LMFDB - Embedded newform 300.2.w.a.103.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			103.15
Character	$\chi$	$=$	300.103
Dual form			300.2.w.a.67.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.194555 + 1.40077i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-1.92430 - 0.545051i) q^{4} +(1.56105 - 1.60098i) q^{5} +(-0.0269690 - 1.41396i) q^{6} +(1.26539 + 1.26539i) q^{7} +(1.13787 - 2.58945i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})$	\(q+(-0.194555 + 1.40077i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-1.92430 - 0.545051i) q^{4} +(1.56105 - 1.60098i) q^{5} +(-0.0269690 - 1.41396i) q^{6} +(1.26539 + 1.26539i) q^{7} +(1.13787 - 2.58945i) q^{8} +(0.951057 - 0.309017i) q^{9} +(1.93889 + 2.49814i) q^{10} +(2.45369 + 0.797253i) q^{11} +(1.98587 + 0.237314i) q^{12} +(0.719314 - 1.41173i) q^{13} +(-2.01871 + 1.52633i) q^{14} +(-1.29138 + 1.82547i) q^{15} +(3.40584 + 2.09768i) q^{16} +(-0.968521 + 6.11500i) q^{17} +(0.247828 + 1.39233i) q^{18} +(4.18468 - 3.04035i) q^{19} +(-3.87653 + 2.22991i) q^{20} +(-1.44777 - 1.05186i) q^{21} +(-1.59414 + 3.28194i) q^{22} +(2.77576 + 5.44773i) q^{23} +(-0.718783 + 2.73557i) q^{24} +(-0.126271 - 4.99841i) q^{25} +(1.83756 + 1.28225i) q^{26} +(-0.891007 + 0.453990i) q^{27} +(-1.74529 - 3.12470i) q^{28} +(-2.10923 + 2.90311i) q^{29} +(-2.30582 - 2.16407i) q^{30} +(-3.46723 - 4.77223i) q^{31} +(-3.60098 + 4.36267i) q^{32} +(-2.54820 - 0.403595i) q^{33} +(-8.37726 - 2.54637i) q^{34} +(4.00121 - 0.0505318i) q^{35} +(-1.99855 + 0.0762659i) q^{36} +(8.50512 + 4.33357i) q^{37} +(3.44467 + 6.45327i) q^{38} +(-0.489614 + 1.50688i) q^{39} +(-2.36939 - 5.86396i) q^{40} +(-2.24529 - 6.91028i) q^{41} +(1.75509 - 1.82334i) q^{42} +(1.96263 - 1.96263i) q^{43} +(-4.28709 - 2.87154i) q^{44} +(0.989913 - 2.00501i) q^{45} +(-8.17104 + 2.82831i) q^{46} +(0.00589566 + 0.0372238i) q^{47} +(-3.69206 - 1.53906i) q^{48} -3.79756i q^{49} +(7.02617 + 0.795586i) q^{50} -6.19122i q^{51} +(-2.15364 + 2.32453i) q^{52} +(-1.13623 - 7.17385i) q^{53} +(-0.462586 - 1.33642i) q^{54} +(5.10671 - 2.68376i) q^{55} +(4.71653 - 1.83682i) q^{56} +(-3.65754 + 3.65754i) q^{57} +(-3.65622 - 3.51935i) q^{58} +(2.91440 + 8.96960i) q^{59} +(3.47997 - 2.80888i) q^{60} +(-0.911425 + 2.80508i) q^{61} +(7.35935 - 3.92832i) q^{62} +(1.59449 + 0.812433i) q^{63} +(-5.41050 - 5.89292i) q^{64} +(-1.13727 - 3.35539i) q^{65} +(1.06111 - 3.49091i) q^{66} +(-6.72692 - 1.06544i) q^{67} +(5.19671 - 11.2392i) q^{68} +(-3.59380 - 4.94644i) q^{69} +(-0.707670 + 5.61459i) q^{70} +(1.78138 - 2.45186i) q^{71} +(0.281995 - 2.81433i) q^{72} +(6.68488 - 3.40612i) q^{73} +(-7.72504 + 11.0706i) q^{74} +(0.906640 + 4.91711i) q^{75} +(-9.70971 + 3.56967i) q^{76} +(2.09605 + 4.11372i) q^{77} +(-2.01553 - 0.979005i) q^{78} +(-3.75981 - 2.73166i) q^{79} +(8.67501 - 2.17810i) q^{80} +(0.809017 - 0.587785i) q^{81} +(10.1165 - 1.80070i) q^{82} +(-1.32439 + 8.36187i) q^{83} +(2.21261 + 2.81320i) q^{84} +(8.27808 + 11.0964i) q^{85} +(2.36735 + 3.13103i) q^{86} +(1.62912 - 3.19732i) q^{87} +(4.85643 - 5.44654i) q^{88} +(-2.83952 - 0.922614i) q^{89} +(2.61596 + 1.77672i) q^{90} +(2.69661 - 0.876183i) q^{91} +(-2.37209 - 11.9960i) q^{92} +(4.17109 + 4.17109i) q^{93} +(-0.0532888 + 0.00101640i) q^{94} +(1.66494 - 11.4457i) q^{95} +(2.87418 - 4.87228i) q^{96} +(-12.1121 + 1.91837i) q^{97} +(5.31949 + 0.738832i) q^{98} +2.57996 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−0.194555	+	1.40077i	−0.137571	+	0.990492i
$2$	−0.194555	+	1.40077i	−0.137571	+	0.990492i
$3$	−0.987688	+	0.156434i	−0.570242	+	0.0903175i
$3$	−0.987688	+	0.156434i	−0.570242	+	0.0903175i
$4$	−1.92430	−	0.545051i	−0.962149	−	0.272526i
$5$	1.56105	−	1.60098i	0.698121	−	0.715980i
$5$	1.56105	−	1.60098i	0.698121	−	0.715980i
$6$	−0.0269690	−	1.41396i	−0.0110100	−	0.577245i
$7$	1.26539	+	1.26539i	0.478274	+	0.478274i	0.904579	−	0.426305i	$-0.140185\pi$
$7$	1.26539	+	1.26539i	0.478274	+	0.478274i	−0.426305	+	0.904579i	$0.640185\pi$
$8$	1.13787	−	2.58945i	0.402298	−	0.915509i
$9$	0.951057	−	0.309017i	0.317019	−	0.103006i
$10$	1.93889	+	2.49814i	0.613131	+	0.789981i
$11$	2.45369	+	0.797253i	0.739816	+	0.240381i	0.654593	−	0.755981i	$-0.272840\pi$
$11$	2.45369	+	0.797253i	0.739816	+	0.240381i	0.0852225	+	0.996362i	$0.472840\pi$
$12$	1.98587	+	0.237314i	0.573271	+	0.0685068i
$13$	0.719314	−	1.41173i	0.199502	−	0.391544i	−0.769482	−	0.638668i	$-0.779486\pi$
$13$	0.719314	−	1.41173i	0.199502	−	0.391544i	0.968984	+	0.247124i	$0.0794856\pi$
$14$	−2.01871	+	1.52633i	−0.539523	+	0.407930i
$15$	−1.29138	+	1.82547i	−0.333432	+	0.471334i
$16$	3.40584	+	2.09768i	0.851460	+	0.524420i
$17$	−0.968521	+	6.11500i	−0.234901	+	1.48310i	0.534952	+	0.844883i	$0.320330\pi$
$17$	−0.968521	+	6.11500i	−0.234901	+	1.48310i	−0.769852	+	0.638222i	$0.779670\pi$
$18$	0.247828	+	1.39233i	0.0584137	+	0.328175i
$19$	4.18468	−	3.04035i	0.960031	−	0.697503i	0.00687313	−	0.999976i	$-0.497812\pi$
$19$	4.18468	−	3.04035i	0.960031	−	0.697503i	0.953158	+	0.302473i	$0.0978122\pi$
$20$	−3.87653	+	2.22991i	−0.866819	+	0.498623i
$21$	−1.44777	−	1.05186i	−0.315928	−	0.229535i
$22$	−1.59414	+	3.28194i	−0.339872	+	0.699712i
$23$	2.77576	+	5.44773i	0.578786	+	1.13593i	0.975912	+	0.218167i	$0.0700077\pi$
$23$	2.77576	+	5.44773i	0.578786	+	1.13593i	−0.397126	+	0.917764i	$0.629992\pi$
$24$	−0.718783	+	2.73557i	−0.146721	+	0.558396i
$25$	−0.126271	−	4.99841i	−0.0252543	−	0.999681i
$26$	1.83756	+	1.28225i	0.360376	+	0.251470i
$27$	−0.891007	+	0.453990i	−0.171474	+	0.0873705i
$28$	−1.74529	−	3.12470i	−0.329829	−	0.590512i
$29$	−2.10923	+	2.90311i	−0.391674	+	0.539093i	−0.958630	−	0.284655i	$-0.908121\pi$
$29$	−2.10923	+	2.90311i	−0.391674	+	0.539093i	0.566956	+	0.823748i	$0.308121\pi$
$30$	−2.30582	−	2.16407i	−0.420982	−	0.395104i
$31$	−3.46723	−	4.77223i	−0.622733	−	0.857119i	0.374815	−	0.927100i	$-0.377706\pi$
$31$	−3.46723	−	4.77223i	−0.622733	−	0.857119i	−0.997548	+	0.0699809i	$0.977706\pi$
$32$	−3.60098	+	4.36267i	−0.636570	+	0.771219i
$33$	−2.54820	−	0.403595i	−0.443585	−	0.0702569i
$34$	−8.37726	−	2.54637i	−1.43669	−	0.436699i
$35$	4.00121	−	0.0505318i	0.676328	−	0.00854144i
$36$	−1.99855	+	0.0762659i	−0.333091	+	0.0127110i
$37$	8.50512	+	4.33357i	1.39823	+	0.712435i	0.980570	−	0.196167i	$-0.0628495\pi$
$37$	8.50512	+	4.33357i	1.39823	+	0.712435i	0.417662	+	0.908602i	$0.362850\pi$
$38$	3.44467	+	6.45327i	0.558799	+	1.04686i
$39$	−0.489614	+	1.50688i	−0.0784010	+	0.241293i
$40$	−2.36939	−	5.86396i	−0.374633	−	0.927173i
$41$	−2.24529	−	6.91028i	−0.350655	−	1.07920i	−0.958486	−	0.285139i	$-0.907960\pi$
$41$	−2.24529	−	6.91028i	−0.350655	−	1.07920i	0.607831	−	0.794066i	$-0.292040\pi$
$42$	1.75509	−	1.82334i	0.270816	−	0.281347i
$43$	1.96263	−	1.96263i	0.299299	−	0.299299i	−0.541440	−	0.840739i	$-0.682121\pi$
$43$	1.96263	−	1.96263i	0.299299	−	0.299299i	0.840739	+	0.541440i	$0.182121\pi$
$44$	−4.28709	−	2.87154i	−0.646303	−	0.432901i
$45$	0.989913	−	2.00501i	0.147568	−	0.298890i
$46$	−8.17104	+	2.82831i	−1.20475	+	0.417012i
$47$	0.00589566	+	0.0372238i	0.000859971	+	0.00542964i	0.988115	−	0.153719i	$-0.0491251\pi$
$47$	0.00589566	+	0.0372238i	0.000859971	+	0.00542964i	−0.987255	+	0.159149i	$0.949125\pi$
$48$	−3.69206	−	1.53906i	−0.532902	−	0.222145i
$49$		−	3.79756i		−	0.542508i
$50$	7.02617	+	0.795586i	0.993650	+	0.112513i
$51$		−	6.19122i		−	0.866944i
$52$	−2.15364	+	2.32453i	−0.298656	+	0.322354i
$53$	−1.13623	−	7.17385i	−0.156073	−	0.985404i	−0.934058	−	0.357122i	$-0.883758\pi$
$53$	−1.13623	−	7.17385i	−0.156073	−	0.985404i	0.777985	−	0.628283i	$-0.216242\pi$
$54$	−0.462586	−	1.33642i	−0.0629499	−	0.181864i
$55$	5.10671	−	2.68376i	0.688589	−	0.361878i
$56$	4.71653	−	1.83682i	0.630273	−	0.245455i
$57$	−3.65754	+	3.65754i	−0.484453	+	0.484453i
$58$	−3.65622	−	3.51935i	−0.480085	−	0.462114i
$59$	2.91440	+	8.96960i	0.379422	+	1.16774i	0.940446	+	0.339942i	$0.110408\pi$
$59$	2.91440	+	8.96960i	0.379422	+	1.16774i	−0.561024	+	0.827800i	$0.689592\pi$
$60$	3.47997	−	2.80888i	0.449262	−	0.362625i
$61$	−0.911425	+	2.80508i	−0.116696	+	0.359153i	−0.992297	−	0.123882i	$-0.960466\pi$
$61$	−0.911425	+	2.80508i	−0.116696	+	0.359153i	0.875601	+	0.483035i	$0.160466\pi$
$62$	7.35935	−	3.92832i	0.934639	−	0.498898i
$63$	1.59449	+	0.812433i	0.200887	+	0.102357i
$64$	−5.41050	−	5.89292i	−0.676313	−	0.736615i
$65$	−1.13727	−	3.35539i	−0.141061	−	0.416184i
$66$	1.06111	−	3.49091i	0.130613	−	0.429702i
$67$	−6.72692	−	1.06544i	−0.821825	−	0.130164i	−0.268659	−	0.963235i	$-0.586580\pi$
$67$	−6.72692	−	1.06544i	−0.821825	−	0.130164i	−0.553166	+	0.833071i	$0.686580\pi$
$68$	5.19671	−	11.2392i	0.630194	−	1.36295i
$69$	−3.59380	−	4.94644i	−0.432642	−	0.595481i
$70$	−0.707670	+	5.61459i	−0.0845827	+	0.671072i
$71$	1.78138	−	2.45186i	0.211411	−	0.290982i	−0.690122	−	0.723693i	$-0.742443\pi$
$71$	1.78138	−	2.45186i	0.211411	−	0.290982i	0.901533	+	0.432711i	$0.142443\pi$
$72$	0.281995	−	2.81433i	0.0332335	−	0.331672i
$73$	6.68488	−	3.40612i	0.782406	−	0.398656i	−0.0166887	−	0.999861i	$-0.505312\pi$
$73$	6.68488	−	3.40612i	0.782406	−	0.398656i	0.799095	+	0.601205i	$0.205312\pi$
$74$	−7.72504	+	11.0706i	−0.898017	+	1.28693i
$75$	0.906640	+	4.91711i	0.104690	+	0.567779i
$76$	−9.70971	+	3.56967i	−1.11378	+	0.409469i
$77$	2.09605	+	4.11372i	0.238867	+	0.468802i
$78$	−2.01553	−	0.979005i	−0.228214	−	0.110851i
$79$	−3.75981	−	2.73166i	−0.423012	−	0.307336i	0.355837	−	0.934548i	$-0.384196\pi$
$79$	−3.75981	−	2.73166i	−0.423012	−	0.307336i	−0.778848	+	0.627212i	$0.784196\pi$
$80$	8.67501	−	2.17810i	0.969896	−	0.243519i
$81$	0.809017	−	0.587785i	0.0898908	−	0.0653095i
$82$	10.1165	−	1.80070i	1.11718	−	0.198854i
$83$	−1.32439	+	8.36187i	−0.145371	+	0.917835i	0.801913	+	0.597440i	$0.203815\pi$
$83$	−1.32439	+	8.36187i	−0.145371	+	0.917835i	−0.947284	+	0.320395i	$0.896185\pi$
$84$	2.21261	+	2.81320i	0.241416	+	0.306946i
$85$	8.27808	+	11.0964i	0.897884	+	1.20357i
$86$	2.36735	+	3.13103i	0.255278	+	0.337628i
$87$	1.62912	−	3.19732i	0.174660	−	0.342789i
$88$	4.85643	−	5.44654i	0.517697	−	0.580603i
$89$	−2.83952	−	0.922614i	−0.300988	−	0.0977969i	0.154630	−	0.987973i	$-0.450582\pi$
$89$	−2.83952	−	0.922614i	−0.300988	−	0.0977969i	−0.455618	+	0.890176i	$0.650582\pi$
$90$	2.61596	+	1.77672i	0.275747	+	0.187283i
$91$	2.69661	−	0.876183i	0.282682	−	0.0918489i
$92$	−2.37209	−	11.9960i	−0.247307	−	1.25067i
$93$	4.17109	+	4.17109i	0.432521	+	0.432521i
$94$	−0.0532888	+	0.00101640i	−0.00549632	+	0.000104834i
$95$	1.66494	−	11.4457i	0.170819	−	1.17430i
$96$	2.87418	−	4.87228i	0.293345	−	0.497275i
$97$	−12.1121	+	1.91837i	−1.22980	+	0.194781i	−0.737320	−	0.675543i	$-0.763909\pi$
$97$	−12.1121	+	1.91837i	−1.22980	+	0.194781i	−0.492479	+	0.870324i	$0.663909\pi$
$98$	5.31949	+	0.738832i	0.537350	+	0.0746333i
$99$	2.57996			0.259296
$100$	−2.48140	+	9.68724i	−0.248140	+	0.968724i
$101$	−18.4944			−1.84026			−0.920129	−	0.391616i	$-0.871916\pi$
$101$	−18.4944			−1.84026			−0.920129	+	0.391616i	$0.871916\pi$
$102$	8.67246	+	1.20453i	0.858702	+	0.119266i
$103$	−19.8981	+	3.15155i	−1.96062	+	0.310532i	−0.961225	+	0.275767i	$0.911068\pi$
$103$	−19.8981	+	3.15155i	−1.96062	+	0.310532i	−0.999396	+	0.0347649i	$0.988932\pi$
$104$	−2.83712	−	3.46900i	−0.278203	−	0.340163i
$105$	−3.94404	+	0.675836i	−0.384899	+	0.0659549i
$106$	10.2700	−	0.195883i	0.997506	−	0.0190258i
$107$	−9.72003	−	9.72003i	−0.939671	−	0.939671i	0.0586099	−	0.998281i	$-0.481333\pi$
$107$	−9.72003	−	9.72003i	−0.939671	−	0.939671i	−0.998281	+	0.0586099i	$0.981333\pi$
$108$	1.96201	−	0.387968i	0.188794	−	0.0373323i
$109$	9.37929	−	3.04752i	0.898373	−	0.291899i	0.176808	−	0.984245i	$-0.443423\pi$
$109$	9.37929	−	3.04752i	0.898373	−	0.291899i	0.721565	+	0.692346i	$0.243423\pi$
$110$	2.76579	+	7.67545i	0.263708	+	0.731825i
$111$	−9.07833	−	2.94973i	−0.861677	−	0.279976i
$112$	1.65533	+	6.96412i	0.156414	+	0.658047i
$113$	−2.97994	+	5.84847i	−0.280330	+	0.550178i	−0.987643	−	0.156723i	$-0.949907\pi$
$113$	−2.97994	+	5.84847i	−0.280330	+	0.550178i	0.707313	+	0.706900i	$0.249907\pi$
$114$	−4.41177	−	5.83496i	−0.413201	−	0.546494i
$115$	13.0548	+	4.06023i	1.21737	+	0.378618i
$116$	5.64113	−	4.43680i	0.523766	−	0.411947i
$117$	0.247859	−	1.56492i	0.0229145	−	0.144677i
$118$	−13.1313	+	2.33732i	−1.20884	+	0.215168i
$119$	−8.96344	+	6.51232i	−0.821677	+	0.596983i
$120$	3.25754	+	5.42111i	0.297372	+	0.494877i
$121$	−3.51420	−	2.55321i	−0.319473	−	0.232110i
$122$	−3.75194	−	1.82243i	−0.339684	−	0.164995i
$123$	3.29865	+	6.47397i	0.297429	+	0.583738i
$124$	4.07087	+	11.0730i	0.365575	+	0.994386i
$125$	−8.19946	−	7.60058i	−0.733382	−	0.679817i
$126$	−1.44824	+	2.07545i	−0.129020	+	0.184895i
$127$	−15.0362	+	7.66131i	−1.33424	+	0.679831i	−0.968062	−	0.250712i	$-0.919335\pi$
$127$	−15.0362	+	7.66131i	−1.33424	+	0.679831i	−0.366182	+	0.930543i	$0.619335\pi$
$128$	9.30724	−	6.43236i	0.822652	−	0.568545i
$129$	−1.63145	+	2.24550i	−0.143641	+	0.197705i
$130$	4.92138	−	0.940250i	0.431633	−	0.0824653i
$131$	−2.64378	−	3.63885i	−0.230988	−	0.317928i	0.677752	−	0.735291i	$-0.262954\pi$
$131$	−2.64378	−	3.63885i	−0.230988	−	0.317928i	−0.908740	+	0.417363i	$0.862954\pi$
$132$	4.68351	+	2.16554i	0.407648	+	0.188486i
$133$	9.14250	+	1.44803i	0.792756	+	0.125560i
$134$	2.80119	−	9.21557i	0.241986	−	0.796104i
$135$	−0.664073	+	2.13518i	−0.0571543	+	0.183767i
$136$	14.7324	+	9.46601i	1.26330	+	0.811704i
$137$	15.3805	+	7.83674i	1.31404	+	0.669538i	0.963676	−	0.267074i	$-0.0860569\pi$
$137$	15.3805	+	7.83674i	1.31404	+	0.669538i	0.350367	+	0.936613i	$0.386057\pi$
$138$	7.62800	−	4.07172i	0.649338	−	0.346608i
$139$	4.36271	−	13.4270i	0.370040	−	1.13887i	−0.576724	−	0.816939i	$-0.695669\pi$
$139$	4.36271	−	13.4270i	0.370040	−	1.13887i	0.946764	−	0.321928i	$-0.104331\pi$
$140$	−7.72705	−	2.08363i	−0.653055	−	0.176098i
$141$	−0.0116462	−	0.0358432i	−0.000980783	−	0.00301854i
$142$	3.08791	+	2.97232i	0.259131	+	0.249431i
$143$	2.89048	−	2.89048i	0.241714	−	0.241714i
$144$	3.88736	+	0.942552i	0.323947	+	0.0785460i
$145$	1.35521	+	7.90872i	0.112544	+	0.656783i
$146$	3.47060	+	10.0266i	0.287229	+	0.829811i
$147$	0.594069	+	3.75080i	0.0489980	+	0.309361i
$148$	−14.0044	−	12.9748i	−1.15115	−	1.06652i
$149$			17.2353i			1.41197i	0.708227	+	0.705985i	$0.249495\pi$
$149$			17.2353i			1.41197i	−0.708227	+	0.705985i	$0.750505\pi$
$150$	−7.06412	+	0.313344i	−0.576783	+	0.0255844i
$151$		−	9.16179i		−	0.745576i	−0.927917	−	0.372788i	$-0.878402\pi$
$151$		−	9.16179i		−	0.745576i	0.927917	−	0.372788i	$-0.121598\pi$
$152$	−3.11120	−	14.2955i	−0.252352	−	1.15952i
$153$	0.968521	+	6.11500i	0.0783002	+	0.494368i
$154$	−6.17017	+	2.13573i	−0.497206	+	0.172102i
$155$	−13.0528	−	1.89871i	−1.04842	−	0.152508i
$156$	1.76349	−	2.63281i	0.141192	−	0.210794i
$157$	−3.35617	+	3.35617i	−0.267851	+	0.267851i	−0.828234	−	0.560383i	$-0.810654\pi$
$157$	−3.35617	+	3.35617i	−0.267851	+	0.267851i	0.560383	+	0.828234i	$0.310654\pi$
$158$	4.55791	−	4.73516i	0.362608	−	0.376709i
$159$	2.24447	+	6.90778i	0.177998	+	0.547823i
$160$	1.36325	+	12.5754i	0.107774	+	0.994175i
$161$	−3.38110	+	10.4060i	−0.266468	+	0.820104i
$162$	0.665952	+	1.24760i	0.0523222	+	0.0980208i
$163$	4.84163	+	2.46694i	0.379226	+	0.193225i	0.633204	−	0.773985i	$-0.281739\pi$
$163$	4.84163	+	2.46694i	0.379226	+	0.193225i	−0.253978	+	0.967210i	$0.581739\pi$
$164$	0.554140	+	14.5212i	0.0432711	+	1.13392i
$165$	−4.62400	+	3.44959i	−0.359978	+	0.268550i
$166$	−11.4554	−	3.48200i	−0.889109	−	0.270256i
$167$	−16.3746	−	2.59348i	−1.26710	−	0.200690i	−0.513541	−	0.858065i	$-0.671667\pi$
$167$	−16.3746	−	2.59348i	−1.26710	−	0.200690i	−0.753563	+	0.657375i	$0.771667\pi$
$168$	−4.37112	+	2.55203i	−0.337239	+	0.196894i
$169$	6.16563	+	8.48626i	0.474279	+	0.652789i
$170$	−17.1540	+	9.43681i	−1.31565	+	0.723771i
$171$	3.04035	−	4.18468i	0.232501	−	0.320010i
$172$	−4.84643	+	2.70696i	−0.369537	+	0.206403i
$173$	17.8380	−	9.08892i	1.35620	−	0.691018i	0.383598	−	0.923500i	$-0.374685\pi$
$173$	17.8380	−	9.08892i	1.35620	−	0.691018i	0.972601	+	0.232483i	$0.0746849\pi$
$174$	4.16175	+	2.90407i	0.315501	+	0.220157i
$175$	6.16517	−	6.48473i	0.466043	−	0.490200i
$176$	6.68449	+	7.86238i	0.503863	+	0.592649i
$177$	−4.28167	−	8.40325i	−0.321830	−	0.631627i
$178$	1.84481	−	3.79800i	0.138274	−	0.284672i
$179$	16.1069	+	11.7023i	1.20389	+	0.874674i	0.994661	−	0.103194i	$-0.0329062\pi$
$179$	16.1069	+	11.7023i	1.20389	+	0.874674i	0.209224	+	0.977868i	$0.432906\pi$
$180$	−2.99772	+	3.31868i	−0.223437	+	0.247360i
$181$	−8.23772	+	5.98505i	−0.612305	+	0.444866i	−0.850225	−	0.526419i	$-0.823534\pi$
$181$	−8.23772	+	5.98505i	−0.612305	+	0.444866i	0.237920	+	0.971285i	$0.423534\pi$
$182$	0.702690	+	3.94779i	0.0520868	+	0.292630i
$183$	0.461393	−	2.91312i	0.0341071	−	0.215344i
$184$	17.2651	−	0.988871i	1.27280	−	0.0729006i
$185$	20.2148	−	6.85161i	1.48622	−	0.503741i
$186$	−6.65422	+	5.03122i	−0.487911	+	0.368907i
$187$	−7.25165	+	14.2322i	−0.530293	+	1.04076i
$188$	0.00894385	−	0.0748430i	0.000652297	−	0.00545849i
$189$	−1.70195	−	0.552997i	−0.123799	−	0.0402246i
$190$	15.7088	+	4.55901i	1.13964	+	0.330745i
$191$	−12.1738	+	3.95551i	−0.880866	+	0.286211i	−0.714317	−	0.699823i	$-0.753262\pi$
$191$	−12.1738	+	3.95551i	−0.880866	+	0.286211i	−0.166549	+	0.986033i	$0.553262\pi$
$192$	6.26574	+	4.97398i	0.452191	+	0.358966i
$193$	3.19755	+	3.19755i	0.230165	+	0.230165i	0.812761	−	0.582597i	$-0.197963\pi$
$193$	3.19755	+	3.19755i	0.230165	+	0.230165i	−0.582597	+	0.812761i	$0.697963\pi$
$194$	−0.330723	−	17.3395i	−0.0237445	−	1.24490i
$195$	1.64817	+	3.13617i	0.118028	+	0.224586i
$196$	−2.06986	+	7.30763i	−0.147847	+	0.521973i
$197$	−11.4480	+	1.81319i	−0.815639	+	0.129184i	−0.550296	−	0.834970i	$-0.685485\pi$
$197$	−11.4480	+	1.81319i	−0.815639	+	0.129184i	−0.265343	+	0.964154i	$0.585485\pi$
$198$	−0.501944	+	3.61393i	−0.0356716	+	0.256831i
$199$	8.34981			0.591902			0.295951	−	0.955203i	$-0.404363\pi$
$199$	8.34981			0.591902			0.295951	+	0.955203i	$0.404363\pi$
$200$	−13.0868	−	5.36057i	−0.925376	−	0.379049i
$201$	6.81078			0.480395
$202$	3.59816	−	25.9063i	0.253166	−	1.82276i
$203$	−6.34258	+	1.00457i	−0.445162	+	0.0705067i
$204$	−3.37453	+	11.9138i	−0.236265	+	0.834129i
$205$	−14.5682	−	7.19261i	−1.01749	−	0.502354i
$206$	−0.543321	−	28.4858i	−0.0378550	−	1.98470i
$207$	4.32335	+	4.32335i	0.300493	+	0.300493i
$208$	5.41123	−	3.29924i	0.375201	−	0.228761i
$209$	12.6918	−	4.12383i	0.877912	−	0.285251i
$210$	−0.179358	−	5.65617i	−0.0123769	−	0.390313i
$211$	14.6855	+	4.77161i	1.01099	+	0.328491i	0.767250	−	0.641348i	$-0.221625\pi$
$211$	14.6855	+	4.77161i	1.01099	+	0.328491i	0.243743	+	0.969840i	$0.421625\pi$
$212$	−1.72368	+	14.4239i	−0.118383	+	0.990639i
$213$	−1.37589	+	2.70034i	−0.0942745	+	0.185024i
$214$	15.5066	−	11.7244i	1.06001	−	0.801465i
$215$	−0.0783752	−	6.20590i	−0.00534515	−	0.423239i
$216$	0.161735	+	2.82380i	0.0110047	+	0.192135i
$217$	1.65134	−	10.4262i	0.112100	−	0.707775i
$218$	2.44408	+	13.7311i	0.165534	+	0.929988i
$219$	−6.06975	+	4.40993i	−0.410155	+	0.297995i
$220$	−11.2896	+	2.38094i	−0.761146	+	0.160523i
$221$	7.93607	+	5.76589i	0.533838	+	0.387856i
$222$	5.89811	−	12.1427i	0.395855	−	0.814967i
$223$	−3.75855	−	7.37657i	−0.251691	−	0.493972i	0.730245	−	0.683186i	$-0.239406\pi$
$223$	−3.75855	−	7.37657i	−0.251691	−	0.493972i	−0.981936	+	0.189214i	$0.939406\pi$
$224$	−10.0772	+	0.963835i	−0.673309	+	0.0643990i
$225$	−1.66468	−	4.71475i	−0.110979	−	0.314316i
$226$	−7.61258	−	5.31205i	−0.506381	−	0.353353i
$227$	24.4631	−	12.4646i	1.62367	−	0.827303i	0.624755	−	0.780821i	$-0.285199\pi$
$227$	24.4631	−	12.4646i	1.62367	−	0.827303i	0.998919	−	0.0464825i	$-0.0148012\pi$
$228$	9.03175	−	5.04465i	0.598142	−	0.334090i
$229$	10.4537	−	14.3883i	0.690803	−	0.950808i	−0.309197	−	0.950998i	$-0.600060\pi$
$229$	10.4537	−	14.3883i	0.690803	−	0.950808i	1.00000		0.000189558i	$6.03382e-5\pi$
$230$	−8.22731	+	17.4968i	−0.542492	+	1.15370i
$231$	−2.71377	−	3.73518i	−0.178553	−	0.245757i
$232$	5.11742	+	8.76511i	0.335975	+	0.575457i
$233$	−5.32769	−	0.843823i	−0.349029	−	0.0552807i	−0.0205411	−	0.999789i	$-0.506539\pi$
$233$	−5.32769	−	0.843823i	−0.349029	−	0.0552807i	−0.328488	+	0.944508i	$0.606539\pi$
$234$	2.14386	+	0.651654i	0.140149	+	0.0426000i
$235$	0.0687979	+	0.0486692i	0.00448788	+	0.00317483i
$236$	−0.719278	−	18.8487i	−0.0468210	−	1.22694i
$237$	4.14085	+	2.10987i	0.268977	+	0.137051i
$238$	−7.37837	−	13.8227i	−0.478268	−	0.895992i
$239$	3.11661	−	9.59193i	0.201596	−	0.620450i	−0.798240	−	0.602340i	$-0.794235\pi$
$239$	3.11661	−	9.59193i	0.201596	−	0.620450i	0.999836	−	0.0181100i	$-0.00576491\pi$
$240$	−8.22748	+	3.50836i	−0.531082	+	0.226463i
$241$	−1.59822	−	4.91881i	−0.102950	−	0.316848i	0.886294	−	0.463124i	$-0.153271\pi$
$241$	−1.59822	−	4.91881i	−0.102950	−	0.316848i	−0.989244	+	0.146275i	$0.953271\pi$
$242$	4.26016	−	4.42583i	0.273854	−	0.284503i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	3.28276	−	4.90103i	0.210157	−	0.313756i
$245$	−6.07981	−	5.92816i	−0.388425	−	0.378736i
$246$	−9.71028	+	3.36110i	−0.619105	+	0.214296i
$247$	−1.28206	−	8.09461i	−0.0815756	−	0.515048i
$248$	−16.3027	+	3.54804i	−1.03522	+	0.225300i
$249$		−	8.46610i		−	0.536518i
$250$	12.2419	−	10.0068i	0.774245	−	0.632886i
$251$			13.6267i			0.860111i	0.902803	+	0.430055i	$0.141506\pi$
$251$			13.6267i			0.860111i	−0.902803	+	0.430055i	$0.858494\pi$
$252$	−2.62545	−	2.43244i	−0.165388	−	0.153229i
$253$	2.46764	+	15.5800i	0.155139	+	0.979508i
$254$	−7.80635	−	22.5527i	−0.489814	−	1.41508i
$255$	−9.91202	−	9.66478i	−0.620715	−	0.605232i
$256$	7.19947	+	14.2887i	0.449967	+	0.893045i
$257$	10.7300	−	10.7300i	0.669319	−	0.669319i	−0.288239	−	0.957558i	$-0.593070\pi$
$257$	10.7300	−	10.7300i	0.669319	−	0.669319i	0.957558	+	0.288239i	$0.0930698\pi$
$258$	−2.82801	−	2.72215i	−0.176064	−	0.169474i
$259$	5.27865	+	16.2460i	0.327999	+	1.00948i
$260$	0.359594	+	7.07663i	0.0223011	+	0.438874i
$261$	−1.10889	+	3.41281i	−0.0686384	+	0.211247i
$262$	5.61154	−	2.99536i	0.346682	−	0.185054i
$263$	−16.1259	−	8.21657i	−0.994367	−	0.506655i	−0.120444	−	0.992720i	$-0.538432\pi$
$263$	−16.1259	−	8.21657i	−0.994367	−	0.506655i	−0.873923	+	0.486065i	$0.838432\pi$
$264$	−3.94461	+	6.13920i	−0.242774	+	0.377841i
$265$	−13.2589	−	9.37963i	−0.814487	−	0.576186i
$266$	−3.80707	+	12.5248i	−0.233426	+	0.767945i
$267$	2.94888	+	0.467057i	0.180469	+	0.0285835i
$268$	12.3639	+	5.71674i	0.755244	+	0.349206i
$269$	−9.43653	−	12.9883i	−0.575355	−	0.791908i	0.417821	−	0.908529i	$-0.362794\pi$
$269$	−9.43653	−	12.9883i	−0.575355	−	0.791908i	−0.993177	+	0.116621i	$0.962794\pi$
$270$	−2.86170	−	1.34562i	−0.174157	−	0.0818919i
$271$	1.76045	−	2.42305i	0.106940	−	0.147190i	−0.752193	−	0.658943i	$-0.771004\pi$
$271$	1.76045	−	2.42305i	0.106940	−	0.147190i	0.859132	+	0.511753i	$0.171004\pi$
$272$	−16.1259	+	18.7950i	−0.977779	+	1.13962i
$273$	−2.52635	+	1.28724i	−0.152902	+	0.0779072i
$274$	−13.9698	+	20.0198i	−0.843946	+	1.20944i
$275$	3.67516	−	12.3652i	0.221621	−	0.745650i
$276$	4.21947	+	11.4772i	0.253982	+	0.690847i
$277$	−7.87265	−	15.4509i	−0.473022	−	0.928357i	−0.997057	−	0.0766608i	$-0.975574\pi$
$277$	−7.87265	−	15.4509i	−0.473022	−	0.928357i	0.524036	−	0.851696i	$-0.324426\pi$
$278$	17.9594	+	8.72344i	1.07713	+	0.523197i
$279$	−4.77223	−	3.46723i	−0.285706	−	0.207578i
$280$	4.42201	−	10.4184i	0.264266	−	0.622620i
$281$	−8.05625	+	5.85321i	−0.480595	+	0.349173i	−0.801556	−	0.597920i	$-0.795994\pi$
$281$	−8.05625	+	5.85321i	−0.480595	+	0.349173i	0.320961	+	0.947092i	$0.395994\pi$
$282$	0.0524738	−	0.00934010i	0.00312477	−	0.000556195i
$283$	−1.77033	+	11.1775i	−0.105235	+	0.664431i	0.877523	+	0.479535i	$0.159195\pi$
$283$	−1.77033	+	11.1775i	−0.105235	+	0.664431i	−0.982758	+	0.184896i	$0.940805\pi$
$284$	−4.76429	+	3.74716i	−0.282709	+	0.222353i
$285$	0.146059	+	11.5652i	0.00865180	+	0.685066i
$286$	3.48653	+	4.61125i	0.206163	+	0.272669i
$287$	5.90306	−	11.5854i	0.348446	−	0.683865i
$288$	−2.07660	+	5.26191i	−0.122365	+	0.310061i
$289$	−20.2872	−	6.59171i	−1.19337	−	0.387748i
$290$	−11.3419	+	0.359655i	−0.666021	+	0.0211197i
$291$	11.6629	−	3.78951i	0.683691	−	0.222145i
$292$	−14.7202	+	2.91078i	−0.861435	+	0.170340i
$293$	−19.4066	−	19.4066i	−1.13375	−	1.13375i	−0.989549	−	0.144199i	$-0.953940\pi$
$293$	−19.4066	−	19.4066i	−1.13375	−	1.13375i	−0.144199	−	0.989549i	$-0.546060\pi$
$294$	−5.36958	+	0.102416i	−0.313160	+	0.00597303i
$295$	18.9097	+	9.33606i	1.10096	+	0.543566i
$296$	20.8993	−	17.0925i	1.21475	−	0.993483i
$297$	−2.54820	+	0.403595i	−0.147862	+	0.0234190i
$298$	−24.1426	−	3.35320i	−1.39854	−	0.194246i
$299$	9.68738			0.560236
$300$	0.935435	−	9.95615i	0.0540074	−	0.574819i
$301$	4.96701			0.286294
$302$	12.8335	+	1.78247i	0.738487	+	0.102570i
$303$	18.2667	−	2.89315i	1.04939	−	0.166207i
$304$	20.6300	−	1.57681i	1.18321	−	0.0904361i
$305$	3.06809	+	5.83803i	0.175679	+	0.334284i
$306$	−8.75412	+	0.166971i	−0.500440	+	0.00954509i
$307$	3.83564	+	3.83564i	0.218912	+	0.218912i	0.808040	−	0.589128i	$-0.200529\pi$
$307$	3.83564	+	3.83564i	0.218912	+	0.218912i	−0.589128	+	0.808040i	$0.700529\pi$
$308$	−1.79123	−	9.05848i	−0.102065	−	0.516155i
$309$	19.1601	−	6.22550i	1.08998	−	0.354157i
$310$	5.19913	−	17.9145i	0.295290	−	1.01747i
$311$	−7.89005	−	2.56363i	−0.447404	−	0.145370i	0.0766452	−	0.997058i	$-0.475579\pi$
$311$	−7.89005	−	2.56363i	−0.447404	−	0.145370i	−0.524049	+	0.851688i	$0.675579\pi$
$312$	3.34487	+	2.98246i	0.189366	+	0.168849i
$313$	−8.49876	+	16.6797i	−0.480378	+	0.942795i	0.515904	+	0.856646i	$0.327456\pi$
$313$	−8.49876	+	16.6797i	−0.480378	+	0.942795i	−0.996282	+	0.0861488i	$0.972544\pi$
$314$	−4.04825	−	5.35417i	−0.228456	−	0.302153i
$315$	3.78976	−	1.28450i	0.213529	−	0.0723734i
$316$	5.74609	+	7.30582i	0.323243	+	0.410984i
$317$	−0.165705	+	1.04622i	−0.00930692	+	0.0587616i	−0.991905	−	0.126984i	$-0.959470\pi$
$317$	−0.165705	+	1.04622i	−0.00930692	+	0.0587616i	0.982598	+	0.185746i	$0.0594702\pi$
$318$	−10.1129	+	1.80005i	−0.567101	+	0.100942i
$319$	−7.48991	+	5.44174i	−0.419354	+	0.304679i
$320$	−17.8805	−	0.537016i	−0.999549	−	0.0300201i
$321$	11.1209	+	8.07981i	0.620709	+	0.450971i
$322$	−13.9185	−	6.76066i	−0.775648	−	0.376757i
$323$	14.5388	+	28.5339i	0.808959	+	1.58767i
$324$	−1.87716	+	0.690118i	−0.104287	+	0.0383399i
$325$	−7.14724	−	3.41716i	−0.396458	−	0.189550i
$326$	−4.39756	+	6.30205i	−0.243559	+	0.349038i
$327$	−8.78708	+	4.47724i	−0.485927	+	0.247592i
$328$	−20.4487	−	2.04895i	−1.12909	−	0.113134i
$329$	−0.0396424	+	0.0545630i	−0.00218555	+	0.00300816i
$330$	−3.93244	−	7.14829i	−0.216474	−	0.393500i
$331$	18.5262	+	25.4991i	1.01829	+	1.40156i	0.913394	+	0.407077i	$0.133452\pi$
$331$	18.5262	+	25.4991i	1.01829	+	1.40156i	0.104899	+	0.994483i	$0.466548\pi$
$332$	7.10617	−	15.3689i	0.390002	−	0.843476i
$333$	9.42800	+	1.49325i	0.516651	+	0.0818295i
$334$	6.81862	−	22.4324i	0.373098	−	1.22745i
$335$	−12.2068	+	9.10647i	−0.666928	+	0.497539i
$336$	−2.72438	−	6.61943i	−0.148627	−	0.361119i
$337$	−18.0272	−	9.18532i	−0.982004	−	0.500356i	−0.112164	−	0.993690i	$-0.535778\pi$
$337$	−18.0272	−	9.18532i	−0.982004	−	0.500356i	−0.869840	+	0.493333i	$0.835778\pi$
$338$	−13.0868	+	6.98557i	−0.711830	+	0.379965i
$339$	2.02835	−	6.24263i	0.110165	−	0.339053i
$340$	−9.88139	−	25.8647i	−0.535894	−	1.40271i
$341$	−4.70284	−	14.4738i	−0.254673	−	0.783803i
$342$	5.27025	+	5.07297i	0.284982	+	0.274315i
$343$	13.6632	−	13.6632i	0.737741	−	0.737741i
$344$	−2.84892	−	7.31537i	−0.153603	−	0.394418i
$345$	−13.5292	−	1.96802i	−0.728389	−	0.105955i
$346$	9.26099	+	26.7552i	0.497874	+	1.43837i
$347$	0.0503563	+	0.317937i	0.00270327	+	0.0170678i	0.989003	−	0.147895i	$-0.0472497\pi$
$347$	0.0503563	+	0.317937i	0.00270327	+	0.0170678i	−0.986300	+	0.164963i	$0.947250\pi$
$348$	−4.87761	+	5.26464i	−0.261467	+	0.282214i
$349$		−	1.90739i		−	0.102100i	−0.998696	−	0.0510501i	$-0.983743\pi$
$349$		−	1.90739i		−	0.102100i	0.998696	−	0.0510501i	$-0.0162568\pi$
$350$	7.88414	+	9.89760i	0.421425	+	0.529049i
$351$			1.58442i			0.0845703i
$352$	−12.3139	+	7.83376i	−0.656331	+	0.417541i
$353$	1.39657	+	8.81760i	0.0743319	+	0.469313i	0.996574	+	0.0827014i	$0.0263548\pi$
$353$	1.39657	+	8.81760i	0.0743319	+	0.469313i	−0.922242	+	0.386612i	$0.873645\pi$
$354$	12.6040	−	4.36273i	0.669896	−	0.231877i
$355$	−1.14456	−	6.67941i	−0.0607469	−	0.354506i
$356$	4.96120	+	3.32307i	0.262943	+	0.176122i
$357$	7.83433	−	7.83433i	0.414637	−	0.414637i
$358$	−19.5259	+	20.2853i	−1.03198	+	1.07211i
$359$	6.39407	+	19.6789i	0.337466	+	1.03861i	0.965494	+	0.260424i	$0.0838623\pi$
$359$	6.39407	+	19.6789i	0.337466	+	1.03861i	−0.628028	+	0.778191i	$0.716138\pi$
$360$	−4.06548	−	4.84477i	−0.214270	−	0.255342i
$361$	2.39650	−	7.37568i	0.126132	−	0.388193i
$362$	−6.78098	−	12.7035i	−0.356400	−	0.667684i
$363$	3.87034	+	1.97204i	0.203140	+	0.103505i
$364$	−5.66665	+	0.216243i	−0.297013	+	0.0113342i
$365$	4.98228	−	16.0195i	0.260785	−	0.838497i
$366$	3.99084	+	1.21306i	0.208604	+	0.0634079i
$367$	15.3559	+	2.43213i	0.801569	+	0.126956i	0.543761	−	0.839240i	$-0.317000\pi$
$367$	15.3559	+	2.43213i	0.801569	+	0.126956i	0.257808	+	0.966196i	$0.417000\pi$
$368$	−1.97382	+	24.3768i	−0.102893	+	1.27073i
$369$	−4.27079	−	5.87824i	−0.222328	−	0.306009i
$370$	5.66462	+	29.6493i	0.294490	+	1.54139i
$371$	7.63997	−	10.5155i	0.396648	−	0.545939i
$372$	−5.75295	−	10.2999i	−0.298277	−	0.534023i
$373$	−6.75054	+	3.43957i	−0.349530	+	0.178094i	−0.619937	−	0.784652i	$-0.712842\pi$
$373$	−6.75054	+	3.43957i	−0.349530	+	0.178094i	0.270407	+	0.962746i	$0.412842\pi$
$374$	−18.5251	−	12.9268i	−0.957910	−	0.668429i
$375$	9.28750	+	6.22433i	0.479605	+	0.321423i
$376$	0.103098	+	0.0270893i	0.00531685	+	0.00139702i
$377$	2.58121	+	5.06591i	0.132939	+	0.260908i
$378$	1.10574	−	2.27645i	0.0568733	−	0.117088i
$379$	−28.3717	−	20.6132i	−1.45735	−	1.05883i	−0.984042	−	0.177935i	$-0.943058\pi$
$379$	−28.3717	−	20.6132i	−1.45735	−	1.05883i	−0.473312	−	0.880895i	$-0.656942\pi$
$380$	−9.44234	+	21.1175i	−0.484382	+	1.08330i
$381$	13.6525	−	9.91916i	0.699441	−	0.508174i
$382$	−3.17228	−	17.8222i	−0.162308	−	0.911864i
$383$	1.80034	−	11.3669i	0.0919932	−	0.580822i	−0.898032	−	0.439931i	$-0.855003\pi$
$383$	1.80034	−	11.3669i	0.0919932	−	0.580822i	0.990025	−	0.140892i	$-0.0449970\pi$
$384$	−8.18641	+	7.80914i	−0.417761	+	0.398508i
$385$	9.85801	+	3.06598i	0.502411	+	0.156257i
$386$	−5.10113	+	3.85693i	−0.259640	+	0.196313i
$387$	1.26009	−	2.47306i	0.0640539	−	0.125713i
$388$	24.3529	+	2.91021i	1.23633	+	0.147744i
$389$	−9.99966	−	3.24909i	−0.507003	−	0.164735i	0.0443360	−	0.999017i	$-0.485883\pi$
$389$	−9.99966	−	3.24909i	−0.507003	−	0.164735i	−0.551339	+	0.834282i	$0.685883\pi$
$390$	−4.71370	+	1.69855i	−0.238687	+	0.0860092i
$391$	−36.0013	+	11.6975i	−1.82066	+	0.591569i
$392$	−9.83358	−	4.32113i	−0.496671	−	0.218250i
$393$	3.18047	+	3.18047i	0.160434	+	0.160434i
$394$	−0.312590	−	16.3888i	−0.0157481	−	0.825656i
$395$	−10.2426	+	1.75513i	−0.515360	+	0.0883101i
$396$	−4.96462	−	1.40621i	−0.249481	−	0.0706648i
$397$	−6.35706	+	1.00686i	−0.319052	+	0.0505328i	−0.313906	−	0.949454i	$-0.601638\pi$
$397$	−6.35706	+	1.00686i	−0.319052	+	0.0505328i	−0.00514536	+	0.999987i	$0.501638\pi$
$398$	−1.62449	+	11.6961i	−0.0814285	+	0.586274i
$399$	−9.25647			−0.463403
$400$	10.0550	−	17.2886i	0.502750	−	0.864432i
$401$	21.4858			1.07295			0.536476	−	0.843916i	$-0.319755\pi$
$401$	21.4858			1.07295			0.536476	+	0.843916i	$0.319755\pi$
$402$	−1.32507	+	9.54031i	−0.0660884	+	0.475827i
$403$	−9.23115	+	1.46207i	−0.459836	+	0.0728309i
$404$	35.5886	+	10.0804i	1.77060	+	0.501517i
$405$	0.321880	−	2.21278i	0.0159944	−	0.109954i
$406$	−0.173185	−	9.07992i	−0.00859503	−	0.450629i
$407$	17.4140	+	17.4140i	0.863179	+	0.863179i
$408$	−16.0319	−	7.04481i	−0.793695	−	0.348770i
$409$	25.1912	−	8.18512i	1.24563	−	0.404728i	0.389274	−	0.921122i	$-0.372726\pi$
$409$	25.1912	−	8.18512i	1.24563	−	0.404728i	0.856351	+	0.516394i	$0.172726\pi$
$410$	12.9095	−	19.0073i	0.637554	−	0.938705i
$411$	−16.4171	−	5.33422i	−0.809794	−	0.263118i
$412$	40.0077	+	4.78097i	1.97104	+	0.235542i
$413$	−7.66221	+	15.0379i	−0.377033	+	0.739968i
$414$	−6.89713	+	5.21487i	−0.338975	+	0.256297i
$415$	11.3198	+	15.1736i	0.555665	+	0.744842i
$416$	3.56869	+	8.22176i	0.174969	+	0.403105i
$417$	−2.20855	+	13.9442i	−0.108153	+	0.682851i
$418$	3.30727	+	18.5806i	0.161764	+	0.908807i
$419$	24.4346	−	17.7528i	1.19371	−	0.867280i	0.200058	−	0.979784i	$-0.435887\pi$
$419$	24.4346	−	17.7528i	1.19371	−	0.867280i	0.993651	+	0.112504i	$0.0358871\pi$
$420$	7.95787	+	0.849195i	0.388304	+	0.0414365i
$421$	30.7065	+	22.3096i	1.49655	+	1.08730i	0.971732	+	0.236087i	$0.0758650\pi$
$421$	30.7065	+	22.3096i	1.49655	+	1.08730i	0.524814	+	0.851217i	$0.324135\pi$
$422$	−9.54105	+	19.6426i	−0.464451	+	0.956189i
$423$	0.0171099	+	0.0335800i	0.000831911	+	0.00163272i
$424$	−19.8692	−	5.22071i	−0.964934	−	0.253540i
$425$	30.6875	+	4.06891i	1.48856	+	0.197371i
$426$	−3.51486	−	2.45267i	−0.170296	−	0.118832i
$427$	−4.70284	+	2.39622i	−0.227586	+	0.115961i
$428$	13.4063	+	24.0021i	0.648019	+	1.16019i
$429$	−2.40272	+	3.30707i	−0.116005	+	0.159667i
$430$	8.70827	+	1.09760i	0.419950	+	0.0529310i
$431$	2.67391	+	3.68032i	0.128798	+	0.177275i	0.868545	−	0.495609i	$-0.165055\pi$
$431$	2.67391	+	3.68032i	0.128798	+	0.177275i	−0.739748	+	0.672884i	$0.765055\pi$
$432$	−3.98695	−	0.322830i	−0.191822	−	0.0155321i
$433$	−12.1409	−	1.92293i	−0.583456	−	0.0924104i	−0.142273	−	0.989827i	$-0.545441\pi$
$433$	−12.1409	−	1.92293i	−0.583456	−	0.0924104i	−0.441183	+	0.897417i	$0.645441\pi$
$434$	14.2834	+	4.34161i	0.685623	+	0.208404i
$435$	−2.57572	−	7.59935i	−0.123496	−	0.364361i
$436$	−19.7096	+	0.752132i	−0.943919	+	0.0360206i
$437$	28.1787	+	14.3577i	1.34797	+	0.686824i
$438$	−4.99639	−	9.36027i	−0.238737	−	0.447251i
$439$	−4.19717	+	12.9175i	−0.200320	+	0.616521i	0.799553	+	0.600595i	$0.205070\pi$
$439$	−4.19717	+	12.9175i	−0.200320	+	0.616521i	−0.999873	+	0.0159259i	$0.994930\pi$
$440$	−1.13869	−	16.2773i	−0.0542849	−	0.775992i
$441$	−1.17351	−	3.61169i	−0.0558814	−	0.171985i
$442$	−9.62067	+	9.99481i	−0.457609	+	0.475405i
$443$	10.9593	−	10.9593i	0.520692	−	0.520692i	−0.397088	−	0.917780i	$-0.629979\pi$
$443$	10.9593	−	10.9593i	0.520692	−	0.520692i	0.917780	+	0.397088i	$0.129979\pi$
$444$	15.8616	+	10.6243i	0.752760	+	0.504207i
$445$	−5.90970	+	3.10576i	−0.280147	+	0.147227i
$446$	11.0641	−	3.82971i	0.523900	−	0.181342i
$447$	−2.69619	−	17.0231i	−0.127526	−	0.805164i
$448$	0.610449	−	14.3033i	0.0288410	−	0.675766i
$449$			30.6804i			1.44790i	0.689853	+	0.723950i	$0.257675\pi$
$449$			30.6804i			1.44790i	−0.689853	+	0.723950i	$0.742325\pi$
$450$	6.92813	−	1.41456i	0.326595	−	0.0666829i
$451$		−	18.7458i		−	0.882703i
$452$	8.92201	−	9.62997i	0.419656	−	0.452956i
$453$	1.43322	+	9.04900i	0.0673386	+	0.425159i
$454$	12.7006	+	36.6922i	0.596067	+	1.72205i
$455$	2.80679	−	5.68498i	0.131584	−	0.266516i
$456$	5.30921	+	13.6328i	0.248627	+	0.638416i
$457$	−4.67954	+	4.67954i	−0.218900	+	0.218900i	−0.808035	−	0.589135i	$-0.799469\pi$
$457$	−4.67954	+	4.67954i	−0.218900	+	0.218900i	0.589135	+	0.808035i	$0.299469\pi$
$458$	18.1209	+	17.4426i	0.846734	+	0.815038i
$459$	−1.91319	−	5.88820i	−0.0893002	−	0.274838i
$460$	−22.9083	−	14.9286i	−1.06810	−	0.696051i
$461$	−2.33115	+	7.17453i	−0.108572	+	0.334151i	−0.990552	−	0.137136i	$-0.956210\pi$
$461$	−2.33115	+	7.17453i	−0.108572	+	0.334151i	0.881980	+	0.471287i	$0.156210\pi$
$462$	5.76010	−	3.07466i	0.267984	−	0.143046i
$463$	−15.1118	−	7.69983i	−0.702303	−	0.357841i	0.0660950	−	0.997813i	$-0.478946\pi$
$463$	−15.1118	−	7.69983i	−0.702303	−	0.357841i	−0.768398	+	0.639972i	$0.778946\pi$
$464$	−13.2735	+	5.46302i	−0.616206	+	0.253614i
$465$	13.1891	−	0.166567i	0.611629	−	0.00772435i
$466$	2.21853	−	7.29869i	0.102771	−	0.338105i
$467$	6.42804	+	1.01810i	0.297454	+	0.0471121i	0.303378	−	0.952870i	$-0.401886\pi$
$467$	6.42804	+	1.01810i	0.297454	+	0.0471121i	−0.00592362	+	0.999982i	$0.501886\pi$
$468$	−1.32991	+	2.87627i	−0.0614753	+	0.132956i
$469$	−7.16401	−	9.86041i	−0.330803	−	0.455311i
$470$	−0.0815591	+	0.0869010i	−0.00376204	+	0.00400844i
$471$	2.78983	−	3.83987i	0.128549	−	0.176932i
$472$	26.5425	+	2.65955i	1.22172	+	0.122416i
$473$	6.38042	−	3.25098i	0.293372	−	0.149480i
$474$	−3.76105	+	5.38988i	−0.172751	+	0.247565i
$475$	−15.7253	−	20.5328i	−0.721526	−	0.942110i
$476$	20.7979	−	7.64610i	0.953269	−	0.350459i
$477$	−3.29746	−	6.47162i	−0.150980	−	0.296315i
$478$	12.8297	+	6.23179i	0.586817	+	0.285036i
$479$	−5.30790	−	3.85642i	−0.242524	−	0.176204i	0.459883	−	0.887980i	$-0.347891\pi$
$479$	−5.30790	−	3.85642i	−0.242524	−	0.176204i	−0.702407	+	0.711775i	$0.747891\pi$
$480$	−3.31370	−	12.2074i	−0.151249	−	0.557187i
$481$	12.2357	−	8.88975i	0.557900	−	0.405338i
$482$	7.20104	−	1.28175i	0.327999	−	0.0583823i
$483$	1.71162	−	10.8068i	0.0778815	−	0.491725i
$484$	5.37073	+	6.82856i	0.244124	+	0.310389i
$485$	−15.8363	+	22.3859i	−0.719089	+	1.01649i
$486$	−0.852921	−	1.12806i	−0.0386893	−	0.0511700i
$487$	−12.8302	+	25.1807i	−0.581391	+	1.14104i	0.393700	+	0.919239i	$0.371195\pi$
$487$	−12.8302	+	25.1807i	−0.581391	+	1.14104i	−0.975091	+	0.221806i	$0.928805\pi$
$488$	6.22652	+	5.55190i	0.281861	+	0.251323i
$489$	−5.16794	−	1.67917i	−0.233702	−	0.0759345i
$490$	9.48683	−	7.36305i	0.428571	−	0.332629i
$491$	9.75331	−	3.16904i	0.440161	−	0.143017i	−0.0805490	−	0.996751i	$-0.525667\pi$
$491$	9.75331	−	3.16904i	0.440161	−	0.143017i	0.520710	+	0.853734i	$0.325667\pi$
$492$	−2.81894	−	14.2558i	−0.127088	−	0.642700i
$493$	−15.7097	−	15.7097i	−0.707527	−	0.707527i
$494$	11.5881	−	0.221024i	0.521373	−	0.00994436i
$495$	4.02744	−	4.13047i	0.181020	−	0.185651i
$496$	−1.79820	−	23.5266i	−0.0807416	−	1.05638i
$497$	5.35671	−	0.848420i	0.240281	−	0.0380568i
$498$	11.8590	+	1.64712i	0.531416	+	0.0738092i
$499$	−12.4397			−0.556877			−0.278438	−	0.960454i	$-0.589817\pi$
$499$	−12.4397			−0.556877			−0.278438	+	0.960454i	$0.589817\pi$
$500$	11.6355	+	19.0949i	0.520355	+	0.853950i
$501$	16.5787			0.740682
$502$	−19.0879	−	2.65114i	−0.851933	−	0.118326i
$503$	−37.7591	+	5.98046i	−1.68360	+	0.266655i	−0.923624	−	0.383300i	$-0.874787\pi$
$503$	−37.7591	+	5.98046i	−1.68360	+	0.266655i	−0.759972	+	0.649956i	$0.774787\pi$
$504$	3.91808	−	3.20441i	0.174525	−	0.142736i
$505$	−28.8705	+	29.6091i	−1.28472	+	1.31759i
$506$	−22.3041	+	0.425415i	−0.991538	+	0.0189120i
$507$	−7.41727	−	7.41727i	−0.329412	−	0.329412i
$508$	33.1098	−	6.54715i	1.46901	−	0.290483i
$509$	8.26830	−	2.68653i	0.366486	−	0.119078i	−0.119984	−	0.992776i	$-0.538284\pi$
$509$	8.26830	−	2.68653i	0.366486	−	0.119078i	0.486470	+	0.873697i	$0.338284\pi$
$510$	15.4665	−	12.0041i	0.684870	−	0.531551i
$511$	12.7691	+	4.14893i	0.564871	+	0.183538i
$512$	−21.4159	+	7.30484i	−0.946457	+	0.322831i
$513$	−2.34829	+	4.60877i	−0.103679	+	0.203482i
$514$	12.9427	+	17.1178i	0.570876	+	0.755034i
$515$	−26.0163	+	36.7762i	−1.14642	+	1.62055i
$516$	4.36330	−	3.43178i	0.192084	−	0.151076i
$517$	−0.0152106	+	0.0960359i	−0.000668961	+	0.00422366i
$518$	−23.7839	+	4.23342i	−1.04500	+	0.186006i
$519$	−16.1966	+	11.7675i	−0.710950	+	0.516536i
$520$	−9.98267	−	0.873083i	−0.437769	−	0.0382872i
$521$	−16.2717	−	11.8221i	−0.712877	−	0.517935i	0.171224	−	0.985232i	$-0.445228\pi$
$521$	−16.2717	−	11.8221i	−0.712877	−	0.517935i	−0.884100	+	0.467297i	$0.845228\pi$
$522$	−4.56481	−	2.21727i	−0.199796	−	0.0970473i
$523$	12.0208	+	23.5921i	0.525632	+	1.03161i	0.989340	+	0.145623i	$0.0465186\pi$
$523$	12.0208	+	23.5921i	0.525632	+	1.03161i	−0.463708	+	0.885988i	$0.653481\pi$
$524$	3.10406	+	8.44322i	0.135601	+	0.368844i
$525$	−5.07483	+	7.36934i	−0.221484	+	0.321624i
$526$	14.6469	−	20.9901i	0.638634	−	0.915212i
$527$	32.5403	−	16.5801i	1.41748	−	0.722241i
$528$	−7.83214	−	6.71989i	−0.340850	−	0.292446i
$529$	−8.45390	+	11.6358i	−0.367561	+	0.505904i
$530$	15.7183	−	16.7478i	0.682758	−	0.727476i
$531$	5.54352	+	7.62999i	0.240568	+	0.331114i
$532$	−16.8036	−	7.76957i	−0.728530	−	0.336854i
$533$	−11.3705	−	1.80092i	−0.492513	−	0.0780063i
$534$	−1.22796	+	4.03983i	−0.0531389	+	0.174821i
$535$	−30.7350	+	0.388157i	−1.32879	+	0.0167815i
$536$	−10.4133	+	16.2067i	−0.449785	+	0.700023i
$537$	−17.7392	−	9.03859i	−0.765505	−	0.390044i
$538$	20.0295	−	10.6914i	0.863531	−	0.460941i
$539$	3.02761	−	9.31803i	0.130408	−	0.401356i
$540$	2.44166	−	3.74677i	0.105072	−	0.161235i
$541$	5.50745	+	16.9502i	0.236784	+	0.728746i	0.996880	+	0.0789350i	$0.0251520\pi$
$541$	5.50745	+	16.9502i	0.236784	+	0.728746i	−0.760096	+	0.649811i	$0.774848\pi$
$542$	3.05162	+	2.93739i	0.131078	+	0.126172i
$543$	7.20003	−	7.20003i	0.308983	−	0.308983i
$544$	−23.1901	−	26.2453i	−0.994268	−	1.12526i
$545$	9.76249	−	19.7734i	0.418179	−	0.846998i
$546$	−1.31161	−	3.78926i	−0.0561317	−	0.162166i
$547$	−3.96056	−	25.0060i	−0.169341	−	1.06918i	−0.915178	−	0.403050i	$-0.867950\pi$
$547$	−3.96056	−	25.0060i	−0.169341	−	1.06918i	0.745837	−	0.666129i	$-0.232050\pi$
$548$	−25.3252	−	23.4634i	−1.08184	−	1.00231i
$549$			2.94943i			0.125879i
$550$	16.6058	+	7.55375i	0.708072	+	0.322093i
$551$			18.5614i			0.790740i
$552$	−16.8978	+	3.67755i	−0.719219	+	0.156527i
$553$	−1.30101	−	8.21427i	−0.0553247	−	0.349306i
$554$	23.1748	−	8.02169i	0.984604	−	0.340809i
$555$	−18.8941	+	9.92956i	−0.802011	+	0.421486i
$556$	−15.7136	+	23.4597i	−0.666404	+	0.994914i
$557$	10.1259	−	10.1259i	0.429048	−	0.429048i	−0.459256	−	0.888304i	$-0.651884\pi$
$557$	10.1259	−	10.1259i	0.429048	−	0.429048i	0.888304	+	0.459256i	$0.151884\pi$
$558$	5.78524	−	6.01022i	0.244909	−	0.254433i
$559$	−1.35897	−	4.18247i	−0.0574781	−	0.176899i
$560$	13.7335	+	8.22116i	0.580345	+	0.347407i
$561$	4.93597	−	15.1913i	0.208397	−	0.641379i
$562$	−6.63160	−	12.4237i	−0.279737	−	0.524062i
$563$	−38.7259	−	19.7318i	−1.63210	−	0.831597i	−0.998311	−	0.0580911i	$-0.981499\pi$
$563$	−38.7259	−	19.7318i	−1.63210	−	0.831597i	−0.633789	−	0.773506i	$-0.718501\pi$
$564$	0.00287429	+	0.0753207i	0.000121029	+	0.00317157i
$565$	4.71145	+	13.9006i	0.198212	+	0.584801i
$566$	−15.3126	−	4.65445i	−0.643636	−	0.195641i
$567$	1.76751	+	0.279945i	0.0742282	+	0.0117566i
$568$	−4.32198	−	7.40269i	−0.181346	−	0.310610i
$569$	19.2119	+	26.4429i	0.805405	+	1.10855i	0.992016	+	0.126111i	$0.0402497\pi$
$569$	19.2119	+	26.4429i	0.805405	+	1.10855i	−0.186611	+	0.982434i	$0.559750\pi$
$570$	−16.2286	−	2.04548i	−0.679743	−	0.0856756i
$571$	−22.6330	+	31.1516i	−0.947160	+	1.30365i	0.00561699	+	0.999984i	$0.498212\pi$
$571$	−22.6330	+	31.1516i	−0.947160	+	1.30365i	−0.952777	+	0.303670i	$0.901788\pi$
$572$	−7.13761	+	3.98668i	−0.298438	+	0.166692i
$573$	11.4051	−	5.81121i	0.476457	−	0.242767i
$574$	15.0800	+	10.5228i	0.629426	+	0.439213i
$575$	26.8795	−	14.5623i	1.12095	−	0.607288i
$576$	−6.96670	−	3.93256i	−0.290279	−	0.163857i
$577$	0.778351	+	1.52760i	0.0324032	+	0.0635948i	0.906641	−	0.421904i	$-0.138638\pi$
$577$	0.778351	+	1.52760i	0.0324032	+	0.0635948i	−0.874237	+	0.485499i	$0.838638\pi$
$578$	13.1804	−	27.1352i	0.548233	−	1.12868i
$579$	−3.65839	−	2.65798i	−0.152038	−	0.110462i
$580$	1.70283	−	15.9574i	0.0707063	−	0.662594i
$581$	−12.2569	+	8.90519i	−0.508503	+	0.369449i
$582$	3.03914	+	17.0743i	0.125977	+	0.707751i
$583$	2.93142	−	18.5083i	0.121407	−	0.766534i
$584$	−1.21344	−	21.1859i	−0.0502124	−	0.876678i
$585$	−2.11848	−	2.83973i	−0.0875885	−	0.117408i
$586$	30.9598	−	23.4085i	1.27894	−	0.966997i
$587$	10.0460	−	19.7163i	0.414642	−	0.813780i	−0.585354	−	0.810778i	$-0.699044\pi$
$587$	10.0460	−	19.7163i	0.414642	−	0.813780i	0.999995	−	0.00300205i	$-0.000955585\pi$
$588$	0.901215	−	7.54146i	0.0371655	−	0.311004i
$589$	−29.0185	−	9.42868i	−1.19569	−	0.388502i
$590$	−16.7566	+	24.6716i	−0.689859	+	1.01572i
$591$	11.0234	−	3.58173i	0.453444	−	0.147333i
$592$	19.8766	+	32.6005i	0.816923	+	1.33987i
$593$	−24.7989	−	24.7989i	−1.01837	−	1.01837i	−0.999828	−	0.0185411i	$-0.994098\pi$
$593$	−24.7989	−	24.7989i	−1.01837	−	1.01837i	−0.0185411	−	0.999828i	$-0.505902\pi$
$594$	−0.0695789	−	3.64796i	−0.00285486	−	0.149677i
$595$	−3.56625	+	24.5163i	−0.146202	+	1.00507i
$596$	9.39411	−	33.1658i	0.384798	−	1.35852i
$597$	−8.24701	+	1.30620i	−0.337528	+	0.0534591i
$598$	−1.88473	+	13.5698i	−0.0770721	+	0.554909i
$599$	5.41697			0.221331			0.110666	−	0.993858i	$-0.464702\pi$
$599$	5.41697			0.221331			0.110666	+	0.993858i	$0.464702\pi$
$600$	13.7643	+	3.24734i	0.561923	+	0.132572i
$601$	−13.7486			−0.560819			−0.280409	−	0.959881i	$-0.590470\pi$
$601$	−13.7486			−0.560819			−0.280409	+	0.959881i	$0.590470\pi$
$602$	−0.966355	+	6.95763i	−0.0393857	+	0.283572i
$603$	−6.72692	+	1.06544i	−0.273942	+	0.0433881i
$604$	−4.99365	+	17.6300i	−0.203189	+	0.717355i
$605$	−9.57347	+	1.64047i	−0.389217	+	0.0666948i
$606$	0.498774	+	26.1502i	0.0202613	+	1.06228i
$607$	25.1868	+	25.1868i	1.02230	+	1.02230i	0.999746	+	0.0225567i	$0.00718063\pi$
$607$	25.1868	+	25.1868i	1.02230	+	1.02230i	0.0225567	+	0.999746i	$0.492819\pi$
$608$	−1.80492	+	29.2046i	−0.0731993	+	1.18440i
$609$	6.10734	−	1.98440i	0.247482	−	0.0804118i
$610$	−8.77463	+	3.16187i	−0.355274	+	0.128020i
$611$	0.0567908	+	0.0184525i	0.00229751	+	0.000746506i
$612$	1.46927	−	12.2950i	0.0593916	−	0.496995i
$613$	9.17652	−	18.0099i	0.370636	−	0.727415i	−0.628076	−	0.778152i	$-0.716157\pi$
$613$	9.17652	−	18.0099i	0.370636	−	0.727415i	0.998712	+	0.0507375i	$0.0161572\pi$
$614$	−6.11908	+	4.62660i	−0.246946	+	0.186714i
$615$	15.5140	+	4.82509i	0.625586	+	0.194566i
$616$	13.0373	−	0.746722i	0.525288	−	0.0300863i
$617$	−2.43800	+	15.3930i	−0.0981503	+	0.619697i	0.888753	+	0.458386i	$0.151572\pi$
$617$	−2.43800	+	15.3930i	−0.0981503	+	0.619697i	−0.986904	+	0.161311i	$0.948428\pi$
$618$	4.99279	+	28.0501i	0.200839	+	1.12834i
$619$	11.5048	−	8.35870i	0.462415	−	0.335964i	−0.332063	−	0.943257i	$-0.607745\pi$
$619$	11.5048	−	8.35870i	0.462415	−	0.335964i	0.794478	+	0.607293i	$0.207745\pi$
$620$	24.0825	+	10.7681i	0.967176	+	0.432458i
$621$	−4.94644	−	3.59380i	−0.198494	−	0.144214i
$622$	5.12610	−	10.5534i	0.205538	−	0.423151i
$623$	−2.42563	−	4.76058i	−0.0971810	−	0.190728i
$624$	−4.82850	+	4.10513i	−0.193295	+	0.164337i
$625$	−24.9681	+	1.26231i	−0.998724	+	0.0504924i
$626$	−21.7110	−	15.1499i	−0.867745	−	0.605512i
$627$	−11.8905	+	6.05850i	−0.474860	+	0.241953i
$628$	8.28755	−	4.62898i	0.330709	−	0.184716i
$629$	−34.7372	+	47.8116i	−1.38506	+	1.90637i
$630$	1.06197	+	5.55848i	0.0423099	+	0.221455i
$631$	−12.7859	−	17.5983i	−0.508999	−	0.700577i	0.474751	−	0.880120i	$-0.342538\pi$
$631$	−12.7859	−	17.5983i	−0.508999	−	0.700577i	−0.983750	+	0.179543i	$0.942538\pi$
$632$	−11.3517	+	6.62756i	−0.451545	+	0.263630i
$633$	−15.2512	−	2.41555i	−0.606179	−	0.0960093i
$634$	−1.43327	−	0.435661i	−0.0569225	−	0.0173023i
$635$	−11.2065	+	36.0322i	−0.444718	+	1.42990i
$636$	−0.553940	−	14.5160i	−0.0219651	−	0.575596i
$637$	−5.36114	−	2.73163i	−0.212416	−	0.108231i
$638$	−6.16541	−	11.5503i	−0.244091	−	0.457282i
$639$	0.936526	−	2.88233i	0.0370484	−	0.114023i
$640$	4.23096	−	24.9419i	0.167244	−	0.985916i
$641$	3.91015	+	12.0342i	0.154442	+	0.475322i	0.998104	−	0.0615520i	$-0.0196050\pi$
$641$	3.91015	+	12.0342i	0.154442	+	0.475322i	−0.843662	+	0.536874i	$0.819605\pi$
$642$	−13.4816	+	14.0058i	−0.532075	+	0.552766i
$643$	31.0681	−	31.0681i	1.22521	−	1.22521i	0.259450	−	0.965756i	$-0.416459\pi$
$643$	31.0681	−	31.0681i	1.22521	−	1.22521i	0.965756	−	0.259450i	$-0.0835414\pi$
$644$	12.1780	−	18.1813i	0.479881	−	0.716443i
$645$	1.04823	+	6.11724i	0.0412739	+	0.240866i
$646$	−42.7980	+	14.8140i	−1.68386	+	0.582850i
$647$	7.56645	+	47.7727i	0.297468	+	1.87814i	0.454803	+	0.890592i	$0.349710\pi$
$647$	7.56645	+	47.7727i	0.297468	+	1.87814i	−0.157336	+	0.987545i	$0.550290\pi$
$648$	−0.601484	−	2.76373i	−0.0236285	−	0.108570i
$649$			24.3321i			0.955120i
$650$	6.17717	−	9.34680i	0.242289	−	0.366612i
$651$			10.5561i			0.413727i
$652$	−7.97214	−	7.38606i	−0.312213	−	0.289260i
$653$	−0.865641	−	5.46544i	−0.0338752	−	0.213879i	0.964944	−	0.262454i	$-0.0845320\pi$
$653$	−0.865641	−	5.46544i	−0.0338752	−	0.213879i	−0.998820	+	0.0485752i	$0.984532\pi$
$654$	−4.56201	−	13.1797i	−0.178389	−	0.515368i
$655$	−9.95278	−	1.44777i	−0.388887	−	0.0565692i
$656$	6.84849	−	28.2452i	0.267388	−	1.10279i
$657$	5.30515	−	5.30515i	0.206974	−	0.206974i
$658$	−0.0687175	−	0.0661452i	−0.00267889	−	0.00257861i
$659$	−14.2601	−	43.8880i	−0.555494	−	1.70963i	−0.694635	−	0.719362i	$-0.744434\pi$
$659$	−14.2601	−	43.8880i	−0.555494	−	1.70963i	0.139141	−	0.990273i	$-0.455566\pi$
$660$	10.7782	−	4.11771i	0.419539	−	0.160282i
$661$	10.7448	−	33.0690i	0.417923	−	1.28624i	−0.491687	−	0.870772i	$-0.663619\pi$
$661$	10.7448	−	33.0690i	0.417923	−	1.28624i	0.909610	−	0.415463i	$-0.136381\pi$
$662$	−39.3227	+	20.9899i	−1.52832	+	0.815797i
$663$	−8.74035	−	4.45343i	−0.339447	−	0.172957i
$664$	20.1457	+	12.9442i	0.781803	+	0.502331i
$665$	16.5901	−	12.3765i	0.643338	−	0.479941i
$666$	−3.92595	+	12.9159i	−0.152128	+	0.500481i
$667$	−21.6701	−	3.43220i	−0.839068	−	0.132895i
$668$	30.0960	+	13.9156i	1.16445	+	0.538412i
$669$	4.86623	+	6.69779i	0.188139	+	0.258951i
$670$	−10.3812	−	18.8706i	−0.401059	−	0.729034i
$671$	−4.47271	+	6.15616i	−0.172667	+	0.237656i
$672$	9.80232	−	2.52838i	0.378133	−	0.0975346i
$673$	22.2414	−	11.3325i	0.857342	−	0.436838i	0.0306753	−	0.999529i	$-0.490234\pi$
$673$	22.2414	−	11.3325i	0.857342	−	0.436838i	0.826667	+	0.562692i	$0.190234\pi$
$674$	16.3738	−	23.4649i	0.630694	−	0.903833i
$675$	2.38174	+	4.39629i	0.0916731	+	0.169213i
$676$	−7.23906	−	19.6907i	−0.278425	−	0.757334i
$677$	−8.19739	−	16.0883i	−0.315051	−	0.618323i	0.678125	−	0.734947i	$-0.262793\pi$
$677$	−8.19739	−	16.0883i	−0.315051	−	0.618323i	−0.993176	+	0.116624i	$0.962793\pi$
$678$	8.34985	+	4.05578i	0.320674	+	0.155761i
$679$	−17.7541	−	12.8991i	−0.681340	−	0.495022i
$680$	38.1529	−	8.80944i	1.46310	−	0.337826i
$681$	−22.2120	+	16.1380i	−0.851167	+	0.618409i
$682$	21.1895	−	3.77163i	0.811386	−	0.144423i
$683$	−3.32035	+	20.9639i	−0.127050	+	0.802161i	0.839062	+	0.544036i	$0.183105\pi$
$683$	−3.32035	+	20.9639i	−0.127050	+	0.802161i	−0.966112	+	0.258125i	$0.916895\pi$
$684$	−8.13140	+	6.39542i	−0.310912	+	0.244535i
$685$	36.5561	−	12.3903i	1.39674	−	0.473409i
$686$	16.4807	+	21.7971i	0.629235	+	0.832219i
$687$	−8.07421	+	15.8465i	−0.308050	+	0.604583i
$688$	10.8014	−	2.56743i	0.411800	−	0.0978825i
$689$	−10.9449	−	3.55620i	−0.416966	−	0.135480i
$690$	5.38891	−	18.5684i	0.205152	−	0.706887i
$691$	27.8609	−	9.05257i	1.05988	−	0.344376i	0.273342	−	0.961917i	$-0.411871\pi$
$691$	27.8609	−	9.05257i	1.05988	−	0.344376i	0.786539	+	0.617541i	$0.211871\pi$
$692$	−39.2795	+	7.76715i	−1.49318	+	0.295263i
$693$	3.26467	+	3.26467i	0.124015	+	0.124015i
$694$	−0.455153	+	0.00868131i	−0.0172774	+	0.000329538i
$695$	−14.6860	−	27.9449i	−0.557073	−	1.06001i
$696$	−6.42558	−	7.85665i	−0.243561	−	0.297806i
$697$	44.4310	−	7.03717i	1.68294	−	0.266552i
$698$	2.67181	+	0.371092i	0.101130	+	0.0140460i
$699$	5.39410			0.204024
$700$	−15.3981	+	9.11822i	−0.581995	+	0.344636i
$701$	−26.3853			−0.996559			−0.498279	−	0.867016i	$-0.666035\pi$
$701$	−26.3853			−0.996559			−0.498279	+	0.867016i	$0.666035\pi$
$702$	−2.21941	−	0.308257i	−0.0837662	−	0.0116344i
$703$	48.7668	−	7.72390i	1.83927	−	0.291312i
$704$	−8.57755	−	18.7729i	−0.323279	−	0.707532i
$705$	−0.0755644	−	0.0373076i	−0.00284592	−	0.00140509i
$706$	−12.6231	+	0.240766i	−0.475077	+	0.00906134i
$707$	−23.4026	−	23.4026i	−0.880147	−	0.880147i
$708$	3.65900	+	18.5041i	0.137514	+	0.695426i
$709$	−12.9991	+	4.22365i	−0.488190	+	0.158623i	−0.542761	−	0.839887i	$-0.682621\pi$
$709$	−12.9991	+	4.22365i	−0.488190	+	0.158623i	0.0545707	+	0.998510i	$0.482621\pi$
$710$	9.57898	−	0.303751i	0.359493	−	0.0113996i
$711$	−4.41992	−	1.43612i	−0.165760	−	0.0538587i
$712$	−5.62007	+	6.30297i	−0.210621	+	0.236214i
$713$	16.3737	−	32.1351i	0.613198	−	1.20347i
$714$	9.44987	+	12.4983i	0.353653	+	0.467737i
$715$	−0.115428	−	9.13978i	−0.00431674	−	0.341808i
$716$	−24.6161	−	31.2979i	−0.919945	−	1.16966i
$717$	−1.57773	+	9.96138i	−0.0589213	+	0.372015i
$718$	−28.8096	+	5.12798i	−1.07516	+	0.191375i
$719$	−28.1664	+	20.4641i	−1.05043	+	0.763183i	−0.972294	−	0.233760i	$-0.924897\pi$
$719$	−28.1664	+	20.4641i	−1.05043	+	0.763183i	−0.0781367	+	0.996943i	$0.524897\pi$
$720$	7.57736	−	4.75222i	0.282392	−	0.177105i
$721$	−29.1669	−	21.1910i	−1.08623	−	0.789194i
$722$	9.86535	+	4.79191i	0.367150	+	0.178337i
$723$	2.34801	+	4.60823i	0.0873235	+	0.171382i
$724$	19.1140	−	7.02704i	0.710366	−	0.261158i
$725$	14.7772	+	10.1762i	0.548813	+	0.377935i
$726$	−3.51536	+	5.03778i	−0.130467	+	0.186970i
$727$	31.4045	−	16.0014i	1.16473	−	0.593458i	0.238766	−	0.971077i	$-0.423257\pi$
$727$	31.4045	−	16.0014i	1.16473	−	0.593458i	0.925961	+	0.377619i	$0.123257\pi$
$728$	0.799566	−	7.97973i	0.0296339	−	0.295748i
$729$	0.587785	−	0.809017i	0.0217698	−	0.0299636i
$730$	21.4702	+	10.0957i	0.794648	+	0.373658i
$731$	10.1007	+	13.9024i	0.373586	+	0.514197i
$732$	−2.47566	+	5.35422i	−0.0915029	+	0.197898i
$733$	−21.4328	−	3.39462i	−0.791637	−	0.125383i	−0.252495	−	0.967598i	$-0.581251\pi$
$733$	−21.4328	−	3.39462i	−0.791637	−	0.125383i	−0.539142	+	0.842215i	$0.681251\pi$
$734$	−6.39440	+	21.0368i	−0.236022	+	0.776482i
$735$	6.93233	+	4.90408i	0.255703	+	0.180890i
$736$	−33.7621	−	7.50748i	−1.24449	−	0.276729i
$737$	−15.6564	−	7.97732i	−0.576710	−	0.293848i
$738$	9.06494	−	4.83874i	0.333685	−	0.178117i
$739$	7.04674	−	21.6876i	0.259219	−	0.797793i	−0.733751	−	0.679419i	$-0.762232\pi$
$739$	7.04674	−	21.6876i	0.259219	−	0.797793i	0.992969	−	0.118374i	$-0.0377681\pi$
$740$	−42.6338	+	2.16641i	−1.56725	+	0.0796388i
$741$	2.53255	+	7.79439i	0.0930356	+	0.286334i
$742$	13.2434	+	12.7477i	0.486181	+	0.467981i
$743$	12.9863	−	12.9863i	0.476422	−	0.476422i	−0.427563	−	0.903985i	$-0.640628\pi$
$743$	12.9863	−	12.9863i	0.476422	−	0.476422i	0.903985	+	0.427563i	$0.140628\pi$
$744$	15.5470	−	6.05466i	0.569980	−	0.221975i
$745$	27.5933	+	26.9051i	1.01094	+	0.985725i
$746$	−3.50469	−	10.1251i	−0.128316	−	0.370707i
$747$	1.32439	+	8.36187i	0.0484569	+	0.305945i
$748$	21.7116	−	23.4344i	0.793854	−	0.856846i
$749$		−	24.5993i		−	0.898840i
$750$	−10.5258	+	11.7987i	−0.384346	+	0.430826i
$751$		−	17.3842i		−	0.634360i	−0.948365	−	0.317180i	$-0.897264\pi$
$751$		−	17.3842i		−	0.634360i	0.948365	−	0.317180i	$-0.102736\pi$
$752$	−0.0580039	+	0.139145i	−0.00211518	+	0.00507411i
$753$	−2.13169	−	13.4589i	−0.0776830	−	0.490471i
$754$	−7.59835	+	2.63008i	−0.276716	+	0.0957819i
$755$	−14.6678	−	14.3020i	−0.533817	−	0.520502i
$756$	2.97365	+	1.99178i	0.108151	+	0.0724404i
$757$	−0.770220	+	0.770220i	−0.0279941	+	0.0279941i	−0.720965	−	0.692971i	$-0.756301\pi$
$757$	−0.770220	+	0.770220i	−0.0279941	+	0.0279941i	0.692971	+	0.720965i	$0.256301\pi$
$758$	34.3942	−	35.7317i	1.24925	−	1.29783i
$759$	−4.87451	−	15.0022i	−0.176933	−	0.544545i
$760$	−27.7436	−	17.3350i	−1.00637	−	0.628807i
$761$	5.86337	−	18.0456i	0.212547	−	0.654152i	−0.786772	−	0.617244i	$-0.788249\pi$
$761$	5.86337	−	18.0456i	0.212547	−	0.654152i	0.999319	−	0.0369083i	$-0.0117509\pi$
$762$	11.2383	+	21.0539i	0.407119	+	0.762701i
$763$	15.7248	+	8.01219i	0.569276	+	0.290061i
$764$	25.5820	−	0.976226i	0.925523	−	0.0353186i
$765$	11.3019	+	7.99521i	0.408621	+	0.289067i
$766$	15.5721	+	4.73335i	0.562644	+	0.171023i
$767$	14.7590	+	2.33760i	0.532918	+	0.0844059i
$768$	−9.34608	−	12.9866i	−0.337248	−	0.468612i
$769$	23.8890	+	32.8804i	0.861459	+	1.18570i	0.981220	+	0.192894i	$0.0617872\pi$
$769$	23.8890	+	32.8804i	0.861459	+	1.18570i	−0.119761	+	0.992803i	$0.538213\pi$
$770$	−6.21265	+	13.2123i	−0.223888	+	0.476138i
$771$	−8.91936	+	12.2764i	−0.321223	+	0.442125i
$772$	−4.41021	−	7.89587i	−0.158727	−	0.284179i
$773$	8.89205	−	4.53072i	0.319825	−	0.162959i	−0.286707	−	0.958018i	$-0.592560\pi$
$773$	8.89205	−	4.53072i	0.319825	−	0.162959i	0.606531	+	0.795060i	$0.292560\pi$
$774$	3.21903	+	2.24624i	0.115706	+	0.0807393i
$775$	−23.4158	+	17.9332i	−0.841119	+	0.644180i
$776$	−8.81450	+	33.5466i	−0.316422	+	1.20425i
$777$	−7.75509	−	15.2202i	−0.278212	−	0.546023i
$778$	6.49669	−	13.3751i	0.232918	−	0.479519i
$779$	−30.4055	−	22.0909i	−1.08939	−	0.791487i
$780$	−1.46220	−	6.93325i	−0.0523550	−	0.248250i
$781$	6.32570	−	4.59589i	0.226351	−	0.164454i
$782$	−9.38129	−	52.7052i	−0.335474	−	1.88473i
$783$	0.561355	−	3.54426i	0.0200612	−	0.126661i
$784$	7.96606	−	12.9339i	0.284502	−	0.461924i
$785$	0.134024	+	10.6123i	0.00478353	+	0.378769i
$786$	−5.07387	+	3.83632i	−0.180979	+	0.136837i
$787$	18.5177	−	36.3430i	0.660084	−	1.29549i	−0.281775	−	0.959480i	$-0.590923\pi$
$787$	18.5177	−	36.3430i	0.660084	−	1.29549i	0.941859	−	0.336007i	$-0.109077\pi$
$788$	23.0177	+	2.75065i	0.819972	+	0.0979878i
$789$	17.2127	+	5.59276i	0.612790	+	0.199107i
$790$	−0.465788	−	14.6889i	−0.0165720	−	0.522608i
$791$	−11.1714	+	3.62981i	−0.397210	+	0.129061i
$792$	2.93567	−	6.68069i	0.104314	−	0.237388i
$793$	3.30442	+	3.30442i	0.117343	+	0.117343i
$794$	−0.173580	−	9.10065i	−0.00616014	−	0.322970i
$795$	14.5629	+	7.19001i	0.516494	+	0.255003i
$796$	−16.0675	−	4.55107i	−0.569498	−	0.161309i
$797$	4.72778	−	0.748807i	0.167467	−	0.0265241i	−0.0721379	−	0.997395i	$-0.522982\pi$
$797$	4.72778	−	0.748807i	0.167467	−	0.0265241i	0.239605	+	0.970871i	$0.422982\pi$
$798$	1.80089	−	12.9662i	0.0637507	−	0.458997i
$799$	−0.233333			−0.00825474
$800$	22.2611	+	17.4483i	0.787049	+	0.616891i
$801$	−2.98564			−0.105493
$802$	−4.18017	+	30.0967i	−0.147607	+	1.06275i
$803$	19.1182	−	3.02802i	0.674666	−	0.106857i
$804$	−13.1060	−	3.71222i	−0.462211	−	0.130920i
$805$	11.3817	+	21.6572i	0.401151	+	0.763318i
$806$	−0.252058	−	13.2151i	−0.00887835	−	0.465483i
$807$	11.3522	+	11.3522i	0.399615	+	0.399615i
$808$	−21.0442	+	47.8902i	−0.740332	+	1.68477i
$809$	−2.35381	+	0.764801i	−0.0827557	+	0.0268890i	−0.350102	−	0.936711i	$-0.613853\pi$
$809$	−2.35381	+	0.764801i	−0.0827557	+	0.0268890i	0.267347	+	0.963600i	$0.413853\pi$
$810$	3.03697	+	0.881386i	0.106708	+	0.0309687i
$811$	11.1441	+	3.62095i	0.391323	+	0.127149i	0.498068	−	0.867138i	$-0.334043\pi$
$811$	11.1441	+	3.62095i	0.391323	+	0.127149i	−0.106745	+	0.994286i	$0.534043\pi$
$812$	12.7525	+	1.52395i	0.447527	+	0.0534801i
$813$	−1.35972	+	2.66861i	−0.0476876	+	0.0935922i
$814$	−27.7809	+	21.0050i	−0.973720	+	0.736224i
$815$	11.5075	−	3.90036i	0.403091	−	0.136624i
$816$	12.9872	−	21.0863i	0.454643	−	0.738168i
$817$	2.24591	−	14.1801i	0.0785743	−	0.496098i
$818$	6.56438	+	36.8795i	0.229518	+	1.28946i
$819$	2.29388	−	1.66660i	0.0801545	−	0.0582357i
$820$	24.1132	+	21.7811i	0.842071	+	0.760631i
$821$	−36.4321	−	26.4694i	−1.27149	−	0.923790i	−0.272227	−	0.962233i	$-0.587760\pi$
$821$	−36.4321	−	26.4694i	−1.27149	−	0.923790i	−0.999261	+	0.0384434i	$0.987760\pi$
$822$	10.6660	−	21.9587i	0.372020	−	0.765897i
$823$	6.03211	+	11.8387i	0.210266	+	0.412670i	0.971919	−	0.235314i	$-0.0756120\pi$
$823$	6.03211	+	11.8387i	0.210266	+	0.412670i	−0.761653	+	0.647985i	$0.775612\pi$
$824$	−14.4807	+	55.1112i	−0.504459	+	1.91989i
$825$	−1.69557	+	12.7879i	−0.0590321	+	0.445217i
$826$	−19.5739	−	13.6587i	−0.681064	−	0.475246i
$827$	−24.7640	+	12.6179i	−0.861127	+	0.438766i	−0.828029	−	0.560686i	$-0.810538\pi$
$827$	−24.7640	+	12.6179i	−0.861127	+	0.438766i	−0.0330987	+	0.999452i	$0.510538\pi$
$828$	−5.96296	−	10.6758i	−0.207227	−	0.371011i
$829$	12.5423	−	17.2630i	0.435612	−	0.599568i	−0.533618	−	0.845725i	$-0.679168\pi$
$829$	12.5423	−	17.2630i	0.435612	−	0.599568i	0.969230	+	0.246158i	$0.0791681\pi$
$830$	−23.4570	+	12.9042i	−0.814203	+	0.447913i
$831$	10.1928	+	14.0292i	0.353584	+	0.486666i
$832$	−12.2111	+	3.39932i	−0.423343	+	0.117850i
$833$	23.2221	+	3.67801i	0.804596	+	0.127436i
$834$	−19.1029	−	5.80657i	−0.661480	−	0.201065i
$835$	−29.7136	+	22.1669i	−1.02828	+	0.767116i
$836$	−26.6706	+	1.01777i	−0.922420	+	0.0352002i
$837$	5.25587	+	2.67800i	0.181670	+	0.0925653i
$838$	20.1137	+	37.6811i	0.694815	+	1.30167i
$839$	4.45524	−	13.7118i	0.153812	−	0.473385i	−0.844227	−	0.535987i	$-0.819940\pi$
$839$	4.45524	−	13.7118i	0.153812	−	0.473385i	0.998039	+	0.0626017i	$0.0199398\pi$
$840$	−2.73776	+	10.9819i	−0.0944619	+	0.378912i
$841$	4.98232	+	15.3340i	0.171804	+	0.528759i
$842$	−37.2247	+	38.6723i	−1.28285	+	1.33273i
$843$	7.04142	−	7.04142i	0.242519	−	0.242519i
$844$	−25.6585	−	17.1864i	−0.883203	−	0.591579i
$845$	23.2112	+	3.37640i	0.798488	+	0.116152i
$846$	−0.0503666	+	0.0174338i	−0.00173164	+	0.000599387i
$847$	−1.21602	−	7.67767i	−0.0417830	−	0.263808i
$848$	11.1786	−	26.8164i	0.383876	−	0.920879i
$849$		−	11.3168i		−	0.388391i
$850$	−11.6700	+	42.1945i	−0.400278	+	1.44726i
$851$			58.3626i			2.00064i
$852$	4.11945	−	4.44632i	0.141130	−	0.152329i
$853$	6.23886	+	39.3906i	0.213615	+	1.34871i	0.828454	+	0.560057i	$0.189221\pi$
$853$	6.23886	+	39.3906i	0.213615	+	1.34871i	−0.614840	+	0.788652i	$0.710779\pi$
$854$	−2.44158	−	7.05377i	−0.0835492	−	0.241375i
$855$	−1.95346	−	11.4000i	−0.0668071	−	0.389872i
$856$	−36.2297	+	14.1094i	−1.23830	+	0.482249i
$857$	11.2607	−	11.2607i	0.384659	−	0.384659i	−0.488119	−	0.872777i	$-0.662317\pi$
$857$	11.2607	−	11.2607i	0.384659	−	0.384659i	0.872777	+	0.488119i	$0.162317\pi$
$858$	−4.16497	−	4.00906i	−0.142190	−	0.136867i
$859$	15.0260	+	46.2452i	0.512680	+	1.57787i	0.787465	+	0.616360i	$0.211393\pi$
$859$	15.0260	+	46.2452i	0.512680	+	1.57787i	−0.274785	+	0.961506i	$0.588607\pi$
$860$	−3.23172	+	11.9847i	−0.110201	+	0.408675i
$861$	−4.01802	+	12.3662i	−0.136934	+	0.421439i
$862$	−5.67549	+	3.02950i	−0.193308	+	0.103185i
$863$	11.9945	+	6.11151i	0.408298	+	0.208038i	0.646062	−	0.763285i	$-0.276415\pi$
$863$	11.9945	+	6.11151i	0.408298	+	0.208038i	−0.237764	+	0.971323i	$0.576415\pi$
$864$	1.22789	−	5.52198i	0.0417736	−	0.187862i
$865$	13.2948	−	42.7465i	0.452036	−	1.45342i
$866$	5.05566	−	16.6325i	0.171798	−	0.565195i
$867$	21.0686	+	3.33694i	0.715527	+	0.113328i
$868$	−8.86047	+	19.1630i	−0.300744	+	0.650434i
$869$	−7.04759	−	9.70017i	−0.239073	−	0.329056i
$870$	11.1460	−	2.12950i	0.377886	−	0.0721967i
$871$	−6.34289	+	8.73023i	−0.214920	+	0.295813i
$872$	2.78103	−	27.7549i	0.0941776	−	0.939899i
$873$	−10.9265	+	5.56733i	−0.369806	+	0.188426i
$874$	−25.5941	+	36.6784i	−0.865735	+	1.24066i
$875$	−0.757816	−	19.9933i	−0.0256189	−	0.675896i
$876$	14.0836	−	5.17769i	0.475842	−	0.174938i
$877$	24.5889	+	48.2585i	0.830309	+	1.62957i	0.775731	+	0.631064i	$0.217382\pi$
$877$	24.5889	+	48.2585i	0.830309	+	1.62957i	0.0545785	+	0.998509i	$0.482618\pi$
$878$	−17.2779	−	8.39242i	−0.583101	−	0.283230i
$879$	22.2036	+	16.1318i	0.748908	+	0.544113i
$880$	23.0223	+	1.57179i	0.776082	+	0.0529851i
$881$	15.7949	−	11.4757i	0.532145	−	0.386626i	−0.289014	−	0.957325i	$-0.593328\pi$
$881$	15.7949	−	11.4757i	0.532145	−	0.386626i	0.821160	+	0.570699i	$0.193328\pi$
$882$	5.28745	−	0.941143i	0.178038	−	0.0316899i
$883$	−3.04871	+	19.2488i	−0.102597	+	0.647774i	0.881774	+	0.471671i	$0.156349\pi$
$883$	−3.04871	+	19.2488i	−0.102597	+	0.647774i	−0.984372	+	0.176103i	$0.943651\pi$
$884$	−12.1287	−	15.4209i	−0.407931	−	0.518660i
$885$	−20.1373	−	6.26300i	−0.676909	−	0.210528i
$886$	13.2192	+	17.4836i	0.444109	+	0.587373i
$887$	−5.86298	+	11.5067i	−0.196860	+	0.386359i	−0.968243	−	0.250012i	$-0.919565\pi$
$887$	−5.86298	+	11.5067i	−0.196860	+	0.386359i	0.771383	+	0.636371i	$0.219565\pi$
$888$	−17.9681	+	20.1515i	−0.602971	+	0.676239i
$889$	−28.7212	−	9.33210i	−0.963279	−	0.312988i
$890$	−3.20069	−	8.88235i	−0.107287	−	0.297737i
$891$	2.45369	−	0.797253i	0.0822017	−	0.0267090i
$892$	3.21196	+	16.2433i	0.107544	+	0.543867i
$893$	0.137845	+	0.137845i	0.00461279	+	0.00461279i
$894$	24.3699	−	0.464818i	0.815053	−	0.0155458i
$895$	43.8788	−	7.51891i	1.46671	−	0.251329i
$896$	19.9168	+	3.63787i	0.665373	+	0.121533i
$897$	−9.56812	+	1.51544i	−0.319470	+	0.0505991i
$898$	−42.9762	−	5.96902i	−1.43413	−	0.199189i
$899$	21.1675			0.705975
$900$	0.633567	+	9.97991i	0.0211189	+	0.332664i
$901$	44.9685			1.49812
$902$	26.2584	+	3.64707i	0.874311	+	0.121434i
$903$	−4.90586	+	0.777012i	−0.163257	+	0.0258573i
$904$	11.7535	+	14.3712i	0.390916	+	0.477980i
$905$	−3.27751	+	22.5314i	−0.108948	+	0.748968i
$906$	−12.9544	+	0.247084i	−0.430380	+	0.00820882i
$907$	−10.8696	−	10.8696i	−0.360919	−	0.360919i	0.503232	−	0.864151i	$-0.332144\pi$
$907$	−10.8696	−	10.8696i	−0.360919	−	0.360919i	−0.864151	+	0.503232i	$0.832144\pi$
$908$	−53.8681	+	10.6519i	−1.78768	+	0.353496i
$909$	−17.5892	+	5.71507i	−0.583396	+	0.189557i
$910$	7.41727	+	5.03769i	0.245880	+	0.166998i
$911$	30.7028	+	9.97593i	1.01723	+	0.330517i	0.769729	−	0.638371i	$-0.220391\pi$
$911$	30.7028	+	9.97593i	1.01723	+	0.330517i	0.247499	+	0.968888i	$0.420391\pi$
$912$	−20.1294	+	4.78464i	−0.666550	+	0.158435i
$913$	−9.91617	+	19.4616i	−0.328177	+	0.644084i
$914$	−5.64452	−	7.46537i	−0.186704	−	0.246933i
$915$	−3.94359	−	5.28619i	−0.130371	−	0.174756i
$916$	−27.9585	+	21.9896i	−0.923774	+	0.726557i
$917$	1.25916	−	7.95000i	0.0415810	−	0.262532i
$918$	8.62022	−	1.53436i	0.284510	−	0.0506415i
$919$	−20.5334	+	14.9184i	−0.677333	+	0.492111i	−0.872472	−	0.488664i	$-0.837484\pi$
$919$	−20.5334	+	14.9184i	−0.677333	+	0.492111i	0.195139	+	0.980776i	$0.437484\pi$
$920$	25.3684	−	29.1847i	0.836372	−	0.962192i
$921$	−4.38844	−	3.18839i	−0.144604	−	0.105061i
$922$	−9.59631	−	4.66123i	−0.316038	−	0.153509i
$923$	−2.18000	−	4.27848i	−0.0717555	−	0.140828i
$924$	3.18623	+	8.66675i	0.104819	+	0.285115i
$925$	20.5870	−	43.0592i	0.676897	−	1.41578i
$926$	13.7257	−	19.6700i	0.451055	−	0.646397i
$927$	−17.9504	+	9.14616i	−0.589567	+	0.300399i
$928$	−5.07000	−	19.6559i	−0.166431	−	0.645237i
$929$	−17.0561	+	23.4756i	−0.559591	+	0.770211i	−0.991274	−	0.131814i	$-0.957920\pi$
$929$	−17.0561	+	23.4756i	−0.559591	+	0.770211i	0.431683	+	0.902025i	$0.357920\pi$
$930$	−2.33267	+	18.5072i	−0.0764914	+	0.606876i
$931$	−11.5459	−	15.8916i	−0.378401	−	0.520825i
$932$	9.79213	+	4.52763i	0.320752	+	0.148308i
$933$	8.19395	+	1.29779i	0.268258	+	0.0424879i
$934$	−2.67673	+	8.80611i	−0.0875852	+	0.288145i
$935$	11.4652	+	33.8268i	0.374954	+	1.10625i
$936$	−3.77024	−	2.42249i	−0.123234	−	0.0791816i
$937$	−37.0127	−	18.8589i	−1.20915	−	0.616093i	−0.271087	−	0.962555i	$-0.587383\pi$
$937$	−37.0127	−	18.8589i	−1.20915	−	0.616093i	−0.938064	+	0.346461i	$0.887383\pi$
$938$	15.2059	−	8.11672i	0.496491	−	0.265020i
$939$	5.78484	−	17.8039i	0.188781	−	0.581008i
$940$	−0.105860	−	0.131152i	−0.00345278	−	0.00427772i
$941$	−0.494245	−	1.52113i	−0.0161119	−	0.0495874i	0.942677	−	0.333706i	$-0.108299\pi$
$941$	−0.494245	−	1.52113i	−0.0161119	−	0.0495874i	−0.958789	+	0.284118i	$0.908299\pi$
$942$	4.83599	+	4.65496i	0.157565	+	0.151667i
$943$	31.4130	−	31.4130i	1.02295	−	1.02295i
$944$	−8.88939	+	36.6625i	−0.289325	+	1.19326i
$945$	−3.54216	+	1.86153i	−0.115227	+	0.0605557i
$946$	3.31253	+	9.56997i	0.107700	+	0.311147i
$947$	4.82272	+	30.4494i	0.156717	+	0.989474i	0.933206	+	0.359342i	$0.116999\pi$
$947$	4.82272	+	30.4494i	0.156717	+	0.989474i	−0.776489	+	0.630131i	$0.783001\pi$
$948$	−6.81823	−	6.31698i	−0.221446	−	0.205166i
$949$		−	11.8873i		−	0.385879i
$950$	31.8211	−	18.0327i	1.03241	−	0.585059i
$951$		−	1.05926i		−	0.0343489i
$952$	6.66409	+	30.6206i	0.215984	+	0.992418i
$953$	−2.81647	−	17.7825i	−0.0912344	−	0.576031i	−0.990379	−	0.138380i	$-0.955810\pi$
$953$	−2.81647	−	17.7825i	−0.0912344	−	0.576031i	0.899145	−	0.437651i	$-0.144190\pi$
$954$	9.70677	−	3.35988i	0.314268	−	0.108780i
$955$	−12.6712	+	25.6647i	−0.410030	+	0.830492i
$956$	−11.2254	+	16.7590i	−0.363054	+	0.542025i
$957$	6.54642	−	6.54642i	0.211616	−	0.211616i
$958$	6.43462	−	6.68485i	0.207893	−	0.215978i
$959$	9.54579	+	29.3789i	0.308250	+	0.948695i
$960$	17.7444	−	2.26672i	0.572696	−	0.0731580i
$961$	−1.17300	+	3.61013i	−0.0378388	+	0.116456i
$962$	10.0720	+	18.8689i	0.324733	+	0.608358i
$963$	−12.2480	−	6.24065i	−0.394685	−	0.201102i
$964$	0.394442	+	10.3364i	0.0127041	+	0.332912i
$965$	10.1107	−	0.127690i	0.325476	−	0.00411049i
$966$	14.8048	+	4.50009i	0.476335	+	0.144788i
$967$	49.1784	+	7.78910i	1.58147	+	0.250481i	0.884473	−	0.466592i	$-0.154518\pi$
$967$	49.1784	+	7.78910i	1.58147	+	0.250481i	0.696999	+	0.717072i	$0.254518\pi$
$968$	−10.6101	+	6.19461i	−0.341022	+	0.199102i
$969$	−18.8235	−	25.9083i	−0.604697	−	0.832294i
$970$	−28.2764	−	26.5383i	−0.907902	−	0.852092i
$971$	17.0745	−	23.5010i	0.547945	−	0.754182i	−0.441786	−	0.897120i	$-0.645655\pi$
$971$	17.0745	−	23.5010i	0.547945	−	0.754182i	0.989732	+	0.142938i	$0.0456550\pi$
$972$	1.74609	−	0.975274i	0.0560060	−	0.0312819i
$973$	22.5111	−	11.4700i	0.721671	−	0.367710i
$974$	−32.7761	−	22.8711i	−1.05021	−	0.732838i
$975$	7.59381	+	2.25701i	0.243197	+	0.0722823i
$976$	−8.98832	+	7.64176i	−0.287709	+	0.244607i
$977$	12.5647	+	24.6595i	0.401979	+	0.788928i	0.999920	−	0.0126118i	$-0.00401455\pi$
$977$	12.5647	+	24.6595i	0.401979	+	0.788928i	−0.597942	+	0.801540i	$0.704015\pi$
$978$	3.35757	−	6.91239i	0.107363	−	0.221034i
$979$	−6.23174	−	4.52762i	−0.199167	−	0.144703i
$980$	8.46821	+	14.7214i	0.270507	+	0.470256i
$981$	7.97850	−	5.79672i	0.254734	−	0.185075i
$982$	2.54154	+	14.2787i	0.0811038	+	0.455651i
$983$	8.49682	−	53.6468i	0.271006	−	1.71107i	−0.358046	−	0.933704i	$-0.616557\pi$
$983$	8.49682	−	53.6468i	0.271006	−	1.71107i	0.629053	−	0.777363i	$-0.283443\pi$
$984$	20.5174	−	1.17515i	0.654072	−	0.0374625i
$985$	−14.9680	+	21.1585i	−0.476921	+	0.674167i
$986$	25.0620	−	18.9492i	0.798135	−	0.603465i
$987$	0.0306188	−	0.0600927i	0.000974606	−	0.00191277i
$988$	−1.94491	+	16.2752i	−0.0618759	+	0.517784i
$989$	16.1397	+	5.24411i	0.513213	+	0.166753i
$990$	5.00227	+	6.44511i	0.158983	+	0.204839i
$991$	21.6353	−	7.02975i	0.687269	−	0.223307i	0.0554940	−	0.998459i	$-0.482327\pi$
$991$	21.6353	−	7.02975i	0.687269	−	0.223307i	0.631775	+	0.775152i	$0.282327\pi$
$992$	33.3051	+	2.05835i	1.05744	+	0.0653526i
$993$	−22.2871	−	22.2871i	−0.707259	−	0.707259i
$994$	0.146266	+	7.66857i	0.00463927	+	0.243232i
$995$	13.0344	−	13.3679i	0.413219	−	0.423790i
$996$	−4.61446	+	16.2913i	−0.146215	+	0.516210i
$997$	17.7115	−	2.80523i	0.560929	−	0.0888425i	0.130470	−	0.991452i	$-0.458351\pi$
$997$	17.7115	−	2.80523i	0.560929	−	0.0888425i	0.430460	+	0.902610i	$0.358351\pi$
$998$	2.42020	−	17.4251i	0.0766100	−	0.551582i
$999$	−9.54552			−0.302007

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.103.15	yes	240
3.2	odd	2		900.2.bj.f.703.16		240
4.3	odd	2	inner	300.2.w.a.103.26	yes	240
12.11	even	2		900.2.bj.f.703.5		240
25.17	odd	20	inner	300.2.w.a.67.26	yes	240
75.17	even	20		900.2.bj.f.667.5		240
100.67	even	20	inner	300.2.w.a.67.15	✓	240
300.167	odd	20		900.2.bj.f.667.16		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.67.15	✓	240	100.67	even	20	inner
300.2.w.a.67.26	yes	240	25.17	odd	20	inner
300.2.w.a.103.15	yes	240	1.1	even	1	trivial
300.2.w.a.103.26	yes	240	4.3	odd	2	inner
900.2.bj.f.667.5		240	75.17	even	20
900.2.bj.f.667.16		240	300.167	odd	20
900.2.bj.f.703.5		240	12.11	even	2
900.2.bj.f.703.16		240	3.2	odd	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.194555 + 1.40077i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-1.92430 - 0.545051i) q^{4} +(1.56105 - 1.60098i) q^{5} +(-0.0269690 - 1.41396i) q^{6} +(1.26539 + 1.26539i) q^{7} +(1.13787 - 2.58945i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})\)	\(q+(-0.194555 + 1.40077i) q^{2} +(-0.987688 + 0.156434i) q^{3} +(-1.92430 - 0.545051i) q^{4} +(1.56105 - 1.60098i) q^{5} +(-0.0269690 - 1.41396i) q^{6} +(1.26539 + 1.26539i) q^{7} +(1.13787 - 2.58945i) q^{8} +(0.951057 - 0.309017i) q^{9} +(1.93889 + 2.49814i) q^{10} +(2.45369 + 0.797253i) q^{11} +(1.98587 + 0.237314i) q^{12} +(0.719314 - 1.41173i) q^{13} +(-2.01871 + 1.52633i) q^{14} +(-1.29138 + 1.82547i) q^{15} +(3.40584 + 2.09768i) q^{16} +(-0.968521 + 6.11500i) q^{17} +(0.247828 + 1.39233i) q^{18} +(4.18468 - 3.04035i) q^{19} +(-3.87653 + 2.22991i) q^{20} +(-1.44777 - 1.05186i) q^{21} +(-1.59414 + 3.28194i) q^{22} +(2.77576 + 5.44773i) q^{23} +(-0.718783 + 2.73557i) q^{24} +(-0.126271 - 4.99841i) q^{25} +(1.83756 + 1.28225i) q^{26} +(-0.891007 + 0.453990i) q^{27} +(-1.74529 - 3.12470i) q^{28} +(-2.10923 + 2.90311i) q^{29} +(-2.30582 - 2.16407i) q^{30} +(-3.46723 - 4.77223i) q^{31} +(-3.60098 + 4.36267i) q^{32} +(-2.54820 - 0.403595i) q^{33} +(-8.37726 - 2.54637i) q^{34} +(4.00121 - 0.0505318i) q^{35} +(-1.99855 + 0.0762659i) q^{36} +(8.50512 + 4.33357i) q^{37} +(3.44467 + 6.45327i) q^{38} +(-0.489614 + 1.50688i) q^{39} +(-2.36939 - 5.86396i) q^{40} +(-2.24529 - 6.91028i) q^{41} +(1.75509 - 1.82334i) q^{42} +(1.96263 - 1.96263i) q^{43} +(-4.28709 - 2.87154i) q^{44} +(0.989913 - 2.00501i) q^{45} +(-8.17104 + 2.82831i) q^{46} +(0.00589566 + 0.0372238i) q^{47} +(-3.69206 - 1.53906i) q^{48} -3.79756i q^{49} +(7.02617 + 0.795586i) q^{50} -6.19122i q^{51} +(-2.15364 + 2.32453i) q^{52} +(-1.13623 - 7.17385i) q^{53} +(-0.462586 - 1.33642i) q^{54} +(5.10671 - 2.68376i) q^{55} +(4.71653 - 1.83682i) q^{56} +(-3.65754 + 3.65754i) q^{57} +(-3.65622 - 3.51935i) q^{58} +(2.91440 + 8.96960i) q^{59} +(3.47997 - 2.80888i) q^{60} +(-0.911425 + 2.80508i) q^{61} +(7.35935 - 3.92832i) q^{62} +(1.59449 + 0.812433i) q^{63} +(-5.41050 - 5.89292i) q^{64} +(-1.13727 - 3.35539i) q^{65} +(1.06111 - 3.49091i) q^{66} +(-6.72692 - 1.06544i) q^{67} +(5.19671 - 11.2392i) q^{68} +(-3.59380 - 4.94644i) q^{69} +(-0.707670 + 5.61459i) q^{70} +(1.78138 - 2.45186i) q^{71} +(0.281995 - 2.81433i) q^{72} +(6.68488 - 3.40612i) q^{73} +(-7.72504 + 11.0706i) q^{74} +(0.906640 + 4.91711i) q^{75} +(-9.70971 + 3.56967i) q^{76} +(2.09605 + 4.11372i) q^{77} +(-2.01553 - 0.979005i) q^{78} +(-3.75981 - 2.73166i) q^{79} +(8.67501 - 2.17810i) q^{80} +(0.809017 - 0.587785i) q^{81} +(10.1165 - 1.80070i) q^{82} +(-1.32439 + 8.36187i) q^{83} +(2.21261 + 2.81320i) q^{84} +(8.27808 + 11.0964i) q^{85} +(2.36735 + 3.13103i) q^{86} +(1.62912 - 3.19732i) q^{87} +(4.85643 - 5.44654i) q^{88} +(-2.83952 - 0.922614i) q^{89} +(2.61596 + 1.77672i) q^{90} +(2.69661 - 0.876183i) q^{91} +(-2.37209 - 11.9960i) q^{92} +(4.17109 + 4.17109i) q^{93} +(-0.0532888 + 0.00101640i) q^{94} +(1.66494 - 11.4457i) q^{95} +(2.87418 - 4.87228i) q^{96} +(-12.1121 + 1.91837i) q^{97} +(5.31949 + 0.738832i) q^{98} +2.57996 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

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