LMFDB - Embedded newform 637.2.bz.a.4.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(4,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 7]))

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

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

chi := DirichletCharacter("637.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bz (of order $42$, degree $12$, 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:	$756$
Relative dimension:	$63$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			4.8
Character	$\chi$	$=$	637.4
Dual form			637.2.bz.a.478.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02936 - 2.13750i) q^{2} +(-2.28640 + 0.705259i) q^{3} +(-2.26233 + 2.83687i) q^{4} +(-0.329479 - 1.06814i) q^{5} +(3.86103 + 4.16120i) q^{6} +(-1.23633 - 2.33912i) q^{7} +(3.76664 + 0.859710i) q^{8} +(2.25150 - 1.53504i) q^{9} +(-1.94400 + 1.80377i) q^{10} +(-1.91062 + 2.80236i) q^{11} +(3.17184 - 8.08173i) q^{12} +(-0.516250 + 3.56840i) q^{13} +(-3.72724 + 5.05046i) q^{14} +(1.50664 + 2.20983i) q^{15} +(-0.424784 - 1.86110i) q^{16} +(1.44084 + 1.80675i) q^{17} +(-5.59876 - 3.23245i) q^{18} +(-1.06362 - 0.614080i) q^{19} +(3.77557 + 1.48180i) q^{20} +(4.47642 + 4.47623i) q^{21} +(7.95676 + 1.19929i) q^{22} +(-2.33524 + 2.92830i) q^{23} +(-9.21834 + 0.690819i) q^{24} +(3.09882 - 2.11274i) q^{25} +(8.15886 - 2.56970i) q^{26} +(0.410261 - 0.514451i) q^{27} +(9.43276 + 1.78456i) q^{28} +(-1.16255 + 0.175226i) q^{29} +(3.17263 - 5.49516i) q^{30} +(-7.21091 - 4.16322i) q^{31} +(2.50037 - 1.99398i) q^{32} +(2.39203 - 7.75478i) q^{33} +(2.37878 - 4.93959i) q^{34} +(-2.09118 + 2.09127i) q^{35} +(-0.738902 + 9.85997i) q^{36} +(5.58435 - 4.45337i) q^{37} +(-0.217744 + 2.90560i) q^{38} +(-1.33630 - 8.52286i) q^{39} +(-0.322733 - 4.30657i) q^{40} +(0.191060 - 0.205914i) q^{41} +(4.96006 - 14.1760i) q^{42} +(6.47620 - 6.00903i) q^{43} +(-3.62749 - 11.7600i) q^{44} +(-2.38147 - 1.89916i) q^{45} +(8.66304 + 1.97728i) q^{46} +(0.702141 - 1.02985i) q^{47} +(2.28378 + 3.95563i) q^{48} +(-3.94299 + 5.78384i) q^{49} +(-7.70579 - 4.44894i) q^{50} +(-4.56855 - 3.11478i) q^{51} +(-8.95516 - 9.53742i) q^{52} +(2.12481 + 5.41394i) q^{53} +(-1.52194 - 0.347374i) q^{54} +(3.62283 + 1.11750i) q^{55} +(-2.64583 - 9.87351i) q^{56} +(2.86494 + 0.653903i) q^{57} +(1.57123 + 2.30457i) q^{58} +(-0.476532 + 0.108765i) q^{59} +(-9.67751 - 0.725229i) q^{60} +(6.42058 - 0.967746i) q^{61} +(-1.47622 + 19.6988i) q^{62} +(-6.37424 - 3.36871i) q^{63} +(-10.2758 - 4.94855i) q^{64} +(3.98166 - 0.624284i) q^{65} +(-19.0381 + 2.86953i) q^{66} +(11.6003 - 6.69745i) q^{67} -8.38515 q^{68} +(3.27407 - 8.34219i) q^{69} +(6.62266 + 2.31721i) q^{70} +(-0.421887 + 2.79904i) q^{71} +(9.80026 - 3.84632i) q^{72} +(0.772794 + 1.13348i) q^{73} +(-15.2674 - 7.35239i) q^{74} +(-5.59509 + 7.01603i) q^{75} +(4.14832 - 1.62809i) q^{76} +(8.91721 + 1.00453i) q^{77} +(-16.8421 + 11.6295i) q^{78} +(4.37875 + 7.58422i) q^{79} +(-1.84797 + 1.06692i) q^{80} +(-3.56185 + 9.07545i) q^{81} +(-0.636812 - 0.196431i) q^{82} +(1.46582 - 3.04381i) q^{83} +(-22.8256 + 2.57232i) q^{84} +(1.45515 - 2.13431i) q^{85} +(-19.5107 - 7.65737i) q^{86} +(2.53446 - 1.22053i) q^{87} +(-9.60581 + 8.91289i) q^{88} +(-3.88609 + 8.06955i) q^{89} +(-1.60805 + 7.04531i) q^{90} +(8.98518 - 3.20414i) q^{91} +(-3.02412 - 13.2495i) q^{92} +(19.4231 + 4.43321i) q^{93} +(-2.92407 - 0.440732i) q^{94} +(-0.305487 + 1.33842i) q^{95} +(-4.31057 + 6.32244i) q^{96} +(8.94651 - 5.16527i) q^{97} +(16.4217 + 2.47445i) q^{98} +9.24238i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 756 q - 21 q^{2} - 5 q^{3} + 115 q^{4} - 15 q^{6} - 14 q^{7} + 50 q^{9} - 16 q^{10} - 24 q^{11} - 26 q^{12} - 10 q^{13} - 38 q^{14} - 6 q^{15} - 125 q^{16} + 15 q^{17} - 9 q^{18} - 27 q^{19} - 15 q^{20}+ \cdots + 105 q^{98}+O(q^{100}) $ 756 * q - 21 * q^2 - 5 * q^3 + 115 * q^4 - 15 * q^6 - 14 * q^7 + 50 * q^9 - 16 * q^10 - 24 * q^11 - 26 * q^12 - 10 * q^13 - 38 * q^14 - 6 * q^15 - 125 * q^16 + 15 * q^17 - 9 * q^18 - 27 * q^19 - 15 * q^20 - 16 * q^21 - q^22 - 5 * q^23 - 39 * q^24 - 79 * q^25 - 34 * q^26 - 50 * q^27 - 142 * q^28 - 3 * q^29 - 11 * q^30 - 15 * q^31 - 21 * q^32 - 6 * q^33 - 12 * q^35 - 84 * q^36 + 7 * q^37 - 2 * q^38 - 6 * q^39 - 24 * q^40 - 6 * q^41 + 88 * q^42 - 5 * q^43 + 108 * q^44 - 21 * q^45 - 21 * q^46 + 63 * q^47 - 154 * q^48 - 34 * q^49 + 135 * q^50 + 26 * q^51 + 89 * q^52 + 16 * q^53 - 21 * q^54 - 4 * q^55 + 58 * q^56 - 63 * q^57 - 18 * q^58 - 21 * q^59 + 15 * q^60 - 75 * q^61 - 87 * q^62 + 147 * q^63 + 4 * q^64 - 20 * q^65 + 85 * q^66 - 27 * q^67 + 312 * q^68 - 182 * q^69 - 228 * q^70 - 30 * q^71 - 120 * q^72 + 6 * q^73 - 43 * q^74 + 83 * q^75 + 21 * q^76 + 3 * q^77 + 79 * q^78 + 12 * q^79 + 57 * q^80 + 72 * q^81 - 248 * q^82 + 147 * q^83 - 14 * q^84 - 24 * q^85 - 60 * q^86 - 37 * q^87 + 70 * q^88 - 126 * q^89 + 117 * q^90 - 55 * q^91 + 88 * q^92 - 21 * q^93 + 210 * q^94 + 9 * q^95 - 12 * q^96 - 156 * q^97 + 105 * q^98

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{21}\right)$

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 $

$2$	−1.02936	−	2.13750i	−0.727871	−	1.51144i	−0.854479	−	0.519487i	$-0.826123\pi$
$2$	−1.02936	−	2.13750i	−0.727871	−	1.51144i	0.126608	−	0.991953i	$-0.459591\pi$
$3$	−2.28640	+	0.705259i	−1.32005	+	0.407182i	−0.873172	−	0.487413i	$-0.837941\pi$
$3$	−2.28640	+	0.705259i	−1.32005	+	0.407182i	−0.446879	+	0.894594i	$0.647465\pi$
$4$	−2.26233	+	2.83687i	−1.13116	+	1.41843i
$5$	−0.329479	−	1.06814i	−0.147347	−	0.477689i	0.851568	−	0.524244i	$-0.175652\pi$
$5$	−0.329479	−	1.06814i	−0.147347	−	0.477689i	−0.998916	+	0.0465551i	$0.985176\pi$
$6$	3.86103	+	4.16120i	1.57626	+	1.69880i
$7$	−1.23633	−	2.33912i	−0.467288	−	0.884105i
$7$	−1.23633	−	2.33912i	−0.467288	−	0.884105i
$8$	3.76664	+	0.859710i	1.33171	+	0.303953i
$9$	2.25150	−	1.53504i	0.750498	−	0.511681i
$10$	−1.94400	+	1.80377i	−0.614747	+	0.570402i
$11$	−1.91062	+	2.80236i	−0.576073	+	0.844943i	−0.998098	−	0.0616406i	$-0.980367\pi$
$11$	−1.91062	+	2.80236i	−0.576073	+	0.844943i	0.422026	+	0.906584i	$0.361319\pi$
$12$	3.17184	−	8.08173i	0.915633	−	2.33299i
$13$	−0.516250	+	3.56840i	−0.143182	+	0.989696i
$13$	−0.516250	+	3.56840i	−0.143182	+	0.989696i
$14$	−3.72724	+	5.05046i	−0.996147	+	1.34979i
$15$	1.50664	+	2.20983i	0.389012	+	0.570576i
$16$	−0.424784	−	1.86110i	−0.106196	−	0.465275i
$17$	1.44084	+	1.80675i	0.349454	+	0.438201i	0.925230	−	0.379406i	$-0.123872\pi$
$17$	1.44084	+	1.80675i	0.349454	+	0.438201i	−0.575776	+	0.817607i	$0.695300\pi$
$18$	−5.59876	−	3.23245i	−1.31964	−	0.761895i
$19$	−1.06362	−	0.614080i	−0.244011	−	0.140880i	0.373008	−	0.927828i	$-0.378326\pi$
$19$	−1.06362	−	0.614080i	−0.244011	−	0.140880i	−0.617019	+	0.786948i	$0.711660\pi$
$20$	3.77557	+	1.48180i	0.844244	+	0.331341i
$21$	4.47642	+	4.47623i	0.976835	+	0.976793i
$22$	7.95676	+	1.19929i	1.69639	+	0.255689i
$23$	−2.33524	+	2.92830i	−0.486931	+	0.610592i	−0.963226	−	0.268694i	$-0.913408\pi$
$23$	−2.33524	+	2.92830i	−0.486931	+	0.610592i	0.476295	+	0.879286i	$0.341980\pi$
$24$	−9.21834	+	0.690819i	−1.88169	+	0.141013i
$25$	3.09882	−	2.11274i	0.619764	−	0.422548i
$26$	8.15886	−	2.56970i	1.60008	−	0.503960i
$27$	0.410261	−	0.514451i	0.0789547	−	0.0990060i
$28$	9.43276	+	1.78456i	1.78262	+	0.337251i
$29$	−1.16255	+	0.175226i	−0.215879	+	0.0325386i	−0.256091	−	0.966653i	$-0.582435\pi$
$29$	−1.16255	+	0.175226i	−0.215879	+	0.0325386i	0.0402119	+	0.999191i	$0.487197\pi$
$30$	3.17263	−	5.49516i	0.579241	−	1.00327i
$31$	−7.21091	−	4.16322i	−1.29512	−	0.747737i	−0.315562	−	0.948905i	$-0.602193\pi$
$31$	−7.21091	−	4.16322i	−1.29512	−	0.747737i	−0.979557	+	0.201168i	$0.935526\pi$
$32$	2.50037	−	1.99398i	0.442008	−	0.352490i
$33$	2.39203	−	7.75478i	0.416400	−	1.34993i
$34$	2.37878	−	4.93959i	0.407958	−	0.847132i
$35$	−2.09118	+	2.09127i	−0.353473	+	0.353489i
$36$	−0.738902	+	9.85997i	−0.123150	+	1.64333i
$37$	5.58435	−	4.45337i	0.918061	−	0.732129i	−0.0456837	−	0.998956i	$-0.514547\pi$
$37$	5.58435	−	4.45337i	0.918061	−	0.732129i	0.963744	+	0.266827i	$0.0859752\pi$
$38$	−0.217744	+	2.90560i	−0.0353228	+	0.471350i
$39$	−1.33630	−	8.52286i	−0.213979	−	1.36475i
$40$	−0.322733	−	4.30657i	−0.0510285	−	0.680928i
$41$	0.191060	−	0.205914i	0.0298386	−	0.0321584i	−0.717956	−	0.696088i	$-0.754922\pi$
$41$	0.191060	−	0.205914i	0.0298386	−	0.0321584i	0.747795	+	0.663930i	$0.231113\pi$
$42$	4.96006	−	14.1760i	0.765354	−	2.18741i
$43$	6.47620	−	6.00903i	0.987611	−	0.916369i	−0.00888930	−	0.999960i	$-0.502830\pi$
$43$	6.47620	−	6.00903i	0.987611	−	0.916369i	0.996500	+	0.0835916i	$0.0266391\pi$
$44$	−3.62749	−	11.7600i	−0.546864	−	1.77289i
$45$	−2.38147	−	1.89916i	−0.355008	−	0.283110i
$46$	8.66304	+	1.97728i	1.27730	+	0.291534i
$47$	0.702141	−	1.02985i	0.102418	−	0.150219i	−0.771609	−	0.636097i	$-0.780548\pi$
$47$	0.702141	−	1.02985i	0.102418	−	0.150219i	0.874027	+	0.485878i	$0.161500\pi$
$48$	2.28378	+	3.95563i	0.329636	+	0.570946i
$49$	−3.94299	+	5.78384i	−0.563284	+	0.826263i
$50$	−7.70579	−	4.44894i	−1.08976	−	0.629175i
$51$	−4.56855	−	3.11478i	−0.639725	−	0.436157i
$52$	−8.95516	−	9.53742i	−1.24186	−	1.32260i
$53$	2.12481	+	5.41394i	0.291866	+	0.743661i	0.999319	+	0.0369012i	$0.0117487\pi$
$53$	2.12481	+	5.41394i	0.291866	+	0.743661i	−0.707453	+	0.706760i	$0.750156\pi$
$54$	−1.52194	−	0.347374i	−0.207110	−	0.0472716i
$55$	3.62283	+	1.11750i	0.488503	+	0.150683i
$56$	−2.64583	−	9.87351i	−0.353563	−	1.31940i
$57$	2.86494	+	0.653903i	0.379470	+	0.0866116i
$58$	1.57123	+	2.30457i	0.206312	+	0.302605i
$59$	−0.476532	+	0.108765i	−0.0620392	+	0.0141600i	−0.253428	−	0.967354i	$-0.581558\pi$
$59$	−0.476532	+	0.108765i	−0.0620392	+	0.0141600i	0.191389	+	0.981514i	$0.438701\pi$
$60$	−9.67751	−	0.725229i	−1.24936	−	0.0936266i
$61$	6.42058	−	0.967746i	0.822070	−	0.123907i	0.275480	−	0.961307i	$-0.411163\pi$
$61$	6.42058	−	0.967746i	0.822070	−	0.123907i	0.546591	+	0.837400i	$0.315925\pi$
$62$	−1.47622	+	19.6988i	−0.187480	+	2.50175i
$63$	−6.37424	−	3.36871i	−0.803079	−	0.424417i
$64$	−10.2758	−	4.94855i	−1.28447	−	0.618568i
$65$	3.98166	−	0.624284i	0.493864	−	0.0774329i
$66$	−19.0381	+	2.86953i	−2.34343	+	0.353215i
$67$	11.6003	−	6.69745i	1.41721	−	0.818224i	0.421153	−	0.906989i	$-0.361625\pi$
$67$	11.6003	−	6.69745i	1.41721	−	0.818224i	0.996053	+	0.0887653i	$0.0282921\pi$
$68$	−8.38515			−1.01685
$69$	3.27407	−	8.34219i	0.394152	−	1.00428i
$70$	6.62266	+	2.31721i	0.791560	+	0.276960i
$71$	−0.421887	+	2.79904i	−0.0500688	+	0.332185i	0.949747	+	0.313017i	$0.101340\pi$
$71$	−0.421887	+	2.79904i	−0.0500688	+	0.332185i	−0.999816	+	0.0191677i	$0.993898\pi$
$72$	9.80026	−	3.84632i	1.15497	−	0.453293i
$73$	0.772794	+	1.13348i	0.0904486	+	0.132664i	0.868796	−	0.495170i	$-0.164894\pi$
$73$	0.772794	+	1.13348i	0.0904486	+	0.132664i	−0.778348	+	0.627834i	$0.783942\pi$
$74$	−15.2674	−	7.35239i	−1.77480	−	0.854698i
$75$	−5.59509	+	7.01603i	−0.646066	+	0.810141i
$76$	4.14832	−	1.62809i	0.475845	−	0.186755i
$77$	8.91721	+	1.00453i	1.01621	+	0.114477i
$78$	−16.8421	+	11.6295i	−1.90699	+	1.31678i
$79$	4.37875	+	7.58422i	0.492648	+	0.853292i	0.999964	−	0.00846851i	$-0.00269564\pi$
$79$	4.37875	+	7.58422i	0.492648	+	0.853292i	−0.507316	+	0.861760i	$0.669362\pi$
$80$	−1.84797	+	1.06692i	−0.206609	+	0.119286i
$81$	−3.56185	+	9.07545i	−0.395761	+	1.00838i
$82$	−0.636812	−	0.196431i	−0.0703241	−	0.0216921i
$83$	1.46582	−	3.04381i	0.160895	−	0.334101i	−0.804899	−	0.593411i	$-0.797781\pi$
$83$	1.46582	−	3.04381i	0.160895	−	0.334101i	0.965794	+	0.259310i	$0.0834951\pi$
$84$	−22.8256	+	2.57232i	−2.49048	+	0.280664i
$85$	1.45515	−	2.13431i	0.157833	−	0.231498i
$86$	−19.5107	−	7.65737i	−2.10389	−	0.825716i
$87$	2.53446	−	1.22053i	0.271723	−	0.130855i
$88$	−9.60581	+	8.91289i	−1.02398	+	0.950118i
$89$	−3.88609	+	8.06955i	−0.411925	+	0.855371i	0.587026	+	0.809568i	$0.300299\pi$
$89$	−3.88609	+	8.06955i	−0.411925	+	0.855371i	−0.998951	+	0.0458024i	$0.985416\pi$
$90$	−1.60805	+	7.04531i	−0.169503	+	0.742641i
$91$	8.98518	−	3.20414i	0.941903	−	0.335885i
$92$	−3.02412	−	13.2495i	−0.315286	−	1.38136i
$93$	19.4231	+	4.43321i	2.01409	+	0.459702i
$94$	−2.92407	−	0.440732i	−0.301594	−	0.0454580i
$95$	−0.305487	+	1.33842i	−0.0313423	+	0.137319i
$96$	−4.31057	+	6.32244i	−0.439946	+	0.645282i
$97$	8.94651	−	5.16527i	0.908380	−	0.524454i	0.0284706	−	0.999595i	$-0.490936\pi$
$97$	8.94651	−	5.16527i	0.908380	−	0.524454i	0.879910	+	0.475141i	$0.157603\pi$
$98$	16.4217	+	2.47445i	1.65884	+	0.249958i
$99$			9.24238i			0.928894i
$100$	−1.01698	+	13.5706i	−0.101698	+	1.35706i
$101$	−15.1932	+	4.68647i	−1.51178	+	0.466321i	−0.936212	−	0.351435i	$-0.885694\pi$
$101$	−15.1932	+	4.68647i	−1.51178	+	0.466321i	−0.575564	+	0.817757i	$0.695218\pi$
$102$	−1.95514	+	12.9715i	−0.193588	+	1.28437i
$103$	−11.6901	+	3.60590i	−1.15186	+	0.355300i	−0.811132	−	0.584863i	$-0.801148\pi$
$103$	−11.6901	+	3.60590i	−1.15186	+	0.355300i	−0.340723	+	0.940164i	$0.610672\pi$
$104$	−5.01232	+	12.9970i	−0.491498	+	1.27446i
$105$	3.30637	−	6.25628i	0.322669	−	0.610551i
$106$	9.38507	−	10.1147i	0.911558	−	0.982426i
$107$	12.6165	+	6.07577i	1.21968	+	0.587366i	0.929222	−	0.369522i	$-0.120478\pi$
$107$	12.6165	+	6.07577i	1.21968	+	0.587366i	0.290457	+	0.956888i	$0.406193\pi$
$108$	0.531285	+	2.32771i	0.0511229	+	0.223984i
$109$	14.0758	+	1.05484i	1.34822	+	0.101035i	0.729178	−	0.684324i	$-0.239903\pi$
$109$	14.0758	+	1.05484i	1.34822	+	0.101035i	0.619040	+	0.785359i	$0.287522\pi$
$110$	−1.34057	−	8.89411i	−0.127818	−	0.848020i
$111$	−9.62724	+	14.1206i	−0.913777	+	1.34027i
$112$	−3.82817	+	3.29455i	−0.361728	+	0.311306i
$113$	−0.817266	−	10.9057i	−0.0768819	−	1.02592i	−0.893595	−	0.448874i	$-0.851825\pi$
$113$	−0.817266	−	10.9057i	−0.0768819	−	1.02592i	0.816713	−	0.577044i	$-0.195794\pi$
$114$	−1.55135	−	6.79691i	−0.145297	−	0.636589i
$115$	3.89726	+	1.52956i	0.363421	+	0.142632i
$116$	2.13297	−	3.69441i	0.198041	−	0.343017i
$117$	4.31532	+	8.82670i	0.398951	+	0.816029i
$118$	0.723011	+	0.906627i	0.0665585	+	0.0834618i
$119$	2.44487	−	5.60403i	0.224121	−	0.513720i
$120$	3.77514	+	9.61890i	0.344622	+	0.878082i
$121$	−0.184013	−	0.468857i	−0.0167284	−	0.0426234i
$122$	−8.67767	−	12.7278i	−0.785639	−	1.15232i
$123$	−0.291617	+	0.605548i	−0.0262942	+	0.0546005i
$124$	28.1240	−	11.0378i	2.52561	−	0.991227i
$125$	−7.64738	−	6.09858i	−0.684003	−	0.545474i
$126$	−0.639189	+	17.0926i	−0.0569435	+	1.52273i
$127$	−5.03122	+	0.758334i	−0.446449	+	0.0672913i	−0.368419	−	0.929660i	$-0.620101\pi$
$127$	−5.03122	+	0.758334i	−0.446449	+	0.0672913i	−0.0780293	+	0.996951i	$0.524863\pi$
$128$			20.6621i			1.82629i
$129$	−10.5692	+	18.3064i	−0.930568	+	1.61179i
$130$	−5.43299	−	7.86818i	−0.476504	−	0.690085i
$131$	7.79406	−	7.23183i	0.680970	−	0.631848i	−0.261866	−	0.965104i	$-0.584338\pi$
$131$	7.79406	−	7.23183i	0.680970	−	0.631848i	0.942836	+	0.333256i	$0.108147\pi$
$132$	16.5877	+	24.3297i	1.44378	+	2.11763i
$133$	−0.121429	+	3.24714i	−0.0105293	+	0.281563i
$134$	−26.2568	−	17.9016i	−2.26824	−	1.54646i
$135$	−0.684680	−	0.268717i	−0.0589278	−	0.0231275i
$136$	3.87382	+	8.04407i	0.332177	+	0.689774i
$137$	5.60146	−	1.27850i	0.478565	−	0.109229i	0.0235677	−	0.999722i	$-0.492497\pi$
$137$	5.60146	−	1.27850i	0.478565	−	0.109229i	0.454997	+	0.890493i	$0.349640\pi$
$138$	−21.2016	+	1.58884i	−1.80480	+	0.135251i
$139$	−8.93327	+	2.75555i	−0.757710	+	0.233723i	−0.649454	−	0.760401i	$-0.725003\pi$
$139$	−8.93327	+	2.75555i	−0.757710	+	0.233723i	−0.108255	+	0.994123i	$0.534526\pi$
$140$	−1.20172	−	10.6635i	−0.101564	−	0.901232i
$141$	−0.879059	+	2.84984i	−0.0740301	+	0.240000i
$142$	6.41722	−	1.97945i	0.538521	−	0.166112i
$143$	−9.01359	−	8.26456i	−0.753754	−	0.691117i
$144$	−3.81327	−	3.53820i	−0.317772	−	0.294850i
$145$	0.570201	+	1.18403i	0.0473526	+	0.0983287i
$146$	1.62732	−	2.81861i	0.134678	−	0.233270i
$147$	4.93613	−	16.0050i	0.407125	−	1.32007i
$148$			25.9170i			2.13037i
$149$	15.4947	+	1.16117i	1.26938	+	0.0951265i	0.692327	−	0.721584i	$-0.256585\pi$
$149$	15.4947	+	1.16117i	1.26938	+	0.0951265i	0.577048	+	0.816710i	$0.304205\pi$
$150$	20.7561	+	4.73745i	1.69473	+	0.386811i
$151$	14.0632	−	5.51941i	1.14445	−	0.449163i	0.284063	−	0.958806i	$-0.408318\pi$
$151$	14.0632	−	5.51941i	1.14445	−	0.449163i	0.860386	+	0.509643i	$0.170222\pi$
$152$	−3.47833	−	3.22742i	−0.282130	−	0.261778i
$153$	6.01748	+	1.85615i	0.486484	+	0.150060i
$154$	−7.03187	−	20.0946i	−0.566645	−	1.61927i
$155$	−2.07108	+	9.07399i	−0.166353	+	0.728840i
$156$	27.2014	+	15.4906i	2.17785	+	1.24024i
$157$	20.8271	+	6.42432i	1.66219	+	0.512717i	0.976562	−	0.215238i	$-0.0690528\pi$
$157$	20.8271	+	6.42432i	1.66219	+	0.512717i	0.685625	+	0.727955i	$0.259529\pi$
$158$	11.7039	−	17.1665i	0.931114	−	1.36569i
$159$	−8.67639	−	10.8799i	−0.688083	−	0.862828i
$160$	−2.95368	−	2.01379i	−0.233509	−	0.159204i
$161$	9.73677	+	1.84208i	0.767365	+	0.145176i
$162$	23.0652	−	1.72850i	1.81217	−	0.135804i
$163$	3.05291	−	9.89728i	0.239122	−	0.775214i	−0.753869	−	0.657025i	$-0.771815\pi$
$163$	3.05291	−	9.89728i	0.239122	−	0.775214i	0.992991	−	0.118190i	$-0.0377091\pi$
$164$	0.151910	+	1.00786i	0.0118622	+	0.0787005i
$165$	−9.07135			−0.706204
$166$	−8.01500			−0.622085
$167$	1.61575	+	10.7198i	0.125031	+	0.829524i	0.960156	+	0.279465i	$0.0901570\pi$
$167$	1.61575	+	10.7198i	0.125031	+	0.829524i	−0.835125	+	0.550060i	$0.814605\pi$
$168$	13.0128	+	20.7087i	1.00396	+	1.59771i
$169$	−12.4670	−	3.68437i	−0.958998	−	0.283413i
$170$	−6.05995	−	0.913391i	−0.464777	−	0.0700539i
$171$	−3.33737	+	0.250101i	−0.255215	+	0.0191257i
$172$	2.39556	+	31.9665i	0.182660	+	2.43742i
$173$	0.444291	+	1.13203i	0.0337788	+	0.0860670i	0.946768	−	0.321917i	$-0.104327\pi$
$173$	0.444291	+	1.13203i	0.0337788	+	0.0860670i	−0.912989	+	0.407984i	$0.866232\pi$
$174$	−5.21777	−	4.16103i	−0.395558	−	0.315447i
$175$	−8.77311	−	4.63648i	−0.663185	−	0.350485i
$176$	6.02707	+	2.36545i	0.454308	+	0.178303i
$177$	1.01283	−	0.584759i	0.0761291	−	0.0439532i
$178$	21.2489			1.59267
$179$	−9.35890	+	23.8461i	−0.699517	+	1.78234i	−0.0807939	+	0.996731i	$0.525746\pi$
$179$	−9.35890	+	23.8461i	−0.699517	+	1.78234i	−0.618723	+	0.785609i	$0.712350\pi$
$180$	10.7753	−	2.45940i	0.803145	−	0.183313i
$181$	21.5831	+	10.3939i	1.60426	+	0.772569i	0.999712	−	0.0240021i	$-0.00764084\pi$
$181$	21.5831	+	10.3939i	1.60426	+	0.772569i	0.604545	+	0.796571i	$0.293355\pi$
$182$	−16.0979	−	15.9076i	−1.19325	−	1.17915i
$183$	−13.9975	+	6.74082i	−1.03472	+	0.498296i
$184$	−11.3135	+	9.02220i	−0.834041	+	0.665125i
$185$	−6.59676	−	4.49760i	−0.485004	−	0.330670i
$186$	−10.5175	−	46.0803i	−0.771183	−	3.37877i
$187$	−7.81605	+	0.585732i	−0.571566	+	0.0428330i
$188$	1.33308	+	4.32174i	0.0972249	+	0.315195i
$189$	−1.71058	−	0.323621i	−0.124426	−	0.0235400i
$190$	3.17534	−	0.724750i	0.230363	−	0.0525789i
$191$	−4.77611	−	4.43158i	−0.345587	−	0.320658i	0.488213	−	0.872724i	$-0.337649\pi$
$191$	−4.77611	−	4.43158i	−0.345587	−	0.320658i	−0.833800	+	0.552067i	$0.813839\pi$
$192$	26.9845	+	4.06725i	1.94744	+	0.293529i
$193$	5.67628	+	18.4020i	0.408588	+	1.32461i	0.893113	+	0.449831i	$0.148516\pi$
$193$	5.67628	+	18.4020i	0.408588	+	1.32461i	−0.484526	+	0.874777i	$0.661008\pi$
$194$	−20.2500	−	13.8062i	−1.45386	−	0.991227i
$195$	−8.66337	+	4.23546i	−0.620397	+	0.303308i
$196$	−7.48766	−	24.2707i	−0.534833	−	1.73362i
$197$	0.156289	+	0.0902333i	0.0111351	+	0.00642886i	0.505557	−	0.862793i	$-0.331287\pi$
$197$	0.156289	+	0.0902333i	0.0111351	+	0.00642886i	−0.494422	+	0.869222i	$0.664620\pi$
$198$	19.7556	−	9.51378i	1.40397	−	0.676115i
$199$	−2.81902	+	12.3509i	−0.199835	+	0.875534i	0.771199	+	0.636594i	$0.219657\pi$
$199$	−2.81902	+	12.3509i	−0.199835	+	0.875534i	−0.971034	+	0.238940i	$0.923200\pi$
$200$	13.4885	−	5.29383i	0.953778	−	0.374330i
$201$	−21.7995	+	23.4943i	−1.53762	+	1.65716i
$202$	25.6566	+	27.6513i	1.80519	+	1.94554i
$203$	1.84716	+	2.50270i	0.129645	+	0.175655i
$204$	19.1718	−	5.91371i	1.34229	−	0.414042i
$205$	−0.282896	−	0.136236i	−0.0197583	−	0.00951512i
$206$	19.7409	+	21.2757i	1.37542	+	1.48235i
$207$	−0.762716	+	10.1777i	−0.0530124	+	0.707402i
$208$	6.86045	−	0.555007i	0.475686	−	0.0384828i
$209$	3.75304	−	1.80737i	0.259603	−	0.125018i
$210$	−16.7763	−	0.627361i	−1.15767	−	0.0432920i
$211$	5.48127	−	3.73707i	0.377346	−	0.257270i	−0.359763	−	0.933044i	$-0.617143\pi$
$211$	5.48127	−	3.73707i	0.377346	−	0.257270i	0.737110	+	0.675773i	$0.236190\pi$
$212$	−20.1656	−	6.22028i	−1.38498	−	0.427210i
$213$	−1.00945	−	6.69725i	−0.0691662	−	0.458888i
$214$		−	33.2218i		−	2.27100i
$215$	−8.55228	−	4.93766i	−0.583261	−	0.336746i
$216$	1.98758	−	1.58504i	0.135238	−	0.107848i
$217$	−0.823243	+	22.0143i	−0.0558853	+	1.49443i
$218$	−12.2344	−	31.1728i	−0.828620	−	2.11129i
$219$	−2.56631	−	2.04656i	−0.173415	−	0.138294i
$220$	−11.3662	+	7.74936i	−0.766310	+	0.522461i
$221$	−7.19104	+	4.20874i	−0.483722	+	0.283111i
$222$	40.0926	+	6.04299i	2.69084	+	0.405579i
$223$	−14.8560	+	5.83055i	−0.994831	+	0.390442i	−0.806224	−	0.591610i	$-0.798492\pi$
$223$	−14.8560	+	5.83055i	−0.994831	+	0.390442i	−0.188607	+	0.982053i	$0.560397\pi$
$224$	−7.75545	−	3.38347i	−0.518183	−	0.226068i
$225$	3.73383	−	9.51364i	0.248922	−	0.634243i
$226$	−22.4696	+	12.9728i	−1.49465	+	0.862938i
$227$			0.596443i			0.0395873i	0.999804	+	0.0197937i	$0.00630093\pi$
$227$			0.596443i			0.0395873i	−0.999804	+	0.0197937i	$0.993699\pi$
$228$	−8.33646	+	6.64811i	−0.552096	+	0.440282i
$229$	5.78727	+	6.23719i	0.382433	+	0.412165i	0.894704	−	0.446659i	$-0.147386\pi$
$229$	5.78727	+	6.23719i	0.382433	+	0.412165i	−0.512271	+	0.858824i	$0.671196\pi$
$230$	−0.742266	−	9.90485i	−0.0489436	−	0.653107i
$231$	−21.0967	+	3.99219i	−1.38806	+	0.262667i
$232$	−4.52953	−	0.339442i	−0.297378	−	0.0222854i
$233$	9.85509	−	25.1103i	0.645628	−	1.64503i	−0.113067	−	0.993587i	$-0.536067\pi$
$233$	9.85509	−	25.1103i	0.645628	−	1.64503i	0.758695	−	0.651446i	$-0.225837\pi$
$234$	14.4250	−	18.3099i	0.942994	−	1.19695i
$235$	−1.33137	−	0.410673i	−0.0868490	−	0.0267894i
$236$	0.769518	−	1.59792i	0.0500914	−	0.104016i
$237$	−15.3604	−	14.2524i	−0.997765	−	0.925791i
$238$	−14.4953	+	0.542687i	−0.939588	+	0.0351772i
$239$	−0.0825068	+	0.0188316i	−0.00533692	+	0.00121812i	−0.225189	−	0.974315i	$-0.572300\pi$
$239$	−0.0825068	+	0.0188316i	−0.00533692	+	0.00121812i	0.219852	+	0.975533i	$0.429443\pi$
$240$	3.47272	−	3.74270i	0.224163	−	0.241591i
$241$	−4.06084	−	3.23841i	−0.261582	−	0.208605i	0.483913	−	0.875116i	$-0.339215\pi$
$241$	−4.06084	−	3.23841i	−0.261582	−	0.208605i	−0.745495	+	0.666512i	$0.767787\pi$
$242$	−0.812765	+	0.875952i	−0.0522465	+	0.0563083i
$243$	1.59573	−	21.2936i	0.102366	−	1.36598i
$244$	−11.7801	+	20.4037i	−0.754142	+	1.30621i
$245$	7.47711	+	2.30603i	0.477695	+	0.147327i
$246$	1.59454			0.101664
$247$	2.74038	−	3.47840i	0.174366	−	0.221325i
$248$	−23.5817	−	21.8806i	−1.49744	−	1.38942i
$249$	−1.20477	+	7.99313i	−0.0763492	+	0.506544i
$250$	−5.16376	+	22.6239i	−0.326585	+	1.43086i
$251$	2.56750	−	2.38229i	0.162059	−	0.150369i	−0.594975	−	0.803744i	$-0.702838\pi$
$251$	2.56750	−	2.38229i	0.162059	−	0.150369i	0.757034	+	0.653375i	$0.226648\pi$
$252$	23.9772	−	10.4618i	1.51042	−	0.659029i
$253$	−3.74440	−	12.1390i	−0.235408	−	0.763174i
$254$	6.79990	+	9.97362i	0.426664	+	0.625801i
$255$	−1.82180	+	5.90612i	−0.114085	+	0.369856i
$256$	23.6136	−	11.3717i	1.47585	−	0.710733i
$257$	−2.33551	−	2.92864i	−0.145685	−	0.182683i	0.703635	−	0.710562i	$-0.251559\pi$
$257$	−2.33551	−	2.92864i	−0.145685	−	0.182683i	−0.849320	+	0.527878i	$0.822988\pi$
$258$	50.0095	+	3.74770i	3.11346	+	0.233321i
$259$	−17.3210	−	7.55665i	−1.07628	−	0.469548i
$260$	−7.23681	+	12.7078i	−0.448808	+	0.788103i
$261$	−2.34849	+	2.17908i	−0.145368	+	0.134882i
$262$	−23.4809	−	9.21559i	−1.45066	−	0.569341i
$263$	12.5332	+	21.7082i	0.772832	+	1.33858i	0.936005	+	0.351987i	$0.114494\pi$
$263$	12.5332	+	21.7082i	0.772832	+	1.33858i	−0.163173	+	0.986598i	$0.552173\pi$
$264$	15.6768	−	27.1530i	0.964839	−	1.67115i
$265$	5.08278	−	4.05338i	0.312233	−	0.248997i
$266$	7.06575	−	3.08294i	0.433229	−	0.189027i
$267$	3.19401	−	21.1909i	0.195470	−	1.29686i
$268$	−7.24394	+	48.0604i	−0.442494	+	2.93576i
$269$	15.8740	+	7.64450i	0.967853	+	0.466094i	0.849911	−	0.526927i	$-0.176656\pi$
$269$	15.8740	+	7.64450i	0.967853	+	0.466094i	0.117943	+	0.993020i	$0.462370\pi$
$270$	0.130403	+	1.74011i	0.00793608	+	0.105900i
$271$	9.54728	+	7.61370i	0.579956	+	0.462500i	0.868997	−	0.494817i	$-0.164765\pi$
$271$	9.54728	+	7.61370i	0.579956	+	0.462500i	−0.289041	+	0.957317i	$0.593336\pi$
$272$	2.75050	−	3.44902i	0.166774	−	0.209127i
$273$	−18.2839	+	13.6628i	−1.10659	+	0.826911i
$274$	−8.49873	−	10.6571i	−0.513427	−	0.643817i
$275$			12.7206i			0.767083i
$276$	16.2587	+	28.1609i	0.978658	+	1.69509i
$277$	−0.368984	−	0.462691i	−0.0221701	−	0.0278004i	0.770623	−	0.637291i	$-0.219945\pi$
$277$	−0.368984	−	0.462691i	−0.0221701	−	0.0278004i	−0.792793	+	0.609491i	$0.791374\pi$
$278$	15.0856	+	16.2584i	0.904772	+	0.975113i
$279$	−22.6261	+	1.69559i	−1.35459	+	0.101512i
$280$	−9.67459	+	6.07924i	−0.578167	+	0.363304i
$281$	−0.977992	−	2.03082i	−0.0583421	−	0.121149i	0.869759	−	0.493476i	$-0.164274\pi$
$281$	−0.977992	−	2.03082i	−0.0583421	−	0.121149i	−0.928101	+	0.372328i	$0.878560\pi$
$282$	6.99640	−	1.05454i	0.416629	−	0.0627968i
$283$	−16.2332	−	11.0676i	−0.964965	−	0.657902i	−0.0251853	−	0.999683i	$-0.508018\pi$
$283$	−16.2332	−	11.0676i	−0.964965	−	0.657902i	−0.939780	+	0.341781i	$0.888970\pi$
$284$	−6.98606	−	7.52918i	−0.414546	−	0.446775i
$285$	−0.245473	−	3.27561i	−0.0145406	−	0.194031i
$286$	−8.38722	+	27.7738i	−0.495947	+	1.64230i
$287$	−0.717872	−	0.192337i	−0.0423746	−	0.0113533i
$288$	2.56873	−	8.32763i	0.151364	−	0.490710i
$289$	2.59452	−	11.3673i	0.152619	−	0.668666i
$290$	1.94393	−	2.43761i	0.114151	−	0.143141i
$291$	−16.8124	+	18.1195i	−0.985560	+	1.06218i
$292$	−4.96384	−	0.371989i	−0.290487	−	0.0217690i
$293$	−26.5682	+	15.3392i	−1.55213	+	0.896123i	−0.554162	+	0.832409i	$0.686961\pi$
$293$	−26.5682	+	15.3392i	−1.55213	+	0.896123i	−0.997968	+	0.0637141i	$0.979705\pi$
$294$	−39.2917	+	5.92400i	−2.29154	+	0.345495i
$295$	0.273184	+	0.473169i	0.0159054	+	0.0275490i
$296$	24.8628	−	11.9733i	1.44512	−	0.695934i
$297$	0.657825	+	2.13262i	0.0381709	+	0.123747i
$298$	−13.4677	−	34.3152i	−0.780163	−	1.98782i
$299$	−9.24377	−	9.84480i	−0.534581	−	0.569340i
$300$	−7.24561	−	31.7451i	−0.418325	−	1.83280i
$301$	−22.0626	−	7.71949i	−1.27166	−	0.444944i
$302$	−26.2739	−	24.3786i	−1.51189	−	1.40283i
$303$	31.4324	−	21.4302i	1.80574	−	1.23114i
$304$	−0.691057	+	2.24035i	−0.0396348	+	0.128493i
$305$	−3.14914	−	6.53925i	−0.180319	−	0.374436i
$306$	−2.22667	−	14.7730i	−0.127290	−	0.844516i
$307$	−5.23842	−	10.8777i	−0.298972	−	0.620822i	0.696321	−	0.717730i	$-0.254819\pi$
$307$	−5.23842	−	10.8777i	−0.298972	−	0.620822i	−0.995293	+	0.0969081i	$0.969105\pi$
$308$	−23.0234	+	23.0244i	−1.31188	+	1.31193i
$309$	24.1850	−	16.4890i	1.37584	−	0.938029i
$310$	21.5275	−	4.91352i	1.22268	−	0.279069i
$311$	5.57396	−	0.840139i	0.316070	−	0.0476399i	0.0109086	−	0.999940i	$-0.496528\pi$
$311$	5.57396	−	0.840139i	0.316070	−	0.0476399i	0.305162	+	0.952301i	$0.401290\pi$
$312$	2.29384	−	33.2514i	0.129863	−	1.88249i
$313$	16.8216	+	29.1359i	0.950815	+	1.64686i	0.743666	+	0.668551i	$0.233085\pi$
$313$	16.8216	+	29.1359i	0.950815	+	1.64686i	0.207149	+	0.978309i	$0.433582\pi$
$314$	−7.70675	−	51.1309i	−0.434917	−	2.88549i
$315$	−1.49809	+	7.91853i	−0.0844078	+	0.446158i
$316$	−31.4216	−	4.73604i	−1.76760	−	0.266423i
$317$	4.19056	−	27.8025i	0.235365	−	1.56155i	−0.489096	−	0.872230i	$-0.662673\pi$
$317$	4.19056	−	27.8025i	0.235365	−	1.56155i	0.724461	−	0.689315i	$-0.242089\pi$
$318$	−14.3245	+	29.7451i	−0.803277	+	1.66802i
$319$	1.73013	−	3.59266i	0.0968689	−	0.201150i
$320$	−1.90011	+	12.6064i	−0.106220	+	0.704721i
$321$	−33.1312	−	4.99372i	−1.84920	−	0.278723i
$322$	−6.08525	−	22.7085i	−0.339117	−	1.26549i
$323$	−0.423009	−	2.80648i	−0.0235369	−	0.156157i
$324$	−17.6878	−	30.6361i	−0.982655	−	1.70201i
$325$	5.93933	+	12.1485i	0.329455	+	0.673879i
$326$	−24.2980	+	3.66233i	−1.34574	+	0.202838i
$327$	−32.9268	+	7.51533i	−1.82086	+	0.415598i
$328$	0.896682	−	0.611347i	0.0495110	−	0.0337560i
$329$	−3.27703	−	0.369161i	−0.180668	−	0.0203525i
$330$	9.33773	+	19.3900i	0.514025	+	1.06738i
$331$	−1.55347	−	10.3066i	−0.0853864	−	0.566502i	−0.990087	−	0.140454i	$-0.955144\pi$
$331$	−1.55347	−	10.3066i	−0.0853864	−	0.566502i	0.904701	−	0.426048i	$-0.140094\pi$
$332$	5.31872	+	11.0444i	0.291902	+	0.606142i
$333$	5.73702	−	18.5989i	0.314387	−	1.01922i
$334$	21.2504	−	14.4883i	1.16277	−	0.792763i
$335$	−10.9759	−	10.1842i	−0.599678	−	0.556420i
$336$	6.42920	−	10.2325i	0.350741	−	0.558228i
$337$	−3.09100	−	13.5425i	−0.168377	−	0.737710i	−0.986647	−	0.162875i	$-0.947923\pi$
$337$	−3.09100	−	13.5425i	−0.168377	−	0.737710i	0.818269	−	0.574835i	$-0.194934\pi$
$338$	4.95773	+	30.4407i	0.269665	+	1.65576i
$339$	9.55991	+	24.3583i	0.519223	+	1.32296i
$340$	2.76273	+	8.95655i	0.149830	+	0.485737i
$341$	25.4441	−	12.2533i	1.37788	−	0.663551i
$342$	3.96997	+	6.87618i	0.214671	+	0.371821i
$343$	18.4039	+	2.07242i	0.993719	+	0.111900i
$344$	29.5595	−	17.0662i	1.59374	−	0.920147i
$345$	−9.98940	−	0.748602i	−0.537811	−	0.0403034i
$346$	1.96238	−	2.11495i	0.105498	−	0.113700i
$347$	−14.1071	+	17.6898i	−0.757310	+	0.949636i	−0.999789	−	0.0205201i	$-0.993468\pi$
$347$	−14.1071	+	17.6898i	−0.757310	+	0.949636i	0.242480	+	0.970156i	$0.422039\pi$
$348$	−2.27129	+	9.95117i	−0.121754	+	0.533439i
$349$	9.18657	−	29.7821i	0.491746	−	1.59420i	−0.281148	−	0.959664i	$-0.590715\pi$
$349$	9.18657	−	29.7821i	0.491746	−	1.59420i	0.772894	−	0.634536i	$-0.218809\pi$
$350$	−0.879741	+	23.5251i	−0.0470241	+	1.25747i
$351$	1.62397	+	1.72956i	0.0866810	+	0.0923170i
$352$	0.810598	+	10.8167i	0.0432050	+	0.576531i
$353$	−14.5499	−	15.6810i	−0.774411	−	0.834617i	0.215471	−	0.976510i	$-0.430871\pi$
$353$	−14.5499	−	15.6810i	−0.774411	−	0.834617i	−0.989882	+	0.141894i	$0.954681\pi$
$354$	−2.29250	−	1.56300i	−0.121845	−	0.0830724i
$355$	3.12878	−	0.471588i	0.166058	−	0.0250293i
$356$	−14.1006	−	29.2803i	−0.747333	−	1.55185i
$357$	−1.63764	+	14.5373i	−0.0866732	+	0.769395i
$358$	60.6047	−	4.54169i	3.20306	−	0.240036i
$359$	23.7013	+	25.5440i	1.25091	+	1.34816i	0.913520	+	0.406793i	$0.133353\pi$
$359$	23.7013	+	25.5440i	1.25091	+	1.34816i	0.337388	+	0.941366i	$0.390457\pi$
$360$	−7.33740	−	9.20081i	−0.386715	−	0.484925i
$361$	−8.74581	−	15.1482i	−0.460306	−	0.797273i
$362$		−	56.8328i		−	2.98707i
$363$	0.751392	+	0.942216i	0.0394379	+	0.0494535i
$364$	−11.2377	+	32.7386i	−0.589015	+	1.71597i
$365$	0.956101	−	1.19891i	0.0500446	−	0.0627540i
$366$	28.8170	+	22.9808i	1.50629	+	1.20122i
$367$	−2.03576	−	27.1654i	−0.106266	−	1.41802i	−0.754360	−	0.656461i	$-0.772053\pi$
$367$	−2.03576	−	27.1654i	−0.106266	−	1.41802i	0.648094	−	0.761560i	$-0.275566\pi$
$368$	6.44183	+	3.10222i	0.335803	+	0.161714i
$369$	0.114084	−	0.756901i	0.00593900	−	0.0394027i
$370$	−2.82313	+	18.7302i	−0.146767	+	0.973738i
$371$	10.0369	−	11.6636i	0.521090	−	0.605544i
$372$	−56.5179	+	45.0715i	−2.93032	+	2.33685i
$373$	−4.86819	+	8.43195i	−0.252065	+	0.436590i	−0.964094	−	0.265560i	$-0.914443\pi$
$373$	−4.86819	+	8.43195i	−0.252065	+	0.436590i	0.712029	+	0.702150i	$0.247776\pi$
$374$	9.29757	+	16.1039i	0.480766	+	0.832711i
$375$	21.7860	+	8.55038i	1.12503	+	0.441540i
$376$	3.53008	−	3.27544i	0.182050	−	0.168918i
$377$	−0.0251114	−	4.23889i	−0.00129330	−	0.218314i
$378$	1.06907	+	3.98948i	0.0549871	+	0.205197i
$379$	3.94637	+	0.295740i	0.202711	+	0.0151911i	0.175699	−	0.984444i	$-0.443782\pi$
$379$	3.94637	+	0.295740i	0.202711	+	0.0151911i	0.0270126	+	0.999635i	$0.491401\pi$
$380$	−3.10582	−	3.89458i	−0.159325	−	0.199788i
$381$	10.9685	−	5.28217i	0.561935	−	0.270614i
$382$	−4.55614	+	14.7706i	−0.233112	+	0.755731i
$383$	16.1588	+	23.7006i	0.825675	+	1.21104i	0.974989	+	0.222253i	$0.0713409\pi$
$383$	16.1588	+	23.7006i	0.825675	+	1.21104i	−0.149314	+	0.988790i	$0.547707\pi$
$384$	−14.5721	−	47.2417i	−0.743631	−	2.41079i
$385$	−1.86505	−	9.85584i	−0.0950515	−	0.502300i
$386$	33.4914	−	31.0755i	1.70467	−	1.58170i
$387$	5.35700	−	23.4706i	0.272312	−	1.19308i
$388$	−5.58674	+	37.0656i	−0.283624	+	1.88172i
$389$	24.4420	+	22.6789i	1.23926	+	1.14987i	0.983068	+	0.183240i	$0.0586584\pi$
$389$	24.4420	+	22.6789i	1.23926	+	1.14987i	0.256192	+	0.966626i	$0.417532\pi$
$390$	17.9711	+	14.1581i	0.910000	+	0.716923i
$391$	−8.65540			−0.437722
$392$	−19.8242	+	18.3958i	−1.00128	+	0.929128i
$393$	−12.7200	+	22.0316i	−0.641638	+	1.11135i
$394$	0.0319955	−	0.426950i	0.00161191	−	0.0215094i
$395$	6.65834	−	7.17598i	0.335017	−	0.361063i
$396$	−26.2194	−	20.9093i	−1.31757	−	1.05073i
$397$	6.30903	−	6.79951i	0.316641	−	0.341258i	−0.554597	−	0.832119i	$-0.687127\pi$
$397$	6.30903	−	6.79951i	0.316641	−	0.341258i	0.871238	+	0.490861i	$0.163318\pi$
$398$	29.3019	−	6.68796i	1.46877	−	0.335237i
$399$	−2.01244	−	7.50988i	−0.100748	−	0.375964i
$400$	−5.24835	−	4.86975i	−0.262417	−	0.243488i
$401$	0.616703	−	1.28060i	0.0307967	−	0.0639499i	−0.885003	−	0.465585i	$-0.845844\pi$
$401$	0.616703	−	1.28060i	0.0307967	−	0.0639499i	0.915800	+	0.401635i	$0.131558\pi$
$402$	72.6586	+	22.4122i	3.62388	+	1.11782i
$403$	18.5787	−	23.5822i	0.925470	−	1.17471i
$404$	21.0770	−	53.7033i	1.04862	−	2.67184i
$405$	10.8674	+	0.814403i	0.540008	+	0.0404680i
$406$	3.44812	−	6.52450i	0.171127	−	0.323805i
$407$	1.81039	+	24.1580i	0.0897379	+	1.19747i
$408$	−14.5302	−	15.6599i	−0.719354	−	0.775280i
$409$	−5.92709	+	4.72669i	−0.293076	+	0.233720i	−0.758978	−	0.651116i	$-0.774301\pi$
$409$	−5.92709	+	4.72669i	−0.293076	+	0.233720i	0.465903	+	0.884836i	$0.345730\pi$
$410$			0.744927i			0.0367893i
$411$	−11.9055	+	6.87363i	−0.587254	+	0.339051i
$412$	16.2172	−	41.3209i	0.798966	−	2.03573i
$413$	0.843565	+	0.980197i	0.0415091	+	0.0482323i
$414$	22.5400	−	8.84630i	1.10778	−	0.434772i
$415$	−3.73418	−	0.562837i	−0.183304	−	0.0276286i
$416$	5.82451	+	9.95173i	0.285570	+	0.487924i
$417$	18.4816	−	12.6005i	0.905048	−	0.617051i
$418$	−7.72650	−	6.16168i	−0.377915	−	0.301377i
$419$	−12.5037	−	31.8589i	−0.610846	−	1.55641i	−0.816229	−	0.577728i	$-0.803939\pi$
$419$	−12.5037	−	31.8589i	−0.610846	−	1.55641i	0.205383	−	0.978682i	$-0.434156\pi$
$420$	10.2682	+	23.5335i	0.501035	+	1.14832i
$421$	−6.55429	+	5.22687i	−0.319436	+	0.254742i	−0.770059	−	0.637972i	$-0.779773\pi$
$421$	−6.55429	+	5.22687i	−0.319436	+	0.254742i	0.450623	+	0.892714i	$0.351202\pi$
$422$	−13.6302	−	7.86940i	−0.663508	−	0.383076i
$423$		−	3.39652i		−	0.165145i
$424$	3.34898	+	22.2190i	0.162641	+	1.07905i
$425$	8.28208	+	2.55468i	0.401740	+	0.123920i
$426$	−13.2763	+	9.05161i	−0.643237	+	0.438552i
$427$	−10.2016	−	13.8221i	−0.493690	−	0.668897i
$428$	−45.7787	+	22.0459i	−2.21280	+	1.06563i
$429$	26.4373	+	12.5391i	1.27640	+	0.605395i
$430$	−1.75083	+	23.3631i	−0.0844323	+	1.12667i
$431$	−4.34107	−	4.67856i	−0.209102	−	0.225358i	0.619789	−	0.784768i	$-0.287218\pi$
$431$	−4.34107	−	4.67856i	−0.209102	−	0.225358i	−0.828891	+	0.559410i	$0.811028\pi$
$432$	−1.13172	−	0.545006i	−0.0544497	−	0.0262216i
$433$	−1.18972	+	0.366980i	−0.0571743	+	0.0176359i	−0.323210	−	0.946327i	$-0.604762\pi$
$433$	−1.18972	+	0.366980i	−0.0571743	+	0.0176359i	0.266036	+	0.963963i	$0.414286\pi$
$434$	47.9030	−	20.9011i	2.29942	−	1.00328i
$435$	−2.13876	−	2.30503i	−0.102545	−	0.110518i
$436$	−34.8365	+	37.5448i	−1.66837	+	1.79807i
$437$	4.28201	−	1.68057i	0.204836	−	0.0803924i
$438$	−1.73286	+	7.59214i	−0.0827991	+	0.362767i
$439$	32.9733	−	15.8791i	1.57373	−	0.757869i	0.575527	−	0.817783i	$-0.304797\pi$
$439$	32.9733	−	15.8791i	1.57373	−	0.757869i	0.998204	+	0.0599145i	$0.0190828\pi$
$440$	12.6852	+	7.32378i	0.604742	+	0.349148i
$441$	0.000822133		19.0750i	3.91492e−5		0.908331i
$442$	16.3984	+	11.0385i	0.779992	+	0.525048i
$443$	−4.40926	−	3.00618i	−0.209490	−	0.142828i	0.454030	−	0.890986i	$-0.349986\pi$
$443$	−4.40926	−	3.00618i	−0.209490	−	0.142828i	−0.663520	+	0.748158i	$0.730938\pi$
$444$	−18.2782	−	59.2566i	−0.867446	−	2.81219i
$445$	9.89983	+	1.49216i	0.469297	+	0.0707351i
$446$	27.7550	+	25.7529i	1.31424	+	1.21944i
$447$	−36.2459	+	8.27290i	−1.71437	+	0.391295i
$448$	1.12894	+	30.1543i	0.0533376	+	1.42466i
$449$	3.02085	+	9.79336i	0.142563	+	0.462177i	0.998491	−	0.0549177i	$-0.0174897\pi$
$449$	3.02085	+	9.79336i	0.142563	+	0.462177i	−0.855928	+	0.517095i	$0.827013\pi$
$450$	−24.1789	+	1.81196i	−1.13980	+	0.0854164i
$451$	0.212002	+	0.928843i	0.00998280	+	0.0437375i
$452$	32.7868	+	22.3537i	1.54216	+	1.05143i
$453$	−28.2615	+	22.5378i	−1.32784	+	1.05892i
$454$	1.27490	−	0.613957i	0.0598338	−	0.0288144i
$455$	−6.38291	−	8.54177i	−0.299235	−	0.400445i
$456$	10.2290	+	4.92603i	0.479017	+	0.230683i
$457$	−21.2734	+	4.85552i	−0.995130	+	0.227132i	−0.688924	−	0.724834i	$-0.741917\pi$
$457$	−21.2734	+	4.85552i	−0.995130	+	0.227132i	−0.306206	+	0.951965i	$0.599060\pi$
$458$	7.37477	−	18.7906i	0.344600	−	0.878028i
$459$	1.52060			0.0709756
$460$	−13.1560	+	7.59563i	−0.613403	+	0.354148i
$461$	33.7312	+	13.2385i	1.57102	+	0.616580i	0.981549	−	0.191210i	$-0.0612411\pi$
$461$	33.7312	+	13.2385i	1.57102	+	0.616580i	0.589471	+	0.807790i	$0.299336\pi$
$462$	30.2495	+	40.9848i	1.40733	+	1.90678i
$463$	5.95639	+	4.75006i	0.276817	+	0.220754i	0.752050	−	0.659106i	$-0.229065\pi$
$463$	5.95639	+	4.75006i	0.276817	+	0.220754i	−0.475233	+	0.879860i	$0.657636\pi$
$464$	0.819944	+	2.08918i	0.0380649	+	0.0969878i
$465$	−1.66421	−	22.2074i	−0.0771760	−	1.02984i
$466$	−63.8178	+	4.78248i	−2.95630	+	0.221544i
$467$	13.0719	+	1.97027i	0.604895	+	0.0911733i	0.444347	−	0.895855i	$-0.353436\pi$
$467$	13.0719	+	1.97027i	0.604895	+	0.0911733i	0.160548	+	0.987028i	$0.448674\pi$
$468$	−34.8029	−	7.72690i	−1.60876	−	0.357176i
$469$	−30.0080	−	18.8544i	−1.38564	−	0.870613i
$470$	0.492652	+	3.26854i	0.0227244	+	0.150766i
$471$	−52.1499			−2.40294
$472$	−1.88843			−0.0869220
$473$	4.46594	+	29.6296i	0.205344	+	1.36237i
$474$	−14.6530	+	47.5037i	−0.673033	+	2.18192i
$475$	−4.59335	+	0.344224i	−0.210757	+	0.0157941i
$476$	10.3668	+	19.6139i	0.475161	+	0.899002i
$477$	13.0946	+	8.92777i	0.599562	+	0.408774i
$478$	0.125182	+	0.156974i	0.00572570	+	0.00717981i
$479$	−17.2395	+	25.2857i	−0.787692	+	1.15533i	0.196893	+	0.980425i	$0.436915\pi$
$479$	−17.2395	+	25.2857i	−0.787692	+	1.15533i	−0.984585	+	0.174907i	$0.944038\pi$
$480$	8.17352	+	2.52120i	0.373069	+	0.115076i
$481$	13.0085	+	22.2262i	0.593136	+	1.01343i
$482$	−2.74202	+	12.0136i	−0.124895	+	0.547202i
$483$	−23.5612	+	2.65523i	−1.07207	+	0.120817i
$484$	1.74638	+	0.538688i	0.0793810	+	0.0244858i
$485$	−8.46494	−	7.85431i	−0.384373	−	0.356646i
$486$	−47.1576	+	18.5080i	−2.13911	+	0.839540i
$487$	−2.15268	−	0.491334i	−0.0975470	−	0.0222645i	0.173469	−	0.984839i	$-0.444502\pi$
$487$	−2.15268	−	0.491334i	−0.0975470	−	0.0222645i	−0.271016	+	0.962575i	$0.587360\pi$
$488$	25.0160	+	1.87469i	1.13242	+	0.0848631i
$489$			24.7822i			1.12069i
$490$	−2.76754	−	18.3561i	−0.125025	−	0.829242i
$491$	5.41804	−	9.38431i	0.244512	−	0.423508i	−0.717482	−	0.696577i	$-0.754705\pi$
$491$	5.41804	−	9.38431i	0.244512	−	0.423508i	0.961994	+	0.273069i	$0.0880387\pi$
$492$	−1.05813	−	2.19723i	−0.0477041	−	0.0990586i
$493$	−1.99163	−	1.84796i	−0.0896984	−	0.0832279i
$494$	−10.2559	−	2.27701i	−0.461436	−	0.102448i
$495$	9.87219	−	3.04517i	0.443722	−	0.136870i
$496$	−4.68509	+	15.1887i	−0.210367	+	0.681993i
$497$	7.06889	−	2.47368i	0.317083	−	0.110960i
$498$	18.3255	−	5.65265i	0.821183	−	0.253301i
$499$	−13.7110	+	1.02750i	−0.613789	+	0.0459972i	−0.377998	−	0.925806i	$-0.623387\pi$
$499$	−13.7110	+	1.02750i	−0.613789	+	0.0459972i	−0.235792	+	0.971804i	$0.575768\pi$
$500$	34.6017	−	7.89762i	1.54744	−	0.353192i
$501$	−11.2545	−	23.3702i	−0.502814	−	1.04410i
$502$	−7.73505	−	3.03578i	−0.345232	−	0.135494i
$503$	−4.26189	−	2.90571i	−0.190028	−	0.129559i	0.464569	−	0.885537i	$-0.346209\pi$
$503$	−4.26189	−	2.90571i	−0.190028	−	0.129559i	−0.654597	+	0.755978i	$0.727162\pi$
$504$	−21.1133	−	18.1687i	−0.940462	−	0.809298i
$505$	10.0117	+	14.6844i	0.445513	+	0.653447i
$506$	−22.0928	+	20.4991i	−0.982145	+	0.911298i
$507$	31.1029	−	0.368522i	1.38133	−	0.0163666i
$508$	9.23097	−	15.9885i	0.409558	−	0.709375i
$509$		−	6.58287i		−	0.291781i	−0.989301	−	0.145890i	$-0.953395\pi$
$509$		−	6.58287i		−	0.291781i	0.989301	−	0.145890i	$-0.0466046\pi$
$510$	14.4996	−	2.18547i	0.642054	−	0.0967741i
$511$	1.69592	−	3.20901i	0.0750232	−	0.141958i
$512$	−16.3056	−	13.0033i	−0.720611	−	0.574668i
$513$	−0.752275	+	0.295246i	−0.0332137	+	0.0130354i
$514$	−3.85587	+	8.00679i	−0.170075	+	0.353164i
$515$	7.70325	+	11.2986i	0.339446	+	0.497875i
$516$	−28.0219	−	71.3986i	−1.23359	−	3.14315i
$517$	1.54449	+	3.93530i	0.0679267	+	0.173074i
$518$	1.67735	+	44.8023i	0.0736985	+	1.96850i
$519$	−1.81420	−	2.27494i	−0.0796346	−	0.0998587i
$520$	15.5342	+	1.07162i	0.681218	+	0.0469938i
$521$	17.4821	−	30.2799i	0.765905	−	1.32659i	−0.173862	−	0.984770i	$-0.555625\pi$
$521$	17.4821	−	30.2799i	0.765905	−	1.32659i	0.939767	−	0.341816i	$-0.111042\pi$
$522$	7.07523	+	2.77682i	0.309674	+	0.121538i
$523$	3.18645	+	13.9607i	0.139334	+	0.610460i	0.995582	+	0.0938959i	$0.0299321\pi$
$523$	3.18645	+	13.9607i	0.139334	+	0.610460i	−0.856248	+	0.516564i	$0.827211\pi$
$524$	2.88304	+	38.4715i	0.125946	+	1.68063i
$525$	23.3287	+	4.41351i	1.01815	+	0.192621i
$526$	33.5000	−	49.1354i	1.46067	−	2.14241i
$527$	−2.86783	−	19.0268i	−0.124925	−	0.828822i
$528$	−15.4485	−	1.15771i	−0.672311	−	0.0503827i
$529$	1.99640	+	8.74680i	0.0868000	+	0.380295i
$530$	−13.8961	−	6.69203i	−0.603610	−	0.290683i
$531$	−0.905950	+	0.976382i	−0.0393149	+	0.0423714i
$532$	−8.93699	−	7.69057i	−0.387468	−	0.333428i
$533$	0.636149	+	0.788083i	0.0275547	+	0.0341357i
$534$	−48.5833	+	14.9860i	−2.10240	+	0.648506i
$535$	2.33294	−	15.4780i	0.100862	−	0.669174i
$536$	49.4521	−	15.2539i	2.13600	−	0.658870i
$537$	4.58046	−	61.1220i	0.197662	−	2.63761i
$538$		−	41.7996i		−	1.80211i
$539$	−8.67486	−	22.1004i	−0.373653	−	0.951931i
$540$	2.31128	−	1.33442i	0.0994618	−	0.0574243i
$541$	−8.13138	+	11.9266i	−0.349596	+	0.512762i	−0.960253	−	0.279133i	$-0.909953\pi$
$541$	−8.13138	+	11.9266i	−0.349596	+	0.512762i	0.610657	+	0.791895i	$0.290905\pi$
$542$	6.44664	−	28.2446i	0.276907	−	1.21321i
$543$	−56.6778	−	8.54280i	−2.43228	−	0.366607i
$544$	7.20526	+	1.64455i	0.308923	+	0.0705096i
$545$	−3.51096	−	15.3825i	−0.150393	−	0.658916i
$546$	48.0251	+	25.0178i	2.05528	+	1.07066i
$547$	−0.134582	+	0.589642i	−0.00575431	+	0.0252113i	−0.977724	−	0.209897i	$-0.932687\pi$
$547$	−0.134582	+	0.589642i	−0.00575431	+	0.0252113i	0.971969	+	0.235108i	$0.0755444\pi$
$548$	−9.04540	+	18.7830i	−0.386400	+	0.802369i
$549$	12.9704	−	12.0347i	0.553562	−	0.513630i
$550$	27.1903	−	13.0942i	1.15940	−	0.558338i
$551$	1.34411	+	0.527524i	0.0572609	+	0.0224733i
$552$	19.5041	−	28.6073i	0.830150	−	1.21761i
$553$	12.3269	−	19.6190i	0.524191	−	0.834285i
$554$	−0.609183	+	1.26498i	−0.0258817	+	0.0537439i
$555$	18.2548	+	5.63085i	0.774872	+	0.239016i
$556$	12.3928	−	31.5764i	0.525574	−	1.33914i
$557$	−35.2475	+	20.3502i	−1.49348	+	0.862264i	−0.999972	−	0.00747477i	$-0.997621\pi$
$557$	−35.2475	+	20.3502i	−1.49348	+	0.862264i	−0.493513	+	0.869739i	$0.664287\pi$
$558$	26.9148	+	46.6178i	1.13939	+	1.97349i
$559$	18.0993	+	26.2118i	0.765519	+	1.10864i
$560$	4.78036	+	3.00355i	0.202007	+	0.126923i
$561$	17.4575	−	6.85156i	0.737055	−	0.289273i
$562$	−3.33417	+	4.18091i	−0.140643	+	0.176361i
$563$	15.8837	+	7.64921i	0.669420	+	0.322376i	0.737542	−	0.675301i	$-0.235986\pi$
$563$	15.8837	+	7.64921i	0.669420	+	0.322376i	−0.0681221	+	0.997677i	$0.521701\pi$
$564$	−6.09590	−	8.94104i	−0.256684	−	0.376486i
$565$	−11.3795	+	4.46614i	−0.478741	+	0.187892i
$566$	−6.94712	+	46.0911i	−0.292009	+	1.93735i
$567$	25.6322	−	2.88862i	1.07645	−	0.121310i
$568$	−3.99546	+	10.1803i	−0.167646	+	0.427154i
$569$	−8.34625			−0.349893			−0.174946	−	0.984578i	$-0.555975\pi$
$569$	−8.34625			−0.349893			−0.174946	+	0.984578i	$0.555975\pi$
$570$	−6.74894	+	3.89650i	−0.282682	+	0.163206i
$571$	−25.4962	+	3.84293i	−1.06698	+	0.160822i	−0.658981	−	0.752159i	$-0.729012\pi$
$571$	−25.4962	+	3.84293i	−1.06698	+	0.160822i	−0.408002	+	0.912981i	$0.633774\pi$
$572$	43.8372	−	6.87322i	1.83292	−	0.287384i
$573$	14.0455	+	6.76395i	0.586758	+	0.282568i
$574$	0.327833	+	1.73243i	0.0136835	+	0.0723104i
$575$	−1.04976	+	14.0080i	−0.0437778	+	0.584174i
$576$	−30.7321	+	4.63211i	−1.28050	+	0.193005i
$577$	−27.7169	−	2.07709i	−1.15387	−	0.0864705i	−0.515981	−	0.856600i	$-0.672572\pi$
$577$	−27.7169	−	2.07709i	−1.15387	−	0.0864705i	−0.637888	+	0.770130i	$0.720192\pi$
$578$	−26.9683	+	6.15534i	−1.12173	+	0.256028i
$579$	−25.9564	−	38.0711i	−1.07871	−	1.58218i
$580$	−4.64893	−	1.06109i	−0.193036	−	0.0440593i
$581$	−8.93207	+	0.334407i	−0.370565	+	0.0138736i
$582$	56.0364	+	17.2849i	2.32278	+	0.716484i
$583$	−19.2315	−	4.38946i	−0.796487	−	0.181793i
$584$	1.93637	+	4.93379i	0.0801275	+	0.204161i
$585$	8.00639	−	7.51759i	0.331023	−	0.310814i
$586$	60.1358	+	40.9999i	2.48419	+	1.69369i
$587$	−0.735853	−	0.424845i	−0.0303719	−	0.0175352i	0.484737	−	0.874660i	$-0.338915\pi$
$587$	−0.735853	−	0.424845i	−0.0303719	−	0.0175352i	−0.515109	+	0.857125i	$0.672249\pi$
$588$	34.2369	+	50.2116i	1.41191	+	2.07069i
$589$	5.11311	+	8.85616i	0.210682	+	0.364912i
$590$	0.730191	−	1.07099i	0.0300615	−	0.0440921i
$591$	−0.420975	−	0.0960849i	−0.0173166	−	0.00395240i
$592$	−10.6603	−	8.50131i	−0.438136	−	0.349402i
$593$	−13.0712	−	42.3759i	−0.536771	−	1.74017i	−0.663445	−	0.748225i	$-0.730906\pi$
$593$	−13.0712	−	42.3759i	−0.536771	−	1.74017i	0.126674	−	0.991944i	$-0.459570\pi$
$594$	3.88132	−	3.60134i	0.159252	−	0.147765i
$595$	−6.79144	−	0.765063i	−0.278422	−	0.0313645i
$596$	−38.3482	+	41.3295i	−1.57080	+	1.69292i
$597$	−2.26522	−	30.2272i	−0.0927092	−	1.23712i
$598$	−11.5280	+	29.8924i	−0.471416	+	1.22239i
$599$	−1.21246	+	16.1791i	−0.0495397	+	0.661062i	0.916062	+	0.401036i	$0.131350\pi$
$599$	−1.21246	+	16.1791i	−0.0495397	+	0.661062i	−0.965602	+	0.260025i	$0.916269\pi$
$600$	−27.1064	+	21.6167i	−1.10662	+	0.882496i
$601$	1.56063	−	20.8251i	0.0636593	−	0.849474i	−0.870398	−	0.492350i	$-0.836138\pi$
$601$	1.56063	−	20.8251i	0.0636593	−	0.849474i	0.934057	−	0.357124i	$-0.116243\pi$
$602$	6.21003	+	55.1049i	0.253102	+	2.24591i
$603$	15.8372	−	32.8863i	0.644941	−	1.33923i
$604$	−16.1578	+	52.3822i	−0.657451	+	2.13140i
$605$	−0.440179	+	0.351031i	−0.0178958	+	0.0142714i
$606$	−78.1625	−	45.1272i	−3.17514	−	1.83317i
$607$	1.58373	−	2.74310i	0.0642816	−	0.111339i	−0.832093	−	0.554635i	$-0.812858\pi$
$607$	1.58373	−	2.74310i	0.0642816	−	0.111339i	0.896375	+	0.443296i	$0.146191\pi$
$608$	−3.88391	+	0.585405i	−0.157513	+	0.0237413i
$609$	−5.98840	−	4.41944i	−0.242662	−	0.179085i
$610$	−10.7360	+	13.4625i	−0.434689	+	0.545083i
$611$	3.31244	+	3.03718i	0.134007	+	0.122871i
$612$	−18.8791	+	12.8716i	−0.763144	+	0.520303i
$613$	35.1041	−	2.63069i	1.41784	−	0.106253i	0.656365	−	0.754443i	$-0.272093\pi$
$613$	35.1041	−	2.63069i	1.41784	−	0.106253i	0.761478	+	0.648191i	$0.224474\pi$
$614$	−17.8588	+	22.3942i	−0.720722	+	0.903757i
$615$	0.742894	+	0.111973i	0.0299564	+	0.00451520i
$616$	32.7243	+	11.4499i	1.31850	+	0.461331i
$617$	−35.0348	−	13.7501i	−1.41045	−	0.553560i	−0.466756	−	0.884386i	$-0.654577\pi$
$617$	−35.0348	−	13.7501i	−1.41045	−	0.553560i	−0.943692	+	0.330827i	$0.892672\pi$
$618$	−60.1405	−	34.7221i	−2.41920	−	1.39673i
$619$	16.2664	+	9.39142i	0.653802	+	0.377473i	0.789912	−	0.613221i	$-0.210126\pi$
$619$	16.2664	+	9.39142i	0.653802	+	0.377473i	−0.136109	+	0.990694i	$0.543460\pi$
$620$	−21.0563	−	26.4037i	−0.845639	−	1.06040i
$621$	0.548407	+	2.40273i	0.0220068	+	0.0964182i
$622$	−7.53343	−	11.0495i	−0.302063	−	0.443045i
$623$	23.6802	−	0.886560i	0.948725	−	0.0355193i
$624$	−15.2943	+	6.10736i	−0.612261	+	0.244490i
$625$	2.85656	−	7.27841i	0.114263	−	0.291136i
$626$	44.9624	−	65.9477i	1.79706	−	2.63580i
$627$	−7.30627	+	6.77923i	−0.291784	+	0.270736i
$628$	−65.3427	+	44.5499i	−2.60746	+	1.77774i
$629$	16.0922	+	3.67295i	0.641640	+	0.146450i
$630$	18.4679	−	4.94889i	0.735779	−	0.197168i
$631$	23.2672	+	25.0761i	0.926252	+	0.998262i	1.00000		0.000985285i	$0.000313626\pi$
$631$	23.2672	+	25.0761i	0.926252	+	0.998262i	−0.0737475	+	0.997277i	$0.523496\pi$
$632$	9.97294	+	32.3315i	0.396702	+	1.28608i
$633$	−9.89675	+	12.4101i	−0.393360	+	0.493258i
$634$	−63.7415	+	19.6616i	−2.53150	+	0.780863i
$635$	2.46769	+	5.12421i	0.0979273	+	0.203348i
$636$	50.4935			2.00220
$637$	−18.6035	−	17.0561i	−0.737097	−	0.675786i
$638$	−9.46025			−0.374535
$639$	3.34677	+	6.94964i	0.132396	+	0.274923i
$640$	22.0701	−	6.80772i	0.872397	−	0.269099i
$641$	−14.9637	+	18.7639i	−0.591032	+	0.741130i	−0.983950	−	0.178443i	$-0.942894\pi$
$641$	−14.9637	+	18.7639i	−0.591032	+	0.741130i	0.392919	+	0.919573i	$0.371465\pi$
$642$	23.4300	+	75.9582i	0.924709	+	2.99783i
$643$	9.93834	+	10.7110i	0.391930	+	0.422400i	0.897933	−	0.440132i	$-0.145068\pi$
$643$	9.93834	+	10.7110i	0.391930	+	0.422400i	−0.506004	+	0.862531i	$0.668878\pi$
$644$	−27.2535	+	23.4545i	−1.07394	+	0.924238i
$645$	23.0362	+	5.25787i	0.907051	+	0.207028i
$646$	−5.56342	+	3.79308i	−0.218890	+	0.149237i
$647$	18.3074	−	16.9868i	0.719739	−	0.667820i	−0.232700	−	0.972549i	$-0.574756\pi$
$647$	18.3074	−	16.9868i	0.719739	−	0.667820i	0.952439	+	0.304728i	$0.0985656\pi$
$648$	−21.2185	+	31.1218i	−0.833540	+	1.22258i
$649$	0.605670	−	1.54322i	0.0237746	−	0.0605768i
$650$	19.8537	−	25.2006i	0.778727	−	0.988448i
$651$	−13.6435	−	50.9140i	−0.534733	−	1.99548i
$652$	21.1706	+	31.0516i	0.829104	+	1.21607i
$653$	8.79120	+	38.5168i	0.344026	+	1.50728i	0.790490	+	0.612475i	$0.209826\pi$
$653$	8.79120	+	38.5168i	0.344026	+	1.50728i	−0.446463	+	0.894802i	$0.647317\pi$
$654$	49.9577	+	62.6449i	1.95350	+	2.44961i
$655$	−10.2926	−	5.94244i	−0.402166	−	0.232190i
$656$	−0.464386	−	0.268114i	−0.0181312	−	0.0104681i
$657$	3.47988	+	1.36575i	0.135763	+	0.0532831i
$658$	2.58417	+	7.38464i	0.100742	+	0.287883i
$659$	−33.5352	−	5.05462i	−1.30635	−	0.196900i	−0.541275	−	0.840846i	$-0.682058\pi$
$659$	−33.5352	−	5.05462i	−1.30635	−	0.196900i	−0.765071	+	0.643946i	$0.777296\pi$
$660$	20.5224	−	25.7342i	0.798832	−	1.00170i
$661$	−34.8836	+	2.61417i	−1.35682	+	0.101679i	−0.733180	−	0.680035i	$-0.761965\pi$
$661$	−34.8836	+	2.61417i	−1.35682	+	0.101679i	−0.623637	+	0.781714i	$0.714346\pi$
$662$	−20.4312	+	13.9298i	−0.794083	+	0.541396i
$663$	13.4733	−	14.6944i	0.523260	−	0.570683i
$664$	8.13801	−	10.2047i	0.315816	−	0.396021i
$665$	3.50842	−	0.940160i	0.136051	−	0.0364578i
$666$	−45.6607	+	6.88224i	−1.76932	+	0.266682i
$667$	2.20171	−	3.81347i	0.0852506	−	0.147658i
$668$	−34.0661	−	19.6681i	−1.31806	−	0.760980i
$669$	29.8546	−	23.8083i	1.15425	−	0.920481i
$670$	−10.4704	+	33.9442i	−0.404507	+	1.31138i
$671$	−9.55528	+	19.8418i	−0.368878	+	0.765982i
$672$	20.1182	+	2.26634i	0.776078	+	0.0874261i
$673$	0.0650244	−	0.867691i	0.00250651	−	0.0334470i	−0.995810	−	0.0914431i	$-0.970852\pi$
$673$	0.0650244	−	0.867691i	0.00250651	−	0.0334470i	0.998317	+	0.0579961i	$0.0184711\pi$
$674$	−25.7654	+	20.5472i	−0.992446	+	0.791450i
$675$	0.184424	−	2.46096i	0.00709847	−	0.0947225i
$676$	38.6564	−	27.0319i	1.48679	−	1.03969i
$677$	1.33308	+	17.7888i	0.0512346	+	0.683678i	0.962400	+	0.271637i	$0.0875650\pi$
$677$	1.33308	+	17.7888i	0.0512346	+	0.683678i	−0.911165	+	0.412041i	$0.864816\pi$
$678$	42.2251	−	45.5078i	1.62165	−	1.74772i
$679$	−23.1430	−	14.5410i	−0.888147	−	0.558033i
$680$	7.31589	−	6.78815i	0.280551	−	0.260314i
$681$	−0.420647	−	1.36370i	−0.0161192	−	0.0522572i
$682$	−52.3826	−	41.7737i	−2.00583	−	1.59960i
$683$	−9.90682	−	2.26117i	−0.379074	−	0.0865212i	0.0287382	−	0.999587i	$-0.490851\pi$
$683$	−9.90682	−	2.26117i	−0.379074	−	0.0865212i	−0.407812	+	0.913066i	$0.633708\pi$
$684$	6.84072	−	10.0335i	0.261562	−	0.383640i
$685$	−3.21118	−	5.56193i	−0.122693	−	0.212510i
$686$	−14.5146	−	41.4717i	−0.554169	−	1.58340i
$687$	−17.6308	−	10.1792i	−0.672657	−	0.388359i
$688$	−13.9344	−	9.50031i	−0.531244	−	0.362196i
$689$	−20.4160	+	4.78724i	−0.777789	+	0.182379i
$690$	8.68260	+	22.1229i	0.330541	+	0.842205i
$691$	8.21731	+	1.87555i	0.312601	+	0.0713492i	0.375943	−	0.926643i	$-0.377319\pi$
$691$	8.21731	+	1.87555i	0.312601	+	0.0713492i	−0.0633420	+	0.997992i	$0.520176\pi$
$692$	−4.21656	−	1.30064i	−0.160290	−	0.0494428i
$693$	21.6191	−	11.4266i	0.821240	−	0.434061i
$694$	52.3332	+	11.9447i	1.98654	+	0.453415i
$695$	5.88664	+	8.63412i	0.223293	+	0.327511i
$696$	10.5957	−	2.41840i	0.401629	−	0.0916691i
$697$	0.647322	+	0.0485101i	0.0245191	+	0.00183745i
$698$	−73.1155	+	11.0204i	−2.76746	+	0.417128i
$699$	−4.82331	+	64.3626i	−0.182434	+	2.43442i
$700$	33.0007	−	14.3989i	1.24731	−	0.544228i
$701$	−45.3306	−	21.8301i	−1.71211	−	0.824510i	−0.991337	−	0.131341i	$-0.958072\pi$
$701$	−45.3306	−	21.8301i	−1.71211	−	0.824510i	−0.720775	−	0.693169i	$-0.756214\pi$
$702$	2.02527	−	5.25158i	0.0764390	−	0.198208i
$703$	−8.67434	+	1.30745i	−0.327159	+	0.0493113i
$704$	33.5006	−	19.3416i	1.26260	−	0.728964i
$705$	3.33367			0.125553
$706$	−18.5410	+	47.2418i	−0.697801	+	1.77797i
$707$	29.7460	+	29.7447i	1.11871	+	1.11866i
$708$	−0.632474	+	4.19619i	−0.0237698	+	0.157702i
$709$	24.0023	−	9.42021i	0.901425	−	0.353783i	0.131051	−	0.991376i	$-0.458165\pi$
$709$	24.0023	−	9.42021i	0.901425	−	0.353783i	0.770374	+	0.637592i	$0.220070\pi$
$710$	−4.22867	−	6.20233i	−0.158699	−	0.232769i
$711$	21.5009	+	10.3543i	0.806345	+	0.388315i
$712$	−21.5750	+	27.0542i	−0.808556	+	1.01390i
$713$	29.0304	−	11.3936i	1.08720	−	0.426693i
$714$	32.7591	−	11.4637i	1.22598	−	0.429019i
$715$	−5.85796	+	12.3508i	−0.219075	+	0.461894i
$716$	−46.4753	−	80.4976i	−1.73686	−	3.00834i
$717$	0.175362	−	0.101245i	0.00654902	−	0.00378108i
$718$	30.2028	−	76.9556i	1.12716	−	2.87196i
$719$	2.01438	+	0.621354i	0.0751237	+	0.0231726i	0.332089	−	0.943248i	$-0.392246\pi$
$719$	2.01438	+	0.621354i	0.0751237	+	0.0231726i	−0.256966	+	0.966421i	$0.582723\pi$
$720$	−2.52291	+	5.23888i	−0.0940234	+	0.195242i
$721$	22.8874	+	22.8864i	0.852370	+	0.852334i
$722$	−23.3766	+	34.2872i	−0.869987	+	1.27604i
$723$	11.5686	+	4.54035i	0.430241	+	0.168857i
$724$	−78.3139	+	37.7140i	−2.91051	+	1.40163i
$725$	−3.23231	+	2.99915i	−0.120045	+	0.111386i
$726$	1.24053	−	2.57598i	0.0460403	−	0.0956037i
$727$	0.360235	−	1.57829i	0.0133604	−	0.0585357i	−0.967808	−	0.251688i	$-0.919014\pi$
$727$	0.360235	−	1.57829i	0.0133604	−	0.0585357i	0.981169	+	0.193153i	$0.0618713\pi$
$728$	36.5985	−	4.34418i	1.35643	−	0.161006i
$729$	4.86070	+	21.2961i	0.180026	+	0.788745i
$730$	−3.54685	−	0.809545i	−0.131275	−	0.0299626i
$731$	20.1880	+	3.04285i	0.746679	+	0.112544i
$732$	12.5440	−	54.9589i	0.463640	−	2.03134i
$733$	7.89958	−	11.5866i	0.291778	−	0.427959i	−0.652161	−	0.758081i	$-0.726137\pi$
$733$	7.89958	−	11.5866i	0.291778	−	0.427959i	0.943938	+	0.330121i	$0.107090\pi$
$734$	−55.9704	+	32.3145i	−2.06590	+	1.19275i
$735$	−18.7220		0.000806919i	−0.690570		2.97637e-5i
$736$			11.9783i			0.441525i
$737$	−3.39511	+	45.3046i	−0.125060	+	1.66881i
$738$	−1.73531	+	0.535272i	−0.0638776	+	0.0197036i
$739$	−0.318797	+	2.11508i	−0.0117271	+	0.0778045i	−0.993929	−	0.110025i	$-0.964907\pi$
$739$	−0.318797	+	2.11508i	−0.0117271	+	0.0778045i	0.982202	+	0.187829i	$0.0601451\pi$
$740$	27.6831	−	8.53911i	1.01765	−	0.313904i
$741$	−3.81241	+	9.88567i	−0.140053	+	0.363159i
$742$	−35.2625	−	9.44775i	−1.29453	−	0.346838i
$743$	21.3291	−	22.9873i	0.782490	−	0.843324i	−0.208393	−	0.978045i	$-0.566823\pi$
$743$	21.3291	−	22.9873i	0.782490	−	0.843324i	0.990884	+	0.134721i	$0.0430138\pi$
$744$	69.3487	+	33.3966i	2.54245	+	1.22438i
$745$	−3.86488	−	16.9332i	−0.141598	−	0.620383i
$746$	23.0344	+	1.72619i	0.843350	+	0.0632003i
$747$	−1.37209	−	9.10322i	−0.0502021	−	0.333069i
$748$	16.0208	−	23.4982i	0.585779	−	0.859180i
$749$	−1.38610	−	37.0231i	−0.0506472	−	1.35279i
$750$	−4.14934	−	55.3690i	−0.151512	−	2.02179i
$751$	0.777862	+	3.40804i	0.0283846	+	0.124361i	0.987135	−	0.159887i	$-0.0511131\pi$
$751$	0.777862	+	3.40804i	0.0283846	+	0.124361i	−0.958751	+	0.284248i	$0.908256\pi$
$752$	−2.21492	−	0.869290i	−0.0807697	−	0.0316998i
$753$	−4.19019	+	7.25762i	−0.152699	+	0.264482i
$754$	−9.03477	+	4.41704i	−0.329027	+	0.160859i
$755$	−10.5291	−	13.2030i	−0.383192	−	0.480507i
$756$	4.78796	−	4.12055i	0.174136	−	0.149863i
$757$	14.3400	+	36.5376i	0.521195	+	1.32798i	0.913009	+	0.407939i	$0.133752\pi$
$757$	14.3400	+	36.5376i	0.521195	+	1.32798i	−0.391814	+	0.920044i	$0.628152\pi$
$758$	−3.43011	−	8.73978i	−0.124587	−	0.317443i
$759$	17.1223	+	25.1139i	0.621501	+	0.911575i
$760$	−2.30131	+	4.77873i	−0.0834774	+	0.173343i
$761$	−20.0934	+	7.88609i	−0.728386	+	0.285871i	−0.700413	−	0.713738i	$-0.747001\pi$
$761$	−20.0934	+	7.88609i	−0.728386	+	0.285871i	−0.0279736	+	0.999609i	$0.508905\pi$
$762$	−22.5812	−	18.0079i	−0.818032	−	0.652359i
$763$	−14.9349	−	34.2292i	−0.540680	−	1.23918i
$764$	23.3769	−	3.52350i	0.845747	−	0.127476i
$765$		−	7.03909i		−	0.254499i
$766$	34.0266	−	58.9359i	1.22943	−	2.12944i
$767$	−0.142109	−	1.75661i	−0.00513125	−	0.0634274i
$768$	−45.9701	+	42.6540i	−1.65880	+	1.53914i
$769$	−2.48085	−	3.63873i	−0.0894616	−	0.131216i	0.778899	−	0.627149i	$-0.215778\pi$
$769$	−2.48085	−	3.63873i	−0.0894616	−	0.131216i	−0.868361	+	0.495933i	$0.834826\pi$
$770$	−19.1470	+	14.1318i	−0.690011	+	0.509274i
$771$	7.40535	+	5.04888i	0.266697	+	0.181831i
$772$	−65.0458	−	25.5286i	−2.34105	−	0.918794i
$773$	−8.57104	−	17.7980i	−0.308279	−	0.640148i	0.688059	−	0.725655i	$-0.258463\pi$
$773$	−8.57104	−	17.7980i	−0.308279	−	0.640148i	−0.996338	+	0.0855073i	$0.972749\pi$
$774$	−55.6826	+	12.7092i	−2.00147	+	0.456822i
$775$	−31.1411	+	2.33370i	−1.11862	+	0.0838291i
$776$	38.1389	−	11.7643i	1.36911	−	0.422313i
$777$	44.9322	+	5.06166i	1.61193	+	0.181586i
$778$	23.3163	−	75.5897i	0.835931	−	2.71002i
$779$	−0.329663	+	0.101688i	−0.0118114	+	0.00364334i
$780$	7.58392	−	34.1588i	0.271548	−	1.22308i
$781$	−7.03785	−	6.53017i	−0.251834	−	0.233668i
$782$	8.90956	+	18.5009i	0.318605	+	0.661591i
$783$	−0.386802	+	0.669961i	−0.0138232	+	0.0239424i
$784$	12.4392	+	4.88142i	0.444258	+	0.174336i
$785$		−	24.3631i		−	0.869555i
$786$	60.1861	+	4.51033i	2.14677	+	0.160878i
$787$	−4.10882	−	0.937810i	−0.146463	−	0.0334293i	0.148661	−	0.988888i	$-0.452504\pi$
$787$	−4.10882	−	0.937810i	−0.146463	−	0.0334293i	−0.295124	+	0.955459i	$0.595361\pi$
$788$	−0.609556	+	0.239233i	−0.0217145	+	0.00852233i
$789$	−43.9658	−	40.7943i	−1.56522	−	1.45232i
$790$	−22.1925	−	6.84548i	−0.789574	−	0.243551i
$791$	−24.4993	+	15.3946i	−0.871094	+	0.547371i
$792$	−7.94577	+	34.8127i	−0.282341	+	1.23701i
$793$	0.138686	+	23.4108i	0.00492490	+	0.831341i
$794$	−21.0282	−	6.48635i	−0.746264	−	0.230192i
$795$	−8.76256	+	12.8523i	−0.310776	+	0.455825i
$796$	−28.6604	−	35.9390i	−1.01584	−	1.27382i
$797$	35.5451	+	24.2343i	1.25907	+	0.858421i	0.994376	−	0.105910i	$-0.0337756\pi$
$797$	35.5451	+	24.2343i	1.25907	+	0.858421i	0.264697	+	0.964332i	$0.414728\pi$
$798$	−13.9808	+	12.0320i	−0.494916	+	0.425928i
$799$	2.87235	−	0.215253i	0.101617	−	0.00761511i
$800$	3.53544	−	11.4616i	0.124997	−	0.405230i
$801$	3.63760	+	24.1339i	0.128528	+	0.852729i
$802$	−3.37208			−0.119072
$803$	−4.65293			−0.164198
$804$	−17.3326	−	114.994i	−0.611272	−	4.05553i
$805$	−1.24045	−	11.0072i	−0.0437202	−	0.387953i
$806$	−69.5311	−	15.4372i	−2.44913	−	0.543754i
$807$	−41.6855	−	6.28308i	−1.46740	−	0.221175i
$808$	−61.2561	+	4.59051i	−2.15498	+	0.161494i
$809$	−2.19304	−	29.2641i	−0.0771033	−	1.02887i	−0.892818	−	0.450417i	$-0.851275\pi$
$809$	−2.19304	−	29.2641i	−0.0771033	−	1.02887i	0.815715	−	0.578454i	$-0.196344\pi$
$810$	−9.44578	−	24.0675i	−0.331891	−	0.845644i
$811$	−0.585330	−	0.466785i	−0.0205537	−	0.0163911i	0.613159	−	0.789959i	$-0.289898\pi$
$811$	−0.585330	−	0.466785i	−0.0205537	−	0.0163911i	−0.633713	+	0.773568i	$0.718470\pi$
$812$	−11.2787	−	0.421777i	−0.395805	−	0.0148015i
$813$	−27.1985	−	10.6746i	−0.953893	−	0.374375i
$814$	49.7742	−	28.7371i	1.74458	−	1.00724i
$815$	−11.5776			−0.405545
$816$	−3.85628	+	9.82563i	−0.134997	+	0.343966i
$817$	−10.5782	+	2.41441i	−0.370086	+	0.0844696i
$818$	16.2044	+	7.80364i	0.566575	+	0.272848i
$819$	15.3116	−	21.0067i	0.535031	−	0.734035i
$820$	1.02649	−	0.494330i	0.0358465	−	0.0172628i
$821$	0.870916	−	0.694533i	0.0303952	−	0.0242394i	−0.608174	−	0.793803i	$-0.708098\pi$
$821$	0.870916	−	0.694533i	0.0303952	−	0.0242394i	0.638570	+	0.769564i	$0.279526\pi$
$822$	26.9474	+	18.3725i	0.939900	+	0.640813i
$823$	−1.57908	−	6.91840i	−0.0550432	−	0.241160i	0.939921	−	0.341393i	$-0.110899\pi$
$823$	−1.57908	−	6.91840i	−0.0550432	−	0.241160i	−0.994964	+	0.100232i	$0.968041\pi$
$824$	−47.1322	+	3.53207i	−1.64193	+	0.123046i
$825$	−8.97135	−	29.0844i	−0.312342	−	1.01259i
$826$	1.22683	−	2.81210i	0.0426870	−	0.0978454i
$827$	21.7688	−	4.96859i	0.756975	−	0.172775i	0.173420	−	0.984848i	$-0.444518\pi$
$827$	21.7688	−	4.96859i	0.756975	−	0.172775i	0.583555	+	0.812073i	$0.301661\pi$
$828$	−27.1474	−	25.1891i	−0.943437	−	0.875382i
$829$	54.0134	+	8.14121i	1.87596	+	0.282756i	0.985161	−	0.171635i	$-0.0549050\pi$
$829$	54.0134	+	8.14121i	1.87596	+	0.282756i	0.890802	+	0.454391i	$0.150143\pi$
$830$	2.64077	+	8.56117i	0.0916625	+	0.297163i
$831$	1.16996	+	0.797666i	0.0405855	+	0.0276707i
$832$	22.9633	−	34.1134i	0.796108	−	1.18267i
$833$	−16.1312	+	1.20956i	−0.558912	+	0.0419089i
$834$	−45.9579	−	26.5338i	−1.59139	−	0.918791i
$835$	10.9180	−	5.25781i	0.377831	−	0.181954i
$836$	−3.36334	+	14.7357i	−0.116323	+	0.509646i
$837$	−5.10013	+	2.00165i	−0.176286	+	0.0691872i
$838$	−55.2275	+	59.5211i	−1.90780	+	2.05612i
$839$	33.0667	+	35.6375i	1.14159	+	1.23034i	0.969455	+	0.245269i	$0.0788764\pi$
$839$	33.0667	+	35.6375i	1.14159	+	1.23034i	0.172136	+	0.985073i	$0.444933\pi$
$840$	17.8325	−	20.7226i	0.615279	−	0.714999i
$841$	−26.3908	+	8.14048i	−0.910028	+	0.280706i
$842$	17.9192	+	8.62942i	0.617535	+	0.297389i
$843$	3.66833	+	3.95352i	0.126344	+	0.136167i
$844$	−1.79886	+	24.0041i	−0.0619193	+	0.826255i
$845$	0.172164	+	14.5304i	0.00592262	+	0.499863i
$846$	−7.26006	+	3.49626i	−0.249606	+	0.120204i
$847$	−0.869214	+	1.01009i	−0.0298666	+	0.0347071i
$848$	9.17329	−	6.25424i	0.315012	−	0.214772i
$849$	44.9211	+	13.8563i	1.54169	+	0.475548i
$850$	−3.06465	−	20.3326i	−0.105117	−	0.697403i
$851$			26.7523i			0.917057i
$852$	21.2829	+	12.2877i	0.729141	+	0.420969i
$853$	−2.88817	+	2.30324i	−0.0988892	+	0.0788615i	−0.671686	−	0.740836i	$-0.734430\pi$
$853$	−2.88817	+	2.30324i	−0.0988892	+	0.0788615i	0.572797	+	0.819697i	$0.305858\pi$
$854$	−19.0435	+	36.0339i	−0.651654	+	1.23305i
$855$	1.36674	+	3.48239i	0.0467415	+	0.119095i
$856$	42.2982	+	33.7317i	1.44572	+	1.15293i
$857$	−22.6068	+	15.4130i	−0.772232	+	0.526499i	−0.884141	−	0.467220i	$-0.845256\pi$
$857$	−22.6068	+	15.4130i	−0.772232	+	0.526499i	0.111909	+	0.993718i	$0.464303\pi$
$858$	−0.411229	−	69.4170i	−0.0140391	−	2.36986i
$859$	−23.1950	−	3.49608i	−0.791402	−	0.119285i	−0.259113	−	0.965847i	$-0.583430\pi$
$859$	−23.1950	−	3.49608i	−0.791402	−	0.119285i	−0.532290	+	0.846562i	$0.678668\pi$
$860$	33.3556	−	13.0911i	1.13742	−	0.446403i
$861$	1.77699	−	0.0665285i	0.0605595	−	0.00226728i
$862$	−5.53187	+	14.0950i	−0.188416	+	0.480077i
$863$	−11.3191	+	6.53510i	−0.385308	+	0.222458i	−0.680125	−	0.733096i	$-0.738075\pi$
$863$	−11.3191	+	6.53510i	−0.385308	+	0.222458i	0.294817	+	0.955554i	$0.404741\pi$
$864$		−	2.10437i		−	0.0715922i
$865$	1.06279	−	0.847548i	0.0361360	−	0.0288175i
$866$	2.00908	+	2.16527i	0.0682712	+	0.0735788i
$867$	2.08482	+	27.8200i	0.0708042	+	0.944816i
$868$	−60.5893	−	52.1390i	−2.05653	−	1.76971i
$869$	−29.6198	−	2.21970i	−1.00478	−	0.0752981i
$870$	−2.72544	+	6.94430i	−0.0924010	+	0.235434i
$871$	17.9105	+	44.8522i	0.606875	+	1.51976i
$872$	52.1116	+	16.0743i	1.76472	+	0.544344i
$873$	12.2141	−	25.3629i	0.413385	−	0.858403i
$874$	−7.99996	−	7.42288i	−0.270603	−	0.251083i
$875$	−4.81067	+	25.4280i	−0.162630	+	0.859623i
$876$	11.6117	−	2.65029i	0.392322	−	0.0895448i
$877$	29.1477	−	31.4138i	0.984249	−	1.06077i	−0.0138967	−	0.999903i	$-0.504424\pi$
$877$	29.1477	−	31.4138i	0.984249	−	1.06077i	0.998146	−	0.0608651i	$-0.0193859\pi$
$878$	−67.8831	−	54.1350i	−2.29094	−	1.82697i
$879$	49.9273	−	53.8088i	1.68401	−	1.81493i
$880$	0.540850	−	7.21715i	0.0182321	−	0.243290i
$881$	−5.44721	+	9.43485i	−0.183521	+	0.317868i	−0.943077	−	0.332574i	$-0.892083\pi$
$881$	−5.44721	+	9.43485i	−0.183521	+	0.317868i	0.759556	+	0.650442i	$0.225416\pi$
$882$	40.7718	−	19.6368i	1.37286	−	0.661207i
$883$	12.2135			0.411016			0.205508	−	0.978655i	$-0.434115\pi$
$883$	12.2135			0.411016			0.205508	+	0.978655i	$0.434115\pi$
$884$	4.32883	−	29.9216i	0.145594	−	1.00637i
$885$	−0.958314	−	0.889185i	−0.0322134	−	0.0298896i
$886$	−1.88697	+	12.5192i	−0.0633940	+	0.420592i
$887$	−11.0283	+	48.3182i	−0.370295	+	1.62237i	0.355653	+	0.934618i	$0.384258\pi$
$887$	−11.0283	+	48.3182i	−0.370295	+	1.62237i	−0.725948	+	0.687750i	$0.758599\pi$
$888$	−48.4019	+	44.9104i	−1.62426	+	1.50709i
$889$	7.99407	+	10.8311i	0.268112	+	0.363263i
$890$	−7.00105	−	22.6968i	−0.234676	−	0.760800i
$891$	−18.6273	−	27.3213i	−0.624040	−	0.915298i
$892$	17.0686	−	55.3351i	0.571500	−	1.85276i
$893$	−1.37922	+	0.664198i	−0.0461539	+	0.0222265i
$894$	54.9936	+	68.9598i	1.83926	+	2.30636i
$895$	28.5546	+	2.13987i	0.954476	+	0.0715281i
$896$	48.3312	−	25.5451i	1.61463	−	0.853402i
$897$	28.0781	+	15.9898i	0.937499	+	0.533885i
$898$	17.8237	−	16.5380i	0.594785	−	0.551880i
$899$	9.11252	+	3.57640i	0.303920	+	0.119280i
$900$	18.5418	+	32.1153i	0.618060	+	1.07051i
$901$	−6.72012	+	11.6396i	−0.223880	+	0.387771i
$902$	1.76717	−	1.40927i	0.0588404	−	0.0469237i
$903$	55.8880	+	2.08997i	1.85984	+	0.0695500i
$904$	6.29736	−	41.7803i	0.209447	−	1.38959i
$905$	3.99097	−	26.4784i	0.132664	−	0.880171i
$906$	77.2658	+	37.2093i	2.56698	+	1.23619i
$907$	3.62871	+	48.4218i	0.120489	+	1.60782i	0.650282	+	0.759693i	$0.274651\pi$
$907$	3.62871	+	48.4218i	0.120489	+	1.60782i	−0.529792	+	0.848127i	$0.677730\pi$
$908$	−1.69203	−	1.34935i	−0.0561520	−	0.0447797i
$909$	−27.0134	+	33.8737i	−0.895978	+	1.12352i
$910$	−11.6877	+	22.4361i	−0.387443	+	0.743748i
$911$	10.9140	+	13.6857i	0.361598	+	0.453429i	0.929037	−	0.369986i	$-0.120637\pi$
$911$	10.9140	+	13.6857i	0.361598	+	0.453429i	−0.567440	+	0.823415i	$0.692066\pi$
$912$		−	5.60971i		−	0.185756i
$913$	5.72922	+	9.92331i	0.189610	+	0.328413i
$914$	32.2768	+	40.4738i	1.06762	+	1.33876i
$915$	11.8120	+	12.7303i	0.390494	+	0.420852i
$916$	−30.7868	+	2.30715i	−1.01722	+	0.0762304i
$917$	−26.5521	−	9.29035i	−0.876829	−	0.306794i
$918$	−1.56525	−	3.25028i	−0.0516611	−	0.107275i
$919$	32.0070	−	4.82427i	1.05581	−	0.159138i	0.401881	−	0.915692i	$-0.368357\pi$
$919$	32.0070	−	4.82427i	1.05581	−	0.159138i	0.653931	+	0.756554i	$0.273118\pi$
$920$	13.3646	+	9.11181i	0.440617	+	0.300407i
$921$	19.6487	+	21.1762i	0.647446	+	0.697781i
$922$	−6.42440	−	85.7277i	−0.211577	−	2.82329i
$923$	−9.77029	−	2.95047i	−0.321593	−	0.0971158i
$924$	36.4024	−	68.8802i	1.19755	−	2.26599i
$925$	7.89607	−	25.5984i	0.259621	−	0.841671i
$926$	4.02195	−	17.6213i	0.132170	−	0.579073i
$927$	−20.7849	+	26.0634i	−0.682665	+	0.856035i
$928$	−2.55740	+	2.75623i	−0.0839509	+	0.0904776i
$929$	38.8382	+	2.91052i	1.27424	+	0.0954911i	0.694609	−	0.719388i	$-0.255577\pi$
$929$	38.8382	+	2.91052i	1.27424	+	0.0954911i	0.579632	+	0.814879i	$0.303196\pi$
$930$	−45.7551	+	26.4167i	−1.50037	+	0.866239i
$931$	7.74558	−	3.73049i	0.253851	−	0.122262i
$932$	48.9393	+	84.7654i	1.60306	+	2.77658i
$933$	−12.1518	+	5.85198i	−0.397831	+	0.191585i
$934$	−9.24430	−	29.9693i	−0.302483	−	0.980625i
$935$	3.20087	+	8.15568i	0.104680	+	0.266719i
$936$	8.66582	+	36.9569i	0.283251	+	1.20797i
$937$	−7.80572	−	34.1991i	−0.255002	−	1.11724i	−0.926519	−	0.376247i	$-0.877214\pi$
$937$	−7.80572	−	34.1991i	−0.255002	−	1.11724i	0.671518	−	0.740989i	$-0.265643\pi$
$938$	−9.41200	+	83.5500i	−0.307313	+	2.72800i
$939$	−59.0093	−	54.7526i	−1.92570	−	1.78678i
$940$	4.17702	−	2.84785i	0.136239	−	0.0928865i
$941$	−0.990586	+	3.21140i	−0.0322922	+	0.104689i	−0.970284	−	0.241968i	$-0.922207\pi$
$941$	−0.990586	+	3.21140i	−0.0322922	+	0.104689i	0.937992	+	0.346657i	$0.112683\pi$
$942$	53.6813	+	111.470i	1.74903	+	3.63190i
$943$	0.156806	+	1.04034i	0.00510631	+	0.0338781i
$944$	0.404846	+	0.840672i	0.0131766	+	0.0273615i
$945$	0.217926	+	1.93377i	0.00708913	+	0.0629056i
$946$	58.7361	−	40.0456i	1.90968	−	1.30199i
$947$	43.5033	−	9.92934i	1.41367	−	0.322660i	0.553575	−	0.832799i	$-0.313263\pi$
$947$	43.5033	−	9.92934i	1.41367	−	0.322660i	0.860092	+	0.510139i	$0.170406\pi$
$948$	75.1823	−	11.3319i	2.44181	−	0.368043i
$949$	−4.44367	+	2.17248i	−0.144247	+	0.0705216i
$950$	5.46401	+	9.46395i	0.177276	+	0.307051i
$951$	10.0267	+	66.5230i	0.325139	+	2.15716i
$952$	14.0268	−	19.0064i	0.454610	−	0.616003i
$953$	2.91637	+	0.439572i	0.0944704	+	0.0142391i	0.196107	−	0.980582i	$-0.437170\pi$
$953$	2.91637	+	0.439572i	0.0944704	+	0.0142391i	−0.101637	+	0.994822i	$0.532408\pi$
$954$	5.60394	−	37.1797i	0.181434	−	1.20374i
$955$	−3.15994	+	6.56168i	−0.102253	+	0.212331i
$956$	0.133235	−	0.276664i	0.00430911	−	0.00894797i
$957$	−1.42201	+	9.43444i	−0.0459671	+	0.304972i
$958$	71.7938	+	10.8212i	2.31955	+	0.349616i
$959$	−9.91579	−	11.5219i	−0.320198	−	0.372060i
$960$	−4.54640	−	30.1634i	−0.146734	−	0.973519i
$961$	19.1648	+	33.1945i	0.618221	+	1.07079i
$962$	34.1181	−	50.6845i	1.10001	−	1.63413i
$963$	37.7325	−	5.68725i	1.21591	−	0.183269i
$964$	18.3739	−	4.19372i	0.591784	−	0.135071i
$965$	17.7858	−	12.1262i	0.572546	−	0.390355i
$966$	29.9287	+	47.6289i	0.962939	+	1.53243i
$967$	−1.29407	−	2.68716i	−0.0416144	−	0.0864132i	0.879125	−	0.476591i	$-0.158128\pi$
$967$	−1.29407	−	2.68716i	−0.0416144	−	0.0864132i	−0.920739	+	0.390178i	$0.872413\pi$
$968$	−0.290028	−	1.92421i	−0.00932186	−	0.0618465i
$969$	2.94646	+	6.11840i	0.0946541	+	0.196551i
$970$	−8.07507	+	26.1787i	−0.259275	+	0.840549i
$971$	37.1456	−	25.3254i	1.19206	−	0.812732i	0.205906	−	0.978572i	$-0.433986\pi$
$971$	37.1456	−	25.3254i	1.19206	−	0.812732i	0.986153	+	0.165840i	$0.0530334\pi$
$972$	56.7971	+	52.7000i	1.82177	+	1.69035i
$973$	17.4900	+	17.4892i	0.560704	+	0.560680i
$974$	1.16566	+	5.10710i	0.0373502	+	0.163642i
$975$	−22.1475	−	23.5876i	−0.709289	−	0.755406i
$976$	−4.52843	−	11.5383i	−0.144952	−	0.369330i
$977$	12.9853	+	42.0974i	0.415437	+	1.34681i	0.885688	+	0.464281i	$0.153687\pi$
$977$	12.9853	+	42.0974i	0.415437	+	1.34681i	−0.470251	+	0.882533i	$0.655837\pi$
$978$	52.9718	−	25.5099i	1.69385	−	0.815717i
$979$	−15.1890	−	26.3080i	−0.485441	−	0.840809i
$980$	−23.4576	+	15.9946i	−0.749324	+	0.510928i
$981$	33.3108	−	19.2320i	1.06353	−	0.614031i
$982$	−25.6361	−	1.92116i	−0.818080	−	0.0613066i
$983$	22.5343	−	24.2862i	0.718733	−	0.774610i	−0.263016	−	0.964791i	$-0.584717\pi$
$983$	22.5343	−	24.2862i	0.718733	−	0.774610i	0.981749	+	0.190182i	$0.0609077\pi$
$984$	−1.61901	+	2.03017i	−0.0516122	+	0.0647196i
$985$	0.0448884	−	0.196669i	0.00143026	−	0.00626639i
$986$	−1.89990	+	6.15932i	−0.0605051	+	0.196153i
$987$	7.75293	−	1.46711i	0.246778	−	0.0466985i
$988$	3.66813	+	15.6434i	0.116699	+	0.497682i
$989$	2.47276	+	32.9968i	0.0786294	+	1.04924i
$990$	−16.6711	−	17.9672i	−0.529843	−	0.571035i
$991$	−32.7131	−	22.3034i	−1.03917	−	0.708491i	−0.0815879	−	0.996666i	$-0.525999\pi$
$991$	−32.7131	−	22.3034i	−1.03917	−	0.708491i	−0.957578	+	0.288175i	$0.906952\pi$
$992$	−26.3314	+	3.96882i	−0.836022	+	0.126010i
$993$	10.8207	+	22.4693i	0.343384	+	0.713043i
$994$	−12.5640	−	12.5634i	−0.398504	−	0.398487i
$995$	14.1214	−	1.05825i	0.447678	−	0.0335488i
$996$	−19.9499	−	21.5009i	−0.632136	−	0.681281i
$997$	−32.9373	−	41.3020i	−1.04313	−	1.30805i	−0.949951	−	0.312399i	$-0.898867\pi$
$997$	−32.9373	−	41.3020i	−1.04313	−	1.30805i	−0.0931827	−	0.995649i	$-0.529704\pi$
$998$	16.3099	+	28.2496i	0.516281	+	0.894226i
$999$		−	4.69991i		−	0.148699i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bz.a.4.8	yes	756
13.10	even	6		637.2.bp.a.543.8	✓	756
49.37	even	21		637.2.bp.a.576.8	yes	756
637.478	even	42	inner	637.2.bz.a.478.8	yes	756

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bp.a.543.8	✓	756	13.10	even	6
637.2.bp.a.576.8	yes	756	49.37	even	21
637.2.bz.a.4.8	yes	756	1.1	even	1	trivial
637.2.bz.a.478.8	yes	756	637.478	even	42	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bz (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.02936 - 2.13750i) q^{2} +(-2.28640 + 0.705259i) q^{3} +(-2.26233 + 2.83687i) q^{4} +(-0.329479 - 1.06814i) q^{5} +(3.86103 + 4.16120i) q^{6} +(-1.23633 - 2.33912i) q^{7} +(3.76664 + 0.859710i) q^{8} +(2.25150 - 1.53504i) q^{9} +(-1.94400 + 1.80377i) q^{10} +(-1.91062 + 2.80236i) q^{11} +(3.17184 - 8.08173i) q^{12} +(-0.516250 + 3.56840i) q^{13} +(-3.72724 + 5.05046i) q^{14} +(1.50664 + 2.20983i) q^{15} +(-0.424784 - 1.86110i) q^{16} +(1.44084 + 1.80675i) q^{17} +(-5.59876 - 3.23245i) q^{18} +(-1.06362 - 0.614080i) q^{19} +(3.77557 + 1.48180i) q^{20} +(4.47642 + 4.47623i) q^{21} +(7.95676 + 1.19929i) q^{22} +(-2.33524 + 2.92830i) q^{23} +(-9.21834 + 0.690819i) q^{24} +(3.09882 - 2.11274i) q^{25} +(8.15886 - 2.56970i) q^{26} +(0.410261 - 0.514451i) q^{27} +(9.43276 + 1.78456i) q^{28} +(-1.16255 + 0.175226i) q^{29} +(3.17263 - 5.49516i) q^{30} +(-7.21091 - 4.16322i) q^{31} +(2.50037 - 1.99398i) q^{32} +(2.39203 - 7.75478i) q^{33} +(2.37878 - 4.93959i) q^{34} +(-2.09118 + 2.09127i) q^{35} +(-0.738902 + 9.85997i) q^{36} +(5.58435 - 4.45337i) q^{37} +(-0.217744 + 2.90560i) q^{38} +(-1.33630 - 8.52286i) q^{39} +(-0.322733 - 4.30657i) q^{40} +(0.191060 - 0.205914i) q^{41} +(4.96006 - 14.1760i) q^{42} +(6.47620 - 6.00903i) q^{43} +(-3.62749 - 11.7600i) q^{44} +(-2.38147 - 1.89916i) q^{45} +(8.66304 + 1.97728i) q^{46} +(0.702141 - 1.02985i) q^{47} +(2.28378 + 3.95563i) q^{48} +(-3.94299 + 5.78384i) q^{49} +(-7.70579 - 4.44894i) q^{50} +(-4.56855 - 3.11478i) q^{51} +(-8.95516 - 9.53742i) q^{52} +(2.12481 + 5.41394i) q^{53} +(-1.52194 - 0.347374i) q^{54} +(3.62283 + 1.11750i) q^{55} +(-2.64583 - 9.87351i) q^{56} +(2.86494 + 0.653903i) q^{57} +(1.57123 + 2.30457i) q^{58} +(-0.476532 + 0.108765i) q^{59} +(-9.67751 - 0.725229i) q^{60} +(6.42058 - 0.967746i) q^{61} +(-1.47622 + 19.6988i) q^{62} +(-6.37424 - 3.36871i) q^{63} +(-10.2758 - 4.94855i) q^{64} +(3.98166 - 0.624284i) q^{65} +(-19.0381 + 2.86953i) q^{66} +(11.6003 - 6.69745i) q^{67} -8.38515 q^{68} +(3.27407 - 8.34219i) q^{69} +(6.62266 + 2.31721i) q^{70} +(-0.421887 + 2.79904i) q^{71} +(9.80026 - 3.84632i) q^{72} +(0.772794 + 1.13348i) q^{73} +(-15.2674 - 7.35239i) q^{74} +(-5.59509 + 7.01603i) q^{75} +(4.14832 - 1.62809i) q^{76} +(8.91721 + 1.00453i) q^{77} +(-16.8421 + 11.6295i) q^{78} +(4.37875 + 7.58422i) q^{79} +(-1.84797 + 1.06692i) q^{80} +(-3.56185 + 9.07545i) q^{81} +(-0.636812 - 0.196431i) q^{82} +(1.46582 - 3.04381i) q^{83} +(-22.8256 + 2.57232i) q^{84} +(1.45515 - 2.13431i) q^{85} +(-19.5107 - 7.65737i) q^{86} +(2.53446 - 1.22053i) q^{87} +(-9.60581 + 8.91289i) q^{88} +(-3.88609 + 8.06955i) q^{89} +(-1.60805 + 7.04531i) q^{90} +(8.98518 - 3.20414i) q^{91} +(-3.02412 - 13.2495i) q^{92} +(19.4231 + 4.43321i) q^{93} +(-2.92407 - 0.440732i) q^{94} +(-0.305487 + 1.33842i) q^{95} +(-4.31057 + 6.32244i) q^{96} +(8.94651 - 5.16527i) q^{97} +(16.4217 + 2.47445i) q^{98} +9.24238i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 756 q - 21 q^{2} - 5 q^{3} + 115 q^{4} - 15 q^{6} - 14 q^{7} + 50 q^{9} - 16 q^{10} - 24 q^{11} - 26 q^{12} - 10 q^{13} - 38 q^{14} - 6 q^{15} - 125 q^{16} + 15 q^{17} - 9 q^{18} - 27 q^{19} - 15 q^{20}+ \cdots + 105 q^{98}+O(q^{100}) \) 756 * q - 21 * q^2 - 5 * q^3 + 115 * q^4 - 15 * q^6 - 14 * q^7 + 50 * q^9 - 16 * q^10 - 24 * q^11 - 26 * q^12 - 10 * q^13 - 38 * q^14 - 6 * q^15 - 125 * q^16 + 15 * q^17 - 9 * q^18 - 27 * q^19 - 15 * q^20 - 16 * q^21 - q^22 - 5 * q^23 - 39 * q^24 - 79 * q^25 - 34 * q^26 - 50 * q^27 - 142 * q^28 - 3 * q^29 - 11 * q^30 - 15 * q^31 - 21 * q^32 - 6 * q^33 - 12 * q^35 - 84 * q^36 + 7 * q^37 - 2 * q^38 - 6 * q^39 - 24 * q^40 - 6 * q^41 + 88 * q^42 - 5 * q^43 + 108 * q^44 - 21 * q^45 - 21 * q^46 + 63 * q^47 - 154 * q^48 - 34 * q^49 + 135 * q^50 + 26 * q^51 + 89 * q^52 + 16 * q^53 - 21 * q^54 - 4 * q^55 + 58 * q^56 - 63 * q^57 - 18 * q^58 - 21 * q^59 + 15 * q^60 - 75 * q^61 - 87 * q^62 + 147 * q^63 + 4 * q^64 - 20 * q^65 + 85 * q^66 - 27 * q^67 + 312 * q^68 - 182 * q^69 - 228 * q^70 - 30 * q^71 - 120 * q^72 + 6 * q^73 - 43 * q^74 + 83 * q^75 + 21 * q^76 + 3 * q^77 + 79 * q^78 + 12 * q^79 + 57 * q^80 + 72 * q^81 - 248 * q^82 + 147 * q^83 - 14 * q^84 - 24 * q^85 - 60 * q^86 - 37 * q^87 + 70 * q^88 - 126 * q^89 + 117 * q^90 - 55 * q^91 + 88 * q^92 - 21 * q^93 + 210 * q^94 + 9 * q^95 - 12 * q^96 - 156 * q^97 + 105 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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