LMFDB - Embedded newform 300.2.w.a.223.9

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			223.9
Character	$\chi$	$=$	300.223
Dual form			300.2.w.a.187.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.852164 - 1.12863i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-0.547633 + 1.92356i) q^{4} +(1.99077 - 1.01825i) q^{5} +(-0.618747 + 1.27167i) q^{6} +(2.49130 + 2.49130i) q^{7} +(2.63767 - 1.02111i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(-0.852164 - 1.12863i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-0.547633 + 1.92356i) q^{4} +(1.99077 - 1.01825i) q^{5} +(-0.618747 + 1.27167i) q^{6} +(2.49130 + 2.49130i) q^{7} +(2.63767 - 1.02111i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(-2.84569 - 1.37914i) q^{10} +(0.801993 + 1.10385i) q^{11} +(1.96253 - 0.385335i) q^{12} +(0.636851 + 4.02092i) q^{13} +(0.688770 - 4.93475i) q^{14} +(-1.81106 - 1.31152i) q^{15} +(-3.40020 - 2.10681i) q^{16} +(5.08043 + 2.58861i) q^{17} +(1.41397 - 0.0260204i) q^{18} +(-1.33319 - 4.10314i) q^{19} +(0.868448 + 4.38700i) q^{20} +(1.08874 - 3.35078i) q^{21} +(0.562412 - 1.84582i) q^{22} +(1.11924 - 7.06662i) q^{23} +(-2.10730 - 1.88661i) q^{24} +(2.92635 - 4.05419i) q^{25} +(3.99545 - 4.14525i) q^{26} +(0.987688 + 0.156434i) q^{27} +(-6.15648 + 3.42785i) q^{28} +(-8.75004 - 2.84306i) q^{29} +(0.0630915 + 3.16165i) q^{30} +(-3.06381 + 0.995491i) q^{31} +(0.519703 + 5.63293i) q^{32} +(0.619439 - 1.21572i) q^{33} +(-1.40777 - 7.93987i) q^{34} +(7.49635 + 2.42285i) q^{35} +(-1.23431 - 1.57369i) q^{36} +(0.129150 - 0.0204553i) q^{37} +(-3.49485 + 5.00124i) q^{38} +(3.29354 - 2.39290i) q^{39} +(4.21126 - 4.71861i) q^{40} +(3.36019 + 2.44132i) q^{41} +(-4.70959 + 1.62663i) q^{42} +(-5.22481 + 5.22481i) q^{43} +(-2.56252 + 0.938181i) q^{44} +(-0.346369 + 2.20908i) q^{45} +(-8.92941 + 4.75870i) q^{46} +(7.83453 - 3.99189i) q^{47} +(-0.333527 + 3.98607i) q^{48} +5.41311i q^{49} +(-7.06943 + 0.152052i) q^{50} -5.70190i q^{51} +(-8.08325 - 0.976963i) q^{52} +(-4.72153 + 2.40574i) q^{53} +(-0.665115 - 1.24805i) q^{54} +(2.72057 + 1.38089i) q^{55} +(9.11512 + 4.02733i) q^{56} +(-3.05067 + 3.05067i) q^{57} +(4.24769 + 12.2983i) q^{58} +(2.82088 + 2.04949i) q^{59} +(3.51458 - 2.76545i) q^{60} +(2.94802 - 2.14186i) q^{61} +(3.73441 + 2.60960i) q^{62} +(-3.47985 + 0.551154i) q^{63} +(5.91465 - 5.38674i) q^{64} +(5.36211 + 7.35626i) q^{65} +(-1.89996 + 0.336870i) q^{66} +(2.58207 - 5.06761i) q^{67} +(-7.76157 + 8.35493i) q^{68} +(-6.80453 + 2.21093i) q^{69} +(-3.65361 - 10.5253i) q^{70} +(1.20429 + 0.391299i) q^{71} +(-0.724287 + 2.73412i) q^{72} +(-3.00337 - 0.475687i) q^{73} +(-0.133143 - 0.128332i) q^{74} +(-4.94085 - 0.766836i) q^{75} +(8.62276 - 0.317464i) q^{76} +(-0.752011 + 4.74801i) q^{77} +(-5.50734 - 1.67806i) q^{78} +(-4.80819 + 14.7981i) q^{79} +(-8.91427 - 0.731952i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(-0.108074 - 5.87284i) q^{82} +(-4.03896 - 2.05795i) q^{83} +(5.84922 + 3.92925i) q^{84} +(12.7498 - 0.0197929i) q^{85} +(10.3493 + 1.44451i) q^{86} +(1.43925 + 9.08706i) q^{87} +(3.24255 + 2.09267i) q^{88} +(-8.38047 - 11.5347i) q^{89} +(2.78841 - 1.49157i) q^{90} +(-8.43071 + 11.6039i) q^{91} +(12.9802 + 6.02285i) q^{92} +(2.27793 + 2.27793i) q^{93} +(-11.1817 - 5.44057i) q^{94} +(-6.83209 - 6.81091i) q^{95} +(4.78304 - 3.02036i) q^{96} +(7.56046 + 14.8382i) q^{97} +(6.10942 - 4.61285i) q^{98} -1.36443 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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	−0.852164	−	1.12863i	−0.602571	−	0.798065i
$2$	−0.852164	−	1.12863i	−0.602571	−	0.798065i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$4$	−0.547633	+	1.92356i	−0.273816	+	0.961782i
$5$	1.99077	−	1.01825i	0.890301	−	0.455373i
$5$	1.99077	−	1.01825i	0.890301	−	0.455373i
$6$	−0.618747	+	1.27167i	−0.252602	+	0.519158i
$7$	2.49130	+	2.49130i	0.941621	+	0.941621i	0.998387	−	0.0567663i	$-0.0180790\pi$
$7$	2.49130	+	2.49130i	0.941621	+	0.941621i	−0.0567663	+	0.998387i	$0.518079\pi$
$8$	2.63767	−	1.02111i	0.932559	−	0.361019i
$9$	−0.587785	+	0.809017i	−0.195928	+	0.269672i
$10$	−2.84569	−	1.37914i	−0.899887	−	0.436123i
$11$	0.801993	+	1.10385i	0.241810	+	0.332823i	0.912622	−	0.408805i	$-0.134054\pi$
$11$	0.801993	+	1.10385i	0.241810	+	0.332823i	−0.670812	+	0.741627i	$0.734054\pi$
$12$	1.96253	−	0.385335i	0.566533	−	0.111237i
$13$	0.636851	+	4.02092i	0.176631	+	1.11520i	0.903551	+	0.428480i	$0.140951\pi$
$13$	0.636851	+	4.02092i	0.176631	+	1.11520i	−0.726921	+	0.686722i	$0.759049\pi$
$14$	0.688770	−	4.93475i	0.184082	−	1.31887i
$15$	−1.81106	−	1.31152i	−0.467612	−	0.338632i
$16$	−3.40020	−	2.10681i	−0.850049	−	0.526703i
$17$	5.08043	+	2.58861i	1.23219	+	0.627830i	0.944064	−	0.329764i	$-0.106969\pi$
$17$	5.08043	+	2.58861i	1.23219	+	0.627830i	0.288122	+	0.957594i	$0.406969\pi$
$18$	1.41397	−	0.0260204i	0.333277	−	0.00613306i
$19$	−1.33319	−	4.10314i	−0.305855	−	0.941325i	−0.979357	−	0.202140i	$-0.935211\pi$
$19$	−1.33319	−	4.10314i	−0.305855	−	0.941325i	0.673502	−	0.739186i	$-0.264789\pi$
$20$	0.868448	+	4.38700i	0.194191	+	0.980964i
$21$	1.08874	−	3.35078i	0.237582	−	0.731201i
$22$	0.562412	−	1.84582i	0.119907	−	0.393529i
$23$	1.11924	−	7.06662i	0.233378	−	1.47349i	−0.541136	−	0.840935i	$-0.682005\pi$
$23$	1.11924	−	7.06662i	0.233378	−	1.47349i	0.774514	−	0.632557i	$-0.217995\pi$
$24$	−2.10730	−	1.88661i	−0.430151	−	0.385102i
$25$	2.92635	−	4.05419i	0.585271	−	0.810838i
$26$	3.99545	−	4.14525i	0.783571	−	0.812951i
$27$	0.987688	+	0.156434i	0.190081	+	0.0301058i
$28$	−6.15648	+	3.42785i	−1.16347	+	0.647803i
$29$	−8.75004	−	2.84306i	−1.62484	−	0.527943i	−0.651764	−	0.758422i	$-0.725971\pi$
$29$	−8.75004	−	2.84306i	−1.62484	−	0.527943i	−0.973077	+	0.230479i	$0.925971\pi$
$30$	0.0630915	+	3.16165i	0.0115189	+	0.577235i
$31$	−3.06381	+	0.995491i	−0.550276	+	0.178795i	−0.570941	−	0.820991i	$-0.693422\pi$
$31$	−3.06381	+	0.995491i	−0.550276	+	0.178795i	0.0206653	+	0.999786i	$0.493422\pi$
$32$	0.519703	+	5.63293i	0.0918713	+	0.995771i
$33$	0.619439	−	1.21572i	0.107830	−	0.211629i
$34$	−1.40777	−	7.93987i	−0.241430	−	1.36168i
$35$	7.49635	+	2.42285i	1.26711	+	0.409537i
$36$	−1.23431	−	1.57369i	−0.205718	−	0.262281i
$37$	0.129150	−	0.0204553i	0.0212321	−	0.00336283i	−0.145809	−	0.989313i	$-0.546579\pi$
$37$	0.129150	−	0.0204553i	0.0212321	−	0.00336283i	0.167041	+	0.985950i	$0.446579\pi$
$38$	−3.49485	+	5.00124i	−0.566940	+	0.811308i
$39$	3.29354	−	2.39290i	0.527388	−	0.383170i
$40$	4.21126	−	4.71861i	0.665859	−	0.746077i
$41$	3.36019	+	2.44132i	0.524774	+	0.381271i	0.818399	−	0.574650i	$-0.194862\pi$
$41$	3.36019	+	2.44132i	0.524774	+	0.381271i	−0.293625	+	0.955921i	$0.594862\pi$
$42$	−4.70959	+	1.62663i	−0.726706	+	0.250995i
$43$	−5.22481	+	5.22481i	−0.796776	+	0.796776i	−0.982586	−	0.185810i	$-0.940509\pi$
$43$	−5.22481	+	5.22481i	−0.796776	+	0.796776i	0.185810	+	0.982586i	$0.440509\pi$
$44$	−2.56252	+	0.938181i	−0.386315	+	0.141436i
$45$	−0.346369	+	2.20908i	−0.0516337	+	0.329310i
$46$	−8.92941	+	4.75870i	−1.31657	+	0.701633i
$47$	7.83453	−	3.99189i	1.14278	−	0.582277i	0.223045	−	0.974808i	$-0.428400\pi$
$47$	7.83453	−	3.99189i	1.14278	−	0.582277i	0.919739	+	0.392531i	$0.128400\pi$
$48$	−0.333527	+	3.98607i	−0.0481405	+	0.575340i
$49$			5.41311i			0.773301i
$50$	−7.06943	+	0.152052i	−0.999769	+	0.0215034i
$51$		−	5.70190i		−	0.798426i
$52$	−8.08325	−	0.976963i	−1.12095	−	0.135480i
$53$	−4.72153	+	2.40574i	−0.648552	+	0.330454i	−0.747132	−	0.664675i	$-0.768570\pi$
$53$	−4.72153	+	2.40574i	−0.648552	+	0.330454i	0.0985800	+	0.995129i	$0.468570\pi$
$54$	−0.665115	−	1.24805i	−0.0905107	−	0.169838i
$55$	2.72057	+	1.38089i	0.366842	+	0.186199i
$56$	9.11512	+	4.02733i	1.21806	+	0.538174i
$57$	−3.05067	+	3.05067i	−0.404071	+	0.404071i
$58$	4.24769	+	12.2983i	0.557749	+	1.61485i
$59$	2.82088	+	2.04949i	0.367248	+	0.266821i	0.756069	−	0.654492i	$-0.227118\pi$
$59$	2.82088	+	2.04949i	0.367248	+	0.266821i	−0.388821	+	0.921313i	$0.627118\pi$
$60$	3.51458	−	2.76545i	0.453731	−	0.357018i
$61$	2.94802	−	2.14186i	0.377455	−	0.274237i	−0.382840	−	0.923815i	$-0.625054\pi$
$61$	2.94802	−	2.14186i	0.377455	−	0.274237i	0.760296	+	0.649577i	$0.225054\pi$
$62$	3.73441	+	2.60960i	0.474271	+	0.331419i
$63$	−3.47985	+	0.551154i	−0.438420	+	0.0694388i
$64$	5.91465	−	5.38674i	0.739331	−	0.673342i
$65$	5.36211	+	7.35626i	0.665087	+	0.912432i
$66$	−1.89996	+	0.336870i	−0.233869	+	0.0414659i
$67$	2.58207	−	5.06761i	0.315451	−	0.619107i	−0.677780	−	0.735265i	$-0.737058\pi$
$67$	2.58207	−	5.06761i	0.315451	−	0.619107i	0.993231	+	0.116158i	$0.0370579\pi$
$68$	−7.76157	+	8.35493i	−0.941228	+	1.01318i
$69$	−6.80453	+	2.21093i	−0.819169	+	0.266164i
$70$	−3.65361	−	10.5253i	−0.436689	−	1.25802i
$71$	1.20429	+	0.391299i	0.142923	+	0.0464386i	0.379605	−	0.925149i	$-0.376060\pi$
$71$	1.20429	+	0.391299i	0.142923	+	0.0464386i	−0.236682	+	0.971587i	$0.576060\pi$
$72$	−0.724287	+	2.73412i	−0.0853580	+	0.322219i
$73$	−3.00337	−	0.475687i	−0.351518	−	0.0556749i	−0.0218211	−	0.999762i	$-0.506946\pi$
$73$	−3.00337	−	0.475687i	−0.351518	−	0.0556749i	−0.329696	+	0.944087i	$0.606946\pi$
$74$	−0.133143	−	0.128332i	−0.0154776	−	0.0149183i
$75$	−4.94085	−	0.766836i	−0.570520	−	0.0885466i
$76$	8.62276	−	0.317464i	0.989098	−	0.0364157i
$77$	−0.752011	+	4.74801i	−0.0856997	+	0.541086i
$78$	−5.50734	−	1.67806i	−0.623584	−	0.190003i
$79$	−4.80819	+	14.7981i	−0.540963	+	1.66491i	0.189436	+	0.981893i	$0.439334\pi$
$79$	−4.80819	+	14.7981i	−0.540963	+	1.66491i	−0.730399	+	0.683020i	$0.760666\pi$
$80$	−8.91427	−	0.731952i	−0.996646	−	0.0818348i
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	−0.108074	−	5.87284i	−0.0119347	−	0.648547i
$83$	−4.03896	−	2.05795i	−0.443333	−	0.225889i	0.218050	−	0.975938i	$-0.430030\pi$
$83$	−4.03896	−	2.05795i	−0.443333	−	0.225889i	−0.661383	+	0.750048i	$0.730030\pi$
$84$	5.84922	+	3.92925i	0.638202	+	0.428717i
$85$	12.7498	−	0.0197929i	1.38291	−	0.00214684i
$86$	10.3493	+	1.44451i	1.11599	+	0.155765i
$87$	1.43925	+	9.08706i	0.154304	+	0.974235i
$88$	3.24255	+	2.09267i	0.345657	+	0.223079i
$89$	−8.38047	−	11.5347i	−0.888328	−	1.22268i	−0.974044	−	0.226359i	$-0.927318\pi$
$89$	−8.38047	−	11.5347i	−0.888328	−	1.22268i	0.0857164	−	0.996320i	$-0.472682\pi$
$90$	2.78841	−	1.49157i	0.293924	−	0.157226i
$91$	−8.43071	+	11.6039i	−0.883779	+	1.21642i
$92$	12.9802	+	6.02285i	1.35328	+	0.627925i
$93$	2.27793	+	2.27793i	0.236210	+	0.236210i
$94$	−11.1817	−	5.44057i	−1.15330	−	0.561152i
$95$	−6.83209	−	6.81091i	−0.700957	−	0.698784i
$96$	4.78304	−	3.02036i	0.488167	−	0.308264i
$97$	7.56046	+	14.8382i	0.767648	+	1.50659i	0.859677	+	0.510838i	$0.170665\pi$
$97$	7.56046	+	14.8382i	0.767648	+	1.50659i	−0.0920287	+	0.995756i	$0.529335\pi$
$98$	6.10942	−	4.61285i	0.617144	−	0.465969i
$99$	−1.36443			−0.137131
$100$	6.19593	+	7.84923i	0.619593	+	0.784923i
$101$	−15.0905			−1.50156			−0.750779	−	0.660554i	$-0.770322\pi$
$101$	−15.0905			−1.50156			−0.750779	+	0.660554i	$0.770322\pi$
$102$	−6.43537	+	4.85896i	−0.637196	+	0.481108i
$103$	0.449746	+	0.882676i	0.0443148	+	0.0869727i	0.912102	−	0.409963i	$-0.134458\pi$
$103$	0.449746	+	0.882676i	0.0443148	+	0.0869727i	−0.867787	+	0.496936i	$0.834458\pi$
$104$	5.78562	+	9.95557i	0.567327	+	0.976224i
$105$	−1.24449	−	7.77925i	−0.121450	−	0.759177i
$106$	6.73872	+	3.27880i	0.654523	+	0.318465i
$107$	−8.30034	−	8.30034i	−0.802424	−	0.802424i	0.181050	−	0.983474i	$-0.442050\pi$
$107$	−8.30034	−	8.30034i	−0.802424	−	0.802424i	−0.983474	+	0.181050i	$0.942050\pi$
$108$	−0.841802	+	1.81421i	−0.0810025	+	0.174573i
$109$	−1.44527	+	1.98924i	−0.138432	+	0.190535i	−0.872604	−	0.488428i	$-0.837570\pi$
$109$	−1.44527	+	1.98924i	−0.138432	+	0.190535i	0.734172	+	0.678963i	$0.237570\pi$
$110$	−0.759859	−	4.24728i	−0.0724498	−	0.404962i
$111$	−0.0768586	−	0.105787i	−0.00729510	−	0.0100408i
$112$	−3.22220	−	13.7196i	−0.304469	−	1.29638i
$113$	−2.40655	−	15.1943i	−0.226389	−	1.42936i	−0.794926	−	0.606706i	$-0.792490\pi$
$113$	−2.40655	−	15.1943i	−0.226389	−	1.42936i	0.568537	−	0.822658i	$-0.307510\pi$
$114$	6.04276	+	0.843421i	0.565957	+	0.0789936i
$115$	−4.96739	−	15.2077i	−0.463212	−	1.41813i
$116$	10.2606	−	15.2743i	0.952674	−	1.41818i
$117$	−3.62732	−	1.84821i	−0.335346	−	0.170867i
$118$	−0.0907278	−	4.93025i	−0.00835217	−	0.453866i
$119$	6.20787	+	19.1058i	0.569074	+	1.75143i
$120$	−6.11618	−	1.61006i	−0.558329	−	0.146978i
$121$	2.82390	−	8.69106i	0.256718	−	0.790097i
$122$	−4.92958	−	1.50202i	−0.446303	−	0.135987i
$123$	0.649739	−	4.10229i	0.0585850	−	0.369891i
$124$	−0.237050	−	6.43859i	−0.0212877	−	0.578202i
$125$	1.69754	−	11.0507i	0.151833	−	0.988406i
$126$	3.58745	+	3.45780i	0.319596	+	0.308046i
$127$	0.361353	+	0.0572327i	0.0320649	+	0.00507858i	0.172446	−	0.985019i	$-0.444833\pi$
$127$	0.361353	+	0.0572327i	0.0320649	+	0.00507858i	−0.140381	+	0.990098i	$0.544833\pi$
$128$	−11.1199	−	2.08510i	−0.982870	−	0.184298i
$129$	7.02736	+	2.28333i	0.618724	+	0.201036i
$130$	3.73314	−	12.3206i	0.327418	−	1.08059i
$131$	−8.57410	+	2.78589i	−0.749123	+	0.243405i	−0.658604	−	0.752490i	$-0.728853\pi$
$131$	−8.57410	+	2.78589i	−0.749123	+	0.243405i	−0.0905190	+	0.995895i	$0.528853\pi$
$132$	1.99929	+	1.85730i	0.174015	+	0.161657i
$133$	6.90077	−	13.5435i	0.598372	−	1.17437i
$134$	−7.91983	+	1.40421i	−0.684169	+	0.121306i
$135$	2.12555	−	0.694284i	0.182938	−	0.0597544i
$136$	16.0438	+	1.64020i	1.37574	+	0.140646i
$137$	−13.9447	+	2.20862i	−1.19138	+	0.188695i	−0.720469	−	0.693487i	$-0.756073\pi$
$137$	−13.9447	+	2.20862i	−1.19138	+	0.188695i	−0.470907	+	0.882183i	$0.656073\pi$
$138$	8.29390	+	5.79576i	0.706024	+	0.493368i
$139$	4.83671	−	3.51407i	0.410244	−	0.298060i	−0.363456	−	0.931611i	$-0.618403\pi$
$139$	4.83671	−	3.51407i	0.410244	−	0.298060i	0.773701	+	0.633551i	$0.218403\pi$
$140$	−8.76576	+	13.0929i	−0.740842	+	1.10655i
$141$	−7.11360	−	5.16833i	−0.599073	−	0.435252i
$142$	−0.584623	−	1.69266i	−0.0490605	−	0.142045i
$143$	−3.92773	+	3.92773i	−0.328454	+	0.328454i
$144$	3.70303	−	1.51246i	0.308586	−	0.126039i
$145$	−20.3143	+	3.24980i	−1.68701	+	0.269881i
$146$	2.02249	+	3.79507i	0.167382	+	0.314082i
$147$	4.82311	−	2.45750i	0.397804	−	0.202691i
$148$	−0.0313796	+	0.259630i	−0.00257938	+	0.0213414i
$149$			4.74359i			0.388610i	0.980941	+	0.194305i	$0.0622452\pi$
$149$			4.74359i			0.388610i	−0.980941	+	0.194305i	$0.937755\pi$
$150$	3.34493	+	6.22988i	0.273113	+	0.508668i
$151$			12.6752i			1.03149i	0.856742	+	0.515746i	$0.172485\pi$
$151$			12.6752i			1.03149i	−0.856742	+	0.515746i	$0.827515\pi$
$152$	−7.70631	−	9.46141i	−0.625064	−	0.767422i
$153$	−5.08043	+	2.58861i	−0.410729	+	0.209277i
$154$	5.99961	−	3.19734i	0.483462	−	0.257649i
$155$	−5.08569	+	5.10150i	−0.408492	+	0.409763i
$156$	2.79924	+	7.64576i	0.224119	+	0.612151i
$157$	6.11797	−	6.11797i	0.488268	−	0.488268i	−0.419492	−	0.907759i	$-0.637792\pi$
$157$	6.11797	−	6.11797i	0.488268	−	0.488268i	0.907759	+	0.419492i	$0.137792\pi$
$158$	20.7990	−	7.18370i	1.65468	−	0.571505i
$159$	4.28706	+	3.11473i	0.339986	+	0.247014i
$160$	6.77032	+	10.6847i	0.535240	+	0.844700i
$161$	20.3934	−	14.8167i	1.60723	−	1.16772i
$162$	−0.810062	+	1.15922i	−0.0636445	+	0.0910772i
$163$	13.9503	−	2.20951i	1.09267	−	0.173063i	0.416014	−	0.909358i	$-0.363427\pi$
$163$	13.9503	−	2.20951i	1.09267	−	0.173063i	0.676660	+	0.736296i	$0.263427\pi$
$164$	−6.53620	+	5.12660i	−0.510391	+	0.400320i
$165$	−0.00473632	−	3.05096i	−0.000368722	−	0.237517i
$166$	1.11918	+	6.31222i	0.0868651	+	0.489923i
$167$	−1.93455	+	3.79676i	−0.149700	+	0.293802i	−0.953663	−	0.300877i	$-0.902721\pi$
$167$	−1.93455	+	3.79676i	−0.149700	+	0.293802i	0.803963	+	0.594679i	$0.202721\pi$
$168$	−0.549805	−	9.95000i	−0.0424184	−	0.767659i
$169$	−3.39846	+	1.10423i	−0.261420	+	0.0849406i
$170$	−10.8873	−	14.3730i	−0.835016	−	1.10236i
$171$	4.10314	+	1.33319i	0.313775	+	0.101952i
$172$	−7.18898	−	12.9115i	−0.548155	−	0.984495i
$173$	6.87016	+	1.08813i	0.522329	+	0.0827287i	0.412031	−	0.911170i	$-0.364820\pi$
$173$	6.87016	+	1.08813i	0.522329	+	0.0827287i	0.110298	+	0.993899i	$0.464820\pi$
$174$	9.02950	−	9.36806i	0.684524	−	0.710190i
$175$	17.3906	−	2.80978i	1.31461	−	0.212399i
$176$	−0.401331	−	5.44295i	−0.0302514	−	0.410278i
$177$	0.545456	−	3.44387i	0.0409990	−	0.258857i
$178$	−5.87696	+	19.2880i	−0.440496	+	1.44569i
$179$	2.78914	−	8.58410i	0.208470	−	0.641606i	−0.791083	−	0.611709i	$-0.790482\pi$
$179$	2.78914	−	8.58410i	0.208470	−	0.641606i	0.999553	−	0.0298964i	$-0.00951772\pi$
$180$	−4.05962	−	1.87603i	−0.302586	−	0.139831i
$181$	−0.855610	−	2.63330i	−0.0635970	−	0.195731i	0.914209	−	0.405242i	$-0.132813\pi$
$181$	−0.855610	−	2.63330i	−0.0635970	−	0.195731i	−0.977806	+	0.209511i	$0.932813\pi$
$182$	20.2809	−	0.373215i	1.50332	−	0.0276645i
$183$	−3.24679	−	1.65432i	−0.240009	−	0.122291i
$184$	−4.26363	−	19.7823i	−0.314319	−	1.45837i
$185$	0.236279	−	0.172228i	0.0173716	−	0.0126625i
$186$	0.629780	−	4.51212i	0.0461777	−	0.330844i
$187$	1.21704	+	7.68407i	0.0889986	+	0.561915i
$188$	3.38821	+	17.2563i	0.247111	+	1.25855i
$189$	2.07090	+	2.85035i	0.150636	+	0.207332i
$190$	−1.86497	+	13.5149i	−0.135299	+	0.980477i
$191$	−1.91873	+	2.64090i	−0.138834	+	0.191089i	−0.872772	−	0.488127i	$-0.837680\pi$
$191$	−1.91873	+	2.64090i	−0.138834	+	0.191089i	0.733938	+	0.679216i	$0.237680\pi$
$192$	−7.48481	−	2.82446i	−0.540170	−	0.203838i
$193$	5.18695	+	5.18695i	0.373365	+	0.373365i	0.868701	−	0.495336i	$-0.164955\pi$
$193$	5.18695	+	5.18695i	0.373365	+	0.373365i	−0.495336	+	0.868701i	$0.664955\pi$
$194$	10.3042	−	21.1776i	0.739798	−	1.52046i
$195$	4.12013	−	8.11734i	0.295049	−	0.581295i
$196$	−10.4125	−	2.96439i	−0.743747	−	0.211742i
$197$	10.2744	+	20.1646i	0.732020	+	1.43667i	0.893161	+	0.449738i	$0.148483\pi$
$197$	10.2744	+	20.1646i	0.732020	+	1.43667i	−0.161141	+	0.986931i	$0.551517\pi$
$198$	1.16272	+	1.53994i	0.0826309	+	0.109439i
$199$	−25.4743			−1.80583			−0.902914	−	0.429822i	$-0.858576\pi$
$199$	−25.4743			−1.80583			−0.902914	+	0.429822i	$0.858576\pi$
$200$	3.57897	−	13.6818i	0.253072	−	0.967448i
$201$	−5.68751			−0.401166
$202$	12.8596	+	17.0316i	0.904795	+	1.19834i
$203$	−14.7160	−	28.8818i	−1.03286	−	2.02711i
$204$	10.9680	+	3.12255i	0.767912	+	0.218622i
$205$	9.17525	+	1.43862i	0.640827	+	0.100478i
$206$	0.612962	−	1.25978i	0.0427071	−	0.0877733i
$207$	5.05914	+	5.05914i	0.351635	+	0.351635i
$208$	6.30590	−	15.0136i	0.437236	−	1.04101i
$209$	3.46004	−	4.76233i	0.239336	−	0.329417i
$210$	−7.71942	+	8.03378i	−0.532691	+	0.554383i
$211$	−6.05539	−	8.33453i	−0.416870	−	0.573773i	0.548007	−	0.836474i	$-0.315387\pi$
$211$	−6.05539	−	8.33453i	−0.416870	−	0.573773i	−0.964877	+	0.262701i	$0.915387\pi$
$212$	−2.04193	−	10.3996i	−0.140240	−	0.714250i
$213$	−0.198088	−	1.25068i	−0.0135728	−	0.0856952i
$214$	−2.29480	+	16.4413i	−0.156869	+	1.12390i
$215$	−5.08127	+	15.7216i	−0.346540	+	1.07220i
$216$	2.76494	−	0.595920i	0.188130	−	0.0405472i
$217$	−10.1129	−	5.15278i	−0.686509	−	0.349794i
$218$	3.47673	−	0.0639798i	0.235474	−	0.00433326i
$219$	0.939660	+	2.89198i	0.0634964	+	0.195422i
$220$	−4.14610	+	4.47698i	−0.279530	+	0.301838i
$221$	−7.17311	+	22.0766i	−0.482515	+	1.48503i
$222$	−0.0538985	+	0.176893i	−0.00361743	+	0.0118723i
$223$	−4.17730	+	26.3745i	−0.279733	+	1.76616i	0.302507	+	0.953147i	$0.402177\pi$
$223$	−4.17730	+	26.3745i	−0.279733	+	1.76616i	−0.582240	+	0.813017i	$0.697823\pi$
$224$	−12.7386	+	15.3280i	−0.851131	+	1.02415i
$225$	1.55984	+	4.75046i	0.103989	+	0.316697i
$226$	−15.0981	+	15.6642i	−1.00431	+	1.04197i
$227$	−6.78898	−	1.07527i	−0.450601	−	0.0713681i	−0.0729901	−	0.997333i	$-0.523254\pi$
$227$	−6.78898	−	1.07527i	−0.450601	−	0.0713681i	−0.377610	+	0.925965i	$0.623254\pi$
$228$	−4.19751	−	7.53881i	−0.277987	−	0.499270i
$229$	−16.4996	−	5.36104i	−1.09032	−	0.354268i	−0.291952	−	0.956433i	$-0.594305\pi$
$229$	−16.4996	−	5.36104i	−1.09032	−	0.354268i	−0.798371	+	0.602165i	$0.794305\pi$
$230$	−12.9309	+	18.5658i	−0.852638	+	1.22419i
$231$	4.57192	−	1.48551i	0.300810	−	0.0977391i
$232$	−25.9828	+	1.43573i	−1.70586	+	0.0942601i
$233$	6.52557	−	12.8071i	0.427504	−	0.839024i	−0.572316	−	0.820033i	$-0.693955\pi$
$233$	6.52557	−	12.8071i	0.427504	−	0.839024i	0.999820	−	0.0189905i	$-0.00604523\pi$
$234$	1.00512	+	5.66890i	0.0657065	+	0.370588i
$235$	11.5320	−	15.9244i	0.752267	−	1.03879i
$236$	−5.48713	+	4.30378i	−0.357182	+	0.280152i
$237$	15.3681	−	2.43406i	0.998262	−	0.158109i
$238$	16.2734	−	23.2877i	1.05485	−	1.50952i
$239$	2.34753	−	1.70558i	0.151849	−	0.110325i	−0.509266	−	0.860609i	$-0.670083\pi$
$239$	2.34753	−	1.70558i	0.151849	−	0.110325i	0.661116	+	0.750284i	$0.270083\pi$
$240$	3.39482	+	8.27497i	0.219135	+	0.534147i
$241$	−18.7376	−	13.6136i	−1.20699	−	0.876931i	−0.212038	−	0.977261i	$-0.568010\pi$
$241$	−18.7376	−	13.6136i	−1.20699	−	0.876931i	−0.994954	+	0.100330i	$0.968010\pi$
$242$	−12.2155	+	4.21906i	−0.785240	+	0.271212i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	2.50558	+	6.84366i	0.160403	+	0.438121i
$245$	5.51187	+	10.7763i	0.352140	+	0.688470i
$246$	−5.18368	+	2.76251i	−0.330499	+	0.176131i
$247$	15.6494	−	7.97374i	0.995745	−	0.507357i
$248$	−7.06481	+	5.75428i	−0.448616	+	0.365397i
$249$			4.53303i			0.287269i
$250$	−13.9188	+	7.50112i	−0.880303	+	0.474412i
$251$			3.00762i			0.189839i	0.995485	+	0.0949195i	$0.0302594\pi$
$251$			3.00762i			0.189839i	−0.995485	+	0.0949195i	$0.969741\pi$
$252$	0.845499	−	6.99554i	0.0532614	−	0.440677i
$253$	8.69810	−	4.43190i	0.546845	−	0.278631i
$254$	−0.243337	−	0.456608i	−0.0152683	−	0.0286501i
$255$	−5.80594	−	11.3512i	−0.363582	−	0.710839i
$256$	7.12267	+	14.3272i	0.445167	+	0.895447i
$257$	−9.92699	+	9.92699i	−0.619228	+	0.619228i	−0.945334	−	0.326105i	$-0.894264\pi$
$257$	−9.92699	+	9.92699i	−0.619228	+	0.619228i	0.326105	+	0.945334i	$0.394264\pi$
$258$	−3.41142	−	9.87709i	−0.212386	−	0.614921i
$259$	0.372711	+	0.270790i	0.0231591	+	0.0168261i
$260$	−17.0867	+	6.28582i	−1.05967	+	0.389830i
$261$	7.44323	−	5.40782i	0.460724	−	0.334736i
$262$	10.4508	+	7.30299i	0.645652	+	0.451180i
$263$	−4.42292	+	0.700522i	−0.272729	+	0.0431961i	−0.291301	−	0.956631i	$-0.594088\pi$
$263$	−4.42292	+	0.700522i	−0.272729	+	0.0431961i	0.0185717	+	0.999828i	$0.494088\pi$
$264$	0.392491	−	3.83918i	0.0241562	−	0.236285i
$265$	−6.94986	+	9.59696i	−0.426927	+	0.589537i
$266$	−21.1663	+	3.75285i	−1.29779	+	0.230102i
$267$	−6.47286	+	12.7037i	−0.396133	+	0.777454i
$268$	8.33384	+	7.74197i	0.509070	+	0.472916i
$269$	6.18147	−	2.00848i	0.376891	−	0.122459i	−0.114445	−	0.993430i	$-0.536509\pi$
$269$	6.18147	−	2.00848i	0.376891	−	0.122459i	0.491335	+	0.870970i	$0.336509\pi$
$270$	−2.59491	−	1.80733i	−0.157921	−	0.109990i
$271$	11.9688	+	3.88889i	0.727052	+	0.236233i	0.649078	−	0.760722i	$-0.275155\pi$
$271$	11.9688	+	3.88889i	0.727052	+	0.236233i	0.0779738	+	0.996955i	$0.475155\pi$
$272$	−11.8208	−	19.5053i	−0.716738	−	1.18268i
$273$	14.1666	+	2.24377i	0.857401	+	0.135799i
$274$	14.3759	+	13.8564i	0.868480	+	0.837093i
$275$	6.82213	−	0.0211814i	0.411390	−	0.00127729i
$276$	−0.526474	−	14.2997i	−0.0316900	−	0.860742i
$277$	−0.828491	+	5.23089i	−0.0497792	+	0.314293i	0.950217	+	0.311588i	$0.100861\pi$
$277$	−0.828491	+	5.23089i	−0.0497792	+	0.314293i	−0.999996	+	0.00270498i	$0.999139\pi$
$278$	−8.08778	−	2.46431i	−0.485073	−	0.147799i
$279$	0.995491	−	3.06381i	0.0595985	−	0.183425i
$280$	22.2469	−	1.26394i	1.32951	−	0.0755348i
$281$	7.54433	+	23.2191i	0.450057	+	1.38513i	0.876842	+	0.480779i	$0.159646\pi$
$281$	7.54433	+	23.2191i	0.450057	+	1.38513i	−0.426785	+	0.904353i	$0.640354\pi$
$282$	0.228794	+	12.4329i	0.0136245	+	0.740370i
$283$	3.54673	+	1.80715i	0.210831	+	0.107424i	0.556218	−	0.831037i	$-0.312252\pi$
$283$	3.54673	+	1.80715i	0.210831	+	0.107424i	−0.345386	+	0.938461i	$0.612252\pi$
$284$	−1.41220	+	2.10225i	−0.0837986	+	0.124746i
$285$	−2.96686	+	9.17952i	−0.175742	+	0.543748i
$286$	7.78005	+	1.08590i	0.460044	+	0.0642108i
$287$	2.28918	+	14.4533i	0.135126	+	0.853151i
$288$	−4.86261	−	2.89051i	−0.286532	−	0.170325i
$289$	9.11754	+	12.5492i	0.536326	+	0.738189i
$290$	20.9789	+	20.1580i	1.23193	+	1.18372i
$291$	9.78859	−	13.4728i	0.573817	−	0.789792i
$292$	2.55976	−	5.51667i	0.149798	−	0.322839i
$293$	−13.6906	−	13.6906i	−0.799811	−	0.799811i	0.183255	−	0.983065i	$-0.441337\pi$
$293$	−13.6906	−	13.6906i	−0.799811	−	0.799811i	−0.983065	+	0.183255i	$0.941337\pi$
$294$	−6.88370	−	3.34934i	−0.401466	−	0.195337i
$295$	7.70262	+	1.20772i	0.448464	+	0.0703162i
$296$	0.319768	−	0.185831i	0.0185861	−	0.0108012i
$297$	0.619439	+	1.21572i	0.0359435	+	0.0705431i
$298$	5.35379	−	4.04232i	0.310136	−	0.234165i
$299$	29.1271			1.68446
$300$	4.18083	−	9.08409i	0.241380	−	0.524470i
$301$	−26.0331			−1.50052
$302$	14.3057	−	10.8013i	0.823198	−	0.621547i
$303$	6.85093	+	13.4457i	0.393576	+	0.772436i
$304$	−4.11144	+	16.7603i	−0.235807	+	0.961268i
$305$	3.68790	−	7.26577i	0.211168	−	0.416037i
$306$	7.25096	+	3.52803i	0.414510	+	0.201684i
$307$	−18.8904	−	18.8904i	−1.07813	−	1.07813i	−0.996677	−	0.0814535i	$-0.974044\pi$
$307$	−18.8904	−	18.8904i	−1.07813	−	1.07813i	−0.0814535	−	0.996677i	$-0.525956\pi$
$308$	−8.72128	−	4.04671i	−0.496941	−	0.230583i
$309$	0.582290	−	0.801453i	0.0331253	−	0.0455931i
$310$	10.0916	+	1.39257i	0.573163	+	0.0790925i
$311$	−11.1415	−	15.3349i	−0.631775	−	0.869564i	0.366368	−	0.930470i	$-0.380601\pi$
$311$	−11.1415	−	15.3349i	−0.631775	−	0.869564i	−0.998144	+	0.0609059i	$0.980601\pi$
$312$	6.24386	−	9.67476i	0.353489	−	0.547726i
$313$	3.79538	+	23.9631i	0.214528	+	1.35447i	0.826206	+	0.563368i	$0.190495\pi$
$313$	3.79538	+	23.9631i	0.214528	+	1.35447i	−0.611678	+	0.791107i	$0.709505\pi$
$314$	−12.1185	−	1.69144i	−0.683885	−	0.0954535i
$315$	−6.36638	+	4.64056i	−0.358705	+	0.261466i
$316$	−25.8319	−	17.3528i	−1.45316	−	0.976169i
$317$	−7.14229	−	3.63918i	−0.401151	−	0.204397i	0.241762	−	0.970335i	$-0.422275\pi$
$317$	−7.14229	−	3.63918i	−0.401151	−	0.204397i	−0.642913	+	0.765939i	$0.722275\pi$
$318$	−0.137884	−	7.49279i	−0.00773218	−	0.420175i
$319$	−3.87916	−	11.9388i	−0.217191	−	0.668446i
$320$	6.28971	−	16.7463i	0.351605	−	0.936148i
$321$	−3.62738	+	11.1639i	−0.202461	+	0.623110i
$322$	−34.1011	−	10.3905i	−1.90038	−	0.579038i
$323$	3.84824	−	24.2969i	0.214122	−	1.35191i
$324$	1.99865	−	0.0735842i	0.111036	−	0.00408801i
$325$	18.1652	+	9.18471i	1.00762	+	0.509476i
$326$	−14.3817	−	13.8620i	−0.796529	−	0.767742i
$327$	2.42857	+	0.384647i	0.134300	+	0.0212710i
$328$	11.3560	+	3.00827i	0.627029	+	0.166104i
$329$	29.4631	+	9.57314i	1.62435	+	0.527784i
$330$	−3.43938	+	2.60526i	−0.189332	+	0.143415i
$331$	−14.2143	+	4.61851i	−0.781289	+	0.253856i	−0.672390	−	0.740197i	$-0.734732\pi$
$331$	−14.2143	+	4.61851i	−0.781289	+	0.253856i	−0.108898	+	0.994053i	$0.534732\pi$
$332$	6.17047	−	6.64219i	0.338648	−	0.364537i
$333$	−0.0593636	+	0.116508i	−0.00325311	+	0.00638458i
$334$	5.93371	−	1.05207i	0.324678	−	0.0575666i
$335$	−0.0197429	−	12.7176i	−0.00107867	−	0.694839i
$336$	−10.7614	+	9.09956i	−0.587082	+	0.496422i
$337$	−10.1786	+	1.61213i	−0.554464	+	0.0878185i	−0.427378	−	0.904073i	$-0.640563\pi$
$337$	−10.1786	+	1.61213i	−0.554464	+	0.0878185i	−0.127086	+	0.991892i	$0.540563\pi$
$338$	4.14232	+	2.89464i	0.225312	+	0.157448i
$339$	−12.4457	+	9.04234i	−0.675958	+	0.491112i
$340$	−6.94415	+	24.5359i	−0.376599	+	1.33065i
$341$	−3.55602	−	2.58360i	−0.192569	−	0.139910i
$342$	−1.99186	−	5.76705i	−0.107708	−	0.311846i
$343$	3.95342	−	3.95342i	0.213465	−	0.213465i
$344$	−8.44622	+	19.1165i	−0.455390	+	1.03069i
$345$	−11.2950	+	11.3301i	−0.608103	+	0.609994i
$346$	−4.62641	−	8.68116i	−0.248717	−	0.466702i
$347$	−1.43149	+	0.729383i	−0.0768467	+	0.0391553i	−0.491992	−	0.870600i	$-0.663731\pi$
$347$	−1.43149	+	0.729383i	−0.0768467	+	0.0391553i	0.415145	+	0.909755i	$0.363731\pi$
$348$	−18.2677	−	2.20789i	−0.979253	−	0.118355i
$349$			11.4754i			0.614266i	0.951667	+	0.307133i	$0.0993697\pi$
$349$			11.4754i			0.614266i	−0.951667	+	0.307133i	$0.900630\pi$
$350$	−17.9909	−	17.2332i	−0.961651	−	0.921155i
$351$			4.07104i			0.217296i
$352$	−5.80110	+	5.09124i	−0.309200	+	0.271364i
$353$	−11.6493	+	5.93560i	−0.620028	+	0.315920i	−0.735638	−	0.677375i	$-0.763118\pi$
$353$	−11.6493	+	5.93560i	−0.620028	+	0.315920i	0.115610	+	0.993295i	$0.463118\pi$
$354$	−4.35169	+	2.31912i	−0.231290	+	0.123260i
$355$	2.79591	−	0.447280i	0.148392	−	0.0237391i
$356$	26.7772	−	9.80357i	1.41919	−	0.519588i
$357$	14.2051	−	14.2051i	0.751815	−	0.751815i
$358$	−12.0651	+	4.16714i	−0.637661	+	0.220240i
$359$	16.4363	+	11.9417i	0.867476	+	0.630258i	0.929908	−	0.367791i	$-0.119886\pi$
$359$	16.4363	+	11.9417i	0.867476	+	0.630258i	−0.0624327	+	0.998049i	$0.519886\pi$
$360$	1.34211	+	6.18051i	0.0707356	+	0.325742i
$361$	0.312944	−	0.227367i	0.0164707	−	0.0119667i
$362$	−2.24291	+	3.20967i	−0.117885	+	0.168697i
$363$	−9.02582	+	1.42955i	−0.473733	+	0.0750319i
$364$	−17.7039	−	22.5717i	−0.927935	−	1.18308i
$365$	−6.46339	+	2.11118i	−0.338309	+	0.110504i
$366$	0.899672	+	5.07419i	0.0470266	+	0.265232i
$367$	13.2055	−	25.9173i	0.689322	−	1.35287i	−0.235277	−	0.971928i	$-0.575600\pi$
$367$	13.2055	−	25.9173i	0.689322	−	1.35287i	0.924599	−	0.380942i	$-0.124400\pi$
$368$	−18.6937	+	21.6699i	−0.974476	+	1.12962i
$369$	−3.95015	+	1.28348i	−0.205636	+	0.0668153i
$370$	−0.395731	−	0.119907i	−0.0205731	−	0.00623364i
$371$	−17.7561	−	5.76932i	−0.921853	−	0.299528i
$372$	−5.62921	+	3.13427i	−0.291861	+	0.162504i
$373$	20.6375	+	3.26865i	1.06857	+	0.169245i	0.665854	−	0.746082i	$-0.268067\pi$
$373$	20.6375	+	3.26865i	1.06857	+	0.169245i	0.402713	+	0.915326i	$0.368067\pi$
$374$	7.63540	−	7.92168i	0.394817	−	0.409620i
$375$	−10.6169	+	3.50440i	−0.548256	+	0.180966i
$376$	16.5888	−	18.5293i	0.855500	−	0.955574i
$377$	5.85924	−	36.9938i	0.301766	−	1.90528i
$378$	1.45226	−	4.76625i	0.0746960	−	0.245150i
$379$	3.51944	−	10.8317i	0.180781	−	0.556388i	−0.819069	−	0.573695i	$-0.805509\pi$
$379$	3.51944	−	10.8317i	0.180781	−	0.556388i	0.999850	+	0.0173073i	$0.00550935\pi$
$380$	16.8427	−	9.41208i	0.864012	−	0.482830i
$381$	−0.113056	−	0.347951i	−0.00579204	−	0.0178261i
$382$	4.61569	−	0.0849392i	0.236159	−	0.00434587i
$383$	32.0719	+	16.3414i	1.63880	+	0.835009i	0.997717	+	0.0675348i	$0.0215134\pi$
$383$	32.0719	+	16.3414i	1.63880	+	0.835009i	0.641080	+	0.767474i	$0.278487\pi$
$384$	3.19050	+	10.8545i	0.162814	+	0.553918i
$385$	3.33756	+	10.2179i	0.170098	+	0.520755i
$386$	1.43404	−	10.2743i	0.0729907	−	0.522948i
$387$	−1.15589	−	7.29803i	−0.0587574	−	0.370980i
$388$	−32.6826	+	6.41712i	−1.65921	+	0.325780i
$389$	0.975123	+	1.34214i	0.0494407	+	0.0680493i	0.833022	−	0.553241i	$-0.186609\pi$
$389$	0.975123	+	1.34214i	0.0494407	+	0.0680493i	−0.783581	+	0.621290i	$0.786609\pi$
$390$	−12.6725	+	2.26718i	−0.641699	+	0.114803i
$391$	23.9790	−	33.0042i	1.21267	−	1.66909i
$392$	5.52740	+	14.2780i	0.279176	+	0.721148i
$393$	6.37481	+	6.37481i	0.321567	+	0.321567i
$394$	14.0030	−	28.7796i	0.705462	−	1.44989i
$395$	5.49606	+	34.3555i	0.276537	+	1.72861i
$396$	0.747208	−	2.62457i	0.0375486	−	0.131890i
$397$	−11.8881	−	23.3318i	−0.596649	−	1.17099i	−0.969956	−	0.243282i	$-0.921776\pi$
$397$	−11.8881	−	23.3318i	−0.596649	−	1.17099i	0.373307	−	0.927708i	$-0.378224\pi$
$398$	21.7083	+	28.7512i	1.08814	+	1.44117i
$399$	−15.2002			−0.760964
$400$	−18.4916	+	7.61976i	−0.924580	+	0.380988i
$401$	−2.17523			−0.108626			−0.0543130	−	0.998524i	$-0.517297\pi$
$401$	−2.17523			−0.108626			−0.0543130	+	0.998524i	$0.517297\pi$
$402$	4.84669	+	6.41912i	0.241731	+	0.320156i
$403$	−5.95397	−	11.6853i	−0.296589	−	0.582088i
$404$	8.26403	−	29.0275i	0.411151	−	1.44417i
$405$	−1.58359	−	1.57868i	−0.0786893	−	0.0784454i
$406$	−20.0566	+	41.2211i	−0.995391	+	2.04577i
$407$	0.126157	+	0.126157i	0.00625336	+	0.00625336i
$408$	−5.82230	−	15.0398i	−0.288247	−	0.744579i
$409$	11.9578	−	16.4586i	0.591277	−	0.813823i	−0.403598	−	0.914937i	$-0.632240\pi$
$409$	11.9578	−	16.4586i	0.591277	−	0.813823i	0.994875	+	0.101113i	$0.0322405\pi$
$410$	−6.19514	−	11.5814i	−0.305956	−	0.571967i
$411$	8.29866	+	11.4221i	0.409343	+	0.563412i
$412$	−1.94418	+	0.381733i	−0.0957828	+	0.0188066i
$413$	1.92176	+	12.1335i	0.0945638	+	0.597052i
$414$	1.39870	−	10.0211i	0.0687426	−	0.492512i
$415$	−10.1361	+	0.0157354i	−0.497564	+	0.000772419i
$416$	−22.3186	+	5.67702i	−1.09426	+	0.278339i
$417$	−5.32688	−	2.71418i	−0.260859	−	0.132914i
$418$	−8.32345	+	0.153171i	−0.407113	+	0.00749182i
$419$	−0.0483649	−	0.148852i	−0.00236278	−	0.00727189i	0.949868	−	0.312651i	$-0.101217\pi$
$419$	−0.0483649	−	0.148852i	−0.00236278	−	0.00727189i	−0.952231	+	0.305379i	$0.901217\pi$
$420$	15.6454	+	1.86631i	0.763418	+	0.0910665i
$421$	−4.99608	+	15.3764i	−0.243494	+	0.749398i	0.752386	+	0.658722i	$0.228903\pi$
$421$	−4.99608	+	15.3764i	−0.243494	+	0.749398i	−0.995880	+	0.0906756i	$0.971097\pi$
$422$	−4.24646	+	13.9367i	−0.206714	+	0.678429i
$423$	−1.37551	+	8.68464i	−0.0668797	+	0.422262i
$424$	−9.99733	+	11.1668i	−0.485513	+	0.542307i
$425$	25.3619	−	13.0219i	1.23023	−	0.631653i
$426$	−1.24276	+	1.28935i	−0.0602118	+	0.0624694i
$427$	12.6804	+	2.00838i	0.613648	+	0.0971923i
$428$	20.5118	−	11.4207i	0.991474	−	0.552040i
$429$	5.28279	+	1.71648i	0.255056	+	0.0828726i
$430$	22.0740	−	7.66244i	1.06450	−	0.369516i
$431$	−6.19043	+	2.01139i	−0.298183	+	0.0968854i	−0.454288	−	0.890855i	$-0.650106\pi$
$431$	−6.19043	+	2.01139i	−0.298183	+	0.0968854i	0.156105	+	0.987740i	$0.450106\pi$
$432$	−3.02876	−	2.61278i	−0.145721	−	0.125708i
$433$	11.0775	−	21.7408i	0.532350	−	1.04480i	−0.455623	−	0.890173i	$-0.650584\pi$
$433$	11.0775	−	21.7408i	0.532350	−	1.04480i	0.987973	−	0.154624i	$-0.0494165\pi$
$434$	2.80225	+	15.8048i	0.134512	+	0.758654i
$435$	12.1181	+	16.6248i	0.581017	+	0.797097i
$436$	−3.03496	−	3.86944i	−0.145348	−	0.185313i
$437$	−30.4875	+	4.82875i	−1.45842	+	0.230990i
$438$	2.46324	−	3.52497i	0.117698	−	0.168430i
$439$	−3.16414	+	2.29888i	−0.151016	+	0.109720i	−0.660728	−	0.750626i	$-0.729752\pi$
$439$	−3.16414	+	2.29888i	−0.151016	+	0.109720i	0.509712	+	0.860345i	$0.329752\pi$
$440$	8.58603	+	0.864309i	0.409323	+	0.0412043i
$441$	−4.37929	−	3.18174i	−0.208538	−	0.151512i
$442$	31.0290	−	10.7170i	1.47590	−	0.509757i
$443$	−0.304670	+	0.304670i	−0.0144753	+	0.0144753i	−0.714307	−	0.699832i	$-0.753258\pi$
$443$	−0.304670	+	0.304670i	−0.0144753	+	0.0144753i	0.699832	+	0.714307i	$0.253258\pi$
$444$	0.245578	−	0.0899101i	0.0116546	−	0.00426695i
$445$	−28.4288	−	14.4296i	−1.34765	−	0.684031i
$446$	33.3269	−	17.7607i	1.57807	−	0.840994i
$447$	4.22657	−	2.15355i	0.199910	−	0.101859i
$448$	28.1551	+	1.31519i	1.33020	+	0.0621368i
$449$		−	12.7116i		−	0.599898i	−0.953955	−	0.299949i	$-0.903030\pi$
$449$		−	12.7116i		−	0.599898i	0.953955	−	0.299949i	$-0.0969696\pi$
$450$	4.03230	−	5.80867i	0.190084	−	0.273823i
$451$			5.66707i			0.266852i
$452$	30.5452	+	3.69177i	1.43673	+	0.173646i
$453$	11.2937	−	5.75441i	0.530623	−	0.270366i
$454$	4.57174	+	8.57859i	0.214562	+	0.402613i
$455$	−4.96803	+	31.6852i	−0.232905	+	1.48543i
$456$	−4.93159	+	11.1618i	−0.230943	+	0.522697i
$457$	29.0219	−	29.0219i	1.35759	−	1.35759i	0.480709	−	0.876880i	$-0.340380\pi$
$457$	29.0219	−	29.0219i	1.35759	−	1.35759i	0.876880	−	0.480709i	$-0.159620\pi$
$458$	8.00970	+	23.1905i	0.374269	+	1.08362i
$459$	4.61294	+	3.35149i	0.215313	+	0.156434i
$460$	31.9733	−	1.22687i	1.49076	−	0.0572030i
$461$	17.2511	−	12.5337i	0.803465	−	0.583752i	−0.108463	−	0.994100i	$-0.534593\pi$
$461$	17.2511	−	12.5337i	0.803465	−	0.583752i	0.911929	+	0.410349i	$0.134593\pi$
$462$	−5.57262	−	3.89413i	−0.259262	−	0.181171i
$463$	−13.6679	+	2.16478i	−0.635201	+	0.100606i	−0.465727	−	0.884929i	$-0.654207\pi$
$463$	−13.6679	+	2.16478i	−0.635201	+	0.100606i	−0.169474	+	0.985535i	$0.554207\pi$
$464$	23.7621	+	28.1017i	1.10313	+	1.30459i
$465$	6.85433	+	2.21535i	0.317862	+	0.102734i
$466$	−20.0154	+	3.54881i	−0.927197	+	0.164395i
$467$	2.00669	−	3.93835i	0.0928585	−	0.182245i	−0.839906	−	0.542733i	$-0.817390\pi$
$467$	2.00669	−	3.93835i	0.0928585	−	0.182245i	0.932764	+	0.360488i	$0.117390\pi$
$468$	5.54160	−	5.96524i	0.256160	−	0.275744i
$469$	19.0576	−	6.19219i	0.879999	−	0.285929i
$470$	−27.8000	+	0.554757i	−1.28232	+	0.0255890i
$471$	−8.22866	−	2.67365i	−0.379157	−	0.123195i
$472$	9.53333	+	2.52544i	0.438807	+	0.116243i
$473$	−9.95766	−	1.57714i	−0.457854	−	0.0725169i
$474$	−15.8433	−	15.2707i	−0.727705	−	0.701406i
$475$	−20.5363	−	6.60223i	−0.942271	−	0.302931i
$476$	−40.1510	+	1.47824i	−1.84032	+	0.0677550i
$477$	0.828962	−	5.23386i	0.0379556	−	0.239642i
$478$	−3.92546	−	1.19607i	−0.179546	−	0.0547070i
$479$	9.92975	−	30.5606i	0.453702	−	1.39635i	−0.418951	−	0.908009i	$-0.637602\pi$
$479$	9.92975	−	30.5606i	0.453702	−	1.39635i	0.872653	−	0.488341i	$-0.162398\pi$
$480$	6.44648	−	10.8831i	0.294240	−	0.496745i
$481$	0.164498	+	0.506274i	0.00750048	+	0.0230841i
$482$	0.602655	+	32.7489i	0.0274502	+	1.49167i
$483$	−22.4602	−	11.4440i	−1.02197	−	0.520721i
$484$	15.1714	+	10.1915i	0.689607	+	0.463248i
$485$	30.1601	+	21.8412i	1.36950	+	0.991756i
$486$	1.40064	+	0.195494i	0.0635342	+	0.00886780i
$487$	5.05186	+	31.8962i	0.228921	+	1.44535i	0.787712	+	0.616044i	$0.211266\pi$
$487$	5.05186	+	31.8962i	0.228921	+	1.44535i	−0.558790	+	0.829309i	$0.688734\pi$
$488$	5.58883	−	8.65980i	0.252995	−	0.392011i
$489$	−8.30201	−	11.4267i	−0.375430	−	0.516735i
$490$	7.46545	−	15.4040i	0.337255	−	0.695883i
$491$	4.07703	−	5.61155i	0.183994	−	0.253246i	−0.707050	−	0.707164i	$-0.749974\pi$
$491$	4.07703	−	5.61155i	0.183994	−	0.253246i	0.891043	+	0.453918i	$0.149974\pi$
$492$	7.53520	+	3.49637i	0.339713	+	0.157628i
$493$	−37.0944	−	37.0944i	−1.67065	−	1.67065i
$494$	−22.3353	−	10.8675i	−1.00491	−	0.488950i
$495$	−2.71627	+	1.38933i	−0.122087	+	0.0624456i
$496$	12.5149	+	3.07000i	0.561934	+	0.137847i
$497$	2.02541	+	3.97509i	0.0908521	+	0.178307i
$498$	5.11613	−	3.86288i	0.229259	−	0.173100i
$499$	−2.75484			−0.123323			−0.0616617	−	0.998097i	$-0.519640\pi$
$499$	−2.75484			−0.123323			−0.0616617	+	0.998097i	$0.519640\pi$
$500$	20.3271	+	9.31707i	0.909057	+	0.416672i
$501$	4.26121			0.190377
$502$	3.39450	−	2.56298i	0.151504	−	0.114391i
$503$	18.0885	+	35.5006i	0.806524	+	1.58289i	0.812536	+	0.582911i	$0.198086\pi$
$503$	18.0885	+	35.5006i	0.806524	+	1.58289i	−0.00601199	+	0.999982i	$0.501914\pi$
$504$	−8.61591	+	5.00709i	−0.383783	+	0.223033i
$505$	−30.0417	+	15.3658i	−1.33684	+	0.683769i
$506$	−12.4142	−	6.04027i	−0.551879	−	0.268523i
$507$	2.52674	+	2.52674i	0.112217	+	0.112217i
$508$	−0.307980	+	0.663744i	−0.0136644	+	0.0294489i
$509$	2.10528	−	2.89767i	0.0933148	−	0.128437i	−0.759807	−	0.650149i	$-0.774706\pi$
$509$	2.10528	−	2.89767i	0.0933148	−	0.128437i	0.853122	+	0.521712i	$0.174706\pi$
$510$	−7.86374	+	16.2259i	−0.348212	+	0.718493i
$511$	−6.29720	−	8.66735i	−0.278572	−	0.383421i
$512$	10.1004	−	20.2480i	0.446381	−	0.894843i
$513$	−0.674905	−	4.26118i	−0.0297978	−	0.188136i
$514$	19.6634	+	2.74452i	0.867314	+	0.121056i
$515$	1.79412	+	1.29926i	0.0790585	+	0.0572521i
$516$	−8.24053	+	12.2671i	−0.362769	+	0.540031i
$517$	10.6897	+	5.44666i	0.470131	+	0.239544i
$518$	−0.0119875	−	0.651412i	−0.000526699	−	0.0286214i
$519$	−2.14946	−	6.61536i	−0.0943508	−	0.290382i
$520$	21.6551	+	13.9281i	0.949638	+	0.610788i
$521$	−7.11130	+	21.8863i	−0.311552	+	0.958857i	0.665599	+	0.746310i	$0.268176\pi$
$521$	−7.11130	+	21.8863i	−0.311552	+	0.958857i	−0.977151	+	0.212548i	$0.931824\pi$
$522$	−12.4463	−	3.79233i	−0.544760	−	0.165986i
$523$	−2.70501	+	17.0788i	−0.118282	+	0.746802i	0.855244	+	0.518225i	$0.173407\pi$
$523$	−2.70501	+	17.0788i	−0.118282	+	0.746802i	−0.973526	+	0.228577i	$0.926593\pi$
$524$	−0.663387	−	18.0185i	−0.0289802	−	0.787141i
$525$	−10.3987	−	14.2195i	−0.453836	−	0.620591i
$526$	4.55969	+	4.39491i	0.198812	+	0.191627i
$527$	−18.1424	−	2.87347i	−0.790295	−	0.125170i
$528$	−4.66750	+	2.82864i	−0.203127	+	0.123101i
$529$	−26.8101	−	8.71113i	−1.16566	−	0.378745i
$530$	16.7539	−	0.334328i	0.727743	−	0.0145223i
$531$	−3.31615	+	1.07748i	−0.143908	+	0.0467587i
$532$	22.2727	+	20.6909i	0.965645	+	0.897066i
$533$	−7.67642	+	15.0658i	−0.332503	+	0.652573i
$534$	19.8538	−	3.52015i	0.859157	−	0.152332i
$535$	−24.9759	−	8.07231i	−1.07980	−	0.348996i
$536$	1.63606	−	16.0033i	0.0706672	−	0.691237i
$537$	−8.91473	+	1.41195i	−0.384699	+	0.0609303i
$538$	−7.53446	−	5.26506i	−0.324834	−	0.226993i
$539$	−5.97525	+	4.34127i	−0.257372	+	0.186992i
$540$	0.171477	+	4.46885i	0.00737919	+	0.192309i
$541$	31.4706	+	22.8648i	1.35303	+	0.983033i	0.998854	+	0.0478534i	$0.0152380\pi$
$541$	31.4706	+	22.8648i	1.35303	+	0.983033i	0.354174	+	0.935179i	$0.384762\pi$
$542$	−5.81023	−	16.8224i	−0.249571	−	0.722582i
$543$	−1.95785	+	1.95785i	−0.0840192	+	0.0840192i
$544$	−11.9411	+	29.9630i	−0.511972	+	1.28465i
$545$	−0.851666	+	5.43177i	−0.0364813	+	0.232671i
$546$	−9.53987	−	17.9010i	−0.408269	−	0.766091i
$547$	−13.4042	+	6.82978i	−0.573122	+	0.292020i	−0.716431	−	0.697658i	$-0.754226\pi$
$547$	−13.4042	+	6.82978i	−0.573122	+	0.292020i	0.143309	+	0.989678i	$0.454226\pi$
$548$	3.38815	−	28.0330i	0.144734	−	1.19751i
$549$			3.64395i			0.155520i
$550$	−5.83748	−	7.68164i	−0.248911	−	0.327546i
$551$			39.6930i			1.69098i
$552$	−15.6905	+	12.7799i	−0.667833	+	0.543949i
$553$	−48.8450	+	24.8878i	−2.07710	+	1.05834i
$554$	6.60977	−	3.52251i	0.280822	−	0.149657i
$555$	−0.260725	−	0.132337i	−0.0110672	−	0.00561737i
$556$	4.11081	+	11.2281i	0.174337	+	0.476179i
$557$	−5.19301	+	5.19301i	−0.220035	+	0.220035i	−0.808513	−	0.588478i	$-0.799727\pi$
$557$	−5.19301	+	5.19301i	−0.220035	+	0.220035i	0.588478	+	0.808513i	$0.299727\pi$
$558$	−4.30624	+	1.48732i	−0.182298	+	0.0629633i
$559$	−24.3360	−	17.6811i	−1.02930	−	0.747831i
$560$	−20.3846	−	24.0316i	−0.861406	−	1.01552i
$561$	6.29404	−	4.57288i	0.265734	−	0.193067i
$562$	19.7768	−	28.3012i	0.834235	−	1.19382i
$563$	−3.06650	+	0.485685i	−0.129237	+	0.0204692i	−0.220718	−	0.975338i	$-0.570840\pi$
$563$	−3.06650	+	0.485685i	−0.129237	+	0.0204692i	0.0914806	+	0.995807i	$0.470840\pi$
$564$	13.8373	−	10.8531i	0.582654	−	0.456999i
$565$	−20.2625	−	27.7980i	−0.852448	−	1.16947i
$566$	−0.982785	−	5.54296i	−0.0413096	−	0.232988i
$567$	1.59951	−	3.13922i	0.0671731	−	0.131835i
$568$	3.57610	−	0.197604i	0.150050	−	0.00829126i
$569$	0.605838	−	0.196849i	0.0253981	−	0.00825233i	−0.296290	−	0.955098i	$-0.595750\pi$
$569$	0.605838	−	0.196849i	0.0253981	−	0.00825233i	0.321688	+	0.946846i	$0.395750\pi$
$570$	12.8886	−	4.47396i	0.539843	−	0.187393i
$571$	32.9971	+	10.7214i	1.38089	+	0.448677i	0.902961	−	0.429722i	$-0.141389\pi$
$571$	32.9971	+	10.7214i	1.38089	+	0.448677i	0.477926	+	0.878400i	$0.341389\pi$
$572$	−5.40429	−	9.70620i	−0.225965	−	0.405837i
$573$	3.22415	+	0.510655i	0.134691	+	0.0213329i
$574$	14.3617	−	14.9002i	0.599447	−	0.621923i
$575$	−25.3741	−	25.2170i	−1.05817	−	1.05162i
$576$	0.881417	+	7.95130i	0.0367257	+	0.331304i
$577$	2.68723	−	16.9665i	0.111871	−	0.706325i	−0.866455	−	0.499255i	$-0.833607\pi$
$577$	2.68723	−	16.9665i	0.111871	−	0.706325i	0.978326	−	0.207070i	$-0.0663928\pi$
$578$	6.39384	−	20.9844i	0.265949	−	0.872835i
$579$	2.26678	−	6.97643i	0.0942042	−	0.289931i
$580$	4.87356	−	40.8555i	0.202364	−	1.69643i
$581$	−4.93527	−	15.1892i	−0.204749	−	0.630154i
$582$	−23.5474	+	0.433326i	−0.976071	+	0.0179619i
$583$	−6.44221	−	3.28247i	−0.266809	−	0.135946i
$584$	−8.40763	+	1.81208i	−0.347910	+	0.0749842i
$585$	−9.10311	+	0.0141317i	−0.376367	+	0.000584273i
$586$	−3.78504	+	27.1182i	−0.156358	+	1.12024i
$587$	−0.678884	−	4.28630i	−0.0280205	−	0.176915i	0.969709	−	0.244263i	$-0.0785461\pi$
$587$	−0.678884	−	4.28630i	−0.0280205	−	0.176915i	−0.997730	+	0.0673485i	$0.978546\pi$
$588$	2.08586	+	10.6234i	0.0860195	+	0.438100i
$589$	8.16928	+	11.2441i	0.336609	+	0.463303i
$590$	−5.20082	−	9.72262i	−0.214114	−	0.400274i
$591$	13.3023	−	18.3091i	0.547185	−	0.753135i
$592$	−0.482230	−	0.202542i	−0.0198195	−	0.00832444i
$593$	8.39438	+	8.39438i	0.344716	+	0.344716i	0.858137	−	0.513421i	$-0.171622\pi$
$593$	8.39438	+	8.39438i	0.344716	+	0.344716i	−0.513421	+	0.858137i	$0.671622\pi$
$594$	0.844237	−	1.73511i	0.0346395	−	0.0711925i
$595$	31.8129	+	31.7143i	1.30420	+	1.30016i
$596$	−9.12461	−	2.59775i	−0.373759	−	0.106408i
$597$	11.5651	+	22.6978i	0.473328	+	0.928959i
$598$	−24.8211	−	32.8738i	−1.01501	−	1.34431i
$599$	−12.7341			−0.520302			−0.260151	−	0.965568i	$-0.583772\pi$
$599$	−12.7341			−0.520302			−0.260151	+	0.965568i	$0.583772\pi$
$600$	−13.8154	+	3.02251i	−0.564010	+	0.123393i
$601$	5.75412			0.234715			0.117358	−	0.993090i	$-0.462558\pi$
$601$	5.75412			0.234715			0.117358	+	0.993090i	$0.462558\pi$
$602$	22.1845	+	29.3819i	0.904171	+	1.19752i
$603$	2.58207	+	5.06761i	0.105150	+	0.206369i
$604$	−24.3815	−	6.94135i	−0.992071	−	0.282439i
$605$	−3.22790	−	20.1774i	−0.131233	−	0.820326i
$606$	9.33717	−	19.1901i	0.379297	−	0.779546i
$607$	−21.1094	−	21.1094i	−0.856803	−	0.856803i	0.134157	−	0.990960i	$-0.457167\pi$
$607$	−21.1094	−	21.1094i	−0.856803	−	0.856803i	−0.990960	+	0.134157i	$0.957167\pi$
$608$	22.4199	−	9.64219i	0.909245	−	0.391043i
$609$	−19.0530	+	26.2242i	−0.772065	+	1.06266i
$610$	−11.3431	+	2.02934i	−0.459269	+	0.0821655i
$611$	21.0405	+	28.9598i	0.851207	+	1.17159i
$612$	−2.19714	−	11.1901i	−0.0888143	−	0.452335i
$613$	4.32963	+	27.3362i	0.174872	+	1.10410i	0.906441	+	0.422332i	$0.138788\pi$
$613$	4.32963	+	27.3362i	0.174872	+	1.10410i	−0.731569	+	0.681767i	$0.761212\pi$
$614$	−5.22263	+	37.4180i	−0.210768	+	1.51007i
$615$	−2.88366	−	8.82833i	−0.116280	−	0.355993i
$616$	2.86471	+	13.2916i	0.115422	+	0.535534i
$617$	−11.3531	−	5.78472i	−0.457060	−	0.232884i	0.210273	−	0.977643i	$-0.432565\pi$
$617$	−11.3531	−	5.78472i	−0.457060	−	0.232884i	−0.667334	+	0.744759i	$0.732565\pi$
$618$	−1.40075	+	0.0257771i	−0.0563466	+	0.00103691i
$619$	−6.42998	−	19.7894i	−0.258443	−	0.795405i	−0.993132	−	0.117001i	$-0.962672\pi$
$619$	−6.42998	−	19.7894i	−0.258443	−	0.795405i	0.734689	−	0.678404i	$-0.237328\pi$
$620$	−7.02798	−	12.5764i	−0.282250	−	0.505080i
$621$	2.21093	−	6.80453i	0.0887214	−	0.273056i
$622$	−7.81317	+	25.6425i	−0.313279	+	1.02817i
$623$	7.85818	−	49.6146i	0.314831	−	1.98777i
$624$	−16.2401	+	1.19745i	−0.650123	+	0.0479362i
$625$	−7.87292	−	23.7280i	−0.314917	−	0.949119i
$626$	23.8113	−	24.7041i	0.951691	−	0.987374i
$627$	−5.81409	−	0.920862i	−0.232193	−	0.0367757i
$628$	8.41791	+	15.1187i	0.335911	+	0.603303i
$629$	0.709088	+	0.230397i	0.0282732	+	0.00918651i
$630$	10.6627	+	3.23079i	0.424812	+	0.128718i
$631$	34.4907	−	11.2067i	1.37305	−	0.446131i	0.472672	−	0.881238i	$-0.343289\pi$
$631$	34.4907	−	11.2067i	1.37305	−	0.446131i	0.900379	+	0.435107i	$0.143289\pi$
$632$	2.42810	+	43.9422i	0.0965848	+	1.74793i
$633$	−4.67703	+	9.17919i	−0.185895	+	0.364840i
$634$	1.97910	+	11.1622i	0.0786001	+	0.443308i
$635$	0.777649	−	0.254009i	0.0308601	−	0.0100800i
$636$	−8.33912	+	6.54071i	−0.330668	+	0.259356i
$637$	−21.7656	+	3.44734i	−0.862386	+	0.136589i
$638$	−10.1689	+	14.5520i	−0.402590	+	0.576119i
$639$	−1.02443	+	0.744295i	−0.0405260	+	0.0294439i
$640$	−24.2604	+	7.17184i	−0.958975	+	0.283492i
$641$	−2.65216	−	1.92691i	−0.104754	−	0.0761083i	0.534175	−	0.845374i	$-0.320622\pi$
$641$	−2.65216	−	1.92691i	−0.104754	−	0.0761083i	−0.638929	+	0.769266i	$0.720622\pi$
$642$	15.6911	−	5.41951i	0.619279	−	0.213891i
$643$	30.5991	−	30.5991i	1.20671	−	1.20671i	0.234623	−	0.972086i	$-0.424614\pi$
$643$	30.5991	−	30.5991i	1.20671	−	1.20671i	0.972086	−	0.234623i	$-0.0753856\pi$
$644$	17.3327	+	47.3421i	0.683005	+	1.86554i
$645$	16.3149	−	2.60999i	0.642397	−	0.102768i
$646$	−30.7016	+	16.3616i	−1.20794	+	0.643740i
$647$	−5.55651	+	2.83118i	−0.218449	+	0.111305i	−0.559791	−	0.828634i	$-0.689119\pi$
$647$	−5.55651	+	2.83118i	−0.218449	+	0.111305i	0.341342	+	0.939939i	$0.389119\pi$
$648$	−1.78622	−	2.19304i	−0.0701695	−	0.0861506i
$649$			4.75750i			0.186748i
$650$	−5.11356	−	28.3288i	−0.200570	−	1.11115i
$651$			11.3500i			0.444841i
$652$	−3.38951	+	28.0443i	−0.132744	+	1.09830i
$653$	−24.3791	+	12.4218i	−0.954027	+	0.486101i	−0.860463	−	0.509512i	$-0.829826\pi$
$653$	−24.3791	+	12.4218i	−0.954027	+	0.486101i	−0.0935636	+	0.995613i	$0.529826\pi$
$654$	−1.63541	−	3.06875i	−0.0639496	−	0.119997i
$655$	−14.2324	+	14.2766i	−0.556104	+	0.557834i
$656$	−6.28191	−	15.3803i	−0.245267	−	0.600499i
$657$	2.15017	−	2.15017i	0.0838863	−	0.0838863i
$658$	−14.3028	−	41.4110i	−0.557582	−	1.61437i
$659$	−16.3088	−	11.8491i	−0.635302	−	0.461574i	0.222931	−	0.974834i	$-0.428438\pi$
$659$	−16.3088	−	11.8491i	−0.635302	−	0.461574i	−0.858233	+	0.513260i	$0.828438\pi$
$660$	5.87131	+	1.66169i	0.228540	+	0.0646814i
$661$	28.6158	−	20.7906i	1.11302	−	0.808660i	0.129888	−	0.991529i	$-0.458538\pi$
$661$	28.6158	−	20.7906i	1.11302	−	0.808660i	0.983137	+	0.182869i	$0.0585384\pi$
$662$	17.3255	+	12.1070i	0.673376	+	0.470553i
$663$	22.9269	−	3.63126i	0.890406	−	0.141026i
$664$	−12.7549	−	1.30397i	−0.494984	−	0.0506037i
$665$	−0.0527642	−	33.9887i	−0.00204611	−	1.31803i
$666$	0.182082	−	0.0322838i	0.00705554	−	0.00125097i
$667$	−29.8842	+	58.6511i	−1.15712	+	2.27098i
$668$	−6.24389	−	5.80046i	−0.241583	−	0.224426i
$669$	25.3963	−	8.25175i	0.981877	−	0.319031i
$670$	−14.3367	+	10.8598i	−0.553877	+	0.419550i
$671$	4.72858	+	1.53641i	0.182545	+	0.0593124i
$672$	19.4406	+	4.39136i	0.749936	+	0.169400i
$673$	9.60732	+	1.52165i	0.370335	+	0.0586553i	0.338828	−	0.940848i	$-0.389969\pi$
$673$	9.60732	+	1.52165i	0.370335	+	0.0586553i	0.0315068	+	0.999504i	$0.489969\pi$
$674$	10.4934	+	10.1141i	0.404189	+	0.389582i
$675$	3.52454	−	3.54649i	0.135660	−	0.136505i
$676$	−0.262943	−	7.14187i	−0.0101132	−	0.274687i
$677$	−1.11431	+	7.03549i	−0.0428265	+	0.270396i	−0.999805	−	0.0197640i	$-0.993709\pi$
$677$	−1.11431	+	7.03549i	−0.0428265	+	0.270396i	0.956978	+	0.290160i	$0.0937085\pi$
$678$	20.8113	+	6.34111i	0.799252	+	0.243529i
$679$	−18.1311	+	55.8018i	−0.695807	+	2.14147i
$680$	33.6097	−	13.0712i	1.28887	−	0.501259i
$681$	2.12406	+	6.53719i	0.0813942	+	0.250506i
$682$	0.114372	+	6.21510i	0.00437953	+	0.237989i
$683$	44.5512	+	22.7000i	1.70470	+	0.868590i	0.984622	+	0.174700i	$0.0558956\pi$
$683$	44.5512	+	22.7000i	1.70470	+	0.868590i	0.720082	+	0.693889i	$0.244104\pi$
$684$	−4.81150	+	7.16256i	−0.183972	+	0.273867i
$685$	−25.5118	+	18.5960i	−0.974756	+	0.710516i
$686$	−7.83094	−	1.09301i	−0.298987	−	0.0417312i
$687$	2.71393	+	17.1351i	0.103543	+	0.653745i
$688$	28.7731	−	6.75768i	1.09696	−	0.257634i
$689$	−12.6802	−	17.4528i	−0.483077	−	0.664899i
$690$	22.4128	+	3.09281i	0.853240	+	0.117741i
$691$	−19.7591	+	27.1961i	−0.751673	+	1.03459i	0.246188	+	0.969222i	$0.420822\pi$
$691$	−19.7591	+	27.1961i	−0.751673	+	1.03459i	−0.997861	+	0.0653672i	$0.979178\pi$
$692$	−5.85541	+	12.6193i	−0.222589	+	0.479714i
$693$	−3.39920	−	3.39920i	−0.129125	−	0.129125i
$694$	2.04308	+	0.994081i	0.0775541	+	0.0377348i
$695$	6.05060	−	11.9207i	0.229512	−	0.452177i
$696$	13.0752	+	22.4991i	0.495614	+	0.852825i
$697$	10.7516	+	21.1012i	0.407246	+	0.799265i
$698$	12.9516	−	9.77895i	0.490224	−	0.370139i
$699$	−14.3738			−0.543667
$700$	−4.11888	+	34.9906i	−0.155679	+	1.32252i
$701$	31.0425			1.17246			0.586229	−	0.810146i	$-0.300612\pi$
$701$	31.0425			1.17246			0.586229	+	0.810146i	$0.300612\pi$
$702$	4.59472	−	3.46919i	0.173416	−	0.130936i
$703$	−0.256113	−	0.502649i	−0.00965947	−	0.0189578i
$704$	10.6896	+	2.20875i	0.402881	+	0.0832455i
$705$	−19.4242	−	3.04559i	−0.731558	−	0.114703i
$706$	16.6262	+	8.08967i	0.625736	+	0.304459i
$707$	−37.5948	−	37.5948i	−1.41390	−	1.41390i
$708$	6.32580	+	2.93520i	0.237738	+	0.110311i
$709$	−17.2385	+	23.7268i	−0.647407	+	0.891079i	−0.998983	−	0.0450801i	$-0.985646\pi$
$709$	−17.2385	+	23.7268i	−0.647407	+	0.891079i	0.351577	+	0.936159i	$0.385646\pi$
$710$	−2.88739	−	2.77441i	−0.108362	−	0.104122i
$711$	−9.14571	−	12.5880i	−0.342991	−	0.472087i
$712$	−33.8832	−	21.8674i	−1.26983	−	0.819516i
$713$	3.60561	+	22.7649i	0.135031	+	0.852554i
$714$	−28.1375	−	3.92730i	−1.05302	−	0.146976i
$715$	−3.81983	+	11.8186i	−0.142854	+	0.441991i
$716$	14.9846	+	10.0660i	0.560002	+	0.376185i
$717$	−2.58544	−	1.31735i	−0.0965551	−	0.0491973i
$718$	−0.528640	−	28.7269i	−0.0197287	−	1.07208i
$719$	−2.12647	−	6.54461i	−0.0793040	−	0.244073i	0.903542	−	0.428499i	$-0.140957\pi$
$719$	−2.12647	−	6.54461i	−0.0793040	−	0.244073i	−0.982846	+	0.184426i	$0.940957\pi$
$720$	5.83184	−	6.78157i	0.217340	−	0.252734i
$721$	−1.07856	+	3.31946i	−0.0401676	+	0.123623i
$722$	−0.523293	−	0.159445i	−0.0194750	−	0.00593393i
$723$	−3.62316	+	22.8758i	−0.134747	+	0.850758i
$724$	5.53387	−	0.203741i	0.205665	−	0.00757197i
$725$	−37.1320	+	27.1545i	−1.37905	+	1.00849i
$726$	9.30492	+	8.96864i	0.345338	+	0.332858i
$727$	12.4912	+	1.97841i	0.463272	+	0.0733750i	0.383707	−	0.923455i	$-0.374647\pi$
$727$	12.4912	+	1.97841i	0.463272	+	0.0733750i	0.0795643	+	0.996830i	$0.474647\pi$
$728$	−10.3886	+	39.2160i	−0.385026	+	1.45344i
$729$	0.951057	+	0.309017i	0.0352243	+	0.0114451i
$730$	7.89062	+	5.49573i	0.292045	+	0.203406i
$731$	−40.0693	+	13.0193i	−1.48202	+	0.481536i
$732$	4.96024	−	5.33944i	0.183336	−	0.197351i
$733$	−13.2521	+	26.0087i	−0.489477	+	0.960652i	0.505714	+	0.862701i	$0.331229\pi$
$733$	−13.2521	+	26.0087i	−0.489477	+	0.960652i	−0.995191	+	0.0979512i	$0.968771\pi$
$734$	−40.5044	+	7.18157i	−1.49504	+	0.265076i
$735$	7.09938	−	9.80343i	0.261865	−	0.361605i
$736$	40.3875	+	2.63208i	1.48870	+	0.0970196i
$737$	7.66467	−	1.21396i	0.282332	−	0.0447170i
$738$	4.81475	+	3.36454i	0.177233	+	0.123850i
$739$	30.8033	−	22.3799i	1.13312	−	0.823257i	0.146971	−	0.989141i	$-0.453048\pi$
$739$	30.8033	−	22.3799i	1.13312	−	0.823257i	0.986145	+	0.165884i	$0.0530477\pi$
$740$	0.201897	+	0.548816i	0.00742190	+	0.0201749i
$741$	−14.2093	−	10.3237i	−0.521992	−	0.379250i
$742$	8.61969	+	24.9566i	0.316439	+	0.916186i
$743$	−17.1276	+	17.1276i	−0.628352	+	0.628352i	−0.947653	−	0.319301i	$-0.896552\pi$
$743$	−17.1276	+	17.1276i	−0.628352	+	0.628352i	0.319301	+	0.947653i	$0.396552\pi$
$744$	8.33446	+	3.68241i	0.305556	+	0.135004i
$745$	4.83014	+	9.44342i	0.176963	+	0.345980i
$746$	−13.8974	−	26.0776i	−0.508820	−	0.954769i
$747$	4.03896	−	2.05795i	0.147778	−	0.0752965i
$748$	−15.4473	−	1.86700i	−0.564809	−	0.0682643i
$749$		−	41.3572i		−	1.51116i
$750$	13.0026	+	8.99631i	0.474786	+	0.328499i
$751$		−	51.4238i		−	1.87648i	−0.345986	−	0.938240i	$-0.612456\pi$
$751$		−	51.4238i		−	1.87648i	0.345986	−	0.938240i	$-0.387544\pi$
$752$	−35.0491	−	2.93267i	−1.27811	−	0.106944i
$753$	2.67981	−	1.36543i	0.0976575	−	0.0497590i
$754$	−46.7455	+	24.9118i	−1.70237	+	0.907235i
$755$	12.9065	+	25.2334i	0.469714	+	0.918338i
$756$	−6.61692	+	2.42256i	−0.240655	+	0.0881078i
$757$	13.9717	−	13.9717i	0.507810	−	0.507810i	−0.406044	−	0.913854i	$-0.633092\pi$
$757$	13.9717	−	13.9717i	0.507810	−	0.507810i	0.913854	+	0.406044i	$0.133092\pi$
$758$	−15.2242	+	5.25824i	−0.552968	+	0.190988i
$759$	−7.89771	−	5.73802i	−0.286669	−	0.208277i
$760$	−24.9755	−	10.9886i	−0.905958	−	0.398599i
$761$	17.6783	−	12.8440i	0.640837	−	0.465596i	−0.219300	−	0.975657i	$-0.570377\pi$
$761$	17.6783	−	12.8440i	0.640837	−	0.465596i	0.860138	+	0.510062i	$0.170377\pi$
$762$	−0.296367	+	0.424111i	−0.0107363	+	0.0153639i
$763$	−8.55638	+	1.35520i	−0.309762	+	0.0490614i
$764$	−4.02919	−	5.13704i	−0.145771	−	0.185852i
$765$	−7.47815	+	10.3265i	−0.270373	+	0.373354i
$766$	−8.88699	−	50.1230i	−0.321100	−	1.81102i
$767$	−6.44435	+	12.6478i	−0.232692	+	0.456684i
$768$	9.53197	−	12.8507i	0.343955	−	0.463711i
$769$	17.9380	−	5.82841i	0.646861	−	0.210178i	0.0328314	−	0.999461i	$-0.489548\pi$
$769$	17.9380	−	5.82841i	0.646861	−	0.210178i	0.614030	+	0.789283i	$0.289548\pi$
$770$	8.68818	−	12.4743i	0.313100	−	0.449541i
$771$	13.3518	+	4.33825i	0.480852	+	0.156238i
$772$	−12.8180	+	7.13689i	−0.461329	+	0.256862i
$773$	−30.5110	−	4.83247i	−1.09740	−	0.173812i	−0.418629	−	0.908157i	$-0.637489\pi$
$773$	−30.5110	−	4.83247i	−1.09740	−	0.173812i	−0.678776	+	0.734346i	$0.737489\pi$
$774$	−7.25180	+	7.52370i	−0.260660	+	0.270434i
$775$	−4.92987	+	15.3344i	−0.177086	+	0.550828i
$776$	35.0936	+	31.4183i	1.25979	+	1.12785i
$777$	0.0720687	−	0.455024i	0.00258545	−	0.0163239i
$778$	0.683823	−	2.24428i	0.0245162	−	0.0804615i
$779$	5.53732	−	17.0421i	0.198395	−	0.610597i
$780$	13.3579	+	12.3707i	0.478290	+	0.442941i
$781$	0.533901	+	1.64318i	0.0191045	+	0.0587975i
$782$	−57.6837	+	1.06151i	−2.06276	+	0.0379596i
$783$	−8.19756	−	4.17686i	−0.292957	−	0.149269i
$784$	11.4044	−	18.4056i	0.407300	−	0.657344i
$785$	5.94990	−	18.4091i	0.212361	−	0.657049i
$786$	1.76245	−	12.6272i	0.0628644	−	0.450398i
$787$	0.323147	+	2.04027i	0.0115189	+	0.0727277i	0.992778	−	0.119965i	$-0.0382781\pi$
$787$	0.323147	+	2.04027i	0.0115189	+	0.0727277i	−0.981259	+	0.192692i	$0.938278\pi$
$788$	−44.4145	+	8.72063i	−1.58220	+	0.310660i
$789$	2.63214	+	3.62282i	0.0937065	+	0.128976i
$790$	34.0913	−	35.4796i	1.21291	−	1.26231i
$791$	31.8582	−	43.8490i	1.13275	−	1.55909i
$792$	−3.59893	+	1.39324i	−0.127882	+	0.0495067i
$793$	10.4897	+	10.4897i	0.372500	+	0.372500i
$794$	−16.2024	+	33.2999i	−0.575003	+	1.18177i
$795$	11.7061	+	1.83544i	0.415174	+	0.0650965i
$796$	13.9506	−	49.0015i	0.494465	−	1.73681i
$797$	21.0945	+	41.4003i	0.747205	+	1.46647i	0.879821	+	0.475305i	$0.157662\pi$
$797$	21.0945	+	41.4003i	0.747205	+	1.46647i	−0.132616	+	0.991168i	$0.542338\pi$
$798$	12.9531	+	17.1555i	0.458535	+	0.607299i
$799$	50.1362			1.77369
$800$	24.3578	+	14.3770i	0.861179	+	0.508303i
$801$	14.2577			0.503771
$802$	1.85365	+	2.45504i	0.0654548	+	0.0866906i
$803$	−1.88359	−	3.69676i	−0.0664705	−	0.130456i
$804$	3.11467	−	10.9403i	0.109846	−	0.385834i
$805$	25.5116	−	50.2621i	0.899166	−	1.77151i
$806$	−8.11471	+	16.6777i	−0.285828	+	0.587446i
$807$	−4.59590	−	4.59590i	−0.161783	−	0.161783i
$808$	−39.8037	+	15.4091i	−1.40029	+	0.542090i
$809$	18.4766	−	25.4309i	0.649604	−	0.894103i	−0.349478	−	0.936945i	$-0.613641\pi$
$809$	18.4766	−	25.4309i	0.649604	−	0.894103i	0.999082	+	0.0428417i	$0.0136411\pi$
$810$	−0.432276	+	3.13259i	−0.0151886	+	0.110068i
$811$	−22.4918	−	30.9573i	−0.789795	−	1.08706i	−0.994134	−	0.108159i	$-0.965504\pi$
$811$	−22.4918	−	30.9573i	−0.789795	−	1.08706i	0.204339	−	0.978900i	$-0.434496\pi$
$812$	63.6150	−	12.4906i	2.23245	−	0.438334i
$813$	−1.96868	−	12.4298i	−0.0690448	−	0.435931i
$814$	0.0348786	−	0.249891i	0.00122250	−	0.00875868i
$815$	25.5221	−	18.6035i	0.894000	−	0.651652i
$816$	−12.0128	+	19.3876i	−0.420534	+	0.678701i
$817$	28.4038	+	14.4725i	0.993724	+	0.506328i
$818$	−28.7657	+	0.529355i	−1.00577	+	0.0185085i
$819$	−4.43229	−	13.6412i	−0.154877	−	0.476661i
$820$	−7.79194	+	16.8613i	−0.272107	+	0.588824i
$821$	−6.78167	+	20.8718i	−0.236682	+	0.728432i	0.760212	+	0.649675i	$0.225095\pi$
$821$	−6.78167	+	20.8718i	−0.236682	+	0.728432i	−0.996894	+	0.0787568i	$0.974905\pi$
$822$	5.81959	−	19.0997i	0.202981	−	0.666178i
$823$	−7.68914	+	48.5473i	−0.268027	+	1.69225i	0.375494	+	0.926825i	$0.377473\pi$
$823$	−7.68914	+	48.5473i	−0.268027	+	1.69225i	−0.643521	+	0.765429i	$0.722527\pi$
$824$	2.08760	+	1.86897i	0.0727249	+	0.0651086i
$825$	−3.11605	−	6.06894i	−0.108487	−	0.211293i
$826$	12.0567	−	12.5087i	0.419505	−	0.435235i
$827$	−47.8026	−	7.57119i	−1.66226	−	0.263276i	−0.746612	−	0.665259i	$-0.768321\pi$
$827$	−47.8026	−	7.57119i	−1.66226	−	0.263276i	−0.915647	+	0.401983i	$0.868321\pi$
$828$	−12.5021	+	6.96103i	−0.434479	+	0.241913i
$829$	20.3434	+	6.60997i	0.706556	+	0.229574i	0.640185	−	0.768221i	$-0.278858\pi$
$829$	20.3434	+	6.60997i	0.706556	+	0.229574i	0.0663712	+	0.997795i	$0.478858\pi$
$830$	8.65542	+	11.4266i	0.300434	+	0.396623i
$831$	5.03688	−	1.63658i	0.174727	−	0.0567724i
$832$	25.4264	+	20.3518i	0.881501	+	0.705571i
$833$	−14.0124	+	27.5009i	−0.485501	+	0.952850i
$834$	1.47606	+	8.32503i	0.0511117	+	0.288272i
$835$	0.0147918	+	9.52833i	0.000511892	+	0.329742i
$836$	7.26582	+	9.26361i	0.251294	+	0.320389i
$837$	−3.18181	+	0.503950i	−0.109980	+	0.0174191i
$838$	−0.126785	+	0.181433i	−0.00437970	+	0.00626749i
$839$	−36.8226	+	26.7532i	−1.27126	+	0.923624i	−0.999252	−	0.0386716i	$-0.987687\pi$
$839$	−36.8226	+	26.7532i	−1.27126	+	0.923624i	−0.272007	+	0.962295i	$0.587687\pi$
$840$	−11.2261	−	19.2484i	−0.387337	−	0.664131i
$841$	45.0187	+	32.7080i	1.55237	+	1.12786i
$842$	21.6118	−	7.46443i	0.744791	−	0.257241i
$843$	17.2633	−	17.2633i	0.594579	−	0.594579i
$844$	19.3481	−	7.08367i	0.665991	−	0.243830i
$845$	−5.64119	+	5.65874i	−0.194063	+	0.194666i
$846$	10.9739	−	5.84829i	0.377292	−	0.201068i
$847$	28.6872	−	14.6168i	0.985703	−	0.502241i
$848$	21.1226	+	1.76740i	0.725353	+	0.0606926i
$849$		−	3.98059i		−	0.136614i
$850$	−36.3094	−	17.5275i	−1.24540	−	0.601189i
$851$		−	0.935547i		−	0.0320701i
$852$	2.51424	+	0.303878i	0.0861365	+	0.0104107i
$853$	39.3011	−	20.0249i	1.34564	−	0.685640i	0.375194	−	0.926946i	$-0.377576\pi$
$853$	39.3011	−	20.0249i	1.34564	−	0.685640i	0.970449	+	0.241307i	$0.0775759\pi$
$854$	−8.53906	−	16.0230i	−0.292201	−	0.548296i
$855$	9.52594	−	1.52392i	0.325780	−	0.0521171i
$856$	−30.3692	−	13.4180i	−1.03800	−	0.458617i
$857$	27.2666	−	27.2666i	0.931409	−	0.931409i	−0.0663848	−	0.997794i	$-0.521147\pi$
$857$	27.2666	−	27.2666i	0.931409	−	0.931409i	0.997794	+	0.0663848i	$0.0211465\pi$
$858$	−2.56452	−	7.42507i	−0.0875513	−	0.253488i
$859$	13.2204	+	9.60521i	0.451076	+	0.327726i	0.790020	−	0.613081i	$-0.210070\pi$
$859$	13.2204	+	9.60521i	0.451076	+	0.327726i	−0.338945	+	0.940806i	$0.610070\pi$
$860$	−27.4587	−	18.3838i	−0.936335	−	0.626882i
$861$	11.8387	−	8.60133i	0.403462	−	0.293133i
$862$	7.54540	+	5.27270i	0.256997	+	0.179589i
$863$	28.7174	−	4.54838i	0.977551	−	0.154829i	0.352839	−	0.935684i	$-0.385216\pi$
$863$	28.7174	−	4.54838i	0.977551	−	0.154829i	0.624712	+	0.780855i	$0.285216\pi$
$864$	−0.367880	+	5.64488i	−0.0125155	+	0.192043i
$865$	14.7849	−	4.82930i	0.502702	−	0.164201i
$866$	−33.9773	+	6.02429i	−1.15459	+	0.204714i
$867$	7.04216	−	13.8210i	0.239164	−	0.469386i
$868$	15.4499	−	16.6310i	0.524403	−	0.564493i
$869$	−20.1910	+	6.56044i	−0.684931	+	0.222548i
$870$	8.43670	−	27.8439i	0.286031	−	0.943997i
$871$	22.0208	+	7.15500i	0.746147	+	0.242438i
$872$	−1.78090	+	6.72276i	−0.0603090	+	0.227661i
$873$	−16.4483	−	2.60516i	−0.556691	−	0.0881712i
$874$	31.4303	+	30.2944i	1.06314	+	1.02472i
$875$	31.7597	−	23.3015i	1.07367	−	0.787735i
$876$	−6.07749	+	0.223755i	−0.205339	+	0.00755999i
$877$	−0.814105	+	5.14006i	−0.0274904	+	0.173567i	−0.997613	−	0.0690457i	$-0.978005\pi$
$877$	−0.814105	+	5.14006i	−0.0274904	+	0.173567i	0.970123	+	0.242613i	$0.0780046\pi$
$878$	5.29096	+	1.61213i	0.178561	+	0.0544068i
$879$	−5.98299	+	18.4138i	−0.201801	+	0.621081i
$880$	−6.34122	−	10.4270i	−0.213762	−	0.351495i
$881$	6.53025	+	20.0980i	0.220010	+	0.677120i	0.998760	+	0.0497860i	$0.0158539\pi$
$881$	6.53025	+	20.0980i	0.220010	+	0.677120i	−0.778750	+	0.627334i	$0.784146\pi$
$882$	0.140851	+	7.65399i	0.00474270	+	0.257723i
$883$	−24.2485	−	12.3552i	−0.816027	−	0.415787i	−0.00442009	−	0.999990i	$-0.501407\pi$
$883$	−24.2485	−	12.3552i	−0.816027	−	0.415787i	−0.811607	+	0.584204i	$0.801407\pi$
$884$	−38.5374	−	25.8878i	−1.29615	−	0.870700i
$885$	−2.42083	−	7.41138i	−0.0813753	−	0.249131i
$886$	0.603490	+	0.0842323i	0.0202746	+	0.00282984i
$887$	−6.09005	−	38.4511i	−0.204484	−	1.29106i	−0.849784	−	0.527131i	$-0.823268\pi$
$887$	−6.09005	−	38.4511i	−0.204484	−	1.29106i	0.645300	−	0.763929i	$-0.276732\pi$
$888$	−0.310748	−	0.200550i	−0.0104280	−	0.00673001i
$889$	0.757654	+	1.04282i	0.0254109	+	0.0349751i
$890$	7.94019	+	44.3821i	0.266156	+	1.48769i
$891$	0.801993	−	1.10385i	0.0268678	−	0.0369803i
$892$	−48.4453	−	22.4788i	−1.62207	−	0.752647i
$893$	−26.8242	−	26.8242i	−0.897639	−	0.897639i
$894$	−6.03230	−	2.93508i	−0.201750	−	0.0981639i
$895$	−3.18817	−	19.9290i	−0.106569	−	0.666154i
$896$	−22.5084	−	32.8976i	−0.751952	−	1.09903i
$897$	−13.2234	−	25.9524i	−0.441517	−	0.866526i
$898$	−14.3468	+	10.8324i	−0.478758	+	0.361481i
$899$	29.6387			0.988505
$900$	−9.99204	+	0.398946i	−0.333068	+	0.0132982i
$901$	−30.2150			−1.00661
$902$	6.39605	−	4.82927i	0.212965	−	0.160797i
$903$	11.8188	+	23.1957i	0.393304	+	0.771903i
$904$	−21.8629	−	37.6204i	−0.727148	−	1.25123i
$905$	−4.38467	−	4.37107i	−0.145751	−	0.145299i
$906$	−16.1187	−	7.84273i	−0.535508	−	0.260557i
$907$	25.5328	+	25.5328i	0.847804	+	0.847804i	0.989859	−	0.142055i	$-0.0453709\pi$
$907$	25.5328	+	25.5328i	0.847804	+	0.847804i	−0.142055	+	0.989859i	$0.545371\pi$
$908$	5.78622	−	12.4702i	0.192022	−	0.413838i
$909$	8.86995	−	12.2084i	0.294198	−	0.404929i
$910$	39.9946	−	21.3939i	1.32581	−	0.709201i
$911$	−24.6515	−	33.9299i	−0.816741	−	1.12415i	−0.990248	−	0.139315i	$-0.955510\pi$
$911$	−24.6515	−	33.9299i	−0.816741	−	1.12415i	0.173507	−	0.984833i	$-0.444490\pi$
$912$	16.8001	−	3.94569i	0.556306	−	0.130655i
$913$	−0.967548	−	6.10886i	−0.0320212	−	0.202174i
$914$	−57.4866	−	8.02371i	−1.90149	−	0.265401i
$915$	−8.14812	+	0.0126492i	−0.269369	+	0.000418168i
$916$	19.3480	−	28.8021i	0.639277	−	0.951649i
$917$	−28.3011	−	14.4201i	−0.934585	−	0.476195i
$918$	−0.148366	−	8.06234i	−0.00489679	−	0.266097i
$919$	5.41980	+	16.6804i	0.178783	+	0.550237i	0.999786	−	0.0206867i	$-0.00658524\pi$
$919$	5.41980	+	16.6804i	0.178783	+	0.550237i	−0.821003	+	0.570924i	$0.806585\pi$
$920$	−28.6312	−	35.0407i	−0.943942	−	1.15526i
$921$	−8.25540	+	25.4075i	−0.272025	+	0.837206i
$922$	−28.8467	−	8.78947i	−0.950017	−	0.289466i
$923$	−0.806425	+	5.09157i	−0.0265438	+	0.167591i
$924$	0.353734	+	9.60789i	0.0116370	+	0.316076i
$925$	0.295008	−	0.583457i	0.00969981	−	0.0191840i
$926$	14.0905	+	13.5813i	0.463044	+	0.446310i
$927$	−0.978454	−	0.154972i	−0.0321366	−	0.00508994i
$928$	11.4673	−	50.7659i	0.376434	−	1.66647i
$929$	−10.9899	−	3.57083i	−0.360567	−	0.117155i	0.123131	−	0.992390i	$-0.460707\pi$
$929$	−10.9899	−	3.57083i	−0.360567	−	0.117155i	−0.483698	+	0.875235i	$0.660707\pi$
$930$	−3.34069	−	9.62387i	−0.109546	−	0.315579i
$931$	22.2107	−	7.21671i	0.727928	−	0.236518i
$932$	21.0617	+	19.5660i	0.689900	+	0.640904i
$933$	−8.60540	+	16.8890i	−0.281728	+	0.552922i
$934$	−6.15498	+	1.09130i	−0.201397	+	0.0357084i
$935$	10.2471	+	14.0580i	0.335117	+	0.459746i
$936$	−11.4549	−	1.17107i	−0.374416	−	0.0382777i
$937$	−15.4514	+	2.44727i	−0.504777	+	0.0799488i	−0.403629	−	0.914923i	$-0.632251\pi$
$937$	−15.4514	+	2.44727i	−0.504777	+	0.0799488i	−0.101148	+	0.994871i	$0.532251\pi$
$938$	−23.2289	−	16.2323i	−0.758452	−	0.530004i
$939$	19.6282	−	14.2607i	0.640543	−	0.465381i
$940$	24.3163	+	30.9034i	0.793111	+	1.00796i
$941$	24.3401	+	17.6841i	0.793465	+	0.576486i	0.908990	−	0.416819i	$-0.136855\pi$
$941$	24.3401	+	17.6841i	0.793465	+	0.576486i	−0.115525	+	0.993305i	$0.536855\pi$
$942$	3.99459	+	11.5655i	0.130151	+	0.376826i
$943$	21.0128	−	21.0128i	0.684270	−	0.684270i
$944$	−5.27366	−	12.9117i	−0.171643	−	0.420241i
$945$	7.02504	+	3.56571i	0.228525	+	0.115993i
$946$	6.70555	+	12.5825i	0.218016	+	0.409094i
$947$	46.3140	−	23.5982i	1.50500	−	0.766838i	0.509403	−	0.860528i	$-0.329866\pi$
$947$	46.3140	−	23.5982i	1.50500	−	0.766838i	0.995601	+	0.0936904i	$0.0298664\pi$
$948$	−3.73398	+	30.8944i	−0.121274	+	1.00340i
$949$		−	12.3792i		−	0.401847i
$950$	10.0488	+	28.8042i	0.326026	+	0.934531i
$951$			8.01598i			0.259936i
$952$	35.8836	+	44.0561i	1.16299	+	1.42786i
$953$	50.1648	−	25.5603i	1.62500	−	0.827978i	0.626165	−	0.779691i	$-0.284624\pi$
$953$	50.1648	−	25.5603i	1.62500	−	0.827978i	0.998833	−	0.0482873i	$-0.0153763\pi$
$954$	−6.61353	+	3.52451i	−0.214121	+	0.114110i
$955$	−1.13067	+	7.21118i	−0.0365875	+	0.233348i
$956$	1.99521	+	5.44966i	0.0645297	+	0.176255i
$957$	−8.87647	+	8.87647i	−0.286936	+	0.286936i
$958$	−42.9536	+	14.8356i	−1.38777	+	0.479317i
$959$	−40.2427	−	29.2380i	−1.29950	−	0.944145i
$960$	−17.7766	+	1.99851i	−0.573736	+	0.0645015i
$961$	−16.6836	+	12.1214i	−0.538181	+	0.391012i
$962$	0.431219	−	0.617087i	0.0139030	−	0.0198957i
$963$	11.5939	−	1.83630i	0.373609	−	0.0591739i
$964$	36.4480	−	28.5876i	1.17391	−	0.920745i
$965$	15.6076	+	5.04445i	0.502427	+	0.162387i
$966$	6.22362	+	35.1015i	0.200242	+	1.12937i
$967$	−2.94839	+	5.78655i	−0.0948139	+	0.186083i	−0.933542	−	0.358467i	$-0.883300\pi$
$967$	−2.94839	+	5.78655i	−0.0948139	+	0.186083i	0.838728	+	0.544550i	$0.183300\pi$
$968$	−1.42605	−	25.8077i	−0.0458350	−	0.829492i
$969$	−23.3957	+	7.60173i	−0.751579	+	0.244203i
$970$	−1.05068	−	52.6520i	−0.0337354	−	1.69055i
$971$	23.8146	+	7.73784i	0.764247	+	0.248319i	0.665101	−	0.746754i	$-0.268389\pi$
$971$	23.8146	+	7.73784i	0.764247	+	0.248319i	0.0991468	+	0.995073i	$0.468389\pi$
$972$	−0.972930	−	1.74740i	−0.0312068	−	0.0560479i
$973$	20.8043	+	3.29507i	0.666954	+	0.105635i
$974$	31.6941	−	32.8825i	1.01554	−	1.05362i
$975$	−0.0631988	−	20.3551i	−0.00202398	−	0.651885i
$976$	−14.5364	+	1.07182i	−0.465297	+	0.0343083i
$977$	−5.36907	+	33.8990i	−0.171772	+	1.08452i	0.739632	+	0.673011i	$0.235000\pi$
$977$	−5.36907	+	33.8990i	−0.171772	+	1.08452i	−0.911404	+	0.411513i	$0.865000\pi$
$978$	−5.82193	+	19.1074i	−0.186165	+	0.610987i
$979$	6.01151	−	18.5015i	0.192129	−	0.591311i
$980$	−23.7473	+	4.70100i	−0.758580	+	0.150168i
$981$	−0.759823	−	2.33849i	−0.0242593	−	0.0746624i
$982$	−9.80769	+	0.180484i	−0.312976	+	0.00575947i
$983$	−40.7656	−	20.7711i	−1.30022	−	0.662496i	−0.339656	−	0.940550i	$-0.610311\pi$
$983$	−40.7656	−	20.7711i	−1.30022	−	0.662496i	−0.960566	+	0.278054i	$0.910311\pi$
$984$	−2.47511	−	11.4840i	−0.0789037	−	0.366096i
$985$	40.9865	+	29.6813i	1.30594	+	0.945726i
$986$	−10.2555	+	73.4765i	−0.326602	+	2.33997i
$987$	−4.84624	−	30.5979i	−0.154257	−	0.973943i
$988$	6.76791	+	34.4692i	0.215316	+	1.09661i
$989$	31.0739	+	42.7696i	0.988093	+	1.35999i
$990$	3.88275	+	1.88175i	0.123402	+	0.0598058i
$991$	−9.20377	+	12.6679i	−0.292367	+	0.402409i	−0.929781	−	0.368112i	$-0.880004\pi$
$991$	−9.20377	+	12.6679i	−0.292367	+	0.402409i	0.637414	+	0.770522i	$0.280004\pi$
$992$	−7.19980	−	16.7408i	−0.228594	−	0.531522i
$993$	10.5683	+	10.5683i	0.335374	+	0.335374i
$994$	2.76045	−	5.67338i	0.0875560	−	0.179949i
$995$	−50.7136	+	25.9391i	−1.60773	+	0.822325i
$996$	−8.71957	−	2.48243i	−0.276290	−	0.0786589i
$997$	5.01016	+	9.83299i	0.158673	+	0.311414i	0.956632	−	0.291298i	$-0.0940870\pi$
$997$	5.01016	+	9.83299i	0.158673	+	0.311414i	−0.797959	+	0.602712i	$0.794087\pi$
$998$	2.34757	+	3.10920i	0.0743111	+	0.0984201i
$999$	0.130760			0.00413705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.223.9	yes	240
3.2	odd	2		900.2.bj.f.523.22		240
4.3	odd	2	inner	300.2.w.a.223.24	yes	240
12.11	even	2		900.2.bj.f.523.7		240
25.12	odd	20	inner	300.2.w.a.187.24	yes	240
75.62	even	20		900.2.bj.f.487.7		240
100.87	even	20	inner	300.2.w.a.187.9	✓	240
300.287	odd	20		900.2.bj.f.487.22		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.9	✓	240	100.87	even	20	inner
300.2.w.a.187.24	yes	240	25.12	odd	20	inner
300.2.w.a.223.9	yes	240	1.1	even	1	trivial
300.2.w.a.223.24	yes	240	4.3	odd	2	inner
900.2.bj.f.487.7		240	75.62	even	20
900.2.bj.f.487.22		240	300.287	odd	20
900.2.bj.f.523.7		240	12.11	even	2
900.2.bj.f.523.22		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)

\(f(q)\)	\(=\)	\(q+(-0.852164 - 1.12863i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-0.547633 + 1.92356i) q^{4} +(1.99077 - 1.01825i) q^{5} +(-0.618747 + 1.27167i) q^{6} +(2.49130 + 2.49130i) q^{7} +(2.63767 - 1.02111i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(-0.852164 - 1.12863i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(-0.547633 + 1.92356i) q^{4} +(1.99077 - 1.01825i) q^{5} +(-0.618747 + 1.27167i) q^{6} +(2.49130 + 2.49130i) q^{7} +(2.63767 - 1.02111i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(-2.84569 - 1.37914i) q^{10} +(0.801993 + 1.10385i) q^{11} +(1.96253 - 0.385335i) q^{12} +(0.636851 + 4.02092i) q^{13} +(0.688770 - 4.93475i) q^{14} +(-1.81106 - 1.31152i) q^{15} +(-3.40020 - 2.10681i) q^{16} +(5.08043 + 2.58861i) q^{17} +(1.41397 - 0.0260204i) q^{18} +(-1.33319 - 4.10314i) q^{19} +(0.868448 + 4.38700i) q^{20} +(1.08874 - 3.35078i) q^{21} +(0.562412 - 1.84582i) q^{22} +(1.11924 - 7.06662i) q^{23} +(-2.10730 - 1.88661i) q^{24} +(2.92635 - 4.05419i) q^{25} +(3.99545 - 4.14525i) q^{26} +(0.987688 + 0.156434i) q^{27} +(-6.15648 + 3.42785i) q^{28} +(-8.75004 - 2.84306i) q^{29} +(0.0630915 + 3.16165i) q^{30} +(-3.06381 + 0.995491i) q^{31} +(0.519703 + 5.63293i) q^{32} +(0.619439 - 1.21572i) q^{33} +(-1.40777 - 7.93987i) q^{34} +(7.49635 + 2.42285i) q^{35} +(-1.23431 - 1.57369i) q^{36} +(0.129150 - 0.0204553i) q^{37} +(-3.49485 + 5.00124i) q^{38} +(3.29354 - 2.39290i) q^{39} +(4.21126 - 4.71861i) q^{40} +(3.36019 + 2.44132i) q^{41} +(-4.70959 + 1.62663i) q^{42} +(-5.22481 + 5.22481i) q^{43} +(-2.56252 + 0.938181i) q^{44} +(-0.346369 + 2.20908i) q^{45} +(-8.92941 + 4.75870i) q^{46} +(7.83453 - 3.99189i) q^{47} +(-0.333527 + 3.98607i) q^{48} +5.41311i q^{49} +(-7.06943 + 0.152052i) q^{50} -5.70190i q^{51} +(-8.08325 - 0.976963i) q^{52} +(-4.72153 + 2.40574i) q^{53} +(-0.665115 - 1.24805i) q^{54} +(2.72057 + 1.38089i) q^{55} +(9.11512 + 4.02733i) q^{56} +(-3.05067 + 3.05067i) q^{57} +(4.24769 + 12.2983i) q^{58} +(2.82088 + 2.04949i) q^{59} +(3.51458 - 2.76545i) q^{60} +(2.94802 - 2.14186i) q^{61} +(3.73441 + 2.60960i) q^{62} +(-3.47985 + 0.551154i) q^{63} +(5.91465 - 5.38674i) q^{64} +(5.36211 + 7.35626i) q^{65} +(-1.89996 + 0.336870i) q^{66} +(2.58207 - 5.06761i) q^{67} +(-7.76157 + 8.35493i) q^{68} +(-6.80453 + 2.21093i) q^{69} +(-3.65361 - 10.5253i) q^{70} +(1.20429 + 0.391299i) q^{71} +(-0.724287 + 2.73412i) q^{72} +(-3.00337 - 0.475687i) q^{73} +(-0.133143 - 0.128332i) q^{74} +(-4.94085 - 0.766836i) q^{75} +(8.62276 - 0.317464i) q^{76} +(-0.752011 + 4.74801i) q^{77} +(-5.50734 - 1.67806i) q^{78} +(-4.80819 + 14.7981i) q^{79} +(-8.91427 - 0.731952i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(-0.108074 - 5.87284i) q^{82} +(-4.03896 - 2.05795i) q^{83} +(5.84922 + 3.92925i) q^{84} +(12.7498 - 0.0197929i) q^{85} +(10.3493 + 1.44451i) q^{86} +(1.43925 + 9.08706i) q^{87} +(3.24255 + 2.09267i) q^{88} +(-8.38047 - 11.5347i) q^{89} +(2.78841 - 1.49157i) q^{90} +(-8.43071 + 11.6039i) q^{91} +(12.9802 + 6.02285i) q^{92} +(2.27793 + 2.27793i) q^{93} +(-11.1817 - 5.44057i) q^{94} +(-6.83209 - 6.81091i) q^{95} +(4.78304 - 3.02036i) q^{96} +(7.56046 + 14.8382i) q^{97} +(6.10942 - 4.61285i) q^{98} -1.36443 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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