LMFDB - Embedded newform 637.2.u.h.30.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (of order $6$, degree $2$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			30.5
Root			$0.759479 - 1.19298i$ of defining polynomial
Character	$\chi$	$=$	637.30
Dual form			637.2.u.h.361.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.20027 - 0.692976i) q^{2} -2.82577 q^{3} +(-0.0395678 + 0.0685334i) q^{4} +(-0.449430 - 0.259479i) q^{5} +(-3.39169 + 1.95819i) q^{6} +2.88158i q^{8} +4.98500 q^{9} -0.719250 q^{10} -1.62416i q^{11} +(0.111810 - 0.193660i) q^{12} +(1.42641 - 3.31140i) q^{13} +(1.26999 + 0.733228i) q^{15} +(1.91773 + 3.32161i) q^{16} +(0.974127 - 1.68724i) q^{17} +(5.98335 - 3.45449i) q^{18} +2.49115i q^{19} +(0.0355659 - 0.0205340i) q^{20} +(-1.12550 - 1.94943i) q^{22} +(-4.57029 - 7.91598i) q^{23} -8.14270i q^{24} +(-2.36534 - 4.09689i) q^{25} +(-0.582637 - 4.96304i) q^{26} -5.60916 q^{27} +(2.61498 - 4.52928i) q^{29} +2.03244 q^{30} +(5.01767 - 2.89695i) q^{31} +(-0.387453 - 0.223696i) q^{32} +4.58951i q^{33} -2.70019i q^{34} +(-0.197245 + 0.341639i) q^{36} +(8.85879 - 5.11463i) q^{37} +(1.72631 + 2.99006i) q^{38} +(-4.03072 + 9.35726i) q^{39} +(0.747709 - 1.29507i) q^{40} +(3.64513 + 2.10452i) q^{41} +(-0.498655 - 0.863697i) q^{43} +(0.111309 + 0.0642644i) q^{44} +(-2.24041 - 1.29350i) q^{45} +(-10.9712 - 6.33421i) q^{46} +(-3.91206 - 2.25863i) q^{47} +(-5.41908 - 9.38612i) q^{48} +(-5.67810 - 3.27825i) q^{50} +(-2.75266 + 4.76775i) q^{51} +(0.170501 + 0.228782i) q^{52} +(4.44825 + 7.70460i) q^{53} +(-6.73251 + 3.88701i) q^{54} +(-0.421434 + 0.729946i) q^{55} -7.03944i q^{57} -7.24847i q^{58} +(5.37392 + 3.10263i) q^{59} +(-0.100501 + 0.0580244i) q^{60} -13.4707 q^{61} +(4.01504 - 6.95426i) q^{62} -8.29100 q^{64} +(-1.50031 + 1.11812i) q^{65} +(3.18042 + 5.50865i) q^{66} +8.37266i q^{67} +(0.0770880 + 0.133520i) q^{68} +(12.9146 + 22.3688i) q^{69} +(-4.50168 + 2.59905i) q^{71} +14.3647i q^{72} +(10.2533 - 5.91976i) q^{73} +(7.08863 - 12.2779i) q^{74} +(6.68392 + 11.5769i) q^{75} +(-0.170727 - 0.0985694i) q^{76} +(1.64640 + 14.0244i) q^{78} +(-0.491155 + 0.850705i) q^{79} -1.99044i q^{80} +0.895217 q^{81} +5.83352 q^{82} -8.91851i q^{83} +(-0.875603 + 0.505530i) q^{85} +(-1.19704 - 0.691113i) q^{86} +(-7.38934 + 12.7987i) q^{87} +4.68015 q^{88} +(10.4087 - 6.00949i) q^{89} -3.58546 q^{90} +0.723345 q^{92} +(-14.1788 + 8.18614i) q^{93} -6.26070 q^{94} +(0.646401 - 1.11960i) q^{95} +(1.09485 + 0.632114i) q^{96} +(3.82981 - 2.21114i) q^{97} -8.09643i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} - 24 q^{10} + 2 q^{12} + 4 q^{13} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} + 24 q^{26} + 12 q^{27} + 8 q^{29}+ \cdots + 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 - 6 * q^5 - 18 * q^6 + 8 * q^9 - 24 * q^10 + 2 * q^12 + 4 * q^13 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^18 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 10 * q^25 + 24 * q^26 + 12 * q^27 + 8 * q^29 - 16 * q^30 + 18 * q^31 - 36 * q^32 - 10 * q^36 + 42 * q^37 - 2 * q^38 - 10 * q^39 - 46 * q^40 + 30 * q^41 + 2 * q^43 + 24 * q^44 - 12 * q^46 + 42 * q^47 - 2 * q^48 - 18 * q^50 - 26 * q^51 + 26 * q^52 + 22 * q^53 - 12 * q^54 - 6 * q^55 - 18 * q^59 + 66 * q^60 - 28 * q^61 - 4 * q^62 - 52 * q^64 - 42 * q^65 + 26 * q^66 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 30 * q^73 + 6 * q^74 + 46 * q^75 - 18 * q^76 - 10 * q^78 + 28 * q^79 - 4 * q^81 - 28 * q^82 - 48 * q^85 - 60 * q^86 - 2 * q^87 + 28 * q^88 + 12 * q^89 + 24 * q^90 + 24 * q^92 + 18 * q^93 - 8 * q^94 - 22 * q^95 + 6 * q^96 + 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.20027	−	0.692976i	0.848719	−	0.490008i	−0.0114993	−	0.999934i	$-0.503660\pi$
$2$	1.20027	−	0.692976i	0.848719	−	0.490008i	0.860218	+	0.509926i	$0.170327\pi$
$3$	−2.82577			−1.63146			−0.815731	−	0.578432i	$-0.803665\pi$
$3$	−2.82577			−1.63146			−0.815731	+	0.578432i	$0.803665\pi$
$4$	−0.0395678	+	0.0685334i	−0.0197839	+	0.0342667i
$5$	−0.449430	−	0.259479i	−0.200991	−	0.116042i	0.396127	−	0.918196i	$-0.370354\pi$
$5$	−0.449430	−	0.259479i	−0.200991	−	0.116042i	−0.597118	+	0.802154i	$0.703687\pi$
$6$	−3.39169	+	1.95819i	−1.38465	+	0.799429i
$7$		0			0
$7$		0			0
$8$			2.88158i			1.01879i
$9$	4.98500			1.66167
$10$	−0.719250			−0.227447
$11$		−	1.62416i		−	0.489702i	−0.969561	−	0.244851i	$-0.921261\pi$
$11$		−	1.62416i		−	0.489702i	0.969561	−	0.244851i	$-0.0787391\pi$
$12$	0.111810	−	0.193660i	0.0322766	−	0.0559048i
$13$	1.42641	−	3.31140i	0.395616	−	0.918416i
$13$	1.42641	−	3.31140i	0.395616	−	0.918416i
$14$		0			0
$15$	1.26999	+	0.733228i	0.327909	+	0.189319i
$16$	1.91773	+	3.32161i	0.479433	+	0.830403i
$17$	0.974127	−	1.68724i	0.236260	−	0.409215i	−0.723378	−	0.690452i	$-0.757411\pi$
$17$	0.974127	−	1.68724i	0.236260	−	0.409215i	0.959638	+	0.281237i	$0.0907448\pi$
$18$	5.98335	−	3.45449i	1.41029	−	0.814230i
$19$			2.49115i			0.571510i	0.958303	+	0.285755i	$0.0922444\pi$
$19$			2.49115i			0.571510i	−0.958303	+	0.285755i	$0.907756\pi$
$20$	0.0355659	−	0.0205340i	0.00795277	−	0.00459154i
$21$		0			0
$22$	−1.12550	−	1.94943i	−0.239958	−	0.415620i
$23$	−4.57029	−	7.91598i	−0.952971	−	1.65059i	−0.738943	−	0.673767i	$-0.764675\pi$
$23$	−4.57029	−	7.91598i	−0.952971	−	1.65059i	−0.214028	−	0.976828i	$-0.568658\pi$
$24$		−	8.14270i		−	1.66212i
$25$	−2.36534	−	4.09689i	−0.473068	−	0.819378i
$26$	−0.582637	−	4.96304i	−0.114265	−	0.973332i
$27$	−5.60916			−1.07948
$28$		0			0
$29$	2.61498	−	4.52928i	0.485589	−	0.841065i	−0.514274	−	0.857626i	$-0.671938\pi$
$29$	2.61498	−	4.52928i	0.485589	−	0.841065i	0.999863	+	0.0165608i	$0.00527172\pi$
$30$	2.03244			0.371071
$31$	5.01767	−	2.89695i	0.901201	−	0.520308i	0.0236111	−	0.999721i	$-0.492484\pi$
$31$	5.01767	−	2.89695i	0.901201	−	0.520308i	0.877590	+	0.479413i	$0.159150\pi$
$32$	−0.387453	−	0.223696i	−0.0684926	−	0.0395442i
$33$			4.58951i			0.798931i
$34$		−	2.70019i		−	0.463078i
$35$		0			0
$36$	−0.197245	+	0.341639i	−0.0328742	+	0.0569398i
$37$	8.85879	−	5.11463i	1.45638	−	0.840840i	0.457546	−	0.889186i	$-0.348728\pi$
$37$	8.85879	−	5.11463i	1.45638	−	0.840840i	0.998831	+	0.0483462i	$0.0153951\pi$
$38$	1.72631	+	2.99006i	0.280045	+	0.485052i
$39$	−4.03072	+	9.35726i	−0.645432	+	1.49836i
$40$	0.747709	−	1.29507i	0.118223	−	0.204769i
$41$	3.64513	+	2.10452i	0.569273	+	0.328670i	0.756859	−	0.653578i	$-0.226733\pi$
$41$	3.64513	+	2.10452i	0.569273	+	0.328670i	−0.187586	+	0.982248i	$0.560066\pi$
$42$		0			0
$43$	−0.498655	−	0.863697i	−0.0760442	−	0.131712i	0.825496	−	0.564408i	$-0.190896\pi$
$43$	−0.498655	−	0.863697i	−0.0760442	−	0.131712i	−0.901540	+	0.432696i	$0.857562\pi$
$44$	0.111309	+	0.0642644i	0.0167805	+	0.00968822i
$45$	−2.24041	−	1.29350i	−0.333980	−	0.192824i
$46$	−10.9712	−	6.33421i	−1.61761	−	0.933928i
$47$	−3.91206	−	2.25863i	−0.570632	−	0.329455i	0.186770	−	0.982404i	$-0.440198\pi$
$47$	−3.91206	−	2.25863i	−0.570632	−	0.329455i	−0.757402	+	0.652949i	$0.773532\pi$
$48$	−5.41908	−	9.38612i	−0.782177	−	1.35477i
$49$		0			0
$50$	−5.67810	−	3.27825i	−0.803004	−	0.463615i
$51$	−2.75266	+	4.76775i	−0.385450	+	0.667618i
$52$	0.170501	+	0.228782i	0.0236443	+	0.0317263i
$53$	4.44825	+	7.70460i	0.611015	+	1.05831i	0.991070	+	0.133344i	$0.0425717\pi$
$53$	4.44825	+	7.70460i	0.611015	+	1.05831i	−0.380055	+	0.924964i	$0.624095\pi$
$54$	−6.73251	+	3.88701i	−0.916178	+	0.528956i
$55$	−0.421434	+	0.729946i	−0.0568262	+	0.0984259i
$56$		0			0
$57$		−	7.03944i		−	0.932397i
$58$		−	7.24847i		−	0.951771i
$59$	5.37392	+	3.10263i	0.699624	+	0.403928i	0.807207	−	0.590268i	$-0.200978\pi$
$59$	5.37392	+	3.10263i	0.699624	+	0.403928i	−0.107583	+	0.994196i	$0.534311\pi$
$60$	−0.100501	+	0.0580244i	−0.0129746	+	0.00749091i
$61$	−13.4707			−1.72475			−0.862375	−	0.506270i	$-0.831024\pi$
$61$	−13.4707			−1.72475			−0.862375	+	0.506270i	$0.831024\pi$
$62$	4.01504	−	6.95426i	0.509911	−	0.883191i
$63$		0			0
$64$	−8.29100			−1.03637
$65$	−1.50031	+	1.11812i	−0.186090	+	0.138685i
$66$	3.18042	+	5.50865i	0.391483	+	0.678068i
$67$			8.37266i			1.02288i	0.859318	+	0.511442i	$0.170888\pi$
$67$			8.37266i			1.02288i	−0.859318	+	0.511442i	$0.829112\pi$
$68$	0.0770880	+	0.133520i	0.00934830	+	0.0161917i
$69$	12.9146	+	22.3688i	1.55474	+	2.69288i
$70$		0			0
$71$	−4.50168	+	2.59905i	−0.534251	+	0.308450i	−0.742746	−	0.669573i	$-0.766477\pi$
$71$	−4.50168	+	2.59905i	−0.534251	+	0.308450i	0.208495	+	0.978023i	$0.433144\pi$
$72$			14.3647i			1.69289i
$73$	10.2533	−	5.91976i	1.20006	−	0.692856i	0.239493	−	0.970898i	$-0.423019\pi$
$73$	10.2533	−	5.91976i	1.20006	−	0.692856i	0.960569	+	0.278042i	$0.0896855\pi$
$74$	7.08863	−	12.2779i	0.824037	−	1.42727i
$75$	6.68392	+	11.5769i	0.771793	+	1.33678i
$76$	−0.170727	−	0.0985694i	−0.0195838	−	0.0113067i
$77$		0			0
$78$	1.64640	+	14.0244i	0.186418	+	1.58795i
$79$	−0.491155	+	0.850705i	−0.0552592	+	0.0957118i	−0.892332	−	0.451380i	$-0.850932\pi$
$79$	−0.491155	+	0.850705i	−0.0552592	+	0.0957118i	0.837073	+	0.547092i	$0.184265\pi$
$80$		−	1.99044i		−	0.222538i
$81$	0.895217			0.0994686
$82$	5.83352			0.644204
$83$		−	8.91851i		−	0.978934i	−0.872022	−	0.489467i	$-0.837191\pi$
$83$		−	8.91851i		−	0.978934i	0.872022	−	0.489467i	$-0.162809\pi$
$84$		0			0
$85$	−0.875603	+	0.505530i	−0.0949725	+	0.0548324i
$86$	−1.19704	−	0.691113i	−0.129080	−	0.0745246i
$87$	−7.38934	+	12.7987i	−0.792220	+	1.37217i
$88$	4.68015			0.498906
$89$	10.4087	−	6.00949i	1.10332	−	0.637005i	0.166233	−	0.986087i	$-0.446840\pi$
$89$	10.4087	−	6.00949i	1.10332	−	0.637005i	0.937092	+	0.349082i	$0.113506\pi$
$90$	−3.58546			−0.377941
$91$		0			0
$92$	0.723345			0.0754139
$93$	−14.1788	+	8.18614i	−1.47027	+	0.848863i
$94$	−6.26070			−0.645742
$95$	0.646401	−	1.11960i	0.0663194	−	0.114869i
$96$	1.09485	+	0.632114i	0.111743	+	0.0645149i
$97$	3.82981	−	2.21114i	0.388858	−	0.224507i	−0.292807	−	0.956172i	$-0.594589\pi$
$97$	3.82981	−	2.21114i	0.388858	−	0.224507i	0.681665	+	0.731664i	$0.261256\pi$
$98$		0			0
$99$		−	8.09643i		−	0.813722i
$100$	0.374365			0.0374365
$101$	−18.3026			−1.82118			−0.910591	−	0.413309i	$-0.864373\pi$
$101$	−18.3026			−1.82118			−0.910591	+	0.413309i	$0.864373\pi$
$102$			7.63012i			0.755494i
$103$	2.51023	−	4.34784i	0.247340	−	0.428406i	−0.715447	−	0.698667i	$-0.753777\pi$
$103$	2.51023	−	4.34784i	0.247340	−	0.428406i	0.962787	+	0.270262i	$0.0871102\pi$
$104$	9.54206	+	4.11033i	0.935676	+	0.403051i
$105$		0			0
$106$	10.6782	+	6.16507i	1.03716	+	0.598804i
$107$	−3.07228	−	5.32134i	−0.297008	−	0.514434i	0.678442	−	0.734654i	$-0.262656\pi$
$107$	−3.07228	−	5.32134i	−0.297008	−	0.514434i	−0.975450	+	0.220221i	$0.929322\pi$
$108$	0.221942	−	0.384415i	0.0213564	−	0.0369903i
$109$	10.3025	−	5.94812i	0.986796	−	0.569727i	0.0824809	−	0.996593i	$-0.473716\pi$
$109$	10.3025	−	5.94812i	0.986796	−	0.569727i	0.904315	+	0.426866i	$0.140382\pi$
$110$			1.16818i			0.111381i
$111$	−25.0330	+	14.4528i	−2.37602	+	1.37180i
$112$		0			0
$113$	−1.77806	−	3.07969i	−0.167266	−	0.289713i	0.770192	−	0.637812i	$-0.220161\pi$
$113$	−1.77806	−	3.07969i	−0.167266	−	0.289713i	−0.937458	+	0.348099i	$0.886827\pi$
$114$	−4.87817	−	8.44923i	−0.456882	−	0.791343i
$115$			4.74357i			0.442340i
$116$	0.206938	+	0.358427i	0.0192137	+	0.0332791i
$117$	7.11067	−	16.5073i	0.657382	−	1.52610i
$118$	8.60020			0.791713
$119$		0			0
$120$	−2.11286	+	3.65957i	−0.192877	+	0.334072i
$121$	8.36211			0.760191
$122$	−16.1685	+	9.33489i	−1.46383	+	0.845141i
$123$	−10.3003	−	5.94689i	−0.928748	−	0.536213i
$124$			0.458504i			0.0411749i
$125$			5.04981i			0.451668i
$126$		0			0
$127$	−0.711749	+	1.23279i	−0.0631575	+	0.109392i	−0.895875	−	0.444306i	$-0.853450\pi$
$127$	−0.711749	+	1.23279i	−0.0631575	+	0.109392i	0.832718	+	0.553698i	$0.186784\pi$
$128$	−9.17653	+	5.29807i	−0.811098	+	0.468288i
$129$	1.40909	+	2.44061i	0.124063	+	0.214884i
$130$	−1.02595	+	2.38172i	−0.0899816	+	0.208891i
$131$	−4.33687	+	7.51168i	−0.378914	+	0.656298i	−0.990905	−	0.134567i	$-0.957036\pi$
$131$	−4.33687	+	7.51168i	−0.378914	+	0.656298i	0.611990	+	0.790865i	$0.290369\pi$
$132$	−0.314535	−	0.181597i	−0.0273767	−	0.0158060i
$133$		0			0
$134$	5.80205	+	10.0495i	0.501221	+	0.868141i
$135$	2.52092	+	1.45546i	0.216967	+	0.125266i
$136$	4.86191	+	2.80703i	0.416906	+	0.240701i
$137$	−7.37667	−	4.25892i	−0.630231	−	0.363864i	0.150611	−	0.988593i	$-0.451876\pi$
$137$	−7.37667	−	4.25892i	−0.630231	−	0.363864i	−0.780842	+	0.624729i	$0.785209\pi$
$138$	31.0020	+	17.8990i	2.63907	+	1.52367i
$139$	2.51922	+	4.36342i	0.213677	+	0.370100i	0.952863	−	0.303402i	$-0.0981225\pi$
$139$	2.51922	+	4.36342i	0.213677	+	0.370100i	−0.739185	+	0.673502i	$0.764789\pi$
$140$		0			0
$141$	11.0546	+	6.38237i	0.930964	+	0.537493i
$142$	−3.60215	+	6.23912i	−0.302286	+	0.523575i
$143$	−5.37824	−	2.31672i	−0.449751	−	0.193734i
$144$	9.55990	+	16.5582i	0.796658	+	1.37985i
$145$	−2.35050	+	1.35706i	−0.195198	+	0.112698i
$146$	8.20451	−	14.2106i	0.679010	−	1.17608i
$147$		0			0
$148$			0.809498i			0.0665403i
$149$			3.36490i			0.275663i	0.990456	+	0.137832i	$0.0440133\pi$
$149$			3.36490i			0.275663i	−0.990456	+	0.137832i	$0.955987\pi$
$150$	16.0450	+	9.26360i	1.31007	+	0.756370i
$151$	−10.9610	+	6.32831i	−0.891990	+	0.514991i	−0.874593	−	0.484858i	$-0.838871\pi$
$151$	−10.9610	+	6.32831i	−0.891990	+	0.514991i	−0.0173971	+	0.999849i	$0.505538\pi$
$152$	−7.17847			−0.582251
$153$	4.85602	−	8.41087i	0.392586	−	0.679979i
$154$		0			0
$155$	−3.00679			−0.241511
$156$	−0.481798	−	0.646485i	−0.0385747	−	0.0517602i
$157$	−5.18457	−	8.97993i	−0.413773	−	0.716677i	0.581525	−	0.813528i	$-0.302456\pi$
$157$	−5.18457	−	8.97993i	−0.413773	−	0.716677i	−0.995299	+	0.0968517i	$0.969123\pi$
$158$			1.36143i			0.108310i
$159$	−12.5698	−	21.7715i	−0.996847	−	1.72659i
$160$	0.116089	+	0.201071i	0.00917761	+	0.0158961i
$161$		0			0
$162$	1.07450	−	0.620364i	0.0844209	−	0.0487404i
$163$			15.7534i			1.23390i	0.787002	+	0.616950i	$0.211632\pi$
$163$			15.7534i			1.23390i	−0.787002	+	0.616950i	$0.788368\pi$
$164$	−0.288459	+	0.166542i	−0.0225249	+	0.0130047i
$165$	1.19088	−	2.06266i	0.0927098	−	0.160578i
$166$	−6.18032	−	10.7046i	−0.479686	−	0.830840i
$167$	−14.2016	−	8.19930i	−1.09895	−	0.634481i	−0.163007	−	0.986625i	$-0.552119\pi$
$167$	−14.2016	−	8.19930i	−1.09895	−	0.634481i	−0.935946	+	0.352144i	$0.885453\pi$
$168$		0			0
$169$	−8.93069	−	9.44684i	−0.686976	−	0.726680i
$170$	−0.700640	+	1.21354i	−0.0537367	+	0.0930746i
$171$			12.4184i			0.949659i
$172$	0.0789227			0.00601780
$173$	0.301355			0.0229116			0.0114558	−	0.999934i	$-0.496353\pi$
$173$	0.301355			0.0229116			0.0114558	+	0.999934i	$0.496353\pi$
$174$			20.4825i			1.55278i
$175$		0			0
$176$	5.39483	−	3.11470i	0.406650	−	0.234780i
$177$	−15.1855	−	8.76734i	−1.14141	−	0.658993i
$178$	8.32887	−	14.4260i	0.624275	−	1.08128i
$179$	9.81582			0.733669			0.366834	−	0.930286i	$-0.380442\pi$
$179$	9.81582			0.733669			0.366834	+	0.930286i	$0.380442\pi$
$180$	0.177296	−	0.102362i	0.0132149	−	0.00762960i
$181$	12.4320			0.924062			0.462031	−	0.886864i	$-0.347121\pi$
$181$	12.4320			0.924062			0.462031	+	0.886864i	$0.347121\pi$
$182$		0			0
$183$	38.0652			2.81386
$184$	22.8105	−	13.1697i	1.68162	−	0.970881i
$185$	−5.30854			−0.390292
$186$	−11.3456	+	19.6512i	−0.831900	+	1.44089i
$187$	−2.74034	−	1.58214i	−0.200394	−	0.115697i
$188$	0.309583	−	0.178738i	0.0225786	−	0.0130358i
$189$		0			0
$190$		−	1.79176i		−	0.129988i
$191$	−12.2469			−0.886156			−0.443078	−	0.896483i	$-0.646114\pi$
$191$	−12.2469			−0.886156			−0.443078	+	0.896483i	$0.646114\pi$
$192$	23.4285			1.69081
$193$			11.6338i			0.837422i	0.908119	+	0.418711i	$0.137518\pi$
$193$			11.6338i			0.837422i	−0.908119	+	0.418711i	$0.862482\pi$
$194$	3.06454	−	5.30794i	0.220021	−	0.381088i
$195$	4.23953	−	3.15955i	0.303599	−	0.226260i
$196$		0			0
$197$	−1.55984	−	0.900572i	−0.111134	−	0.0641631i	0.443403	−	0.896322i	$-0.353771\pi$
$197$	−1.55984	−	0.900572i	−0.111134	−	0.0641631i	−0.554537	+	0.832159i	$0.687104\pi$
$198$	−5.61064	−	9.71791i	−0.398731	−	0.690622i
$199$	3.29657	−	5.70982i	0.233687	−	0.404759i	−0.725203	−	0.688535i	$-0.758254\pi$
$199$	3.29657	−	5.70982i	0.233687	−	0.404759i	0.958890	+	0.283777i	$0.0915874\pi$
$200$	11.8055	−	6.81593i	0.834777	−	0.481959i
$201$		−	23.6592i		−	1.66879i
$202$	−21.9681	+	12.6833i	−1.54567	+	0.892394i
$203$		0			0
$204$	−0.217833	−	0.377298i	−0.0152514	−	0.0264162i
$205$	−1.09215	−	1.89166i	−0.0762793	−	0.132120i
$206$		−	6.95811i		−	0.484795i
$207$	−22.7829	−	39.4611i	−1.58352	−	2.74274i
$208$	13.7347	−	1.61238i	0.952327	−	0.111799i
$209$	4.04603			0.279870
$210$		0			0
$211$	−5.35996	+	9.28373i	−0.368995	+	0.639118i	−0.989409	−	0.145157i	$-0.953631\pi$
$211$	−5.35996	+	9.28373i	−0.368995	+	0.639118i	0.620414	+	0.784275i	$0.286965\pi$
$212$	−0.704030			−0.0483530
$213$	12.7207	−	7.34432i	0.871610	−	0.503224i
$214$	−7.37513	−	4.25803i	−0.504154	−	0.291073i
$215$			0.517562i			0.0352974i
$216$		−	16.1633i		−	1.09977i
$217$		0			0
$218$	8.24382	−	14.2787i	0.558342	−	0.967076i
$219$	−28.9736	+	16.7279i	−1.95785	+	1.13037i
$220$	−0.0333504	−	0.0577647i	−0.00224849	−	0.00389449i
$221$	−4.19760	−	5.63242i	−0.282361	−	0.378877i
$222$	−20.0309	+	34.6945i	−1.34438	+	2.32854i
$223$	−11.1612	−	6.44392i	−0.747409	−	0.431517i	0.0773480	−	0.997004i	$-0.475355\pi$
$223$	−11.1612	−	6.44392i	−0.747409	−	0.431517i	−0.824757	+	0.565487i	$0.808688\pi$
$224$		0			0
$225$	−11.7912	−	20.4230i	−0.786082	−	1.36153i
$226$	−4.26831	−	2.46431i	−0.283924	−	0.163923i
$227$	0.605486	+	0.349577i	0.0401875	+	0.0232023i	0.519959	−	0.854191i	$-0.325947\pi$
$227$	0.605486	+	0.349577i	0.0401875	+	0.0232023i	−0.479772	+	0.877393i	$0.659280\pi$
$228$	0.482437	+	0.278535i	0.0319502	+	0.0184464i
$229$	15.8369	+	9.14342i	1.04653	+	0.604214i	0.921676	−	0.387961i	$-0.126820\pi$
$229$	15.8369	+	9.14342i	1.04653	+	0.604214i	0.124854	+	0.992175i	$0.460154\pi$
$230$	3.28718	+	5.69356i	0.216750	+	0.375422i
$231$		0			0
$232$	13.0515	+	7.53528i	0.856872	+	0.494715i
$233$	13.3898	−	23.1918i	0.877194	−	1.51934i	0.0227864	−	0.999740i	$-0.492746\pi$
$233$	13.3898	−	23.1918i	0.877194	−	1.51934i	0.854407	−	0.519604i	$-0.173920\pi$
$234$	−2.90445	−	24.7408i	−0.189870	−	1.61735i
$235$	1.17213	+	2.03019i	0.0764614	+	0.132435i
$236$	−0.425268	+	0.245528i	−0.0276826	+	0.0159825i
$237$	1.38789	−	2.40390i	0.0901533	−	0.156150i
$238$		0			0
$239$		−	16.6177i		−	1.07491i	−0.843293	−	0.537454i	$-0.819386\pi$
$239$		−	16.6177i		−	1.07491i	0.843293	−	0.537454i	$-0.180614\pi$
$240$			5.62454i			0.363063i
$241$	−15.0800	−	8.70643i	−0.971387	−	0.560830i	−0.0717279	−	0.997424i	$-0.522851\pi$
$241$	−15.0800	−	8.70643i	−0.971387	−	0.560830i	−0.899659	+	0.436594i	$0.856185\pi$
$242$	10.0368	−	5.79474i	0.645189	−	0.372500i
$243$	14.2978			0.917204
$244$	0.533007	−	0.923194i	0.0341222	−	0.0591015i
$245$		0			0
$246$	−16.4842			−1.05099
$247$	8.24920	+	3.55342i	0.524884	+	0.226099i
$248$	8.34782	+	14.4588i	0.530087	+	0.918137i
$249$			25.2017i			1.59709i
$250$	3.49940	+	6.06113i	0.221321	+	0.383340i
$251$	−3.22491	−	5.58571i	−0.203554	−	0.352567i	0.746117	−	0.665815i	$-0.231916\pi$
$251$	−3.22491	−	5.58571i	−0.203554	−	0.352567i	−0.949671	+	0.313249i	$0.898583\pi$
$252$		0			0
$253$	−12.8568	+	7.42288i	−0.808300	+	0.466672i
$254$			1.97290i			0.123791i
$255$	2.47426	−	1.42851i	0.154944	−	0.0894570i
$256$	0.948120	−	1.64219i	0.0592575	−	0.102637i
$257$	−1.83578	−	3.17966i	−0.114513	−	0.198342i	0.803072	−	0.595882i	$-0.203197\pi$
$257$	−1.83578	−	3.17966i	−0.114513	−	0.198342i	−0.917585	+	0.397540i	$0.869864\pi$
$258$	3.38257	+	1.95293i	0.210590	+	0.121584i
$259$		0			0
$260$	−0.0172645	−	0.147063i	−0.00107070	−	0.00912044i
$261$	13.0357	−	22.5784i	0.806887	−	1.39757i
$262$			12.0214i			0.742684i
$263$	18.3193			1.12961			0.564807	−	0.825223i	$-0.308950\pi$
$263$	18.3193			1.12961			0.564807	+	0.825223i	$0.308950\pi$
$264$	−13.2250			−0.813945
$265$		−	4.61690i		−	0.283614i
$266$		0			0
$267$	−29.4128	+	16.9815i	−1.80003	+	1.03925i
$268$	−0.573807	−	0.331287i	−0.0350508	−	0.0202366i
$269$	−13.7715	+	23.8529i	−0.839661	+	1.45434i	0.0505171	+	0.998723i	$0.483913\pi$
$269$	−13.7715	+	23.8529i	−0.839661	+	1.45434i	−0.890178	+	0.455613i	$0.849420\pi$
$270$	4.03439			0.245525
$271$	−5.64582	+	3.25961i	−0.342959	+	0.198007i	−0.661580	−	0.749875i	$-0.730114\pi$
$271$	−5.64582	+	3.25961i	−0.342959	+	0.198007i	0.318621	+	0.947882i	$0.396780\pi$
$272$	7.47246			0.453084
$273$		0			0
$274$	−11.8053			−0.713186
$275$	−6.65401	+	3.84169i	−0.401252	+	0.231663i
$276$	−2.04401			−0.123035
$277$	2.72093	−	4.71279i	0.163485	−	0.283164i	−0.772631	−	0.634855i	$-0.781060\pi$
$277$	2.72093	−	4.71279i	0.163485	−	0.283164i	0.936116	+	0.351691i	$0.114393\pi$
$278$	6.04749	+	3.49152i	0.362704	+	0.209407i
$279$	25.0131	−	14.4413i	1.49749	−	0.864579i
$280$		0			0
$281$		−	3.54237i		−	0.211320i	−0.994402	−	0.105660i	$-0.966304\pi$
$281$		−	3.54237i		−	0.211320i	0.994402	−	0.105660i	$-0.0336955\pi$
$282$	17.6913			1.05350
$283$	14.1391			0.840484			0.420242	−	0.907412i	$-0.361945\pi$
$283$	14.1391			0.840484			0.420242	+	0.907412i	$0.361945\pi$
$284$		−	0.411354i		−	0.0244094i
$285$	−1.82658	+	3.16374i	−0.108197	+	0.187404i
$286$	−8.06077	+	0.946296i	−0.476643	+	0.0559556i
$287$		0			0
$288$	−1.93145	−	1.11512i	−0.113812	−	0.0657093i
$289$	6.60215	+	11.4353i	0.388362	+	0.672663i
$290$	−1.88082	+	3.25768i	−0.110446	+	0.191298i
$291$	−10.8222	+	6.24819i	−0.634407	+	0.366275i
$292$			0.936928i			0.0548295i
$293$	−7.23071	+	4.17465i	−0.422423	+	0.243886i	−0.696113	−	0.717932i	$-0.745089\pi$
$293$	−7.23071	+	4.17465i	−0.422423	+	0.243886i	0.273691	+	0.961818i	$0.411756\pi$
$294$		0			0
$295$	−1.61013	−	2.78883i	−0.0937455	−	0.162372i
$296$	14.7382	+	25.5274i	0.856642	+	1.48375i
$297$			9.11017i			0.528626i
$298$	2.33180	+	4.03879i	0.135077	+	0.233961i
$299$	−32.7321	+	3.84259i	−1.89294	+	0.222223i
$300$	−1.05787			−0.0610762
$301$		0			0
$302$	−8.77074	+	15.1914i	−0.504699	+	0.874165i
$303$	51.7192			2.97119
$304$	−8.27465	+	4.77737i	−0.474584	+	0.274001i
$305$	6.05415	+	3.49536i	0.346659	+	0.200144i
$306$		−	13.4604i		−	0.769481i
$307$			8.33362i			0.475625i	0.971311	+	0.237813i	$0.0764304\pi$
$307$			8.33362i			0.475625i	−0.971311	+	0.237813i	$0.923570\pi$
$308$		0			0
$309$	−7.09334	+	12.2860i	−0.403526	+	0.698927i
$310$	−3.60896	+	2.08363i	−0.204975	+	0.118342i
$311$	−7.31134	−	12.6636i	−0.414588	−	0.718088i	0.580797	−	0.814048i	$-0.302741\pi$
$311$	−7.31134	−	12.6636i	−0.414588	−	0.718088i	−0.995385	+	0.0959606i	$0.969408\pi$
$312$	−26.9637	−	11.6149i	−1.52652	−	0.657562i
$313$	−8.56641	+	14.8375i	−0.484202	+	0.838663i	−0.999835	−	0.0181467i	$-0.994223\pi$
$313$	−8.56641	+	14.8375i	−0.484202	+	0.838663i	0.515633	+	0.856809i	$0.327557\pi$
$314$	−12.4458	−	7.18556i	−0.702355	−	0.405505i
$315$		0			0
$316$	−0.0388678	−	0.0673210i	−0.00218649	−	0.00378710i
$317$	12.1244	+	7.00002i	0.680973	+	0.393160i	0.800222	−	0.599704i	$-0.204715\pi$
$317$	12.1244	+	7.00002i	0.680973	+	0.393160i	−0.119248	+	0.992864i	$0.538048\pi$
$318$	−30.1742	−	17.4211i	−1.69209	−	0.976926i
$319$	−7.35627	−	4.24714i	−0.411872	−	0.237794i
$320$	3.72622	+	2.15134i	0.208302	+	0.120263i
$321$	8.68157	+	15.0369i	0.484558	+	0.839279i
$322$		0			0
$323$	4.20317	+	2.42670i	0.233871	+	0.135025i
$324$	−0.0354217	+	0.0613523i	−0.00196787	+	0.00340846i
$325$	−16.9404	+	1.98872i	−0.939684	+	0.110314i
$326$	10.9167	+	18.9083i	0.604621	+	1.04724i
$327$	−29.1124	+	16.8081i	−1.60992	+	0.929487i
$328$	−6.06434	+	10.5037i	−0.334847	+	0.579972i
$329$		0			0
$330$		−	3.30100i		−	0.181714i
$331$			6.91996i			0.380355i	0.981750	+	0.190178i	$0.0609064\pi$
$331$			6.91996i			0.380355i	−0.981750	+	0.190178i	$0.939094\pi$
$332$	0.611216	+	0.352886i	0.0335448	+	0.0193671i
$333$	44.1611	−	25.4964i	2.42001	−	1.39719i
$334$	−22.7277			−1.24360
$335$	2.17253	−	3.76292i	0.118698	−	0.205591i
$336$		0			0
$337$	11.1559			0.607703			0.303852	−	0.952719i	$-0.401727\pi$
$337$	11.1559			0.607703			0.303852	+	0.952719i	$0.401727\pi$
$338$	−17.2657	−	5.15001i	−0.939129	−	0.280123i
$339$	5.02440	+	8.70251i	0.272888	+	0.472656i
$340$		−	0.0800108i		−	0.00433919i
$341$	−4.70512	−	8.14950i	−0.254796	−	0.441320i
$342$	8.60566	+	14.9054i	0.465341	+	0.805994i
$343$		0			0
$344$	2.48881	−	1.43692i	0.134188	−	0.0774734i
$345$		−	13.4043i		−	0.721661i
$346$	0.361707	−	0.208832i	0.0194455	−	0.0112269i
$347$	2.46255	−	4.26527i	0.132197	−	0.228971i	−0.792326	−	0.610097i	$-0.791130\pi$
$347$	2.46255	−	4.26527i	0.132197	−	0.228971i	0.924523	+	0.381126i	$0.124464\pi$
$348$	−0.584759	−	1.01283i	−0.0313464	−	0.0542935i
$349$	1.31926	+	0.761675i	0.0706183	+	0.0407715i	0.534893	−	0.844920i	$-0.320352\pi$
$349$	1.31926	+	0.761675i	0.0706183	+	0.0407715i	−0.464275	+	0.885691i	$0.653685\pi$
$350$		0			0
$351$	−8.00098	+	18.5741i	−0.427061	+	0.991415i
$352$	−0.363318	+	0.629285i	−0.0193649	+	0.0335410i
$353$		−	17.9280i		−	0.954212i	−0.878846	−	0.477106i	$-0.841686\pi$
$353$		−	17.9280i		−	0.954212i	0.878846	−	0.477106i	$-0.158314\pi$
$354$	−24.3022			−1.29165
$355$	2.69759			0.143173
$356$			0.951129i			0.0504097i
$357$		0			0
$358$	11.7816	−	6.80213i	0.622679	−	0.359504i
$359$	−17.3217	−	10.0007i	−0.914204	−	0.527816i	−0.0324227	−	0.999474i	$-0.510322\pi$
$359$	−17.3217	−	10.0007i	−0.914204	−	0.527816i	−0.881781	+	0.471658i	$0.843656\pi$
$360$	3.72733	−	6.45592i	0.196447	−	0.340257i
$361$	12.7941			0.673376
$362$	14.9217	−	8.61507i	0.784269	−	0.452798i
$363$	−23.6294			−1.24022
$364$		0			0
$365$	−6.14421			−0.321602
$366$	45.6885	−	26.3783i	2.38818	−	1.37882i
$367$	27.4157			1.43109			0.715544	−	0.698568i	$-0.246179\pi$
$367$	27.4157			1.43109			0.715544	+	0.698568i	$0.246179\pi$
$368$	17.5292	−	30.3615i	0.913772	−	1.58270i
$369$	18.1710	+	10.4910i	0.945942	+	0.546140i
$370$	−6.37169	+	3.67870i	−0.331248	+	0.191246i
$371$		0			0
$372$		−	1.29563i		−	0.0671752i
$373$	−15.8929			−0.822901			−0.411451	−	0.911432i	$-0.634978\pi$
$373$	−15.8929			−0.822901			−0.411451	+	0.911432i	$0.634978\pi$
$374$	−4.38553			−0.226771
$375$		−	14.2696i		−	0.736880i
$376$	6.50842	−	11.2729i	0.335646	−	0.581356i
$377$	−11.2682	−	15.1199i	−0.580341	−	0.778712i
$378$		0			0
$379$	7.60284	+	4.38950i	0.390532	+	0.225474i	0.682390	−	0.730988i	$-0.260940\pi$
$379$	7.60284	+	4.38950i	0.390532	+	0.225474i	−0.291859	+	0.956461i	$0.594274\pi$
$380$	0.0511533	+	0.0886001i	0.00262411	+	0.00454509i
$381$	2.01124	−	3.48357i	0.103039	−	0.178469i
$382$	−14.6996	+	8.48682i	−0.752098	+	0.434224i
$383$			7.96237i			0.406858i	0.979090	+	0.203429i	$0.0652086\pi$
$383$			7.96237i			0.406858i	−0.979090	+	0.203429i	$0.934791\pi$
$384$	25.9308	−	14.9712i	1.32328	−	0.763994i
$385$		0			0
$386$	8.06198	+	13.9638i	0.410344	+	0.710736i
$387$	−2.48580	−	4.30553i	−0.126360	−	0.218862i
$388$			0.349960i			0.0177665i
$389$	16.0217	+	27.7504i	0.812333	+	1.40700i	0.911227	+	0.411904i	$0.135136\pi$
$389$	16.0217	+	27.7504i	0.812333	+	1.40700i	−0.0988938	+	0.995098i	$0.531530\pi$
$390$	2.89910	−	6.73021i	0.146801	−	0.340797i
$391$	−17.8082			−0.900598
$392$		0			0
$393$	12.2550	−	21.2263i	0.618184	−	1.07073i
$394$	−2.49630			−0.125762
$395$	0.441479	−	0.254888i	0.0222132	−	0.0128248i
$396$	0.554876	+	0.320358i	0.0278836	+	0.0160986i
$397$			6.43457i			0.322942i	0.986877	+	0.161471i	$0.0516238\pi$
$397$			6.43457i			0.322942i	−0.986877	+	0.161471i	$0.948376\pi$
$398$		−	9.13777i		−	0.458035i
$399$		0			0
$400$	9.07219	−	15.7135i	0.453609	−	0.785675i
$401$	0.462092	−	0.266789i	0.0230758	−	0.0133228i	−0.488418	−	0.872610i	$-0.662426\pi$
$401$	0.462092	−	0.266789i	0.0230758	−	0.0133228i	0.511494	+	0.859287i	$0.329092\pi$
$402$	−16.3953	−	28.3975i	−0.817723	−	1.41634i
$403$	−2.43569	−	20.7478i	−0.121330	−	1.03352i
$404$	0.724195	−	1.25434i	0.0360301	−	0.0624059i
$405$	−0.402337	−	0.232290i	−0.0199923	−	0.0115426i
$406$		0			0
$407$	−8.30697	−	14.3881i	−0.411761	−	0.713191i
$408$	−13.7387	−	7.93202i	−0.680165	−	0.392694i
$409$	34.4269	+	19.8764i	1.70230	+	0.982824i	0.943424	+	0.331590i	$0.107585\pi$
$409$	34.4269	+	19.8764i	1.70230	+	0.982824i	0.758877	+	0.651234i	$0.225748\pi$
$410$	−2.62176	−	1.51367i	−0.129479	−	0.0747550i
$411$	20.8448	+	12.0347i	1.02820	+	0.593630i
$412$	0.198648	+	0.344069i	0.00978670	+	0.0169511i
$413$		0			0
$414$	−54.6913	−	31.5760i	−2.68793	−	1.55188i
$415$	−2.31416	+	4.00825i	−0.113598	+	0.196757i
$416$	−1.29341	+	0.963926i	−0.0634148	+	0.0472604i
$417$	−7.11875	−	12.3300i	−0.348607	−	0.603804i
$418$	4.85633	−	2.80380i	0.237531	−	0.137139i
$419$	−11.9088	+	20.6266i	−0.581783	+	1.00768i	0.413485	+	0.910511i	$0.364311\pi$
$419$	−11.9088	+	20.6266i	−0.581783	+	1.00768i	−0.995268	+	0.0971665i	$0.969022\pi$
$420$		0			0
$421$			23.2419i			1.13274i	0.824151	+	0.566370i	$0.191653\pi$
$421$			23.2419i			1.13274i	−0.824151	+	0.566370i	$0.808347\pi$
$422$			14.8573i			0.723243i
$423$	−19.5016	−	11.2593i	−0.948200	−	0.547444i
$424$	−22.2014	+	12.8180i	−1.07820	+	0.622498i
$425$	−9.21657			−0.447069
$426$	10.1789	−	17.6303i	0.493168	−	0.854192i
$427$		0			0
$428$	0.486253			0.0235039
$429$	15.1977	+	6.54654i	0.733751	+	0.316070i
$430$	0.358658	+	0.621214i	0.0172960	+	0.0299576i
$431$			2.70689i			0.130386i	0.997873	+	0.0651932i	$0.0207664\pi$
$431$			2.70689i			0.130386i	−0.997873	+	0.0651932i	$0.979234\pi$
$432$	−10.7569	−	18.6314i	−0.517540	−	0.896406i
$433$	−2.90945	−	5.03932i	−0.139819	−	0.242174i	0.787609	−	0.616176i	$-0.211319\pi$
$433$	−2.90945	−	5.03932i	−0.139819	−	0.242174i	−0.927428	+	0.374002i	$0.877985\pi$
$434$		0			0
$435$	6.64198	−	3.83475i	0.318459	−	0.183862i
$436$			0.941416i			0.0450856i
$437$	19.7199	−	11.3853i	0.943332	−	0.544633i
$438$	−23.1841	+	40.1560i	−1.10778	+	1.91873i
$439$	19.0851	+	33.0563i	0.910882	+	1.57769i	0.812822	+	0.582513i	$0.197930\pi$
$439$	19.0851	+	33.0563i	0.910882	+	1.57769i	0.0980599	+	0.995181i	$0.468736\pi$
$440$	−2.10340	−	1.21440i	−0.100276	−	0.0578942i
$441$		0			0
$442$	−8.94139	−	3.85158i	−0.425298	−	0.183201i
$443$	15.8370	−	27.4305i	0.752440	−	1.30326i	−0.194198	−	0.980962i	$-0.562210\pi$
$443$	15.8370	−	27.4305i	0.752440	−	1.30326i	0.946637	−	0.322301i	$-0.104456\pi$
$444$		−	2.28746i		−	0.108558i
$445$	−6.23734			−0.295678
$446$	−17.8619			−0.845787
$447$		−	9.50845i		−	0.449734i
$448$		0			0
$449$	27.1975	−	15.7025i	1.28353	−	0.741045i	0.306036	−	0.952020i	$-0.400997\pi$
$449$	27.1975	−	15.7025i	1.28353	−	0.741045i	0.977491	+	0.210975i	$0.0676638\pi$
$450$	−28.3053	−	16.3421i	−1.33433	−	0.770373i
$451$	3.41807	−	5.92027i	0.160951	−	0.278775i
$452$	0.281416			0.0132367
$453$	30.9732	−	17.8824i	1.45525	−	0.840187i
$454$	0.968995			0.0454772
$455$		0			0
$456$	20.2847			0.949920
$457$	−27.5640	+	15.9141i	−1.28939	+	0.744429i	−0.978545	−	0.206032i	$-0.933945\pi$
$457$	−27.5640	+	15.9141i	−1.28939	+	0.744429i	−0.310844	+	0.950461i	$0.600612\pi$
$458$	25.3447			1.18428
$459$	−5.46403	+	9.46398i	−0.255039	+	0.441741i
$460$	−0.325093	−	0.187692i	−0.0151575	−	0.00875121i
$461$	1.01005	−	0.583153i	0.0470427	−	0.0271601i	−0.476294	−	0.879286i	$-0.658020\pi$
$461$	1.01005	−	0.583153i	0.0470427	−	0.0271601i	0.523337	+	0.852126i	$0.324687\pi$
$462$		0			0
$463$		−	20.3441i		−	0.945469i	−0.881205	−	0.472734i	$-0.843267\pi$
$463$		−	20.3441i		−	0.945469i	0.881205	−	0.472734i	$-0.156733\pi$
$464$	20.0593			0.931231
$465$	8.49651			0.394016
$466$		−	37.1152i		−	1.71933i
$467$	−0.784697	+	1.35913i	−0.0363114	+	0.0628932i	−0.883610	−	0.468224i	$-0.844894\pi$
$467$	−0.784697	+	1.35913i	−0.0363114	+	0.0628932i	0.847299	+	0.531117i	$0.178227\pi$
$468$	0.849948	+	1.14048i	0.0392889	+	0.0527185i
$469$		0			0
$470$	2.81375	+	1.62452i	0.129788	+	0.0749334i
$471$	14.6504	+	25.3753i	0.675055	+	1.16923i
$472$	−8.94049	+	15.4854i	−0.411519	+	0.712773i
$473$	−1.40278	+	0.809896i	−0.0644999	+	0.0372391i
$474$		−	3.84711i		−	0.176703i
$475$	10.2060	−	5.89243i	0.468283	−	0.270363i
$476$		0			0
$477$	22.1745	+	38.4074i	1.01530	+	1.75856i
$478$	−11.5157	−	19.9457i	−0.526714	−	0.912295i
$479$		−	7.71918i		−	0.352699i	−0.984328	−	0.176349i	$-0.943571\pi$
$479$		−	7.71918i		−	0.352699i	0.984328	−	0.176349i	$-0.0564288\pi$
$480$	−0.328040	−	0.568182i	−0.0149729	−	0.0259338i
$481$	−4.30025	−	36.6306i	−0.196075	−	1.67021i
$482$	−24.1334			−1.09925
$483$		0			0
$484$	−0.330870	+	0.573083i	−0.0150395	+	0.0260492i
$485$	−2.29498			−0.104209
$486$	17.1612	−	9.90803i	0.778448	−	0.449437i
$487$	0.0659739	+	0.0380900i	0.00298956	+	0.00172602i	0.501494	−	0.865161i	$-0.332784\pi$
$487$	0.0659739	+	0.0380900i	0.00298956	+	0.00172602i	−0.498504	+	0.866887i	$0.666117\pi$
$488$		−	38.8170i		−	1.75716i
$489$		−	44.5155i		−	2.01306i
$490$		0			0
$491$	0.893574	−	1.54772i	0.0403264	−	0.0698474i	−0.845158	−	0.534517i	$-0.820494\pi$
$491$	0.893574	−	1.54772i	0.0403264	−	0.0698474i	0.885484	+	0.464670i	$0.153827\pi$
$492$	0.815121	−	0.470610i	0.0367485	−	0.0212167i
$493$	−5.09464	−	8.82418i	−0.229451	−	0.397421i
$494$	12.3637	−	1.45144i	0.556269	−	0.0653034i
$495$	−2.10085	+	3.63878i	−0.0944262	+	0.163551i
$496$	19.2451	+	11.1112i	0.864131	+	0.498906i
$497$		0			0
$498$	17.4642	+	30.2488i	0.782589	+	1.35548i
$499$	−7.21826	−	4.16747i	−0.323134	−	0.186561i	0.329655	−	0.944102i	$-0.393068\pi$
$499$	−7.21826	−	4.16747i	−0.323134	−	0.186561i	−0.652789	+	0.757540i	$0.726401\pi$
$500$	−0.346080	−	0.199810i	−0.0154772	−	0.00893576i
$501$	40.1305	+	23.1694i	1.79290	+	1.03513i
$502$	−7.74152	−	4.46957i	−0.345521	−	0.199487i
$503$	−0.720238	−	1.24749i	−0.0321138	−	0.0556228i	0.849522	−	0.527554i	$-0.176891\pi$
$503$	−0.720238	−	1.24749i	−0.0321138	−	0.0556228i	−0.881636	+	0.471931i	$0.843557\pi$
$504$		0			0
$505$	8.22576	+	4.74914i	0.366041	+	0.211334i
$506$	−10.2878	+	17.8189i	−0.457347	+	0.792148i
$507$	25.2361	+	26.6946i	1.12077	+	1.18555i
$508$	−0.0563247	−	0.0975572i	−0.00249900	−	0.00432840i
$509$	−12.8394	+	7.41282i	−0.569096	+	0.328568i	−0.756788	−	0.653660i	$-0.773233\pi$
$509$	−12.8394	+	7.41282i	−0.569096	+	0.328568i	0.187692	+	0.982228i	$0.439899\pi$
$510$	1.97985	−	3.42920i	0.0876693	−	0.151848i
$511$		0			0
$512$		−	23.8204i		−	1.05272i
$513$		−	13.9733i		−	0.616935i
$514$	−4.40686	−	2.54430i	−0.194378	−	0.112224i
$515$	−2.25634	+	1.30270i	−0.0994264	+	0.0574038i
$516$	−0.223018			−0.00981781
$517$	−3.66837	+	6.35380i	−0.161335	+	0.279440i
$518$		0			0
$519$	−0.851561			−0.0373794
$520$	−3.22195	−	4.32327i	−0.141292	−	0.189588i
$521$	0.167194	+	0.289588i	0.00732489	+	0.0126871i	0.869665	−	0.493643i	$-0.164335\pi$
$521$	0.167194	+	0.289588i	0.00732489	+	0.0126871i	−0.862340	+	0.506330i	$0.831002\pi$
$522$		−	36.1336i		−	1.58153i
$523$	16.2533	+	28.1515i	0.710705	+	1.23098i	0.964593	+	0.263744i	$0.0849574\pi$
$523$	16.2533	+	28.1515i	0.710705	+	1.23098i	−0.253887	+	0.967234i	$0.581709\pi$
$524$	−0.343201	−	0.594441i	−0.0149928	−	0.0259683i
$525$		0			0
$526$	21.9881	−	12.6948i	0.958726	−	0.553521i
$527$		−	11.2880i		−	0.491713i
$528$	−15.2446	+	8.80145i	−0.663434	+	0.383034i
$529$	−30.2751	+	52.4380i	−1.31631	+	2.27991i
$530$	−3.19941	−	5.54153i	−0.138973	−	0.240709i
$531$	26.7890	+	15.4666i	1.16254	+	0.671194i
$532$		0			0
$533$	12.1683	−	9.06855i	0.527070	−	0.392803i
$534$	−23.5355	+	40.7647i	−1.01848	+	1.76406i
$535$			3.18876i			0.137862i
$536$	−24.1265			−1.04211
$537$	−27.7373			−1.19695
$538$			38.1732i			1.64576i
$539$		0			0
$540$	−0.199495	+	0.115178i	−0.00858488	+	0.00495649i
$541$	9.18120	+	5.30077i	0.394731	+	0.227898i	0.684208	−	0.729287i	$-0.260148\pi$
$541$	9.18120	+	5.30077i	0.394731	+	0.227898i	−0.289477	+	0.957185i	$0.593481\pi$
$542$	−4.51767	+	7.82483i	−0.194051	+	0.336105i
$543$	−35.1300			−1.50757
$544$	−0.754856	+	0.435816i	−0.0323642	+	0.0186855i
$545$	−6.17364			−0.264450
$546$		0			0
$547$	10.2327			0.437519			0.218760	−	0.975779i	$-0.429799\pi$
$547$	10.2327			0.437519			0.218760	+	0.975779i	$0.429799\pi$
$548$	0.583756	−	0.337032i	0.0249368	−	0.0143973i
$549$	−67.1515			−2.86596
$550$	−5.32440	+	9.22214i	−0.227033	+	0.393233i
$551$	11.2831	+	6.51432i	0.480677	+	0.277519i
$552$	−64.4574	+	37.2145i	−2.74349	+	1.58396i
$553$		0			0
$554$		−	7.54216i		−	0.320436i
$555$	15.0007			0.636746
$556$	−0.398720			−0.0169095
$557$		−	31.9930i		−	1.35559i	−0.735253	−	0.677793i	$-0.762937\pi$
$557$		−	31.9930i		−	1.35559i	0.735253	−	0.677793i	$-0.237063\pi$
$558$	20.0150	−	34.6670i	0.847302	−	1.46757i
$559$	−3.57133	+	0.419257i	−0.151051	+	0.0177327i
$560$		0			0
$561$	7.74359	+	4.47076i	0.326934	+	0.188756i
$562$	−2.45478	−	4.25180i	−0.103549	−	0.179351i
$563$	5.39566	−	9.34556i	0.227400	−	0.393868i	−0.729637	−	0.683835i	$-0.760311\pi$
$563$	5.39566	−	9.34556i	0.227400	−	0.393868i	0.957037	+	0.289967i	$0.0936442\pi$
$564$	−0.874811	+	0.505072i	−0.0368362	+	0.0212674i
$565$			1.84547i			0.0776397i
$566$	16.9708	−	9.79808i	0.713335	−	0.411844i
$567$		0			0
$568$	−7.48937	−	12.9720i	−0.314247	−	0.544292i
$569$	−12.3007	−	21.3054i	−0.515672	−	0.893170i	−0.999835	−	0.0181917i	$-0.994209\pi$
$569$	−12.3007	−	21.3054i	−0.515672	−	0.893170i	0.484163	−	0.874978i	$-0.339124\pi$
$570$			5.06312i			0.212071i
$571$	8.28621	+	14.3521i	0.346767	+	0.600618i	0.985673	−	0.168667i	$-0.0539461\pi$
$571$	8.28621	+	14.3521i	0.346767	+	0.600618i	−0.638906	+	0.769285i	$0.720613\pi$
$572$	0.371578	−	0.276921i	0.0155364	−	0.0115787i
$573$	34.6070			1.44573
$574$		0			0
$575$	−21.6206	+	37.4480i	−0.901641	+	1.56169i
$576$	−41.3306			−1.72211
$577$	12.6969	−	7.33053i	0.528577	−	0.305174i	−0.211860	−	0.977300i	$-0.567952\pi$
$577$	12.6969	−	7.33053i	0.528577	−	0.305174i	0.740437	+	0.672126i	$0.234619\pi$
$578$	15.8487	+	9.15027i	0.659221	+	0.380601i
$579$		−	32.8746i		−	1.36622i
$580$		−	0.214784i		−	0.00891840i
$581$		0			0
$582$	−8.65969	+	14.9990i	−0.358956	+	0.621730i
$583$	12.5135	−	7.22467i	0.518256	−	0.299215i
$584$	17.0583	+	29.5458i	0.705877	+	1.22262i
$585$	−7.47904	+	5.57381i	−0.309220	+	0.230449i
$586$	−5.78587	+	10.0214i	−0.239012	+	0.413981i
$587$	30.5998	+	17.6668i	1.26299	+	0.729186i	0.973652	−	0.228041i	$-0.0732320\pi$
$587$	30.5998	+	17.6668i	1.26299	+	0.729186i	0.289336	+	0.957227i	$0.406565\pi$
$588$		0			0
$589$	7.21676	+	12.4998i	0.297362	+	0.515045i
$590$	−3.86519	−	2.23157i	−0.159127	−	0.0918722i
$591$	4.40775	+	2.54481i	0.181310	+	0.104680i
$592$	33.9776	+	19.6170i	1.39647	+	0.806253i
$593$	14.2283	+	8.21471i	0.584286	+	0.337338i	0.762835	−	0.646593i	$-0.223807\pi$
$593$	14.2283	+	8.21471i	0.584286	+	0.337338i	−0.178549	+	0.983931i	$0.557140\pi$
$594$	6.31313	+	10.9347i	0.259031	+	0.448655i
$595$		0			0
$596$	−0.230608	−	0.133142i	−0.00944608	−	0.00545370i
$597$	−9.31535	+	16.1347i	−0.381252	+	0.660348i
$598$	−36.6245	+	27.2947i	−1.49769	+	1.11616i
$599$	−6.04094	−	10.4632i	−0.246826	−	0.427516i	0.715817	−	0.698288i	$-0.246054\pi$
$599$	−6.04094	−	10.4632i	−0.246826	−	0.427516i	−0.962644	+	0.270772i	$0.912721\pi$
$600$	−33.3598	+	19.2603i	−1.36191	+	0.786297i
$601$	−3.90743	+	6.76787i	−0.159387	+	0.276067i	−0.934648	−	0.355574i	$-0.884285\pi$
$601$	−3.90743	+	6.76787i	−0.159387	+	0.276067i	0.775261	+	0.631642i	$0.217619\pi$
$602$		0			0
$603$			41.7377i			1.69969i
$604$		−	1.00159i		−	0.0407541i
$605$	−3.75818	−	2.16979i	−0.152792	−	0.0882144i
$606$	62.0770	−	35.8401i	2.52170	−	1.45591i
$607$	35.5649			1.44354			0.721768	−	0.692135i	$-0.243330\pi$
$607$	35.5649			1.44354			0.721768	+	0.692135i	$0.243330\pi$
$608$	0.557261	−	0.965205i	0.0225999	−	0.0391442i
$609$		0			0
$610$	9.68882			0.392289
$611$	−13.0594	+	9.73263i	−0.528328	+	0.393740i
$612$	0.384284	+	0.665599i	0.0155338	+	0.0269052i
$613$			11.9368i			0.482122i	0.970510	+	0.241061i	$0.0774954\pi$
$613$			11.9368i			0.482122i	−0.970510	+	0.241061i	$0.922505\pi$
$614$	5.77500	+	10.0026i	0.233060	+	0.403672i
$615$	3.08618	+	5.34542i	0.124447	+	0.215548i
$616$		0			0
$617$	−20.4124	+	11.7851i	−0.821772	+	0.474450i	−0.851027	−	0.525122i	$-0.824020\pi$
$617$	−20.4124	+	11.7851i	−0.821772	+	0.474450i	0.0292550	+	0.999572i	$0.490687\pi$
$618$			19.6621i			0.790924i
$619$	−24.7312	+	14.2786i	−0.994031	+	0.573904i	−0.906477	−	0.422256i	$-0.861238\pi$
$619$	−24.7312	+	14.2786i	−0.994031	+	0.573904i	−0.0875541	+	0.996160i	$0.527905\pi$
$620$	0.118972	−	0.206066i	0.00477803	−	0.00827579i
$621$	25.6355	+	44.4020i	1.02872	+	1.78179i
$622$	−17.5512	−	10.1332i	−0.703738	−	0.406303i
$623$		0			0
$624$	−38.8110	+	4.55623i	−1.55368	+	0.182395i
$625$	−10.5164	+	18.2149i	−0.420656	+	0.728597i
$626$			23.7453i			0.949052i
$627$	−11.4332			−0.456597
$628$	0.820567			0.0327442
$629$		−	19.9292i		−	0.794628i
$630$		0			0
$631$	−38.9646	+	22.4962i	−1.55116	+	0.895561i	−0.553109	+	0.833109i	$0.686559\pi$
$631$	−38.9646	+	22.4962i	−1.55116	+	0.895561i	−0.998048	+	0.0624526i	$0.980108\pi$
$632$	−2.45138	−	1.41530i	−0.0975106	−	0.0562978i
$633$	15.1460	−	26.2337i	0.602001	−	1.04270i
$634$	19.4034			0.770607
$635$	0.639763	−	0.369367i	0.0253882	−	0.0146579i
$636$	1.98943			0.0788860
$637$		0			0
$638$	−11.7727			−0.466085
$639$	−22.4409	+	12.9562i	−0.887747	+	0.512541i
$640$	5.49894			0.217365
$641$	−1.26650	+	2.19364i	−0.0500238	+	0.0866437i	−0.889953	−	0.456052i	$-0.849263\pi$
$641$	−1.26650	+	2.19364i	−0.0500238	+	0.0866437i	0.839929	+	0.542696i	$0.182596\pi$
$642$	20.8405	+	12.0322i	0.822507	+	0.474875i
$643$	15.9150	−	9.18853i	0.627627	−	0.362360i	−0.152206	−	0.988349i	$-0.548638\pi$
$643$	15.9150	−	9.18853i	0.627627	−	0.362360i	0.779832	+	0.625988i	$0.215304\pi$
$644$		0			0
$645$		−	1.46251i		−	0.0575863i
$646$	6.72658			0.264654
$647$	−20.9287			−0.822791			−0.411396	−	0.911457i	$-0.634959\pi$
$647$	−20.9287			−0.822791			−0.411396	+	0.911457i	$0.634959\pi$
$648$			2.57964i			0.101338i
$649$	5.03917	−	8.72810i	0.197805	−	0.342608i
$650$	−18.9549	+	14.1263i	−0.743473	+	0.554079i
$651$		0			0
$652$	−1.07963	−	0.623326i	−0.0422817	−	0.0244113i
$653$	24.0580	+	41.6696i	0.941461	+	1.63066i	0.762686	+	0.646769i	$0.223880\pi$
$653$	24.0580	+	41.6696i	0.941461	+	1.63066i	0.178775	+	0.983890i	$0.442786\pi$
$654$	−23.2952	+	40.3484i	−0.910913	+	1.57775i
$655$	3.89824	−	2.25065i	0.152317	−	0.0879401i
$656$			16.1436i			0.630302i
$657$	51.1129	−	29.5100i	1.99410	−	1.15130i
$658$		0			0
$659$	1.10819	+	1.91944i	0.0431690	+	0.0747708i	0.886803	−	0.462148i	$-0.152921\pi$
$659$	1.10819	+	1.91944i	0.0431690	+	0.0747708i	−0.843634	+	0.536919i	$0.819588\pi$
$660$	0.0942408	+	0.163230i	0.00366832	+	0.00635371i
$661$			0.637434i			0.0247933i	0.999923	+	0.0123966i	$0.00394608\pi$
$661$			0.637434i			0.0247933i	−0.999923	+	0.0123966i	$0.996054\pi$
$662$	4.79537	+	8.30582i	0.186377	+	0.322815i
$663$	11.8615	+	15.9159i	0.460661	+	0.618124i
$664$	25.6994			0.997331
$665$		0			0
$666$	35.3368	−	61.2052i	1.36927	−	2.37165i
$667$	−47.8048			−1.85101
$668$	1.12385	−	0.648856i	0.0434831	−	0.0251050i
$669$	31.5390	+	18.2091i	1.21937	+	0.704003i
$670$		−	6.02203i		−	0.232651i
$671$			21.8786i			0.844614i
$672$		0			0
$673$	7.70343	−	13.3427i	0.296945	−	0.514324i	−0.678490	−	0.734609i	$-0.737365\pi$
$673$	7.70343	−	13.3427i	0.296945	−	0.514324i	0.975436	+	0.220285i	$0.0706988\pi$
$674$	13.3901	−	7.73081i	0.515769	−	0.297780i
$675$	13.2676	+	22.9801i	0.510669	+	0.884505i
$676$	1.00079	−	0.238260i	0.0384920	−	0.00916384i
$677$	5.84060	−	10.1162i	0.224473	−	0.388798i	−0.731689	−	0.681639i	$-0.761267\pi$
$677$	5.84060	−	10.1162i	0.224473	−	0.388798i	0.956161	+	0.292841i	$0.0946008\pi$
$678$	12.0613	+	6.96358i	0.463210	+	0.267435i
$679$		0			0
$680$	−1.45673	−	2.52312i	−0.0558629	−	0.0967574i
$681$	−1.71097	−	0.987826i	−0.0655643	−	0.0378536i
$682$	−11.2948	−	6.52107i	−0.432501	−	0.249705i
$683$	−19.8419	−	11.4557i	−0.759227	−	0.438340i	0.0697909	−	0.997562i	$-0.477767\pi$
$683$	−19.8419	−	11.4557i	−0.759227	−	0.438340i	−0.829018	+	0.559221i	$0.811100\pi$
$684$	−0.851075	−	0.491369i	−0.0325417	−	0.0187879i
$685$	2.21020	+	3.82817i	0.0844473	+	0.146267i
$686$		0			0
$687$	−44.7514	−	25.8372i	−1.70737	−	0.985752i
$688$	1.91258	−	3.31268i	0.0729163	−	0.126295i
$689$	31.8580	−	3.73998i	1.21369	−	0.142482i
$690$	−9.28883	−	16.0887i	−0.353620	−	0.612487i
$691$	40.9046	−	23.6163i	1.55608	−	0.898405i	0.558458	−	0.829533i	$-0.311393\pi$
$691$	40.9046	−	23.6163i	1.55608	−	0.898405i	0.997625	−	0.0688729i	$-0.0219403\pi$
$692$	−0.0119239	+	0.0206529i	−0.000453280	+	0.000785104i
$693$		0			0
$694$		−	6.82596i		−	0.259110i
$695$		−	2.61473i		−	0.0991825i
$696$	−36.8805	−	21.2930i	−1.39795	−	0.807109i
$697$	7.10163	−	4.10013i	0.268994	−	0.155303i
$698$	2.11129			0.0799135
$699$	−37.8365	+	65.5347i	−1.43111	+	2.47875i
$700$		0			0
$701$	12.2098			0.461158			0.230579	−	0.973054i	$-0.425938\pi$
$701$	12.2098			0.461158			0.230579	+	0.973054i	$0.425938\pi$
$702$	3.26810	+	27.8385i	0.123347	+	1.05070i
$703$	12.7413	+	22.0686i	0.480548	+	0.832334i
$704$			13.4659i			0.507515i
$705$	−3.31218	−	5.73686i	−0.124744	−	0.216063i
$706$	−12.4237	−	21.5185i	−0.467572	−	0.809858i
$707$		0			0
$708$	1.20171	−	0.693808i	0.0451630	−	0.0260749i
$709$		−	17.8875i		−	0.671778i	−0.941902	−	0.335889i	$-0.890963\pi$
$709$		−	17.8875i		−	0.671778i	0.941902	−	0.335889i	$-0.109037\pi$
$710$	3.23783	−	1.86936i	0.121514	−	0.0701560i
$711$	−2.44841	+	4.24076i	−0.0918224	+	0.159041i
$712$	17.3169	+	29.9937i	0.648977	+	1.12406i
$713$	−45.8644	−	26.4798i	−1.71764	−	0.991678i
$714$		0			0
$715$	1.81600	+	2.43674i	0.0679146	+	0.0911290i
$716$	−0.388390	+	0.672711i	−0.0145148	+	0.0251404i
$717$			46.9578i			1.75367i
$718$	−27.7210			−1.03454
$719$	−9.12634			−0.340355			−0.170178	−	0.985413i	$-0.554434\pi$
$719$	−9.12634			−0.340355			−0.170178	+	0.985413i	$0.554434\pi$
$720$		−	9.92235i		−	0.369784i
$721$		0			0
$722$	15.3564	−	8.86604i	0.571507	−	0.329960i
$723$	42.6126	+	24.6024i	1.58478	+	0.914973i
$724$	−0.491906	+	0.852006i	−0.0182815	+	0.0316646i
$725$	−24.7413			−0.918868
$726$	−28.3617	+	16.3746i	−1.05260	+	0.607719i
$727$	33.6859			1.24934			0.624670	−	0.780889i	$-0.285233\pi$
$727$	33.6859			1.24934			0.624670	+	0.780889i	$0.285233\pi$
$728$		0			0
$729$	−43.0880			−1.59585
$730$	−7.37471	+	4.25779i	−0.272950	+	0.157588i
$731$	−1.94301			−0.0718650
$732$	−1.50616	+	2.60874i	−0.0556691	+	0.0964218i
$733$	−40.2134	−	23.2172i	−1.48532	−	0.857547i	−0.485455	−	0.874262i	$-0.661346\pi$
$733$	−40.2134	−	23.2172i	−1.48532	−	0.857547i	−0.999860	+	0.0167147i	$0.994679\pi$
$734$	32.9062	−	18.9984i	1.21459	−	0.701245i
$735$		0			0
$736$			4.08942i			0.150738i
$737$	13.5985			0.500908
$738$	29.0801			1.07045
$739$			1.85025i			0.0680627i	0.999421	+	0.0340314i	$0.0108346\pi$
$739$			1.85025i			0.0680627i	−0.999421	+	0.0340314i	$0.989165\pi$
$740$	0.210047	−	0.363813i	0.00772149	−	0.0133740i
$741$	−23.3104	−	10.0412i	−0.856328	−	0.368871i
$742$		0			0
$743$	28.7095	+	16.5755i	1.05325	+	0.608094i	0.923558	−	0.383460i	$-0.125268\pi$
$743$	28.7095	+	16.5755i	1.05325	+	0.608094i	0.129693	+	0.991554i	$0.458601\pi$
$744$	−23.5890	−	40.8574i	−0.864816	−	1.49791i
$745$	0.873120	−	1.51229i	0.0319886	−	0.0554059i
$746$	−19.0757	+	11.0134i	−0.698412	+	0.403228i
$747$		−	44.4588i		−	1.62666i
$748$	0.216858	−	0.125203i	0.00792913	−	0.00457788i
$749$		0			0
$750$	−9.88850	−	17.1274i	−0.361077	−	0.625404i
$751$	−10.3871	−	17.9910i	−0.379032	−	0.656503i	0.611890	−	0.790943i	$-0.290410\pi$
$751$	−10.3871	−	17.9910i	−0.379032	−	0.656503i	−0.990922	+	0.134441i	$0.957076\pi$
$752$		−	17.3258i		−	0.631806i
$753$	9.11286	+	15.7839i	0.332091	+	0.575199i
$754$	−24.0026	−	10.3393i	−0.874122	−	0.376536i
$755$	6.56824			0.239043
$756$		0			0
$757$	−21.8075	+	37.7717i	−0.792607	+	1.37283i	0.131741	+	0.991284i	$0.457943\pi$
$757$	−21.8075	+	37.7717i	−0.792607	+	1.37283i	−0.924348	+	0.381551i	$0.875390\pi$
$758$	12.1673			0.441936
$759$	36.3304	−	20.9754i	1.31871	−	0.761358i
$760$	3.22622	+	1.86266i	0.117027	+	0.0675657i
$761$			12.3902i			0.449145i	0.974457	+	0.224573i	$0.0720986\pi$
$761$			12.3902i			0.449145i	−0.974457	+	0.224573i	$0.927901\pi$
$762$		−	5.57497i		−	0.201960i
$763$		0			0
$764$	0.484583	−	0.839323i	0.0175316	−	0.0303656i
$765$	−4.36488	+	2.52007i	−0.157813	+	0.0911132i
$766$	5.51773	+	9.55700i	0.199364	+	0.345308i
$767$	17.9395	−	13.3695i	0.647757	−	0.482746i
$768$	−2.67917	+	4.64046i	−0.0966763	+	0.167448i
$769$	−4.80955	−	2.77680i	−0.173437	−	0.100134i	0.410769	−	0.911740i	$-0.365260\pi$
$769$	−4.80955	−	2.77680i	−0.173437	−	0.100134i	−0.584205	+	0.811606i	$0.698594\pi$
$770$		0			0
$771$	5.18750	+	8.98501i	0.186823	+	0.323587i
$772$	−0.797307	−	0.460325i	−0.0286957	−	0.0165675i
$773$	−37.9355	−	21.9021i	−1.36445	−	0.787764i	−0.374235	−	0.927334i	$-0.622095\pi$
$773$	−37.9355	−	21.9021i	−1.36445	−	0.787764i	−0.990212	+	0.139570i	$0.955428\pi$
$774$	−5.96726	−	3.44520i	−0.214489	−	0.123835i
$775$	−23.7370	−	13.7046i	−0.852659	−	0.492283i
$776$	6.37159	+	11.0359i	0.228727	+	0.396166i
$777$		0			0
$778$	38.4608	+	22.2053i	1.37889	+	0.796100i
$779$	−5.24267	+	9.08058i	−0.187838	+	0.325346i
$780$	0.0487854	+	0.415566i	0.00174680	+	0.0148796i
$781$	4.22127	+	7.31145i	0.151049	+	0.261624i
$782$	−21.3746	+	12.3406i	−0.764354	+	0.441300i
$783$	−14.6678	+	25.4054i	−0.524185	+	0.907916i
$784$		0			0
$785$			5.38113i			0.192061i
$786$		−	33.9697i		−	1.21166i
$787$	−21.4782	−	12.4005i	−0.765616	−	0.442029i	0.0656923	−	0.997840i	$-0.479074\pi$
$787$	−21.4782	−	12.4005i	−0.765616	−	0.442029i	−0.831309	+	0.555811i	$0.812408\pi$
$788$	0.123439	−	0.0712673i	0.00439732	−	0.00253879i
$789$	−51.7661			−1.84292
$790$	0.353263	−	0.611870i	0.0125685	−	0.0217693i
$791$		0			0
$792$	23.3305			0.829015
$793$	−19.2148	+	44.6069i	−0.682338	+	1.58404i
$794$	4.45901	+	7.72323i	0.158244	+	0.274087i
$795$			13.0463i			0.462706i
$796$	0.260876	+	0.451850i	0.00924649	+	0.0160154i
$797$	−8.23575	−	14.2647i	−0.291725	−	0.505283i	0.682492	−	0.730893i	$-0.260896\pi$
$797$	−8.23575	−	14.2647i	−0.291725	−	0.505283i	−0.974218	+	0.225610i	$0.927563\pi$
$798$		0			0
$799$	−7.62168	+	4.40038i	−0.269636	+	0.155674i
$800$			2.11647i			0.0748285i
$801$	51.8876	−	29.9573i	1.83336	−	1.05849i
$802$	0.369756	−	0.640437i	0.0130566	−	0.0226146i
$803$	−9.61464	−	16.6530i	−0.339293	−	0.587673i
$804$	1.62145	+	0.936144i	0.0571841	+	0.0330152i
$805$		0			0
$806$	−17.3012	−	23.2150i	−0.609408	−	0.817715i
$807$	38.9151	−	67.4028i	1.36987	−	2.37269i
$808$		−	52.7406i		−	1.85541i
$809$	1.38194			0.0485863			0.0242932	−	0.999705i	$-0.492266\pi$
$809$	1.38194			0.0485863			0.0242932	+	0.999705i	$0.492266\pi$
$810$	−0.643885			−0.0226238
$811$		−	6.83571i		−	0.240034i	−0.992772	−	0.120017i	$-0.961705\pi$
$811$		−	6.83571i		−	0.240034i	0.992772	−	0.120017i	$-0.0382950\pi$
$812$		0			0
$813$	15.9538	−	9.21093i	0.559524	−	0.323041i
$814$	−19.9412	−	11.5131i	−0.698939	−	0.403533i
$815$	4.08767	−	7.08004i	0.143185	−	0.248003i
$816$	−21.1155			−0.739190
$817$	2.15160	−	1.24223i	0.0752750	−	0.0434601i
$818$	55.0954			1.92637
$819$		0			0
$820$	0.172856			0.00603640
$821$	9.13009	−	5.27126i	0.318642	−	0.183968i	−0.332145	−	0.943228i	$-0.607772\pi$
$821$	9.13009	−	5.27126i	0.318642	−	0.183968i	0.650787	+	0.759260i	$0.274439\pi$
$822$	33.3592			1.16353
$823$	7.41652	−	12.8458i	0.258524	−	0.447776i	−0.707323	−	0.706891i	$-0.750097\pi$
$823$	7.41652	−	12.8458i	0.258524	−	0.447776i	0.965847	+	0.259114i	$0.0834307\pi$
$824$	12.5287	+	7.23343i	0.436457	+	0.251988i
$825$	18.8027	−	10.8558i	0.654627	−	0.377949i
$826$		0			0
$827$		−	55.6758i		−	1.93604i	−0.250879	−	0.968018i	$-0.580720\pi$
$827$		−	55.6758i		−	1.93604i	0.250879	−	0.968018i	$-0.419280\pi$
$828$	3.60587			0.125313
$829$	0.0464848			0.00161448			0.000807242	−	1.00000i	$-0.499743\pi$
$829$	0.0464848			0.00161448			0.000807242		1.00000i	$0.499743\pi$
$830$			6.41464i			0.222655i
$831$	−7.68873	+	13.3173i	−0.266719	+	0.461971i
$832$	−11.8264	+	27.4548i	−0.410006	+	0.951823i
$833$		0			0
$834$	−17.0888	−	9.86624i	−0.591738	−	0.341640i
$835$	4.25508	+	7.37002i	0.147253	+	0.255050i
$836$	−0.160092	+	0.277288i	−0.00553691	+	0.00959022i
$837$	−28.1449	+	16.2495i	−0.972831	+	0.561664i
$838$			33.0100i			1.14031i
$839$	22.1248	−	12.7738i	0.763833	−	0.440999i	−0.0668370	−	0.997764i	$-0.521291\pi$
$839$	22.1248	−	12.7738i	0.763833	−	0.440999i	0.830670	+	0.556765i	$0.187957\pi$
$840$		0			0
$841$	0.823775	+	1.42682i	0.0284060	+	0.0492007i
$842$	16.1061	+	27.8965i	0.555052	+	0.961378i
$843$			10.0099i			0.344761i
$844$	−0.424164	−	0.734673i	−0.0146003	−	0.0252885i
$845$	1.56247	+	6.56302i	0.0537505	+	0.225775i
$846$	−31.2096			−1.07301
$847$		0			0
$848$	−17.0611	+	29.5507i	−0.585881	+	1.01478i
$849$	−39.9540			−1.37122
$850$	−11.0624	+	6.38686i	−0.379436	+	0.219068i
$851$	−80.9745	−	46.7507i	−2.77577	−	1.60259i
$852$			1.16239i			0.0398229i
$853$			22.6671i			0.776105i	0.921637	+	0.388053i	$0.126852\pi$
$853$			22.6671i			0.776105i	−0.921637	+	0.388053i	$0.873148\pi$
$854$		0			0
$855$	3.22231	−	5.58120i	0.110201	−	0.190873i
$856$	15.3339	−	8.85303i	0.524102	−	0.302590i
$857$	−18.5268	−	32.0893i	−0.632862	−	1.09615i	−0.986964	−	0.160943i	$-0.948547\pi$
$857$	−18.5268	−	32.0893i	−0.632862	−	1.09615i	0.354101	−	0.935207i	$-0.384787\pi$
$858$	22.7779	−	2.67402i	0.777625	−	0.0912895i
$859$	2.12169	−	3.67488i	0.0723912	−	0.125385i	−0.827558	−	0.561381i	$-0.810270\pi$
$859$	2.12169	−	3.67488i	0.0723912	−	0.125385i	0.899949	+	0.435996i	$0.143604\pi$
$860$	−0.0354702	−	0.0204788i	−0.00120953	−	0.000698320i
$861$		0			0
$862$	1.87581	+	3.24900i	0.0638904	+	0.110661i
$863$	6.49563	+	3.75025i	0.221114	+	0.127660i	0.606466	−	0.795110i	$-0.292587\pi$
$863$	6.49563	+	3.75025i	0.221114	+	0.127660i	−0.385352	+	0.922770i	$0.625920\pi$
$864$	2.17328	+	1.25475i	0.0739366	+	0.0426873i
$865$	−0.135438	−	0.0781951i	−0.00460503	−	0.00265871i
$866$	−6.98425	−	4.03236i	−0.237335	−	0.137025i
$867$	−18.6562	−	32.3135i	−0.633598	−	1.09742i
$868$		0			0
$869$	1.38168	+	0.797714i	0.0468703	+	0.0270606i
$870$	5.31478	−	9.20547i	0.180188	−	0.312095i
$871$	27.7252	+	11.9429i	0.939432	+	0.404669i
$872$	17.1400	+	29.6874i	0.580434	+	1.00534i
$873$	19.0916	−	11.0225i	0.646153	−	0.373057i
$874$	15.7795	−	27.3309i	0.533749	−	0.924481i
$875$		0			0
$876$		−	2.64755i		−	0.0894523i
$877$		−	28.2897i		−	0.955274i	−0.878557	−	0.477637i	$-0.841493\pi$
$877$		−	28.2897i		−	0.955274i	0.878557	−	0.477637i	$-0.158507\pi$
$878$	45.8145	+	26.4510i	1.54617	+	0.892679i
$879$	20.4324	−	11.7966i	0.689166	−	0.397890i
$880$	−3.23280			−0.108978
$881$	−19.7860	+	34.2704i	−0.666609	+	1.15460i	0.312238	+	0.950004i	$0.398921\pi$
$881$	−19.7860	+	34.2704i	−0.666609	+	1.15460i	−0.978846	+	0.204596i	$0.934412\pi$
$882$		0			0
$883$	−28.3609			−0.954419			−0.477209	−	0.878790i	$-0.658352\pi$
$883$	−28.3609			−0.954419			−0.477209	+	0.878790i	$0.658352\pi$
$884$	0.552098	−	0.0648137i	0.0185691	−	0.00217992i
$885$	4.54987	+	7.88061i	0.152942	+	0.264904i
$886$		−	43.8987i		−	1.47481i
$887$	21.8593	+	37.8614i	0.733963	+	1.27126i	0.955177	+	0.296036i	$0.0956648\pi$
$887$	21.8593	+	37.8614i	0.733963	+	1.27126i	−0.221214	+	0.975225i	$0.571002\pi$
$888$	−41.6469	−	72.1345i	−1.39758	−	2.42068i
$889$		0			0
$890$	−7.48649	+	4.32233i	−0.250948	+	0.144885i
$891$		−	1.45398i		−	0.0487100i
$892$	0.883247	−	0.509943i	0.0295733	−	0.0170742i
$893$	5.62659	−	9.74554i	0.188287	−	0.326122i
$894$	−6.58913	−	11.4127i	−0.220374	−	0.381698i
$895$	−4.41152	−	2.54699i	−0.147461	−	0.0851366i
$896$		0			0
$897$	92.4934	−	10.8583i	3.08826	−	0.362547i
$898$	21.7629	−	37.6944i	0.726236	−	1.25788i
$899$		−	30.3019i		−	1.01062i
$900$	1.86621			0.0622070
$901$	17.3326			0.577434
$902$		−	9.47456i		−	0.315468i
$903$		0			0
$904$	8.87439	−	5.12363i	0.295158	−	0.170409i
$905$	−5.58731	−	3.22583i	−0.185728	−	0.107230i
$906$	24.7841	−	42.9274i	0.823397	−	1.42617i
$907$	36.6985			1.21855			0.609277	−	0.792957i	$-0.291460\pi$
$907$	36.6985			1.21855			0.609277	+	0.792957i	$0.291460\pi$
$908$	−0.0479154	+	0.0276640i	−0.00159013	+	0.000918062i
$909$	−91.2387			−3.02620
$910$		0			0
$911$	−35.5211			−1.17686			−0.588432	−	0.808546i	$-0.700255\pi$
$911$	−35.5211			−1.17686			−0.588432	+	0.808546i	$0.700255\pi$
$912$	23.3823	−	13.4998i	0.774265	−	0.447022i
$913$	−14.4851			−0.479386
$914$	−22.0562	+	38.2024i	−0.729553	+	1.26362i
$915$	−17.1077	−	9.87711i	−0.565562	−	0.326527i
$916$	−1.25326	+	0.723569i	−0.0414088	+	0.0239074i
$917$		0			0
$918$			15.1458i			0.499885i
$919$	21.9334			0.723516			0.361758	−	0.932272i	$-0.382177\pi$
$919$	21.9334			0.723516			0.361758	+	0.932272i	$0.382177\pi$
$920$	−13.6690			−0.450653
$921$		−	23.5489i		−	0.775964i
$922$	0.808222	−	1.39988i	0.0266174	−	0.0461026i
$923$	2.18521	+	18.6142i	0.0719272	+	0.612693i
$924$		0			0
$925$	−41.9082	−	24.1957i	−1.37793	−	0.795549i
$926$	−14.0980	−	24.4184i	−0.463287	−	0.802437i
$927$	12.5135	−	21.6740i	0.410997	−	0.711867i
$928$	−2.02636	+	1.16992i	−0.0665186	+	0.0384045i
$929$		−	15.5172i		−	0.509102i	−0.967059	−	0.254551i	$-0.918072\pi$
$929$		−	15.5172i		−	0.509102i	0.967059	−	0.254551i	$-0.0819276\pi$
$930$	10.1981	−	5.88788i	0.334409	−	0.193071i
$931$		0			0
$932$	1.05961	+	1.83529i	0.0347086	+	0.0601171i
$933$	20.6602	+	35.7845i	0.676385	+	1.17153i
$934$			2.17510i			0.0711716i
$935$	0.821061	+	1.42212i	0.0268516	+	0.0465083i
$936$	47.5672	+	20.4900i	1.55478	+	0.669736i
$937$	40.8110			1.33324			0.666618	−	0.745399i	$-0.267741\pi$
$937$	40.8110			1.33324			0.666618	+	0.745399i	$0.267741\pi$
$938$		0			0
$939$	24.2067	−	41.9273i	0.789957	−	1.36825i
$940$	−0.185514			−0.00605081
$941$	−44.6814	+	25.7968i	−1.45657	+	0.840952i	−0.998841	−	0.0481384i	$-0.984671\pi$
$941$	−44.6814	+	25.7968i	−1.45657	+	0.840952i	−0.457731	+	0.889091i	$0.651338\pi$
$942$	35.1689	+	20.3048i	1.14586	+	0.661565i
$943$		−	38.4730i		−	1.25285i
$944$			23.8001i			0.774627i
$945$		0			0
$946$	−1.12248	+	1.94419i	−0.0364949	+	0.0632110i
$947$	4.31462	−	2.49105i	0.140206	−	0.0809482i	−0.428256	−	0.903657i	$-0.640872\pi$
$947$	4.31462	−	2.49105i	0.140206	−	0.0809482i	0.568462	+	0.822709i	$0.307539\pi$
$948$	0.109832	+	0.190234i	0.00356717	+	0.00617851i
$949$	−4.97719	−	42.3969i	−0.161566	−	1.37626i
$950$	8.16663	−	14.1450i	0.264961	−	0.458925i
$951$	−34.2608	−	19.7805i	−1.11098	−	0.641426i
$952$		0			0
$953$	15.1163	+	26.1822i	0.489664	+	0.848123i	0.999929	−	0.0118941i	$-0.00378608\pi$
$953$	15.1163	+	26.1822i	0.489664	+	0.848123i	−0.510265	+	0.860017i	$0.670453\pi$
$954$	53.2309	+	30.7329i	1.72341	+	0.995013i
$955$	5.50413	+	3.17781i	0.178110	+	0.102832i
$956$	1.13887	+	0.657525i	0.0368336	+	0.0212659i
$957$	20.7871	+	12.0015i	0.671953	+	0.387952i
$958$	−5.34921	−	9.26511i	−0.172825	−	0.299342i
$959$		0			0
$960$	−10.5295	−	6.07919i	−0.339837	−	0.196205i
$961$	1.28469	−	2.22516i	0.0414418	−	0.0717792i
$962$	−30.5456	−	40.9866i	−0.984829	−	1.32146i
$963$	−15.3153	−	26.5269i	−0.493529	−	0.854817i
$964$	1.19336	−	0.688988i	0.0384356	−	0.0221908i
$965$	3.01873	−	5.22860i	0.0971764	−	0.168315i
$966$		0			0
$967$		−	29.9990i		−	0.964703i	−0.875978	−	0.482352i	$-0.839783\pi$
$967$		−	29.9990i		−	0.964703i	0.875978	−	0.482352i	$-0.160217\pi$
$968$			24.0961i			0.774478i
$969$	−11.8772	−	6.85731i	−0.381551	−	0.220288i
$970$	−2.75459	+	1.59036i	−0.0884446	+	0.0510635i
$971$	44.1240			1.41601			0.708003	−	0.706209i	$-0.249596\pi$
$971$	44.1240			1.41601			0.708003	+	0.706209i	$0.249596\pi$
$972$	−0.565732	+	0.979876i	−0.0181459	+	0.0314295i
$973$		0			0
$974$	0.105582			0.00338306
$975$	47.8697	−	5.61968i	1.53306	−	0.179974i
$976$	−25.8333	−	44.7445i	−0.826902	−	1.43224i
$977$			15.0024i			0.479970i	0.970777	+	0.239985i	$0.0771425\pi$
$977$			15.0024i			0.479970i	−0.970777	+	0.239985i	$0.922858\pi$
$978$	−30.8482	−	53.4306i	−0.986417	−	1.70852i
$979$	−9.76037	−	16.9055i	−0.311943	−	0.540301i
$980$		0			0
$981$	51.3577	−	29.6514i	1.63973	−	0.946696i
$982$		−	2.47690i		−	0.0790411i
$983$	5.21223	−	3.00928i	0.166244	−	0.0959812i	−0.414569	−	0.910018i	$-0.636068\pi$
$983$	5.21223	−	3.00928i	0.166244	−	0.0959812i	0.580814	+	0.814037i	$0.302734\pi$
$984$	17.1364	−	29.6812i	0.546290	−	0.946202i
$985$	0.467358	+	0.809488i	0.0148913	+	0.0257924i
$986$	−12.2299	−	7.06093i	−0.389479	−	0.224866i
$987$		0			0
$988$	−0.569930	+	0.424745i	−0.0181319	+	0.0135129i
$989$	−4.55800	+	7.89469i	−0.144936	+	0.251036i
$990$			5.82336i			0.185078i
$991$	33.8400			1.07496			0.537482	−	0.843275i	$-0.319376\pi$
$991$	33.8400			1.07496			0.537482	+	0.843275i	$0.319376\pi$
$992$	−2.59215			−0.0823008
$993$		−	19.5542i		−	0.620535i
$994$		0			0
$995$	−2.96315	+	1.71078i	−0.0939382	+	0.0542353i
$996$	−1.72716	−	0.997175i	−0.0547271	−	0.0315967i
$997$	−13.1608	+	22.7951i	−0.416805	+	0.721928i	−0.995616	−	0.0935340i	$-0.970184\pi$
$997$	−13.1608	+	22.7951i	−0.416805	+	0.721928i	0.578811	+	0.815462i	$0.303517\pi$
$998$	−11.5518			−0.365666
$999$	−49.6904	+	28.6888i	−1.57213	+	0.907672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.h.30.5		12
7.2	even	3		91.2.q.a.43.2	yes	12
7.3	odd	6		637.2.k.g.459.5		12
7.4	even	3		637.2.k.h.459.5		12
7.5	odd	6		637.2.q.h.589.2		12
7.6	odd	2		637.2.u.i.30.5		12
13.10	even	6		637.2.k.h.569.2		12
21.2	odd	6		819.2.ct.a.316.5		12
28.23	odd	6		1456.2.cc.c.225.1		12
91.9	even	3		1183.2.c.i.337.10		12
91.10	odd	6		637.2.u.i.361.5		12
91.19	even	12		8281.2.a.by.1.6		6
91.23	even	6		91.2.q.a.36.2	✓	12
91.30	even	6		1183.2.c.i.337.3		12
91.33	even	12		8281.2.a.ch.1.1		6
91.58	odd	12		1183.2.a.m.1.6		6
91.62	odd	6		637.2.k.g.569.2		12
91.72	odd	12		1183.2.a.p.1.1		6
91.75	odd	6		637.2.q.h.491.2		12
91.88	even	6	inner	637.2.u.h.361.5		12
273.23	odd	6		819.2.ct.a.127.5		12
364.23	odd	6		1456.2.cc.c.673.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.2	✓	12	91.23	even	6
91.2.q.a.43.2	yes	12	7.2	even	3
637.2.k.g.459.5		12	7.3	odd	6
637.2.k.g.569.2		12	91.62	odd	6
637.2.k.h.459.5		12	7.4	even	3
637.2.k.h.569.2		12	13.10	even	6
637.2.q.h.491.2		12	91.75	odd	6
637.2.q.h.589.2		12	7.5	odd	6
637.2.u.h.30.5		12	1.1	even	1	trivial
637.2.u.h.361.5		12	91.88	even	6	inner
637.2.u.i.30.5		12	7.6	odd	2
637.2.u.i.361.5		12	91.10	odd	6
819.2.ct.a.127.5		12	273.23	odd	6
819.2.ct.a.316.5		12	21.2	odd	6
1183.2.a.m.1.6		6	91.58	odd	12
1183.2.a.p.1.1		6	91.72	odd	12
1183.2.c.i.337.3		12	91.30	even	6
1183.2.c.i.337.10		12	91.9	even	3
1456.2.cc.c.225.1		12	28.23	odd	6
1456.2.cc.c.673.1		12	364.23	odd	6
8281.2.a.by.1.6		6	91.19	even	12
8281.2.a.ch.1.1		6	91.33	even	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.20027 - 0.692976i) q^{2} -2.82577 q^{3} +(-0.0395678 + 0.0685334i) q^{4} +(-0.449430 - 0.259479i) q^{5} +(-3.39169 + 1.95819i) q^{6} +2.88158i q^{8} +4.98500 q^{9} -0.719250 q^{10} -1.62416i q^{11} +(0.111810 - 0.193660i) q^{12} +(1.42641 - 3.31140i) q^{13} +(1.26999 + 0.733228i) q^{15} +(1.91773 + 3.32161i) q^{16} +(0.974127 - 1.68724i) q^{17} +(5.98335 - 3.45449i) q^{18} +2.49115i q^{19} +(0.0355659 - 0.0205340i) q^{20} +(-1.12550 - 1.94943i) q^{22} +(-4.57029 - 7.91598i) q^{23} -8.14270i q^{24} +(-2.36534 - 4.09689i) q^{25} +(-0.582637 - 4.96304i) q^{26} -5.60916 q^{27} +(2.61498 - 4.52928i) q^{29} +2.03244 q^{30} +(5.01767 - 2.89695i) q^{31} +(-0.387453 - 0.223696i) q^{32} +4.58951i q^{33} -2.70019i q^{34} +(-0.197245 + 0.341639i) q^{36} +(8.85879 - 5.11463i) q^{37} +(1.72631 + 2.99006i) q^{38} +(-4.03072 + 9.35726i) q^{39} +(0.747709 - 1.29507i) q^{40} +(3.64513 + 2.10452i) q^{41} +(-0.498655 - 0.863697i) q^{43} +(0.111309 + 0.0642644i) q^{44} +(-2.24041 - 1.29350i) q^{45} +(-10.9712 - 6.33421i) q^{46} +(-3.91206 - 2.25863i) q^{47} +(-5.41908 - 9.38612i) q^{48} +(-5.67810 - 3.27825i) q^{50} +(-2.75266 + 4.76775i) q^{51} +(0.170501 + 0.228782i) q^{52} +(4.44825 + 7.70460i) q^{53} +(-6.73251 + 3.88701i) q^{54} +(-0.421434 + 0.729946i) q^{55} -7.03944i q^{57} -7.24847i q^{58} +(5.37392 + 3.10263i) q^{59} +(-0.100501 + 0.0580244i) q^{60} -13.4707 q^{61} +(4.01504 - 6.95426i) q^{62} -8.29100 q^{64} +(-1.50031 + 1.11812i) q^{65} +(3.18042 + 5.50865i) q^{66} +8.37266i q^{67} +(0.0770880 + 0.133520i) q^{68} +(12.9146 + 22.3688i) q^{69} +(-4.50168 + 2.59905i) q^{71} +14.3647i q^{72} +(10.2533 - 5.91976i) q^{73} +(7.08863 - 12.2779i) q^{74} +(6.68392 + 11.5769i) q^{75} +(-0.170727 - 0.0985694i) q^{76} +(1.64640 + 14.0244i) q^{78} +(-0.491155 + 0.850705i) q^{79} -1.99044i q^{80} +0.895217 q^{81} +5.83352 q^{82} -8.91851i q^{83} +(-0.875603 + 0.505530i) q^{85} +(-1.19704 - 0.691113i) q^{86} +(-7.38934 + 12.7987i) q^{87} +4.68015 q^{88} +(10.4087 - 6.00949i) q^{89} -3.58546 q^{90} +0.723345 q^{92} +(-14.1788 + 8.18614i) q^{93} -6.26070 q^{94} +(0.646401 - 1.11960i) q^{95} +(1.09485 + 0.632114i) q^{96} +(3.82981 - 2.21114i) q^{97} -8.09643i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} - 24 q^{10} + 2 q^{12} + 4 q^{13} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} + 24 q^{26} + 12 q^{27} + 8 q^{29}+ \cdots + 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 - 6 * q^5 - 18 * q^6 + 8 * q^9 - 24 * q^10 + 2 * q^12 + 4 * q^13 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^18 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 10 * q^25 + 24 * q^26 + 12 * q^27 + 8 * q^29 - 16 * q^30 + 18 * q^31 - 36 * q^32 - 10 * q^36 + 42 * q^37 - 2 * q^38 - 10 * q^39 - 46 * q^40 + 30 * q^41 + 2 * q^43 + 24 * q^44 - 12 * q^46 + 42 * q^47 - 2 * q^48 - 18 * q^50 - 26 * q^51 + 26 * q^52 + 22 * q^53 - 12 * q^54 - 6 * q^55 - 18 * q^59 + 66 * q^60 - 28 * q^61 - 4 * q^62 - 52 * q^64 - 42 * q^65 + 26 * q^66 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 30 * q^73 + 6 * q^74 + 46 * q^75 - 18 * q^76 - 10 * q^78 + 28 * q^79 - 4 * q^81 - 28 * q^82 - 48 * q^85 - 60 * q^86 - 2 * q^87 + 28 * q^88 + 12 * q^89 + 24 * q^90 + 24 * q^92 + 18 * q^93 - 8 * q^94 - 22 * q^95 + 6 * q^96 + 6 * q^97

Introduction

L-functions

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