LMFDB - Embedded newform 224.2.bd.a.37.14

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			37.14
Character	$\chi$	$=$	224.37
Dual form			224.2.bd.a.109.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.399779 - 1.35653i) q^{2} +(1.62045 - 2.11181i) q^{3} +(-1.68035 + 1.08463i) q^{4} +(1.05240 - 0.807534i) q^{5} +(-3.51256 - 1.35393i) q^{6} +(2.64452 - 0.0808662i) q^{7} +(2.14310 + 1.84584i) q^{8} +(-1.05744 - 3.94640i) q^{9} +O(q^{10})$	\(q+(-0.399779 - 1.35653i) q^{2} +(1.62045 - 2.11181i) q^{3} +(-1.68035 + 1.08463i) q^{4} +(1.05240 - 0.807534i) q^{5} +(-3.51256 - 1.35393i) q^{6} +(2.64452 - 0.0808662i) q^{7} +(2.14310 + 1.84584i) q^{8} +(-1.05744 - 3.94640i) q^{9} +(-1.51617 - 1.10478i) q^{10} +(-1.69616 + 0.223304i) q^{11} +(-0.432405 + 5.30618i) q^{12} +(-0.550667 + 0.228094i) q^{13} +(-1.16692 - 3.55504i) q^{14} -3.53104i q^{15} +(1.64718 - 3.64511i) q^{16} +(-4.66215 + 2.69169i) q^{17} +(-4.93068 + 3.01213i) q^{18} +(-0.654477 + 4.97125i) q^{19} +(-0.892530 + 2.49840i) q^{20} +(4.11453 - 5.71576i) q^{21} +(0.981009 + 2.21162i) q^{22} +(1.35463 + 5.05554i) q^{23} +(7.37086 - 1.53473i) q^{24} +(-0.838663 + 3.12993i) q^{25} +(0.529562 + 0.655810i) q^{26} +(-2.66982 - 1.10587i) q^{27} +(-4.35601 + 3.00419i) q^{28} +(-3.87939 - 9.36567i) q^{29} +(-4.78996 + 1.41163i) q^{30} +(1.43967 + 2.49358i) q^{31} +(-5.60321 - 0.777209i) q^{32} +(-2.27697 + 3.94383i) q^{33} +(5.51519 + 5.24827i) q^{34} +(2.71778 - 2.22064i) q^{35} +(6.05724 + 5.48443i) q^{36} +(4.83651 - 3.71118i) q^{37} +(7.00530 - 1.09958i) q^{38} +(-0.410638 + 1.53252i) q^{39} +(3.74597 + 0.211937i) q^{40} +(2.70535 - 2.70535i) q^{41} +(-9.39851 - 3.29645i) q^{42} +(1.10066 - 2.65723i) q^{43} +(2.60795 - 2.21493i) q^{44} +(-4.29970 - 3.29928i) q^{45} +(6.31644 - 3.85869i) q^{46} +(-8.38206 - 4.83939i) q^{47} +(-5.02862 - 9.38525i) q^{48} +(6.98692 - 0.427704i) q^{49} +(4.58113 - 0.113609i) q^{50} +(-1.87043 + 14.2073i) q^{51} +(0.677920 - 0.980546i) q^{52} +(6.88442 - 0.906351i) q^{53} +(-0.432817 + 4.06380i) q^{54} +(-1.60471 + 1.60471i) q^{55} +(5.81672 + 4.70805i) q^{56} +(9.43780 + 9.43780i) q^{57} +(-11.1539 + 9.00670i) q^{58} +(-0.0283506 - 0.215344i) q^{59} +(3.82985 + 5.93339i) q^{60} +(4.05592 + 0.533972i) q^{61} +(2.80707 - 2.94984i) q^{62} +(-3.11554 - 10.3508i) q^{63} +(1.18574 + 7.91164i) q^{64} +(-0.395328 + 0.684728i) q^{65} +(6.26022 + 1.51212i) q^{66} +(-8.41153 + 10.9621i) q^{67} +(4.91458 - 9.57968i) q^{68} +(12.8715 + 5.33153i) q^{69} +(-4.09888 - 2.79899i) q^{70} +(6.41498 + 6.41498i) q^{71} +(5.01825 - 10.4094i) q^{72} +(-9.61077 - 2.57520i) q^{73} +(-6.96787 - 5.07722i) q^{74} +(5.25082 + 6.84301i) q^{75} +(-4.29219 - 9.06332i) q^{76} +(-4.46747 + 0.727693i) q^{77} +(2.24308 - 0.0556267i) q^{78} +(4.05809 + 2.34294i) q^{79} +(-1.21006 - 5.16626i) q^{80} +(3.95304 - 2.28229i) q^{81} +(-4.75143 - 2.58835i) q^{82} +(9.11873 - 3.77710i) q^{83} +(-0.714412 + 14.0672i) q^{84} +(-2.73281 + 6.59758i) q^{85} +(-4.04464 - 0.430776i) q^{86} +(-26.0649 - 6.98407i) q^{87} +(-4.04723 - 2.65228i) q^{88} +(-16.1173 + 4.31863i) q^{89} +(-2.75664 + 7.15166i) q^{90} +(-1.43780 + 0.647728i) q^{91} +(-7.75962 - 7.02583i) q^{92} +(7.59889 + 1.00041i) q^{93} +(-3.21381 + 13.3052i) q^{94} +(3.32568 + 5.76025i) q^{95} +(-10.7210 + 10.5735i) q^{96} -9.28832 q^{97} +(-3.37342 - 9.30699i) q^{98} +(2.67483 + 6.45761i) 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 $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.399779	−	1.35653i	−0.282686	−	0.959212i
$2$	−0.399779	−	1.35653i	−0.282686	−	0.959212i
$3$	1.62045	−	2.11181i	0.935568	−	1.21926i	−0.0399198	−	0.999203i	$-0.512710\pi$
$3$	1.62045	−	2.11181i	0.935568	−	1.21926i	0.975488	−	0.220053i	$-0.0706231\pi$
$4$	−1.68035	+	1.08463i	−0.840177	+	0.542313i
$5$	1.05240	−	0.807534i	0.470647	−	0.361140i	−0.346041	−	0.938219i	$-0.612474\pi$
$5$	1.05240	−	0.807534i	0.470647	−	0.361140i	0.816688	+	0.577079i	$0.195808\pi$
$6$	−3.51256	−	1.35393i	−1.43400	−	0.552741i
$7$	2.64452	−	0.0808662i	0.999533	−	0.0305646i
$7$	2.64452	−	0.0808662i	0.999533	−	0.0305646i
$8$	2.14310	+	1.84584i	0.757700	+	0.652604i
$9$	−1.05744	−	3.94640i	−0.352479	−	1.31547i
$10$	−1.51617	−	1.10478i	−0.479456	−	0.349361i
$11$	−1.69616	+	0.223304i	−0.511412	+	0.0673287i	−0.381816	−	0.924238i	$-0.624701\pi$
$11$	−1.69616	+	0.223304i	−0.511412	+	0.0673287i	−0.129596	+	0.991567i	$0.541368\pi$
$12$	−0.432405	+	5.30618i	−0.124825	+	1.53176i
$13$	−0.550667	+	0.228094i	−0.152728	+	0.0632619i	−0.457738	−	0.889087i	$-0.651340\pi$
$13$	−0.550667	+	0.228094i	−0.152728	+	0.0632619i	0.305010	+	0.952349i	$0.401340\pi$
$14$	−1.16692	−	3.55504i	−0.311872	−	0.950124i
$15$		−	3.53104i		−	0.911710i
$16$	1.64718	−	3.64511i	0.411794	−	0.911277i
$17$	−4.66215	+	2.69169i	−1.13074	+	0.652831i	−0.944120	−	0.329601i	$-0.893086\pi$
$17$	−4.66215	+	2.69169i	−1.13074	+	0.652831i	−0.186617	+	0.982433i	$0.559752\pi$
$18$	−4.93068	+	3.01213i	−1.16217	+	0.709967i
$19$	−0.654477	+	4.97125i	−0.150147	+	1.14048i	0.735967	+	0.677017i	$0.236728\pi$
$19$	−0.654477	+	4.97125i	−0.150147	+	1.14048i	−0.886115	+	0.463466i	$0.846606\pi$
$20$	−0.892530	+	2.49840i	−0.199576	+	0.558659i
$21$	4.11453	−	5.71576i	0.897865	−	1.24728i
$22$	0.981009	+	2.21162i	0.209152	+	0.471520i
$23$	1.35463	+	5.05554i	0.282459	+	1.05415i	0.950676	+	0.310186i	$0.100391\pi$
$23$	1.35463	+	5.05554i	0.282459	+	1.05415i	−0.668217	+	0.743967i	$0.732942\pi$
$24$	7.37086	−	1.53473i	1.50457	−	0.313275i
$25$	−0.838663	+	3.12993i	−0.167733	+	0.625987i
$26$	0.529562	+	0.655810i	0.103856	+	0.128615i
$27$	−2.66982	−	1.10587i	−0.513807	−	0.212826i
$28$	−4.35601	+	3.00419i	−0.823209	+	0.567739i
$29$	−3.87939	−	9.36567i	−0.720384	−	1.73916i	−0.672255	−	0.740319i	$-0.734674\pi$
$29$	−3.87939	−	9.36567i	−0.720384	−	1.73916i	−0.0481284	−	0.998841i	$-0.515326\pi$
$30$	−4.78996	+	1.41163i	−0.874524	+	0.257728i
$31$	1.43967	+	2.49358i	0.258572	+	0.447860i	0.965860	−	0.259066i	$-0.0834147\pi$
$31$	1.43967	+	2.49358i	0.258572	+	0.447860i	−0.707288	+	0.706926i	$0.750081\pi$
$32$	−5.60321	−	0.777209i	−0.990517	−	0.137392i
$33$	−2.27697	+	3.94383i	−0.396370	+	0.686533i
$34$	5.51519	+	5.24827i	0.945848	+	0.900071i
$35$	2.71778	−	2.22064i	0.459389	−	0.375356i
$36$	6.05724	+	5.48443i	1.00954	+	0.914072i
$37$	4.83651	−	3.71118i	0.795117	−	0.610115i	−0.129253	−	0.991612i	$-0.541258\pi$
$37$	4.83651	−	3.71118i	0.795117	−	0.610115i	0.924370	+	0.381497i	$0.124591\pi$
$38$	7.00530	−	1.09958i	1.13641	−	0.178376i
$39$	−0.410638	+	1.53252i	−0.0657547	+	0.245400i
$40$	3.74597	+	0.211937i	0.592290	+	0.0335102i
$41$	2.70535	−	2.70535i	0.422505	−	0.422505i	−0.463561	−	0.886065i	$-0.653428\pi$
$41$	2.70535	−	2.70535i	0.422505	−	0.422505i	0.886065	+	0.463561i	$0.153428\pi$
$42$	−9.39851	−	3.29645i	−1.45022	−	0.508654i
$43$	1.10066	−	2.65723i	0.167849	−	0.405224i	−0.817464	−	0.575980i	$-0.804621\pi$
$43$	1.10066	−	2.65723i	0.167849	−	0.405224i	0.985313	+	0.170755i	$0.0546208\pi$
$44$	2.60795	−	2.21493i	0.393163	−	0.333913i
$45$	−4.29970	−	3.29928i	−0.640961	−	0.491827i
$46$	6.31644	−	3.85869i	0.931309	−	0.568933i
$47$	−8.38206	−	4.83939i	−1.22265	−	0.705897i	−0.257168	−	0.966367i	$-0.582789\pi$
$47$	−8.38206	−	4.83939i	−1.22265	−	0.705897i	−0.965482	+	0.260470i	$0.916123\pi$
$48$	−5.02862	−	9.38525i	−0.725818	−	1.35464i
$49$	6.98692	−	0.427704i	0.998132	−	0.0611005i
$50$	4.58113	−	0.113609i	0.647870	−	0.0160667i
$51$	−1.87043	+	14.2073i	−0.261913	+	1.98943i
$52$	0.677920	−	0.980546i	0.0940105	−	0.135977i
$53$	6.88442	−	0.906351i	0.945648	−	0.124497i	0.358097	−	0.933684i	$-0.383426\pi$
$53$	6.88442	−	0.906351i	0.945648	−	0.124497i	0.587551	+	0.809187i	$0.300092\pi$
$54$	−0.432817	+	4.06380i	−0.0588989	+	0.553013i
$55$	−1.60471	+	1.60471i	−0.216379	+	0.216379i
$56$	5.81672	+	4.70805i	0.777292	+	0.629140i
$57$	9.43780	+	9.43780i	1.25007	+	1.25007i
$58$	−11.1539	+	9.00670i	−1.46458	+	1.18264i
$59$	−0.0283506	−	0.215344i	−0.00369093	−	0.0280354i	0.989500	−	0.144531i	$-0.0461673\pi$
$59$	−0.0283506	−	0.215344i	−0.00369093	−	0.0280354i	−0.993191	+	0.116495i	$0.962834\pi$
$60$	3.82985	+	5.93339i	0.494432	+	0.765998i
$61$	4.05592	+	0.533972i	0.519308	+	0.0683682i	0.385624	−	0.922656i	$-0.373986\pi$
$61$	4.05592	+	0.533972i	0.519308	+	0.0683682i	0.133684	+	0.991024i	$0.457319\pi$
$62$	2.80707	−	2.94984i	0.356498	−	0.374629i
$63$	−3.11554	−	10.3508i	−0.392521	−	1.30408i
$64$	1.18574	+	7.91164i	0.148217	+	0.988955i
$65$	−0.395328	+	0.684728i	−0.0490344	+	0.0849301i
$66$	6.26022	+	1.51212i	0.770579	+	0.186129i
$67$	−8.41153	+	10.9621i	−1.02763	+	1.33924i	−0.0883499	+	0.996089i	$0.528159\pi$
$67$	−8.41153	+	10.9621i	−1.02763	+	1.33924i	−0.939282	+	0.343146i	$0.888507\pi$
$68$	4.91458	−	9.57968i	0.595980	−	1.16171i
$69$	12.8715	+	5.33153i	1.54954	+	0.641841i
$70$	−4.09888	−	2.79899i	−0.489910	−	0.334543i
$71$	6.41498	+	6.41498i	0.761319	+	0.761319i	0.976561	−	0.215242i	$-0.0690541\pi$
$71$	6.41498	+	6.41498i	0.761319	+	0.761319i	−0.215242	+	0.976561i	$0.569054\pi$
$72$	5.01825	−	10.4094i	0.591406	−	1.22676i
$73$	−9.61077	−	2.57520i	−1.12486	−	0.301404i	−0.352009	−	0.935997i	$-0.614501\pi$
$73$	−9.61077	−	2.57520i	−1.12486	−	0.301404i	−0.772847	+	0.634593i	$0.781168\pi$
$74$	−6.96787	−	5.07722i	−0.809999	−	0.590215i
$75$	5.25082	+	6.84301i	0.606313	+	0.790162i
$76$	−4.29219	−	9.06332i	−0.492348	−	1.03963i
$77$	−4.46747	+	0.727693i	−0.509115	+	0.0829283i
$78$	2.24308	−	0.0556267i	0.253979	−	0.00629849i
$79$	4.05809	+	2.34294i	0.456571	+	0.263601i	0.710601	−	0.703595i	$-0.248423\pi$
$79$	4.05809	+	2.34294i	0.456571	+	0.263601i	−0.254030	+	0.967196i	$0.581756\pi$
$80$	−1.21006	−	5.16626i	−0.135289	−	0.577605i
$81$	3.95304	−	2.28229i	0.439226	−	0.253587i
$82$	−4.75143	−	2.58835i	−0.524708	−	0.285835i
$83$	9.11873	−	3.77710i	1.00091	−	0.414591i	0.178780	−	0.983889i	$-0.442785\pi$
$83$	9.11873	−	3.77710i	1.00091	−	0.414591i	0.822131	+	0.569298i	$0.192785\pi$
$84$	−0.714412	+	14.0672i	−0.0779488	+	1.53486i
$85$	−2.73281	+	6.59758i	−0.296414	+	0.715608i
$86$	−4.04464	−	0.430776i	−0.436145	−	0.0464518i
$87$	−26.0649	−	6.98407i	−2.79445	−	0.748771i
$88$	−4.04723	−	2.65228i	−0.431436	−	0.282735i
$89$	−16.1173	+	4.31863i	−1.70844	+	0.457774i	−0.975040	−	0.222028i	$-0.928732\pi$
$89$	−16.1173	+	4.31863i	−1.70844	+	0.457774i	−0.733395	+	0.679802i	$0.762066\pi$
$90$	−2.75664	+	7.15166i	−0.290575	+	0.753851i
$91$	−1.43780	+	0.647728i	−0.150723	+	0.0679004i
$92$	−7.75962	−	7.02583i	−0.808996	−	0.732493i
$93$	7.59889	+	1.00041i	0.787968	+	0.103738i
$94$	−3.21381	+	13.3052i	−0.331479	+	1.37233i
$95$	3.32568	+	5.76025i	0.341208	+	0.590989i
$96$	−10.7210	+	10.5735i	−1.09421	+	1.07915i
$97$	−9.28832			−0.943086			−0.471543	−	0.881843i	$-0.656303\pi$
$97$	−9.28832			−0.943086			−0.471543	+	0.881843i	$0.656303\pi$
$98$	−3.37342	−	9.30699i	−0.340767	−	0.940148i
$99$	2.67483	+	6.45761i	0.268831	+	0.649015i
$100$	−1.98555	−	6.16903i	−0.198555	−	0.616903i
$101$	−1.94029	−	14.7380i	−0.193066	−	1.46648i	−0.763855	−	0.645388i	$-0.776696\pi$
$101$	−1.94029	−	14.7380i	−0.193066	−	1.46648i	0.570789	−	0.821097i	$-0.306637\pi$
$102$	20.0205	−	3.14250i	1.98232	−	0.311154i
$103$	6.26364	−	1.67834i	0.617175	−	0.165372i	0.0633318	−	0.997993i	$-0.479827\pi$
$103$	6.26364	−	1.67834i	0.617175	−	0.165372i	0.553843	+	0.832621i	$0.313161\pi$
$104$	−1.60116	−	0.527617i	−0.157007	−	0.0517371i
$105$	−0.285542	−	9.33789i	−0.0278660	−	0.911284i
$106$	−3.98174	−	8.97659i	−0.386741	−	0.871884i
$107$	1.46810	+	1.91327i	0.141927	+	0.184963i	0.858908	−	0.512130i	$-0.171143\pi$
$107$	1.46810	+	1.91327i	0.141927	+	0.184963i	−0.716981	+	0.697093i	$0.754477\pi$
$108$	5.68570	−	1.03749i	0.547107	−	0.0998326i
$109$	1.07390	+	0.824034i	0.102861	+	0.0789282i	0.658912	−	0.752220i	$-0.271017\pi$
$109$	1.07390	+	0.824034i	0.102861	+	0.0789282i	−0.556050	+	0.831149i	$0.687684\pi$
$110$	2.81837	+	1.53531i	0.268721	+	0.146386i
$111$		−	16.2276i		−	1.54026i
$112$	4.06122	−	9.77274i	0.383749	−	0.923437i
$113$		−	9.70571i		−	0.913036i	−0.889714	−	0.456518i	$-0.849096\pi$
$113$		−	9.70571i		−	0.913036i	0.889714	−	0.456518i	$-0.150904\pi$
$114$	9.02964	−	16.5757i	0.845703	−	1.55246i
$115$	5.50813	+	4.22653i	0.513635	+	0.394126i
$116$	16.6770	+	11.5300i	1.54842	+	1.07053i
$117$	1.48245	+	1.93196i	0.137052	+	0.178610i
$118$	−0.280787	+	0.124548i	−0.0258485	+	0.0114656i
$119$	−12.1115	+	7.49523i	−1.11026	+	0.687087i
$120$	6.51774	−	7.56736i	0.594985	−	0.690802i
$121$	−7.79808	+	2.08949i	−0.708917	+	0.189954i
$122$	−0.897123	−	5.71546i	−0.0812217	−	0.517453i
$123$	−1.32931	−	10.0971i	−0.119860	−	0.910423i
$124$	−5.12375	−	2.62859i	−0.460126	−	0.236055i
$125$	4.18310	+	10.0989i	0.374148	+	0.903274i
$126$	−12.7957	+	8.36436i	−1.13993	+	0.745156i
$127$	−15.3584			−1.36283			−0.681417	−	0.731895i	$-0.738636\pi$
$127$	−15.3584			−1.36283			−0.681417	+	0.731895i	$0.738636\pi$
$128$	10.2584	−	4.77140i	0.906719	−	0.421736i
$129$	−3.82801	−	6.63031i	−0.337038	−	0.583766i
$130$	1.08690	+	0.262535i	0.0953273	+	0.0230258i
$131$	−13.2843	−	1.74892i	−1.16066	−	0.152804i	−0.474500	−	0.880256i	$-0.657371\pi$
$131$	−13.2843	−	1.74892i	−1.16066	−	0.152804i	−0.686158	+	0.727452i	$0.740704\pi$
$132$	−0.451461	−	9.09669i	−0.0392946	−	0.791766i
$133$	−1.32877	+	13.1995i	−0.115219	+	1.14454i
$134$	18.2332	+	7.02808i	1.57511	+	0.607133i
$135$	−3.70274	+	0.992147i	−0.318681	+	0.0853904i
$136$	−14.9599	−	2.83703i	−1.28280	−	0.243273i
$137$	7.49981	+	2.00957i	0.640752	+	0.171689i	0.564544	−	0.825403i	$-0.309052\pi$
$137$	7.49981	+	2.00957i	0.640752	+	0.171689i	0.0762081	+	0.997092i	$0.475719\pi$
$138$	2.08665	−	19.5920i	0.177628	−	1.66778i
$139$	0.525559	−	1.26881i	0.0445774	−	0.107619i	−0.900023	−	0.435843i	$-0.856450\pi$
$139$	0.525559	−	1.26881i	0.0445774	−	0.107619i	0.944600	+	0.328224i	$0.106450\pi$
$140$	−2.15827	+	6.67923i	−0.182407	+	0.564498i
$141$	−23.8026	+	9.85936i	−2.00454	+	0.830308i
$142$	6.13755	−	11.2667i	0.515052	−	0.945481i
$143$	0.883087	−	0.509851i	0.0738474	−	0.0426358i
$144$	−16.1269	−	2.64596i	−1.34390	−	0.220496i
$145$	−11.6458	−	6.72368i	−0.967127	−	0.558371i
$146$	0.348847	+	14.0668i	0.0288708	+	1.16418i
$147$	10.4187	−	15.4481i	0.859323	−	1.27414i
$148$	−4.10180	+	11.4819i	−0.337166	+	0.943807i
$149$	−5.81887	−	7.58329i	−0.476700	−	0.621248i	0.491665	−	0.870784i	$-0.336388\pi$
$149$	−5.81887	−	7.58329i	−0.476700	−	0.621248i	−0.968365	+	0.249537i	$0.919722\pi$
$150$	7.18358	−	9.85860i	0.586537	−	0.804951i
$151$	10.0907	+	2.70380i	0.821172	+	0.220032i	0.644859	−	0.764302i	$-0.276916\pi$
$151$	10.0907	+	2.70380i	0.821172	+	0.220032i	0.176313	+	0.984334i	$0.443583\pi$
$152$	−10.5787	+	9.44581i	−0.858050	+	0.766157i
$153$	15.5524	+	15.5524i	1.25734	+	1.25734i
$154$	2.77314	+	5.76935i	0.223466	+	0.464907i
$155$	3.52875	+	1.46166i	0.283436	+	0.117403i
$156$	−0.972195	−	3.02057i	−0.0778379	−	0.241839i
$157$	−8.51876	+	11.1019i	−0.679871	+	0.886026i	−0.998076	−	0.0619963i	$-0.980253\pi$
$157$	−8.51876	+	11.1019i	−0.679871	+	0.886026i	0.318205	+	0.948022i	$0.396920\pi$
$158$	1.55593	−	6.44159i	0.123783	−	0.512465i
$159$	9.24183	−	16.0073i	0.732925	−	1.26946i
$160$	−6.52443	+	3.70685i	−0.515802	+	0.293052i
$161$	3.99116	+	13.2599i	0.314547	+	1.04503i
$162$	−4.67634	−	4.45001i	−0.367408	−	0.349626i
$163$	19.8763	+	2.61676i	1.55683	+	0.204961i	0.859254	−	0.511549i	$-0.170928\pi$
$163$	19.8763	+	2.61676i	1.55683	+	0.204961i	0.697577	+	0.716510i	$0.254262\pi$
$164$	−1.61165	+	7.48024i	−0.125849	+	0.584108i
$165$	0.788495	+	5.98921i	0.0613843	+	0.466260i
$166$	−8.76923	−	10.8598i	−0.680624	−	0.842887i
$167$	−6.01405	−	6.01405i	−0.465381	−	0.465381i	0.435033	−	0.900414i	$-0.356737\pi$
$167$	−6.01405	−	6.01405i	−0.465381	−	0.465381i	−0.900414	+	0.435033i	$0.856737\pi$
$168$	19.3682	−	4.65466i	1.49429	−	0.359115i
$169$	−8.94118	+	8.94118i	−0.687783	+	0.687783i
$170$	10.0423	+	1.06956i	0.770212	+	0.0820318i
$171$	20.3106	−	2.67395i	1.55319	−	0.204482i
$172$	1.03260	+	5.65890i	0.0787350	+	0.431487i
$173$	−0.741181	+	5.62983i	−0.0563510	+	0.428028i	0.939895	+	0.341463i	$0.110922\pi$
$173$	−0.741181	+	5.62983i	−0.0563510	+	0.428028i	−0.996246	+	0.0865651i	$0.972411\pi$
$174$	0.946091	+	38.1499i	0.0717230	+	2.89214i
$175$	−1.96475	+	8.34498i	−0.148521	+	0.630821i
$176$	−1.97991	+	6.55052i	−0.149241	+	0.493764i
$177$	−0.500707	−	0.289083i	−0.0376354	−	0.0217288i
$178$	12.3017	+	20.1372i	0.922054	+	1.50935i
$179$	4.22574	+	3.24253i	0.315847	+	0.242358i	0.754502	−	0.656298i	$-0.227878\pi$
$179$	4.22574	+	3.24253i	0.315847	+	0.242358i	−0.438655	+	0.898655i	$0.644545\pi$
$180$	10.8035	+	0.880387i	0.805245	+	0.0656202i
$181$	0.166639	−	0.402302i	0.0123862	−	0.0299029i	−0.917565	−	0.397585i	$-0.869848\pi$
$181$	0.166639	−	0.402302i	0.0123862	−	0.0299029i	0.929952	+	0.367682i	$0.119848\pi$
$182$	1.45347	+	1.69148i	0.107738	+	0.125381i
$183$	7.70008	−	7.70008i	0.569206	−	0.569206i
$184$	−6.42863	+	13.3349i	−0.473925	+	0.983065i
$185$	2.09303	−	7.81129i	0.153883	−	0.574298i
$186$	−1.68078	−	10.7081i	−0.123241	−	0.785154i
$187$	7.30670	−	5.60662i	0.534319	−	0.409997i
$188$	19.3337	−	0.959516i	1.41006	−	0.0699799i
$189$	−7.14980	−	2.70860i	−0.520072	−	0.197022i
$190$	6.48442	−	6.81422i	0.470429	−	0.494355i
$191$	−2.23881	+	3.87774i	−0.161995	+	0.280583i	−0.935584	−	0.353104i	$-0.885126\pi$
$191$	−2.23881	+	3.87774i	−0.161995	+	0.280583i	0.773589	+	0.633687i	$0.218459\pi$
$192$	18.6293	+	10.3164i	1.34446	+	0.744520i
$193$	−11.3376	−	19.6373i	−0.816098	−	1.41352i	−0.908537	−	0.417805i	$-0.862800\pi$
$193$	−11.3376	−	19.6373i	−0.816098	−	1.41352i	0.0924389	−	0.995718i	$-0.470534\pi$
$194$	3.71328	+	12.5999i	0.266598	+	0.904620i
$195$	0.805408	+	1.94443i	0.0576765	+	0.139243i
$196$	−11.2766	+	8.29688i	−0.805471	+	0.592635i
$197$	−9.07205	−	3.75777i	−0.646357	−	0.267730i	0.0353278	−	0.999376i	$-0.488752\pi$
$197$	−9.07205	−	3.75777i	−0.646357	−	0.267730i	−0.681685	+	0.731646i	$0.738752\pi$
$198$	7.69061	−	6.21011i	0.546548	−	0.441333i
$199$	1.01507	−	3.78831i	0.0719567	−	0.268546i	−0.920569	−	0.390579i	$-0.872275\pi$
$199$	1.01507	−	3.78831i	0.0719567	−	0.268546i	0.992526	+	0.122033i	$0.0389414\pi$
$200$	−7.57470	+	5.15972i	−0.535612	+	0.364847i
$201$	9.51947	+	35.5272i	0.671452	+	2.50589i
$202$	−19.2168	+	8.52400i	−1.35209	+	0.599747i
$203$	−11.0165	−	24.4539i	−0.773204	−	1.71633i
$204$	−12.2667	−	25.9021i	−0.858838	−	1.81351i
$205$	0.662445	−	5.03177i	0.0462672	−	0.351434i
$206$	−4.78079	−	7.82586i	−0.333093	−	0.545254i
$207$	18.5188	−	10.6918i	1.28714	−	0.743133i
$208$	−0.0756195	+	2.38295i	−0.00524327	+	0.165228i
$209$		−	8.57819i		−	0.593366i
$210$	−12.5530	+	4.12044i	−0.866238	+	0.284337i
$211$	20.7378	−	8.58990i	1.42765	−	0.591353i	0.470882	−	0.882196i	$-0.343936\pi$
$211$	20.7378	−	8.58990i	1.42765	−	0.591353i	0.956771	+	0.290843i	$0.0939359\pi$
$212$	−10.5852	+	8.99001i	−0.726995	+	0.617436i
$213$	23.9424	−	3.15208i	1.64051	−	0.215977i
$214$	2.00849	−	2.75642i	0.137298	−	0.188425i
$215$	−0.987470	−	3.68529i	−0.0673449	−	0.251335i
$216$	−3.68041	−	7.29806i	−0.250420	−	0.496570i
$217$	4.00887	+	6.47789i	0.272140	+	0.439748i
$218$	0.688505	−	1.78621i	0.0466314	−	0.120978i
$219$	−21.0121	+	16.1232i	−1.41987	+	1.08950i
$220$	0.955973	−	4.43700i	0.0644517	−	0.299142i
$221$	1.95333	−	2.54564i	0.131395	−	0.171238i
$222$	−22.0132	+	6.48745i	−1.47743	+	0.435409i
$223$	16.6980			1.11818			0.559091	−	0.829106i	$-0.311150\pi$
$223$	16.6980			1.11818			0.559091	+	0.829106i	$0.311150\pi$
$224$	−14.8806	−	1.60223i	−0.994253	−	0.107054i
$225$	13.2388			0.882588
$226$	−13.1661	+	3.88014i	−0.875796	+	0.258103i
$227$	−1.78212	+	2.32250i	−0.118284	+	0.154150i	−0.848742	−	0.528807i	$-0.822640\pi$
$227$	−1.78212	+	2.32250i	−0.118284	+	0.154150i	0.730459	+	0.682957i	$0.239306\pi$
$228$	−26.0953	−	5.62237i	−1.72821	−	0.372350i
$229$	12.9898	−	9.96740i	0.858388	−	0.658664i	−0.0827933	−	0.996567i	$-0.526384\pi$
$229$	12.9898	−	9.96740i	0.858388	−	0.658664i	0.941181	+	0.337903i	$0.109717\pi$
$230$	3.53139	−	9.16162i	0.232853	−	0.604100i
$231$	−5.70257	+	10.6137i	−0.375201	+	0.698327i
$232$	8.97363	−	27.2323i	0.589148	−	1.78789i
$233$	2.69076	+	10.0420i	0.176277	+	0.657876i	0.996331	+	0.0855886i	$0.0272771\pi$
$233$	2.69076	+	10.0420i	0.176277	+	0.657876i	−0.820053	+	0.572287i	$0.806056\pi$
$234$	2.02812	−	2.78334i	0.132582	−	0.181953i
$235$	−12.7292	+	1.67584i	−0.830364	+	0.109319i
$236$	0.281206	+	0.331104i	0.0183050	+	0.0215530i
$237$	11.5238	−	4.77331i	0.748551	−	0.310060i
$238$	15.0094	+	13.4331i	0.972916	+	0.870741i
$239$		−	1.67622i		−	0.108426i	−0.998529	−	0.0542128i	$-0.982735\pi$
$239$		−	1.67622i		−	0.108426i	0.998529	−	0.0542128i	$-0.0172649\pi$
$240$	−12.8710	−	5.81624i	−0.830820	−	0.375437i
$241$	6.58959	−	3.80450i	0.424473	−	0.245070i	−0.272516	−	0.962151i	$-0.587856\pi$
$241$	6.58959	−	3.80450i	0.424473	−	0.245070i	0.696989	+	0.717082i	$0.254523\pi$
$242$	5.95197	+	9.74301i	0.382607	+	0.626304i
$243$	2.71752	−	20.6416i	0.174329	−	1.32416i
$244$	−7.39455	+	3.50189i	−0.473387	+	0.224186i
$245$	7.00764	−	6.09229i	0.447702	−	0.389222i
$246$	−13.1656	+	5.83985i	−0.839407	+	0.372335i
$247$	−0.773512	−	2.88679i	−0.0492174	−	0.183682i
$248$	−1.51740	+	8.00138i	−0.0963551	+	0.508088i
$249$	6.79993	−	25.3777i	0.430928	−	1.60824i
$250$	12.0272	−	9.71184i	0.760665	−	0.614231i
$251$	−28.1259	−	11.6501i	−1.77529	−	0.735350i	−0.993767	−	0.111474i	$-0.964443\pi$
$251$	−28.1259	−	11.6501i	−1.77529	−	0.735350i	−0.781524	−	0.623876i	$-0.785557\pi$
$252$	16.4620	+	14.0138i	1.03701	+	0.882789i
$253$	−3.42659	−	8.27252i	−0.215428	−	0.520089i
$254$	6.13995	+	20.8341i	0.385255	+	1.30725i
$255$	9.50447	+	16.4622i	0.595193	+	1.03090i
$256$	−10.5736	−	12.0083i	−0.660851	−	0.750517i
$257$	−7.21889	+	12.5035i	−0.450302	+	0.779946i	−0.998405	−	0.0564650i	$-0.982017\pi$
$257$	−7.21889	+	12.5035i	−0.450302	+	0.779946i	0.548102	+	0.836411i	$0.315350\pi$
$258$	−7.46386	+	7.84347i	−0.464680	+	0.488313i
$259$	12.4901	−	10.2054i	0.776098	−	0.634132i
$260$	−0.0783826	−	1.57937i	−0.00486108	−	0.0979483i
$261$	−32.8585	+	25.2132i	−2.03389	+	1.56066i
$262$	2.93834	+	18.7198i	0.181531	+	1.15651i
$263$	−3.07789	+	11.4868i	−0.189791	+	0.708309i	0.803763	+	0.594949i	$0.202828\pi$
$263$	−3.07789	+	11.4868i	−0.189791	+	0.708309i	−0.993554	+	0.113360i	$0.963839\pi$
$264$	−12.1595	+	4.24909i	−0.748363	+	0.261513i
$265$	6.51325	−	6.51325i	0.400106	−	0.400106i
$266$	18.4367	−	3.47435i	1.13043	−	0.213026i
$267$	−16.9972	+	41.0350i	−1.04021	+	2.51130i
$268$	2.24455	−	27.5436i	0.137108	−	1.68249i
$269$	5.35148	+	4.10634i	0.326286	+	0.250368i	0.758894	−	0.651214i	$-0.225740\pi$
$269$	5.35148	+	4.10634i	0.326286	+	0.250368i	−0.432608	+	0.901582i	$0.642407\pi$
$270$	2.82616	+	4.62625i	0.171994	+	0.281544i
$271$	23.2482	+	13.4224i	1.41223	+	0.815351i	0.995598	−	0.0937244i	$-0.0298773\pi$
$271$	23.2482	+	13.4224i	1.41223	+	0.815351i	0.416631	+	0.909076i	$0.363211\pi$
$272$	2.13213	+	21.4277i	0.129279	+	1.29925i
$273$	−0.962009	+	4.08598i	−0.0582234	+	0.247295i
$274$	−0.272224	−	10.9771i	−0.0164457	−	0.663152i
$275$	0.723582	−	5.49615i	0.0436337	−	0.331431i
$276$	−27.4113	+	5.00185i	−1.64997	+	0.301076i
$277$	−11.1523	+	1.46823i	−0.670077	+	0.0882173i	−0.457886	−	0.889011i	$-0.651393\pi$
$277$	−11.1523	+	1.46823i	−0.670077	+	0.0882173i	−0.212191	+	0.977228i	$0.568060\pi$
$278$	−1.93129	−	0.205693i	−0.115831	−	0.0123367i
$279$	8.31831	−	8.31831i	0.498004	−	0.498004i
$280$	9.92342	+	0.257549i	0.593038	+	0.0153915i
$281$	13.0894	+	13.0894i	0.780849	+	0.780849i	0.979974	−	0.199125i	$-0.0638100\pi$
$281$	13.0894	+	13.0894i	0.780849	+	0.780849i	−0.199125	+	0.979974i	$0.563810\pi$
$282$	22.8903	+	28.3474i	1.36310	+	1.68806i
$283$	−1.17342	−	8.91302i	−0.0697526	−	0.529824i	−0.990274	−	0.139131i	$-0.955569\pi$
$283$	−1.17342	−	8.91302i	−0.0697526	−	0.529824i	0.920521	−	0.390692i	$-0.127764\pi$
$284$	−17.7373	−	3.82159i	−1.05251	−	0.226770i
$285$	17.5537	+	2.31099i	1.03979	+	0.136891i
$286$	−1.04467	−	0.994108i	−0.0617725	−	0.0587828i
$287$	6.93557	−	7.37311i	0.409394	−	0.435221i
$288$	2.85785	+	22.9344i	0.168401	+	1.35142i
$289$	5.99042	−	10.3757i	0.352378	−	0.610336i
$290$	−4.46515	+	18.4858i	−0.262203	+	1.08552i
$291$	−15.0513	+	19.6152i	−0.882321	+	1.14986i
$292$	18.9426	−	6.09684i	1.10853	−	0.356791i
$293$	−7.53848	−	3.12254i	−0.440403	−	0.182421i	0.151453	−	0.988464i	$-0.451605\pi$
$293$	−7.53848	−	3.12254i	−0.440403	−	0.182421i	−0.591856	+	0.806044i	$0.701605\pi$
$294$	−25.1211	−	7.95750i	−1.46509	−	0.464091i
$295$	−0.203734	−	0.203734i	−0.0118618	−	0.0118618i
$296$	17.2154	+	0.974000i	1.00062	+	0.0566126i
$297$	4.77539	+	1.27956i	0.277096	+	0.0742477i
$298$	−7.96071	+	10.9251i	−0.461152	+	0.632875i
$299$	−1.89909	−	2.47494i	−0.109827	−	0.143129i
$300$	−16.2453	−	5.80350i	−0.937925	−	0.335065i
$301$	2.69584	−	7.11610i	0.155385	−	0.410165i
$302$	−0.366268	−	14.7693i	−0.0210764	−	0.849878i
$303$	−34.2680	−	19.7847i	−1.96865	−	1.13660i
$304$	17.0427	+	10.5742i	0.977466	+	0.606470i
$305$	4.69965	−	2.71334i	0.269101	−	0.155366i
$306$	14.8798	−	27.3149i	0.850623	−	1.56149i
$307$	−23.7853	+	9.85221i	−1.35750	+	0.562295i	−0.938370	−	0.345631i	$-0.887665\pi$
$307$	−23.7853	+	9.85221i	−1.35750	+	0.562295i	−0.419130	+	0.907926i	$0.637665\pi$
$308$	6.71765	−	6.06831i	0.382774	−	0.345774i
$309$	6.60559	−	15.9473i	0.375779	−	0.907211i
$310$	0.572063	−	5.37120i	0.0324910	−	0.305064i
$311$	−23.0690	−	6.18132i	−1.30812	−	0.350510i	−0.463607	−	0.886041i	$-0.653445\pi$
$311$	−23.0690	−	6.18132i	−1.30812	−	0.350510i	−0.844516	+	0.535531i	$0.820112\pi$
$312$	−3.70883	+	2.52637i	−0.209971	+	0.143028i
$313$	−12.7761	+	3.42336i	−0.722151	+	0.193500i	−0.601131	−	0.799150i	$-0.705283\pi$
$313$	−12.7761	+	3.42336i	−0.722151	+	0.193500i	−0.121020	+	0.992650i	$0.538616\pi$
$314$	18.4657	+	7.11768i	1.04208	+	0.401674i
$315$	−11.6374	−	8.37728i	−0.655694	−	0.472006i
$316$	−9.36024	+	0.464540i	−0.526555	+	0.0261324i
$317$	29.9430	+	3.94206i	1.68176	+	0.221408i	0.910031	−	0.414539i	$-0.136057\pi$
$317$	29.9430	+	3.94206i	1.68176	+	0.221408i	0.771732	+	0.635948i	$0.219391\pi$
$318$	−25.4091	−	6.13744i	−1.42487	−	0.344171i
$319$	8.67146	+	15.0194i	0.485508	+	0.840925i
$320$	7.63678	+	7.36867i	0.426909	+	0.411921i
$321$	6.41947			0.358300
$322$	16.3919	−	10.7152i	0.913485	−	0.597132i
$323$	−10.3298	−	24.9384i	−0.574766	−	1.38761i
$324$	−4.16707	+	8.12261i	−0.231504	+	0.451256i
$325$	−0.252094	−	1.91485i	−0.0139837	−	0.106217i
$326$	−4.39640	−	28.0089i	−0.243494	−	1.55127i
$327$	3.48041	−	0.932574i	0.192467	−	0.0515715i
$328$	10.7915	−	0.804182i	0.595860	−	0.0444035i
$329$	−22.5578	−	12.1200i	−1.24365	−	0.668197i
$330$	7.80933	−	3.46398i	0.429890	−	0.190686i
$331$	−9.77869	−	12.7438i	−0.537485	−	0.700464i	0.443119	−	0.896463i	$-0.353872\pi$
$331$	−9.77869	−	12.7438i	−0.537485	−	0.700464i	−0.980604	+	0.195998i	$0.937205\pi$
$332$	−11.2260	+	16.2373i	−0.616104	+	0.891136i
$333$	−19.7601	−	15.1625i	−1.08285	−	0.830899i
$334$	−5.75396	+	10.5625i	−0.314843	+	0.577957i
$335$			18.3291i			1.00143i
$336$	−14.0572	−	24.4128i	−0.766883	−	1.33183i
$337$		−	12.3378i		−	0.672081i	−0.941848	−	0.336041i	$-0.890912\pi$
$337$		−	12.3378i		−	0.672081i	0.941848	−	0.336041i	$-0.109088\pi$
$338$	15.7035	+	8.55449i	0.854157	+	0.465303i
$339$	−20.4966	−	15.7276i	−1.11323	−	0.854208i
$340$	−2.56382	−	14.0503i	−0.139043	−	0.761986i
$341$	−2.99874	−	3.90803i	−0.162391	−	0.211632i
$342$	−11.7471	−	26.4830i	−0.635208	−	1.43204i
$343$	18.4424	−	1.69608i	0.995798	−	0.0915794i
$344$	7.26366	−	3.66306i	0.391630	−	0.197499i
$345$	17.8513	−	4.78324i	0.961082	−	0.257521i
$346$	7.93335	−	1.24525i	0.426499	−	0.0669452i
$347$	0.350030	+	2.65874i	0.0187906	+	0.142729i	0.998268	−	0.0588232i	$-0.0187348\pi$
$347$	0.350030	+	2.65874i	0.0187906	+	0.142729i	−0.979478	+	0.201552i	$0.935402\pi$
$348$	51.3733	−	16.5349i	2.75390	−	0.886366i
$349$	−7.04548	−	17.0093i	−0.377136	−	0.910487i	−0.992500	−	0.122244i	$-0.960991\pi$
$349$	−7.04548	−	17.0093i	−0.377136	−	0.910487i	0.615364	−	0.788243i	$-0.289009\pi$
$350$	12.1057	−	0.670899i	0.647076	−	0.0358611i
$351$	1.72242			0.0919362
$352$	9.67751	+	0.0670535i	0.515813	+	0.00357396i
$353$	−7.72069	−	13.3726i	−0.410931	−	0.711753i	0.584061	−	0.811710i	$-0.301463\pi$
$353$	−7.72069	−	13.3726i	−0.410931	−	0.711753i	−0.994992	+	0.0999565i	$0.968130\pi$
$354$	−0.191978	+	0.794794i	−0.0102035	+	0.0422428i
$355$	11.9314	+	1.57080i	0.633255	+	0.0833696i
$356$	22.3988	−	24.7381i	1.18713	−	1.31112i
$357$	−3.79749	+	37.7228i	−0.200985	+	1.99650i
$358$	2.70923	−	7.02865i	0.143187	−	0.371476i
$359$	0.280573	−	0.0751793i	0.0148081	−	0.00396781i	−0.251407	−	0.967881i	$-0.580893\pi$
$359$	0.280573	−	0.0751793i	0.0148081	−	0.00396781i	0.266215	+	0.963914i	$0.414227\pi$
$360$	−3.12474	−	15.0072i	−0.164688	−	0.790951i
$361$	−5.93239	−	1.58958i	−0.312231	−	0.0836621i
$362$	−0.612354	−	0.0652190i	−0.0321846	−	0.00342784i
$363$	−8.22380	+	19.8540i	−0.431638	+	1.04207i
$364$	1.71348	−	2.64789i	0.0898105	−	0.138787i
$365$	−12.1939	+	5.05089i	−0.638259	+	0.264376i
$366$	−13.5237	−	7.36707i	−0.706896	−	0.385083i
$367$	21.4497	−	12.3840i	1.11966	−	0.646438i	0.178348	−	0.983968i	$-0.442925\pi$
$367$	21.4497	−	12.3840i	1.11966	−	0.646438i	0.941315	+	0.337530i	$0.109591\pi$
$368$	20.6593	+	3.38960i	1.07694	+	0.176695i
$369$	−13.5371	−	7.81567i	−0.704715	−	0.406868i
$370$	−11.4330	+	0.283530i	−0.594374	+	0.0147400i
$371$	18.1327	−	2.95358i	0.941401	−	0.153342i
$372$	−13.8539	+	6.56090i	−0.718291	+	0.340167i
$373$	−1.37170	−	1.78763i	−0.0710240	−	0.0925602i	0.756490	−	0.654005i	$-0.226912\pi$
$373$	−1.37170	−	1.78763i	−0.0710240	−	0.0925602i	−0.827514	+	0.561445i	$0.810246\pi$
$374$	−10.5266	−	7.67035i	−0.544319	−	0.396624i
$375$	28.1055	+	7.53085i	1.45136	+	0.388892i
$376$	−9.03084	−	25.8432i	−0.465730	−	1.33276i
$377$	4.27250	+	4.27250i	0.220045	+	0.220045i
$378$	−0.815966	+	10.7818i	−0.0419688	+	0.554555i
$379$	11.1490	+	4.61806i	0.572685	+	0.237214i	0.650182	−	0.759779i	$-0.274693\pi$
$379$	11.1490	+	4.61806i	0.572685	+	0.237214i	−0.0774966	+	0.996993i	$0.524693\pi$
$380$	−11.8360	−	6.07214i	−0.607176	−	0.311494i
$381$	−24.8875	+	32.4340i	−1.27502	+	1.66164i
$382$	6.15530	+	1.48678i	0.314932	+	0.0760703i
$383$	−14.4746	+	25.0707i	−0.739616	+	1.28105i	0.213052	+	0.977041i	$0.431660\pi$
$383$	−14.4746	+	25.0707i	−0.739616	+	1.28105i	−0.952668	+	0.304012i	$0.901674\pi$
$384$	6.54686	−	29.3955i	0.334093	−	1.50008i
$385$	−4.11392	+	4.37346i	−0.209665	+	0.222892i
$386$	−22.1061	+	23.2304i	−1.12517	+	1.18240i
$387$	−11.6504	−	1.53380i	−0.592223	−	0.0779676i
$388$	15.6077	−	10.0743i	0.792359	−	0.511448i
$389$	−0.794882	−	6.03773i	−0.0403021	−	0.306125i	−0.999710	−	0.0241012i	$-0.992328\pi$
$389$	−0.794882	−	6.03773i	−0.0403021	−	0.306125i	0.959407	−	0.282024i	$-0.0910057\pi$
$390$	2.31569	−	1.86990i	0.117260	−	0.0946862i
$391$	−19.9234	−	19.9234i	−1.00757	−	1.00757i
$392$	15.7631	+	11.9801i	0.796158	+	0.605088i
$393$	−25.2200	+	25.2200i	−1.27218	+	1.27218i
$394$	−1.47071	+	13.8088i	−0.0740934	+	0.695677i
$395$	6.16274	−	0.811340i	0.310081	−	0.0408229i
$396$	−11.4988	−	7.94989i	−0.577834	−	0.399497i
$397$	2.87380	−	21.8287i	0.144232	−	1.09555i	−0.754265	−	0.656570i	$-0.772006\pi$
$397$	2.87380	−	21.8287i	0.144232	−	1.09555i	0.898497	−	0.438980i	$-0.144660\pi$
$398$	−5.54477	+	0.137506i	−0.277934	+	0.00689256i
$399$	25.7216	+	24.1952i	1.28769	+	1.21128i
$400$	10.0275	+	8.21257i	0.501376	+	0.410629i
$401$	24.3241	+	14.0435i	1.21469	+	0.701300i	0.963777	−	0.266710i	$-0.0859366\pi$
$401$	24.3241	+	14.0435i	1.21469	+	0.701300i	0.250911	+	0.968010i	$0.419270\pi$
$402$	44.3880	−	27.1165i	2.21387	−	1.35245i
$403$	−1.36155	−	1.04475i	−0.0678236	−	0.0520429i
$404$	19.2456	+	22.6605i	0.957503	+	1.12740i
$405$	2.31715	−	5.59409i	0.115140	−	0.277972i
$406$	−28.7684	+	24.7203i	−1.42775	+	1.22685i
$407$	−7.37478	+	7.37478i	−0.365555	+	0.365555i
$408$	−30.2330	+	26.9952i	−1.49676	+	1.33646i
$409$	−4.34197	+	16.2044i	−0.214697	+	0.801258i	0.771577	+	0.636136i	$0.219468\pi$
$409$	−4.34197	+	16.2044i	−0.214697	+	0.801258i	−0.986273	+	0.165122i	$0.947198\pi$
$410$	−7.09058	+	1.11297i	−0.350179	+	0.0549656i
$411$	16.3969	−	12.5818i	0.808800	−	0.620614i
$412$	−8.70477	+	9.61390i	−0.428853	+	0.473643i
$413$	−0.0923875	−	0.567188i	−0.00454609	−	0.0279095i
$414$	−21.9072	−	20.8469i	−1.07668	−	1.02457i
$415$	6.54640	−	11.3387i	0.321350	−	0.556595i
$416$	3.26278	−	0.850074i	0.159971	−	0.0416783i
$417$	−1.82785	−	3.16593i	−0.0895103	−	0.155036i
$418$	−11.6366	+	3.42938i	−0.569164	+	0.167737i
$419$	9.28172	+	22.4081i	0.453442	+	1.09471i	0.971005	+	0.239060i	$0.0768393\pi$
$419$	9.28172	+	22.4081i	0.453442	+	1.09471i	−0.517563	+	0.855645i	$0.673161\pi$
$420$	10.6079	+	15.3812i	0.517613	+	0.750528i
$421$	12.3542	+	5.11727i	0.602106	+	0.249400i	0.662849	−	0.748753i	$-0.269347\pi$
$421$	12.3542	+	5.11727i	0.602106	+	0.249400i	−0.0607433	+	0.998153i	$0.519347\pi$
$422$	−19.9430	−	24.6975i	−0.970811	−	1.20225i
$423$	−10.2347	+	38.1964i	−0.497627	+	1.85717i
$424$	16.4270	+	10.7652i	0.797764	+	0.522802i
$425$	−4.51485	−	16.8496i	−0.219002	−	0.817328i
$426$	−13.8476	−	31.2185i	−0.670917	−	1.51254i
$427$	10.7691	+	1.08411i	0.521155	+	0.0524638i
$428$	−4.54212	−	1.62263i	−0.219552	−	0.0784327i
$429$	0.354290	−	2.69110i	0.0171053	−	0.129928i
$430$	−4.60444	+	2.81283i	−0.222046	+	0.135647i
$431$	−8.96739	+	5.17733i	−0.431944	+	0.249383i	−0.700175	−	0.713972i	$-0.746894\pi$
$431$	−8.96739	+	5.17733i	−0.431944	+	0.249383i	0.268230	+	0.963355i	$0.413561\pi$
$432$	−8.42869	+	7.91020i	−0.405526	+	0.380580i
$433$			18.5114i			0.889599i	0.895630	+	0.444800i	$0.146725\pi$
$433$			18.5114i			0.889599i	−0.895630	+	0.444800i	$0.853275\pi$
$434$	7.18479	−	8.02788i	0.344881	−	0.385351i
$435$	−33.0705	+	13.6983i	−1.58561	+	0.656781i
$436$	−2.69830	−	0.219887i	−0.129225	−	0.0105307i
$437$	−26.0189	+	3.42546i	−1.24465	+	0.163862i
$438$	30.2718	+	22.0579i	1.44644	+	1.05397i
$439$	5.08206	+	18.9665i	0.242554	+	0.905222i	0.974597	+	0.223965i	$0.0719000\pi$
$439$	5.08206	+	18.9665i	0.242554	+	0.905222i	−0.732044	+	0.681258i	$0.761433\pi$
$440$	−6.40110	+	0.477011i	−0.305161	+	0.0227406i
$441$	−9.07611	−	27.1210i	−0.432196	−	1.29147i
$442$	−4.23414	−	1.63207i	−0.201397	−	0.0776295i
$443$	23.7835	−	18.2498i	1.12999	−	0.867072i	0.137635	−	0.990483i	$-0.456050\pi$
$443$	23.7835	−	18.2498i	1.12999	−	0.867072i	0.992356	+	0.123411i	$0.0393834\pi$
$444$	17.6009	+	27.2681i	0.835300	+	1.29409i
$445$	−13.4744	+	17.5602i	−0.638749	+	0.832434i
$446$	−6.67552	−	22.6514i	−0.316095	−	1.07257i
$447$	−25.4437			−1.20345
$448$	3.77548	+	20.8266i	0.178375	+	0.983963i
$449$	27.2364			1.28536			0.642682	−	0.766133i	$-0.277822\pi$
$449$	27.2364			1.28536			0.642682	+	0.766133i	$0.277822\pi$
$450$	−5.29260	−	17.9589i	−0.249496	−	0.846589i
$451$	−3.98460	+	5.19283i	−0.187627	+	0.244521i
$452$	10.5271	+	16.3090i	0.495151	+	0.767112i
$453$	22.0615	−	16.9284i	1.03654	−	0.795363i
$454$	3.86300	+	1.48901i	0.181300	+	0.0698829i
$455$	−0.990080	+	1.84274i	−0.0464156	+	0.0863891i
$456$	2.80544	+	37.6468i	0.131377	+	1.76297i
$457$	−4.47114	−	16.6865i	−0.209151	−	0.780562i	−0.988144	−	0.153529i	$-0.950936\pi$
$457$	−4.47114	−	16.6865i	−0.209151	−	0.780562i	0.778993	−	0.627032i	$-0.215731\pi$
$458$	−18.7141	−	13.6363i	−0.874453	−	0.637181i
$459$	15.4238	−	2.03058i	0.719920	−	0.0947792i
$460$	−13.8398	−	1.12782i	−0.645284	−	0.0525848i
$461$	8.36744	−	3.46591i	0.389711	−	0.161423i	−0.179220	−	0.983809i	$-0.557357\pi$
$461$	8.36744	−	3.46591i	0.389711	−	0.161423i	0.568931	+	0.822386i	$0.307357\pi$
$462$	16.6775	+	3.49259i	0.775908	+	0.162490i
$463$		−	11.8044i		−	0.548599i	−0.961644	−	0.274299i	$-0.911554\pi$
$463$		−	11.8044i		−	0.548599i	0.961644	−	0.274299i	$-0.0884459\pi$
$464$	−40.5289	−	1.28613i	−1.88151	−	0.0597069i
$465$	8.80492	−	5.08352i	0.408319	−	0.235743i
$466$	12.5466	−	7.66469i	0.581211	−	0.355060i
$467$	1.79383	−	13.6255i	0.0830086	−	0.630513i	−0.898483	−	0.439008i	$-0.855330\pi$
$467$	1.79383	−	13.6255i	0.0830086	−	0.630513i	0.981492	−	0.191505i	$-0.0613368\pi$
$468$	−4.58649	−	1.63848i	−0.212010	−	0.0757388i
$469$	−21.3580	+	29.6697i	−0.986219	+	1.37002i
$470$	7.36220	+	16.5976i	0.339593	+	0.765592i
$471$	9.64083	+	35.9801i	0.444226	+	1.65787i
$472$	0.336733	−	0.513834i	0.0154994	−	0.0236511i
$473$	−1.27353	+	4.75288i	−0.0585570	+	0.218538i
$474$	−11.0821	−	13.7241i	−0.509019	−	0.630370i
$475$	−15.0108	−	6.21768i	−0.688743	−	0.285287i
$476$	12.2220	−	25.7310i	0.560195	−	1.17938i
$477$	−10.8567	−	26.2103i	−0.497093	−	1.20009i
$478$	−2.27384	+	0.670117i	−0.104003	+	0.0306504i
$479$	0.255055	+	0.441769i	0.0116538	+	0.0201849i	0.871793	−	0.489874i	$-0.162957\pi$
$479$	0.255055	+	0.441769i	0.0116538	+	0.0201849i	−0.860140	+	0.510059i	$0.829624\pi$
$480$	−2.74435	+	19.7851i	−0.125262	+	0.903064i
$481$	−1.81681	+	3.14681i	−0.0828394	+	0.143482i
$482$	−7.79531	−	7.41803i	−0.355067	−	0.337882i
$483$	34.4699	+	13.0585i	1.56844	+	0.594180i
$484$	10.8372	−	11.9691i	0.492601	−	0.544049i
$485$	−9.77502	+	7.50063i	−0.443861	+	0.340586i
$486$	−29.0874	+	4.56568i	−1.31943	+	0.207104i
$487$	6.03562	−	22.5252i	0.273500	−	1.02072i	−0.683340	−	0.730100i	$-0.739473\pi$
$487$	6.03562	−	22.5252i	0.273500	−	1.02072i	0.956840	−	0.290615i	$-0.0938600\pi$
$488$	7.70661	+	8.63095i	0.348862	+	0.390705i
$489$	37.7347	−	37.7347i	1.70642	−	1.70642i
$490$	−11.0659	−	7.07051i	−0.499906	−	0.319413i
$491$	0.893235	−	2.15646i	0.0403111	−	0.0973197i	−0.902442	−	0.430812i	$-0.858227\pi$
$491$	0.893235	−	2.15646i	0.0403111	−	0.0973197i	0.942753	+	0.333492i	$0.108227\pi$
$492$	13.1853	+	15.5249i	0.594437	+	0.699915i
$493$	43.2958	+	33.2220i	1.94994	+	1.49624i
$494$	−3.60678	+	2.20337i	−0.162277	+	0.0991343i
$495$	8.02973	+	4.63597i	0.360910	+	0.208371i
$496$	11.4608	−	1.14038i	0.514603	−	0.0512047i
$497$	17.4833	+	16.4458i	0.784232	+	0.737693i
$498$	−37.1441	+	0.921146i	−1.66447	+	0.0412775i
$499$	−4.22841	+	32.1180i	−0.189290	+	1.43780i	0.588104	+	0.808785i	$0.299874\pi$
$499$	−4.22841	+	32.1180i	−0.189290	+	1.43780i	−0.777394	+	0.629014i	$0.783459\pi$
$500$	−17.9826	−	12.4326i	−0.804207	−	0.556004i
$501$	−22.4460	+	2.95508i	−1.00281	+	0.132023i
$502$	−4.55962	+	42.8111i	−0.203506	+	1.91075i
$503$	−18.0124	+	18.0124i	−0.803132	+	0.803132i	−0.983584	−	0.180452i	$-0.942244\pi$
$503$	−18.0124	+	18.0124i	−0.803132	+	0.803132i	0.180452	+	0.983584i	$0.442244\pi$
$504$	12.4291	−	27.9336i	0.553635	−	1.24426i
$505$	−13.9434	−	13.9434i	−0.620472	−	0.620472i
$506$	−9.85205	+	7.95546i	−0.437977	+	0.353663i
$507$	4.39336	+	33.3709i	0.195116	+	1.48205i
$508$	25.8075	−	16.6581i	1.14502	−	0.739082i
$509$	−29.1195	−	3.83365i	−1.29070	−	0.169924i	−0.546260	−	0.837616i	$-0.683949\pi$
$509$	−29.1195	−	3.83365i	−1.29070	−	0.169924i	−0.744437	+	0.667692i	$0.767282\pi$
$510$	18.5318	−	19.4744i	0.820604	−	0.862339i
$511$	−25.6241	−	6.03296i	−1.13354	−	0.266883i
$512$	−12.0625	+	19.1441i	−0.533091	+	0.846058i
$513$	7.24492	−	12.5486i	0.319871	−	0.554033i
$514$	19.8473	+	4.79402i	0.875428	+	0.211455i
$515$	5.23653	−	6.82438i	0.230749	−	0.300718i
$516$	13.6238	+	6.98931i	0.599755	+	0.307687i
$517$	15.2980	+	6.33664i	0.672805	+	0.278685i
$518$	−18.8372	−	12.8633i	−0.827660	−	0.565182i
$519$	10.6881	+	10.6881i	0.469156	+	0.469156i
$520$	−2.11113	+	0.737727i	−0.0925790	+	0.0323514i
$521$	15.4615	+	4.14291i	0.677382	+	0.181504i	0.581078	−	0.813848i	$-0.302631\pi$
$521$	15.4615	+	4.14291i	0.677382	+	0.181504i	0.0963044	+	0.995352i	$0.469298\pi$
$522$	47.3387	+	34.4939i	2.07196	+	1.50976i
$523$	−13.0166	−	16.9636i	−0.569176	−	0.741764i	0.416737	−	0.909027i	$-0.363174\pi$
$523$	−13.0166	−	16.9636i	−0.569176	−	0.741764i	−0.985912	+	0.167263i	$0.946507\pi$
$524$	24.2193	−	11.4697i	1.05803	−	0.501057i
$525$	14.4393	+	17.6718i	0.630181	+	0.771262i
$526$	16.8127	−	0.416944i	0.733070	−	0.0181796i
$527$	−13.4239	−	7.75029i	−0.584754	−	0.337608i
$528$	10.6251	+	14.7960i	0.462399	+	0.643913i
$529$	−3.80487	+	2.19674i	−0.165429	+	0.0955106i
$530$	−11.4393	−	6.23156i	−0.496891	−	0.270682i
$531$	−0.819855	+	0.339595i	−0.0355787	+	0.0147372i
$532$	−12.0837	−	23.6210i	−0.523894	−	1.02410i
$533$	−0.872674	+	2.10682i	−0.0377997	+	0.0912566i
$534$	62.4603	+	6.65237i	2.70292	+	0.287876i
$535$	3.09006	+	0.827980i	0.133595	+	0.0357967i
$536$	−38.2611	+	7.96654i	−1.65263	+	0.344102i
$537$	13.6952	−	3.66962i	0.590993	−	0.158356i
$538$	3.43096	−	8.90108i	0.147919	−	0.383753i
$539$	−11.7554	+	2.28566i	−0.506343	+	0.0984505i
$540$	5.14581	−	5.68325i	0.221440	−	0.244568i
$541$	−4.12687	−	0.543312i	−0.177428	−	0.0233588i	0.0412887	−	0.999147i	$-0.486854\pi$
$541$	−4.12687	−	0.543312i	−0.177428	−	0.0233588i	−0.218717	+	0.975788i	$0.570187\pi$
$542$	8.91371	−	36.9029i	0.382877	−	1.58512i
$543$	−0.579556	−	1.00382i	−0.0248711	−	0.0430781i
$544$	28.2150	−	11.4587i	1.20971	−	0.491286i
$545$	1.79561			0.0769154
$546$	5.92736	−	0.328495i	0.253667	−	0.0140583i
$547$	−13.2421	−	31.9692i	−0.566190	−	1.36690i	−0.904744	−	0.425956i	$-0.859938\pi$
$547$	−13.2421	−	31.9692i	−0.566190	−	1.36690i	0.338554	−	0.940947i	$-0.390062\pi$
$548$	−14.7820	+	4.75770i	−0.631454	+	0.203239i
$549$	−2.18161	−	16.5710i	−0.0931088	−	0.707231i
$550$	−7.74498	+	1.21568i	−0.330247	+	0.0518370i
$551$	49.0980	−	13.1558i	2.09165	−	0.560455i
$552$	17.7436	+	35.1847i	0.755219	+	1.49756i
$553$	10.9212	+	5.86778i	0.464415	+	0.249523i
$554$	6.45015	+	14.5415i	0.274041	+	0.617808i
$555$	−13.1043	−	17.0779i	−0.556248	−	0.724917i
$556$	0.493060	+	2.70209i	0.0209104	+	0.114594i
$557$	−0.576651	−	0.442480i	−0.0244335	−	0.0187485i	0.596473	−	0.802634i	$-0.296568\pi$
$557$	−0.576651	−	0.442480i	−0.0244335	−	0.0187485i	−0.620906	+	0.783885i	$0.713235\pi$
$558$	−14.6095	−	7.95857i	−0.618471	−	0.336913i
$559$			1.71431i			0.0725074i
$560$	−3.61780	−	13.5644i	−0.152880	−	0.573200i
$561$		−	24.5156i		−	1.03505i
$562$	12.5233	−	22.9891i	0.528265	−	0.969735i
$563$	8.72655	+	6.69612i	0.367780	+	0.282208i	0.776073	−	0.630644i	$-0.217209\pi$
$563$	8.72655	+	6.69612i	0.367780	+	0.282208i	−0.408292	+	0.912851i	$0.633876\pi$
$564$	29.3031	−	42.3841i	1.23388	−	1.78469i
$565$	−7.83769	−	10.2143i	−0.329734	−	0.429718i
$566$	−11.6217	+	5.15502i	−0.488496	+	0.216682i
$567$	10.2693	−	6.35521i	0.431270	−	0.266894i
$568$	1.90689	+	25.5890i	0.0800115	+	1.07369i
$569$	−4.48148	+	1.20081i	−0.187873	+	0.0503405i	−0.351529	−	0.936177i	$-0.614338\pi$
$569$	−4.48148	+	1.20081i	−0.187873	+	0.0503405i	0.163656	+	0.986518i	$0.447671\pi$
$570$	−3.88267	−	24.7360i	−0.162627	−	1.03608i
$571$	3.02103	+	22.9470i	0.126426	+	0.960301i	0.930633	+	0.365953i	$0.119257\pi$
$571$	3.02103	+	22.9470i	0.126426	+	0.960301i	−0.804207	+	0.594349i	$0.797410\pi$
$572$	−0.930902	+	1.81455i	−0.0389230	+	0.0758700i
$573$	4.56117	+	11.0116i	0.190546	+	0.460018i
$574$	−12.7745	−	6.46070i	−0.533199	−	0.269664i
$575$	−16.9596			−0.707263
$576$	29.9687	−	13.0454i	1.24870	−	0.543560i
$577$	0.147694	+	0.255814i	0.00614858	+	0.0106497i	0.869083	−	0.494666i	$-0.164709\pi$
$577$	0.147694	+	0.255814i	0.00614858	+	0.0106497i	−0.862935	+	0.505315i	$0.831376\pi$
$578$	−16.4698	−	3.97820i	−0.685054	−	0.165471i
$579$	−59.8423	−	7.87839i	−2.48696	−	0.327415i
$580$	26.8616	−	1.33312i	1.11537	−	0.0553548i
$581$	23.8092	−	10.7260i	0.987771	−	0.444989i
$582$	32.6258	+	12.5758i	1.35238	+	0.521283i
$583$	−11.4747	+	3.07464i	−0.475234	+	0.127339i
$584$	−15.8434	−	23.2589i	−0.655605	−	0.962459i
$585$	3.12025	+	0.836068i	0.129006	+	0.0345672i
$586$	−1.22210	+	11.4745i	−0.0504844	+	0.474008i
$587$	3.80781	−	9.19287i	0.157165	−	0.379430i	−0.825608	−	0.564243i	$-0.809168\pi$
$587$	3.80781	−	9.19287i	0.157165	−	0.379430i	0.982774	+	0.184813i	$0.0591680\pi$
$588$	−0.751711	+	37.2588i	−0.0310000	+	1.53653i
$589$	−13.3384	+	5.52496i	−0.549601	+	0.227652i
$590$	−0.194923	+	0.357819i	−0.00802483	+	0.0147312i
$591$	−22.6365	+	13.0692i	−0.931142	+	0.537595i
$592$	−5.56108	−	23.7426i	−0.228559	−	0.975814i
$593$	−1.47253	−	0.850168i	−0.0604698	−	0.0349122i	0.469460	−	0.882954i	$-0.344448\pi$
$593$	−1.47253	−	0.850168i	−0.0604698	−	0.0349122i	−0.529930	+	0.848041i	$0.677782\pi$
$594$	−0.173335	−	6.98951i	−0.00711201	−	0.286783i
$595$	−6.69342	+	17.6684i	−0.274404	+	0.724333i
$596$	18.0028	+	6.43133i	0.737423	+	0.263437i
$597$	−6.35532	−	8.28242i	−0.260106	−	0.338977i
$598$	−2.59812	+	3.56560i	−0.106245	+	0.145808i
$599$	−5.37460	−	1.44012i	−0.219600	−	0.0588417i	0.147341	−	0.989086i	$-0.452928\pi$
$599$	−5.37460	−	1.44012i	−0.219600	−	0.0588417i	−0.366942	+	0.930244i	$0.619595\pi$
$600$	−1.37808	+	24.3574i	−0.0562598	+	0.994388i
$601$	−22.0815	−	22.0815i	−0.900723	−	0.900723i	0.0947758	−	0.995499i	$-0.469787\pi$
$601$	−22.0815	−	22.0815i	−0.900723	−	0.900723i	−0.995499	+	0.0947758i	$0.969787\pi$
$602$	−10.7309	−	0.812120i	−0.437361	−	0.0330995i
$603$	52.1556	+	21.6036i	2.12394	+	0.879765i
$604$	−19.8886	+	6.40131i	−0.809256	+	0.260466i
$605$	−6.51936	+	8.49619i	−0.265050	+	0.345419i
$606$	−13.1389	+	54.3951i	−0.533730	+	2.20965i
$607$	−8.55391	+	14.8158i	−0.347193	+	0.601355i	−0.985750	−	0.168219i	$-0.946198\pi$
$607$	−8.55391	+	14.8158i	−0.347193	+	0.601355i	0.638557	+	0.769575i	$0.279532\pi$
$608$	7.53087	−	27.3463i	0.305417	−	1.10904i
$609$	−69.4938	−	16.3617i	−2.81603	−	0.663010i
$610$	−5.55956	−	5.29048i	−0.225100	−	0.214205i
$611$	5.71956	+	0.752995i	0.231389	+	0.0304629i
$612$	−43.0021	−	9.26503i	−1.73826	−	0.374517i
$613$	−4.23641	−	32.1788i	−0.171107	−	1.29969i	−0.834330	−	0.551266i	$-0.814145\pi$
$613$	−4.23641	−	32.1788i	−0.171107	−	1.29969i	0.663223	−	0.748422i	$-0.269188\pi$
$614$	22.8737	+	28.3268i	0.923107	+	1.14318i
$615$	−9.55270	−	9.55270i	−0.385202	−	0.385202i
$616$	−10.9174	−	6.68672i	−0.439876	−	0.269416i
$617$	31.1039	−	31.1039i	1.25220	−	1.25220i	0.297465	−	0.954733i	$-0.403859\pi$
$617$	31.1039	−	31.1039i	1.25220	−	1.25220i	0.954733	−	0.297465i	$-0.0961411\pi$
$618$	−24.2738	−	2.58529i	−0.976435	−	0.103996i
$619$	8.98941	−	1.18348i	0.361315	−	0.0475680i	0.0523164	−	0.998631i	$-0.483340\pi$
$619$	8.98941	−	1.18348i	0.361315	−	0.0475680i	0.308998	+	0.951063i	$0.400006\pi$
$620$	−7.51491	+	1.37127i	−0.301806	+	0.0550717i
$621$	1.97418	−	14.9954i	0.0792213	−	0.601745i
$622$	0.837347	+	33.7650i	0.0335745	+	1.35385i
$623$	−42.2733	+	12.7240i	−1.69365	+	0.509778i
$624$	4.90981	+	4.02115i	0.196550	+	0.160975i
$625$	−1.47361	−	0.850790i	−0.0589444	−	0.0340316i
$626$	9.75153	+	15.9627i	0.389749	+	0.637996i
$627$	−18.1155	−	13.9005i	−0.723465	−	0.555134i
$628$	2.27317	−	27.8947i	0.0907093	−	1.11312i
$629$	−12.5592	+	30.3205i	−0.500767	+	1.20896i
$630$	−6.71165	+	19.1356i	−0.267399	+	0.762380i
$631$	34.6058	−	34.6058i	1.37763	−	1.37763i	0.529034	−	0.848600i	$-0.322554\pi$
$631$	34.6058	−	34.6058i	1.37763	−	1.37763i	0.848600	−	0.529034i	$-0.177446\pi$
$632$	4.37219	+	12.5118i	0.173916	+	0.497691i
$633$	15.4644	−	57.7140i	0.614655	−	2.29392i
$634$	−6.62303	−	42.1945i	−0.263034	−	1.67576i
$635$	−16.1631	+	12.4024i	−0.641414	+	0.492174i
$636$	1.83240	+	36.9219i	0.0726593	+	1.46405i
$637$	−3.74991	+	1.82920i	−0.148577	+	0.0724754i
$638$	16.9076	−	17.7675i	0.669379	−	0.703424i
$639$	18.5327	−	32.0996i	0.733142	−	1.26984i
$640$	6.94281	−	13.3054i	0.274439	−	0.525941i
$641$	16.1845	+	28.0324i	0.639250	+	1.10721i	0.985598	+	0.169108i	$0.0540886\pi$
$641$	16.1845	+	28.0324i	0.639250	+	1.10721i	−0.346347	+	0.938106i	$0.612578\pi$
$642$	−2.56637	−	8.70820i	−0.101286	−	0.343685i
$643$	1.89126	+	4.56590i	0.0745839	+	0.180061i	0.956774	−	0.290831i	$-0.0939319\pi$
$643$	1.89126	+	4.56590i	0.0745839	+	0.180061i	−0.882190	+	0.470893i	$0.843932\pi$
$644$	−21.0886	−	17.9524i	−0.831006	−	0.707425i
$645$	−9.38279	−	3.88648i	−0.369447	−	0.153030i
$646$	−29.7000	+	23.9825i	−1.16853	+	0.943580i
$647$	7.18841	−	26.8275i	0.282606	−	1.05470i	−0.667965	−	0.744192i	$-0.732835\pi$
$647$	7.18841	−	26.8275i	0.282606	−	1.05470i	0.950571	−	0.310507i	$-0.100499\pi$
$648$	12.6845	+	2.40552i	0.498294	+	0.0944976i
$649$	0.0961743	+	0.358927i	0.00377517	+	0.0140891i
$650$	−2.49677	+	1.10749i	−0.0979313	+	0.0434393i
$651$	20.1763	+	2.03111i	0.790770	+	0.0796056i
$652$	−36.2374	+	17.1612i	−1.41917	+	0.672086i
$653$	−3.36747	+	25.5785i	−0.131779	+	1.00096i	0.789961	+	0.613157i	$0.210101\pi$
$653$	−3.36747	+	25.5785i	−0.131779	+	1.00096i	−0.921741	+	0.387807i	$0.873233\pi$
$654$	−2.65646	−	4.34847i	−0.103876	−	0.170038i
$655$	−15.3927	+	8.88699i	−0.601444	+	0.347244i
$656$	−5.40510	−	14.3175i	−0.211034	−	0.559004i
$657$			40.6511i			1.58595i
$658$	−7.42302	+	35.4457i	−0.289379	+	1.38182i
$659$	−10.6410	+	4.40765i	−0.414515	+	0.171698i	−0.580187	−	0.814483i	$-0.697021\pi$
$659$	−10.6410	+	4.40765i	−0.414515	+	0.171698i	0.165672	+	0.986181i	$0.447021\pi$
$660$	−7.82100	−	9.20878i	−0.304432	−	0.358451i
$661$	41.8739	−	5.51280i	1.62870	−	0.214423i	0.739902	−	0.672714i	$-0.234872\pi$
$661$	41.8739	−	5.51280i	1.62870	−	0.214423i	0.888802	+	0.458291i	$0.151538\pi$
$662$	−13.3781	+	18.3598i	−0.519954	+	0.713574i
$663$	−2.21062	−	8.25016i	−0.0858535	−	0.320410i
$664$	26.5143	+	8.73703i	1.02895	+	0.339063i
$665$	9.26062	+	14.9641i	0.359112	+	0.580284i
$666$	−12.6687	+	32.8669i	−0.490902	+	1.27357i
$667$	42.0934	−	32.2994i	1.62986	−	1.25064i
$668$	16.6287	+	3.58274i	0.643385	+	0.138620i
$669$	27.0583	−	35.2631i	1.04614	−	1.36335i
$670$	24.8640	−	7.32759i	0.960581	−	0.283090i
$671$	−6.99874			−0.270183
$672$	−27.4969	+	28.8288i	−1.06072	+	1.11209i
$673$	44.7537			1.72513			0.862563	−	0.505949i	$-0.168858\pi$
$673$	44.7537			1.72513			0.862563	+	0.505949i	$0.168858\pi$
$674$	−16.7366	+	4.93238i	−0.644669	+	0.189988i
$675$	5.70039	−	7.42890i	0.219408	−	0.285938i
$676$	5.32652	−	24.7222i	0.204866	−	0.950853i
$677$	−5.59437	+	4.29271i	−0.215009	+	0.164982i	−0.710651	−	0.703545i	$-0.751599\pi$
$677$	−5.59437	+	4.29271i	−0.215009	+	0.164982i	0.495642	+	0.868527i	$0.334933\pi$
$678$	−13.1409	+	34.0919i	−0.504673	+	1.30929i
$679$	−24.5631	+	0.751111i	−0.942646	+	0.0288250i
$680$	−18.0348	+	9.09492i	−0.691601	+	0.348774i
$681$	2.01686	+	7.52701i	0.0772861	+	0.288436i
$682$	−4.10253	+	5.63023i	−0.157094	+	0.215593i
$683$	−10.4129	+	1.37088i	−0.398437	+	0.0524552i	−0.327082	−	0.944996i	$-0.606065\pi$
$683$	−10.4129	+	1.37088i	−0.398437	+	0.0524552i	−0.0713545	+	0.997451i	$0.522732\pi$
$684$	−31.2288	+	26.5226i	−1.19406	+	1.01412i
$685$	9.51559	−	3.94148i	0.363572	−	0.150596i
$686$	−9.67367	−	24.3397i	−0.369343	−	0.929293i
$687$		−	43.5836i		−	1.66282i
$688$	−7.87291	−	8.38896i	−0.300152	−	0.319826i
$689$	−3.58429	+	2.06939i	−0.136551	+	0.0788376i
$690$	−13.6252	−	22.3036i	−0.518702	−	0.849084i
$691$	−3.87592	+	29.4406i	−0.147447	+	1.11997i	0.744432	+	0.667698i	$0.232720\pi$
$691$	−3.87592	+	29.4406i	−0.147447	+	1.11997i	−0.891879	+	0.452273i	$0.850613\pi$
$692$	−4.86081	−	10.2640i	−0.184780	−	0.390179i
$693$	7.59583	+	16.8610i	0.288542	+	0.640495i
$694$	3.46673	−	1.53774i	0.131595	−	0.0583716i
$695$	−0.471511	−	1.75970i	−0.0178854	−	0.0667493i
$696$	−42.9681	−	63.0792i	−1.62870	−	2.39101i
$697$	−5.33077	+	19.8947i	−0.201917	+	0.753566i
$698$	−20.2570	+	16.3574i	−0.766739	+	0.619136i
$699$	25.5671	+	10.5903i	0.967038	+	0.400560i
$700$	−5.74970	−	16.1535i	−0.217318	−	0.610546i
$701$	7.49691	+	18.0991i	0.283154	+	0.683595i	0.999906	−	0.0137337i	$-0.00437171\pi$
$701$	7.49691	+	18.0991i	0.283154	+	0.683595i	−0.716751	+	0.697329i	$0.754372\pi$
$702$	−0.688589	−	2.33652i	−0.0259891	−	0.0881864i
$703$	15.2838	+	26.4724i	0.576441	+	0.998425i
$704$	−3.77790	−	13.1546i	−0.142385	−	0.495784i
$705$	−17.0881	+	29.5974i	−0.643574	+	1.11470i
$706$	−15.0538	+	15.8195i	−0.566558	+	0.595373i
$707$	−6.32294	−	38.8179i	−0.237799	−	1.45990i
$708$	1.15491	−	0.0573172i	0.0434042	−	0.00215411i
$709$	14.8796	−	11.4175i	0.558815	−	0.428794i	−0.290350	−	0.956920i	$-0.593772\pi$
$709$	14.8796	−	11.4175i	0.558815	−	0.428794i	0.849166	+	0.528126i	$0.177105\pi$
$710$	−2.63909	−	16.8133i	−0.0990434	−	0.630993i
$711$	4.95502	−	18.4924i	0.185828	−	0.693519i
$712$	−42.5126	−	20.4948i	−1.59323	−	0.768076i
$713$	−10.6562	+	10.6562i	−0.399077	+	0.399077i
$714$	52.6903	−	9.92936i	1.97189	−	0.371597i
$715$	0.517638	−	1.24969i	0.0193586	−	0.0467357i
$716$	−10.6177	−	0.865244i	−0.396801	−	0.0323357i
$717$	−3.53986	−	2.71623i	−0.132198	−	0.101439i
$718$	−0.214150	−	0.350551i	−0.00799202	−	0.0130824i
$719$	10.9538	+	6.32419i	0.408509	+	0.235853i	0.690149	−	0.723667i	$-0.257545\pi$
$719$	10.9538	+	6.32419i	0.408509	+	0.235853i	−0.281640	+	0.959520i	$0.590878\pi$
$720$	−19.1086	+	10.2384i	−0.712135	+	0.381562i
$721$	16.4286	−	4.94491i	0.611832	−	0.184158i
$722$	0.215331	+	8.68295i	0.00801379	+	0.323146i
$723$	2.64371	−	20.0810i	0.0983208	−	0.746821i
$724$	0.156334	+	0.856750i	0.00581013	+	0.0318409i
$725$	32.5674	−	4.28758i	1.20952	−	0.159237i
$726$	30.2203	+	3.21863i	1.12158	+	0.119454i
$727$	−8.10183	+	8.10183i	−0.300480	+	0.300480i	−0.841202	−	0.540721i	$-0.818151\pi$
$727$	−8.10183	+	8.10183i	−0.300480	+	0.300480i	0.540721	+	0.841202i	$0.318151\pi$
$728$	−4.27696	−	1.26581i	−0.158515	−	0.0469141i
$729$	−29.5047	−	29.5047i	−1.09277	−	1.09277i
$730$	11.7266	+	14.5222i	0.434019	+	0.537491i
$731$	2.02100	+	15.3511i	0.0747496	+	0.567779i
$732$	−4.58716	+	21.2906i	−0.169546	+	0.786921i
$733$	−30.3827	−	3.99996i	−1.12221	−	0.147742i	−0.453495	−	0.891259i	$-0.649823\pi$
$733$	−30.3827	−	3.99996i	−1.12221	−	0.147742i	−0.668717	+	0.743517i	$0.733156\pi$
$734$	−25.3743	−	24.1463i	−0.936584	−	0.891255i
$735$	−1.51024	−	24.6711i	−0.0557060	−	0.910007i
$736$	−3.66105	−	29.3801i	−0.134948	−	1.08296i
$737$	11.8194	−	20.4719i	0.435374	−	0.754091i
$738$	−5.19034	+	21.4881i	−0.191059	+	0.790988i
$739$	10.2948	−	13.4165i	0.378702	−	0.493534i	−0.564649	−	0.825331i	$-0.690988\pi$
$739$	10.2948	−	13.4165i	0.378702	−	0.493534i	0.943351	+	0.331797i	$0.107655\pi$
$740$	4.95529	+	15.3959i	0.182160	+	0.565964i
$741$	−7.34980	−	3.04438i	−0.270001	−	0.111838i
$742$	−11.2557	−	23.4168i	−0.413209	−	0.859656i
$743$	−0.628600	−	0.628600i	−0.0230611	−	0.0230611i	0.695482	−	0.718543i	$-0.255191\pi$
$743$	−0.628600	−	0.628600i	−0.0230611	−	0.0230611i	−0.718543	+	0.695482i	$0.755191\pi$
$744$	14.4386	+	16.1703i	0.529343	+	0.592833i
$745$	−12.2475	−	3.28172i	−0.448715	−	0.120233i
$746$	−1.87661	+	2.57541i	−0.0687074	+	0.0942926i
$747$	−24.5484	−	31.9922i	−0.898181	−	1.17053i
$748$	−6.19675	+	17.3461i	−0.226575	+	0.634238i
$749$	4.03714	+	4.94096i	0.147514	+	0.180539i
$750$	−1.02016	−	41.1367i	−0.0372510	−	1.50210i
$751$	−8.64463	−	4.99098i	−0.315447	−	0.182124i	0.333914	−	0.942603i	$-0.391630\pi$
$751$	−8.64463	−	4.99098i	−0.315447	−	0.182124i	−0.649361	+	0.760480i	$0.724964\pi$
$752$	−31.4468	+	22.5822i	−1.14675	+	0.823488i
$753$	−70.1795	+	40.5182i	−2.55748	+	1.47656i
$754$	4.08773	−	7.50384i	0.148866	−	0.273274i
$755$	12.8029	−	5.30313i	0.465944	−	0.193001i
$756$	14.9520	−	3.20344i	0.543800	−	0.116508i
$757$	−6.50215	+	15.6976i	−0.236325	+	0.570539i	−0.996897	−	0.0787146i	$-0.974918\pi$
$757$	−6.50215	+	15.6976i	−0.236325	+	0.570539i	0.760572	+	0.649253i	$0.224918\pi$
$758$	1.80742	−	16.9702i	0.0656483	−	0.616384i
$759$	−23.0226	−	6.16890i	−0.835669	−	0.223917i
$760$	−3.50525	+	18.4835i	−0.127149	+	0.670465i
$761$	−0.398743	+	0.106843i	−0.0144544	+	0.00387305i	−0.266039	−	0.963962i	$-0.585715\pi$
$761$	−0.398743	+	0.106843i	−0.0144544	+	0.00387305i	0.251585	+	0.967835i	$0.419048\pi$
$762$	53.9472	+	20.7942i	1.95430	+	0.753295i
$763$	2.90659	+	2.09233i	0.105226	+	0.0757474i
$764$	−0.443894	−	8.94424i	−0.0160595	−	0.323591i
$765$	28.9265	+	3.80824i	1.04584	+	0.137687i
$766$	39.7958	+	9.61248i	1.43788	+	0.347313i
$767$	0.0647303	+	0.112116i	0.00233728	+	0.00404828i
$768$	−42.4933	+	2.87069i	−1.53334	+	0.103587i
$769$	4.31950			0.155765			0.0778826	−	0.996963i	$-0.475184\pi$
$769$	4.31950			0.155765			0.0778826	+	0.996963i	$0.475184\pi$
$770$	7.57739	+	3.83225i	0.273070	+	0.138105i
$771$	14.7072	+	35.5063i	0.529666	+	1.27873i
$772$	40.3503	+	20.7006i	1.45224	+	0.745029i
$773$	−4.02147	−	30.5461i	−0.144642	−	1.09867i	−0.897667	−	0.440675i	$-0.854739\pi$
$773$	−4.02147	−	30.5461i	−0.144642	−	1.09867i	0.753025	−	0.657992i	$-0.228594\pi$
$774$	2.57693	+	16.4173i	0.0926258	+	0.590108i
$775$	−9.01214	+	2.41479i	−0.323725	+	0.0867420i
$776$	−19.9058	−	17.1448i	−0.714576	−	0.615461i
$777$	−1.31226	−	42.9141i	−0.0470772	−	1.53954i
$778$	−7.87259	+	3.49204i	−0.282246	+	0.125196i
$779$	11.6784	+	15.2196i	0.418421	+	0.545297i
$780$	−3.46235	−	2.39376i	−0.123972	−	0.0857104i
$781$	−12.3133	−	9.44836i	−0.440606	−	0.338089i
$782$	−19.0618	+	34.9917i	−0.681648	+	1.25130i
$783$			29.2947i			1.04691i
$784$	9.94967	−	26.1726i	0.355345	−	0.934735i
$785$			18.5628i			0.662534i
$786$	44.2942	+	24.1293i	1.57992	+	0.860664i
$787$	−17.6022	−	13.5067i	−0.627452	−	0.481461i	0.245416	−	0.969418i	$-0.421076\pi$
$787$	−17.6022	−	13.5067i	−0.627452	−	0.481461i	−0.872868	+	0.487957i	$0.837742\pi$
$788$	19.3200	−	3.52540i	0.688247	−	0.125587i
$789$	19.2705	+	25.1138i	0.686048	+	0.894075i
$790$	−3.56434	−	8.03559i	−0.126813	−	0.285893i
$791$	−0.784864	−	25.6669i	−0.0279065	−	0.912610i
$792$	−6.18731	+	18.7766i	−0.219856	+	0.667198i
$793$	−2.35526	+	0.631090i	−0.0836378	+	0.0224107i
$794$	−30.7602	+	4.82825i	−1.09164	+	0.171348i
$795$	−3.20036	−	24.3092i	−0.113505	−	0.862157i
$796$	2.40321	+	7.46668i	0.0851796	+	0.264649i
$797$	−16.0161	−	38.6663i	−0.567319	−	1.36963i	−0.903806	−	0.427942i	$-0.859239\pi$
$797$	−16.0161	−	38.6663i	−0.567319	−	1.36963i	0.336487	−	0.941688i	$-0.390761\pi$
$798$	22.5386	−	44.5649i	0.797858	−	1.57758i
$799$	52.1046			1.84333
$800$	7.13182	−	16.8859i	0.252148	−	0.597005i
$801$	34.0861	+	59.0389i	1.20437	+	2.08604i
$802$	9.32622	−	38.6107i	0.329320	−	1.36339i
$803$	16.8765	+	2.22183i	0.595558	+	0.0784067i
$804$	−54.5297	−	49.3731i	−1.92312	−	1.74126i
$805$	14.9081	+	10.7317i	0.525442	+	0.378243i
$806$	−0.872922	+	2.26465i	−0.0307473	+	0.0797690i
$807$	17.3436	−	4.64721i	0.610525	−	0.163590i
$808$	23.0458	−	35.1664i	0.810747	−	1.23715i
$809$	25.4770	+	6.82653i	0.895723	+	0.240008i	0.677178	−	0.735819i	$-0.263203\pi$
$809$	25.4770	+	6.82653i	0.895723	+	0.240008i	0.218544	+	0.975827i	$0.429869\pi$
$810$	−8.51490	−	0.906884i	−0.299183	−	0.0318646i
$811$	1.07609	−	2.59792i	0.0377868	−	0.0912253i	−0.903859	−	0.427829i	$-0.859278\pi$
$811$	1.07609	−	2.59792i	0.0377868	−	0.0912253i	0.941646	+	0.336604i	$0.109278\pi$
$812$	45.0349	+	29.1425i	1.58042	+	1.02270i
$813$	66.0182	−	27.3456i	2.31536	−	0.959053i
$814$	12.9524	+	7.05584i	0.453982	+	0.247307i
$815$	23.0309	−	13.2969i	0.806737	−	0.465770i
$816$	48.7064	+	30.2199i	1.70506	+	1.05791i
$817$	12.4894	+	7.21076i	0.436949	+	0.252273i
$818$	23.7177	−	0.588181i	0.829269	−	0.0205653i
$819$	4.07658	+	4.98922i	0.142447	+	0.174338i
$820$	4.34444	+	9.17365i	0.151714	+	0.320358i
$821$	−8.28284	−	10.7944i	−0.289073	−	0.376728i	0.626131	−	0.779718i	$-0.284637\pi$
$821$	−8.28284	−	10.7944i	−0.289073	−	0.376728i	−0.915204	+	0.402990i	$0.867971\pi$
$822$	−23.6227	−	17.2130i	−0.823938	−	0.600372i
$823$	−9.74972	−	2.61243i	−0.339854	−	0.0910636i	0.0848556	−	0.996393i	$-0.472957\pi$
$823$	−9.74972	−	2.61243i	−0.339854	−	0.0910636i	−0.424710	+	0.905330i	$0.639624\pi$
$824$	16.5215	+	7.96485i	0.575555	+	0.277469i
$825$	−10.4343	−	10.4343i	−0.363276	−	0.363276i
$826$	−0.732473	+	0.352076i	−0.0254860	+	0.0122503i
$827$	8.63772	+	3.57786i	0.300363	+	0.124414i	0.527775	−	0.849384i	$-0.323026\pi$
$827$	8.63772	+	3.57786i	0.300363	+	0.124414i	−0.227412	+	0.973799i	$0.573026\pi$
$828$	−19.5215	+	38.0520i	−0.678418	+	1.32240i
$829$	−7.46453	+	9.72797i	−0.259254	+	0.337866i	−0.904786	−	0.425867i	$-0.859969\pi$
$829$	−7.46453	+	9.72797i	−0.259254	+	0.337866i	0.645532	+	0.763733i	$0.276636\pi$
$830$	−17.9984	−	4.34742i	−0.624734	−	0.150901i
$831$	−14.9711	+	25.9308i	−0.519343	+	0.899529i
$832$	−2.45754	−	4.08622i	−0.0852000	−	0.141664i
$833$	−31.4228	+	20.8007i	−1.08874	+	0.720700i
$834$	−3.56395	+	3.74521i	−0.123409	+	0.129686i
$835$	−11.1857	−	1.47263i	−0.387098	−	0.0509624i
$836$	9.30413	+	14.4144i	0.321790	+	0.498532i
$837$	−1.08607	−	8.24949i	−0.0375400	−	0.285144i
$838$	26.6866	−	21.5492i	0.921873	−	0.744405i
$839$	25.1919	+	25.1919i	0.869721	+	0.869721i	0.992441	−	0.122720i	$-0.0391618\pi$
$839$	25.1919	+	25.1919i	0.869721	+	0.869721i	−0.122720	+	0.992441i	$0.539162\pi$
$840$	16.6243	−	20.5391i	0.573593	−	0.708665i
$841$	−52.1600	+	52.1600i	−1.79862	+	1.79862i
$842$	2.00279	−	18.8046i	0.0690208	−	0.648049i
$843$	48.8532	−	6.43164i	1.68259	−	0.221517i
$844$	−25.5301	+	36.9269i	−0.878782	+	1.27107i
$845$	−2.18938	+	16.6300i	−0.0753170	+	0.572089i
$846$	55.9062	−	1.38643i	1.92209	−	0.0476665i
$847$	−20.4532	+	6.15629i	−0.702779	+	0.211533i
$848$	8.03611	−	26.5874i	0.275961	−	0.913015i
$849$	−20.7241	−	11.9651i	−0.711249	−	0.410640i
$850$	−21.0521	+	12.8607i	−0.722082	+	0.441117i
$851$	25.3137	+	19.4239i	0.867743	+	0.665842i
$852$	−36.8129	+	31.2652i	−1.26119	+	1.07113i
$853$	−8.82371	+	21.3023i	−0.302118	+	0.729378i	0.697796	+	0.716296i	$0.254164\pi$
$853$	−8.82371	+	21.3023i	−0.302118	+	0.729378i	−0.999914	+	0.0130814i	$0.995836\pi$
$854$	−2.83464	−	15.0421i	−0.0969994	−	0.514729i
$855$	19.2156	−	19.2156i	0.657159	−	0.657159i
$856$	−0.385304	+	6.81022i	−0.0131694	+	0.232768i
$857$	−0.479471	+	1.78941i	−0.0163784	+	0.0611250i	−0.973631	−	0.228127i	$-0.926740\pi$
$857$	−0.479471	+	1.78941i	−0.0163784	+	0.0611250i	0.957253	+	0.289252i	$0.0934065\pi$
$858$	−3.79220	+	0.595240i	−0.129464	+	0.0203212i
$859$	−4.44475	+	3.41058i	−0.151653	+	0.116367i	−0.681801	−	0.731538i	$-0.738803\pi$
$859$	−4.44475	+	3.41058i	−0.151653	+	0.116367i	0.530148	+	0.847905i	$0.322136\pi$
$860$	5.65646	+	5.12155i	0.192884	+	0.174644i
$861$	−4.33188	−	26.5944i	−0.147630	−	0.906335i
$862$	10.6082	+	10.0948i	0.361316	+	0.343829i
$863$	1.82430	−	3.15978i	0.0620999	−	0.107560i	−0.833304	−	0.552815i	$-0.813554\pi$
$863$	1.82430	−	3.15978i	0.0620999	−	0.107560i	0.895404	+	0.445255i	$0.146887\pi$
$864$	14.1001	+	8.27145i	0.479693	+	0.281401i
$865$	3.76626	+	6.52335i	0.128057	+	0.221801i
$866$	25.1112	−	7.40045i	0.853315	−	0.251478i
$867$	−12.2044	−	29.4640i	−0.414483	−	1.00065i
$868$	−13.7624	−	6.53702i	−0.467126	−	0.221881i
$869$	−7.40637	−	3.06782i	−0.251244	−	0.104069i
$870$	31.8030	+	39.3849i	1.07822	+	1.33527i
$871$	2.13156	−	7.95510i	0.0722252	−	0.269548i
$872$	0.780441	+	3.74824i	0.0264291	+	0.126931i
$873$	9.82181	+	36.6555i	0.332418	+	1.24060i
$874$	15.0486	+	33.9260i	0.509025	+	1.14757i
$875$	11.8789	+	26.3684i	0.401582	+	0.891416i
$876$	17.8202	−	49.8829i	0.602089	−	1.68539i
$877$	3.27416	−	24.8697i	0.110560	−	0.839790i	−0.842857	−	0.538137i	$-0.819128\pi$
$877$	3.27416	−	24.8697i	0.110560	−	0.839790i	0.953418	−	0.301653i	$-0.0975384\pi$
$878$	23.6970	−	14.4764i	0.799734	−	0.488554i
$879$	−18.8100	+	10.8599i	−0.634444	+	0.366297i
$880$	3.20611	+	8.49260i	0.108078	+	0.286285i
$881$			25.2286i			0.849972i	0.905200	+	0.424986i	$0.139721\pi$
$881$			25.2286i			0.849972i	−0.905200	+	0.424986i	$0.860279\pi$
$882$	−33.1620	+	23.1544i	−1.11662	+	0.779650i
$883$	−42.5118	+	17.6089i	−1.43063	+	0.592588i	−0.957508	−	0.288406i	$-0.906875\pi$
$883$	−42.5118	+	17.6089i	−1.43063	+	0.592588i	−0.473126	+	0.880995i	$0.656875\pi$
$884$	−0.521233	+	6.39620i	−0.0175310	+	0.215128i
$885$	−0.760388	+	0.100107i	−0.0255601	+	0.00336506i
$886$	−34.2645	−	24.9673i	−1.15114	−	0.838791i
$887$	2.77928	+	10.3724i	0.0933190	+	0.348271i	0.996759	−	0.0804428i	$-0.0256334\pi$
$887$	2.77928	+	10.3724i	0.0933190	+	0.348271i	−0.903440	+	0.428714i	$0.858967\pi$
$888$	29.9536	−	34.7773i	1.00518	−	1.16705i
$889$	−40.6154	+	1.24197i	−1.36220	+	0.0416544i
$890$	29.2078	+	11.2583i	0.979047	+	0.377378i
$891$	−6.19535	+	4.75386i	−0.207552	+	0.159260i
$892$	−28.0586	+	18.1111i	−0.939471	+	0.606404i
$893$	29.5437	−	38.5021i	0.988641	−	1.28842i
$894$	10.1719	+	34.5152i	0.340198	+	1.15436i
$895$	7.06562			0.236178
$896$	26.7425	−	13.4476i	0.893405	−	0.449252i
$897$	−8.30399			−0.277262
$898$	−10.8885	−	36.9470i	−0.363355	−	1.23294i
$899$	17.7690	−	23.1570i	0.592629	−	0.772329i
$900$	−22.2459	+	14.3592i	−0.741530	+	0.478639i
$901$	−29.6566	+	22.7563i	−0.988004	+	0.758122i
$902$	8.63719	+	3.32925i	0.287587	+	0.110852i
$903$	−10.6594	−	17.2244i	−0.354723	−	0.573192i
$904$	17.9152	−	20.8003i	0.595851	−	0.691807i
$905$	−0.149502	−	0.557948i	−0.00496961	−	0.0185468i
$906$	−31.7835	−	23.1595i	−1.05594	−	0.769421i
$907$	−13.1217	+	1.72751i	−0.435700	+	0.0573610i	−0.345186	−	0.938534i	$-0.612184\pi$
$907$	−13.1217	+	1.72751i	−0.435700	+	0.0573610i	−0.0905138	+	0.995895i	$0.528851\pi$
$908$	0.475546	−	5.83556i	0.0157815	−	0.193660i
$909$	−56.1103	+	23.2417i	−1.86106	+	0.770877i
$910$	2.89555	+	0.606384i	0.0959866	+	0.0201014i
$911$			17.1732i			0.568975i	0.958680	+	0.284487i	$0.0918234\pi$
$911$			17.1732i			0.568975i	−0.958680	+	0.284487i	$0.908177\pi$
$912$	49.9475	−	18.8561i	1.65393	−	0.624387i
$913$	−14.6234	+	8.44283i	−0.483964	+	0.279417i
$914$	−20.8483	+	12.7361i	−0.689601	+	0.421274i
$915$	1.88548	−	14.3216i	0.0623320	−	0.473458i
$916$	−11.0165	+	30.8378i	−0.363996	+	1.01891i
$917$	−35.2721	−	3.55078i	−1.16479	−	0.117257i
$918$	−8.92064	−	20.1110i	−0.294425	−	0.663763i
$919$	−8.07953	−	30.1532i	−0.266519	−	0.994663i	−0.961314	−	0.275455i	$-0.911172\pi$
$919$	−8.07953	−	30.1532i	−0.266519	−	0.994663i	0.694795	−	0.719208i	$-0.255495\pi$
$920$	4.00294	+	19.2250i	0.131973	+	0.633830i
$921$	−17.7369	+	66.1952i	−0.584452	+	2.18121i
$922$	−8.04674	−	9.96510i	−0.265005	−	0.328183i
$923$	−4.99574	−	2.06930i	−0.164437	−	0.0681120i
$924$	−1.92951	−	24.0198i	−0.0634762	−	0.790195i
$925$	7.55956	+	18.2504i	0.248557	+	0.600069i
$926$	−16.0131	+	4.71916i	−0.526223	+	0.155081i
$927$	−13.2468	−	22.9441i	−0.435082	−	0.753584i
$928$	14.4579	+	55.4929i	0.474605	+	1.82164i
$929$	17.7486	−	30.7415i	0.582314	−	1.00860i	−0.412891	−	0.910781i	$-0.635481\pi$
$929$	17.7486	−	30.7415i	0.582314	−	1.00860i	0.995204	−	0.0978163i	$-0.0311858\pi$
$930$	−10.4160	−	9.91187i	−0.341554	−	0.325023i
$931$	−2.44656	+	35.0137i	−0.0801828	+	1.14753i
$932$	−15.4133	−	13.9557i	−0.504878	−	0.457135i
$933$	−50.4360	+	38.7009i	−1.65120	+	1.26701i
$934$	−19.2006	+	3.01380i	−0.628262	+	0.0986146i
$935$	3.16202	−	11.8008i	0.103409	−	0.385928i
$936$	−0.389068	+	6.87674i	−0.0127171	+	0.224773i
$937$	−3.04316	+	3.04316i	−0.0994158	+	0.0994158i	−0.755065	−	0.655650i	$-0.772395\pi$
$937$	−3.04316	+	3.04316i	−0.0994158	+	0.0994158i	0.655650	+	0.755065i	$0.272395\pi$
$938$	48.7863	+	17.1114i	1.59293	+	0.558707i
$939$	−13.4736	+	32.5282i	−0.439695	+	1.06152i
$940$	19.5720	−	16.6224i	0.638367	−	0.542165i
$941$	13.3746	+	10.2627i	0.435998	+	0.334553i	0.803327	−	0.595538i	$-0.203061\pi$
$941$	13.3746	+	10.2627i	0.435998	+	0.334553i	−0.367329	+	0.930091i	$0.619728\pi$
$942$	44.9539	−	27.4622i	1.46468	−	0.894766i
$943$	17.3417	+	10.0123i	0.564725	+	0.326044i
$944$	−0.831650	−	0.251369i	−0.0270679	−	0.00818135i
$945$	−9.71173	+	2.92318i	−0.315923	+	0.0950909i
$946$	6.95656	−	0.172518i	0.226177	−	0.00560903i
$947$	−6.43786	+	48.9004i	−0.209202	+	1.58905i	0.488437	+	0.872599i	$0.337567\pi$
$947$	−6.43786	+	48.9004i	−0.209202	+	1.58905i	−0.697639	+	0.716449i	$0.745766\pi$
$948$	−14.1868	+	20.5199i	−0.460766	+	0.666454i
$949$	5.87972	−	0.774080i	0.190864	−	0.0251277i
$950$	−2.43347	+	22.8483i	−0.0789522	+	0.741297i
$951$	56.8460	−	56.8460i	1.84336	−	1.84336i
$952$	−39.7910	−	6.29281i	−1.28964	−	0.203951i
$953$	36.4273	+	36.4273i	1.18000	+	1.18000i	0.979744	+	0.200253i	$0.0641764\pi$
$953$	36.4273	+	36.4273i	1.18000	+	1.18000i	0.200253	+	0.979744i	$0.435824\pi$
$954$	−31.2148	+	25.2057i	−1.01062	+	0.816066i
$955$	0.775280	+	5.88884i	0.0250875	+	0.190558i
$956$	1.81807	+	2.81664i	0.0588005	+	0.0910966i
$957$	45.7699	+	6.02572i	1.47953	+	0.194784i
$958$	0.497308	−	0.522601i	0.0160673	−	0.0168845i
$959$	19.9959	+	4.70785i	0.645700	+	0.152025i
$960$	27.9363	−	4.18688i	0.901640	−	0.135131i
$961$	11.3547	−	19.6669i	0.366281	−	0.634417i
$962$	4.99506	+	1.20653i	0.161047	+	0.0389002i
$963$	5.99812	−	7.81690i	0.193287	−	0.251896i
$964$	−6.94639	+	13.5401i	−0.223728	+	0.436099i
$965$	−27.7894	−	11.5108i	−0.894574	−	0.370545i
$966$	3.93386	−	51.9800i	0.126570	−	1.67243i
$967$	2.44248	+	2.44248i	0.0785448	+	0.0785448i	0.745288	−	0.666743i	$-0.232312\pi$
$967$	2.44248	+	2.44248i	0.0785448	+	0.0785448i	−0.666743	+	0.745288i	$0.732312\pi$
$968$	−20.5689	−	9.91604i	−0.661110	−	0.318714i
$969$	−69.4041	−	18.5968i	−2.22958	−	0.597414i
$970$	14.0827	+	10.2615i	0.452168	+	0.329478i
$971$	−5.16730	−	6.73416i	−0.165827	−	0.216109i	0.703047	−	0.711143i	$-0.251822\pi$
$971$	−5.16730	−	6.73416i	−0.165827	−	0.216109i	−0.868874	+	0.495034i	$0.835156\pi$
$972$	17.8220	+	37.6327i	0.571642	+	1.20707i
$973$	1.28725	−	3.39789i	0.0412672	−	0.108931i
$974$	−32.9691	+	0.817610i	−1.05640	+	0.0261979i
$975$	−4.45231	−	2.57054i	−0.142588	−	0.0823232i
$976$	8.62721	−	13.9047i	0.276150	−	0.445080i
$977$	14.2021	−	8.19960i	0.454366	−	0.262328i	−0.255306	−	0.966860i	$-0.582176\pi$
$977$	14.2021	−	8.19960i	0.454366	−	0.262328i	0.709672	+	0.704532i	$0.248843\pi$
$978$	−66.2738	−	36.1027i	−2.11920	−	1.15444i
$979$	26.3733	−	10.9242i	0.842894	−	0.349138i
$980$	−5.16746	+	17.8379i	−0.165069	+	0.569810i
$981$	2.11639	−	5.10942i	0.0675711	−	0.163131i
$982$	−3.28240	−	0.349594i	−0.104746	−	0.0111560i
$983$	36.5269	+	9.78736i	1.16503	+	0.312168i	0.788972	−	0.614429i	$-0.210613\pi$
$983$	36.5269	+	9.78736i	1.16503	+	0.312168i	0.376056	+	0.926597i	$0.377280\pi$
$984$	15.7888	−	24.0927i	0.503328	−	0.768048i
$985$	−12.5819	+	3.37132i	−0.400894	+	0.107419i
$986$	27.7580	−	72.0135i	0.883993	−	2.29338i
$987$	−62.1491	+	27.9981i	−1.97823	+	0.891188i
$988$	4.43086	+	4.01185i	0.140964	+	0.127634i
$989$	14.9247	+	1.96488i	0.474579	+	0.0624795i
$990$	3.07872	−	12.7459i	0.0978480	−	0.405093i
$991$	−25.3302	−	43.8732i	−0.804640	−	1.39368i	−0.916534	−	0.399958i	$-0.869025\pi$
$991$	−25.3302	−	43.8732i	−0.804640	−	1.39368i	0.111893	−	0.993720i	$-0.464308\pi$
$992$	−6.12873	−	15.0910i	−0.194587	−	0.479139i
$993$	−42.7585			−1.35690
$994$	15.3197	−	30.2913i	0.485913	−	0.960781i
$995$	−1.99093	−	4.80652i	−0.0631166	−	0.152377i
$996$	16.0990	+	50.0188i	0.510116	+	1.58491i
$997$	2.09044	+	15.8785i	0.0662049	+	0.502876i	0.992134	+	0.125179i	$0.0399506\pi$
$997$	2.09044	+	15.8785i	0.0662049	+	0.502876i	−0.925929	+	0.377697i	$0.876716\pi$
$998$	45.2595	−	7.10412i	1.43266	−	0.224877i
$999$	−17.0167	+	4.55961i	−0.538385	+	0.144260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.37.14	✓	240
4.3	odd	2		896.2.bh.a.625.4		240
7.4	even	3	inner	224.2.bd.a.165.28	yes	240
28.11	odd	6		896.2.bh.a.753.27		240
32.13	even	8	inner	224.2.bd.a.205.28	yes	240
32.19	odd	8		896.2.bh.a.401.27		240
224.109	even	24	inner	224.2.bd.a.109.14	yes	240
224.179	odd	24		896.2.bh.a.529.4		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.14	✓	240	1.1	even	1	trivial
224.2.bd.a.109.14	yes	240	224.109	even	24	inner
224.2.bd.a.165.28	yes	240	7.4	even	3	inner
224.2.bd.a.205.28	yes	240	32.13	even	8	inner
896.2.bh.a.401.27		240	32.19	odd	8
896.2.bh.a.529.4		240	224.179	odd	24
896.2.bh.a.625.4		240	4.3	odd	2
896.2.bh.a.753.27		240	28.11	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-0.399779 - 1.35653i) q^{2} +(1.62045 - 2.11181i) q^{3} +(-1.68035 + 1.08463i) q^{4} +(1.05240 - 0.807534i) q^{5} +(-3.51256 - 1.35393i) q^{6} +(2.64452 - 0.0808662i) q^{7} +(2.14310 + 1.84584i) q^{8} +(-1.05744 - 3.94640i) q^{9} +O(q^{10})\)	\(q+(-0.399779 - 1.35653i) q^{2} +(1.62045 - 2.11181i) q^{3} +(-1.68035 + 1.08463i) q^{4} +(1.05240 - 0.807534i) q^{5} +(-3.51256 - 1.35393i) q^{6} +(2.64452 - 0.0808662i) q^{7} +(2.14310 + 1.84584i) q^{8} +(-1.05744 - 3.94640i) q^{9} +(-1.51617 - 1.10478i) q^{10} +(-1.69616 + 0.223304i) q^{11} +(-0.432405 + 5.30618i) q^{12} +(-0.550667 + 0.228094i) q^{13} +(-1.16692 - 3.55504i) q^{14} -3.53104i q^{15} +(1.64718 - 3.64511i) q^{16} +(-4.66215 + 2.69169i) q^{17} +(-4.93068 + 3.01213i) q^{18} +(-0.654477 + 4.97125i) q^{19} +(-0.892530 + 2.49840i) q^{20} +(4.11453 - 5.71576i) q^{21} +(0.981009 + 2.21162i) q^{22} +(1.35463 + 5.05554i) q^{23} +(7.37086 - 1.53473i) q^{24} +(-0.838663 + 3.12993i) q^{25} +(0.529562 + 0.655810i) q^{26} +(-2.66982 - 1.10587i) q^{27} +(-4.35601 + 3.00419i) q^{28} +(-3.87939 - 9.36567i) q^{29} +(-4.78996 + 1.41163i) q^{30} +(1.43967 + 2.49358i) q^{31} +(-5.60321 - 0.777209i) q^{32} +(-2.27697 + 3.94383i) q^{33} +(5.51519 + 5.24827i) q^{34} +(2.71778 - 2.22064i) q^{35} +(6.05724 + 5.48443i) q^{36} +(4.83651 - 3.71118i) q^{37} +(7.00530 - 1.09958i) q^{38} +(-0.410638 + 1.53252i) q^{39} +(3.74597 + 0.211937i) q^{40} +(2.70535 - 2.70535i) q^{41} +(-9.39851 - 3.29645i) q^{42} +(1.10066 - 2.65723i) q^{43} +(2.60795 - 2.21493i) q^{44} +(-4.29970 - 3.29928i) q^{45} +(6.31644 - 3.85869i) q^{46} +(-8.38206 - 4.83939i) q^{47} +(-5.02862 - 9.38525i) q^{48} +(6.98692 - 0.427704i) q^{49} +(4.58113 - 0.113609i) q^{50} +(-1.87043 + 14.2073i) q^{51} +(0.677920 - 0.980546i) q^{52} +(6.88442 - 0.906351i) q^{53} +(-0.432817 + 4.06380i) q^{54} +(-1.60471 + 1.60471i) q^{55} +(5.81672 + 4.70805i) q^{56} +(9.43780 + 9.43780i) q^{57} +(-11.1539 + 9.00670i) q^{58} +(-0.0283506 - 0.215344i) q^{59} +(3.82985 + 5.93339i) q^{60} +(4.05592 + 0.533972i) q^{61} +(2.80707 - 2.94984i) q^{62} +(-3.11554 - 10.3508i) q^{63} +(1.18574 + 7.91164i) q^{64} +(-0.395328 + 0.684728i) q^{65} +(6.26022 + 1.51212i) q^{66} +(-8.41153 + 10.9621i) q^{67} +(4.91458 - 9.57968i) q^{68} +(12.8715 + 5.33153i) q^{69} +(-4.09888 - 2.79899i) q^{70} +(6.41498 + 6.41498i) q^{71} +(5.01825 - 10.4094i) q^{72} +(-9.61077 - 2.57520i) q^{73} +(-6.96787 - 5.07722i) q^{74} +(5.25082 + 6.84301i) q^{75} +(-4.29219 - 9.06332i) q^{76} +(-4.46747 + 0.727693i) q^{77} +(2.24308 - 0.0556267i) q^{78} +(4.05809 + 2.34294i) q^{79} +(-1.21006 - 5.16626i) q^{80} +(3.95304 - 2.28229i) q^{81} +(-4.75143 - 2.58835i) q^{82} +(9.11873 - 3.77710i) q^{83} +(-0.714412 + 14.0672i) q^{84} +(-2.73281 + 6.59758i) q^{85} +(-4.04464 - 0.430776i) q^{86} +(-26.0649 - 6.98407i) q^{87} +(-4.04723 - 2.65228i) q^{88} +(-16.1173 + 4.31863i) q^{89} +(-2.75664 + 7.15166i) q^{90} +(-1.43780 + 0.647728i) q^{91} +(-7.75962 - 7.02583i) q^{92} +(7.59889 + 1.00041i) q^{93} +(-3.21381 + 13.3052i) q^{94} +(3.32568 + 5.76025i) q^{95} +(-10.7210 + 10.5735i) q^{96} -9.28832 q^{97} +(-3.37342 - 9.30699i) q^{98} +(2.67483 + 6.45761i) 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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