LMFDB - Embedded newform 110.2.k.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,2,Mod(7,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 14]))

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

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

chi := DirichletCharacter("110.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.k (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:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	110.17
Dual form			110.2.k.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 - 0.453990i) q^{2} +(-2.20142 + 0.348671i) q^{3} +(0.587785 + 0.809017i) q^{4} +(2.18748 - 0.463629i) q^{5} +(2.11978 + 0.688757i) q^{6} +(0.620489 - 3.91761i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(1.87153 - 0.608097i) q^{9} +O(q^{10})$	\(q+(-0.891007 - 0.453990i) q^{2} +(-2.20142 + 0.348671i) q^{3} +(0.587785 + 0.809017i) q^{4} +(2.18748 - 0.463629i) q^{5} +(2.11978 + 0.688757i) q^{6} +(0.620489 - 3.91761i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(1.87153 - 0.608097i) q^{9} +(-2.15954 - 0.579997i) q^{10} +(2.83922 - 1.71431i) q^{11} +(-1.57605 - 1.57605i) q^{12} +(1.35296 - 2.65534i) q^{13} +(-2.33142 + 3.20892i) q^{14} +(-4.65391 + 1.78335i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(2.11841 + 4.15761i) q^{17} +(-1.94362 - 0.307838i) q^{18} +(-2.59693 - 1.88678i) q^{19} +(1.66085 + 1.49719i) q^{20} +8.84068i q^{21} +(-3.30804 + 0.238480i) q^{22} +(-5.14200 + 5.14200i) q^{23} +(0.688757 + 2.11978i) q^{24} +(4.57010 - 2.02835i) q^{25} +(-2.41100 + 1.75169i) q^{26} +(2.04980 - 1.04442i) q^{27} +(3.53413 - 1.80073i) q^{28} +(-0.0660203 + 0.0479665i) q^{29} +(4.95629 + 0.523850i) q^{30} +(-0.600717 - 1.84882i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-5.65259 + 4.76387i) q^{33} -4.66620i q^{34} +(-0.459014 - 8.85736i) q^{35} +(1.59202 + 1.15667i) q^{36} +(-5.78725 - 0.916611i) q^{37} +(1.45730 + 2.86011i) q^{38} +(-2.05261 + 6.31728i) q^{39} +(-0.800117 - 2.08802i) q^{40} +(1.64181 - 2.25975i) q^{41} +(4.01358 - 7.87710i) q^{42} +(2.07213 + 2.07213i) q^{43} +(3.05575 + 1.28933i) q^{44} +(3.81199 - 2.19789i) q^{45} +(6.91597 - 2.24713i) q^{46} +(1.92981 + 12.1843i) q^{47} +(0.348671 - 2.20142i) q^{48} +(-8.30529 - 2.69855i) q^{49} +(-4.99284 - 0.267505i) q^{50} +(-6.11316 - 8.41404i) q^{51} +(2.94347 - 0.466200i) q^{52} +(-3.28846 - 1.67555i) q^{53} -2.30054 q^{54} +(5.41592 - 5.06634i) q^{55} -3.96645 q^{56} +(6.37480 + 3.24812i) q^{57} +(0.0806009 - 0.0127659i) q^{58} +(1.48475 + 2.04358i) q^{59} +(-4.17826 - 2.71686i) q^{60} +(1.70602 + 0.554319i) q^{61} +(-0.304102 + 1.92003i) q^{62} +(-1.22102 - 7.70925i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(1.72848 - 6.43577i) q^{65} +(7.19925 - 1.67841i) q^{66} +(2.34748 + 2.34748i) q^{67} +(-2.11841 + 4.15761i) q^{68} +(9.52685 - 13.1126i) q^{69} +(-3.61217 + 8.10035i) q^{70} +(-1.98584 + 6.11179i) q^{71} +(-0.893382 - 1.75336i) q^{72} +(7.72040 + 1.22279i) q^{73} +(4.74035 + 3.44406i) q^{74} +(-9.35350 + 6.05873i) q^{75} -3.20998i q^{76} +(-4.95428 - 12.1867i) q^{77} +(4.69687 - 4.69687i) q^{78} +(3.80642 + 11.7150i) q^{79} +(-0.235030 + 2.22368i) q^{80} +(-8.92437 + 6.48393i) q^{81} +(-2.48877 + 1.26809i) q^{82} +(13.4709 - 6.86376i) q^{83} +(-7.15226 + 5.19642i) q^{84} +(6.56156 + 8.11252i) q^{85} +(-0.905554 - 2.78701i) q^{86} +(0.128614 - 0.128614i) q^{87} +(-2.13735 - 2.53609i) q^{88} +5.99094i q^{89} +(-4.39433 + 0.227727i) q^{90} +(-9.56310 - 6.94800i) q^{91} +(-7.18235 - 1.13757i) q^{92} +(1.96706 + 3.86058i) q^{93} +(3.81210 - 11.7324i) q^{94} +(-6.55548 - 2.92327i) q^{95} +(-1.31009 + 1.80319i) q^{96} +(-4.98351 + 9.78069i) q^{97} +(6.17495 + 6.17495i) q^{98} +(4.27122 - 4.93489i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$3$	−2.20142	+	0.348671i	−1.27099	+	0.201306i	−0.755250	−	0.655437i	$-0.772484\pi$
$3$	−2.20142	+	0.348671i	−1.27099	+	0.201306i	−0.515744	+	0.856743i	$0.672484\pi$
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$	2.18748	−	0.463629i	0.978269	−	0.207341i
$5$	2.18748	−	0.463629i	0.978269	−	0.207341i
$6$	2.11978	+	0.688757i	0.865396	+	0.281184i
$7$	0.620489	−	3.91761i	0.234523	−	1.48072i	−0.536494	−	0.843904i	$-0.680252\pi$
$7$	0.620489	−	3.91761i	0.234523	−	1.48072i	0.771017	−	0.636815i	$-0.219748\pi$
$8$	−0.156434	−	0.987688i	−0.0553079	−	0.349201i
$9$	1.87153	−	0.608097i	0.623843	−	0.202699i
$10$	−2.15954	−	0.579997i	−0.682906	−	0.183411i
$11$	2.83922	−	1.71431i	0.856056	−	0.516883i
$11$	2.83922	−	1.71431i	0.856056	−	0.516883i
$12$	−1.57605	−	1.57605i	−0.454965	−	0.454965i
$13$	1.35296	−	2.65534i	0.375245	−	0.736460i	−0.623734	−	0.781637i	$-0.714385\pi$
$13$	1.35296	−	2.65534i	0.375245	−	0.736460i	0.998979	+	0.0451771i	$0.0143852\pi$
$14$	−2.33142	+	3.20892i	−0.623098	+	0.857621i
$15$	−4.65391	+	1.78335i	−1.20163	+	0.460460i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	2.11841	+	4.15761i	0.513790	+	1.00837i	0.991531	+	0.129869i	$0.0414555\pi$
$17$	2.11841	+	4.15761i	0.513790	+	1.00837i	−0.477742	+	0.878500i	$0.658544\pi$
$18$	−1.94362	−	0.307838i	−0.458115	−	0.0725582i
$19$	−2.59693	−	1.88678i	−0.595776	−	0.432856i	0.248601	−	0.968606i	$-0.420029\pi$
$19$	−2.59693	−	1.88678i	−0.595776	−	0.432856i	−0.844377	+	0.535750i	$0.820029\pi$
$20$	1.66085	+	1.49719i	0.371377	+	0.334782i
$21$			8.84068i			1.92919i
$22$	−3.30804	+	0.238480i	−0.705276	+	0.0508440i
$23$	−5.14200	+	5.14200i	−1.07218	+	1.07218i	−0.0749964	+	0.997184i	$0.523895\pi$
$23$	−5.14200	+	5.14200i	−1.07218	+	1.07218i	−0.997184	+	0.0749964i	$0.976105\pi$
$24$	0.688757	+	2.11978i	0.140592	+	0.432698i
$25$	4.57010	−	2.02835i	0.914019	−	0.405671i
$26$	−2.41100	+	1.75169i	−0.472836	+	0.343536i
$27$	2.04980	−	1.04442i	0.394483	−	0.200999i
$28$	3.53413	−	1.80073i	0.667888	−	0.340306i
$29$	−0.0660203	+	0.0479665i	−0.0122597	+	0.00890716i	−0.593898	−	0.804540i	$-0.702412\pi$
$29$	−0.0660203	+	0.0479665i	−0.0122597	+	0.00890716i	0.581639	+	0.813447i	$0.302412\pi$
$30$	4.95629	+	0.523850i	0.904890	+	0.0956415i
$31$	−0.600717	−	1.84882i	−0.107892	−	0.332057i	0.882506	−	0.470300i	$-0.155854\pi$
$31$	−0.600717	−	1.84882i	−0.107892	−	0.332057i	−0.990398	+	0.138243i	$0.955854\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−5.65259	+	4.76387i	−0.983990	+	0.829283i
$34$		−	4.66620i		−	0.800246i
$35$	−0.459014	−	8.85736i	−0.0775875	−	1.49717i
$36$	1.59202	+	1.15667i	0.265336	+	0.192778i
$37$	−5.78725	−	0.916611i	−0.951419	−	0.150690i	−0.338615	−	0.940925i	$-0.609958\pi$
$37$	−5.78725	−	0.916611i	−0.951419	−	0.150690i	−0.612804	+	0.790235i	$0.709958\pi$
$38$	1.45730	+	2.86011i	0.236405	+	0.463971i
$39$	−2.05261	+	6.31728i	−0.328680	+	1.01157i
$40$	−0.800117	−	2.08802i	−0.126510	−	0.330144i
$41$	1.64181	−	2.25975i	0.256407	−	0.352914i	−0.661335	−	0.750090i	$-0.730010\pi$
$41$	1.64181	−	2.25975i	0.256407	−	0.352914i	0.917742	+	0.397177i	$0.130010\pi$
$42$	4.01358	−	7.87710i	0.619309	−	1.21546i
$43$	2.07213	+	2.07213i	0.315997	+	0.315997i	0.847227	−	0.531231i	$-0.178270\pi$
$43$	2.07213	+	2.07213i	0.315997	+	0.315997i	−0.531231	+	0.847227i	$0.678270\pi$
$44$	3.05575	+	1.28933i	0.460672	+	0.194374i
$45$	3.81199	−	2.19789i	0.568259	−	0.327642i
$46$	6.91597	−	2.24713i	1.01970	−	0.331322i
$47$	1.92981	+	12.1843i	0.281492	+	1.77727i	0.571858	+	0.820352i	$0.306223\pi$
$47$	1.92981	+	12.1843i	0.281492	+	1.77727i	−0.290367	+	0.956915i	$0.593777\pi$
$48$	0.348671	−	2.20142i	0.0503264	−	0.317748i
$49$	−8.30529	−	2.69855i	−1.18647	−	0.385507i
$50$	−4.99284	−	0.267505i	−0.706094	−	0.0378309i
$51$	−6.11316	−	8.41404i	−0.856013	−	1.17820i
$52$	2.94347	−	0.466200i	0.408186	−	0.0646503i
$53$	−3.28846	−	1.67555i	−0.451704	−	0.230155i	0.213311	−	0.976984i	$-0.431575\pi$
$53$	−3.28846	−	1.67555i	−0.451704	−	0.230155i	−0.665016	+	0.746830i	$0.731575\pi$
$54$	−2.30054			−0.313064
$55$	5.41592	−	5.06634i	0.730282	−	0.683146i
$56$	−3.96645			−0.530039
$57$	6.37480	+	3.24812i	0.844363	+	0.430225i
$58$	0.0806009	−	0.0127659i	0.0105834	−	0.00167625i
$59$	1.48475	+	2.04358i	0.193298	+	0.266052i	0.894654	−	0.446759i	$-0.147422\pi$
$59$	1.48475	+	2.04358i	0.193298	+	0.266052i	−0.701356	+	0.712811i	$0.747422\pi$
$60$	−4.17826	−	2.71686i	−0.539411	−	0.350745i
$61$	1.70602	+	0.554319i	0.218433	+	0.0709733i	0.416189	−	0.909278i	$-0.363365\pi$
$61$	1.70602	+	0.554319i	0.218433	+	0.0709733i	−0.197756	+	0.980251i	$0.563365\pi$
$62$	−0.304102	+	1.92003i	−0.0386210	+	0.243844i
$63$	−1.22102	−	7.70925i	−0.153835	−	0.971274i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$	1.72848	−	6.43577i	0.214392	−	0.798259i
$66$	7.19925	−	1.67841i	0.886166	−	0.206599i
$67$	2.34748	+	2.34748i	0.286790	+	0.286790i	0.835809	−	0.549020i	$-0.184999\pi$
$67$	2.34748	+	2.34748i	0.286790	+	0.286790i	−0.549020	+	0.835809i	$0.684999\pi$
$68$	−2.11841	+	4.15761i	−0.256895	+	0.504184i
$69$	9.52685	−	13.1126i	1.14690	−	1.57857i
$70$	−3.61217	+	8.10035i	−0.431737	+	0.968177i
$71$	−1.98584	+	6.11179i	−0.235676	+	0.725336i	0.761355	+	0.648335i	$0.224534\pi$
$71$	−1.98584	+	6.11179i	−0.235676	+	0.725336i	−0.997031	+	0.0770011i	$0.975466\pi$
$72$	−0.893382	−	1.75336i	−0.105286	−	0.206636i
$73$	7.72040	+	1.22279i	0.903604	+	0.143117i	0.590911	−	0.806737i	$-0.298769\pi$
$73$	7.72040	+	1.22279i	0.903604	+	0.143117i	0.312694	+	0.949854i	$0.398769\pi$
$74$	4.74035	+	3.44406i	0.551054	+	0.400364i
$75$	−9.35350	+	6.05873i	−1.08005	+	0.699602i
$76$		−	3.20998i		−	0.368210i
$77$	−4.95428	−	12.1867i	−0.564593	−	1.38880i
$78$	4.69687	−	4.69687i	0.531816	−	0.531816i
$79$	3.80642	+	11.7150i	0.428256	+	1.31803i	0.899842	+	0.436215i	$0.143681\pi$
$79$	3.80642	+	11.7150i	0.428256	+	1.31803i	−0.471587	+	0.881820i	$0.656319\pi$
$80$	−0.235030	+	2.22368i	−0.0262771	+	0.248615i
$81$	−8.92437	+	6.48393i	−0.991596	+	0.720437i
$82$	−2.48877	+	1.26809i	−0.274838	+	0.140037i
$83$	13.4709	−	6.86376i	1.47862	−	0.753396i	0.485922	−	0.874002i	$-0.338484\pi$
$83$	13.4709	−	6.86376i	1.47862	−	0.753396i	0.992700	+	0.120606i	$0.0384838\pi$
$84$	−7.15226	+	5.19642i	−0.780375	+	0.566976i
$85$	6.56156	+	8.11252i	0.711701	+	0.879926i
$86$	−0.905554	−	2.78701i	−0.0976484	−	0.300531i
$87$	0.128614	−	0.128614i	0.0137889	−	0.0137889i
$88$	−2.13735	−	2.53609i	−0.227842	−	0.270348i
$89$			5.99094i			0.635038i	0.948252	+	0.317519i	$0.102850\pi$
$89$			5.99094i			0.635038i	−0.948252	+	0.317519i	$0.897150\pi$
$90$	−4.39433	+	0.227727i	−0.463203	+	0.0240045i
$91$	−9.56310	−	6.94800i	−1.00249	−	0.728349i
$92$	−7.18235	−	1.13757i	−0.748812	−	0.118600i
$93$	1.96706	+	3.86058i	0.203975	+	0.400323i
$94$	3.81210	−	11.7324i	0.393188	−	1.21011i
$95$	−6.55548	−	2.92327i	−0.672578	−	0.299921i
$96$	−1.31009	+	1.80319i	−0.133711	+	0.184037i
$97$	−4.98351	+	9.78069i	−0.505999	+	0.993078i	0.486826	+	0.873499i	$0.338155\pi$
$97$	−4.98351	+	9.78069i	−0.505999	+	0.993078i	−0.992825	+	0.119579i	$0.961845\pi$
$98$	6.17495	+	6.17495i	0.623764	+	0.623764i
$99$	4.27122	−	4.93489i	0.429273	−	0.495976i
$100$	4.32721	+	2.50505i	0.432721	+	0.250505i
$101$	−7.31649	+	2.37727i	−0.728018	+	0.236547i	−0.649496	−	0.760365i	$-0.725020\pi$
$101$	−7.31649	+	2.37727i	−0.728018	+	0.236547i	−0.0785218	+	0.996912i	$0.525020\pi$
$102$	1.62697	+	10.2723i	0.161094	+	1.01711i
$103$	0.891762	−	5.63036i	0.0878679	−	0.554776i	−0.904003	−	0.427526i	$-0.859385\pi$
$103$	0.891762	−	5.63036i	0.0878679	−	0.554776i	0.991871	−	0.127250i	$-0.0406149\pi$
$104$	−2.83430	−	0.920920i	−0.277926	−	0.0903037i
$105$	4.09879	+	19.3388i	0.400001	+	1.88727i
$106$	2.16935	+	2.98586i	0.210706	+	0.290012i
$107$	−12.4391	+	1.97017i	−1.20254	+	0.190463i	−0.725376	−	0.688353i	$-0.758334\pi$
$107$	−12.4391	+	1.97017i	−1.20254	+	0.190463i	−0.477161	+	0.878816i	$0.658334\pi$
$108$	2.04980	+	1.04442i	0.197242	+	0.100500i
$109$	−13.0770			−1.25255			−0.626273	−	0.779604i	$-0.715420\pi$
$109$	−13.0770			−1.25255			−0.626273	+	0.779604i	$0.715420\pi$
$110$	−7.12569	+	2.05537i	−0.679408	+	0.195972i
$111$	13.0598			1.23958
$112$	3.53413	+	1.80073i	0.333944	+	0.170153i
$113$	−0.413613	+	0.0655098i	−0.0389094	+	0.00616264i	−0.175859	−	0.984415i	$-0.556270\pi$
$113$	−0.413613	+	0.0655098i	−0.0389094	+	0.00616264i	0.136949	+	0.990578i	$0.456270\pi$
$114$	−4.20537	−	5.78820i	−0.393869	−	0.542115i
$115$	−8.86401	+	13.6320i	−0.826573	+	1.27119i
$116$	−0.0776115	−	0.0252175i	−0.00720605	−	0.00234139i
$117$	0.917408	−	5.79229i	0.0848144	−	0.535497i
$118$	−0.395154	−	2.49491i	−0.0363769	−	0.229675i
$119$	17.6024	−	5.71935i	1.61361	−	0.524292i
$120$	2.48943	+	4.31763i	0.227253	+	0.394144i
$121$	5.12231	−	9.73457i	0.465665	−	0.884961i
$122$	−1.26842	−	1.26842i	−0.114837	−	0.114837i
$123$	−2.82640	+	5.54712i	−0.254848	+	0.500167i
$124$	1.14263	−	1.57270i	0.102611	−	0.141232i
$125$	9.05657	−	6.55580i	0.810044	−	0.586369i
$126$	−2.41198	+	7.42332i	−0.214877	+	0.661322i
$127$	−3.94067	−	7.73399i	−0.349678	−	0.686281i	0.647443	−	0.762114i	$-0.275838\pi$
$127$	−3.94067	−	7.73399i	−0.349678	−	0.686281i	−0.997121	+	0.0758331i	$0.975838\pi$
$128$	0.987688	+	0.156434i	0.0873001	+	0.0138270i
$129$	−5.28413	−	3.83915i	−0.465242	−	0.338018i
$130$	−4.46187	+	4.94960i	−0.391332	+	0.434108i
$131$		−	1.31996i		−	0.115326i	−0.998336	−	0.0576628i	$-0.981635\pi$
$131$		−	1.31996i		−	0.115326i	0.998336	−	0.0576628i	$-0.0183648\pi$
$132$	−7.17656	−	1.77291i	−0.624640	−	0.154312i
$133$	−9.00303	+	9.00303i	−0.780661	+	0.780661i
$134$	−1.02588	−	3.15735i	−0.0886229	−	0.272753i
$135$	3.99965	−	3.23499i	0.344235	−	0.278424i
$136$	3.77503	−	2.74272i	0.323706	−	0.235186i
$137$	15.9711	−	8.13766i	1.36450	−	0.695248i	0.390248	−	0.920710i	$-0.372389\pi$
$137$	15.9711	−	8.13766i	1.36450	−	0.695248i	0.974252	+	0.225462i	$0.0723892\pi$
$138$	−14.4415	+	7.35830i	−1.22934	+	0.626380i
$139$	2.00508	−	1.45677i	0.170068	−	0.123562i	−0.499495	−	0.866317i	$-0.666481\pi$
$139$	2.00508	−	1.45677i	0.170068	−	0.123562i	0.669564	+	0.742755i	$0.266481\pi$
$140$	6.89595	−	5.57757i	0.582814	−	0.471391i
$141$	−8.49666	−	26.1500i	−0.715548	−	2.20223i
$142$	4.54409	−	4.54409i	0.381332	−	0.381332i
$143$	−0.710708	−	9.85849i	−0.0594324	−	0.824408i
$144$			1.96784i			0.163987i
$145$	−0.122179	+	0.135535i	−0.0101464	+	0.0112555i
$146$	−6.32379	−	4.59450i	−0.523361	−	0.380244i
$147$	19.2244	+	3.04484i	1.58560	+	0.251134i
$148$	−2.66011	−	5.22076i	−0.218660	−	0.429144i
$149$	3.39237	−	10.4406i	0.277914	−	0.855331i	−0.710520	−	0.703677i	$-0.751540\pi$
$149$	3.39237	−	10.4406i	0.277914	−	0.855331i	0.988434	−	0.151654i	$-0.0484598\pi$
$150$	11.0846	−	1.15197i	0.905056	−	0.0940578i
$151$	−7.30350	+	10.0524i	−0.594350	+	0.818053i	−0.995176	−	0.0981010i	$-0.968723\pi$
$151$	−7.30350	+	10.0524i	−0.594350	+	0.818053i	0.400826	+	0.916154i	$0.368723\pi$
$152$	−1.45730	+	2.86011i	−0.118203	+	0.231986i
$153$	6.49290	+	6.49290i	0.524920	+	0.524920i
$154$	−1.11833	+	13.1076i	−0.0901177	+	1.05624i
$155$	−2.17122	−	3.76573i	−0.174396	−	0.302471i
$156$	−6.31728	+	2.05261i	−0.505787	+	0.164340i
$157$	0.889545	+	5.61637i	0.0709934	+	0.448235i	0.997422	+	0.0717635i	$0.0228627\pi$
$157$	0.889545	+	5.61637i	0.0709934	+	0.448235i	−0.926428	+	0.376471i	$0.877137\pi$
$158$	1.92693	−	12.1662i	0.153299	−	0.967889i
$159$	7.82350	+	2.54201i	0.620444	+	0.201595i
$160$	1.21894	−	1.87461i	0.0963660	−	0.148201i
$161$	16.9538	+	23.3349i	1.33615	+	1.83905i
$162$	10.8953	−	1.72565i	0.856017	−	0.135580i
$163$	10.7990	+	5.50237i	0.845843	+	0.430979i	0.822511	−	0.568749i	$-0.192573\pi$
$163$	10.7990	+	5.50237i	0.845843	+	0.430979i	0.0233320	+	0.999728i	$0.492573\pi$
$164$	2.79321			0.218113
$165$	−10.1562	+	13.0416i	−0.790663	+	1.01528i
$166$	−15.1187			−1.17344
$167$	−3.65804	−	1.86387i	−0.283068	−	0.144230i	0.306692	−	0.951809i	$-0.400778\pi$
$167$	−3.65804	−	1.86387i	−0.283068	−	0.144230i	−0.589760	+	0.807578i	$0.700778\pi$
$168$	8.73183	−	1.38299i	0.673676	−	0.106700i
$169$	2.42088	+	3.33205i	0.186221	+	0.256312i
$170$	−2.16338	−	10.2072i	−0.165924	−	0.782856i
$171$	−6.00757	−	1.95198i	−0.459410	−	0.149271i
$172$	−0.458421	+	2.89436i	−0.0349543	+	0.220693i
$173$	−2.03097	−	12.8231i	−0.154412	−	0.974919i	−0.936224	−	0.351405i	$-0.885704\pi$
$173$	−2.03097	−	12.8231i	−0.154412	−	0.974919i	0.781812	−	0.623515i	$-0.214296\pi$
$174$	−0.172986	+	0.0562064i	−0.0131140	+	0.00426100i
$175$	−5.11061	−	19.1624i	−0.386326	−	1.44854i
$176$	0.753035	+	3.23001i	0.0567622	+	0.243471i
$177$	−3.98110	−	3.98110i	−0.299238	−	0.299238i
$178$	2.71983	−	5.33796i	0.203860	−	0.400097i
$179$	−4.78324	+	6.58357i	−0.357516	+	0.492079i	−0.949455	−	0.313904i	$-0.898363\pi$
$179$	−4.78324	+	6.58357i	−0.357516	+	0.492079i	0.591938	+	0.805983i	$0.298363\pi$
$180$	4.01877	+	1.79208i	0.299541	+	0.133574i
$181$	5.23127	−	16.1002i	0.388837	−	1.19672i	−0.544821	−	0.838552i	$-0.683402\pi$
$181$	5.23127	−	16.1002i	0.388837	−	1.19672i	0.933658	−	0.358165i	$-0.116598\pi$
$182$	5.36646	+	10.5323i	0.397789	+	0.780704i
$183$	−3.94895	−	0.625452i	−0.291915	−	0.0462348i
$184$	5.88307	+	4.27430i	0.433706	+	0.315106i
$185$	−13.0844	+	0.678073i	−0.961987	+	0.0498529i
$186$		−	4.33283i		−	0.317698i
$187$	13.1420	+	8.17276i	0.961041	+	0.597652i
$188$	−8.72302	+	8.72302i	−0.636192	+	0.636192i
$189$	−2.81977	−	8.67836i	−0.205108	−	0.631258i
$190$	4.51384	+	5.58078i	0.327468	+	0.404872i
$191$	−8.26779	+	6.00690i	−0.598236	+	0.434644i	−0.845252	−	0.534367i	$-0.820550\pi$
$191$	−8.26779	+	6.00690i	−0.598236	+	0.434644i	0.247016	+	0.969011i	$0.420550\pi$
$192$	1.98593	−	1.01188i	0.143322	−	0.0730264i
$193$	−19.6510	+	10.0127i	−1.41451	+	0.720728i	−0.983379	−	0.181563i	$-0.941885\pi$
$193$	−19.6510	+	10.0127i	−1.41451	+	0.720728i	−0.431129	+	0.902290i	$0.641885\pi$
$194$	8.88068	−	6.45219i	0.637596	−	0.463240i
$195$	−1.56116	+	14.7705i	−0.111797	+	1.05774i
$196$	−2.69855	−	8.30529i	−0.192754	−	0.593235i
$197$	−10.9542	+	10.9542i	−0.780453	+	0.780453i	−0.979907	−	0.199454i	$-0.936083\pi$
$197$	−10.9542	+	10.9542i	−0.780453	+	0.780453i	0.199454	+	0.979907i	$0.436083\pi$
$198$	−6.04608	+	2.45793i	−0.429676	+	0.174678i
$199$		−	7.77743i		−	0.551327i	−0.961254	−	0.275664i	$-0.911102\pi$
$199$		−	7.77743i		−	0.551327i	0.961254	−	0.275664i	$-0.0888976\pi$
$200$	−2.71830	−	4.19653i	−0.192213	−	0.296739i
$201$	−5.98629	−	4.34929i	−0.422240	−	0.306776i
$202$	7.59830	+	1.20345i	0.534614	+	0.0846746i
$203$	0.146949	+	0.288405i	0.0103138	+	0.0202420i
$204$	3.21388	−	9.89130i	0.225016	−	0.692529i
$205$	2.54372	−	5.70434i	0.177661	−	0.398408i
$206$	−3.35070	+	4.61184i	−0.233454	+	0.321322i
$207$	−6.49657	+	12.7502i	−0.451543	+	0.886202i
$208$	2.10729	+	2.10729i	0.146114	+	0.146114i
$209$	−10.6078	−	0.905046i	−0.733753	−	0.0626033i
$210$	5.12756	−	19.0918i	0.353836	−	1.31746i
$211$	9.07668	−	2.94919i	0.624864	−	0.203031i	0.0205655	−	0.999789i	$-0.493453\pi$
$211$	9.07668	−	2.94919i	0.624864	−	0.203031i	0.604299	+	0.796758i	$0.293453\pi$
$212$	−0.577356	−	3.64528i	−0.0396530	−	0.250359i
$213$	2.24067	−	14.1471i	0.153528	−	0.969340i
$214$	11.9778	+	3.89182i	0.818785	+	0.266039i
$215$	5.49343	+	3.57203i	0.374649	+	0.243611i
$216$	−1.35222	−	1.86118i	−0.0920071	−	0.126637i
$217$	−7.61569	+	1.20621i	−0.516986	+	0.0818826i
$218$	11.6517	+	5.93682i	0.789150	+	0.402092i
$219$	−17.4222			−1.17729
$220$	7.28215	+	1.40365i	0.490963	+	0.0946338i
$221$	13.9060			0.935420
$222$	−11.6364	−	5.92903i	−0.780982	−	0.397930i
$223$	18.3320	−	2.90351i	1.22760	−	0.194433i	0.491243	−	0.871023i	$-0.336543\pi$
$223$	18.3320	−	2.90351i	1.22760	−	0.194433i	0.736361	+	0.676589i	$0.236543\pi$
$224$	−2.33142	−	3.20892i	−0.155774	−	0.214405i
$225$	7.31964	−	6.57519i	0.487976	−	0.438346i
$226$	0.398272	+	0.129407i	0.0264927	+	0.00860799i
$227$	1.76089	−	11.1178i	0.116874	−	0.737915i	−0.857750	−	0.514067i	$-0.828138\pi$
$227$	1.76089	−	11.1178i	0.116874	−	0.737915i	0.974624	−	0.223848i	$-0.0718619\pi$
$228$	1.11923	+	7.06652i	0.0741226	+	0.467992i
$229$	4.10397	−	1.33346i	0.271198	−	0.0881177i	−0.170261	−	0.985399i	$-0.554461\pi$
$229$	4.10397	−	1.33346i	0.271198	−	0.0881177i	0.441459	+	0.897281i	$0.354461\pi$
$230$	14.0867	−	8.12199i	0.928848	−	0.535548i
$231$	15.1556	+	25.1006i	0.997167	+	1.65150i
$232$	0.0577038	+	0.0577038i	0.00378844	+	0.00378844i
$233$	−6.64117	+	13.0340i	−0.435077	+	0.853887i	0.564518	+	0.825421i	$0.309062\pi$
$233$	−6.64117	+	13.0340i	−0.435077	+	0.853887i	−0.999595	+	0.0284660i	$0.990938\pi$
$234$	−3.44706	+	4.74447i	−0.225341	+	0.310156i
$235$	9.87042	+	25.7582i	0.643875	+	1.68028i
$236$	−0.780579	+	2.40237i	−0.0508113	+	0.156381i
$237$	−12.4642	−	24.4624i	−0.809638	−	1.58900i
$238$	−18.2804	−	2.89532i	−1.18494	−	0.187676i
$239$	−6.12048	−	4.44679i	−0.395901	−	0.287639i	0.371968	−	0.928245i	$-0.378683\pi$
$239$	−6.12048	−	4.44679i	−0.395901	−	0.287639i	−0.767869	+	0.640606i	$0.778683\pi$
$240$	−0.257934	−	4.97722i	−0.0166495	−	0.321278i
$241$			6.31704i			0.406917i	0.979084	+	0.203458i	$0.0652181\pi$
$241$			6.31704i			0.406917i	−0.979084	+	0.203458i	$0.934782\pi$
$242$	−8.98342	+	6.34809i	−0.577476	+	0.408070i
$243$	12.5054	−	12.5054i	0.802220	−	0.802220i
$244$	0.554319	+	1.70602i	0.0354867	+	0.109217i
$245$	−19.4187	−	2.05245i	−1.24062	−	0.131126i
$246$	5.03668	−	3.65936i	0.321127	−	0.233313i
$247$	−8.52359	+	4.34299i	−0.542343	+	0.276338i
$248$	−1.73208	+	0.882540i	−0.109987	+	0.0560413i
$249$	−27.2620	+	19.8070i	−1.72766	+	1.25522i
$250$	−11.0457	+	1.72966i	−0.698594	+	0.109394i
$251$	6.45616	+	19.8700i	0.407509	+	1.25418i	0.918782	+	0.394765i	$0.129174\pi$
$251$	6.45616	+	19.8700i	0.407509	+	1.25418i	−0.511273	+	0.859418i	$0.670826\pi$
$252$	5.51921	−	5.51921i	0.347678	−	0.347678i
$253$	−5.78429	+	23.4142i	−0.363655	+	1.47204i
$254$			8.68006i			0.544636i
$255$	−17.2734	−	15.5713i	−1.08170	−	0.975111i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	6.07028	+	0.961438i	0.378654	+	0.0599729i	0.342860	−	0.939386i	$-0.388604\pi$
$257$	6.07028	+	0.961438i	0.378654	+	0.0599729i	0.0357933	+	0.999359i	$0.488604\pi$
$258$	2.96526	+	5.81965i	0.184609	+	0.362315i
$259$	−7.18185	+	22.1035i	−0.446259	+	1.37344i
$260$	6.22262	−	2.38448i	0.385911	−	0.147879i
$261$	−0.0943906	+	0.129918i	−0.00584263	+	0.00804169i
$262$	−0.599250	+	1.17609i	−0.0370218	+	0.0726594i
$263$	−17.2139	−	17.2139i	−1.06145	−	1.06145i	−0.997984	−	0.0634691i	$-0.979784\pi$
$263$	−17.2139	−	17.2139i	−1.06145	−	1.06145i	−0.0634691	−	0.997984i	$-0.520216\pi$
$264$	5.58948	+	4.83777i	0.344009	+	0.297744i
$265$	−7.97025	−	2.14061i	−0.489609	−	0.131496i
$266$	12.1090	−	3.93447i	0.742453	−	0.241238i
$267$	−2.08887	−	13.1886i	−0.127837	−	0.807129i
$268$	−0.519336	+	3.27896i	−0.0317235	+	0.200294i
$269$	25.5811	+	8.31179i	1.55971	+	0.506779i	0.956729	−	0.290980i	$-0.0939814\pi$
$269$	25.5811	+	8.31179i	1.55971	+	0.506779i	0.602976	+	0.797759i	$0.293981\pi$
$270$	−5.03237	+	1.06660i	−0.306260	+	0.0649110i
$271$	13.3592	+	18.3874i	0.811515	+	1.11695i	0.991088	+	0.133210i	$0.0425284\pi$
$271$	13.3592	+	18.3874i	0.811515	+	1.11695i	−0.179573	+	0.983745i	$0.557472\pi$
$272$	−4.60875	+	0.729954i	−0.279446	+	0.0442600i
$273$	23.4750	+	11.9611i	1.42077	+	0.723920i
$274$	−17.9247			−1.08287
$275$	9.49828	−	13.5935i	0.572768	−	0.819718i
$276$	16.2080			0.975610
$277$	−18.5311	−	9.44205i	−1.11342	−	0.567318i	−0.202247	−	0.979334i	$-0.564825\pi$
$277$	−18.5311	−	9.44205i	−1.11342	−	0.567318i	−0.911176	+	0.412017i	$0.864825\pi$
$278$	−2.44790	+	0.387709i	−0.146815	+	0.0232532i
$279$	−2.24852	−	3.09482i	−0.134615	−	0.185282i
$280$	−8.67650	+	1.83896i	−0.518520	+	0.109899i
$281$	−6.11005	−	1.98528i	−0.364495	−	0.118432i	0.121043	−	0.992647i	$-0.461376\pi$
$281$	−6.11005	−	1.98528i	−0.364495	−	0.118432i	−0.485538	+	0.874216i	$0.661376\pi$
$282$	−4.30129	+	27.1572i	−0.256138	+	1.61719i
$283$	−0.151673	−	0.957628i	−0.00901605	−	0.0569251i	0.982770	−	0.184832i	$-0.0591741\pi$
$283$	−0.151673	−	0.957628i	−0.00901605	−	0.0569251i	−0.991786	+	0.127907i	$0.959174\pi$
$284$	−6.11179	+	1.98584i	−0.362668	+	0.117838i
$285$	15.4506	+	4.14965i	0.915217	+	0.245804i
$286$	−3.84242	+	9.10663i	−0.227207	+	0.538487i
$287$	−7.83411	−	7.83411i	−0.462433	−	0.462433i
$288$	0.893382	−	1.75336i	0.0526430	−	0.103318i
$289$	−2.80573	+	3.86175i	−0.165043	+	0.227162i
$290$	0.170394	−	0.0652940i	0.0100059	−	0.00383420i
$291$	7.56058	−	23.2691i	0.443209	−	1.36406i
$292$	3.54868	+	6.96467i	0.207671	+	0.407577i
$293$	4.28056	+	0.677974i	0.250073	+	0.0396077i	0.280212	−	0.959938i	$-0.409595\pi$
$293$	4.28056	+	0.677974i	0.250073	+	0.0396077i	−0.0301394	+	0.999546i	$0.509595\pi$
$294$	−15.7467	−	11.4407i	−0.918367	−	0.667233i
$295$	4.19531	+	3.78191i	0.244261	+	0.220191i
$296$			5.85939i			0.340570i
$297$	4.02936	−	6.47932i	0.233807	−	0.375968i
$298$	−7.76258	+	7.76258i	−0.449674	+	0.449674i
$299$	6.69682	+	20.6107i	0.387287	+	1.19195i
$300$	−10.3995	−	4.00591i	−0.600413	−	0.231281i
$301$	9.40354	−	6.83207i	0.542011	−	0.393794i
$302$	11.0712	−	5.64104i	0.637074	−	0.324605i
$303$	15.2778	−	7.78443i	0.877687	−	0.447204i
$304$	2.59693	−	1.88678i	0.148944	−	0.108214i
$305$	3.98887	+	0.421600i	0.228402	+	0.0241408i
$306$	−2.83750	−	8.73293i	−0.162209	−	0.499228i
$307$	13.5031	−	13.5031i	0.770662	−	0.770662i	−0.207560	−	0.978222i	$-0.566552\pi$
$307$	13.5031	−	13.5031i	0.770662	−	0.770662i	0.978222	+	0.207560i	$0.0665522\pi$
$308$	6.94716	−	11.1712i	0.395851	−	0.636540i
$309$			12.7058i			0.722805i
$310$	0.224963	+	4.34100i	0.0127771	+	0.246552i
$311$	−18.7825	−	13.6463i	−1.06506	−	0.773812i	−0.0900427	−	0.995938i	$-0.528700\pi$
$311$	−18.7825	−	13.6463i	−1.06506	−	0.773812i	−0.975018	+	0.222126i	$0.928700\pi$
$312$	6.56060	+	1.03910i	0.371421	+	0.0588273i
$313$	−15.3478	−	30.1218i	−0.867510	−	1.70258i	−0.696803	−	0.717263i	$-0.745395\pi$
$313$	−15.3478	−	30.1218i	−0.867510	−	1.70258i	−0.170707	−	0.985322i	$-0.554605\pi$
$314$	1.75719	−	5.40807i	0.0991638	−	0.305195i
$315$	−6.24519	−	16.2977i	−0.351877	−	0.918271i
$316$	−7.24024	+	9.96533i	−0.407295	+	0.560594i
$317$	−5.38910	+	10.5767i	−0.302682	+	0.594047i	−0.991382	−	0.130999i	$-0.958182\pi$
$317$	−5.38910	+	10.5767i	−0.302682	+	0.594047i	0.688700	+	0.725046i	$0.258182\pi$
$318$	−5.81674	−	5.81674i	−0.326187	−	0.326187i
$319$	−0.105217	+	0.249366i	−0.00589100	+	0.0139618i
$320$	−1.93714	+	1.11690i	−0.108290	+	0.0624368i
$321$	26.6969	−	8.67435i	1.49008	−	0.484155i
$322$	−4.51212	−	28.4884i	−0.251451	−	1.58760i
$323$	2.34314	−	14.7940i	0.130376	−	0.823159i
$324$	−10.4912	−	3.40880i	−0.582846	−	0.189378i
$325$	0.797208	−	14.8795i	0.0442211	−	0.825364i
$326$	−7.12396	−	9.80529i	−0.394560	−	0.543065i
$327$	28.7879	−	4.55956i	1.59198	−	0.252144i
$328$	−2.48877	−	1.26809i	−0.137419	−	0.0700185i
$329$	48.9309			2.69765
$330$	14.9700	−	7.00927i	0.824073	−	0.385848i
$331$	11.2700			0.619456			0.309728	−	0.950825i	$-0.399762\pi$
$331$	11.2700			0.619456			0.309728	+	0.950825i	$0.399762\pi$
$332$	13.4709	+	6.86376i	0.739311	+	0.376698i
$333$	−11.3884	+	1.80375i	−0.624081	+	0.0988447i
$334$	2.41316	+	3.32144i	0.132042	+	0.181741i
$335$	6.22340	+	4.04669i	0.340021	+	0.221094i
$336$	−8.40798	−	2.73192i	−0.458693	−	0.149038i
$337$	2.62548	−	16.5766i	0.143019	−	0.902987i	−0.806945	−	0.590627i	$-0.798881\pi$
$337$	2.62548	−	16.5766i	0.143019	−	0.902987i	0.949964	−	0.312360i	$-0.101119\pi$
$338$	−0.644298	−	4.06794i	−0.0350452	−	0.221267i
$339$	0.887696	−	0.288430i	0.0482130	−	0.0156654i
$340$	−2.70638	+	10.0768i	−0.146774	+	0.546493i
$341$	−4.87500	−	4.21938i	−0.263996	−	0.228492i
$342$	4.46660	+	4.46660i	0.241526	+	0.241526i
$343$	−3.12012	+	6.12358i	−0.168471	+	0.330642i
$344$	1.72247	−	2.37077i	0.0928691	−	0.127823i
$345$	14.7604	−	33.1004i	0.794672	−	1.78206i
$346$	−4.01194	+	12.3475i	−0.215683	+	0.663804i
$347$	−3.11106	−	6.10579i	−0.167010	−	0.327776i	0.792299	−	0.610133i	$-0.208884\pi$
$347$	−3.11106	−	6.10579i	−0.167010	−	0.327776i	−0.959309	+	0.282357i	$0.908884\pi$
$348$	0.179649	+	0.0284535i	0.00963017	+	0.00152527i
$349$	−9.07565	−	6.59384i	−0.485808	−	0.352960i	0.317762	−	0.948171i	$-0.397069\pi$
$349$	−9.07565	−	6.59384i	−0.485808	−	0.352960i	−0.803570	+	0.595210i	$0.797069\pi$
$350$	−4.14598	+	19.3940i	−0.221612	+	1.03665i
$351$		−	6.85598i		−	0.365945i
$352$	0.795433	−	3.21983i	0.0423967	−	0.171617i
$353$	−15.7594	+	15.7594i	−0.838790	+	0.838790i	−0.988700	−	0.149910i	$-0.952102\pi$
$353$	−15.7594	+	15.7594i	−0.838790	+	0.838790i	0.149910	+	0.988700i	$0.452102\pi$
$354$	1.73981	+	5.35457i	0.0924696	+	0.284592i
$355$	−1.51038	+	14.2901i	−0.0801625	+	0.758439i
$356$	−4.84677	+	3.52138i	−0.256878	+	0.186633i
$357$	−36.7561	+	18.7282i	−1.94534	+	0.991200i
$358$	7.25077	−	3.69445i	0.383215	−	0.195258i
$359$	−12.7399	+	9.25607i	−0.672386	+	0.488517i	−0.870823	−	0.491597i	$-0.836413\pi$
$359$	−12.7399	+	9.25607i	−0.672386	+	0.488517i	0.198437	+	0.980114i	$0.436413\pi$
$360$	−2.76716	−	3.42124i	−0.145842	−	0.180315i
$361$	−2.68723	−	8.27043i	−0.141433	−	0.435286i
$362$	−11.9704	+	11.9704i	−0.629152	+	0.629152i
$363$	−7.88222	+	23.2159i	−0.413709	+	1.21852i
$364$		−	11.8206i		−	0.619570i
$365$	17.4551	−	0.904574i	0.913642	−	0.0473475i
$366$	3.23459	+	2.35007i	0.169075	+	0.122840i
$367$	27.4914	+	4.35420i	1.43504	+	0.227288i	0.825021	−	0.565102i	$-0.191163\pi$
$367$	27.4914	+	4.35420i	1.43504	+	0.227288i	0.610016	+	0.792389i	$0.291163\pi$
$368$	−3.30136	−	6.47929i	−0.172096	−	0.337756i
$369$	1.69854	−	5.22757i	0.0884225	−	0.272136i
$370$	11.9662	+	5.33605i	0.622091	+	0.277408i
$371$	−8.60461	+	11.8432i	−0.446729	+	0.614870i
$372$	−1.96706	+	3.86058i	−0.101987	+	0.200162i
$373$	19.2605	+	19.2605i	0.997270	+	0.997270i	0.999996	−	0.00272613i	$-0.000867755\pi$
$373$	19.2605	+	19.2605i	0.997270	+	0.997270i	−0.00272613	+	0.999996i	$0.500868\pi$
$374$	−7.99929	−	13.2483i	−0.413633	−	0.685056i
$375$	−17.6515	+	17.5899i	−0.911522	+	0.908337i
$376$	11.7324	−	3.81210i	0.605054	−	0.196594i
$377$	0.0380445	+	0.240203i	0.00195939	+	0.0123711i
$378$	−1.42746	+	9.01262i	−0.0734206	+	0.463559i
$379$	−20.6465	−	6.70844i	−1.06054	−	0.344590i	−0.273742	−	0.961803i	$-0.588261\pi$
$379$	−20.6465	−	6.70844i	−1.06054	−	0.344590i	−0.786796	+	0.617214i	$0.788261\pi$
$380$	−1.48824	−	7.02175i	−0.0763450	−	0.360208i
$381$	11.3717	+	15.6518i	0.582590	+	0.801866i
$382$	10.0937	−	1.59869i	0.516440	−	0.0817960i
$383$	−28.8865	−	14.7184i	−1.47603	−	0.752075i	−0.483647	−	0.875263i	$-0.660688\pi$
$383$	−28.8865	−	14.7184i	−1.47603	−	0.752075i	−0.992383	+	0.123188i	$0.960688\pi$
$384$	−2.22887			−0.113741
$385$	−16.4875	−	24.3611i	−0.840279	−	1.24156i
$386$	22.0548			1.12256
$387$	5.13811	+	2.61800i	0.261185	+	0.133080i
$388$	−10.8420	+	1.71720i	−0.550418	+	0.0871776i
$389$	−6.37358	−	8.77248i	−0.323153	−	0.444782i	0.616273	−	0.787532i	$-0.288642\pi$
$389$	−6.37358	−	8.77248i	−0.323153	−	0.444782i	−0.939427	+	0.342750i	$0.888642\pi$
$390$	8.09668	−	12.4519i	0.409992	−	0.630526i
$391$	−32.2713	−	10.4856i	−1.63203	−	0.530278i
$392$	−1.36610	+	8.62518i	−0.0689982	+	0.435638i
$393$	0.460233	+	2.90580i	0.0232157	+	0.146578i
$394$	14.7333	−	4.78715i	0.742255	−	0.241173i
$395$	13.7578	+	23.8614i	0.692232	+	1.20060i
$396$	6.50297	+	0.554829i	0.326787	+	0.0278812i
$397$	−1.10287	−	1.10287i	−0.0553516	−	0.0553516i	0.678889	−	0.734241i	$-0.262462\pi$
$397$	−1.10287	−	1.10287i	−0.0553516	−	0.0553516i	−0.734241	+	0.678889i	$0.762462\pi$
$398$	−3.53088	+	6.92974i	−0.176987	+	0.347356i
$399$	16.6804	−	22.9586i	0.835064	−	1.14937i
$400$	0.516841	+	4.97322i	0.0258420	+	0.248661i
$401$	−6.24701	+	19.2263i	−0.311961	+	0.960116i	0.665027	+	0.746820i	$0.268420\pi$
$401$	−6.24701	+	19.2263i	−0.311961	+	0.960116i	−0.976987	+	0.213297i	$0.931580\pi$
$402$	3.35928	+	6.59297i	0.167546	+	0.328827i
$403$	−5.72199	−	0.906274i	−0.285033	−	0.0451447i
$404$	−6.22378	−	4.52184i	−0.309644	−	0.224970i
$405$	−16.5157	+	18.3210i	−0.820671	+	0.910379i
$406$		−	0.323684i		−	0.0160642i
$407$	−18.0026	+	7.31866i	−0.892357	+	0.362773i
$408$	−7.35414	+	7.35414i	−0.364084	+	0.364084i
$409$	−6.20451	−	19.0955i	−0.306793	−	0.944212i	−0.979002	−	0.203851i	$-0.934654\pi$
$409$	−6.20451	−	19.0955i	−0.306793	−	0.944212i	0.672209	−	0.740362i	$-0.265346\pi$
$410$	−4.85619	+	3.92778i	−0.239830	+	0.193979i
$411$	−32.3217	+	23.4831i	−1.59431	+	1.15834i
$412$	5.07922	−	2.58799i	0.250235	−	0.127501i
$413$	8.92723	−	4.54865i	0.439280	−	0.223825i
$414$	11.5770	−	8.41116i	0.568977	−	0.413386i
$415$	26.2850	−	21.2598i	1.29028	−	1.04360i
$416$	−0.920920	−	2.83430i	−0.0451518	−	0.138963i
$417$	−3.90609	+	3.90609i	−0.191282	+	0.191282i
$418$	9.04069	+	5.62222i	0.442195	+	0.274992i
$419$		−	0.0907865i		−	0.00443521i	−0.999998	−	0.00221761i	$-0.999294\pi$
$419$		−	0.0907865i		−	0.00443521i	0.999998	−	0.00221761i	$-0.000705886\pi$
$420$	−13.2362	+	14.6830i	−0.645859	+	0.716459i
$421$	25.5580	+	18.5690i	1.24562	+	0.904997i	0.997960	−	0.0638492i	$-0.0203377\pi$
$421$	25.5580	+	18.5690i	1.24562	+	0.904997i	0.247662	+	0.968846i	$0.420338\pi$
$422$	−9.42628	−	1.49298i	−0.458864	−	0.0726770i
$423$	11.0210	+	21.6298i	0.535857	+	1.05168i
$424$	−1.14050	+	3.51008i	−0.0553873	+	0.170465i
$425$	18.1144	+	14.7038i	0.878679	+	0.713239i
$426$	−8.41909	+	11.5879i	−0.407906	+	0.561434i
$427$	3.23018	−	6.33958i	0.156319	−	0.306794i
$428$	−8.90544	−	8.90544i	−0.430461	−	0.430461i
$429$	5.00194	+	21.4549i	0.241496	+	1.03585i
$430$	−3.27301	−	5.67667i	−0.157839	−	0.273753i
$431$	−6.52048	+	2.11863i	−0.314081	+	0.102051i	−0.461815	−	0.886976i	$-0.652802\pi$
$431$	−6.52048	+	2.11863i	−0.314081	+	0.102051i	0.147735	+	0.989027i	$0.452802\pi$
$432$	0.359884	+	2.27222i	0.0173149	+	0.109322i
$433$	−2.60280	+	16.4334i	−0.125083	+	0.789740i	0.842780	+	0.538259i	$0.180918\pi$
$433$	−2.60280	+	16.4334i	−0.125083	+	0.789740i	−0.967862	+	0.251481i	$0.919082\pi$
$434$	7.33323	+	2.38271i	0.352006	+	0.114374i
$435$	0.221711	−	0.340969i	0.0106302	−	0.0163482i
$436$	−7.68644	−	10.5795i	−0.368114	−	0.506665i
$437$	23.0552	−	3.65158i	1.10288	−	0.174679i
$438$	15.5233	+	7.90953i	0.741733	+	0.377932i
$439$	0.201886			0.00963548			0.00481774	−	0.999988i	$-0.498466\pi$
$439$	0.201886			0.00963548			0.00481774	+	0.999988i	$0.498466\pi$
$440$	−5.85121	−	4.55669i	−0.278945	−	0.217232i
$441$	−17.1846			−0.818313
$442$	−12.3904	−	6.31320i	−0.589349	−	0.300288i
$443$	−9.22116	+	1.46049i	−0.438111	+	0.0693899i	−0.371594	−	0.928395i	$-0.621189\pi$
$443$	−9.22116	+	1.46049i	−0.438111	+	0.0693899i	−0.0665168	+	0.997785i	$0.521189\pi$
$444$	7.67636	+	10.5656i	0.364304	+	0.501421i
$445$	2.77757	+	13.1050i	0.131669	+	0.621238i
$446$	−17.6521	−	5.73552i	−0.835852	−	0.271585i
$447$	−3.82769	+	24.1671i	−0.181044	+	1.14307i
$448$	0.620489	+	3.91761i	0.0293153	+	0.185090i
$449$	28.7015	−	9.32569i	1.35451	−	0.440107i	0.460303	−	0.887762i	$-0.347741\pi$
$449$	28.7015	−	9.32569i	1.35451	−	0.440107i	0.894206	+	0.447655i	$0.147741\pi$
$450$	−9.50692	+	2.53549i	−0.448160	+	0.119524i
$451$	0.787538	−	9.23048i	0.0370837	−	0.434647i
$452$	−0.296114	−	0.296114i	−0.0139280	−	0.0139280i
$453$	12.5731	−	24.6761i	0.590737	−	1.15939i
$454$	−6.61634	+	9.10662i	−0.310520	+	0.427395i
$455$	−24.1403	−	10.7649i	−1.13172	−	0.504664i
$456$	2.21090	−	6.80444i	0.103535	−	0.318647i
$457$	12.4675	+	24.4688i	0.583203	+	1.14460i	0.974511	+	0.224340i	$0.0720227\pi$
$457$	12.4675	+	24.4688i	0.583203	+	1.14460i	−0.391308	+	0.920260i	$0.627977\pi$
$458$	−4.26205	−	0.675042i	−0.199152	−	0.0315426i
$459$	8.68461	+	6.30974i	0.405363	+	0.294513i
$460$	−16.2386	+	0.841532i	−0.757130	+	0.0392366i
$461$		−	14.8765i		−	0.692866i	−0.938075	−	0.346433i	$-0.887393\pi$
$461$		−	14.8765i		−	0.692866i	0.938075	−	0.346433i	$-0.112607\pi$
$462$	−2.10832	−	29.2453i	−0.0980880	−	1.36062i
$463$	19.4801	−	19.4801i	0.905318	−	0.905318i	−0.0905720	−	0.995890i	$-0.528870\pi$
$463$	19.4801	−	19.4801i	0.905318	−	0.905318i	0.995890	+	0.0905720i	$0.0288695\pi$
$464$	−0.0252175	−	0.0776115i	−0.00117069	−	0.00360302i
$465$	6.09278	+	7.53293i	0.282546	+	0.349331i
$466$	11.8346	−	8.59837i	0.548229	−	0.398312i
$467$	−27.2368	+	13.8779i	−1.26037	+	0.642191i	−0.951129	−	0.308793i	$-0.900075\pi$
$467$	−27.2368	+	13.8779i	−1.26037	+	0.642191i	−0.309241	+	0.950984i	$0.600075\pi$
$468$	5.22530	−	2.66242i	0.241539	−	0.123071i
$469$	10.6531	−	7.73992i	0.491914	−	0.357396i
$470$	2.89938	−	27.4318i	0.133738	−	1.26534i
$471$	−3.91653	−	12.0539i	−0.180464	−	0.555412i
$472$	1.78616	−	1.78616i	0.0822145	−	0.0822145i
$473$	9.43549	+	2.33096i	0.433844	+	0.107178i
$474$			27.4548i			1.26104i
$475$	−15.6953	−	3.35527i	−0.720148	−	0.153950i
$476$	14.9735	+	10.8789i	0.686308	+	0.498632i
$477$	−7.17334	−	1.13615i	−0.328445	−	0.0520205i
$478$	3.43459	+	6.74076i	0.157094	+	0.308315i
$479$	3.79842	−	11.6903i	0.173554	−	0.534145i	−0.826010	−	0.563655i	$-0.809395\pi$
$479$	3.79842	−	11.6903i	0.173554	−	0.534145i	0.999564	+	0.0295100i	$0.00939470\pi$
$480$	−2.02979	+	4.55183i	−0.0926467	+	0.207762i
$481$	−10.2639	+	14.1270i	−0.467992	+	0.644136i
$482$	2.86788	−	5.62853i	0.130628	−	0.256372i
$483$	−45.4587	−	45.4587i	−2.06844	−	2.06844i
$484$	10.8863	−	1.57780i	0.494830	−	0.0717182i
$485$	−6.36670	+	23.7055i	−0.289097	+	1.07641i
$486$	−16.8197	+	5.46505i	−0.762957	+	0.247900i
$487$	−0.991932	−	6.26281i	−0.0449487	−	0.283795i	0.954968	−	0.296709i	$-0.0958892\pi$
$487$	−0.991932	−	6.26281i	−0.0449487	−	0.283795i	−0.999917	+	0.0129141i	$0.995889\pi$
$488$	0.280615	−	1.77173i	0.0127028	−	0.0802025i
$489$	−25.6917	−	8.34774i	−1.16182	−	0.377498i
$490$	16.3704	+	10.6447i	0.739541	+	0.480877i
$491$	−13.6000	−	18.7188i	−0.613761	−	0.844770i	0.383119	−	0.923699i	$-0.374850\pi$
$491$	−13.6000	−	18.7188i	−0.613761	−	0.844770i	−0.996880	+	0.0789292i	$0.974850\pi$
$492$	−6.14903	+	0.973911i	−0.277220	+	0.0439073i
$493$	−0.339284	−	0.172874i	−0.0152806	−	0.00778585i
$494$	9.56625			0.430406
$495$	7.05522	−	12.7752i	0.317109	−	0.574203i
$496$	1.94396			0.0872864
$497$	22.7114	+	11.5721i	1.01875	+	0.519078i
$498$	33.2828	−	5.27147i	1.49144	−	0.236220i
$499$	−24.4517	−	33.6549i	−1.09461	−	1.50660i	−0.842345	−	0.538939i	$-0.818825\pi$
$499$	−24.4517	−	33.6549i	−1.09461	−	1.50660i	−0.252263	−	0.967659i	$-0.581175\pi$
$500$	10.6271	+	3.47352i	0.475257	+	0.155340i
$501$	8.70279	+	2.82771i	0.388812	+	0.126333i
$502$	3.26832	−	20.6353i	0.145872	−	0.921000i
$503$	2.33868	+	14.7659i	0.104277	+	0.658377i	0.983354	+	0.181698i	$0.0581594\pi$
$503$	2.33868	+	14.7659i	0.104277	+	0.658377i	−0.879078	+	0.476678i	$0.841841\pi$
$504$	−7.42332	+	2.41198i	−0.330661	+	0.107438i
$505$	−14.9025	+	8.59236i	−0.663151	+	0.382355i
$506$	15.7837	−	18.2362i	0.701669	−	0.810697i
$507$	−6.49117	−	6.49117i	−0.288283	−	0.288283i
$508$	3.94067	−	7.73399i	0.174839	−	0.343140i
$509$	−14.5639	+	20.0455i	−0.645534	+	0.888501i	−0.998896	−	0.0469857i	$-0.985038\pi$
$509$	−14.5639	+	20.0455i	−0.645534	+	0.888501i	0.353362	+	0.935487i	$0.385038\pi$
$510$	8.32148	+	21.7161i	0.368481	+	0.961603i
$511$	9.58085	−	29.4868i	0.423832	−	1.30442i
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$	−7.29376	−	1.15522i	−0.322027	−	0.0510041i
$514$	−4.97218	−	3.61250i	−0.219313	−	0.159340i
$515$	−0.659691	−	12.7297i	−0.0290694	−	0.560939i
$516$		−	6.53154i		−	0.287535i
$517$	26.3668	+	31.2857i	1.15961	+	1.37594i
$518$	16.4338	−	16.4338i	0.722062	−	0.722062i
$519$	8.94207	+	27.5209i	0.392513	+	1.20803i
$520$	−6.62693	−	0.700427i	−0.290610	−	0.0307158i
$521$	−2.66594	+	1.93692i	−0.116797	+	0.0848580i	−0.644650	−	0.764477i	$-0.722997\pi$
$521$	−2.66594	+	1.93692i	−0.116797	+	0.0848580i	0.527853	+	0.849336i	$0.322997\pi$
$522$	0.143084	−	0.0729049i	0.00626262	−	0.00319096i
$523$	29.8077	−	15.1878i	1.30340	−	0.664116i	0.342112	−	0.939659i	$-0.388858\pi$
$523$	29.8077	−	15.1878i	1.30340	−	0.664116i	0.961289	+	0.275543i	$0.0888577\pi$
$524$	1.06787	−	0.775854i	0.0466502	−	0.0338933i
$525$	17.9320	+	40.4028i	0.782617	+	1.76332i
$526$	7.52274	+	23.1526i	0.328007	+	1.00950i
$527$	6.41410	−	6.41410i	0.279402	−	0.279402i
$528$	−2.78396	−	6.84805i	−0.121156	−	0.298023i
$529$		−	29.8802i		−	1.29914i
$530$	6.12973	+	5.52571i	0.266258	+	0.240022i
$531$	4.02145	+	2.92175i	0.174516	+	0.126793i
$532$	−12.5754	−	1.99176i	−0.545215	−	0.0863535i
$533$	−3.77911	−	7.41692i	−0.163691	−	0.321262i
$534$	−4.12630	+	12.6994i	−0.178563	+	0.549559i
$535$	−26.2969	+	10.0768i	−1.13691	+	0.435660i
$536$	1.95135	−	2.68580i	0.0842854	−	0.116009i
$537$	8.23444	−	16.1610i	0.355342	−	0.697399i
$538$	−19.0194	−	19.0194i	−0.819986	−	0.819986i
$539$	−28.2067	+	6.57603i	−1.21495	+	0.283250i
$540$	4.96810	+	1.33431i	0.213793	+	0.0574194i
$541$	−1.96815	+	0.639490i	−0.0846173	+	0.0274938i	−0.351020	−	0.936368i	$-0.614165\pi$
$541$	−1.96815	+	0.639490i	−0.0846173	+	0.0274938i	0.266402	+	0.963862i	$0.414165\pi$
$542$	−3.55545	−	22.4482i	−0.152720	−	0.964235i
$543$	−5.90257	+	37.2674i	−0.253303	+	1.59930i
$544$	4.43782	+	1.44193i	0.190270	+	0.0618224i
$545$	−28.6055	+	6.06285i	−1.22533	+	0.259704i
$546$	−15.4862	−	21.3149i	−0.662747	−	0.912193i
$547$	−14.2143	+	2.25132i	−0.607758	+	0.0962595i	−0.452726	−	0.891650i	$-0.649548\pi$
$547$	−14.2143	+	2.25132i	−0.607758	+	0.0962595i	−0.155033	+	0.987909i	$0.549548\pi$
$548$	15.9711	+	8.13766i	0.682250	+	0.347624i
$549$	3.52995			0.150654
$550$	−14.6343	+	7.79975i	−0.624010	+	0.332582i
$551$	0.261952			0.0111595
$552$	−14.4415	−	7.35830i	−0.614670	−	0.313190i
$553$	48.2565	−	7.64308i	2.05207	−	0.325017i
$554$	12.2247	+	16.8259i	0.519378	+	0.714862i
$555$	28.5680	−	6.05490i	1.21264	−	0.257016i
$556$	2.35711	+	0.765872i	0.0999637	+	0.0324802i
$557$	2.82606	−	17.8430i	0.119744	−	0.756033i	−0.852615	−	0.522540i	$-0.824984\pi$
$557$	2.82606	−	17.8430i	0.119744	−	0.756033i	0.972359	−	0.233493i	$-0.0750155\pi$
$558$	0.598426	+	3.77831i	0.0253334	+	0.159949i
$559$	8.30573	−	2.69870i	0.351295	−	0.114143i
$560$	8.56569	+	2.30053i	0.361967	+	0.0972150i
$561$	−31.7808	−	13.4095i	−1.34179	−	0.566148i
$562$	4.54280	+	4.54280i	0.191626	+	0.191626i
$563$	−18.7859	+	36.8694i	−0.791731	+	1.55386i	0.0403368	+	0.999186i	$0.487157\pi$
$563$	−18.7859	+	36.8694i	−0.791731	+	1.55386i	−0.832068	+	0.554674i	$0.812843\pi$
$564$	16.1616	−	22.2445i	0.680526	−	0.936664i
$565$	−0.874395	+	0.335064i	−0.0367861	+	0.0140962i
$566$	−0.299612	+	0.922111i	−0.0125936	+	0.0387592i
$567$	19.8641	+	38.9854i	0.834212	+	1.63723i
$568$	6.34720	+	1.00530i	0.266323	+	0.0421814i
$569$	−16.9040	−	12.2815i	−0.708653	−	0.514867i	0.174086	−	0.984731i	$-0.444303\pi$
$569$	−16.9040	−	12.2815i	−0.708653	−	0.514867i	−0.882739	+	0.469864i	$0.844303\pi$
$570$	−11.8827	−	10.7118i	−0.497713	−	0.448668i
$571$			0.865366i			0.0362145i	0.999836	+	0.0181072i	$0.00576403\pi$
$571$			0.865366i			0.0362145i	−0.999836	+	0.0181072i	$0.994236\pi$
$572$	7.55794	−	6.36965i	0.316013	−	0.266328i
$573$	16.1065	−	16.1065i	0.672858	−	0.672858i
$574$	3.42363	+	10.5369i	0.142900	+	0.439800i
$575$	−13.0696	+	33.9292i	−0.545041	+	1.41495i
$576$	−1.59202	+	1.15667i	−0.0663341	+	0.0481945i
$577$	10.9934	−	5.60142i	0.457661	−	0.233190i	−0.209932	−	0.977716i	$-0.567324\pi$
$577$	10.9934	−	5.60142i	0.457661	−	0.233190i	0.667594	+	0.744526i	$0.267324\pi$
$578$	4.25312	−	2.16707i	0.176907	−	0.0901384i
$579$	39.7690	−	28.8939i	1.65274	−	1.20079i
$580$	−0.181465	−	0.0191797i	−0.00753492	−	0.000796396i
$581$	−18.5310	−	57.0326i	−0.768797	−	2.36611i
$582$	−17.3005	+	17.3005i	−0.717127	+	0.717127i
$583$	−12.2090	+	0.880162i	−0.505647	+	0.0364526i
$584$		−	7.81664i		−	0.323455i
$585$	−0.678663	−	13.0958i	−0.0280593	−	0.541446i
$586$	−3.50621	−	2.54741i	−0.144840	−	0.105233i
$587$	−8.22614	−	1.30289i	−0.339529	−	0.0537761i	−0.0156582	−	0.999877i	$-0.504984\pi$
$587$	−8.22614	−	1.30289i	−0.339529	−	0.0537761i	−0.323871	+	0.946101i	$0.604984\pi$
$588$	8.83648	+	17.3426i	0.364410	+	0.715195i
$589$	−1.92829	+	5.93466i	−0.0794537	+	0.244533i
$590$	−2.02110	−	5.27434i	−0.0832074	−	0.217141i
$591$	20.2954	−	27.9342i	0.834841	−	1.14906i
$592$	2.66011	−	5.22076i	0.109330	−	0.214572i
$593$	21.2622	+	21.2622i	0.873133	+	0.873133i	0.992813	−	0.119680i	$-0.0381868\pi$
$593$	21.2622	+	21.2622i	0.873133	+	0.873133i	−0.119680	+	0.992813i	$0.538187\pi$
$594$	−6.53173	+	3.94383i	−0.268000	+	0.161817i
$595$	35.8531	−	20.6719i	1.46983	−	0.847466i
$596$	10.4406	−	3.39237i	0.427665	−	0.138957i
$597$	2.71177	+	17.1214i	0.110985	+	0.700733i
$598$	3.39015	−	21.4046i	0.138634	−	0.875297i
$599$	31.8537	+	10.3499i	1.30151	+	0.422885i	0.876105	−	0.482120i	$-0.160133\pi$
$599$	31.8537	+	10.3499i	1.30151	+	0.422885i	0.425401	+	0.905005i	$0.360133\pi$
$600$	7.44734	+	8.29054i	0.304037	+	0.338460i
$601$	−12.4882	−	17.1885i	−0.509403	−	0.701133i	0.474415	−	0.880301i	$-0.342659\pi$
$601$	−12.4882	−	17.1885i	−0.509403	−	0.701133i	−0.983819	+	0.179168i	$0.942659\pi$
$602$	−11.4803	+	1.81830i	−0.467902	+	0.0741084i
$603$	5.82086	+	2.96588i	0.237044	+	0.120780i
$604$	−12.4255			−0.505585
$605$	6.69170	−	23.6690i	0.272056	−	0.962281i
$606$	−17.1467			−0.696537
$607$	−29.9613	−	15.2661i	−1.21609	−	0.619630i	−0.276200	−	0.961100i	$-0.589075\pi$
$607$	−29.9613	−	15.2661i	−1.21609	−	0.619630i	−0.939893	+	0.341470i	$0.889075\pi$
$608$	−3.17046	+	0.502151i	−0.128579	+	0.0203649i
$609$	−0.424057	−	0.583664i	−0.0171836	−	0.0236513i
$610$	−3.36271	−	2.18656i	−0.136152	−	0.0885312i
$611$	34.9645	+	11.3607i	1.41451	+	0.459604i
$612$	−1.43643	+	9.06929i	−0.0580644	+	0.366604i
$613$	−2.69721	−	17.0295i	−0.108939	−	0.687816i	−0.980351	−	0.197263i	$-0.936795\pi$
$613$	−2.69721	−	17.0295i	−0.108939	−	0.687816i	0.871411	−	0.490553i	$-0.163205\pi$
$614$	−18.1616	+	5.90107i	−0.732943	+	0.238148i
$615$	−3.61088	+	13.4446i	−0.145605	+	0.542139i
$616$	−11.2616	+	6.79970i	−0.453743	+	0.273968i
$617$	−15.8379	−	15.8379i	−0.637611	−	0.637611i	0.312355	−	0.949965i	$-0.398882\pi$
$617$	−15.8379	−	15.8379i	−0.637611	−	0.637611i	−0.949965	+	0.312355i	$0.898882\pi$
$618$	5.76829	−	11.3209i	0.232035	−	0.455394i
$619$	−7.27397	+	10.0118i	−0.292366	+	0.402407i	−0.929781	−	0.368114i	$-0.880004\pi$
$619$	−7.27397	+	10.0118i	−0.292366	+	0.402407i	0.637415	+	0.770521i	$0.280004\pi$
$620$	1.77033	−	3.96999i	0.0710982	−	0.159439i
$621$	−5.16962	+	15.9105i	−0.207450	+	0.638465i
$622$	10.5401	+	20.6861i	0.422618	+	0.829435i
$623$	23.4702	+	3.71731i	0.940312	+	0.148931i
$624$	−5.37380	−	3.90429i	−0.215124	−	0.156297i
$625$	16.7716	−	18.5395i	0.670863	−	0.741582i
$626$			33.8065i			1.35118i
$627$	23.6677	−	1.70623i	0.945198	−	0.0681402i
$628$	−4.02088	+	4.02088i	−0.160450	+	0.160450i
$629$	−8.44886	−	26.0029i	−0.336878	−	1.03680i
$630$	−1.83449	+	17.3566i	−0.0730878	+	0.691504i
$631$	−32.0471	+	23.2836i	−1.27577	+	0.926905i	−0.999417	−	0.0341502i	$-0.989128\pi$
$631$	−32.0471	+	23.2836i	−1.27577	+	0.926905i	−0.276358	+	0.961055i	$0.589128\pi$
$632$	10.9753	−	5.59218i	0.436573	−	0.222445i
$633$	−18.9533	+	9.65720i	−0.753327	+	0.383839i
$634$	9.60345	−	6.97731i	0.381402	−	0.277104i
$635$	−12.2058	−	15.0909i	−0.484373	−	0.598864i
$636$	2.54201	+	7.82350i	0.100797	+	0.310222i
$637$	−18.4023	+	18.4023i	−0.729127	+	0.729127i
$638$	0.206959	−	0.174420i	0.00819357	−	0.00690534i
$639$			12.6460i			0.500268i
$640$	2.23307	−	0.115724i	0.0882699	−	0.00457440i
$641$	26.3762	+	19.1634i	1.04180	+	0.756910i	0.970636	−	0.240555i	$-0.0773294\pi$
$641$	26.3762	+	19.1634i	1.04180	+	0.756910i	0.0711615	+	0.997465i	$0.477329\pi$
$642$	−27.7252	−	4.39124i	−1.09423	−	0.173308i
$643$	5.85631	+	11.4937i	0.230950	+	0.453266i	0.977177	−	0.212426i	$-0.0681365\pi$
$643$	5.85631	+	11.4937i	0.230950	+	0.453266i	−0.746227	+	0.665692i	$0.768137\pi$
$644$	−8.91314	+	27.4318i	−0.351227	+	1.08097i
$645$	−13.3388	−	5.94816i	−0.525216	−	0.234209i
$646$	−8.80407	+	12.1178i	−0.346392	+	0.476767i
$647$	−0.360903	+	0.708311i	−0.0141885	+	0.0278466i	−0.897992	−	0.440012i	$-0.854974\pi$
$647$	−0.360903	+	0.708311i	−0.0141885	+	0.0278466i	0.883803	+	0.467858i	$0.154974\pi$
$648$	7.80018	+	7.80018i	0.306420	+	0.306420i
$649$	7.71885	+	3.25686i	0.302991	+	0.127843i
$650$	−7.46545	+	12.8958i	−0.292819	+	0.505814i
$651$	16.3448	−	5.31074i	0.640603	−	0.208144i
$652$	1.89599	+	11.9708i	0.0742525	+	0.468812i
$653$	0.611758	−	3.86249i	0.0239400	−	0.151151i	−0.972823	−	0.231551i	$-0.925620\pi$
$653$	0.611758	−	3.86249i	0.0239400	−	0.151151i	0.996763	+	0.0804004i	$0.0256199\pi$
$654$	−27.7202	−	9.00685i	−1.08395	−	0.352196i
$655$	−0.611972	−	2.88738i	−0.0239117	−	0.112819i
$656$	1.64181	+	2.25975i	0.0641017	+	0.0882285i
$657$	15.1925	−	2.40626i	0.592717	−	0.0938772i
$658$	−43.5978	−	22.2142i	−1.69962	−	0.865999i
$659$	−2.33997			−0.0911522			−0.0455761	−	0.998961i	$-0.514512\pi$
$659$	−2.33997			−0.0911522			−0.0455761	+	0.998961i	$0.514512\pi$
$660$	−16.5205	−	0.550943i	−0.643061	−	0.0214454i
$661$	−28.1337			−1.09428			−0.547138	−	0.837043i	$-0.684283\pi$
$661$	−28.1337			−1.09428			−0.547138	+	0.837043i	$0.684283\pi$
$662$	−10.0417	−	5.11648i	−0.390280	−	0.198858i
$663$	−30.6130	+	4.84863i	−1.18891	+	0.188305i
$664$	−8.88657	−	12.2313i	−0.344866	−	0.474667i
$665$	−15.5198	+	23.8680i	−0.601833	+	0.925560i
$666$	10.9660	+	3.56308i	0.424925	+	0.138067i
$667$	0.0928322	−	0.586120i	0.00359448	−	0.0226946i
$668$	−0.642245	−	4.05497i	−0.0248492	−	0.156892i
$669$	−39.3442	+	12.7837i	−1.52114	+	0.494247i
$670$	−3.70793	−	6.43099i	−0.143250	−	0.248451i
$671$	5.79403	−	1.35081i	0.223676	−	0.0521473i
$672$	6.25130	+	6.25130i	0.241149	+	0.241149i
$673$	−9.37899	+	18.4073i	−0.361534	+	0.709550i	−0.998096	−	0.0616753i	$-0.980356\pi$
$673$	−9.37899	+	18.4073i	−0.361534	+	0.709550i	0.636563	+	0.771225i	$0.280356\pi$
$674$	−9.86495	+	13.5779i	−0.379984	+	0.523003i
$675$	7.24931	−	8.93082i	0.279026	−	0.343748i
$676$	−1.27273	+	3.91706i	−0.0489512	+	0.150656i
$677$	1.30583	+	2.56283i	0.0501870	+	0.0984976i	0.914738	−	0.404048i	$-0.132397\pi$
$677$	1.30583	+	2.56283i	0.0501870	+	0.0984976i	−0.864551	+	0.502545i	$0.832397\pi$
$678$	−0.921887	−	0.146013i	−0.0354049	−	0.00560758i
$679$	35.2247	+	25.5923i	1.35180	+	0.982141i
$680$	6.98619	−	7.74985i	0.267908	−	0.297193i
$681$			25.0890i			0.961413i
$682$	2.42810	+	5.97270i	0.0929768	+	0.228706i
$683$	4.54465	−	4.54465i	0.173896	−	0.173896i	−0.614793	−	0.788689i	$-0.710760\pi$
$683$	4.54465	−	4.54465i	0.173896	−	0.173896i	0.788689	+	0.614793i	$0.210760\pi$
$684$	−1.95198	−	6.00757i	−0.0746357	−	0.229705i
$685$	31.1635	−	25.2056i	1.19069	−	0.963056i
$686$	5.56010	−	4.03965i	0.212285	−	0.154234i
$687$	−8.56965	+	4.36646i	−0.326953	+	0.166591i
$688$	−2.61104	+	1.33039i	−0.0995448	+	0.0507206i
$689$	−8.89833	+	6.46501i	−0.338999	+	0.246297i
$690$	−28.1788	+	22.7916i	−1.07275	+	0.867661i
$691$	6.11570	+	18.8222i	0.232652	+	0.716030i	0.997424	+	0.0717289i	$0.0228516\pi$
$691$	6.11570	+	18.8222i	0.232652	+	0.716030i	−0.764772	+	0.644301i	$0.777148\pi$
$692$	9.18030	−	9.18030i	0.348983	−	0.348983i
$693$	−16.6828	−	19.7950i	−0.633726	−	0.751951i
$694$			6.85269i			0.260124i
$695$	3.71066	−	4.11627i	0.140753	−	0.156139i
$696$	−0.147150	−	0.106911i	−0.00557772	−	0.00405245i
$697$	12.8732	+	2.03891i	0.487607	+	0.0772293i
$698$	5.09292	+	9.99542i	0.192770	+	0.378332i
$699$	10.0754	−	31.0090i	0.381088	−	1.17287i
$700$	12.4988	−	15.3980i	0.472410	−	0.581988i
$701$	−3.26547	+	4.49454i	−0.123335	+	0.169756i	−0.866220	−	0.499663i	$-0.833457\pi$
$701$	−3.26547	+	4.49454i	−0.123335	+	0.169756i	0.742885	+	0.669420i	$0.233457\pi$
$702$	−3.11255	+	6.10872i	−0.117476	+	0.230559i
$703$	13.2996	+	13.2996i	0.501605	+	0.501605i
$704$	−2.17051	+	2.50777i	−0.0818041	+	0.0945151i
$705$	−30.7101	−	53.2632i	−1.15661	−	2.00601i
$706$	21.1964	−	6.88712i	0.797737	−	0.259200i
$707$	4.77343	+	30.1382i	0.179523	+	1.13347i
$708$	0.880746	−	5.56081i	0.0331005	−	0.208988i
$709$	31.7561	+	10.3182i	1.19262	+	0.387507i	0.837042	−	0.547138i	$-0.184283\pi$
$709$	31.7561	+	10.3182i	1.19262	+	0.387507i	0.355582	+	0.934645i	$0.384283\pi$
$710$	7.83332	−	12.0469i	0.293979	−	0.452111i
$711$	14.2477	+	19.6102i	0.534329	+	0.735440i
$712$	5.91718	−	0.937189i	0.221756	−	0.0351226i
$713$	12.5955	+	6.41772i	0.471705	+	0.240346i
$714$	41.2523			1.54383
$715$	−6.12534	−	21.2357i	−0.229075	−	0.794170i
$716$	−8.13773			−0.304121
$717$	15.0242	+	7.65524i	0.561091	+	0.285890i
$718$	15.5535	−	2.46343i	0.580451	−	0.0919344i
$719$	−11.8552	−	16.3173i	−0.442125	−	0.608532i	0.528558	−	0.848897i	$-0.322733\pi$
$719$	−11.8552	−	16.3173i	−0.442125	−	0.608532i	−0.970683	+	0.240365i	$0.922733\pi$
$720$	0.912349	+	4.30461i	0.0340012	+	0.160423i
$721$	−21.5043	−	6.98716i	−0.800860	−	0.260215i
$722$	−1.36036	+	8.58898i	−0.0506274	+	0.319649i
$723$	−2.20257	−	13.9065i	−0.0819146	−	0.517188i
$724$	16.1002	−	5.23127i	0.598359	−	0.194419i
$725$	−0.204426	+	0.353124i	−0.00759219	+	0.0131147i
$726$	17.5629	−	17.1071i	0.651821	−	0.634904i
$727$	3.28024	+	3.28024i	0.121657	+	0.121657i	0.765314	−	0.643657i	$-0.222584\pi$
$727$	3.28024	+	3.28024i	0.121657	+	0.121657i	−0.643657	+	0.765314i	$0.722584\pi$
$728$	−5.36646	+	10.5323i	−0.198894	+	0.390352i
$729$	−3.71759	+	5.11682i	−0.137688	+	0.189512i
$730$	−15.9633	−	7.11847i	−0.590828	−	0.263466i
$731$	−4.22549	+	13.0047i	−0.156285	+	0.480997i
$732$	−1.81513	−	3.56240i	−0.0670892	−	0.131670i
$733$	−33.9874	−	5.38308i	−1.25535	−	0.198828i	−0.506894	−	0.862009i	$-0.669206\pi$
$733$	−33.9874	−	5.38308i	−1.25535	−	0.198828i	−0.748460	+	0.663180i	$0.769206\pi$
$734$	−22.5182	−	16.3604i	−0.831162	−	0.603875i
$735$	43.4645	−	2.25246i	1.60321	−	0.0830831i
$736$			7.27188i			0.268045i
$737$	10.6893	+	2.64070i	0.393745	+	0.0972716i
$738$	−3.88668	+	3.88668i	−0.143071	+	0.143071i
$739$	−0.0954132	−	0.293652i	−0.00350983	−	0.0108022i	0.949286	−	0.314413i	$-0.101808\pi$
$739$	−0.0954132	−	0.293652i	−0.00350983	−	0.0108022i	−0.952796	+	0.303611i	$0.901808\pi$
$740$	−8.23942	−	10.1870i	−0.302887	−	0.374481i
$741$	17.2498	−	12.5327i	0.633686	−	0.460400i
$742$	13.0435	−	6.64599i	0.478841	−	0.243982i
$743$	−1.10902	+	0.565075i	−0.0406860	+	0.0207306i	−0.474215	−	0.880409i	$-0.657268\pi$
$743$	−1.10902	+	0.565075i	−0.0406860	+	0.0207306i	0.433529	+	0.901140i	$0.357268\pi$
$744$	3.50533	−	2.54677i	0.128512	−	0.0933692i
$745$	2.58014	−	24.4114i	0.0945292	−	0.894366i
$746$	−8.41714	−	25.9053i	−0.308173	−	0.948460i
$747$	21.0374	−	21.0374i	0.769716	−	0.769716i
$748$	1.11279	+	15.4360i	0.0406878	+	0.564395i
$749$			49.9542i			1.82529i
$750$	23.7133	−	7.65906i	0.865886	−	0.279669i
$751$	−19.6696	−	14.2908i	−0.717754	−	0.521479i	0.167912	−	0.985802i	$-0.446298\pi$
$751$	−19.6696	−	14.2908i	−0.717754	−	0.521479i	−0.885666	+	0.464323i	$0.846298\pi$
$752$	−12.1843	−	1.92981i	−0.444317	−	0.0703729i
$753$	−21.1408	−	41.4912i	−0.770415	−	1.51202i
$754$	0.0751522	−	0.231295i	0.00273688	−	0.00842326i
$755$	−11.3156	+	25.3755i	−0.411818	+	0.923509i
$756$	5.36352	−	7.38225i	0.195069	−	0.268490i
$757$	−12.8369	+	25.1939i	−0.466566	+	0.915688i	0.531093	+	0.847313i	$0.321781\pi$
$757$	−12.8369	+	25.1939i	−0.466566	+	0.915688i	−0.997660	+	0.0683747i	$0.978219\pi$
$758$	15.3506	+	15.3506i	0.557558	+	0.557558i
$759$	4.56982	−	53.5614i	0.165874	−	1.94416i
$760$	−1.86178	+	6.93207i	−0.0675337	+	0.251453i
$761$	−32.7506	+	10.6413i	−1.18721	+	0.385747i	−0.835040	−	0.550190i	$-0.814555\pi$
$761$	−32.7506	+	10.6413i	−1.18721	+	0.385747i	−0.352168	+	0.935937i	$0.614555\pi$
$762$	−3.02649	−	19.1085i	−0.109638	−	0.692228i
$763$	−8.11411	+	51.2305i	−0.293750	+	1.85467i
$764$	−9.71936	−	3.15801i	−0.351634	−	0.114253i
$765$	17.2133	+	11.1928i	0.622350	+	0.404675i
$766$	19.0560	+	26.2284i	0.688522	+	0.947670i
$767$	7.43522	−	1.17762i	0.268470	−	0.0425215i
$768$	1.98593	+	1.01188i	0.0716612	+	0.0365132i
$769$	−22.6026			−0.815072			−0.407536	−	0.913189i	$-0.633612\pi$
$769$	−22.6026			−0.815072			−0.407536	+	0.913189i	$0.633612\pi$
$770$	3.63074	+	29.1910i	0.130843	+	1.05197i
$771$	−13.6985			−0.493339
$772$	−19.6510	−	10.0127i	−0.707254	−	0.360364i
$773$	−43.4361	+	6.87959i	−1.56229	+	0.247442i	−0.876876	−	0.480716i	$-0.840377\pi$
$773$	−43.4361	+	6.87959i	−1.56229	+	0.247442i	−0.685410	+	0.728158i	$0.740377\pi$
$774$	−3.38954	−	4.66530i	−0.121835	−	0.167691i
$775$	−6.49539	−	7.23080i	−0.233321	−	0.259738i
$776$	10.4399	+	3.39212i	0.374769	+	0.121770i
$777$	8.10346	−	51.1632i	0.290710	−	1.83547i
$778$	1.69628	+	10.7099i	0.0608145	+	0.383968i
$779$	−8.52730	+	2.77069i	−0.305522	+	0.0992701i
$780$	−12.8672	+	7.41890i	−0.460721	+	0.265639i
$781$	4.83924	+	20.7570i	0.173162	+	0.742746i
$782$	23.9936	+	23.9936i	0.858008	+	0.858008i
$783$	−0.0852307	+	0.167275i	−0.00304590	+	0.00597791i
$784$	5.13295	−	7.06490i	0.183320	−	0.252318i
$785$	4.54977	+	11.8732i	0.162388	+	0.423774i
$786$	0.909134	−	2.79803i	0.0324277	−	0.0998023i
$787$	−8.70928	−	17.0929i	−0.310452	−	0.609297i	0.682080	−	0.731277i	$-0.261075\pi$
$787$	−8.70928	−	17.0929i	−0.310452	−	0.609297i	−0.992533	+	0.121980i	$0.961075\pi$
$788$	−15.3008	−	2.42341i	−0.545069	−	0.0863305i
$789$	43.8970	+	31.8931i	1.56278	+	1.13542i
$790$	−1.42547	−	27.5066i	−0.0507160	−	0.978641i
$791$			1.66102i			0.0590592i
$792$	−5.54230	−	3.44664i	−0.196937	−	0.122471i
$793$	3.78009	−	3.78009i	0.134235	−	0.134235i
$794$	0.481974	+	1.48336i	0.0171046	+	0.0526425i
$795$	18.2923	+	1.93338i	0.648760	+	0.0685701i
$796$	6.29207	−	4.57146i	0.223017	−	0.162031i
$797$	3.43669	−	1.75108i	0.121734	−	0.0620265i	−0.392063	−	0.919938i	$-0.628238\pi$
$797$	3.43669	−	1.75108i	0.121734	−	0.0620265i	0.513797	+	0.857912i	$0.328238\pi$
$798$	−25.2853	+	12.8835i	−0.895090	+	0.456071i
$799$	−46.5696	+	33.8348i	−1.64751	+	1.19699i
$800$	1.79728	−	4.66581i	0.0635436	−	0.164961i
$801$	3.64307	+	11.2122i	0.128722	+	0.396164i
$802$	14.2947	−	14.2947i	0.504763	−	0.504763i
$803$	24.0161	−	9.76335i	0.847511	−	0.344541i
$804$		−	7.39946i		−	0.260959i
$805$	47.9047	+	43.1843i	1.68842	+	1.52204i
$806$	4.68689	+	3.40522i	0.165089	+	0.119944i
$807$	−59.2129	−	9.37840i	−2.08439	−	0.330135i
$808$	3.49255	+	6.85452i	0.122868	+	0.241141i
$809$	9.68199	−	29.7981i	0.340400	−	1.04764i	−0.623600	−	0.781744i	$-0.714330\pi$
$809$	9.68199	−	29.7981i	0.340400	−	1.04764i	0.964000	−	0.265901i	$-0.0856695\pi$
$810$	23.0332	−	8.82619i	0.809303	−	0.310121i
$811$	29.8031	−	41.0204i	1.04653	−	1.44042i	0.154746	−	0.987954i	$-0.450544\pi$
$811$	29.8031	−	41.0204i	1.04653	−	1.44042i	0.891781	−	0.452467i	$-0.149456\pi$
$812$	−0.146949	+	0.288405i	−0.00515692	+	0.0101210i
$813$	−35.8205	−	35.8205i	−1.25628	−	1.25628i
$814$	19.3631	+	1.65204i	0.678675	+	0.0579041i
$815$	26.1736	+	7.02956i	0.916821	+	0.246235i
$816$	9.89130	−	3.21388i	0.346265	−	0.112508i
$817$	−1.47152	−	9.29081i	−0.0514820	−	0.325044i
$818$	−3.14092	+	19.8310i	−0.109820	+	0.693375i
$819$	−22.1227	−	7.18810i	−0.773030	−	0.251173i
$820$	6.11007	−	1.29501i	0.213373	−	0.0452237i
$821$	−3.78341	−	5.20742i	−0.132042	−	0.181740i	0.737877	−	0.674936i	$-0.235829\pi$
$821$	−3.78341	−	5.20742i	−0.132042	−	0.181740i	−0.869918	+	0.493196i	$0.835829\pi$
$822$	39.4600	−	6.24985i	1.37632	−	0.217988i
$823$	10.2211	+	5.20789i	0.356284	+	0.181536i	0.622966	−	0.782249i	$-0.285927\pi$
$823$	10.2211	+	5.20789i	0.356284	+	0.181536i	−0.266682	+	0.963784i	$0.585927\pi$
$824$	−5.70055			−0.198588
$825$	−16.1701	+	33.2368i	−0.562971	+	1.15716i
$826$	−10.0193			−0.348615
$827$	17.0635	+	8.69429i	0.593356	+	0.302330i	0.724763	−	0.688999i	$-0.241949\pi$
$827$	17.0635	+	8.69429i	0.593356	+	0.302330i	−0.131407	+	0.991329i	$0.541949\pi$
$828$	−14.1337	+	2.23856i	−0.491181	+	0.0777955i
$829$	1.12936	+	1.55443i	0.0392242	+	0.0539875i	0.828179	−	0.560464i	$-0.189377\pi$
$829$	1.12936	+	1.55443i	0.0392242	+	0.0539875i	−0.788954	+	0.614452i	$0.789377\pi$
$830$	−33.0719	+	7.00948i	−1.14794	+	0.243303i
$831$	44.0869	+	14.3247i	1.52936	+	0.496919i
$832$	−0.466200	+	2.94347i	−0.0161626	+	0.102046i
$833$	−6.37447	−	40.2468i	−0.220862	−	1.39447i
$834$	5.25368	−	1.70703i	0.181920	−	0.0591094i
$835$	−8.86603	−	2.38119i	−0.306821	−	0.0824044i
$836$	−5.50288	−	9.11382i	−0.190321	−	0.315208i
$837$	−3.16229	−	3.16229i	−0.109305	−	0.109305i
$838$	−0.0412162	+	0.0808914i	−0.00142379	+	0.00279435i
$839$	−1.68441	+	2.31839i	−0.0581522	+	0.0800396i	−0.837103	−	0.547046i	$-0.815752\pi$
$839$	−1.68441	+	2.31839i	−0.0581522	+	0.0800396i	0.778950	+	0.627085i	$0.215752\pi$
$840$	18.4595	−	7.07358i	0.636913	−	0.244062i
$841$	−8.95943	+	27.5743i	−0.308946	+	0.950838i
$842$	−14.3422	−	28.1482i	−0.494266	−	0.970051i
$843$	14.1430	+	2.24004i	0.487112	+	0.0771509i
$844$	7.72108	+	5.60970i	0.265771	+	0.193094i
$845$	6.84045	+	6.16639i	0.235318	+	0.212130i
$846$		−	24.2757i		−	0.834617i
$847$	−34.9580	−	26.1074i	−1.20117	−	0.897062i
$848$	2.60973	−	2.60973i	0.0896186	−	0.0896186i
$849$	0.667795	+	2.05526i	0.0229187	+	0.0705364i
$850$	−9.46469	−	21.3250i	−0.324636	−	0.731440i
$851$	34.4712	−	25.0448i	1.18166	−	0.858526i
$852$	12.7622	−	6.50269i	0.437227	−	0.222778i
$853$	−16.9233	+	8.62287i	−0.579444	+	0.295241i	−0.719042	−	0.694967i	$-0.755419\pi$
$853$	−16.9233	+	8.62287i	−0.579444	+	0.295241i	0.139598	+	0.990208i	$0.455419\pi$
$854$	−5.75621	+	4.18213i	−0.196974	+	0.143110i
$855$	−14.0464	−	1.48462i	−0.480377	−	0.0507730i
$856$	3.89182	+	11.9778i	0.133020	+	0.409393i
$857$	9.24508	−	9.24508i	0.315806	−	0.315806i	−0.531348	−	0.847154i	$-0.678314\pi$
$857$	9.24508	−	9.24508i	0.315806	−	0.315806i	0.847154	+	0.531348i	$0.178314\pi$
$858$	5.28357	−	21.3873i	0.180378	−	0.730151i
$859$			0.806684i			0.0275237i	0.999905	+	0.0137619i	$0.00438067\pi$
$859$			0.806684i			0.0275237i	−0.999905	+	0.0137619i	$0.995619\pi$
$860$	0.339122	+	6.54387i	0.0115640	+	0.223144i
$861$	19.9777	+	14.5147i	0.680839	+	0.494659i
$862$	6.77163	+	1.07252i	0.230643	+	0.0365302i
$863$	4.95462	+	9.72398i	0.168657	+	0.331008i	0.959829	−	0.280586i	$-0.0905287\pi$
$863$	4.95462	+	9.72398i	0.168657	+	0.331008i	−0.791172	+	0.611594i	$0.790529\pi$
$864$	0.710906	−	2.18794i	0.0241855	−	0.0744353i
$865$	−10.3878	−	27.1085i	−0.353197	−	0.921717i
$866$	9.77973	−	13.4607i	0.332329	−	0.457412i
$867$	4.83012	−	9.47964i	0.164039	−	0.321945i
$868$	−5.45223	−	5.45223i	−0.185061	−	0.185061i
$869$	30.8903	+	26.7359i	1.04788	+	0.906954i
$870$	−0.352343	+	0.203151i	−0.0119455	+	0.00688747i
$871$	9.40940	−	3.05730i	0.318825	−	0.103593i
$872$	2.04569	+	12.9160i	0.0692757	+	0.437390i
$873$	−3.37918	+	21.3353i	−0.114368	+	0.722091i
$874$	−22.2001	−	7.21325i	−0.750930	−	0.243992i
$875$	−20.0636	−	39.5479i	−0.678273	−	1.33696i
$876$	−10.2405	−	14.0949i	−0.345995	−	0.476222i
$877$	−32.3552	+	5.12456i	−1.09256	+	0.173044i	−0.676608	−	0.736344i	$-0.736551\pi$
$877$	−32.3552	+	5.12456i	−1.09256	+	0.173044i	−0.415949	+	0.909388i	$0.636551\pi$
$878$	−0.179882	−	0.0916542i	−0.00607071	−	0.00309318i
$879$	−9.65972			−0.325814
$880$	3.14477	+	6.71643i	0.106010	+	0.226411i
$881$	54.9218			1.85036			0.925181	−	0.379526i	$-0.123913\pi$
$881$	54.9218			1.85036			0.925181	+	0.379526i	$0.123913\pi$
$882$	15.3116	+	7.80164i	0.515567	+	0.262695i
$883$	−13.9402	+	2.20791i	−0.469125	+	0.0743021i	−0.386522	−	0.922280i	$-0.626324\pi$
$883$	−13.9402	+	2.20791i	−0.469125	+	0.0743021i	−0.0826036	+	0.996582i	$0.526324\pi$
$884$	8.17375	+	11.2502i	0.274913	+	0.378385i
$885$	−10.5543	−	6.86281i	−0.354779	−	0.230691i
$886$	8.87916	+	2.88501i	0.298301	+	0.0969240i
$887$	5.10680	−	32.2431i	0.171470	−	1.08262i	−0.740409	−	0.672157i	$-0.765368\pi$
$887$	5.10680	−	32.2431i	0.171470	−	1.08262i	0.911878	−	0.410460i	$-0.134632\pi$
$888$	−2.04300	−	12.8990i	−0.0685587	−	0.432863i
$889$	−32.7439	+	10.6391i	−1.09820	+	0.356826i
$890$	3.47472	−	12.9377i	0.116473	−	0.433671i
$891$	−14.2228	+	33.7084i	−0.476481	+	1.12927i
$892$	13.1243	+	13.1243i	0.439434	+	0.439434i
$893$	17.9776	−	35.2829i	0.601596	−	1.18070i
$894$	14.3821	−	19.7953i	0.481011	−	0.662054i
$895$	−7.41089	+	16.6190i	−0.247719	+	0.555513i
$896$	1.22570	−	3.77231i	0.0409477	−	0.126024i
$897$	−21.9289	−	43.0379i	−0.732185	−	1.43699i
$898$	−29.8070	−	4.72097i	−0.994673	−	0.157541i
$899$	0.128341	+	0.0932451i	0.00428041	+	0.00310990i
$900$	9.62181	+	2.05691i	0.320727	+	0.0685638i
$901$		−	17.2216i		−	0.573735i
$902$	−4.89225	+	7.86689i	−0.162894	+	0.261939i
$903$	−18.3190	+	18.3190i	−0.609619	+	0.609619i
$904$	0.129407	+	0.398272i	0.00430400	+	0.0132463i
$905$	3.97876	−	37.6441i	0.132258	−	1.25133i
$906$	−22.4055	+	16.2785i	−0.744372	+	0.540818i
$907$	−9.48671	+	4.83372i	−0.315001	+	0.160501i	−0.604342	−	0.796725i	$-0.706564\pi$
$907$	−9.48671	+	4.83372i	−0.315001	+	0.160501i	0.289341	+	0.957226i	$0.406564\pi$
$908$	10.0295	−	5.11030i	0.332841	−	0.169591i
$909$	−12.2474	+	8.89827i	−0.406221	+	0.295137i
$910$	16.6221	+	20.5510i	0.551016	+	0.681260i
$911$	0.763148	+	2.34873i	0.0252842	+	0.0778168i	0.962902	−	0.269850i	$-0.0869741\pi$
$911$	0.763148	+	2.34873i	0.0252842	+	0.0778168i	−0.937618	+	0.347667i	$0.886974\pi$
$912$	−5.05907	+	5.05907i	−0.167523	+	0.167523i
$913$	26.4802	−	42.5810i	0.876367	−	1.40922i
$914$		−	27.4619i		−	0.908360i
$915$	−8.92821	+	0.462685i	−0.295157	+	0.0152959i
$916$	3.49105	+	2.53640i	0.115348	+	0.0838049i
$917$	−5.17110	−	0.819022i	−0.170765	−	0.0270465i
$918$	−4.87348	−	9.56475i	−0.160849	−	0.315684i
$919$	−12.9101	+	39.7333i	−0.425866	+	1.31068i	0.476297	+	0.879285i	$0.341979\pi$
$919$	−12.9101	+	39.7333i	−0.425866	+	1.31068i	−0.902163	+	0.431396i	$0.858021\pi$
$920$	14.8508	+	6.62237i	0.489615	+	0.218333i
$921$	−25.0179	+	34.4342i	−0.824368	+	1.13465i
$922$	−6.75377	+	13.2550i	−0.222424	+	0.436531i
$923$	13.5421	+	13.5421i	0.445745	+	0.445745i
$924$	−11.3986	+	27.0149i	−0.374985	+	0.888726i
$925$	−28.3075	+	7.54959i	−0.930746	+	0.248229i
$926$	−26.2007	+	8.51312i	−0.861008	+	0.279759i
$927$	−1.75485	−	11.0797i	−0.0576367	−	0.363904i
$928$	−0.0127659	+	0.0806009i	−0.000419062	+	0.00264585i
$929$	−28.4482	−	9.24339i	−0.933356	−	0.303266i	−0.197422	−	0.980319i	$-0.563257\pi$
$929$	−28.4482	−	9.24339i	−0.933356	−	0.303266i	−0.735934	+	0.677053i	$0.763257\pi$
$930$	−2.00882	−	9.47795i	−0.0658719	−	0.310794i
$931$	16.4767	+	22.6782i	0.540001	+	0.743247i
$932$	−14.4483	+	2.28839i	−0.473271	+	0.0749587i
$933$	46.1065	+	23.4924i	1.50946	+	0.769107i
$934$	30.5686			1.00024
$935$	32.5370	+	11.7847i	1.06407	+	0.385401i
$936$	−5.86449			−0.191687
$937$	27.0607	+	13.7881i	0.884036	+	0.450439i	0.836205	−	0.548417i	$-0.184769\pi$
$937$	27.0607	+	13.7881i	0.884036	+	0.450439i	0.0478305	+	0.998855i	$0.484769\pi$
$938$	−13.0058	+	2.05992i	−0.424655	+	0.0672587i
$939$	44.2897	+	60.9595i	1.44534	+	1.98934i
$940$	−15.0372	+	23.1256i	−0.490458	+	0.754275i
$941$	37.8725	+	12.3055i	1.23461	+	0.401149i	0.852382	−	0.522920i	$-0.175157\pi$
$941$	37.8725	+	12.3055i	1.23461	+	0.401149i	0.382227	+	0.924068i	$0.375157\pi$
$942$	−1.98268	+	12.5181i	−0.0645991	+	0.407863i
$943$	3.17748	+	20.0618i	0.103473	+	0.653302i
$944$	−2.40237	+	0.780579i	−0.0781906	+	0.0254057i
$945$	−10.1917	−	17.6764i	−0.331536	−	0.575012i
$946$	−7.34885	−	6.36053i	−0.238932	−	0.206799i
$947$	−4.82949	−	4.82949i	−0.156937	−	0.156937i	0.624271	−	0.781208i	$-0.285396\pi$
$947$	−4.82949	−	4.82949i	−0.156937	−	0.156937i	−0.781208	+	0.624271i	$0.785396\pi$
$948$	12.4642	−	24.4624i	0.404819	−	0.794502i
$949$	13.6924	−	18.8459i	0.444473	−	0.611764i
$950$	12.4613	+	10.1151i	0.404298	+	0.328176i
$951$	8.17590	−	25.1628i	0.265122	−	0.815961i
$952$	−8.40256	−	16.4909i	−0.272328	−	0.534475i
$953$	19.5290	+	3.09310i	0.632608	+	0.100195i	0.464499	−	0.885573i	$-0.346234\pi$
$953$	19.5290	+	3.09310i	0.632608	+	0.100195i	0.168108	+	0.985769i	$0.446234\pi$
$954$	5.87569	+	4.26894i	0.190233	+	0.138212i
$955$	−15.3006	+	16.9731i	−0.495116	+	0.549237i
$956$		−	7.56533i		−	0.244680i
$957$	0.144680	−	0.585647i	0.00467683	−	0.0189313i
$958$	−8.69172	+	8.69172i	−0.280817	+	0.280817i
$959$	−21.9704	−	67.6178i	−0.709460	−	2.18349i
$960$	3.87504	−	3.13421i	0.125066	−	0.101156i
$961$	22.0223	−	16.0001i	0.710396	−	0.516133i
$962$	15.5587	−	7.92755i	0.501632	−	0.255595i
$963$	−22.0822	+	11.2514i	−0.711588	+	0.362572i
$964$	−5.11060	+	3.71307i	−0.164601	+	0.119590i
$965$	−38.3439	+	31.0132i	−1.23433	+	0.998351i
$966$	19.8662	+	61.1418i	0.639184	+	1.96721i
$967$	−1.05132	+	1.05132i	−0.0338081	+	0.0338081i	−0.723809	−	0.690001i	$-0.757610\pi$
$967$	−1.05132	+	1.05132i	−0.0338081	+	0.0338081i	0.690001	+	0.723809i	$0.257610\pi$
$968$	−10.4160	−	3.53643i	−0.334784	−	0.113665i
$969$			33.3848i			1.07247i
$970$	16.4348	−	18.2313i	0.527691	−	0.585373i
$971$	−36.1581	−	26.2704i	−1.16037	−	0.843057i	−0.170544	−	0.985350i	$-0.554553\pi$
$971$	−36.1581	−	26.2704i	−1.16037	−	0.843057i	−0.989825	+	0.142293i	$0.954553\pi$
$972$	17.4675	+	2.76659i	0.560272	+	0.0887383i
$973$	−4.46295	−	8.75903i	−0.143076	−	0.280802i
$974$	−1.95944	+	6.03053i	−0.0627845	+	0.193231i
$975$	3.43305	+	33.0340i	0.109946	+	1.05793i
$976$	−1.05438	+	1.45123i	−0.0337498	+	0.0464526i
$977$	6.15577	−	12.0814i	0.196940	−	0.386517i	−0.771325	−	0.636441i	$-0.780406\pi$
$977$	6.15577	−	12.0814i	0.196940	−	0.386517i	0.968265	+	0.249924i	$0.0804057\pi$
$978$	19.1017	+	19.1017i	0.610804	+	0.610804i
$979$	10.2703	+	17.0096i	0.328240	+	0.543628i
$980$	−9.75359	−	16.9165i	−0.311567	−	0.540377i
$981$	−24.4739	+	7.95206i	−0.781392	+	0.253890i
$982$	3.61954	+	22.8529i	0.115504	+	0.729265i
$983$	4.07455	−	25.7257i	0.129958	−	0.820523i	−0.833472	−	0.552562i	$-0.813650\pi$
$983$	4.07455	−	25.7257i	0.129958	−	0.820523i	0.963430	−	0.267961i	$-0.0863497\pi$
$984$	5.92098	+	1.92384i	0.188754	+	0.0613298i
$985$	−18.8833	+	29.0407i	−0.601673	+	0.925313i
$986$	0.223821	+	0.308064i	0.00712792	+	0.00981074i
$987$	−107.718	+	17.0608i	−3.42869	+	0.543052i
$988$	−8.52359	−	4.34299i	−0.271171	−	0.138169i
$989$	−21.3098			−0.677611
$990$	−12.0861	+	8.17980i	−0.384121	+	0.259971i
$991$	34.9392			1.10988			0.554940	−	0.831890i	$-0.312741\pi$
$991$	34.9392			1.10988			0.554940	+	0.831890i	$0.312741\pi$
$992$	−1.73208	−	0.882540i	−0.0549936	−	0.0280207i
$993$	−24.8101	+	3.92953i	−0.787324	+	0.124700i
$994$	−14.9824	−	20.6216i	−0.475214	−	0.654076i
$995$	−3.60584	−	17.0129i	−0.114313	−	0.539346i
$996$	−32.0484	−	10.4131i	−1.01549	−	0.329953i
$997$	−8.55527	+	54.0159i	−0.270948	+	1.71070i	0.358393	+	0.933571i	$0.383325\pi$
$997$	−8.55527	+	54.0159i	−0.270948	+	1.71070i	−0.629341	+	0.777129i	$0.716675\pi$
$998$	6.50762	+	41.0875i	0.205995	+	1.30060i
$999$	−12.8200	+	4.16548i	−0.405607	+	0.131790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.k.a.17.1	yes	48
3.2	odd	2		990.2.bh.c.127.4		48
4.3	odd	2		880.2.cm.c.17.5		48
5.2	odd	4		550.2.bh.b.193.6		48
5.3	odd	4	inner	110.2.k.a.83.1	yes	48
5.4	even	2		550.2.bh.b.457.6		48
11.2	odd	10	inner	110.2.k.a.57.1	yes	48
15.8	even	4		990.2.bh.c.523.5		48
20.3	even	4		880.2.cm.c.193.5		48
33.2	even	10		990.2.bh.c.937.5		48
44.35	even	10		880.2.cm.c.497.5		48
55.2	even	20		550.2.bh.b.343.6		48
55.13	even	20	inner	110.2.k.a.13.1	✓	48
55.24	odd	10		550.2.bh.b.57.6		48
165.68	odd	20		990.2.bh.c.343.4		48
220.123	odd	20		880.2.cm.c.673.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.13.1	✓	48	55.13	even	20	inner
110.2.k.a.17.1	yes	48	1.1	even	1	trivial
110.2.k.a.57.1	yes	48	11.2	odd	10	inner
110.2.k.a.83.1	yes	48	5.3	odd	4	inner
550.2.bh.b.57.6		48	55.24	odd	10
550.2.bh.b.193.6		48	5.2	odd	4
550.2.bh.b.343.6		48	55.2	even	20
550.2.bh.b.457.6		48	5.4	even	2
880.2.cm.c.17.5		48	4.3	odd	2
880.2.cm.c.193.5		48	20.3	even	4
880.2.cm.c.497.5		48	44.35	even	10
880.2.cm.c.673.5		48	220.123	odd	20
990.2.bh.c.127.4		48	3.2	odd	2
990.2.bh.c.343.4		48	165.68	odd	20
990.2.bh.c.523.5		48	15.8	even	4
990.2.bh.c.937.5		48	33.2	even	10

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.891007 - 0.453990i) q^{2} +(-2.20142 + 0.348671i) q^{3} +(0.587785 + 0.809017i) q^{4} +(2.18748 - 0.463629i) q^{5} +(2.11978 + 0.688757i) q^{6} +(0.620489 - 3.91761i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(1.87153 - 0.608097i) q^{9} +O(q^{10})\)	\(q+(-0.891007 - 0.453990i) q^{2} +(-2.20142 + 0.348671i) q^{3} +(0.587785 + 0.809017i) q^{4} +(2.18748 - 0.463629i) q^{5} +(2.11978 + 0.688757i) q^{6} +(0.620489 - 3.91761i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(1.87153 - 0.608097i) q^{9} +(-2.15954 - 0.579997i) q^{10} +(2.83922 - 1.71431i) q^{11} +(-1.57605 - 1.57605i) q^{12} +(1.35296 - 2.65534i) q^{13} +(-2.33142 + 3.20892i) q^{14} +(-4.65391 + 1.78335i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(2.11841 + 4.15761i) q^{17} +(-1.94362 - 0.307838i) q^{18} +(-2.59693 - 1.88678i) q^{19} +(1.66085 + 1.49719i) q^{20} +8.84068i q^{21} +(-3.30804 + 0.238480i) q^{22} +(-5.14200 + 5.14200i) q^{23} +(0.688757 + 2.11978i) q^{24} +(4.57010 - 2.02835i) q^{25} +(-2.41100 + 1.75169i) q^{26} +(2.04980 - 1.04442i) q^{27} +(3.53413 - 1.80073i) q^{28} +(-0.0660203 + 0.0479665i) q^{29} +(4.95629 + 0.523850i) q^{30} +(-0.600717 - 1.84882i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-5.65259 + 4.76387i) q^{33} -4.66620i q^{34} +(-0.459014 - 8.85736i) q^{35} +(1.59202 + 1.15667i) q^{36} +(-5.78725 - 0.916611i) q^{37} +(1.45730 + 2.86011i) q^{38} +(-2.05261 + 6.31728i) q^{39} +(-0.800117 - 2.08802i) q^{40} +(1.64181 - 2.25975i) q^{41} +(4.01358 - 7.87710i) q^{42} +(2.07213 + 2.07213i) q^{43} +(3.05575 + 1.28933i) q^{44} +(3.81199 - 2.19789i) q^{45} +(6.91597 - 2.24713i) q^{46} +(1.92981 + 12.1843i) q^{47} +(0.348671 - 2.20142i) q^{48} +(-8.30529 - 2.69855i) q^{49} +(-4.99284 - 0.267505i) q^{50} +(-6.11316 - 8.41404i) q^{51} +(2.94347 - 0.466200i) q^{52} +(-3.28846 - 1.67555i) q^{53} -2.30054 q^{54} +(5.41592 - 5.06634i) q^{55} -3.96645 q^{56} +(6.37480 + 3.24812i) q^{57} +(0.0806009 - 0.0127659i) q^{58} +(1.48475 + 2.04358i) q^{59} +(-4.17826 - 2.71686i) q^{60} +(1.70602 + 0.554319i) q^{61} +(-0.304102 + 1.92003i) q^{62} +(-1.22102 - 7.70925i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(1.72848 - 6.43577i) q^{65} +(7.19925 - 1.67841i) q^{66} +(2.34748 + 2.34748i) q^{67} +(-2.11841 + 4.15761i) q^{68} +(9.52685 - 13.1126i) q^{69} +(-3.61217 + 8.10035i) q^{70} +(-1.98584 + 6.11179i) q^{71} +(-0.893382 - 1.75336i) q^{72} +(7.72040 + 1.22279i) q^{73} +(4.74035 + 3.44406i) q^{74} +(-9.35350 + 6.05873i) q^{75} -3.20998i q^{76} +(-4.95428 - 12.1867i) q^{77} +(4.69687 - 4.69687i) q^{78} +(3.80642 + 11.7150i) q^{79} +(-0.235030 + 2.22368i) q^{80} +(-8.92437 + 6.48393i) q^{81} +(-2.48877 + 1.26809i) q^{82} +(13.4709 - 6.86376i) q^{83} +(-7.15226 + 5.19642i) q^{84} +(6.56156 + 8.11252i) q^{85} +(-0.905554 - 2.78701i) q^{86} +(0.128614 - 0.128614i) q^{87} +(-2.13735 - 2.53609i) q^{88} +5.99094i q^{89} +(-4.39433 + 0.227727i) q^{90} +(-9.56310 - 6.94800i) q^{91} +(-7.18235 - 1.13757i) q^{92} +(1.96706 + 3.86058i) q^{93} +(3.81210 - 11.7324i) q^{94} +(-6.55548 - 2.92327i) q^{95} +(-1.31009 + 1.80319i) q^{96} +(-4.98351 + 9.78069i) q^{97} +(6.17495 + 6.17495i) q^{98} +(4.27122 - 4.93489i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7}+O(q^{10}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36} + 20 q^{37} - 36 q^{38} - 20 q^{41} - 20 q^{42} + 16 q^{45} + 40 q^{46} + 40 q^{47} + 4 q^{48} + 40 q^{50} + 40 q^{51} + 40 q^{52} + 96 q^{55} - 8 q^{56} + 48 q^{58} + 20 q^{60} + 80 q^{61} + 40 q^{62} + 100 q^{63} + 24 q^{66} + 20 q^{68} - 56 q^{70} - 56 q^{71} - 20 q^{73} - 76 q^{75} - 96 q^{77} + 16 q^{78} - 12 q^{80} - 68 q^{81} - 80 q^{85} - 56 q^{86} - 4 q^{88} - 80 q^{90} - 68 q^{91} - 12 q^{92} + 76 q^{93} + 20 q^{95} + 72 q^{97}+O(q^{100}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Introduction

L-functions

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