LMFDB - Embedded newform 224.2.bd.a.109.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(37,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("224.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, degree $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			109.9
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.760837 - 1.19211i) q^{2} +(-1.44087 - 1.87778i) q^{3} +(-0.842255 + 1.81400i) q^{4} +(-2.75892 - 2.11700i) q^{5} +(-1.14225 + 3.14636i) q^{6} +(-1.14468 + 2.38531i) q^{7} +(2.80331 - 0.376098i) q^{8} +(-0.673491 + 2.51350i) q^{9} +O(q^{10})$	\(q+(-0.760837 - 1.19211i) q^{2} +(-1.44087 - 1.87778i) q^{3} +(-0.842255 + 1.81400i) q^{4} +(-2.75892 - 2.11700i) q^{5} +(-1.14225 + 3.14636i) q^{6} +(-1.14468 + 2.38531i) q^{7} +(2.80331 - 0.376098i) q^{8} +(-0.673491 + 2.51350i) q^{9} +(-0.424604 + 4.89963i) q^{10} +(2.68201 + 0.353093i) q^{11} +(4.61988 - 1.03217i) q^{12} +(1.84002 + 0.762162i) q^{13} +(3.71447 - 0.450247i) q^{14} +8.23097i q^{15} +(-2.58121 - 3.05571i) q^{16} +(-6.86527 - 3.96366i) q^{17} +(3.50879 - 1.10949i) q^{18} +(0.226114 + 1.71751i) q^{19} +(6.16395 - 3.22164i) q^{20} +(6.12843 - 1.28747i) q^{21} +(-1.61964 - 3.46589i) q^{22} +(-1.20290 + 4.48927i) q^{23} +(-4.74544 - 4.72209i) q^{24} +(1.83589 + 6.85163i) q^{25} +(-0.491375 - 2.77339i) q^{26} +(-0.869948 + 0.360344i) q^{27} +(-3.36285 - 4.08549i) q^{28} +(0.0946303 - 0.228458i) q^{29} +(9.81223 - 6.26242i) q^{30} +(-4.72355 + 8.18143i) q^{31} +(-1.67886 + 5.40198i) q^{32} +(-3.20140 - 5.54498i) q^{33} +(0.498221 + 11.1999i) q^{34} +(8.20778 - 4.15761i) q^{35} +(-3.99225 - 3.33872i) q^{36} +(-3.74651 - 2.87479i) q^{37} +(1.87542 - 1.57629i) q^{38} +(-1.22006 - 4.55333i) q^{39} +(-8.53032 - 4.89697i) q^{40} +(0.823484 + 0.823484i) q^{41} +(-6.19754 - 6.32621i) q^{42} +(-2.05302 - 4.95643i) q^{43} +(-2.89945 + 4.56777i) q^{44} +(7.17918 - 5.50878i) q^{45} +(6.26691 - 1.98162i) q^{46} +(0.844781 - 0.487734i) q^{47} +(-2.01875 + 9.24983i) q^{48} +(-4.37942 - 5.46083i) q^{49} +(6.77109 - 7.40155i) q^{50} +(2.44908 + 18.6026i) q^{51} +(-2.93233 + 2.69587i) q^{52} +(-7.52554 - 0.990756i) q^{53} +(1.09146 + 0.762911i) q^{54} +(-6.65195 - 6.65195i) q^{55} +(-2.31178 + 7.11728i) q^{56} +(2.89930 - 2.89930i) q^{57} +(-0.344345 + 0.0610092i) q^{58} +(0.187527 - 1.42441i) q^{59} +(-14.9310 - 6.93258i) q^{60} +(-5.51757 + 0.726402i) q^{61} +(13.3470 - 0.593736i) q^{62} +(-5.22455 - 4.48364i) q^{63} +(7.71710 - 2.10864i) q^{64} +(-3.46298 - 5.99807i) q^{65} +(-4.17449 + 8.03524i) q^{66} +(-7.06937 - 9.21298i) q^{67} +(12.9724 - 9.11520i) q^{68} +(10.1631 - 4.20969i) q^{69} +(-11.2011 - 6.62132i) q^{70} +(-0.823109 + 0.823109i) q^{71} +(-0.942681 + 7.29942i) q^{72} +(13.8498 - 3.71104i) q^{73} +(-0.576595 + 6.65350i) q^{74} +(10.2206 - 13.3197i) q^{75} +(-3.30601 - 1.03641i) q^{76} +(-3.91227 + 5.99324i) q^{77} +(-4.49981 + 4.91879i) q^{78} +(-0.377642 + 0.218032i) q^{79} +(0.652444 + 13.8949i) q^{80} +(8.69076 + 5.01761i) q^{81} +(0.355147 - 1.60822i) q^{82} +(-8.69345 - 3.60095i) q^{83} +(-2.82623 + 12.2014i) q^{84} +(10.5497 + 25.4692i) q^{85} +(-4.34660 + 6.21846i) q^{86} +(-0.565344 + 0.151483i) q^{87} +(7.65129 - 0.0188683i) q^{88} +(6.94761 + 1.86161i) q^{89} +(-12.0293 - 4.36710i) q^{90} +(-3.92423 + 3.51659i) q^{91} +(-7.13040 - 5.96317i) q^{92} +(22.1690 - 2.91860i) q^{93} +(-1.22417 - 0.635986i) q^{94} +(3.01212 - 5.21715i) q^{95} +(12.5628 - 4.63103i) q^{96} -9.00485 q^{97} +(-3.17790 + 9.37555i) q^{98} +(-2.69381 + 6.50342i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−0.760837	−	1.19211i	−0.537993	−	0.842949i
$2$	−0.760837	−	1.19211i	−0.537993	−	0.842949i
$3$	−1.44087	−	1.87778i	−0.831887	−	1.08414i	−0.995229	−	0.0975672i	$-0.968894\pi$
$3$	−1.44087	−	1.87778i	−0.831887	−	1.08414i	0.163341	−	0.986570i	$-0.447773\pi$
$4$	−0.842255	+	1.81400i	−0.421128	+	0.907001i
$5$	−2.75892	−	2.11700i	−1.23383	−	0.946749i	−0.234152	−	0.972200i	$-0.575231\pi$
$5$	−2.75892	−	2.11700i	−1.23383	−	0.946749i	−0.999676	+	0.0254506i	$0.991898\pi$
$6$	−1.14225	+	3.14636i	−0.466323	+	1.28450i
$7$	−1.14468	+	2.38531i	−0.432648	+	0.901563i
$7$	−1.14468	+	2.38531i	−0.432648	+	0.901563i
$8$	2.80331	−	0.376098i	0.991120	−	0.132971i
$9$	−0.673491	+	2.51350i	−0.224497	+	0.837834i
$10$	−0.424604	+	4.89963i	−0.134272	+	1.54940i
$11$	2.68201	+	0.353093i	0.808655	+	0.106461i	0.523506	−	0.852022i	$-0.324624\pi$
$11$	2.68201	+	0.353093i	0.808655	+	0.106461i	0.285149	+	0.958483i	$0.407957\pi$
$12$	4.61988	−	1.03217i	1.33364	−	0.297963i
$13$	1.84002	+	0.762162i	0.510330	+	0.211386i	0.622963	−	0.782251i	$-0.285929\pi$
$13$	1.84002	+	0.762162i	0.510330	+	0.211386i	−0.112633	+	0.993637i	$0.535929\pi$
$14$	3.71447	−	0.450247i	0.992734	−	0.120334i
$15$			8.23097i			2.12523i
$16$	−2.58121	−	3.05571i	−0.645303	−	0.763927i
$17$	−6.86527	−	3.96366i	−1.66507	−	0.961330i	−0.970236	−	0.242161i	$-0.922144\pi$
$17$	−6.86527	−	3.96366i	−1.66507	−	0.961330i	−0.694836	−	0.719168i	$-0.744523\pi$
$18$	3.50879	−	1.10949i	0.827029	−	0.261509i
$19$	0.226114	+	1.71751i	0.0518741	+	0.394023i	0.997611	+	0.0690882i	$0.0220090\pi$
$19$	0.226114	+	1.71751i	0.0518741	+	0.394023i	−0.945736	+	0.324935i	$0.894658\pi$
$20$	6.16395	−	3.22164i	1.37830	−	0.720381i
$21$	6.12843	−	1.28747i	1.33733	−	0.280949i
$22$	−1.61964	−	3.46589i	−0.345309	−	0.738931i
$23$	−1.20290	+	4.48927i	−0.250821	+	0.936077i	0.719546	+	0.694444i	$0.244350\pi$
$23$	−1.20290	+	4.48927i	−0.250821	+	0.936077i	−0.970368	+	0.241633i	$0.922317\pi$
$24$	−4.74544	−	4.72209i	−0.968659	−	0.963893i
$25$	1.83589	+	6.85163i	0.367178	+	1.37033i
$26$	−0.491375	−	2.77339i	−0.0963665	−	0.543907i
$27$	−0.869948	+	0.360344i	−0.167421	+	0.0693483i
$28$	−3.36285	−	4.08549i	−0.635518	−	0.772086i
$29$	0.0946303	−	0.228458i	0.0175724	−	0.0424235i	−0.914850	−	0.403794i	$-0.867691\pi$
$29$	0.0946303	−	0.228458i	0.0175724	−	0.0424235i	0.932422	+	0.361371i	$0.117691\pi$
$30$	9.81223	−	6.26242i	1.79146	−	1.14336i
$31$	−4.72355	+	8.18143i	−0.848375	+	1.46943i	0.0342833	+	0.999412i	$0.489085\pi$
$31$	−4.72355	+	8.18143i	−0.848375	+	1.46943i	−0.882658	+	0.470016i	$0.844248\pi$
$32$	−1.67886	+	5.40198i	−0.296783	+	0.954945i
$33$	−3.20140	−	5.54498i	−0.557291	−	0.965257i
$34$	0.498221	+	11.1999i	0.0854441	+	1.92076i
$35$	8.20778	−	4.15761i	1.38737	−	0.702764i
$36$	−3.99225	−	3.33872i	−0.665375	−	0.556454i
$37$	−3.74651	−	2.87479i	−0.615922	−	0.472613i	0.253065	−	0.967449i	$-0.418561\pi$
$37$	−3.74651	−	2.87479i	−0.615922	−	0.472613i	−0.868986	+	0.494836i	$0.835228\pi$
$38$	1.87542	−	1.57629i	0.304233	−	0.255709i
$39$	−1.22006	−	4.55333i	−0.195366	−	0.729117i
$40$	−8.53032	−	4.89697i	−1.34876	−	0.774279i
$41$	0.823484	+	0.823484i	0.128607	+	0.128607i	0.768480	−	0.639874i	$-0.221013\pi$
$41$	0.823484	+	0.823484i	0.128607	+	0.128607i	−0.639874	+	0.768480i	$0.721013\pi$
$42$	−6.19754	−	6.32621i	−0.956301	−	0.976155i
$43$	−2.05302	−	4.95643i	−0.313082	−	0.755848i	−0.999587	−	0.0287228i	$-0.990856\pi$
$43$	−2.05302	−	4.95643i	−0.313082	−	0.755848i	0.686505	−	0.727125i	$-0.259144\pi$
$44$	−2.89945	+	4.56777i	−0.437108	+	0.688618i
$45$	7.17918	−	5.50878i	1.07021	−	0.821200i
$46$	6.26691	−	1.98162i	0.924006	−	0.292173i
$47$	0.844781	−	0.487734i	0.123224	−	0.0711434i	−0.437121	−	0.899403i	$-0.644002\pi$
$47$	0.844781	−	0.487734i	0.123224	−	0.0711434i	0.560345	+	0.828259i	$0.310669\pi$
$48$	−2.01875	+	9.24983i	−0.291382	+	1.33510i
$49$	−4.37942	−	5.46083i	−0.625631	−	0.780119i
$50$	6.77109	−	7.40155i	0.957577	−	1.04674i
$51$	2.44908	+	18.6026i	0.342939	+	2.60488i
$52$	−2.93233	+	2.69587i	−0.406641	+	0.373850i
$53$	−7.52554	−	0.990756i	−1.03371	−	0.136091i	−0.405470	−	0.914108i	$-0.632892\pi$
$53$	−7.52554	−	0.990756i	−1.03371	−	0.136091i	−0.628242	+	0.778018i	$0.716225\pi$
$54$	1.09146	+	0.762911i	0.148529	+	0.103819i
$55$	−6.65195	−	6.65195i	−0.896949	−	0.896949i
$56$	−2.31178	+	7.11728i	−0.308925	+	0.951086i
$57$	2.89930	−	2.89930i	0.384021	−	0.384021i
$58$	−0.344345	+	0.0610092i	−0.0452147	+	0.00801091i
$59$	0.187527	−	1.42441i	0.0244139	−	0.185442i	−0.974893	−	0.222675i	$-0.928521\pi$
$59$	0.187527	−	1.42441i	0.0244139	−	0.185442i	0.999307	+	0.0372330i	$0.0118544\pi$
$60$	−14.9310	−	6.93258i	−1.92758	−	0.894992i
$61$	−5.51757	+	0.726402i	−0.706452	+	0.0930062i	−0.475187	−	0.879885i	$-0.657620\pi$
$61$	−5.51757	+	0.726402i	−0.706452	+	0.0930062i	−0.231265	+	0.972891i	$0.574286\pi$
$62$	13.3470	−	0.593736i	1.69507	−	0.0754046i
$63$	−5.22455	−	4.48364i	−0.658232	−	0.564885i
$64$	7.71710	−	2.10864i	0.964638	−	0.263580i
$65$	−3.46298	−	5.99807i	−0.429530	−	0.743968i
$66$	−4.17449	+	8.03524i	−0.513844	+	0.989070i
$67$	−7.06937	−	9.21298i	−0.863661	−	1.12554i	−0.991023	−	0.133688i	$-0.957318\pi$
$67$	−7.06937	−	9.21298i	−0.863661	−	1.12554i	0.127363	−	0.991856i	$-0.459349\pi$
$68$	12.9724	−	9.11520i	1.57314	−	1.10538i
$69$	10.1631	−	4.20969i	1.22349	−	0.506787i
$70$	−11.2011	−	6.62132i	−1.33879	−	0.791399i
$71$	−0.823109	+	0.823109i	−0.0976851	+	0.0976851i	−0.754260	−	0.656575i	$-0.772004\pi$
$71$	−0.823109	+	0.823109i	−0.0976851	+	0.0976851i	0.656575	+	0.754260i	$0.272004\pi$
$72$	−0.942681	+	7.29942i	−0.111096	+	0.860245i
$73$	13.8498	−	3.71104i	1.62100	−	0.434345i	0.669702	−	0.742630i	$-0.266422\pi$
$73$	13.8498	−	3.71104i	1.62100	−	0.434345i	0.951294	+	0.308285i	$0.0997552\pi$
$74$	−0.576595	+	6.65350i	−0.0670278	+	0.773453i
$75$	10.2206	−	13.3197i	1.18017	−	1.53803i
$76$	−3.30601	−	1.03641i	−0.379225	−	0.118884i
$77$	−3.91227	+	5.99324i	−0.445845	+	0.682993i
$78$	−4.49981	+	4.91879i	−0.509503	+	0.556943i
$79$	−0.377642	+	0.218032i	−0.0424880	+	0.0245305i	−0.521094	−	0.853500i	$-0.674476\pi$
$79$	−0.377642	+	0.218032i	−0.0424880	+	0.0245305i	0.478606	+	0.878030i	$0.341142\pi$
$80$	0.652444	+	13.8949i	0.0729455	+	1.55349i
$81$	8.69076	+	5.01761i	0.965640	+	0.557513i
$82$	0.355147	−	1.60822i	0.0392194	−	0.177598i
$83$	−8.69345	−	3.60095i	−0.954230	−	0.395255i	−0.149411	−	0.988775i	$-0.547738\pi$
$83$	−8.69345	−	3.60095i	−0.954230	−	0.395255i	−0.804819	+	0.593520i	$0.797738\pi$
$84$	−2.82623	+	12.2014i	−0.308367	+	1.33128i
$85$	10.5497	+	25.4692i	1.14427	+	2.76252i
$86$	−4.34660	+	6.21846i	−0.468706	+	0.670553i
$87$	−0.565344	+	0.151483i	−0.0606112	+	0.0162407i
$88$	7.65129	−	0.0188683i	0.815631	−	0.00201137i
$89$	6.94761	+	1.86161i	0.736445	+	0.197330i	0.607498	−	0.794322i	$-0.292173\pi$
$89$	6.94761	+	1.86161i	0.736445	+	0.197330i	0.128948	+	0.991651i	$0.458840\pi$
$90$	−12.0293	−	4.36710i	−1.26800	−	0.460332i
$91$	−3.92423	+	3.51659i	−0.411371	+	0.368639i
$92$	−7.13040	−	5.96317i	−0.743396	−	0.621703i
$93$	22.1690	−	2.91860i	2.29881	−	0.302644i
$94$	−1.22417	−	0.635986i	−0.126264	−	0.0655969i
$95$	3.01212	−	5.21715i	0.309037	−	0.535268i
$96$	12.5628	−	4.63103i	1.28218	−	0.472653i
$97$	−9.00485			−0.914304			−0.457152	−	0.889389i	$-0.651131\pi$
$97$	−9.00485			−0.914304			−0.457152	+	0.889389i	$0.651131\pi$
$98$	−3.17790	+	9.37555i	−0.321016	+	0.947074i
$99$	−2.69381	+	6.50342i	−0.270738	+	0.653618i
$100$	−13.9752	−	2.44052i	−1.39752	−	0.244052i
$101$	1.14590	−	8.70397i	0.114021	−	0.866077i	−0.834864	−	0.550456i	$-0.814454\pi$
$101$	1.14590	−	8.70397i	0.114021	−	0.866077i	0.948885	−	0.315621i	$-0.102213\pi$
$102$	20.3130	−	17.0731i	2.01129	−	1.69049i
$103$	16.7898	+	4.49881i	1.65435	+	0.443281i	0.960825	−	0.277156i	$-0.0893918\pi$
$103$	16.7898	+	4.49881i	1.65435	+	0.443281i	0.693521	+	0.720437i	$0.256059\pi$
$104$	5.44480	+	1.44455i	0.533907	+	0.141650i
$105$	−19.6334	−	9.42183i	−1.91603	−	0.919476i
$106$	4.54461	+	9.72508i	0.441412	+	0.944583i
$107$	−1.12333	+	1.46395i	−0.108596	+	0.141526i	−0.844489	−	0.535572i	$-0.820096\pi$
$107$	−1.12333	+	1.46395i	−0.108596	+	0.141526i	0.735893	+	0.677098i	$0.236763\pi$
$108$	0.0790529	−	1.88159i	0.00760687	−	0.181056i
$109$	−6.62330	+	5.08224i	−0.634398	+	0.486790i	−0.875186	−	0.483787i	$-0.839261\pi$
$109$	−6.62330	+	5.08224i	−0.634398	+	0.486790i	0.240788	+	0.970578i	$0.422594\pi$
$110$	−2.86881	+	12.9909i	−0.273531	+	1.23863i
$111$			11.1773i			1.06090i
$112$	10.2435	−	2.65919i	0.967917	−	0.251269i
$113$			0.411718i			0.0387312i	0.999812	+	0.0193656i	$0.00616464\pi$
$113$			0.411718i			0.0387312i	−0.999812	+	0.0193656i	$0.993835\pi$
$114$	−5.66217	−	1.25039i	−0.530311	−	0.117110i
$115$	12.8225	−	9.83902i	1.19570	−	0.917494i
$116$	0.334720	+	0.364079i	0.0310780	+	0.0338039i
$117$	−3.15493	+	4.11159i	−0.291674	+	0.380116i
$118$	−1.84073	+	0.860189i	−0.169453	+	0.0791869i
$119$	17.3131	−	11.8387i	1.58709	−	1.08525i
$120$	3.09565	+	23.0740i	0.282593	+	2.10636i
$121$	−3.55670	−	0.953015i	−0.323336	−	0.0866377i
$122$	5.06392	+	6.02488i	0.458466	+	0.545467i
$123$	0.359787	−	2.73286i	0.0324409	−	0.246413i
$124$	−10.8627	−	15.4594i	−0.975499	−	1.38829i
$125$	2.78580	−	6.72552i	0.249170	−	0.601549i
$126$	−1.36996	+	9.63956i	−0.122046	+	0.858760i
$127$	−11.2634			−0.999464			−0.499732	−	0.866180i	$-0.666568\pi$
$127$	−11.2634			−0.999464			−0.499732	+	0.866180i	$0.666568\pi$
$128$	−8.38518	−	7.59531i	−0.741153	−	0.671337i
$129$	−6.34894	+	10.9967i	−0.558993	+	0.968205i
$130$	−4.51559	+	8.69181i	−0.396044	+	0.762322i
$131$	−14.7315	+	1.93944i	−1.28710	+	0.169450i	−0.742840	−	0.669469i	$-0.766522\pi$
$131$	−14.7315	+	1.93944i	−1.28710	+	0.169450i	−0.544257	+	0.838919i	$0.683188\pi$
$132$	12.7550	−	1.13705i	1.11018	−	0.0989676i
$133$	−4.35561	−	1.42664i	−0.377680	−	0.123706i
$134$	−5.60426	+	15.4370i	−0.484134	+	1.33356i
$135$	3.16297	+	0.847514i	0.272225	+	0.0729424i
$136$	−20.7362	−	8.52937i	−1.77811	−	0.731387i
$137$	−6.28819	+	1.68492i	−0.537236	+	0.143952i	−0.517228	−	0.855848i	$-0.673036\pi$
$137$	−6.28819	+	1.68492i	−0.537236	+	0.143952i	−0.0200085	+	0.999800i	$0.506369\pi$
$138$	−12.7509	−	8.91263i	−1.08542	−	0.758694i
$139$	0.00331720	+	0.00800842i	0.000281361	+	0.000679266i	0.924020	−	0.382344i	$-0.124883\pi$
$139$	0.00331720	+	0.00800842i	0.000281361	+	0.000679266i	−0.923739	+	0.383023i	$0.874883\pi$
$140$	0.628864	+	18.3907i	0.0531487	+	1.55430i
$141$	−2.13308	−	0.883550i	−0.179638	−	0.0744083i
$142$	1.60749	+	0.354986i	0.134897	+	0.0297897i
$143$	4.66584	+	2.69382i	0.390177	+	0.225269i
$144$	9.41895	−	4.42989i	0.784912	−	0.369157i
$145$	−0.744722	+	0.429965i	−0.0618458	+	0.0357067i
$146$	−14.9614	−	13.6870i	−1.23821	−	1.13274i
$147$	−3.94407	+	16.0919i	−0.325302	+	1.32724i
$148$	8.37040	−	4.37486i	0.688043	−	0.359611i
$149$	−8.39232	+	10.9371i	−0.687525	+	0.896001i	−0.998519	−	0.0544116i	$-0.982672\pi$
$149$	−8.39232	+	10.9371i	−0.687525	+	0.896001i	0.310993	+	0.950412i	$0.399338\pi$
$150$	−23.6548	−	2.04993i	−1.93140	−	0.167376i
$151$	4.06949	−	1.09042i	0.331170	−	0.0887368i	−0.0894026	−	0.995996i	$-0.528496\pi$
$151$	4.06949	−	1.09042i	0.331170	−	0.0887368i	0.420573	+	0.907259i	$0.361829\pi$
$152$	1.27982	+	4.72966i	0.103807	+	0.383626i
$153$	14.5864	−	14.5864i	1.17924	−	1.17924i
$154$	10.1212	+	0.103988i	0.815590	+	0.00837956i
$155$	30.3520	−	12.5722i	2.43793	−	1.00982i
$156$	9.28736	+	1.62187i	0.743584	+	0.129854i
$157$	9.39972	+	12.2500i	0.750180	+	0.977653i	0.999956	+	0.00934970i	$0.00297615\pi$
$157$	9.39972	+	12.2500i	0.750180	+	0.977653i	−0.249777	+	0.968303i	$0.580357\pi$
$158$	0.547241	+	0.284304i	0.0435362	+	0.0226180i
$159$	8.98291	+	15.5589i	0.712391	+	1.23390i
$160$	16.0678	−	11.3495i	1.27027	−	0.897258i
$161$	−9.33137	−	8.00806i	−0.735415	−	0.631123i
$162$	−0.630699	−	14.1779i	−0.0495524	−	1.11392i
$163$	5.81892	−	0.766076i	0.455773	−	0.0600037i	0.100855	−	0.994901i	$-0.467842\pi$
$163$	5.81892	−	0.766076i	0.455773	−	0.0600037i	0.354918	+	0.934897i	$0.384509\pi$
$164$	−2.18739	+	0.800218i	−0.170806	+	0.0624865i
$165$	−2.90630	+	22.0755i	−0.226255	+	1.71858i
$166$	2.32157	+	13.1033i	0.180189	+	1.01701i
$167$	−3.20407	+	3.20407i	−0.247938	+	0.247938i	−0.820124	−	0.572186i	$-0.806096\pi$
$167$	−3.20407	+	3.20407i	−0.247938	+	0.247938i	0.572186	+	0.820124i	$0.306096\pi$
$168$	16.6957	−	5.91406i	1.28810	−	0.456280i
$169$	−6.38760	−	6.38760i	−0.491354	−	0.491354i
$170$	22.3355	−	31.9543i	1.71305	−	2.45078i
$171$	−4.46924	−	0.588386i	−0.341771	−	0.0449950i
$172$	10.7201	+	0.450395i	0.817403	+	0.0343423i
$173$	−2.02443	−	15.3771i	−0.153915	−	1.16910i	−0.877747	−	0.479124i	$-0.840954\pi$
$173$	−2.02443	−	15.3771i	−0.153915	−	1.16910i	0.723832	−	0.689976i	$-0.242379\pi$
$174$	0.610719	+	0.558698i	0.0462985	+	0.0423548i
$175$	−18.4448	−	3.46376i	−1.39429	−	0.261835i
$176$	−5.84388	−	9.10683i	−0.440499	−	0.686453i
$177$	−2.94493	+	1.70026i	−0.221354	+	0.127799i
$178$	−3.06675	−	9.69870i	−0.229863	−	0.726948i
$179$	6.63005	−	5.08741i	0.495553	−	0.380251i	−0.330534	−	0.943794i	$-0.607229\pi$
$179$	6.63005	−	5.08741i	0.495553	−	0.380251i	0.826087	+	0.563543i	$0.190562\pi$
$180$	3.94624	+	17.6629i	0.294135	+	1.31651i
$181$	−6.21583	−	15.0064i	−0.462019	−	1.11541i	−0.967567	−	0.252615i	$-0.918710\pi$
$181$	−6.21583	−	15.0064i	−0.462019	−	1.11541i	0.505548	−	0.862799i	$-0.331290\pi$
$182$	7.17786	+	2.00256i	0.532059	+	0.148440i
$183$	9.31413	+	9.31413i	0.688520	+	0.688520i
$184$	−1.68369	+	13.0372i	−0.124123	+	0.961117i
$185$	4.25039	+	15.8627i	0.312495	+	1.16625i
$186$	−20.3462	−	24.2073i	−1.49186	−	1.77496i
$187$	−17.0131	−	13.0546i	−1.24412	−	0.954650i
$188$	0.173230	+	1.94323i	0.0126341	+	0.141725i
$189$	0.136279	−	2.48757i	0.00991282	−	0.180944i
$190$	−8.51115	+	0.378615i	−0.617464	+	0.0274676i
$191$	−7.87208	−	13.6348i	−0.569604	−	0.986583i	−0.996605	−	0.0823317i	$-0.973763\pi$
$191$	−7.87208	−	13.6348i	−0.569604	−	0.986583i	0.427001	−	0.904251i	$-0.359570\pi$
$192$	−15.0789	−	11.4527i	−1.08823	−	0.826530i
$193$	7.16214	−	12.4052i	0.515542	−	0.892945i	−0.484295	−	0.874905i	$-0.660924\pi$
$193$	7.16214	−	12.4052i	0.515542	−	0.892945i	0.999837	−	0.0180405i	$-0.00574277\pi$
$194$	6.85122	+	10.7348i	0.491889	+	0.770712i
$195$	−6.27333	+	15.1452i	−0.449243	+	1.08457i
$196$	13.5946	−	3.34485i	0.971040	−	0.238918i
$197$	8.63148	−	3.57528i	0.614967	−	0.254728i	−0.0533834	−	0.998574i	$-0.517001\pi$
$197$	8.63148	−	3.57528i	0.614967	−	0.254728i	0.668351	+	0.743846i	$0.267001\pi$
$198$	9.80234	−	1.73673i	0.696622	−	0.123424i
$199$	2.44416	+	9.12172i	0.173262	+	0.646622i	0.996841	+	0.0794207i	$0.0253070\pi$
$199$	2.44416	+	9.12172i	0.173262	+	0.646622i	−0.823579	+	0.567201i	$0.808026\pi$
$200$	7.72345	+	18.5168i	0.546130	+	1.30933i
$201$	−7.11390	+	26.5494i	−0.501776	+	1.87265i
$202$	−11.2479	+	5.25626i	−0.791402	+	0.369829i
$203$	0.436621	+	0.487234i	0.0306448	+	0.0341971i
$204$	−35.8079	−	11.2255i	−2.50705	−	0.785942i
$205$	−0.528616	−	4.01524i	−0.0369202	−	0.280437i
$206$	−7.41120	−	23.4381i	−0.516363	−	1.63301i
$207$	−10.4736	−	6.04696i	−0.727969	−	0.420293i
$208$	−2.42054	−	7.58987i	−0.167834	−	0.526263i
$209$			4.68620i			0.324151i
$210$	3.70597	+	30.5737i	0.255736	+	2.10978i
$211$	10.7623	+	4.45790i	0.740908	+	0.306894i	0.721026	−	0.692908i	$-0.243671\pi$
$211$	10.7623	+	4.45790i	0.740908	+	0.306894i	0.0198823	+	0.999802i	$0.493671\pi$
$212$	8.13566	−	12.8169i	0.558759	−	0.880267i
$213$	2.73161	+	0.359624i	0.187167	+	0.0246410i
$214$	2.59986	+	0.225305i	0.177723	+	0.0154015i
$215$	−4.82861	+	18.0206i	−0.329309	+	1.22900i
$216$	−2.30321	+	1.33734i	−0.156713	+	0.0909946i
$217$	−14.1083	−	20.6323i	−0.957734	−	1.40061i
$218$	11.0978	+	4.02896i	0.751641	+	0.272875i
$219$	−26.9243	−	20.6597i	−1.81937	−	1.39606i
$220$	17.6693	−	6.46402i	1.19126	−	0.435804i
$221$	−9.61129	−	12.5257i	−0.646525	−	0.842568i
$222$	13.3246	−	8.50412i	0.894289	−	0.570759i
$223$	−20.9534			−1.40315			−0.701573	−	0.712597i	$-0.747519\pi$
$223$	−20.9534			−1.40315			−0.701573	+	0.712597i	$0.747519\pi$
$224$	−10.9637	−	10.1881i	−0.732540	−	0.680724i
$225$	−18.4580			−1.23054
$226$	0.490813	−	0.313250i	0.0326484	−	0.0208371i
$227$	0.300327	+	0.391394i	0.0199334	+	0.0259777i	0.803214	−	0.595691i	$-0.203122\pi$
$227$	0.300327	+	0.391394i	0.0199334	+	0.0259777i	−0.783280	+	0.621669i	$0.786455\pi$
$228$	2.81738	+	7.70128i	0.186586	+	0.510030i
$229$	13.0467	+	10.0111i	0.862152	+	0.661552i	0.942131	−	0.335244i	$-0.108819\pi$
$229$	13.0467	+	10.0111i	0.862152	+	0.661552i	−0.0799794	+	0.996797i	$0.525485\pi$
$230$	−21.4850	−	7.79991i	−1.41668	−	0.514311i
$231$	16.8911	−	1.28910i	1.11135	−	0.0848163i
$232$	0.179356	−	0.676028i	0.0117753	−	0.0443834i
$233$	−3.09783	+	11.5613i	−0.202946	+	0.757404i	0.787120	+	0.616800i	$0.211571\pi$
$233$	−3.09783	+	11.5613i	−0.202946	+	0.757404i	−0.990066	+	0.140604i	$0.955095\pi$
$234$	7.30186	+	0.632782i	0.477337	+	0.0413662i
$235$	−3.36322	−	0.442776i	−0.219392	−	0.0288835i
$236$	2.42594	+	1.53989i	0.157915	+	0.100238i
$237$	0.953548	+	0.394973i	0.0619396	+	0.0256562i
$238$	−27.2854	−	11.6318i	−1.76865	−	0.753980i
$239$		−	21.1899i		−	1.37066i	−0.728234	−	0.685329i	$-0.759658\pi$
$239$		−	21.1899i		−	1.37066i	0.728234	−	0.685329i	$-0.240342\pi$
$240$	25.1514	−	21.2459i	1.62352	−	1.37142i
$241$	−2.64873	−	1.52924i	−0.170620	−	0.0985073i	0.412258	−	0.911067i	$-0.364740\pi$
$241$	−2.64873	−	1.52924i	−0.170620	−	0.0985073i	−0.582878	+	0.812560i	$0.698073\pi$
$242$	1.56997	+	4.96507i	0.100921	+	0.319167i
$243$	−2.73157	−	20.7484i	−0.175231	−	1.33101i
$244$	3.32951	−	10.6207i	0.213150	−	0.679921i
$245$	0.521906	+	24.3372i	0.0333433	+	1.55485i
$246$	−3.53161	+	1.65035i	−0.225167	+	0.105222i
$247$	−0.892963	+	3.33258i	−0.0568179	+	0.212047i
$248$	−10.1646	+	24.7116i	−0.645450	+	1.56919i
$249$	5.76436	+	21.5129i	0.365302	+	1.36332i
$250$	−10.1371	+	1.79604i	−0.641127	+	0.113591i
$251$	−1.84890	+	0.765839i	−0.116701	+	0.0483393i	−0.440270	−	0.897865i	$-0.645117\pi$
$251$	−1.84890	+	0.765839i	−0.116701	+	0.0483393i	0.323569	+	0.946205i	$0.395117\pi$
$252$	12.5337	−	5.70098i	0.789551	−	0.359128i
$253$	−4.81130	+	11.6155i	−0.302484	+	0.730261i
$254$	8.56960	+	13.4272i	0.537705	+	0.842498i
$255$	32.6248	−	56.5078i	2.04304	−	3.53866i
$256$	−2.67469	+	15.7749i	−0.167168	+	0.985928i
$257$	−4.12526	−	7.14516i	−0.257327	−	0.445703i	0.708198	−	0.706014i	$-0.249508\pi$
$257$	−4.12526	−	7.14516i	−0.257327	−	0.445703i	−0.965525	+	0.260311i	$0.916175\pi$
$258$	17.9398	−	0.798043i	1.11688	−	0.0496840i
$259$	11.1458	−	5.64586i	0.692568	−	0.350817i
$260$	13.7972	−	1.22996i	0.855668	−	0.0762789i
$261$	0.510496	+	0.391718i	0.0315989	+	0.0242467i
$262$	13.5203	+	16.0860i	0.835286	+	0.993795i
$263$	−2.34212	−	8.74090i	−0.144421	−	0.538987i	−0.999780	−	0.0209518i	$-0.993330\pi$
$263$	−2.34212	−	8.74090i	−0.144421	−	0.538987i	0.855359	−	0.518035i	$-0.173336\pi$
$264$	−11.0600	−	14.3403i	−0.680694	−	0.882582i
$265$	18.6650	+	18.6650i	1.14658	+	1.14658i
$266$	1.61319	+	6.27781i	0.0989113	+	0.384917i
$267$	−6.51492	−	15.7284i	−0.398707	−	0.962563i
$268$	22.6666	−	5.06417i	1.38458	−	0.309343i
$269$	4.43119	−	3.40017i	0.270174	−	0.207312i	−0.464784	−	0.885424i	$-0.653868\pi$
$269$	4.43119	−	3.40017i	0.270174	−	0.207312i	0.734959	+	0.678112i	$0.237201\pi$
$270$	−1.39617	−	4.41542i	−0.0849682	−	0.268714i
$271$	5.37806	−	3.10502i	0.326694	−	0.188617i	−0.327678	−	0.944789i	$-0.606266\pi$
$271$	5.37806	−	3.10502i	0.326694	−	0.188617i	0.654372	+	0.756173i	$0.272933\pi$
$272$	5.60891	+	31.2093i	0.340090	+	1.89234i
$273$	12.2577	+	2.30188i	0.741870	+	0.139316i
$274$	6.79289	+	6.21427i	0.410373	+	0.375418i
$275$	2.50460	+	19.0244i	0.151033	+	1.14721i
$276$	−0.923528	+	21.9815i	−0.0555899	+	1.32313i
$277$	−4.95715	−	0.652622i	−0.297846	−	0.0392122i	−0.0198780	−	0.999802i	$-0.506328\pi$
$277$	−4.95715	−	0.652622i	−0.297846	−	0.0392122i	−0.277969	+	0.960590i	$0.589661\pi$
$278$	0.00702308	−	0.0100476i	0.000421216	−	0.000602613i
$279$	−17.3828	−	17.3828i	−1.04068	−	1.04068i
$280$	21.4453	−	14.7420i	1.28160	−	0.881002i
$281$	12.7750	−	12.7750i	0.762093	−	0.762093i	−0.214607	−	0.976700i	$-0.568847\pi$
$281$	12.7750	−	12.7750i	0.762093	−	0.762093i	0.976700	+	0.214607i	$0.0688472\pi$
$282$	0.569635	+	3.21510i	0.0339213	+	0.191457i
$283$	−2.65472	+	20.1646i	−0.157806	+	1.19866i	0.710886	+	0.703307i	$0.248294\pi$
$283$	−2.65472	+	20.1646i	−0.157806	+	1.19866i	−0.868693	+	0.495352i	$0.835039\pi$
$284$	−0.799854	−	2.18639i	−0.0474626	−	0.129738i
$285$	−14.1367	+	1.86114i	−0.837388	+	0.110244i
$286$	−0.338605	−	7.61175i	−0.0200222	−	0.450092i
$287$	−2.90689	+	1.02164i	−0.171588	+	0.0603055i
$288$	−12.4472	−	7.85800i	−0.733458	−	0.463037i
$289$	22.9213	+	39.7008i	1.34831	+	2.33534i
$290$	1.07918	+	0.560658i	0.0633715	+	0.0329229i
$291$	12.9748	+	16.9091i	0.760598	+	0.991231i
$292$	−4.93323	+	28.2492i	−0.288695	+	1.65316i
$293$	−23.9894	+	9.93674i	−1.40148	+	0.580510i	−0.950134	−	0.311841i	$-0.899054\pi$
$293$	−23.9894	+	9.93674i	−1.40148	+	0.580510i	−0.451341	+	0.892351i	$0.649054\pi$
$294$	22.1842	−	7.54157i	1.29381	−	0.439833i
$295$	−3.53284	+	3.53284i	−0.205690	+	0.205690i
$296$	−11.5838	−	6.64989i	−0.673296	−	0.386517i
$297$	−2.46044	+	0.659273i	−0.142769	+	0.0382549i
$298$	19.4234	+	1.68324i	1.12517	+	0.0975074i
$299$	−5.63491	+	7.34355i	−0.325875	+	0.424689i
$300$	15.5537	+	29.7587i	0.897991	+	1.71812i
$301$	14.1727	+	0.776433i	0.816899	+	0.0447528i
$302$	−4.39611	−	4.02165i	−0.252968	−	0.231420i
$303$	−17.9952	+	10.3895i	−1.03380	+	0.596864i
$304$	4.66455	−	5.12418i	0.267530	−	0.293892i
$305$	16.7603	+	9.67659i	0.959694	+	0.554080i
$306$	−28.4864	−	6.29072i	−1.62846	−	0.359617i
$307$	−1.52272	−	0.630732i	−0.0869063	−	0.0359978i	0.338807	−	0.940856i	$-0.389977\pi$
$307$	−1.52272	−	0.630732i	−0.0869063	−	0.0359978i	−0.425713	+	0.904858i	$0.639977\pi$
$308$	−7.57662	−	12.1447i	−0.431718	−	0.692009i
$309$	−15.7441	−	38.0097i	−0.895653	−	2.16230i
$310$	−38.0803	−	26.6175i	−2.16282	−	1.51177i
$311$	−22.4323	+	6.01071i	−1.27202	+	0.340836i	−0.830804	−	0.556566i	$-0.812119\pi$
$311$	−22.4323	+	6.01071i	−1.27202	+	0.340836i	−0.441214	+	0.897402i	$0.645452\pi$
$312$	−5.13271	−	12.3055i	−0.290583	−	0.696664i
$313$	15.0729	+	4.03878i	0.851971	+	0.228285i	0.658276	−	0.752777i	$-0.271286\pi$
$313$	15.0729	+	4.03878i	0.851971	+	0.228285i	0.193695	+	0.981062i	$0.437953\pi$
$314$	7.45165	−	20.5257i	0.420521	−	1.15833i
$315$	4.92229	+	23.4304i	0.277339	+	1.32015i
$316$	−0.0774390	−	0.868681i	−0.00435629	−	0.0488671i
$317$	7.27433	−	0.957684i	0.408567	−	0.0537889i	0.0765581	−	0.997065i	$-0.475607\pi$
$317$	7.27433	−	0.957684i	0.408567	−	0.0537889i	0.332009	+	0.943276i	$0.392274\pi$
$318$	11.7134	−	22.5464i	0.656852	−	1.26434i
$319$	0.334466	−	0.579312i	0.0187265	−	0.0324352i
$320$	−25.7549	−	10.5195i	−1.43974	−	0.588058i
$321$	4.36755			0.243773
$322$	−2.44684	+	17.2169i	−0.136357	+	0.959458i
$323$	5.25528	−	12.6874i	0.292412	−	0.705944i
$324$	−16.4218	+	11.5390i	−0.912322	+	0.641053i
$325$	−1.84398	+	14.0064i	−0.102285	+	0.776935i
$326$	−5.34050	−	6.35394i	−0.295783	−	0.351912i
$327$	19.0867	+	5.11426i	1.05549	+	0.282819i
$328$	2.61819	+	1.99877i	0.144565	+	0.110364i
$329$	0.196395	+	2.57336i	0.0108276	+	0.141874i
$330$	28.5277	−	13.3312i	1.57040	−	0.733860i
$331$	−0.486928	+	0.634576i	−0.0267640	+	0.0348795i	−0.806544	−	0.591175i	$-0.798664\pi$
$331$	−0.486928	+	0.634576i	−0.0267640	+	0.0348795i	0.779780	+	0.626054i	$0.215331\pi$
$332$	13.8542	−	12.7370i	0.760350	−	0.699035i
$333$	9.74904	−	7.48070i	0.534244	−	0.409940i
$334$	6.25738	+	1.38183i	0.342389	+	0.0756105i
$335$			40.3837i			2.20640i
$336$	−19.7529	−	15.4034i	−1.07761	−	0.840327i
$337$			31.5554i			1.71893i	0.511193	+	0.859466i	$0.329204\pi$
$337$			31.5554i			1.71893i	−0.511193	+	0.859466i	$0.670796\pi$
$338$	−2.75481	+	12.4746i	−0.149842	+	0.678531i
$339$	0.773116	−	0.593232i	0.0419899	−	0.0322200i
$340$	−55.0867	−	2.31441i	−2.98750	−	0.125516i
$341$	−15.5574	+	20.2748i	−0.842480	+	1.09794i
$342$	2.69894	+	5.77549i	0.145942	+	0.312303i
$343$	18.0388	−	4.19536i	0.974005	−	0.226528i
$344$	−7.61935	−	13.1223i	−0.410808	−	0.707505i
$345$	−36.9510	−	9.90100i	−1.98938	−	0.533052i
$346$	−16.7910	+	14.1128i	−0.902687	+	0.758710i
$347$	−4.20229	+	31.9196i	−0.225591	+	1.71353i	0.386117	+	0.922450i	$0.373816\pi$
$347$	−4.20229	+	31.9196i	−0.225591	+	1.71353i	−0.611708	+	0.791084i	$0.709517\pi$
$348$	0.201372	−	1.15312i	0.0107947	−	0.0618139i
$349$	12.9498	−	31.2635i	0.693185	−	1.67350i	−0.0450790	−	0.998983i	$-0.514354\pi$
$349$	12.9498	−	31.2635i	0.693185	−	1.67350i	0.738264	−	0.674512i	$-0.235646\pi$
$350$	9.90427	+	24.6236i	0.529406	+	1.31618i
$351$	−1.87536			−0.100099
$352$	−6.41012	+	13.8954i	−0.341660	+	0.740625i
$353$	16.4146	−	28.4310i	0.873664	−	1.51323i	0.0154841	−	0.999880i	$-0.495071\pi$
$353$	16.4146	−	28.4310i	0.873664	−	1.51323i	0.858180	−	0.513350i	$-0.171596\pi$
$354$	4.26750	+	2.21706i	0.226815	+	0.117836i
$355$	4.01341	−	0.528376i	0.213010	−	0.0280433i
$356$	−9.22862	+	11.0350i	−0.489116	+	0.584856i
$357$	−47.1764	−	15.4522i	−2.49684	−	0.817817i
$358$	−11.1091	−	4.03306i	−0.587136	−	0.213154i
$359$	−29.7349	−	7.96745i	−1.56935	−	0.420506i	−0.633741	−	0.773546i	$-0.718481\pi$
$359$	−29.7349	−	7.96745i	−1.56935	−	0.420506i	−0.935608	+	0.353040i	$0.885148\pi$
$360$	18.0536	−	18.1429i	0.951510	−	0.956215i
$361$	15.4539	−	4.14086i	0.813363	−	0.217940i
$362$	−13.1600	+	18.8273i	−0.691674	+	0.989543i
$363$	3.33520	+	8.05187i	0.175052	+	0.422614i
$364$	−3.07391	−	10.0804i	−0.161116	−	0.528358i
$365$	−46.0668	−	19.0815i	−2.41125	−	0.998770i
$366$	4.01694	−	18.1900i	0.209969	−	0.950807i
$367$	4.58516	+	2.64724i	0.239343	+	0.138185i	0.614875	−	0.788625i	$-0.289207\pi$
$367$	4.58516	+	2.64724i	0.239343	+	0.138185i	−0.375532	+	0.926810i	$0.622540\pi$
$368$	16.8228	−	7.91206i	0.876950	−	0.412444i
$369$	−2.62444	+	1.51522i	−0.136623	+	0.0788791i
$370$	15.6762	−	17.1358i	0.814967	−	0.890850i
$371$	10.9776	−	16.8167i	0.569928	−	0.873077i
$372$	−13.3776	+	42.6727i	−0.693595	+	2.21248i
$373$	7.79880	−	10.1636i	0.403807	−	0.526251i	−0.546545	−	0.837430i	$-0.684057\pi$
$373$	7.79880	−	10.1636i	0.403807	−	0.526251i	0.950351	+	0.311179i	$0.100724\pi$
$374$	−2.61836	+	30.2140i	−0.135392	+	1.56233i
$375$	−16.6430	+	4.45948i	−0.859442	+	0.230287i
$376$	2.18475	−	1.68499i	0.112670	−	0.0868968i
$377$	0.348244	−	0.348244i	0.0179355	−	0.0179355i
$378$	−3.06915	+	1.73018i	−0.157860	+	0.0889907i
$379$	−5.09850	+	2.11187i	−0.261892	+	0.108479i	−0.509766	−	0.860313i	$-0.670268\pi$
$379$	−5.09850	+	2.11187i	−0.261892	+	0.108479i	0.247874	+	0.968792i	$0.420268\pi$
$380$	6.92695	+	9.85817i	0.355345	+	0.505713i
$381$	16.2291	+	21.1502i	0.831442	+	1.08356i
$382$	−10.2649	+	19.7583i	−0.525197	+	1.01092i
$383$	3.57816	+	6.19756i	0.182836	+	0.316681i	0.942845	−	0.333231i	$-0.108139\pi$
$383$	3.57816	+	6.19756i	0.182836	+	0.316681i	−0.760009	+	0.649912i	$0.774806\pi$
$384$	−2.18035	+	26.6894i	−0.111265	+	1.36199i
$385$	23.4813	−	8.25262i	1.19672	−	0.420592i
$386$	−20.2376	+	0.900259i	−1.03007	+	0.0458220i
$387$	13.8407	−	1.82216i	0.703561	−	0.0926256i
$388$	7.58439	−	16.3348i	0.385039	−	0.829275i
$389$	0.357906	−	2.71857i	0.0181466	−	0.137837i	−0.979973	−	0.199129i	$-0.936189\pi$
$389$	0.357906	−	2.71857i	0.0181466	−	0.137837i	0.998120	+	0.0612920i	$0.0195221\pi$
$390$	22.8277	−	4.04449i	1.15593	−	0.204801i
$391$	26.0522	−	26.0522i	1.31751	−	1.31751i
$392$	−14.3307	−	13.6613i	−0.723808	−	0.690001i
$393$	24.8680	+	24.8680i	1.25443	+	1.25443i
$394$	−10.8293	−	7.56948i	−0.545571	−	0.381345i
$395$	1.50346	+	0.197934i	0.0756471	+	0.00995913i
$396$	−9.52835	−	10.3641i	−0.478818	−	0.520816i
$397$	0.537590	+	4.08340i	0.0269809	+	0.204940i	0.999626	−	0.0273571i	$-0.00870912\pi$
$397$	0.537590	+	4.08340i	0.0269809	+	0.204940i	−0.972645	+	0.232297i	$0.925376\pi$
$398$	9.01450	−	9.85385i	0.451856	−	0.493929i
$399$	3.59696	+	10.2345i	0.180073	+	0.512365i
$400$	16.1978	−	23.2954i	0.809888	−	1.16477i
$401$	30.4012	−	17.5522i	1.51817	−	0.876513i	0.518394	−	0.855142i	$-0.326530\pi$
$401$	30.4012	−	17.5522i	1.51817	−	0.876513i	0.999772	−	0.0213718i	$-0.00680336\pi$
$402$	37.0624	−	11.7192i	1.84850	−	0.584502i
$403$	−14.9270	+	11.4539i	−0.743567	+	0.570559i
$404$	14.8239	+	9.40963i	0.737516	+	0.468146i
$405$	−13.3549	−	32.2415i	−0.663609	−	1.60209i
$406$	0.248639	−	0.891206i	0.0123397	−	0.0442298i
$407$	−9.03308	−	9.03308i	−0.447753	−	0.447753i
$408$	13.8619	+	51.2277i	0.686267	+	2.53615i
$409$	2.50492	+	9.34849i	0.123860	+	0.462253i	0.999796	−	0.0201740i	$-0.00642203\pi$
$409$	2.50492	+	9.34849i	0.123860	+	0.462253i	−0.875936	+	0.482427i	$0.839755\pi$
$410$	−4.38442	+	3.68511i	−0.216531	+	0.181995i
$411$	12.2244	+	9.38009i	0.602984	+	0.462686i
$412$	−22.3021	+	26.6676i	−1.09875	+	1.31382i
$413$	3.18300	+	2.07780i	0.156625	+	0.102242i
$414$	0.760085	+	17.0865i	0.0373561	+	0.839755i
$415$	16.3614	+	28.3387i	0.803148	+	1.39109i
$416$	−7.20633	+	8.66020i	−0.353319	+	0.424601i
$417$	0.0102584	−	0.0177681i	0.000502356	−	0.000870107i
$418$	5.58647	−	3.56543i	0.273243	−	0.174391i
$419$	−3.83604	+	9.26102i	−0.187403	+	0.452430i	−0.989458	−	0.144819i	$-0.953740\pi$
$419$	−3.83604	+	9.26102i	−0.187403	+	0.452430i	0.802055	+	0.597250i	$0.203740\pi$
$420$	33.6276	−	27.6795i	1.64086	−	1.35062i
$421$	21.6933	−	8.98568i	1.05727	−	0.437935i	0.214788	−	0.976661i	$-0.431094\pi$
$421$	21.6933	−	8.98568i	1.05727	−	0.437935i	0.842481	+	0.538726i	$0.181094\pi$
$422$	−2.87406	−	16.2216i	−0.139907	−	0.789655i
$423$	0.656969	+	2.45184i	0.0319429	+	0.119213i
$424$	−21.4690	+	0.0529434i	−1.04263	+	0.00257116i
$425$	14.5537	−	54.3151i	0.705958	−	2.63467i
$426$	−1.64960	−	3.53000i	−0.0799234	−	0.171029i
$427$	4.58316	−	13.9926i	0.221794	−	0.677150i
$428$	−1.70948	−	3.27074i	−0.0826309	−	0.158097i
$429$	−1.66446	−	12.6429i	−0.0803611	−	0.610403i
$430$	25.1564	−	7.95452i	1.21315	−	0.383601i
$431$	−21.6047	−	12.4735i	−1.04066	−	0.600827i	−0.120642	−	0.992696i	$-0.538495\pi$
$431$	−21.6047	−	12.4735i	−1.04066	−	0.600827i	−0.920021	+	0.391869i	$0.871829\pi$
$432$	3.34662	+	1.72818i	0.161015	+	0.0831471i
$433$		−	27.3257i		−	1.31319i	−0.754243	−	0.656596i	$-0.771996\pi$
$433$		−	27.3257i		−	1.31319i	0.754243	−	0.656596i	$-0.228004\pi$
$434$	−13.8618	+	32.5164i	−0.665389	+	1.56084i
$435$	1.88043	+	0.778899i	0.0901597	+	0.0373454i
$436$	−3.64068	−	16.2952i	−0.174357	−	0.780400i
$437$	−7.98234	−	1.05089i	−0.381847	−	0.0502711i
$438$	−4.14370	+	47.8154i	−0.197994	+	2.28471i
$439$	0.645658	−	2.40963i	0.0308156	−	0.115005i	−0.948805	−	0.315863i	$-0.897706\pi$
$439$	0.645658	−	2.40963i	0.0308156	−	0.115005i	0.979621	+	0.200857i	$0.0643728\pi$
$440$	−21.1493	−	16.1457i	−1.00825	−	0.769716i
$441$	16.6753	−	7.32985i	0.794062	−	0.349040i
$442$	−7.61937	+	20.9877i	−0.362416	+	0.998283i
$443$	−16.3557	−	12.5501i	−0.777081	−	0.596275i	0.142218	−	0.989835i	$-0.454577\pi$
$443$	−16.3557	−	12.5501i	−0.777081	−	0.596275i	−0.919299	+	0.393560i	$0.871243\pi$
$444$	−20.2757	−	9.41416i	−0.962242	−	0.446776i
$445$	−15.2269	−	19.8441i	−0.721825	−	0.940700i
$446$	15.9422	+	24.9788i	0.754883	+	1.18278i
$447$	32.6297			1.54333
$448$	−3.80385	+	20.8214i	−0.179715	+	0.983719i
$449$	−16.6657			−0.786502			−0.393251	−	0.919431i	$-0.628650\pi$
$449$	−16.6657			−0.786502			−0.393251	+	0.919431i	$0.628650\pi$
$450$	14.0435	+	22.0040i	0.662019	+	1.03728i
$451$	1.91782	+	2.49935i	0.0903067	+	0.117690i
$452$	−0.746857	−	0.346772i	−0.0351292	−	0.0163108i
$453$	−7.91117	−	6.07045i	−0.371699	−	0.285215i
$454$	0.238085	−	0.655810i	0.0111739	−	0.0307787i
$455$	18.2713	−	1.39443i	0.856570	−	0.0653719i
$456$	7.03721	−	9.21805i	0.329548	−	0.431675i
$457$	−1.00153	+	3.73775i	−0.0468494	+	0.174844i	−0.985386	−	0.170335i	$-0.945515\pi$
$457$	−1.00153	+	3.73775i	−0.0468494	+	0.174844i	0.938537	+	0.345179i	$0.112182\pi$
$458$	2.00792	−	23.1700i	0.0938239	−	1.08266i
$459$	7.40071	+	0.974321i	0.345435	+	0.0454774i
$460$	7.04822	+	31.5470i	0.328625	+	1.47088i
$461$	14.0710	+	5.82839i	0.655351	+	0.271455i	0.685481	−	0.728091i	$-0.259592\pi$
$461$	14.0710	+	5.82839i	0.655351	+	0.271455i	−0.0301296	+	0.999546i	$0.509592\pi$
$462$	−14.3881	−	19.1552i	−0.669395	−	0.891182i
$463$		−	25.2657i		−	1.17420i	−0.809515	−	0.587099i	$-0.800270\pi$
$463$		−	25.2657i		−	1.17420i	0.809515	−	0.587099i	$-0.199730\pi$
$464$	−0.942361	+	0.300535i	−0.0437480	+	0.0139520i
$465$	−67.3411	−	38.8794i	−3.12287	−	1.80299i
$466$	16.1393	−	5.10328i	0.747637	−	0.236405i
$467$	1.49931	+	11.3884i	0.0693797	+	0.526991i	0.990479	+	0.137663i	$0.0439592\pi$
$467$	1.49931	+	11.3884i	0.0693797	+	0.526991i	−0.921099	+	0.389327i	$0.872707\pi$
$468$	−4.80117	−	9.18606i	−0.221934	−	0.424626i
$469$	30.0680	−	6.31673i	1.38841	−	0.291679i
$470$	2.03102	+	4.34621i	0.0936840	+	0.200476i
$471$	9.45894	−	35.3012i	0.435845	−	1.62659i
$472$	−0.0100209	−	4.06359i	−0.000461251	−	0.187042i
$473$	−3.75613	−	14.0181i	−0.172707	−	0.644552i
$474$	−0.254643	−	1.43724i	−0.0116962	−	0.0660148i
$475$	−11.3526	+	4.70240i	−0.520893	+	0.215761i
$476$	6.89332	+	41.3772i	0.315955	+	1.89652i
$477$	7.55865	−	18.2482i	0.346087	−	0.835527i
$478$	−25.2606	+	16.1220i	−1.15540	+	0.737404i
$479$	1.40022	−	2.42526i	0.0639778	−	0.110813i	−0.832262	−	0.554382i	$-0.812955\pi$
$479$	1.40022	−	2.42526i	0.0639778	−	0.110813i	0.896240	+	0.443569i	$0.146288\pi$
$480$	−44.4636	−	13.8187i	−2.02947	−	0.630732i
$481$	−4.70259	−	8.14513i	−0.214420	−	0.371386i
$482$	0.192221	+	4.32108i	0.00875544	+	0.196820i
$483$	−1.59206	+	29.0608i	−0.0724414	+	1.32231i
$484$	4.72442	−	5.64918i	0.214746	−	0.256781i
$485$	24.8437	+	19.0632i	1.12809	+	0.865617i
$486$	−22.6561	+	19.0425i	−1.02770	+	0.863783i
$487$	−3.28151	−	12.2468i	−0.148699	−	0.554953i	−0.999563	−	0.0295666i	$-0.990587\pi$
$487$	−3.28151	−	12.2468i	−0.148699	−	0.554953i	0.850863	−	0.525387i	$-0.176079\pi$
$488$	−15.1943	+	4.11148i	−0.687812	+	0.186118i
$489$	−9.82284	−	9.82284i	−0.444204	−	0.444204i
$490$	28.6156	−	19.1388i	1.29272	−	0.864604i
$491$	15.7884	+	38.1167i	0.712523	+	1.72018i	0.693599	+	0.720361i	$0.256024\pi$
$491$	15.7884	+	38.1167i	0.712523	+	1.72018i	0.0189236	+	0.999821i	$0.493976\pi$
$492$	4.65437	+	2.95442i	0.209835	+	0.133195i
$493$	−1.55519	+	1.19334i	−0.0700423	+	0.0537454i
$494$	4.65221	−	1.47104i	0.209313	−	0.0661852i
$495$	21.1997	−	12.2397i	0.952857	−	0.550132i
$496$	37.1925	−	6.68421i	1.66999	−	0.300130i
$497$	−1.02118	−	2.90557i	−0.0458060	−	0.130333i
$498$	21.2600	−	23.2396i	0.952684	−	1.04139i
$499$	−1.58992	−	12.0767i	−0.0711748	−	0.540626i	−0.989471	−	0.144732i	$-0.953768\pi$
$499$	−1.58992	−	12.0767i	−0.0711748	−	0.540626i	0.918296	−	0.395894i	$-0.129565\pi$
$500$	9.85375	+	10.7181i	0.440673	+	0.479326i
$501$	10.6332	+	1.39989i	0.475056	+	0.0625423i
$502$	2.31967	+	1.62141i	0.103532	+	0.0723672i
$503$	18.3719	+	18.3719i	0.819162	+	0.819162i	0.985987	−	0.166824i	$-0.0533513\pi$
$503$	18.3719	+	18.3719i	0.819162	+	0.819162i	−0.166824	+	0.985987i	$0.553351\pi$
$504$	−16.3323	−	10.6041i	−0.727500	−	0.472344i
$505$	−21.5877	+	21.5877i	−0.960641	+	0.960641i
$506$	17.5076	−	3.10190i	0.778308	−	0.137896i
$507$	−2.79080	+	21.1982i	−0.123944	+	0.941446i
$508$	9.48665	−	20.4318i	0.420902	−	0.906516i
$509$	−20.5602	+	2.70680i	−0.911314	+	0.119977i	−0.571582	−	0.820545i	$-0.693670\pi$
$509$	−20.5602	+	2.70680i	−0.911314	+	0.119977i	−0.339733	+	0.940522i	$0.610337\pi$
$510$	−92.1857	+	4.10084i	−4.08205	+	0.181588i
$511$	−7.00159	+	37.2840i	−0.309732	+	1.64935i
$512$	20.8404	−	8.81356i	0.921023	−	0.389508i
$513$	−0.815600	−	1.41266i	−0.0360096	−	0.0623705i
$514$	−5.37917	+	10.3541i	−0.237265	+	0.456698i
$515$	−36.7977	−	47.9558i	−1.62150	−	2.11318i
$516$	−14.6006	−	20.7790i	−0.642755	−	0.914745i
$517$	2.43792	−	1.00982i	0.107220	−	0.0444119i
$518$	−15.2106	−	8.99148i	−0.668317	−	0.395063i
$519$	−25.9579	+	25.9579i	−1.13942	+	1.13942i
$520$	−11.9637	−	15.5120i	−0.524642	−	0.680247i
$521$	−11.2859	+	3.02404i	−0.494444	+	0.132486i	−0.497420	−	0.867510i	$-0.665719\pi$
$521$	−11.2859	+	3.02404i	−0.494444	+	0.132486i	0.00297645	+	0.999996i	$0.499053\pi$
$522$	0.0785664	−	0.906601i	0.00343876	−	0.0396809i
$523$	−7.43424	+	9.68849i	−0.325077	+	0.423648i	−0.927091	−	0.374838i	$-0.877698\pi$
$523$	−7.43424	+	9.68849i	−0.325077	+	0.423648i	0.602014	+	0.798486i	$0.294365\pi$
$524$	8.88954	−	28.3565i	0.388341	−	1.23876i
$525$	20.0724	+	39.6261i	0.876030	+	1.72942i
$526$	−8.63815	+	9.44246i	−0.376641	+	0.411711i
$527$	64.8569	−	37.4451i	2.82521	−	1.63114i
$528$	−8.68035	+	24.0953i	−0.377764	+	1.04861i
$529$	1.21200	+	0.699749i	0.0526957	+	0.0304239i
$530$	8.04971	−	36.4517i	0.349657	−	1.58336i
$531$	3.45396	+	1.43068i	0.149889	+	0.0620860i
$532$	6.25647	−	6.69950i	0.271252	−	0.290460i
$533$	0.887600	+	2.14286i	0.0384462	+	0.0928174i
$534$	−13.7932	+	19.7333i	−0.596891	+	0.853942i
$535$	6.19836	−	1.66085i	0.267978	−	0.0718046i
$536$	−23.2826	−	23.1681i	−1.00566	−	1.00071i
$537$	−19.1061	−	5.11946i	−0.824489	−	0.220921i
$538$	−7.42479	−	2.69549i	−0.320105	−	0.116211i
$539$	−9.81744	−	16.1923i	−0.422867	−	0.697453i
$540$	−4.20142	+	5.02380i	−0.180800	+	0.216190i
$541$	−13.8708	+	1.82612i	−0.596351	+	0.0785111i	−0.422659	−	0.906289i	$-0.638903\pi$
$541$	−13.8708	+	1.82612i	−0.596351	+	0.0785111i	−0.173692	+	0.984800i	$0.555570\pi$
$542$	−7.79336	−	4.04883i	−0.334753	−	0.173912i
$543$	−19.2224	+	33.2942i	−0.824913	+	1.42879i
$544$	32.9375	−	30.4316i	1.41218	−	1.30474i
$545$	29.0323			1.24361
$546$	−6.58201	−	16.3639i	−0.281684	−	0.700310i
$547$	−9.20321	+	22.2185i	−0.393501	+	0.949995i	0.595670	+	0.803229i	$0.296886\pi$
$547$	−9.20321	+	22.2185i	−0.393501	+	0.949995i	−0.989171	+	0.146766i	$0.953114\pi$
$548$	2.23982	−	12.8259i	0.0956804	−	0.547896i
$549$	1.89022	−	14.3576i	0.0806726	−	0.612769i
$550$	20.7735	−	17.4602i	0.885787	−	0.744505i
$551$	0.413775	+	0.110871i	0.0176274	+	0.00472325i
$552$	26.9070	−	15.6234i	1.14524	−	0.664975i
$553$	−0.0877941	−	1.15037i	−0.00373339	−	0.0489187i
$554$	2.99359	+	6.40601i	0.127185	+	0.272165i
$555$	23.6623	−	30.8374i	1.00441	−	1.30897i
$556$	−0.0173212		0.000727733i	−0.000734584		3.08627e-5i
$557$	−12.4764	+	9.57349i	−0.528643	+	0.405642i	−0.838302	−	0.545206i	$-0.816452\pi$
$557$	−12.4764	+	9.57349i	−0.528643	+	0.405642i	0.309659	+	0.950848i	$0.399785\pi$
$558$	−7.49674	+	33.9476i	−0.317362	+	1.43712i
$559$		−	10.6847i		−	0.451913i
$560$	−33.8904	−	14.3489i	−1.43213	−	0.606352i
$561$			50.7570i			2.14296i
$562$	−24.9489	−	5.50953i	−1.05241	−	0.232405i
$563$	−14.0673	+	10.7942i	−0.592866	+	0.454922i	−0.861103	−	0.508431i	$-0.830226\pi$
$563$	−14.0673	+	10.7942i	−0.592866	+	0.454922i	0.268237	+	0.963353i	$0.413559\pi$
$564$	3.39936	−	3.12524i	0.143139	−	0.131596i
$565$	0.871605	−	1.13590i	0.0366687	−	0.0477876i
$566$	26.0582	−	12.1772i	1.09531	−	0.511847i
$567$	−21.9167	+	14.9866i	−0.920415	+	0.629378i
$568$	−1.99786	+	2.61700i	−0.0838284	+	0.109807i
$569$	18.4201	+	4.93565i	0.772211	+	0.206913i	0.623348	−	0.781944i	$-0.285772\pi$
$569$	18.4201	+	4.93565i	0.772211	+	0.206913i	0.148863	+	0.988858i	$0.452439\pi$
$570$	12.9744	+	15.4365i	0.543439	+	0.646565i
$571$	5.35143	−	40.6481i	0.223950	−	1.70107i	−0.397488	−	0.917607i	$-0.630118\pi$
$571$	5.35143	−	40.6481i	0.223950	−	1.70107i	0.621438	−	0.783463i	$-0.286549\pi$
$572$	−8.81643	+	6.19495i	−0.368633	+	0.259024i
$573$	−14.2606	+	34.4281i	−0.595744	+	1.43825i
$574$	3.42958	+	2.68803i	0.143148	+	0.112196i
$575$	−32.9672			−1.37483
$576$	0.102672	+	20.8171i	0.00427800	+	0.867379i
$577$	−15.8000	+	27.3664i	−0.657764	+	1.13928i	0.323430	+	0.946252i	$0.395164\pi$
$577$	−15.8000	+	27.3664i	−0.657764	+	1.13928i	−0.981193	+	0.193028i	$0.938169\pi$
$578$	29.8884	−	57.5305i	1.24319	−	2.39295i
$579$	−33.6139	+	4.42536i	−1.39695	+	0.183912i
$580$	−0.152712	−	1.71307i	−0.00634104	−	0.0711313i
$581$	18.5406	−	16.6147i	0.769194	−	0.689292i
$582$	10.2858	−	28.3325i	0.426361	−	1.17442i
$583$	−19.8337	−	5.31443i	−0.821428	−	0.220101i
$584$	37.4296	−	15.6121i	1.54885	−	0.646033i
$585$	17.4084	−	4.66458i	0.719750	−	0.192856i
$586$	30.0977	+	21.0378i	1.24332	+	0.869063i
$587$	8.61161	+	20.7903i	0.355439	+	0.858106i	0.995929	+	0.0901398i	$0.0287314\pi$
$587$	8.61161	+	20.7903i	0.355439	+	0.858106i	−0.640490	+	0.767967i	$0.721269\pi$
$588$	−25.8689	−	20.7081i	−1.06682	−	0.853987i
$589$	−15.1197	−	6.26279i	−0.622997	−	0.258054i
$590$	6.89945	+	1.52362i	0.284046	+	0.0627265i
$591$	−19.1504	−	11.0565i	−0.787743	−	0.454804i
$592$	0.885993	+	18.8687i	0.0364141	+	0.775498i
$593$	10.5063	−	6.06579i	0.431440	−	0.249092i	−0.268520	−	0.963274i	$-0.586534\pi$
$593$	10.5063	−	6.06579i	0.431440	−	0.249092i	0.699960	+	0.714182i	$0.253201\pi$
$594$	2.65792	+	2.43152i	0.109056	+	0.0997664i
$595$	−72.8279	−	3.98979i	−2.98565	−	0.163566i
$596$	−12.7714	−	24.4355i	−0.523138	−	1.00092i
$597$	13.6069	−	17.7328i	0.556892	−	0.725756i
$598$	13.0416	+	1.13019i	0.533309	+	0.0462168i
$599$	19.3969	−	5.19739i	0.792537	−	0.212360i	0.160232	−	0.987079i	$-0.448776\pi$
$599$	19.3969	−	5.19739i	0.792537	−	0.212360i	0.632305	+	0.774720i	$0.282109\pi$
$600$	23.6419	−	41.1832i	0.965178	−	1.68130i
$601$	−26.4614	+	26.4614i	−1.07938	+	1.07938i	−0.0828178	+	0.996565i	$0.526392\pi$
$601$	−26.4614	+	26.4614i	−1.07938	+	1.07938i	−0.996565	+	0.0828178i	$0.973608\pi$
$602$	−9.85749	−	17.4861i	−0.401761	−	0.712681i
$603$	27.9180	−	11.5640i	1.13691	−	0.470923i
$604$	−1.44953	+	8.30047i	−0.0589806	+	0.337741i
$605$	7.79514	+	10.1588i	0.316917	+	0.413015i
$606$	26.0769	+	13.5476i	1.05930	+	0.550332i
$607$	8.97752	+	15.5495i	0.364386	+	0.631136i	0.988677	−	0.150056i	$-0.0479454\pi$
$607$	8.97752	+	15.5495i	0.364386	+	0.631136i	−0.624291	+	0.781192i	$0.714612\pi$
$608$	−9.65755	−	1.66199i	−0.391665	−	0.0674026i
$609$	0.285803	−	1.52192i	0.0115813	−	0.0616713i
$610$	−1.21632	−	27.3425i	−0.0492473	−	1.10706i
$611$	1.92615	−	0.253582i	0.0779236	−	0.0102588i
$612$	14.1743	+	38.7452i	0.572961	+	1.56618i
$613$	−0.963901	+	7.32155i	−0.0389316	+	0.295715i	0.960892	+	0.276924i	$0.0893150\pi$
$613$	−0.963901	+	7.32155i	−0.0389316	+	0.295715i	−0.999823	+	0.0187908i	$0.994018\pi$
$614$	0.406640	+	2.29514i	0.0164107	+	0.0926242i
$615$	−6.77807	+	6.77807i	−0.273318	+	0.273318i
$616$	−8.71328	+	18.2723i	−0.351068	+	0.736212i
$617$	−8.61926	−	8.61926i	−0.346999	−	0.346999i	0.511992	−	0.858990i	$-0.328908\pi$
$617$	−8.61926	−	8.61926i	−0.346999	−	0.346999i	−0.858990	+	0.511992i	$0.828908\pi$
$618$	−33.3331	+	47.6879i	−1.34085	+	1.91829i
$619$	−39.9239	−	5.25608i	−1.60468	−	0.211260i	−0.725661	−	0.688053i	$-0.758466\pi$
$619$	−39.9239	−	5.25608i	−1.60468	−	0.211260i	−0.879016	+	0.476793i	$0.841799\pi$
$620$	−2.75811	+	65.6475i	−0.110768	+	2.63647i
$621$	−0.571225	−	4.33889i	−0.0229225	−	0.174113i
$622$	24.2327	+	22.1686i	0.971644	+	0.888879i
$623$	−12.3933	+	14.4413i	−0.496527	+	0.578577i
$624$	−10.7644	+	15.4813i	−0.430922	+	0.619747i
$625$	8.79131	−	5.07567i	0.351652	−	0.203027i
$626$	−6.65336	−	21.0414i	−0.265922	−	0.840985i
$627$	8.79965	−	6.75221i	0.351424	−	0.269657i
$628$	−30.1384	+	6.73353i	−1.20265	+	0.268697i
$629$	14.3260	+	34.5861i	0.571217	+	1.37904i
$630$	24.1865	−	23.6946i	0.963615	−	0.944015i
$631$	2.16966	+	2.16966i	0.0863726	+	0.0863726i	0.748973	−	0.662600i	$-0.230547\pi$
$631$	2.16966	+	2.16966i	0.0863726	+	0.0863726i	−0.662600	+	0.748973i	$0.730547\pi$
$632$	−0.976646	+	0.753240i	−0.0388489	+	0.0299623i
$633$	−7.13616	−	26.6325i	−0.283637	−	1.05855i
$634$	−6.67624	−	7.94316i	−0.265147	−	0.315463i
$635$	31.0748	+	23.8446i	1.23317	+	0.946242i
$636$	−35.7897	+	3.19049i	−1.41915	+	0.126511i
$637$	−3.89618	−	13.3859i	−0.154372	−	0.530368i
$638$	−0.945078	+	0.0420414i	−0.0374160	+	0.00166443i
$639$	−1.51453	−	2.62324i	−0.0599139	−	0.103774i
$640$	7.05484	+	38.7063i	0.278867	+	1.53000i
$641$	−1.28091	+	2.21860i	−0.0505930	+	0.0876296i	−0.890213	−	0.455545i	$-0.849444\pi$
$641$	−1.28091	+	2.21860i	−0.0505930	+	0.0876296i	0.839620	+	0.543174i	$0.182778\pi$
$642$	−3.32299	−	5.20660i	−0.131148	−	0.205488i
$643$	1.92686	−	4.65185i	0.0759880	−	0.183451i	−0.881321	−	0.472518i	$-0.843345\pi$
$643$	1.92686	−	4.65185i	0.0759880	−	0.183451i	0.957309	+	0.289067i	$0.0933451\pi$
$644$	22.3860	−	10.1823i	0.882133	−	0.401239i
$645$	40.7962	−	16.8983i	1.60635	−	0.665371i
$646$	−19.1232	+	3.38814i	−0.752391	+	0.133305i
$647$	−5.66762	−	21.1519i	−0.222817	−	0.831565i	−0.983267	−	0.182169i	$-0.941688\pi$
$647$	−5.66762	−	21.1519i	−0.222817	−	0.831565i	0.760450	−	0.649396i	$-0.224978\pi$
$648$	26.2500	+	10.7973i	1.03120	+	0.424160i
$649$	1.00590	−	3.75406i	0.0394849	−	0.147360i
$650$	18.1001	−	8.45835i	0.709946	−	0.331764i
$651$	−18.4146	+	56.2207i	−0.721725	+	2.20346i
$652$	−3.51136	+	11.2008i	−0.137515	+	0.438656i
$653$	4.72054	+	35.8560i	0.184729	+	1.40316i	0.792901	+	0.609350i	$0.208570\pi$
$653$	4.72054	+	35.8560i	0.184729	+	1.40316i	−0.608172	+	0.793805i	$0.708097\pi$
$654$	−8.42507	−	26.6445i	−0.329446	−	1.04188i
$655$	44.7488	+	25.8358i	1.74848	+	1.00949i
$656$	0.390739	−	4.64191i	0.0152558	−	0.181236i
$657$			37.3108i			1.45563i
$658$	2.91831	−	2.19203i	0.113768	−	0.0854544i
$659$	15.1726	+	6.28471i	0.591041	+	0.244817i	0.658099	−	0.752932i	$-0.271361\pi$
$659$	15.1726	+	6.28471i	0.591041	+	0.244817i	−0.0670571	+	0.997749i	$0.521361\pi$
$660$	−37.5972	−	23.8652i	−1.46347	−	0.928954i
$661$	31.5018	+	4.14729i	1.22528	+	0.161311i	0.715263	−	0.698855i	$-0.246307\pi$
$661$	31.5018	+	4.14729i	1.22528	+	0.161311i	0.510014	+	0.860166i	$0.329640\pi$
$662$	1.12696	+	0.0976626i	0.0438005	+	0.00379577i
$663$	−9.67183	+	36.0958i	−0.375623	+	1.40184i
$664$	−25.7248	−	6.82498i	−0.998314	−	0.264861i
$665$	8.99661	+	13.1568i	0.348873	+	0.510199i
$666$	−16.3352	−	5.93034i	−0.632978	−	0.229796i
$667$	0.911778	+	0.699632i	0.0353042	+	0.0270899i
$668$	−3.11355	−	8.51084i	−0.120467	−	0.329294i
$669$	30.1912	+	39.3460i	1.16726	+	1.52120i
$670$	48.1419	−	30.7254i	1.85988	−	1.18703i
$671$	−15.0546			−0.581178
$672$	−3.33389	+	35.2671i	−0.128607	+	1.36046i
$673$	33.1865			1.27924			0.639622	−	0.768689i	$-0.279091\pi$
$673$	33.1865			1.27924			0.639622	+	0.768689i	$0.279091\pi$
$674$	37.6175	−	24.0085i	1.44897	−	0.924773i
$675$	−4.06607	−	5.29901i	−0.156503	−	0.203959i
$676$	16.9671	−	6.20713i	0.652581	−	0.238736i
$677$	−34.1214	−	26.1823i	−1.31139	−	1.00627i	−0.998402	−	0.0565108i	$-0.982002\pi$
$677$	−34.1214	−	26.1823i	−1.31139	−	1.00627i	−0.312991	−	0.949756i	$-0.601331\pi$
$678$	−1.29541	−	0.470286i	−0.0497501	−	0.0180612i
$679$	10.3077	−	21.4794i	0.395572	−	0.824303i
$680$	39.1529	+	67.4303i	1.50145	+	2.58583i
$681$	0.302219	−	1.12790i	0.0115811	−	0.0432211i
$682$	36.0064	+	3.12033i	1.37876	+	0.119484i
$683$	19.5305	+	2.57124i	0.747314	+	0.0983857i	0.494558	−	0.869144i	$-0.335330\pi$
$683$	19.5305	+	2.57124i	0.747314	+	0.0983857i	0.252755	+	0.967530i	$0.418663\pi$
$684$	4.83157	−	7.61164i	0.184740	−	0.291038i
$685$	20.9156	+	8.66352i	0.799144	+	0.331016i
$686$	−18.7259	−	18.3123i	−0.714959	−	0.699166i
$687$		−	38.9236i		−	1.48503i
$688$	−9.84611	+	19.0670i	−0.375380	+	0.726923i
$689$	−13.0920	−	7.55869i	−0.498767	−	0.287963i
$690$	16.3106	+	51.5828i	0.620935	+	1.96372i
$691$	−4.88106	−	37.0753i	−0.185684	−	1.41041i	−0.789727	−	0.613459i	$-0.789778\pi$
$691$	−4.88106	−	37.0753i	−0.185684	−	1.41041i	0.604043	−	0.796952i	$-0.293556\pi$
$692$	29.5992	+	9.27912i	1.12519	+	0.352739i
$693$	−12.4291	−	13.8699i	−0.472144	−	0.526874i
$694$	41.2489	−	19.2760i	1.56579	−	0.731707i
$695$	0.00780191	−	0.0291171i	0.000295943	−	0.00110448i
$696$	−1.52786	+	0.637279i	−0.0579134	+	0.0241560i
$697$	−2.38942	−	8.91745i	−0.0905059	−	0.337772i
$698$	−47.1222	+	8.34886i	−1.78360	+	0.316009i
$699$	26.1731	−	10.8413i	0.989958	−	0.410054i
$700$	21.8185	−	30.5415i	0.824661	−	1.15436i
$701$	−2.62484	+	6.33692i	−0.0991388	+	0.239342i	−0.965666	−	0.259788i	$-0.916347\pi$
$701$	−2.62484	+	6.33692i	−0.0991388	+	0.239342i	0.866527	+	0.499131i	$0.166347\pi$
$702$	1.42684	+	2.23564i	0.0538528	+	0.0843788i
$703$	4.09034	−	7.08468i	0.154270	−	0.267204i
$704$	21.4419	−	2.93053i	0.808120	−	0.110449i
$705$	4.01453	+	6.95336i	0.151196	+	0.261879i
$706$	−46.3818	+	2.06327i	−1.74560	+	0.0776523i
$707$	19.4500	+	12.6966i	0.731492	+	0.477504i
$708$	−0.603886	−	6.77416i	−0.0226954	−	0.254588i
$709$	−23.9384	−	18.3686i	−0.899027	−	0.689848i	0.0521017	−	0.998642i	$-0.483408\pi$
$709$	−23.9384	−	18.3686i	−0.899027	−	0.689848i	−0.951129	+	0.308794i	$0.900075\pi$
$710$	−3.68344	−	4.38243i	−0.138237	−	0.164470i
$711$	−0.293684	−	1.09604i	−0.0110140	−	0.0411049i
$712$	20.1765	+	2.60568i	0.756145	+	0.0976519i
$713$	−31.0467	−	31.0467i	−1.16271	−	1.16271i
$714$	17.4728	+	67.9961i	0.653902	+	2.54469i
$715$	−7.16987	−	17.3096i	−0.268138	−	0.647342i
$716$	3.64439	+	16.3118i	0.136197	+	0.609602i
$717$	−39.7899	+	30.5319i	−1.48598	+	1.14023i
$718$	13.1253	+	41.5092i	0.489833	+	1.54911i
$719$	3.28187	−	1.89479i	0.122393	−	0.0706637i	−0.437554	−	0.899192i	$-0.644155\pi$
$719$	3.28187	−	1.89479i	0.122393	−	0.0706637i	0.559947	+	0.828529i	$0.310822\pi$
$720$	−35.3642	−	7.71815i	−1.31795	−	0.287638i
$721$	−29.9500	+	34.8991i	−1.11540	+	1.29971i
$722$	−16.6942	−	15.2722i	−0.621296	−	0.568374i
$723$	0.944893	+	7.17717i	0.0351409	+	0.266922i
$724$	32.4569	+	1.36364i	1.20625	+	0.0506793i
$725$	1.73904	+	0.228949i	0.0645863	+	0.00850294i
$726$	7.06119	−	10.1021i	0.262065	−	0.374923i
$727$	10.0645	+	10.0645i	0.373272	+	0.373272i	0.868668	−	0.495395i	$-0.164977\pi$
$727$	10.0645	+	10.0645i	0.373272	+	0.373272i	−0.495395	+	0.868668i	$0.664977\pi$
$728$	−9.67825	+	11.3340i	−0.358700	+	0.420066i
$729$	−13.7371	+	13.7371i	−0.508781	+	0.508781i
$730$	12.3020	+	69.4346i	0.455319	+	2.56989i
$731$	−5.55108	+	42.1647i	−0.205314	+	1.55952i
$732$	−24.7407	+	9.05098i	−0.914444	+	0.334534i
$733$	−3.00160	+	0.395168i	−0.110866	+	0.0145958i	−0.185755	−	0.982596i	$-0.559473\pi$
$733$	−3.00160	+	0.395168i	−0.110866	+	0.0145958i	0.0748888	+	0.997192i	$0.476140\pi$
$734$	−0.332750	−	7.48013i	−0.0122820	−	0.276097i
$735$	44.9480	−	36.0468i	1.65793	−	1.32961i
$736$	−22.2315	−	14.0349i	−0.819463	−	0.517333i
$737$	−15.7071	−	27.2054i	−0.578577	−	1.00212i
$738$	3.80308	+	1.97578i	0.139993	+	0.0727296i
$739$	5.27338	+	6.87241i	0.193985	+	0.252806i	0.880211	−	0.474582i	$-0.157401\pi$
$739$	5.27338	+	6.87241i	0.193985	+	0.252806i	−0.686227	+	0.727388i	$0.740734\pi$
$740$	−32.3549	−	5.65020i	−1.18939	−	0.207706i
$741$	7.54450	−	3.12504i	0.277154	−	0.114801i
$742$	−28.3995	−	0.291783i	−1.04258	−	0.0107117i
$743$	−30.6105	+	30.6105i	−1.12299	+	1.12299i	−0.131699	+	0.991290i	$0.542043\pi$
$743$	−30.6105	+	30.6105i	−1.12299	+	1.12299i	−0.991290	+	0.131699i	$0.957957\pi$
$744$	61.0488	−	16.5194i	2.23816	−	0.605632i
$745$	46.3075	−	12.4081i	1.69658	−	0.454596i
$746$	−18.0497	−	1.56420i	−0.660848	−	0.0572694i
$747$	14.9059	−	19.4258i	0.545380	−	0.710753i
$748$	38.0106	−	19.8665i	1.38980	−	0.726393i
$749$	−2.20613	−	4.35525i	−0.0806101	−	0.159137i
$750$	17.9788	+	16.4474i	0.656494	+	0.600574i
$751$	−43.0634	+	24.8627i	−1.57141	+	0.907252i	−0.575410	+	0.817865i	$0.695157\pi$
$751$	−43.0634	+	24.8627i	−1.57141	+	0.907252i	−0.995997	+	0.0893869i	$0.971509\pi$
$752$	−3.67093	−	1.32246i	−0.133865	−	0.0482250i
$753$	4.10210	+	2.36835i	0.149489	+	0.0863074i
$754$	−0.680102	−	0.150188i	−0.0247678	−	0.00546954i
$755$	−13.5358	−	5.60672i	−0.492619	−	0.204049i
$756$	4.39768	+	2.34238i	0.159942	+	0.0851916i
$757$	−2.17686	−	5.25541i	−0.0791193	−	0.191011i	0.879370	−	0.476139i	$-0.157964\pi$
$757$	−2.17686	−	5.25541i	−0.0791193	−	0.191011i	−0.958490	+	0.285128i	$0.907964\pi$
$758$	6.39671	+	4.47119i	0.232339	+	0.162401i
$759$	28.7439	−	7.70189i	1.04334	−	0.279561i
$760$	6.48175	−	15.7581i	0.235118	−	0.571608i
$761$	15.1537	+	4.06042i	0.549321	+	0.147190i	0.522796	−	0.852458i	$-0.324889\pi$
$761$	15.1537	+	4.06042i	0.549321	+	0.147190i	0.0265254	+	0.999648i	$0.491556\pi$
$762$	12.8657	−	35.4387i	0.466073	−	1.28381i
$763$	−4.54116	−	21.6162i	−0.164401	−	0.782558i
$764$	31.3640	−	2.79596i	1.13471	−	0.101154i
$765$	−71.1219	+	9.36338i	−2.57142	+	0.338534i
$766$	4.66578	−	8.98090i	0.168582	−	0.324493i
$767$	1.43068	−	2.47802i	0.0516590	−	0.0894760i
$768$	33.4756	−	17.7070i	1.20795	−	0.638948i
$769$	−5.19904			−0.187482			−0.0937411	−	0.995597i	$-0.529883\pi$
$769$	−5.19904			−0.187482			−0.0937411	+	0.995597i	$0.529883\pi$
$770$	−27.7035	−	21.7135i	−0.998364	−	0.782498i
$771$	−7.47307	+	18.0416i	−0.269136	+	0.649752i
$772$	16.4707	+	23.4405i	0.592793	+	0.843641i
$773$	−2.37738	+	18.0580i	−0.0855084	+	0.649500i	0.893996	+	0.448076i	$0.147890\pi$
$773$	−2.37738	+	18.0580i	−0.0855084	+	0.649500i	−0.979504	+	0.201425i	$0.935443\pi$
$774$	−12.7027	−	15.1132i	−0.456589	−	0.543235i
$775$	−64.7280	−	17.3438i	−2.32510	−	0.623009i
$776$	−25.2434	+	3.38671i	−0.906185	+	0.121576i
$777$	−26.6614	−	12.7945i	−0.956472	−	0.458999i
$778$	−3.51314	+	1.64172i	−0.125952	+	0.0588586i
$779$	−1.22814	+	1.60054i	−0.0440026	+	0.0573453i
$780$	−22.1896	−	24.1359i	−0.794516	−	0.864205i
$781$	−2.49822	+	1.91695i	−0.0893933	+	0.0685939i
$782$	−50.8785	−	11.2356i	−1.81941	−	0.401785i
$783$			0.232846i			0.00832123i
$784$	−5.38251	+	27.4778i	−0.192233	+	0.981349i
$785$		−	53.6959i		−	1.91649i
$786$	10.7249	−	48.5659i	0.382546	−	1.73229i
$787$	7.32521	−	5.62083i	0.261116	−	0.200361i	−0.469904	−	0.882718i	$-0.655711\pi$
$787$	7.32521	−	5.62083i	0.261116	−	0.200361i	0.731020	+	0.682356i	$0.239045\pi$
$788$	−0.784350	+	18.6688i	−0.0279413	+	0.665049i
$789$	−13.0388	+	16.9925i	−0.464193	+	0.604949i
$790$	−0.907925	−	1.94288i	−0.0323025	−	0.0691246i
$791$	−0.982075	−	0.471285i	−0.0349186	−	0.0167570i
$792$	−5.10565	+	19.2442i	−0.181421	+	0.683814i
$793$	−10.7061	−	2.86869i	−0.380184	−	0.101870i
$794$	4.45885	−	3.74767i	0.158239	−	0.133000i
$795$	8.15488	−	61.9425i	0.289224	−	2.19687i
$796$	−18.6054	−	3.24911i	−0.659452	−	0.115162i
$797$	−3.28952	+	7.94160i	−0.116521	+	0.281306i	−0.971371	−	0.237570i	$-0.923649\pi$
$797$	−3.28952	+	7.94160i	−0.116521	+	0.281306i	0.854850	+	0.518876i	$0.173649\pi$
$798$	9.46395	−	12.0747i	0.335020	−	0.427441i
$799$	−7.73286			−0.273569
$800$	−40.0946	−	1.58549i	−1.41756	−	0.0560556i
$801$	−9.35830	+	16.2091i	−0.330659	+	0.572719i
$802$	−44.0545	−	22.8873i	−1.55562	−	0.808179i
$803$	38.4556	−	5.06277i	1.35707	−	0.178661i
$804$	−42.1690	−	35.2660i	−1.48719	−	1.24374i
$805$	8.79151	+	41.8481i	0.309860	+	1.47495i
$806$	25.0113	+	9.08010i	0.880986	+	0.319833i
$807$	−12.7695	−	3.42159i	−0.449509	−	0.120446i
$808$	−0.0612338	−	24.8309i	−0.00215420	−	0.873548i
$809$	−26.2561	+	7.03530i	−0.923115	+	0.247348i	−0.688917	−	0.724841i	$-0.741913\pi$
$809$	−26.2561	+	7.03530i	−0.923115	+	0.247348i	−0.234199	+	0.972189i	$0.575247\pi$
$810$	−28.2746	+	40.4510i	−0.993467	+	1.42130i
$811$	8.45170	+	20.4042i	0.296779	+	0.716489i	0.999985	+	0.00550212i	$0.00175139\pi$
$811$	8.45170	+	20.4042i	0.296779	+	0.716489i	−0.703205	+	0.710987i	$0.748249\pi$
$812$	−1.25159	+	0.381657i	−0.0439222	+	0.0133935i
$813$	−13.5796	−	5.62487i	−0.476259	−	0.197273i
$814$	−3.89573	+	17.6411i	−0.136545	+	0.618321i
$815$	−17.6757	−	10.2051i	−0.619154	−	0.357469i
$816$	50.5225	−	55.5009i	1.76864	−	1.94292i
$817$	8.04848	−	4.64679i	0.281580	−	0.162571i
$818$	9.23860	−	10.0988i	0.323020	−	0.353097i
$819$	−6.19603	−	12.2319i	−0.216507	−	0.427419i
$820$	7.72889	+	2.42295i	0.269904	+	0.0846129i
$821$	8.21023	−	10.6998i	0.286539	−	0.373425i	−0.627800	−	0.778375i	$-0.716044\pi$
$821$	8.21023	−	10.6998i	0.286539	−	0.373425i	0.914339	+	0.404950i	$0.132711\pi$
$822$	1.88136	−	21.7095i	0.0656198	−	0.757206i
$823$	2.05346	−	0.550223i	0.0715791	−	0.0191796i	−0.222852	−	0.974852i	$-0.571537\pi$
$823$	2.05346	−	0.550223i	0.0715791	−	0.0191796i	0.294431	+	0.955673i	$0.404870\pi$
$824$	48.7590	+	6.29695i	1.69860	+	0.219365i
$825$	32.1147	−	32.1147i	1.11809	−	1.11809i
$826$	0.0552276	−	5.37536i	0.00192162	−	0.187033i
$827$	24.8151	−	10.2787i	0.862905	−	0.357427i	0.0930623	−	0.995660i	$-0.470334\pi$
$827$	24.8151	−	10.2787i	0.862905	−	0.357427i	0.769843	+	0.638233i	$0.220334\pi$
$828$	19.7907	−	13.9061i	0.687774	−	0.483272i
$829$	−25.8651	−	33.7080i	−0.898331	−	1.17073i	−0.984664	−	0.174461i	$-0.944182\pi$
$829$	−25.8651	−	33.7080i	−0.898331	−	1.17073i	0.0863332	−	0.996266i	$-0.472485\pi$
$830$	21.3346	−	41.0657i	0.740534	−	1.42541i
$831$	5.91714	+	10.2488i	0.205263	+	0.355527i
$832$	15.8068	+	2.00174i	0.548001	+	0.0693978i
$833$	8.42095	+	54.8486i	0.291769	+	1.90039i
$834$	−0.0289865	+	0.00128945i	−0.00100372	+	4.46500e-5i
$835$	15.6228	−	2.05678i	0.540649	−	0.0711778i
$836$	−8.50078	−	3.94698i	−0.294006	−	0.136509i
$837$	1.16111	−	8.81952i	0.0401339	−	0.304847i
$838$	13.9588	−	2.47314i	0.482197	−	0.0854332i
$839$	−21.6483	+	21.6483i	−0.747383	+	0.747383i	−0.973987	−	0.226604i	$-0.927238\pi$
$839$	−21.6483	+	21.6483i	−0.747383	+	0.747383i	0.226604	+	0.973987i	$0.427238\pi$
$840$	−58.5821	−	19.0282i	−2.02127	−	0.656536i
$841$	20.4629	+	20.4629i	0.705616	+	0.705616i
$842$	−27.2170	−	19.0242i	−0.937960	−	0.655619i
$843$	−42.3958	−	5.58151i	−1.46019	−	0.192238i
$844$	−17.1513	+	15.7682i	−0.590371	+	0.542763i
$845$	4.10037	+	31.1454i	0.141057	+	1.07143i
$846$	2.42302	−	2.64863i	0.0833052	−	0.0910618i
$847$	6.34452	−	7.39294i	0.218000	−	0.254024i
$848$	16.3975	+	25.5532i	0.563094	+	0.877500i
$849$	41.6897	−	24.0696i	1.43079	−	0.826065i
$850$	−75.8226	+	23.9753i	−2.60069	+	0.822346i
$851$	17.4124	−	13.3610i	0.596889	−	0.458009i
$852$	−2.95307	+	4.65226i	−0.101171	+	0.159384i
$853$	−12.9262	−	31.2066i	−0.442585	−	1.06849i	−0.975039	−	0.222036i	$-0.928730\pi$
$853$	−12.9262	−	31.2066i	−0.442585	−	1.06849i	0.532454	−	0.846459i	$-0.321270\pi$
$854$	−20.1678	+	5.18246i	−0.690127	+	0.177340i
$855$	11.0847	+	11.0847i	0.379088	+	0.379088i
$856$	−2.59845	+	4.52639i	−0.0888133	+	0.154709i
$857$	11.9622	+	44.6435i	0.408621	+	1.52499i	0.797279	+	0.603611i	$0.206272\pi$
$857$	11.9622	+	44.6435i	0.408621	+	1.52499i	−0.388659	+	0.921382i	$0.627061\pi$
$858$	−13.8053	+	11.6034i	−0.471305	+	0.396133i
$859$	−22.2045	−	17.0381i	−0.757606	−	0.581332i	0.156084	−	0.987744i	$-0.450113\pi$
$859$	−22.2045	−	17.0381i	−0.757606	−	0.581332i	−0.913690	+	0.406412i	$0.866780\pi$
$860$	−28.6226	−	23.9371i	−0.976021	−	0.816248i
$861$	6.10687	+	3.98645i	0.208122	+	0.135858i
$862$	1.56788	+	35.2455i	0.0534022	+	1.20047i
$863$	−7.85966	−	13.6133i	−0.267546	−	0.463403i	0.700681	−	0.713474i	$-0.252879\pi$
$863$	−7.85966	−	13.6133i	−0.267546	−	0.463403i	−0.968228	+	0.250071i	$0.919546\pi$
$864$	−0.486052	−	5.30441i	−0.0165358	−	0.180460i
$865$	−26.9680	+	46.7100i	−0.916940	+	1.58819i
$866$	−32.5753	+	20.7904i	−1.10695	+	0.706487i
$867$	41.5228	−	100.245i	1.41019	−	3.40449i
$868$	49.3098	−	8.21487i	1.67368	−	0.278831i
$869$	−1.08982	+	0.451419i	−0.0369697	+	0.0153134i
$870$	−0.502165	−	2.83429i	−0.0170250	−	0.0960916i
$871$	−5.98601	−	22.3401i	−0.202828	−	0.756965i
$872$	−16.6558	+	16.7381i	−0.564035	+	0.566824i
$873$	6.06468	−	22.6337i	0.205258	−	0.766035i
$874$	4.82047	+	10.3154i	0.163055	+	0.348923i
$875$	12.8536	+	14.3436i	0.434531	+	0.484901i
$876$	60.1539	−	31.4400i	2.03241	−	1.06226i
$877$	−5.25920	−	39.9476i	−0.177590	−	1.34893i	−0.815471	−	0.578798i	$-0.803522\pi$
$877$	−5.25920	−	39.9476i	−0.177590	−	1.34893i	0.637880	−	0.770136i	$-0.279811\pi$
$878$	−3.36379	+	1.06364i	−0.113522	+	0.0358960i
$879$	53.2246	+	30.7293i	1.79522	+	1.03647i
$880$	−3.15632	+	37.4965i	−0.106400	+	1.26401i
$881$			2.08556i			0.0702642i	0.999383	+	0.0351321i	$0.0111852\pi$
$881$			2.08556i			0.0702642i	−0.999383	+	0.0351321i	$0.988815\pi$
$882$	−21.4252	−	14.3020i	−0.721423	−	0.481573i
$883$	10.3216	+	4.27536i	0.347351	+	0.143877i	0.549536	−	0.835470i	$-0.314804\pi$
$883$	10.3216	+	4.27536i	0.347351	+	0.143877i	−0.202186	+	0.979347i	$0.564804\pi$
$884$	30.8168	−	6.88508i	1.03648	−	0.231570i
$885$	11.7243	+	1.54353i	0.394107	+	0.0518852i
$886$	−2.51717	+	29.0464i	−0.0845660	+	0.975832i
$887$	10.5997	−	39.5585i	0.355902	−	1.32824i	−0.523444	−	0.852060i	$-0.675353\pi$
$887$	10.5997	−	39.5585i	0.355902	−	1.32824i	0.879346	−	0.476184i	$-0.157980\pi$
$888$	4.20377	+	31.3335i	0.141069	+	1.05148i
$889$	12.8930	−	26.8667i	0.432417	−	0.901080i
$890$	−12.0712	+	33.2503i	−0.404626	+	1.11455i
$891$	21.5370	+	16.5259i	0.721516	+	0.553639i
$892$	17.6482	−	38.0096i	0.590904	−	1.27266i
$893$	1.02870	+	1.34063i	0.0344242	+	0.0448625i
$894$	−24.8259	−	38.8982i	−0.830301	−	1.30095i
$895$	−29.0618			−0.971430
$896$	27.7155	−	11.3071i	0.925911	−	0.377743i
$897$	21.9088			0.731512
$898$	12.6799	+	19.8673i	0.423132	+	0.662981i
$899$	1.42212	+	1.85334i	0.0474304	+	0.0618124i
$900$	15.5464	−	33.4829i	0.518213	−	1.11610i
$901$	47.7378	+	36.6305i	1.59038	+	1.22034i
$902$	1.52036	−	4.18786i	0.0506224	−	0.139440i
$903$	−18.9630	−	27.7319i	−0.631050	−	0.922860i
$904$	0.154846	+	1.15417i	0.00515011	+	0.0383872i
$905$	−14.6194	+	54.5603i	−0.485965	+	1.81364i
$906$	−1.21755	+	14.0496i	−0.0404502	+	0.466767i
$907$	−0.556878	−	0.0733143i	−0.0184908	−	0.00243436i	0.121275	−	0.992619i	$-0.461302\pi$
$907$	−0.556878	−	0.0733143i	−0.0184908	−	0.00243436i	−0.139766	+	0.990185i	$0.544635\pi$
$908$	−0.962942	+	0.215141i	−0.0319563	+	0.00713969i
$909$	21.1057	+	8.74226i	0.700031	+	0.289962i
$910$	−15.5638	−	20.7204i	−0.515934	−	0.686876i
$911$			30.4575i			1.00910i	0.863382	+	0.504551i	$0.168342\pi$
$911$			30.4575i			1.00910i	−0.863382	+	0.504551i	$0.831658\pi$
$912$	−16.3431	−	1.37570i	−0.541174	−	0.0455541i
$913$	−22.0444	−	12.7274i	−0.729564	−	0.421214i
$914$	5.21781	−	1.64988i	0.172590	−	0.0545733i
$915$	−5.97899	−	45.4149i	−0.197659	−	1.50137i
$916$	−29.1488	+	15.2349i	−0.963105	+	0.503375i
$917$	12.2367	−	37.3592i	0.404091	−	1.23371i
$918$	−4.46923	−	9.56376i	−0.147507	−	0.315651i
$919$	−8.69186	+	32.4385i	−0.286718	+	1.07005i	0.660857	+	0.750512i	$0.270193\pi$
$919$	−8.69186	+	32.4385i	−0.286718	+	1.07005i	−0.947575	+	0.319534i	$0.896474\pi$
$920$	32.2449	−	32.4043i	1.06308	−	1.06834i
$921$	1.00967	+	3.76814i	0.0332698	+	0.124164i
$922$	−3.75763	−	21.2086i	−0.123751	−	0.698469i
$923$	−2.14188	+	0.887197i	−0.0705009	+	0.0292024i
$924$	−11.8882	+	31.7262i	−0.391092	+	1.04372i
$925$	12.8189	−	30.9475i	0.421482	−	1.01755i
$926$	−30.1196	+	19.2231i	−0.989790	+	0.631710i
$927$	−22.6155	+	39.1712i	−0.742791	+	1.28655i
$928$	1.07525	+	0.894740i	0.0352969	+	0.0293713i
$929$	22.1332	+	38.3359i	0.726168	+	1.25776i	0.958492	+	0.285121i	$0.0920338\pi$
$929$	22.1332	+	38.3359i	0.726168	+	1.25776i	−0.232324	+	0.972639i	$0.574633\pi$
$930$	4.88702	+	109.859i	0.160252	+	3.60242i
$931$	8.38877	−	8.75644i	0.274931	−	0.286981i
$932$	−18.3630	−	15.3570i	−0.601500	−	0.503036i
$933$	43.6088	+	33.4622i	1.42769	+	1.09550i
$934$	12.4355	−	10.4520i	0.406901	−	0.342001i
$935$	19.3013	+	72.0335i	0.631221	+	2.35575i
$936$	−7.29790	+	12.7126i	−0.238539	+	0.415525i
$937$	−30.0129	−	30.0129i	−0.980480	−	0.980480i	0.0193331	−	0.999813i	$-0.493846\pi$
$937$	−30.0129	−	30.0129i	−0.980480	−	0.980480i	−0.999813	+	0.0193331i	$0.993846\pi$
$938$	−30.4071	−	31.0384i	−0.992826	−	1.01344i
$939$	−14.1342	−	34.1230i	−0.461252	−	1.11356i
$940$	3.63588	−	5.72795i	0.118589	−	0.186825i
$941$	−9.67554	+	7.42430i	−0.315414	+	0.242025i	−0.754319	−	0.656508i	$-0.772033\pi$
$941$	−9.67554	+	7.42430i	−0.315414	+	0.242025i	0.438906	+	0.898533i	$0.355366\pi$
$942$	−49.2797	+	15.5824i	−1.60562	+	0.507701i
$943$	−4.68741	+	2.70628i	−0.152643	+	0.0881284i
$944$	−4.83662	+	3.10367i	−0.157419	+	0.101016i
$945$	−5.64217	+	6.57452i	−0.183540	+	0.213869i
$946$	−13.8533	+	15.1432i	−0.450409	+	0.492348i
$947$	5.79803	+	44.0404i	0.188411	+	1.43112i	0.780453	+	0.625214i	$0.214988\pi$
$947$	5.79803	+	44.0404i	0.188411	+	1.43112i	−0.592042	+	0.805907i	$0.701678\pi$
$948$	−1.51961	+	1.39707i	−0.0493547	+	0.0453748i
$949$	28.3123	+	3.72739i	0.919057	+	0.120996i
$950$	14.2432	+	9.95579i	0.462112	+	0.323008i
$951$	−12.2797	−	12.2797i	−0.398196	−	0.398196i
$952$	44.0815	−	39.6989i	1.42869	−	1.28665i
$953$	−18.1908	+	18.1908i	−0.589258	+	0.589258i	−0.937430	−	0.348173i	$-0.886802\pi$
$953$	−18.1908	+	18.1908i	−0.589258	+	0.589258i	0.348173	+	0.937430i	$0.386802\pi$
$954$	−27.5048	+	4.87315i	−0.890499	+	0.157774i
$955$	−7.14645	+	54.2827i	−0.231254	+	1.75655i
$956$	38.4384	+	17.8473i	1.24319	+	0.577222i
$957$	−1.56974	+	0.206661i	−0.0507426	+	0.00668039i
$958$	−3.95652	+	0.176004i	−0.127829	+	0.00568643i
$959$	3.17892	−	16.9280i	0.102653	−	0.546633i
$960$	17.3561	+	63.5192i	0.560167	+	2.05007i
$961$	−29.1239	−	50.4440i	−0.939479	−	1.62723i
$962$	−6.13199	+	11.8031i	−0.197703	+	0.380548i
$963$	−2.92309	−	3.80945i	−0.0941953	−	0.122758i
$964$	5.00496	−	3.51679i	0.161199	−	0.113268i
$965$	−46.0215	+	19.0627i	−1.48149	+	0.613651i
$966$	35.8550	−	20.2126i	1.15362	−	0.650331i
$967$	6.72772	−	6.72772i	0.216349	−	0.216349i	−0.590609	−	0.806958i	$-0.701112\pi$
$967$	6.72772	−	6.72772i	0.216349	−	0.216349i	0.806958	+	0.590609i	$0.201112\pi$
$968$	−10.3290	−	1.33393i	−0.331986	−	0.0428741i
$969$	−31.3963	+	8.41261i	−1.00859	+	0.270252i
$970$	3.82350	−	44.1204i	0.122765	−	1.41662i
$971$	29.2178	−	38.0774i	0.937645	−	1.22196i	−0.0372522	−	0.999306i	$-0.511860\pi$
$971$	29.2178	−	38.0774i	0.937645	−	1.22196i	0.974897	−	0.222657i	$-0.0714728\pi$
$972$	39.9383	+	12.5203i	1.28102	+	0.401590i
$973$	−0.0228997	−	0.00125453i	−0.000734131	−	4.02185e-5i
$974$	−12.1028	+	13.2297i	−0.387799	+	0.423907i
$975$	28.9579	−	16.7188i	0.927394	−	0.535431i
$976$	16.4617	+	14.9851i	0.526926	+	0.479661i
$977$	−10.7981	−	6.23428i	−0.345462	−	0.199452i	0.317223	−	0.948351i	$-0.397250\pi$
$977$	−10.7981	−	6.23428i	−0.345462	−	0.199452i	−0.662685	+	0.748899i	$0.730583\pi$
$978$	−4.23634	+	19.1835i	−0.135463	+	0.613420i
$979$	17.9762	+	7.44599i	0.574522	+	0.237975i
$980$	−44.5874	−	19.5514i	−1.42429	−	0.624547i
$981$	−8.31348	−	20.0705i	−0.265429	−	0.640803i
$982$	33.4269	−	47.8221i	1.06669	−	1.52607i
$983$	6.79271	−	1.82010i	0.216654	−	0.0580522i	−0.148859	−	0.988858i	$-0.547560\pi$
$983$	6.79271	−	1.82010i	0.216654	−	0.0580522i	0.365513	+	0.930806i	$0.380894\pi$
$984$	−0.0192261	−	7.79636i	−0.000612905	−	0.248539i
$985$	−31.3824	−	8.40890i	−0.999927	−	0.267930i
$986$	2.60584	+	0.946024i	0.0829869	+	0.0301275i
$987$	4.54923	−	4.07667i	0.144804	−	0.129762i
$988$	−5.29321	−	4.42672i	−0.168400	−	0.140833i
$989$	24.7203	−	3.25449i	0.786060	−	0.103487i
$990$	−30.7206	−	15.9600i	−0.976363	−	0.507243i
$991$	14.3047	−	24.7765i	0.454404	−	0.787050i	−0.544250	−	0.838923i	$-0.683186\pi$
$991$	14.3047	−	24.7765i	0.454404	−	0.787050i	0.998654	+	0.0518729i	$0.0165191\pi$
$992$	−36.2658	−	39.2520i	−1.15144	−	1.24625i
$993$	1.89320			0.0600787
$994$	−2.68681	+	3.42802i	−0.0852205	+	0.108730i
$995$	12.5674	−	30.3404i	0.398414	−	0.961855i
$996$	−43.8795	−	7.66278i	−1.39038	−	0.242805i
$997$	5.68821	−	43.2063i	0.180148	−	1.36836i	−0.627466	−	0.778644i	$-0.715908\pi$
$997$	5.68821	−	43.2063i	0.180148	−	1.36836i	0.807613	−	0.589712i	$-0.200759\pi$
$998$	−13.1871	+	11.0837i	−0.417429	+	0.350850i
$999$	4.29518	+	1.15089i	0.135893	+	0.0364125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.9	yes	240
4.3	odd	2		896.2.bh.a.529.27		240
7.2	even	3	inner	224.2.bd.a.205.11	yes	240
28.23	odd	6		896.2.bh.a.401.4		240
32.5	even	8	inner	224.2.bd.a.165.11	yes	240
32.27	odd	8		896.2.bh.a.753.4		240
224.37	even	24	inner	224.2.bd.a.37.9	✓	240
224.219	odd	24		896.2.bh.a.625.27		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.9	✓	240	224.37	even	24	inner
224.2.bd.a.109.9	yes	240	1.1	even	1	trivial
224.2.bd.a.165.11	yes	240	32.5	even	8	inner
224.2.bd.a.205.11	yes	240	7.2	even	3	inner
896.2.bh.a.401.4		240	28.23	odd	6
896.2.bh.a.529.27		240	4.3	odd	2
896.2.bh.a.625.27		240	224.219	odd	24
896.2.bh.a.753.4		240	32.27	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.760837 - 1.19211i) q^{2} +(-1.44087 - 1.87778i) q^{3} +(-0.842255 + 1.81400i) q^{4} +(-2.75892 - 2.11700i) q^{5} +(-1.14225 + 3.14636i) q^{6} +(-1.14468 + 2.38531i) q^{7} +(2.80331 - 0.376098i) q^{8} +(-0.673491 + 2.51350i) q^{9} +O(q^{10})\)	\(q+(-0.760837 - 1.19211i) q^{2} +(-1.44087 - 1.87778i) q^{3} +(-0.842255 + 1.81400i) q^{4} +(-2.75892 - 2.11700i) q^{5} +(-1.14225 + 3.14636i) q^{6} +(-1.14468 + 2.38531i) q^{7} +(2.80331 - 0.376098i) q^{8} +(-0.673491 + 2.51350i) q^{9} +(-0.424604 + 4.89963i) q^{10} +(2.68201 + 0.353093i) q^{11} +(4.61988 - 1.03217i) q^{12} +(1.84002 + 0.762162i) q^{13} +(3.71447 - 0.450247i) q^{14} +8.23097i q^{15} +(-2.58121 - 3.05571i) q^{16} +(-6.86527 - 3.96366i) q^{17} +(3.50879 - 1.10949i) q^{18} +(0.226114 + 1.71751i) q^{19} +(6.16395 - 3.22164i) q^{20} +(6.12843 - 1.28747i) q^{21} +(-1.61964 - 3.46589i) q^{22} +(-1.20290 + 4.48927i) q^{23} +(-4.74544 - 4.72209i) q^{24} +(1.83589 + 6.85163i) q^{25} +(-0.491375 - 2.77339i) q^{26} +(-0.869948 + 0.360344i) q^{27} +(-3.36285 - 4.08549i) q^{28} +(0.0946303 - 0.228458i) q^{29} +(9.81223 - 6.26242i) q^{30} +(-4.72355 + 8.18143i) q^{31} +(-1.67886 + 5.40198i) q^{32} +(-3.20140 - 5.54498i) q^{33} +(0.498221 + 11.1999i) q^{34} +(8.20778 - 4.15761i) q^{35} +(-3.99225 - 3.33872i) q^{36} +(-3.74651 - 2.87479i) q^{37} +(1.87542 - 1.57629i) q^{38} +(-1.22006 - 4.55333i) q^{39} +(-8.53032 - 4.89697i) q^{40} +(0.823484 + 0.823484i) q^{41} +(-6.19754 - 6.32621i) q^{42} +(-2.05302 - 4.95643i) q^{43} +(-2.89945 + 4.56777i) q^{44} +(7.17918 - 5.50878i) q^{45} +(6.26691 - 1.98162i) q^{46} +(0.844781 - 0.487734i) q^{47} +(-2.01875 + 9.24983i) q^{48} +(-4.37942 - 5.46083i) q^{49} +(6.77109 - 7.40155i) q^{50} +(2.44908 + 18.6026i) q^{51} +(-2.93233 + 2.69587i) q^{52} +(-7.52554 - 0.990756i) q^{53} +(1.09146 + 0.762911i) q^{54} +(-6.65195 - 6.65195i) q^{55} +(-2.31178 + 7.11728i) q^{56} +(2.89930 - 2.89930i) q^{57} +(-0.344345 + 0.0610092i) q^{58} +(0.187527 - 1.42441i) q^{59} +(-14.9310 - 6.93258i) q^{60} +(-5.51757 + 0.726402i) q^{61} +(13.3470 - 0.593736i) q^{62} +(-5.22455 - 4.48364i) q^{63} +(7.71710 - 2.10864i) q^{64} +(-3.46298 - 5.99807i) q^{65} +(-4.17449 + 8.03524i) q^{66} +(-7.06937 - 9.21298i) q^{67} +(12.9724 - 9.11520i) q^{68} +(10.1631 - 4.20969i) q^{69} +(-11.2011 - 6.62132i) q^{70} +(-0.823109 + 0.823109i) q^{71} +(-0.942681 + 7.29942i) q^{72} +(13.8498 - 3.71104i) q^{73} +(-0.576595 + 6.65350i) q^{74} +(10.2206 - 13.3197i) q^{75} +(-3.30601 - 1.03641i) q^{76} +(-3.91227 + 5.99324i) q^{77} +(-4.49981 + 4.91879i) q^{78} +(-0.377642 + 0.218032i) q^{79} +(0.652444 + 13.8949i) q^{80} +(8.69076 + 5.01761i) q^{81} +(0.355147 - 1.60822i) q^{82} +(-8.69345 - 3.60095i) q^{83} +(-2.82623 + 12.2014i) q^{84} +(10.5497 + 25.4692i) q^{85} +(-4.34660 + 6.21846i) q^{86} +(-0.565344 + 0.151483i) q^{87} +(7.65129 - 0.0188683i) q^{88} +(6.94761 + 1.86161i) q^{89} +(-12.0293 - 4.36710i) q^{90} +(-3.92423 + 3.51659i) q^{91} +(-7.13040 - 5.96317i) q^{92} +(22.1690 - 2.91860i) q^{93} +(-1.22417 - 0.635986i) q^{94} +(3.01212 - 5.21715i) q^{95} +(12.5628 - 4.63103i) q^{96} -9.00485 q^{97} +(-3.17790 + 9.37555i) q^{98} +(-2.69381 + 6.50342i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21} - 24 q^{22} - 12 q^{23} + 36 q^{24} - 4 q^{25} - 4 q^{26} - 16 q^{27} + 12 q^{28} - 16 q^{29} + 44 q^{30} - 56 q^{31} - 4 q^{32} - 8 q^{33} - 32 q^{34} - 32 q^{35} - 96 q^{36} - 4 q^{37} + 36 q^{38} - 4 q^{39} - 68 q^{40} - 16 q^{41} - 28 q^{42} + 44 q^{44} + 8 q^{45} - 4 q^{46} - 16 q^{48} + 8 q^{50} - 28 q^{51} - 28 q^{52} - 20 q^{53} - 92 q^{54} - 16 q^{55} - 48 q^{56} - 16 q^{57} + 28 q^{58} - 36 q^{59} + 60 q^{60} - 4 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{65} - 36 q^{66} + 36 q^{67} - 36 q^{68} - 16 q^{69} - 44 q^{70} + 48 q^{71} - 4 q^{72} - 4 q^{73} + 68 q^{74} + 16 q^{75} - 16 q^{76} - 8 q^{77} - 120 q^{78} - 16 q^{80} - 44 q^{82} - 96 q^{83} - 28 q^{84} - 56 q^{85} - 4 q^{86} - 4 q^{87} + 40 q^{88} - 4 q^{89} + 224 q^{90} - 56 q^{91} - 80 q^{92} + 20 q^{93} + 4 q^{94} - 8 q^{95} - 32 q^{96} - 32 q^{97} + 96 q^{98} + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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