−	12.5553i	−0.761983	−	0.599230i	−0.921687	+	0.387935i	$0.873189\pi$
$440$		0			0
$441$	6.79668	−	18.0107i	0.323651	−	0.857652i
$442$		0			0
$443$	−4.95066	+	20.4069i	−0.235213	+	0.969561i	0.724656	+	0.689111i	$0.241999\pi$
$443$	−4.95066	+	20.4069i	−0.235213	+	0.969561i	−0.959869	+	0.280450i	$0.909516\pi$
$444$		0			0
$445$	6.87378	−	0.656367i	0.325849	−	0.0311148i
$446$		0			0
$447$	−2.02675	+	1.30251i	−0.0958620	+	0.0616068i
$448$		0			0
$449$	−1.86423	−	12.9660i	−0.0879785	−	0.611904i	−0.985339	−	0.170606i	$-0.945427\pi$
$449$	−1.86423	−	12.9660i	−0.0879785	−	0.611904i	0.897361	−	0.441298i	$-0.145482\pi$
$450$		0			0
$451$	−27.1872	−	5.23990i	−1.28019	−	0.246737i
$452$		0			0
$453$	−4.90739	+	2.52994i	−0.230569	+	0.118867i
$454$		0			0
$455$	−5.38233	−	12.2303i	−0.252328	−	0.573365i
$456$		0			0
$457$	−11.6585	−	1.11326i	−0.545364	−	0.0520759i	−0.181262	−	0.983435i	$-0.558018\pi$
$457$	−11.6585	−	1.11326i	−0.545364	−	0.0520759i	−0.364102	+	0.931359i	$0.618624\pi$
$458$		0			0
$459$	6.04281	+	10.4665i	0.282054	+	0.488532i
$460$		0			0
$461$	32.6873			1.52240			0.761200	−	0.648517i	$-0.224611\pi$
$461$	32.6873			1.52240			0.761200	+	0.648517i	$0.224611\pi$
$462$		0			0
$463$	−5.76985	−	12.6342i	−0.268148	−	0.587161i	0.726880	−	0.686765i	$-0.240970\pi$
$463$	−5.76985	−	12.6342i	−0.268148	−	0.587161i	−0.995027	+	0.0996035i	$0.968243\pi$
$464$		0			0
$465$	2.67173	−	7.71945i	0.123898	−	0.357981i
$466$		0			0
$467$	−13.8691	+	7.15000i	−0.641784	+	0.330862i	−0.748214	−	0.663458i	$-0.769088\pi$
$467$	−13.8691	+	7.15000i	−0.641784	+	0.330862i	0.106430	+	0.994320i	$0.466058\pi$
$468$		0			0
$469$	−0.581318	−	17.2041i	−0.0268428	−	0.794413i
$470$		0			0
$471$	8.19915	+	3.28245i	0.377797	+	0.151247i
$472$		0			0
$473$	−43.6908	−	22.5242i	−2.00891	−	1.03566i
$474$		0			0
$475$	3.44524	−	7.54402i	0.158078	−	0.346143i
$476$		0			0
$477$	17.1213	−	5.02727i	0.783931	−	0.230183i
$478$		0			0
$479$	−1.70839	−	7.04207i	−0.0780583	−	0.321761i	0.919373	−	0.393386i	$-0.128696\pi$
$479$	−1.70839	−	7.04207i	−0.0780583	−	0.321761i	−0.997432	+	0.0716256i	$0.977181\pi$
$480$		0			0
$481$	−20.6695	−	16.2547i	−0.942450	−	0.741151i
$482$		0			0
$483$	6.13411	−	1.61623i	0.279112	−	0.0735409i
$484$		0			0
$485$	−13.1975	−	10.3786i	−0.599266	−	0.471268i
$486$		0			0
$487$	−0.508522	−	2.09616i	−0.0230433	−	0.0949859i	0.959129	−	0.282970i	$-0.0913198\pi$
$487$	−0.508522	−	2.09616i	−0.0230433	−	0.0949859i	−0.982172	+	0.187984i	$0.939805\pi$
$488$		0			0
$489$	−3.34517	+	0.982232i	−0.151274	+	0.0444181i
$490$		0			0
$491$	−5.84248	+	12.7932i	−0.263667	+	0.577351i	−0.994444	−	0.105266i	$-0.966431\pi$
$491$	−5.84248	+	12.7932i	−0.263667	+	0.577351i	0.730777	+	0.682616i	$0.239158\pi$
$492$		0			0
$493$	3.87631	+	1.99838i	0.174580	+	0.0900025i
$494$		0			0
$495$	24.1467	+	9.66689i	1.08531	+	0.434494i
$496$		0			0
$497$	−22.9297	−	12.2252i	−1.02854	−	0.548375i
$498$		0			0
$499$	12.3402	−	6.36180i	0.552422	−	0.284793i	−0.159329	−	0.987226i	$-0.550933\pi$
$499$	12.3402	−	6.36180i	0.552422	−	0.284793i	0.711751	+	0.702432i	$0.247903\pi$
$500$		0			0
$501$	−0.568628	+	1.64294i	−0.0254044	+	0.0734013i
$502$		0			0
$503$	−16.5354	−	36.2074i	−0.737275	−	1.61441i	−0.787985	−	0.615694i	$-0.788876\pi$
$503$	−16.5354	−	36.2074i	−0.737275	−	1.61441i	0.0507101	−	0.998713i	$-0.483852\pi$
$504$		0			0
$505$	−9.42193			−0.419270
$506$		0			0
$507$	1.44815	+	2.50827i	0.0643145	+	0.111396i
$508$		0			0
$509$	−29.4679	−	2.81384i	−1.30614	−	0.124721i	−0.581330	−	0.813668i	$-0.697467\pi$
$509$	−29.4679	−	2.81384i	−1.30614	−	0.124721i	−0.724812	+	0.688947i	$0.758073\pi$
$510$		0			0
$511$	2.52118	+	0.275961i	0.111530	+	0.0122078i
$512$		0			0
$513$	−14.5080	+	7.47937i	−0.640542	+	0.330222i
$514$		0			0
$515$	−16.8074	−	3.23935i	−0.740621	−	0.142743i
$516$		0			0
$517$	−6.68299	−	46.4812i	−0.293918	−	2.04424i
$518$		0			0
$519$	−3.74449	+	2.40644i	−0.164365	+	0.105631i
$520$		0			0
$521$	−1.00734	+	0.0961896i	−0.0441325	+	0.00421414i	−0.117099	−	0.993120i	$-0.537359\pi$
$521$	−1.00734	+	0.0961896i	−0.0441325	+	0.00421414i	0.0729664	+	0.997334i	$0.476753\pi$
$522$		0			0
$523$	−0.301423	+	1.24248i	−0.0131803	+	0.0543300i	−0.978022	−	0.208502i	$-0.933141\pi$
$523$	−0.301423	+	1.24248i	−0.0131803	+	0.0543300i	0.964842	+	0.262832i	$0.0846564\pi$
$524$		0			0
$525$	−1.61068	−	1.06687i	−0.0702960	−	0.0465620i
$526$		0			0
$527$	28.7020	+	22.5715i	1.25028	+	0.983229i
$528$		0			0
$529$	−17.6697	−	14.7235i	−0.768248	−	0.640153i
$530$		0			0
$531$	−3.69293	+	25.6849i	−0.160259	+	1.11463i
$532$		0			0
$533$	14.1860	+	4.16540i	0.614465	+	0.180423i
$534$		0			0
$535$	−26.4036	−	25.1758i	−1.14153	−	1.08845i
$536$		0			0
$537$	−5.89736	−	8.28169i	−0.254490	−	0.357381i
$538$		0			0
$539$	−35.1774	−	0.972784i	−1.51520	−	0.0419008i
$540$		0			0
$541$	27.8710	+	11.1579i	1.19827	+	0.479715i	0.883039	−	0.469300i	$-0.155494\pi$
$541$	27.8710	+	11.1579i	1.19827	+	0.479715i	0.315231	+	0.949015i	$0.397918\pi$
$542$		0			0
$543$	4.06411	+	0.783294i	0.174408	+	0.0336143i
$544$		0			0
$545$	17.6609	+	11.3499i	0.756508	+	0.486178i
$546$		0			0
$547$	−9.25208	−	10.6775i	−0.395590	−	0.456536i	0.522657	−	0.852543i	$-0.324941\pi$
$547$	−9.25208	−	10.6775i	−0.395590	−	0.456536i	−0.918247	+	0.396008i	$0.870395\pi$
$548$		0			0
$549$	−14.6579	+	20.5842i	−0.625585	+	0.878512i
$550$		0			0
$551$	−2.94499	+	5.10087i	−0.125461	+	0.217304i
$552$		0			0
$553$	42.7103	+	13.1848i	1.81623	+	0.560676i
$554$		0			0
$555$	9.17103	+	0.875727i	0.389289	+	0.0371725i
$556$		0			0
$557$	5.56500	−	16.0790i	0.235797	−	0.681290i	−0.763571	−	0.645724i	$-0.776556\pi$
$557$	5.56500	−	16.0790i	0.235797	−	0.681290i	0.999367	−	0.0355656i	$-0.0113233\pi$
$558$		0			0
$559$	22.0816	+	14.1910i	0.933953	+	0.600215i
$560$		0			0
$561$	6.91953	−	7.98557i	0.292143	−	0.337151i
$562$		0			0
$563$	−0.241490	+	0.189910i	−0.0101776	+	0.00800374i	−0.623235	−	0.782035i	$-0.714182\pi$
$563$	−0.241490	+	0.189910i	−0.0101776	+	0.00800374i	0.613057	+	0.790038i	$0.289939\pi$
$564$		0			0
$565$	−0.604672	−	12.6936i	−0.0254387	−	0.534025i
$566$		0			0
$567$	−5.65959	−	17.1141i	−0.237680	−	0.718725i
$568$		0			0
$569$	7.63433	−	31.4691i	0.320048	−	1.31925i	−0.553635	−	0.832759i	$-0.686760\pi$
$569$	7.63433	−	31.4691i	0.320048	−	1.31925i	0.873683	−	0.486496i	$-0.161725\pi$
$570$		0			0
$571$	7.77510	+	32.0494i	0.325378	+	1.34123i	0.866035	+	0.499983i	$0.166661\pi$
$571$	7.77510	+	32.0494i	0.325378	+	1.34123i	−0.540657	+	0.841243i	$0.681824\pi$
$572$		0			0
$573$	0.681622	−	4.74078i	0.0284751	−	0.198049i
$574$		0			0
$575$	0.234275	+	7.00098i	0.00976994	+	0.291961i
$576$		0			0
$577$	−16.0208	+	6.41375i	−0.666953	+	0.267008i	−0.680333	−	0.732903i	$-0.738165\pi$
$577$	−16.0208	+	6.41375i	−0.666953	+	0.267008i	0.0133803	+	0.999910i	$0.495741\pi$
$578$		0			0
$579$	−2.98154	+	2.84289i	−0.123908	+	0.118146i
$580$		0			0
$581$	−14.6938	−	26.2829i	−0.609601	−	1.09040i
$582$		0			0
$583$	−18.9215	−	26.5715i	−0.783647	−	1.10048i
$584$		0			0
$585$	−12.3451	−	6.36434i	−0.510407	−	0.263133i
$586$		0			0
$587$	4.65987	+	32.4101i	0.192333	+	1.33771i	0.825811	+	0.563947i	$0.190718\pi$
$587$	4.65987	+	32.4101i	0.192333	+	1.33771i	−0.633478	+	0.773761i	$0.718373\pi$
$588$		0			0
$589$	−32.2942	+	37.2695i	−1.33066	+	1.53566i
$590$		0			0
$591$	−0.401683	+	8.43235i	−0.0165230	+	0.346861i
$592$		0			0
$593$	−41.5969	+	8.01714i	−1.70818	+	0.329225i	−0.947464	−	0.319861i	$-0.896364\pi$
$593$	−41.5969	+	8.01714i	−1.70818	+	0.329225i	−0.760715	+	0.649086i	$0.775152\pi$
$594$		0			0
$595$	−16.6265	+	12.7072i	−0.681621	+	0.520946i
$596$		0			0
$597$	6.29345	−	10.9006i	0.257574	−	0.446131i
$598$		0			0
$599$	5.72489	+	9.91580i	0.233913	+	0.405148i	0.958956	−	0.283555i	$-0.0915137\pi$
$599$	5.72489	+	9.91580i	0.233913	+	0.405148i	−0.725044	+	0.688703i	$0.758180\pi$
$600$		0			0
$601$	12.7032	+	27.8161i	0.518174	+	1.13464i	0.970126	+	0.242601i	$0.0780007\pi$
$601$	12.7032	+	27.8161i	0.518174	+	1.13464i	−0.451952	+	0.892042i	$0.649272\pi$
$602$		0			0
$603$	−11.7172	−	13.5224i	−0.477161	−	0.550673i
$604$		0			0
$605$	1.27771	−	26.8224i	0.0519463	−	1.09049i
$606$		0			0
$607$	12.8011	+	36.9864i	0.519581	+	1.50123i	0.833901	+	0.551914i	$0.186102\pi$
$607$	12.8011	+	36.9864i	0.519581	+	1.50123i	−0.314320	+	0.949317i	$0.601776\pi$
$608$		0			0
$609$	1.06670	+	0.862987i	0.0432247	+	0.0349700i
$610$		0			0
$611$	1.19316	+	25.0474i	0.0482700	+	1.01331i
$612$		0			0
$613$	3.56166	−	0.340098i	0.143854	−	0.0137364i	−0.0228805	−	0.999738i	$-0.507284\pi$
$613$	3.56166	−	0.340098i	0.143854	−	0.0137364i	0.166735	+	0.986002i	$0.446678\pi$
$614$		0			0
$615$	−4.97017	+	1.45937i	−0.200416	+	0.0588476i
$616$		0			0
$617$	−14.0208	−	4.11688i	−0.564457	−	0.165739i	−0.0129593	−	0.999916i	$-0.504125\pi$
$617$	−14.0208	−	4.11688i	−0.564457	−	0.165739i	−0.551497	+	0.834177i	$0.685943\pi$
$618$		0			0
$619$	−14.3217	+	5.73354i	−0.575637	+	0.230450i	−0.641169	−	0.767400i	$-0.721550\pi$
$619$	−14.3217	+	5.73354i	−0.575637	+	0.230450i	0.0655312	+	0.997851i	$0.479126\pi$
$620$		0			0
$621$	8.15497	−	11.1158i	0.327248	−	0.446061i
$622$		0			0
$623$	−4.15570	+	8.77660i	−0.166495	+	0.351627i
$624$		0			0
$625$	−11.2638	+	10.7400i	−0.450552	+	0.429601i
$626$		0			0
$627$	10.3282	+	9.84788i	0.412467	+	0.393286i
$628$		0			0
$629$	−17.1071	+	37.4594i	−0.682106	+	1.49360i
$630$		0			0
$631$	5.74655	−	3.69308i	0.228766	−	0.147019i	−0.421237	−	0.906951i	$-0.638404\pi$
$631$	5.74655	−	3.69308i	0.228766	−	0.147019i	0.650003	+	0.759931i	$0.274768\pi$
$632$		0			0
$633$	−0.384781	+	0.302595i	−0.0152937	+	0.0120271i
$634$		0			0
$635$	−2.13475	−	6.16796i	−0.0847151	−	0.244768i
$636$		0			0
$637$	18.6500	+	2.30268i	0.738941	+	0.0912357i
$638$		0			0
$639$	−26.5215	+	5.11161i	−1.04918	+	0.202212i
$640$		0			0
$641$	8.94970	−	12.5681i	0.353492	−	0.496410i	−0.599094	−	0.800678i	$-0.704473\pi$
$641$	8.94970	−	12.5681i	0.353492	−	0.496410i	0.952586	+	0.304268i	$0.0984120\pi$
$642$		0			0
$643$	4.07292			0.160620			0.0803101	−	0.996770i	$-0.474409\pi$
$643$	4.07292			0.160620			0.0803101	+	0.996770i	$0.474409\pi$
$644$		0			0
$645$	−9.19632			−0.362105
$646$		0			0
$647$	11.5319	−	16.1942i	0.453364	−	0.636661i	−0.523118	−	0.852261i	$-0.675231\pi$
$647$	11.5319	−	16.1942i	0.453364	−	0.636661i	0.976482	+	0.215599i	$0.0691705\pi$
$648$		0			0
$649$	46.5789	−	8.97735i	1.82838	−	0.352392i
$650$		0			0
$651$	7.40223	+	8.78512i	0.290116	+	0.344316i
$652$		0			0
$653$	−5.48892	−	15.8592i	−0.214798	−	0.620619i	−0.999999	−	0.00137741i	$-0.999562\pi$
$653$	−5.48892	−	15.8592i	−0.214798	−	0.620619i	0.785201	−	0.619241i	$-0.212560\pi$
$654$		0			0
$655$	−5.71995	+	4.49822i	−0.223497	+	0.175760i
$656$		0			0
$657$	2.21774	−	1.42526i	0.0865223	−	0.0556045i
$658$		0			0
$659$	15.3370	−	33.5834i	0.597446	−	1.30822i	−0.333391	−	0.942789i	$-0.608193\pi$
$659$	15.3370	−	33.5834i	0.597446	−	1.30822i	0.930837	−	0.365436i	$-0.119080\pi$
$660$		0			0
$661$	−2.90150	−	2.76657i	−0.112855	−	0.107607i	0.631551	−	0.775335i	$-0.282419\pi$
$661$	−2.90150	−	2.76657i	−0.112855	−	0.107607i	−0.744406	+	0.667727i	$0.767267\pi$
$662$		0			0
$663$	−4.08359	+	3.89369i	−0.158593	+	0.151218i
$664$		0			0
$665$	−16.0741	−	23.2464i	−0.623326	−	0.901456i
$666$		0			0
$667$	0.306997	−	4.96536i	0.0118870	−	0.192259i
$668$		0			0
$669$	−3.98450	+	1.59515i	−0.154050	+	0.0616722i
$670$		0			0
$671$	44.3234	+	13.0145i	1.71108	+	0.502420i
$672$		0			0
$673$	−30.1575	+	8.85503i	−1.16248	+	0.341336i	−0.805398	−	0.592735i	$-0.798048\pi$
$673$	−30.1575	+	8.85503i	−1.16248	+	0.341336i	−0.357087	+	0.934071i	$0.616230\pi$
$674$		0			0
$675$	−4.17978	+	0.399121i	−0.160880	+	0.0153622i
$676$		0			0
$677$	−1.47883	−	31.0445i	−0.0568361	−	1.19314i	−0.829569	−	0.558405i	$-0.811414\pi$
$677$	−1.47883	−	31.0445i	−0.0568361	−	1.19314i	0.772733	−	0.634732i	$-0.218889\pi$
$678$		0			0
$679$	22.0394	−	8.47169i	0.845795	−	0.325114i
$680$		0			0
$681$	1.12367	+	3.24663i	0.0430591	+	0.124411i
$682$		0			0
$683$	0.440181	−	9.24054i	0.0168431	−	0.353579i	−0.974676	−	0.223620i	$-0.928212\pi$
$683$	0.440181	−	9.24054i	0.0168431	−	0.353579i	0.991519	−	0.129959i	$-0.0414846\pi$
$684$		0			0
$685$	−19.4778	−	22.4786i	−0.744208	−	0.858861i
$686$		0			0
$687$	−5.67138	−	12.4186i	−0.216377	−	0.473799i
$688$		0			0
$689$	8.70942	+	15.0852i	0.331802	+	0.574698i
$690$		0			0
$691$	1.78279	−	3.08789i	0.0678206	−	0.117469i	−0.830121	−	0.557583i	$-0.811729\pi$
$691$	1.78279	−	3.08789i	0.0678206	−	0.117469i	0.897942	+	0.440114i	$0.145062\pi$
$692$		0			0
$693$	−29.0623	+	22.2116i	−1.10399	+	0.843750i
$694$		0			0
$695$	−19.9711	+	3.84912i	−0.757548	+	0.146005i
$696$		0			0
$697$	1.10173	−	23.1283i	0.0417312	−	0.876045i
$698$		0			0
$699$	−0.490019	+	0.565512i	−0.0185342	+	0.0213896i
$700$		0			0
$701$	5.59323	+	38.9018i	0.211253	+	1.46930i	0.768979	+	0.639275i	$0.220765\pi$
$701$	5.59323	+	38.9018i	0.211253	+	1.46930i	−0.557725	+	0.830026i	$0.688326\pi$
$702$		0			0
$703$	−49.4347	−	25.4854i	−1.86447	−	0.961199i
$704$		0			0
$705$	−5.09608	−	7.15644i	−0.191929	−	0.269527i
$706$		0			0
$707$	6.78313	−	11.3824i	0.255106	−	0.428080i
$708$		0			0
$709$	−6.58017	+	6.27418i	−0.247124	+	0.235632i	−0.803509	−	0.595292i	$-0.797036\pi$
$709$	−6.58017	+	6.27418i	−0.247124	+	0.235632i	0.556386	+	0.830924i	$0.312188\pi$
$710$		0			0
$711$	43.1333	−	17.2680i	1.61762	−	0.647599i
$712$		0			0
$713$	10.3917	−	40.3354i	0.389172	−	1.51057i
$714$		0			0
$715$	−3.61337	+	25.1315i	−0.135132	+	0.939866i
$716$		0			0
$717$	−1.73734	−	7.16143i	−0.0648823	−	0.267448i
$718$		0			0
$719$	2.51035	−	10.3478i	0.0936203	−	0.385908i	−0.905653	−	0.424019i	$-0.860619\pi$
$719$	2.51035	−	10.3478i	0.0936203	−	0.385908i	0.999274	+	0.0381110i	$0.0121340\pi$
$720$		0			0
$721$	16.0135	−	17.9725i	0.596374	−	0.669330i
$722$		0			0
$723$	−0.528837	−	11.1017i	−0.0196677	−	0.412875i
$724$		0			0
$725$	−1.19098	+	0.936598i	−0.0442319	+	0.0347844i
$726$		0			0
$727$	−21.4500	+	24.7547i	−0.795538	+	0.918100i	−0.998128	−	0.0611641i	$-0.980519\pi$
$727$	−21.4500	+	24.7547i	−0.795538	+	0.918100i	0.202590	+	0.979264i	$0.435064\pi$
$728$		0			0
$729$	−12.1350	−	7.79870i	−0.449445	−	0.288841i
$730$		0			0
$731$	13.4449	−	38.8465i	0.497278	−	1.43679i
$732$		0			0
$733$	10.8454	+	1.03561i	0.400585	+	0.0382512i	0.293405	−	0.955988i	$-0.405212\pi$
$733$	10.8454	+	1.03561i	0.400585	+	0.0382512i	0.107180	+	0.994240i	$0.465818\pi$
$734$		0			0
$735$	−5.93305	+	2.85394i	−0.218844	+	0.105269i
$736$		0			0
$737$	−16.3543	+	28.3266i	−0.602420	+	1.04342i
$738$		0			0
$739$	−2.50922	+	3.52370i	−0.0923030	+	0.129621i	−0.858145	−	0.513407i	$-0.828383\pi$
$739$	−2.50922	+	3.52370i	−0.0923030	+	0.129621i	0.765842	+	0.643029i	$0.222322\pi$
$740$		0			0
$741$	−4.99031	−	5.75913i	−0.183324	−	0.211567i
$742$		0			0
$743$	3.72900	+	2.39649i	0.136804	+	0.0879185i	0.607253	−	0.794509i	$-0.292272\pi$
$743$	3.72900	+	2.39649i	0.136804	+	0.0879185i	−0.470449	+	0.882427i	$0.655908\pi$
$744$		0			0
$745$	−8.90232	−	1.71578i	−0.326156	−	0.0628614i
$746$		0			0
$747$	−29.0566	−	11.6325i	−1.06313	−	0.425611i
$748$		0			0
$749$	49.4231	−	13.7728i	1.80588	−	0.503247i
$750$		0			0
$751$	−9.74905	−	13.6906i	−0.355748	−	0.499578i	0.597458	−	0.801900i	$-0.296178\pi$
$751$	−9.74905	−	13.6906i	−0.355748	−	0.499578i	−0.953206	+	0.302322i	$0.902238\pi$
$752$		0			0
$753$	−1.85814	−	1.77173i	−0.0677145	−	0.0645656i
$754$		0			0
$755$	−19.9352	−	5.85351i	−0.725517	−	0.213031i
$756$		0			0
$757$	0.137328	−	0.955138i	0.00499127	−	0.0347151i	−0.987174	−	0.159650i	$-0.948963\pi$
$757$	0.137328	−	0.955138i	0.00499127	−	0.0347151i	0.992165	+	0.124935i	$0.0398724\pi$
$758$		0			0
$759$	−11.5159	−	3.55912i	−0.418002	−	0.129188i
$760$		0			0
$761$	24.6009	+	19.3464i	0.891782	+	0.701305i	0.954972	−	0.296696i	$-0.0958849\pi$
$761$	24.6009	+	19.3464i	0.891782	+	0.701305i	−0.0631898	+	0.998002i	$0.520127\pi$
$762$		0			0
$763$	−26.4262	+	13.1645i	−0.956693	+	0.476587i
$764$		0			0
$765$	−5.12811	+	21.1383i	−0.185407	+	0.764259i
$766$		0			0
$767$	−25.2158	+	2.40782i	−0.910491	+	0.0869414i
$768$		0			0
$769$	31.8551	−	20.4721i	1.14873	−	0.738241i	0.179341	−	0.983787i	$-0.442603\pi$
$769$	31.8551	−	20.4721i	1.14873	−	0.738241i	0.969385	+	0.245546i	$0.0789671\pi$
$770$		0			0
$771$	0.483902	+	3.36562i	0.0174273	+	0.121210i
$772$		0			0
$773$	−33.9366	−	6.54074i	−1.22061	−	0.235254i	−0.462051	−	0.886854i	$-0.652886\pi$
$773$	−33.9366	−	6.54074i	−1.22061	−	0.235254i	−0.758563	+	0.651599i	$0.774098\pi$
$774$		0			0
$775$	−11.2755	+	5.81294i	−0.405029	+	0.208807i
$776$		0			0
$777$	−7.66045	+	10.4488i	−0.274817	+	0.374850i
$778$		0			0
$779$	31.1301	+	2.97256i	1.11535	+	0.106503i
$780$		0			0
$781$	24.6875	+	42.7601i	0.883389	+	1.53008i
$782$		0			0
$783$	2.98196			0.106566
$784$		0			0
$785$	13.8064	+	30.2318i	0.492772	+	1.07902i
$786$		0			0
$787$	−5.92516	+	17.1196i	−0.211209	+	0.610248i	−0.999990	−	0.00442568i	$-0.998591\pi$
$787$	−5.92516	+	17.1196i	−0.211209	+	0.610248i	0.788781	+	0.614674i	$0.210712\pi$
$788$		0			0
$789$	13.6105	−	7.01672i	0.484548	−	0.249802i
$790$		0			0
$791$	15.7702	+	8.40803i	0.560723	+	0.298955i
$792$		0			0
$793$	−22.9006	−	9.16800i	−0.813223	−	0.325565i
$794$		0			0
$795$	−5.42438	−	2.79646i	−0.192383	−	0.0991804i
$796$		0			0
$797$	1.30252	−	2.85212i	0.0461375	−	0.101027i	−0.885160	−	0.465288i	$-0.845951\pi$
$797$	1.30252	−	2.85212i	0.0461375	−	0.101027i	0.931297	+	0.364260i	$0.118678\pi$
$798$		0			0
$799$	37.6802	−	11.0639i	1.33303	−	0.391413i
$800$		0			0
$801$	2.37966	+	9.80908i	0.0840811	+	0.346587i
$802$		0			0
$803$	−3.78813	−	2.97902i	−0.133680	−	0.105127i
$804$		0			0
$805$	20.9034	+	11.5276i	0.736749	+	0.406295i
$806$		0			0
$807$	7.74592	+	6.09146i	0.272669	+	0.214429i
$808$		0			0
$809$	3.35877	+	13.8451i	0.118088	+	0.486766i	0.999885	+	0.0151374i	$0.00481856\pi$
$809$	3.35877	+	13.8451i	0.118088	+	0.486766i	−0.881797	+	0.471629i	$0.843666\pi$
$810$		0			0
$811$	−14.4155	+	4.23277i	−0.506197	+	0.148633i	−0.524853	−	0.851193i	$-0.675880\pi$
$811$	−14.4155	+	4.23277i	−0.506197	+	0.148633i	0.0186557	+	0.999826i	$0.494061\pi$
$812$		0			0
$813$	−4.45239	+	9.74938i	−0.156152	+	0.341926i
$814$		0			0
$815$	−11.6613	−	6.01184i	−0.408479	−	0.210585i
$816$		0			0
$817$	51.5414	+	20.6341i	1.80320	+	0.721894i
$818$		0			0
$819$	16.5762	−	10.3319i	0.579220	−	0.361027i
$820$		0			0
$821$	−13.9100	+	7.17111i	−0.485463	+	0.250274i	−0.683540	−	0.729913i	$-0.739561\pi$
$821$	−13.9100	+	7.17111i	−0.485463	+	0.250274i	0.198077	+	0.980186i	$0.436530\pi$
$822$		0			0
$823$	−6.39654	+	18.4816i	−0.222969	+	0.644227i	0.776924	+	0.629595i	$0.216779\pi$
$823$	−6.39654	+	18.4816i	−0.222969	+	0.644227i	−0.999893	+	0.0146325i	$0.995342\pi$
$824$		0			0
$825$	1.52499	+	3.33925i	0.0530932	+	0.116258i
$826$		0			0
$827$	−4.65367			−0.161824			−0.0809119	−	0.996721i	$-0.525783\pi$
$827$	−4.65367			−0.161824			−0.0809119	+	0.996721i	$0.525783\pi$
$828$		0			0
$829$	−2.74311	−	4.75120i	−0.0952720	−	0.165016i	0.814450	−	0.580234i	$-0.197039\pi$
$829$	−2.74311	−	4.75120i	−0.0952720	−	0.165016i	−0.909722	+	0.415218i	$0.863705\pi$
$830$		0			0
$831$	−0.817918	−	0.0781017i	−0.0283733	−	0.00270932i
$832$		0			0
$833$	−3.38140	−	29.2344i	−0.117158	−	1.01291i
$834$		0			0
$835$	−5.81516	+	2.99792i	−0.201242	+	0.103747i
$836$		0			0
$837$	24.5157	+	4.72500i	0.847385	+	0.163320i
$838$		0			0
$839$	−0.271822	−	1.89057i	−0.00938435	−	0.0652696i	0.984591	−	0.174872i	$-0.0559513\pi$
$839$	−0.271822	−	1.89057i	−0.00938435	−	0.0652696i	−0.993975	+	0.109603i	$0.965042\pi$
$840$		0			0
$841$	−23.4911	+	15.0968i	−0.810039	+	0.520580i
$842$		0			0
$843$	2.48396	−	0.237190i	0.0855522	−	0.00816924i
$844$		0			0
$845$	−2.56957	+	10.5919i	−0.0883960	+	0.364373i
$846$		0			0
$847$	31.4837	+	20.8539i	1.08179	+	0.716547i
$848$		0			0
$849$	9.18075	+	7.21982i	0.315082	+	0.247784i
$850$		0			0
$851$	46.9713	+	0.664652i	1.61016	+	0.0227840i
$852$		0			0
$853$	1.58334	−	11.0123i	0.0542124	−	0.377056i	−0.944595	−	0.328237i	$-0.893545\pi$
$853$	1.58334	−	11.0123i	0.0542124	−	0.377056i	0.998808	−	0.0488182i	$-0.0155455\pi$
$854$		0			0
$855$	−28.1869	−	8.27641i	−0.963971	−	0.283047i
$856$		0			0
$857$	−8.12947	−	7.75143i	−0.277697	−	0.264784i	0.538412	−	0.842682i	$-0.319025\pi$
$857$	−8.12947	−	7.75143i	−0.277697	−	0.264784i	−0.816109	+	0.577898i	$0.803873\pi$
$858$		0			0
$859$	22.1139	+	31.0546i	0.754516	+	1.05957i	0.996017	+	0.0891687i	$0.0284210\pi$
$859$	22.1139	+	31.0546i	0.754516	+	1.05957i	−0.241501	+	0.970401i	$0.577640\pi$
$860$		0			0
$861$	1.81514	−	7.05499i	0.0618598	−	0.240433i
$862$		0			0
$863$	−10.9590	−	4.38731i	−0.373048	−	0.149346i	0.177560	−	0.984110i	$-0.443180\pi$
$863$	−10.9590	−	4.38731i	−0.373048	−	0.149346i	−0.550608	+	0.834764i	$0.685604\pi$
$864$		0			0
$865$	−16.4474	−	3.16997i	−0.559227	−	0.107782i
$866$		0			0
$867$	0.283986	+	0.182507i	0.00964466	+	0.00619825i
$868$		0			0
$869$	−55.6199	−	64.1888i	−1.88678	−	2.17746i
$870$		0			0
$871$	10.1314	−	14.2275i	0.343289	−	0.482082i
$872$		0			0
$873$	12.2712	−	21.2544i	0.415319	−	0.719353i
$874$		0			0
$875$	−7.14879	−	31.3532i	−0.241673	−	1.05993i
$876$		0			0
$877$	−20.3224	−	1.94056i	−0.686239	−	0.0655279i	−0.253889	−	0.967233i	$-0.581710\pi$
$877$	−20.3224	−	1.94056i	−0.686239	−	0.0655279i	−0.432351	+	0.901706i	$0.642316\pi$
$878$		0			0
$879$	2.11590	−	6.11349i	0.0713675	−	0.206203i
$880$		0			0
$881$	40.3017	+	25.9003i	1.35780	+	0.872604i	0.998169	−	0.0604917i	$-0.0192669\pi$
$881$	40.3017	+	25.9003i	1.35780	+	0.872604i	0.359629	+	0.933095i	$0.382903\pi$
$882$		0			0
$883$	−19.7062	+	22.7421i	−0.663166	+	0.765334i	−0.983291	−	0.182041i	$-0.941730\pi$
$883$	−19.7062	+	22.7421i	−0.663166	+	0.765334i	0.320125	+	0.947375i	$0.396275\pi$
$884$		0			0
$885$	6.97600	−	5.48598i	0.234496	−	0.184409i
$886$		0			0
$887$	1.36219	+	28.5958i	0.0457377	+	0.960154i	0.898804	+	0.438351i	$0.144437\pi$
$887$	1.36219	+	28.5958i	0.0457377	+	0.960154i	−0.853066	+	0.521803i	$0.825260\pi$
$888$		0			0
$889$	8.98825	+	1.86156i	0.301456	+	0.0624347i
$890$		0			0
$891$	−8.07499	+	33.2855i	−0.270522	+	1.11511i
$892$		0			0
$893$	12.5042	+	51.5430i	0.418437	+	1.72482i
$894$		0			0
$895$	5.44487	−	37.8699i	0.182002	−	1.26585i
$896$		0			0
$897$	5.94092	+	2.47648i	0.198361	+	0.0826872i
$898$		0			0
$899$	8.36397	−	3.34843i	0.278954	−	0.111676i
$900$		0			0
$901$	19.7430	−	18.8249i	0.657736	−	0.627150i
$902$		0			0
$903$	6.62071	−	11.1099i	0.220323	−	0.369713i
$904$		0			0
$905$	9.03455	+	12.6872i	0.300319	+	0.421738i
$906$		0			0
$907$	−37.6293	−	19.3993i	−1.24946	−	0.644142i	−0.298783	−	0.954321i	$-0.596581\pi$
$907$	−37.6293	−	19.3993i	−1.24946	−	0.644142i	−0.950678	+	0.310179i	$0.899611\pi$
$908$		0			0
$909$	−1.96006	−	13.6325i	−0.0650111	−	0.452162i
$910$		0			0
$911$	−3.83356	+	4.42416i	−0.127011	+	0.146579i	−0.815693	−	0.578485i	$-0.803644\pi$
$911$	−3.83356	+	4.42416i	−0.127011	+	0.146579i	0.688682	+	0.725064i	$0.258190\pi$
$912$		0			0
$913$	−2.72242	+	57.1507i	−0.0900990	+	1.89141i
$914$		0			0
$915$	8.48625	−	1.63559i	0.280547	−	0.0540710i
$916$		0			0
$917$	−1.31623	−	10.1485i	−0.0434657	−	0.335134i
$918$		0			0
$919$	−13.3684	+	23.1548i	−0.440984	+	0.763806i	−0.997763	−	0.0668544i	$-0.978704\pi$
$919$	−13.3684	+	23.1548i	−0.440984	+	0.763806i	0.556779	+	0.830661i	$0.312037\pi$
$920$		0			0
$921$	−3.30759	−	5.72891i	−0.108989	−	0.188774i
$922$		0			0
$923$	−10.9528	−	23.9833i	−0.360516	−	0.789419i
$924$		0			0
$925$	−9.36913	−	10.8126i	−0.308055	−	0.355515i
$926$		0			0
$927$	1.19053	−	24.9923i	0.0391022	−	0.820856i
$928$		0			0
$929$	6.80855	+	19.6720i	0.223381	+	0.645418i	0.999883	+	0.0153027i	$0.00487120\pi$
$929$	6.80855	+	19.6720i	0.223381	+	0.645418i	−0.776502	+	0.630115i	$0.783008\pi$
$930$		0			0
$931$	39.6556	−	2.68295i	1.29966	−	0.0879300i
$932$		0			0
$933$	0.268931	+	5.64556i	0.00880440	+	0.184827i
$934$		0			0
$935$	39.5828	−	3.77970i	1.29450	−	0.123609i
$936$		0			0
$937$	18.0638	−	5.30402i	0.590119	−	0.173275i	0.0269792	−	0.999636i	$-0.491411\pi$
$937$	18.0638	−	5.30402i	0.590119	−	0.173275i	0.563140	+	0.826361i	$0.309593\pi$
$938$		0			0
$939$	8.49777	+	2.49517i	0.277314	+	0.0814268i
$940$		0			0
$941$	7.06022	−	2.82649i	0.230157	−	0.0921408i	−0.253718	−	0.967278i	$-0.581653\pi$
$941$	7.06022	−	2.82649i	0.230157	−	0.0921408i	0.483874	+	0.875137i	$0.339229\pi$
$942$		0			0
$943$	−24.6573	+	9.46877i	−0.802954	+	0.308345i
$944$		0			0
$945$	−6.12337	+	12.9322i	−0.199193	+	0.420684i
$946$		0			0
$947$	−2.72869	+	2.60180i	−0.0886704	+	0.0845470i	−0.733118	−	0.680101i	$-0.761936\pi$
$947$	−2.72869	+	2.60180i	−0.0886704	+	0.0845470i	0.644448	+	0.764648i	$0.277087\pi$
$948$		0			0
$949$	1.86246	+	1.77585i	0.0604580	+	0.0576466i
$950$		0			0
$951$	5.20354	−	11.3942i	0.168736	−	0.369481i
$952$		0			0
$953$	−7.66192	+	4.92402i	−0.248194	+	0.159505i	−0.658823	−	0.752298i	$-0.728945\pi$
$953$	−7.66192	+	4.92402i	−0.248194	+	0.159505i	0.410629	+	0.911802i	$0.365309\pi$
$954$		0			0
$955$	14.1676	−	11.1415i	0.458451	−	0.360530i
$956$		0			0
$957$	−0.852704	−	2.46373i	−0.0275640	−	0.0796409i
$958$		0			0
$959$	41.1785	−	7.34766i	1.32972	−	0.237268i
$960$		0			0
$961$	43.6289	−	8.40878i	1.40738	−	0.271251i
$962$		0			0
$963$	30.9339	−	43.4406i	0.996832	−	1.39985i
$964$		0			0
$965$	−15.5028			−0.499054
$966$		0			0
$967$	51.7785			1.66508			0.832542	−	0.553962i	$-0.186885\pi$
$967$	51.7785			1.66508			0.832542	+	0.553962i	$0.186885\pi$
$968$		0			0
$969$	−6.92254	+	9.72134i	−0.222384	+	0.312295i
$970$		0			0
$971$	−38.9927	+	7.51523i	−1.25134	+	0.241175i	−0.771526	−	0.636197i	$-0.780506\pi$
$971$	−38.9927	+	7.51523i	−1.25134	+	0.241175i	−0.479810	+	0.877373i	$0.659294\pi$
$972$		0			0
$973$	9.72779	−	26.8978i	0.311859	−	0.862303i
$974$		0			0
$975$	−0.641145	−	1.85247i	−0.0205331	−	0.0593264i
$976$		0			0
$977$	33.4698	−	26.3209i	1.07079	−	0.842081i	0.0827981	−	0.996566i	$-0.473614\pi$
$977$	33.4698	−	26.3209i	1.07079	−	0.842081i	0.987995	+	0.154485i	$0.0493719\pi$
$978$		0			0
$979$	15.5225	−	9.97571i	0.496102	−	0.318825i
$980$		0			0
$981$	−12.7481	+	27.9145i	−0.407017	+	0.891242i
$982$		0			0
$983$	3.17396	+	3.02636i	0.101233	+	0.0965259i	0.739006	−	0.673699i	$-0.235296\pi$
$983$	3.17396	+	3.02636i	0.101233	+	0.0965259i	−0.637772	+	0.770225i	$0.720144\pi$
$984$		0			0
$985$	−22.9916	+	21.9225i	−0.732575	+	0.698509i
$986$		0			0
$987$	12.3144	−	1.00432i	0.391970	−	0.0319678i
$988$		0			0
$989$	−46.7383	+	3.79648i	−1.48619	+	0.120721i
$990$		0			0
$991$	−36.2990	+	14.5319i	−1.15307	+	0.461621i	−0.867844	−	0.496837i	$-0.834495\pi$
$991$	−36.2990	+	14.5319i	−1.15307	+	0.461621i	−0.285231	+	0.958459i	$0.592070\pi$
$992$		0			0
$993$	1.87479	+	0.550488i	0.0594947	+	0.0174692i
$994$		0			0
$995$	45.4476	−	13.3446i	1.44078	−	0.423053i
$996$		0			0
$997$	12.1892	−	1.16393i	0.386035	−	0.0368619i	0.0997655	−	0.995011i	$-0.468191\pi$
$997$	12.1892	−	1.16393i	0.386035	−	0.0368619i	0.286270	+	0.958149i	$0.407585\pi$
$998$		0			0
$999$	1.33980	+	28.1259i	0.0423894	+	0.889864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.y.a.261.9	yes	320
7.4	even	3	inner	644.2.y.a.445.8	yes	320
23.3	even	11	inner	644.2.y.a.233.8	✓	320
161.95	even	33	inner	644.2.y.a.417.9	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.y.a.233.8	✓	320	23.3	even	11	inner
644.2.y.a.261.9	yes	320	1.1	even	1	trivial
644.2.y.a.417.9	yes	320	161.95	even	33	inner
644.2.y.a.445.8	yes	320	7.4	even	3	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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.289991 - 0.407235i) q^{3} +(1.84733 - 0.356043i) q^{5} +(-0.899818 + 2.48804i) q^{7} +(0.899458 + 2.59881i) q^{9} +O(q^{10})\)	\(q+(0.289991 - 0.407235i) q^{3} +(1.84733 - 0.356043i) q^{5} +(-0.899818 + 2.48804i) q^{7} +(0.899458 + 2.59881i) q^{9} +(3.95170 - 3.10765i) q^{11} +(-2.25836 + 1.45136i) q^{13} +(0.390714 - 0.855544i) q^{15} +(3.04272 + 2.90123i) q^{17} +(-4.10939 + 3.91830i) q^{19} +(0.752277 + 1.08794i) q^{21} +(1.63253 - 4.50942i) q^{23} +(-1.35600 + 0.542859i) q^{25} +(2.75821 + 0.809885i) q^{27} +(0.995306 - 0.292248i) q^{29} +(8.64582 - 0.825576i) q^{31} +(-0.119588 - 2.51046i) q^{33} +(-0.776409 + 4.91659i) q^{35} +(3.20369 + 9.25645i) q^{37} +(-0.0638590 + 1.34057i) q^{39} +(-3.60663 - 4.16227i) q^{41} +(-4.06181 - 8.89412i) q^{43} +(2.58688 + 4.48061i) q^{45} +(4.67045 - 8.08946i) q^{47} +(-5.38065 - 4.47756i) q^{49} +(2.06384 - 0.397773i) q^{51} +(0.308741 - 6.48127i) q^{53} +(6.19361 - 7.14781i) q^{55} +(0.403982 + 2.80976i) q^{57} +(8.38685 + 4.32372i) q^{59} +(5.33003 + 7.48498i) q^{61} +(-7.27529 - 0.100575i) q^{63} +(-3.65518 + 3.48521i) q^{65} +(-6.04020 + 2.41813i) q^{67} +(-1.36297 - 1.97251i) q^{69} +(-1.39774 + 9.72149i) q^{71} +(-0.226000 - 0.931586i) q^{73} +(-0.172155 + 0.709633i) q^{75} +(4.17614 + 12.6283i) q^{77} +(-0.803880 - 16.8755i) q^{79} +(-5.35542 + 4.21155i) q^{81} +(-7.45299 + 8.60121i) q^{83} +(6.65385 + 4.27617i) q^{85} +(0.169616 - 0.490073i) q^{87} +(3.65370 + 0.348886i) q^{89} +(-1.57893 - 6.92485i) q^{91} +(2.17100 - 3.76029i) q^{93} +(-6.19630 + 8.70149i) q^{95} +(-5.84419 - 6.74456i) q^{97} +(11.6306 + 7.47452i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9	\( 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9} - 2 q^{11} - 16 q^{15} + 4 q^{17} - 50 q^{21} + 25 q^{23} + 44 q^{25} + 54 q^{27} + 12 q^{29} + 2 q^{31} - 12 q^{33} - 22 q^{35} - 44 q^{37} - 4 q^{39} + 12 q^{41} + 76 q^{43} - 114 q^{45} - 10 q^{47} - 74 q^{49} - 30 q^{51} - 20 q^{53} + 32 q^{55} + 52 q^{57} - 32 q^{59} + 74 q^{61} + 87 q^{63} - 75 q^{65} - 8 q^{67} + 10 q^{69} + 8 q^{73} + 118 q^{75} + 5 q^{77} - 40 q^{79} - 44 q^{81} - 52 q^{83} - 100 q^{85} + 84 q^{87} + 36 q^{89} + 30 q^{91} - 12 q^{93} - 25 q^{95} + 72 q^{97} + 2 q^{99}+O(q^{100}) \) 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9 - 2 * q^11 - 16 * q^15 + 4 * q^17 - 50 * q^21 + 25 * q^23 + 44 * q^25 + 54 * q^27 + 12 * q^29 + 2 * q^31 - 12 * q^33 - 22 * q^35 - 44 * q^37 - 4 * q^39 + 12 * q^41 + 76 * q^43 - 114 * q^45 - 10 * q^47 - 74 * q^49 - 30 * q^51 - 20 * q^53 + 32 * q^55 + 52 * q^57 - 32 * q^59 + 74 * q^61 + 87 * q^63 - 75 * q^65 - 8 * q^67 + 10 * q^69 + 8 * q^73 + 118 * q^75 + 5 * q^77 - 40 * q^79 - 44 * q^81 - 52 * q^83 - 100 * q^85 + 84 * q^87 + 36 * q^89 + 30 * q^91 - 12 * q^93 - 25 * q^95 + 72 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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