LMFDB - Embedded newform 300.2.w.a.223.10

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			223.10
Character	$\chi$	$=$	300.223
Dual form			300.2.w.a.187.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.696395 - 1.23087i) q^{2} +(0.453990 + 0.891007i) q^{3} +(-1.03007 + 1.71434i) q^{4} +(0.328085 - 2.21187i) q^{5} +(0.780554 - 1.17929i) q^{6} +(-3.17506 - 3.17506i) q^{7} +(2.82746 + 0.0740164i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(-0.696395 - 1.23087i) q^{2} +(0.453990 + 0.891007i) q^{3} +(-1.03007 + 1.71434i) q^{4} +(0.328085 - 2.21187i) q^{5} +(0.780554 - 1.17929i) q^{6} +(-3.17506 - 3.17506i) q^{7} +(2.82746 + 0.0740164i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(-2.95099 + 1.13651i) q^{10} +(1.22267 + 1.68286i) q^{11} +(-1.99513 - 0.139502i) q^{12} +(-0.339738 - 2.14502i) q^{13} +(-1.69698 + 6.11917i) q^{14} +(2.11974 - 0.711841i) q^{15} +(-1.87792 - 3.53177i) q^{16} +(-2.26334 - 1.15323i) q^{17} +(1.40512 + 0.160090i) q^{18} +(-1.87987 - 5.78563i) q^{19} +(3.45394 + 2.84082i) q^{20} +(1.38755 - 4.27044i) q^{21} +(1.21991 - 2.67687i) q^{22} +(0.703414 - 4.44118i) q^{23} +(1.21769 + 2.55289i) q^{24} +(-4.78472 - 1.45136i) q^{25} +(-2.40365 + 1.91196i) q^{26} +(-0.987688 - 0.156434i) q^{27} +(8.71365 - 2.17261i) q^{28} +(1.37225 + 0.445870i) q^{29} +(-2.35236 - 2.11339i) q^{30} +(-1.68210 + 0.546548i) q^{31} +(-3.03936 + 4.77098i) q^{32} +(-0.944357 + 1.85340i) q^{33} +(0.156708 + 3.58897i) q^{34} +(-8.06450 + 5.98112i) q^{35} +(-0.781472 - 1.84101i) q^{36} +(8.87863 - 1.40624i) q^{37} +(-5.81222 + 6.34296i) q^{38} +(1.75699 - 1.27653i) q^{39} +(1.09136 - 6.22968i) q^{40} +(5.90311 + 4.28886i) q^{41} +(-6.22263 + 1.26603i) q^{42} +(-4.19804 + 4.19804i) q^{43} +(-4.14442 + 0.362612i) q^{44} +(1.59660 + 1.56553i) q^{45} +(-5.95636 + 2.22701i) q^{46} +(-1.82245 + 0.928585i) q^{47} +(2.29427 - 3.27663i) q^{48} +13.1620i q^{49} +(1.54562 + 6.90008i) q^{50} -2.54021i q^{51} +(4.02725 + 1.62709i) q^{52} +(10.2866 - 5.24127i) q^{53} +(0.495272 + 1.32465i) q^{54} +(4.12339 - 2.15226i) q^{55} +(-8.74233 - 9.21235i) q^{56} +(4.30160 - 4.30160i) q^{57} +(-0.406820 - 1.99956i) q^{58} +(3.92021 + 2.84820i) q^{59} +(-0.963132 + 4.36719i) q^{60} +(-11.1415 + 8.09476i) q^{61} +(1.84414 + 1.68983i) q^{62} +(4.43493 - 0.702423i) q^{63} +(7.98904 + 0.418557i) q^{64} +(-4.85597 + 0.0477062i) q^{65} +(2.93894 - 0.128325i) q^{66} +(3.16115 - 6.20411i) q^{67} +(4.30842 - 2.69223i) q^{68} +(4.27647 - 1.38951i) q^{69} +(12.9780 + 5.76110i) q^{70} +(8.47778 + 2.75460i) q^{71} +(-1.72182 + 2.24396i) q^{72} +(-0.968954 - 0.153467i) q^{73} +(-7.91392 - 9.94911i) q^{74} +(-0.879045 - 4.92212i) q^{75} +(11.8549 + 2.73686i) q^{76} +(1.46113 - 9.22520i) q^{77} +(-2.79480 - 1.27365i) q^{78} +(4.20734 - 12.9489i) q^{79} +(-8.42793 + 2.99500i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(1.16812 - 10.2527i) q^{82} +(4.17938 + 2.12950i) q^{83} +(5.89172 + 6.77757i) q^{84} +(-3.29336 + 4.62785i) q^{85} +(8.09073 + 2.24373i) q^{86} +(0.225714 + 1.42510i) q^{87} +(3.33248 + 4.84870i) q^{88} +(9.07416 + 12.4895i) q^{89} +(0.815097 - 3.05542i) q^{90} +(-5.73188 + 7.88926i) q^{91} +(6.88914 + 5.78061i) q^{92} +(-1.25064 - 1.25064i) q^{93} +(2.41211 + 1.59653i) q^{94} +(-13.4138 + 2.25984i) q^{95} +(-5.63082 - 0.542109i) q^{96} +(-4.76437 - 9.35061i) q^{97} +(16.2006 - 9.16594i) q^{98} -2.08012 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 $

$2$	−0.696395	−	1.23087i	−0.492426	−	0.870354i
$2$	−0.696395	−	1.23087i	−0.492426	−	0.870354i
$3$	0.453990	+	0.891007i	0.262112	+	0.514423i
$3$	0.453990	+	0.891007i	0.262112	+	0.514423i
$4$	−1.03007	+	1.71434i	−0.515033	+	0.857170i
$5$	0.328085	−	2.21187i	0.146724	−	0.989177i
$5$	0.328085	−	2.21187i	0.146724	−	0.989177i
$6$	0.780554	−	1.17929i	0.318660	−	0.481445i
$7$	−3.17506	−	3.17506i	−1.20006	−	1.20006i	−0.974148	−	0.225911i	$-0.927464\pi$
$7$	−3.17506	−	3.17506i	−1.20006	−	1.20006i	−0.225911	−	0.974148i	$-0.572536\pi$
$8$	2.82746	+	0.0740164i	0.999658	+	0.0261688i
$9$	−0.587785	+	0.809017i	−0.195928	+	0.269672i
$10$	−2.95099	+	1.13651i	−0.933186	+	0.359395i
$11$	1.22267	+	1.68286i	0.368648	+	0.507400i	0.952533	−	0.304436i	$-0.0984681\pi$
$11$	1.22267	+	1.68286i	0.368648	+	0.507400i	−0.583885	+	0.811836i	$0.698468\pi$
$12$	−1.99513	−	0.139502i	−0.575944	−	0.0402708i
$13$	−0.339738	−	2.14502i	−0.0942265	−	0.594923i	−0.988944	−	0.148290i	$-0.952623\pi$
$13$	−0.339738	−	2.14502i	−0.0942265	−	0.594923i	0.894717	−	0.446633i	$-0.147377\pi$
$14$	−1.69698	+	6.11917i	−0.453536	+	1.63542i
$15$	2.11974	−	0.711841i	0.547314	−	0.183797i
$16$	−1.87792	−	3.53177i	−0.469481	−	0.882942i
$17$	−2.26334	−	1.15323i	−0.548941	−	0.279699i	0.157443	−	0.987528i	$-0.449675\pi$
$17$	−2.26334	−	1.15323i	−0.548941	−	0.279699i	−0.706384	+	0.707829i	$0.749675\pi$
$18$	1.40512	+	0.160090i	0.331191	+	0.0377335i
$19$	−1.87987	−	5.78563i	−0.431271	−	1.32732i	−0.896860	−	0.442315i	$-0.854157\pi$
$19$	−1.87987	−	5.78563i	−0.431271	−	1.32732i	0.465589	−	0.885001i	$-0.345843\pi$
$20$	3.45394	+	2.84082i	0.772326	+	0.635227i
$21$	1.38755	−	4.27044i	0.302788	−	0.931887i
$22$	1.21991	−	2.67687i	0.260086	−	0.570711i
$23$	0.703414	−	4.44118i	0.146672	−	0.926051i	−0.799095	−	0.601205i	$-0.794688\pi$
$23$	0.703414	−	4.44118i	0.146672	−	0.926051i	0.945767	−	0.324846i	$-0.105312\pi$
$24$	1.21769	+	2.55289i	0.248560	+	0.521106i
$25$	−4.78472	−	1.45136i	−0.956944	−	0.290272i
$26$	−2.40365	+	1.91196i	−0.471394	+	0.374966i
$27$	−0.987688	−	0.156434i	−0.190081	−	0.0301058i
$28$	8.71365	−	2.17261i	1.64672	−	0.410584i
$29$	1.37225	+	0.445870i	0.254820	+	0.0827960i	0.433641	−	0.901086i	$-0.357228\pi$
$29$	1.37225	+	0.445870i	0.254820	+	0.0827960i	−0.178822	+	0.983882i	$0.557228\pi$
$30$	−2.35236	−	2.11339i	−0.429480	−	0.385851i
$31$	−1.68210	+	0.546548i	−0.302114	+	0.0981629i	−0.456151	−	0.889902i	$-0.650772\pi$
$31$	−1.68210	+	0.546548i	−0.302114	+	0.0981629i	0.154037	+	0.988065i	$0.450772\pi$
$32$	−3.03936	+	4.77098i	−0.537288	+	0.843399i
$33$	−0.944357	+	1.85340i	−0.164391	+	0.322636i
$34$	0.156708	+	3.58897i	0.0268752	+	0.615504i
$35$	−8.06450	+	5.98112i	−1.36315	+	1.01099i
$36$	−0.781472	−	1.84101i	−0.130245	−	0.306834i
$37$	8.87863	−	1.40624i	1.45964	−	0.231184i	0.624413	−	0.781094i	$-0.285338\pi$
$37$	8.87863	−	1.40624i	1.45964	−	0.231184i	0.835224	+	0.549910i	$0.185338\pi$
$38$	−5.81222	+	6.34296i	−0.942866	+	1.02896i
$39$	1.75699	−	1.27653i	0.281344	−	0.204408i
$40$	1.09136	−	6.22968i	0.172559	−	0.984999i
$41$	5.90311	+	4.28886i	0.921911	+	0.669807i	0.943999	−	0.329949i	$-0.107031\pi$
$41$	5.90311	+	4.28886i	0.921911	+	0.669807i	−0.0220881	+	0.999756i	$0.507031\pi$
$42$	−6.22263	+	1.26603i	−0.960173	+	0.195352i
$43$	−4.19804	+	4.19804i	−0.640195	+	0.640195i	−0.950603	−	0.310408i	$-0.899534\pi$
$43$	−4.19804	+	4.19804i	−0.640195	+	0.640195i	0.310408	+	0.950603i	$0.399534\pi$
$44$	−4.14442	+	0.362612i	−0.624794	+	0.0546658i
$45$	1.59660	+	1.56553i	0.238006	+	0.233375i
$46$	−5.95636	+	2.22701i	−0.878218	+	0.328355i
$47$	−1.82245	+	0.928585i	−0.265832	+	0.135448i	−0.581827	−	0.813313i	$-0.697662\pi$
$47$	−1.82245	+	0.928585i	−0.265832	+	0.135448i	0.315995	+	0.948761i	$0.397662\pi$
$48$	2.29427	−	3.27663i	0.331149	−	0.472941i
$49$			13.1620i			1.88028i
$50$	1.54562	+	6.90008i	0.218584	+	0.975818i
$51$		−	2.54021i		−	0.355700i
$52$	4.02725	+	1.62709i	0.558480	+	0.225637i
$53$	10.2866	−	5.24127i	1.41297	−	0.719944i	0.429848	−	0.902901i	$-0.358567\pi$
$53$	10.2866	−	5.24127i	1.41297	−	0.719944i	0.983121	+	0.182957i	$0.0585670\pi$
$54$	0.495272	+	1.32465i	0.0673979	+	0.180262i
$55$	4.12339	−	2.15226i	0.555998	−	0.290210i
$56$	−8.74233	−	9.21235i	−1.16824	−	1.23105i
$57$	4.30160	−	4.30160i	0.569760	−	0.569760i
$58$	−0.406820	−	1.99956i	−0.0534181	−	0.262554i
$59$	3.92021	+	2.84820i	0.510367	+	0.370804i	0.812963	−	0.582315i	$-0.197853\pi$
$59$	3.92021	+	2.84820i	0.510367	+	0.370804i	−0.302596	+	0.953119i	$0.597853\pi$
$60$	−0.963132	+	4.36719i	−0.124340	+	0.563802i
$61$	−11.1415	+	8.09476i	−1.42652	+	1.03643i	−0.435869	+	0.900010i	$0.643559\pi$
$61$	−11.1415	+	8.09476i	−1.42652	+	1.03643i	−0.990651	+	0.136417i	$0.956441\pi$
$62$	1.84414	+	1.68983i	0.234205	+	0.214609i
$63$	4.43493	−	0.702423i	0.558748	−	0.0884970i
$64$	7.98904	+	0.418557i	0.998630	+	0.0523196i
$65$	−4.85597	+	0.0477062i	−0.602309	+	0.00591722i
$66$	2.93894	−	0.128325i	0.361758	−	0.0157957i
$67$	3.16115	−	6.20411i	0.386196	−	0.757953i	−0.613295	−	0.789854i	$-0.710156\pi$
$67$	3.16115	−	6.20411i	0.386196	−	0.757953i	0.999491	+	0.0319014i	$0.0101563\pi$
$68$	4.30842	−	2.69223i	0.522473	−	0.326481i
$69$	4.27647	−	1.38951i	0.514826	−	0.167277i
$70$	12.9780	+	5.76110i	1.55117	+	0.688583i
$71$	8.47778	+	2.75460i	1.00613	+	0.326911i	0.765312	−	0.643660i	$-0.222585\pi$
$71$	8.47778	+	2.75460i	1.00613	+	0.326911i	0.240816	+	0.970571i	$0.422585\pi$
$72$	−1.72182	+	2.24396i	−0.202918	+	0.264453i
$73$	−0.968954	−	0.153467i	−0.113407	−	0.0179620i	0.0994727	−	0.995040i	$-0.468284\pi$
$73$	−0.968954	−	0.153467i	−0.113407	−	0.0179620i	−0.212880	+	0.977078i	$0.568284\pi$
$74$	−7.91392	−	9.94911i	−0.919975	−	1.15656i
$75$	−0.879045	−	4.92212i	−0.101503	−	0.568358i
$76$	11.8549	+	2.73686i	1.35985	+	0.313939i
$77$	1.46113	−	9.22520i	0.166511	−	1.05131i
$78$	−2.79480	−	1.27365i	−0.316449	−	0.144213i
$79$	4.20734	−	12.9489i	0.473363	−	1.45686i	−0.374790	−	0.927110i	$-0.622285\pi$
$79$	4.20734	−	12.9489i	0.473363	−	1.45686i	0.848153	−	0.529751i	$-0.177715\pi$
$80$	−8.42793	+	2.99500i	−0.942271	+	0.334851i
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	1.16812	−	10.2527i	0.128997	−	1.13222i
$83$	4.17938	+	2.12950i	0.458747	+	0.233743i	0.668063	−	0.744105i	$-0.267124\pi$
$83$	4.17938	+	2.12950i	0.458747	+	0.233743i	−0.209316	+	0.977848i	$0.567124\pi$
$84$	5.89172	+	6.77757i	0.642839	+	0.739494i
$85$	−3.29336	+	4.62785i	−0.357215	+	0.501961i
$86$	8.09073	+	2.24373i	0.872446	+	0.241948i
$87$	0.225714	+	1.42510i	0.0241991	+	0.152787i
$88$	3.33248	+	4.84870i	0.355243	+	0.516873i
$89$	9.07416	+	12.4895i	0.961859	+	1.32389i	0.946053	+	0.324011i	$0.105031\pi$
$89$	9.07416	+	12.4895i	0.961859	+	1.32389i	0.0158059	+	0.999875i	$0.494969\pi$
$90$	0.815097	−	3.05542i	0.0859188	−	0.322070i
$91$	−5.73188	+	7.88926i	−0.600865	+	0.827019i
$92$	6.88914	+	5.78061i	0.718242	+	0.602670i
$93$	−1.25064	−	1.25064i	−0.129685	−	0.129685i
$94$	2.41211	+	1.59653i	0.248790	+	0.164670i
$95$	−13.4138	+	2.25984i	−1.37623	+	0.231854i
$96$	−5.63082	−	0.542109i	−0.574693	−	0.0553287i
$97$	−4.76437	−	9.35061i	−0.483749	−	0.949410i	−0.995895	−	0.0905123i	$-0.971150\pi$
$97$	−4.76437	−	9.35061i	−0.483749	−	0.949410i	0.512147	−	0.858898i	$-0.328850\pi$
$98$	16.2006	−	9.16594i	1.63651	−	0.925899i
$99$	−2.08012			−0.209060
$100$	7.41671	−	6.70764i	0.741671	−	0.670764i
$101$	−11.3317			−1.12755			−0.563775	−	0.825928i	$-0.690652\pi$
$101$	−11.3317			−1.12755			−0.563775	+	0.825928i	$0.690652\pi$
$102$	−3.12666	+	1.76899i	−0.309585	+	0.175156i
$103$	8.24729	+	16.1862i	0.812630	+	1.59488i	0.803789	+	0.594915i	$0.202814\pi$
$103$	8.24729	+	16.1862i	0.812630	+	1.59488i	0.00884143	+	0.999961i	$0.497186\pi$
$104$	−0.801829	−	6.09011i	−0.0786258	−	0.597185i
$105$	−8.99042	−	4.47015i	−0.877375	−	0.436242i
$106$	−13.6148	−	9.01140i	−1.32239	−	0.875265i
$107$	−1.76369	−	1.76369i	−0.170502	−	0.170502i	0.616698	−	0.787200i	$-0.288470\pi$
$107$	−1.76369	−	1.76369i	−0.170502	−	0.170502i	−0.787200	+	0.616698i	$0.788470\pi$
$108$	1.28557	−	1.53210i	0.123704	−	0.147426i
$109$	−2.27144	+	3.12637i	−0.217564	+	0.299452i	−0.903823	−	0.427905i	$-0.859252\pi$
$109$	−2.27144	+	3.12637i	−0.217564	+	0.299452i	0.686259	+	0.727357i	$0.259252\pi$
$110$	−5.52065	−	3.57653i	−0.526374	−	0.341008i
$111$	5.28378	+	7.27250i	0.501514	+	0.690275i
$112$	−5.25105	+	17.1761i	−0.496178	+	1.62299i
$113$	−0.815870	−	5.15120i	−0.0767506	−	0.484584i	−0.995884	−	0.0906377i	$-0.971109\pi$
$113$	−0.815870	−	5.15120i	−0.0767506	−	0.484584i	0.919133	−	0.393947i	$-0.128891\pi$
$114$	−8.29031	−	2.29908i	−0.776458	−	0.215329i
$115$	−9.59253	−	3.01295i	−0.894508	−	0.280959i
$116$	−2.17788	+	1.89322i	−0.202211	+	0.175781i
$117$	1.93505	+	0.985959i	0.178896	+	0.0911520i
$118$	0.775737	−	6.80872i	0.0714124	−	0.626794i
$119$	3.52466	+	10.8478i	0.323105	+	0.994416i
$120$	6.04615	−	1.85581i	0.551936	−	0.169411i
$121$	2.06210	−	6.34648i	0.187463	−	0.576953i
$122$	17.7224	+	8.07653i	1.60451	+	0.731214i
$123$	−1.14145	+	7.20681i	−0.102921	+	0.649816i
$124$	0.795708	−	3.44667i	0.0714567	−	0.309521i
$125$	−4.78002	+	10.1070i	−0.427538	+	0.903998i
$126$	−3.95305	−	4.96964i	−0.352166	−	0.442731i
$127$	1.55836	+	0.246821i	0.138282	+	0.0219018i	0.225192	−	0.974314i	$-0.427699\pi$
$127$	1.55836	+	0.246821i	0.138282	+	0.0219018i	−0.0869095	+	0.996216i	$0.527699\pi$
$128$	−5.04835	−	10.1249i	−0.446215	−	0.894926i
$129$	−5.64635	−	1.83461i	−0.497134	−	0.161529i
$130$	3.44040	+	5.94383i	0.301743	+	0.521309i
$131$	9.13047	−	2.96667i	0.797733	−	0.259199i	0.118339	−	0.992973i	$-0.462243\pi$
$131$	9.13047	−	2.96667i	0.797733	−	0.259199i	0.679394	+	0.733774i	$0.262243\pi$
$132$	−2.20461	−	3.52808i	−0.191887	−	0.307080i
$133$	−12.4010	+	24.3384i	−1.07531	+	2.11041i
$134$	−9.83784	+	0.429556i	−0.849860	+	0.0371080i
$135$	−0.670058	+	2.13331i	−0.0576694	+	0.183606i
$136$	−6.31414	−	3.42823i	−0.541433	−	0.293968i
$137$	7.72018	−	1.22276i	0.659579	−	0.104467i	0.182333	−	0.983237i	$-0.441635\pi$
$137$	7.72018	−	1.22276i	0.659579	−	0.104467i	0.477246	+	0.878770i	$0.341635\pi$
$138$	−4.68841	−	4.29611i	−0.399104	−	0.365710i
$139$	−2.48469	+	1.80523i	−0.210748	+	0.153118i	−0.688152	−	0.725566i	$-0.741578\pi$
$139$	−2.48469	+	1.80523i	−0.210748	+	0.153118i	0.477404	+	0.878684i	$0.341578\pi$
$140$	−1.94670	−	19.9862i	−0.164526	−	1.68915i
$141$	−1.65475	−	1.20225i	−0.139355	−	0.101247i
$142$	−2.51335	−	12.3533i	−0.210915	−	1.03667i
$143$	3.19438	−	3.19438i	0.267127	−	0.267127i
$144$	3.96108	+	0.556649i	0.330090	+	0.0463874i
$145$	1.43642	−	2.88895i	0.119288	−	0.239914i
$146$	0.485877	+	1.29953i	0.0402115	+	0.107550i
$147$	−11.7274	+	5.97541i	−0.967260	+	0.492843i
$148$	−6.73481	+	16.6695i	−0.553598	+	1.37022i
$149$		−	16.9988i		−	1.39260i	−0.717753	−	0.696298i	$-0.754829\pi$
$149$		−	16.9988i		−	1.39260i	0.717753	−	0.696298i	$-0.245171\pi$
$150$	−5.44631	+	4.50973i	−0.444690	+	0.368218i
$151$		−	13.8505i		−	1.12714i	−0.826070	−	0.563568i	$-0.809428\pi$
$151$		−	13.8505i		−	1.12714i	0.826070	−	0.563568i	$-0.190572\pi$
$152$	−4.88701	−	16.4978i	−0.396389	−	1.33815i
$153$	2.26334	−	1.15323i	0.182980	−	0.0932331i
$154$	−12.3725	+	4.62593i	−0.997006	+	0.372768i
$155$	0.657019	+	3.89990i	0.0527731	+	0.313248i
$156$	0.378587	+	4.32699i	0.0303112	+	0.346437i
$157$	−1.80291	+	1.80291i	−0.143888	+	0.143888i	−0.775381	−	0.631494i	$-0.782442\pi$
$157$	−1.80291	+	1.80291i	−0.143888	+	0.143888i	0.631494	+	0.775381i	$0.282442\pi$
$158$	−18.8683	+	3.83885i	−1.50108	+	0.305403i
$159$	9.34001	+	6.78592i	0.740711	+	0.538158i
$160$	9.55562	+	8.28795i	0.755438	+	0.655220i
$161$	−16.3344	+	11.8676i	−1.28733	+	0.935300i
$162$	−0.955426	+	1.04267i	−0.0750654	+	0.0819199i
$163$	−20.4868	+	3.24480i	−1.60465	+	0.254152i	−0.893559	−	0.448946i	$-0.851800\pi$
$163$	−20.4868	+	3.24480i	−1.60465	+	0.254152i	−0.711093	+	0.703098i	$0.751800\pi$
$164$	−13.4332	+	5.70213i	−1.04895	+	0.445261i
$165$	3.78966	+	2.69687i	0.295024	+	0.209951i
$166$	−0.289369	−	6.62723i	−0.0224594	−	0.514373i
$167$	7.83909	−	15.3851i	0.606607	−	1.19053i	−0.359682	−	0.933075i	$-0.617115\pi$
$167$	7.83909	−	15.3851i	0.606607	−	1.19053i	0.966289	−	0.257459i	$-0.0828851\pi$
$168$	4.23932	−	11.9718i	0.327071	−	0.923644i
$169$	7.87803	−	2.55973i	0.606002	−	0.196902i
$170$	7.98975	+	0.830872i	0.612786	+	0.0637250i
$171$	5.78563	+	1.87987i	0.442439	+	0.143757i
$172$	−2.87261	−	11.5211i	−0.219034	−	0.878478i
$173$	−24.0008	−	3.80135i	−1.82474	−	0.289011i	−0.852457	−	0.522798i	$-0.824888\pi$
$173$	−24.0008	−	3.80135i	−1.82474	−	0.289011i	−0.972288	+	0.233787i	$0.924888\pi$
$174$	1.59692	−	1.27026i	0.121063	−	0.0962980i
$175$	10.5836	+	19.7999i	0.800045	+	1.49673i
$176$	3.64738	−	7.47845i	0.274932	−	0.563710i
$177$	−0.758025	+	4.78598i	−0.0569767	+	0.359737i
$178$	9.05372	−	19.8667i	0.678605	−	1.48907i
$179$	3.94945	−	12.1551i	0.295195	−	0.908518i	−0.687960	−	0.725748i	$-0.741494\pi$
$179$	3.94945	−	12.1551i	0.295195	−	0.908518i	0.983156	−	0.182770i	$-0.0585063\pi$
$180$	−4.32845	+	1.12451i	−0.322624	+	0.0838158i
$181$	−3.21626	−	9.89864i	−0.239063	−	0.735760i	−0.996556	−	0.0829173i	$-0.973576\pi$
$181$	−3.21626	−	9.89864i	−0.239063	−	0.735760i	0.757494	−	0.652843i	$-0.226424\pi$
$182$	13.7023	+	1.56114i	1.01568	+	0.115719i
$183$	−12.2706	−	6.25219i	−0.907069	−	0.462175i
$184$	2.31760	−	12.5052i	0.170855	−	0.921896i
$185$	−0.197464	−	20.0997i	−0.0145179	−	1.47776i
$186$	−0.668429	+	2.41030i	−0.0490116	+	0.176732i
$187$	−0.826591	−	5.21889i	−0.0604463	−	0.381643i
$188$	0.285335	−	4.08081i	0.0208102	−	0.297623i
$189$	2.63928	+	3.63265i	0.191979	+	0.264237i
$190$	12.1229	+	14.9369i	0.879486	+	1.08364i
$191$	−1.34116	+	1.84595i	−0.0970428	+	0.133568i	−0.854777	−	0.518995i	$-0.826306\pi$
$191$	−1.34116	+	1.84595i	−0.0970428	+	0.133568i	0.757734	+	0.652563i	$0.226306\pi$
$192$	3.25401	+	7.30831i	0.234838	+	0.527432i
$193$	2.06189	+	2.06189i	0.148418	+	0.148418i	0.777411	−	0.628993i	$-0.216533\pi$
$193$	2.06189	+	2.06189i	0.148418	+	0.148418i	−0.628993	+	0.777411i	$0.716533\pi$
$194$	−8.19147	+	12.3760i	−0.588113	+	0.888547i
$195$	−2.24707	−	4.30504i	−0.160916	−	0.308291i
$196$	−22.5641	−	13.5577i	−1.61172	−	0.968408i
$197$	2.02095	+	3.96633i	0.143986	+	0.282589i	0.951725	−	0.306951i	$-0.0993088\pi$
$197$	2.02095	+	3.96633i	0.143986	+	0.282589i	−0.807739	+	0.589541i	$0.799309\pi$
$198$	1.44859	+	2.56036i	0.102947	+	0.181957i
$199$	18.6400			1.32135			0.660676	−	0.750671i	$-0.270270\pi$
$199$	18.6400			1.32135			0.660676	+	0.750671i	$0.270270\pi$
$200$	−13.4212	−	4.45781i	−0.949020	−	0.315215i
$201$	6.96303			0.491135
$202$	7.89137	+	13.9479i	0.555235	+	0.981368i
$203$	−2.94130	−	5.77262i	−0.206439	−	0.405159i
$204$	4.35478	+	2.61658i	0.304895	+	0.183197i
$205$	11.4231	−	11.6498i	0.797825	−	0.813657i
$206$	14.1797	−	21.4233i	0.987947	−	1.49263i
$207$	3.17954	+	3.17954i	0.220993	+	0.220993i
$208$	−6.93773	+	5.22807i	−0.481045	+	0.362502i
$209$	7.43794	−	10.2374i	0.514493	−	0.708139i
$210$	0.758730	+	14.1790i	0.0523574	+	0.978444i
$211$	6.16496	+	8.48534i	0.424413	+	0.584155i	0.966660	−	0.256065i	$-0.0824261\pi$
$211$	6.16496	+	8.48534i	0.424413	+	0.584155i	−0.542246	+	0.840220i	$0.682426\pi$
$212$	−1.61054	+	23.0335i	−0.110612	+	1.58195i
$213$	1.39447	+	8.80432i	0.0955473	+	0.603262i
$214$	−0.942640	+	3.39909i	−0.0644376	+	0.232357i
$215$	7.90820	+	10.6628i	0.539335	+	0.727199i
$216$	−2.78107	−	0.515417i	−0.189228	−	0.0350697i
$217$	7.07609	+	3.60545i	0.480356	+	0.244754i
$218$	5.42996	+	0.618651i	0.367763	+	0.0419003i
$219$	−0.303155	−	0.933017i	−0.0204853	−	0.0630474i
$220$	−0.557671	+	9.28587i	−0.0375981	+	0.626053i
$221$	−1.70476	+	5.24671i	−0.114675	+	0.352932i
$222$	5.27188	−	11.5682i	0.353825	−	0.776404i
$223$	−2.55430	+	16.1272i	−0.171049	+	1.07996i	0.741489	+	0.670965i	$0.234120\pi$
$223$	−2.55430	+	16.1272i	−0.171049	+	1.07996i	−0.912538	+	0.408993i	$0.865880\pi$
$224$	24.7983	−	5.49800i	1.65691	−	0.367351i
$225$	3.98656	−	3.01783i	0.265771	−	0.201189i
$226$	−5.77228	+	4.59150i	−0.383966	+	0.305422i
$227$	−9.94776	−	1.57557i	−0.660256	−	0.104574i	−0.182691	−	0.983170i	$-0.558481\pi$
$227$	−9.94776	−	1.57557i	−0.660256	−	0.104574i	−0.477565	+	0.878596i	$0.658481\pi$
$228$	2.94347	+	11.8053i	0.194936	+	0.781827i
$229$	−14.6534	−	4.76117i	−0.968323	−	0.314627i	−0.218184	−	0.975908i	$-0.570013\pi$
$229$	−14.6534	−	4.76117i	−0.968323	−	0.314627i	−0.750139	+	0.661281i	$0.770013\pi$
$230$	2.97166	+	13.9053i	0.195945	+	0.916891i
$231$	8.88305	−	2.88628i	0.584462	−	0.189903i
$232$	3.84697	+	1.36225i	0.252566	+	0.0894360i
$233$	−2.87986	+	5.65205i	−0.188666	+	0.370278i	−0.965893	−	0.258943i	$-0.916626\pi$
$233$	−2.87986	+	5.65205i	−0.188666	+	0.370278i	0.777227	+	0.629221i	$0.216626\pi$
$234$	−0.133978	−	3.06841i	−0.00875842	−	0.200588i
$235$	1.45599	+	4.33568i	0.0949783	+	0.282828i
$236$	−8.92085	+	3.78673i	−0.580698	+	0.246495i
$237$	13.4476	−	2.12989i	0.873516	−	0.138351i
$238$	10.8976	−	11.8928i	0.706389	−	0.770893i
$239$	0.780902	−	0.567359i	0.0505124	−	0.0366994i	−0.562243	−	0.826972i	$-0.690061\pi$
$239$	0.780902	−	0.567359i	0.0505124	−	0.0366994i	0.612755	+	0.790273i	$0.290061\pi$
$240$	−6.49476	−	6.14964i	−0.419235	−	0.396957i
$241$	19.0484	+	13.8395i	1.22701	+	0.891478i	0.996663	−	0.0816289i	$-0.0260122\pi$
$241$	19.0484	+	13.8395i	1.22701	+	0.891478i	0.230352	+	0.973107i	$0.426012\pi$
$242$	−9.24771	+	1.88149i	−0.594465	+	0.120947i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−2.40070	−	27.4384i	−0.153689	−	1.75657i
$245$	29.1125	+	4.31825i	1.85993	+	0.275883i
$246$	9.66552	−	3.61382i	0.616251	−	0.230409i
$247$	−11.7717	+	5.99796i	−0.749013	+	0.381641i
$248$	−4.79653	+	1.42084i	−0.304580	+	0.0902233i
$249$			4.69063i			0.297256i
$250$	15.7692	−	1.15490i	0.997329	−	0.0730426i
$251$		−	4.80127i		−	0.303053i	−0.988453	−	0.151527i	$-0.951581\pi$
$251$		−	4.80127i		−	0.303053i	0.988453	−	0.151527i	$-0.0484190\pi$
$252$	−3.36408	+	8.32652i	−0.211917	+	0.524521i
$253$	8.33391	−	4.24634i	0.523949	−	0.266965i
$254$	−0.781434	−	2.09002i	−0.0490315	−	0.131140i
$255$	−5.61860	−	0.833404i	−0.351850	−	0.0521898i
$256$	−8.94680	+	13.2648i	−0.559175	+	0.829050i
$257$	−21.3134	+	21.3134i	−1.32949	+	1.32949i	−0.423684	+	0.905810i	$0.639263\pi$
$257$	−21.3134	+	21.3134i	−1.32949	+	1.32949i	−0.905810	+	0.423684i	$0.860737\pi$
$258$	1.67393	+	8.22753i	0.104214	+	0.512223i
$259$	−32.6550	−	23.7253i	−2.02908	−	1.47422i
$260$	4.92019	−	8.37393i	0.305137	−	0.519329i
$261$	−1.16730	+	0.848095i	−0.0722542	+	0.0524958i
$262$	−10.0100	−	9.17242i	−0.618419	−	0.566674i
$263$	18.2989	−	2.89826i	1.12836	−	0.178714i	0.435777	−	0.900055i	$-0.356474\pi$
$263$	18.2989	−	2.89826i	1.12836	−	0.178714i	0.692581	+	0.721340i	$0.256474\pi$
$264$	−2.80731	+	5.17053i	−0.172778	+	0.318224i
$265$	−8.21813	−	24.4721i	−0.504835	−	1.50331i
$266$	38.5934	−	1.68513i	2.36631	−	0.103322i
$267$	−7.00865	+	13.7553i	−0.428923	+	0.841808i
$268$	7.37976	+	11.8099i	0.450790	+	0.721407i
$269$	23.2869	−	7.56638i	1.41983	−	0.461330i	0.504281	−	0.863540i	$-0.331758\pi$
$269$	23.2869	−	7.56638i	1.41983	−	0.461330i	0.915548	+	0.402209i	$0.131758\pi$
$270$	3.09245	−	0.660877i	0.188200	−	0.0402197i
$271$	−11.5568	−	3.75503i	−0.702026	−	0.228102i	−0.0638128	−	0.997962i	$-0.520326\pi$
$271$	−11.5568	−	3.75503i	−0.702026	−	0.228102i	−0.638213	+	0.769860i	$0.720326\pi$
$272$	0.177442	+	10.1593i	0.0107590	+	0.615996i
$273$	−9.63160	−	1.52550i	−0.582931	−	0.0923272i
$274$	−6.88135	−	8.65099i	−0.415717	−	0.522625i
$275$	−3.40768	−	9.82653i	−0.205491	−	0.592562i
$276$	−2.02296	+	8.76261i	−0.121768	+	0.527447i
$277$	−1.14142	+	7.20665i	−0.0685813	+	0.433005i	0.929377	+	0.369133i	$0.120345\pi$
$277$	−1.14142	+	7.20665i	−0.0685813	+	0.433005i	−0.997958	+	0.0638728i	$0.979655\pi$
$278$	3.95232	+	1.80116i	0.237045	+	0.108027i
$279$	0.546548	−	1.68210i	0.0327210	−	0.100705i
$280$	−23.2447	+	16.3145i	−1.38914	+	0.974975i
$281$	3.36566	+	10.3584i	0.200779	+	0.617933i	0.999860	+	0.0167105i	$0.00531937\pi$
$281$	3.36566	+	10.3584i	0.200779	+	0.617933i	−0.799082	+	0.601222i	$0.794681\pi$
$282$	−0.327445	+	2.87402i	−0.0194991	+	0.171145i
$283$	−3.85499	−	1.96422i	−0.229156	−	0.116761i	0.335643	−	0.941989i	$-0.391046\pi$
$283$	−3.85499	−	1.96422i	−0.229156	−	0.116761i	−0.564799	+	0.825229i	$0.691046\pi$
$284$	−13.4550	+	11.6964i	−0.798408	+	0.694053i
$285$	−8.10327	−	10.9259i	−0.479997	−	0.647192i
$286$	−6.15641	−	1.70730i	−0.364036	−	0.100955i
$287$	−5.12533	−	32.3601i	−0.302539	−	1.91016i
$288$	−2.07332	−	5.26321i	−0.122171	−	0.310138i
$289$	−6.19958	−	8.53299i	−0.364681	−	0.501941i
$290$	−4.55622	+	0.243807i	−0.267551	+	0.0143169i
$291$	6.16847	−	8.49017i	0.361602	−	0.497703i
$292$	1.26118	−	1.50303i	0.0738051	−	0.0879585i
$293$	−11.6800	−	11.6800i	−0.682355	−	0.682355i	0.278176	−	0.960530i	$-0.410270\pi$
$293$	−11.6800	−	11.6800i	−0.682355	−	0.682355i	−0.960530	+	0.278176i	$0.910270\pi$
$294$	15.5218	+	10.2736i	0.905252	+	0.599170i
$295$	7.58600	−	7.73653i	0.441674	−	0.450438i
$296$	25.2080	−	3.31891i	1.46519	−	0.192908i
$297$	−0.944357	−	1.85340i	−0.0547971	−	0.107545i
$298$	−20.9233	+	11.8379i	−1.21205	+	0.685750i
$299$	−9.76542			−0.564749
$300$	9.34367	+	3.56313i	0.539457	+	0.205718i
$301$	26.6580			1.53654
$302$	−17.0481	+	9.64540i	−0.981007	+	0.555031i
$303$	−5.14450	−	10.0967i	−0.295544	−	0.580038i
$304$	−16.9033	+	17.5042i	−0.969470	+	1.00394i
$305$	14.2492	+	27.2992i	0.815906	+	1.56315i
$306$	−2.99565	−	1.98277i	−0.171250	−	0.113347i
$307$	7.80956	+	7.80956i	0.445715	+	0.445715i	0.893927	−	0.448212i	$-0.147939\pi$
$307$	7.80956	+	7.80956i	0.445715	+	0.445715i	−0.448212	+	0.893927i	$0.647939\pi$
$308$	14.3101	+	12.0074i	0.815392	+	0.684187i
$309$	−10.6778	+	14.6968i	−0.607441	+	0.836071i
$310$	4.34271	−	3.52458i	0.246650	−	0.200182i
$311$	2.70660	+	3.72531i	0.153477	+	0.211243i	0.878831	−	0.477133i	$-0.158324\pi$
$311$	2.70660	+	3.72531i	0.153477	+	0.211243i	−0.725354	+	0.688376i	$0.758324\pi$
$312$	5.06231	−	3.47929i	0.286597	−	0.196976i
$313$	−2.19947	−	13.8869i	−0.124321	−	0.784933i	−0.968526	−	0.248912i	$-0.919927\pi$
$313$	−2.19947	−	13.8869i	−0.124321	−	0.784933i	0.844205	−	0.536021i	$-0.180073\pi$
$314$	3.47468	+	0.963602i	0.196087	+	0.0543792i
$315$	−0.0986345	−	10.0399i	−0.00555743	−	0.565686i
$316$	17.8649	+	20.5510i	1.00498	+	1.15608i
$317$	−4.05926	−	2.06830i	−0.227991	−	0.116167i	0.336264	−	0.941768i	$-0.390837\pi$
$317$	−4.05926	−	2.06830i	−0.227991	−	0.116167i	−0.564255	+	0.825601i	$0.690837\pi$
$318$	1.84822	−	16.2220i	0.103643	−	0.909684i
$319$	0.927465	+	2.85444i	0.0519281	+	0.159818i
$320$	3.54688	−	17.5334i	0.198277	−	0.980146i
$321$	0.770759	−	2.37215i	0.0430196	−	0.132401i
$322$	25.9827	+	11.8409i	1.44796	+	0.659868i
$323$	−2.41739	+	15.2628i	−0.134507	+	0.849244i
$324$	1.94874	+	0.449891i	0.108263	+	0.0249940i
$325$	−1.48765	+	10.7564i	−0.0825201	+	0.596659i
$326$	18.2608	+	22.9569i	1.01137	+	1.27147i
$327$	−3.81683	−	0.604526i	−0.211071	−	0.0334304i
$328$	16.3734	+	12.5635i	0.904067	+	0.693703i
$329$	8.73470	+	2.83808i	0.481559	+	0.156468i
$330$	0.680384	−	6.54265i	0.0374539	−	0.360161i
$331$	24.1401	−	7.84361i	1.32686	−	0.431124i	0.442016	−	0.897007i	$-0.354263\pi$
$331$	24.1401	−	7.84361i	1.32686	−	0.431124i	0.884846	+	0.465883i	$0.154263\pi$
$332$	−7.95573	+	4.97135i	−0.436627	+	0.272838i
$333$	−4.08106	+	8.00952i	−0.223641	+	0.438919i
$334$	−24.3961	+	1.06522i	−1.33490	+	0.0582864i
$335$	−12.6855	−	9.02753i	−0.693085	−	0.493226i
$336$	−17.6879	+	3.11906i	−0.964956	+	0.170159i
$337$	2.81142	−	0.445285i	0.153148	−	0.0242562i	−0.0793897	−	0.996844i	$-0.525297\pi$
$337$	2.81142	−	0.445285i	0.153148	−	0.0242562i	0.232537	+	0.972587i	$0.425297\pi$
$338$	−8.63691	−	7.91422i	−0.469786	−	0.430477i
$339$	4.21936	−	3.06554i	0.229164	−	0.166497i
$340$	−4.54133	−	10.4129i	−0.246288	−	0.564721i
$341$	−2.97641	−	2.16249i	−0.161182	−	0.117105i
$342$	−1.71522	−	8.43048i	−0.0927487	−	0.455868i
$343$	19.5646	−	19.5646i	1.05639	−	1.05639i
$344$	−12.1805	+	11.5591i	−0.656729	+	0.623223i
$345$	−1.67036	−	9.91486i	−0.0899294	−	0.533798i
$346$	12.0351	+	32.1890i	0.647009	+	1.73049i
$347$	−6.72865	+	3.42842i	−0.361213	+	0.184047i	−0.625173	−	0.780487i	$-0.714971\pi$
$347$	−6.72865	+	3.42842i	−0.361213	+	0.184047i	0.263960	+	0.964534i	$0.414971\pi$
$348$	−2.67561	−	1.08100i	−0.143428	−	0.0579477i
$349$			0.864340i			0.0462670i	0.999732	+	0.0231335i	$0.00736428\pi$
$349$			0.864340i			0.0462670i	−0.999732	+	0.0231335i	$0.992636\pi$
$350$	17.0007	−	26.8156i	0.908725	−	1.43335i
$351$			2.17176i			0.115920i
$352$	−11.7450	+	0.718516i	−0.626011	+	0.0382970i
$353$	−0.498575	+	0.254037i	−0.0265365	+	0.0135210i	−0.467208	−	0.884147i	$-0.654740\pi$
$353$	−0.498575	+	0.254037i	−0.0265365	+	0.0135210i	0.440672	+	0.897668i	$0.354740\pi$
$354$	6.41879	−	2.39991i	0.341155	−	0.127554i
$355$	8.87424	−	17.8480i	0.470996	−	0.947273i
$356$	−30.7583	+	2.69117i	−1.63018	+	0.142632i
$357$	−8.06530	+	8.06530i	−0.426861	+	0.426861i
$358$	−17.7117	+	3.60354i	−0.936095	+	0.190453i
$359$	8.80968	+	6.40061i	0.464957	+	0.337811i	0.795473	−	0.605989i	$-0.207223\pi$
$359$	8.80968	+	6.40061i	0.464957	+	0.337811i	−0.330516	+	0.943801i	$0.607223\pi$
$360$	4.39843	+	4.54464i	0.231818	+	0.239524i
$361$	−14.5683	+	10.5845i	−0.766755	+	0.557080i
$362$	−9.94412	+	10.8522i	−0.522651	+	0.570377i
$363$	6.59093	−	1.04390i	0.345934	−	0.0547906i
$364$	−7.62065	−	17.9529i	−0.399431	−	0.940986i
$365$	−0.657348	+	2.09285i	−0.0344072	+	0.109545i
$366$	0.849585	+	19.4575i	0.0444085	+	1.01706i
$367$	2.00355	−	3.93219i	0.104585	−	0.205259i	−0.832784	−	0.553598i	$-0.813254\pi$
$367$	2.00355	−	3.93219i	0.104585	−	0.205259i	0.937368	+	0.348339i	$0.113254\pi$
$368$	−17.0062	+	5.85591i	−0.886509	+	0.305260i
$369$	−6.93952	+	2.25479i	−0.361257	+	0.117380i
$370$	−24.6026	+	14.2404i	−1.27903	+	0.740323i
$371$	−49.3018	−	16.0191i	−2.55962	−	0.831671i
$372$	3.43225	−	0.855777i	0.177954	−	0.0443700i
$373$	30.4365	+	4.82066i	1.57594	+	0.249604i	0.882290	−	0.470707i	$-0.156001\pi$
$373$	30.4365	+	4.82066i	1.57594	+	0.249604i	0.693651	+	0.720311i	$0.256001\pi$
$374$	−5.84812	+	4.65183i	−0.302399	+	0.240541i
$375$	−11.1755	+	0.329456i	−0.577100	+	0.0170131i
$376$	−5.22164	+	2.49065i	−0.269285	+	0.128445i
$377$	0.490197	−	3.09498i	0.0252464	−	0.159400i
$378$	2.63333	−	5.77836i	0.135444	−	0.297207i
$379$	−5.63128	+	17.3313i	−0.289259	+	0.890248i	0.695830	+	0.718206i	$0.255037\pi$
$379$	−5.63128	+	17.3313i	−0.289259	+	0.890248i	−0.985090	+	0.172042i	$0.944963\pi$
$380$	9.94300	−	25.3236i	0.510065	−	1.29907i
$381$	0.487564	+	1.50057i	0.0249786	+	0.0768763i
$382$	3.20609	+	0.365279i	0.164038	+	0.0186893i
$383$	25.7096	+	13.0997i	1.31370	+	0.669364i	0.963600	−	0.267348i	$-0.0861473\pi$
$383$	25.7096	+	13.0997i	1.31370	+	0.669364i	0.350101	+	0.936712i	$0.386147\pi$
$384$	6.72948	−	9.09473i	0.343412	−	0.464114i
$385$	−19.9255	−	6.25847i	−1.01550	−	0.318961i
$386$	1.10202	−	3.97381i	0.0560915	−	0.202261i
$387$	−0.928740	−	5.86383i	−0.0472105	−	0.298075i
$388$	20.9377	+	1.46399i	1.06295	+	0.0743231i
$389$	−7.36949	−	10.1432i	−0.373648	−	0.514282i	0.580240	−	0.814446i	$-0.302959\pi$
$389$	−7.36949	−	10.1432i	−0.373648	−	0.514282i	−0.953888	+	0.300163i	$0.902959\pi$
$390$	−3.73409	+	5.76386i	−0.189083	+	0.291864i
$391$	−6.71377	+	9.24071i	−0.339530	+	0.467323i
$392$	−0.974202	+	37.2149i	−0.0492046	+	1.87964i
$393$	6.78847	+	6.78847i	0.342433	+	0.342433i
$394$	3.47465	−	5.24965i	0.175050	−	0.264474i
$395$	−27.2608	−	13.5544i	−1.37164	−	0.681996i
$396$	2.14267	−	3.56604i	0.107673	−	0.179200i
$397$	−0.707656	−	1.38885i	−0.0355163	−	0.0697046i	0.872566	−	0.488495i	$-0.162454\pi$
$397$	−0.707656	−	1.38885i	−0.0355163	−	0.0697046i	−0.908083	+	0.418791i	$0.862454\pi$
$398$	−12.9808	−	22.9433i	−0.650668	−	1.15005i
$399$	−27.3156			−1.36749
$400$	3.85947	+	19.6241i	0.192973	+	0.981204i
$401$	32.2568			1.61083			0.805415	−	0.592712i	$-0.201943\pi$
$401$	32.2568			1.61083			0.805415	+	0.592712i	$0.201943\pi$
$402$	−4.84903	−	8.57057i	−0.241847	−	0.427461i
$403$	1.74383	+	3.42246i	0.0868665	+	0.170485i
$404$	11.6725	−	19.4265i	0.580726	−	0.966503i
$405$	−2.20500	+	0.371477i	−0.109567	+	0.0184589i
$406$	−5.05703	+	7.64038i	−0.250976	+	0.379186i
$407$	13.2221	+	13.2221i	0.655395	+	0.655395i
$408$	0.188017	−	7.18233i	0.00930823	−	0.355578i
$409$	13.1897	−	18.1540i	0.652187	−	0.897659i	−0.347004	−	0.937864i	$-0.612801\pi$
$409$	13.1897	−	18.1540i	0.652187	−	0.897659i	0.999191	+	0.0402050i	$0.0128011\pi$
$410$	−22.2943	−	5.94747i	−1.10104	−	0.293725i
$411$	4.59437	+	6.32361i	0.226624	+	0.311921i
$412$	−36.2440	−	2.53423i	−1.78561	−	0.124852i
$413$	−3.40369	−	21.4901i	−0.167485	−	1.05746i
$414$	1.69937	−	6.12780i	0.0835196	−	0.301165i
$415$	6.08137	−	8.54558i	0.298523	−	0.419486i
$416$	11.2665	+	4.89861i	0.552384	+	0.240174i
$417$	−2.73650	−	1.39431i	−0.134007	−	0.0682799i
$418$	−17.7807	−	2.02580i	−0.869681	−	0.0990853i
$419$	7.45146	+	22.9332i	0.364028	+	1.12036i	0.950588	+	0.310456i	$0.100482\pi$
$419$	7.45146	+	22.9332i	0.364028	+	1.12036i	−0.586560	+	0.809906i	$0.699518\pi$
$420$	16.9241	−	10.8081i	0.825811	−	0.527381i
$421$	4.41337	−	13.5829i	0.215094	−	0.661992i	−0.784053	−	0.620694i	$-0.786851\pi$
$421$	4.41337	−	13.5829i	0.215094	−	0.661992i	0.999147	−	0.0412979i	$-0.0131493\pi$
$422$	6.15107	−	13.4974i	0.299430	−	0.657043i
$423$	0.319969	−	2.02020i	0.0155574	−	0.0982256i
$424$	29.4728	−	14.0581i	1.43133	−	0.682722i
$425$	9.15570	+	8.80280i	0.444116	+	0.426999i
$426$	9.86585	−	7.84769i	0.478002	−	0.380222i
$427$	61.0761	+	9.67351i	2.95568	+	0.468134i
$428$	4.84027	−	1.20684i	0.233964	−	0.0583350i
$429$	4.29643	+	1.39599i	0.207434	+	0.0673993i
$430$	7.61729	−	17.1595i	0.367338	−	0.827504i
$431$	−25.9632	+	8.43597i	−1.25060	+	0.406346i	−0.858138	−	0.513420i	$-0.828378\pi$
$431$	−25.9632	+	8.43597i	−1.25060	+	0.406346i	−0.392467	+	0.919766i	$0.628378\pi$
$432$	1.30231	+	3.78206i	0.0626576	+	0.181964i
$433$	14.2105	−	27.8897i	0.682913	−	1.34029i	−0.245738	−	0.969336i	$-0.579030\pi$
$433$	14.2105	−	27.8897i	0.682913	−	1.34029i	0.928651	−	0.370956i	$-0.120970\pi$
$434$	−0.489930	−	11.2205i	−0.0235174	−	0.538603i
$435$	3.22619	−	0.0316948i	0.154684	−	0.00151965i
$436$	−3.01992	−	7.11439i	−0.144628	−	0.340717i
$437$	−27.0174	+	4.27913i	−1.29242	+	0.204699i
$438$	−0.937303	+	1.02289i	−0.0447861	+	0.0488757i
$439$	20.9443	−	15.2169i	0.999616	−	0.726263i	0.0376099	−	0.999292i	$-0.488026\pi$
$439$	20.9443	−	15.2169i	0.999616	−	0.726263i	0.962006	+	0.273029i	$0.0880256\pi$
$440$	11.8180	−	5.78022i	0.563402	−	0.275561i
$441$	−10.6483	−	7.73641i	−0.507060	−	0.368401i
$442$	7.64519	−	1.55545i	0.363645	−	0.0739854i
$443$	−15.0847	+	15.0847i	−0.716694	+	0.716694i	−0.967927	−	0.251233i	$-0.919164\pi$
$443$	−15.0847	+	15.0847i	−0.716694	+	0.716694i	0.251233	+	0.967927i	$0.419164\pi$
$444$	−17.9102	+	1.56704i	−0.849979	+	0.0743682i
$445$	30.6023	−	15.9732i	1.45069	−	0.757204i
$446$	21.6293	−	8.08691i	1.02417	−	0.382926i
$447$	15.1460	−	7.71729i	0.716383	−	0.365015i
$448$	−24.0367	−	26.6946i	−1.13563	−	1.26120i
$449$			4.78357i			0.225750i	0.993609	+	0.112875i	$0.0360060\pi$
$449$			4.78357i			0.225750i	−0.993609	+	0.112875i	$0.963994\pi$
$450$	−6.49077	−	2.80533i	−0.305978	−	0.132244i
$451$			15.1779i			0.714701i
$452$	9.67131	+	3.90740i	0.454900	+	0.183789i
$453$	12.3409	−	6.28798i	0.579824	−	0.295435i
$454$	4.98826	+	13.3416i	0.234111	+	0.626152i
$455$	15.5695	+	15.2665i	0.729907	+	0.715705i
$456$	12.4810	−	11.8442i	0.584475	−	0.554655i
$457$	4.80645	−	4.80645i	0.224836	−	0.224836i	−0.585695	−	0.810531i	$-0.699178\pi$
$457$	4.80645	−	4.80645i	0.224836	−	0.224836i	0.810531	+	0.585695i	$0.199178\pi$
$458$	4.34418	+	21.3520i	0.202990	+	0.997714i
$459$	2.05507	+	1.49310i	0.0959224	+	0.0696917i
$460$	15.0462	−	13.3413i	0.701531	−	0.622043i
$461$	−0.725727	+	0.527271i	−0.0338005	+	0.0245575i	−0.604557	−	0.796562i	$-0.706650\pi$
$461$	−0.725727	+	0.527271i	−0.0338005	+	0.0245575i	0.570757	+	0.821119i	$0.306650\pi$
$462$	−9.73874	−	8.92386i	−0.453087	−	0.415176i
$463$	−29.7408	+	4.71048i	−1.38217	+	0.218914i	−0.802848	−	0.596184i	$-0.796683\pi$
$463$	−29.7408	+	4.71048i	−1.38217	+	0.218914i	−0.579323	+	0.815098i	$0.696683\pi$
$464$	−1.00227	−	5.68377i	−0.0465290	−	0.263862i
$465$	−3.17656	+	2.35593i	−0.147309	+	0.109253i
$466$	8.96244	−	0.391333i	0.415177	−	0.0181282i
$467$	−7.71551	+	15.1425i	−0.357031	+	0.700713i	−0.997749	−	0.0670634i	$-0.978637\pi$
$467$	−7.71551	+	15.1425i	−0.357031	+	0.700713i	0.640717	+	0.767777i	$0.278637\pi$
$468$	−3.68350	+	2.30174i	−0.170270	+	0.106398i
$469$	−29.7352	+	9.66156i	−1.37305	+	0.446130i
$470$	4.32270	−	4.81147i	0.199391	−	0.221937i
$471$	−2.42490	−	0.787899i	−0.111734	−	0.0363045i
$472$	10.8734	+	8.34332i	0.500489	+	0.384032i
$473$	−12.1975	−	1.93189i	−0.560842	−	0.0888286i
$474$	−11.9865	−	15.0690i	−0.550557	−	0.692141i
$475$	0.597587	+	30.4110i	0.0274192	+	1.39535i
$476$	−22.2275	−	5.13149i	−1.01879	−	0.235201i
$477$	−1.80602	+	11.4028i	−0.0826919	+	0.522096i
$478$	−1.24216	−	0.566081i	−0.0568151	−	0.0258919i
$479$	−6.57174	+	20.2257i	−0.300270	+	0.924137i	0.681130	+	0.732163i	$0.261489\pi$
$479$	−6.57174	+	20.2257i	−0.300270	+	0.924137i	−0.981400	+	0.191974i	$0.938511\pi$
$480$	−3.04646	+	12.2768i	−0.139051	+	0.560355i
$481$	−6.03282	−	18.5671i	−0.275073	−	0.846587i
$482$	3.76933	−	33.0838i	0.171688	−	1.50692i
$483$	−17.9898	−	9.16626i	−0.818564	−	0.417079i
$484$	8.75593	+	10.0724i	0.397997	+	0.457838i
$485$	−22.2454	+	7.47037i	−1.01011	+	0.339212i
$486$	−1.36278	−	0.377928i	−0.0618170	−	0.0171432i
$487$	−0.734244	−	4.63584i	−0.0332718	−	0.210070i	0.965452	−	0.260582i	$-0.0839145\pi$
$487$	−0.734244	−	4.63584i	−0.0332718	−	0.210070i	−0.998723	+	0.0505125i	$0.983915\pi$
$488$	−32.1012	+	22.0629i	−1.45315	+	0.998742i
$489$	−12.1920	−	16.7808i	−0.551339	−	0.758854i
$490$	−14.9587	−	38.8409i	−0.675763	−	1.75465i
$491$	12.0866	−	16.6358i	0.545460	−	0.750762i	−0.443927	−	0.896063i	$-0.646415\pi$
$491$	12.0866	−	16.6358i	0.545460	−	0.750762i	0.989387	+	0.145301i	$0.0464151\pi$
$492$	−11.1792	−	9.38032i	−0.503995	−	0.422898i
$493$	−2.59167	−	2.59167i	−0.116723	−	0.116723i
$494$	15.5804	+	10.3124i	0.700996	+	0.463977i
$495$	−0.682458	+	4.60096i	−0.0306742	+	0.206798i
$496$	5.08914	+	4.91442i	0.228509	+	0.220664i
$497$	−18.1714	−	35.6635i	−0.815100	−	1.59972i
$498$	5.77354	−	3.26653i	0.258718	−	0.146377i
$499$	−23.3972			−1.04740			−0.523702	−	0.851901i	$-0.675450\pi$
$499$	−23.3972			−1.04740			−0.523702	+	0.851901i	$0.675450\pi$
$500$	−12.4031	−	18.6055i	−0.554684	−	0.832061i
$501$	17.2671			0.771436
$502$	−5.90972	+	3.34358i	−0.263764	+	0.149231i
$503$	−6.50796	−	12.7726i	−0.290176	−	0.569502i	0.699193	−	0.714933i	$-0.253543\pi$
$503$	−6.50796	−	12.7726i	−0.290176	−	0.569502i	−0.989368	+	0.145432i	$0.953543\pi$
$504$	12.5916	−	1.65782i	0.560873	−	0.0738450i
$505$	−3.71778	+	25.0643i	−0.165439	+	1.11535i
$506$	−11.0304	−	7.30081i	−0.490360	−	0.324560i
$507$	5.85728	+	5.85728i	0.260131	+	0.260131i
$508$	−2.02835	+	2.41732i	−0.0899936	+	0.107251i
$509$	−16.0722	+	22.1215i	−0.712388	+	0.980517i	0.287355	+	0.957824i	$0.407224\pi$
$509$	−16.0722	+	22.1215i	−0.712388	+	0.980517i	−0.999742	+	0.0226933i	$0.992776\pi$
$510$	2.88696	+	7.49613i	0.127837	+	0.331934i
$511$	2.58922	+	3.56375i	0.114540	+	0.157651i
$512$	22.5577	+	1.77477i	0.996919	+	0.0784346i
$513$	0.951650	+	6.00848i	0.0420164	+	0.265281i
$514$	41.0765	+	11.3914i	1.81181	+	0.502454i
$515$	38.5076	−	12.9315i	1.69685	−	0.569828i
$516$	8.96127	−	7.79000i	0.394498	−	0.342936i
$517$	−3.79092	−	1.93157i	−0.166725	−	0.0849505i
$518$	−6.46183	+	56.7161i	−0.283917	+	2.49196i
$519$	−7.50909	−	23.1106i	−0.329613	−	1.01444i
$520$	−13.7336	−	0.224535i	−0.602258	−	0.00984649i
$521$	−8.57371	+	26.3872i	−0.375621	+	1.15604i	0.567437	+	0.823417i	$0.307935\pi$
$521$	−8.57371	+	26.3872i	−0.375621	+	1.15604i	−0.943059	+	0.332627i	$0.892065\pi$
$522$	1.85680	+	0.846185i	0.0812698	+	0.0370365i
$523$	2.86352	−	18.0796i	0.125213	−	0.790565i	−0.842534	−	0.538643i	$-0.818937\pi$
$523$	2.86352	−	18.0796i	0.125213	−	0.790565i	0.967747	−	0.251922i	$-0.0810627\pi$
$524$	−4.31911	+	18.7086i	−0.188681	+	0.817289i
$525$	−12.8370	+	18.4190i	−0.560253	+	0.803872i
$526$	−16.3106	−	20.5052i	−0.711177	−	0.894068i
$527$	4.43746	+	0.702825i	0.193299	+	0.0306155i
$528$	8.31923	−	0.145304i	0.362048	−	0.00632352i
$529$	2.64498	+	0.859405i	0.114999	+	0.0373654i
$530$	−24.3989	+	27.1577i	−1.05982	+	1.17965i
$531$	−4.60848	+	1.49739i	−0.199991	+	0.0649810i
$532$	−28.9504	−	46.3298i	−1.25516	−	2.00865i
$533$	7.19419	−	14.1194i	0.311615	−	0.611579i
$534$	21.8117	−	0.952378i	0.943884	−	0.0412134i
$535$	−4.47968	+	3.32240i	−0.193674	+	0.143640i
$536$	9.39723	−	17.3079i	0.405899	−	0.747587i
$537$	12.6233	−	1.99934i	0.544737	−	0.0862778i
$538$	−25.5301	−	23.3939i	−1.10068	−	1.00858i
$539$	−22.1497	+	16.0927i	−0.954055	+	0.693162i
$540$	−2.96702	−	3.34616i	−0.127680	−	0.143996i
$541$	−2.99298	−	2.17453i	−0.128678	−	0.0934902i	0.521584	−	0.853200i	$-0.325341\pi$
$541$	−2.99298	−	2.17453i	−0.128678	−	0.0934902i	−0.650263	+	0.759709i	$0.725341\pi$
$542$	3.42616	+	16.8399i	0.147166	+	0.723334i
$543$	7.35960	−	7.35960i	0.315831	−	0.315831i
$544$	12.3811	−	7.29328i	0.530837	−	0.312697i
$545$	6.16989	+	6.04984i	0.264289	+	0.259147i
$546$	4.82972	+	12.9176i	0.206693	+	0.552821i
$547$	−36.8218	+	18.7616i	−1.57439	+	0.802190i	−0.999867	−	0.0163019i	$-0.994811\pi$
$547$	−36.8218	+	18.7616i	−1.57439	+	0.802190i	−0.574519	+	0.818492i	$0.694811\pi$
$548$	−5.85608	+	14.4945i	−0.250159	+	0.619176i
$549$		−	13.7716i		−	0.587759i
$550$	−9.72205	+	11.0376i	−0.414550	+	0.470643i
$551$		−	8.77749i		−	0.373934i
$552$	12.1944	−	3.61225i	0.519027	−	0.153748i
$553$	−54.4719	+	27.7548i	−2.31638	+	1.18026i
$554$	9.66530	−	3.61374i	0.410639	−	0.153533i
$555$	17.8193	−	9.30102i	0.756388	−	0.394806i
$556$	−0.535386	−	6.11910i	−0.0227054	−	0.259508i
$557$	−13.3650	+	13.3650i	−0.566292	+	0.566292i	−0.931088	−	0.364795i	$-0.881139\pi$
$557$	−13.3650	+	13.3650i	−0.566292	+	0.566292i	0.364795	+	0.931088i	$0.381139\pi$
$558$	−2.45106	+	0.498680i	−0.103761	+	0.0211108i
$559$	10.4311	+	7.57866i	0.441190	+	0.320543i
$560$	36.2684	+	17.2499i	1.53262	+	0.728939i
$561$	4.27480	−	3.10582i	0.180482	−	0.131128i
$562$	10.4060	−	11.3563i	0.438952	−	0.479035i
$563$	0.762754	−	0.120808i	0.0321463	−	0.00509147i	−0.140341	−	0.990103i	$-0.544820\pi$
$563$	0.762754	−	0.120808i	0.0321463	−	0.00509147i	0.172487	+	0.985012i	$0.444820\pi$
$564$	3.76556	−	1.59841i	0.158559	−	0.0673053i
$565$	−11.6615	+	0.114565i	−0.490601	+	0.00481978i
$566$	0.266910	+	6.11285i	0.0112191	+	0.256942i
$567$	−2.03851	+	4.00080i	−0.0856095	+	0.168018i
$568$	23.7667	+	8.41601i	0.997228	+	0.353128i
$569$	4.42737	−	1.43854i	0.185605	−	0.0603068i	−0.214740	−	0.976671i	$-0.568890\pi$
$569$	4.42737	−	1.43854i	0.185605	−	0.0603068i	0.400345	+	0.916365i	$0.368890\pi$
$570$	−7.80519	+	17.5828i	−0.326923	+	0.736461i
$571$	25.9192	+	8.42167i	1.08469	+	0.352436i	0.796191	−	0.605045i	$-0.206845\pi$
$571$	25.9192	+	8.42167i	1.08469	+	0.352436i	0.288496	+	0.957481i	$0.406845\pi$
$572$	2.18583	+	8.76668i	0.0913941	+	0.366553i
$573$	−2.25362	−	0.356939i	−0.0941465	−	0.0149113i
$574$	−36.2617	+	28.8440i	−1.51353	+	1.20393i
$575$	−9.81141	+	20.2289i	−0.409164	+	0.843604i
$576$	−5.03446	+	6.21725i	−0.209769	+	0.259052i
$577$	−3.36036	+	21.2165i	−0.139894	+	0.883253i	0.813509	+	0.581552i	$0.197554\pi$
$577$	−3.36036	+	21.2165i	−0.139894	+	0.883253i	−0.953403	+	0.301701i	$0.902446\pi$
$578$	−6.18562	+	13.5732i	−0.257288	+	0.564570i
$579$	−0.901080	+	2.77324i	−0.0374476	+	0.115252i
$580$	3.47303	+	5.43832i	0.144210	+	0.225814i
$581$	−6.50848	−	20.0311i	−0.270017	−	0.831028i
$582$	−14.7460	−	1.68005i	−0.611240	−	0.0696403i
$583$	21.3973	+	10.9025i	0.886187	+	0.451535i
$584$	−2.72832	−	0.505641i	−0.112899	−	0.0209236i
$585$	2.81567	−	3.95661i	0.116414	−	0.163585i
$586$	−6.24264	+	22.5105i	−0.257881	+	0.929900i
$587$	0.100781	+	0.636305i	0.00415967	+	0.0262631i	0.989681	−	0.143289i	$-0.0457679\pi$
$587$	0.100781	+	0.636305i	0.00415967	+	0.0262631i	−0.985521	+	0.169552i	$0.945768\pi$
$588$	1.83612	−	26.2598i	0.0757204	−	1.08294i
$589$	6.32425	+	8.70459i	0.260586	+	0.358666i
$590$	−14.8055	−	3.94967i	−0.609532	−	0.162605i
$591$	−2.61654	+	3.60135i	−0.107630	+	0.148140i
$592$	−21.6399	−	28.7165i	−0.889394	−	1.18024i
$593$	26.5567	+	26.5567i	1.09055	+	1.09055i	0.995469	+	0.0950849i	$0.0303123\pi$
$593$	26.5567	+	26.5567i	1.09055	+	1.09055i	0.0950849	+	0.995469i	$0.469688\pi$
$594$	−1.62365	+	2.45308i	−0.0666191	+	0.100651i
$595$	25.1503	−	4.23709i	1.03106	−	0.173704i
$596$	29.1417	+	17.5099i	1.19369	+	0.717233i
$597$	8.46237	+	16.6083i	0.346342	+	0.679734i
$598$	6.80060	+	12.0199i	0.278097	+	0.491532i
$599$	43.2901			1.76879			0.884393	−	0.466743i	$-0.154573\pi$
$599$	43.2901			1.76879			0.884393	+	0.466743i	$0.154573\pi$
$600$	−2.12114	−	13.9822i	−0.0865954	−	0.570819i
$601$	−5.53025			−0.225584			−0.112792	−	0.993619i	$-0.535979\pi$
$601$	−5.53025			−0.225584			−0.112792	+	0.993619i	$0.535979\pi$
$602$	−18.5645	−	32.8125i	−0.756634	−	1.33734i
$603$	3.16115	+	6.20411i	0.128732	+	0.252651i
$604$	23.7444	+	14.2669i	0.966147	+	0.580512i
$605$	−13.3610	−	6.64327i	−0.543203	−	0.270087i
$606$	−8.84503	+	13.3635i	−0.359305	+	0.542854i
$607$	10.5049	+	10.5049i	0.426379	+	0.426379i	0.887393	−	0.461014i	$-0.152514\pi$
$607$	10.5049	+	10.5049i	0.426379	+	0.426379i	−0.461014	+	0.887393i	$0.652514\pi$
$608$	33.3168	+	8.61582i	1.35117	+	0.349417i
$609$	3.80812	−	5.24143i	0.154313	−	0.212394i
$610$	23.6787	−	36.5499i	0.958722	−	1.47986i
$611$	2.61099	+	3.59373i	0.105630	+	0.145387i
$612$	−0.354364	+	5.06804i	−0.0143243	+	0.204863i
$613$	3.99442	+	25.2198i	0.161333	+	1.01862i	0.926913	+	0.375276i	$0.122452\pi$
$613$	3.99442	+	25.2198i	0.161333	+	1.01862i	−0.765580	+	0.643341i	$0.777548\pi$
$614$	4.17399	−	15.0511i	0.168448	−	0.607412i
$615$	15.5660	+	4.88918i	0.627683	+	0.197151i
$616$	4.81409	−	25.9757i	0.193965	−	1.04659i
$617$	11.1407	+	5.67648i	0.448509	+	0.228527i	0.663630	−	0.748061i	$-0.269015\pi$
$617$	11.1407	+	5.67648i	0.448509	+	0.228527i	−0.215122	+	0.976587i	$0.569015\pi$
$618$	25.5258	+	2.90823i	1.02680	+	0.116986i
$619$	−3.93346	−	12.1059i	−0.158099	−	0.486579i	0.840363	−	0.542024i	$-0.182342\pi$
$619$	−3.93346	−	12.1059i	−0.158099	−	0.486579i	−0.998462	+	0.0554458i	$0.982342\pi$
$620$	−7.36253	−	2.89080i	−0.295686	−	0.116097i
$621$	−1.38951	+	4.27647i	−0.0557591	+	0.171609i
$622$	2.70050	−	5.92575i	0.108280	−	0.237601i
$623$	10.8439	−	68.4659i	0.434453	−	2.74303i
$624$	−7.80791	−	3.80807i	−0.312566	−	0.152445i
$625$	20.7871	+	13.8887i	0.831484	+	0.555549i
$626$	−15.5612	+	12.3780i	−0.621951	+	0.494725i
$627$	12.4984	+	1.97955i	0.499137	+	0.0790556i
$628$	−1.23368	−	4.94791i	−0.0492293	−	0.197443i
$629$	−21.7171	−	7.05630i	−0.865916	−	0.281353i
$630$	−12.2891	+	7.11316i	−0.489610	+	0.283395i
$631$	−33.2425	+	10.8011i	−1.32336	+	0.429986i	−0.883648	−	0.468152i	$-0.844920\pi$
$631$	−33.2425	+	10.8011i	−1.32336	+	0.429986i	−0.439713	+	0.898138i	$0.644920\pi$
$632$	12.8545	−	36.3010i	0.511325	−	1.44397i
$633$	−4.76166	+	9.34528i	−0.189259	+	0.371442i
$634$	0.281053	+	6.43677i	0.0111620	+	0.255637i
$635$	1.05721	−	3.36592i	0.0419541	−	0.133572i
$636$	−21.2542	+	9.02201i	−0.842784	+	0.357746i
$637$	28.2327	−	4.47163i	1.11862	−	0.177172i
$638$	2.86756	−	3.12941i	0.113528	−	0.123894i
$639$	−7.21163	+	5.23956i	−0.285288	+	0.207274i
$640$	−24.0513	+	7.84444i	−0.950711	+	0.310079i
$641$	−12.4082	−	9.01507i	−0.490094	−	0.356074i	0.315127	−	0.949050i	$-0.397953\pi$
$641$	−12.4082	−	9.01507i	−0.490094	−	0.356074i	−0.805220	+	0.592976i	$0.797953\pi$
$642$	−3.45656	+	0.703255i	−0.136419	+	0.0277552i
$643$	4.12183	−	4.12183i	0.162549	−	0.162549i	−0.621146	−	0.783695i	$-0.713333\pi$
$643$	4.12183	−	4.12183i	0.162549	−	0.162549i	0.783695	+	0.621146i	$0.213333\pi$
$644$	−3.51964	−	40.2272i	−0.138693	−	1.58517i
$645$	−5.91040	+	11.8871i	−0.232722	+	0.468053i
$646$	20.4699	−	7.65345i	0.805378	−	0.301121i
$647$	−29.6311	+	15.0978i	−1.16492	+	0.593556i	−0.926015	−	0.377488i	$-0.876788\pi$
$647$	−29.6311	+	15.0978i	−1.16492	+	0.593556i	−0.238904	+	0.971043i	$0.576788\pi$
$648$	−0.803339	−	2.71195i	−0.0315581	−	0.106535i
$649$			10.0795i			0.395656i
$650$	14.2757	−	5.65962i	0.559940	−	0.221989i
$651$			7.94168i			0.311259i
$652$	15.5401	−	38.4638i	0.608598	−	1.50636i
$653$	31.3131	−	15.9548i	1.22538	−	0.624360i	0.283065	−	0.959101i	$-0.408649\pi$
$653$	31.3131	−	15.9548i	1.22538	−	0.624360i	0.942310	+	0.334741i	$0.108649\pi$
$654$	1.91393	+	5.11899i	0.0748406	+	0.200168i
$655$	−3.56631	−	21.1687i	−0.139347	−	0.827130i
$656$	4.06167	−	28.9026i	0.158582	−	1.12846i
$657$	0.693694	−	0.693694i	0.0270636	−	0.0270636i
$658$	−2.58951	−	12.7277i	−0.100950	−	0.496176i
$659$	10.8923	+	7.91373i	0.424304	+	0.308275i	0.779367	−	0.626567i	$-0.215541\pi$
$659$	10.8923	+	7.91373i	0.424304	+	0.308275i	−0.355063	+	0.934842i	$0.615541\pi$
$660$	−8.52695	+	3.71881i	−0.331911	+	0.144754i
$661$	−14.4788	+	10.5195i	−0.563160	+	0.409159i	−0.832614	−	0.553854i	$-0.813157\pi$
$661$	−14.4788	+	10.5195i	−0.563160	+	0.409159i	0.269454	+	0.963013i	$0.413157\pi$
$662$	−26.4655	−	24.2511i	−1.02861	−	0.942544i
$663$	−5.44880	+	0.863005i	−0.211614	+	0.0335164i
$664$	11.6594	+	6.33042i	0.452473	+	0.245668i
$665$	49.7647	+	35.4145i	1.92979	+	1.37332i
$666$	12.7007	−	0.554559i	0.492142	−	0.0214887i
$667$	2.94545	−	5.78077i	0.114048	−	0.223832i
$668$	18.3005	+	29.2865i	0.708067	+	1.13313i
$669$	−15.5291	+	5.04570i	−0.600389	+	0.195078i
$670$	−2.27753	+	21.9009i	−0.0879886	+	0.846107i
$671$	−27.2446	−	8.85231i	−1.05177	−	0.341740i
$672$	16.1569	+	19.5994i	0.623268	+	0.756063i
$673$	1.17648	+	0.186337i	0.0453501	+	0.00718275i	0.179068	−	0.983837i	$-0.442692\pi$
$673$	1.17648	+	0.186337i	0.0453501	+	0.00718275i	−0.133718	+	0.991019i	$0.542692\pi$
$674$	−2.50595	−	3.15039i	−0.0965254	−	0.121348i
$675$	4.49877	+	2.18199i	0.173158	+	0.0839848i
$676$	−3.72665	+	16.1423i	−0.143333	+	0.620858i
$677$	−4.65493	+	29.3901i	−0.178904	+	1.12955i	0.720829	+	0.693113i	$0.243761\pi$
$677$	−4.65493	+	29.3901i	−0.178904	+	1.12955i	−0.899733	+	0.436441i	$0.856239\pi$
$678$	−6.71162	−	3.05864i	−0.257758	−	0.117466i
$679$	−14.5616	+	44.8159i	−0.558821	+	1.71988i
$680$	−9.65437	+	12.8413i	−0.370228	+	0.492441i
$681$	−3.11234	−	9.57881i	−0.119265	−	0.367061i
$682$	−0.588977	+	5.16951i	−0.0225531	+	0.197951i
$683$	15.7957	+	8.04833i	0.604407	+	0.307961i	0.729283	−	0.684212i	$-0.239854\pi$
$683$	15.7957	+	8.04833i	0.604407	+	0.307961i	−0.124877	+	0.992172i	$0.539854\pi$
$684$	−9.18232	+	7.98216i	−0.351095	+	0.305205i
$685$	−0.171700	−	17.4772i	−0.00656031	−	0.667769i
$686$	−37.7061	−	10.4567i	−1.43963	−	0.399240i
$687$	−2.41026	−	15.2178i	−0.0919572	−	0.580595i
$688$	22.7101	+	6.94291i	0.865815	+	0.264696i
$689$	−14.7374	−	20.2843i	−0.561450	−	0.772769i
$690$	−11.0406	+	8.96066i	−0.420310	+	0.341126i
$691$	−5.11148	+	7.03535i	−0.194450	+	0.267637i	−0.895098	−	0.445870i	$-0.852894\pi$
$691$	−5.11148	+	7.03535i	−0.194450	+	0.267637i	0.700648	+	0.713507i	$0.252894\pi$
$692$	31.2392	−	37.2298i	1.18754	−	1.41527i
$693$	6.60451	+	6.60451i	0.250885	+	0.250885i
$694$	8.90573	+	5.89454i	0.338057	+	0.223754i
$695$	3.17774	+	6.08807i	0.120539	+	0.230934i
$696$	0.532716	+	4.04612i	0.0201925	+	0.153368i
$697$	−8.41470	−	16.5148i	−0.318730	−	0.625542i
$698$	1.06389	−	0.601922i	0.0402687	−	0.0227831i
$699$	−6.34344			−0.239931
$700$	−44.8456	−	2.25134i	−1.69500	−	0.0850926i
$701$	17.7811			0.671583			0.335792	−	0.941936i	$-0.390996\pi$
$701$	17.7811			0.671583			0.335792	+	0.941936i	$0.390996\pi$
$702$	2.67315	−	1.51240i	0.100892	−	0.0570820i
$703$	−24.8266	−	48.7249i	−0.936353	−	1.83770i
$704$	9.06356	+	13.9562i	0.341596	+	0.525993i
$705$	−3.20211	+	3.26565i	−0.120598	+	0.122992i
$706$	0.659891	+	0.436769i	0.0248353	+	0.0164380i
$707$	35.9789	+	35.9789i	1.35313	+	1.35313i
$708$	−7.42399	−	6.22940i	−0.279011	−	0.234115i
$709$	5.90417	−	8.12640i	0.221736	−	0.305193i	−0.683627	−	0.729831i	$-0.739599\pi$
$709$	5.90417	−	8.12640i	0.221736	−	0.305193i	0.905363	+	0.424638i	$0.139599\pi$
$710$	−28.1485	+	1.50625i	−1.05639	+	0.0565286i
$711$	8.00284	+	11.0150i	0.300130	+	0.413093i
$712$	24.7324	+	35.9852i	0.926885	+	1.34860i
$713$	1.24411	+	7.85497i	0.0465921	+	0.294171i
$714$	15.5439	+	4.31067i	0.581718	+	0.161323i
$715$	−6.01752	−	8.11357i	−0.225042	−	0.303430i
$716$	16.7699	+	19.2913i	0.626719	+	0.720950i
$717$	0.860042	+	0.438213i	0.0321189	+	0.0163654i
$718$	1.74327	−	15.3009i	0.0650584	−	0.571024i
$719$	0.629430	+	1.93719i	0.0234738	+	0.0722449i	0.962107	−	0.272672i	$-0.0879072\pi$
$719$	0.629430	+	1.93719i	0.0234738	+	0.0722449i	−0.938633	+	0.344916i	$0.887907\pi$
$720$	2.53081	−	8.57875i	0.0943175	−	0.319711i
$721$	25.2066	−	77.5778i	0.938741	−	2.88915i
$722$	23.1735	+	10.5607i	0.862427	+	0.393028i
$723$	−3.68327	+	23.2552i	−0.136982	+	0.864871i
$724$	20.2826	+	4.68249i	0.753797	+	0.174023i
$725$	−5.91870	−	4.12499i	−0.219815	−	0.153198i
$726$	−5.87479	−	7.38559i	−0.218034	−	0.274105i
$727$	−30.0171	−	4.75424i	−1.11327	−	0.176325i	−0.427411	−	0.904058i	$-0.640574\pi$
$727$	−30.0171	−	4.75424i	−1.11327	−	0.176325i	−0.685861	+	0.727733i	$0.740574\pi$
$728$	−16.7906	+	21.8823i	−0.622301	+	0.811012i
$729$	0.951057	+	0.309017i	0.0352243	+	0.0114451i
$730$	3.03379	−	0.648341i	0.112286	−	0.0239962i
$731$	14.3429	−	4.66029i	0.530491	−	0.172367i
$732$	23.3579	−	14.5958i	0.863334	−	0.539477i
$733$	1.85241	−	3.63556i	0.0684203	−	0.134282i	−0.854263	−	0.519841i	$-0.825991\pi$
$733$	1.85241	−	3.63556i	0.0684203	−	0.134282i	0.922683	+	0.385559i	$0.125991\pi$
$734$	−6.23527	+	0.272255i	−0.230148	+	0.0100491i
$735$	9.36923	+	27.8999i	0.345589	+	1.02910i
$736$	19.0509	+	16.8543i	0.702225	+	0.621259i
$737$	14.3057	−	2.26579i	0.526956	−	0.0834616i
$738$	7.60799	+	6.97140i	0.280054	+	0.256621i
$739$	3.36210	−	2.44271i	0.123677	−	0.0898564i	−0.524227	−	0.851578i	$-0.675646\pi$
$739$	3.36210	−	2.44271i	0.123677	−	0.0898564i	0.647904	+	0.761722i	$0.275646\pi$
$740$	34.6612	+	20.3655i	1.27417	+	0.748652i
$741$	−10.6884	−	7.76561i	−0.392650	−	0.285277i
$742$	14.6161	+	71.8396i	0.536575	+	2.63731i
$743$	−1.67808	+	1.67808i	−0.0615626	+	0.0615626i	−0.737218	−	0.675655i	$-0.763861\pi$
$743$	−1.67808	+	1.67808i	−0.0615626	+	0.0615626i	0.675655	+	0.737218i	$0.263861\pi$
$744$	−3.44355	−	3.62869i	−0.126247	−	0.133034i
$745$	−37.5991	−	5.57705i	−1.37752	−	0.204327i
$746$	−15.2622	−	40.8203i	−0.558790	−	1.49454i
$747$	−4.17938	+	2.12950i	−0.152916	+	0.0779143i
$748$	9.79840	+	3.95875i	0.358265	+	0.144746i
$749$			11.1996i			0.409225i
$750$	8.18807	+	13.5261i	0.298986	+	0.493903i
$751$		−	30.7328i		−	1.12145i	−0.828001	−	0.560727i	$-0.810522\pi$
$751$		−	30.7328i		−	1.12145i	0.828001	−	0.560727i	$-0.189478\pi$
$752$	6.70198	+	4.69267i	0.244396	+	0.171124i
$753$	4.27796	−	2.17973i	0.155898	−	0.0794338i
$754$	−4.15088	+	1.55196i	−0.151166	+	0.0565192i
$755$	−30.6354	−	4.54413i	−1.11494	−	0.165378i
$756$	−8.94624	+	0.782744i	−0.325372	+	0.0284681i
$757$	−3.48566	+	3.48566i	−0.126688	+	0.126688i	−0.767608	−	0.640920i	$-0.778553\pi$
$757$	−3.48566	+	3.48566i	−0.126688	+	0.126688i	0.640920	+	0.767608i	$0.278553\pi$
$758$	25.2541	−	5.13808i	0.917270	−	0.186623i
$759$	7.56703	+	5.49777i	0.274666	+	0.199557i
$760$	−38.0943	+	5.39675i	−1.38182	+	0.195761i
$761$	−23.6585	+	17.1889i	−0.857620	+	0.623097i	−0.927236	−	0.374477i	$-0.877822\pi$
$761$	−23.6585	+	17.1889i	−0.857620	+	0.623097i	0.0696167	+	0.997574i	$0.477822\pi$
$762$	1.50746	−	1.64511i	0.0546095	−	0.0595962i
$763$	17.1383	−	2.71445i	0.620450	−	0.0982696i
$764$	−1.78310	−	4.20065i	−0.0645102	−	0.151974i
$765$	−1.80822	−	5.38457i	−0.0653764	−	0.194679i
$766$	−1.78007	−	40.7677i	−0.0643165	−	1.47300i
$767$	4.77760	−	9.37658i	0.172509	−	0.338569i
$768$	−15.8808	−	1.94956i	−0.573048	−	0.0703488i
$769$	−20.4125	+	6.63242i	−0.736093	+	0.239171i	−0.652986	−	0.757370i	$-0.726484\pi$
$769$	−20.4125	+	6.63242i	−0.736093	+	0.239171i	−0.0831064	+	0.996541i	$0.526484\pi$
$770$	6.17271	+	28.8841i	0.222449	+	1.04091i
$771$	−28.6665	−	9.31430i	−1.03240	−	0.335446i
$772$	−5.65867	+	1.41090i	−0.203660	+	0.0507793i
$773$	15.1378	+	2.39759i	0.544468	+	0.0862353i	0.422609	−	0.906312i	$-0.361114\pi$
$773$	15.1378	+	2.39759i	0.544468	+	0.0862353i	0.121859	+	0.992547i	$0.461114\pi$
$774$	−6.57083	+	5.22670i	−0.236184	+	0.187870i
$775$	8.84162	−	0.173741i	0.317600	−	0.00624096i
$776$	−12.7790	−	26.7911i	−0.458738	−	0.961744i
$777$	6.31429	−	39.8669i	0.226524	−	1.43022i
$778$	−7.35289	+	16.1346i	−0.263614	+	0.578452i
$779$	13.7167	−	42.2157i	0.491452	−	1.51254i
$780$	9.69495	+	0.582238i	0.347135	+	0.0208475i
$781$	5.72991	+	17.6348i	0.205032	+	0.631024i
$782$	16.0495	+	1.82857i	0.573930	+	0.0653895i
$783$	−1.28560	−	0.655047i	−0.0459437	−	0.0234095i
$784$	46.4851	−	24.7172i	1.66018	−	0.882757i
$785$	3.39629	+	4.57930i	0.121219	+	0.163442i
$786$	3.62824	−	13.0832i	0.129415	−	0.466661i
$787$	1.41565	+	8.93807i	0.0504625	+	0.318608i	0.999988	+	0.00491769i	$0.00156536\pi$
$787$	1.41565	+	8.93807i	0.0504625	+	0.318608i	−0.949525	+	0.313690i	$0.898435\pi$
$788$	−8.88135	−	0.620996i	−0.316385	−	0.0221221i
$789$	10.8899	+	14.9886i	0.387690	+	0.533610i
$790$	2.30063	+	42.9937i	0.0818526	+	1.52965i
$791$	−13.7649	+	18.9458i	−0.489424	+	0.673635i
$792$	−5.88146	−	0.153963i	−0.208989	−	0.00547085i
$793$	21.1486	+	21.1486i	0.751010	+	0.751010i
$794$	−1.21669	+	1.83822i	−0.0431786	+	0.0652361i
$795$	18.0739	−	18.4325i	0.641014	−	0.653734i
$796$	−19.2004	+	31.9553i	−0.680541	+	1.13262i
$797$	−22.7616	−	44.6721i	−0.806257	−	1.58237i	−0.812909	−	0.582391i	$-0.802117\pi$
$797$	−22.7616	−	44.6721i	−0.806257	−	1.58237i	0.00665213	−	0.999978i	$-0.497883\pi$
$798$	19.0225	+	33.6219i	0.673388	+	1.19020i
$799$	5.19570			0.183811
$800$	21.4669	−	18.4166i	0.758970	−	0.651126i
$801$	−15.4379			−0.545471
$802$	−22.4635	−	39.7039i	−0.793214	−	1.40199i
$803$	−0.926444	−	1.81825i	−0.0326935	−	0.0641646i
$804$	−7.17239	+	11.9370i	−0.252951	+	0.420986i
$805$	20.8906	+	40.0231i	0.736296	+	1.41063i
$806$	2.99820	−	4.52981i	0.105607	−	0.159556i
$807$	17.3137	+	17.3137i	0.609472	+	0.609472i
$808$	−32.0400	−	0.838735i	−1.12716	−	0.0295066i
$809$	6.38491	−	8.78807i	0.224481	−	0.308972i	−0.681889	−	0.731455i	$-0.738841\pi$
$809$	6.38491	−	8.78807i	0.224481	−	0.308972i	0.906371	+	0.422483i	$0.138841\pi$
$810$	1.99279	+	2.45536i	0.0700194	+	0.0862726i
$811$	−13.6381	−	18.7712i	−0.478898	−	0.659147i	0.499395	−	0.866375i	$-0.333556\pi$
$811$	−13.6381	−	18.7712i	−0.478898	−	0.659147i	−0.978293	+	0.207228i	$0.933556\pi$
$812$	12.9260	+	0.903801i	0.453613	+	0.0317172i
$813$	−1.90092	−	12.0019i	−0.0666682	−	0.420926i
$814$	7.06683	−	25.4824i	0.247692	−	0.893159i
$815$	0.455635	+	46.3787i	0.0159602	+	1.62458i
$816$	−8.97142	+	4.77032i	−0.314063	+	0.166994i
$817$	32.1801	+	16.3966i	1.12584	+	0.573644i
$818$	−31.5304	−	3.59235i	−1.10243	−	0.125604i
$819$	−3.01343	−	9.27438i	−0.105298	−	0.324073i
$820$	8.20513	+	31.5832i	0.286536	+	1.10293i
$821$	6.43852	−	19.8157i	0.224706	−	0.691573i	−0.773616	−	0.633655i	$-0.781554\pi$
$821$	6.43852	−	19.8157i	0.224706	−	0.691573i	0.998321	−	0.0579181i	$-0.0184462\pi$
$822$	4.58402	−	10.0588i	0.159886	−	0.350841i
$823$	−2.40540	+	15.1871i	−0.0838469	+	0.529389i	0.909636	+	0.415407i	$0.136361\pi$
$823$	−2.40540	+	15.1871i	−0.0838469	+	0.529389i	−0.993483	+	0.113982i	$0.963639\pi$
$824$	22.1208	+	46.3763i	0.770616	+	1.61560i
$825$	7.20844	−	7.49742i	0.250966	−	0.261027i
$826$	−24.0811	+	19.1551i	−0.837888	+	0.666490i
$827$	24.7345	+	3.91756i	0.860103	+	0.136227i	0.570879	−	0.821034i	$-0.306603\pi$
$827$	24.7345	+	3.91756i	0.860103	+	0.136227i	0.289224	+	0.957261i	$0.406603\pi$
$828$	−8.72594	+	2.17567i	−0.303247	+	0.0756098i
$829$	0.129955	+	0.0422250i	0.00451353	+	0.00146654i	0.311273	−	0.950321i	$-0.399245\pi$
$829$	0.129955	+	0.0422250i	0.00451353	+	0.00146654i	−0.306759	+	0.951787i	$0.599245\pi$
$830$	−14.7535	−	1.53425i	−0.512102	−	0.0532546i
$831$	−6.93936	+	2.25474i	−0.240724	+	0.0782159i
$832$	−1.81637	−	17.2789i	−0.0629713	−	0.599038i
$833$	15.1788	−	29.7900i	0.525913	−	1.03216i
$834$	0.189468	+	4.33926i	0.00656074	+	0.150256i
$835$	−31.4579	−	22.3867i	−1.08865	−	0.774722i
$836$	9.88889	+	23.2964i	0.342014	+	0.805723i
$837$	1.74689	−	0.276680i	0.0603814	−	0.00956347i
$838$	23.0386	−	25.1424i	0.795855	−	0.868528i
$839$	−22.1804	+	16.1150i	−0.765752	+	0.556352i	−0.900669	−	0.434505i	$-0.856923\pi$
$839$	−22.1804	+	16.1150i	−0.765752	+	0.556352i	0.134917	+	0.990857i	$0.456923\pi$
$840$	−25.0892	−	13.3046i	−0.865659	−	0.459052i
$841$	−21.7772	−	15.8221i	−0.750939	−	0.545589i
$842$	−19.7922	+	4.02683i	−0.682086	+	0.138774i
$843$	−7.70146	+	7.70146i	−0.265252	+	0.265252i
$844$	−20.8971	+	1.82837i	−0.719307	+	0.0629352i
$845$	−3.07711	−	18.2650i	−0.105856	−	0.628334i
$846$	−2.70943	+	1.01302i	−0.0931520	+	0.0348284i
$847$	−26.6977	+	13.6032i	−0.917344	+	0.467410i
$848$	−37.8284	−	26.4871i	−1.29903	−	0.909570i
$849$		−	4.32656i		−	0.148487i
$850$	4.45910	−	17.3997i	0.152946	−	0.596804i
$851$		−	40.4208i		−	1.38561i
$852$	−16.5300	−	6.67845i	−0.566308	−	0.228800i
$853$	40.6991	−	20.7372i	1.39351	−	0.710029i	0.413785	−	0.910375i	$-0.364207\pi$
$853$	40.6991	−	20.7372i	1.39351	−	0.710029i	0.979725	+	0.200346i	$0.0642067\pi$
$854$	−30.6263	−	81.9132i	−1.04801	−	2.80301i
$855$	6.05620	−	12.1803i	0.207118	−	0.416558i
$856$	−4.85621	−	5.11729i	−0.165982	−	0.174905i
$857$	7.89955	−	7.89955i	0.269844	−	0.269844i	−0.559194	−	0.829037i	$-0.688889\pi$
$857$	7.89955	−	7.89955i	0.269844	−	0.269844i	0.829037	+	0.559194i	$0.188889\pi$
$858$	−1.27373	−	6.26050i	−0.0434844	−	0.213730i
$859$	−10.1313	−	7.36085i	−0.345677	−	0.251149i	0.401376	−	0.915913i	$-0.368532\pi$
$859$	−10.1313	−	7.36085i	−0.345677	−	0.251149i	−0.747053	+	0.664764i	$0.768532\pi$
$860$	−26.4257	+	2.57392i	−0.901109	+	0.0877699i
$861$	26.5062	−	19.2579i	0.903329	−	0.656307i
$862$	28.4642	+	26.0825i	0.969495	+	0.888374i
$863$	−7.46119	+	1.18174i	−0.253982	+	0.0402268i	−0.282127	−	0.959377i	$-0.591040\pi$
$863$	−7.46119	+	1.18174i	−0.253982	+	0.0402268i	0.0281451	+	0.999604i	$0.491040\pi$
$864$	3.74829	−	4.23678i	0.127519	−	0.144138i
$865$	−16.2824	+	51.8394i	−0.553617	+	1.76259i
$866$	−44.2246	+	1.93101i	−1.50281	+	0.0656183i
$867$	4.78840	−	9.39776i	0.162623	−	0.319165i
$868$	−13.4698	+	8.41697i	−0.457195	+	0.285691i
$869$	26.9352	−	8.75179i	0.913715	−	0.296884i
$870$	−2.28572	−	3.94894i	−0.0774930	−	0.133882i
$871$	−14.3819	−	4.67297i	−0.487313	−	0.158338i
$872$	−6.65380	+	8.67155i	−0.225326	+	0.293656i
$873$	10.3652	+	1.64169i	0.350810	+	0.0555628i
$874$	24.0818	+	30.2748i	0.814580	+	1.02406i
$875$	47.2671	−	16.9135i	1.59792	−	0.571780i
$876$	1.91178	+	0.441358i	0.0645930	+	0.0149121i
$877$	−0.531340	+	3.35475i	−0.0179421	+	0.113282i	−0.995034	−	0.0995361i	$-0.968264\pi$
$877$	−0.531340	+	3.35475i	−0.0179421	+	0.113282i	0.977092	+	0.212818i	$0.0682641\pi$
$878$	−33.3155	−	15.1826i	−1.12434	−	0.512389i
$879$	5.10436	−	15.7096i	0.172166	−	0.529872i
$880$	−15.3447	−	10.5211i	−0.517270	−	0.354666i
$881$	3.43530	+	10.5728i	0.115738	+	0.356205i	0.992100	−	0.125448i	$-0.0400367\pi$
$881$	3.43530	+	10.5728i	0.115738	+	0.356205i	−0.876362	+	0.481653i	$0.840037\pi$
$882$	−2.10710	+	18.4942i	−0.0709496	+	0.622732i
$883$	−38.6913	−	19.7142i	−1.30206	−	0.663435i	−0.341079	−	0.940034i	$-0.610793\pi$
$883$	−38.6913	−	19.7142i	−1.30206	−	0.663435i	−0.960985	+	0.276599i	$0.910793\pi$
$884$	−7.23864	−	8.32701i	−0.243462	−	0.280068i
$885$	10.3373	+	3.24686i	0.347483	+	0.109142i
$886$	29.0721	+	8.06232i	0.976696	+	0.270859i
$887$	−4.86134	−	30.6933i	−0.163228	−	1.03058i	−0.924232	−	0.381832i	$-0.875293\pi$
$887$	−4.86134	−	30.6933i	−0.163228	−	1.03058i	0.761004	−	0.648747i	$-0.224707\pi$
$888$	14.4014	+	20.9538i	0.483279	+	0.703162i
$889$	−4.16422	−	5.73156i	−0.139664	−	0.192230i
$890$	−40.9722	−	26.5436i	−1.37339	−	0.889744i
$891$	1.22267	−	1.68286i	0.0409609	−	0.0563778i
$892$	−25.0164	−	20.9910i	−0.837612	−	0.702832i
$893$	8.79842	+	8.79842i	0.294428	+	0.294428i
$894$	−20.0466	−	13.2685i	−0.670458	−	0.443764i
$895$	−25.5898	−	12.7236i	−0.855373	−	0.425302i
$896$	−16.1184	+	48.1760i	−0.538479	+	1.60945i
$897$	−4.43341	−	8.70105i	−0.148027	−	0.290520i
$898$	5.88793	−	3.33125i	0.196483	−	0.111165i
$899$	−2.55195			−0.0851122
$900$	1.06716	+	9.94290i	0.0355720	+	0.331430i
$901$	−29.3264			−0.977004
$902$	18.6820	−	10.5698i	0.622043	−	0.351937i
$903$	12.1025	+	23.7525i	0.402746	+	0.790433i
$904$	−1.92557	−	14.6252i	−0.0640434	−	0.486427i
$905$	−22.9497	+	3.86635i	−0.762874	+	0.128522i
$906$	−16.3338	−	10.8110i	−0.542654	−	0.359173i
$907$	15.6082	+	15.6082i	0.518261	+	0.518261i	0.917045	−	0.398784i	$-0.130568\pi$
$907$	15.6082	+	15.6082i	0.518261	+	0.518261i	−0.398784	+	0.917045i	$0.630568\pi$
$908$	12.9479	−	15.4309i	0.429692	−	0.512092i
$909$	6.66063	−	9.16757i	0.220919	−	0.304069i
$910$	7.94855	−	29.7955i	0.263492	−	0.987710i
$911$	−10.5675	−	14.5449i	−0.350117	−	0.481895i	0.597245	−	0.802059i	$-0.296262\pi$
$911$	−10.5675	−	14.5449i	−0.350117	−	0.481895i	−0.947362	+	0.320164i	$0.896262\pi$
$912$	−23.2703	−	7.11417i	−0.770557	−	0.235574i
$913$	1.52634	+	9.63696i	0.0505146	+	0.318937i
$914$	−9.26329	−	2.56891i	−0.306402	−	0.0849720i
$915$	−17.8548	+	25.0897i	−0.590262	+	0.829440i
$916$	23.2562	−	20.2166i	0.768407	−	0.667974i
$917$	−38.4091	−	19.5704i	−1.26838	−	0.646272i
$918$	0.406661	−	3.56930i	0.0134218	−	0.117805i
$919$	6.00600	+	18.4846i	0.198120	+	0.609749i	0.999926	+	0.0121655i	$0.00387251\pi$
$919$	6.00600	+	18.4846i	0.198120	+	0.609749i	−0.801806	+	0.597584i	$0.796127\pi$
$920$	−26.8995	−	9.22899i	−0.886850	−	0.304271i
$921$	−3.41290	+	10.5038i	−0.112459	+	0.346113i
$922$	1.15439	+	0.526084i	0.0380179	+	0.0173256i
$923$	3.02845	−	19.1209i	0.0996827	−	0.629372i
$924$	−4.20207	+	18.2016i	−0.138238	+	0.598790i
$925$	−44.5227	−	6.15765i	−1.46390	−	0.202462i
$926$	26.5093	+	33.3266i	0.871150	+	1.09518i
$927$	−17.9426	−	2.84182i	−0.589311	−	0.0933377i
$928$	−6.29799	+	5.19181i	−0.206742	+	0.170429i
$929$	31.4701	+	10.2253i	1.03250	+	0.335480i	0.775779	−	0.631005i	$-0.217357\pi$
$929$	31.4701	+	10.2253i	1.03250	+	0.335480i	0.256723	+	0.966485i	$0.417357\pi$
$930$	5.11197	+	2.26926i	0.167628	+	0.0744120i
$931$	76.1504	−	24.7427i	2.49573	−	0.810911i
$932$	−6.72308	−	10.7590i	−0.220222	−	0.352424i
$933$	−2.09051	+	4.10285i	−0.0684401	+	0.134321i
$934$	24.0115	−	1.04843i	0.785680	−	0.0343057i
$935$	−11.8147	+	0.116070i	−0.386382	+	0.00379590i
$936$	5.39831	+	2.93098i	0.176449	+	0.0958022i
$937$	−4.63859	+	0.734681i	−0.151536	+	0.0240010i	−0.231742	−	0.972777i	$-0.574442\pi$
$937$	−4.63859	+	0.734681i	−0.151536	+	0.0240010i	0.0802054	+	0.996778i	$0.474442\pi$
$938$	32.5996	+	29.8718i	1.06441	+	0.975350i
$939$	11.3748	−	8.26425i	0.371202	−	0.269694i
$940$	−8.93259	−	1.96998i	−0.291349	−	0.0642535i
$941$	−30.0646	−	21.8432i	−0.980077	−	0.712068i	−0.0223514	−	0.999750i	$-0.507115\pi$
$941$	−30.0646	−	21.8432i	−0.980077	−	0.712068i	−0.957726	+	0.287682i	$0.907115\pi$
$942$	0.718893	+	3.53342i	0.0234228	+	0.115125i
$943$	23.1999	−	23.1999i	0.755494	−	0.755494i
$944$	2.69732	−	19.1940i	0.0877904	−	0.624710i
$945$	8.90086	−	4.64592i	0.289545	−	0.151132i
$946$	6.11638	+	16.3589i	0.198861	+	0.531873i
$947$	28.1072	−	14.3213i	0.913361	−	0.465381i	0.0668570	−	0.997763i	$-0.478703\pi$
$947$	28.1072	−	14.3213i	0.913361	−	0.465381i	0.846504	+	0.532382i	$0.178703\pi$
$948$	−10.2006	+	25.2477i	−0.331299	+	0.820008i
$949$			2.13057i			0.0691611i
$950$	37.0157	−	21.9136i	1.20095	−	0.710972i
$951$		−	4.55582i		−	0.147733i
$952$	9.16293	+	30.9326i	0.296972	+	1.00253i
$953$	−23.5416	+	11.9951i	−0.762588	+	0.388558i	−0.791615	−	0.611020i	$-0.790759\pi$
$953$	−23.5416	+	11.9951i	−0.762588	+	0.388558i	0.0290264	+	0.999579i	$0.490759\pi$
$954$	15.2930	−	5.71786i	0.495128	−	0.185122i
$955$	3.64298	+	3.57209i	0.117884	+	0.115590i
$956$	0.168264	+	1.92315i	0.00544206	+	0.0621991i
$957$	−2.12227	+	2.12227i	−0.0686032	+	0.0686032i
$958$	29.4717	−	5.99617i	0.952187	−	0.193727i
$959$	−28.3943	−	20.6297i	−0.916900	−	0.666167i
$960$	17.2326	−	4.79970i	0.556180	−	0.154910i
$961$	−22.5488	+	16.3826i	−0.727380	+	0.528472i
$962$	−18.6524	+	20.3557i	−0.601378	+	0.656293i
$963$	2.46352	−	0.390184i	0.0793859	−	0.0125735i
$964$	−43.3467	+	18.3998i	−1.39610	+	0.592619i
$965$	5.23711	−	3.88416i	0.168589	−	0.125035i
$966$	1.24557	+	28.5264i	0.0400755	+	0.917821i
$967$	2.30501	−	4.52383i	0.0741240	−	0.145477i	−0.850971	−	0.525213i	$-0.823985\pi$
$967$	2.30501	−	4.52383i	0.0741240	−	0.145477i	0.925095	+	0.379737i	$0.123985\pi$
$968$	6.30024	−	17.7918i	0.202497	−	0.571849i
$969$	−14.6967	+	4.77525i	−0.472126	+	0.153403i
$970$	24.6866	+	22.1788i	0.792640	+	0.712119i
$971$	30.8515	+	10.0243i	0.990072	+	0.321694i	0.758892	−	0.651217i	$-0.225741\pi$
$971$	30.8515	+	10.0243i	0.990072	+	0.321694i	0.231181	+	0.972911i	$0.425741\pi$
$972$	0.483854	+	1.94059i	0.0155196	+	0.0622444i
$973$	13.6207	+	2.15731i	0.436660	+	0.0691602i
$974$	−5.19477	+	4.13213i	−0.166451	+	0.132402i
$975$	−10.2594	+	3.55781i	−0.328564	+	0.113941i
$976$	49.5117	+	24.1478i	1.58483	+	0.772952i
$977$	0.473153	−	2.98737i	0.0151375	−	0.0955745i	−0.978963	−	0.204038i	$-0.934593\pi$
$977$	0.473153	−	2.98737i	0.0151375	−	0.0955745i	0.994100	+	0.108464i	$0.0345932\pi$
$978$	−12.1645	+	26.6927i	−0.388978	+	0.853540i
$979$	−9.92338	+	30.5410i	−0.317152	+	0.976095i
$980$	−37.3908	+	45.4607i	−1.19441	+	1.45219i
$981$	−1.19417	−	3.67527i	−0.0381268	−	0.117342i
$982$	−28.8935	−	3.29192i	−0.922028	−	0.105049i
$983$	6.89254	+	3.51193i	0.219838	+	0.112013i	0.560442	−	0.828194i	$-0.310631\pi$
$983$	6.89254	+	3.51193i	0.219838	+	0.112013i	−0.340604	+	0.940207i	$0.610631\pi$
$984$	−3.76082	+	20.2925i	−0.119890	+	0.646900i
$985$	9.43604	−	3.16877i	0.300657	−	0.100965i
$986$	−1.38517	+	4.99483i	−0.0441129	+	0.159068i
$987$	1.43673	+	9.07113i	0.0457315	+	0.288737i
$988$	1.84305	−	26.3589i	0.0586353	−	0.838589i
$989$	15.6913	+	21.5972i	0.498955	+	0.686752i
$990$	6.13843	−	2.36407i	0.195092	−	0.0751352i
$991$	−28.7622	+	39.5878i	−0.913661	+	1.25755i	0.0522398	+	0.998635i	$0.483364\pi$
$991$	−28.7622	+	39.5878i	−0.913661	+	1.25755i	−0.965901	+	0.258912i	$0.916636\pi$
$992$	2.50494	−	9.68643i	0.0795320	−	0.307545i
$993$	17.9481	+	17.9481i	0.569566	+	0.569566i
$994$	−31.2425	+	47.2025i	−0.990951	+	1.49717i
$995$	6.11550	−	41.2292i	0.193874	−	1.30705i
$996$	−8.04133	−	4.83166i	−0.254799	−	0.153097i
$997$	−5.99814	−	11.7720i	−0.189963	−	0.372824i	0.776307	−	0.630355i	$-0.217091\pi$
$997$	−5.99814	−	11.7720i	−0.189963	−	0.372824i	−0.966270	+	0.257532i	$0.917091\pi$
$998$	16.2937	+	28.7989i	0.515769	+	0.911613i
$999$	−8.98930			−0.284409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.223.10	yes	240
3.2	odd	2		900.2.bj.f.523.21		240
4.3	odd	2	inner	300.2.w.a.223.22	yes	240
12.11	even	2		900.2.bj.f.523.9		240
25.12	odd	20	inner	300.2.w.a.187.22	yes	240
75.62	even	20		900.2.bj.f.487.9		240
100.87	even	20	inner	300.2.w.a.187.10	✓	240
300.287	odd	20		900.2.bj.f.487.21		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.10	✓	240	100.87	even	20	inner
300.2.w.a.187.22	yes	240	25.12	odd	20	inner
300.2.w.a.223.10	yes	240	1.1	even	1	trivial
300.2.w.a.223.22	yes	240	4.3	odd	2	inner
900.2.bj.f.487.9		240	75.62	even	20
900.2.bj.f.487.21		240	300.287	odd	20
900.2.bj.f.523.9		240	12.11	even	2
900.2.bj.f.523.21		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)

\(f(q)\)	\(=\)	\(q+(-0.696395 - 1.23087i) q^{2} +(0.453990 + 0.891007i) q^{3} +(-1.03007 + 1.71434i) q^{4} +(0.328085 - 2.21187i) q^{5} +(0.780554 - 1.17929i) q^{6} +(-3.17506 - 3.17506i) q^{7} +(2.82746 + 0.0740164i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(-0.696395 - 1.23087i) q^{2} +(0.453990 + 0.891007i) q^{3} +(-1.03007 + 1.71434i) q^{4} +(0.328085 - 2.21187i) q^{5} +(0.780554 - 1.17929i) q^{6} +(-3.17506 - 3.17506i) q^{7} +(2.82746 + 0.0740164i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(-2.95099 + 1.13651i) q^{10} +(1.22267 + 1.68286i) q^{11} +(-1.99513 - 0.139502i) q^{12} +(-0.339738 - 2.14502i) q^{13} +(-1.69698 + 6.11917i) q^{14} +(2.11974 - 0.711841i) q^{15} +(-1.87792 - 3.53177i) q^{16} +(-2.26334 - 1.15323i) q^{17} +(1.40512 + 0.160090i) q^{18} +(-1.87987 - 5.78563i) q^{19} +(3.45394 + 2.84082i) q^{20} +(1.38755 - 4.27044i) q^{21} +(1.21991 - 2.67687i) q^{22} +(0.703414 - 4.44118i) q^{23} +(1.21769 + 2.55289i) q^{24} +(-4.78472 - 1.45136i) q^{25} +(-2.40365 + 1.91196i) q^{26} +(-0.987688 - 0.156434i) q^{27} +(8.71365 - 2.17261i) q^{28} +(1.37225 + 0.445870i) q^{29} +(-2.35236 - 2.11339i) q^{30} +(-1.68210 + 0.546548i) q^{31} +(-3.03936 + 4.77098i) q^{32} +(-0.944357 + 1.85340i) q^{33} +(0.156708 + 3.58897i) q^{34} +(-8.06450 + 5.98112i) q^{35} +(-0.781472 - 1.84101i) q^{36} +(8.87863 - 1.40624i) q^{37} +(-5.81222 + 6.34296i) q^{38} +(1.75699 - 1.27653i) q^{39} +(1.09136 - 6.22968i) q^{40} +(5.90311 + 4.28886i) q^{41} +(-6.22263 + 1.26603i) q^{42} +(-4.19804 + 4.19804i) q^{43} +(-4.14442 + 0.362612i) q^{44} +(1.59660 + 1.56553i) q^{45} +(-5.95636 + 2.22701i) q^{46} +(-1.82245 + 0.928585i) q^{47} +(2.29427 - 3.27663i) q^{48} +13.1620i q^{49} +(1.54562 + 6.90008i) q^{50} -2.54021i q^{51} +(4.02725 + 1.62709i) q^{52} +(10.2866 - 5.24127i) q^{53} +(0.495272 + 1.32465i) q^{54} +(4.12339 - 2.15226i) q^{55} +(-8.74233 - 9.21235i) q^{56} +(4.30160 - 4.30160i) q^{57} +(-0.406820 - 1.99956i) q^{58} +(3.92021 + 2.84820i) q^{59} +(-0.963132 + 4.36719i) q^{60} +(-11.1415 + 8.09476i) q^{61} +(1.84414 + 1.68983i) q^{62} +(4.43493 - 0.702423i) q^{63} +(7.98904 + 0.418557i) q^{64} +(-4.85597 + 0.0477062i) q^{65} +(2.93894 - 0.128325i) q^{66} +(3.16115 - 6.20411i) q^{67} +(4.30842 - 2.69223i) q^{68} +(4.27647 - 1.38951i) q^{69} +(12.9780 + 5.76110i) q^{70} +(8.47778 + 2.75460i) q^{71} +(-1.72182 + 2.24396i) q^{72} +(-0.968954 - 0.153467i) q^{73} +(-7.91392 - 9.94911i) q^{74} +(-0.879045 - 4.92212i) q^{75} +(11.8549 + 2.73686i) q^{76} +(1.46113 - 9.22520i) q^{77} +(-2.79480 - 1.27365i) q^{78} +(4.20734 - 12.9489i) q^{79} +(-8.42793 + 2.99500i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(1.16812 - 10.2527i) q^{82} +(4.17938 + 2.12950i) q^{83} +(5.89172 + 6.77757i) q^{84} +(-3.29336 + 4.62785i) q^{85} +(8.09073 + 2.24373i) q^{86} +(0.225714 + 1.42510i) q^{87} +(3.33248 + 4.84870i) q^{88} +(9.07416 + 12.4895i) q^{89} +(0.815097 - 3.05542i) q^{90} +(-5.73188 + 7.88926i) q^{91} +(6.88914 + 5.78061i) q^{92} +(-1.25064 - 1.25064i) q^{93} +(2.41211 + 1.59653i) q^{94} +(-13.4138 + 2.25984i) q^{95} +(-5.63082 - 0.542109i) q^{96} +(-4.76437 - 9.35061i) q^{97} +(16.2006 - 9.16594i) q^{98} -2.08012 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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