LMFDB - Embedded newform 300.2.w.a.223.25

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			223.25
Character	$\chi$	$=$	300.223
Dual form			300.2.w.a.187.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16035 + 0.808445i) q^{2} +(0.453990 + 0.891007i) q^{3} +(0.692833 + 1.87616i) q^{4} +(2.17065 + 0.536923i) q^{5} +(-0.193541 + 1.40091i) q^{6} +(-0.403183 - 0.403183i) q^{7} +(-0.712844 + 2.73712i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(1.16035 + 0.808445i) q^{2} +(0.453990 + 0.891007i) q^{3} +(0.692833 + 1.87616i) q^{4} +(2.17065 + 0.536923i) q^{5} +(-0.193541 + 1.40091i) q^{6} +(-0.403183 - 0.403183i) q^{7} +(-0.712844 + 2.73712i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(2.08464 + 2.37787i) q^{10} +(-2.68322 - 3.69314i) q^{11} +(-1.35713 + 1.46908i) q^{12} +(-0.669605 - 4.22772i) q^{13} +(-0.141883 - 0.793785i) q^{14} +(0.507052 + 2.17782i) q^{15} +(-3.03997 + 2.59973i) q^{16} +(1.13184 + 0.576699i) q^{17} +(-1.33608 + 0.463552i) q^{18} +(-0.214045 - 0.658762i) q^{19} +(0.496541 + 4.44448i) q^{20} +(0.176197 - 0.542280i) q^{21} +(-0.127782 - 6.45458i) q^{22} +(-0.103651 + 0.654427i) q^{23} +(-2.76242 + 0.607480i) q^{24} +(4.42343 + 2.33094i) q^{25} +(2.64090 - 5.44698i) q^{26} +(-0.987688 - 0.156434i) q^{27} +(0.477098 - 1.03577i) q^{28} +(5.48448 + 1.78201i) q^{29} +(-1.17229 + 2.93696i) q^{30} +(-7.87705 + 2.55941i) q^{31} +(-5.62917 + 0.558959i) q^{32} +(2.07245 - 4.06742i) q^{33} +(0.847098 + 1.58420i) q^{34} +(-0.658690 - 1.09165i) q^{35} +(-1.92508 - 0.542267i) q^{36} +(-0.551102 + 0.0872860i) q^{37} +(0.284206 - 0.937440i) q^{38} +(3.46293 - 2.51597i) q^{39} +(-3.01696 + 5.55859i) q^{40} +(-3.58374 - 2.60374i) q^{41} +(0.642854 - 0.486789i) q^{42} +(-2.72923 + 2.72923i) q^{43} +(5.06990 - 7.59289i) q^{44} +(-1.71026 + 1.44050i) q^{45} +(-0.649340 + 0.675569i) q^{46} +(9.06571 - 4.61921i) q^{47} +(-3.69649 - 1.52838i) q^{48} -6.67489i q^{49} +(3.24829 + 6.28081i) q^{50} +1.27029i q^{51} +(7.46797 - 4.18539i) q^{52} +(7.66275 - 3.90436i) q^{53} +(-1.01960 - 0.980011i) q^{54} +(-3.84140 - 9.45719i) q^{55} +(1.39097 - 0.816155i) q^{56} +(0.489787 - 0.489787i) q^{57} +(4.92326 + 6.50166i) q^{58} +(5.72938 + 4.16264i) q^{59} +(-3.73464 + 2.46018i) q^{60} +(-10.7384 + 7.80192i) q^{61} +(-11.2093 - 3.39835i) q^{62} +(0.563167 - 0.0891968i) q^{63} +(-6.98371 - 3.90229i) q^{64} +(0.816485 - 9.53642i) q^{65} +(5.69306 - 3.04417i) q^{66} +(4.20759 - 8.25787i) q^{67} +(-0.297808 + 2.52306i) q^{68} +(-0.630155 + 0.204750i) q^{69} +(0.118224 - 1.79921i) q^{70} +(-1.71079 - 0.555870i) q^{71} +(-1.79538 - 2.18554i) q^{72} +(-6.95389 - 1.10139i) q^{73} +(-0.710038 - 0.344253i) q^{74} +(-0.0686916 + 4.99953i) q^{75} +(1.08765 - 0.857995i) q^{76} +(-0.407181 + 2.57084i) q^{77} +(6.05224 - 0.119817i) q^{78} +(-2.36601 + 7.28182i) q^{79} +(-7.99455 + 4.01088i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(-2.05342 - 5.91851i) q^{82} +(7.97834 + 4.06517i) q^{83} +(1.13948 - 0.0451344i) q^{84} +(2.14717 + 1.85952i) q^{85} +(-5.37330 + 0.960434i) q^{86} +(0.902114 + 5.69572i) q^{87} +(12.0213 - 4.71169i) q^{88} +(3.05003 + 4.19801i) q^{89} +(-3.14906 + 0.288834i) q^{90} +(-1.43457 + 1.97452i) q^{91} +(-1.29962 + 0.258942i) q^{92} +(-5.85655 - 5.85655i) q^{93} +(14.2538 + 1.96922i) q^{94} +(-0.110911 - 1.54487i) q^{95} +(-3.05363 - 4.76187i) q^{96} +(5.74169 + 11.2687i) q^{97} +(5.39628 - 7.74522i) q^{98} +4.56497 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 $

$2$	1.16035	+	0.808445i	0.820493	+	0.571657i
$2$	1.16035	+	0.808445i	0.820493	+	0.571657i
$3$	0.453990	+	0.891007i	0.262112	+	0.514423i
$3$	0.453990	+	0.891007i	0.262112	+	0.514423i
$4$	0.692833	+	1.87616i	0.346416	+	0.938081i
$5$	2.17065	+	0.536923i	0.970743	+	0.240119i
$5$	2.17065	+	0.536923i	0.970743	+	0.240119i
$6$	−0.193541	+	1.40091i	−0.0790129	+	0.571918i
$7$	−0.403183	−	0.403183i	−0.152389	−	0.152389i	0.626795	−	0.779184i	$-0.284366\pi$
$7$	−0.403183	−	0.403183i	−0.152389	−	0.152389i	−0.779184	+	0.626795i	$0.784366\pi$
$8$	−0.712844	+	2.73712i	−0.252028	+	0.967720i
$9$	−0.587785	+	0.809017i	−0.195928	+	0.269672i
$10$	2.08464	+	2.37787i	0.659222	+	0.751949i
$11$	−2.68322	−	3.69314i	−0.809022	−	1.11352i	−0.991473	−	0.130309i	$-0.958403\pi$
$11$	−2.68322	−	3.69314i	−0.809022	−	1.11352i	0.182451	−	0.983215i	$-0.441597\pi$
$12$	−1.35713	+	1.46908i	−0.391771	+	0.424086i
$13$	−0.669605	−	4.22772i	−0.185715	−	1.17256i	−0.887719	−	0.460386i	$-0.847711\pi$
$13$	−0.669605	−	4.22772i	−0.185715	−	1.17256i	0.702004	−	0.712173i	$-0.252289\pi$
$14$	−0.141883	−	0.793785i	−0.0379197	−	0.212148i
$15$	0.507052	+	2.17782i	0.130920	+	0.562311i
$16$	−3.03997	+	2.59973i	−0.759991	+	0.649933i
$17$	1.13184	+	0.576699i	0.274511	+	0.139870i	0.585827	−	0.810436i	$-0.300770\pi$
$17$	1.13184	+	0.576699i	0.274511	+	0.139870i	−0.311316	+	0.950306i	$0.600770\pi$
$18$	−1.33608	+	0.463552i	−0.314918	+	0.109260i
$19$	−0.214045	−	0.658762i	−0.0491053	−	0.151130i	0.923497	−	0.383605i	$-0.125318\pi$
$19$	−0.214045	−	0.658762i	−0.0491053	−	0.151130i	−0.972602	+	0.232475i	$0.925318\pi$
$20$	0.496541	+	4.44448i	0.111030	+	0.993817i
$21$	0.176197	−	0.542280i	0.0384494	−	0.118335i
$22$	−0.127782	−	6.45458i	−0.0272432	−	1.37612i
$23$	−0.103651	+	0.654427i	−0.0216127	+	0.136457i	−0.996135	−	0.0878321i	$-0.972006\pi$
$23$	−0.103651	+	0.654427i	−0.0216127	+	0.136457i	0.974523	+	0.224289i	$0.0720061\pi$
$24$	−2.76242	+	0.607480i	−0.563877	+	0.124001i
$25$	4.42343	+	2.33094i	0.884685	+	0.466189i
$26$	2.64090	−	5.44698i	0.517924	−	1.06824i
$27$	−0.987688	−	0.156434i	−0.190081	−	0.0301058i
$28$	0.477098	−	1.03577i	0.0901630	−	0.195743i
$29$	5.48448	+	1.78201i	1.01844	+	0.330912i	0.770211	−	0.637789i	$-0.220151\pi$
$29$	5.48448	+	1.78201i	1.01844	+	0.330912i	0.248231	+	0.968701i	$0.420151\pi$
$30$	−1.17229	+	2.93696i	−0.214030	+	0.536213i
$31$	−7.87705	+	2.55941i	−1.41476	+	0.459683i	−0.913933	−	0.405865i	$-0.866970\pi$
$31$	−7.87705	+	2.55941i	−1.41476	+	0.459683i	−0.500826	+	0.865548i	$0.666970\pi$
$32$	−5.62917	+	0.558959i	−0.995106	+	0.0988109i
$33$	2.07245	−	4.06742i	0.360768	−	0.708047i
$34$	0.847098	+	1.58420i	0.145276	+	0.271688i
$35$	−0.658690	−	1.09165i	−0.111339	−	0.184522i
$36$	−1.92508	−	0.542267i	−0.320847	−	0.0903778i
$37$	−0.551102	+	0.0872860i	−0.0906006	+	0.0143497i	−0.201570	−	0.979474i	$-0.564604\pi$
$37$	−0.551102	+	0.0872860i	−0.0906006	+	0.0143497i	0.110970	+	0.993824i	$0.464604\pi$
$38$	0.284206	−	0.937440i	0.0461043	−	0.152073i
$39$	3.46293	−	2.51597i	0.554513	−	0.402877i
$40$	−3.01696	+	5.55859i	−0.477023	+	0.878891i
$41$	−3.58374	−	2.60374i	−0.559686	−	0.406636i	0.271658	−	0.962394i	$-0.412428\pi$
$41$	−3.58374	−	2.60374i	−0.559686	−	0.406636i	−0.831344	+	0.555758i	$0.812428\pi$
$42$	0.642854	−	0.486789i	0.0991946	−	0.0751132i
$43$	−2.72923	+	2.72923i	−0.416204	+	0.416204i	−0.883893	−	0.467689i	$-0.845087\pi$
$43$	−2.72923	+	2.72923i	−0.416204	+	0.416204i	0.467689	+	0.883893i	$0.345087\pi$
$44$	5.06990	−	7.59289i	0.764317	−	1.14467i
$45$	−1.71026	+	1.44050i	−0.254950	+	0.214736i
$46$	−0.649340	+	0.675569i	−0.0957399	+	0.0996072i
$47$	9.06571	−	4.61921i	1.32237	−	0.673781i	0.356863	−	0.934157i	$-0.383846\pi$
$47$	9.06571	−	4.61921i	1.32237	−	0.673781i	0.965507	+	0.260375i	$0.0838463\pi$
$48$	−3.69649	−	1.52838i	−0.533543	−	0.220602i
$49$		−	6.67489i		−	0.953555i
$50$	3.24829	+	6.28081i	0.459378	+	0.888241i
$51$			1.27029i			0.177876i
$52$	7.46797	−	4.18539i	1.03562	−	0.580410i
$53$	7.66275	−	3.90436i	1.05256	−	0.536306i	0.159944	−	0.987126i	$-0.448868\pi$
$53$	7.66275	−	3.90436i	1.05256	−	0.536306i	0.892615	+	0.450820i	$0.148868\pi$
$54$	−1.01960	−	0.980011i	−0.138750	−	0.133363i
$55$	−3.84140	−	9.45719i	−0.517974	−	1.27521i
$56$	1.39097	−	0.816155i	0.185876	−	0.109063i
$57$	0.489787	−	0.489787i	0.0648739	−	0.0648739i
$58$	4.92326	+	6.50166i	0.646456	+	0.853710i
$59$	5.72938	+	4.16264i	0.745902	+	0.541929i	0.894554	−	0.446960i	$-0.147493\pi$
$59$	5.72938	+	4.16264i	0.745902	+	0.541929i	−0.148652	+	0.988890i	$0.547493\pi$
$60$	−3.73464	+	2.46018i	−0.482140	+	0.317607i
$61$	−10.7384	+	7.80192i	−1.37491	+	0.998934i	−0.377579	+	0.925977i	$0.623243\pi$
$61$	−10.7384	+	7.80192i	−1.37491	+	0.998934i	−0.997335	+	0.0729561i	$0.976757\pi$
$62$	−11.2093	−	3.39835i	−1.42358	−	0.431590i
$63$	0.563167	−	0.0891968i	0.0709523	−	0.0112377i
$64$	−6.98371	−	3.90229i	−0.872963	−	0.487786i
$65$	0.816485	−	9.53642i	0.101272	−	1.18285i
$66$	5.69306	−	3.04417i	0.700768	−	0.374712i
$67$	4.20759	−	8.25787i	0.514039	−	1.00886i	−0.477448	−	0.878660i	$-0.658438\pi$
$67$	4.20759	−	8.25787i	0.514039	−	1.00886i	0.991488	−	0.130199i	$-0.0415618\pi$
$68$	−0.297808	+	2.52306i	−0.0361145	+	0.305966i
$69$	−0.630155	+	0.204750i	−0.0758618	+	0.0246490i
$70$	0.118224	−	1.79921i	0.0141305	−	0.215047i
$71$	−1.71079	−	0.555870i	−0.203034	−	0.0659696i	0.205735	−	0.978608i	$-0.434042\pi$
$71$	−1.71079	−	0.555870i	−0.203034	−	0.0659696i	−0.408768	+	0.912638i	$0.634042\pi$
$72$	−1.79538	−	2.18554i	−0.211588	−	0.257569i
$73$	−6.95389	−	1.10139i	−0.813892	−	0.128908i	−0.264407	−	0.964411i	$-0.585176\pi$
$73$	−6.95389	−	1.10139i	−0.813892	−	0.128908i	−0.549485	+	0.835504i	$0.685176\pi$
$74$	−0.710038	−	0.344253i	−0.0825402	−	0.0400186i
$75$	−0.0686916	+	4.99953i	−0.00793183	+	0.577296i
$76$	1.08765	−	0.857995i	0.124762	−	0.0984188i
$77$	−0.407181	+	2.57084i	−0.0464026	+	0.292974i
$78$	6.05224	−	0.119817i	0.685282	−	0.0135666i
$79$	−2.36601	+	7.28182i	−0.266197	+	0.819269i	0.725219	+	0.688518i	$0.241739\pi$
$79$	−2.36601	+	7.28182i	−0.266197	+	0.819269i	−0.991415	+	0.130750i	$0.958261\pi$
$80$	−7.99455	+	4.01088i	−0.893818	+	0.448430i
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	−2.05342	−	5.91851i	−0.226762	−	0.653590i
$83$	7.97834	+	4.06517i	0.875737	+	0.446210i	0.833256	−	0.552887i	$-0.186474\pi$
$83$	7.97834	+	4.06517i	0.875737	+	0.446210i	0.0424806	+	0.999097i	$0.486474\pi$
$84$	1.13948	−	0.0451344i	0.124327	−	0.00492457i
$85$	2.14717	+	1.85952i	0.232894	+	0.201693i
$86$	−5.37330	+	0.960434i	−0.579418	+	0.103566i
$87$	0.902114	+	5.69572i	0.0967168	+	0.610646i
$88$	12.0213	−	4.71169i	1.28148	−	0.502267i
$89$	3.05003	+	4.19801i	0.323303	+	0.444988i	0.939472	−	0.342626i	$-0.111316\pi$
$89$	3.05003	+	4.19801i	0.323303	+	0.444988i	−0.616169	+	0.787614i	$0.711316\pi$
$90$	−3.14906	+	0.288834i	−0.331940	+	0.0304458i
$91$	−1.43457	+	1.97452i	−0.150384	+	0.206986i
$92$	−1.29962	+	0.258942i	−0.135495	+	0.0269966i
$93$	−5.85655	−	5.85655i	−0.607296	−	0.607296i
$94$	14.2538	+	1.96922i	1.47017	+	0.203110i
$95$	−0.110911	−	1.54487i	−0.0113793	−	0.158500i
$96$	−3.05363	−	4.76187i	−0.311659	−	0.486006i
$97$	5.74169	+	11.2687i	0.582981	+	1.14416i	0.974582	+	0.224029i	$0.0719210\pi$
$97$	5.74169	+	11.2687i	0.582981	+	1.14416i	−0.391602	+	0.920135i	$0.628079\pi$
$98$	5.39628	−	7.74522i	0.545107	−	0.782385i
$99$	4.56497			0.458797
$100$	−1.30853	+	9.91402i	−0.130853	+	0.991402i
$101$	−18.5684			−1.84763			−0.923813	−	0.382845i	$-0.874945\pi$
$101$	−18.5684			−1.84763			−0.923813	+	0.382845i	$0.874945\pi$
$102$	−1.02696	+	1.47398i	−0.101684	+	0.145946i
$103$	−3.40490	−	6.68249i	−0.335495	−	0.658445i	0.660205	−	0.751085i	$-0.270469\pi$
$103$	−3.40490	−	6.68249i	−0.335495	−	0.658445i	−0.995700	+	0.0926401i	$0.970469\pi$
$104$	12.0491	+	1.18091i	1.18151	+	0.115798i
$105$	0.673625	−	1.08249i	0.0657391	−	0.105641i
$106$	12.0479	+	1.66447i	1.17020	+	0.161668i
$107$	0.808322	+	0.808322i	0.0781434	+	0.0781434i	0.745098	−	0.666955i	$-0.232403\pi$
$107$	0.808322	+	0.808322i	0.0781434	+	0.0781434i	−0.666955	+	0.745098i	$0.732403\pi$
$108$	−0.390806	−	1.96145i	−0.0376054	−	0.188740i
$109$	−10.5714	+	14.5503i	−1.01256	+	1.39367i	−0.0952690	+	0.995452i	$0.530371\pi$
$109$	−10.5714	+	14.5503i	−1.01256	+	1.39367i	−0.917291	+	0.398218i	$0.869629\pi$
$110$	3.18825	−	14.0792i	0.303987	−	1.34240i
$111$	−0.327967	−	0.451408i	−0.0311293	−	0.0428458i
$112$	2.27383	+	0.177494i	0.214857	+	0.0167716i
$113$	−1.84765	−	11.6656i	−0.173813	−	1.09741i	−0.908156	−	0.418632i	$-0.862510\pi$
$113$	−1.84765	−	11.6656i	−0.173813	−	1.09741i	0.734343	−	0.678778i	$-0.237490\pi$
$114$	0.964292	−	0.172359i	0.0903142	−	0.0161429i
$115$	−0.576367	+	1.36488i	−0.0537465	+	0.127276i
$116$	0.456478	+	11.5244i	0.0423829	+	1.07001i
$117$	3.81388	+	1.94327i	0.352594	+	0.179655i
$118$	3.28283	+	9.46201i	0.302209	+	0.871049i
$119$	−0.223822	−	0.688852i	−0.0205177	−	0.0631469i
$120$	−6.32241	−	0.164583i	−0.577155	−	0.0150243i
$121$	−3.04041	+	9.35742i	−0.276401	+	0.850675i
$122$	−18.7678	+	0.371547i	−1.69915	+	0.0336383i
$123$	0.692965	−	4.37521i	0.0624825	−	0.394499i
$124$	−10.2593	−	13.0054i	−0.921316	−	1.16792i
$125$	8.35017	+	7.43470i	0.746862	+	0.664980i
$126$	0.725582	+	0.351790i	0.0646400	+	0.0313399i
$127$	−19.6106	−	3.10602i	−1.74016	−	0.275614i	−0.796047	−	0.605235i	$-0.793079\pi$
$127$	−19.6106	−	3.10602i	−1.74016	−	0.275614i	−0.944113	+	0.329621i	$0.893079\pi$
$128$	−4.94877	−	10.1740i	−0.437414	−	0.899260i
$129$	−3.67081	−	1.19272i	−0.323196	−	0.105013i
$130$	8.65709	−	10.4055i	0.759277	−	0.912625i
$131$	21.6599	−	7.03773i	1.89243	−	0.614889i	0.915083	−	0.403264i	$-0.132125\pi$
$131$	21.6599	−	7.03773i	1.89243	−	0.614889i	0.977351	−	0.211625i	$-0.0678755\pi$
$132$	9.06700	+	1.07022i	0.789181	+	0.0931505i
$133$	−0.179302	+	0.351901i	−0.0155475	+	0.0305137i
$134$	11.5583	−	6.18042i	0.998487	−	0.533907i
$135$	−2.05993	−	0.869877i	−0.177291	−	0.0748671i
$136$	−2.38532	+	2.68688i	−0.204540	+	0.230398i
$137$	−16.5163	+	2.61593i	−1.41109	+	0.223494i	−0.815016	−	0.579438i	$-0.803272\pi$
$137$	−16.5163	+	2.61593i	−1.41109	+	0.223494i	−0.596070	+	0.802932i	$0.703272\pi$
$138$	−0.896731	−	0.271864i	−0.0763348	−	0.0231426i
$139$	0.991605	−	0.720443i	0.0841068	−	0.0611072i	−0.544937	−	0.838477i	$-0.683447\pi$
$139$	0.991605	−	0.720443i	0.0841068	−	0.0611072i	0.629044	+	0.777370i	$0.283447\pi$
$140$	1.59174	−	1.99214i	0.134527	−	0.168366i
$141$	8.23150	+	5.98053i	0.693217	+	0.503652i
$142$	−1.53573	−	2.02809i	−0.128876	−	0.170193i
$143$	−13.8169	+	13.8169i	−1.15542	+	1.15542i
$144$	−0.316381	−	3.98747i	−0.0263651	−	0.332289i
$145$	10.9481	+	6.81287i	0.909187	+	0.565778i
$146$	−7.17855	−	6.89984i	−0.594101	−	0.571035i
$147$	5.94737	−	3.03034i	0.490531	−	0.249938i
$148$	−0.545584	−	0.973482i	−0.0448467	−	0.0800197i
$149$			13.9644i			1.14401i	0.820251	+	0.572003i	$0.193834\pi$
$149$			13.9644i			1.14401i	−0.820251	+	0.572003i	$0.806166\pi$
$150$	−4.12155	+	5.74568i	−0.336523	+	0.469133i
$151$			19.3040i			1.57094i	0.618901	+	0.785469i	$0.287578\pi$
$151$			19.3040i			1.57094i	−0.618901	+	0.785469i	$0.712422\pi$
$152$	1.95570	−	0.116273i	0.158628	−	0.00943096i
$153$	−1.13184	+	0.576699i	−0.0915035	+	0.0466234i
$154$	−2.55086	+	2.65390i	−0.205554	+	0.213857i
$155$	−18.4725	+	1.32620i	−1.48375	+	0.106523i
$156$	7.11960	+	4.75388i	0.570024	+	0.380615i
$157$	11.6248	−	11.6248i	0.927763	−	0.927763i	−0.0697978	−	0.997561i	$-0.522235\pi$
$157$	11.6248	−	11.6248i	0.927763	−	0.927763i	0.997561	+	0.0697978i	$0.0222354\pi$
$158$	−8.63235	+	6.53669i	−0.686753	+	0.520031i
$159$	6.95763	+	5.05501i	0.551776	+	0.400889i
$160$	−12.5191	−	1.80913i	−0.989719	−	0.143024i
$161$	0.305644	−	0.222063i	0.0240881	−	0.0175010i
$162$	0.410309	−	1.35338i	0.0322369	−	0.106332i
$163$	17.3839	−	2.75333i	1.36161	−	0.215658i	0.567470	−	0.823394i	$-0.307922\pi$
$163$	17.3839	−	2.75333i	1.36161	−	0.215658i	0.794139	+	0.607736i	$0.207922\pi$
$164$	2.40210	−	8.52763i	0.187573	−	0.665896i
$165$	6.68246	−	7.71619i	0.520229	−	0.600705i
$166$	5.97122	+	11.1671i	0.463456	+	0.866733i
$167$	−3.04644	+	5.97897i	−0.235741	+	0.462667i	−0.978322	−	0.207089i	$-0.933601\pi$
$167$	−3.04644	+	5.97897i	−0.235741	+	0.462667i	0.742582	+	0.669756i	$0.233601\pi$
$168$	1.35869	+	0.868835i	0.104825	+	0.0670321i
$169$	−5.06153	+	1.64459i	−0.389349	+	0.126507i
$170$	0.988157	+	3.89357i	0.0757882	+	0.298623i
$171$	0.658762	+	0.214045i	0.0503768	+	0.0163684i
$172$	−7.01138	−	3.22958i	−0.534612	−	0.246253i
$173$	−0.974029	−	0.154271i	−0.0740540	−	0.0117290i	0.119297	−	0.992859i	$-0.461936\pi$
$173$	−0.974029	−	0.154271i	−0.0740540	−	0.0117290i	−0.193352	+	0.981130i	$0.561936\pi$
$174$	−3.55791	+	7.33835i	−0.269725	+	0.556319i
$175$	−0.843653	−	2.72325i	−0.0637742	−	0.205858i
$176$	17.7581	+	4.25136i	1.33857	+	0.320458i
$177$	−1.10785	+	6.99471i	−0.0832714	+	0.525755i
$178$	0.145250	+	7.33695i	0.0108870	+	0.549928i
$179$	−5.08238	+	15.6420i	−0.379875	+	1.16914i	0.560255	+	0.828320i	$0.310703\pi$
$179$	−5.08238	+	15.6420i	−0.379875	+	1.16914i	−0.940130	+	0.340815i	$0.889297\pi$
$180$	−3.88752	−	2.21069i	−0.289759	−	0.164775i
$181$	−7.05393	−	21.7098i	−0.524314	−	1.61367i	−0.765668	−	0.643236i	$-0.777591\pi$
$181$	−7.05393	−	21.7098i	−0.524314	−	1.61367i	0.241353	−	0.970437i	$-0.422409\pi$
$182$	−3.26090	+	1.13136i	−0.241714	+	0.0838622i
$183$	−11.8267	−	6.02601i	−0.874255	−	0.445455i
$184$	−1.71736	−	0.750210i	−0.126606	−	0.0553062i
$185$	−1.24311	−	0.106432i	−0.0913956	−	0.00782506i
$186$	−2.06096	−	11.5304i	−0.151117	−	0.845447i
$187$	−0.907138	−	5.72744i	−0.0663365	−	0.418832i
$188$	14.9474	+	13.8084i	1.09015	+	1.00708i
$189$	0.335147	+	0.461291i	0.0243784	+	0.0335540i
$190$	1.12024	−	1.88226i	0.0812711	−	0.136553i
$191$	−5.09993	+	7.01945i	−0.369018	+	0.507910i	−0.952634	−	0.304120i	$-0.901638\pi$
$191$	−5.09993	+	7.01945i	−0.369018	+	0.507910i	0.583616	+	0.812030i	$0.301638\pi$
$192$	0.306427	−	7.99413i	0.0221145	−	0.576927i
$193$	3.60845	+	3.60845i	0.259742	+	0.259742i	0.824949	−	0.565207i	$-0.191204\pi$
$193$	3.60845	+	3.60845i	0.259742	+	0.259742i	−0.565207	+	0.824949i	$0.691204\pi$
$194$	−2.44775	+	17.7175i	−0.175738	+	1.27204i
$195$	8.86769	−	3.60195i	0.635029	−	0.257941i
$196$	12.5232	−	4.62458i	0.894512	−	0.330327i
$197$	5.27204	+	10.3470i	0.375617	+	0.737190i	0.998999	−	0.0447274i	$-0.0142419\pi$
$197$	5.27204	+	10.3470i	0.375617	+	0.737190i	−0.623382	+	0.781917i	$0.714242\pi$
$198$	5.29697	+	3.69053i	0.376440	+	0.262275i
$199$	1.27147			0.0901321			0.0450661	−	0.998984i	$-0.485650\pi$
$199$	1.27147			0.0901321			0.0450661	+	0.998984i	$0.485650\pi$
$200$	−9.53330	+	10.4459i	−0.674106	+	0.738635i
$201$	9.26802			0.653716
$202$	−21.5459	−	15.0115i	−1.51596	−	1.05621i
$203$	−1.49277	−	2.92972i	−0.104772	−	0.205626i
$204$	−2.38327	+	0.880098i	−0.166862	+	0.0616192i
$205$	−6.38103	−	7.57599i	−0.445670	−	0.529130i
$206$	1.45155	−	10.5067i	0.101134	−	0.732037i
$207$	−0.468518	−	0.468518i	−0.0325642	−	0.0325642i
$208$	13.0265	+	11.1113i	0.903227	+	0.770432i
$209$	−1.85857	+	2.55811i	−0.128560	+	0.176948i
$210$	1.65678	−	0.711485i	0.114329	−	0.0490971i
$211$	2.56831	+	3.53497i	0.176810	+	0.243358i	0.888219	−	0.459420i	$-0.151943\pi$
$211$	2.56831	+	3.53497i	0.176810	+	0.243358i	−0.711409	+	0.702778i	$0.751943\pi$
$212$	12.6342	+	11.6715i	0.867722	+	0.801601i
$213$	−0.281399	−	1.77669i	−0.0192812	−	0.121736i
$214$	0.284454	+	1.59142i	0.0194449	+	0.108787i
$215$	−7.38958	+	4.45881i	−0.503965	+	0.304088i
$216$	1.13225	−	2.59191i	0.0770398	−	0.176357i
$217$	4.20780	+	2.14398i	0.285644	+	0.145543i
$218$	−24.0297	+	8.33708i	−1.62750	+	0.564658i
$219$	−2.17566	−	6.69598i	−0.147017	−	0.452473i
$220$	15.0818	−	13.7593i	1.01681	−	0.927655i
$221$	1.68024	−	5.17125i	0.113025	−	0.347856i
$222$	−0.0156186	−	0.788936i	−0.00104825	−	0.0529499i
$223$	1.79466	−	11.3311i	0.120180	−	0.758784i	−0.851826	−	0.523825i	$-0.824504\pi$
$223$	1.79466	−	11.3311i	0.120180	−	0.758784i	0.972005	−	0.234959i	$-0.0754955\pi$
$224$	2.49495	+	2.04422i	0.166701	+	0.136585i
$225$	−4.48580	+	2.20853i	−0.299053	+	0.147236i
$226$	7.28709	−	15.0300i	0.484730	−	0.999778i
$227$	29.6086	+	4.68955i	1.96519	+	0.311256i	0.998460	+	0.0554697i	$0.0176656\pi$
$227$	29.6086	+	4.68955i	1.96519	+	0.311256i	0.966733	+	0.255786i	$0.0823344\pi$
$228$	1.25826	+	0.579580i	0.0833304	+	0.0383836i
$229$	0.824628	+	0.267938i	0.0544929	+	0.0177058i	0.336137	−	0.941813i	$-0.390880\pi$
$229$	0.824628	+	0.267938i	0.0544929	+	0.0177058i	−0.281644	+	0.959519i	$0.590880\pi$
$230$	−1.77222	+	1.11778i	−0.116857	+	0.0737041i
$231$	−2.47549	+	0.804336i	−0.162875	+	0.0529214i
$232$	−8.78718	+	13.7414i	−0.576906	+	0.902167i
$233$	−4.29817	+	8.43563i	−0.281582	+	0.552637i	−0.987869	−	0.155289i	$-0.950369\pi$
$233$	−4.29817	+	8.43563i	−0.281582	+	0.552637i	0.706287	+	0.707926i	$0.250369\pi$
$234$	2.85442	+	5.33819i	0.186599	+	0.348969i
$235$	22.1586	−	5.15909i	1.44547	−	0.336542i
$236$	−3.84028	+	13.6333i	−0.249981	+	0.887449i
$237$	−7.56229	+	1.19775i	−0.491224	+	0.0778022i
$238$	0.297187	−	0.980258i	0.0192638	−	0.0635407i
$239$	−8.95405	+	6.50550i	−0.579190	+	0.420806i	−0.838432	−	0.545006i	$-0.816527\pi$
$239$	−8.95405	+	6.50550i	−0.579190	+	0.420806i	0.259242	+	0.965812i	$0.416527\pi$
$240$	−7.20317	−	5.30230i	−0.464962	−	0.342262i
$241$	−0.593499	−	0.431202i	−0.0382306	−	0.0277762i	0.568506	−	0.822679i	$-0.307522\pi$
$241$	−0.593499	−	0.431202i	−0.0382306	−	0.0277762i	−0.606736	+	0.794903i	$0.707522\pi$
$242$	−11.0929	+	8.39990i	−0.713079	+	0.539966i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−22.0776	−	14.7416i	−1.41337	−	0.943734i
$245$	3.58390	−	14.4888i	0.228967	−	0.925658i
$246$	4.34120	−	4.51656i	0.276785	−	0.287965i
$247$	−2.64174	+	1.34603i	−0.168090	+	0.0856461i
$248$	−1.39031	−	23.3849i	−0.0882849	−	1.48494i
$249$			8.95430i			0.567456i
$250$	3.67858	+	15.3775i	0.232654	+	0.972560i
$251$		−	13.1418i		−	0.829505i	−0.909934	−	0.414753i	$-0.863868\pi$
$251$		−	13.1418i		−	0.829505i	0.909934	−	0.414753i	$-0.136132\pi$
$252$	0.557528	+	0.994793i	0.0351210	+	0.0626661i
$253$	2.69501	−	1.37318i	0.169434	−	0.0863308i
$254$	−20.2442	−	19.4582i	−1.27023	−	1.22091i
$255$	−0.682048	+	2.75735i	−0.0427115	+	0.172672i
$256$	2.48278	−	15.8062i	0.155174	−	0.987887i
$257$	11.0515	−	11.0515i	0.689375	−	0.689375i	−0.272719	−	0.962094i	$-0.587923\pi$
$257$	11.0515	−	11.0515i	0.689375	−	0.689375i	0.962094	+	0.272719i	$0.0879230\pi$
$258$	−3.29518	−	4.35162i	−0.205149	−	0.270920i
$259$	0.257387	+	0.187003i	0.0159932	+	0.0116198i
$260$	18.4576	−	5.07529i	1.14469	−	0.314756i
$261$	−4.66538	+	3.38959i	−0.288779	+	0.209811i
$262$	30.8227	+	9.34460i	1.90423	+	0.577311i
$263$	−13.8057	+	2.18660i	−0.851294	+	0.134832i	−0.566810	−	0.823849i	$-0.691822\pi$
$263$	−13.8057	+	2.18660i	−0.851294	+	0.134832i	−0.284485	+	0.958681i	$0.591822\pi$
$264$	9.65570	+	8.57200i	0.594267	+	0.527570i
$265$	18.7295	−	4.36069i	1.15054	−	0.267875i
$266$	−0.492547	+	0.263373i	−0.0302000	+	0.0161484i
$267$	−2.35577	+	4.62346i	−0.144171	+	0.282951i
$268$	18.4083	+	2.17281i	1.12446	+	0.132725i
$269$	−5.95656	+	1.93540i	−0.363178	+	0.118004i	−0.484921	−	0.874558i	$-0.661152\pi$
$269$	−5.95656	+	1.93540i	−0.363178	+	0.118004i	0.121743	+	0.992562i	$0.461152\pi$
$270$	−1.68700	−	2.67470i	−0.102667	−	0.162777i
$271$	19.0797	+	6.19936i	1.15901	+	0.376584i	0.824529	−	0.565820i	$-0.191440\pi$
$271$	19.0797	+	6.19936i	1.15901	+	0.376584i	0.334478	+	0.942404i	$0.391440\pi$
$272$	−4.94001	+	1.18932i	−0.299532	+	0.0721134i
$273$	−2.41059	−	0.381800i	−0.145896	−	0.0231076i
$274$	−21.2796	−	10.3172i	−1.28555	−	0.623282i
$275$	−3.26054	−	22.5908i	−0.196618	−	1.36228i
$276$	−0.820736	−	1.04042i	−0.0494025	−	0.0626257i
$277$	1.56268	−	9.86635i	0.0938922	−	0.592812i	−0.895217	−	0.445630i	$-0.852980\pi$
$277$	1.56268	−	9.86635i	0.0938922	−	0.592812i	0.989109	−	0.147182i	$-0.0470203\pi$
$278$	1.73305	−	0.0343093i	0.103941	−	0.00205774i
$279$	2.55941	−	7.87705i	0.153228	−	0.471586i
$280$	3.45752	−	1.02474i	0.206626	−	0.0612401i
$281$	−8.65459	−	26.6361i	−0.516290	−	1.58898i	−0.780923	−	0.624627i	$-0.785251\pi$
$281$	−8.65459	−	26.6361i	−0.516290	−	1.58898i	0.264633	−	0.964349i	$-0.414749\pi$
$282$	4.71650	+	13.5942i	0.280863	+	0.809525i
$283$	−8.54906	−	4.35596i	−0.508189	−	0.258935i	0.181044	−	0.983475i	$-0.442052\pi$
$283$	−8.54906	−	4.35596i	−0.508189	−	0.258935i	−0.689233	+	0.724540i	$0.742052\pi$
$284$	−0.142391	−	3.59485i	−0.00844933	−	0.213315i
$285$	1.32613	−	0.800178i	0.0785534	−	0.0473984i
$286$	−27.2026	+	4.86225i	−1.60852	+	0.287511i
$287$	0.395119	+	2.49468i	0.0233232	+	0.147257i
$288$	2.85654	−	4.88264i	0.168323	−	0.287712i
$289$	−9.04388	−	12.4478i	−0.531993	−	0.732225i
$290$	7.19578	+	16.7562i	0.422551	+	0.983960i
$291$	−7.43382	+	10.2318i	−0.435778	+	0.599797i
$292$	−2.75150	−	13.8097i	−0.161019	−	0.808152i
$293$	−0.365499	−	0.365499i	−0.0213527	−	0.0213527i	0.696350	−	0.717703i	$-0.254806\pi$
$293$	−0.365499	−	0.365499i	−0.0213527	−	0.0213527i	−0.717703	+	0.696350i	$0.754806\pi$
$294$	9.35090	+	1.29187i	0.545356	+	0.0753431i
$295$	10.2014	+	12.1119i	0.593951	+	0.705180i
$296$	0.153937	−	1.57066i	0.00894742	−	0.0912925i
$297$	2.07245	+	4.06742i	0.120256	+	0.236016i
$298$	−11.2894	+	16.2036i	−0.653979	+	0.938649i
$299$	2.83614			0.164018
$300$	−9.42752	+	3.33496i	−0.544298	+	0.192544i
$301$	2.20076			0.126850
$302$	−15.6062	+	22.3994i	−0.898038	+	1.28894i
$303$	−8.42988	−	16.5446i	−0.484284	−	0.950461i
$304$	2.36330	+	1.44616i	0.135544	+	0.0829427i
$305$	−27.4984	+	11.1695i	−1.57455	+	0.639565i
$306$	−1.77956	−	0.245853i	−0.101731	−	0.0140545i
$307$	−7.86266	−	7.86266i	−0.448745	−	0.448745i	0.446192	−	0.894937i	$-0.352780\pi$
$307$	−7.86266	−	7.86266i	−0.448745	−	0.448745i	−0.894937	+	0.446192i	$0.852780\pi$
$308$	−5.10542	+	1.01722i	−0.290908	+	0.0579618i
$309$	4.40835	−	6.06757i	0.250782	−	0.345172i
$310$	−22.5068	−	13.3951i	−1.27830	−	0.760793i
$311$	−11.2964	−	15.5482i	−0.640562	−	0.881658i	0.358084	−	0.933689i	$-0.383430\pi$
$311$	−11.2964	−	15.5482i	−0.640562	−	0.881658i	−0.998645	+	0.0520319i	$0.983430\pi$
$312$	4.41799	+	11.2720i	0.250119	+	0.638150i
$313$	1.18066	+	7.45438i	0.0667347	+	0.421346i	0.998326	+	0.0578387i	$0.0184209\pi$
$313$	1.18066	+	7.45438i	0.0667347	+	0.421346i	−0.931591	+	0.363508i	$0.881579\pi$
$314$	22.8870	−	4.09086i	1.29159	−	0.230861i
$315$	1.27033	+	0.108762i	0.0715749	+	0.00612806i
$316$	−15.3011	+	0.606072i	−0.860755	+	0.0340942i
$317$	10.8062	+	5.50604i	0.606937	+	0.309250i	0.730316	−	0.683110i	$-0.239373\pi$
$317$	10.8062	+	5.50604i	0.606937	+	0.309250i	−0.123379	+	0.992360i	$0.539373\pi$
$318$	3.98660	+	11.4905i	0.223557	+	0.644353i
$319$	−8.13485	−	25.0365i	−0.455464	−	1.40177i
$320$	−13.0639	−	12.2202i	−0.730296	−	0.683130i
$321$	−0.353250	+	1.08719i	−0.0197165	+	0.0606811i
$322$	0.534181	−	0.0105752i	0.0297687	−	0.000589333i
$323$	0.137644	−	0.869050i	0.00765872	−	0.0483553i
$324$	1.57024	−	1.23869i	0.0872355	−	0.0688161i
$325$	6.89263	−	20.2618i	0.382334	−	1.12392i
$326$	22.3973	+	10.8591i	1.24047	+	0.601428i
$327$	−17.7638	−	2.81351i	−0.982339	−	0.155587i
$328$	9.68141	−	7.95308i	0.534566	−	0.439136i
$329$	−5.51753	−	1.79275i	−0.304191	−	0.0988377i
$330$	13.9921	−	3.55109i	0.770241	−	0.195481i
$331$	1.45790	−	0.473702i	0.0801336	−	0.0260370i	−0.268676	−	0.963231i	$-0.586586\pi$
$331$	1.45790	−	0.473702i	0.0801336	−	0.0260370i	0.348809	+	0.937194i	$0.386586\pi$
$332$	−2.09926	+	17.7851i	−0.115212	+	0.976086i
$333$	0.253314	−	0.497156i	0.0138815	−	0.0272440i
$334$	−8.36861	+	4.47483i	−0.457910	+	0.244852i
$335$	13.5670	−	15.6658i	0.741247	−	0.855913i
$336$	0.874148	+	2.10658i	0.0476887	+	0.114923i
$337$	1.08031	−	0.171104i	0.0588481	−	0.00932062i	−0.126941	−	0.991910i	$-0.540516\pi$
$337$	1.08031	−	0.171104i	0.0588481	−	0.00932062i	0.185789	+	0.982590i	$0.440516\pi$
$338$	−7.20272	−	2.18367i	−0.391776	−	0.118776i
$339$	9.55533	−	6.94235i	0.518974	−	0.377057i
$340$	−2.00113	+	5.31678i	−0.108526	+	0.288343i
$341$	30.5881	+	22.2236i	1.65644	+	1.20347i
$342$	0.591353	+	0.780941i	0.0319767	+	0.0422284i
$343$	−5.51348	+	5.51348i	−0.297700	+	0.297700i
$344$	−5.52473	−	9.41576i	−0.297873	−	0.507664i
$345$	−1.47778	+	0.106095i	−0.0795610	+	0.00571196i
$346$	−1.00550	−	0.966458i	−0.0540558	−	0.0519571i
$347$	20.4311	−	10.4102i	1.09680	−	0.558846i	0.190586	−	0.981670i	$-0.438961\pi$
$347$	20.4311	−	10.4102i	1.09680	−	0.558846i	0.906212	+	0.422824i	$0.138961\pi$
$348$	−10.0611	+	5.63870i	−0.539331	+	0.302266i
$349$		−	20.7955i		−	1.11316i	−0.830795	−	0.556578i	$-0.812114\pi$
$349$		−	20.7955i		−	1.11316i	0.830795	−	0.556578i	$-0.187886\pi$
$350$	1.22266	−	3.84197i	0.0653539	−	0.205362i
$351$			4.28042i			0.228472i
$352$	17.1686	+	19.2895i	0.915092	+	1.02813i
$353$	20.9677	−	10.6836i	1.11600	−	0.568628i	0.204059	−	0.978959i	$-0.434587\pi$
$353$	20.9677	−	10.6836i	1.11600	−	0.568628i	0.911937	+	0.410330i	$0.134587\pi$
$354$	−6.94034	+	7.22069i	−0.368875	+	0.383775i
$355$	−3.41507	−	2.12516i	−0.181253	−	0.112792i
$356$	−5.76298	+	8.63087i	−0.305437	+	0.457435i
$357$	0.512159	−	0.512159i	0.0271063	−	0.0271063i
$358$	−18.5430	+	14.0414i	−0.980029	+	0.742109i
$359$	−28.2460	−	20.5219i	−1.49077	−	1.08311i	−0.973883	−	0.227051i	$-0.927092\pi$
$359$	−28.2460	−	20.5219i	−1.49077	−	1.08311i	−0.516885	−	0.856055i	$-0.672908\pi$
$360$	−2.72367	−	5.70803i	−0.143550	−	0.300840i
$361$	14.9832	−	10.8859i	0.788588	−	0.572943i
$362$	9.36611	−	30.8937i	0.492272	−	1.62374i
$363$	−9.71784	+	1.53916i	−0.510055	+	0.0807847i
$364$	−4.69843	−	1.32348i	−0.246265	−	0.0693691i
$365$	−14.5031	−	6.12443i	−0.759127	−	0.320568i
$366$	−8.85144	−	16.5535i	−0.462672	−	0.865267i
$367$	−7.31720	+	14.3608i	−0.381955	+	0.749628i	−0.999313	−	0.0370536i	$-0.988203\pi$
$367$	−7.31720	+	14.3608i	−0.381955	+	0.749628i	0.617359	+	0.786682i	$0.288203\pi$
$368$	−1.38624	−	2.25890i	−0.0722627	−	0.117753i
$369$	4.21294	−	1.36887i	0.219317	−	0.0712604i
$370$	−1.35641	−	1.12849i	−0.0705161	−	0.0586673i
$371$	−4.66366	−	1.51531i	−0.242125	−	0.0786712i
$372$	6.93023	−	15.0455i	0.359316	−	0.780070i
$373$	−11.3634	−	1.79978i	−0.588373	−	0.0931891i	−0.144852	−	0.989453i	$-0.546271\pi$
$373$	−11.3634	−	1.79978i	−0.588373	−	0.0931891i	−0.443520	+	0.896264i	$0.646271\pi$
$374$	3.57772	−	7.37922i	0.185000	−	0.381570i
$375$	−2.83347	+	10.8153i	−0.146320	+	0.558501i
$376$	6.18092	+	28.1068i	0.318757	+	1.44950i
$377$	3.86143	−	24.3801i	0.198874	−	1.25564i
$378$	0.0159605	+	0.806208i	0.000820922	+	0.0414668i
$379$	−3.02441	+	9.30816i	−0.155353	+	0.478128i	−0.998197	−	0.0600309i	$-0.980880\pi$
$379$	−3.02441	+	9.30816i	−0.155353	+	0.478128i	0.842843	+	0.538159i	$0.180880\pi$
$380$	2.82158	−	1.27842i	0.144744	−	0.0655817i
$381$	−6.13555	−	18.8833i	−0.314334	−	0.967420i
$382$	−11.5926	+	4.02202i	−0.593127	+	0.205784i
$383$	14.8289	+	7.55569i	0.757720	+	0.386078i	0.789766	−	0.613409i	$-0.210202\pi$
$383$	14.8289	+	7.55569i	0.757720	+	0.386078i	−0.0320454	+	0.999486i	$0.510202\pi$
$384$	6.81838	−	9.02827i	0.347949	−	0.460722i
$385$	−2.26419	+	5.36176i	−0.115394	+	0.273261i
$386$	1.26984	+	7.10430i	0.0646330	+	0.361600i
$387$	−0.603792	−	3.81219i	−0.0306925	−	0.193785i
$388$	−17.1639	+	18.5797i	−0.871364	+	0.943240i
$389$	8.71062	+	11.9891i	0.441646	+	0.607873i	0.970577	−	0.240792i	$-0.0774070\pi$
$389$	8.71062	+	11.9891i	0.441646	+	0.607873i	−0.528931	+	0.848665i	$0.677407\pi$
$390$	13.2016	+	2.98951i	0.668490	+	0.151380i
$391$	−0.494723	+	0.680928i	−0.0250192	+	0.0344360i
$392$	18.2700	+	4.75815i	0.922774	+	0.240323i
$393$	16.1041	+	16.1041i	0.812342	+	0.812342i
$394$	−2.24753	+	16.2683i	−0.113229	+	0.819583i
$395$	−9.04555	+	14.5359i	−0.455131	+	0.731381i
$396$	3.16276	+	8.56463i	0.158935	+	0.430389i
$397$	16.9966	+	33.3577i	0.853034	+	1.67417i	0.731768	+	0.681554i	$0.238696\pi$
$397$	16.9966	+	33.3577i	0.853034	+	1.67417i	0.121267	+	0.992620i	$0.461304\pi$
$398$	1.47535	+	1.02791i	0.0739528	+	0.0515247i
$399$	−0.394948			−0.0197721
$400$	−19.5069	+	4.41374i	−0.975345	+	0.220687i
$401$	6.38092			0.318648			0.159324	−	0.987226i	$-0.449069\pi$
$401$	6.38092			0.318648			0.159324	+	0.987226i	$0.449069\pi$
$402$	10.7542	+	7.49269i	0.536369	+	0.373701i
$403$	16.0950	+	31.5882i	0.801748	+	1.57352i
$404$	−12.8648	−	34.8373i	−0.640048	−	1.73322i
$405$	−0.160123	−	2.23033i	−0.00795657	−	0.110826i
$406$	0.636384	−	4.60633i	0.0315832	−	0.228608i
$407$	1.80109	+	1.80109i	0.0892767	+	0.0892767i
$408$	−3.47694	−	0.905518i	−0.172134	−	0.0448298i
$409$	7.75145	−	10.6690i	0.383285	−	0.527546i	−0.573166	−	0.819439i	$-0.694285\pi$
$409$	7.75145	−	10.6690i	0.383285	−	0.527546i	0.956451	+	0.291893i	$0.0942851\pi$
$410$	−1.27946	−	13.9495i	−0.0631882	−	0.688918i
$411$	−9.82907	−	13.5286i	−0.484832	−	0.667315i
$412$	10.1784	−	11.0180i	0.501454	−	0.542817i
$413$	−0.631683	−	3.98829i	−0.0310831	−	0.196251i
$414$	−0.164875	−	0.922417i	−0.00810314	−	0.0453343i
$415$	15.1355	+	13.1078i	0.742972	+	0.643437i
$416$	6.13245	+	23.4243i	0.300668	+	1.14847i
$417$	1.09210	+	0.556452i	0.0534803	+	0.0272496i
$418$	−4.22469	+	1.46575i	−0.206636	+	0.0716921i
$419$	1.32767	+	4.08615i	0.0648610	+	0.199622i	0.978235	−	0.207500i	$-0.0665326\pi$
$419$	1.32767	+	4.08615i	0.0648610	+	0.199622i	−0.913374	+	0.407121i	$0.866533\pi$
$420$	2.49764	+	0.513842i	0.121872	+	0.0250729i
$421$	−1.80550	+	5.55676i	−0.0879948	+	0.270820i	−0.985365	−	0.170459i	$-0.945475\pi$
$421$	−1.80550	+	5.55676i	−0.0879948	+	0.270820i	0.897370	+	0.441279i	$0.145475\pi$
$422$	0.122309	+	6.17815i	0.00595392	+	0.300748i
$423$	−1.59167	+	10.0494i	−0.0773897	+	0.488620i
$424$	5.22439	+	23.7571i	0.253719	+	1.15375i
$425$	3.66234	+	5.18923i	0.177650	+	0.251715i
$426$	1.10983	−	2.28908i	0.0537715	−	0.110906i
$427$	7.47515	+	1.18395i	0.361748	+	0.0572952i
$428$	−0.956511	+	2.07657i	−0.0462347	+	0.100375i
$429$	−18.5837	−	6.03819i	−0.897227	−	0.291527i
$430$	−12.1792	−	0.800285i	−0.587334	−	0.0385932i
$431$	2.92353	−	0.949912i	0.140821	−	0.0457556i	−0.237758	−	0.971324i	$-0.576413\pi$
$431$	2.92353	−	0.949912i	0.140821	−	0.0457556i	0.378580	+	0.925569i	$0.376413\pi$
$432$	3.40923	−	2.09217i	0.164026	−	0.100660i
$433$	−12.4138	+	24.3634i	−0.596568	+	1.17083i	0.373416	+	0.927664i	$0.378186\pi$
$433$	−12.4138	+	24.3634i	−0.596568	+	1.17083i	−0.969984	+	0.243167i	$0.921814\pi$
$434$	3.14924	+	5.88955i	0.151168	+	0.282707i
$435$	−1.09999	+	12.8478i	−0.0527407	+	0.616004i
$436$	−34.6230	−	9.75278i	−1.65814	−	0.467073i
$437$	0.453298	−	0.0717953i	0.0216842	−	0.00343444i
$438$	2.88881	−	9.52860i	0.138033	−	0.455294i
$439$	19.5015	−	14.1687i	0.930757	−	0.676235i	−0.0154210	−	0.999881i	$-0.504909\pi$
$439$	19.5015	−	14.1687i	0.930757	−	0.676235i	0.946178	+	0.323646i	$0.104909\pi$
$440$	28.6238	−	3.77289i	1.36459	−	0.179865i
$441$	5.40010	+	3.92340i	0.257147	+	0.186829i
$442$	6.13034	−	4.64209i	0.291591	−	0.220801i
$443$	−17.8280	+	17.8280i	−0.847032	+	0.847032i	−0.989762	−	0.142730i	$-0.954412\pi$
$443$	−17.8280	+	17.8280i	−0.847032	+	0.847032i	0.142730	+	0.989762i	$0.454412\pi$
$444$	0.619689	−	0.928070i	0.0294091	−	0.0440443i
$445$	4.36654	+	10.7500i	0.206994	+	0.509601i
$446$	11.2430	−	11.6971i	0.532371	−	0.553875i
$447$	−12.4424	+	6.33969i	−0.588503	+	0.299857i
$448$	1.24238	+	4.38905i	0.0586967	+	0.207363i
$449$			10.8433i			0.511725i	0.966713	+	0.255862i	$0.0823594\pi$
$449$			10.8433i			0.511725i	−0.966713	+	0.255862i	$0.917641\pi$
$450$	−6.99058	−	1.06385i	−0.329539	−	0.0501502i
$451$			20.2217i			0.952201i
$452$	20.6065	−	11.5488i	0.969248	−	0.543211i
$453$	−17.2000	+	8.76384i	−0.808127	+	0.411761i
$454$	30.5652	+	29.3785i	1.43450	+	1.37880i
$455$	−4.17411	+	3.51573i	−0.195686	+	0.164820i
$456$	0.991467	+	1.68975i	0.0464297	+	0.0791298i
$457$	−10.7529	+	10.7529i	−0.502999	+	0.502999i	−0.912369	−	0.409369i	$-0.865749\pi$
$457$	−10.7529	+	10.7529i	−0.502999	+	0.502999i	0.409369	+	0.912369i	$0.365749\pi$
$458$	0.740245	+	0.977568i	0.0345894	+	0.0456788i
$459$	−1.02769	−	0.746657i	−0.0479682	−	0.0348510i
$460$	−2.96006	−	0.135726i	−0.138013	−	0.00632823i
$461$	−6.99954	+	5.08547i	−0.326001	+	0.236854i	−0.738732	−	0.673999i	$-0.764575\pi$
$461$	−6.99954	+	5.08547i	−0.326001	+	0.236854i	0.412731	+	0.910853i	$0.364575\pi$
$462$	−3.52270	−	1.06799i	−0.163891	−	0.0496872i
$463$	6.98414	−	1.10618i	0.324581	−	0.0514085i	0.00798209	−	0.999968i	$-0.497459\pi$
$463$	6.98414	−	1.10618i	0.324581	−	0.0514085i	0.316599	+	0.948560i	$0.397459\pi$
$464$	−21.3054	+	8.84091i	−0.989078	+	0.410429i
$465$	−9.56800	−	15.8570i	−0.443705	−	0.735352i
$466$	−11.8071	+	6.31347i	−0.546955	+	0.292466i
$467$	−8.40547	+	16.4967i	−0.388959	+	0.763374i	−0.999593	−	0.0285385i	$-0.990915\pi$
$467$	−8.40547	+	16.4967i	−0.388959	+	0.763374i	0.610634	+	0.791913i	$0.290915\pi$
$468$	−1.00351	+	8.50182i	−0.0463871	+	0.392997i
$469$	−5.02586	+	1.63300i	−0.232073	+	0.0754050i
$470$	29.8827	+	11.9277i	1.37838	+	0.550183i
$471$	15.6354	+	5.08024i	0.720440	+	0.234085i
$472$	−15.4778	+	12.7147i	−0.712424	+	0.585242i
$473$	17.4026	+	2.75630i	0.800171	+	0.126735i
$474$	−9.74324	−	4.72389i	−0.447522	−	0.216975i
$475$	0.588726	−	3.41291i	0.0270126	−	0.156595i
$476$	1.13733	−	0.897185i	0.0521293	−	0.0411224i
$477$	−1.34535	+	8.49422i	−0.0615994	+	0.388924i
$478$	−15.6492	+	0.309808i	−0.715778	+	0.0141703i
$479$	7.81425	−	24.0498i	0.357042	−	1.09886i	−0.597774	−	0.801665i	$-0.703948\pi$
$479$	7.81425	−	24.0498i	0.357042	−	1.09886i	0.954816	−	0.297198i	$-0.0960521\pi$
$480$	−4.07159	−	11.9759i	−0.185842	−	0.546622i
$481$	0.738042	+	2.27146i	0.0336518	+	0.103570i
$482$	−0.340064	−	0.980158i	−0.0154895	−	0.0446450i
$483$	0.336619	+	0.171516i	0.0153167	+	0.00780425i
$484$	−19.6625	+	0.778826i	−0.893752	+	0.0354012i
$485$	6.41276	+	27.5432i	0.291189	+	1.25067i
$486$	1.39215	−	0.248836i	0.0631492	−	0.0112874i
$487$	3.69540	+	23.3318i	0.167455	+	1.05727i	0.918038	+	0.396491i	$0.129772\pi$
$487$	3.69540	+	23.3318i	0.167455	+	1.05727i	−0.750584	+	0.660775i	$0.770228\pi$
$488$	−13.7000	−	34.9540i	−0.620170	−	1.58229i
$489$	10.3453	+	14.2391i	0.467833	+	0.643917i
$490$	15.8720	−	13.9148i	0.717025	−	0.628605i
$491$	14.0618	−	19.3544i	0.634599	−	0.873451i	−0.363714	−	0.931511i	$-0.618491\pi$
$491$	14.0618	−	19.3544i	0.634599	−	0.873451i	0.998313	+	0.0580598i	$0.0184914\pi$
$492$	8.68871	−	1.73117i	0.391717	−	0.0780473i
$493$	5.17984	+	5.17984i	0.233288	+	0.233288i
$494$	−4.15354	−	0.573829i	−0.186877	−	0.0258178i
$495$	9.90895	+	2.45104i	0.445374	+	0.110166i
$496$	17.2922	−	28.2587i	0.776441	−	1.26885i
$497$	0.465644	+	0.913879i	0.0208870	+	0.0409931i
$498$	−7.23906	+	10.3901i	−0.324390	+	0.465593i
$499$	3.20194			0.143339			0.0716693	−	0.997428i	$-0.477167\pi$
$499$	3.20194			0.143339			0.0716693	+	0.997428i	$0.477167\pi$
$500$	−8.16343	+	20.8173i	−0.365080	+	0.930976i
$501$	−6.71036			−0.299797
$502$	10.6245	−	15.2492i	0.474193	−	0.680603i
$503$	5.20750	+	10.2203i	0.232191	+	0.455701i	0.977476	−	0.211045i	$-0.0676867\pi$
$503$	5.20750	+	10.2203i	0.232191	+	0.455701i	−0.745285	+	0.666746i	$0.767687\pi$
$504$	−0.157307	+	1.60504i	−0.00700702	+	0.0714942i
$505$	−40.3055	−	9.96981i	−1.79357	−	0.443651i
$506$	4.23730	+	0.585400i	0.188371	+	0.0260242i
$507$	−3.76323	−	3.76323i	−0.167131	−	0.167131i
$508$	−7.75948	−	38.9446i	−0.344271	−	1.72789i
$509$	13.6267	−	18.7556i	0.603994	−	0.831327i	−0.392072	−	0.919934i	$-0.628242\pi$
$509$	13.6267	−	18.7556i	0.603994	−	0.831327i	0.996067	+	0.0886075i	$0.0282417\pi$
$510$	−3.02058	+	2.64810i	−0.133754	+	0.117260i
$511$	2.35963	+	3.24775i	0.104384	+	0.143672i
$512$	15.6593	−	16.3336i	0.692052	−	0.721848i
$513$	0.108357	+	0.684136i	0.00478406	+	0.0302053i
$514$	21.7582	−	3.88910i	0.959713	−	0.171541i
$515$	−3.80285	−	16.3335i	−0.167574	−	0.719740i
$516$	−0.305524	−	7.71338i	−0.0134500	−	0.339563i
$517$	−41.3847	−	21.0866i	−1.82010	−	0.927387i
$518$	0.147478	+	0.425072i	0.00647982	+	0.0186766i
$519$	−0.304743	−	0.937904i	−0.0133767	−	0.0411694i
$520$	25.5204	+	9.03281i	1.11914	+	0.396115i
$521$	−4.78400	+	14.7236i	−0.209591	+	0.645054i	0.789903	+	0.613232i	$0.210131\pi$
$521$	−4.78400	+	14.7236i	−0.209591	+	0.645054i	−0.999494	+	0.0318218i	$0.989869\pi$
$522$	−8.15378	+	0.161421i	−0.356881	+	0.00706520i
$523$	1.35911	−	8.58111i	0.0594299	−	0.375226i	−0.939991	−	0.341199i	$-0.889167\pi$
$523$	1.35911	−	8.58111i	0.0594299	−	0.375226i	0.999421	−	0.0340265i	$-0.0108331\pi$
$524$	28.2106	+	35.7615i	1.23239	+	1.56225i
$525$	2.04342	−	1.98803i	0.0891821	−	0.0867647i
$526$	−17.7872	−	8.62390i	−0.775558	−	0.376020i
$527$	−10.3915	−	1.64586i	−0.452662	−	0.0716946i
$528$	4.27402	+	17.7526i	0.186003	+	0.772585i
$529$	21.4568	+	6.97173i	0.932903	+	0.303119i
$530$	25.2582	+	10.0818i	1.09714	+	0.437926i
$531$	−6.73529	+	2.18843i	−0.292287	+	0.0949697i
$532$	−0.784450	−	0.0925920i	−0.0340102	−	0.00401437i
$533$	−8.60819	+	16.8945i	−0.372862	+	0.731783i
$534$	−6.47133	+	3.46033i	−0.280042	+	0.149743i
$535$	1.32058	+	2.18859i	0.0570935	+	0.0946210i
$536$	19.6035	+	17.4033i	0.846740	+	0.751707i
$537$	−16.2445	+	2.57287i	−0.701000	+	0.111027i
$538$	−8.47637	−	2.56980i	−0.365442	−	0.110792i
$539$	−24.6513	+	17.9102i	−1.06181	+	0.771448i
$540$	0.204843	−	4.46744i	0.00881502	−	0.192248i
$541$	30.7034	+	22.3073i	1.32004	+	0.959067i	0.999932	+	0.0116875i	$0.00372033\pi$
$541$	30.7034	+	22.3073i	1.32004	+	0.959067i	0.320111	+	0.947380i	$0.396280\pi$
$542$	17.1273	+	22.6183i	0.735680	+	0.971539i
$543$	16.1411	−	16.1411i	0.692682	−	0.692682i
$544$	−6.69365	−	2.61369i	−0.286988	−	0.112061i
$545$	−30.7593	+	25.9076i	−1.31758	+	1.10976i
$546$	−2.48847	−	2.39185i	−0.106497	−	0.102362i
$547$	12.8211	−	6.53267i	0.548190	−	0.279317i	−0.157881	−	0.987458i	$-0.550466\pi$
$547$	12.8211	−	6.53267i	0.548190	−	0.279317i	0.706071	+	0.708141i	$0.250466\pi$
$548$	−16.3510	−	29.1749i	−0.698479	−	1.24629i
$549$		−	13.2734i		−	0.566496i
$550$	14.4800	−	28.8492i	0.617431	−	1.23014i
$551$		−	3.99440i		−	0.170167i
$552$	−0.111223	−	1.87077i	−0.00473398	−	0.0796252i
$553$	3.88984	−	1.98197i	0.165413	−	0.0842820i
$554$	9.78966	−	10.1851i	0.415923	−	0.432724i
$555$	−0.469530	−	1.15594i	−0.0199304	−	0.0490670i
$556$	2.03868	+	1.36126i	0.0864595	+	0.0577305i
$557$	22.6217	−	22.6217i	0.958513	−	0.958513i	−0.0406596	−	0.999173i	$-0.512946\pi$
$557$	22.6217	−	22.6217i	0.958513	−	0.958513i	0.999173	+	0.0406596i	$0.0129459\pi$
$558$	9.33797	−	7.07100i	0.395308	−	0.299339i
$559$	13.3659	+	9.71092i	0.565319	+	0.410728i
$560$	4.84038	+	1.60615i	0.204543	+	0.0678722i
$561$	4.69136	−	3.40847i	0.198069	−	0.143906i
$562$	11.4915	−	37.9040i	0.484738	−	1.59888i
$563$	33.9090	−	5.37066i	1.42909	−	0.226346i	0.606549	−	0.795046i	$-0.292553\pi$
$563$	33.9090	−	5.37066i	1.42909	−	0.226346i	0.822545	+	0.568700i	$0.192553\pi$
$564$	−5.51740	+	19.5871i	−0.232324	+	0.824767i
$565$	2.25294	−	26.3140i	0.0947819	−	1.10704i
$566$	−6.39836	−	11.9659i	−0.268943	−	0.502964i
$567$	−0.258859	+	0.508040i	−0.0108711	+	0.0213357i
$568$	2.74101	−	4.28640i	0.115010	−	0.179853i
$569$	−13.8272	+	4.49274i	−0.579667	+	0.188345i	−0.584151	−	0.811645i	$-0.698573\pi$
$569$	−13.8272	+	4.49274i	−0.579667	+	0.188345i	0.00448435	+	0.999990i	$0.498573\pi$
$570$	2.18568	+	0.143619i	0.0915481	+	0.00601554i
$571$	−32.5728	−	10.5835i	−1.36313	−	0.442908i	−0.466043	−	0.884762i	$-0.654321\pi$
$571$	−32.5728	−	10.5835i	−1.36313	−	0.442908i	−0.897087	+	0.441854i	$0.854321\pi$
$572$	−35.4955	−	16.3499i	−1.48414	−	0.683624i
$573$	−8.56970	−	1.35731i	−0.358004	−	0.0567023i
$574$	−1.55834	+	3.21414i	−0.0650438	+	0.134156i
$575$	−1.98392	+	2.65320i	−0.0827354	+	0.110646i
$576$	7.26194	−	3.35623i	0.302581	−	0.139843i
$577$	4.65814	−	29.4103i	0.193921	−	1.22437i	−0.678126	−	0.734945i	$-0.737208\pi$
$577$	4.65814	−	29.4103i	0.193921	−	1.22437i	0.872047	−	0.489422i	$-0.162792\pi$
$578$	−0.430692	−	21.7553i	−0.0179144	−	0.904903i
$579$	−1.57695	+	4.85335i	−0.0655358	+	0.201698i
$580$	−5.19687	+	25.2605i	−0.215788	+	1.04889i
$581$	−1.57772	−	4.85574i	−0.0654550	−	0.201450i
$582$	−16.8977	+	5.86262i	−0.700431	+	0.243013i
$583$	−34.9802	−	17.8233i	−1.44873	−	0.738166i
$584$	7.97168	−	18.2486i	0.329870	−	0.755131i
$585$	7.23521	+	6.26592i	0.299139	+	0.259064i
$586$	−0.128621	−	0.719593i	−0.00531330	−	0.0297261i
$587$	−0.417161	−	2.63385i	−0.0172181	−	0.108711i	0.977583	−	0.210553i	$-0.0675264\pi$
$587$	−0.417161	−	2.63385i	−0.0172181	−	0.108711i	−0.994801	+	0.101842i	$0.967526\pi$
$588$	9.80593	+	9.05871i	0.404390	+	0.373575i
$589$	3.37208	+	4.64127i	0.138944	+	0.191240i
$590$	2.04550	+	22.3013i	0.0842118	+	0.918131i
$591$	−6.82575	+	9.39484i	−0.280774	+	0.386452i
$592$	1.44841	−	1.69806i	0.0595293	−	0.0697900i
$593$	−4.29407	−	4.29407i	−0.176336	−	0.176336i	0.613420	−	0.789757i	$-0.289793\pi$
$593$	−4.29407	−	4.29407i	−0.176336	−	0.176336i	−0.789757	+	0.613420i	$0.789793\pi$
$594$	−0.883510	+	6.39510i	−0.0362509	+	0.262394i
$595$	−0.115977	−	1.61543i	−0.00475460	−	0.0662262i
$596$	−26.1994	+	9.67498i	−1.07317	+	0.396303i
$597$	0.577235	+	1.13289i	0.0236247	+	0.0463660i
$598$	3.29092	+	2.29286i	0.134576	+	0.0937622i
$599$	1.90922			0.0780086			0.0390043	−	0.999239i	$-0.487581\pi$
$599$	1.90922			0.0780086			0.0390043	+	0.999239i	$0.487581\pi$
$600$	−13.6354	−	3.75190i	−0.556662	−	0.153171i
$601$	−19.9000			−0.811739			−0.405869	−	0.913931i	$-0.633031\pi$
$601$	−19.9000			−0.811739			−0.405869	+	0.913931i	$0.633031\pi$
$602$	2.55365	+	1.77919i	0.104079	+	0.0725144i
$603$	4.20759	+	8.25787i	0.171346	+	0.336286i
$604$	−36.2175	+	13.3745i	−1.47367	+	0.544199i
$605$	−11.6239	+	18.6792i	−0.472578	+	0.759418i
$606$	3.59375	−	26.0126i	0.145986	−	1.05669i
$607$	−6.68008	−	6.68008i	−0.271136	−	0.271136i	0.558421	−	0.829557i	$-0.311407\pi$
$607$	−6.68008	−	6.68008i	−0.271136	−	0.271136i	−0.829557	+	0.558421i	$0.811407\pi$
$608$	1.57312	+	3.58864i	0.0637983	+	0.145539i
$609$	1.93270	−	2.66013i	0.0783170	−	0.107794i
$610$	−40.9377	−	9.27036i	−1.65752	−	0.375346i
$611$	−25.5992	−	35.2343i	−1.03563	−	1.42543i
$612$	−1.86615	−	1.72395i	−0.0754348	−	0.0696866i
$613$	1.64882	+	10.4102i	0.0665950	+	0.420465i	0.998352	+	0.0573826i	$0.0182755\pi$
$613$	1.64882	+	10.4102i	0.0665950	+	0.420465i	−0.931757	+	0.363082i	$0.881725\pi$
$614$	−2.76692	−	15.4800i	−0.111664	−	0.624721i
$615$	3.85333	−	9.12497i	0.155381	−	0.367954i
$616$	−6.74645	−	2.94711i	−0.271822	−	0.118743i
$617$	−33.5664	−	17.1029i	−1.35133	−	0.688538i	−0.379717	−	0.925103i	$-0.623979\pi$
$617$	−33.5664	−	17.1029i	−1.35133	−	0.688538i	−0.971616	+	0.236564i	$0.923979\pi$
$618$	10.0205	−	3.47661i	0.403085	−	0.139850i
$619$	11.4354	+	35.1945i	0.459627	+	1.41459i	0.865616	+	0.500708i	$0.166927\pi$
$619$	11.4354	+	35.1945i	0.459627	+	1.41459i	−0.405989	+	0.913878i	$0.633073\pi$
$620$	−15.2865	−	33.7386i	−0.613922	−	1.35497i
$621$	0.204750	−	0.630155i	0.00821633	−	0.0252873i
$622$	−0.537964	−	27.1739i	−0.0215704	−	1.08958i
$623$	0.462845	−	2.92229i	0.0185435	−	0.117079i
$624$	−3.98635	+	16.6512i	−0.159582	+	0.666580i
$625$	14.1334	+	20.6215i	0.565336	+	0.824860i
$626$	−4.65648	+	9.60420i	−0.186110	+	0.383861i
$627$	−3.12306	−	0.494644i	−0.124723	−	0.0197542i
$628$	29.8642	+	13.7560i	1.19171	+	0.548925i
$629$	−0.674095	−	0.219027i	−0.0268779	−	0.00873316i
$630$	1.38610	+	1.15319i	0.0552235	+	0.0459443i
$631$	−11.9182	+	3.87246i	−0.474456	+	0.154160i	−0.536477	−	0.843915i	$-0.680245\pi$
$631$	−11.9182	+	3.87246i	−0.474456	+	0.154160i	0.0620213	+	0.998075i	$0.480245\pi$
$632$	−18.2447	−	11.6669i	−0.725733	−	0.464083i
$633$	−1.98370	+	3.89322i	−0.0788449	+	0.154742i
$634$	8.08768	+	15.1252i	0.321203	+	0.600697i
$635$	−40.9000	−	17.2715i	−1.62307	−	0.685397i
$636$	−4.66355	+	16.5559i	−0.184922	+	0.656485i
$637$	−28.2196	+	4.46954i	−1.11810	+	0.177090i
$638$	10.8013	−	35.6277i	0.427629	−	1.41051i
$639$	1.45529	−	1.05733i	0.0575702	−	0.0418272i
$640$	−5.27940	−	24.7412i	−0.208687	−	0.977983i
$641$	12.9136	+	9.38230i	0.510058	+	0.370579i	0.812845	−	0.582479i	$-0.197917\pi$
$641$	12.9136	+	9.38230i	0.510058	+	0.370579i	−0.302788	+	0.953058i	$0.597917\pi$
$642$	−1.28883	+	0.975941i	−0.0508660	+	0.0385173i
$643$	18.8472	−	18.8472i	0.743260	−	0.743260i	−0.229944	−	0.973204i	$-0.573854\pi$
$643$	18.8472	−	18.8472i	0.743260	−	0.743260i	0.973204	+	0.229944i	$0.0738544\pi$
$644$	0.628387	+	0.419585i	0.0247619	+	0.0165340i
$645$	−7.32763	−	4.55991i	−0.288525	−	0.179546i
$646$	0.862295	−	0.897127i	0.0339266	−	0.0352970i
$647$	−9.13665	+	4.65536i	−0.359199	+	0.183021i	−0.624271	−	0.781207i	$-0.714604\pi$
$647$	−9.13665	+	4.65536i	−0.359199	+	0.183021i	0.265073	+	0.964228i	$0.414604\pi$
$648$	2.82344	−	0.167863i	0.110915	−	0.00659428i
$649$		−	32.3287i		−	1.26901i
$650$	24.3785	−	17.9385i	0.956202	−	0.703608i
$651$			4.72252i			0.185090i
$652$	17.2098	+	30.7073i	0.673988	+	1.20259i
$653$	−16.6573	+	8.48730i	−0.651849	+	0.332134i	−0.748452	−	0.663189i	$-0.769202\pi$
$653$	−16.6573	+	8.48730i	−0.651849	+	0.332134i	0.0966028	+	0.995323i	$0.469202\pi$
$654$	−18.3377	−	17.6257i	−0.717059	−	0.689219i
$655$	50.7947	−	3.64673i	1.98472	−	0.142489i
$656$	17.6635	−	1.40149i	0.689643	−	0.0547189i
$657$	4.97844	−	4.97844i	0.194227	−	0.194227i
$658$	−4.95293	−	6.54084i	−0.193085	−	0.254989i
$659$	−2.98224	−	2.16672i	−0.116171	−	0.0844035i	0.528183	−	0.849131i	$-0.322874\pi$
$659$	−2.98224	−	2.16672i	−0.116171	−	0.0844035i	−0.644354	+	0.764727i	$0.722874\pi$
$660$	19.1066	+	7.19135i	0.743725	+	0.279923i
$661$	19.7563	−	14.3538i	0.768432	−	0.558299i	−0.133053	−	0.991109i	$-0.542478\pi$
$661$	19.7563	−	14.3538i	0.768432	−	0.558299i	0.901485	+	0.432810i	$0.142478\pi$
$662$	2.07464	+	0.628975i	0.0806333	+	0.0244458i
$663$	5.37043	−	0.850592i	0.208570	−	0.0330343i
$664$	−16.8142	+	18.9399i	−0.652517	+	0.735010i
$665$	−0.578146	+	0.667581i	−0.0224196	+	0.0258877i
$666$	0.695857	−	0.372086i	0.0269639	−	0.0144180i
$667$	−1.73467	+	3.40448i	−0.0671667	+	0.131822i
$668$	−13.3282	−	1.57318i	−0.515683	−	0.0608683i
$669$	10.9108	−	3.54514i	0.421836	−	0.137063i
$670$	28.4075	−	7.20959i	1.09748	−	0.278531i
$671$	57.6272	+	18.7242i	2.22467	+	0.722840i
$672$	−0.688733	+	3.15107i	−0.0265684	+	0.121555i
$673$	−23.5644	−	3.73224i	−0.908342	−	0.143867i	−0.315256	−	0.949007i	$-0.602090\pi$
$673$	−23.5644	−	3.73224i	−0.908342	−	0.143867i	−0.593086	+	0.805139i	$0.702090\pi$
$674$	1.39186	+	0.674828i	0.0536126	+	0.0259934i
$675$	−4.00433	−	2.99422i	−0.154127	−	0.115248i
$676$	−6.59231	−	8.35682i	−0.253550	−	0.321416i
$677$	1.26062	−	7.95924i	0.0484495	−	0.305898i	−0.951549	−	0.307497i	$-0.900509\pi$
$677$	1.26062	−	7.95924i	0.0484495	−	0.305898i	0.999999	+	0.00159823i	$0.000508732\pi$
$678$	16.7001	−	0.330612i	0.641362	−	0.0126971i
$679$	2.22840	−	6.85830i	0.0855180	−	0.263197i
$680$	−6.62034	+	4.55154i	−0.253878	+	0.174543i
$681$	9.26362	+	28.5105i	0.354983	+	1.09252i
$682$	17.5264	+	50.5160i	0.671122	+	1.93436i
$683$	35.5849	+	18.1314i	1.36162	+	0.693780i	0.973683	−	0.227906i	$-0.0731880\pi$
$683$	35.5849	+	18.1314i	1.36162	+	0.693780i	0.387937	+	0.921686i	$0.373188\pi$
$684$	0.0548294	+	1.38424i	0.00209645	+	0.0529278i
$685$	−37.2557	−	3.18974i	−1.42347	−	0.121874i
$686$	−10.8549	+	1.94023i	−0.414443	+	0.0740783i
$687$	0.135639	+	0.856390i	0.00517494	+	0.0326733i
$688$	1.20150	−	15.3920i	0.0458066	−	0.586816i
$689$	−21.6376	−	29.7816i	−0.824326	−	1.13459i
$690$	−1.80052	−	1.07160i	−0.0685445	−	0.0407950i
$691$	28.5593	−	39.3084i	1.08645	−	1.49536i	0.234223	−	0.972183i	$-0.424745\pi$
$691$	28.5593	−	39.3084i	1.08645	−	1.49536i	0.852222	−	0.523181i	$-0.175255\pi$
$692$	−0.385402	−	1.93432i	−0.0146508	−	0.0735318i
$693$	−1.84052	−	1.84052i	−0.0699155	−	0.0699155i
$694$	32.1233	+	4.43797i	1.21938	+	0.168463i
$695$	2.53925	−	1.03141i	0.0963192	−	0.0391237i
$696$	−16.2330	−	1.59096i	−0.615309	−	0.0603054i
$697$	−2.55463	−	5.01374i	−0.0967635	−	0.189909i
$698$	16.8120	−	24.1301i	0.636344	−	0.913337i
$699$	−9.46753			−0.358095
$700$	4.52474	−	3.46958i	0.171019	−	0.131138i
$701$	−0.239240			−0.00903597			−0.00451799	−	0.999990i	$-0.501438\pi$
$701$	−0.239240			−0.00903597			−0.00451799	+	0.999990i	$0.501438\pi$
$702$	−3.46049	+	4.96679i	−0.130608	+	0.187460i
$703$	0.175461	+	0.344362i	0.00661765	+	0.0129879i
$704$	4.32715	+	36.2625i	0.163086	+	1.36670i
$705$	14.6566	+	17.4013i	0.551999	+	0.655371i
$706$	32.9669	+	4.55452i	1.24073	+	0.171412i
$707$	7.48646	+	7.48646i	0.281557	+	0.281557i
$708$	−13.8908	+	2.76765i	−0.522047	+	0.104015i
$709$	−8.43241	+	11.6062i	−0.316686	+	0.435881i	−0.937452	−	0.348115i	$-0.886822\pi$
$709$	−8.43241	+	11.6062i	−0.316686	+	0.435881i	0.620766	+	0.783996i	$0.286822\pi$
$710$	−2.24460	−	5.22683i	−0.0842384	−	0.196159i
$711$	−4.50041	−	6.19429i	−0.168779	−	0.232304i
$712$	−13.6647	+	5.35579i	−0.512105	+	0.200717i
$713$	−0.858481	−	5.42024i	−0.0321504	−	0.202989i
$714$	1.00834	−	0.180232i	0.0377360	−	0.00674501i
$715$	−37.4102	+	22.5730i	−1.39906	+	0.844181i
$716$	−32.8681	+	1.30189i	−1.22834	+	0.0486541i
$717$	−9.86150	−	5.02469i	−0.368284	−	0.187650i
$718$	−16.1845	−	46.6480i	−0.603999	−	1.74089i
$719$	9.40688	+	28.9514i	0.350818	+	1.07971i	0.958395	+	0.285445i	$0.0921414\pi$
$719$	9.40688	+	28.9514i	0.350818	+	1.07971i	−0.607578	+	0.794260i	$0.707859\pi$
$720$	1.45421	−	8.82526i	0.0541953	−	0.328898i
$721$	−1.32147	+	4.06706i	−0.0492141	+	0.151465i
$722$	26.1864	−	0.518414i	0.974557	−	0.0192934i
$723$	0.114761	−	0.724573i	0.00426801	−	0.0269472i
$724$	35.8438	−	28.2755i	1.33213	−	1.05085i
$725$	20.1064	+	20.6666i	0.746733	+	0.767539i
$726$	−12.5204	−	6.07038i	−0.464677	−	0.225293i
$727$	−21.2294	−	3.36240i	−0.787354	−	0.124705i	−0.250206	−	0.968193i	$-0.580498\pi$
$727$	−21.2294	−	3.36240i	−0.787354	−	0.124705i	−0.537148	+	0.843488i	$0.680498\pi$
$728$	−4.38188	−	5.33413i	−0.162403	−	0.197696i
$729$	0.951057	+	0.309017i	0.0352243	+	0.0114451i
$730$	−11.8774	−	18.8315i	−0.439603	−	0.696983i
$731$	−4.66298	+	1.51510i	−0.172467	+	0.0560378i
$732$	3.11184	−	26.3638i	0.115017	−	0.974435i
$733$	14.4461	−	28.3522i	0.533581	−	1.04721i	−0.454133	−	0.890934i	$-0.650051\pi$
$733$	14.4461	−	28.3522i	0.533581	−	1.04721i	0.987713	−	0.156277i	$-0.0499492\pi$
$734$	−20.1005	+	10.7480i	−0.741921	+	0.396717i
$735$	14.5367	−	3.38451i	0.536194	−	0.124840i
$736$	0.217672	−	3.74182i	0.00802348	−	0.137925i
$737$	−41.7874	+	6.61847i	−1.53926	+	0.243795i
$738$	5.99514	+	1.81756i	0.220684	+	0.0669054i
$739$	−9.06553	+	6.58650i	−0.333481	+	0.242288i	−0.741906	−	0.670504i	$-0.766078\pi$
$739$	−9.06553	+	6.58650i	−0.333481	+	0.242288i	0.408425	+	0.912792i	$0.366078\pi$
$740$	−0.661586	−	2.40602i	−0.0243204	−	0.0884472i
$741$	−2.39865	−	1.74272i	−0.0881166	−	0.0640204i
$742$	−4.18644	−	5.52861i	−0.153689	−	0.202962i
$743$	22.0818	−	22.0818i	0.810104	−	0.810104i	−0.174545	−	0.984649i	$-0.555846\pi$
$743$	22.0818	−	22.0818i	0.810104	−	0.810104i	0.984649	+	0.174545i	$0.0558455\pi$
$744$	20.2049	−	11.8553i	0.740748	−	0.434637i
$745$	−7.49780	+	30.3118i	−0.274698	+	1.11054i
$746$	−11.7305	−	11.2750i	−0.429483	−	0.412808i
$747$	−7.97834	+	4.06517i	−0.291912	+	0.148737i
$748$	10.1171	−	5.67010i	0.369918	−	0.207319i
$749$		−	0.651803i		−	0.0238164i
$750$	−12.0314	+	10.2589i	−0.439326	+	0.374602i
$751$			3.26645i			0.119194i	0.998223	+	0.0595972i	$0.0189816\pi$
$751$			3.26645i			0.119194i	−0.998223	+	0.0595972i	$0.981018\pi$
$752$	−15.5507	+	37.6107i	−0.567077	+	1.37152i
$753$	11.7095	−	5.96627i	0.426716	−	0.217423i
$754$	24.1906	−	25.1677i	0.880969	−	0.916555i
$755$	−10.3648	+	41.9022i	−0.377213	+	1.52498i
$756$	−0.633255	+	0.948388i	−0.0230313	+	0.0344925i
$757$	−1.58095	+	1.58095i	−0.0574608	+	0.0574608i	−0.735253	−	0.677792i	$-0.762937\pi$
$757$	−1.58095	+	1.58095i	−0.0574608	+	0.0574608i	0.677792	+	0.735253i	$0.262937\pi$
$758$	−11.0345	+	8.35568i	−0.400792	+	0.303492i
$759$	2.44702	+	1.77786i	0.0888211	+	0.0645323i
$760$	4.30756	+	0.797672i	0.156252	+	0.0289346i
$761$	−0.114145	+	0.0829313i	−0.00413776	+	0.00300626i	−0.589852	−	0.807511i	$-0.700814\pi$
$761$	−0.114145	+	0.0829313i	−0.00413776	+	0.00300626i	0.585714	+	0.810517i	$0.300814\pi$
$762$	8.14670	−	26.8715i	0.295124	−	0.973452i
$763$	10.1287	−	1.60422i	0.366682	−	0.0580768i
$764$	−16.7030	−	4.70499i	−0.604294	−	0.170221i
$765$	−2.76646	+	0.644102i	−0.100022	+	0.0232876i
$766$	11.0984	+	20.7556i	0.401000	+	0.749930i
$767$	13.7621	−	27.0096i	0.496919	−	0.975258i
$768$	15.2106	−	4.96369i	0.548865	−	0.179112i
$769$	30.9057	−	10.0419i	1.11449	−	0.362120i	0.306828	−	0.951765i	$-0.400733\pi$
$769$	30.9057	−	10.0419i	1.11449	−	0.362120i	0.807662	+	0.589645i	$0.200733\pi$
$770$	−6.96195	+	4.39106i	−0.250891	+	0.158243i
$771$	14.8643	+	4.82969i	0.535323	+	0.173937i
$772$	−4.26998	+	9.27009i	−0.153680	+	0.333638i
$773$	35.2942	+	5.59005i	1.26944	+	0.201060i	0.754578	−	0.656210i	$-0.227842\pi$
$773$	35.2942	+	5.59005i	1.26944	+	0.201060i	0.514866	+	0.857271i	$0.327842\pi$
$774$	2.38134	−	4.91162i	0.0855955	−	0.176545i
$775$	−40.8094	−	7.03959i	−1.46592	−	0.252870i
$776$	−34.9368	+	7.68290i	−1.25416	+	0.275800i
$777$	−0.0497693	+	0.314231i	−0.00178546	+	0.0112730i
$778$	0.414821	+	20.9537i	0.0148721	+	0.751225i
$779$	−0.948164	+	2.91815i	−0.0339715	+	0.104554i
$780$	12.9017	+	14.1417i	0.461954	+	0.506353i
$781$	2.53753	+	7.80972i	0.0908000	+	0.279454i
$782$	−1.12455	+	0.390160i	−0.0402137	+	0.0139521i
$783$	−5.13819	−	2.61804i	−0.183624	−	0.0935610i
$784$	17.3529	+	20.2914i	0.619747	+	0.724694i
$785$	31.4751	−	18.9918i	1.12339	−	0.677846i
$786$	5.66712	+	31.7056i	0.202140	+	1.13090i
$787$	2.87851	+	18.1742i	0.102608	+	0.647841i	0.984365	+	0.176138i	$0.0563605\pi$
$787$	2.87851	+	18.1742i	0.102608	+	0.647841i	−0.881758	+	0.471703i	$0.843639\pi$
$788$	−15.7599	+	17.0599i	−0.561424	+	0.607734i
$789$	−8.21592	−	11.3082i	−0.292495	−	0.402584i
$790$	−22.2475	+	9.55394i	−0.791530	+	0.339914i
$791$	−3.95844	+	5.44832i	−0.140746	+	0.193720i
$792$	−3.25411	+	12.4949i	−0.115630	+	0.443987i
$793$	40.1749	+	40.1749i	1.42665	+	1.42665i
$794$	−7.24584	+	52.4475i	−0.257145	+	1.86129i
$795$	12.3884	+	14.7084i	0.439372	+	0.521652i
$796$	0.880916	+	2.38548i	0.0312232	+	0.0845512i
$797$	−0.180269	−	0.353797i	−0.00638545	−	0.0125322i	0.887792	−	0.460245i	$-0.152239\pi$
$797$	−0.180269	−	0.353797i	−0.00638545	−	0.0125322i	−0.894177	+	0.447713i	$0.852239\pi$
$798$	−0.458278	−	0.319293i	−0.0162229	−	0.0113029i
$799$	12.9248			0.457246
$800$	−26.2031	−	10.6488i	−0.926420	−	0.376491i
$801$	−5.18903			−0.183345
$802$	7.40411	+	5.15862i	0.261448	+	0.182157i
$803$	14.5913	+	28.6370i	0.514915	+	1.01058i
$804$	6.42119	+	17.3883i	0.226458	+	0.613238i
$805$	0.782676	−	0.317914i	0.0275857	−	0.0112050i
$806$	−6.86147	+	49.6653i	−0.241685	+	1.74939i
$807$	−4.42868	−	4.42868i	−0.155897	−	0.155897i
$808$	13.2364	−	50.8241i	0.465654	−	1.78798i
$809$	27.2343	−	37.4848i	0.957506	−	1.31789i	0.00939488	−	0.999956i	$-0.497009\pi$
$809$	27.2343	−	37.4848i	0.957506	−	1.31789i	0.948111	−	0.317938i	$-0.102991\pi$
$810$	1.61730	−	2.71742i	0.0568261	−	0.0954802i
$811$	−10.0855	−	13.8814i	−0.354148	−	0.487443i	0.594358	−	0.804200i	$-0.297406\pi$
$811$	−10.0855	−	13.8814i	−0.354148	−	0.487443i	−0.948507	+	0.316757i	$0.897406\pi$
$812$	4.46240	−	4.83049i	0.156599	−	0.169517i
$813$	3.13832	+	19.8146i	0.110066	+	0.694927i
$814$	0.633815	+	3.54598i	0.0222152	+	0.124286i
$815$	39.2126	+	3.35728i	1.37356	+	0.117600i
$816$	−3.30241	−	3.86163i	−0.115608	−	0.135184i
$817$	2.38209	+	1.21374i	0.0833388	+	0.0424633i
$818$	17.6197	−	6.11312i	0.616058	−	0.213740i
$819$	−0.754199	−	2.32119i	−0.0263538	−	0.0811088i
$820$	9.79280	−	17.2207i	0.341980	−	0.601374i
$821$	−7.99259	+	24.5987i	−0.278943	+	0.858499i	0.709206	+	0.705002i	$0.249054\pi$
$821$	−7.99259	+	24.5987i	−0.278943	+	0.858499i	−0.988149	+	0.153498i	$0.950946\pi$
$822$	−0.468085	−	23.6442i	−0.0163263	−	0.824685i
$823$	4.34747	−	27.4488i	0.151543	−	0.956806i	−0.788323	−	0.615262i	$-0.789050\pi$
$823$	4.34747	−	27.4488i	0.151543	−	0.956806i	0.939866	−	0.341544i	$-0.110950\pi$
$824$	20.7180	−	4.55606i	0.721745	−	0.158718i
$825$	18.6483	−	13.1612i	0.649250	−	0.458213i
$826$	2.49134	−	5.13850i	0.0866848	−	0.178791i
$827$	−27.6226	−	4.37499i	−0.960533	−	0.152133i	−0.343571	−	0.939127i	$-0.611637\pi$
$827$	−27.6226	−	4.37499i	−0.960533	−	0.152133i	−0.616962	+	0.786993i	$0.711637\pi$
$828$	0.554411	−	1.20362i	0.0192671	−	0.0418287i
$829$	26.8128	+	8.71201i	0.931248	+	0.302581i	0.735073	−	0.677988i	$-0.237148\pi$
$829$	26.8128	+	8.71201i	0.931248	+	0.302581i	0.196175	+	0.980569i	$0.437148\pi$
$830$	6.96555	+	27.4459i	0.241778	+	0.952660i
$831$	9.50043	−	3.08688i	0.329566	−	0.107083i
$832$	−11.8215	+	32.1382i	−0.409835	+	1.11419i
$833$	3.84940	−	7.55488i	0.133374	−	0.261761i
$834$	0.817358	+	1.52858i	0.0283028	+	0.0529305i
$835$	−9.82300	+	11.3425i	−0.339939	+	0.392525i
$836$	−6.08710	−	1.71464i	−0.210527	−	0.0593022i
$837$	8.18045	−	1.29566i	0.282758	−	0.0447844i
$838$	−1.76287	+	5.81473i	−0.0608972	+	0.200866i
$839$	−26.1157	+	18.9742i	−0.901615	+	0.655062i	−0.938880	−	0.344244i	$-0.888135\pi$
$839$	−26.1157	+	18.9742i	−0.901615	+	0.655062i	0.0372654	+	0.999305i	$0.488135\pi$
$840$	2.48273	+	2.61545i	0.0856624	+	0.0902414i
$841$	3.44243	+	2.50107i	0.118704	+	0.0862438i
$842$	−6.58736	+	4.98815i	−0.227015	+	0.171903i
$843$	19.8038	−	19.8038i	0.682080	−	0.682080i
$844$	−4.85277	+	7.26771i	−0.167039	+	0.250165i
$845$	−11.8698	+	0.852175i	−0.408334	+	0.0293157i
$846$	−9.97131	+	10.3741i	−0.342821	+	0.356668i
$847$	4.99859	−	2.54691i	0.171754	−	0.0875129i
$848$	−13.1442	+	31.7902i	−0.451373	+	1.09168i
$849$		−	9.59484i		−	0.329294i
$850$	0.0543940	+	8.98214i	0.00186570	+	0.308085i
$851$		−	0.369703i		−	0.0126733i
$852$	3.13839	−	1.75890i	0.107519	−	0.0602588i
$853$	11.7252	−	5.97427i	0.401462	−	0.204555i	−0.241589	−	0.970379i	$-0.577668\pi$
$853$	11.7252	−	5.97427i	0.401462	−	0.204555i	0.643051	+	0.765824i	$0.277668\pi$
$854$	7.71664	+	7.41704i	0.264058	+	0.253806i
$855$	1.31502	+	0.818321i	0.0449726	+	0.0279860i
$856$	−2.78869	+	1.63627i	−0.0953153	+	0.0559266i
$857$	17.3368	−	17.3368i	0.592213	−	0.592213i	−0.346015	−	0.938229i	$-0.612466\pi$
$857$	17.3368	−	17.3368i	0.592213	−	0.592213i	0.938229	+	0.346015i	$0.112466\pi$
$858$	−16.6820	−	22.0303i	−0.569515	−	0.752102i
$859$	−26.4354	−	19.2065i	−0.901966	−	0.655317i	0.0370044	−	0.999315i	$-0.488218\pi$
$859$	−26.4354	−	19.2065i	−0.901966	−	0.655317i	−0.938970	+	0.343999i	$0.888218\pi$
$860$	−13.4852	−	10.7748i	−0.459841	−	0.367419i
$861$	−2.04340	+	1.48462i	−0.0696389	+	0.0505956i
$862$	4.16027	+	1.26128i	0.141699	+	0.0429594i
$863$	−25.5766	+	4.05093i	−0.870637	+	0.137895i	−0.575739	−	0.817634i	$-0.695286\pi$
$863$	−25.5766	+	4.05093i	−0.870637	+	0.137895i	−0.294898	+	0.955529i	$0.595286\pi$
$864$	5.64731	+	0.328519i	0.192125	+	0.0111764i
$865$	−2.03144	−	0.857847i	−0.0690711	−	0.0291677i
$866$	−34.1008	+	18.2343i	−1.15879	+	0.619626i
$867$	6.98526	−	13.7094i	0.237232	−	0.465594i
$868$	−1.10715	+	9.37993i	−0.0375792	+	0.318376i
$869$	33.2413	−	10.8008i	1.12763	−	0.366391i
$870$	−11.6631	+	14.0187i	−0.395416	+	0.475277i
$871$	−37.7294	−	12.2590i	−1.27841	−	0.415381i
$872$	−32.2903	−	39.3075i	−1.09349	−	1.33112i
$873$	−12.4915	−	1.97845i	−0.422772	−	0.0669605i
$874$	0.584028	+	0.283159i	0.0197550	+	0.00957798i
$875$	−0.369101	−	6.36419i	−0.0124779	−	0.215149i
$876$	11.0554	−	8.72108i	0.373527	−	0.294658i
$877$	−2.40885	+	15.2089i	−0.0813410	+	0.513567i	0.913054	+	0.407839i	$0.133717\pi$
$877$	−2.40885	+	15.2089i	−0.0813410	+	0.513567i	−0.994395	+	0.105728i	$0.966283\pi$
$878$	34.0832	−	0.674748i	1.15025	−	0.0227716i
$879$	0.159729	−	0.491595i	0.00538752	−	0.0165811i
$880$	36.2639	+	18.7629i	1.22246	+	0.632498i
$881$	−6.30400	−	19.4017i	−0.212387	−	0.653660i	−0.999329	−	0.0366329i	$-0.988337\pi$
$881$	−6.30400	−	19.4017i	−0.212387	−	0.653660i	0.786942	−	0.617027i	$-0.211663\pi$
$882$	3.09416	+	8.91821i	0.104186	+	0.300292i
$883$	−42.2974	−	21.5516i	−1.42342	−	0.725270i	−0.438575	−	0.898694i	$-0.644517\pi$
$883$	−42.2974	−	21.5516i	−1.42342	−	0.725270i	−0.984847	+	0.173424i	$0.944517\pi$
$884$	10.8662	−	0.430407i	0.365471	−	0.0144762i
$885$	−6.16038	+	14.5882i	−0.207079	+	0.490378i
$886$	−35.0996	+	6.27377i	−1.17919	+	0.210772i
$887$	5.53478	+	34.9452i	0.185840	+	1.17335i	0.887491	+	0.460825i	$0.152447\pi$
$887$	5.53478	+	34.9452i	0.185840	+	1.17335i	−0.701651	+	0.712521i	$0.747553\pi$
$888$	1.46935	−	0.575904i	0.0493082	−	0.0193261i
$889$	6.65437	+	9.15895i	0.223180	+	0.307181i
$890$	−3.62409	+	16.0039i	−0.121480	+	0.536453i
$891$	−2.68322	+	3.69314i	−0.0898914	+	0.123725i
$892$	22.5023	−	4.48345i	0.753433	−	0.150117i
$893$	−4.98343	−	4.98343i	−0.166764	−	0.166764i
$894$	−19.5628	−	2.70268i	−0.654278	−	0.0903912i
$895$	−19.4306	+	31.2244i	−0.649493	+	1.04372i
$896$	−2.10671	+	6.09723i	−0.0703802	+	0.203694i
$897$	1.28758	+	2.52702i	0.0429911	+	0.0843747i
$898$	−8.76617	+	12.5820i	−0.292531	+	0.419866i
$899$	−47.7624			−1.59296
$900$	−7.25147	−	6.88594i	−0.241716	−	0.229531i
$901$	10.9246			0.363952
$902$	−16.3481	+	23.4642i	−0.544333	+	0.781274i
$903$	0.999123	+	1.96089i	0.0332487	+	0.0652543i
$904$	33.2474	+	3.25851i	1.10579	+	0.108377i
$905$	−3.65512	−	50.9117i	−0.121500	−	1.69236i
$906$	−27.0431	−	3.73612i	−0.898448	−	0.124124i
$907$	−25.9955	−	25.9955i	−0.863166	−	0.863166i	0.128538	−	0.991705i	$-0.458971\pi$
$907$	−25.9955	−	25.9955i	−0.863166	−	0.863166i	−0.991705	+	0.128538i	$0.958971\pi$
$908$	11.7155	+	58.7996i	0.388792	+	1.95133i
$909$	10.9142	−	15.0222i	0.362002	−	0.498254i
$910$	−7.68572	+	0.704940i	−0.254779	+	0.0233685i
$911$	4.91355	+	6.76292i	0.162793	+	0.224065i	0.882619	−	0.470089i	$-0.155778\pi$
$911$	4.91355	+	6.76292i	0.162793	+	0.224065i	−0.719826	+	0.694155i	$0.755778\pi$
$912$	−0.215621	+	2.76225i	−0.00713991	+	0.0914673i
$913$	−6.39444	−	40.3729i	−0.211625	−	1.33615i
$914$	−21.1703	+	3.78402i	−0.700250	+	0.125164i
$915$	−22.4361	−	19.4304i	−0.741715	−	0.642348i
$916$	0.0686345	+	1.73277i	0.00226775	+	0.0572524i
$917$	−11.5704	−	5.89541i	−0.382088	−	0.194684i
$918$	−0.588845	−	1.69721i	−0.0194348	−	0.0560164i
$919$	−12.4509	−	38.3200i	−0.410718	−	1.26406i	−0.916025	−	0.401121i	$-0.868621\pi$
$919$	−12.4509	−	38.3200i	−0.410718	−	1.26406i	0.505307	−	0.862940i	$-0.331379\pi$
$920$	−3.32498	−	2.55053i	−0.109621	−	0.0840886i
$921$	3.43611	−	10.5752i	0.113224	−	0.348466i
$922$	−12.2333	+	0.242183i	−0.402881	+	0.00797586i
$923$	−1.20451	+	7.60496i	−0.0396469	+	0.250320i
$924$	−3.22417	−	4.08715i	−0.106067	−	0.134457i
$925$	−2.64122	−	0.898484i	−0.0868427	−	0.0295420i
$926$	8.99835	+	4.36274i	0.295704	+	0.143369i
$927$	7.40760	+	1.17325i	0.243297	+	0.0385345i
$928$	−31.8691	−	6.96567i	−1.04616	−	0.228659i
$929$	15.1027	+	4.90715i	0.495502	+	0.160998i	0.546099	−	0.837721i	$-0.316112\pi$
$929$	15.1027	+	4.90715i	0.495502	+	0.160998i	−0.0505966	+	0.998719i	$0.516112\pi$
$930$	1.71730	−	26.1349i	0.0563125	−	0.856998i
$931$	−4.39717	+	1.42873i	−0.144111	+	0.0468246i
$932$	−18.8045	−	2.21958i	−0.615962	−	0.0727047i
$933$	8.72508	−	17.1239i	0.285646	−	0.560612i
$934$	−23.0899	+	12.3466i	−0.755526	+	0.403992i
$935$	1.10612	−	12.9193i	0.0361740	−	0.422507i
$936$	−8.03768	+	9.05383i	−0.262720	+	0.295934i
$937$	−2.53917	+	0.402165i	−0.0829512	+	0.0131382i	−0.197772	−	0.980248i	$-0.563371\pi$
$937$	−2.53917	+	0.402165i	−0.0829512	+	0.0131382i	0.114821	+	0.993386i	$0.463371\pi$
$938$	−7.15196	−	2.16828i	−0.233520	−	0.0707967i
$939$	−6.10589	+	4.43619i	−0.199258	+	0.144770i
$940$	25.0315	+	37.9988i	0.816438	+	1.23938i
$941$	−13.7615	−	9.99831i	−0.448612	−	0.325935i	0.340436	−	0.940268i	$-0.389425\pi$
$941$	−13.7615	−	9.99831i	−0.448612	−	0.325935i	−0.789047	+	0.614332i	$0.789425\pi$
$942$	14.0354	+	18.5352i	0.457299	+	0.603910i
$943$	2.07541	−	2.07541i	0.0675848	−	0.0675848i
$944$	−28.2389	+	2.24058i	−0.919097	+	0.0729246i
$945$	0.479809	+	1.18125i	0.0156082	+	0.0384260i
$946$	17.9648	+	17.2673i	0.584085	+	0.561408i
$947$	25.4121	−	12.9481i	0.825782	−	0.420757i	0.0105872	−	0.999944i	$-0.496630\pi$
$947$	25.4121	−	12.9481i	0.825782	−	0.420757i	0.815195	+	0.579187i	$0.196630\pi$
$948$	−7.48658	−	13.3582i	−0.243153	−	0.433856i
$949$			30.1366i			0.978276i
$950$	3.44228	−	3.48423i	0.111682	−	0.113043i
$951$			12.1281i			0.393280i
$952$	2.04502	−	0.121583i	0.0662796	−	0.00394054i
$953$	−13.9573	+	7.11160i	−0.452121	+	0.230367i	−0.665196	−	0.746669i	$-0.731652\pi$
$953$	−13.9573	+	7.11160i	−0.452121	+	0.230367i	0.213075	+	0.977036i	$0.431652\pi$
$954$	−8.42819	+	8.76864i	−0.272873	+	0.283895i
$955$	−14.8391	+	12.4985i	−0.480181	+	0.404442i
$956$	−18.4090	−	12.2920i	−0.595391	−	0.397553i
$957$	18.6145	−	18.6145i	0.601722	−	0.601722i
$958$	28.5102	−	21.5888i	0.921123	−	0.697503i
$959$	7.71380	+	5.60441i	0.249092	+	0.180976i
$960$	4.95738	−	17.1879i	0.159999	−	0.554738i
$961$	30.4178	−	22.0998i	0.981218	−	0.712897i
$962$	−0.979962	+	3.23236i	−0.0315952	+	0.104215i
$963$	−1.12907	+	0.178826i	−0.0363836	+	0.00576260i
$964$	0.397810	−	1.41225i	0.0128126	−	0.0454855i
$965$	5.89521	+	9.77013i	0.189774	+	0.314512i
$966$	0.251935	+	0.471157i	0.00810589	+	0.0151592i
$967$	−1.53584	+	3.01425i	−0.0493891	+	0.0969316i	−0.914382	−	0.404853i	$-0.867323\pi$
$967$	−1.53584	+	3.01425i	−0.0493891	+	0.0969316i	0.864993	+	0.501784i	$0.167323\pi$
$968$	−23.4451	−	14.9924i	−0.753554	−	0.481873i
$969$	0.836819	−	0.271899i	0.0268825	−	0.00873465i
$970$	−14.8261	+	37.1442i	−0.476039	+	1.19263i
$971$	−0.924449	−	0.300372i	−0.0296670	−	0.00963939i	0.294146	−	0.955761i	$-0.404965\pi$
$971$	−0.924449	−	0.300372i	−0.0296670	−	0.00963939i	−0.323813	+	0.946121i	$0.604965\pi$
$972$	1.81655	+	0.836740i	0.0582660	+	0.0268384i
$973$	−0.690268	−	0.109328i	−0.0221290	−	0.00350489i
$974$	−14.5746	+	30.0607i	−0.466999	+	0.963206i
$975$	21.1826	−	3.05730i	0.678387	−	0.0979120i
$976$	12.3615	−	51.6346i	0.395683	−	1.65278i
$977$	−1.61466	+	10.1946i	−0.0516576	+	0.326153i	0.948304	+	0.317364i	$0.102798\pi$
$977$	−1.61466	+	10.1946i	−0.0516576	+	0.326153i	−0.999961	+	0.00878920i	$0.997202\pi$
$978$	0.492671	+	24.8861i	0.0157539	+	0.795769i
$979$	7.31992	−	22.5284i	0.233946	−	0.720011i
$980$	29.6664	−	3.31436i	0.947660	−	0.105873i
$981$	−5.55773	−	17.1049i	−0.177445	−	0.546119i
$982$	31.9636	−	11.0897i	1.02000	−	0.353887i
$983$	2.23630	+	1.13945i	0.0713268	+	0.0363428i	0.489290	−	0.872121i	$-0.337256\pi$
$983$	2.23630	+	1.13945i	0.0713268	+	0.0363428i	−0.417963	+	0.908464i	$0.637256\pi$
$984$	11.4815	+	5.01557i	0.366017	+	0.159891i
$985$	5.88821	+	25.2903i	0.187614	+	0.805815i
$986$	1.82282	+	10.1981i	0.0580504	+	0.324772i
$987$	−0.907550	−	5.73005i	−0.0288876	−	0.182389i
$988$	−4.35566	−	4.02375i	−0.138572	−	0.128013i
$989$	−1.50319	−	2.06897i	−0.0477988	−	0.0657894i
$990$	9.51634	+	10.8549i	0.302449	+	0.344992i
$991$	22.1826	−	30.5317i	0.704653	−	0.969871i	−0.295243	−	0.955422i	$-0.595401\pi$
$991$	22.1826	−	30.5317i	0.704653	−	0.969871i	0.999896	−	0.0144492i	$-0.00459947\pi$
$992$	42.9106	−	18.8103i	1.36241	−	0.597227i
$993$	1.08395	+	1.08395i	0.0343980	+	0.0343980i
$994$	−0.198509	+	1.43687i	−0.00629634	+	0.0455747i
$995$	2.75991	+	0.682682i	0.0874952	+	0.0216425i
$996$	−16.7997	+	6.20383i	−0.532319	+	0.196576i
$997$	3.03505	+	5.95663i	0.0961211	+	0.188648i	0.934060	−	0.357115i	$-0.116240\pi$
$997$	3.03505	+	5.95663i	0.0961211	+	0.188648i	−0.837939	+	0.545764i	$0.816240\pi$
$998$	3.71538	+	2.58859i	0.117608	+	0.0819405i
$999$	0.557971			0.0176534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.223.25	yes	240
3.2	odd	2		900.2.bj.f.523.6		240
4.3	odd	2	inner	300.2.w.a.223.3	yes	240
12.11	even	2		900.2.bj.f.523.28		240
25.12	odd	20	inner	300.2.w.a.187.3	✓	240
75.62	even	20		900.2.bj.f.487.28		240
100.87	even	20	inner	300.2.w.a.187.25	yes	240
300.287	odd	20		900.2.bj.f.487.6		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.3	✓	240	25.12	odd	20	inner
300.2.w.a.187.25	yes	240	100.87	even	20	inner
300.2.w.a.223.3	yes	240	4.3	odd	2	inner
300.2.w.a.223.25	yes	240	1.1	even	1	trivial
900.2.bj.f.487.6		240	300.287	odd	20
900.2.bj.f.487.28		240	75.62	even	20
900.2.bj.f.523.6		240	3.2	odd	2
900.2.bj.f.523.28		240	12.11	even	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)

\(f(q)\)	\(=\)	\(q+(1.16035 + 0.808445i) q^{2} +(0.453990 + 0.891007i) q^{3} +(0.692833 + 1.87616i) q^{4} +(2.17065 + 0.536923i) q^{5} +(-0.193541 + 1.40091i) q^{6} +(-0.403183 - 0.403183i) q^{7} +(-0.712844 + 2.73712i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(1.16035 + 0.808445i) q^{2} +(0.453990 + 0.891007i) q^{3} +(0.692833 + 1.87616i) q^{4} +(2.17065 + 0.536923i) q^{5} +(-0.193541 + 1.40091i) q^{6} +(-0.403183 - 0.403183i) q^{7} +(-0.712844 + 2.73712i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(2.08464 + 2.37787i) q^{10} +(-2.68322 - 3.69314i) q^{11} +(-1.35713 + 1.46908i) q^{12} +(-0.669605 - 4.22772i) q^{13} +(-0.141883 - 0.793785i) q^{14} +(0.507052 + 2.17782i) q^{15} +(-3.03997 + 2.59973i) q^{16} +(1.13184 + 0.576699i) q^{17} +(-1.33608 + 0.463552i) q^{18} +(-0.214045 - 0.658762i) q^{19} +(0.496541 + 4.44448i) q^{20} +(0.176197 - 0.542280i) q^{21} +(-0.127782 - 6.45458i) q^{22} +(-0.103651 + 0.654427i) q^{23} +(-2.76242 + 0.607480i) q^{24} +(4.42343 + 2.33094i) q^{25} +(2.64090 - 5.44698i) q^{26} +(-0.987688 - 0.156434i) q^{27} +(0.477098 - 1.03577i) q^{28} +(5.48448 + 1.78201i) q^{29} +(-1.17229 + 2.93696i) q^{30} +(-7.87705 + 2.55941i) q^{31} +(-5.62917 + 0.558959i) q^{32} +(2.07245 - 4.06742i) q^{33} +(0.847098 + 1.58420i) q^{34} +(-0.658690 - 1.09165i) q^{35} +(-1.92508 - 0.542267i) q^{36} +(-0.551102 + 0.0872860i) q^{37} +(0.284206 - 0.937440i) q^{38} +(3.46293 - 2.51597i) q^{39} +(-3.01696 + 5.55859i) q^{40} +(-3.58374 - 2.60374i) q^{41} +(0.642854 - 0.486789i) q^{42} +(-2.72923 + 2.72923i) q^{43} +(5.06990 - 7.59289i) q^{44} +(-1.71026 + 1.44050i) q^{45} +(-0.649340 + 0.675569i) q^{46} +(9.06571 - 4.61921i) q^{47} +(-3.69649 - 1.52838i) q^{48} -6.67489i q^{49} +(3.24829 + 6.28081i) q^{50} +1.27029i q^{51} +(7.46797 - 4.18539i) q^{52} +(7.66275 - 3.90436i) q^{53} +(-1.01960 - 0.980011i) q^{54} +(-3.84140 - 9.45719i) q^{55} +(1.39097 - 0.816155i) q^{56} +(0.489787 - 0.489787i) q^{57} +(4.92326 + 6.50166i) q^{58} +(5.72938 + 4.16264i) q^{59} +(-3.73464 + 2.46018i) q^{60} +(-10.7384 + 7.80192i) q^{61} +(-11.2093 - 3.39835i) q^{62} +(0.563167 - 0.0891968i) q^{63} +(-6.98371 - 3.90229i) q^{64} +(0.816485 - 9.53642i) q^{65} +(5.69306 - 3.04417i) q^{66} +(4.20759 - 8.25787i) q^{67} +(-0.297808 + 2.52306i) q^{68} +(-0.630155 + 0.204750i) q^{69} +(0.118224 - 1.79921i) q^{70} +(-1.71079 - 0.555870i) q^{71} +(-1.79538 - 2.18554i) q^{72} +(-6.95389 - 1.10139i) q^{73} +(-0.710038 - 0.344253i) q^{74} +(-0.0686916 + 4.99953i) q^{75} +(1.08765 - 0.857995i) q^{76} +(-0.407181 + 2.57084i) q^{77} +(6.05224 - 0.119817i) q^{78} +(-2.36601 + 7.28182i) q^{79} +(-7.99455 + 4.01088i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(-2.05342 - 5.91851i) q^{82} +(7.97834 + 4.06517i) q^{83} +(1.13948 - 0.0451344i) q^{84} +(2.14717 + 1.85952i) q^{85} +(-5.37330 + 0.960434i) q^{86} +(0.902114 + 5.69572i) q^{87} +(12.0213 - 4.71169i) q^{88} +(3.05003 + 4.19801i) q^{89} +(-3.14906 + 0.288834i) q^{90} +(-1.43457 + 1.97452i) q^{91} +(-1.29962 + 0.258942i) q^{92} +(-5.85655 - 5.85655i) q^{93} +(14.2538 + 1.96922i) q^{94} +(-0.110911 - 1.54487i) q^{95} +(-3.05363 - 4.76187i) q^{96} +(5.74169 + 11.2687i) q^{97} +(5.39628 - 7.74522i) q^{98} +4.56497 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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