LMFDB - Embedded newform 260.2.bg.c.23.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(23,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("260.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bg (of order $12$, degree $4$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.15
Character	$\chi$	$=$	260.23
Dual form			260.2.bg.c.147.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.565829 + 1.29609i) q^{2} +(2.90282 + 0.777809i) q^{3} +(-1.35968 - 1.46672i) q^{4} +(0.446275 - 2.19108i) q^{5} +(-2.65061 + 3.32220i) q^{6} +(-0.874770 - 3.26469i) q^{7} +(2.67034 - 0.932342i) q^{8} +(5.22332 + 3.01568i) q^{9} +(2.58731 + 1.81819i) q^{10} +(1.15104 + 1.99367i) q^{11} +(-2.80607 - 5.31521i) q^{12} +(0.690411 + 3.53883i) q^{13} +(4.72628 + 0.713476i) q^{14} +(2.99970 - 6.01320i) q^{15} +(-0.302562 + 3.98854i) q^{16} +(0.868722 + 3.24211i) q^{17} +(-6.86408 + 5.06350i) q^{18} +(-3.12105 - 1.80194i) q^{19} +(-3.82050 + 2.32460i) q^{20} -10.1572i q^{21} +(-3.23526 + 0.363778i) q^{22} +(-6.82930 - 1.82991i) q^{23} +(8.47672 - 0.629405i) q^{24} +(-4.60168 - 1.95565i) q^{25} +(-4.97728 - 1.10754i) q^{26} +(6.44169 + 6.44169i) q^{27} +(-3.59899 + 5.72196i) q^{28} +(3.11068 - 1.79595i) q^{29} +(6.09631 + 7.29031i) q^{30} -3.41729 q^{31} +(-4.99829 - 2.64898i) q^{32} +(1.79058 + 6.68255i) q^{33} +(-4.69361 - 0.708543i) q^{34} +(-7.54358 + 0.459745i) q^{35} +(-2.67884 - 11.7615i) q^{36} +(-1.15462 + 4.30910i) q^{37} +(4.10144 - 3.02555i) q^{38} +(-0.748393 + 10.8096i) q^{39} +(-0.851129 - 6.26702i) q^{40} +(4.54947 - 2.62664i) q^{41} +(13.1646 + 5.74724i) q^{42} +(2.04769 + 7.64209i) q^{43} +(1.35911 - 4.39901i) q^{44} +(8.93864 - 10.0989i) q^{45} +(6.23593 - 7.81594i) q^{46} +(2.06802 - 2.06802i) q^{47} +(-3.98061 + 11.3427i) q^{48} +(-3.83078 + 2.21170i) q^{49} +(5.13845 - 4.85761i) q^{50} +10.0870i q^{51} +(4.25176 - 5.82431i) q^{52} +(1.47596 + 1.47596i) q^{53} +(-11.9939 + 4.70409i) q^{54} +(4.88197 - 1.63231i) q^{55} +(-5.37974 - 7.90225i) q^{56} +(-7.65828 - 7.65828i) q^{57} +(0.567595 + 5.04790i) q^{58} +(-7.88272 - 4.55109i) q^{59} +(-12.8983 + 3.77628i) q^{60} +(-6.75570 + 11.7012i) q^{61} +(1.93360 - 4.42910i) q^{62} +(5.27606 - 19.6905i) q^{63} +(6.26148 - 4.97935i) q^{64} +(8.06198 + 0.0665445i) q^{65} +(-9.67432 - 1.46043i) q^{66} +(-3.73572 - 1.00098i) q^{67} +(3.57411 - 5.68240i) q^{68} +(-18.4009 - 10.6238i) q^{69} +(3.67251 - 10.0373i) q^{70} +(4.21945 - 7.30830i) q^{71} +(16.7597 + 3.18300i) q^{72} +(-0.802185 + 0.802185i) q^{73} +(-4.93165 - 3.93470i) q^{74} +(-11.8367 - 9.25613i) q^{75} +(1.60067 + 7.02776i) q^{76} +(5.50180 - 5.50180i) q^{77} +(-13.5867 - 7.08637i) q^{78} -1.05896 q^{79} +(8.60419 + 2.44293i) q^{80} +(4.64163 + 8.03955i) q^{81} +(0.830127 + 7.38273i) q^{82} +(5.65651 + 5.65651i) q^{83} +(-14.8978 + 13.8105i) q^{84} +(7.49143 - 0.456566i) q^{85} +(-11.0634 - 1.67013i) q^{86} +(10.4266 - 2.79381i) q^{87} +(4.93246 + 4.25061i) q^{88} +(-1.40915 - 2.44071i) q^{89} +(8.03128 + 17.2995i) q^{90} +(10.9492 - 5.34964i) q^{91} +(6.60167 + 12.5048i) q^{92} +(-9.91978 - 2.65800i) q^{93} +(1.51019 + 3.85048i) q^{94} +(-5.34103 + 6.03431i) q^{95} +(-12.4488 - 11.5772i) q^{96} +(-10.6238 + 2.84663i) q^{97} +(-0.698989 - 6.21646i) q^{98} +13.8847i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 6 q^{2} - 12 q^{6} + 12 q^{10} - 12 q^{12} + 4 q^{13} - 12 q^{16} - 24 q^{17} - 42 q^{20} - 12 q^{22} - 24 q^{25} - 36 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 76 q^{36} + 48 q^{37} - 16 q^{38}+ \cdots - 162 q^{98}+O(q^{100}) $ 144 * q - 6 * q^2 - 12 * q^6 + 12 * q^10 - 12 * q^12 + 4 * q^13 - 12 * q^16 - 24 * q^17 - 42 * q^20 - 12 * q^22 - 24 * q^25 - 36 * q^26 - 6 * q^28 - 36 * q^32 - 12 * q^33 - 76 * q^36 + 48 * q^37 - 16 * q^38 + 76 * q^40 - 72 * q^41 + 40 * q^42 - 120 * q^45 - 12 * q^46 - 40 * q^48 + 120 * q^50 - 10 * q^52 + 8 * q^53 - 20 * q^56 + 126 * q^58 + 16 * q^61 - 44 * q^62 + 32 * q^65 + 96 * q^66 - 64 * q^68 - 54 * q^72 - 12 * q^76 + 40 * q^77 - 100 * q^78 - 24 * q^80 - 32 * q^81 - 78 * q^82 - 24 * q^85 - 10 * q^88 - 8 * q^90 + 100 * q^92 - 48 * q^93 - 12 * q^97 - 162 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.565829	+	1.29609i	−0.400101	+	0.916471i
$2$	−0.565829	+	1.29609i	−0.400101	+	0.916471i
$3$	2.90282	+	0.777809i	1.67595	+	0.449068i	0.966704	−	0.255898i	$-0.0823710\pi$
$3$	2.90282	+	0.777809i	1.67595	+	0.449068i	0.709241	+	0.704966i	$0.249038\pi$
$4$	−1.35968	−	1.46672i	−0.679838	−	0.733362i
$5$	0.446275	−	2.19108i	0.199580	−	0.979881i
$5$	0.446275	−	2.19108i	0.199580	−	0.979881i
$6$	−2.65061	+	3.32220i	−1.08211	+	1.35628i
$7$	−0.874770	−	3.26469i	−0.330632	−	1.23394i	−0.908528	−	0.417825i	$-0.862793\pi$
$7$	−0.874770	−	3.26469i	−0.330632	−	1.23394i	0.577896	−	0.816111i	$-0.303874\pi$
$8$	2.67034	−	0.932342i	0.944109	−	0.329633i
$9$	5.22332	+	3.01568i	1.74111	+	1.00523i
$10$	2.58731	+	1.81819i	0.818181	+	0.574961i
$11$	1.15104	+	1.99367i	0.347053	+	0.601113i	0.985725	−	0.168366i	$-0.0538491\pi$
$11$	1.15104	+	1.99367i	0.347053	+	0.601113i	−0.638672	+	0.769479i	$0.720516\pi$
$12$	−2.80607	−	5.31521i	−0.810042	−	1.53437i
$13$	0.690411	+	3.53883i	0.191486	+	0.981495i
$13$	0.690411	+	3.53883i	0.191486	+	0.981495i
$14$	4.72628	+	0.713476i	1.26315	+	0.190684i
$15$	2.99970	−	6.01320i	0.774519	−	1.55260i
$16$	−0.302562	+	3.98854i	−0.0756406	+	0.997135i
$17$	0.868722	+	3.24211i	0.210696	+	0.786328i	0.987637	+	0.156755i	$0.0501035\pi$
$17$	0.868722	+	3.24211i	0.210696	+	0.786328i	−0.776941	+	0.629573i	$0.783230\pi$
$18$	−6.86408	+	5.06350i	−1.61788	+	1.19348i
$19$	−3.12105	−	1.80194i	−0.716017	−	0.413393i	0.0972680	−	0.995258i	$-0.468990\pi$
$19$	−3.12105	−	1.80194i	−0.716017	−	0.413393i	−0.813285	+	0.581866i	$0.802323\pi$
$20$	−3.82050	+	2.32460i	−0.854290	+	0.519796i
$21$		−	10.1572i		−	2.21648i
$22$	−3.23526	+	0.363778i	−0.689759	+	0.0775577i
$23$	−6.82930	−	1.82991i	−1.42401	−	0.381562i	−0.537104	−	0.843516i	$-0.680482\pi$
$23$	−6.82930	−	1.82991i	−1.42401	−	0.381562i	−0.886904	+	0.461954i	$0.847148\pi$
$24$	8.47672	−	0.629405i	1.73030	−	0.128477i
$25$	−4.60168	−	1.95565i	−0.920335	−	0.391130i
$26$	−4.97728	−	1.10754i	−0.976126	−	0.217206i
$27$	6.44169	+	6.44169i	1.23970	+	1.23970i
$28$	−3.59899	+	5.72196i	−0.680146	+	1.08135i
$29$	3.11068	−	1.79595i	0.577638	−	0.333499i	−0.182556	−	0.983195i	$-0.558437\pi$
$29$	3.11068	−	1.79595i	0.577638	−	0.333499i	0.760194	+	0.649696i	$0.225104\pi$
$30$	6.09631	+	7.29031i	1.11303	+	1.33102i
$31$	−3.41729			−0.613763			−0.306882	−	0.951748i	$-0.599286\pi$
$31$	−3.41729			−0.613763			−0.306882	+	0.951748i	$0.599286\pi$
$32$	−4.99829	−	2.64898i	−0.883581	−	0.468277i
$33$	1.79058	+	6.68255i	0.311701	+	1.16328i
$34$	−4.69361	−	0.708543i	−0.804947	−	0.121514i
$35$	−7.54358	+	0.459745i	−1.27510	+	0.0777110i
$36$	−2.67884	−	11.7615i	−0.446473	−	1.96025i
$37$	−1.15462	+	4.30910i	−0.189818	+	0.708412i	0.803729	+	0.594995i	$0.202846\pi$
$37$	−1.15462	+	4.30910i	−0.189818	+	0.708412i	−0.993548	+	0.113416i	$0.963821\pi$
$38$	4.10144	−	3.02555i	0.665342	−	0.490810i
$39$	−0.748393	+	10.8096i	−0.119839	+	1.73092i
$40$	−0.851129	−	6.26702i	−0.134575	−	0.990903i
$41$	4.54947	−	2.62664i	0.710508	−	0.410212i	−0.100741	−	0.994913i	$-0.532121\pi$
$41$	4.54947	−	2.62664i	0.710508	−	0.410212i	0.811249	+	0.584701i	$0.198788\pi$
$42$	13.1646	+	5.74724i	2.03134	+	0.886818i
$43$	2.04769	+	7.64209i	0.312270	+	1.16541i	0.926504	+	0.376284i	$0.122798\pi$
$43$	2.04769	+	7.64209i	0.312270	+	1.16541i	−0.614234	+	0.789124i	$0.710535\pi$
$44$	1.35911	−	4.39901i	0.204894	−	0.663175i
$45$	8.93864	−	10.0989i	1.33249	−	1.50545i
$46$	6.23593	−	7.81594i	0.919437	−	1.15240i
$47$	2.06802	−	2.06802i	0.301652	−	0.301652i	−0.540008	−	0.841660i	$-0.681579\pi$
$47$	2.06802	−	2.06802i	0.301652	−	0.301652i	0.841660	+	0.540008i	$0.181579\pi$
$48$	−3.98061	+	11.3427i	−0.574551	+	1.63718i
$49$	−3.83078	+	2.21170i	−0.547254	+	0.315957i
$50$	5.13845	−	4.85761i	0.726687	−	0.686969i
$51$			10.0870i			1.41246i
$52$	4.25176	−	5.82431i	0.589613	−	0.807686i
$53$	1.47596	+	1.47596i	0.202739	+	0.202739i	0.801172	−	0.598433i	$-0.204210\pi$
$53$	1.47596	+	1.47596i	0.202739	+	0.202739i	−0.598433	+	0.801172i	$0.704210\pi$
$54$	−11.9939	+	4.70409i	−1.63216	+	0.640146i
$55$	4.88197	−	1.63231i	0.658284	−	0.220100i
$56$	−5.37974	−	7.90225i	−0.718898	−	1.05598i
$57$	−7.65828	−	7.65828i	−1.01436	−	1.01436i
$58$	0.567595	+	5.04790i	0.0745289	+	0.662822i
$59$	−7.88272	−	4.55109i	−1.02624	−	0.592502i	−0.110337	−	0.993894i	$-0.535193\pi$
$59$	−7.88272	−	4.55109i	−1.02624	−	0.592502i	−0.915906	+	0.401392i	$0.868526\pi$
$60$	−12.8983	+	3.77628i	−1.66517	+	0.487515i
$61$	−6.75570	+	11.7012i	−0.864979	+	1.49819i	0.00208956	+	0.999998i	$0.499335\pi$
$61$	−6.75570	+	11.7012i	−0.864979	+	1.49819i	−0.867068	+	0.498189i	$0.833998\pi$
$62$	1.93360	−	4.42910i	0.245567	−	0.562496i
$63$	5.27606	−	19.6905i	0.664721	−	2.48077i
$64$	6.26148	−	4.97935i	0.782685	−	0.622418i
$65$	8.06198	+	0.0665445i	0.999966	+	0.00825383i
$66$	−9.67432	−	1.46043i	−1.19083	−	0.179766i
$67$	−3.73572	−	1.00098i	−0.456390	−	0.122289i	0.0232977	−	0.999729i	$-0.492583\pi$
$67$	−3.73572	−	1.00098i	−0.456390	−	0.122289i	−0.479688	+	0.877439i	$0.659250\pi$
$68$	3.57411	−	5.68240i	0.433424	−	0.689092i
$69$	−18.4009	−	10.6238i	−2.21521	−	1.27895i
$70$	3.67251	−	10.0373i	0.438948	−	1.19968i
$71$	4.21945	−	7.30830i	0.500757	−	0.867336i	−0.499243	−	0.866462i	$-0.666388\pi$
$71$	4.21945	−	7.30830i	0.500757	−	0.867336i	1.00000		0.000874105i	$-0.000278236\pi$
$72$	16.7597	+	3.18300i	1.97515	+	0.375120i
$73$	−0.802185	+	0.802185i	−0.0938887	+	0.0938887i	−0.752491	−	0.658602i	$-0.771148\pi$
$73$	−0.802185	+	0.802185i	−0.0938887	+	0.0938887i	0.658602	+	0.752491i	$0.271148\pi$
$74$	−4.93165	−	3.93470i	−0.573292	−	0.457399i
$75$	−11.8367	−	9.25613i	−1.36679	−	1.06881i
$76$	1.60067	+	7.02776i	0.183609	+	0.806140i
$77$	5.50180	−	5.50180i	0.626988	−	0.626988i
$78$	−13.5867	−	7.08637i	−1.53839	−	0.802373i
$79$	−1.05896			−0.119142			−0.0595711	−	0.998224i	$-0.518973\pi$
$79$	−1.05896			−0.119142			−0.0595711	+	0.998224i	$0.518973\pi$
$80$	8.60419	+	2.44293i	0.961978	+	0.273127i
$81$	4.64163	+	8.03955i	0.515737	+	0.893283i
$82$	0.830127	+	7.38273i	0.0916722	+	0.815286i
$83$	5.65651	+	5.65651i	0.620882	+	0.620882i	0.945757	−	0.324875i	$-0.105322\pi$
$83$	5.65651	+	5.65651i	0.620882	+	0.620882i	−0.324875	+	0.945757i	$0.605322\pi$
$84$	−14.8978	+	13.8105i	−1.62549	+	1.50685i
$85$	7.49143	−	0.456566i	0.812559	−	0.0495215i
$86$	−11.0634	−	1.67013i	−1.19300	−	0.180095i
$87$	10.4266	−	2.79381i	1.11785	−	0.299528i
$88$	4.93246	+	4.25061i	0.525802	+	0.453117i
$89$	−1.40915	−	2.44071i	−0.149369	−	0.258715i	0.781625	−	0.623748i	$-0.214391\pi$
$89$	−1.40915	−	2.44071i	−0.149369	−	0.258715i	−0.930995	+	0.365033i	$0.881058\pi$
$90$	8.03128	+	17.2995i	0.846571	+	1.82353i
$91$	10.9492	−	5.34964i	1.14779	−	0.560795i
$92$	6.60167	+	12.5048i	0.688271	+	1.30371i
$93$	−9.91978	−	2.65800i	−1.02863	−	0.275621i
$94$	1.51019	+	3.85048i	0.155764	+	0.397146i
$95$	−5.34103	+	6.03431i	−0.547979	+	0.619107i
$96$	−12.4488	−	11.5772i	−1.27055	−	1.18160i
$97$	−10.6238	+	2.84663i	−1.07868	+	0.289032i	−0.754056	−	0.656811i	$-0.771905\pi$
$97$	−10.6238	+	2.84663i	−1.07868	+	0.289032i	−0.324626	+	0.945842i	$0.605238\pi$
$98$	−0.698989	−	6.21646i	−0.0706086	−	0.627957i
$99$			13.8847i			1.39547i
$100$	3.38839	+	9.40844i	0.338839	+	0.940844i
$101$	−2.37776	−	4.11840i	−0.236596	−	0.409796i	0.723139	−	0.690702i	$-0.242698\pi$
$101$	−2.37776	−	4.11840i	−0.236596	−	0.409796i	−0.959735	+	0.280906i	$0.909365\pi$
$102$	−13.0736	−	5.70750i	−1.29448	−	0.565127i
$103$	1.99725	−	1.99725i	0.196795	−	0.196795i	−0.601829	−	0.798625i	$-0.705561\pi$
$103$	1.99725	−	1.99725i	0.196795	−	0.196795i	0.798625	+	0.601829i	$0.205561\pi$
$104$	5.14304	+	8.80620i	0.504316	+	0.863519i
$105$	−22.2553	−	4.53291i	−2.17189	−	0.442367i
$106$	−2.74812	+	1.07783i	−0.266921	+	0.104688i
$107$	0.507737	−	1.89490i	0.0490848	−	0.183187i	−0.937031	−	0.349246i	$-0.886438\pi$
$107$	0.507737	−	1.89490i	0.0490848	−	0.183187i	0.986116	+	0.166059i	$0.0531043\pi$
$108$	0.689575	−	18.2068i	0.0663543	−	1.75195i
$109$	8.90824			0.853255			0.426627	−	0.904427i	$-0.359702\pi$
$109$	8.90824			0.853255			0.426627	+	0.904427i	$0.359702\pi$
$110$	−0.646747	+	7.25106i	−0.0616649	+	0.691361i
$111$	−6.70331	+	11.6105i	−0.636250	+	1.10202i
$112$	13.2860	−	2.50128i	1.25541	−	0.236349i
$113$	5.31798	−	1.42495i	0.500274	−	0.134048i	0.000146769	−	1.00000i	$-0.499953\pi$
$113$	5.31798	−	1.42495i	0.500274	−	0.134048i	0.500127	+	0.865952i	$0.333287\pi$
$114$	14.2591	−	5.59251i	1.33548	−	0.523787i
$115$	−7.05722	+	14.1469i	−0.658089	+	1.31921i
$116$	−6.86367	−	2.12060i	−0.637276	−	0.196892i
$117$	−7.06576	+	20.5665i	−0.653229	+	1.90137i
$118$	10.3589	−	7.64155i	0.953612	−	0.703461i
$119$	9.82456	−	5.67221i	0.900616	−	0.519971i
$120$	2.40387	−	18.8541i	0.219442	−	1.72113i
$121$	2.85020	−	4.93668i	0.259109	−	0.448789i
$122$	−11.3432	−	15.3768i	−1.02697	−	1.39215i
$123$	15.2493	−	4.08604i	1.37499	−	0.368426i
$124$	4.64640	+	5.01222i	0.417259	+	0.450111i
$125$	−6.33860	+	9.20989i	−0.566942	+	0.823758i
$126$	22.5352	+	17.9797i	2.00760	+	1.60176i
$127$	−4.29043	+	16.0121i	−0.380714	+	1.42084i	0.464099	+	0.885783i	$0.346378\pi$
$127$	−4.29043	+	16.0121i	−0.380714	+	1.42084i	−0.844813	+	0.535061i	$0.820289\pi$
$128$	2.91074	+	10.9329i	0.257275	+	0.966338i
$129$			23.7763i			2.09339i
$130$	−4.64795	+	10.4114i	−0.407652	+	0.913137i
$131$		−	8.68888i		−	0.759151i	−0.925161	−	0.379575i	$-0.876070\pi$
$131$		−	8.68888i		−	0.759151i	0.925161	−	0.379575i	$-0.123930\pi$
$132$	7.36685	−	11.7124i	0.641202	−	1.01943i
$133$	−3.15256	+	11.7655i	−0.273362	+	1.02020i
$134$	3.41113	−	4.27542i	0.294677	−	0.369340i
$135$	16.9890	−	11.2395i	1.46218	−	0.967343i
$136$	5.34255	+	7.84762i	0.458120	+	0.672928i
$137$	3.28355	−	0.879825i	0.280533	−	0.0751685i	−0.115809	−	0.993271i	$-0.536946\pi$
$137$	3.28355	−	0.879825i	0.280533	−	0.0751685i	0.396342	+	0.918103i	$0.370279\pi$
$138$	24.1811	−	17.8379i	2.05843	−	1.51847i
$139$	10.9319	−	18.9347i	0.927235	−	1.60602i	0.139309	−	0.990249i	$-0.455512\pi$
$139$	10.9319	−	18.9347i	0.927235	−	1.60602i	0.787927	−	0.615769i	$-0.211155\pi$
$140$	10.9311	+	10.4393i	0.923850	+	0.882278i
$141$	7.61162	−	4.39457i	0.641014	−	0.370090i
$142$	7.08470	+	9.60402i	0.594535	+	0.805951i
$143$	−6.26056	+	5.44980i	−0.523534	+	0.455735i
$144$	−13.6086	+	19.9210i	−1.13405	+	1.66008i
$145$	−2.54685	−	7.61723i	−0.211505	−	0.632577i
$146$	−0.585801	−	1.49360i	−0.0484813	−	0.123611i
$147$	−12.8403	+	3.44056i	−1.05905	+	0.283773i
$148$	7.89017	−	4.16547i	0.648568	−	0.342400i
$149$	10.2922	−	17.8267i	0.843172	−	1.46042i	−0.0440271	−	0.999030i	$-0.514019\pi$
$149$	10.2922	−	17.8267i	0.843172	−	1.46042i	0.887199	−	0.461387i	$-0.152648\pi$
$150$	18.6943	−	10.1040i	1.52638	−	0.824991i
$151$	−12.3291			−1.00333			−0.501666	−	0.865062i	$-0.667279\pi$
$151$	−12.3291			−1.00333			−0.501666	+	0.865062i	$0.667279\pi$
$152$	−10.0143	−	1.90191i	−0.812266	−	0.154265i
$153$	−5.23958	+	19.5544i	−0.423595	+	1.58088i
$154$	4.01773	+	10.2439i	0.323758	+	0.825475i
$155$	−1.52505	+	7.48756i	−0.122495	+	0.601415i
$156$	16.8723	−	13.5999i	1.35086	−	1.08886i
$157$	−2.20785	+	2.20785i	−0.176206	+	0.176206i	−0.789699	−	0.613494i	$-0.789764\pi$
$157$	−2.20785	+	2.20785i	−0.176206	+	0.176206i	0.613494	+	0.789699i	$0.289764\pi$
$158$	0.599189	−	1.37250i	0.0476689	−	0.109190i
$159$	3.13644	+	5.43247i	0.248736	+	0.430823i
$160$	−8.03474	+	9.76949i	−0.635202	+	0.772346i
$161$			23.8963i			1.88329i
$162$	−13.0463	+	1.46695i	−1.02501	+	0.115254i
$163$	−10.1608	+	2.72259i	−0.795858	+	0.213249i	−0.633765	−	0.773526i	$-0.718491\pi$
$163$	−10.1608	+	2.72259i	−0.795858	+	0.213249i	−0.162093	+	0.986775i	$0.551825\pi$
$164$	−10.0384	−	3.10144i	−0.783864	−	0.242182i
$165$	15.4411	−	0.941061i	1.20209	−	0.0732615i
$166$	−10.5319	+	4.13071i	−0.817437	+	0.320605i
$167$	4.32642	+	1.15926i	0.334788	+	0.0897062i	0.422297	−	0.906458i	$-0.361224\pi$
$167$	4.32642	+	1.15926i	0.334788	+	0.0897062i	−0.0875088	+	0.996164i	$0.527891\pi$
$168$	−9.46999	−	27.1232i	−0.730626	−	2.09260i
$169$	−12.0467	+	4.88650i	−0.926666	+	0.375885i
$170$	−3.64712	+	9.96787i	−0.279721	+	0.764501i
$171$	−10.8681	−	18.8242i	−0.831107	−	1.43952i
$172$	8.42464	−	13.3942i	0.642373	−	1.02130i
$173$	10.1421	−	2.71758i	0.771093	−	0.206614i	0.148239	−	0.988952i	$-0.452640\pi$
$173$	10.1421	−	2.71758i	0.771093	−	0.206614i	0.622854	+	0.782338i	$0.285973\pi$
$174$	−2.27868	+	15.0946i	−0.172746	+	1.14432i
$175$	−2.35917	+	16.7338i	−0.178337	+	1.26495i
$176$	−8.30008	+	3.98778i	−0.625642	+	0.300590i
$177$	−19.3423	−	19.3423i	−1.45385	−	1.45385i
$178$	3.96071	−	0.445349i	0.296868	−	0.0333803i
$179$	−5.26857	−	9.12543i	−0.393791	−	0.682067i	0.599155	−	0.800633i	$-0.295503\pi$
$179$	−5.26857	−	9.12543i	−0.393791	−	0.682067i	−0.992946	+	0.118566i	$0.962170\pi$
$180$	−26.9659	+	0.620687i	−2.00992	+	0.0462633i
$181$	16.6531			1.23782			0.618908	−	0.785464i	$-0.287576\pi$
$181$	16.6531			1.23782			0.618908	+	0.785464i	$0.287576\pi$
$182$	0.738208	+	17.2181i	0.0547196	+	1.27629i
$183$	−28.7119	+	28.7119i	−2.12245	+	2.12245i
$184$	−19.9427	+	1.48076i	−1.47019	+	0.109163i
$185$	8.92631	+	4.45291i	0.656276	+	0.327385i
$186$	9.05789	−	11.3529i	0.664156	−	0.832436i
$187$	−5.46376	+	5.46376i	−0.399550	+	0.399550i
$188$	−5.84505	−	0.221379i	−0.426294	−	0.0161457i
$189$	15.3951	−	26.6651i	1.11983	−	1.93960i
$190$	−4.79887	−	10.3368i	−0.348146	−	0.749912i
$191$	−8.25265	−	4.76467i	−0.597141	−	0.344760i	0.170775	−	0.985310i	$-0.445373\pi$
$191$	−8.25265	−	4.76467i	−0.597141	−	0.344760i	−0.767916	+	0.640550i	$0.778706\pi$
$192$	22.0489	−	9.58393i	1.59125	−	0.691660i
$193$	−2.22403	−	0.595926i	−0.160089	−	0.0428957i	0.177884	−	0.984051i	$-0.443075\pi$
$193$	−2.22403	−	0.595926i	−0.160089	−	0.0428957i	−0.337973	+	0.941156i	$0.609741\pi$
$194$	2.32176	−	15.3800i	0.166693	−	1.10422i
$195$	23.3507	+	6.46385i	1.67218	+	0.462886i
$196$	8.45257	+	2.61150i	0.603755	+	0.186536i
$197$	−1.49892	+	5.59405i	−0.106794	+	0.398559i	−0.998542	−	0.0539713i	$-0.982812\pi$
$197$	−1.49892	+	5.59405i	−0.106794	+	0.398559i	0.891749	+	0.452531i	$0.149479\pi$
$198$	−17.9958	−	7.85638i	−1.27891	−	0.558329i
$199$	9.74870	−	16.8852i	0.691067	−	1.19696i	−0.280422	−	0.959877i	$-0.590474\pi$
$199$	9.74870	−	16.8852i	0.691067	−	1.19696i	0.971489	−	0.237086i	$-0.0761923\pi$
$200$	−14.1114	−	0.931923i	−0.997826	−	0.0658969i
$201$	−10.0655	−	5.81135i	−0.709969	−	0.409901i
$202$	6.68320	−	0.751471i	0.470229	−	0.0528733i
$203$	−8.58434	−	8.58434i	−0.602502	−	0.602502i
$204$	14.7948	−	13.7150i	1.03585	−	0.960244i
$205$	−3.72486	−	11.1405i	−0.260156	−	0.778083i
$206$	1.45851	+	3.71871i	0.101619	+	0.259095i
$207$	−30.1532	−	30.1532i	−2.09579	−	2.09579i
$208$	−14.3237	+	1.68302i	−0.993168	+	0.116696i
$209$		−	8.29643i		−	0.573876i
$210$	18.4677	−	26.2799i	1.27439	−	1.81348i
$211$	6.42243	−	3.70799i	0.442138	−	0.255269i	−0.262366	−	0.964968i	$-0.584503\pi$
$211$	6.42243	−	3.70799i	0.442138	−	0.255269i	0.704504	+	0.709700i	$0.251169\pi$
$212$	0.158000	−	4.17166i	0.0108515	−	0.286511i
$213$	17.9328	−	17.9328i	1.22873	−	1.22873i
$214$	2.16866	+	1.73026i	0.148247	+	0.118278i
$215$	17.6583	−	1.07619i	1.20428	−	0.0733953i
$216$	23.2074	+	11.1957i	1.57906	+	0.761769i
$217$	2.98934	+	11.1564i	0.202930	+	0.757344i
$218$	−5.04054	+	11.5458i	−0.341388	+	0.781983i
$219$	−2.95255	+	1.70465i	−0.199515	+	0.115190i
$220$	−9.03204	−	4.94109i	−0.608940	−	0.333128i
$221$	−10.8735	+	5.31265i	−0.731432	+	0.357368i
$222$	−11.2553	−	15.2576i	−0.755403	−	1.02402i
$223$	−0.942268	+	3.51659i	−0.0630989	+	0.235488i	−0.990272	−	0.139145i	$-0.955565\pi$
$223$	−0.942268	+	3.51659i	−0.0630989	+	0.235488i	0.927173	+	0.374633i	$0.122231\pi$
$224$	−4.27572	+	18.6351i	−0.285684	+	1.24511i
$225$	−18.1384	−	24.0922i	−1.20923	−	1.60614i
$226$	−1.16221	+	7.69884i	−0.0773091	+	0.512119i
$227$	5.05868	+	18.8793i	0.335757	+	1.25306i	0.903047	+	0.429543i	$0.141325\pi$
$227$	5.05868	+	18.8793i	0.335757	+	1.25306i	−0.567290	+	0.823518i	$0.692008\pi$
$228$	−0.819809	+	21.6454i	−0.0542931	+	1.43350i
$229$	−8.65456			−0.571909			−0.285955	−	0.958243i	$-0.592311\pi$
$229$	−8.65456			−0.571909			−0.285955	+	0.958243i	$0.592311\pi$
$230$	−14.3424	−	17.1515i	−0.945712	−	1.13094i
$231$	20.2501	−	11.6914i	1.33236	−	0.769237i
$232$	6.63214	−	7.69602i	0.435421	−	0.505268i
$233$	−0.0588996	−	0.0588996i	−0.00385864	−	0.00385864i	0.705175	−	0.709033i	$-0.250869\pi$
$233$	−0.0588996	−	0.0588996i	−0.00385864	−	0.00385864i	−0.709033	+	0.705175i	$0.750869\pi$
$234$	−22.6579	−	20.7949i	−1.48120	−	1.35941i
$235$	−3.60830	−	5.45411i	−0.235379	−	0.355787i
$236$	4.04275	+	17.7498i	0.263161	+	1.15541i
$237$	−3.07397	−	0.823668i	−0.199676	−	0.0535030i
$238$	1.79266	+	15.9430i	0.116201	+	1.03343i
$239$			26.8110i			1.73426i	0.498081	+	0.867131i	$0.334038\pi$
$239$			26.8110i			1.73426i	−0.498081	+	0.867131i	$0.665962\pi$
$240$	23.0763	+	13.7838i	1.48957	+	0.889740i
$241$	1.63445	+	0.943652i	0.105284	+	0.0607860i	0.551718	−	0.834031i	$-0.313973\pi$
$241$	1.63445	+	0.943652i	0.105284	+	0.0607860i	−0.446433	+	0.894817i	$0.647306\pi$
$242$	4.78564	+	6.48741i	0.307633	+	0.417027i
$243$	0.147141	+	0.549136i	0.00943907	+	0.0352271i
$244$	26.3480	−	6.00111i	1.68676	−	0.384182i
$245$	3.13643	+	9.38057i	0.200379	+	0.599302i
$246$	−3.33264	+	22.0764i	−0.212481	+	1.40754i
$247$	4.22194	−	12.2889i	0.268636	−	0.781926i
$248$	−9.12534	+	3.18608i	−0.579459	+	0.202316i
$249$	12.0202	+	20.8195i	0.761747	+	1.31938i
$250$	−8.35025	−	13.4266i	−0.528116	−	0.849172i
$251$	22.9219	+	13.2340i	1.44682	+	0.835321i	0.998290	−	0.0584479i	$-0.0186152\pi$
$251$	22.9219	+	13.2340i	1.44682	+	0.835321i	0.448528	+	0.893769i	$0.351948\pi$
$252$	−36.0543	+	19.0342i	−2.27121	+	1.19904i
$253$	−4.21260	−	15.7216i	−0.264844	−	0.988412i
$254$	−18.3254	−	14.6209i	−1.14984	−	0.917395i
$255$	22.1014	+	4.50157i	1.38404	+	0.281899i
$256$	−15.8169	−	2.41357i	−0.988557	−	0.150848i
$257$	5.14695	+	1.37912i	0.321058	+	0.0860272i	0.415749	−	0.909480i	$-0.363520\pi$
$257$	5.14695	+	1.37912i	0.321058	+	0.0860272i	−0.0946908	+	0.995507i	$0.530186\pi$
$258$	−30.8162	−	13.4533i	−1.91853	−	0.837568i
$259$	15.0779			0.936894
$260$	−10.8641	−	11.9152i	−0.673762	−	0.738949i
$261$	21.6641			1.34097
$262$	11.2615	+	4.91641i	0.695739	+	0.303737i
$263$	13.0672	+	3.50136i	0.805761	+	0.215903i	0.638112	−	0.769944i	$-0.279716\pi$
$263$	13.0672	+	3.50136i	0.805761	+	0.215903i	0.167649	+	0.985847i	$0.446382\pi$
$264$	11.0119	+	16.1753i	0.677736	+	0.995520i
$265$	3.89264	−	2.57527i	0.239123	−	0.158197i
$266$	−13.4653	−	10.7433i	−0.825611	−	0.658711i
$267$	−2.19209	−	8.18101i	−0.134154	−	0.500670i
$268$	3.61120	+	6.84028i	0.220589	+	0.417836i
$269$	−8.95560	−	5.17052i	−0.546032	−	0.315252i	0.201488	−	0.979491i	$-0.435422\pi$
$269$	−8.95560	−	5.17052i	−0.546032	−	0.315252i	−0.747520	+	0.664239i	$0.768756\pi$
$270$	4.95448	+	28.3789i	0.301520	+	1.72708i
$271$	2.88198	+	4.99174i	0.175068	+	0.303227i	0.940185	−	0.340665i	$-0.110652\pi$
$271$	2.88198	+	4.99174i	0.175068	+	0.303227i	−0.765117	+	0.643892i	$0.777319\pi$
$272$	−13.1941	+	2.48399i	−0.800013	+	0.150614i
$273$	35.9447	−	7.01265i	2.17547	−	0.424425i
$274$	−0.717599	+	4.75360i	−0.0433517	+	0.287175i
$275$	−1.39782	−	11.4252i	−0.0842916	−	0.688968i
$276$	9.43714	+	41.4340i	0.568049	+	2.49403i
$277$	−7.85448	−	29.3133i	−0.471930	−	1.76127i	−0.632824	−	0.774296i	$-0.718104\pi$
$277$	−7.85448	−	29.3133i	−0.471930	−	1.76127i	0.160894	−	0.986972i	$-0.448562\pi$
$278$	18.3554	+	24.8825i	1.10088	+	1.49235i
$279$	−17.8496	−	10.3055i	−1.06863	−	0.616971i
$280$	−19.7153	+	8.26087i	−1.17822	+	0.493682i
$281$			13.8635i			0.827027i	0.910498	+	0.413513i	$0.135698\pi$
$281$			13.8635i			0.827027i	−0.910498	+	0.413513i	$0.864302\pi$
$282$	1.38887	+	12.3519i	0.0827059	+	0.735544i
$283$	27.5000	+	7.36860i	1.63471	+	0.438018i	0.955274	−	0.295721i	$-0.0955600\pi$
$283$	27.5000	+	7.36860i	1.63471	+	0.438018i	0.679431	+	0.733739i	$0.262227\pi$
$284$	−16.4564	+	3.74815i	−0.976505	+	0.222412i
$285$	−20.1976	+	13.3622i	−1.19640	+	0.791509i
$286$	−3.52101	−	11.1979i	−0.208202	−	0.662144i
$287$	−12.5549	−	12.5549i	−0.741091	−	0.741091i
$288$	−18.1192	−	28.9097i	−1.06768	−	1.70352i
$289$	4.96580	−	2.86701i	0.292106	−	0.168647i
$290$	11.3137	+	1.00911i	0.664361	+	0.0592567i
$291$	−33.0531			−1.93761
$292$	2.26730	+	0.0858729i	0.132683	+	0.00502533i
$293$	−5.17729	−	19.3219i	−0.302460	−	1.12880i	−0.935109	−	0.354359i	$-0.884699\pi$
$293$	−5.17729	−	19.3219i	−0.302460	−	1.12880i	0.632649	−	0.774439i	$-0.281968\pi$
$294$	2.80617	−	18.5889i	0.163659	−	1.08413i
$295$	−13.4897	+	15.2407i	−0.785399	+	0.887345i
$296$	0.934321	+	12.5833i	0.0543063	+	0.731388i
$297$	−5.42792	+	20.2573i	−0.314960	+	1.17545i
$298$	17.2812	+	23.4264i	1.00108	+	1.35706i
$299$	1.76070	−	25.4311i	0.101824	−	1.47072i
$300$	2.51792	+	29.9466i	0.145372	+	1.72897i
$301$	23.1578	−	13.3701i	1.33479	−	0.770642i
$302$	6.97618	−	15.9796i	0.401434	−	0.919524i
$303$	−3.69888	−	13.8044i	−0.212495	−	0.793044i
$304$	8.13141	−	11.9032i	0.466368	−	0.682696i
$305$	22.6234	+	20.0242i	1.29541	+	1.14659i
$306$	−22.3794	−	17.8554i	−1.27935	−	1.02072i
$307$	1.60523	−	1.60523i	0.0916155	−	0.0916155i	−0.659814	−	0.751429i	$-0.729365\pi$
$307$	1.60523	−	1.60523i	0.0916155	−	0.0916155i	0.751429	+	0.659814i	$0.229365\pi$
$308$	−15.5503	−	0.588960i	−0.886060	−	0.0335591i
$309$	7.35115	−	4.24419i	0.418192	−	0.241443i
$310$	−8.84160	−	6.21327i	−0.502169	−	0.352890i
$311$			25.2906i			1.43410i	0.697022	+	0.717050i	$0.254508\pi$
$311$			25.2906i			1.43410i	−0.697022	+	0.717050i	$0.745492\pi$
$312$	8.07978	+	29.5631i	0.457428	+	1.67368i
$313$	−8.19990	−	8.19990i	−0.463486	−	0.463486i	0.436311	−	0.899796i	$-0.356285\pi$
$313$	−8.19990	−	8.19990i	−0.463486	−	0.463486i	−0.899796	+	0.436311i	$0.856285\pi$
$314$	−1.61230	−	4.11083i	−0.0909872	−	0.231987i
$315$	−40.7889	−	20.3477i	−2.29820	−	1.14646i
$316$	1.43984	+	1.55320i	0.0809974	+	0.0873744i
$317$	−1.34515	−	1.34515i	−0.0755513	−	0.0755513i	0.668321	−	0.743873i	$-0.267013\pi$
$317$	−1.34515	−	1.34515i	−0.0755513	−	0.0755513i	−0.743873	+	0.668321i	$0.767013\pi$
$318$	−8.81564	+	0.991246i	−0.494356	+	0.0555863i
$319$	7.16105	+	4.13443i	0.400942	+	0.231484i
$320$	−8.11581	−	15.9416i	−0.453688	−	0.891161i
$321$	2.94774	−	5.10564i	0.164527	−	0.284969i
$322$	−30.9716	−	13.5212i	−1.72598	−	0.753507i
$323$	3.13076	−	11.6842i	0.174200	−	0.650125i
$324$	5.48068	−	17.7392i	0.304482	−	0.985510i
$325$	3.74367	−	17.6348i	0.207661	−	0.978201i
$326$	2.22058	−	14.7098i	0.122987	−	0.814702i
$327$	25.8590	+	6.92891i	1.43001	+	0.383170i
$328$	9.69973	−	11.2557i	0.535578	−	0.621491i
$329$	−8.56048	−	4.94240i	−0.471955	−	0.272483i
$330$	−7.51733	+	20.5455i	−0.413815	+	1.13099i
$331$	7.54301	−	13.0649i	0.414601	−	0.718111i	−0.580785	−	0.814057i	$-0.697254\pi$
$331$	7.54301	−	13.0649i	0.414601	−	0.718111i	0.995387	+	0.0959462i	$0.0305877\pi$
$332$	0.605522	−	15.9876i	0.0332323	−	0.877431i
$333$	−19.0258	+	19.0258i	−1.04261	+	1.04261i
$334$	−3.95051	+	4.95147i	−0.216162	+	0.270932i
$335$	−3.86039	+	7.73854i	−0.210916	+	0.422802i
$336$	40.5124	+	3.07319i	2.21013	+	0.167656i
$337$	−14.7209	+	14.7209i	−0.801901	+	0.801901i	−0.983392	−	0.181492i	$-0.941907\pi$
$337$	−14.7209	+	14.7209i	−0.801901	+	0.801901i	0.181492	+	0.983392i	$0.441907\pi$
$338$	0.483025	−	18.3784i	0.0262731	−	0.999655i
$339$	16.5455			0.898628
$340$	−10.8556	−	10.3671i	−0.588726	−	0.562234i
$341$	−3.93345	−	6.81293i	−0.213008	−	0.368941i
$342$	30.5472	−	3.43478i	1.65181	−	0.185732i
$343$	−6.15786	−	6.15786i	−0.332493	−	0.332493i
$344$	12.5931	+	18.4979i	0.678973	+	0.997338i
$345$	−31.4894	+	35.5768i	−1.69533	+	1.91539i
$346$	−2.21650	+	14.6828i	−0.119160	+	0.789351i
$347$	19.2104	−	5.14741i	1.03127	−	0.276328i	0.296778	−	0.954946i	$-0.404088\pi$
$347$	19.2104	−	5.14741i	1.03127	−	0.276328i	0.734491	+	0.678619i	$0.237421\pi$
$348$	−18.2746	−	11.4943i	−0.979622	−	0.616161i
$349$	16.3213	+	28.2693i	0.873658	+	1.51322i	0.858186	+	0.513339i	$0.171592\pi$
$349$	16.3213	+	28.2693i	0.873658	+	1.51322i	0.0154720	+	0.999880i	$0.495075\pi$
$350$	−20.3535	−	12.5261i	−1.08794	−	0.669550i
$351$	−18.3486	+	27.2435i	−0.979378	+	1.45415i
$352$	−0.472076	−	13.0140i	−0.0251617	−	0.693649i
$353$	18.7204	+	5.01612i	0.996388	+	0.266981i	0.719931	−	0.694045i	$-0.244173\pi$
$353$	18.7204	+	5.01612i	0.996388	+	0.266981i	0.276456	+	0.961026i	$0.410840\pi$
$354$	36.0136	−	14.1248i	1.91410	−	0.750726i
$355$	−14.1301	−	12.5067i	−0.749946	−	0.663786i
$356$	−1.66387	+	5.38541i	−0.0881851	+	0.285426i
$357$	32.9308	−	8.82379i	1.74288	−	0.467005i
$358$	14.8084	−	1.66509i	0.782651	−	0.0880027i
$359$			6.34293i			0.334767i	0.985892	+	0.167384i	$0.0535319\pi$
$359$			6.34293i			0.334767i	−0.985892	+	0.167384i	$0.946468\pi$
$360$	14.4536	−	35.3014i	0.761774	−	1.86055i
$361$	−3.00605	−	5.20663i	−0.158213	−	0.274033i
$362$	−9.42280	+	21.5838i	−0.495251	+	1.13442i
$363$	12.1134	−	12.1134i	0.635789	−	0.635789i
$364$	−22.7338	−	8.78572i	−1.19158	−	0.460497i
$365$	1.39966	+	2.11565i	0.0732614	+	0.110738i
$366$	−20.9671	−	53.4591i	−1.09597	−	2.79435i
$367$	−3.83216	+	14.3018i	−0.200037	+	0.746548i	0.790868	+	0.611986i	$0.209629\pi$
$367$	−3.83216	+	14.3018i	−0.200037	+	0.746548i	−0.990905	+	0.134561i	$0.957037\pi$
$368$	9.36494	−	26.6853i	0.488181	−	1.39107i
$369$	31.6844			1.64942
$370$	−10.8221	+	9.04968i	−0.562615	+	0.470471i
$371$	3.52743	−	6.10968i	0.183135	−	0.317199i
$372$	9.58914	+	18.1636i	0.497174	+	0.941739i
$373$	−23.1168	+	6.19414i	−1.19694	+	0.320720i	−0.801627	−	0.597824i	$-0.796032\pi$
$373$	−23.1168	+	6.19414i	−1.19694	+	0.320720i	−0.395317	+	0.918545i	$0.629365\pi$
$374$	−3.98995	−	10.1731i	−0.206315	−	0.526036i
$375$	−25.5634	+	21.8045i	−1.32009	+	1.12598i
$376$	3.59423	−	7.45043i	0.185358	−	0.384227i
$377$	8.50321	+	9.76821i	0.437938	+	0.503089i
$378$	25.8493	+	35.0412i	1.32954	+	1.80233i
$379$	−27.7410	+	16.0163i	−1.42496	+	0.822700i	−0.996717	−	0.0809651i	$-0.974200\pi$
$379$	−27.7410	+	16.0163i	−1.42496	+	0.822700i	−0.428241	+	0.903665i	$0.640866\pi$
$380$	16.1127	−	0.370874i	0.826566	−	0.0190254i
$381$	−24.9087	+	43.1432i	−1.27611	+	2.21029i
$382$	10.8450	−	8.00016i	0.554879	−	0.409324i
$383$	−27.2616	+	7.30472i	−1.39300	+	0.373254i	−0.875827	−	0.482626i	$-0.839683\pi$
$383$	−27.2616	+	7.30472i	−1.39300	+	0.373254i	−0.517175	+	0.855880i	$0.673016\pi$
$384$	−0.0543300	+	34.0002i	−0.00277252	+	1.73506i
$385$	−9.59957	−	14.5102i	−0.489239	−	0.739508i
$386$	2.03079	−	2.54534i	0.103364	−	0.129554i
$387$	−12.3504	+	46.0922i	−0.627805	+	2.34300i
$388$	18.6201	+	11.7117i	0.945294	+	0.594570i
$389$		−	5.50488i		−	0.279108i	−0.990214	−	0.139554i	$-0.955433\pi$
$389$		−	5.50488i		−	0.279108i	0.990214	−	0.139554i	$-0.0445669\pi$
$390$	−21.5902	+	26.6071i	−1.09326	+	1.34730i
$391$		−	23.7311i		−	1.20013i
$392$	−8.16743	+	9.47759i	−0.412518	+	0.478691i
$393$	6.75829	−	25.2223i	0.340910	−	1.27229i
$394$	−6.40223	−	5.10800i	−0.322540	−	0.257337i
$395$	−0.472587	+	2.32027i	−0.0237784	+	0.116745i
$396$	20.3651	−	18.8787i	1.02338	−	0.948692i
$397$	2.09369	−	0.561003i	0.105079	−	0.0281559i	−0.205896	−	0.978574i	$-0.566011\pi$
$397$	2.09369	−	0.561003i	0.105079	−	0.0281559i	0.310976	+	0.950418i	$0.399344\pi$
$398$	16.3686	+	22.1893i	0.820485	+	1.11225i
$399$	−18.3026	+	31.7011i	−0.916278	+	1.58704i
$400$	9.19248	−	17.7623i	0.459624	−	0.888114i
$401$	0.454400	−	0.262348i	0.0226917	−	0.0131010i	−0.488611	−	0.872502i	$-0.662496\pi$
$401$	0.454400	−	0.262348i	0.0226917	−	0.0131010i	0.511303	+	0.859401i	$0.329163\pi$
$402$	13.2274	−	9.75758i	0.659721	−	0.486664i
$403$	−2.35933	−	12.0932i	−0.117527	−	0.602406i
$404$	−2.80758	+	9.08721i	−0.139682	+	0.452105i
$405$	19.6867	−	6.58235i	0.978242	−	0.327080i
$406$	15.9833	−	6.26877i	0.793238	−	0.311114i
$407$	−9.91993	+	2.65804i	−0.491713	+	0.131754i
$408$	9.40452	+	26.9357i	0.465593	+	1.33352i
$409$	−0.796852	+	1.38019i	−0.0394018	+	0.0682459i	−0.885054	−	0.465489i	$-0.845879\pi$
$409$	−0.796852	+	1.38019i	−0.0394018	+	0.0682459i	0.845652	+	0.533735i	$0.179212\pi$
$410$	16.5466	+	1.47585i	0.817180	+	0.0728871i
$411$	10.2159			0.503913
$412$	−5.64504	−	0.213803i	−0.278111	−	0.0105333i
$413$	−7.96232	+	29.7158i	−0.391800	+	1.46222i
$414$	56.1426	−	22.0196i	2.75926	−	1.08220i
$415$	14.9182	−	9.86951i	0.732307	−	0.484475i
$416$	5.92341	−	19.5170i	0.290419	−	0.956900i
$417$	46.4610	−	46.4610i	2.27521	−	2.27521i
$418$	10.7529	+	4.69436i	0.525941	+	0.229609i
$419$	−6.74726	−	11.6866i	−0.329625	−	0.570928i	0.652812	−	0.757520i	$-0.273589\pi$
$419$	−6.74726	−	11.6866i	−0.329625	−	0.570928i	−0.982437	+	0.186592i	$0.940256\pi$
$420$	23.6114	+	38.8056i	1.15212	+	1.89352i
$421$		−	39.3681i		−	1.91868i	−0.282248	−	0.959341i	$-0.591080\pi$
$421$		−	39.3681i		−	1.91868i	0.282248	−	0.959341i	$-0.408920\pi$
$422$	1.17188	+	10.4221i	0.0570462	+	0.507340i
$423$	17.0384	−	4.56543i	0.828436	−	0.221979i
$424$	5.31743	+	2.56523i	0.258237	+	0.124578i
$425$	2.34286	−	16.6181i	0.113646	−	0.806095i
$426$	13.0955	+	33.3893i	0.634481	+	1.61772i
$427$	44.1105	+	11.8194i	2.13466	+	0.571979i
$428$	−3.46966	+	1.83174i	−0.167712	+	0.0885406i
$429$	−22.4122	+	10.9503i	−1.08207	+	0.528685i
$430$	−8.59673	+	23.4956i	−0.414571	+	1.13306i
$431$	14.5062	+	25.1254i	0.698737	+	1.21025i	0.968905	+	0.247435i	$0.0795876\pi$
$431$	14.5062	+	25.1254i	0.698737	+	1.21025i	−0.270167	+	0.962813i	$0.587079\pi$
$432$	−27.6420	+	23.7439i	−1.32992	+	1.14238i
$433$	−10.1118	+	2.70944i	−0.485940	+	0.130207i	−0.493467	−	0.869764i	$-0.664271\pi$
$433$	−10.1118	+	2.70944i	−0.485940	+	0.130207i	0.00752724	+	0.999972i	$0.497604\pi$
$434$	−16.1511	−	2.43815i	−0.775276	−	0.117035i
$435$	−1.46832	−	24.0924i	−0.0704004	−	1.15514i
$436$	−12.1123	−	13.0659i	−0.580075	−	0.625745i
$437$	18.0172	+	18.0172i	0.861879	+	0.861879i
$438$	−0.538742	−	4.79130i	−0.0257421	−	0.228937i
$439$	−13.2900	−	23.0189i	−0.634297	−	1.09863i	−0.986664	−	0.162772i	$-0.947956\pi$
$439$	−13.2900	−	23.0189i	−0.634297	−	1.09863i	0.352367	−	0.935862i	$-0.385377\pi$
$440$	11.5147	−	8.91049i	0.548940	−	0.424791i
$441$	−26.6791			−1.27043
$442$	−0.733104	−	17.0991i	−0.0348702	−	0.813320i
$443$	25.3954	−	25.3954i	1.20657	−	1.20657i	0.234440	−	0.972131i	$-0.424674\pi$
$443$	25.3954	−	25.3954i	1.20657	−	1.20657i	0.972131	−	0.234440i	$-0.0753256\pi$
$444$	26.1437	−	5.95458i	1.24073	−	0.282592i
$445$	−5.97667	+	1.99833i	−0.283321	+	0.0947298i
$446$	−4.02464	−	3.21105i	−0.190572	−	0.152048i
$447$	43.7422	−	43.7422i	2.06894	−	2.06894i
$448$	−21.7334	−	16.0860i	−1.02680	−	0.759991i
$449$	13.9306	−	24.1284i	0.657424	−	1.13869i	−0.323856	−	0.946106i	$-0.604979\pi$
$449$	13.9306	−	24.1284i	0.657424	−	1.13869i	0.981280	−	0.192585i	$-0.0616873\pi$
$450$	41.4887	−	9.87687i	1.95580	−	0.465600i
$451$	10.4733	+	6.04675i	0.493167	+	0.284730i
$452$	−9.32074	−	5.86255i	−0.438411	−	0.275751i
$453$	−35.7893	−	9.58972i	−1.68153	−	0.450564i
$454$	−27.3315	−	4.12594i	−1.28273	−	0.193640i
$455$	−6.83513	−	26.3781i	−0.320436	−	1.23662i
$456$	−27.5904	−	13.3101i	−1.29204	−	0.623303i
$457$	−5.82949	+	21.7560i	−0.272692	+	1.01770i	0.684680	+	0.728844i	$0.259942\pi$
$457$	−5.82949	+	21.7560i	−0.272692	+	1.01770i	−0.957372	+	0.288857i	$0.906725\pi$
$458$	4.89700	−	11.2170i	0.228822	−	0.524138i
$459$	−15.2887	+	26.4807i	−0.713614	+	1.23602i
$460$	30.3452	−	8.88422i	1.41485	−	0.414229i
$461$	−13.2574	−	7.65417i	−0.617460	−	0.356490i	0.158420	−	0.987372i	$-0.449360\pi$
$461$	−13.2574	−	7.65417i	−0.617460	−	0.356490i	−0.775879	+	0.630881i	$0.782693\pi$
$462$	3.69497	+	32.8612i	0.171905	+	1.52884i
$463$	−15.5135	−	15.5135i	−0.720976	−	0.720976i	0.247828	−	0.968804i	$-0.420283\pi$
$463$	−15.5135	−	15.5135i	−0.720976	−	0.720976i	−0.968804	+	0.247828i	$0.920283\pi$
$464$	6.22204	+	12.9504i	0.288851	+	0.601209i
$465$	−10.2508	+	20.5488i	−0.475371	+	0.952930i
$466$	0.109666	−	0.0430118i	0.00508018	−	0.00199248i
$467$	7.40023	+	7.40023i	0.342442	+	0.342442i	0.857285	−	0.514843i	$-0.172150\pi$
$467$	7.40023	+	7.40023i	0.342442	+	0.342442i	−0.514843	+	0.857285i	$0.672150\pi$
$468$	39.7725	−	17.6003i	1.83849	−	0.813572i
$469$			13.0716i			0.603589i
$470$	9.11067	−	1.59057i	0.420244	−	0.0733675i
$471$	−8.12628	+	4.69171i	−0.374439	+	0.216183i
$472$	−25.2928	−	4.80359i	−1.16419	−	0.221103i
$473$	−12.8788	+	12.8788i	−0.592168	+	0.592168i
$474$	2.80688	−	3.51807i	0.128924	−	0.161590i
$475$	10.8381	+	14.3956i	0.497286	+	0.660516i
$476$	−21.6778	−	6.69755i	−0.993600	−	0.306982i
$477$	3.25838	+	12.1604i	0.149191	+	0.556789i
$478$	−34.7494	−	15.1704i	−1.58940	−	0.693880i
$479$	−13.2755	+	7.66461i	−0.606573	+	0.350205i	−0.771623	−	0.636080i	$-0.780555\pi$
$479$	−13.2755	+	7.66461i	−0.606573	+	0.350205i	0.165050	+	0.986285i	$0.447221\pi$
$480$	−30.9222	+	22.1096i	−1.41140	+	1.00916i
$481$	−16.0463	−	1.11095i	−0.731650	−	0.0506551i
$482$	−2.14788	+	1.58445i	−0.0978330	+	0.0721696i
$483$	−18.5867	+	69.3666i	−0.845726	+	3.15629i
$484$	−11.1161	+	2.53184i	−0.505277	+	0.115084i
$485$	1.49608	+	24.5480i	0.0679334	+	1.11467i
$486$	−0.794983	−	0.120010i	−0.0360612	−	0.00544377i
$487$	0.694543	+	2.59207i	0.0314728	+	0.117458i	0.979875	−	0.199611i	$-0.0639679\pi$
$487$	0.694543	+	2.59207i	0.0314728	+	0.117458i	−0.948402	+	0.317069i	$0.897301\pi$
$488$	−7.13051	+	37.5449i	−0.322783	+	1.69958i
$489$	−31.6127			−1.42958
$490$	−13.9327	−	1.24271i	−0.629415	−	0.0561397i
$491$	34.5000	−	19.9186i	1.55696	−	0.898912i	0.559416	−	0.828887i	$-0.311025\pi$
$491$	34.5000	−	19.9186i	1.55696	−	0.898912i	0.997545	−	0.0700252i	$-0.0223080\pi$
$492$	−26.7272	−	16.8109i	−1.20496	−	0.757892i
$493$	8.52499	+	8.52499i	0.383946	+	0.383946i
$494$	13.5386	+	12.4254i	0.609131	+	0.559047i
$495$	30.4226	+	6.19641i	1.36739	+	0.278508i
$496$	1.03394	−	13.6300i	0.0464254	−	0.612005i
$497$	−27.5504	−	7.38210i	−1.23580	−	0.331132i
$498$	−33.7852	+	3.79887i	−1.51395	+	0.170232i
$499$		−	11.4530i		−	0.512707i	−0.966583	−	0.256353i	$-0.917479\pi$
$499$		−	11.4530i		−	0.512707i	0.966583	−	0.256353i	$-0.0825211\pi$
$500$	22.1268	−	3.22549i	0.989542	−	0.144248i
$501$	11.6571	+	6.73025i	0.520803	+	0.300685i
$502$	−30.1222	+	22.2206i	−1.34442	+	0.991754i
$503$	−4.40598	−	16.4433i	−0.196453	−	0.733172i	−0.991886	−	0.127131i	$-0.959423\pi$
$503$	−4.40598	−	16.4433i	−0.196453	−	0.733172i	0.795433	−	0.606041i	$-0.207243\pi$
$504$	−4.26940	−	57.4995i	−0.190174	−	2.56123i
$505$	−10.0849	+	3.37193i	−0.448771	+	0.150049i
$506$	22.7602	+	3.43586i	1.01181	+	0.152743i
$507$	−38.7701	+	4.81464i	−1.72184	+	0.213826i
$508$	29.3189	−	15.4784i	1.30082	−	0.686743i
$509$	−0.372516	−	0.645217i	−0.0165115	−	0.0285988i	0.857652	−	0.514231i	$-0.171923\pi$
$509$	−0.372516	−	0.645217i	−0.0165115	−	0.0285988i	−0.874163	+	0.485632i	$0.838589\pi$
$510$	−18.3400	+	26.0982i	−0.812110	+	1.15565i
$511$	3.32061	+	1.91716i	0.146895	+	0.0848099i
$512$	12.0778	−	19.1344i	0.533771	−	0.845629i
$513$	−8.49729	−	31.7123i	−0.375165	−	1.40013i
$514$	−4.69975	+	5.89054i	−0.207297	+	0.259821i
$515$	−3.48482	−	5.26747i	−0.153560	−	0.232112i
$516$	34.8733	−	32.3281i	1.53521	−	1.42317i
$517$	6.50333	+	1.74256i	0.286016	+	0.0766377i
$518$	−8.53150	+	19.5422i	−0.374853	+	0.858636i
$519$	31.5546			1.38509
$520$	21.5903	−	7.33883i	0.946798	−	0.321829i
$521$	−10.8329			−0.474599			−0.237300	−	0.971437i	$-0.576262\pi$
$521$	−10.8329			−0.474599			−0.237300	+	0.971437i	$0.576262\pi$
$522$	−12.2581	+	28.0785i	−0.536524	+	1.22896i
$523$	−13.2677	−	3.55507i	−0.580156	−	0.155452i	−0.0432056	−	0.999066i	$-0.513757\pi$
$523$	−13.2677	−	3.55507i	−0.580156	−	0.155452i	−0.536950	+	0.843614i	$0.680424\pi$
$524$	−12.7442	+	11.8141i	−0.556732	+	0.516099i
$525$	−19.8639	+	46.7402i	−0.866934	+	2.03991i
$526$	−11.9319	+	14.9551i	−0.520255	+	0.652073i
$527$	−2.96867	−	11.0792i	−0.129317	−	0.482619i
$528$	−27.1954	+	5.11993i	−1.18353	+	0.222816i
$529$	23.3722	+	13.4939i	1.01618	+	0.586693i
$530$	1.13520	+	6.50235i	0.0493100	+	0.282444i
$531$	−27.4493	−	47.5436i	−1.19120	−	2.06322i
$532$	21.5432	−	11.3733i	0.934017	−	0.493097i
$533$	12.4362	+	14.2863i	0.538673	+	0.618810i
$534$	11.8436	+	1.78791i	0.512524	+	0.0773703i
$535$	−3.92529	−	1.95814i	−0.169705	−	0.0846578i
$536$	−10.9089	+	0.809997i	−0.471193	+	0.0349865i
$537$	−8.19588	−	30.5875i	−0.353678	−	1.31995i
$538$	11.7688	−	8.68160i	0.507388	−	0.374290i
$539$	−8.81878	−	5.09153i	−0.379852	−	0.219308i
$540$	−39.5848	−	9.63615i	−1.70346	−	0.414674i
$541$			2.45646i			0.105611i	0.998605	+	0.0528057i	$0.0168164\pi$
$541$			2.45646i			0.105611i	−0.998605	+	0.0528057i	$0.983184\pi$
$542$	−8.10044	+	0.910828i	−0.347944	+	0.0391234i
$543$	48.3410	+	12.9529i	2.07451	+	0.555863i
$544$	4.24616	−	18.5063i	0.182053	−	0.793449i
$545$	3.97553	−	19.5187i	0.170293	−	0.836089i
$546$	−11.2495	+	50.5553i	−0.481435	+	2.16357i
$547$	−1.96833	−	1.96833i	−0.0841597	−	0.0841597i	0.663774	−	0.747933i	$-0.268954\pi$
$547$	−1.96833	−	1.96833i	−0.0841597	−	0.0841597i	−0.747933	+	0.663774i	$0.768954\pi$
$548$	−5.75503	−	3.61979i	−0.245843	−	0.154630i
$549$	−70.5743	+	40.7461i	−3.01204	+	1.73900i
$550$	15.5990	+	4.65304i	0.665145	+	0.198406i
$551$	−12.9447			−0.551465
$552$	−59.0418	−	11.2132i	−2.51299	−	0.477265i
$553$	0.926346	+	3.45717i	0.0393922	+	0.147014i
$554$	42.4369	+	6.40624i	1.80297	+	0.272175i
$555$	22.4480	+	19.8690i	0.952864	+	0.843391i
$556$	−42.6359	+	9.71088i	−1.80816	+	0.411833i
$557$	9.36654	−	34.9564i	0.396873	−	1.48115i	−0.421693	−	0.906739i	$-0.638564\pi$
$557$	9.36654	−	34.9564i	0.396873	−	1.48115i	0.818566	−	0.574412i	$-0.194769\pi$
$558$	23.4566	−	17.3035i	0.992995	−	0.732514i
$559$	−25.6303	+	12.5226i	−1.08405	+	0.529650i
$560$	0.448694	−	30.2270i	0.0189608	−	1.27732i
$561$	−20.1101	+	11.6106i	−0.849048	+	0.490198i
$562$	−17.9683	−	7.84436i	−0.757946	−	0.330894i
$563$	1.69972	+	6.34344i	0.0716347	+	0.267344i	0.992449	−	0.122657i	$-0.0391414\pi$
$563$	1.69972	+	6.34344i	0.0716347	+	0.267344i	−0.920814	+	0.390001i	$0.872475\pi$
$564$	−16.7950	−	5.18896i	−0.707196	−	0.218495i
$565$	−0.748897	−	12.2881i	−0.0315063	−	0.516962i
$566$	−25.1106	+	31.4730i	−1.05548	+	1.32291i
$567$	22.1862	−	22.1862i	0.931734	−	0.931734i
$568$	4.45355	−	23.4497i	0.186867	−	0.983926i
$569$	−2.65308	+	1.53176i	−0.111223	+	0.0642145i	−0.554579	−	0.832131i	$-0.687121\pi$
$569$	−2.65308	+	1.53176i	−0.111223	+	0.0642145i	0.443357	+	0.896345i	$0.353788\pi$
$570$	−5.89019	−	33.7386i	−0.246713	−	1.41315i
$571$			32.9475i			1.37881i	0.724377	+	0.689404i	$0.242128\pi$
$571$			32.9475i			1.37881i	−0.724377	+	0.689404i	$0.757872\pi$
$572$	16.5057	+	1.77255i	0.690137	+	0.0741140i
$573$	−20.2500	−	20.2500i	−0.845955	−	0.845955i
$574$	23.3761	−	9.16829i	0.975700	−	0.382677i
$575$	27.8476	+	21.7764i	1.16132	+	0.908137i
$576$	47.7218	−	7.12607i	1.98841	−	0.296920i
$577$	1.46707	+	1.46707i	0.0610751	+	0.0610751i	0.736985	−	0.675910i	$-0.236249\pi$
$577$	1.46707	+	1.46707i	0.0610751	+	0.0610751i	−0.675910	+	0.736985i	$0.736249\pi$
$578$	0.906094	+	8.05834i	0.0376885	+	0.335183i
$579$	−5.99244	−	3.45974i	−0.249037	−	0.143782i
$580$	−7.70948	+	14.0925i	−0.320119	+	0.585159i
$581$	13.5186	−	23.4149i	0.560845	−	0.971413i
$582$	18.7024	−	42.8396i	0.775239	−	1.77576i
$583$	−1.24368	+	4.64147i	−0.0515079	+	0.192230i
$584$	−1.39420	+	2.89002i	−0.0576924	+	0.119590i
$585$	41.9096	+	24.6600i	1.73275	+	1.01956i
$586$	27.9723	+	4.22268i	1.15553	+	0.174437i
$587$	−38.4431	−	10.3008i	−1.58671	−	0.425159i	−0.645718	−	0.763576i	$-0.723442\pi$
$587$	−38.4431	−	10.3008i	−1.58671	−	0.425159i	−0.940996	+	0.338417i	$0.890109\pi$
$588$	22.5051	+	14.1552i	0.928093	+	0.583751i
$589$	10.6655	+	6.15774i	0.439465	+	0.253725i
$590$	−12.1203	−	26.1074i	−0.498987	−	1.07482i
$591$	−8.70220	+	15.0727i	−0.357961	+	0.620006i
$592$	−16.8377	−	5.90902i	−0.692024	−	0.242859i
$593$	13.4170	−	13.4170i	0.550970	−	0.550970i	−0.375751	−	0.926721i	$-0.622615\pi$
$593$	13.4170	−	13.4170i	0.550970	−	0.550970i	0.926721	+	0.375751i	$0.122615\pi$
$594$	−23.1839	−	18.4972i	−0.951246	−	0.758948i
$595$	−8.04382	−	24.0578i	−0.329765	−	0.986272i
$596$	−40.1409	+	9.14262i	−1.64424	+	0.374496i
$597$	41.4322	−	41.4322i	1.69571	−	1.69571i
$598$	31.9647	+	16.6717i	1.30713	+	0.681756i
$599$	12.2948			0.502353			0.251177	−	0.967941i	$-0.419183\pi$
$599$	12.2948			0.502353			0.251177	+	0.967941i	$0.419183\pi$
$600$	−40.2380	−	13.6812i	−1.64271	−	0.558532i
$601$	10.8790	+	18.8430i	0.443764	+	0.768622i	0.997965	−	0.0637606i	$-0.0203094\pi$
$601$	10.8790	+	18.8430i	0.443764	+	0.768622i	−0.554201	+	0.832383i	$0.686976\pi$
$602$	4.22552	+	37.5797i	0.172219	+	1.53163i
$603$	−16.4942	−	16.4942i	−0.671695	−	0.671695i
$604$	16.7636	+	18.0835i	0.682103	+	0.735805i
$605$	−9.54471	−	8.44813i	−0.388047	−	0.343465i
$606$	19.9847	+	3.01687i	0.811821	+	0.122552i
$607$	−4.54830	+	1.21871i	−0.184610	+	0.0494661i	−0.349940	−	0.936772i	$-0.613798\pi$
$607$	−4.54830	+	1.21871i	−0.184610	+	0.0494661i	0.165330	+	0.986238i	$0.447131\pi$
$608$	10.8266	+	17.2742i	0.439077	+	0.700561i
$609$	−18.2418	−	31.5958i	−0.739196	−	1.28033i
$610$	−38.7541	+	17.9916i	−1.56911	+	0.728458i
$611$	8.74616	+	5.89059i	0.353832	+	0.238308i
$612$	35.8050	−	18.9026i	1.44733	−	0.764092i
$613$	−37.9681	−	10.1735i	−1.53352	−	0.410905i	−0.609352	−	0.792899i	$-0.708571\pi$
$613$	−37.9681	−	10.1735i	−1.53352	−	0.410905i	−0.924164	+	0.381995i	$0.875237\pi$
$614$	1.17223	+	2.98881i	0.0473075	+	0.120618i
$615$	−2.14746	−	35.2360i	−0.0865941	−	1.42085i
$616$	9.56214	−	19.8212i	0.385270	−	0.798621i
$617$	28.6066	−	7.66512i	1.15166	−	0.308586i	0.368029	−	0.929814i	$-0.380033\pi$
$617$	28.6066	−	7.66512i	1.15166	−	0.308586i	0.783630	+	0.621228i	$0.213366\pi$
$618$	1.34134	+	11.9292i	0.0539566	+	0.479863i
$619$			36.3076i			1.45933i	0.683807	+	0.729663i	$0.260323\pi$
$619$			36.3076i			1.45933i	−0.683807	+	0.729663i	$0.739677\pi$
$620$	13.0558	−	7.94382i	0.524332	−	0.319032i
$621$	−32.2046	−	55.7799i	−1.29232	−	2.23837i
$622$	−32.7788	−	14.3102i	−1.31431	−	0.573785i
$623$	−6.73549	+	6.73549i	−0.269852	+	0.269852i
$624$	−42.8881	−	6.25558i	−1.71690	−	0.250424i
$625$	17.3509	+	17.9985i	0.694035	+	0.719942i
$626$	15.2675	−	5.98803i	0.610212	−	0.239330i
$627$	6.45304	−	24.0831i	0.257710	−	0.961785i
$628$	6.24027	+	0.236347i	0.249014	+	0.00943129i
$629$	−14.9736			−0.597038
$630$	49.4519	−	41.3527i	1.97021	−	1.64753i
$631$	5.04403	−	8.73652i	0.200800	−	0.347795i	−0.747987	−	0.663714i	$-0.768979\pi$
$631$	5.04403	−	8.73652i	0.200800	−	0.347795i	0.948786	+	0.315919i	$0.102313\pi$
$632$	−2.82778	+	0.987312i	−0.112483	+	0.0392731i
$633$	21.5273	−	5.76822i	0.855633	−	0.229266i
$634$	2.50456	−	0.982307i	0.0994687	−	0.0390124i
$635$	33.1691	+	16.5465i	1.31628	+	0.656627i
$636$	3.70340	−	11.9867i	0.146849	−	0.475303i
$637$	−10.4716	−	12.0295i	−0.414902	−	0.476626i
$638$	−9.41051	+	6.94195i	−0.372566	+	0.274835i
$639$	44.0791	−	25.4491i	1.74374	−	1.00675i
$640$	25.2538	−	1.49860i	0.998244	−	0.0592372i
$641$	−3.90464	+	6.76304i	−0.154224	+	0.267124i	−0.932776	−	0.360456i	$-0.882621\pi$
$641$	−3.90464	+	6.76304i	−0.154224	+	0.267124i	0.778552	+	0.627580i	$0.215954\pi$
$642$	4.94943	+	6.70944i	0.195338	+	0.264801i
$643$	−24.7720	+	6.63764i	−0.976913	+	0.261763i	−0.711744	−	0.702439i	$-0.752094\pi$
$643$	−24.7720	+	6.63764i	−0.976913	+	0.261763i	−0.265169	+	0.964202i	$0.585428\pi$
$644$	35.0492	−	32.4912i	1.38113	−	1.28033i
$645$	52.0959	+	10.6108i	2.05127	+	0.417799i
$646$	13.3722	+	10.6690i	0.526123	+	0.419765i
$647$	−5.83838	+	21.7891i	−0.229531	+	0.856620i	0.751008	+	0.660293i	$0.229568\pi$
$647$	−5.83838	+	21.7891i	−0.229531	+	0.856620i	−0.980539	+	0.196327i	$0.937099\pi$
$648$	19.8904	+	17.1408i	0.781367	+	0.673353i
$649$		−	20.9540i		−	0.822518i
$650$	20.7379	+	14.8304i	0.813407	+	0.581695i
$651$			34.7101i			1.36040i
$652$	17.8087	+	11.2013i	0.697444	+	0.438677i
$653$	3.52243	−	13.1459i	0.137843	−	0.514439i	−0.862127	−	0.506693i	$-0.830868\pi$
$653$	3.52243	−	13.1459i	0.137843	−	0.514439i	0.999970	−	0.00774579i	$-0.00246559\pi$
$654$	−23.6123	+	29.5950i	−0.923312	+	1.15725i
$655$	−19.0380	−	3.87763i	−0.743878	−	0.151511i
$656$	9.09995	+	18.9405i	0.355293	+	0.739501i
$657$	−6.60920	+	1.77093i	−0.257849	+	0.0690906i
$658$	11.2495	−	8.29857i	0.438552	−	0.323512i
$659$	−13.9850	+	24.2226i	−0.544776	+	0.943580i	0.453845	+	0.891081i	$0.350052\pi$
$659$	−13.9850	+	24.2226i	−0.544776	+	0.943580i	−0.998621	+	0.0524995i	$0.983281\pi$
$660$	−22.3752	−	21.3683i	−0.870953	−	0.831761i
$661$	32.1075	−	18.5373i	1.24884	−	0.721016i	0.277960	−	0.960593i	$-0.410342\pi$
$661$	32.1075	−	18.5373i	1.24884	−	0.721016i	0.970878	+	0.239576i	$0.0770085\pi$
$662$	12.6652	+	17.1689i	0.492245	+	0.667287i
$663$	−35.6961	+	6.96417i	−1.38632	+	0.270466i
$664$	20.3786	+	9.83103i	0.790844	+	0.381518i
$665$	24.3723	+	12.1582i	0.945117	+	0.471474i
$666$	−13.8937	−	35.4245i	−0.538372	−	1.37267i
$667$	−24.5302	+	6.57284i	−0.949811	+	0.254501i
$668$	−4.18221	−	7.92188i	−0.161815	−	0.306507i
$669$	−5.47047	+	9.47514i	−0.211501	+	0.366330i
$670$	−7.84550	−	9.38208i	−0.303098	−	0.362462i
$671$	−31.1044			−1.20077
$672$	−26.9062	+	50.7687i	−1.03793	+	1.95844i
$673$	3.14163	−	11.7247i	0.121101	−	0.451955i	−0.878570	−	0.477614i	$-0.841502\pi$
$673$	3.14163	−	11.7247i	0.121101	−	0.451955i	0.999671	+	0.0256592i	$0.00816847\pi$
$674$	−10.7501	−	27.4091i	−0.414077	−	1.05576i
$675$	−17.0449	−	42.2403i	−0.656058	−	1.62583i
$676$	23.5467	+	11.0251i	0.905643	+	0.424042i
$677$	−27.1988	+	27.1988i	−1.04534	+	1.04534i	−0.0464132	+	0.998922i	$0.514779\pi$
$677$	−27.1988	+	27.1988i	−1.04534	+	1.04534i	−0.998922	+	0.0464132i	$0.985221\pi$
$678$	−9.36192	+	21.4444i	−0.359542	+	0.823567i
$679$	18.5867	+	32.1932i	0.713293	+	1.23546i
$680$	19.5790	−	8.20376i	0.750821	−	0.314600i
$681$			58.7378i			2.25084i
$682$	11.0558	−	1.24313i	0.423349	−	0.0476021i
$683$	5.49056	−	1.47119i	0.210090	−	0.0562936i	−0.152239	−	0.988344i	$-0.548648\pi$
$683$	5.49056	−	1.47119i	0.210090	−	0.0562936i	0.362329	+	0.932050i	$0.381982\pi$
$684$	−12.8327	+	41.5353i	−0.490671	+	1.58814i
$685$	−0.462401	−	7.58718i	−0.0176675	−	0.289891i
$686$	11.4654	−	4.49682i	0.437751	−	0.171689i
$687$	−25.1226	−	6.73159i	−0.958489	−	0.256826i
$688$	−31.1003	+	5.85509i	−1.18569	+	0.223223i
$689$	−4.20416	+	6.24220i	−0.160166	+	0.237809i
$690$	−28.2930	−	60.9434i	−1.07709	−	2.32008i
$691$	11.6599	+	20.1956i	0.443565	+	0.768277i	0.997951	−	0.0639825i	$-0.0203802\pi$
$691$	11.6599	+	20.1956i	0.443565	+	0.768277i	−0.554386	+	0.832260i	$0.687047\pi$
$692$	−17.7760	−	11.1807i	−0.675741	−	0.425027i
$693$	45.3293	−	12.1459i	1.72192	−	0.461386i
$694$	−4.19831	+	27.8109i	−0.159366	+	1.05569i
$695$	−36.6088	−	32.4028i	−1.38865	−	1.22911i
$696$	25.2379	−	17.1816i	0.956642	−	0.651268i
$697$	12.4681	+	12.4681i	0.472262	+	0.472262i
$698$	−45.8744	+	5.15820i	−1.73637	+	0.195241i
$699$	−0.125162	−	0.216788i	−0.00473408	−	0.00819966i
$700$	27.7516	−	19.2923i	1.04891	−	0.729179i
$701$	−44.3008			−1.67322			−0.836608	−	0.547802i	$-0.815465\pi$
$701$	−44.3008			−1.67322			−0.836608	+	0.547802i	$0.815465\pi$
$702$	−24.9277	−	39.1966i	−0.940835	−	1.47938i
$703$	11.3683	−	11.3683i	0.428765	−	0.428765i
$704$	17.1344	+	6.75185i	0.645777	+	0.254470i
$705$	−6.23199	−	18.6389i	−0.234710	−	0.701980i
$706$	−17.0939	+	21.4250i	−0.643337	+	0.806341i
$707$	−11.3653	+	11.3653i	−0.427436	+	0.427436i
$708$	−2.07056	+	54.6690i	−0.0778166	+	2.05459i
$709$	−21.1319	+	36.6016i	−0.793626	+	1.37460i	0.130082	+	0.991503i	$0.458476\pi$
$709$	−21.1319	+	36.6016i	−0.793626	+	1.37460i	−0.923708	+	0.383097i	$0.874857\pi$
$710$	24.2049	−	11.2371i	0.908394	−	0.421722i
$711$	−5.53128	−	3.19348i	−0.207439	−	0.119765i
$712$	−6.03849	−	5.20374i	−0.226302	−	0.195018i
$713$	23.3377	+	6.25331i	0.874003	+	0.234188i
$714$	−7.19682	+	47.6739i	−0.269334	+	1.78415i
$715$	9.14703	+	16.1495i	0.342080	+	0.603957i
$716$	−6.22095	+	20.1352i	−0.232488	+	0.752487i
$717$	−20.8539	+	77.8276i	−0.778801	+	2.90653i
$718$	−8.22099	−	3.58901i	−0.306805	−	0.133941i
$719$	21.3610	−	36.9983i	0.796630	−	1.37980i	−0.125169	−	0.992135i	$-0.539947\pi$
$719$	21.3610	−	36.9983i	0.796630	−	1.37980i	0.921799	−	0.387668i	$-0.126719\pi$
$720$	37.5753	+	38.7077i	1.40035	+	1.44255i
$721$	−8.26754	−	4.77327i	−0.307899	−	0.177766i
$722$	8.44915	−	0.950037i	0.314445	−	0.0353567i
$723$	4.01055	+	4.01055i	0.149154	+	0.149154i
$724$	−22.6428	−	24.4255i	−0.841514	−	0.907767i
$725$	−17.8266	+	2.18099i	−0.662062	+	0.0809998i
$726$	8.84590	+	22.5541i	0.328302	+	0.837062i
$727$	13.0144	+	13.0144i	0.482678	+	0.482678i	0.905986	−	0.423308i	$-0.139131\pi$
$727$	13.0144	+	13.0144i	0.482678	+	0.482678i	−0.423308	+	0.905986i	$0.639131\pi$
$728$	24.2505	−	24.4938i	0.898784	−	0.907801i
$729$		−	26.1413i		−	0.968197i
$730$	−3.53403	+	0.616982i	−0.130800	+	0.0228355i
$731$	−22.9977	+	13.2777i	−0.850599	+	0.491094i
$732$	81.1514	+	3.07357i	2.99944	+	0.113602i
$733$	28.0199	−	28.0199i	1.03494	−	1.03494i	0.0355722	−	0.999367i	$-0.488675\pi$
$733$	28.0199	−	28.0199i	1.03494	−	1.03494i	0.999367	−	0.0355722i	$-0.0113254\pi$
$734$	−16.3680	−	13.0592i	−0.604154	−	0.482023i
$735$	1.80822	+	29.6697i	0.0666973	+	1.09438i
$736$	29.2875	+	27.2371i	1.07955	+	1.00397i
$737$	−2.30435	−	8.59994i	−0.0848818	−	0.316783i
$738$	−17.9279	+	41.0657i	−0.659937	+	1.51165i
$739$	28.3149	−	16.3476i	1.04158	−	0.601357i	0.121300	−	0.992616i	$-0.461294\pi$
$739$	28.3149	−	16.3476i	1.04158	−	0.601357i	0.920281	+	0.391259i	$0.127960\pi$
$740$	−5.60570	−	19.1470i	−0.206070	−	0.703856i
$741$	21.8140	−	32.3887i	0.801357	−	1.18983i
$742$	5.92275	+	8.02888i	0.217431	+	0.294749i
$743$	1.51990	−	5.67233i	0.0557596	−	0.208098i	−0.932426	−	0.361362i	$-0.882312\pi$
$743$	1.51990	−	5.67233i	0.0557596	−	0.208098i	0.988185	+	0.153264i	$0.0489786\pi$
$744$	−28.9674	+	2.15086i	−1.06200	+	0.0788543i
$745$	−34.4665	−	30.5067i	−1.26275	−	1.11768i
$746$	5.05203	−	33.4662i	0.184968	−	1.22529i
$747$	12.4875	+	46.6040i	0.456894	+	1.70515i
$748$	15.4428	+	0.584888i	0.564644	+	0.0213856i
$749$	−6.63041			−0.242270
$750$	−13.7960	−	45.4699i	−0.503757	−	1.66033i
$751$	−7.88569	+	4.55281i	−0.287753	+	0.166134i	−0.636928	−	0.770923i	$-0.719795\pi$
$751$	−7.88569	+	4.55281i	−0.287753	+	0.166134i	0.349175	+	0.937058i	$0.386462\pi$
$752$	7.62268	+	8.87409i	0.277970	+	0.323605i
$753$	56.2447	+	56.2447i	2.04967	+	2.04967i
$754$	−17.4718	+	5.49375i	−0.636285	+	0.200071i
$755$	−5.50219	+	27.0142i	−0.200245	+	0.983146i
$756$	−60.0427	+	13.6755i	−2.18373	+	0.497374i
$757$	35.6312	+	9.54735i	1.29504	+	0.347004i	0.839572	−	0.543249i	$-0.182806\pi$
$757$	35.6312	+	9.54735i	1.29504	+	0.347004i	0.455466	+	0.890253i	$0.349473\pi$
$758$	−5.06180	−	45.0171i	−0.183853	−	1.63510i
$759$		−	48.9138i		−	1.77546i
$760$	−8.63637	+	21.0933i	−0.313274	+	0.765136i
$761$	−23.6461	−	13.6521i	−0.857170	−	0.494887i	0.00589388	−	0.999983i	$-0.498124\pi$
$761$	−23.6461	−	13.6521i	−0.857170	−	0.494887i	−0.863063	+	0.505096i	$0.831457\pi$
$762$	−41.8232	−	56.6955i	−1.51509	−	2.05386i
$763$	−7.79266	−	29.0826i	−0.282113	−	1.05286i
$764$	4.23247	+	18.5828i	0.153126	+	0.672301i
$765$	40.5069	+	20.2070i	1.46453	+	0.730585i
$766$	5.95784	−	39.4666i	0.215266	−	1.42598i
$767$	10.6632	−	31.0378i	0.385027	−	1.12071i
$768$	−44.0364	−	19.3087i	−1.58903	−	0.696742i
$769$	0.748752	+	1.29688i	0.0270007	+	0.0467666i	0.879210	−	0.476434i	$-0.158071\pi$
$769$	0.748752	+	1.29688i	0.0270007	+	0.0467666i	−0.852209	+	0.523201i	$0.824738\pi$
$770$	24.2382	−	4.23158i	0.873483	−	0.152496i
$771$	13.8680	+	8.00669i	0.499443	+	0.288354i
$772$	2.14990	+	4.07230i	0.0773765	+	0.146565i
$773$	10.7597	+	40.1557i	0.386999	+	1.44430i	0.834992	+	0.550262i	$0.185472\pi$
$773$	10.7597	+	40.1557i	0.386999	+	1.44430i	−0.447993	+	0.894037i	$0.647861\pi$
$774$	−52.7513	−	42.0874i	−1.89611	−	1.51280i
$775$	15.7253	+	6.68302i	0.564868	+	0.240061i
$776$	−25.7151	+	17.5065i	−0.923119	+	0.628446i
$777$	43.7684	+	11.7277i	1.57018	+	0.420729i
$778$	7.13479	+	3.11482i	0.255795	+	0.111672i
$779$	−18.9321			−0.678314
$780$	−22.2688	−	43.0379i	−0.797350	−	1.54100i
$781$	19.4271			0.695156
$782$	30.7575	+	13.4277i	1.09989	+	0.480174i
$783$	31.6070	+	8.46906i	1.12954	+	0.302660i
$784$	−7.66240	−	15.9484i	−0.273657	−	0.569585i
$785$	3.85227	+	5.82289i	0.137493	+	0.207828i
$786$	28.8662	+	23.0308i	1.02962	+	0.821481i
$787$	−12.9557	−	48.3512i	−0.461820	−	1.72354i	−0.667223	−	0.744858i	$-0.732517\pi$
$787$	−12.9557	−	48.3512i	−0.461820	−	1.72354i	0.205404	−	0.978677i	$-0.434149\pi$
$788$	10.2430	−	5.40759i	0.364891	−	0.192637i
$789$	35.2085	+	20.3276i	1.25346	+	0.723683i
$790$	−2.73986	−	1.92539i	−0.0974798	−	0.0685021i
$791$	−9.30403	−	16.1150i	−0.330813	−	0.572985i
$792$	12.9453	+	37.0770i	0.459992	+	1.31747i
$793$	−46.0728	−	15.8286i	−1.63609	−	0.562091i
$794$	−0.457563	+	3.03103i	−0.0162383	+	0.107567i
$795$	13.3027	−	4.44782i	0.471798	−	0.157748i
$796$	−38.0211	+	8.65980i	−1.34762	+	0.306938i
$797$	7.55304	+	28.1883i	0.267542	+	0.998482i	0.960676	+	0.277673i	$0.0895631\pi$
$797$	7.55304	+	28.1883i	0.267542	+	0.998482i	−0.693133	+	0.720809i	$0.743770\pi$
$798$	−30.7312	−	41.6592i	−1.08787	−	1.47472i
$799$	8.50130	+	4.90823i	0.300754	+	0.173641i
$800$	17.8201	+	21.9646i	0.630034	+	0.776568i
$801$		−	16.9982i		−	0.600600i
$802$	0.0829130	+	0.737386i	0.00292776	+	0.0260380i
$803$	−2.52264	−	0.675939i	−0.0890220	−	0.0238534i
$804$	5.16224	+	22.6649i	0.182058	+	0.799330i
$805$	52.3587	+	10.6643i	1.84540	+	0.375867i
$806$	17.0088	+	3.78478i	0.599110	+	0.133313i
$807$	−21.9748	−	21.9748i	−0.773551	−	0.773551i
$808$	−10.1892	−	8.78066i	−0.358455	−	0.308903i
$809$	−15.3577	+	8.86680i	−0.539950	+	0.311740i	−0.745058	−	0.666999i	$-0.767578\pi$
$809$	−15.3577	+	8.86680i	−0.539950	+	0.311740i	0.205109	+	0.978739i	$0.434245\pi$
$810$	−2.60803	+	29.2402i	−0.0916370	+	1.02740i
$811$	16.4552			0.577819			0.288909	−	0.957356i	$-0.406707\pi$
$811$	16.4552			0.577819			0.288909	+	0.957356i	$0.406707\pi$
$812$	−0.918942	+	24.2628i	−0.0322485	+	0.851457i
$813$	4.48327	+	16.7318i	0.157235	+	0.586809i
$814$	2.16794	−	14.3611i	0.0759861	−	0.503355i
$815$	1.43088	+	23.4782i	0.0501217	+	0.822407i
$816$	−40.2323	−	3.05194i	−1.40841	−	0.106839i
$817$	7.37962	−	27.5411i	0.258180	−	0.963542i
$818$	−1.33796	−	1.81374i	−0.0467807	−	0.0634158i
$819$	73.3241	+	5.07652i	2.56215	+	0.177388i
$820$	−11.2754	+	20.6108i	−0.393753	+	0.719759i
$821$	7.69160	−	4.44075i	0.268439	−	0.154983i	−0.359739	−	0.933053i	$-0.617134\pi$
$821$	7.69160	−	4.44075i	0.268439	−	0.154983i	0.628178	+	0.778070i	$0.283801\pi$
$822$	−5.78045	+	13.2407i	−0.201616	+	0.461822i
$823$	5.51716	+	20.5903i	0.192316	+	0.717734i	0.992945	+	0.118574i	$0.0378322\pi$
$823$	5.51716	+	20.5903i	0.192316	+	0.717734i	−0.800629	+	0.599160i	$0.795501\pi$
$824$	3.47123	−	7.19547i	0.120926	−	0.250666i
$825$	4.82904	−	34.2527i	0.168126	−	1.19253i
$826$	−34.0089	−	27.1339i	−1.18332	−	0.944109i
$827$	−7.19941	+	7.19941i	−0.250348	+	0.250348i	−0.821113	−	0.570765i	$-0.806647\pi$
$827$	−7.19941	+	7.19941i	−0.250348	+	0.250348i	0.570765	+	0.821113i	$0.306647\pi$
$828$	−3.22786	+	85.2249i	−0.112176	+	2.96177i
$829$	13.7469	−	7.93677i	0.477449	−	0.275656i	−0.241904	−	0.970300i	$-0.577772\pi$
$829$	13.7469	−	7.93677i	0.477449	−	0.275656i	0.719353	+	0.694645i	$0.244438\pi$
$830$	4.35057	+	24.9198i	0.151011	+	0.864977i
$831$		−	91.2007i		−	3.16372i
$832$	21.9441	+	18.7205i	0.760774	+	0.649017i
$833$	−10.4985	−	10.4985i	−0.363750	−	0.363750i
$834$	33.9285	+	86.5065i	1.17485	+	2.99547i
$835$	4.47081	−	8.96218i	0.154719	−	0.310149i
$836$	−12.1686	+	11.2805i	−0.420859	+	0.390143i
$837$	−22.0131	−	22.0131i	−0.760885	−	0.760885i
$838$	18.9646	−	2.13242i	0.655122	−	0.0736631i
$839$	16.1870	+	9.34554i	0.558836	+	0.322644i	0.752678	−	0.658389i	$-0.228762\pi$
$839$	16.1870	+	9.34554i	0.558836	+	0.322644i	−0.193842	+	0.981033i	$0.562095\pi$
$840$	−63.6555	+	8.64509i	−2.19632	+	0.298284i
$841$	−8.04913	+	13.9415i	−0.277556	+	0.480742i
$842$	51.0244	+	22.2756i	1.75842	+	0.767667i
$843$	−10.7831	+	40.2433i	−0.371391	+	1.38605i
$844$	−14.1710	−	4.37827i	−0.487787	−	0.150706i
$845$	5.33060	+	28.5759i	0.183378	+	0.983042i
$846$	−3.72364	+	24.6665i	−0.128021	+	0.848052i
$847$	−18.6100	−	4.98653i	−0.639447	−	0.171339i
$848$	−6.33351	+	5.44036i	−0.217493	+	0.186823i
$849$	74.0963	+	42.7795i	2.54298	+	1.46819i
$850$	20.2128	+	12.4395i	0.693293	+	0.426673i
$851$	15.7705	−	27.3153i	0.540606	−	0.936356i
$852$	−50.6852	−	1.91968i	−1.73645	−	0.0657672i
$853$	3.23218	−	3.23218i	0.110668	−	0.110668i	−0.649605	−	0.760272i	$-0.725066\pi$
$853$	3.23218	−	3.23218i	0.110668	−	0.110668i	0.760272	+	0.649605i	$0.225066\pi$
$854$	−40.2779	+	50.4832i	−1.37828	+	1.72750i
$855$	−46.0955	+	15.4122i	−1.57643	+	0.527087i
$856$	−0.410862	−	5.53342i	−0.0140430	−	0.189129i
$857$	−21.7703	+	21.7703i	−0.743660	+	0.743660i	−0.973280	−	0.229620i	$-0.926252\pi$
$857$	−21.7703	+	21.7703i	−0.743660	+	0.743660i	0.229620	+	0.973280i	$0.426252\pi$
$858$	−1.51105	−	35.2441i	−0.0515865	−	1.20321i
$859$	−22.8003			−0.777937			−0.388969	−	0.921251i	$-0.627169\pi$
$859$	−22.8003			−0.777937			−0.388969	+	0.921251i	$0.627169\pi$
$860$	−25.5880	−	24.4366i	−0.872544	−	0.833280i
$861$	−26.6793	−	46.2099i	−0.909228	−	1.57483i
$862$	−40.7727	+	4.58455i	−1.38872	+	0.156150i
$863$	−1.81832	−	1.81832i	−0.0618963	−	0.0618963i	0.675481	−	0.737377i	$-0.263936\pi$
$863$	−1.81832	−	1.81832i	−0.0618963	−	0.0618963i	−0.737377	+	0.675481i	$0.763936\pi$
$864$	−15.1336	−	49.2613i	−0.514854	−	1.67591i
$865$	−1.42825	−	23.4351i	−0.0485620	−	0.796816i
$866$	2.20986	−	14.6388i	0.0750940	−	0.497446i
$867$	16.6448	−	4.45997i	0.565288	−	0.151468i
$868$	12.2988	−	19.5536i	0.417448	−	0.663692i
$869$	−1.21891	−	2.11121i	−0.0413486	−	0.0716179i
$870$	32.0567	+	11.7291i	1.08682	+	0.397655i
$871$	0.963126	−	13.9112i	0.0326343	−	0.471362i
$872$	23.7881	−	8.30553i	0.805566	−	0.281261i
$873$	−64.0759	−	17.1691i	−2.16864	−	0.581086i
$874$	−33.5464	+	13.1572i	−1.13473	+	0.445048i
$875$	35.6122	+	12.6370i	1.20391	+	0.427209i
$876$	6.51477	+	2.01280i	0.220114	+	0.0680061i
$877$	−4.91901	+	1.31805i	−0.166103	+	0.0445072i	−0.340912	−	0.940095i	$-0.610736\pi$
$877$	−4.91901	+	1.31805i	−0.166103	+	0.0445072i	0.174809	+	0.984602i	$0.444069\pi$
$878$	37.3544	−	4.20019i	1.26065	−	0.141750i
$879$		−	60.1150i		−	2.02763i
$880$	5.03343	+	19.9658i	0.169677	+	0.673047i
$881$	−25.8594	−	44.7899i	−0.871226	−	1.50901i	−0.860729	−	0.509064i	$-0.829992\pi$
$881$	−25.8594	−	44.7899i	−0.871226	−	1.50901i	−0.0104976	−	0.999945i	$-0.503342\pi$
$882$	15.0958	−	34.5784i	0.508303	−	1.16432i
$883$	−13.4157	+	13.4157i	−0.451475	+	0.451475i	−0.895844	−	0.444369i	$-0.853428\pi$
$883$	−13.4157	+	13.4157i	−0.451475	+	0.451475i	0.444369	+	0.895844i	$0.353428\pi$
$884$	22.5767	+	8.72498i	0.759336	+	0.293453i
$885$	−51.0125	+	33.7485i	−1.71477	+	1.13444i
$886$	18.5451	+	47.2840i	0.623036	+	1.58854i
$887$	−9.49036	+	35.4185i	−0.318655	+	1.18924i	0.601883	+	0.798584i	$0.294417\pi$
$887$	−9.49036	+	35.4185i	−0.318655	+	1.18924i	−0.920538	+	0.390653i	$0.872249\pi$
$888$	−7.07522	+	37.2538i	−0.237429	+	1.25015i
$889$	56.0276			1.87911
$890$	0.791769	−	8.87699i	0.0265402	−	0.297557i
$891$	−10.6854	+	18.5077i	−0.357976	+	0.620033i
$892$	6.43905	−	3.39938i	0.215595	−	0.113820i
$893$	−10.1808	+	2.72794i	−0.340688	+	0.0912872i
$894$	31.9431	+	81.4443i	1.06834	+	2.72391i
$895$	−22.3458	+	7.47142i	−0.746938	+	0.249742i
$896$	33.1462	−	19.0664i	1.10734	−	0.636963i
$897$	24.8916	−	72.4526i	0.831105	−	2.41912i
$898$	23.3902	+	31.7078i	0.780542	+	1.05810i
$899$	−10.6301	+	6.13728i	−0.354533	+	0.204690i
$900$	−10.6742	+	59.3616i	−0.355808	+	1.97872i
$901$	−3.50304	+	6.06744i	−0.116703	+	0.202136i
$902$	−13.7632	+	10.1528i	−0.458264	+	0.338053i
$903$	77.6223	−	20.7988i	2.58311	−	0.692142i
$904$	12.8723	−	8.76328i	0.428127	−	0.291463i
$905$	7.43186	−	36.4883i	0.247043	−	1.21291i
$906$	32.6797	−	40.9599i	1.08571	−	1.36080i
$907$	11.0141	−	41.1052i	0.365718	−	1.36488i	−0.500727	−	0.865605i	$-0.666934\pi$
$907$	11.0141	−	41.1052i	0.365718	−	1.36488i	0.866445	−	0.499272i	$-0.166399\pi$
$908$	20.8125	−	33.0894i	0.690687	−	1.09811i
$909$		−	28.6823i		−	0.951331i
$910$	38.0557	+	6.06654i	1.26154	+	0.201104i
$911$			15.2275i			0.504511i	0.967661	+	0.252255i	$0.0811723\pi$
$911$			15.2275i			0.504511i	−0.967661	+	0.252255i	$0.918828\pi$
$912$	32.8625	−	28.2282i	1.08818	−	0.934731i
$913$	−4.76630	+	17.7881i	−0.157742	+	0.588700i
$914$	−24.8991	−	19.8657i	−0.823589	−	0.657098i
$915$	50.0967	+	75.7235i	1.65615	+	2.50334i
$916$	11.7674	+	12.6939i	0.388806	+	0.419417i
$917$	−28.3665	+	7.60077i	−0.936743	+	0.250999i
$918$	−25.6705	−	34.7990i	−0.847254	−	1.14854i
$919$	−2.58132	+	4.47098i	−0.0851499	+	0.147484i	−0.905455	−	0.424442i	$-0.860470\pi$
$919$	−2.58132	+	4.47098i	−0.0851499	+	0.147484i	0.820305	+	0.571926i	$0.193804\pi$
$920$	−5.65544	+	44.3569i	−0.186454	+	1.46240i
$921$	5.90827	−	3.41114i	0.194684	−	0.112401i
$922$	17.4219	−	12.8518i	0.573759	−	0.423251i
$923$	28.7760	+	9.88619i	0.947174	+	0.325408i
$924$	−44.6816	−	13.8048i	−1.46992	−	0.454144i
$925$	13.7403	−	17.5711i	0.451778	−	0.577733i
$926$	28.8849	−	11.3289i	0.949216	−	0.372290i
$927$	16.4554	−	4.40920i	0.540465	−	0.144817i
$928$	−20.3055	+	0.736570i	−0.666560	+	0.0241791i
$929$	−24.3139	+	42.1129i	−0.797714	+	1.38168i	0.123388	+	0.992359i	$0.460624\pi$
$929$	−24.3139	+	42.1129i	−0.797714	+	1.38168i	−0.921102	+	0.389322i	$0.872709\pi$
$930$	−20.8329	−	24.9131i	−0.683136	−	0.816932i
$931$	15.9414			0.522457
$932$	−0.00630512	+	0.166474i	−0.000206531	+	0.00545303i
$933$	−19.6713	+	73.4142i	−0.644009	+	2.40347i
$934$	−13.7786	+	5.40407i	−0.450850	+	0.176827i
$935$	9.53320	+	14.4099i	0.311769	+	0.471254i
$936$	0.306999	+	61.5073i	0.0100346	+	2.01043i
$937$	−0.796061	+	0.796061i	−0.0260062	+	0.0260062i	−0.719990	−	0.693984i	$-0.755854\pi$
$937$	−0.796061	+	0.796061i	−0.0260062	+	0.0260062i	0.693984	+	0.719990i	$0.255854\pi$
$938$	−16.9419	−	7.39627i	−0.553172	−	0.241497i
$939$	−17.4249	−	30.1808i	−0.568640	−	0.984913i
$940$	−3.09356	+	12.7082i	−0.100901	+	0.414496i
$941$			19.5161i			0.636206i	0.948056	+	0.318103i	$0.103046\pi$
$941$			19.5161i			0.636206i	−0.948056	+	0.318103i	$0.896954\pi$
$942$	−1.48278	−	13.1871i	−0.0483115	−	0.429658i
$943$	−35.8762	+	9.61299i	−1.16829	+	0.313042i
$944$	20.5372	−	30.0636i	0.668430	−	0.978486i
$945$	−51.5550	−	45.6319i	−1.67708	−	1.48441i
$946$	−9.40483	−	23.9792i	−0.305777	−	0.779631i
$947$	54.5222	+	14.6092i	1.77173	+	0.474735i	0.989037	−	0.147668i	$-0.0471766\pi$
$947$	54.5222	+	14.6092i	1.77173	+	0.474735i	0.782697	+	0.622402i	$0.213843\pi$
$948$	2.97151	+	5.62859i	0.0965101	+	0.182808i
$949$	−3.39264	−	2.28496i	−0.110130	−	0.0741730i
$950$	−24.7904	+	5.90165i	−0.804308	+	0.191475i
$951$	−2.85847	−	4.95101i	−0.0926921	−	0.160547i
$952$	20.9465	−	24.3066i	0.678880	−	0.787781i
$953$	20.4162	−	5.47051i	0.661346	−	0.177207i	0.0874925	−	0.996165i	$-0.472115\pi$
$953$	20.4162	−	5.47051i	0.661346	−	0.177207i	0.573853	+	0.818958i	$0.305448\pi$
$954$	−17.6047	−	2.65759i	−0.569972	−	0.0860426i
$955$	−14.1227	+	15.9559i	−0.457001	+	0.516320i
$956$	39.3244	−	36.4543i	1.27184	−	1.17902i
$957$	17.5715	+	17.5715i	0.568004	+	0.568004i
$958$	−2.42234	−	21.5430i	−0.0782622	−	0.696024i
$959$	−5.74471	−	9.95012i	−0.185506	−	0.321306i
$960$	−11.1593	−	52.5881i	−0.360164	−	1.69727i
$961$	−19.3221			−0.623295
$962$	10.5194	−	20.1688i	0.339158	−	0.650269i
$963$	8.36649	−	8.36649i	0.269606	−	0.269606i
$964$	−0.838249	−	3.68036i	−0.0269982	−	0.118536i
$965$	−2.29825	+	4.60708i	−0.0739833	+	0.148307i
$966$	−79.3882	−	63.3396i	−2.55427	−	2.03792i
$967$	−36.3453	+	36.3453i	−1.16878	+	1.16878i	−0.186290	+	0.982495i	$0.559646\pi$
$967$	−36.3453	+	36.3453i	−1.16878	+	1.16878i	−0.982495	+	0.186290i	$0.940354\pi$
$968$	3.00833	−	15.8400i	0.0966913	−	0.509117i
$969$	18.1761	−	31.4819i	0.583901	−	1.01135i
$970$	−32.6628	−	11.9509i	−1.04874	−	0.383720i
$971$	−47.6672	−	27.5206i	−1.52971	−	0.883180i	−0.999373	−	0.0353935i	$-0.988732\pi$
$971$	−47.6672	−	27.5206i	−1.52971	−	0.883180i	−0.530338	−	0.847786i	$-0.677935\pi$
$972$	0.605368	−	0.962462i	0.0194172	−	0.0308710i
$973$	−71.3787	−	19.1259i	−2.28830	−	0.613147i
$974$	−3.75254	−	0.566480i	−0.120239	−	0.0181512i
$975$	24.5837	−	48.2787i	0.787308	−	1.54616i
$976$	−44.6268	−	30.4857i	−1.42847	−	0.975824i
$977$	8.63680	−	32.2330i	0.276316	−	1.03122i	−0.678639	−	0.734472i	$-0.737430\pi$
$977$	8.63680	−	32.2330i	0.276316	−	1.03122i	0.954955	−	0.296752i	$-0.0959034\pi$
$978$	17.8874	−	40.9728i	0.571976	−	1.31017i
$979$	3.24398	−	5.61874i	0.103678	−	0.179576i
$980$	9.49418	−	17.3548i	0.303280	−	0.554379i
$981$	46.5306	+	26.8644i	1.48561	+	0.857715i
$982$	6.29510	+	55.9854i	0.200885	+	1.78657i
$983$	15.2941	+	15.2941i	0.487807	+	0.487807i	0.907614	−	0.419807i	$-0.137902\pi$
$983$	15.2941	+	15.2941i	0.487807	+	0.487807i	−0.419807	+	0.907614i	$0.637902\pi$
$984$	36.9114	−	25.1287i	1.17669	−	0.801074i
$985$	11.5881	+	5.78074i	0.369227	+	0.184190i
$986$	−15.8728	+	6.22543i	−0.505493	+	0.198258i
$987$	−21.0053	−	21.0053i	−0.668607	−	0.668607i
$988$	−23.7650	+	10.5165i	−0.756064	+	0.334576i
$989$		−	55.9372i		−	1.77870i
$990$	−25.2450	+	35.9242i	−0.802340	+	1.14174i
$991$	−4.43836	+	2.56249i	−0.140989	+	0.0814001i	−0.568835	−	0.822451i	$-0.692606\pi$
$991$	−4.43836	+	2.56249i	−0.140989	+	0.0814001i	0.427846	+	0.903852i	$0.359272\pi$
$992$	17.0806	+	9.05232i	0.542310	+	0.287411i
$993$	32.0580	−	32.0580i	1.01733	−	1.01733i
$994$	25.1566	−	31.5306i	0.797920	−	1.00009i
$995$	−32.6463	−	28.8957i	−1.03496	−	0.916054i
$996$	14.1930	−	45.9381i	0.449722	−	1.45560i
$997$	1.31199	+	4.89640i	0.0415510	+	0.155070i	0.983584	−	0.180449i	$-0.0577550\pi$
$997$	1.31199	+	4.89640i	0.0415510	+	0.155070i	−0.942033	+	0.335519i	$0.891088\pi$
$998$	14.8441	+	6.48044i	0.469881	+	0.205135i
$999$	−35.1956	+	20.3202i	−1.11354	+	0.642902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bg.c.23.15	✓	144
4.3	odd	2	inner	260.2.bg.c.23.18	yes	144
5.2	odd	4	inner	260.2.bg.c.127.5	yes	144
13.4	even	6	inner	260.2.bg.c.43.2	yes	144
20.7	even	4	inner	260.2.bg.c.127.2	yes	144
52.43	odd	6	inner	260.2.bg.c.43.5	yes	144
65.17	odd	12	inner	260.2.bg.c.147.18	yes	144
260.147	even	12	inner	260.2.bg.c.147.15	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bg.c.23.15	✓	144	1.1	even	1	trivial
260.2.bg.c.23.18	yes	144	4.3	odd	2	inner
260.2.bg.c.43.2	yes	144	13.4	even	6	inner
260.2.bg.c.43.5	yes	144	52.43	odd	6	inner
260.2.bg.c.127.2	yes	144	20.7	even	4	inner
260.2.bg.c.127.5	yes	144	5.2	odd	4	inner
260.2.bg.c.147.15	yes	144	260.147	even	12	inner
260.2.bg.c.147.18	yes	144	65.17	odd	12	inner

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.565829 + 1.29609i) q^{2} +(2.90282 + 0.777809i) q^{3} +(-1.35968 - 1.46672i) q^{4} +(0.446275 - 2.19108i) q^{5} +(-2.65061 + 3.32220i) q^{6} +(-0.874770 - 3.26469i) q^{7} +(2.67034 - 0.932342i) q^{8} +(5.22332 + 3.01568i) q^{9} +(2.58731 + 1.81819i) q^{10} +(1.15104 + 1.99367i) q^{11} +(-2.80607 - 5.31521i) q^{12} +(0.690411 + 3.53883i) q^{13} +(4.72628 + 0.713476i) q^{14} +(2.99970 - 6.01320i) q^{15} +(-0.302562 + 3.98854i) q^{16} +(0.868722 + 3.24211i) q^{17} +(-6.86408 + 5.06350i) q^{18} +(-3.12105 - 1.80194i) q^{19} +(-3.82050 + 2.32460i) q^{20} -10.1572i q^{21} +(-3.23526 + 0.363778i) q^{22} +(-6.82930 - 1.82991i) q^{23} +(8.47672 - 0.629405i) q^{24} +(-4.60168 - 1.95565i) q^{25} +(-4.97728 - 1.10754i) q^{26} +(6.44169 + 6.44169i) q^{27} +(-3.59899 + 5.72196i) q^{28} +(3.11068 - 1.79595i) q^{29} +(6.09631 + 7.29031i) q^{30} -3.41729 q^{31} +(-4.99829 - 2.64898i) q^{32} +(1.79058 + 6.68255i) q^{33} +(-4.69361 - 0.708543i) q^{34} +(-7.54358 + 0.459745i) q^{35} +(-2.67884 - 11.7615i) q^{36} +(-1.15462 + 4.30910i) q^{37} +(4.10144 - 3.02555i) q^{38} +(-0.748393 + 10.8096i) q^{39} +(-0.851129 - 6.26702i) q^{40} +(4.54947 - 2.62664i) q^{41} +(13.1646 + 5.74724i) q^{42} +(2.04769 + 7.64209i) q^{43} +(1.35911 - 4.39901i) q^{44} +(8.93864 - 10.0989i) q^{45} +(6.23593 - 7.81594i) q^{46} +(2.06802 - 2.06802i) q^{47} +(-3.98061 + 11.3427i) q^{48} +(-3.83078 + 2.21170i) q^{49} +(5.13845 - 4.85761i) q^{50} +10.0870i q^{51} +(4.25176 - 5.82431i) q^{52} +(1.47596 + 1.47596i) q^{53} +(-11.9939 + 4.70409i) q^{54} +(4.88197 - 1.63231i) q^{55} +(-5.37974 - 7.90225i) q^{56} +(-7.65828 - 7.65828i) q^{57} +(0.567595 + 5.04790i) q^{58} +(-7.88272 - 4.55109i) q^{59} +(-12.8983 + 3.77628i) q^{60} +(-6.75570 + 11.7012i) q^{61} +(1.93360 - 4.42910i) q^{62} +(5.27606 - 19.6905i) q^{63} +(6.26148 - 4.97935i) q^{64} +(8.06198 + 0.0665445i) q^{65} +(-9.67432 - 1.46043i) q^{66} +(-3.73572 - 1.00098i) q^{67} +(3.57411 - 5.68240i) q^{68} +(-18.4009 - 10.6238i) q^{69} +(3.67251 - 10.0373i) q^{70} +(4.21945 - 7.30830i) q^{71} +(16.7597 + 3.18300i) q^{72} +(-0.802185 + 0.802185i) q^{73} +(-4.93165 - 3.93470i) q^{74} +(-11.8367 - 9.25613i) q^{75} +(1.60067 + 7.02776i) q^{76} +(5.50180 - 5.50180i) q^{77} +(-13.5867 - 7.08637i) q^{78} -1.05896 q^{79} +(8.60419 + 2.44293i) q^{80} +(4.64163 + 8.03955i) q^{81} +(0.830127 + 7.38273i) q^{82} +(5.65651 + 5.65651i) q^{83} +(-14.8978 + 13.8105i) q^{84} +(7.49143 - 0.456566i) q^{85} +(-11.0634 - 1.67013i) q^{86} +(10.4266 - 2.79381i) q^{87} +(4.93246 + 4.25061i) q^{88} +(-1.40915 - 2.44071i) q^{89} +(8.03128 + 17.2995i) q^{90} +(10.9492 - 5.34964i) q^{91} +(6.60167 + 12.5048i) q^{92} +(-9.91978 - 2.65800i) q^{93} +(1.51019 + 3.85048i) q^{94} +(-5.34103 + 6.03431i) q^{95} +(-12.4488 - 11.5772i) q^{96} +(-10.6238 + 2.84663i) q^{97} +(-0.698989 - 6.21646i) q^{98} +13.8847i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 6 q^{2} - 12 q^{6} + 12 q^{10} - 12 q^{12} + 4 q^{13} - 12 q^{16} - 24 q^{17} - 42 q^{20} - 12 q^{22} - 24 q^{25} - 36 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 76 q^{36} + 48 q^{37} - 16 q^{38}+ \cdots - 162 q^{98}+O(q^{100}) \) 144 * q - 6 * q^2 - 12 * q^6 + 12 * q^10 - 12 * q^12 + 4 * q^13 - 12 * q^16 - 24 * q^17 - 42 * q^20 - 12 * q^22 - 24 * q^25 - 36 * q^26 - 6 * q^28 - 36 * q^32 - 12 * q^33 - 76 * q^36 + 48 * q^37 - 16 * q^38 + 76 * q^40 - 72 * q^41 + 40 * q^42 - 120 * q^45 - 12 * q^46 - 40 * q^48 + 120 * q^50 - 10 * q^52 + 8 * q^53 - 20 * q^56 + 126 * q^58 + 16 * q^61 - 44 * q^62 + 32 * q^65 + 96 * q^66 - 64 * q^68 - 54 * q^72 - 12 * q^76 + 40 * q^77 - 100 * q^78 - 24 * q^80 - 32 * q^81 - 78 * q^82 - 24 * q^85 - 10 * q^88 - 8 * q^90 + 100 * q^92 - 48 * q^93 - 12 * q^97 - 162 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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