LMFDB - Embedded newform 97.2.k.a.11.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [97,2,Mod(2,97)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(97, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([17])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("97.2"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	97.k (of order $48$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.774548899606$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$8$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	97.11
Dual form			97.2.k.a.53.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.129856 - 0.986358i) q^{2} +(-0.567607 + 0.739719i) q^{3} +(0.975813 - 0.261468i) q^{4} +(0.354879 - 0.120465i) q^{5} +(0.803335 + 0.463806i) q^{6} +(1.84879 - 1.62135i) q^{7} +(-1.14606 - 2.76683i) q^{8} +(0.551450 + 2.05804i) q^{9} +(-0.164905 - 0.334394i) q^{10} +(-1.27328 - 0.167631i) q^{11} +(-0.360465 + 0.870239i) q^{12} +(-0.507390 - 1.49472i) q^{13} +(-1.83931 - 1.61303i) q^{14} +(-0.112321 + 0.330888i) q^{15} +(-0.830477 + 0.479476i) q^{16} +(-5.37653 + 6.13076i) q^{17} +(1.95835 - 0.811176i) q^{18} +(-0.299968 + 1.50804i) q^{19} +(0.314798 - 0.210341i) q^{20} +(0.149955 + 2.28788i) q^{21} +1.27768i q^{22} +(2.75764 - 0.180745i) q^{23} +(2.69718 + 0.722708i) q^{24} +(-3.85534 + 2.95831i) q^{25} +(-1.40844 + 0.694567i) q^{26} +(-4.41964 - 1.83068i) q^{27} +(1.38015 - 2.06553i) q^{28} +(-0.425964 + 0.863770i) q^{29} +(0.340959 + 0.0678210i) q^{30} +(3.06927 + 2.35513i) q^{31} +(-3.06545 - 3.99497i) q^{32} +(0.846722 - 0.846722i) q^{33} +(6.74530 + 4.50707i) q^{34} +(0.460782 - 0.798098i) q^{35} +(1.07622 + 1.86407i) q^{36} +(0.155364 - 2.37040i) q^{37} +(1.52642 + 0.100047i) q^{38} +(1.39367 + 0.473088i) q^{39} +(-0.740017 - 0.843828i) q^{40} +(-4.43346 - 2.18634i) q^{41} +(2.23719 - 0.445005i) q^{42} +(2.44843 - 9.13766i) q^{43} +(-1.28631 + 0.169346i) q^{44} +(0.443620 + 0.663924i) q^{45} +(-0.536376 - 2.69655i) q^{46} +(-4.60960 - 4.60960i) q^{47} +(0.116707 - 0.886474i) q^{48} +(-0.124416 + 0.945035i) q^{49} +(3.41859 + 3.41859i) q^{50} +(-1.48329 - 7.45699i) q^{51} +(-0.885940 - 1.32590i) q^{52} +(4.79978 - 0.631903i) q^{53} +(-1.23178 + 4.59707i) q^{54} +(-0.472054 + 0.0938974i) q^{55} +(-6.60481 - 3.25713i) q^{56} +(-0.945262 - 1.07786i) q^{57} +(0.907300 + 0.307987i) q^{58} +(6.60653 + 0.433015i) q^{59} +(-0.0230879 + 0.352253i) q^{60} +(1.80992 + 3.13488i) q^{61} +(1.92444 - 3.33323i) q^{62} +(4.35631 + 2.91080i) q^{63} +(-4.89856 + 4.89856i) q^{64} +(-0.360124 - 0.469323i) q^{65} +(-0.945123 - 0.725219i) q^{66} +(12.8752 + 2.56103i) q^{67} +(-3.64349 + 7.38827i) q^{68} +(-1.43155 + 2.14247i) q^{69} +(-0.847045 - 0.350858i) q^{70} +(6.72835 - 3.31805i) q^{71} +(5.06224 - 3.88439i) q^{72} +(5.10159 + 1.36697i) q^{73} +(-2.35824 + 0.154567i) q^{74} -4.53102i q^{75} +(0.101592 + 1.55000i) q^{76} +(-2.62582 + 1.75452i) q^{77} +(0.285657 - 1.43609i) q^{78} +(-11.9738 + 4.95969i) q^{79} +(-0.236959 + 0.270200i) q^{80} +(-1.67276 + 0.965766i) q^{81} +(-1.58080 + 4.65689i) q^{82} +(-7.68770 - 6.74193i) q^{83} +(0.744535 + 2.19333i) q^{84} +(-1.16948 + 2.82336i) q^{85} +(-9.33095 - 1.22844i) q^{86} +(-0.397167 - 0.805375i) q^{87} +(0.995447 + 3.71506i) q^{88} +(3.51797 + 8.49314i) q^{89} +(0.597260 - 0.523783i) q^{90} +(-3.36153 - 1.94078i) q^{91} +(2.64368 - 0.897408i) q^{92} +(-3.48427 + 0.933608i) q^{93} +(-3.94813 + 5.14530i) q^{94} +(0.0752140 + 0.571307i) q^{95} +4.69512 q^{96} +(-6.53067 + 7.37227i) q^{97} +0.948299 q^{98} +(-0.357160 - 2.71290i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{2} - 24 q^{3} - 16 q^{4} - 16 q^{5} - 24 q^{6} - 16 q^{7} - 16 q^{8} + 8 q^{9} + 16 q^{10} - 16 q^{11} - 8 q^{12} - 16 q^{13} + 32 q^{14} + 16 q^{15} - 24 q^{16} - 8 q^{17} - 80 q^{18} - 24 q^{19}+ \cdots - 224 q^{99}+O(q^{100}) $ 128 * q - 16 * q^2 - 24 * q^3 - 16 * q^4 - 16 * q^5 - 24 * q^6 - 16 * q^7 - 16 * q^8 + 8 * q^9 + 16 * q^10 - 16 * q^11 - 8 * q^12 - 16 * q^13 + 32 * q^14 + 16 * q^15 - 24 * q^16 - 8 * q^17 - 80 * q^18 - 24 * q^19 - 8 * q^20 - 16 * q^21 + 24 * q^23 - 48 * q^24 - 24 * q^25 + 24 * q^26 + 24 * q^28 - 56 * q^30 - 40 * q^31 + 128 * q^32 - 8 * q^33 - 16 * q^34 - 72 * q^35 + 112 * q^36 + 8 * q^37 - 16 * q^38 + 32 * q^40 + 16 * q^41 - 64 * q^42 - 24 * q^43 + 104 * q^44 + 152 * q^45 - 16 * q^46 + 32 * q^47 - 48 * q^49 + 8 * q^50 - 16 * q^51 - 48 * q^52 - 32 * q^53 + 96 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 + 112 * q^58 + 32 * q^59 + 16 * q^60 - 56 * q^61 + 56 * q^62 + 176 * q^63 - 48 * q^64 - 8 * q^65 - 8 * q^66 - 32 * q^67 - 48 * q^68 - 96 * q^69 + 64 * q^70 + 136 * q^71 + 112 * q^72 - 64 * q^73 + 304 * q^76 - 16 * q^77 - 64 * q^78 + 32 * q^79 - 48 * q^80 + 72 * q^81 - 8 * q^82 - 64 * q^83 - 112 * q^84 - 72 * q^85 - 248 * q^86 + 96 * q^87 - 96 * q^88 - 16 * q^90 - 168 * q^91 - 120 * q^92 + 24 * q^93 + 48 * q^94 + 32 * q^95 - 352 * q^96 - 176 * q^97 + 208 * q^98 - 224 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{43}{48}\right)$

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 $

$2$	−0.129856	−	0.986358i	−0.0918224	−	0.697460i	−0.974001	−	0.226545i	$-0.927257\pi$
$2$	−0.129856	−	0.986358i	−0.0918224	−	0.697460i	0.882178	−	0.470915i	$-0.156076\pi$
$3$	−0.567607	+	0.739719i	−0.327708	+	0.427077i	−0.927929	−	0.372757i	$-0.878413\pi$
$3$	−0.567607	+	0.739719i	−0.327708	+	0.427077i	0.600221	+	0.799834i	$0.295079\pi$
$4$	0.975813	−	0.261468i	0.487906	−	0.130734i
$5$	0.354879	−	0.120465i	0.158707	−	0.0538737i	−0.240955	−	0.970536i	$-0.577461\pi$
$5$	0.354879	−	0.120465i	0.158707	−	0.0538737i	0.399662	+	0.916663i	$0.369127\pi$
$6$	0.803335	+	0.463806i	0.327960	+	0.189348i
$7$	1.84879	−	1.62135i	0.698778	−	0.612812i	−0.234436	−	0.972131i	$-0.575324\pi$
$7$	1.84879	−	1.62135i	0.698778	−	0.612812i	0.933215	+	0.359319i	$0.116991\pi$
$8$	−1.14606	−	2.76683i	−0.405192	−	0.978220i
$9$	0.551450	+	2.05804i	0.183817	+	0.686013i
$10$	−0.164905	−	0.334394i	−0.0521476	−	0.105745i
$11$	−1.27328	−	0.167631i	−0.383909	−	0.0505425i	−0.0638979	−	0.997956i	$-0.520353\pi$
$11$	−1.27328	−	0.167631i	−0.383909	−	0.0505425i	−0.320011	+	0.947414i	$0.603687\pi$
$12$	−0.360465	+	0.870239i	−0.104057	+	0.251216i
$13$	−0.507390	−	1.49472i	−0.140725	−	0.414561i	0.853603	−	0.520925i	$-0.174413\pi$
$13$	−0.507390	−	1.49472i	−0.140725	−	0.414561i	−0.994327	+	0.106363i	$0.966079\pi$
$14$	−1.83931	−	1.61303i	−0.491576	−	0.431100i
$15$	−0.112321	+	0.330888i	−0.0290012	+	0.0854348i
$16$	−0.830477	+	0.479476i	−0.207619	+	0.119869i
$17$	−5.37653	+	6.13076i	−1.30400	+	1.48693i	−0.540088	+	0.841608i	$0.681609\pi$
$17$	−5.37653	+	6.13076i	−1.30400	+	1.48693i	−0.763913	+	0.645320i	$0.776724\pi$
$18$	1.95835	−	0.811176i	0.461588	−	0.191196i
$19$	−0.299968	+	1.50804i	−0.0688173	+	0.345968i	−0.999819	−	0.0190480i	$-0.993936\pi$
$19$	−0.299968	+	1.50804i	−0.0688173	+	0.345968i	0.931001	+	0.365016i	$0.118936\pi$
$20$	0.314798	−	0.210341i	0.0703909	−	0.0470337i
$21$	0.149955	+	2.28788i	0.0327229	+	0.499256i
$22$			1.27768i			0.272402i
$23$	2.75764	−	0.180745i	0.575007	−	0.0376880i	0.224874	−	0.974388i	$-0.427803\pi$
$23$	2.75764	−	0.180745i	0.575007	−	0.0376880i	0.350133	+	0.936700i	$0.386136\pi$
$24$	2.69718	+	0.722708i	0.550560	+	0.147522i
$25$	−3.85534	+	2.95831i	−0.771068	+	0.591661i
$26$	−1.40844	+	0.694567i	−0.276218	+	0.136216i
$27$	−4.41964	−	1.83068i	−0.850560	−	0.352314i
$28$	1.38015	−	2.06553i	0.260823	−	0.390349i
$29$	−0.425964	+	0.863770i	−0.0790995	+	0.160398i	−0.932830	−	0.360318i	$-0.882668\pi$
$29$	−0.425964	+	0.863770i	−0.0790995	+	0.160398i	0.853730	+	0.520716i	$0.174335\pi$
$30$	0.340959	+	0.0678210i	0.0622504	+	0.0123824i
$31$	3.06927	+	2.35513i	0.551257	+	0.422994i	0.846469	−	0.532437i	$-0.178724\pi$
$31$	3.06927	+	2.35513i	0.551257	+	0.422994i	−0.295213	+	0.955432i	$0.595390\pi$
$32$	−3.06545	−	3.99497i	−0.541900	−	0.706217i
$33$	0.846722	−	0.846722i	0.147395	−	0.147395i
$34$	6.74530	+	4.50707i	1.15681	+	0.772956i
$35$	0.460782	−	0.798098i	0.0778864	−	0.134903i
$36$	1.07622	+	1.86407i	0.179371	+	0.310679i
$37$	0.155364	−	2.37040i	0.0255417	−	0.389692i	−0.965880	−	0.258990i	$-0.916610\pi$
$37$	0.155364	−	2.37040i	0.0255417	−	0.389692i	0.991422	−	0.130702i	$-0.0417230\pi$
$38$	1.52642	+	0.100047i	0.247618	+	0.0162297i
$39$	1.39367	+	0.473088i	0.223166	+	0.0757547i
$40$	−0.740017	−	0.843828i	−0.117007	−	0.133421i
$41$	−4.43346	−	2.18634i	−0.692390	−	0.341449i	0.0618153	−	0.998088i	$-0.480311\pi$
$41$	−4.43346	−	2.18634i	−0.692390	−	0.341449i	−0.754205	+	0.656639i	$0.771978\pi$
$42$	2.23719	−	0.445005i	0.345206	−	0.0686658i
$43$	2.44843	−	9.13766i	0.373382	−	1.39348i	−0.482313	−	0.875999i	$-0.660203\pi$
$43$	2.44843	−	9.13766i	0.373382	−	1.39348i	0.855695	−	0.517481i	$-0.173130\pi$
$44$	−1.28631	+	0.169346i	−0.193919	+	0.0255299i
$45$	0.443620	+	0.663924i	0.0661309	+	0.0989719i
$46$	−0.536376	−	2.69655i	−0.0790844	−	0.397584i
$47$	−4.60960	−	4.60960i	−0.672379	−	0.672379i	0.285885	−	0.958264i	$-0.407712\pi$
$47$	−4.60960	−	4.60960i	−0.672379	−	0.672379i	−0.958264	+	0.285885i	$0.907712\pi$
$48$	0.116707	−	0.886474i	0.0168451	−	0.127951i
$49$	−0.124416	+	0.945035i	−0.0177737	+	0.135005i
$50$	3.41859	+	3.41859i	0.483461	+	0.483461i
$51$	−1.48329	−	7.45699i	−0.207702	−	1.04419i
$52$	−0.885940	−	1.32590i	−0.122858	−	0.183870i
$53$	4.79978	−	0.631903i	0.659300	−	0.0867985i	0.206550	−	0.978436i	$-0.433776\pi$
$53$	4.79978	−	0.631903i	0.659300	−	0.0867985i	0.452750	+	0.891637i	$0.350443\pi$
$54$	−1.23178	+	4.59707i	−0.167624	+	0.625582i
$55$	−0.472054	+	0.0938974i	−0.0636518	+	0.0126611i
$56$	−6.60481	−	3.25713i	−0.882605	−	0.435253i
$57$	−0.945262	−	1.07786i	−0.125203	−	0.142767i
$58$	0.907300	+	0.307987i	0.119134	+	0.0404407i
$59$	6.60653	+	0.433015i	0.860098	+	0.0563738i	0.489066	−	0.872247i	$-0.337338\pi$
$59$	6.60653	+	0.433015i	0.860098	+	0.0563738i	0.371031	+	0.928620i	$0.379004\pi$
$60$	−0.0230879	+	0.352253i	−0.00298063	+	0.0454756i
$61$	1.80992	+	3.13488i	0.231737	+	0.401380i	0.958319	−	0.285699i	$-0.0922259\pi$
$61$	1.80992	+	3.13488i	0.231737	+	0.401380i	−0.726583	+	0.687079i	$0.758893\pi$
$62$	1.92444	−	3.33323i	0.244404	−	0.423320i
$63$	4.35631	+	2.91080i	0.548844	+	0.366726i
$64$	−4.89856	+	4.89856i	−0.612320	+	0.612320i
$65$	−0.360124	−	0.469323i	−0.0446679	−	0.0582123i
$66$	−0.945123	−	0.725219i	−0.116337	−	0.0892683i
$67$	12.8752	+	2.56103i	1.57295	+	0.312880i	0.903039	−	0.429558i	$-0.141331\pi$
$67$	12.8752	+	2.56103i	1.57295	+	0.312880i	0.669914	+	0.742438i	$0.266331\pi$
$68$	−3.64349	+	7.38827i	−0.441838	+	0.895959i
$69$	−1.43155	+	2.14247i	−0.172339	+	0.257923i
$70$	−0.847045	−	0.350858i	−0.101241	−	0.0419355i
$71$	6.72835	−	3.31805i	0.798508	−	0.393781i	0.00320662	−	0.999995i	$-0.498979\pi$
$71$	6.72835	−	3.31805i	0.798508	−	0.393781i	0.795301	+	0.606214i	$0.207313\pi$
$72$	5.06224	−	3.88439i	0.596591	−	0.457780i
$73$	5.10159	+	1.36697i	0.597096	+	0.159991i	0.544694	−	0.838635i	$-0.316646\pi$
$73$	5.10159	+	1.36697i	0.597096	+	0.159991i	0.0524019	+	0.998626i	$0.483312\pi$
$74$	−2.35824	+	0.154567i	−0.274140	+	0.0179681i
$75$		−	4.53102i		−	0.523197i
$76$	0.101592	+	1.55000i	0.0116534	+	0.177797i
$77$	−2.62582	+	1.75452i	−0.299240	+	0.199946i
$78$	0.285657	−	1.43609i	0.0323443	−	0.162606i
$79$	−11.9738	+	4.95969i	−1.34715	+	0.558009i	−0.935498	−	0.353331i	$-0.885049\pi$
$79$	−11.9738	+	4.95969i	−1.34715	+	0.558009i	−0.411654	+	0.911340i	$0.635049\pi$
$80$	−0.236959	+	0.270200i	−0.0264928	+	0.0302092i
$81$	−1.67276	+	0.965766i	−0.185862	+	0.107307i
$82$	−1.58080	+	4.65689i	−0.174570	+	0.514267i
$83$	−7.68770	−	6.74193i	−0.843834	−	0.740023i	0.123820	−	0.992305i	$-0.460486\pi$
$83$	−7.68770	−	6.74193i	−0.843834	−	0.740023i	−0.967654	+	0.252282i	$0.918819\pi$
$84$	0.744535	+	2.19333i	0.0812355	+	0.239312i
$85$	−1.16948	+	2.82336i	−0.126847	+	0.306237i
$86$	−9.33095	−	1.22844i	−1.00618	−	0.132466i
$87$	−0.397167	−	0.805375i	−0.0425808	−	0.0863453i
$88$	0.995447	+	3.71506i	0.106115	+	0.396027i
$89$	3.51797	+	8.49314i	0.372904	+	0.900271i	0.993255	+	0.115947i	$0.0369901\pi$
$89$	3.51797	+	8.49314i	0.372904	+	0.900271i	−0.620351	+	0.784324i	$0.713010\pi$
$90$	0.597260	−	0.523783i	0.0629567	−	0.0552115i
$91$	−3.36153	−	1.94078i	−0.352384	−	0.203449i
$92$	2.64368	−	0.897408i	0.275623	−	0.0935612i
$93$	−3.48427	+	0.933608i	−0.361302	+	0.0968107i
$94$	−3.94813	+	5.14530i	−0.407218	+	0.530697i
$95$	0.0752140	+	0.571307i	0.00771679	+	0.0586149i
$96$	4.69512			0.479194
$97$	−6.53067	+	7.37227i	−0.663089	+	0.748541i
$97$	−6.53067	+	7.37227i	−0.663089	+	0.748541i
$98$	0.948299			0.0957926
$99$	−0.357160	−	2.71290i	−0.0358959	−	0.272657i
$100$	−2.98859	+	3.89480i	−0.298859	+	0.389480i
$101$	7.05381	−	1.89006i	0.701880	−	0.188068i	0.109808	−	0.993953i	$-0.464977\pi$
$101$	7.05381	−	1.89006i	0.701880	−	0.188068i	0.592073	+	0.805885i	$0.298310\pi$
$102$	−7.16264	+	2.43139i	−0.709207	+	0.240743i
$103$	−9.46371	−	5.46388i	−0.932487	−	0.538372i	−0.0448898	−	0.998992i	$-0.514294\pi$
$103$	−9.46371	−	5.46388i	−0.932487	−	0.538372i	−0.887597	+	0.460620i	$0.847627\pi$
$104$	−3.55414	+	3.11690i	−0.348512	+	0.305637i
$105$	0.328825	+	0.793855i	0.0320901	+	0.0774723i
$106$	−1.24656	−	4.65224i	−0.121077	−	0.451866i
$107$	−3.17880	−	6.44596i	−0.307306	−	0.623155i	0.687359	−	0.726318i	$-0.258770\pi$
$107$	−3.17880	−	6.44596i	−0.307306	−	0.623155i	−0.994664	+	0.103164i	$0.967103\pi$
$108$	−4.79141	−	0.630801i	−0.461053	−	0.0606988i
$109$	6.36188	−	15.3589i	0.609357	−	1.47112i	−0.254343	−	0.967114i	$-0.581859\pi$
$109$	6.36188	−	15.3589i	0.609357	−	1.47112i	0.863701	−	0.504005i	$-0.168141\pi$
$110$	0.153916	+	0.453421i	0.0146753	+	0.0432320i
$111$	1.66525	+	1.46038i	0.158058	+	0.138613i
$112$	−0.757983	+	2.23295i	−0.0716227	+	0.210994i
$113$	15.5795	−	8.99486i	1.46560	−	0.846165i	0.466340	−	0.884606i	$-0.345572\pi$
$113$	15.5795	−	8.99486i	1.46560	−	0.846165i	0.999261	+	0.0384409i	$0.0122391\pi$
$114$	−0.940412	+	1.07233i	−0.0880776	+	0.100433i
$115$	0.956854	−	0.396342i	0.0892271	−	0.0369591i
$116$	−0.189813	+	0.954254i	−0.0176237	+	0.0886002i
$117$	2.79640	−	1.86849i	0.258527	−	0.172742i
$118$	−0.430793	−	6.57264i	−0.0396577	−	0.605060i
$119$			20.0517i			1.83814i
$120$	1.04423	−	0.0684428i	0.0953252	−	0.00624794i
$121$	−9.03204	−	2.42013i	−0.821095	−	0.220012i
$122$	2.85708	−	2.19231i	0.258668	−	0.198483i
$123$	4.13374	−	2.03853i	0.372727	−	0.183808i
$124$	3.61082	+	1.49565i	0.324262	+	0.134314i
$125$	−2.05286	+	3.07231i	−0.183613	+	0.274796i
$126$	2.30539	−	4.67487i	0.205381	−	0.416471i
$127$	−4.91189	−	0.977036i	−0.435860	−	0.0866979i	−0.0277166	−	0.999616i	$-0.508824\pi$
$127$	−4.91189	−	0.977036i	−0.435860	−	0.0866979i	−0.408143	+	0.912918i	$0.633824\pi$
$128$	−2.52209	−	1.93527i	−0.222923	−	0.171055i
$129$	5.36956	+	6.99775i	0.472763	+	0.616117i
$130$	−0.416156	+	0.416156i	−0.0364993	+	0.0364993i
$131$	9.08081	+	6.06760i	0.793394	+	0.530129i	0.884958	−	0.465670i	$-0.154187\pi$
$131$	9.08081	+	6.06760i	0.793394	+	0.530129i	−0.0915641	+	0.995799i	$0.529187\pi$
$132$	0.604851	−	1.04763i	0.0526456	−	0.0911848i
$133$	1.89048	+	3.27441i	0.163925	+	0.283927i
$134$	0.854169	−	13.0321i	0.0737890	−	1.12580i
$135$	−1.78897	−	0.117255i	−0.153970	−	0.0100917i
$136$	23.1246	+	7.84973i	1.98291	+	0.673109i
$137$	−0.168348	−	0.191964i	−0.0143829	−	0.0164006i	0.744604	−	0.667507i	$-0.232639\pi$
$137$	−0.168348	−	0.191964i	−0.0143829	−	0.0164006i	−0.758987	+	0.651106i	$0.774305\pi$
$138$	2.29914	+	1.13381i	0.195716	+	0.0965163i
$139$	4.72694	−	0.940248i	0.400934	−	0.0797508i	0.00949542	−	0.999955i	$-0.496977\pi$
$139$	4.72694	−	0.940248i	0.400934	−	0.0797508i	0.391439	+	0.920204i	$0.371977\pi$
$140$	0.240960	−	0.899274i	0.0203648	−	0.0760025i
$141$	6.02625	−	0.793370i	0.507502	−	0.0668138i
$142$	−4.14651	−	6.20569i	−0.347967	−	0.520770i
$143$	0.395489	+	1.98826i	0.0330724	+	0.166266i
$144$	−1.44475	−	1.44475i	−0.120396	−	0.120396i
$145$	−0.0471115	+	0.357848i	−0.00391240	+	0.0297176i
$146$	0.685845	−	5.20951i	0.0567609	−	0.431142i
$147$	−0.628441	−	0.628441i	−0.0518329	−	0.0518329i
$148$	−0.468178	−	2.35369i	−0.0384840	−	0.193472i
$149$	−2.02939	−	3.03720i	−0.166254	−	0.248817i	0.738982	−	0.673725i	$-0.235307\pi$
$149$	−2.02939	−	3.03720i	−0.166254	−	0.248817i	−0.905237	+	0.424907i	$0.860307\pi$
$150$	−4.46921	+	0.588383i	−0.364909	+	0.0480412i
$151$	4.02858	−	15.0349i	0.327841	−	1.22352i	−0.583584	−	0.812053i	$-0.698350\pi$
$151$	4.02858	−	15.0349i	0.327841	−	1.22352i	0.911425	−	0.411466i	$-0.134983\pi$
$152$	4.51626	−	0.898340i	0.366317	−	0.0728650i
$153$	−15.5822	−	7.68431i	−1.25975	−	0.621239i
$154$	2.07156	+	2.36216i	0.166931	+	0.190349i
$155$	1.37293	+	0.466047i	0.110276	+	0.0374338i
$156$	1.48366	+	0.0972443i	0.118788	+	0.00778577i
$157$	−1.41677	+	21.6158i	−0.113071	+	1.72513i	0.445167	+	0.895448i	$0.353144\pi$
$157$	−1.41677	+	21.6158i	−0.113071	+	1.72513i	−0.558238	+	0.829681i	$0.688522\pi$
$158$	6.44690	+	11.1664i	0.512888	+	0.888348i
$159$	−2.25696	+	3.90916i	−0.178988	+	0.310017i
$160$	−1.56912	−	1.04845i	−0.124050	−	0.0828873i
$161$	4.80525	−	4.80525i	0.378707	−	0.378707i
$162$	1.16981	+	1.52453i	0.0919089	+	0.119778i
$163$	−14.8027	−	11.3585i	−1.15944	−	0.889669i	−0.164132	−	0.986438i	$-0.552482\pi$
$163$	−14.8027	−	11.3585i	−1.15944	−	0.889669i	−0.995307	+	0.0967699i	$0.969149\pi$
$164$	−4.89789	−	0.974250i	−0.382461	−	0.0760761i
$165$	0.198483	−	0.402484i	0.0154519	−	0.0313334i
$166$	−5.65166	+	8.45830i	−0.438654	+	0.656491i
$167$	8.23888	+	3.41266i	0.637544	+	0.264079i	0.677954	−	0.735104i	$-0.262867\pi$
$167$	8.23888	+	3.41266i	0.637544	+	0.264079i	−0.0404108	+	0.999183i	$0.512867\pi$
$168$	6.15830	−	3.03694i	0.475123	−	0.234305i
$169$	8.33684	−	6.39708i	0.641296	−	0.492083i
$170$	2.93671	+	0.786889i	0.225235	+	0.0603516i
$171$	−3.26902	+	0.214263i	−0.249988	+	0.0163851i
$172$		−	9.55683i		−	0.728701i
$173$	−0.529060	−	8.07189i	−0.0402237	−	0.613695i	−0.969621	−	0.244613i	$-0.921339\pi$
$173$	−0.529060	−	8.07189i	−0.0402237	−	0.613695i	0.929397	−	0.369081i	$-0.120328\pi$
$174$	−0.742813	+	0.496332i	−0.0563125	+	0.0376268i
$175$	−2.33128	+	11.7201i	−0.176228	+	0.885960i
$176$	1.13781	−	0.471295i	0.0857653	−	0.0355252i
$177$	−4.07022	+	4.64120i	−0.305937	+	0.348854i
$178$	7.92044	−	4.57287i	0.593662	−	0.342751i
$179$	−4.87749	+	14.3686i	−0.364561	+	1.07396i	0.597674	+	0.801739i	$0.296092\pi$
$179$	−4.87749	+	14.3686i	−0.364561	+	1.07396i	−0.962235	+	0.272222i	$0.912242\pi$
$180$	0.606485	+	0.531873i	0.0452047	+	0.0396435i
$181$	−5.09546	−	15.0107i	−0.378743	−	1.11574i	−0.954523	−	0.298136i	$-0.903635\pi$
$181$	−5.09546	−	15.0107i	−0.378743	−	1.11574i	0.575781	−	0.817604i	$-0.304698\pi$
$182$	−1.47779	+	3.56769i	−0.109541	+	0.264455i
$183$	−3.34625	−	0.440542i	−0.247362	−	0.0325658i
$184$	−3.66050	−	7.42276i	−0.269856	−	0.547213i
$185$	−0.230415	−	0.859921i	−0.0169405	−	0.0632227i
$186$	1.37333	+	3.31551i	0.100697	+	0.243105i
$187$	7.87354	−	6.90491i	0.575770	−	0.504937i
$188$	−5.70337	−	3.29284i	−0.415961	−	0.240155i
$189$	−11.1392	+	3.78124i	−0.810255	+	0.275045i
$190$	0.553746	−	0.148376i	0.0401730	−	0.0107643i
$191$	5.46597	−	7.12339i	0.395504	−	0.515431i	−0.552576	−	0.833462i	$-0.686355\pi$
$191$	5.46597	−	7.12339i	0.395504	−	0.515431i	0.948080	+	0.318032i	$0.103022\pi$
$192$	−0.843105	−	6.40402i	−0.0608459	−	0.462170i
$193$	−9.10704			−0.655539			−0.327770	−	0.944758i	$-0.606297\pi$
$193$	−9.10704			−0.655539			−0.327770	+	0.944758i	$0.606297\pi$
$194$	8.11975	+	5.48424i	0.582964	+	0.393745i
$195$	0.551576			0.0394992
$196$	0.125690	+	0.954708i	0.00897784	+	0.0681934i
$197$	−11.7678	+	15.3361i	−0.838419	+	1.09265i	0.156063	+	0.987747i	$0.450120\pi$
$197$	−11.7678	+	15.3361i	−0.838419	+	1.09265i	−0.994483	+	0.104902i	$0.966547\pi$
$198$	−2.62951	+	0.704575i	−0.186871	+	0.0500720i
$199$	6.08589	−	2.06588i	0.431418	−	0.146447i	−0.0972795	−	0.995257i	$-0.531014\pi$
$199$	6.08589	−	2.06588i	0.431418	−	0.146447i	0.528697	+	0.848811i	$0.322681\pi$
$200$	12.6036	+	7.27666i	0.891206	+	0.514538i
$201$	−9.20248	+	8.07036i	−0.649093	+	0.569239i
$202$	−2.78026	−	6.71214i	−0.195618	−	0.472265i
$203$	0.612952	+	2.28757i	0.0430208	+	0.160556i
$204$	−3.39718	−	6.88879i	−0.237850	−	0.482312i
$205$	−1.83672	−	0.241809i	−0.128282	−	0.0168887i
$206$	−4.16041	+	10.0441i	−0.289870	+	0.699807i
$207$	1.89268	+	5.57565i	0.131550	+	0.387535i
$208$	1.13806	+	0.998051i	0.0789102	+	0.0692024i
$209$	0.634737	−	1.86987i	0.0439056	−	0.129342i
$210$	0.740325	−	0.427427i	0.0510873	−	0.0294952i
$211$	−0.643424	+	0.733685i	−0.0442952	+	0.0505090i	−0.773563	−	0.633719i	$-0.781527\pi$
$211$	−0.643424	+	0.733685i	−0.0442952	+	0.0505090i	0.729268	+	0.684228i	$0.239861\pi$
$212$	4.51846	−	1.87161i	0.310329	−	0.128543i
$213$	−1.36463	+	6.86044i	−0.0935026	+	0.470069i
$214$	−5.94524	+	3.97248i	−0.406408	+	0.271553i
$215$	−0.231874	−	3.53771i	−0.0158137	−	0.241270i
$216$			14.3264i			0.974790i
$217$	9.49294	−	0.622200i	0.644422	−	0.0422377i
$218$	−15.9755	−	4.28063i	−1.08200	−	0.289921i
$219$	−3.90687	+	2.99785i	−0.264002	+	0.202576i
$220$	−0.436085	+	0.215053i	−0.0294009	+	0.0144989i
$221$	11.8918	+	4.92574i	0.799928	+	0.331341i
$222$	1.22422	−	1.83217i	0.0821640	−	0.122967i
$223$	−11.8011	+	23.9304i	−0.790263	+	1.60249i	0.00783642	+	0.999969i	$0.497506\pi$
$223$	−11.8011	+	23.9304i	−0.790263	+	1.60249i	−0.798099	+	0.602526i	$0.794161\pi$
$224$	−12.1446	−	2.41571i	−0.811446	−	0.161407i
$225$	−8.21433	−	6.30308i	−0.547622	−	0.420205i
$226$	−10.8953	−	14.1990i	−0.724741	−	0.944501i
$227$	2.29507	−	2.29507i	0.152329	−	0.152329i	−0.626828	−	0.779157i	$-0.715647\pi$
$227$	2.29507	−	2.29507i	0.152329	−	0.152329i	0.779157	+	0.626828i	$0.215647\pi$
$228$	−1.20423	−	0.804638i	−0.0797518	−	0.0532885i
$229$	−13.3634	+	23.1461i	−0.883077	+	1.52953i	−0.0351749	+	0.999381i	$0.511199\pi$
$229$	−13.3634	+	23.1461i	−0.883077	+	1.52953i	−0.847902	+	0.530153i	$0.822135\pi$
$230$	−0.515189	−	0.892333i	−0.0339705	−	0.0588387i
$231$	0.192583	−	2.93825i	0.0126710	−	0.193322i
$232$	2.87808	+	0.188639i	0.188955	+	0.0123848i
$233$	9.60773	+	3.26138i	0.629423	+	0.213660i	0.617879	−	0.786273i	$-0.287992\pi$
$233$	9.60773	+	3.26138i	0.629423	+	0.213660i	0.0115439	+	0.999933i	$0.496325\pi$
$234$	−2.20613	−	2.51561i	−0.144219	−	0.164451i
$235$	−2.19115	−	1.08055i	−0.142935	−	0.0704875i
$236$	6.55996	−	1.30486i	0.427017	−	0.0849390i
$237$	3.12760	−	11.6724i	0.203160	−	0.758202i
$238$	19.7782	−	2.60385i	1.28203	−	0.168782i
$239$	15.3271	+	22.9386i	0.991427	+	1.48378i	0.871139	+	0.491036i	$0.163382\pi$
$239$	15.3271	+	22.9386i	0.991427	+	1.48378i	0.120288	+	0.992739i	$0.461618\pi$
$240$	−0.0653725	−	0.328650i	−0.00421978	−	0.0212143i
$241$	−15.3835	−	15.3835i	−0.990939	−	0.990939i	0.00902021	−	0.999959i	$-0.497129\pi$
$241$	−15.3835	−	15.3835i	−0.990939	−	0.990939i	−0.999959	+	0.00902021i	$0.997129\pi$
$242$	−1.21424	+	9.22309i	−0.0780545	+	0.592883i
$243$	2.10830	−	16.0141i	0.135247	−	1.02731i
$244$	2.58581	+	2.58581i	0.165540	+	0.165540i
$245$	0.0696911	+	0.350361i	0.00445240	+	0.0223837i
$246$	−2.54752	−	3.81263i	−0.162424	−	0.243084i
$247$	2.40630	−	0.316795i	0.153109	−	0.0201572i
$248$	2.99869	−	11.1912i	0.190417	−	0.710645i
$249$	9.35072	−	1.85997i	0.592578	−	0.117871i
$250$	3.29698	+	1.62589i	0.208519	+	0.102830i
$251$	−7.00762	−	7.99066i	−0.442317	−	0.504366i	0.487126	−	0.873332i	$-0.338045\pi$
$251$	−7.00762	−	7.99066i	−0.442317	−	0.504366i	−0.929443	+	0.368966i	$0.879712\pi$
$252$	5.01203	+	1.70135i	0.315728	+	0.107175i
$253$	−3.54155	−	0.232125i	−0.222655	−	0.0145936i
$254$	−0.325866	+	4.97176i	−0.0204467	+	0.311956i
$255$	−1.42469	−	2.46764i	−0.0892178	−	0.154530i
$256$	−8.50897	+	14.7380i	−0.531811	+	0.921123i
$257$	23.8566	+	15.9405i	1.48813	+	0.994338i	0.992020	+	0.126080i	$0.0402397\pi$
$257$	23.8566	+	15.9405i	1.48813	+	0.994338i	0.496113	+	0.868258i	$0.334760\pi$
$258$	6.20501	−	6.20501i	0.386307	−	0.386307i
$259$	−3.55601	−	4.63428i	−0.220960	−	0.287960i
$260$	−0.474126	−	0.363810i	−0.0294041	−	0.0225625i
$261$	−2.01257	−	0.400325i	−0.124575	−	0.0247795i
$262$	4.80563	−	9.74485i	0.296893	−	0.602039i
$263$	−16.9081	+	25.3048i	−1.04260	+	1.56036i	−0.233790	+	0.972287i	$0.575113\pi$
$263$	−16.9081	+	25.3048i	−1.04260	+	1.56036i	−0.808809	+	0.588072i	$0.799887\pi$
$264$	−3.31312	−	1.37234i	−0.203909	−	0.0844617i
$265$	1.62722	−	0.802455i	0.0999592	−	0.0492944i
$266$	2.98424	−	2.28989i	0.182976	−	0.140402i
$267$	−8.27936	−	2.21845i	−0.506689	−	0.135767i
$268$	13.2334	−	0.867362i	0.808358	−	0.0529826i
$269$		−	25.3521i		−	1.54574i	−0.634562	−	0.772872i	$-0.718819\pi$
$269$		−	25.3521i		−	1.54574i	0.634562	−	0.772872i	$-0.281181\pi$
$270$	0.116654	+	1.77979i	0.00709932	+	0.108315i
$271$	10.6831	−	7.13825i	0.648955	−	0.433618i	−0.187042	−	0.982352i	$-0.559890\pi$
$271$	10.6831	−	7.13825i	0.648955	−	0.433618i	0.835997	+	0.548734i	$0.184890\pi$
$272$	1.52553	−	7.66938i	0.0924991	−	0.465024i
$273$	3.34365	−	1.38499i	0.202367	−	0.0838232i
$274$	−0.167484	+	0.190979i	−0.0101181	+	0.0115375i
$275$	5.40483	−	3.12048i	0.325924	−	0.188172i
$276$	−0.836739	+	2.46495i	−0.0503658	+	0.148373i
$277$	14.3784	+	12.6095i	0.863914	+	0.757633i	0.971619	−	0.236550i	$-0.0760168\pi$
$277$	14.3784	+	12.6095i	0.863914	+	0.757633i	−0.107705	+	0.994183i	$0.534350\pi$
$278$	−1.54124	−	4.54036i	−0.0924377	−	0.272313i
$279$	−3.15441	+	7.61541i	−0.188849	+	0.455923i
$280$	−2.73628	−	0.360238i	−0.163524	−	0.0215283i
$281$	6.08234	+	12.3338i	0.362842	+	0.735771i	0.999370	−	0.0354824i	$-0.0112968\pi$
$281$	6.08234	+	12.3338i	0.362842	+	0.735771i	−0.636528	+	0.771253i	$0.719630\pi$
$282$	−1.56509	−	5.84101i	−0.0932000	−	0.347827i
$283$	5.30770	+	12.8139i	0.315510	+	0.761709i	0.999481	+	0.0322000i	$0.0102513\pi$
$283$	5.30770	+	12.8139i	0.315510	+	0.761709i	−0.683971	+	0.729509i	$0.739749\pi$
$284$	5.69804	−	4.99705i	0.338117	−	0.296520i
$285$	−0.465299	−	0.268640i	−0.0275619	−	0.0159129i
$286$	1.90977	−	0.648281i	0.112927	−	0.0383337i
$287$	−11.7414	+	3.14609i	−0.693071	+	0.185708i
$288$	6.53136	−	8.51183i	0.384864	−	0.501565i
$289$	−6.46018	−	49.0699i	−0.380010	−	2.88647i
$290$	0.359083			0.0210861
$291$	−1.74656	−	9.01541i	−0.102385	−	0.528493i
$292$	5.33562			0.312243
$293$	−1.15677	−	8.78658i	−0.0675795	−	0.513317i	−0.991438	−	0.130582i	$-0.958315\pi$
$293$	−1.15677	−	8.78658i	−0.0675795	−	0.513317i	0.923858	−	0.382735i	$-0.125018\pi$
$294$	−0.538261	+	0.701475i	−0.0313920	+	0.0409108i
$295$	2.39668	−	0.642189i	0.139540	−	0.0373897i
$296$	−6.73654	+	2.28675i	−0.391554	+	0.132915i
$297$	5.32057	+	3.07183i	0.308731	+	0.178246i
$298$	−2.73224	+	2.39611i	−0.158274	+	0.138803i
$299$	−1.66936	−	4.03019i	−0.0965416	−	0.233072i
$300$	−1.18472	−	4.42143i	−0.0683998	−	0.255271i
$301$	−10.2887	−	20.8634i	−0.593030	−	1.20255i
$302$	−15.3529	−	2.02124i	−0.883459	−	0.116310i
$303$	−2.60567	+	6.29065i	−0.149692	+	0.361388i
$304$	−0.473953	−	1.39622i	−0.0271830	−	0.0800787i
$305$	1.01995	+	0.894469i	0.0584019	+	0.0512171i
$306$	−5.55602	+	16.3675i	−0.317617	+	0.935668i
$307$	13.7723	−	7.95145i	0.786028	−	0.453813i	−0.0525346	−	0.998619i	$-0.516730\pi$
$307$	13.7723	−	7.95145i	0.786028	−	0.453813i	0.838562	+	0.544806i	$0.183397\pi$
$308$	−2.10356	+	2.39865i	−0.119861	+	0.136676i
$309$	9.41340	−	3.89916i	0.535510	−	0.221815i
$310$	0.281405	−	1.41472i	0.0159827	−	0.0803507i
$311$	−1.10646	+	0.739316i	−0.0627418	+	0.0419227i	−0.586546	−	0.809916i	$-0.699513\pi$
$311$	−1.10646	+	0.739316i	−0.0627418	+	0.0419227i	0.523804	+	0.851839i	$0.324513\pi$
$312$	−0.288276	−	4.39823i	−0.0163204	−	0.249001i
$313$			8.62789i			0.487677i	0.969816	+	0.243838i	$0.0784067\pi$
$313$			8.62789i			0.487677i	−0.969816	+	0.243838i	$0.921593\pi$
$314$	21.5049	−	1.40950i	1.21359	−	0.0795430i
$315$	1.89661	+	0.508196i	0.106862	+	0.0286336i
$316$	−10.3873	+	7.97049i	−0.584334	+	0.448375i
$317$	24.0593	−	11.8647i	1.35130	−	0.666389i	0.384790	−	0.923004i	$-0.374274\pi$
$317$	24.0593	−	11.8647i	1.35130	−	0.666389i	0.966514	+	0.256615i	$0.0826073\pi$
$318$	4.14891	+	1.71854i	0.232659	+	0.0963707i
$319$	0.687166	−	1.02842i	0.0384739	−	0.0575803i
$320$	−1.14829	+	2.32850i	−0.0641914	+	0.130167i
$321$	6.57251	+	1.30735i	0.366842	+	0.0729693i
$322$	−5.36369	−	4.11570i	−0.298907	−	0.229359i
$323$	−7.63264	−	9.94705i	−0.424692	−	0.553469i
$324$	−1.37978	+	1.37978i	−0.0766544	+	0.0766544i
$325$	6.37801	+	4.26165i	0.353788	+	0.236394i
$326$	−9.28134	+	16.0758i	−0.514046	+	0.890354i
$327$	7.75026	+	13.4238i	0.428590	+	0.742340i
$328$	−0.968226	+	14.7723i	−0.0534614	+	0.815663i
$329$	−15.9960	−	1.04843i	−0.881886	−	0.0578019i
$330$	−0.422768	−	0.143510i	−0.0232726	−	0.00789999i
$331$	5.66600	+	6.46083i	0.311431	+	0.355119i	0.886288	−	0.463135i	$-0.153275\pi$
$331$	5.66600	+	6.46083i	0.311431	+	0.355119i	−0.574856	+	0.818254i	$0.694942\pi$
$332$	−9.26455	−	4.56877i	−0.508458	−	0.250744i
$333$	4.96405	−	0.987411i	0.272028	−	0.0541098i
$334$	2.29623	−	8.56964i	0.125644	−	0.468910i
$335$	4.87764	−	0.642154i	0.266494	−	0.0350846i
$336$	−1.22152	−	1.82813i	−0.0666392	−	0.0997326i
$337$	−0.298182	−	1.49906i	−0.0162430	−	0.0816590i	0.971814	−	0.235751i	$-0.0757549\pi$
$337$	−0.298182	−	1.49906i	−0.0162430	−	0.0816590i	−0.988057	+	0.154092i	$0.950755\pi$
$338$	−7.39241	−	7.39241i	−0.402094	−	0.402094i
$339$	−2.18939	+	16.6300i	−0.118911	+	0.903219i
$340$	−0.402969	+	3.06085i	−0.0218541	+	0.165998i
$341$	−3.51325	−	3.51325i	−0.190253	−	0.190253i
$342$	0.635843	+	3.19660i	0.0343825	+	0.172852i
$343$	10.8653	+	16.2611i	0.586673	+	0.878019i
$344$	−28.0883	+	3.69790i	−1.51442	+	0.199377i
$345$	−0.249935	+	0.932770i	−0.0134560	+	0.0502186i
$346$	−7.89307	+	1.57003i	−0.424334	+	0.0844053i
$347$	−19.5421	−	9.63710i	−1.04908	−	0.517347i	−0.165780	−	0.986163i	$-0.553014\pi$
$347$	−19.5421	−	9.63710i	−1.04908	−	0.517347i	−0.883296	+	0.468816i	$0.844681\pi$
$348$	−0.598141	−	0.682049i	−0.0320637	−	0.0365617i
$349$	−20.4785	−	6.95151i	−1.09619	−	0.372106i	−0.285973	−	0.958238i	$-0.592317\pi$
$349$	−20.4785	−	6.95151i	−1.09619	−	0.372106i	−0.810216	+	0.586132i	$0.800650\pi$
$350$	11.8630	+	0.777541i	0.634104	+	0.0415613i
$351$	−0.493870	+	7.53500i	−0.0263608	+	0.402189i
$352$	3.23350	+	5.60058i	0.172346	+	0.298512i
$353$	5.00651	−	8.67153i	0.266470	−	0.461539i	−0.701478	−	0.712691i	$-0.747476\pi$
$353$	5.00651	−	8.67153i	0.266470	−	0.461539i	0.967948	+	0.251152i	$0.0808095\pi$
$354$	5.10643	+	3.41201i	0.271404	+	0.181346i
$355$	1.98804	−	1.98804i	0.105514	−	0.105514i
$356$	5.65357	+	7.36787i	0.299639	+	0.390497i
$357$	−14.8327	−	11.3815i	−0.785028	−	0.602373i
$358$	14.8060	+	2.94509i	0.782520	+	0.155653i
$359$	6.49332	−	13.1671i	0.342704	−	0.694935i	−0.655477	−	0.755215i	$-0.727533\pi$
$359$	6.49332	−	13.1671i	0.342704	−	0.694935i	0.998182	+	0.0602796i	$0.0191992\pi$
$360$	1.32855	−	1.98831i	0.0700206	−	0.104793i
$361$	15.3695	+	6.36626i	0.808922	+	0.335066i
$362$	−14.1443	+	6.97519i	−0.743407	+	0.366608i
$363$	6.91686	−	5.30749i	0.363041	−	0.278571i
$364$	−3.78767	−	1.01490i	−0.198528	−	0.0531954i
$365$	1.97512	−	0.129456i	0.103383	−	0.00677605i
$366$			3.35781i			0.175515i
$367$	1.59886	+	24.3939i	0.0834598	+	1.27335i	0.810083	+	0.586315i	$0.199422\pi$
$367$	1.59886	+	24.3939i	0.0834598	+	1.27335i	−0.726624	+	0.687036i	$0.758912\pi$
$368$	−2.20349	+	1.47233i	−0.114865	+	0.0767503i
$369$	2.05474	−	10.3299i	0.106966	−	0.537752i
$370$	−0.818269	+	0.338938i	−0.0425398	+	0.0176206i
$371$	7.84927	−	8.95037i	0.407514	−	0.464680i
$372$	−3.15589	+	1.82205i	−0.163625	+	0.0944691i
$373$	−6.91827	+	20.3806i	−0.358214	+	1.05527i	0.607201	+	0.794548i	$0.292292\pi$
$373$	−6.91827	+	20.3806i	−0.358214	+	1.05527i	−0.965415	+	0.260717i	$0.916041\pi$
$374$	−7.83314	−	6.86948i	−0.405042	−	0.355212i
$375$	−1.10744	−	3.26240i	−0.0571878	−	0.168470i
$376$	−7.47109	+	18.0368i	−0.385292	+	0.930177i
$377$	1.50723	+	0.198430i	0.0776261	+	0.0102197i
$378$	5.17615	+	10.4962i	0.266232	+	0.539866i
$379$	2.56040	+	9.55553i	0.131519	+	0.490835i	0.999988	−	0.00490848i	$-0.00156242\pi$
$379$	2.56040	+	9.55553i	0.131519	+	0.490835i	−0.868469	+	0.495743i	$0.834896\pi$
$380$	0.222773	+	0.537823i	0.0114280	+	0.0275897i
$381$	3.51075	−	3.07885i	0.179861	−	0.157734i
$382$	−7.73601	−	4.46638i	−0.395808	−	0.228520i
$383$	−20.5221	+	6.96633i	−1.04863	+	0.355963i	−0.791984	−	0.610542i	$-0.790952\pi$
$383$	−20.5221	+	6.96633i	−1.04863	+	0.355963i	−0.256649	+	0.966505i	$0.582618\pi$
$384$	2.86311	−	0.767168i	0.146108	−	0.0391494i
$385$	−0.720490	+	0.938961i	−0.0367196	+	0.0478539i
$386$	1.18261	+	8.98280i	0.0601932	+	0.457213i
$387$	20.1558			1.02458
$388$	−4.44509	+	8.90152i	−0.225665	+	0.451906i
$389$	−2.74499			−0.139177			−0.0695883	−	0.997576i	$-0.522169\pi$
$389$	−2.74499			−0.139177			−0.0695883	+	0.997576i	$0.522169\pi$
$390$	−0.0716257	−	0.544051i	−0.00362691	−	0.0275491i
$391$	−13.7184	+	17.8782i	−0.693771	+	0.904139i
$392$	2.75733	−	0.738826i	0.139266	−	0.0373163i
$393$	−9.64265	+	3.27324i	−0.486408	+	0.165113i
$394$	16.6550	+	9.61575i	0.839065	+	0.484435i
$395$	−3.65176	+	3.20251i	−0.183740	+	0.161136i
$396$	−1.05786	−	2.55390i	−0.0531594	−	0.128338i
$397$	−6.58153	−	24.5626i	−0.330317	−	1.23276i	−0.908857	−	0.417107i	$-0.863044\pi$
$397$	−6.58153	−	24.5626i	−0.330317	−	1.23276i	0.578540	−	0.815654i	$-0.303623\pi$
$398$	−2.82799	−	5.73460i	−0.141754	−	0.287450i
$399$	−3.49519	−	0.460150i	−0.174978	−	0.0230363i
$400$	1.78333	−	4.30535i	0.0891667	−	0.215267i
$401$	0.620479	+	1.82787i	0.0309852	+	0.0912796i	0.961322	−	0.275426i	$-0.0888189\pi$
$401$	0.620479	+	1.82787i	0.0309852	+	0.0912796i	−0.930337	+	0.366706i	$0.880486\pi$
$402$	9.15526	+	8.02895i	0.456623	+	0.400448i
$403$	1.96295	−	5.78267i	0.0977817	−	0.288056i
$404$	6.38901	−	3.68869i	0.317865	−	0.183519i
$405$	−0.477285	+	0.544239i	−0.0237165	+	0.0270435i
$406$	2.17677	−	0.901646i	0.108031	−	0.0447479i
$407$	−0.595174	+	2.99214i	−0.0295017	+	0.148315i
$408$	−18.9322	+	12.6501i	−0.937286	+	0.626274i
$409$	1.78666	+	27.2591i	0.0883445	+	1.34788i	0.780059	+	0.625706i	$0.215189\pi$
$409$	1.78666	+	27.2591i	0.0883445	+	1.34788i	−0.691715	+	0.722171i	$0.743144\pi$
$410$			1.84306i			0.0910224i
$411$	0.237555	−	0.0155702i	0.0117177	−	0.000768020i
$412$	−10.6634	−	2.85726i	−0.525350	−	0.140767i
$413$	12.9162	−	9.91094i	0.635564	−	0.487685i
$414$	5.25381	−	2.59089i	0.258211	−	0.127335i
$415$	−3.54037	−	1.46647i	−0.173790	−	0.0719861i
$416$	−4.41599	+	6.60900i	−0.216512	+	0.324033i
$417$	−1.98753	+	4.03030i	−0.0973295	+	0.197365i
$418$	−1.92679	−	0.383262i	−0.0942423	−	0.0187460i
$419$	−25.0380	−	19.2123i	−1.22319	−	0.938584i	−0.223836	−	0.974627i	$-0.571858\pi$
$419$	−25.0380	−	19.2123i	−1.22319	−	0.938584i	−0.999350	+	0.0360433i	$0.988525\pi$
$420$	0.528440	+	0.688676i	0.0257852	+	0.0336040i
$421$	−4.89443	+	4.89443i	−0.238540	+	0.238540i	−0.816245	−	0.577705i	$-0.803948\pi$
$421$	−4.89443	+	4.89443i	−0.238540	+	0.238540i	0.577705	+	0.816245i	$0.303948\pi$
$422$	0.807229	+	0.539373i	0.0392953	+	0.0262563i
$423$	6.94477	−	12.0287i	0.337666	−	0.584855i
$424$	−7.24918	−	12.5560i	−0.352051	−	0.609771i
$425$	2.59169	−	39.5416i	0.125716	−	1.91805i
$426$	6.94405	+	0.455137i	0.336440	+	0.0220515i
$427$	8.42890	+	2.86123i	0.407903	+	0.138464i
$428$	−4.78732	−	5.45890i	−0.231404	−	0.263866i
$429$	−1.69523	−	0.835996i	−0.0818466	−	0.0403623i
$430$	−3.45934	+	0.688106i	−0.166824	+	0.0331834i
$431$	4.68842	−	17.4974i	0.225833	−	0.842821i	−0.756236	−	0.654299i	$-0.772964\pi$
$431$	4.68842	−	17.4974i	0.225833	−	0.842821i	0.982069	−	0.188522i	$-0.0603697\pi$
$432$	4.54818	−	0.598779i	0.218824	−	0.0288088i
$433$	−8.06402	−	12.0687i	−0.387532	−	0.579982i	0.585494	−	0.810676i	$-0.300900\pi$
$433$	−8.06402	−	12.0687i	−0.387532	−	0.579982i	−0.973026	+	0.230694i	$0.925900\pi$
$434$	−1.84643	−	9.28263i	−0.0886315	−	0.445581i
$435$	−0.237966	−	0.237966i	−0.0114096	−	0.0114096i
$436$	2.19213	−	16.6509i	0.104984	−	0.797432i
$437$	−0.554631	+	4.21284i	−0.0265316	+	0.201528i
$438$	3.46428	+	3.46428i	0.165530	+	0.165530i
$439$	−1.81197	−	9.10939i	−0.0864806	−	0.434767i	−0.999631	−	0.0271457i	$-0.991358\pi$
$439$	−1.81197	−	9.10939i	−0.0864806	−	0.434767i	0.913151	−	0.407622i	$-0.133642\pi$
$440$	0.800799	+	1.19848i	0.0381766	+	0.0571353i
$441$	−2.01353	+	0.265086i	−0.0958823	+	0.0126231i
$442$	3.31431	−	12.3692i	0.157646	−	0.588342i
$443$	−27.7104	+	5.51194i	−1.31656	+	0.261880i	−0.802900	−	0.596113i	$-0.796711\pi$
$443$	−27.7104	+	5.51194i	−1.31656	+	0.261880i	−0.513661	+	0.857993i	$0.671711\pi$
$444$	2.00681	+	0.989650i	0.0952391	+	0.0469667i
$445$	2.27158	+	2.59024i	0.107683	+	0.122789i
$446$	25.1363	+	8.53264i	1.19024	+	0.404032i
$447$	3.39858	+	0.222754i	0.160747	+	0.0105359i
$448$	−1.11415	+	16.9987i	−0.0526389	+	0.803114i
$449$	−4.32770	−	7.49580i	−0.204237	−	0.353749i	0.745652	−	0.666335i	$-0.232138\pi$
$449$	−4.32770	−	7.49580i	−0.204237	−	0.353749i	−0.949889	+	0.312586i	$0.898805\pi$
$450$	−5.15041	+	8.92077i	−0.242793	+	0.420529i
$451$	5.27854	+	3.52701i	0.248557	+	0.166080i
$452$	12.8509	−	12.8509i	0.604453	−	0.604453i
$453$	8.83492	+	11.5139i	0.415101	+	0.540970i
$454$	−2.56178	−	1.96573i	−0.120230	−	0.0922561i
$455$	−1.42673	−	0.283794i	−0.0668862	−	0.0133045i
$456$	−1.89894	+	3.85067i	−0.0889260	+	0.180324i
$457$	1.23009	−	1.84096i	0.0575412	−	0.0861164i	−0.801583	−	0.597883i	$-0.796009\pi$
$457$	1.23009	−	1.84096i	0.0575412	−	0.0861164i	0.859125	+	0.511767i	$0.171009\pi$
$458$	24.5656	+	10.1754i	1.14788	+	0.475466i
$459$	34.9858	−	17.2531i	1.63300	−	0.805305i
$460$	0.830079	−	0.636942i	0.0387027	−	0.0296976i
$461$	17.1194	+	4.58712i	0.797329	+	0.213644i	0.634411	−	0.772996i	$-0.281243\pi$
$461$	17.1194	+	4.58712i	0.797329	+	0.213644i	0.162918	+	0.986640i	$0.447909\pi$
$462$	−2.92317	+	0.191595i	−0.135998	+	0.00891379i
$463$			13.7652i			0.639721i	0.947465	+	0.319861i	$0.103636\pi$
$463$			13.7652i			0.639721i	−0.947465	+	0.319861i	$0.896364\pi$
$464$	−0.0604036	−	0.921581i	−0.00280417	−	0.0427833i
$465$	−1.12403	+	0.751052i	−0.0521256	+	0.0348292i
$466$	1.96927	−	9.90017i	0.0912245	−	0.458616i
$467$	−27.3583	+	11.3322i	−1.26599	+	0.524391i	−0.911743	−	0.410760i	$-0.865263\pi$
$467$	−27.3583	+	11.3322i	−1.26599	+	0.524391i	−0.354248	+	0.935151i	$0.615263\pi$
$468$	2.24021	−	2.55447i	0.103554	−	0.118080i
$469$	27.9559	−	16.1403i	1.29088	−	0.745291i
$470$	−0.781278	+	2.30157i	−0.0360376	+	0.106163i
$471$	−15.1855	−	13.3173i	−0.699709	−	0.613628i
$472$	−6.37338	−	18.7754i	−0.293359	−	0.864207i
$473$	−4.64929	+	11.2244i	−0.213775	+	0.516097i
$474$	−11.9193	−	1.56920i	−0.547470	−	0.0720758i
$475$	−3.30476	−	6.70140i	−0.151633	−	0.307481i
$476$	5.24290	+	19.5668i	0.240308	+	0.896841i
$477$	3.94732	+	9.52967i	0.180735	+	0.436333i
$478$	20.6354	−	18.0967i	0.943839	−	0.827725i
$479$	−9.58193	−	5.53213i	−0.437810	−	0.252770i	0.264858	−	0.964287i	$-0.414675\pi$
$479$	−9.58193	−	5.53213i	−0.437810	−	0.252770i	−0.702668	+	0.711518i	$0.748008\pi$
$480$	1.66620	−	0.565599i	0.0760513	−	0.0258159i
$481$	−3.62192	+	0.970491i	−0.165145	+	0.0442506i
$482$	−13.1760	+	17.1713i	−0.600150	+	0.782131i
$483$	0.827045	+	6.28203i	0.0376319	+	0.285842i
$484$	−9.44637			−0.429380
$485$	−1.42949	+	3.40298i	−0.0649100	+	0.154521i
$486$	−16.0694			−0.728924
$487$	3.73492	+	28.3695i	0.169245	+	1.28555i	0.839478	+	0.543394i	$0.182861\pi$
$487$	3.73492	+	28.3695i	0.169245	+	1.28555i	−0.670232	+	0.742151i	$0.733806\pi$
$488$	6.59938	−	8.60048i	0.298740	−	0.389325i
$489$	16.8042	−	4.50268i	0.759914	−	0.203618i
$490$	0.336531	−	0.114237i	0.0152029	−	0.00516070i
$491$	−16.6871	−	9.63432i	−0.753080	−	0.434791i	0.0737257	−	0.997279i	$-0.476511\pi$
$491$	−16.6871	−	9.63432i	−0.753080	−	0.434791i	−0.826806	+	0.562488i	$0.809844\pi$
$492$	3.50074	−	3.07007i	0.157826	−	0.138409i
$493$	−3.00536	−	7.25557i	−0.135354	−	0.326774i
$494$	−0.624947	−	2.33233i	−0.0281177	−	0.104937i
$495$	−0.453559	−	0.919726i	−0.0203859	−	0.0413386i
$496$	−3.67819	−	0.484243i	−0.165155	−	0.0217431i
$497$	7.05961	−	17.0434i	0.316667	−	0.764501i
$498$	−3.04885	−	8.98163i	−0.136622	−	0.402476i
$499$	13.9055	+	12.1948i	0.622495	+	0.545914i	0.911441	−	0.411432i	$-0.134971\pi$
$499$	13.9055	+	12.1948i	0.622495	+	0.545914i	−0.288945	+	0.957346i	$0.593305\pi$
$500$	−1.19989	+	3.53476i	−0.0536607	+	0.158079i
$501$	−7.20085	+	4.15741i	−0.321710	+	0.185740i
$502$	−6.97166	+	7.94966i	−0.311161	+	0.354811i
$503$	33.8527	−	14.0222i	1.50942	−	0.625220i	0.533978	−	0.845498i	$-0.320696\pi$
$503$	33.8527	−	14.0222i	1.50942	−	0.625220i	0.975437	+	0.220278i	$0.0706963\pi$
$504$	3.06108	−	15.3891i	0.136351	−	0.685485i
$505$	2.27556	−	1.52048i	0.101261	−	0.0676605i
$506$	0.230934	+	3.52337i	0.0102663	+	0.156633i
$507$			9.79795i			0.435142i
$508$	−5.04855	+	0.330899i	−0.223993	+	0.0146813i
$509$	15.1219	+	4.05191i	0.670269	+	0.179598i	0.577876	−	0.816125i	$-0.303882\pi$
$509$	15.1219	+	4.05191i	0.670269	+	0.179598i	0.0923927	+	0.995723i	$0.470548\pi$
$510$	−2.24897	+	1.72570i	−0.0995862	+	0.0764152i
$511$	11.6481	−	5.74422i	0.515283	−	0.254109i
$512$	9.76778	+	4.04595i	0.431679	+	0.178807i
$513$	4.08648	−	6.11585i	0.180422	−	0.270021i
$514$	12.6251	−	25.6011i	0.556868	−	1.12922i
$515$	−4.01668	−	0.798967i	−0.176996	−	0.0352067i
$516$	7.06937	+	5.42452i	0.311212	+	0.238801i
$517$	5.09660	+	6.64202i	0.224148	+	0.292116i
$518$	−4.10929	+	4.10929i	−0.180552	+	0.180552i
$519$	6.27123	+	4.19030i	0.275277	+	0.183934i
$520$	−0.885811	+	1.53427i	−0.0388454	+	0.0672822i
$521$	14.0884	+	24.4018i	0.617223	+	1.06906i	0.989990	+	0.141136i	$0.0450756\pi$
$521$	14.0884	+	24.4018i	0.617223	+	1.06906i	−0.372767	+	0.927925i	$0.621591\pi$
$522$	−0.133518	+	2.03710i	−0.00584394	+	0.0891613i
$523$	18.0704	+	1.18440i	0.790165	+	0.0517902i	0.455141	−	0.890419i	$-0.349589\pi$
$523$	18.0704	+	1.18440i	0.790165	+	0.0517902i	0.335024	+	0.942210i	$0.391256\pi$
$524$	10.4477	+	3.54650i	0.456408	+	0.154930i
$525$	−7.34637	−	8.37693i	−0.320622	−	0.365599i
$526$	27.1552	+	13.3915i	1.18402	+	0.583895i
$527$	−30.9408	+	6.15450i	−1.34780	+	0.268094i
$528$	−0.297200	+	1.10917i	−0.0129340	+	0.0482703i
$529$	−15.2313	+	2.00524i	−0.662232	+	0.0871845i
$530$	−1.00281	−	1.50082i	−0.0435594	−	0.0651912i
$531$	2.75201	+	13.8353i	0.119427	+	0.600400i
$532$	2.70091	+	2.70091i	0.117099	+	0.117099i
$533$	−1.01848	+	7.73612i	−0.0441152	+	0.335088i
$534$	−1.11306	+	8.45449i	−0.0481666	+	0.365862i
$535$	−1.90460	−	1.90460i	−0.0823431	−	0.0823431i
$536$	−7.66975	−	38.5585i	−0.331283	−	1.66547i
$537$	−7.86025	−	11.7637i	−0.339195	−	0.507641i
$538$	−25.0062	+	3.29213i	−1.07809	+	0.141934i
$539$	0.316834	−	1.18244i	0.0136470	−	0.0509312i
$540$	−1.77636	+	0.353340i	−0.0764423	+	0.0152053i
$541$	−19.0076	−	9.37352i	−0.817202	−	0.402999i	−0.0148785	−	0.999889i	$-0.504736\pi$
$541$	−19.0076	−	9.37352i	−0.817202	−	0.402999i	−0.802323	+	0.596890i	$0.796403\pi$
$542$	−8.42814	−	9.61045i	−0.362020	−	0.412804i
$543$	13.9960	+	4.75099i	0.600624	+	0.203884i
$544$	40.9737	+	2.68556i	1.75673	+	0.115142i
$545$	0.407480	−	6.21695i	0.0174545	−	0.266305i
$546$	−1.80029	−	3.11819i	−0.0770452	−	0.133446i
$547$	−4.70622	+	8.15141i	−0.201223	+	0.348529i	−0.948923	−	0.315508i	$-0.897825\pi$
$547$	−4.70622	+	8.15141i	−0.201223	+	0.348529i	0.747699	+	0.664037i	$0.231158\pi$
$548$	−0.214469	−	0.143303i	−0.00916165	−	0.00612162i
$549$	−5.45361	+	5.45361i	−0.232755	+	0.232755i
$550$	−3.77976	−	4.92588i	−0.161170	−	0.210040i
$551$	−1.17482	−	0.901473i	−0.0500491	−	0.0384041i
$552$	7.56848	+	1.50546i	0.322136	+	0.0640768i
$553$	−14.0956	+	28.5831i	−0.599406	+	1.21548i
$554$	10.5704	−	15.8197i	0.449092	−	0.672114i
$555$	0.766886	+	0.317654i	0.0325525	+	0.0134837i
$556$	4.36677	−	2.15345i	0.185192	−	0.0913267i
$557$	−29.6340	+	22.7389i	−1.25563	+	0.963479i	−0.999995	−	0.00329365i	$-0.998952\pi$
$557$	−29.6340	+	22.7389i	−1.25563	+	0.963479i	−0.255636	+	0.966773i	$0.582285\pi$
$558$	7.92114	+	2.12246i	0.335329	+	0.0898510i
$559$	−14.9006	+	0.976635i	−0.630227	+	0.0413073i
$560$			0.883736i			0.0373447i
$561$	0.638622	+	9.74348i	0.0269626	+	0.411370i
$562$	11.3757	−	7.60099i	0.479854	−	0.320628i
$563$	5.57856	−	28.0453i	0.235108	−	1.18197i	−0.665183	−	0.746680i	$-0.731647\pi$
$563$	5.57856	−	28.0453i	0.235108	−	1.18197i	0.900291	−	0.435288i	$-0.143353\pi$
$564$	5.67305	−	2.34985i	0.238878	−	0.0989467i
$565$	4.44529	−	5.06888i	0.187015	−	0.213249i
$566$	11.9499	−	6.89926i	0.502291	−	0.289998i
$567$	−1.52674	+	4.49762i	−0.0641170	+	0.188882i
$568$	−16.8915	−	14.8135i	−0.708753	−	0.621560i
$569$	7.85622	+	23.1437i	0.329350	+	0.970233i	0.977902	+	0.209063i	$0.0670415\pi$
$569$	7.85622	+	23.1437i	0.329350	+	0.970233i	−0.648552	+	0.761170i	$0.724625\pi$
$570$	−0.204553	+	0.493836i	−0.00856780	+	0.0206845i
$571$	−15.3720	−	2.02377i	−0.643300	−	0.0846920i	−0.198184	−	0.980165i	$-0.563504\pi$
$571$	−15.3720	−	2.02377i	−0.643300	−	0.0846920i	−0.445116	+	0.895473i	$0.646838\pi$
$572$	0.905788	+	1.83676i	0.0378729	+	0.0767987i
$573$	2.16679	+	8.08657i	0.0905189	+	0.337821i
$574$	4.62787	+	11.1727i	0.193163	+	0.466338i
$575$	−10.0969	+	8.85477i	−0.421071	+	0.369269i
$576$	−12.7827	−	7.38012i	−0.532614	−	0.307505i
$577$	−18.1066	+	6.14636i	−0.753787	+	0.255876i	−0.671775	−	0.740755i	$-0.734468\pi$
$577$	−18.1066	+	6.14636i	−0.753787	+	0.255876i	−0.0820120	+	0.996631i	$0.526135\pi$
$578$	−47.5616	+	12.7441i	−1.97830	+	0.530084i
$579$	5.16922	−	6.73666i	0.214825	−	0.279966i
$580$	0.0475937	+	0.361510i	0.00197622	+	0.0150109i
$581$	−25.1440			−1.04315
$582$	−8.66562	+	2.89345i	−0.359201	+	0.119937i
$583$	−6.21739			−0.257498
$584$	−2.06455	−	15.6818i	−0.0854318	−	0.648919i
$585$	0.767294	−	0.999957i	0.0317237	−	0.0413431i
$586$	−8.51649	+	2.28199i	−0.351813	+	0.0942680i
$587$	−25.7914	+	8.75499i	−1.06452	+	0.361357i	−0.798116	−	0.602504i	$-0.794170\pi$
$587$	−25.7914	+	8.75499i	−1.06452	+	0.361357i	−0.266407	+	0.963861i	$0.585837\pi$
$588$	−0.777558	−	0.448923i	−0.0320660	−	0.0185133i
$589$	−4.47231	+	3.92211i	−0.184278	+	0.161608i
$590$	−0.944653	−	2.28059i	−0.0388908	−	0.0938906i
$591$	−4.66492	−	17.4097i	−0.191889	−	0.716140i
$592$	1.00752	+	2.04306i	0.0414090	+	0.0839691i
$593$	−7.87963	−	1.03737i	−0.323578	−	0.0425998i	−0.0330123	−	0.999455i	$-0.510510\pi$
$593$	−7.87963	−	1.03737i	−0.323578	−	0.0425998i	−0.290565	+	0.956855i	$0.593843\pi$
$594$	2.33901	−	5.64688i	0.0959709	−	0.231694i
$595$	2.41554	+	7.11594i	0.0990274	+	0.291725i
$596$	−2.77444	−	2.43312i	−0.113646	−	0.0996645i
$597$	−1.92622	+	5.67446i	−0.0788350	+	0.232240i
$598$	−3.75844	+	2.16993i	−0.153694	+	0.0887352i
$599$	−11.8772	+	13.5434i	−0.485290	+	0.553367i	−0.941723	−	0.336391i	$-0.890794\pi$
$599$	−11.8772	+	13.5434i	−0.485290	+	0.553367i	0.456432	+	0.889758i	$0.349127\pi$
$600$	−12.5365	+	5.19281i	−0.511803	+	0.211996i
$601$	0.288432	−	1.45005i	0.0117654	−	0.0591486i	−0.974457	−	0.224576i	$-0.927900\pi$
$601$	0.288432	−	1.45005i	0.0117654	−	0.0591486i	0.986222	+	0.165427i	$0.0529003\pi$
$602$	−19.2427	+	12.8576i	−0.784275	+	0.524036i
$603$	1.82931	+	27.9099i	0.0744953	+	1.13658i
$604$		−	15.7245i		−	0.639823i
$605$	−3.49682	+	0.229194i	−0.142166	+	0.00931805i
$606$	6.54320	+	1.75324i	0.265799	+	0.0712207i
$607$	33.4920	−	25.6994i	1.35940	−	1.04310i	0.365736	−	0.930719i	$-0.380817\pi$
$607$	33.4920	−	25.6994i	1.35940	−	1.04310i	0.993665	−	0.112386i	$-0.0358492\pi$
$608$	6.94410	−	3.42445i	0.281621	−	0.138880i
$609$	−2.04007	−	0.845026i	−0.0826680	−	0.0342422i
$610$	0.749820	−	1.12218i	0.0303593	−	0.0454359i
$611$	−4.55120	+	9.22893i	−0.184122	+	0.373363i
$612$	−17.2145	−	3.42418i	−0.695857	−	0.138414i
$613$	34.1213	+	26.1822i	1.37814	+	1.05749i	0.990768	+	0.135566i	$0.0432854\pi$
$613$	34.1213	+	26.1822i	1.37814	+	1.05749i	0.387377	+	0.921922i	$0.373381\pi$
$614$	−9.63140	−	12.5519i	−0.388692	−	0.506553i
$615$	1.22140	−	1.22140i	0.0492518	−	0.0492518i
$616$	7.86378	+	5.25441i	0.316841	+	0.211706i
$617$	−1.51024	+	2.61582i	−0.0608001	+	0.105309i	−0.894823	−	0.446421i	$-0.852699\pi$
$617$	−1.51024	+	2.61582i	−0.0608001	+	0.105309i	0.834023	+	0.551729i	$0.186032\pi$
$618$	−5.06836	−	8.77865i	−0.203879	−	0.353129i
$619$	0.663159	−	10.1179i	0.0266546	−	0.406671i	−0.963595	−	0.267366i	$-0.913847\pi$
$619$	0.663159	−	10.1179i	0.0266546	−	0.406671i	0.990250	−	0.139305i	$-0.0444867\pi$
$620$	1.46158	+	0.0957970i	0.0586984	+	0.00384730i
$621$	−12.5187	−	4.24951i	−0.502356	−	0.170527i
$622$	0.872911	+	0.995365i	0.0350006	+	0.0399105i
$623$	20.2743	+	9.99820i	0.812274	+	0.400569i
$624$	−1.38425	+	0.275344i	−0.0554143	+	0.0110226i
$625$	5.93031	−	22.1322i	0.237212	−	0.885289i
$626$	8.51018	−	1.12039i	0.340135	−	0.0447797i
$627$	1.02290	+	1.53088i	0.0408507	+	0.0611374i
$628$	4.26934	+	21.4634i	0.170365	+	0.856484i
$629$	13.6970	+	13.6970i	0.546137	+	0.546137i
$630$	0.254976	−	1.93673i	0.0101585	−	0.0771613i
$631$	0.246395	−	1.87156i	0.00980884	−	0.0745055i	−0.985840	−	0.167687i	$-0.946370\pi$
$631$	0.246395	−	1.87156i	0.00980884	−	0.0745055i	0.995649	+	0.0931813i	$0.0297036\pi$
$632$	27.4452	+	27.4452i	1.09171	+	1.09171i
$633$	−0.177509	−	0.892398i	−0.00705535	−	0.0354696i
$634$	−14.8271	−	22.1903i	−0.588860	−	0.881291i
$635$	−1.86083	+	0.244982i	−0.0738446	+	0.00972183i
$636$	−1.18024	+	4.40473i	−0.0467997	+	0.174659i
$637$	1.47569	−	0.293533i	0.0584691	−	0.0116302i
$638$	−1.10362	−	0.544245i	−0.0436927	−	0.0215469i
$639$	10.5390	+	12.0175i	0.416917	+	0.475403i
$640$	−1.12817	−	0.382962i	−0.0445948	−	0.0151379i
$641$	33.1860	+	2.17513i	1.31077	+	0.0859124i	0.704704	−	0.709502i	$-0.251080\pi$
$641$	33.1860	+	2.17513i	1.31077	+	0.0859124i	0.606066	+	0.795414i	$0.292747\pi$
$642$	0.436035	−	6.65261i	0.0172089	−	0.262558i
$643$	−4.45638	−	7.71868i	−0.175743	−	0.304395i	0.764675	−	0.644416i	$-0.222899\pi$
$643$	−4.45638	−	7.71868i	−0.175743	−	0.304395i	−0.940418	+	0.340021i	$0.889566\pi$
$644$	3.43261	−	5.94545i	0.135264	−	0.234283i
$645$	2.74853	+	1.83651i	0.108223	+	0.0723124i
$646$	−8.82021	+	8.82021i	−0.347026	+	0.347026i
$647$	−3.46375	−	4.51405i	−0.136174	−	0.177466i	0.720288	−	0.693675i	$-0.244009\pi$
$647$	−3.46375	−	4.51405i	−0.136174	−	0.177466i	−0.856463	+	0.516209i	$0.827343\pi$
$648$	4.58918	+	3.52140i	0.180280	+	0.138334i
$649$	−8.33939	−	1.65881i	−0.327350	−	0.0651139i
$650$	3.37528	−	6.84440i	0.132390	−	0.268459i
$651$	−4.92800	+	7.37527i	−0.193144	+	0.289060i
$652$	−17.4146	−	7.21335i	−0.682008	−	0.282497i
$653$	0.299238	−	0.147568i	0.0117101	−	0.00577478i	−0.436424	−	0.899741i	$-0.643755\pi$
$653$	0.299238	−	0.147568i	0.0117101	−	0.00577478i	0.448134	+	0.893966i	$0.352089\pi$
$654$	12.2343	−	9.38770i	0.478398	−	0.367088i
$655$	3.95352	+	1.05934i	0.154477	+	0.0413920i
$656$	4.73019	−	0.310033i	0.184683	−	0.0121047i
$657$			11.2531i			0.439025i
$658$	1.04305	+	15.9139i	0.0406624	+	0.620388i
$659$	4.97436	−	3.32376i	0.193774	−	0.129475i	−0.454899	−	0.890543i	$-0.650325\pi$
$659$	4.97436	−	3.32376i	0.193774	−	0.129475i	0.648672	+	0.761068i	$0.275325\pi$
$660$	0.0884457	−	0.444647i	0.00344274	−	0.0173078i
$661$	4.05465	−	1.67949i	0.157708	−	0.0653246i	−0.302433	−	0.953171i	$-0.597799\pi$
$661$	4.05465	−	1.67949i	0.157708	−	0.0653246i	0.460141	+	0.887846i	$0.347799\pi$
$662$	5.63692	−	6.42768i	0.219085	−	0.249819i
$663$	−10.3935	+	6.00070i	−0.403651	+	0.233048i
$664$	−9.84320	+	28.9971i	−0.381990	+	1.12531i
$665$	1.06534	+	0.934281i	0.0413122	+	0.0362299i
$666$	−1.61856	−	4.76811i	−0.0627177	−	0.184760i
$667$	−1.01853	+	2.45895i	−0.0394377	+	0.0952111i
$668$	8.93191	+	1.17591i	0.345586	+	0.0454972i
$669$	−11.0033	−	22.3126i	−0.425414	−	0.862653i
$670$	−1.26679	−	4.72771i	−0.0489403	−	0.182648i
$671$	−1.77904	−	4.29498i	−0.0686790	−	0.165806i
$672$	8.68032	−	7.61243i	0.334850	−	0.293656i
$673$	0.667584	+	0.385430i	0.0257335	+	0.0148572i	0.512812	−	0.858501i	$-0.328604\pi$
$673$	0.667584	+	0.385430i	0.0257335	+	0.0148572i	−0.487078	+	0.873358i	$0.661937\pi$
$674$	−1.43989	+	0.488777i	−0.0554625	+	0.0188270i
$675$	22.4549	−	6.01678i	0.864290	−	0.231586i
$676$	6.46256	−	8.42218i	0.248560	−	0.323930i
$677$	−1.03177	−	7.83704i	−0.0396540	−	0.301202i	−0.999767	−	0.0215895i	$-0.993127\pi$
$677$	−1.03177	−	7.83704i	−0.0396540	−	0.301202i	0.960113	−	0.279613i	$-0.0902060\pi$
$678$	16.6875			0.640878
$679$	−0.120829	+	24.2183i	−0.00463700	+	0.929413i
$680$	9.15204			0.350965
$681$	0.395010	+	3.00040i	0.0151368	+	0.114976i
$682$	−3.00910	+	3.92154i	−0.115224	+	0.150163i
$683$	−15.3176	+	4.10435i	−0.586113	+	0.157049i	−0.539676	−	0.841873i	$-0.681453\pi$
$683$	−15.3176	+	4.10435i	−0.586113	+	0.157049i	−0.0464371	+	0.998921i	$0.514787\pi$
$684$	−3.13393	+	1.06383i	−0.119829	+	0.0406764i
$685$	−0.0828682	−	0.0478440i	−0.00316623	−	0.00182802i
$686$	14.6284	−	12.8287i	0.558513	−	0.489803i
$687$	−9.53644	−	23.0230i	−0.363838	−	0.878382i
$688$	2.34793	+	8.76258i	0.0895139	+	0.334070i
$689$	−3.37988	−	6.85371i	−0.128763	−	0.261106i
$690$	0.952500	+	0.125399i	0.0362611	+	0.00477386i
$691$	6.04160	−	14.5857i	0.229833	−	0.554867i	−0.766323	−	0.642455i	$-0.777916\pi$
$691$	6.04160	−	14.5857i	0.229833	−	0.554867i	0.996157	+	0.0875882i	$0.0279160\pi$
$692$	−2.62681	−	7.73832i	−0.0998562	−	0.294167i
$693$	−5.05887	−	4.43651i	−0.192171	−	0.168529i
$694$	−6.96796	+	20.5269i	−0.264500	+	0.779192i
$695$	1.56423	−	0.903106i	0.0593345	−	0.0342568i
$696$	−1.77316	+	2.02190i	−0.0672113	+	0.0766398i
$697$	37.2406	−	15.4256i	1.41059	−	0.584284i
$698$	−4.19741	+	21.1018i	−0.158874	+	0.798716i
$699$	−7.86592	+	5.25584i	−0.297516	+	0.198794i
$700$	0.789551	+	12.0462i	0.0298422	+	0.455305i
$701$		−	4.19103i		−	0.158293i	−0.996863	−	0.0791465i	$-0.974781\pi$
$701$		−	4.19103i		−	0.158293i	0.996863	−	0.0791465i	$-0.0252195\pi$
$702$	7.49634	−	0.491336i	0.282931	−	0.0185443i
$703$	3.52805	+	0.945339i	0.133063	+	0.0356541i
$704$	7.05840	−	5.41610i	0.266023	−	0.204127i
$705$	2.04301	−	1.00750i	0.0769444	−	0.0379448i
$706$	−9.20335	−	3.81215i	−0.346373	−	0.143472i
$707$	9.97659	−	14.9310i	0.375208	−	0.561539i
$708$	−2.75825	+	5.59318i	−0.103661	+	0.210204i
$709$	36.2166	+	7.20394i	1.36014	+	0.270550i	0.820646	−	0.571437i	$-0.193614\pi$
$709$	36.2166	+	7.20394i	1.36014	+	0.270550i	0.539499	+	0.841986i	$0.318614\pi$
$710$	−2.21908	−	1.70276i	−0.0832805	−	0.0639034i
$711$	−16.8102	−	21.9074i	−0.630430	−	0.821593i
$712$	19.4672	−	19.4672i	0.729565	−	0.729565i
$713$	8.88961	+	5.93985i	0.332918	+	0.222449i
$714$	−9.30012	+	16.1083i	−0.348048	+	0.602837i
$715$	0.379866	+	0.657947i	0.0142062	+	0.0246058i
$716$	−1.00258	+	15.2964i	−0.0374681	+	0.571653i
$717$	−25.6679	−	1.68236i	−0.958585	−	0.0628290i
$718$	−13.8307	−	4.69489i	−0.516158	−	0.175212i
$719$	−14.3843	−	16.4021i	−0.536442	−	0.611695i	0.418598	−	0.908172i	$-0.362522\pi$
$719$	−14.3843	−	16.4021i	−0.536442	−	0.611695i	−0.955040	+	0.296477i	$0.904188\pi$
$720$	−0.686752	−	0.338669i	−0.0255937	−	0.0126214i
$721$	−26.3553	+	5.24239i	−0.981523	+	0.195237i
$722$	4.28358	−	15.9865i	0.159418	−	0.594957i
$723$	20.1113	−	2.64770i	0.747946	−	0.0984690i
$724$	−8.89705	−	13.3154i	−0.330656	−	0.494862i
$725$	−0.913059	−	4.59026i	−0.0339102	−	0.170478i
$726$	−6.13329	−	6.13329i	−0.227628	−	0.227628i
$727$	3.09770	−	23.5294i	0.114887	−	0.872657i	−0.832826	−	0.553535i	$-0.813279\pi$
$727$	3.09770	−	23.5294i	0.114887	−	0.872657i	0.947714	−	0.319122i	$-0.103388\pi$
$728$	−1.51729	+	11.5250i	−0.0562347	+	0.427145i
$729$	6.55187	+	6.55187i	0.242662	+	0.242662i
$730$	−0.384172	−	1.93136i	−0.0142189	−	0.0714830i
$731$	42.8568	+	64.1397i	1.58511	+	2.37229i
$732$	−3.38050	+	0.445052i	−0.124947	+	0.0164496i
$733$	−3.25427	+	12.1451i	−0.120199	+	0.448590i	−0.999623	−	0.0274498i	$-0.991261\pi$
$733$	−3.25427	+	12.1451i	−0.120199	+	0.448590i	0.879424	+	0.476039i	$0.157928\pi$
$734$	23.8535	−	4.74475i	0.880448	−	0.175132i
$735$	−0.298726	−	0.147315i	−0.0110187	−	0.00543380i
$736$	−9.17546	−	10.4626i	−0.338212	−	0.385657i
$737$	−15.9644	−	5.41919i	−0.588057	−	0.199618i
$738$	−10.4558	−	0.685308i	−0.384883	−	0.0252266i
$739$	2.54663	−	38.8540i	0.0936792	−	1.42927i	−0.649594	−	0.760281i	$-0.725061\pi$
$739$	2.54663	−	38.8540i	0.0936792	−	1.42927i	0.743273	−	0.668988i	$-0.233272\pi$
$740$	−0.449684	−	0.778876i	−0.0165307	−	0.0286321i
$741$	−1.13149	+	1.95980i	−0.0415664	+	0.0719951i
$742$	−9.84755	−	6.57992i	−0.361515	−	0.241556i
$743$	8.16444	−	8.16444i	0.299524	−	0.299524i	−0.541303	−	0.840827i	$-0.682069\pi$
$743$	8.16444	−	8.16444i	0.299524	−	0.299524i	0.840827	+	0.541303i	$0.182069\pi$
$744$	6.57631	+	8.57041i	0.241099	+	0.314206i
$745$	−1.08607	−	0.833368i	−0.0397904	−	0.0305322i
$746$	21.0009	+	4.17734i	0.768897	+	0.152943i
$747$	9.63577	−	19.5394i	0.352554	−	0.714909i
$748$	5.87769	−	8.79658i	0.214910	−	0.321635i
$749$	−16.3281	−	6.76332i	−0.596615	−	0.247126i
$750$	−3.07409	+	1.51597i	−0.112250	+	0.0553555i
$751$	4.43076	−	3.39984i	0.161681	−	0.124062i	−0.524752	−	0.851255i	$-0.675842\pi$
$751$	4.43076	−	3.39984i	0.161681	−	0.124062i	0.686433	+	0.727193i	$0.259175\pi$
$752$	6.03836	+	1.61797i	0.220196	+	0.0590014i
$753$	9.88842	−	0.648121i	0.360354	−	0.0236188i
$754$		−	1.51243i		−	0.0550795i
$755$	−0.381519	−	5.82086i	−0.0138849	−	0.211843i
$756$	−9.88107	+	6.60232i	−0.359371	+	0.240124i
$757$	2.44098	−	12.2716i	0.0887190	−	0.446021i	−0.910735	−	0.412990i	$-0.864484\pi$
$757$	2.44098	−	12.2716i	0.0887190	−	0.446021i	0.999454	−	0.0330301i	$-0.0105157\pi$
$758$	9.09269	−	3.76631i	0.330261	−	0.136799i
$759$	2.18191	−	2.48799i	0.0791984	−	0.0903085i
$760$	1.49451	−	0.862854i	0.0542115	−	0.0312990i
$761$	4.03174	−	11.8771i	0.146150	−	0.430545i	−0.849061	−	0.528295i	$-0.822831\pi$
$761$	4.03174	−	11.8771i	0.146150	−	0.430545i	0.995211	+	0.0977505i	$0.0311647\pi$
$762$	−3.49274	−	3.06305i	−0.126529	−	0.110963i
$763$	−13.1404	−	38.7103i	−0.475714	−	1.40141i
$764$	3.47122	−	8.38028i	0.125584	−	0.303188i
$765$	−6.45550	−	0.849882i	−0.233399	−	0.0307276i
$766$	9.53623	+	19.3376i	0.344558	+	0.698694i
$767$	−2.70485	−	10.0946i	−0.0976665	−	0.364496i
$768$	−6.07221	−	14.6596i	−0.219112	−	0.528984i
$769$	−25.8496	+	22.6695i	−0.932161	+	0.817483i	−0.983446	−	0.181201i	$-0.942002\pi$
$769$	−25.8496	+	22.6695i	−0.932161	+	0.817483i	0.0512851	+	0.998684i	$0.483668\pi$
$770$	1.01971	+	0.588731i	0.0367479	+	0.0212164i
$771$	−25.3326	+	8.59926i	−0.912332	+	0.309695i
$772$	−8.88677	+	2.38120i	−0.319842	+	0.0857013i
$773$	−28.4579	+	37.0870i	−1.02356	+	1.33393i	−0.0821643	+	0.996619i	$0.526183\pi$
$773$	−28.4579	+	37.0870i	−1.02356	+	1.33393i	−0.941394	+	0.337309i	$0.890483\pi$
$774$	−2.61737	−	19.8809i	−0.0940793	−	0.714603i
$775$	−18.8003			−0.675326
$776$	27.8823	+	9.62017i	1.00092	+	0.345344i
$777$	5.44648			0.195392
$778$	0.356455	+	2.70754i	0.0127795	+	0.0970702i
$779$	4.62698	−	6.03000i	0.165779	−	0.216047i
$780$	0.538235	−	0.144220i	0.0192719	−	0.00516389i
$781$	−9.12328	+	3.09694i	−0.326457	+	0.110817i
$782$	19.4157	+	11.2097i	0.694305	+	0.400857i
$783$	3.46389	−	3.03775i	0.123789	−	0.108560i
$784$	−0.349797	−	0.844485i	−0.0124927	−	0.0301602i
$785$	2.10117	+	7.84166i	0.0749939	+	0.279881i
$786$	4.48075	+	9.08605i	0.159823	+	0.324089i
$787$	−16.6961	−	2.19808i	−0.595152	−	0.0783532i	−0.173068	−	0.984910i	$-0.555368\pi$
$787$	−16.6961	−	2.19808i	−0.595152	−	0.0783532i	−0.422084	+	0.906557i	$0.638701\pi$
$788$	−7.47325	+	18.0420i	−0.266224	+	0.642721i
$789$	−9.12127	−	26.8704i	−0.324726	−	0.956612i
$790$	3.63303	+	3.18608i	0.129257	+	0.113356i
$791$	14.2196	−	41.8895i	0.505590	−	1.48942i
$792$	−7.09680	+	4.09734i	−0.252174	+	0.145593i
$793$	3.76743	−	4.29593i	0.133785	−	0.152553i
$794$	−23.3728	+	9.68135i	−0.829471	+	0.343578i
$795$	−0.330028	+	1.65916i	−0.0117049	+	0.0588445i
$796$	5.39853	−	3.60718i	0.191346	−	0.127853i
$797$	2.32453	+	35.4655i	0.0823390	+	1.25625i	0.816528	+	0.577306i	$0.195896\pi$
$797$	2.32453	+	35.4655i	0.0823390	+	1.25625i	−0.734189	+	0.678945i	$0.762437\pi$
$798$			3.50726i			0.124156i
$799$	53.0440	−	3.47669i	1.87656	−	0.122996i
$800$	23.6367	+	6.33343i	0.835683	+	0.223921i
$801$	−15.5392	+	11.9237i	−0.549051	+	0.421302i
$802$	1.72236	−	0.849375i	0.0608187	−	0.0299925i
$803$	−6.26662	−	2.59572i	−0.221144	−	0.0916009i
$804$	−6.86976	+	10.2813i	−0.242278	+	0.362594i
$805$	1.12642	−	2.28415i	0.0397010	−	0.0805056i
$806$	−5.95869	−	1.18526i	−0.209886	−	0.0417489i
$807$	18.7534	+	14.3900i	0.660152	+	0.506552i
$808$	−13.3135	−	17.3505i	−0.468369	−	0.610390i
$809$	−15.5124	+	15.5124i	−0.545387	+	0.545387i	−0.925103	−	0.379716i	$-0.876022\pi$
$809$	−15.5124	+	15.5124i	−0.545387	+	0.545387i	0.379716	+	0.925103i	$0.376022\pi$
$810$	0.598793	+	0.400101i	0.0210394	+	0.0140581i
$811$	27.7461	−	48.0577i	0.974298	−	1.68753i	0.292066	−	0.956398i	$-0.405657\pi$
$811$	27.7461	−	48.0577i	0.974298	−	1.68753i	0.682232	−	0.731136i	$-0.261009\pi$
$812$	1.19625	+	2.07197i	0.0419802	+	0.0727119i
$813$	−0.783523	+	11.9542i	−0.0274793	+	0.419254i
$814$	3.02861	+	0.198506i	0.106153	+	0.00695762i
$815$	−6.62148	−	2.24769i	−0.231940	−	0.0787331i
$816$	4.80728	+	5.48166i	0.168289	+	0.191896i
$817$	13.0455	+	6.43333i	0.456404	+	0.225074i
$818$	26.6552	−	5.30206i	0.931979	−	0.185382i
$819$	2.14048	−	7.98839i	0.0747945	−	0.279137i
$820$	−1.85552	+	0.244284i	−0.0647976	+	0.00853076i
$821$	21.1435	+	31.6435i	0.737913	+	1.10436i	0.990597	+	0.136816i	$0.0436869\pi$
$821$	21.1435	+	31.6435i	0.737913	+	1.10436i	−0.252684	+	0.967549i	$0.581313\pi$
$822$	−0.0462058	−	0.232292i	−0.00161161	−	0.00810213i
$823$	−26.8515	−	26.8515i	−0.935985	−	0.935985i	0.0620856	−	0.998071i	$-0.480225\pi$
$823$	−26.8515	−	26.8515i	−0.935985	−	0.935985i	−0.998071	+	0.0620856i	$0.980225\pi$
$824$	−4.27164	+	32.4463i	−0.148810	+	1.13032i
$825$	−0.759538	+	5.76927i	−0.0264437	+	0.200860i
$826$	−11.4530	−	11.4530i	−0.398500	−	0.398500i
$827$	6.11337	+	30.7340i	0.212583	+	1.06873i	0.928724	+	0.370771i	$0.120906\pi$
$827$	6.11337	+	30.7340i	0.212583	+	1.06873i	−0.716142	+	0.697955i	$0.754094\pi$
$828$	3.30476	+	4.94592i	0.114848	+	0.171882i
$829$	−22.3829	+	2.94677i	−0.777390	+	0.102345i	−0.508772	−	0.860901i	$-0.669900\pi$
$829$	−22.3829	+	2.94677i	−0.777390	+	0.102345i	−0.268618	+	0.963247i	$0.586567\pi$
$830$	−0.986723	+	3.68250i	−0.0342497	+	0.127821i
$831$	−17.4888	+	3.47873i	−0.606679	+	0.120676i
$832$	9.80747	+	4.83651i	0.340013	+	0.167676i
$833$	−5.12486	−	5.84378i	−0.177566	−	0.202475i
$834$	4.23341	+	1.43705i	0.146591	+	0.0497610i
$835$	3.33491	+	0.218582i	0.115409	+	0.00756433i
$836$	0.130471	−	1.99061i	0.00451245	−	0.0688467i
$837$	−9.25358	−	16.0277i	−0.319851	−	0.553998i
$838$	−15.6989	+	27.1913i	−0.542309	+	0.939307i
$839$	−3.07260	−	2.05304i	−0.106078	−	0.0708789i	0.501400	−	0.865216i	$-0.332819\pi$
$839$	−3.07260	−	2.05304i	−0.106078	−	0.0708789i	−0.607478	+	0.794337i	$0.707819\pi$
$840$	1.81961	−	1.81961i	0.0627823	−	0.0627823i
$841$	17.0894	+	22.2714i	0.589291	+	0.767979i
$842$	5.46324	+	4.19209i	0.188276	+	0.144469i
$843$	−12.5759	−	2.50150i	−0.433137	−	0.0861564i
$844$	−0.436026	+	0.884174i	−0.0150086	+	0.0304345i
$845$	2.18794	−	3.27449i	0.0752676	−	0.112646i
$846$	−12.7664	−	5.28802i	−0.438918	−	0.181806i
$847$	−20.6223	+	10.1698i	−0.708589	+	0.349437i
$848$	−3.68312	+	2.82616i	−0.126479	+	0.0970508i
$849$	−12.4914	−	3.34706i	−0.428704	−	0.114871i
$850$	−39.3387	+	2.57840i	−1.34931	+	0.0884382i
$851$		−	6.56479i		−	0.225038i
$852$	0.462167	+	7.05131i	0.0158336	+	0.241574i
$853$	9.46346	−	6.32328i	0.324023	−	0.216505i	−0.382910	−	0.923786i	$-0.625078\pi$
$853$	9.46346	−	6.32328i	0.324023	−	0.216505i	0.706933	+	0.707280i	$0.250078\pi$
$854$	1.72764	−	8.68546i	0.0591188	−	0.297210i
$855$	−1.13429	+	0.469840i	−0.0387921	+	0.0160682i
$856$	−14.1918	+	16.1826i	−0.485065	+	0.553110i
$857$	−7.06493	+	4.07894i	−0.241333	+	0.139334i	−0.615789	−	0.787911i	$-0.711163\pi$
$857$	−7.06493	+	4.07894i	−0.241333	+	0.139334i	0.374456	+	0.927245i	$0.377829\pi$
$858$	−0.604454	+	1.78067i	−0.0206357	+	0.0607909i
$859$	28.2973	+	24.8161i	0.965492	+	0.846714i	0.988222	−	0.153028i	$-0.0489023\pi$
$859$	28.2973	+	24.8161i	0.965492	+	0.846714i	−0.0227296	+	0.999742i	$0.507236\pi$
$860$	−1.15127	−	3.39152i	−0.0392578	−	0.115650i
$861$	4.33726	−	10.4711i	0.147813	−	0.356853i
$862$	−17.8675	−	2.35231i	−0.608571	−	0.0801199i
$863$	2.08698	+	4.23198i	0.0710416	+	0.144058i	0.929497	−	0.368831i	$-0.120242\pi$
$863$	2.08698	+	4.23198i	0.0710416	+	0.144058i	−0.858455	+	0.512889i	$0.828575\pi$
$864$	6.23469	+	23.2682i	0.212108	+	0.791599i
$865$	−1.16013	−	2.80081i	−0.0394457	−	0.0952304i
$866$	−10.8568	+	9.52120i	−0.368931	+	0.323543i
$867$	39.9648	+	23.0737i	1.35728	+	0.783624i
$868$	9.10064	−	3.08925i	0.308896	−	0.104856i
$869$	16.0773	−	4.30791i	0.545387	−	0.146136i
$870$	−0.203818	+	0.265621i	−0.00691008	+	0.00900539i
$871$	−2.70470	−	20.5443i	−0.0916454	−	0.696116i
$872$	−49.7866			−1.68599
$873$	−18.7738	−	9.37492i	−0.635395	−	0.317293i
$874$	4.22739			0.142994
$875$	1.18599	+	9.00847i	0.0400937	+	0.304542i
$876$	−3.02853	+	3.94686i	−0.102325	+	0.133352i
$877$	−20.1354	+	5.39527i	−0.679925	+	0.182185i	−0.582221	−	0.813030i	$-0.697816\pi$
$877$	−20.1354	+	5.39527i	−0.679925	+	0.182185i	−0.0977032	+	0.995216i	$0.531150\pi$
$878$	−8.74982	+	2.97016i	−0.295292	+	0.100238i
$879$	7.15619	+	4.13163i	0.241372	+	0.139356i
$880$	0.347009	−	0.304318i	0.0116977	−	0.0102586i
$881$	−12.3101	−	29.7192i	−0.414737	−	1.00126i	−0.983848	−	0.179004i	$-0.942713\pi$
$881$	−12.3101	−	29.7192i	−0.414737	−	1.00126i	0.569111	−	0.822261i	$-0.307287\pi$
$882$	0.522939	+	1.95164i	0.0176083	+	0.0657150i
$883$	3.48488	+	7.06664i	0.117276	+	0.237811i	0.947593	−	0.319479i	$-0.103508\pi$
$883$	3.48488	+	7.06664i	0.117276	+	0.237811i	−0.830318	+	0.557290i	$0.811841\pi$
$884$	12.8921	+	1.69727i	0.433608	+	0.0570855i
$885$	−0.885333	+	2.13738i	−0.0297602	+	0.0718474i
$886$	9.03512	+	26.6166i	0.303541	+	0.894202i
$887$	−4.89612	−	4.29379i	−0.164396	−	0.144171i	0.573196	−	0.819419i	$-0.305704\pi$
$887$	−4.89612	−	4.29379i	−0.164396	−	0.144171i	−0.737591	+	0.675247i	$0.764037\pi$
$888$	2.13215	−	6.28112i	0.0715504	−	0.210781i
$889$	−10.6652	+	6.15755i	−0.357699	+	0.206518i
$890$	2.25993	−	2.57695i	0.0757529	−	0.0863796i
$891$	2.29178	−	0.949287i	0.0767775	−	0.0318023i
$892$	−5.25868	+	26.4372i	−0.176074	+	0.885182i
$893$	8.33418	−	5.56872i	0.278893	−	0.186350i
$894$	−0.221611	−	3.38114i	−0.00741180	−	0.113082i
$895$			5.68669i			0.190085i
$896$	−7.80057	+	0.511277i	−0.260599	+	0.0170806i
$897$	3.92875	+	1.05271i	0.131177	+	0.0351488i
$898$	−6.83156	+	5.24204i	−0.227972	+	0.174929i
$899$	−3.34169	+	1.64794i	−0.111452	+	0.0549619i
$900$	−9.66371	−	4.00284i	−0.322124	−	0.133428i
$901$	−21.9321	+	32.8237i	−0.730665	+	1.09352i
$902$	2.79344	−	5.66454i	0.0930114	−	0.188608i
$903$	21.2730	+	4.23146i	0.707921	+	0.140814i
$904$	−42.7422	−	32.7973i	−1.42159	−	1.09082i
$905$	−3.61654	−	4.71317i	−0.120218	−	0.156671i
$906$	10.2095	−	10.2095i	0.339190	−	0.339190i
$907$	−28.7004	−	19.1770i	−0.952982	−	0.636762i	−0.0211981	−	0.999775i	$-0.506748\pi$
$907$	−28.7004	−	19.1770i	−0.952982	−	0.636762i	−0.931784	+	0.363013i	$0.881748\pi$
$908$	1.63947	−	2.83964i	0.0544076	−	0.0942368i
$909$	7.77964	+	13.4747i	0.258034	+	0.446929i
$910$	−0.0946526	+	1.44412i	−0.00313770	+	0.0478721i
$911$	34.1620	+	2.23909i	1.13184	+	0.0741845i	0.619786	−	0.784771i	$-0.287219\pi$
$911$	34.1620	+	2.23909i	1.13184	+	0.0741845i	0.512050	+	0.858955i	$0.328886\pi$
$912$	1.30183	+	0.441911i	0.0431079	+	0.0146332i
$913$	8.65844	+	9.87306i	0.286553	+	0.326751i
$914$	−1.97558	−	0.974248i	−0.0653464	−	0.0322253i
$915$	−1.24058	+	0.246768i	−0.0410124	+	0.00815788i
$916$	−6.98820	+	26.0803i	−0.230897	+	0.861718i
$917$	26.6263	−	3.50541i	0.879276	−	0.115759i
$918$	−21.5608	−	32.2681i	−0.711614	−	1.06501i
$919$	4.37860	+	22.0127i	0.144437	+	0.726132i	0.983329	+	0.181835i	$0.0582037\pi$
$919$	4.37860	+	22.0127i	0.144437	+	0.726132i	−0.838892	+	0.544297i	$0.816796\pi$
$920$	−2.19322	−	2.19322i	−0.0723082	−	0.0723082i
$921$	−1.93542	+	14.7009i	−0.0637741	+	0.484413i
$922$	2.30148	−	17.4815i	0.0757953	−	0.575722i
$923$	−8.37346	−	8.37346i	−0.275616	−	0.275616i
$924$	−0.580333	−	2.91753i	−0.0190916	−	0.0959798i
$925$	6.41339	+	9.59832i	0.210871	+	0.315591i
$926$	13.5774	−	1.78750i	0.446180	−	0.0587407i
$927$	6.02611	−	22.4897i	0.197923	−	0.738660i
$928$	4.75650	−	0.946127i	0.156140	−	0.0310582i
$929$	19.9222	+	9.82454i	0.653626	+	0.322333i	0.738692	−	0.674043i	$-0.235444\pi$
$929$	19.9222	+	9.82454i	0.653626	+	0.322333i	−0.0850665	+	0.996375i	$0.527110\pi$
$930$	0.886768	+	1.01117i	0.0290783	+	0.0331574i
$931$	−1.38783	−	0.471104i	−0.0454843	−	0.0154398i
$932$	10.2281	+	0.670384i	0.335032	+	0.0219592i
$933$	0.0811502	−	1.23811i	0.00265674	−	0.0405340i
$934$	14.7302	+	25.5135i	0.481988	+	0.834828i
$935$	1.96235	−	3.39889i	0.0641758	−	0.111156i
$936$	−8.37462	−	5.59574i	−0.273733	−	0.182903i
$937$	−10.9254	+	10.9254i	−0.356916	+	0.356916i	−0.862675	−	0.505759i	$-0.831213\pi$
$937$	−10.9254	+	10.9254i	−0.356916	+	0.356916i	0.505759	+	0.862675i	$0.331213\pi$
$938$	−19.5504	−	25.4786i	−0.638343	−	0.831905i
$939$	−6.38221	−	4.89725i	−0.208276	−	0.159816i
$940$	−2.42068	−	0.481503i	−0.0789538	−	0.0157049i
$941$	19.0427	−	38.6148i	0.620775	−	1.25881i	−0.328543	−	0.944489i	$-0.606557\pi$
$941$	19.0427	−	38.6148i	0.620775	−	1.25881i	0.949318	−	0.314318i	$-0.101776\pi$
$942$	−11.1637	+	16.7076i	−0.363732	+	0.544364i
$943$	−12.6210	−	5.22781i	−0.410998	−	0.170241i
$944$	−5.69420	+	2.80807i	−0.185330	+	0.0913948i
$945$	−3.49755	+	2.68376i	−0.113775	+	0.0873028i
$946$	11.6750	+	3.12830i	0.379587	+	0.101710i
$947$	26.1537	−	1.71420i	0.849881	−	0.0557042i	0.365764	−	0.930707i	$-0.380808\pi$
$947$	26.1537	−	1.71420i	0.849881	−	0.0557042i	0.484117	+	0.875003i	$0.339141\pi$
$948$		−	12.2078i		−	0.396491i
$949$	−0.545259	−	8.31905i	−0.0176999	−	0.270048i
$950$	−6.18083	+	4.12990i	−0.200533	+	0.133992i
$951$	−4.87964	+	24.5316i	−0.158233	+	0.795492i
$952$	55.4797	−	22.9804i	1.79811	−	0.744800i
$953$	29.2709	−	33.3771i	0.948178	−	1.08119i	−0.0484247	−	0.998827i	$-0.515420\pi$
$953$	29.2709	−	33.3771i	0.948178	−	1.08119i	0.996602	−	0.0823627i	$-0.0262466\pi$
$954$	8.88707	−	5.13096i	0.287730	−	0.166121i
$955$	1.08164	−	3.18640i	0.0350010	−	0.103110i
$956$	20.9541	+	18.3762i	0.677704	+	0.594330i
$957$	0.370700	+	1.09205i	0.0119830	+	0.0353008i
$958$	−4.21238	+	10.1696i	−0.136096	+	0.328565i
$959$	−0.622482	−	0.0819513i	−0.0201010	−	0.00264634i
$960$	−1.07066	−	2.17109i	−0.0345555	−	0.0700715i
$961$	−4.14963	−	15.4866i	−0.133859	−	0.499569i
$962$	1.42758	+	3.44649i	0.0460271	+	0.111119i
$963$	11.5131	−	10.0967i	0.371004	−	0.325362i
$964$	−19.0337	−	10.9891i	−0.613035	−	0.353936i
$965$	−3.23190	+	1.09708i	−0.104038	+	0.0353163i
$966$	6.08893	−	1.63152i	0.195908	−	0.0524934i
$967$	7.97050	−	10.3874i	0.256314	−	0.334035i	−0.647417	−	0.762136i	$-0.724151\pi$
$967$	7.97050	−	10.3874i	0.256314	−	0.334035i	0.903731	+	0.428101i	$0.140817\pi$
$968$	3.65516	+	27.7637i	0.117481	+	0.892358i
$969$	11.6904			0.375549
$970$	3.54219	+	0.968093i	0.113733	+	0.0310836i
$971$	−31.3479			−1.00600			−0.503000	−	0.864286i	$-0.667771\pi$
$971$	−31.3479			−1.00600			−0.503000	+	0.864286i	$0.667771\pi$
$972$	−2.12988	−	16.1780i	−0.0683159	−	0.518911i
$973$	7.21468	−	9.40235i	0.231292	−	0.301426i
$974$	27.4975	−	7.36793i	0.881076	−	0.236084i
$975$	−6.77262	+	2.29900i	−0.216897	+	0.0736268i
$976$	−3.00620	−	1.73563i	−0.0962260	−	0.0555561i
$977$	−9.97262	+	8.74576i	−0.319053	+	0.279802i	−0.803859	−	0.594820i	$-0.797223\pi$
$977$	−9.97262	+	8.74576i	−0.319053	+	0.279802i	0.484806	+	0.874621i	$0.338890\pi$
$978$	−6.62340	−	15.9903i	−0.211793	−	0.511313i
$979$	−3.05566	−	11.4039i	−0.0976592	−	0.364469i
$980$	0.159614	+	0.323665i	0.00509867	+	0.0103391i
$981$	35.1175	+	4.62331i	1.12122	+	0.147611i
$982$	−7.33596	+	17.7106i	−0.234100	+	0.565167i
$983$	−14.1139	−	41.5782i	−0.450164	−	1.32614i	−0.901111	−	0.433589i	$-0.857247\pi$
$983$	−14.1139	−	41.5782i	−0.450164	−	1.32614i	0.450947	−	0.892551i	$-0.351086\pi$
$984$	−10.3778	−	9.10106i	−0.330831	−	0.290131i
$985$	−2.32867	+	6.86005i	−0.0741977	+	0.218579i
$986$	−6.76632	+	3.90654i	−0.215484	+	0.124410i
$987$	9.85496	−	11.2374i	0.313687	−	0.357691i
$988$	2.26527	−	0.938304i	0.0720677	−	0.0298514i
$989$	5.10029	−	25.6409i	0.162180	−	0.815333i
$990$	−0.848281	+	0.566803i	−0.0269601	+	0.0180142i
$991$	−3.15727	−	48.1706i	−0.100294	−	1.53019i	−0.690734	−	0.723109i	$-0.742712\pi$
$991$	−3.15727	−	48.1706i	−0.100294	−	1.53019i	0.590440	−	0.807082i	$-0.298954\pi$
$992$		−	19.4812i		−	0.618528i
$993$	−7.99526	+	0.524037i	−0.253722	+	0.0166298i
$994$	−17.7276	−	4.75010i	−0.562286	−	0.150664i
$995$	1.91089	−	1.46628i	0.0605792	−	0.0464841i
$996$	8.63823	−	4.25990i	0.273713	−	0.134980i
$997$	8.65171	+	3.58365i	0.274002	+	0.113495i	0.515454	−	0.856917i	$-0.327623\pi$
$997$	8.65171	+	3.58365i	0.274002	+	0.113495i	−0.241451	+	0.970413i	$0.577623\pi$
$998$	10.2227	−	15.2994i	0.323594	−	0.484293i
$999$	−5.02609	+	10.1919i	−0.159018	+	0.322457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.2.k.a.11.3	✓	128
3.2	odd	2		873.2.bu.d.496.6		128
97.21	odd	96		9409.2.a.o.1.42		128
97.53	even	48	inner	97.2.k.a.53.3	yes	128
97.76	odd	96		9409.2.a.o.1.41		128
291.53	odd	48		873.2.bu.d.829.6		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.2.k.a.11.3	✓	128	1.1	even	1	trivial
97.2.k.a.53.3	yes	128	97.53	even	48	inner
873.2.bu.d.496.6		128	3.2	odd	2
873.2.bu.d.829.6		128	291.53	odd	48
9409.2.a.o.1.41		128	97.76	odd	96
9409.2.a.o.1.42		128	97.21	odd	96

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	97.k (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.129856 - 0.986358i) q^{2} +(-0.567607 + 0.739719i) q^{3} +(0.975813 - 0.261468i) q^{4} +(0.354879 - 0.120465i) q^{5} +(0.803335 + 0.463806i) q^{6} +(1.84879 - 1.62135i) q^{7} +(-1.14606 - 2.76683i) q^{8} +(0.551450 + 2.05804i) q^{9} +(-0.164905 - 0.334394i) q^{10} +(-1.27328 - 0.167631i) q^{11} +(-0.360465 + 0.870239i) q^{12} +(-0.507390 - 1.49472i) q^{13} +(-1.83931 - 1.61303i) q^{14} +(-0.112321 + 0.330888i) q^{15} +(-0.830477 + 0.479476i) q^{16} +(-5.37653 + 6.13076i) q^{17} +(1.95835 - 0.811176i) q^{18} +(-0.299968 + 1.50804i) q^{19} +(0.314798 - 0.210341i) q^{20} +(0.149955 + 2.28788i) q^{21} +1.27768i q^{22} +(2.75764 - 0.180745i) q^{23} +(2.69718 + 0.722708i) q^{24} +(-3.85534 + 2.95831i) q^{25} +(-1.40844 + 0.694567i) q^{26} +(-4.41964 - 1.83068i) q^{27} +(1.38015 - 2.06553i) q^{28} +(-0.425964 + 0.863770i) q^{29} +(0.340959 + 0.0678210i) q^{30} +(3.06927 + 2.35513i) q^{31} +(-3.06545 - 3.99497i) q^{32} +(0.846722 - 0.846722i) q^{33} +(6.74530 + 4.50707i) q^{34} +(0.460782 - 0.798098i) q^{35} +(1.07622 + 1.86407i) q^{36} +(0.155364 - 2.37040i) q^{37} +(1.52642 + 0.100047i) q^{38} +(1.39367 + 0.473088i) q^{39} +(-0.740017 - 0.843828i) q^{40} +(-4.43346 - 2.18634i) q^{41} +(2.23719 - 0.445005i) q^{42} +(2.44843 - 9.13766i) q^{43} +(-1.28631 + 0.169346i) q^{44} +(0.443620 + 0.663924i) q^{45} +(-0.536376 - 2.69655i) q^{46} +(-4.60960 - 4.60960i) q^{47} +(0.116707 - 0.886474i) q^{48} +(-0.124416 + 0.945035i) q^{49} +(3.41859 + 3.41859i) q^{50} +(-1.48329 - 7.45699i) q^{51} +(-0.885940 - 1.32590i) q^{52} +(4.79978 - 0.631903i) q^{53} +(-1.23178 + 4.59707i) q^{54} +(-0.472054 + 0.0938974i) q^{55} +(-6.60481 - 3.25713i) q^{56} +(-0.945262 - 1.07786i) q^{57} +(0.907300 + 0.307987i) q^{58} +(6.60653 + 0.433015i) q^{59} +(-0.0230879 + 0.352253i) q^{60} +(1.80992 + 3.13488i) q^{61} +(1.92444 - 3.33323i) q^{62} +(4.35631 + 2.91080i) q^{63} +(-4.89856 + 4.89856i) q^{64} +(-0.360124 - 0.469323i) q^{65} +(-0.945123 - 0.725219i) q^{66} +(12.8752 + 2.56103i) q^{67} +(-3.64349 + 7.38827i) q^{68} +(-1.43155 + 2.14247i) q^{69} +(-0.847045 - 0.350858i) q^{70} +(6.72835 - 3.31805i) q^{71} +(5.06224 - 3.88439i) q^{72} +(5.10159 + 1.36697i) q^{73} +(-2.35824 + 0.154567i) q^{74} -4.53102i q^{75} +(0.101592 + 1.55000i) q^{76} +(-2.62582 + 1.75452i) q^{77} +(0.285657 - 1.43609i) q^{78} +(-11.9738 + 4.95969i) q^{79} +(-0.236959 + 0.270200i) q^{80} +(-1.67276 + 0.965766i) q^{81} +(-1.58080 + 4.65689i) q^{82} +(-7.68770 - 6.74193i) q^{83} +(0.744535 + 2.19333i) q^{84} +(-1.16948 + 2.82336i) q^{85} +(-9.33095 - 1.22844i) q^{86} +(-0.397167 - 0.805375i) q^{87} +(0.995447 + 3.71506i) q^{88} +(3.51797 + 8.49314i) q^{89} +(0.597260 - 0.523783i) q^{90} +(-3.36153 - 1.94078i) q^{91} +(2.64368 - 0.897408i) q^{92} +(-3.48427 + 0.933608i) q^{93} +(-3.94813 + 5.14530i) q^{94} +(0.0752140 + 0.571307i) q^{95} +4.69512 q^{96} +(-6.53067 + 7.37227i) q^{97} +0.948299 q^{98} +(-0.357160 - 2.71290i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{2} - 24 q^{3} - 16 q^{4} - 16 q^{5} - 24 q^{6} - 16 q^{7} - 16 q^{8} + 8 q^{9} + 16 q^{10} - 16 q^{11} - 8 q^{12} - 16 q^{13} + 32 q^{14} + 16 q^{15} - 24 q^{16} - 8 q^{17} - 80 q^{18} - 24 q^{19}+ \cdots - 224 q^{99}+O(q^{100}) \) 128 * q - 16 * q^2 - 24 * q^3 - 16 * q^4 - 16 * q^5 - 24 * q^6 - 16 * q^7 - 16 * q^8 + 8 * q^9 + 16 * q^10 - 16 * q^11 - 8 * q^12 - 16 * q^13 + 32 * q^14 + 16 * q^15 - 24 * q^16 - 8 * q^17 - 80 * q^18 - 24 * q^19 - 8 * q^20 - 16 * q^21 + 24 * q^23 - 48 * q^24 - 24 * q^25 + 24 * q^26 + 24 * q^28 - 56 * q^30 - 40 * q^31 + 128 * q^32 - 8 * q^33 - 16 * q^34 - 72 * q^35 + 112 * q^36 + 8 * q^37 - 16 * q^38 + 32 * q^40 + 16 * q^41 - 64 * q^42 - 24 * q^43 + 104 * q^44 + 152 * q^45 - 16 * q^46 + 32 * q^47 - 48 * q^49 + 8 * q^50 - 16 * q^51 - 48 * q^52 - 32 * q^53 + 96 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 + 112 * q^58 + 32 * q^59 + 16 * q^60 - 56 * q^61 + 56 * q^62 + 176 * q^63 - 48 * q^64 - 8 * q^65 - 8 * q^66 - 32 * q^67 - 48 * q^68 - 96 * q^69 + 64 * q^70 + 136 * q^71 + 112 * q^72 - 64 * q^73 + 304 * q^76 - 16 * q^77 - 64 * q^78 + 32 * q^79 - 48 * q^80 + 72 * q^81 - 8 * q^82 - 64 * q^83 - 112 * q^84 - 72 * q^85 - 248 * q^86 + 96 * q^87 - 96 * q^88 - 16 * q^90 - 168 * q^91 - 120 * q^92 + 24 * q^93 + 48 * q^94 + 32 * q^95 - 352 * q^96 - 176 * q^97 + 208 * q^98 - 224 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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