LMFDB - Embedded newform 370.2.v.a.289.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(99,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("370.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$370 = 2 \cdot 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	370.v (of order $18$ , degree $6$ , 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			289.10
Character	$\chi$	$=$	370.289
Dual form			370.2.v.a.169.10

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(1.06706 - 2.93174i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.51333 + 1.64616i) q^{5} +3.11989i q^{6} +(4.22864 - 0.745624i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-5.15832 - 4.32834i) q^{9} +(0.859044 - 2.06447i) q^{10} +(1.53583 - 2.66013i) q^{11} +(-1.06706 - 2.93174i) q^{12} +(1.79913 - 1.50965i) q^{13} +(-3.71861 + 2.14694i) q^{14} +(3.21128 + 6.19324i) q^{15} +(0.173648 - 0.984808i) q^{16} +(0.650675 + 0.545981i) q^{17} +(6.32761 + 2.30306i) q^{18} +(-1.67595 + 4.60463i) q^{19} +(-0.101147 + 2.23378i) q^{20} +(2.32626 - 13.1929i) q^{21} +(-0.533387 + 3.02499i) q^{22} +(-2.03182 - 3.51921i) q^{23} +(2.00543 + 2.38997i) q^{24} +(-0.419673 - 4.98236i) q^{25} +(-1.17430 + 2.03394i) q^{26} +(-10.0881 + 5.82437i) q^{27} +(2.76005 - 3.28930i) q^{28} +(-5.82054 - 3.36049i) q^{29} +(-5.13583 - 4.72142i) q^{30} +1.08237i q^{31} +(0.173648 + 0.984808i) q^{32} +(-6.15997 - 7.34117i) q^{33} +(-0.798171 - 0.290511i) q^{34} +(-5.17191 + 8.08939i) q^{35} -6.73370 q^{36} +(5.56641 - 2.45256i) q^{37} -4.90014i q^{38} +(-2.50610 - 6.88545i) q^{39} +(-0.668950 - 2.13366i) q^{40} +(-9.54326 + 8.00775i) q^{41} +(2.32626 + 13.1929i) q^{42} +4.64976 q^{43} +(-0.533387 - 3.02499i) q^{44} +(14.9314 - 1.94120i) q^{45} +(3.11293 + 2.61206i) q^{46} +(-0.254210 + 0.146768i) q^{47} +(-2.70190 - 1.55994i) q^{48} +(10.7476 - 3.91182i) q^{49} +(2.09843 + 4.53835i) q^{50} +(2.29499 - 1.32501i) q^{51} +(0.407829 - 2.31291i) q^{52} +(3.92105 + 0.691388i) q^{53} +(7.48767 - 8.92345i) q^{54} +(2.05478 + 6.55386i) q^{55} +(-1.46859 + 4.03493i) q^{56} +(11.7112 + 9.82687i) q^{57} +(6.61888 + 1.16709i) q^{58} +(11.5194 + 2.03118i) q^{59} +(6.44092 + 2.68012i) q^{60} +(-0.829028 - 0.987998i) q^{61} +(-0.370192 - 1.01709i) q^{62} +(-25.0400 - 14.4569i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.237553 + 5.24624i) q^{65} +(8.29930 + 4.79161i) q^{66} +(-6.59551 + 1.16297i) q^{67} +0.849396 q^{68} +(-12.4855 + 2.20153i) q^{69} +(2.09327 - 9.37044i) q^{70} +(12.1478 + 4.42144i) q^{71} +(6.32761 - 2.30306i) q^{72} +13.9817i q^{73} +(-4.39189 + 4.20848i) q^{74} +(-15.0548 - 4.08613i) q^{75} +(1.67595 + 4.60463i) q^{76} +(4.51101 - 12.3939i) q^{77} +(4.70993 + 5.61307i) q^{78} +(-7.28405 + 1.28437i) q^{79} +(1.35836 + 1.77619i) q^{80} +(2.80297 + 15.8964i) q^{81} +(6.22892 - 10.7888i) q^{82} +(6.19433 - 7.38212i) q^{83} +(-6.69821 - 11.6016i) q^{84} +(-1.88346 + 0.244865i) q^{85} +(-4.36935 + 1.59031i) q^{86} +(-16.0630 + 13.4784i) q^{87} +(1.53583 + 2.66013i) q^{88} +(11.8301 + 2.08597i) q^{89} +(-13.3670 + 6.93096i) q^{90} +(6.48224 - 7.72523i) q^{91} +(-3.81857 - 1.38985i) q^{92} +(3.17322 + 1.15496i) q^{93} +(0.188681 - 0.224862i) q^{94} +(-5.04369 - 9.72719i) q^{95} +(3.07249 + 0.541763i) q^{96} +(2.11350 + 3.66068i) q^{97} +(-8.76155 + 7.35181i) q^{98} +(-19.4362 + 7.07421i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$60 q - 3 q^{5} - 30 q^{8} - 6 q^{9} + 9 q^{10} + 6 q^{11} - 3 q^{13} + 9 q^{14} + 18 q^{15} + 3 q^{17} + 12 q^{18} + 3 q^{19} - 6 q^{20} + 12 q^{21} - 3 q^{22} - 18 q^{23} - 15 q^{25} - 27 q^{26} + 6 q^{30}+ \cdots - 45 q^{99}+O(q^{100})$ 60 * q - 3 * q^5 - 30 * q^8 - 6 * q^9 + 9 * q^10 + 6 * q^11 - 3 * q^13 + 9 * q^14 + 18 * q^15 + 3 * q^17 + 12 * q^18 + 3 * q^19 - 6 * q^20 + 12 * q^21 - 3 * q^22 - 18 * q^23 - 15 * q^25 - 27 * q^26 + 6 * q^30 - 66 * q^33 + 21 * q^34 - 3 * q^35 - 72 * q^36 + 6 * q^37 + 12 * q^39 + 6 * q^40 - 57 * q^41 + 12 * q^42 + 60 * q^43 - 3 * q^44 + 45 * q^45 - 21 * q^46 - 18 * q^47 - 6 * q^49 + 36 * q^50 - 3 * q^52 - 6 * q^53 + 3 * q^55 + 30 * q^57 + 15 * q^58 - 12 * q^59 + 9 * q^60 + 42 * q^61 - 12 * q^62 - 9 * q^63 - 30 * q^64 - 30 * q^65 - 18 * q^67 - 24 * q^68 + 36 * q^69 + 18 * q^71 + 12 * q^72 + 3 * q^74 - 78 * q^75 - 3 * q^76 + 21 * q^77 + 6 * q^78 - 24 * q^79 - 36 * q^81 + 27 * q^82 + 30 * q^83 + 12 * q^84 + 33 * q^85 - 18 * q^86 - 30 * q^87 + 6 * q^88 + 3 * q^89 - 3 * q^90 + 57 * q^91 + 15 * q^92 + 60 * q^93 + 3 * q^94 - 150 * q^95 + 84 * q^97 - 6 * q^98 - 45 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$ .

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	1.06706	−	2.93174i	0.616070	−	1.69264i	−0.100335	−	0.994954i	$-0.531991\pi$
$3$	1.06706	−	2.93174i	0.616070	−	1.69264i	0.716405	−	0.697685i	$-0.245786\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−1.51333	+	1.64616i	−0.676781	+	0.736184i
$5$	−1.51333	+	1.64616i	−0.676781	+	0.736184i
$6$			3.11989i			1.27369i
$7$	4.22864	−	0.745624i	1.59828	−	0.281819i	0.697659	−	0.716430i	$-0.254225\pi$
$7$	4.22864	−	0.745624i	1.59828	−	0.281819i	0.900618	+	0.434611i	$0.143114\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−5.15832	−	4.32834i	−1.71944	−	1.44278i
$10$	0.859044	−	2.06447i	0.271654	−	0.652843i
$11$	1.53583	−	2.66013i	0.463069	−	0.802059i	−0.536043	−	0.844191i	$-0.680082\pi$
$11$	1.53583	−	2.66013i	0.463069	−	0.802059i	0.999112	+	0.0421316i	$0.0134149\pi$
$12$	−1.06706	−	2.93174i	−0.308035	−	0.846319i
$13$	1.79913	−	1.50965i	0.498988	−	0.418701i	−0.358246	−	0.933627i	$-0.616625\pi$
$13$	1.79913	−	1.50965i	0.498988	−	0.418701i	0.857234	+	0.514927i	$0.172181\pi$
$14$	−3.71861	+	2.14694i	−0.993840	+	0.573794i
$15$	3.21128	+	6.19324i	0.829149	+	1.59909i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	0.650675	+	0.545981i	0.157812	+	0.132420i	0.718275	−	0.695760i	$-0.244932\pi$
$17$	0.650675	+	0.545981i	0.157812	+	0.132420i	−0.560463	+	0.828180i	$0.689377\pi$
$18$	6.32761	+	2.30306i	1.49143	+	0.542837i
$19$	−1.67595	+	4.60463i	−0.384489	+	1.05637i	0.584956	+	0.811065i	$0.301112\pi$
$19$	−1.67595	+	4.60463i	−0.384489	+	1.05637i	−0.969445	+	0.245309i	$0.921111\pi$
$20$	−0.101147	+	2.23378i	−0.0226171	+	0.499488i
$21$	2.32626	−	13.1929i	0.507632	−	2.87893i
$22$	−0.533387	+	3.02499i	−0.113718	+	0.644929i
$23$	−2.03182	−	3.51921i	−0.423664	−	0.733807i	0.572631	−	0.819813i	$-0.305923\pi$
$23$	−2.03182	−	3.51921i	−0.423664	−	0.733807i	−0.996295	+	0.0860065i	$0.972589\pi$
$24$	2.00543	+	2.38997i	0.409356	+	0.487851i
$25$	−0.419673	−	4.98236i	−0.0839346	−	0.996471i
$26$	−1.17430	+	2.03394i	−0.230298	+	0.398889i
$27$	−10.0881	+	5.82437i	−1.94146	+	1.12090i
$28$	2.76005	−	3.28930i	0.521601	−	0.621620i
$29$	−5.82054	−	3.36049i	−1.08085	−	0.624028i	−0.149723	−	0.988728i	$-0.547838\pi$
$29$	−5.82054	−	3.36049i	−1.08085	−	0.624028i	−0.931125	+	0.364701i	$0.881171\pi$
$30$	−5.13583	−	4.72142i	−0.937670	−	0.862009i
$31$			1.08237i			0.194399i	0.995265	+	0.0971995i	$0.0309885\pi$
$31$			1.08237i			0.194399i	−0.995265	+	0.0971995i	$0.969012\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−6.15997	−	7.34117i	−1.07231	−	1.27793i
$34$	−0.798171	−	0.290511i	−0.136885	−	0.0498221i
$35$	−5.17191	+	8.08939i	−0.874213	+	1.36736i
$36$	−6.73370			−1.12228
$37$	5.56641	−	2.45256i	0.915112	−	0.403199i
$37$	5.56641	−	2.45256i	0.915112	−	0.403199i
$38$		−	4.90014i		−	0.794908i
$39$	−2.50610	−	6.88545i	−0.401297	−	1.10256i
$40$	−0.668950	−	2.13366i	−0.105770	−	0.337361i
$41$	−9.54326	+	8.00775i	−1.49041	+	1.25060i	−0.596288	+	0.802771i	$0.703358\pi$
$41$	−9.54326	+	8.00775i	−1.49041	+	1.25060i	−0.894119	+	0.447829i	$0.852197\pi$
$42$	2.32626	+	13.1929i	0.358950	+	2.03571i
$43$	4.64976			0.709082			0.354541	−	0.935040i	$-0.384637\pi$
$43$	4.64976			0.709082			0.354541	+	0.935040i	$0.384637\pi$
$44$	−0.533387	−	3.02499i	−0.0804111	−	0.456034i
$45$	14.9314	−	1.94120i	2.22584	−	0.289377i
$46$	3.11293	+	2.61206i	0.458976	+	0.385127i
$47$	−0.254210	+	0.146768i	−0.0370803	+	0.0214083i	−0.518426	−	0.855123i	$-0.673482\pi$
$47$	−0.254210	+	0.146768i	−0.0370803	+	0.0214083i	0.481345	+	0.876531i	$0.340148\pi$
$48$	−2.70190	−	1.55994i	−0.389986	−	0.225159i
$49$	10.7476	−	3.91182i	1.53538	−	0.558831i
$50$	2.09843	+	4.53835i	0.296763	+	0.641819i
$51$	2.29499	−	1.32501i	0.321362	−	0.185539i
$52$	0.407829	−	2.31291i	0.0565557	−	0.320743i
$53$	3.92105	+	0.691388i	0.538598	+	0.0949694i	0.436329	−	0.899787i	$-0.356278\pi$
$53$	3.92105	+	0.691388i	0.538598	+	0.0949694i	0.102269	+	0.994757i	$0.467390\pi$
$54$	7.48767	−	8.92345i	1.01894	−	1.21433i
$55$	2.05478	+	6.55386i	0.277067	+	0.883722i
$56$	−1.46859	+	4.03493i	−0.196249	+	0.539190i
$57$	11.7112	+	9.82687i	1.55119	+	1.30160i
$58$	6.61888	+	1.16709i	0.869101	+	0.153246i
$59$	11.5194	+	2.03118i	1.49970	+	0.264437i	0.862419	−	0.506195i	$-0.168948\pi$
$59$	11.5194	+	2.03118i	1.49970	+	0.264437i	0.637280	+	0.770632i	$0.280059\pi$
$60$	6.44092	+	2.68012i	0.831519	+	0.346002i
$61$	−0.829028	−	0.987998i	−0.106146	−	0.126500i	0.710356	−	0.703843i	$-0.248534\pi$
$61$	−0.829028	−	0.987998i	−0.106146	−	0.126500i	−0.816502	+	0.577343i	$0.804090\pi$
$62$	−0.370192	−	1.01709i	−0.0470144	−	0.129171i
$63$	−25.0400	−	14.4569i	−3.15474	−	1.82139i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.237553	+	5.24624i	−0.0294648	+	0.650716i
$66$	8.29930	+	4.79161i	1.02157	+	0.589806i
$67$	−6.59551	+	1.16297i	−0.805770	+	0.142079i	−0.561337	−	0.827587i	$-0.689713\pi$
$67$	−6.59551	+	1.16297i	−0.805770	+	0.142079i	−0.244433	+	0.969666i	$0.578602\pi$
$68$	0.849396			0.103004
$69$	−12.4855	+	2.20153i	−1.50308	+	0.265033i
$70$	2.09327	−	9.37044i	0.250194	−	1.11998i
$71$	12.1478	+	4.42144i	1.44168	+	0.524729i	0.940255	−	0.340472i	$-0.110587\pi$
$71$	12.1478	+	4.42144i	1.44168	+	0.524729i	0.501426	+	0.865201i	$0.332809\pi$
$72$	6.32761	−	2.30306i	0.745716	−	0.271419i
$73$			13.9817i			1.63644i	0.574906	+	0.818219i	$0.305039\pi$
$73$			13.9817i			1.63644i	−0.574906	+	0.818219i	$0.694961\pi$
$74$	−4.39189	+	4.20848i	−0.510547	+	0.489226i
$75$	−15.0548	−	4.08613i	−1.73838	−	0.471825i
$76$	1.67595	+	4.60463i	0.192244	+	0.528187i
$77$	4.51101	−	12.3939i	0.514077	−	1.41241i
$78$	4.70993	+	5.61307i	0.533294	+	0.635555i
$79$	−7.28405	+	1.28437i	−0.819520	+	0.144503i	−0.567663	−	0.823261i	$-0.692152\pi$
$79$	−7.28405	+	1.28437i	−0.819520	+	0.144503i	−0.251857	+	0.967764i	$0.581041\pi$
$80$	1.35836	+	1.77619i	0.151870	+	0.198584i
$81$	2.80297	+	15.8964i	0.311441	+	1.76627i
$82$	6.22892	−	10.7888i	0.687869	−	1.19142i
$83$	6.19433	−	7.38212i	0.679916	−	0.810293i	−0.310181	−	0.950678i	$-0.600390\pi$
$83$	6.19433	−	7.38212i	0.679916	−	0.810293i	0.990097	+	0.140385i	$0.0448340\pi$
$84$	−6.69821	−	11.6016i	−0.730835	−	1.26584i
$85$	−1.88346	+	0.244865i	−0.204290	+	0.0265593i
$86$	−4.36935	+	1.59031i	−0.471159	+	0.171488i
$87$	−16.0630	+	13.4784i	−1.72213	+	1.44504i
$88$	1.53583	+	2.66013i	0.163720	+	0.283571i
$89$	11.8301	+	2.08597i	1.25399	+	0.221112i	0.760902	−	0.648867i	$-0.224757\pi$
$89$	11.8301	+	2.08597i	1.25399	+	0.221112i	0.493088	+	0.869979i	$0.335868\pi$
$90$	−13.3670	+	6.93096i	−1.40900	+	0.730587i
$91$	6.48224	−	7.72523i	0.679523	−	0.809824i
$92$	−3.81857	−	1.38985i	−0.398113	−	0.144901i
$93$	3.17322	+	1.15496i	0.329047	+	0.119763i
$94$	0.188681	−	0.224862i	0.0194610	−	0.0231927i
$95$	−5.04369	−	9.72719i	−0.517471	−	0.997989i
$96$	3.07249	+	0.541763i	0.313585	+	0.0552934i
$97$	2.11350	+	3.66068i	0.214593	+	0.371686i	0.953147	−	0.302509i	$-0.0978241\pi$
$97$	2.11350	+	3.66068i	0.214593	+	0.371686i	−0.738554	+	0.674195i	$0.764491\pi$
$98$	−8.76155	+	7.35181i	−0.885050	+	0.742645i
$99$	−19.4362	+	7.07421i	−1.95341	+	0.710984i
$100$	−3.52409	−	3.54695i	−0.352409	−	0.354695i
$101$	3.67967	+	6.37337i	0.366141	+	0.634174i	0.988958	−	0.148193i	$-0.0473456\pi$
$101$	3.67967	+	6.37337i	0.366141	+	0.634174i	−0.622818	+	0.782367i	$0.714012\pi$
$102$	−1.70340	+	2.03003i	−0.168662	+	0.201003i
$103$	−3.27891	+	5.67924i	−0.323081	+	0.559592i	−0.981122	−	0.193390i	$-0.938052\pi$
$103$	−3.27891	+	5.67924i	−0.323081	+	0.559592i	0.658041	+	0.752982i	$0.271385\pi$
$104$	0.407829	+	2.31291i	0.0399909	+	0.226800i
$105$	18.1972	+	23.7946i	1.77586	+	2.32211i
$106$	−3.92105	+	0.691388i	−0.380846	+	0.0671535i
$107$	8.37130	+	9.97653i	0.809284	+	0.964468i	0.999852	−	0.0172065i	$-0.00547728\pi$
$107$	8.37130	+	9.97653i	0.809284	+	0.964468i	−0.190568	+	0.981674i	$0.561033\pi$
$108$	−3.98410	+	10.9462i	−0.383371	+	1.05330i
$109$	−3.72200	−	10.2261i	−0.356503	−	0.979483i	−0.980234	−	0.197844i	$-0.936606\pi$
$109$	−3.72200	−	10.2261i	−0.356503	−	0.979483i	0.623731	−	0.781639i	$-0.285616\pi$
$110$	−4.17242	−	5.45584i	−0.397824	−	0.520194i
$111$	−1.25055	−	18.9363i	−0.118697	−	1.79735i
$112$		−	4.29388i		−	0.405733i
$113$	−13.0995	+	4.76783i	−1.23230	+	0.448520i	−0.874384	−	0.485235i	$-0.838734\pi$
$113$	−13.0995	+	4.76783i	−1.23230	+	0.448520i	−0.357914	+	0.933754i	$0.616512\pi$
$114$	−14.3659	−	5.22877i	−1.34549	−	0.489719i
$115$	8.86799	+	1.98103i	0.826944	+	0.184732i
$116$	−6.61888	+	1.16709i	−0.614547	+	0.108361i
$117$	−15.8147			−1.46207
$118$	−11.5194	+	2.03118i	−1.06045	+	0.186986i
$119$	3.15857	+	1.82360i	0.289546	+	0.167169i
$120$	−6.96914	−	0.315567i	−0.636193	−	0.0288072i
$121$	0.782477	+	1.35529i	0.0711342	+	0.123208i
$122$	1.11695	+	0.644870i	0.101124	+	0.0583837i
$123$	13.2933	+	36.5231i	1.19862	+	3.29318i
$124$	0.695733	+	0.829142i	0.0624786	+	0.0744592i
$125$	8.83685	+	6.84909i	0.790392	+	0.612602i
$126$	28.4744	+	5.02081i	2.53670	+	0.447290i
$127$	5.48175	+	0.966580i	0.486426	+	0.0857701i	0.411483	−	0.911418i	$-0.365011\pi$
$127$	5.48175	+	0.966580i	0.486426	+	0.0857701i	0.0749439	+	0.997188i	$0.476122\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	4.96160	−	13.6319i	0.436845	−	1.20022i
$130$	−1.57109	−	5.01110i	−0.137794	−	0.439502i
$131$	−9.82167	+	11.7050i	−0.858123	+	1.02267i	0.141342	+	0.989961i	$0.454858\pi$
$131$	−9.82167	+	11.7050i	−0.858123	+	1.02267i	−0.999465	+	0.0327106i	$0.989586\pi$
$132$	−9.43762	−	1.66411i	−0.821440	−	0.144842i
$133$	−3.65366	+	20.7210i	−0.316813	+	1.79674i
$134$	5.80000	−	3.34863i	0.501043	−	0.289277i
$135$	5.67878	−	25.4208i	0.488752	−	2.18787i
$136$	−0.798171	+	0.290511i	−0.0684426	+	0.0249111i
$137$	−5.08436	−	2.93546i	−0.434386	−	0.250793i	0.266827	−	0.963744i	$-0.414025\pi$
$137$	−5.08436	−	2.93546i	−0.434386	−	0.250793i	−0.701213	+	0.712951i	$0.747358\pi$
$138$	10.9796	−	6.33905i	0.934642	−	0.539616i
$139$	−2.16050	−	1.81287i	−0.183251	−	0.153766i	0.546548	−	0.837428i	$-0.315942\pi$
$139$	−2.16050	−	1.81287i	−0.183251	−	0.153766i	−0.729799	+	0.683662i	$0.760386\pi$
$140$	1.23785	+	9.52128i	0.104617	+	0.804695i
$141$	0.159027	+	0.901886i	0.0133925	+	0.0759525i
$142$	−12.9274			−1.08485
$143$	−1.25271	−	7.10446i	−0.104757	−	0.594105i
$144$	−5.15832	+	4.32834i	−0.429860	+	0.360695i
$145$	14.3403	−	4.49600i	1.19090	−	0.373373i
$146$	−4.78204	−	13.1385i	−0.395764	−	1.08735i
$147$		−	35.6834i		−	2.94312i
$148$	2.68764	−	5.45679i	0.220923	−	0.448546i
$149$	−4.98214			−0.408153			−0.204077	−	0.978955i	$-0.565419\pi$
$149$	−4.98214			−0.408153			−0.204077	+	0.978955i	$0.565419\pi$
$150$	15.5444	−	1.30933i	1.26919	−	0.106907i
$151$	−7.33514	−	2.66977i	−0.596925	−	0.217263i	0.0258474	−	0.999666i	$-0.491772\pi$
$151$	−7.33514	−	2.66977i	−0.596925	−	0.217263i	−0.622773	+	0.782403i	$0.713994\pi$
$152$	−3.14975	−	3.75373i	−0.255479	−	0.304467i
$153$	−0.993195	−	5.63269i	−0.0802950	−	0.455376i
$154$			13.1893i			1.06282i
$155$	−1.78175	−	1.63798i	−0.143114	−	0.131566i
$156$	−6.34567	−	3.66367i	−0.508060	−	0.293329i
$157$	15.9623	−	19.0231i	1.27393	−	1.51821i	0.534083	−	0.845432i	$-0.320657\pi$
$157$	15.9623	−	19.0231i	1.27393	−	1.51821i	0.739846	−	0.672777i	$-0.234898\pi$
$158$	6.40549	−	3.69821i	0.509593	−	0.294214i
$159$	6.21098	−	10.7577i	0.492563	−	0.853144i
$160$	−1.88394	−	1.20449i	−0.148938	−	0.0952229i
$161$	−11.2159	−	13.3665i	−0.883933	−	1.05343i
$162$	−8.07083	−	13.9791i	−0.634104	−	1.09830i
$163$	2.82751	−	16.0356i	0.221468	−	1.25601i	−0.647856	−	0.761763i	$-0.724334\pi$
$163$	2.82751	−	16.0356i	0.221468	−	1.25601i	0.869324	−	0.494243i	$-0.164555\pi$
$164$	−2.16328	+	12.2686i	−0.168924	+	0.958015i
$165$	21.4068	+	0.969312i	1.66652	+	0.0754609i
$166$	−3.29594	+	9.05551i	−0.255814	+	0.702844i
$167$	8.69328	+	3.16410i	0.672707	+	0.244845i	0.655713	−	0.755010i	$-0.272368\pi$
$167$	8.69328	+	3.16410i	0.672707	+	0.244845i	0.0169938	+	0.999856i	$0.494590\pi$
$168$	10.2623	+	8.61105i	0.791750	+	0.664357i
$169$	−1.29960	+	7.37041i	−0.0999694	+	0.566955i
$170$	1.68612	−	0.874278i	0.129320	−	0.0670541i
$171$	28.5755	−	16.4981i	2.18522	−	1.26164i
$172$	3.56193	−	2.98881i	0.271594	−	0.227895i
$173$	−2.14010	−	5.87989i	−0.162709	−	0.447040i	0.831367	−	0.555723i	$-0.187559\pi$
$173$	−2.14010	−	5.87989i	−0.162709	−	0.447040i	−0.994076	+	0.108684i	$0.965336\pi$
$174$	10.4844	−	18.1594i	0.794817	−	1.37666i
$175$	−5.48961	−	20.7557i	−0.414976	−	1.56898i
$176$	−2.35302	−	1.97442i	−0.177366	−	0.148827i
$177$	18.2468	−	31.6045i	1.37152	−	2.37554i
$178$	−11.8301	+	2.08597i	−0.886705	+	0.156350i
$179$		−	5.85747i		−	0.437808i	−0.975746	−	0.218904i	$-0.929752\pi$
$179$		−	5.85747i		−	0.437808i	0.975746	−	0.218904i	$-0.0702481\pi$
$180$	10.1903	−	11.0847i	0.759541	−	0.826208i
$181$	−8.11917	+	6.81280i	−0.603493	+	0.506391i	−0.892566	−	0.450916i	$-0.851097\pi$
$181$	−8.11917	+	6.81280i	−0.603493	+	0.506391i	0.289073	+	0.957307i	$0.406653\pi$
$182$	−3.44913	+	9.47640i	−0.255666	+	0.702437i
$183$	−3.78117	+	1.37624i	−0.279512	+	0.101734i
$184$	4.06364			0.299575
$185$	−4.38650	+	12.8747i	−0.322502	+	0.946569i
$186$	−3.37687			−0.247604
$187$	2.45170	−	0.892347i	0.179286	−	0.0652549i
$188$	−0.100395	+	0.275834i	−0.00732207	+	0.0201172i
$189$	−38.3162	+	32.1511i	−2.78709	+	2.33865i
$190$	8.06641	+	7.41553i	0.585199	+	0.537979i
$191$			6.56607i			0.475105i	0.971375	+	0.237552i	$0.0763451\pi$
$191$			6.56607i			0.475105i	−0.971375	+	0.237552i	$0.923655\pi$
$192$	−3.07249	+	0.541763i	−0.221738	+	0.0390984i
$193$	−9.02384	+	15.6297i	−0.649550	+	1.12505i	0.333680	+	0.942686i	$0.391709\pi$
$193$	−9.02384	+	15.6297i	−0.649550	+	1.12505i	−0.983230	+	0.182368i	$0.941624\pi$
$194$	−3.23806	−	2.71706i	−0.232479	−	0.195073i
$195$	15.1271	+	6.29452i	1.08327	+	0.450760i
$196$	5.71870	−	9.90507i	0.408478	−	0.707505i
$197$	5.19898	+	14.2841i	0.370412	+	1.01770i	0.975203	+	0.221314i	$0.0710344\pi$
$197$	5.19898	+	14.2841i	0.370412	+	1.01770i	−0.604791	+	0.796384i	$0.706743\pi$
$198$	15.8446	−	13.2952i	1.12602	−	0.944846i
$199$	−3.75123	+	2.16577i	−0.265918	+	0.153528i	−0.627031	−	0.778994i	$-0.715730\pi$
$199$	−3.75123	+	2.16577i	−0.265918	+	0.153528i	0.361113	+	0.932522i	$0.382397\pi$
$200$	4.52468	+	2.12773i	0.319943	+	0.150453i
$201$	−3.62833	+	20.5773i	−0.255922	+	1.45141i
$202$	−5.63758	−	4.73049i	−0.396659	−	0.332836i
$203$	−27.1187	−	9.87039i	−1.90336	−	0.692765i
$204$	0.906361	−	2.49021i	0.0634579	−	0.174349i
$205$	1.26007	−	27.8281i	0.0880073	−	1.94360i
$206$	1.13875	−	6.45819i	0.0793407	−	0.449964i
$207$	−4.75159	+	26.9476i	−0.330259	+	1.87299i
$208$	−1.17430	−	2.03394i	−0.0814228	−	0.141028i
$209$	9.67494	+	11.5301i	0.669230	+	0.797557i
$210$	−25.2380	−	16.1358i	−1.74159	−	1.11348i
$211$	−12.3343	+	21.3636i	−0.849126	+	1.47073i	0.0328629	+	0.999460i	$0.489538\pi$
$211$	−12.3343	+	21.3636i	−0.849126	+	1.47073i	−0.881989	+	0.471270i	$0.843796\pi$
$212$	3.44812	−	1.99077i	0.236818	−	0.136727i
$213$	25.9250	−	30.8962i	1.77635	−	2.11697i
$214$	−11.2786	−	6.51172i	−0.770991	−	0.445132i
$215$	−7.03662	+	7.65425i	−0.479894	+	0.522015i
$216$		−	11.6487i		−	0.792596i
$217$	0.807040	+	4.57695i	0.0547854	+	0.310704i
$218$	6.99506	+	8.33639i	0.473766	+	0.564612i
$219$	40.9908	+	14.9194i	2.76990	+	1.00816i
$220$	5.78680	+	3.69976i	0.390146	+	0.249438i
$221$	1.99489			0.134191
$222$	7.65173	+	17.3666i	0.513550	+	1.16557i
$223$			8.02784i			0.537584i	0.963198	+	0.268792i	$0.0866244\pi$
$223$			8.02784i			0.537584i	−0.963198	+	0.268792i	$0.913376\pi$
$224$	1.46859	+	4.03493i	0.0981245	+	0.269595i
$225$	−19.4005	+	27.5171i	−1.29337	+	1.83447i
$226$	10.6788	−	8.96059i	0.710344	−	0.596050i
$227$	−3.01681	−	17.1092i	−0.200233	−	1.13558i	−0.904767	−	0.425906i	$-0.859955\pi$
$227$	−3.01681	−	17.1092i	−0.200233	−	1.13558i	0.704535	−	0.709670i	$-0.251156\pi$
$228$	15.2879			1.01247
$229$	−2.29183	−	12.9976i	−0.151448	−	0.858906i	−0.961961	−	0.273185i	$-0.911923\pi$
$229$	−2.29183	−	12.9976i	−0.151448	−	0.858906i	0.810513	−	0.585720i	$-0.199188\pi$
$230$	−9.01074	+	1.17147i	−0.594150	+	0.0772445i
$231$	−31.5221	−	26.4502i	−2.07400	−	1.74029i
$232$	5.82054	−	3.36049i	0.382137	−	0.220627i
$233$	−0.374584	−	0.216266i	−0.0245398	−	0.0141681i	0.487680	−	0.873023i	$-0.337843\pi$
$233$	−0.374584	−	0.216266i	−0.0245398	−	0.0141681i	−0.512220	+	0.858854i	$0.671177\pi$
$234$	14.8610	−	5.40896i	0.971493	−	0.353594i
$235$	0.143099	−	0.640577i	0.00933477	−	0.0417867i
$236$	10.1300	−	5.84856i	0.659407	−	0.380709i
$237$	−4.00711	+	22.7254i	−0.260290	+	1.47618i
$238$	−3.59179	−	0.633330i	−0.232821	−	0.0410527i
$239$	−1.89751	+	2.26136i	−0.122740	+	0.146276i	−0.823915	−	0.566714i	$-0.808215\pi$
$239$	−1.89751	+	2.26136i	−0.122740	+	0.146276i	0.701175	+	0.712989i	$0.252659\pi$
$240$	6.65678	−	2.08705i	0.429693	−	0.134719i
$241$	−1.39831	+	3.84182i	−0.0900730	+	0.247474i	−0.976547	−	0.215305i	$-0.930925\pi$
$241$	−1.39831	+	3.84182i	−0.0900730	+	0.247474i	0.886474	+	0.462779i	$0.153148\pi$
$242$	−1.19882	−	1.00593i	−0.0770633	−	0.0646638i
$243$	15.1798	+	2.67660i	0.973783	+	0.171704i
$244$	−1.27015	−	0.223961i	−0.0813127	−	0.0143376i
$245$	−9.82523	+	23.6122i	−0.627711	+	1.50853i
$246$	−24.9833	−	29.7739i	−1.59288	−	1.89832i
$247$	3.93612	+	10.8144i	0.250449	+	0.688104i
$248$	−0.937358	−	0.541184i	−0.0595223	−	0.0343652i
$249$	−15.0327	−	26.0373i	−0.952657	−	1.65005i
$250$	−10.6465	−	3.41366i	−0.673341	−	0.215899i
$251$	−8.35634	−	4.82454i	−0.527447	−	0.304522i	0.212529	−	0.977155i	$-0.431830\pi$
$251$	−8.35634	−	4.82454i	−0.527447	−	0.304522i	−0.739976	+	0.672633i	$0.765163\pi$
$252$	−28.4744	+	5.02081i	−1.79372	+	0.316281i
$253$	−12.4821			−0.784742
$254$	−5.48175	+	0.966580i	−0.343955	+	0.0606486i
$255$	−1.29189	+	5.78309i	−0.0809013	+	0.362151i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	14.1894	−	5.16450i	0.885108	−	0.322153i	0.140839	−	0.990033i	$-0.455020\pi$
$257$	14.1894	−	5.16450i	0.885108	−	0.322153i	0.744269	+	0.667880i	$0.232798\pi$
$258$			14.5067i			0.903151i
$259$	21.7097	−	14.5215i	1.34897	−	0.902320i
$260$	3.19024	+	4.17155i	0.197850	+	0.258708i
$261$	15.4788	+	42.5278i	0.958116	+	2.63240i
$262$	5.22600	−	14.3583i	0.322863	−	0.887060i
$263$	0.648578	+	0.772946i	0.0399931	+	0.0476619i	0.785670	−	0.618646i	$-0.212318\pi$
$263$	0.648578	+	0.772946i	0.0399931	+	0.0476619i	−0.745677	+	0.666307i	$0.767874\pi$
$264$	9.43762	−	1.66411i	0.580845	−	0.102419i
$265$	−7.07198	+	5.40838i	−0.434428	+	0.332234i
$266$	−3.65366	−	20.7210i	−0.224021	−	1.27048i
$267$	18.7390	−	32.4569i	1.14681	−	1.98633i
$268$	−4.30491	+	5.13040i	−0.262964	+	0.313389i
$269$	−12.0801	−	20.9234i	−0.736539	−	1.27572i	−0.954045	−	0.299665i	$-0.903125\pi$
$269$	−12.0801	−	20.9234i	−0.736539	−	1.27572i	0.217505	−	0.976059i	$-0.430208\pi$
$270$	3.35812	+	25.8300i	0.204368	+	1.57196i
$271$	−16.1851	+	5.89088i	−0.983173	+	0.357846i	−0.783073	−	0.621930i	$-0.786349\pi$
$271$	−16.1851	+	5.89088i	−0.983173	+	0.357846i	−0.200100	+	0.979775i	$0.564127\pi$
$272$	0.650675	−	0.545981i	0.0394530	−	0.0331050i
$273$	−15.7314	−	27.2475i	−0.952106	−	1.64910i
$274$	5.78172	+	1.01947i	0.349287	+	0.0615886i
$275$	−13.8983	−	6.53565i	−0.838096	−	0.394114i
$276$	−8.14932	+	9.71198i	−0.490532	+	0.584593i
$277$	−4.00408	−	1.45736i	−0.240582	−	0.0875646i	0.218915	−	0.975744i	$-0.429748\pi$
$277$	−4.00408	−	1.45736i	−0.240582	−	0.0875646i	−0.459497	+	0.888179i	$0.651970\pi$
$278$	2.65024	+	0.964609i	0.158951	+	0.0578534i
$279$	4.68486	−	5.58320i	0.280475	−	0.334257i
$280$	−4.41966	−	8.52370i	−0.264125	−	0.509389i
$281$	12.3341	+	2.17483i	0.735789	+	0.129739i	0.528971	−	0.848640i	$-0.322578\pi$
$281$	12.3341	+	2.17483i	0.735789	+	0.129739i	0.206818	+	0.978379i	$0.433689\pi$
$282$	−0.457900	−	0.793106i	−0.0272675	−	0.0472288i
$283$	−5.98578	+	5.02267i	−0.355818	+	0.298567i	−0.803121	−	0.595816i	$-0.796829\pi$
$283$	−5.98578	+	5.02267i	−0.355818	+	0.298567i	0.447303	+	0.894382i	$0.352384\pi$
$284$	12.1478	−	4.42144i	0.720840	−	0.262364i
$285$	−33.8995	+	4.40722i	−2.00803	+	0.261061i
$286$	3.60703	+	6.24756i	0.213288	+	0.369426i
$287$	−34.3843	+	40.9776i	−2.02964	+	2.41883i
$288$	3.36685	−	5.83156i	0.198394	−	0.343628i
$289$	−2.82674	−	16.0312i	−0.166279	−	0.943013i
$290$	−11.9377	+	9.12953i	−0.701008	+	0.536104i
$291$	12.9874	−	2.29003i	0.761335	−	0.134244i
$292$	8.98729	+	10.7106i	0.525941	+	0.626792i
$293$	3.39709	−	9.33342i	0.198460	−	0.545264i	−0.800044	−	0.599941i	$-0.795191\pi$
$293$	3.39709	−	9.33342i	0.198460	−	0.545264i	0.998504	+	0.0546769i	$0.0174129\pi$
$294$	12.2044	+	33.5314i	0.711777	+	1.95559i
$295$	−20.7763	+	15.8889i	−1.20964	+	0.925089i
$296$	−0.659223	+	6.04694i	−0.0383165	+	0.351471i
$297$			35.7809i			2.07622i
$298$	4.68168	−	1.70399i	0.271203	−	0.0987097i
$299$	−8.96827	−	3.26418i	−0.518648	−	0.188773i
$300$	−14.1591	+	6.54687i	−0.817478	+	0.377984i
$301$	19.6622	−	3.46698i	1.13331	−	0.199833i
$302$	7.80589			0.449179
$303$	22.6115	−	3.98701i	1.29900	−	0.229048i
$304$	4.24365	+	2.45007i	0.243390	+	0.140521i
$305$	2.88099	+	0.130453i	0.164965	+	0.00746973i
$306$	2.85979	+	4.95330i	0.163483	+	0.283161i
$307$	−6.74516	−	3.89432i	−0.384966	−	0.222260i	0.295011	−	0.955494i	$-0.404677\pi$
$307$	−6.74516	−	3.89432i	−0.384966	−	0.222260i	−0.679977	+	0.733234i	$0.738010\pi$
$308$	−4.51101	−	12.3939i	−0.257038	−	0.706207i
$309$	13.1512	+	15.6730i	0.748147	+	0.891607i
$310$	2.23452	+	0.929802i	0.126912	+	0.0528092i
$311$	−5.30935	−	0.936181i	−0.301065	−	0.0530860i	0.0210749	−	0.999778i	$-0.493291\pi$
$311$	−5.30935	−	0.936181i	−0.301065	−	0.0530860i	−0.322140	+	0.946692i	$0.604402\pi$
$312$	7.21603	+	1.27238i	0.408527	+	0.0720344i
$313$	15.4492	+	12.9634i	0.873243	+	0.732737i	0.964778	−	0.263064i	$-0.0847331\pi$
$313$	15.4492	+	12.9634i	0.873243	+	0.732737i	−0.0915358	+	0.995802i	$0.529178\pi$
$314$	−8.49335	+	23.3353i	−0.479307	+	1.31689i
$315$	61.6920	−	19.3418i	3.47595	−	1.08979i
$316$	−4.75433	+	5.66599i	−0.267452	+	0.318737i
$317$	8.18716	+	1.44362i	0.459836	+	0.0810816i	0.398768	−	0.917052i	$-0.369438\pi$
$317$	8.18716	+	1.44362i	0.459836	+	0.0810816i	0.0610688	+	0.998134i	$0.480549\pi$
$318$	−2.15705	+	12.2333i	−0.120961	+	0.686007i
$319$	−17.8787	+	10.3223i	−1.00101	+	0.577936i
$320$	2.18228	+	0.487502i	0.121993	+	0.0272522i
$321$	38.1813	−	13.8968i	2.13107	−	0.775646i
$322$	15.1111	+	8.72438i	0.842107	+	0.486191i
$323$	−3.60454	+	2.08108i	−0.200562	+	0.115794i
$324$	12.3652	+	10.3757i	0.686957	+	0.576425i
$325$	−8.27664	−	8.33033i	−0.459105	−	0.462084i
$326$	2.82751	+	16.0356i	0.156601	+	0.888130i
$327$	−33.9518			−1.87754
$328$	−2.16328	−	12.2686i	−0.119447	−	0.677419i
$329$	−0.965528	+	0.810175i	−0.0532313	+	0.0446664i
$330$	−20.4473	+	6.41069i	−1.12559	+	0.352897i
$331$	−4.14055	−	11.3761i	−0.227585	−	0.625285i	0.772366	−	0.635178i	$-0.219073\pi$
$331$	−4.14055	−	11.3761i	−0.227585	−	0.625285i	−0.999951	+	0.00989263i	$0.996851\pi$
$332$		−	9.63667i		−	0.528881i
$333$	−39.3288	−	11.4422i	−2.15521	−	0.627030i
$334$	−9.25120			−0.506203
$335$	8.06675	−	12.6172i	0.440734	−	0.689352i
$336$	−12.5885	−	4.58185i	−0.686760	−	0.249960i
$337$	6.92421	+	8.25195i	0.377186	+	0.449512i	0.920924	−	0.389743i	$-0.127436\pi$
$337$	6.92421	+	8.25195i	0.377186	+	0.449512i	−0.543738	+	0.839255i	$0.682992\pi$
$338$	−1.29960	−	7.37041i	−0.0706891	−	0.400898i
$339$			43.4919i			2.36216i
$340$	−1.28542	+	1.39824i	−0.0697114	+	0.0758302i
$341$	2.87924	+	1.66233i	0.155920	+	0.0900202i
$342$	−21.2095	+	25.2765i	−1.14688	+	1.36680i
$343$	16.5009	−	9.52681i	0.890966	−	0.514399i
$344$	−2.32488	+	4.02681i	−0.125349	+	0.217111i
$345$	15.2706	−	23.8847i	0.822140	−	1.28591i
$346$	4.02208	+	4.79333i	0.216228	+	0.257691i
$347$	−16.5449	−	28.6566i	−0.888175	−	1.53836i	−0.842030	−	0.539430i	$-0.818640\pi$
$347$	−16.5449	−	28.6566i	−0.888175	−	1.53836i	−0.0461450	−	0.998935i	$-0.514694\pi$
$348$	−3.64118	+	20.6502i	−0.195188	+	1.10696i
$349$	2.84710	−	16.1467i	0.152402	−	0.864315i	−0.808721	−	0.588193i	$-0.799840\pi$
$349$	2.84710	−	16.1467i	0.152402	−	0.864315i	0.961123	−	0.276122i	$-0.0890493\pi$
$350$	12.2574	+	17.6264i	0.655186	+	0.942172i
$351$	−9.35704	+	25.7082i	−0.499442	+	1.37220i
$352$	2.88641	+	1.05057i	0.153846	+	0.0559954i
$353$	−25.2032	−	21.1480i	−1.34143	−	1.12559i	−0.981256	−	0.192709i	$-0.938273\pi$
$353$	−25.2032	−	21.1480i	−1.34143	−	1.12559i	−0.360174	−	0.932885i	$-0.617283\pi$
$354$	−6.33706	+	35.9393i	−0.336811	+	1.91015i
$355$	−25.6620	+	13.3061i	−1.36200	+	0.706216i
$356$	10.4032	−	6.00631i	0.551370	−	0.318334i
$357$	8.71672	−	7.31420i	0.461338	−	0.387108i
$358$	2.00337	+	5.50422i	0.105882	+	0.290907i
$359$	−8.43435	+	14.6087i	−0.445148	+	0.771018i	−0.998063	−	0.0622193i	$-0.980182\pi$
$359$	−8.43435	+	14.6087i	−0.445148	+	0.771018i	0.552915	+	0.833238i	$0.313516\pi$
$360$	−5.78455	+	13.9015i	−0.304873	+	0.732675i
$361$	−3.83895	−	3.22127i	−0.202050	−	0.169540i
$362$	5.29941	−	9.17885i	0.278531	−	0.482430i
$363$	4.80830	−	0.847834i	0.252371	−	0.0444997i
$364$		−	10.0846i		−	0.528575i
$365$	−23.0162	−	21.1590i	−1.20472	−	1.10751i
$366$	3.08244	−	2.58648i	0.161122	−	0.135197i
$367$	−1.95889	+	5.38201i	−0.102253	+	0.280939i	−0.980261	−	0.197708i	$-0.936650\pi$
$367$	−1.95889	+	5.38201i	−0.102253	+	0.280939i	0.878008	+	0.478647i	$0.158872\pi$
$368$	−3.81857	+	1.38985i	−0.199057	+	0.0724507i
$369$	83.8874			4.36700
$370$	−0.281454	−	13.5986i	−0.0146321	−	0.706955i
$371$	17.0963			0.887594
$372$	3.17322	−	1.15496i	0.164524	−	0.0598817i
$373$	10.0502	−	27.6126i	0.520378	−	1.42973i	−0.349723	−	0.936853i	$-0.613724\pi$
$373$	10.0502	−	27.6126i	0.520378	−	1.42973i	0.870101	−	0.492874i	$-0.164054\pi$
$374$	−1.99865	+	1.67706i	−0.103348	+	0.0867189i
$375$	29.5092	−	18.5989i	1.52385	−	0.960442i
$376$		−	0.293536i		−	0.0151380i
$377$	−15.5450	+	2.74101i	−0.800610	+	0.141169i
$378$	25.0091	−	43.3171i	1.28633	−	2.22799i
$379$	−1.15120	−	0.965971i	−0.0591332	−	0.0496186i	0.612742	−	0.790283i	$-0.290066\pi$
$379$	−1.15120	−	0.965971i	−0.0591332	−	0.0496186i	−0.671875	+	0.740664i	$0.734511\pi$
$380$	−10.1162	−	4.20944i	−0.518950	−	0.215940i
$381$	8.68314	−	15.0396i	0.444851	−	0.770504i
$382$	−2.24573	−	6.17009i	−0.114902	−	0.315689i
$383$	−11.1656	+	9.36905i	−0.570535	+	0.478736i	−0.881823	−	0.471580i	$-0.843684\pi$
$383$	−11.1656	+	9.36905i	−0.570535	+	0.478736i	0.311288	+	0.950316i	$0.399240\pi$
$384$	2.70190	−	1.55994i	0.137881	−	0.0796056i
$385$	13.5757	+	26.1819i	0.691880	+	1.33435i
$386$	3.13395	−	17.7735i	0.159514	−	0.904647i
$387$	−23.9850	−	20.1258i	−1.21922	−	1.02305i
$388$	3.97207	+	1.44572i	0.201652	+	0.0733951i
$389$	−1.23410	+	3.39067i	−0.0625715	+	0.171914i	−0.967039	−	0.254629i	$-0.918047\pi$
$389$	−1.23410	+	3.39067i	−0.0625715	+	0.171914i	0.904467	+	0.426543i	$0.140269\pi$
$390$	−16.3677	−	0.741139i	−0.828809	−	0.0375290i
$391$	0.599371	−	3.39920i	0.0303115	−	0.171905i
$392$	−1.98608	+	11.2636i	−0.100312	+	0.568899i
$393$	23.8356	+	41.2845i	1.20235	+	2.08253i
$394$	−9.77088	−	11.6445i	−0.492250	−	0.586640i
$395$	8.90888	−	13.9344i	0.448254	−	0.701115i
$396$	−10.3418	+	17.9125i	−0.519695	+	0.900138i
$397$	13.0598	−	7.54005i	0.655450	−	0.378424i	−0.135091	−	0.990833i	$-0.543133\pi$
$397$	13.0598	−	7.54005i	0.655450	−	0.378424i	0.790541	+	0.612409i	$0.209799\pi$
$398$	2.78427	−	3.31816i	0.139563	−	0.166324i
$399$	56.8497	+	32.8222i	2.84604	+	1.64316i
$400$	−4.97954	−	0.451880i	−0.248977	−	0.0225940i
$401$			2.50997i			0.125342i	0.998034	+	0.0626711i	$0.0199619\pi$
$401$			2.50997i			0.125342i	−0.998034	+	0.0626711i	$0.980038\pi$
$402$	−3.62833	−	20.5773i	−0.180964	−	1.02630i
$403$	1.63399	+	1.94732i	0.0813950	+	0.0970028i
$404$	6.91551	+	2.51704i	0.344060	+	0.125227i
$405$	−30.4098	−	19.4424i	−1.51108	−	0.966100i
$406$	28.8591			1.43225
$407$	2.02490	−	18.5741i	0.100371	−	0.920683i
$408$			2.65002i			0.131196i
$409$	2.78778	+	7.65935i	0.137847	+	0.378730i	0.989338	−	0.145638i	$-0.0465236\pi$
$409$	2.78778	+	7.65935i	0.137847	+	0.378730i	−0.851491	+	0.524369i	$0.824301\pi$
$410$	8.33368	+	26.5808i	0.411571	+	1.31273i
$411$	−14.0313	+	11.7737i	−0.692114	+	0.580753i
$412$	1.13875	+	6.45819i	0.0561024	+	0.318172i
$413$	50.2260			2.47146
$414$	−4.75159	−	26.9476i	−0.233528	−	1.32440i
$415$	2.77807	+	21.3684i	0.136370	+	1.04893i
$416$	1.79913	+	1.50965i	0.0882094	+	0.0740165i
$417$	−7.62025	+	4.39956i	−0.373165	+	0.215447i
$418$	−13.0350	−	7.52577i	−0.637563	−	0.368097i
$419$	3.97119	−	1.44540i	0.194005	−	0.0706122i	−0.243190	−	0.969979i	$-0.578194\pi$
$419$	3.97119	−	1.44540i	0.194005	−	0.0706122i	0.437196	+	0.899366i	$0.355972\pi$
$420$	29.2347	+	6.53078i	1.42651	+	0.318670i
$421$	−15.8189	+	9.13306i	−0.770967	+	0.445118i	−0.833219	−	0.552942i	$-0.813505\pi$
$421$	−15.8189	+	9.13306i	−0.770967	+	0.445118i	0.0622524	+	0.998060i	$0.480172\pi$
$422$	4.28365	−	24.2938i	0.208525	−	1.18260i
$423$	1.94656	+	0.343230i	0.0946448	+	0.0166884i
$424$	−2.55929	+	3.05004i	−0.124290	+	0.148123i
$425$	2.44720	−	3.47103i	0.118707	−	0.168370i
$426$	−13.7944	+	37.8998i	−0.668341	+	1.83625i
$427$	−4.24234	−	3.55975i	−0.205301	−	0.172268i
$428$	12.8256	+	2.26150i	0.619948	+	0.109314i
$429$	−22.1651	−	3.90831i	−1.07014	−	0.188695i
$430$	3.99435	−	9.59931i	0.192625	−	0.462920i
$431$	1.49565	+	1.78244i	0.0720427	+	0.0858572i	0.800862	−	0.598849i	$-0.204375\pi$
$431$	1.49565	+	1.78244i	0.0720427	+	0.0858572i	−0.728819	+	0.684706i	$0.759931\pi$
$432$	3.98410	+	10.9462i	0.191685	+	0.526651i
$433$	7.13671	+	4.12038i	0.342969	+	0.198013i	0.661584	−	0.749871i	$-0.269884\pi$
$433$	7.13671	+	4.12038i	0.342969	+	0.198013i	−0.318615	+	0.947884i	$0.603218\pi$
$434$	−2.32378	−	4.02490i	−0.111545	−	0.193201i
$435$	2.12092	−	46.8395i	0.101690	−	2.24578i
$436$	−9.42442	−	5.44119i	−0.451348	−	0.260586i
$437$	19.6099	−	3.45775i	0.938068	−	0.165407i
$438$	−43.6215			−2.08431
$439$	27.0030	−	4.76136i	1.28878	−	0.227247i	0.513078	−	0.858342i	$-0.328505\pi$
$439$	27.0030	−	4.76136i	1.28878	−	0.227247i	0.775706	+	0.631095i	$0.217394\pi$
$440$	−6.70320	−	1.49744i	−0.319563	−	0.0713875i
$441$	−72.3714	−	26.3410i	−3.44626	−	1.25433i
$442$	−1.87458	+	0.682291i	−0.0891646	+	0.0324533i
$443$		−	6.47116i		−	0.307454i	−0.988113	−	0.153727i	$-0.950872\pi$
$443$		−	6.47116i		−	0.307454i	0.988113	−	0.153727i	$-0.0491276\pi$
$444$	−13.1300	−	13.7022i	−0.623122	−	0.650278i
$445$	−21.3367	+	16.3175i	−1.01146	+	0.773523i
$446$	−2.74568	−	7.54370i	−0.130012	−	0.357204i
$447$	−5.31627	+	14.6063i	−0.251451	+	0.690856i
$448$	−2.76005	−	3.28930i	−0.130400	−	0.155405i
$449$	5.60004	−	0.987437i	0.264282	−	0.0466000i	−0.0399369	−	0.999202i	$-0.512716\pi$
$449$	5.60004	−	0.987437i	0.264282	−	0.0466000i	0.304219	+	0.952602i	$0.401605\pi$
$450$	8.81915	−	32.4930i	0.415739	−	1.53173i
$451$	6.64485	+	37.6848i	0.312894	+	1.77451i
$452$	−6.97010	+	12.0726i	−0.327846	+	0.567846i
$453$	−15.6541	+	18.6559i	−0.735496	+	0.876530i
$454$	8.68656	+	15.0456i	0.407680	+	0.706123i
$455$	2.90719	+	22.3616i	0.136291	+	1.04833i
$456$	−14.3659	+	5.22877i	−0.672746	+	0.244860i
$457$	−31.6523	+	26.5595i	−1.48063	+	1.24240i	−0.575128	+	0.818063i	$0.695048\pi$
$457$	−31.6523	+	26.5595i	−1.48063	+	1.24240i	−0.905505	+	0.424336i	$0.860508\pi$
$458$	6.59906	+	11.4299i	0.308354	+	0.534084i
$459$	−9.74408	−	1.71814i	−0.454814	−	0.0801961i
$460$	8.06666	−	4.18268i	0.376110	−	0.195018i
$461$	20.7945	−	24.7819i	0.968495	−	1.15421i	−0.0195139	−	0.999810i	$-0.506212\pi$
$461$	20.7945	−	24.7819i	0.968495	−	1.15421i	0.988009	−	0.154398i	$-0.0493437\pi$
$462$	38.6675	+	14.0738i	1.79898	+	0.654774i
$463$	−25.6198	−	9.32486i	−1.19066	−	0.433363i	−0.330702	−	0.943735i	$-0.607285\pi$
$463$	−25.6198	−	9.32486i	−1.19066	−	0.433363i	−0.859954	+	0.510372i	$0.829508\pi$
$464$	−4.32016	+	5.14857i	−0.200559	+	0.239016i
$465$	−6.70336	+	3.47579i	−0.310861	+	0.161186i
$466$	0.425962	+	0.0751085i	0.0197323	+	0.00347934i
$467$	11.2813	+	19.5398i	0.522036	+	0.904194i	0.999671	+	0.0256351i	$0.00816081\pi$
$467$	11.2813	+	19.5398i	0.522036	+	0.904194i	−0.477635	+	0.878558i	$0.658506\pi$
$468$	−12.1148	+	10.1655i	−0.560006	+	0.469901i
$469$	−27.0229	+	9.83555i	−1.24780	+	0.454163i
$470$	0.0846210	+	0.650889i	0.00390327	+	0.0300233i
$471$	−38.7379	−	67.0961i	−1.78495	−	3.09162i
$472$	−7.51876	+	8.96051i	−0.346079	+	0.412441i
$473$	7.14123	−	12.3690i	0.328354	−	0.568726i
$474$	−4.00711	−	22.7254i	−0.184052	−	1.04381i
$475$	23.6452	+	6.41773i	1.08492	+	0.294466i
$476$	3.59179	−	0.633330i	0.164630	−	0.0290286i
$477$	−17.2335	−	20.5381i	−0.789067	−	0.940373i
$478$	1.00964	−	2.77397i	0.0461801	−	0.126879i
$479$	3.00815	+	8.26482i	0.137446	+	0.377629i	0.989251	−	0.146230i	$-0.0467140\pi$
$479$	3.00815	+	8.26482i	0.137446	+	0.377629i	−0.851805	+	0.523859i	$0.824492\pi$
$480$	−5.54151	+	4.23794i	−0.252934	+	0.193435i
$481$	6.31217	−	12.8158i	0.287810	−	0.584349i
$482$		−	4.08838i		−	0.186221i
$483$	−51.1552	+	18.6190i	−2.32764	+	0.847192i
$484$	1.47058	+	0.535246i	0.0668443	+	0.0243293i
$485$	−9.22448	−	2.06067i	−0.418862	−	0.0935701i
$486$	−15.1798	+	2.67660i	−0.688569	+	0.121413i
$487$	9.87486			0.447473			0.223736	−	0.974650i	$-0.428175\pi$
$487$	9.87486			0.447473			0.223736	+	0.974650i	$0.428175\pi$
$488$	1.27015	−	0.223961i	0.0574968	−	0.0101382i
$489$	−43.9950	−	25.4005i	−1.98952	−	1.14865i
$490$	1.15686	−	25.5486i	0.0522615	−	1.15417i
$491$	17.2328	+	29.8482i	0.777707	+	1.34703i	0.933260	+	0.359201i	$0.116951\pi$
$491$	17.2328	+	29.8482i	0.777707	+	1.34703i	−0.155553	+	0.987828i	$0.549716\pi$
$492$	33.6599	+	19.4335i	1.51750	+	0.876132i
$493$	−1.95252	−	5.36449i	−0.0879369	−	0.241605i
$494$	−7.39748	−	8.81598i	−0.332828	−	0.396650i
$495$	17.7681	−	42.7007i	0.798618	−	1.91925i
$496$	1.06592	+	0.187951i	0.0478614	+	0.00843926i
$497$	54.6655	+	9.63901i	2.45208	+	0.432369i
$498$	23.0314	+	19.3256i	1.03206	+	0.866002i
$499$	−11.8595	+	32.5837i	−0.530904	+	1.45865i	0.327094	+	0.944992i	$0.393931\pi$
$499$	−11.8595	+	32.5837i	−0.530904	+	1.45865i	−0.857997	+	0.513654i	$0.828292\pi$
$500$	11.1719	−	0.433507i	0.499624	−	0.0193870i
$501$	18.5526	−	22.1101i	0.828869	−	0.987807i
$502$	9.50248	+	1.67554i	0.424116	+	0.0747832i
$503$	2.67834	−	15.1896i	0.119421	−	0.677273i	−0.865044	−	0.501696i	$-0.832710\pi$
$503$	2.67834	−	15.1896i	0.119421	−	0.677273i	0.984466	−	0.175577i	$-0.0561791\pi$
$504$	25.0400	−	14.4569i	1.11537	−	0.643959i
$505$	−16.0601	−	3.58769i	−0.714666	−	0.159650i
$506$	11.7293	−	4.26912i	0.521432	−	0.189786i
$507$	20.2213	+	11.6748i	0.898061	+	0.518496i
$508$	4.82057	−	2.78316i	0.213878	−	0.123483i
$509$	23.8454	+	20.0087i	1.05693	+	0.886869i	0.993805	−	0.111137i	$-0.0354491\pi$
$509$	23.8454	+	20.0087i	1.05693	+	0.886869i	0.0631242	+	0.998006i	$0.479894\pi$
$510$	−0.763952	−	5.87617i	−0.0338284	−	0.260201i
$511$	10.4251	+	59.1238i	0.461180	+	2.61548i
$512$	1.00000			0.0441942
$513$	−9.91192	−	56.2133i	−0.437622	−	2.48188i
$514$	−11.5673	+	9.70609i	−0.510210	+	0.428117i
$515$	−4.38686	−	13.9922i	−0.193308	−	0.616568i
$516$	−4.96160	−	13.6319i	−0.218422	−	0.600110i
$517$			0.901640i			0.0396541i
$518$	−15.4338	+	21.0709i	−0.678122	+	0.925801i
$519$	−19.5219			−0.856917
$520$	−4.42460	−	2.82885i	−0.194031	−	0.124053i
$521$	−38.5662	−	14.0369i	−1.68962	−	0.614970i	−0.695038	−	0.718973i	$-0.744613\pi$
$521$	−38.5662	−	14.0369i	−1.68962	−	0.614970i	−0.994577	+	0.104003i	$0.966835\pi$
$522$	−29.0907	−	34.6690i	−1.27327	−	1.51742i
$523$	2.06523	+	11.7125i	0.0903063	+	0.512152i	0.996085	+	0.0884013i	$0.0281758\pi$
$523$	2.06523	+	11.7125i	0.0903063	+	0.512152i	−0.905779	+	0.423751i	$0.860713\pi$
$524$			15.2798i			0.667501i
$525$	−66.7080	−	6.05357i	−2.91138	−	0.264200i
$526$	−0.873827	−	0.504504i	−0.0381007	−	0.0219974i
$527$	−0.590953	+	0.704270i	−0.0257423	+	0.0306785i
$528$	−8.29930	+	4.79161i	−0.361181	+	0.208528i
$529$	3.24342	−	5.61778i	0.141018	−	0.244251i
$530$	4.79571	−	7.50097i	0.208312	−	0.325821i
$531$	−50.6291	−	60.3374i	−2.19712	−	2.61842i
$532$	10.5203	+	18.2217i	0.456113	+	0.790011i
$533$	−5.08067	+	28.8139i	−0.220068	+	1.24807i
$534$	−6.50799	+	36.9087i	−0.281628	+	1.59719i
$535$	−29.0915	−	1.31728i	−1.25773	−	0.0569510i
$536$	2.29060	−	6.29336i	0.0989387	−	0.271832i
$537$	−17.1726	−	6.25030i	−0.741051	−	0.269720i
$538$	18.5079	+	15.5299i	0.797930	+	0.669543i
$539$	6.10055	−	34.5980i	0.262769	−	1.49024i
$540$	−11.9900	−	23.1237i	−0.515966	−	0.995086i
$541$	−7.85642	+	4.53591i	−0.337774	+	0.195014i	−0.659287	−	0.751891i	$-0.729142\pi$
$541$	−7.85642	+	4.53591i	−0.337774	+	0.195014i	0.321513	+	0.946905i	$0.395809\pi$
$542$	13.1942	−	11.0712i	0.566739	−	0.475550i
$543$	11.3096	+	31.0730i	0.485343	+	1.33347i
$544$	−0.424698	+	0.735599i	−0.0182088	+	0.0315385i
$545$	22.4664	+	9.34846i	0.962354	+	0.400444i
$546$	24.1019	+	20.2239i	1.03146	+	0.865501i
$547$	7.32539	−	12.6880i	0.313211	−	0.542498i	−0.665844	−	0.746091i	$-0.731929\pi$
$547$	7.32539	−	12.6880i	0.313211	−	0.542498i	0.979056	+	0.203593i	$0.0652619\pi$
$548$	−5.78172	+	1.01947i	−0.246983	+	0.0435497i
$549$			8.68472i			0.370655i
$550$	15.2954	+	1.38802i	0.652198	+	0.0591853i
$551$	25.2287	−	21.1694i	1.07478	−	0.901848i
$552$	4.33616	−	11.9135i	0.184559	−	0.507073i
$553$	−29.8440	+	10.8623i	−1.26910	+	0.461913i
$554$	4.26105			0.181035
$555$	33.0646	+	26.5982i	1.40352	+	1.12903i
$556$	−2.82033			−0.119609
$557$	−4.57236	+	1.66420i	−0.193737	+	0.0705145i	−0.437067	−	0.899429i	$-0.643983\pi$
$557$	−4.57236	+	1.66420i	−0.193737	+	0.0705145i	0.243330	+	0.969944i	$0.421760\pi$
$558$	−2.49276	+	6.84881i	−0.105527	+	0.289933i
$559$	8.36551	−	7.01950i	0.353824	−	0.296893i
$560$	7.06840	+	6.49805i	0.298695	+	0.274593i
$561$		−	8.13994i		−	0.343669i
$562$	−12.3341	+	2.17483i	−0.520281	+	0.0917396i
$563$	5.41494	−	9.37895i	0.228213	−	0.395276i	−0.729066	−	0.684444i	$-0.760045\pi$
$563$	5.41494	−	9.37895i	0.228213	−	0.395276i	0.957278	+	0.289168i	$0.0933786\pi$
$564$	0.701543	+	0.588665i	0.0295403	+	0.0247873i
$565$	11.9753	−	28.7792i	0.503803	−	1.21075i
$566$	3.90694	−	6.76702i	0.164221	−	0.284439i
$567$	23.7055	+	65.1304i	0.995538	+	2.73522i
$568$	−9.90299	+	8.30960i	−0.415520	+	0.348663i
$569$	11.3252	−	6.53861i	0.474778	−	0.274113i	−0.243460	−	0.969911i	$-0.578282\pi$
$569$	11.3252	−	6.53861i	0.474778	−	0.274113i	0.718238	+	0.695798i	$0.244949\pi$
$570$	30.3477	−	15.7357i	1.27113	−	0.659098i
$571$	−3.45342	+	19.5853i	−0.144521	+	0.819620i	0.823229	+	0.567709i	$0.192170\pi$
$571$	−3.45342	+	19.5853i	−0.144521	+	0.819620i	−0.967750	+	0.251911i	$0.918941\pi$
$572$	−5.52629	−	4.63711i	−0.231066	−	0.193887i
$573$	19.2500	+	7.00643i	0.804180	+	0.292698i
$574$	18.2955	−	50.2665i	0.763639	−	2.09808i
$575$	−16.6813	+	11.6002i	−0.695657	+	0.483760i
$576$	−1.16930	+	6.63140i	−0.0487206	+	0.276308i
$577$	4.48070	−	25.4113i	0.186534	−	1.05789i	−0.737435	−	0.675418i	$-0.763963\pi$
$577$	4.48070	−	25.4113i	0.186534	−	1.05789i	0.923969	−	0.382468i	$-0.124926\pi$
$578$	8.13926	+	14.0976i	0.338549	+	0.586384i
$579$	36.1933	+	43.1335i	1.50414	+	1.79257i
$580$	8.09533	−	12.6619i	0.336140	−	0.525757i
$581$	20.6893	−	35.8350i	0.858339	−	1.48669i
$582$	−11.4209	+	6.59387i	−0.473412	+	0.273325i
$583$	7.86124	−	9.36866i	0.325579	−	0.388010i
$584$	−12.1085	−	6.99087i	−0.501055	−	0.289284i
$585$	23.9329	−	26.0335i	0.989503	−	1.07635i
$586$			9.93242i			0.410304i
$587$	2.28471	+	12.9572i	0.0942999	+	0.534802i	0.994960	+	0.100276i	$0.0319727\pi$
$587$	2.28471	+	12.9572i	0.0942999	+	0.534802i	−0.900660	+	0.434525i	$0.856916\pi$
$588$	−22.9368	−	27.3351i	−0.945899	−	1.12728i
$589$	−4.98390	−	1.81399i	−0.205358	−	0.0747442i
$590$	14.0890	−	22.0366i	0.580035	−	0.907233i
$591$	47.4248			1.95079
$592$	−1.44871	−	5.90773i	−0.0595415	−	0.242806i
$593$		−	8.00566i		−	0.328753i	−0.986398	−	0.164377i	$-0.947439\pi$
$593$		−	8.00566i		−	0.328753i	0.986398	−	0.164377i	$-0.0525612\pi$
$594$	−12.2378	−	33.6230i	−0.502122	−	1.37957i
$595$	−7.78189	+	2.43980i	−0.319026	+	0.100022i
$596$	−3.81654	+	3.20246i	−0.156332	+	0.131178i
$597$	2.34667	+	13.3086i	0.0960429	+	0.544686i
$598$	9.54383			0.390276
$599$	0.597637	+	3.38937i	0.0244188	+	0.138486i	0.994580	−	0.103975i	$-0.0331564\pi$
$599$	0.597637	+	3.38937i	0.0244188	+	0.138486i	−0.970161	+	0.242461i	$0.922045\pi$
$600$	11.0661	−	10.9948i	0.451771	−	0.448859i
$601$	28.1678	+	23.6356i	1.14899	+	0.964114i	0.999695	−	0.0246789i	$-0.00785634\pi$
$601$	28.1678	+	23.6356i	1.14899	+	0.964114i	0.149291	+	0.988793i	$0.452301\pi$
$602$	−17.2907	+	9.98276i	−0.704714	+	0.406867i
$603$	39.0555	+	22.5487i	1.59046	+	0.918253i
$604$	−7.33514	+	2.66977i	−0.298463	+	0.108632i
$605$	−3.41517	−	0.762918i	−0.138846	−	0.0310170i
$606$	−19.8842	+	11.4802i	−0.807741	+	0.466349i
$607$	1.37416	−	7.79326i	0.0557755	−	0.316319i	−0.944137	−	0.329553i	$-0.893102\pi$
$607$	1.37416	−	7.79326i	0.0557755	−	0.316319i	0.999912	+	0.0132349i	$0.00421291\pi$
$608$	−4.82570	−	0.850901i	−0.195708	−	0.0345086i
$609$	−57.8747	+	68.9724i	−2.34520	+	2.79490i
$610$	−2.75186	+	0.862772i	−0.111420	+	0.0349326i
$611$	−0.235787	+	0.647821i	−0.00953894	+	0.0262080i
$612$	−4.38145	−	3.67648i	−0.177110	−	0.148613i
$613$	−28.9291	−	5.10097i	−1.16843	−	0.206026i	−0.444424	−	0.895817i	$-0.646592\pi$
$613$	−28.9291	−	5.10097i	−1.16843	−	0.206026i	−0.724009	+	0.689790i	$0.757703\pi$
$614$	7.67031	+	1.35248i	0.309548	+	0.0545817i
$615$	−80.2400	−	33.3886i	−3.23559	−	1.34636i
$616$	8.47792	+	10.1036i	0.341585	+	0.407085i
$617$	−6.39279	−	17.5640i	−0.257364	−	0.707102i	−0.999328	−	0.0366616i	$-0.988328\pi$
$617$	−6.39279	−	17.5640i	−0.257364	−	0.707102i	0.741964	−	0.670440i	$-0.233895\pi$
$618$	−17.7186	−	10.2298i	−0.712746	−	0.411504i
$619$	17.2663	+	29.9062i	0.693992	+	1.20203i	0.970519	+	0.241024i	$0.0774832\pi$
$619$	17.2663	+	29.9062i	0.693992	+	1.20203i	−0.276527	+	0.961006i	$0.589183\pi$
$620$	−2.41777	−	0.109478i	−0.0971000	−	0.00439675i
$621$	40.9944	+	23.6681i	1.64505	+	0.949769i
$622$	5.30935	−	0.936181i	0.212885	−	0.0375374i
$623$	51.5807			2.06654
$624$	−7.21603	+	1.27238i	−0.288872	+	0.0509360i
$625$	−24.6477	+	4.18192i	−0.985910	+	0.167277i
$626$	−18.9513	−	6.89771i	−0.757446	−	0.275688i
$627$	44.1271	−	16.0610i	1.76227	−	0.641413i
$628$		−	24.8329i		−	0.990940i
$629$	4.96098	+	1.44333i	0.197807	+	0.0575495i
$630$	−51.3562	+	39.2753i	−2.04608	+	1.56477i
$631$	−6.23514	−	17.1309i	−0.248217	−	0.681970i	−0.999752	−	0.0222771i	$-0.992908\pi$
$631$	−6.23514	−	17.1309i	−0.248217	−	0.681970i	0.751535	−	0.659693i	$-0.229314\pi$
$632$	2.52972	−	6.95036i	0.100627	−	0.276471i
$633$	49.4709	+	58.9572i	1.96629	+	2.34334i
$634$	−8.18716	+	1.44362i	−0.325153	+	0.0573333i
$635$	−9.88683	+	7.56107i	−0.392347	+	0.300052i
$636$	−2.15705	−	12.2333i	−0.0855327	−	0.485080i
$637$	13.4309	−	23.2630i	0.532151	−	0.921713i
$638$	13.2700	−	15.8146i	0.525366	−	0.626107i
$639$	−43.5248	−	75.3871i	−1.72181	−	2.98227i
$640$	−2.21741	+	0.288281i	−0.0876507	+	0.0113953i
$641$	−39.4749	+	14.3677i	−1.55916	+	0.567490i	−0.970545	−	0.240920i	$-0.922551\pi$
$641$	−39.4749	+	14.3677i	−1.55916	+	0.567490i	−0.588620	+	0.808410i	$0.700329\pi$
$642$	−31.1257	+	26.1175i	−1.22843	+	1.03078i
$643$	2.03342	+	3.52199i	0.0801903	+	0.138894i	0.903332	−	0.428943i	$-0.141114\pi$
$643$	2.03342	+	3.52199i	0.0801903	+	0.138894i	−0.823141	+	0.567837i	$0.807781\pi$
$644$	−17.1837	−	3.02995i	−0.677132	−	0.119397i
$645$	14.9317	+	28.7971i	0.587935	+	1.13388i
$646$	2.67539	−	3.18840i	0.105262	−	0.125446i
$647$	−28.4936	−	10.3708i	−1.12020	−	0.407719i	−0.285474	−	0.958386i	$-0.592151\pi$
$647$	−28.4936	−	10.3708i	−1.12020	−	0.407719i	−0.834725	+	0.550668i	$0.814373\pi$
$648$	−15.1682	−	5.52077i	−0.595863	−	0.216876i
$649$	23.0950	−	27.5236i	0.906559	−	1.08039i
$650$	10.6266	+	4.99717i	0.416811	+	0.196005i
$651$	14.2796	+	2.51787i	0.559661	+	0.0986833i
$652$	−8.14149	−	14.1015i	−0.318845	−	0.552256i
$653$	−21.2057	+	17.7937i	−0.829844	+	0.696322i	−0.955255	−	0.295783i	$-0.904419\pi$
$653$	−21.2057	+	17.7937i	−0.829844	+	0.696322i	0.125411	+	0.992105i	$0.459975\pi$
$654$	31.9043	−	11.6122i	1.24756	−	0.454073i
$655$	−4.40488	−	33.8815i	−0.172113	−	1.32386i
$656$	6.22892	+	10.7888i	0.243199	+	0.421232i
$657$	60.5177	−	72.1222i	2.36102	−	2.81376i
$658$	0.630204	−	1.09155i	0.0245679	−	0.0425529i
$659$	−7.70123	−	43.6758i	−0.299997	−	1.70137i	−0.646166	−	0.763197i	$-0.723629\pi$
$659$	−7.70123	−	43.6758i	−0.299997	−	1.70137i	0.346169	−	0.938172i	$-0.387483\pi$
$660$	17.0216	−	13.0175i	0.662565	−	0.506705i
$661$	12.1733	−	2.14649i	0.473488	−	0.0834887i	0.0681882	−	0.997672i	$-0.478278\pi$
$661$	12.1733	−	2.14649i	0.473488	−	0.0834887i	0.405300	+	0.914184i	$0.367167\pi$
$662$	7.78169	+	9.27386i	0.302444	+	0.360439i
$663$	2.12867	−	5.84848i	0.0826708	−	0.227136i
$664$	3.29594	+	9.05551i	0.127907	+	0.351422i
$665$	−28.5808	−	37.3721i	−1.10832	−	1.44923i
$666$	40.8705	−	2.69908i	1.58370	−	0.104587i
$667$			27.3116i			1.05751i
$668$	8.69328	−	3.16410i	0.336353	−	0.122423i
$669$	23.5355	+	8.56622i	0.909935	+	0.331189i
$670$	−3.26493	+	14.6153i	−0.126135	+	0.564638i
$671$	−3.90144	+	0.687930i	−0.150614	+	0.0265572i
$672$	13.3964			0.516778
$673$	19.1947	−	3.38454i	0.739901	−	0.130464i	0.209020	−	0.977911i	$-0.432973\pi$
$673$	19.1947	−	3.38454i	0.739901	−	0.130464i	0.530880	+	0.847447i	$0.321861\pi$
$674$	−9.32896	−	5.38608i	−0.359338	−	0.207464i
$675$	33.2528	+	47.8182i	1.27990	+	1.84052i
$676$	3.74206	+	6.48143i	0.143925	+	0.249286i
$677$	14.6915	+	8.48214i	0.564640	+	0.325995i	0.755006	−	0.655718i	$-0.227634\pi$
$677$	14.6915	+	8.48214i	0.564640	+	0.325995i	−0.190366	+	0.981713i	$0.560967\pi$
$678$	−14.8751	−	40.8690i	−0.571275	−	1.56956i
$679$	11.6667	+	13.9039i	0.447728	+	0.533581i
$680$	0.729669	−	1.75355i	0.0279815	−	0.0672457i
$681$	−53.3787	−	9.41211i	−2.04548	−	0.360673i
$682$	−3.27415	−	0.577321i	−0.125374	−	0.0221068i
$683$	−4.87967	−	4.09453i	−0.186716	−	0.156673i	0.544639	−	0.838671i	$-0.316667\pi$
$683$	−4.87967	−	4.09453i	−0.186716	−	0.156673i	−0.731354	+	0.681998i	$0.761111\pi$
$684$	11.2853	−	31.0062i	0.431506	−	1.18555i
$685$	12.5265	−	3.92735i	0.478614	−	0.150056i
$686$	−12.2474	+	14.5959i	−0.467609	+	0.557275i
$687$	−40.5511	−	7.15025i	−1.54712	−	0.272799i
$688$	0.807423	−	4.57912i	0.0307827	−	0.174577i
$689$	8.09822	−	4.67551i	0.308518	−	0.178123i
$690$	−6.18060	+	27.6671i	−0.235291	+	1.05327i
$691$	−18.7141	+	6.81136i	−0.711916	+	0.259116i	−0.672490	−	0.740106i	$-0.734775\pi$
$691$	−18.7141	+	6.81136i	−0.711916	+	0.259116i	−0.0394261	+	0.999222i	$0.512553\pi$
$692$	−5.41894	−	3.12862i	−0.205997	−	0.118932i
$693$	−76.9142	+	44.4064i	−2.92173	+	1.68686i
$694$	25.3482	+	21.2697i	0.962205	+	0.807386i
$695$	6.25382	−	0.813048i	0.237221	−	0.0308407i
$696$	−3.64118	−	20.6502i	−0.138019	−	0.782742i
$697$	−10.5816			−0.400808
$698$	2.84710	+	16.1467i	0.107765	+	0.611163i
$699$	−1.03374	+	0.867412i	−0.0390997	+	0.0328085i
$700$	−17.5468	−	12.3711i	−0.663206	−	0.467585i
$701$	−16.0277	−	44.0356i	−0.605356	−	1.66320i	−0.740241	−	0.672341i	$-0.765289\pi$
$701$	−16.0277	−	44.0356i	−0.605356	−	1.66320i	0.134885	−	0.990861i	$-0.456933\pi$
$702$		−	27.3581i		−	1.03257i
$703$	1.96413	+	29.7416i	0.0740786	+	1.12173i
$704$	−3.07165			−0.115767
$705$	−1.72531	−	1.10307i	−0.0649788	−	0.0415439i
$706$	30.9163	+	11.2526i	1.16355	+	0.423497i
$707$	20.3121	+	24.2071i	0.763917	+	0.910401i
$708$	−6.33706	−	35.9393i	−0.238161	−	1.35068i
$709$		−	23.8789i		−	0.896792i	−0.893835	−	0.448396i	$-0.851995\pi$
$709$		−	23.8789i		−	0.896792i	0.893835	−	0.448396i	$-0.148005\pi$
$710$	19.5635	−	21.2806i	0.734204	−	0.798647i
$711$	43.1327	+	24.9027i	1.61760	+	0.933922i
$712$	−7.72156	+	9.20220i	−0.289378	+	0.344867i
$713$	3.80908	−	2.19918i	0.142651	−	0.0823598i
$714$	−5.68943	+	9.85439i	−0.212922	+	0.368791i
$715$	13.5908	+	8.68923i	0.508268	+	0.324959i
$716$	−3.76511	−	4.48708i	−0.140709	−	0.167690i
$717$	4.60496	+	7.97602i	0.171975	+	0.297870i
$718$	2.92922	−	16.6124i	0.109317	−	0.619970i
$719$	1.40969	−	7.99473i	0.0525725	−	0.298153i	−0.947173	−	0.320724i	$-0.896074\pi$
$719$	1.40969	−	7.99473i	0.0525725	−	0.298153i	0.999745	+	0.0225705i	$0.00718501\pi$
$720$	0.681093	−	15.0416i	0.0253829	−	0.560568i
$721$	−9.63077	+	26.4603i	−0.358669	+	0.985434i
$722$	4.70917	+	1.71400i	0.175257	+	0.0637885i
$723$	9.77113	+	8.19895i	0.363392	+	0.304922i
$724$	−1.84047	+	10.4378i	−0.0684004	+	0.387918i
$725$	−14.3004	+	30.4103i	−0.531105	+	1.12941i
$726$	−4.22835	+	2.44124i	−0.156929	+	0.0906029i
$727$	11.5610	−	9.70086i	0.428775	−	0.359785i	−0.402714	−	0.915326i	$-0.631933\pi$
$727$	11.5610	−	9.70086i	0.428775	−	0.359785i	0.831489	+	0.555541i	$0.187489\pi$
$728$	3.44913	+	9.47640i	0.127833	+	0.351219i
$729$	−0.167583	+	0.290263i	−0.00620680	+	0.0107505i
$730$	28.8649	+	12.0109i	1.06834	+	0.444545i
$731$	3.02549	+	2.53868i	0.111902	+	0.0938966i
$732$	−2.01192	+	3.48475i	−0.0743627	+	0.128800i
$733$	0.153995	−	0.0271535i	0.00568793	−	0.00100294i	−0.170803	−	0.985305i	$-0.554636\pi$
$733$	0.153995	−	0.0271535i	0.00568793	−	0.00100294i	0.176491	+	0.984302i	$0.443525\pi$
$734$		−	5.72742i		−	0.211403i
$735$	58.7405	+	54.0007i	2.16668	+	1.99185i
$736$	3.11293	−	2.61206i	0.114744	−	0.0962817i
$737$	−7.03592	+	19.3310i	−0.259171	+	0.712067i
$738$	−78.8284	+	28.6912i	−2.90171	+	1.05614i
$739$	−33.1469			−1.21933			−0.609664	−	0.792660i	$-0.708696\pi$
$739$	−33.1469			−1.21933			−0.609664	+	0.792660i	$0.708696\pi$
$740$	4.91546	+	12.6822i	0.180696	+	0.466207i
$741$	35.9050			1.31900
$742$	−16.0652	+	5.84726i	−0.589773	+	0.214660i
$743$	−1.56280	+	4.29376i	−0.0573336	+	0.157523i	−0.965053	−	0.262055i	$-0.915600\pi$
$743$	−1.56280	+	4.29376i	−0.0573336	+	0.157523i	0.907719	+	0.419578i	$0.137822\pi$
$744$	−2.58683	+	2.17061i	−0.0948378	+	0.0795784i
$745$	7.53962	−	8.20140i	0.276230	−	0.300476i
$746$			29.3847i			1.07585i
$747$	−63.9047	+	11.2681i	−2.33815	+	0.412279i
$748$	1.30452	−	2.25950i	0.0476981	−	0.0826156i
$749$	42.8380	+	35.9454i	1.56527	+	1.31341i
$750$	−21.3684	+	27.5700i	−0.780264	+	1.00671i
$751$	−10.1889	+	17.6478i	−0.371800	+	0.643976i	−0.989842	−	0.142168i	$-0.954593\pi$
$751$	−10.1889	+	17.6478i	−0.371800	+	0.643976i	0.618043	+	0.786144i	$0.287926\pi$
$752$	0.100395	+	0.275834i	0.00366104	+	0.0100586i
$753$	−23.0610	+	19.3505i	−0.840390	+	0.705171i
$754$	13.6701	−	7.89243i	0.497835	−	0.287425i
$755$	15.4953	−	8.03456i	0.563933	−	0.292407i
$756$	−8.68558	+	49.2584i	−0.315892	+	1.79151i
$757$	−26.8630	−	22.5407i	−0.976352	−	0.819257i	0.00718280	−	0.999974i	$-0.497714\pi$
$757$	−26.8630	−	22.5407i	−0.976352	−	0.819257i	−0.983535	+	0.180717i	$0.942158\pi$
$758$	1.41216	+	0.513983i	0.0512918	+	0.0186687i
$759$	−13.3192	+	36.5942i	−0.483456	+	1.32828i
$760$	10.9458	+	0.495634i	0.397047	+	0.0179785i
$761$	7.05517	−	40.0119i	0.255750	−	1.45043i	−0.538391	−	0.842695i	$-0.680968\pi$
$761$	7.05517	−	40.0119i	0.255750	−	1.45043i	0.794141	−	0.607734i	$-0.207921\pi$
$762$	−3.01562	+	17.1024i	−0.109244	+	0.619556i
$763$	−23.3638	−	40.4673i	−0.845827	−	1.46502i
$764$	4.22059	+	5.02991i	0.152696	+	0.181976i
$765$	10.7753	+	6.88915i	0.389583	+	0.249078i
$766$	7.28782	−	12.6229i	0.263320	−	0.456083i
$767$	23.7912	−	13.7359i	0.859052	−	0.495974i
$768$	−2.00543	+	2.38997i	−0.0723646	+	0.0862407i
$769$	−22.5381	−	13.0124i	−0.812746	−	0.469239i	0.0351623	−	0.999382i	$-0.488805\pi$
$769$	−22.5381	−	13.0124i	−0.812746	−	0.469239i	−0.847909	+	0.530142i	$0.822139\pi$
$770$	−21.7117	−	19.9597i	−0.782434	−	0.719299i
$771$		−	47.1103i		−	1.69664i
$772$	3.13395	+	17.7735i	0.112793	+	0.639682i
$773$	1.57084	+	1.87206i	0.0564993	+	0.0673332i	0.793554	−	0.608500i	$-0.208228\pi$
$773$	1.57084	+	1.87206i	0.0564993	+	0.0673332i	−0.737055	+	0.675833i	$0.763784\pi$
$774$	29.4219	+	10.7087i	1.05755	+	0.384916i
$775$	5.39274	−	0.454241i	0.193713	−	0.0163168i
$776$	−4.22699			−0.151740
$777$	−19.4075	−	79.1424i	−0.696240	−	2.83922i
$778$		−	3.60827i		−	0.129363i
$779$	−20.8787	−	57.3637i	−0.748057	−	2.05527i
$780$	15.6341	−	4.90163i	0.559789	−	0.175507i
$781$	30.4185	−	25.5242i	1.08846	−	0.913327i
$782$	0.599371	+	3.39920i	0.0214334	+	0.121555i
$783$	78.2910			2.79789
$784$	−1.98608	−	11.2636i	−0.0709315	−	0.402273i
$785$	7.15886	+	55.0646i	0.255511	+	1.96534i
$786$	−36.5183	−	30.6425i	−1.30257	−	1.09298i
$787$	−13.1197	+	7.57465i	−0.467666	+	0.270007i	−0.715262	−	0.698856i	$-0.753693\pi$
$787$	−13.1197	+	7.57465i	−0.467666	+	0.270007i	0.247596	+	0.968863i	$0.420359\pi$
$788$	13.1643	+	7.60040i	0.468958	+	0.270753i
$789$	2.95815	−	1.07668i	0.105313	−	0.0383307i
$790$	−3.60577	+	16.1411i	−0.128288	+	0.574273i
$791$	−51.8382	+	29.9288i	−1.84315	+	1.06414i
$792$	3.59167	−	20.3694i	0.127624	−	0.723794i
$793$	−2.98305	−	0.525993i	−0.105931	−	0.0186786i
$794$	−9.69331	+	11.5520i	−0.344003	+	0.409966i
$795$	8.30968	+	26.5043i	0.294714	+	0.940009i
$796$	−1.48148	+	4.07032i	−0.0525096	+	0.144269i
$797$	32.0421	+	26.8865i	1.13499	+	0.952370i	0.999263	−	0.0383760i	$-0.0122185\pi$
$797$	32.0421	+	26.8865i	1.13499	+	0.952370i	0.135727	+	0.990746i	$0.456663\pi$
$798$	−64.6471	−	11.3990i	−2.28848	−	0.403521i
$799$	−0.245540	−	0.0432954i	−0.00868660	−	0.00153168i
$800$	4.83379	−	1.27847i	0.170900	−	0.0452009i
$801$	−51.9947	−	61.9649i	−1.83714	−	2.18942i
$802$	−0.858462	−	2.35860i	−0.0303133	−	0.0832852i
$803$	37.1932	+	21.4735i	1.31252	+	0.757784i
$804$	10.4473	+	18.0953i	0.368450	+	0.638173i
$805$	38.9767	+	1.76489i	1.37375	+	0.0622042i
$806$	−2.20147	−	1.27102i	−0.0775436	−	0.0447698i
$807$	−74.2323	+	13.0891i	−2.61310	+	0.460760i
$808$	−7.35933			−0.258900
$809$	19.8586	−	3.50161i	0.698192	−	0.123110i	0.186724	−	0.982412i	$-0.440213\pi$
$809$	19.8586	−	3.50161i	0.698192	−	0.123110i	0.511468	+	0.859302i	$0.329102\pi$
$810$	35.2256	+	7.86909i	1.23770	+	0.276492i
$811$	−9.70561	−	3.53255i	−0.340810	−	0.124045i	0.165945	−	0.986135i	$-0.446933\pi$
$811$	−9.70561	−	3.53255i	−0.340810	−	0.124045i	−0.506754	+	0.862090i	$0.669155\pi$
$812$	−27.1187	+	9.87039i	−0.951679	+	0.346383i
$813$			53.7363i			1.88461i
$814$	4.44992	+	18.1465i	0.155970	+	0.636034i
$815$	22.1182	+	28.9217i	0.774766	+	1.01308i
$816$	−0.906361	−	2.49021i	−0.0317290	−	0.0871746i
$817$	−7.79276	+	21.4104i	−0.272634	+	0.749056i
$818$	−5.23930	−	6.24396i	−0.183188	−	0.218315i
$819$	−66.8749	+	11.7918i	−2.33680	+	0.412040i
$820$	−16.9223	−	22.1275i	−0.590951	−	0.772726i
$821$	4.09993	+	23.2519i	0.143089	+	0.811496i	0.968882	+	0.247523i	$0.0796167\pi$
$821$	4.09993	+	23.2519i	0.143089	+	0.811496i	−0.825793	+	0.563973i	$0.809272\pi$
$822$	9.15830	−	15.8626i	0.319432	−	0.553273i
$823$	18.1295	−	21.6059i	0.631956	−	0.753135i	−0.351121	−	0.936330i	$-0.614199\pi$
$823$	18.1295	−	21.6059i	0.631956	−	0.753135i	0.983077	+	0.183195i	$0.0586439\pi$
$824$	−3.27891	−	5.67924i	−0.114226	−	0.197846i
$825$	−33.9911	+	33.7721i	−1.18342	+	1.17579i
$826$	−47.1970	+	17.1783i	−1.64219	+	0.597710i
$827$	10.0642	−	8.44485i	0.349966	−	0.293656i	−0.450811	−	0.892620i	$-0.648865\pi$
$827$	10.0642	−	8.44485i	0.349966	−	0.293656i	0.800776	+	0.598964i	$0.204421\pi$
$828$	13.6817	+	23.6973i	0.475471	+	0.823540i
$829$	−43.1683	−	7.61173i	−1.49930	−	0.264366i	−0.637036	−	0.770834i	$-0.719840\pi$
$829$	−43.1683	−	7.61173i	−1.49930	−	0.264366i	−0.862259	+	0.506467i	$0.830951\pi$
$830$	−9.91896	−	19.1296i	−0.344292	−	0.663998i
$831$	−8.54522	+	10.1838i	−0.296430	+	0.353272i
$832$	−2.20696	−	0.803266i	−0.0765124	−	0.0278482i
$833$	9.12900	+	3.32268i	0.316301	+	0.115124i
$834$	5.65596	−	6.74051i	0.195850	−	0.233405i
$835$	−18.3644	+	9.52220i	−0.635526	+	0.329529i
$836$	14.8229	+	2.61367i	0.512660	+	0.0903957i
$837$	−6.30411	−	10.9190i	−0.217902	−	0.377417i
$838$	−3.23734	+	2.71645i	−0.111832	+	0.0938384i
$839$	−15.2151	+	5.53785i	−0.525285	+	0.191188i	−0.591032	−	0.806648i	$-0.701279\pi$
$839$	−15.2151	+	5.53785i	−0.525285	+	0.191188i	0.0657470	+	0.997836i	$0.479057\pi$
$840$	−29.7053	+	3.86194i	−1.02493	+	0.133250i
$841$	8.08580	+	14.0050i	0.278821	+	0.482932i
$842$	11.7412	−	13.9927i	0.404630	−	0.482219i
$843$	19.5373	−	33.8395i	0.672899	−	1.16550i
$844$	4.28365	+	24.2938i	0.147449	+	0.836226i
$845$	−10.1661	−	13.2932i	−0.349726	−	0.457300i
$846$	−1.94656	+	0.343230i	−0.0669240	+	0.0118005i
$847$	4.31935	+	5.14760i	0.148415	+	0.176874i
$848$	1.36177	−	3.74143i	0.0467633	−	0.128481i
$849$	8.33792	+	22.9082i	0.286157	+	0.786209i
$850$	−1.11246	+	4.09869i	−0.0381569	+	0.140584i
$851$	−19.9410	−	14.6062i	−0.683570	−	0.500695i
$852$		−	40.3322i		−	1.38176i
$853$	47.7554	−	17.3815i	1.63511	−	0.595133i	0.648939	−	0.760841i	$-0.275213\pi$
$853$	47.7554	−	17.3815i	1.63511	−	0.595133i	0.986175	+	0.165708i	$0.0529909\pi$
$854$	5.20400	+	1.89410i	0.178077	+	0.0648148i
$855$	−16.0857	+	72.0067i	−0.550118	+	2.46258i
$856$	−12.8256	+	2.26150i	−0.438369	+	0.0772963i
$857$	−23.6867			−0.809124			−0.404562	−	0.914511i	$-0.632576\pi$
$857$	−23.6867			−0.809124			−0.404562	+	0.914511i	$0.632576\pi$
$858$	22.1651	−	3.90831i	0.756705	−	0.133428i
$859$	0.244556	+	0.141194i	0.00834413	+	0.00481748i	0.504166	−	0.863607i	$-0.331800\pi$
$859$	0.244556	+	0.141194i	0.00834413	+	0.00481748i	−0.495822	+	0.868424i	$0.665133\pi$
$860$	−0.470309	+	10.3865i	−0.0160374	+	0.354178i
$861$	83.4453	+	144.531i	2.84381	+	4.92562i
$862$	−2.01508	−	1.16341i	−0.0686338	−	0.0396258i
$863$	−14.1443	−	38.8611i	−0.481476	−	1.32285i	−0.908228	−	0.418477i	$-0.862564\pi$
$863$	−14.1443	−	38.8611i	−0.481476	−	1.32285i	0.426751	−	0.904369i	$-0.359658\pi$
$864$	−7.48767	−	8.92345i	−0.254736	−	0.303582i
$865$	12.9179	+	5.37525i	0.439222	+	0.182764i
$866$	−8.11557	−	1.43099i	−0.275778	−	0.0486272i
$867$	−50.0156	−	8.81910i	−1.69862	−	0.299512i
$868$	3.56024	+	2.98739i	0.120842	+	0.101399i
$869$	−7.77043	+	21.3491i	−0.263594	+	0.724218i
$870$	14.0270	+	44.7401i	0.475561	+	1.51683i
$871$	−10.1105	+	12.0492i	−0.342581	+	0.408272i
$872$	10.7171	+	1.88971i	0.362925	+	0.0639935i
$873$	4.94260	−	28.0309i	0.167282	−	0.948702i
$874$	−17.2446	+	9.95620i	−0.583309	+	0.336774i
$875$	42.4747	+	22.3734i	1.43591	+	0.756360i
$876$	40.9908	−	14.9194i	1.38495	−	0.504080i
$877$	−33.0200	−	19.0641i	−1.11500	−	0.643748i	−0.174884	−	0.984589i	$-0.555955\pi$
$877$	−33.0200	−	19.0641i	−1.11500	−	0.643748i	−0.940121	+	0.340841i	$0.889288\pi$
$878$	−23.7461	+	13.7098i	−0.801391	+	0.462683i
$879$	−23.7382	−	19.9187i	−0.800670	−	0.671842i
$880$	6.81110	−	0.885500i	0.229602	−	0.0298502i
$881$	−7.97945	−	45.2537i	−0.268834	−	1.52464i	−0.757890	−	0.652383i	$-0.773769\pi$
$881$	−7.97945	−	45.2537i	−0.268834	−	1.52464i	0.489055	−	0.872253i	$-0.337342\pi$
$882$	77.0160			2.59326
$883$	4.39758	+	24.9399i	0.147990	+	0.839295i	0.964917	+	0.262554i	$0.0845648\pi$
$883$	4.39758	+	24.9399i	0.147990	+	0.839295i	−0.816927	+	0.576741i	$0.804324\pi$
$884$	1.52817	−	1.28229i	0.0513979	−	0.0431280i
$885$	24.4125	+	77.8651i	0.820616	+	2.61741i
$886$	2.21327	+	6.08090i	0.0743561	+	0.204292i
$887$		−	11.6262i		−	0.390369i	−0.980767	−	0.195184i	$-0.937469\pi$
$887$		−	11.6262i		−	0.390369i	0.980767	−	0.195184i	$-0.0625305\pi$
$888$	17.0246	+	8.38514i	0.571308	+	0.281387i
$889$	23.9011			0.801616
$890$	14.4690	−	22.6310i	0.485003	−	0.758593i
$891$	46.5914	+	16.9579i	1.56087	+	0.568111i
$892$	5.16019	+	6.14968i	0.172776	+	0.205906i
$893$	−0.249770	−	1.41652i	−0.00835824	−	0.0474019i
$894$		−	15.5437i		−	0.519860i
$895$	9.64232	+	8.86428i	0.322307	+	0.296300i
$896$	3.71861	+	2.14694i	0.124230	+	0.0717242i
$897$	−19.1394	+	22.8095i	−0.639047	+	0.761587i
$898$	−4.92459	+	2.84321i	−0.164336	+	0.0948792i
$899$	3.63729	−	6.29997i	0.121310	−	0.210116i
$900$	2.82595	+	33.5497i	0.0941985	+	1.11832i
$901$	2.17385	+	2.59069i	0.0724214	+	0.0863084i
$902$	−19.1331	−	33.1395i	−0.637062	−	1.10342i
$903$	10.8166	−	61.3439i	0.359953	−	2.04140i
$904$	2.42069	−	13.7284i	0.0805110	−	0.456601i
$905$	1.07204	−	23.6754i	0.0356358	−	0.786998i
$906$	8.32939	−	22.8848i	0.276726	−	0.760297i
$907$	34.5477	+	12.5743i	1.14714	+	0.417523i	0.844486	−	0.535578i	$-0.179906\pi$
$907$	34.5477	+	12.5743i	1.14714	+	0.417523i	0.302650	+	0.953102i	$0.402129\pi$
$908$	−13.3086	−	11.1672i	−0.441661	−	0.370597i
$909$	8.60524	−	48.8027i	0.285418	−	1.61868i
$910$	−10.3800	−	20.0187i	−0.344093	−	0.663614i
$911$	42.1362	−	24.3274i	1.39604	−	0.806001i	0.402061	−	0.915613i	$-0.368294\pi$
$911$	42.1362	−	24.3274i	1.39604	−	0.806001i	0.993975	+	0.109611i	$0.0349607\pi$
$912$	11.7112	−	9.82687i	0.387797	−	0.325400i
$913$	−10.1240	−	27.8154i	−0.335054	−	0.920554i
$914$	20.6596	−	35.7835i	0.683358	−	1.18361i
$915$	3.45666	−	8.30711i	0.114274	−	0.274625i
$916$	−10.1103	−	8.48358i	−0.334055	−	0.280305i
$917$	−32.8048	+	56.8196i	−1.08331	+	1.87635i
$918$	9.74408	−	1.71814i	0.321602	−	0.0567072i
$919$		−	24.5114i		−	0.808557i	−0.914636	−	0.404279i	$-0.867523\pi$
$919$		−	24.5114i		−	0.808557i	0.914636	−	0.404279i	$-0.132477\pi$
$920$	−6.14962	+	6.68939i	−0.202747	+	0.220543i
$921$	−18.6146	+	15.6195i	−0.613373	+	0.514681i
$922$	−11.0645	+	30.3995i	−0.364390	+	1.00115i
$923$	28.5303	−	10.3842i	0.939086	−	0.341799i
$924$	−41.1491			−1.35371
$925$	−14.5556	−	26.7046i	−0.478586	−	0.878041i
$926$	27.2641			0.895953
$927$	41.4953	−	15.1031i	1.36289	−	0.496050i
$928$	2.29871	−	6.31566i	0.0754589	−	0.207322i
$929$	−23.5166	+	19.7327i	−0.771554	+	0.647410i	−0.941106	−	0.338111i	$-0.890212\pi$
$929$	−23.5166	+	19.7327i	−0.771554	+	0.647410i	0.169553	+	0.985521i	$0.445768\pi$
$930$	5.11031	−	5.55886i	0.167574	−	0.182282i
$931$			56.0449i			1.83680i
$932$	−0.425962	+	0.0751085i	−0.0139528	+	0.00246026i
$933$	−8.41005	+	14.5666i	−0.275333	+	0.476890i
$934$	−17.2840	−	14.5030i	−0.565548	−	0.474551i
$935$	−2.24129	+	5.38631i	−0.0732980	+	0.176151i
$936$	7.90736	−	13.6960i	0.258460	−	0.447666i
$937$	−12.1709	−	33.4392i	−0.397605	−	1.09241i	−0.963447	−	0.267897i	$-0.913671\pi$
$937$	−12.1709	−	33.4392i	−0.397605	−	1.09241i	0.565843	−	0.824513i	$-0.308551\pi$
$938$	22.0293	−	18.4848i	0.719282	−	0.603549i
$939$	54.4907	−	31.4602i	1.77824	−	1.02667i
$940$	−0.302135	−	0.582693i	−0.00985455	−	0.0190054i
$941$	0.427767	−	2.42599i	0.0139448	−	0.0790849i	−0.977041	−	0.213051i	$-0.931660\pi$
$941$	0.427767	−	2.42599i	0.0139448	−	0.0790849i	0.990986	+	0.133966i	$0.0427712\pi$
$942$	59.3500	+	49.8005i	1.93373	+	1.62259i
$943$	47.5711	+	17.3145i	1.54913	+	0.563837i
$944$	4.00065	−	10.9917i	0.130210	−	0.357749i
$945$	5.05919	−	111.730i	0.164576	−	3.63457i
$946$	−2.48012	+	14.0655i	−0.0806358	+	0.457308i
$947$	−4.37931	+	24.8363i	−0.142308	+	0.807071i	0.827181	+	0.561936i	$0.189943\pi$
$947$	−4.37931	+	24.8363i	−0.142308	+	0.807071i	−0.969489	+	0.245135i	$0.921168\pi$
$948$	11.5380	+	19.9844i	0.374737	+	0.649063i
$949$	21.1075	+	25.1549i	0.685178	+	0.816563i
$950$	−24.4143	+	2.05646i	−0.792103	+	0.0667203i
$951$	12.9685	−	22.4621i	0.420533	−	0.728385i
$952$	−3.15857	+	1.82360i	−0.102370	+	0.0591033i
$953$	−5.06105	+	6.03152i	−0.163943	+	0.195380i	−0.841762	−	0.539849i	$-0.818481\pi$
$953$	−5.06105	+	6.03152i	−0.163943	+	0.195380i	0.677818	+	0.735230i	$0.262926\pi$
$954$	23.2186	+	13.4053i	0.751730	+	0.434011i
$955$	−10.8088	−	9.93663i	−0.349764	−	0.321542i
$956$			2.95200i			0.0954746i
$957$	11.1844	+	63.4301i	0.361541	+	2.05040i
$958$	−5.65347	−	6.73754i	−0.182655	−	0.217680i
$959$	−23.6887	−	8.62198i	−0.764948	−	0.278418i
$960$	3.75786	−	5.87767i	0.121284	−	0.189701i
$961$	29.8285			0.962209
$962$	−1.54825	+	14.2018i	−0.0499175	+	0.457884i
$963$		−	87.6960i		−	2.82596i
$964$	1.39831	+	3.84182i	0.0450365	+	0.123737i
$965$	−12.0730	−	38.5076i	−0.388644	−	1.23960i
$966$	41.7021	−	34.9922i	1.34174	−	1.12586i
$967$	−4.62210	−	26.2132i	−0.148637	−	0.842960i	−0.964375	−	0.264539i	$-0.914780\pi$
$967$	−4.62210	−	26.2132i	−0.148637	−	0.842960i	0.815738	−	0.578421i	$-0.196331\pi$
$968$	−1.56495			−0.0502995
$969$	2.25491	+	12.7882i	0.0724380	+	0.410816i
$970$	9.37296	−	1.21856i	0.300948	−	0.0391257i
$971$	−0.643379	−	0.539859i	−0.0206470	−	0.0173249i	0.632406	−	0.774637i	$-0.282068\pi$
$971$	−0.643379	−	0.539859i	−0.0206470	−	0.0173249i	−0.653053	+	0.757312i	$0.726512\pi$
$972$	13.3489	−	7.70697i	0.428165	−	0.247201i
$973$	−10.4877	−	6.05508i	−0.336220	−	0.194117i
$974$	−9.27933	+	3.37740i	−0.297329	+	0.108219i
$975$	−33.2540	+	15.3759i	−1.06498	+	0.492424i
$976$	−1.11695	+	0.644870i	−0.0357526	+	0.0206418i
$977$	5.15913	−	29.2589i	0.165055	−	0.936075i	−0.783952	−	0.620821i	$-0.786799\pi$
$977$	5.15913	−	29.2589i	0.165055	−	0.936075i	0.949007	−	0.315253i	$-0.102090\pi$
$978$	50.0293	+	8.82152i	1.59976	+	0.282081i
$979$	23.7180	−	28.2660i	0.758029	−	0.903384i
$980$	7.65105	+	24.4035i	0.244404	+	0.779541i
$981$	−25.0628	+	68.8595i	−0.800194	+	2.19852i
$982$	−26.4023	−	22.1541i	−0.842530	−	0.706966i
$983$	7.62910	+	1.34522i	0.243330	+	0.0429057i	0.293983	−	0.955811i	$-0.405019\pi$
$983$	7.62910	+	1.34522i	0.243330	+	0.0429057i	−0.0506527	+	0.998716i	$0.516130\pi$
$984$	−38.2766	−	6.74920i	−1.22021	−	0.215157i
$985$	−31.3816	−	13.0582i	−0.999901	−	0.416067i
$986$	3.66953	+	4.37318i	0.116862	+	0.139270i
$987$	1.34494	+	3.69518i	0.0428098	+	0.117619i
$988$	9.96660	+	5.75422i	0.317080	+	0.183066i
$989$	−9.44748	−	16.3635i	−0.300412	−	0.520329i
$990$	−2.09208	+	46.2026i	−0.0664907	+	1.46841i
$991$	38.5897	+	22.2798i	1.22584	+	0.707740i	0.966157	−	0.257954i	$-0.0830481\pi$
$991$	38.5897	+	22.2798i	1.22584	+	0.707740i	0.259684	+	0.965694i	$0.416381\pi$
$992$	−1.06592	+	0.187951i	−0.0338431	+	0.00596746i
$993$	−37.7699			−1.19859
$994$	−54.6655	+	9.63901i	−1.73389	+	0.305731i
$995$	2.11164	−	9.45265i	0.0669434	−	0.299669i
$996$	−28.2522	−	10.2830i	−0.895204	−	0.325828i
$997$	−30.0637	+	10.9423i	−0.952127	+	0.346546i	−0.770944	−	0.636903i	$-0.780215\pi$
$997$	−30.0637	+	10.9423i	−0.952127	+	0.346546i	−0.181184	+	0.983449i	$0.557993\pi$
$998$		−	34.6748i		−	1.09761i
$999$	−41.8699	+	57.1626i	−1.32470	+	1.80854i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.v.a.289.10	yes	60
5.4	even	2		370.2.v.b.289.1	yes	60
37.21	even	18		370.2.v.b.169.1	yes	60
185.169	even	18	inner	370.2.v.a.169.10	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.v.a.169.10	✓	60	185.169	even	18	inner
370.2.v.a.289.10	yes	60	1.1	even	1	trivial
370.2.v.b.169.1	yes	60	37.21	even	18
370.2.v.b.289.1	yes	60	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	370.2.v.a.289.10

Level	$370$
Weight	$2$
Character	370.289
Analytic conductor	$2.954$
Analytic rank	$0$
Dimension	$60$
Inner twists	$2$