LMFDB - Embedded newform 241.2.c.a.15.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [241,2,Mod(15,241)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(241, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("241.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	241.c (of order $3$, degree $2$, 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:	$1.92439468871$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			15.1
Character	$\chi$	$=$	241.15
Dual form			241.2.c.a.225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32860 - 2.30120i) q^{2} +(-0.221815 + 0.384194i) q^{3} +(-2.53035 + 4.38269i) q^{4} +1.01184 q^{5} +1.17881 q^{6} +(-0.0424564 - 0.0735367i) q^{7} +8.13288 q^{8} +(1.40160 + 2.42764i) q^{9} +O(q^{10})$	\(q+(-1.32860 - 2.30120i) q^{2} +(-0.221815 + 0.384194i) q^{3} +(-2.53035 + 4.38269i) q^{4} +1.01184 q^{5} +1.17881 q^{6} +(-0.0424564 - 0.0735367i) q^{7} +8.13288 q^{8} +(1.40160 + 2.42764i) q^{9} +(-1.34434 - 2.32846i) q^{10} +(0.707483 + 1.22540i) q^{11} +(-1.12254 - 1.94429i) q^{12} +(2.56031 - 4.43458i) q^{13} +(-0.112815 + 0.195401i) q^{14} +(-0.224442 + 0.388745i) q^{15} +(-5.74463 - 9.94999i) q^{16} +4.67521 q^{17} +(3.72432 - 6.45071i) q^{18} +(-0.463515 - 0.802832i) q^{19} +(-2.56032 + 4.43460i) q^{20} +0.0376698 q^{21} +(1.87992 - 3.25612i) q^{22} +1.79287 q^{23} +(-1.80399 + 3.12461i) q^{24} -3.97617 q^{25} -13.6065 q^{26} -2.57447 q^{27} +0.429718 q^{28} +(3.98069 + 6.89475i) q^{29} +1.19277 q^{30} +(-1.45705 - 2.52369i) q^{31} +(-7.13174 + 12.3525i) q^{32} -0.627720 q^{33} +(-6.21148 - 10.7586i) q^{34} +(-0.0429593 - 0.0744077i) q^{35} -14.1861 q^{36} +(0.0118740 + 0.0205664i) q^{37} +(-1.23165 + 2.13328i) q^{38} +(1.13583 + 1.96731i) q^{39} +8.22921 q^{40} +8.59946 q^{41} +(-0.0500481 - 0.0866858i) q^{42} +8.79820 q^{43} -7.16071 q^{44} +(1.41820 + 2.45639i) q^{45} +(-2.38201 - 4.12575i) q^{46} -8.54150 q^{47} +5.09698 q^{48} +(3.49639 - 6.05593i) q^{49} +(5.28273 + 9.14997i) q^{50} +(-1.03703 + 1.79619i) q^{51} +(12.9569 + 22.4421i) q^{52} +(1.71465 - 2.96986i) q^{53} +(3.42043 + 5.92437i) q^{54} +(0.715862 + 1.23991i) q^{55} +(-0.345293 - 0.598065i) q^{56} +0.411258 q^{57} +(10.5775 - 18.3207i) q^{58} +(2.69946 + 4.67560i) q^{59} +(-1.13583 - 1.96732i) q^{60} -7.46055 q^{61} +(-3.87168 + 6.70594i) q^{62} +(0.119014 - 0.206137i) q^{63} +14.9224 q^{64} +(2.59063 - 4.48711i) q^{65} +(0.833988 + 1.44451i) q^{66} +(5.68120 + 9.84013i) q^{67} +(-11.8299 + 20.4900i) q^{68} +(-0.397685 + 0.688811i) q^{69} +(-0.114151 + 0.197716i) q^{70} +(0.913944 + 1.58300i) q^{71} +(11.3990 + 19.7437i) q^{72} -0.134876 q^{73} +(0.0315517 - 0.0546491i) q^{74} +(0.881973 - 1.52762i) q^{75} +4.69142 q^{76} +(0.0600743 - 0.104052i) q^{77} +(3.01812 - 5.22754i) q^{78} -13.0618 q^{79} +(-5.81267 - 10.0678i) q^{80} +(-3.63373 + 6.29381i) q^{81} +(-11.4252 - 19.7891i) q^{82} +(-5.62834 - 9.74857i) q^{83} +(-0.0953178 + 0.165095i) q^{84} +4.73058 q^{85} +(-11.6893 - 20.2464i) q^{86} -3.53190 q^{87} +(5.75387 + 9.96599i) q^{88} +(-5.84176 - 10.1182i) q^{89} +(3.76843 - 6.52711i) q^{90} -0.434806 q^{91} +(-4.53659 + 7.85760i) q^{92} +1.29278 q^{93} +(11.3482 + 19.6557i) q^{94} +(-0.469005 - 0.812341i) q^{95} +(-3.16385 - 5.47995i) q^{96} +(-7.57860 + 13.1265i) q^{97} -18.5812 q^{98} +(-1.98321 + 3.43502i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + q^{2} + 2 q^{3} - 21 q^{4} - 4 q^{5} - 5 q^{7} - 12 q^{8} - 13 q^{9}+O(q^{10}) $ 38 * q + q^2 + 2 * q^3 - 21 * q^4 - 4 * q^5 - 5 * q^7 - 12 * q^8 - 13 * q^9	\( 38 q + q^{2} + 2 q^{3} - 21 q^{4} - 4 q^{5} - 5 q^{7} - 12 q^{8} - 13 q^{9} - 8 q^{10} - 4 q^{11} + 21 q^{12} - 9 q^{13} + 6 q^{14} + 4 q^{15} - 25 q^{16} - 18 q^{17} + 5 q^{18} + 3 q^{19} - 5 q^{20} + 10 q^{21} - 7 q^{22} - 10 q^{23} - 9 q^{24} + 54 q^{25} + 20 q^{26} - 4 q^{27} + 8 q^{28} + 25 q^{29} - 22 q^{30} - 8 q^{31} + 23 q^{32} - 28 q^{33} - 4 q^{34} - 7 q^{35} + 18 q^{36} + 12 q^{37} + 30 q^{38} + 20 q^{39} - 4 q^{40} - 20 q^{41} - 30 q^{42} + 12 q^{43} - 2 q^{44} - 9 q^{45} - 19 q^{46} - 42 q^{47} - 84 q^{48} + 6 q^{49} + 31 q^{50} + 11 q^{51} - 16 q^{52} + q^{53} + 42 q^{54} - 11 q^{55} - 5 q^{56} - 22 q^{57} - 2 q^{58} + 22 q^{59} + 48 q^{60} - 26 q^{61} - 44 q^{62} - q^{63} + 72 q^{64} - 19 q^{65} + 55 q^{66} + 18 q^{67} - 25 q^{68} + 3 q^{69} + 68 q^{70} - 14 q^{71} - 8 q^{72} - 38 q^{73} + 27 q^{74} + 26 q^{75} + 70 q^{76} + 17 q^{77} + 2 q^{78} + 12 q^{79} - 56 q^{80} + 5 q^{81} - 27 q^{82} + 14 q^{83} - 17 q^{84} - 50 q^{85} + 35 q^{86} + 44 q^{87} - 20 q^{88} - 32 q^{89} - 44 q^{90} + 56 q^{91} + 28 q^{92} + 10 q^{93} + 14 q^{94} + 17 q^{95} - 70 q^{96} - 35 q^{97} - 10 q^{98} - 10 q^{99}+O(q^{100}) \) 38 * q + q^2 + 2 * q^3 - 21 * q^4 - 4 * q^5 - 5 * q^7 - 12 * q^8 - 13 * q^9 - 8 * q^10 - 4 * q^11 + 21 * q^12 - 9 * q^13 + 6 * q^14 + 4 * q^15 - 25 * q^16 - 18 * q^17 + 5 * q^18 + 3 * q^19 - 5 * q^20 + 10 * q^21 - 7 * q^22 - 10 * q^23 - 9 * q^24 + 54 * q^25 + 20 * q^26 - 4 * q^27 + 8 * q^28 + 25 * q^29 - 22 * q^30 - 8 * q^31 + 23 * q^32 - 28 * q^33 - 4 * q^34 - 7 * q^35 + 18 * q^36 + 12 * q^37 + 30 * q^38 + 20 * q^39 - 4 * q^40 - 20 * q^41 - 30 * q^42 + 12 * q^43 - 2 * q^44 - 9 * q^45 - 19 * q^46 - 42 * q^47 - 84 * q^48 + 6 * q^49 + 31 * q^50 + 11 * q^51 - 16 * q^52 + q^53 + 42 * q^54 - 11 * q^55 - 5 * q^56 - 22 * q^57 - 2 * q^58 + 22 * q^59 + 48 * q^60 - 26 * q^61 - 44 * q^62 - q^63 + 72 * q^64 - 19 * q^65 + 55 * q^66 + 18 * q^67 - 25 * q^68 + 3 * q^69 + 68 * q^70 - 14 * q^71 - 8 * q^72 - 38 * q^73 + 27 * q^74 + 26 * q^75 + 70 * q^76 + 17 * q^77 + 2 * q^78 + 12 * q^79 - 56 * q^80 + 5 * q^81 - 27 * q^82 + 14 * q^83 - 17 * q^84 - 50 * q^85 + 35 * q^86 + 44 * q^87 - 20 * q^88 - 32 * q^89 - 44 * q^90 + 56 * q^91 + 28 * q^92 + 10 * q^93 + 14 * q^94 + 17 * q^95 - 70 * q^96 - 35 * q^97 - 10 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/241\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−1.32860	−	2.30120i	−0.939461	−	1.62719i	−0.766479	−	0.642269i	$-0.777993\pi$
$2$	−1.32860	−	2.30120i	−0.939461	−	1.62719i	−0.172982	−	0.984925i	$-0.555340\pi$
$3$	−0.221815	+	0.384194i	−0.128065	+	0.221815i	−0.922927	−	0.384976i	$-0.874210\pi$
$3$	−0.221815	+	0.384194i	−0.128065	+	0.221815i	0.794862	+	0.606790i	$0.207543\pi$
$4$	−2.53035	+	4.38269i	−1.26517	+	2.19135i
$5$	1.01184			0.452511			0.226255	−	0.974068i	$-0.427352\pi$
$5$	1.01184			0.452511			0.226255	+	0.974068i	$0.427352\pi$
$6$	1.17881			0.481248
$7$	−0.0424564	−	0.0735367i	−0.0160470	−	0.0277942i	0.857890	−	0.513833i	$-0.171775\pi$
$7$	−0.0424564	−	0.0735367i	−0.0160470	−	0.0277942i	−0.873937	+	0.486038i	$0.838441\pi$
$8$	8.13288			2.87541
$9$	1.40160	+	2.42764i	0.467199	+	0.809212i
$10$	−1.34434	−	2.32846i	−0.425116	−	0.736323i
$11$	0.707483	+	1.22540i	0.213314	+	0.369471i	0.952750	−	0.303756i	$-0.0982409\pi$
$11$	0.707483	+	1.22540i	0.213314	+	0.369471i	−0.739436	+	0.673227i	$0.764908\pi$
$12$	−1.12254	−	1.94429i	−0.324049	−	0.561269i
$13$	2.56031	−	4.43458i	0.710102	−	1.22993i	−0.254717	−	0.967016i	$-0.581982\pi$
$13$	2.56031	−	4.43458i	0.710102	−	1.22993i	0.964819	−	0.262916i	$-0.0846844\pi$
$14$	−0.112815	+	0.195401i	−0.0301511	+	0.0522232i
$15$	−0.224442	+	0.388745i	−0.0579507	+	0.100374i
$16$	−5.74463	−	9.94999i	−1.43616	−	2.48750i
$17$	4.67521			1.13390			0.566952	−	0.823751i	$-0.308122\pi$
$17$	4.67521			1.13390			0.566952	+	0.823751i	$0.308122\pi$
$18$	3.72432	−	6.45071i	0.877830	−	1.52045i
$19$	−0.463515	−	0.802832i	−0.106338	−	0.184182i	0.807946	−	0.589256i	$-0.200579\pi$
$19$	−0.463515	−	0.802832i	−0.106338	−	0.184182i	−0.914284	+	0.405074i	$0.867246\pi$
$20$	−2.56032	+	4.43460i	−0.572505	+	0.991607i
$21$	0.0376698			0.00822023
$22$	1.87992	−	3.25612i	0.400800	−	0.694207i
$23$	1.79287			0.373839			0.186920	−	0.982375i	$-0.440150\pi$
$23$	1.79287			0.373839			0.186920	+	0.982375i	$0.440150\pi$
$24$	−1.80399	+	3.12461i	−0.368238	+	0.637808i
$25$	−3.97617			−0.795234
$26$	−13.6065			−2.66845
$27$	−2.57447			−0.495457
$28$	0.429718			0.0812091
$29$	3.98069	+	6.89475i	0.739195	+	1.28032i	0.952858	+	0.303416i	$0.0981270\pi$
$29$	3.98069	+	6.89475i	0.739195	+	1.28032i	−0.213664	+	0.976907i	$0.568540\pi$
$30$	1.19277			0.217770
$31$	−1.45705	−	2.52369i	−0.261694	−	0.453268i	0.704998	−	0.709209i	$-0.250948\pi$
$31$	−1.45705	−	2.52369i	−0.261694	−	0.453268i	−0.966692	+	0.255941i	$0.917615\pi$
$32$	−7.13174	+	12.3525i	−1.26073	+	2.18364i
$33$	−0.627720			−0.109272
$34$	−6.21148	−	10.7586i	−1.06526	−	1.84508i
$35$	−0.0429593	−	0.0744077i	−0.00726144	−	0.0125772i
$36$	−14.1861			−2.36435
$37$	0.0118740	+	0.0205664i	0.00195208	+	0.00338110i	0.867000	−	0.498308i	$-0.166045\pi$
$37$	0.0118740	+	0.0205664i	0.00195208	+	0.00338110i	−0.865048	+	0.501690i	$0.832712\pi$
$38$	−1.23165	+	2.13328i	−0.199800	+	0.346064i
$39$	1.13583	+	1.96731i	0.181878	+	0.315022i
$40$	8.22921			1.30115
$41$	8.59946			1.34301			0.671505	−	0.741000i	$-0.265648\pi$
$41$	8.59946			1.34301			0.671505	+	0.741000i	$0.265648\pi$
$42$	−0.0500481	−	0.0866858i	−0.00772259	−	0.0133759i
$43$	8.79820			1.34171			0.670857	−	0.741587i	$-0.265927\pi$
$43$	8.79820			1.34171			0.670857	+	0.741587i	$0.265927\pi$
$44$	−7.16071			−1.07952
$45$	1.41820	+	2.45639i	0.211412	+	0.366177i
$46$	−2.38201	−	4.12575i	−0.351207	−	0.608309i
$47$	−8.54150			−1.24591			−0.622953	−	0.782259i	$-0.714067\pi$
$47$	−8.54150			−1.24591			−0.622953	+	0.782259i	$0.714067\pi$
$48$	5.09698			0.735685
$49$	3.49639	−	6.05593i	0.499485	−	0.865133i
$50$	5.28273	+	9.14997i	0.747092	+	1.29400i
$51$	−1.03703	+	1.79619i	−0.145213	+	0.251517i
$52$	12.9569	+	22.4421i	1.79680	+	3.11216i
$53$	1.71465	−	2.96986i	0.235525	−	0.407942i	−0.723900	−	0.689905i	$-0.757652\pi$
$53$	1.71465	−	2.96986i	0.235525	−	0.407942i	0.959425	+	0.281963i	$0.0909856\pi$
$54$	3.42043	+	5.92437i	0.465462	+	0.806204i
$55$	0.715862	+	1.23991i	0.0965269	+	0.167189i
$56$	−0.345293	−	0.598065i	−0.0461417	−	0.0799197i
$57$	0.411258			0.0544725
$58$	10.5775	−	18.3207i	1.38889	−	2.40563i
$59$	2.69946	+	4.67560i	0.351440	+	0.608712i	0.986502	−	0.163749i	$-0.0523588\pi$
$59$	2.69946	+	4.67560i	0.351440	+	0.608712i	−0.635062	+	0.772461i	$0.719026\pi$
$60$	−1.13583	−	1.96732i	−0.146635	−	0.253980i
$61$	−7.46055			−0.955226			−0.477613	−	0.878570i	$-0.658498\pi$
$61$	−7.46055			−0.955226			−0.477613	+	0.878570i	$0.658498\pi$
$62$	−3.87168	+	6.70594i	−0.491704	+	0.851655i
$63$	0.119014	−	0.206137i	0.0149943	−	0.0259709i
$64$	14.9224			1.86529
$65$	2.59063	−	4.48711i	0.321329	−	0.556557i
$66$	0.833988	+	1.44451i	0.102657	+	0.177807i
$67$	5.68120	+	9.84013i	0.694069	+	1.20216i	0.970494	+	0.241127i	$0.0775171\pi$
$67$	5.68120	+	9.84013i	0.694069	+	1.20216i	−0.276424	+	0.961036i	$0.589150\pi$
$68$	−11.8299	+	20.4900i	−1.43459	+	2.48478i
$69$	−0.397685	+	0.688811i	−0.0478757	+	0.0829231i
$70$	−0.114151	+	0.197716i	−0.0136437	+	0.0236316i
$71$	0.913944	+	1.58300i	0.108465	+	0.187867i	0.915149	−	0.403117i	$-0.132073\pi$
$71$	0.913944	+	1.58300i	0.108465	+	0.187867i	−0.806683	+	0.590984i	$0.798740\pi$
$72$	11.3990	+	19.7437i	1.34339	+	2.32681i
$73$	−0.134876			−0.0157860			−0.00789301	−	0.999969i	$-0.502512\pi$
$73$	−0.134876			−0.0157860			−0.00789301	+	0.999969i	$0.502512\pi$
$74$	0.0315517	−	0.0546491i	0.00366781	−	0.00635283i
$75$	0.881973	−	1.52762i	0.101842	−	0.176395i
$76$	4.69142			0.538143
$77$	0.0600743	−	0.104052i	0.00684611	−	0.0118578i
$78$	3.01812	−	5.22754i	0.341735	−	0.591902i
$79$	−13.0618			−1.46957			−0.734786	−	0.678299i	$-0.762717\pi$
$79$	−13.0618			−1.46957			−0.734786	+	0.678299i	$0.762717\pi$
$80$	−5.81267	−	10.0678i	−0.649876	−	1.12562i
$81$	−3.63373	+	6.29381i	−0.403748	+	0.699312i
$82$	−11.4252	−	19.7891i	−1.26171	−	2.18534i
$83$	−5.62834	−	9.74857i	−0.617790	−	1.07004i	−0.989888	−	0.141851i	$-0.954695\pi$
$83$	−5.62834	−	9.74857i	−0.617790	−	1.07004i	0.372098	−	0.928194i	$-0.378639\pi$
$84$	−0.0953178	+	0.165095i	−0.0104000	+	0.0180134i
$85$	4.73058			0.513104
$86$	−11.6893	−	20.2464i	−1.26049	−	2.18323i
$87$	−3.53190			−0.378659
$88$	5.75387	+	9.96599i	0.613364	+	1.06238i
$89$	−5.84176	−	10.1182i	−0.619226	−	1.07253i	−0.989627	−	0.143659i	$-0.954113\pi$
$89$	−5.84176	−	10.1182i	−0.619226	−	1.07253i	0.370401	−	0.928872i	$-0.379220\pi$
$90$	3.76843	−	6.52711i	0.397227	−	0.688018i
$91$	−0.434806			−0.0455800
$92$	−4.53659	+	7.85760i	−0.472972	+	0.819211i
$93$	1.29278			0.134055
$94$	11.3482	+	19.6557i	1.17048	+	2.02733i
$95$	−0.469005	−	0.812341i	−0.0481189	−	0.0833444i
$96$	−3.16385	−	5.47995i	−0.322909	−	0.559295i
$97$	−7.57860	+	13.1265i	−0.769490	+	1.33280i	0.168350	+	0.985727i	$0.446156\pi$
$97$	−7.57860	+	13.1265i	−0.769490	+	1.33280i	−0.937840	+	0.347069i	$0.887177\pi$
$98$	−18.5812			−1.87699
$99$	−1.98321	+	3.43502i	−0.199320	+	0.345233i
$100$	10.0611	−	17.4263i	1.00611	−	1.74263i
$101$	−8.05192			−0.801196			−0.400598	−	0.916254i	$-0.631198\pi$
$101$	−8.05192			−0.801196			−0.400598	+	0.916254i	$0.631198\pi$
$102$	5.51119			0.545689
$103$	−10.2607			−1.01102			−0.505509	−	0.862821i	$-0.668695\pi$
$103$	−10.2607			−1.01102			−0.505509	+	0.862821i	$0.668695\pi$
$104$	20.8227	−	36.0659i	2.04183	−	3.53655i
$105$	0.0381160			0.00371974
$106$	−9.11233			−0.885068
$107$	−3.11749	+	5.39965i	−0.301379	+	0.522004i	−0.976449	−	0.215750i	$-0.930780\pi$
$107$	−3.11749	+	5.39965i	−0.301379	+	0.522004i	0.675070	+	0.737754i	$0.264114\pi$
$108$	6.51430	−	11.2831i	0.626839	−	1.08572i
$109$	−2.96656	+	5.13824i	−0.284145	+	0.492154i	−0.972402	−	0.233314i	$-0.925043\pi$
$109$	−2.96656	+	5.13824i	−0.284145	+	0.492154i	0.688256	+	0.725468i	$0.258376\pi$
$110$	1.90219	−	3.29469i	0.181366	−	0.314136i
$111$	−0.0105354			−0.000999972
$112$	−0.487793	+	0.844882i	−0.0460921	+	0.0798338i
$113$	9.46173	+	16.3882i	0.890085	+	1.54167i	0.839773	+	0.542938i	$0.182688\pi$
$113$	9.46173	+	16.3882i	0.890085	+	1.54167i	0.0503122	+	0.998734i	$0.483978\pi$
$114$	−0.546397	−	0.946388i	−0.0511748	−	0.0886373i
$115$	1.81411			0.169166
$116$	−40.2901			−3.74084
$117$	14.3541			1.32703
$118$	7.17300	−	12.4240i	0.660328	−	1.14372i
$119$	−0.198493	−	0.343799i	−0.0181958	−	0.0315160i
$120$	−1.82536	+	3.16162i	−0.166632	+	0.288615i
$121$	4.49894	−	7.79239i	0.408994	−	0.708399i
$122$	9.91208	+	17.1682i	0.897398	+	1.55434i
$123$	−1.90749	+	3.30386i	−0.171992	+	0.297899i
$124$	14.7474			1.32436
$125$	−9.08249			−0.812362
$126$	−0.632485			−0.0563462
$127$	−9.86234	−	17.0821i	−0.875141	−	1.51579i	−0.856612	−	0.515961i	$-0.827435\pi$
$127$	−9.86234	−	17.0821i	−0.875141	−	1.51579i	−0.0185290	−	0.999828i	$-0.505898\pi$
$128$	−5.56234	−	9.63426i	−0.491646	−	0.851556i
$129$	−1.95157	+	3.38022i	−0.171826	+	0.297612i
$130$	−13.7676			−1.20750
$131$	−1.49065	+	2.58188i	−0.130239	+	0.225580i	−0.923769	−	0.382951i	$-0.874908\pi$
$131$	−1.49065	+	2.58188i	−0.130239	+	0.225580i	0.793530	+	0.608531i	$0.208241\pi$
$132$	1.58835	−	2.75111i	0.138248	−	0.239453i
$133$	−0.0393584	+	0.0681707i	−0.00341281	+	0.00591115i
$134$	15.0961	−	26.1472i	1.30410	−	2.25877i
$135$	−2.60496			−0.224199
$136$	38.0229			3.26044
$137$	8.29622	−	14.3695i	0.708794	−	1.22767i	−0.256511	−	0.966541i	$-0.582573\pi$
$137$	8.29622	−	14.3695i	0.708794	−	1.22767i	0.965305	−	0.261125i	$-0.0840936\pi$
$138$	2.11346			0.179909
$139$	−22.9219			−1.94421			−0.972106	−	0.234543i	$-0.924641\pi$
$139$	−22.9219			−1.94421			−0.972106	+	0.234543i	$0.924641\pi$
$140$	0.434808			0.0367480
$141$	1.89463	−	3.28160i	0.159557	−	0.276360i
$142$	2.42853	−	4.20634i	0.203798	−	0.352988i
$143$	7.24549			0.605899
$144$	16.1033	−	27.8917i	1.34194	−	2.32431i
$145$	4.02783	+	6.97641i	0.334493	+	0.579360i
$146$	0.179196	+	0.310376i	0.0148304	+	0.0256869i
$147$	1.55110	+	2.68659i	0.127933	+	0.221586i
$148$	−0.120182			−0.00987889
$149$	7.83056	−	13.5629i	0.641504	−	1.11112i	−0.343593	−	0.939119i	$-0.611644\pi$
$149$	7.83056	−	13.5629i	0.641504	−	1.11112i	0.985097	−	0.171999i	$-0.0550226\pi$
$150$	−4.68716			−0.382705
$151$	2.26242	−	3.91862i	0.184113	−	0.318893i	−0.759164	−	0.650899i	$-0.774392\pi$
$151$	2.26242	−	3.91862i	0.184113	−	0.318893i	0.943277	+	0.332006i	$0.107725\pi$
$152$	−3.76971	−	6.52933i	−0.305764	−	0.529599i
$153$	6.55276	+	11.3497i	0.529759	+	0.917569i
$154$	−0.319259			−0.0257266
$155$	−1.47431	−	2.55358i	−0.118420	−	0.205109i
$156$	−11.4962			−0.920430
$157$	4.07265	−	7.05404i	0.325033	−	0.562973i	−0.656486	−	0.754338i	$-0.727958\pi$
$157$	4.07265	−	7.05404i	0.325033	−	0.562973i	0.981519	+	0.191365i	$0.0612913\pi$
$158$	17.3539	+	30.0579i	1.38061	+	2.39128i
$159$	0.760670	+	1.31752i	0.0603250	+	0.104486i
$160$	−7.21621	+	12.4988i	−0.570492	+	0.988120i
$161$	−0.0761188	−	0.131842i	−0.00599901	−	0.0103906i
$162$	19.3111			1.51722
$163$	4.35571	−	7.54431i	0.341166	−	0.590916i	−0.643484	−	0.765460i	$-0.722512\pi$
$163$	4.35571	−	7.54431i	0.341166	−	0.590916i	0.984649	+	0.174543i	$0.0558450\pi$
$164$	−21.7596	+	37.6888i	−1.69914	+	2.94300i
$165$	−0.635155			−0.0494468
$166$	−14.9556	+	25.9039i	−1.16078	+	2.01053i
$167$	3.57288	−	6.18841i	0.276478	−	0.478873i	−0.694029	−	0.719947i	$-0.744166\pi$
$167$	3.57288	−	6.18841i	0.276478	−	0.478873i	0.970507	+	0.241074i	$0.0774995\pi$
$168$	0.306364			0.0236365
$169$	−6.61035	−	11.4495i	−0.508489	−	0.880728i
$170$	−6.28505	−	10.8860i	−0.482041	−	0.834920i
$171$	1.29932	−	2.25049i	0.0993617	−	0.172100i
$172$	−22.2625	+	38.5598i	−1.69750	+	2.94016i
$173$	−7.02463	+	12.1670i	−0.534073	+	0.925042i	0.465135	+	0.885240i	$0.346006\pi$
$173$	−7.02463	+	12.1670i	−0.534073	+	0.925042i	−0.999208	+	0.0398016i	$0.987327\pi$
$174$	4.69248	+	8.12761i	0.355736	+	0.616152i
$175$	0.168814	+	0.292394i	0.0127611	+	0.0221029i
$176$	8.12845	−	14.0789i	0.612705	−	1.06124i
$177$	−2.39512			−0.180028
$178$	−15.5227	+	26.8861i	−1.16348	+	2.01520i
$179$	−8.97401	+	15.5434i	−0.670749	+	1.16177i	0.306943	+	0.951728i	$0.400694\pi$
$179$	−8.97401	+	15.5434i	−0.670749	+	1.16177i	−0.977692	+	0.210043i	$0.932639\pi$
$180$	−14.3541			−1.06989
$181$	−0.989730	−	1.71426i	−0.0735661	−	0.127420i	0.826896	−	0.562355i	$-0.190105\pi$
$181$	−0.989730	−	1.71426i	−0.0735661	−	0.127420i	−0.900462	+	0.434935i	$0.856771\pi$
$182$	0.577683	+	1.00058i	0.0428207	+	0.0741676i
$183$	1.65486	−	2.86630i	0.122331	−	0.211883i
$184$	14.5812			1.07494
$185$	0.0120147	+	0.0208100i	0.000883337	+	0.00152998i
$186$	−1.71759	−	2.97495i	−0.125940	−	0.218134i
$187$	3.30763	+	5.72898i	0.241878	+	0.418945i
$188$	21.6130	−	37.4348i	1.57629	−	2.73021i
$189$	0.109303	+	0.189318i	0.00795060	+	0.0137708i
$190$	−1.24624	+	2.15855i	−0.0904117	+	0.156598i
$191$	−0.376866	−	0.652751i	−0.0272690	−	0.0472314i	0.852069	−	0.523430i	$-0.175348\pi$
$191$	−0.376866	−	0.652751i	−0.0272690	−	0.0472314i	−0.879338	+	0.476198i	$0.842014\pi$
$192$	−3.31000	+	5.73309i	−0.238879	+	0.413750i
$193$	8.36886			0.602404			0.301202	−	0.953560i	$-0.402612\pi$
$193$	8.36886			0.602404			0.301202	+	0.953560i	$0.402612\pi$
$194$	40.2757			2.89162
$195$	1.14928	+	1.99061i	0.0823018	+	0.142551i
$196$	17.6942	+	30.6472i	1.26387	+	2.18909i
$197$	−12.1887			−0.868411			−0.434206	−	0.900814i	$-0.642971\pi$
$197$	−12.1887			−0.868411			−0.434206	+	0.900814i	$0.642971\pi$
$198$	10.5396			0.749014
$199$	−4.22270	−	7.31394i	−0.299340	−	0.518471i	0.676645	−	0.736309i	$-0.263433\pi$
$199$	−4.22270	−	7.31394i	−0.299340	−	0.518471i	−0.975985	+	0.217838i	$0.930100\pi$
$200$	−32.3377			−2.28662
$201$	−5.04070			−0.355543
$202$	10.6978	+	18.5291i	0.752692	+	1.30370i
$203$	0.338011	−	0.585453i	0.0237237	−	0.0410907i
$204$	−5.24810	−	9.08997i	−0.367440	−	0.636425i
$205$	8.70131			0.607726
$206$	13.6324	+	23.6120i	0.949812	+	1.64512i
$207$	2.51288	+	4.35244i	0.174657	+	0.302515i
$208$	−58.8321			−4.07927
$209$	0.655858	−	1.13598i	0.0453667	−	0.0785773i
$210$	−0.0506409	−	0.0877126i	−0.00349455	−	0.00605274i
$211$	−19.6571			−1.35325			−0.676626	−	0.736327i	$-0.736559\pi$
$211$	−19.6571			−1.35325			−0.676626	+	0.736327i	$0.736559\pi$
$212$	8.67733	+	15.0296i	0.595961	+	1.03224i
$213$	−0.810905			−0.0555623
$214$	16.5676			1.13254
$215$	8.90241			0.607139
$216$	−20.9378			−1.42464
$217$	−0.123722	+	0.214294i	−0.00839883	+	0.0145472i
$218$	15.7655			1.06777
$219$	0.0299175	−	0.0518186i	0.00202163	−	0.00350157i
$220$	−7.24552			−0.488493
$221$	11.9700	−	20.7326i	0.805188	−	1.39463i
$222$	0.0139973	+	0.0242440i	0.000939434	+	0.00162715i
$223$	2.60772	−	4.51670i	0.174626	−	0.302461i	−0.765406	−	0.643548i	$-0.777462\pi$
$223$	2.60772	−	4.51670i	0.174626	−	0.302461i	0.940032	+	0.341087i	$0.110795\pi$
$224$	1.21115			0.0809235
$225$	−5.57299	−	9.65270i	−0.371532	−	0.643513i
$226$	25.1417	−	43.5467i	1.67240	−	2.89668i
$227$	7.63299	−	13.2207i	0.506619	−	0.877490i	−0.493352	−	0.869830i	$-0.664228\pi$
$227$	7.63299	−	13.2207i	0.506619	−	0.877490i	0.999971	−	0.00766000i	$-0.00243828\pi$
$228$	−1.04063	+	1.80242i	−0.0689172	+	0.119368i
$229$	−4.39370	−	7.61011i	−0.290344	−	0.502890i	0.683547	−	0.729906i	$-0.260436\pi$
$229$	−4.39370	−	7.61011i	−0.290344	−	0.502890i	−0.973891	+	0.227016i	$0.927103\pi$
$230$	−2.41022	−	4.17462i	−0.158925	−	0.275266i
$231$	0.0266508	+	0.0461605i	0.00175349	+	0.00303714i
$232$	32.3744	+	56.0741i	2.12548	+	3.68145i
$233$	−1.12127			−0.0734566			−0.0367283	−	0.999325i	$-0.511694\pi$
$233$	−1.12127			−0.0734566			−0.0367283	+	0.999325i	$0.511694\pi$
$234$	−19.0708	−	33.0316i	−1.24670	−	2.15934i
$235$	−8.64267			−0.563786
$236$	−27.3223			−1.77853
$237$	2.89731	−	5.01829i	0.188200	−	0.325973i
$238$	−0.527434	+	0.913542i	−0.0341885	+	0.0592162i
$239$	11.4655	+	19.8588i	0.741640	+	1.28456i	0.951748	+	0.306880i	$0.0992851\pi$
$239$	11.4655	+	19.8588i	0.741640	+	1.28456i	−0.210108	+	0.977678i	$0.567382\pi$
$240$	5.15735			0.332905
$241$	13.8471	−	7.01834i	0.891972	−	0.452091i
$241$	13.8471	−	7.01834i	0.891972	−	0.452091i
$242$	−23.9091			−1.53694
$243$	−5.47373	−	9.48079i	−0.351140	−	0.608193i
$244$	18.8778	−	32.6973i	1.20853	−	2.09323i
$245$	3.53781	−	6.12766i	0.226022	−	0.391482i
$246$	10.1371			0.646320
$247$	−4.74697			−0.302042
$248$	−11.8500	−	20.5249i	−0.752478	−	1.30333i
$249$	4.99379			0.316469
$250$	12.0670	+	20.9006i	0.763183	+	1.32187i
$251$	6.14649	+	10.6460i	0.387963	+	0.671972i	0.992175	−	0.124851i	$-0.0398454\pi$
$251$	6.14649	+	10.6460i	0.387963	+	0.671972i	−0.604212	+	0.796823i	$0.706512\pi$
$252$	0.602291	+	1.04320i	0.0379408	+	0.0657154i
$253$	1.26842	+	2.19698i	0.0797452	+	0.138123i
$254$	−26.2062	+	45.3904i	−1.64432	+	2.84805i
$255$	−1.04931	+	1.81746i	−0.0657106	+	0.113814i
$256$	0.142115	−	0.246151i	0.00888219	−	0.0153844i
$257$	−8.44390	−	14.6253i	−0.526716	−	0.912299i	−0.999515	−	0.0311287i	$-0.990090\pi$
$257$	−8.44390	−	14.6253i	−0.526716	−	0.912299i	0.472799	−	0.881170i	$-0.343244\pi$
$258$	10.3714			0.645696
$259$	0.00100826	−	0.00174635i	6.26501e−5	−	0.000108513i
$260$	13.1104	+	22.7079i	0.813073	+	1.40828i
$261$	−11.1586	+	19.3273i	−0.690702	+	1.19633i
$262$	7.92191			0.489417
$263$	−9.96340	+	17.2571i	−0.614369	+	1.06412i	0.376125	+	0.926569i	$0.377256\pi$
$263$	−9.96340	+	17.2571i	−0.614369	+	1.06412i	−0.990495	+	0.137550i	$0.956077\pi$
$264$	−5.10517			−0.314202
$265$	1.73496	−	3.00504i	0.106578	−	0.184598i
$266$	0.209166			0.0128248
$267$	5.18316			0.317204
$268$	−57.5017			−3.51247
$269$	18.2229			1.11107			0.555536	−	0.831492i	$-0.312513\pi$
$269$	18.2229			1.11107			0.555536	+	0.831492i	$0.312513\pi$
$270$	3.46095	+	5.99454i	0.210627	+	0.364816i
$271$	25.9345			1.57541			0.787705	−	0.616053i	$-0.211269\pi$
$271$	25.9345			1.57541			0.787705	+	0.616053i	$0.211269\pi$
$272$	−26.8573	−	46.5183i	−1.62847	−	2.82059i
$273$	0.0964464	−	0.167050i	0.00583720	−	0.0101103i
$274$	−44.0894			−2.66354
$275$	−2.81307	−	4.87238i	−0.169635	−	0.293816i
$276$	−2.01256	−	3.48586i	−0.121142	−	0.209824i
$277$	−10.4721			−0.629209			−0.314604	−	0.949223i	$-0.601872\pi$
$277$	−10.4721			−0.629209			−0.314604	+	0.949223i	$0.601872\pi$
$278$	30.4540	+	52.7479i	1.82651	+	3.16361i
$279$	4.08440	−	7.07439i	0.244527	−	0.423533i
$280$	−0.349383	−	0.605148i	−0.0208796	−	0.0361645i
$281$	3.16985			0.189097			0.0945487	−	0.995520i	$-0.469859\pi$
$281$	3.16985			0.189097			0.0945487	+	0.995520i	$0.469859\pi$
$282$	−10.0688			−0.599589
$283$	−10.0827	−	17.4637i	−0.599351	−	1.03811i	−0.992917	−	0.118811i	$-0.962092\pi$
$283$	−10.0827	−	17.4637i	−0.599351	−	1.03811i	0.393566	−	0.919297i	$-0.371241\pi$
$284$	−9.25039			−0.548909
$285$	0.416129			0.0246494
$286$	−9.62635	−	16.6733i	−0.569218	−	0.985915i
$287$	−0.365102	−	0.632375i	−0.0215513	−	0.0373279i
$288$	−39.9833			−2.35604
$289$	4.85758			0.285740
$290$	10.7028	−	18.5377i	0.628487	−	1.08857i
$291$	−3.36209	−	5.82331i	−0.197089	−	0.341369i
$292$	0.341283	−	0.591119i	0.0199721	−	0.0345926i
$293$	3.44974	+	5.97512i	0.201536	+	0.349070i	0.949024	−	0.315205i	$-0.102073\pi$
$293$	3.44974	+	5.97512i	0.201536	+	0.349070i	−0.747488	+	0.664276i	$0.768740\pi$
$294$	4.12159	−	7.13880i	0.240376	−	0.416343i
$295$	2.73143	+	4.73098i	0.159030	+	0.275448i
$296$	0.0965701	+	0.167264i	0.00561302	+	0.00972204i
$297$	−1.82139	−	3.15474i	−0.105688	−	0.183057i
$298$	−41.6147			−2.41067
$299$	4.59030	−	7.95063i	0.265464	−	0.459797i
$300$	4.46340	+	7.73084i	0.257695	+	0.446340i
$301$	−0.373540	−	0.646990i	−0.0215305	−	0.0372919i
$302$	−12.0234			−0.691868
$303$	1.78603	−	3.09350i	0.102605	−	0.177717i
$304$	−5.32545	+	9.22395i	−0.305435	+	0.529030i
$305$	−7.54892			−0.432250
$306$	17.4120	−	30.1584i	0.995376	−	1.72404i
$307$	14.8871	+	25.7852i	0.849650	+	1.47164i	0.881521	+	0.472145i	$0.156520\pi$
$307$	14.8871	+	25.7852i	0.849650	+	1.47164i	−0.0318712	+	0.999492i	$0.510147\pi$
$308$	0.304018	+	0.526575i	0.0173230	+	0.0300044i
$309$	2.27598	−	3.94211i	0.129476	−	0.224259i
$310$	−3.91754	+	6.78537i	−0.222501	+	0.385383i
$311$	14.9527	−	25.8989i	0.847891	−	1.46859i	−0.0351965	−	0.999380i	$-0.511206\pi$
$311$	14.9527	−	25.8989i	0.847891	−	1.46859i	0.883087	−	0.469209i	$-0.155461\pi$
$312$	9.23755	+	15.9999i	0.522973	+	0.905816i
$313$	−7.80075	−	13.5113i	−0.440925	−	0.763704i	0.556834	−	0.830624i	$-0.312016\pi$
$313$	−7.80075	−	13.5113i	−0.440925	−	0.763704i	−0.997758	+	0.0669201i	$0.978683\pi$
$314$	−21.6437			−1.22142
$315$	0.120423	−	0.208579i	0.00678508	−	0.0117521i
$316$	33.0510	−	57.2460i	1.85926	−	3.22034i
$317$	20.4873			1.15068			0.575340	−	0.817914i	$-0.304870\pi$
$317$	20.4873			1.15068			0.575340	+	0.817914i	$0.304870\pi$
$318$	2.02125	−	3.50091i	0.113346	−	0.196321i
$319$	−5.63253	+	9.75583i	−0.315361	+	0.546222i
$320$	15.0991			0.844066
$321$	−1.38301	−	2.39544i	−0.0771921	−	0.133701i
$322$	−0.202263	+	0.350329i	−0.0112717	+	0.0195231i
$323$	−2.16703	−	3.75341i	−0.120577	−	0.208845i
$324$	−18.3892	−	31.8511i	−1.02162	−	1.76950i
$325$	−10.1802	+	17.6327i	−0.564697	+	0.978084i
$326$	−23.1480			−1.28205
$327$	−1.31606	−	2.27947i	−0.0727780	−	0.126055i
$328$	69.9383			3.86170
$329$	0.362642	+	0.628114i	0.0199931	+	0.0346290i
$330$	0.843867	+	1.46162i	0.0464533	+	0.0804595i
$331$	−16.6055	+	28.7616i	−0.912723	+	1.58088i	−0.102521	+	0.994731i	$0.532691\pi$
$331$	−16.6055	+	28.7616i	−0.912723	+	1.58088i	−0.810202	+	0.586151i	$0.800642\pi$
$332$	56.9666			3.12645
$333$	−0.0332852	+	0.0576517i	−0.00182402	+	0.00315929i
$334$	−18.9877			−1.03896
$335$	5.74849	+	9.95668i	0.314074	+	0.543991i
$336$	−0.216399	−	0.374815i	−0.0118055	−	0.0204478i
$337$	6.27656	+	10.8713i	0.341906	+	0.592198i	0.984787	−	0.173768i	$-0.0555943\pi$
$337$	6.27656	+	10.8713i	0.341906	+	0.592198i	−0.642881	+	0.765966i	$0.722261\pi$
$338$	−17.5650	+	30.4235i	−0.955411	+	1.65482i
$339$	−8.39501			−0.455954
$340$	−11.9700	+	20.7327i	−0.649166	+	1.12439i
$341$	2.06168	−	3.57093i	0.111646	−	0.193377i
$342$	−6.90511			−0.373386
$343$	−1.18817			−0.0641550
$344$	71.5547			3.85797
$345$	−0.402396	+	0.696970i	−0.0216642	+	0.0375236i
$346$	37.3317			2.00696
$347$	−20.3217			−1.09092			−0.545462	−	0.838135i	$-0.683646\pi$
$347$	−20.3217			−1.09092			−0.545462	+	0.838135i	$0.683646\pi$
$348$	8.93694	−	15.4792i	0.479070	−	0.829774i
$349$	−10.6887	+	18.5133i	−0.572152	+	0.990997i	0.424192	+	0.905572i	$0.360558\pi$
$349$	−10.6887	+	18.5133i	−0.572152	+	0.990997i	−0.996345	+	0.0854246i	$0.972775\pi$
$350$	0.448572	−	0.776949i	0.0239772	−	0.0415297i
$351$	−6.59143	+	11.4167i	−0.351825	+	0.609378i
$352$	−20.1823			−1.07572
$353$	11.0873	−	19.2038i	0.590117	−	1.02211i	−0.404099	−	0.914715i	$-0.632415\pi$
$353$	11.0873	−	19.2038i	0.590117	−	1.02211i	0.994216	−	0.107398i	$-0.0342519\pi$
$354$	3.18215	+	5.51165i	0.169130	+	0.292941i
$355$	0.924769	+	1.60175i	0.0490816	+	0.0850119i
$356$	59.1268			3.13371
$357$	0.176114			0.00932096
$358$	47.6914			2.52057
$359$	−9.02981	+	15.6401i	−0.476575	+	0.825452i	−0.999640	−	0.0268407i	$-0.991455\pi$
$359$	−9.02981	+	15.6401i	−0.476575	+	0.825452i	0.523065	+	0.852293i	$0.324789\pi$
$360$	11.5340	+	19.9775i	0.607896	+	1.05291i
$361$	9.07031	−	15.7102i	0.477385	−	0.826854i
$362$	−2.62991	+	4.55514i	−0.138225	+	0.239413i
$363$	1.99586	+	3.45693i	0.104756	+	0.181442i
$364$	1.10021	−	1.90562i	0.0576667	−	0.0998817i
$365$	−0.136473			−0.00714334
$366$	−8.79459			−0.459700
$367$	−20.5185			−1.07106			−0.535529	−	0.844517i	$-0.679888\pi$
$367$	−20.5185			−1.07106			−0.535529	+	0.844517i	$0.679888\pi$
$368$	−10.2994	−	17.8390i	−0.536892	−	0.929924i
$369$	12.0530	+	20.8764i	0.627452	+	1.08678i
$370$	0.0319254	−	0.0552964i	0.00165972	−	0.00287472i
$371$	−0.291192			−0.0151179
$372$	−3.27119	+	5.66587i	−0.169603	+	0.293762i
$373$	3.18886	−	5.52327i	0.165113	−	0.285984i	−0.771582	−	0.636129i	$-0.780534\pi$
$373$	3.18886	−	5.52327i	0.165113	−	0.285984i	0.936695	+	0.350145i	$0.113868\pi$
$374$	8.78902	−	15.2230i	0.454469	−	0.787164i
$375$	2.01463	−	3.48944i	0.104035	−	0.180194i
$376$	−69.4670			−3.58249
$377$	40.7671			2.09961
$378$	0.290439	−	0.503055i	0.0149386	−	0.0258743i
$379$	−9.80630			−0.503716			−0.251858	−	0.967764i	$-0.581042\pi$
$379$	−9.80630			−0.503716			−0.251858	+	0.967764i	$0.581042\pi$
$380$	4.74699			0.243515
$381$	8.75045			0.448299
$382$	−1.00141	+	1.73449i	−0.0512364	+	0.0887441i
$383$	15.0295	−	26.0319i	0.767971	−	1.33017i	−0.170690	−	0.985325i	$-0.554600\pi$
$383$	15.0295	−	26.0319i	0.767971	−	1.33017i	0.938661	−	0.344841i	$-0.112067\pi$
$384$	4.93524			0.251850
$385$	0.0607859	−	0.105284i	0.00309794	−	0.00536578i
$386$	−11.1189	−	19.2584i	−0.565935	−	0.980228i
$387$	12.3315	+	21.3588i	0.626847	+	1.08573i
$388$	−38.3530	−	66.4293i	−1.94708	−	3.37244i
$389$	−25.4035			−1.28801			−0.644004	−	0.765022i	$-0.722728\pi$
$389$	−25.4035			−1.28801			−0.644004	+	0.765022i	$0.722728\pi$
$390$	3.05387	−	5.28945i	0.154639	−	0.267842i
$391$	8.38204			0.423898
$392$	28.4357	−	49.2522i	1.43622	−	2.48761i
$393$	−0.661297	−	1.14540i	−0.0333580	−	0.0577778i
$394$	16.1939	+	28.0487i	0.815839	+	1.41307i
$395$	−13.2166			−0.664997
$396$	−10.0364	−	17.3836i	−0.504349	−	0.873559i
$397$	−9.05614			−0.454515			−0.227257	−	0.973835i	$-0.572976\pi$
$397$	−9.05614			−0.454515			−0.227257	+	0.973835i	$0.572976\pi$
$398$	−11.2206	+	19.4346i	−0.562436	+	0.974167i
$399$	−0.0174605	−	0.0302426i	−0.000874121	−	0.00151402i
$400$	22.8416	+	39.5629i	1.14208	+	1.97814i
$401$	−17.8527	+	30.9218i	−0.891523	+	1.54416i	−0.0534736	+	0.998569i	$0.517029\pi$
$401$	−17.8527	+	30.9218i	−0.891523	+	1.54416i	−0.838050	+	0.545594i	$0.816304\pi$
$402$	6.69706	+	11.5997i	0.334019	+	0.578538i
$403$	−14.9220			−0.743319
$404$	20.3742	−	35.2891i	1.01365	−	1.75570i
$405$	−3.67677	+	6.36836i	−0.182700	+	0.316446i
$406$	−1.79632			−0.0891501
$407$	−0.0168014	+	0.0291008i	−0.000832812	+	0.00144247i
$408$	−8.43404	+	14.6082i	−0.417547	+	0.723213i
$409$	−2.87514			−0.142167			−0.0710833	−	0.997470i	$-0.522646\pi$
$409$	−2.87514			−0.142167			−0.0710833	+	0.997470i	$0.522646\pi$
$410$	−11.5606	−	20.0235i	−0.570935	−	0.988888i
$411$	3.68045	+	6.37472i	0.181543	+	0.314442i
$412$	25.9632	−	44.9696i	1.27911	−	2.21549i
$413$	0.229219	−	0.397019i	0.0112791	−	0.0195360i
$414$	6.67722	−	11.5653i	0.328167	−	0.568403i
$415$	−5.69500	−	9.86403i	−0.279557	−	0.484206i
$416$	36.5189	+	63.2526i	1.79049	+	3.10121i
$417$	5.08442	−	8.80647i	0.248985	−	0.431255i
$418$	−3.48549			−0.170481
$419$	−12.0064	+	20.7958i	−0.586553	+	1.01594i	0.408126	+	0.912925i	$0.366182\pi$
$419$	−12.0064	+	20.7958i	−0.586553	+	1.01594i	−0.994680	+	0.103015i	$0.967151\pi$
$420$	−0.0964468	+	0.167051i	−0.00470612	+	0.00815124i
$421$	16.5998			0.809027			0.404513	−	0.914532i	$-0.367441\pi$
$421$	16.5998			0.809027			0.404513	+	0.914532i	$0.367441\pi$
$422$	26.1164	+	45.2350i	1.27133	+	2.20200i
$423$	−11.9717	−	20.7357i	−0.582086	−	1.00820i
$424$	13.9450	−	24.1535i	0.677231	−	1.17300i
$425$	−18.5894			−0.901720
$426$	1.07737	+	1.86606i	0.0521986	+	0.0904107i
$427$	0.316748	+	0.548624i	0.0153285	+	0.0265498i
$428$	−15.7767	−	27.3260i	−0.762594	−	1.32085i
$429$	−1.60716	+	2.78368i	−0.0775943	+	0.134397i
$430$	−11.8277	−	20.4862i	−0.570384	−	0.987934i
$431$	17.9206	−	31.0393i	0.863204	−	1.49511i	−0.00561619	−	0.999984i	$-0.501788\pi$
$431$	17.9206	−	31.0393i	0.863204	−	1.49511i	0.868820	−	0.495128i	$-0.164879\pi$
$432$	14.7894	+	25.6159i	0.711554	+	1.23245i
$433$	−9.80979	+	16.9911i	−0.471428	+	0.816538i	−0.999466	−	0.0326831i	$-0.989595\pi$
$433$	−9.80979	+	16.9911i	−0.471428	+	0.816538i	0.528037	+	0.849221i	$0.322928\pi$
$434$	0.657510			0.0315615
$435$	−3.57373			−0.171347
$436$	−15.0129	−	26.0031i	−0.718986	−	1.24532i
$437$	−0.831023	−	1.43937i	−0.0397532	−	0.0688546i
$438$	−0.158993			−0.00759699
$439$	15.1096			0.721143			0.360572	−	0.932732i	$-0.382582\pi$
$439$	15.1096			0.721143			0.360572	+	0.932732i	$0.382582\pi$
$440$	5.82202	+	10.0840i	0.277554	+	0.480737i
$441$	19.6021			0.933435
$442$	−63.6132			−3.02577
$443$	−4.90165	−	8.48991i	−0.232884	−	0.403368i	0.725771	−	0.687936i	$-0.241483\pi$
$443$	−4.90165	−	8.48991i	−0.232884	−	0.403368i	−0.958656	+	0.284568i	$0.908150\pi$
$444$	0.0266581	−	0.0461732i	0.00126514	−	0.00219128i
$445$	−5.91096	−	10.2381i	−0.280206	−	0.485331i
$446$	−13.8584			−0.656216
$447$	3.47387	+	6.01691i	0.164308	+	0.284590i
$448$	−0.633550	−	1.09734i	−0.0299324	−	0.0518445i
$449$	−40.6903			−1.92029			−0.960147	−	0.279496i	$-0.909833\pi$
$449$	−40.6903			−1.92029			−0.960147	+	0.279496i	$0.909833\pi$
$450$	−14.8085	+	25.6491i	−0.698081	+	1.20911i
$451$	6.08397	+	10.5377i	0.286483	+	0.496203i
$452$	−95.7659			−4.50445
$453$	1.00368	+	1.73842i	0.0471568	+	0.0816780i
$454$	−40.5647			−1.90380
$455$	−0.439956			−0.0206255
$456$	3.34471			0.156630
$457$	−22.4665			−1.05094			−0.525470	−	0.850812i	$-0.676110\pi$
$457$	−22.4665			−1.05094			−0.525470	+	0.850812i	$0.676110\pi$
$458$	−11.6749	+	20.2216i	−0.545533	+	0.944892i
$459$	−12.0362			−0.561801
$460$	−4.59032	+	7.95067i	−0.214025	+	0.370702i
$461$	−2.44139			−0.113707			−0.0568534	−	0.998383i	$-0.518107\pi$
$461$	−2.44139			−0.113707			−0.0568534	+	0.998383i	$0.518107\pi$
$462$	0.0708163	−	0.122657i	0.00329467	−	0.00570654i
$463$	−17.3739	−	30.0926i	−0.807436	−	1.39852i	−0.914634	−	0.404282i	$-0.867521\pi$
$463$	−17.3739	−	30.0926i	−0.807436	−	1.39852i	0.107198	−	0.994238i	$-0.465812\pi$
$464$	45.7351	−	79.2156i	2.12320	−	3.67749i
$465$	1.30810			0.0606615
$466$	1.48971	+	2.58026i	0.0690096	+	0.119528i
$467$	7.94620	−	13.7632i	0.367706	−	0.636886i	−0.621500	−	0.783414i	$-0.713477\pi$
$467$	7.94620	−	13.7632i	0.367706	−	0.636886i	0.989206	+	0.146528i	$0.0468099\pi$
$468$	−36.3208	+	62.9095i	−1.67893	+	2.90799i
$469$	0.482407	−	0.835553i	0.0222755	−	0.0385823i
$470$	11.4826	+	19.8885i	0.529655	+	0.917389i
$471$	1.80675	+	3.12938i	0.0832505	+	0.144194i
$472$	21.9544	+	38.0261i	1.01053	+	1.75029i
$473$	6.22458	+	10.7813i	0.286206	+	0.495724i
$474$	−15.3974			−0.707228
$475$	1.84302	+	3.19220i	0.0845634	+	0.146468i
$476$	2.00902			0.0920834
$477$	9.61299			0.440149
$478$	30.4660	−	52.7687i	1.39348	−	2.41359i
$479$	0.763513	−	1.32244i	0.0348858	−	0.0604240i	−0.848055	−	0.529908i	$-0.822227\pi$
$479$	0.763513	−	1.32244i	0.0348858	−	0.0604240i	0.882941	+	0.469484i	$0.155560\pi$
$480$	−3.20132	−	5.54486i	−0.146120	−	0.253087i
$481$	0.121605			0.00554470
$482$	−34.5479	−	22.5405i	−1.57361	−	1.02669i
$483$	0.0675371			0.00307305
$484$	22.7678	+	39.4349i	1.03490	+	1.79250i
$485$	−7.66836	+	13.2820i	−0.348202	+	0.603104i
$486$	−14.5448	+	25.1923i	−0.659765	+	1.14275i
$487$	−18.5645			−0.841239			−0.420620	−	0.907237i	$-0.638187\pi$
$487$	−18.5645			−0.841239			−0.420620	+	0.907237i	$0.638187\pi$
$488$	−60.6758			−2.74666
$489$	1.93232	+	3.34688i	0.0873826	+	0.151351i
$490$	−18.8013			−0.849356
$491$	8.28442	+	14.3490i	0.373871	+	0.647563i	0.990157	−	0.139959i	$-0.0446970\pi$
$491$	8.28442	+	14.3490i	0.373871	+	0.647563i	−0.616286	+	0.787522i	$0.711364\pi$
$492$	−9.65321	−	16.7199i	−0.435200	−	0.753789i
$493$	18.6105	+	32.2344i	0.838176	+	1.45176i
$494$	6.30681	+	10.9237i	0.283757	+	0.491482i
$495$	−2.00670	+	3.47571i	−0.0901945	+	0.156221i
$496$	−16.7405	+	28.9953i	−0.751669	+	1.30193i
$497$	0.0776056	−	0.134417i	0.00348109	−	0.00602942i
$498$	−6.63475	−	11.4917i	−0.297310	−	0.514956i
$499$	37.1442			1.66280			0.831402	−	0.555672i	$-0.187539\pi$
$499$	37.1442			1.66280			0.831402	+	0.555672i	$0.187539\pi$
$500$	22.9819	−	39.8058i	1.02778	−	1.78017i
$501$	1.58503	+	2.74536i	0.0708141	+	0.122654i
$502$	16.3324	−	28.2886i	0.728953	−	1.26258i
$503$	18.6684			0.832381			0.416190	−	0.909277i	$-0.363365\pi$
$503$	18.6684			0.832381			0.416190	+	0.909277i	$0.363365\pi$
$504$	0.967922	−	1.67649i	0.0431147	−	0.0746768i
$505$	−8.14729			−0.362549
$506$	3.37045	−	5.83780i	0.149835	−	0.259522i
$507$	5.86510			0.260478
$508$	99.8206			4.42882
$509$	−22.3419			−0.990288			−0.495144	−	0.868811i	$-0.664885\pi$
$509$	−22.3419			−0.990288			−0.495144	+	0.868811i	$0.664885\pi$
$510$	5.57647			0.246930
$511$	0.00572634	+	0.00991832i	0.000253319	+	0.000438761i
$512$	−23.0046			−1.01667
$513$	1.19331	+	2.06687i	0.0526857	+	0.0912543i
$514$	−22.4371	+	38.8622i	−0.989658	+	1.71414i
$515$	−10.3822			−0.457496
$516$	−9.87631	−	17.1063i	−0.434780	−	0.753062i
$517$	−6.04296	−	10.4667i	−0.265769	−	0.460326i
$518$	−0.00535828			−0.000235429
$519$	−3.11634	−	5.39765i	−0.136792	−	0.236931i
$520$	21.0693	−	36.4931i	0.923950	−	1.60033i
$521$	4.63120	+	8.02148i	0.202897	+	0.351427i	0.949461	−	0.313886i	$-0.101631\pi$
$521$	4.63120	+	8.02148i	0.202897	+	0.351427i	−0.746564	+	0.665314i	$0.768298\pi$
$522$	59.3014			2.59555
$523$	29.1689			1.27547			0.637734	−	0.770257i	$-0.279872\pi$
$523$	29.1689			1.27547			0.637734	+	0.770257i	$0.279872\pi$
$524$	−7.54373	−	13.0661i	−0.329550	−	0.570797i
$525$	−0.149782			−0.00653701
$526$	52.9494			2.30870
$527$	−6.81203	−	11.7988i	−0.296737	−	0.513963i
$528$	3.60602	+	6.24581i	0.156932	+	0.271814i
$529$	−19.7856			−0.860244
$530$	−9.22026			−0.400502
$531$	−7.56711	+	13.1066i	−0.328385	+	0.568779i
$532$	−0.199181	−	0.344991i	−0.00863559	−	0.0149573i
$533$	22.0173	−	38.1350i	0.953673	−	1.65181i
$534$	−6.88634	−	11.9275i	−0.298001	−	0.516153i
$535$	−3.15441	+	5.46361i	−0.136377	+	0.236212i
$536$	46.2045	+	80.0285i	1.99573	+	3.45671i
$537$	−3.98114	−	6.89553i	−0.171799	−	0.297564i
$538$	−24.2110	−	41.9346i	−1.04381	−	1.80793i
$539$	9.89455			0.426189
$540$	6.59146	−	11.4167i	0.283651	−	0.491298i
$541$	12.9589	+	22.4455i	0.557147	+	0.965007i	0.997733	+	0.0672966i	$0.0214374\pi$
$541$	12.9589	+	22.4455i	0.557147	+	0.965007i	−0.440586	+	0.897710i	$0.645229\pi$
$542$	−34.4565	−	59.6805i	−1.48004	−	2.56350i
$543$	0.878147			0.0376849
$544$	−33.3424	+	57.7507i	−1.42954	+	2.47604i
$545$	−3.00170	+	5.19910i	−0.128579	+	0.222705i
$546$	−0.512554			−0.0219353
$547$	2.26147	−	3.91698i	0.0966934	−	0.167478i	−0.813621	−	0.581396i	$-0.802507\pi$
$547$	2.26147	−	3.91698i	0.0966934	−	0.167478i	0.910314	+	0.413918i	$0.135840\pi$
$548$	41.9846	+	72.7195i	1.79350	+	3.10642i
$549$	−10.4567	−	18.1115i	−0.446281	−	0.772981i
$550$	−7.47489	+	12.9469i	−0.318730	+	0.552057i
$551$	3.69022	−	6.39164i	0.157209	−	0.272293i
$552$	−3.23432	+	5.60201i	−0.137662	+	0.238438i
$553$	0.554559	+	0.960524i	0.0235822	+	0.0408456i
$554$	13.9132	+	24.0984i	0.591117	+	1.02385i
$555$	−0.0106601			−0.000452498
$556$	58.0004	−	100.460i	2.45977	−	4.26044i
$557$	−8.23009	+	14.2549i	−0.348720	+	0.604001i	−0.986022	−	0.166613i	$-0.946717\pi$
$557$	−8.23009	+	14.2549i	−0.348720	+	0.604001i	0.637302	+	0.770614i	$0.280050\pi$
$558$	−21.7061			−0.918893
$559$	22.5261	−	39.0164i	0.952753	−	1.65022i
$560$	−0.493570	+	0.854889i	−0.0208572	+	0.0361257i
$561$	−2.93472			−0.123904
$562$	−4.21146	−	7.29446i	−0.177650	−	0.307698i
$563$	−4.98680	+	8.63738i	−0.210168	+	0.364022i	−0.951767	−	0.306821i	$-0.900735\pi$
$563$	−4.98680	+	8.63738i	−0.210168	+	0.364022i	0.741599	+	0.670844i	$0.234068\pi$
$564$	9.58816	+	16.6072i	0.403734	+	0.699288i
$565$	9.57380	+	16.5823i	0.402773	+	0.697623i
$566$	−26.7916	+	46.4044i	−1.12613	+	1.95052i
$567$	0.617101			0.0259158
$568$	7.43299	+	12.8743i	0.311881	+	0.540194i
$569$	−14.5087			−0.608236			−0.304118	−	0.952634i	$-0.598362\pi$
$569$	−14.5087			−0.608236			−0.304118	+	0.952634i	$0.598362\pi$
$570$	−0.552869	−	0.957597i	−0.0231571	−	0.0401093i
$571$	14.1861	+	24.5710i	0.593668	+	1.02826i	0.993733	+	0.111777i	$0.0356542\pi$
$571$	14.1861	+	24.5710i	0.593668	+	1.02826i	−0.400065	+	0.916487i	$0.631012\pi$
$572$	−18.3336	+	31.7548i	−0.766567	+	1.32773i
$573$	0.334378			0.0139688
$574$	−0.970148	+	1.68035i	−0.0404932	+	0.0701363i
$575$	−7.12876			−0.297290
$576$	20.9151	+	36.2261i	0.871463	+	1.50942i
$577$	2.61891	+	4.53608i	0.109027	+	0.188840i	0.915376	−	0.402600i	$-0.131893\pi$
$577$	2.61891	+	4.53608i	0.109027	+	0.188840i	−0.806350	+	0.591439i	$0.798560\pi$
$578$	−6.45377	−	11.1783i	−0.268441	−	0.464954i
$579$	−1.85634	+	3.21527i	−0.0771467	+	0.133622i
$580$	−40.7673			−1.69277
$581$	−0.477918	+	0.827778i	−0.0198274	+	0.0343420i
$582$	−8.93374	+	15.4737i	−0.370315	+	0.641405i
$583$	4.85234			0.200963
$584$	−1.09693			−0.0453912
$585$	14.5241			0.600497
$586$	9.16664	−	15.8771i	0.378670	−	0.655876i
$587$	8.95946			0.369796			0.184898	−	0.982758i	$-0.440804\pi$
$587$	8.95946			0.369796			0.184898	+	0.982758i	$0.440804\pi$
$588$	−15.6993			−0.647430
$589$	−1.35073	+	2.33954i	−0.0556560	+	0.0963990i
$590$	7.25796	−	12.5712i	0.298805	−	0.517546i
$591$	2.70364	−	4.68284i	0.111213	−	0.192626i
$592$	0.136424	−	0.236293i	0.00560699	−	0.00971159i
$593$	−8.84225			−0.363108			−0.181554	−	0.983381i	$-0.558113\pi$
$593$	−8.84225			−0.363108			−0.181554	+	0.983381i	$0.558113\pi$
$594$	−4.83980	+	8.38277i	−0.198579	+	0.343949i
$595$	−0.200844	−	0.347871i	−0.00823379	−	0.0142613i
$596$	39.6281	+	68.6378i	1.62323	+	2.81151i
$597$	3.74663			0.153339
$598$	−24.3947			−0.997572
$599$	−5.52278			−0.225655			−0.112827	−	0.993615i	$-0.535991\pi$
$599$	−5.52278			−0.225655			−0.112827	+	0.993615i	$0.535991\pi$
$600$	7.17298	−	12.4240i	0.292836	−	0.507206i
$601$	18.4350	+	31.9304i	0.751979	+	1.30247i	0.946862	+	0.321640i	$0.104234\pi$
$601$	18.4350	+	31.9304i	0.751979	+	1.30247i	−0.194883	+	0.980827i	$0.562433\pi$
$602$	−0.992570	+	1.71918i	−0.0404541	+	0.0700686i
$603$	−15.9255	+	27.5838i	−0.648536	+	1.12330i
$604$	11.4494	+	19.8310i	0.465870	+	0.806911i
$605$	4.55222	−	7.88468i	0.185074	−	0.320558i
$606$	−9.49169			−0.385574
$607$	30.0238			1.21863			0.609315	−	0.792928i	$-0.291444\pi$
$607$	30.0238			1.21863			0.609315	+	0.792928i	$0.291444\pi$
$608$	13.2227			0.536251
$609$	0.149952	+	0.259724i	0.00607635	+	0.0105246i
$610$	10.0295	+	17.3716i	0.406082	+	0.703355i
$611$	−21.8689	+	37.8780i	−0.884720	+	1.53238i
$612$	−66.3230			−2.68095
$613$	16.4478	−	28.4884i	0.664321	−	1.15064i	−0.315148	−	0.949042i	$-0.602054\pi$
$613$	16.4478	−	28.4884i	0.664321	−	1.15064i	0.979469	−	0.201595i	$-0.0646125\pi$
$614$	39.5579	−	68.5163i	1.59643	−	2.76509i
$615$	−1.93008	+	3.34300i	−0.0778283	+	0.134803i
$616$	0.488577	−	0.846240i	0.0196853	−	0.0340960i
$617$	2.00326			0.0806481			0.0403240	−	0.999187i	$-0.487161\pi$
$617$	2.00326			0.0806481			0.0403240	+	0.999187i	$0.487161\pi$
$618$	−12.0954			−0.486550
$619$	−4.30219	+	7.45161i	−0.172920	+	0.299506i	−0.939439	−	0.342715i	$-0.888653\pi$
$619$	−4.30219	+	7.45161i	−0.172920	+	0.299506i	0.766520	+	0.642221i	$0.221987\pi$
$620$	14.9221			0.599285
$621$	−4.61569			−0.185221
$622$	−79.4646			−3.18624
$623$	−0.496041	+	0.859168i	−0.0198735	+	0.0344218i
$624$	13.0498	−	22.6030i	0.522411	−	0.904843i
$625$	10.6908			0.427632
$626$	−20.7281	+	35.9022i	−0.828463	+	1.43494i
$627$	0.290958	+	0.503954i	0.0116197	+	0.0201260i
$628$	20.6104	+	35.6983i	0.822446	+	1.42452i
$629$	0.0555136	+	0.0961524i	0.00221347	+	0.00383385i
$630$	−0.639976			−0.0254973
$631$	−3.22475	+	5.58542i	−0.128375	+	0.222352i	−0.923047	−	0.384687i	$-0.874309\pi$
$631$	−3.22475	+	5.58542i	−0.128375	+	0.222352i	0.794672	+	0.607039i	$0.207643\pi$
$632$	−106.230			−4.22562
$633$	4.36024	−	7.55216i	0.173304	−	0.300171i
$634$	−27.2194	−	47.1453i	−1.08102	−	1.87238i
$635$	−9.97915	−	17.2844i	−0.396011	−	0.685911i
$636$	−7.69904			−0.305287
$637$	−17.9037	−	31.0101i	−0.709370	−	1.22867i
$638$	29.9335			1.18508
$639$	−2.56196	+	4.43745i	−0.101350	+	0.175543i
$640$	−5.62823	−	9.74837i	−0.222475	−	0.385338i
$641$	−8.55599	−	14.8194i	−0.337941	−	0.585331i	0.646104	−	0.763249i	$-0.276397\pi$
$641$	−8.55599	−	14.8194i	−0.337941	−	0.585331i	−0.984045	+	0.177918i	$0.943064\pi$
$642$	−3.67493	+	6.36517i	−0.145038	+	0.251213i
$643$	3.89377	+	6.74420i	0.153555	+	0.265965i	0.932532	−	0.361087i	$-0.117594\pi$
$643$	3.89377	+	6.74420i	0.153555	+	0.265965i	−0.778977	+	0.627053i	$0.784261\pi$
$644$	0.770429			0.0303591
$645$	−1.97469	+	3.42026i	−0.0777532	+	0.134673i
$646$	−5.75823	+	9.97354i	−0.226554	+	0.392404i
$647$	29.3154			1.15251			0.576254	−	0.817271i	$-0.304514\pi$
$647$	29.3154			1.15251			0.576254	+	0.817271i	$0.304514\pi$
$648$	−29.5527	+	51.1868i	−1.16094	+	2.01081i
$649$	−3.81964	+	6.61582i	−0.149934	+	0.259693i
$650$	54.1017			2.12204
$651$	−0.0548870	−	0.0950670i	−0.00215119	−	0.00372597i
$652$	22.0429	+	38.1795i	0.863268	+	1.49522i
$653$	−4.98054	+	8.62655i	−0.194904	+	0.337583i	−0.946869	−	0.321620i	$-0.895773\pi$
$653$	−4.98054	+	8.62655i	−0.194904	+	0.337583i	0.751965	+	0.659203i	$0.229106\pi$
$654$	−3.49702	+	6.05701i	−0.136744	+	0.236848i
$655$	−1.50831	+	2.61246i	−0.0589344	+	0.102077i
$656$	−49.4007	−	85.5645i	−1.92877	−	3.34073i
$657$	−0.189042	−	0.327430i	−0.00737521	−	0.0127742i
$658$	0.963610	−	1.66902i	0.0375654	−	0.0650652i
$659$	39.0376			1.52069			0.760345	−	0.649520i	$-0.225030\pi$
$659$	39.0376			1.52069			0.760345	+	0.649520i	$0.225030\pi$
$660$	1.60716	−	2.78369i	0.0625588	−	0.108355i
$661$	0.859104	−	1.48801i	0.0334153	−	0.0578769i	−0.848834	−	0.528659i	$-0.822695\pi$
$661$	0.859104	−	1.48801i	0.0334153	−	0.0578769i	0.882249	+	0.470782i	$0.156028\pi$
$662$	88.2484			3.42987
$663$	5.31023	+	9.19760i	0.206232	+	0.357205i
$664$	−45.7746	−	79.2839i	−1.77640	−	3.07681i
$665$	−0.0398246	+	0.0689782i	−0.00154433	+	0.00267486i
$666$	0.176891			0.00685438
$667$	7.13685	+	12.3614i	0.276340	+	0.478635i
$668$	18.0813	+	31.3176i	0.699585	+	1.21172i
$669$	1.15686	+	2.00374i	0.0447268	+	0.0774691i
$670$	15.2749	−	26.4569i	0.590120	−	1.02212i
$671$	−5.27821	−	9.14213i	−0.203763	−	0.352928i
$672$	−0.268651	+	0.465318i	−0.0103635	+	0.0179500i
$673$	−7.24992	−	12.5572i	−0.279464	−	0.484045i	0.691788	−	0.722101i	$-0.256823\pi$
$673$	−7.24992	−	12.5572i	−0.279464	−	0.484045i	−0.971252	+	0.238055i	$0.923490\pi$
$674$	16.6781	−	28.8872i	0.642415	−	1.11269i
$675$	10.2365			0.394004
$676$	66.9060			2.57331
$677$	−16.0437	−	27.7885i	−0.616609	−	1.06800i	−0.990100	−	0.140364i	$-0.955173\pi$
$677$	−16.0437	−	27.7885i	−0.616609	−	1.06800i	0.373491	−	0.927634i	$-0.378161\pi$
$678$	11.1536	+	19.3186i	0.428351	+	0.741926i
$679$	1.28704			0.0493921
$680$	38.4733			1.47538
$681$	3.38622	+	5.86510i	0.129760	+	0.224751i
$682$	−10.9566			−0.419549
$683$	20.7314			0.793266			0.396633	−	0.917977i	$-0.370179\pi$
$683$	20.7314			0.793266			0.396633	+	0.917977i	$0.370179\pi$
$684$	6.57548	+	11.3891i	0.251420	+	0.435472i
$685$	8.39448	−	14.5397i	0.320737	−	0.555532i
$686$	1.57860	+	2.73421i	0.0602711	+	0.104393i
$687$	3.89835			0.148731
$688$	−50.5424	−	87.5420i	−1.92691	−	3.33751i
$689$	−8.78007	−	15.2075i	−0.334494	−	0.579360i
$690$	2.13849			0.0814109
$691$	−18.8463	+	32.6427i	−0.716947	+	1.24179i	0.245257	+	0.969458i	$0.421128\pi$
$691$	−18.8463	+	32.6427i	−0.716947	+	1.24179i	−0.962204	+	0.272330i	$0.912206\pi$
$692$	−35.5495	−	61.5736i	−1.35139	−	2.34068i
$693$	0.336800			0.0127940
$694$	26.9993	+	46.7642i	1.02488	+	1.77515i
$695$	−23.1934			−0.879776
$696$	−28.7245			−1.08880
$697$	40.2043			1.52284
$698$	56.8039			2.15006
$699$	0.248713	−	0.430784i	0.00940721	−	0.0162938i
$700$	−1.70863			−0.0645802
$701$	−4.17264	+	7.22722i	−0.157598	+	0.272968i	−0.934002	−	0.357268i	$-0.883708\pi$
$701$	−4.17264	+	7.22722i	−0.157598	+	0.272968i	0.776404	+	0.630236i	$0.217042\pi$
$702$	35.0295			1.32210
$703$	0.0110076	−	0.0190657i	0.000415160	−	0.000719077i
$704$	10.5573	+	18.2858i	0.397893	+	0.689172i
$705$	1.91707	−	3.32047i	0.0722011	−	0.125056i
$706$	−58.9223			−2.21757
$707$	0.341855	+	0.592111i	0.0128568	+	0.0222686i
$708$	6.06049	−	10.4971i	0.227767	−	0.394504i
$709$	−13.6643	+	23.6672i	−0.513172	+	0.888840i	0.486711	+	0.873563i	$0.338196\pi$
$709$	−13.6643	+	23.6672i	−0.513172	+	0.888840i	−0.999883	+	0.0152769i	$0.995137\pi$
$710$	2.45729	−	4.25616i	0.0922206	−	0.159731i
$711$	−18.3074	−	31.7094i	−0.686582	−	1.18920i
$712$	−47.5103	−	82.2903i	−1.78053	−	3.08396i
$713$	−2.61231	−	4.52465i	−0.0978317	−	0.169449i
$714$	−0.233985	−	0.405274i	−0.00875668	−	0.0151670i
$715$	7.33131			0.274176
$716$	−45.4147	−	78.6606i	−1.69723	−	2.93969i
$717$	−10.1728			−0.379912
$718$	47.9880			1.79090
$719$	−9.05015	+	15.6753i	−0.337514	+	0.584591i	−0.983964	−	0.178365i	$-0.942919\pi$
$719$	−9.05015	+	15.6753i	−0.337514	+	0.584591i	0.646451	+	0.762956i	$0.276253\pi$
$720$	16.2940	−	28.2221i	0.607243	−	1.05178i
$721$	0.435633	+	0.754539i	0.0162238	+	0.0281005i
$722$	−48.2032			−1.79394
$723$	−0.375090	+	6.87676i	−0.0139498	+	0.255749i
$724$	10.0175			0.372296
$725$	−15.8279	−	27.4147i	−0.587833	−	1.01816i
$726$	5.30340	−	9.18575i	0.196828	−	0.340915i
$727$	24.4888	−	42.4158i	0.908239	−	1.57312i	0.0917298	−	0.995784i	$-0.470760\pi$
$727$	24.4888	−	42.4158i	0.908239	−	1.57312i	0.816509	−	0.577332i	$-0.195906\pi$
$728$	−3.53622			−0.131061
$729$	−16.9458			−0.627622
$730$	0.181318	+	0.314053i	0.00671089	+	0.0116236i
$731$	41.1334			1.52137
$732$	8.37475	+	14.5055i	0.309540	+	0.536139i
$733$	−0.949151	−	1.64398i	−0.0350577	−	0.0607217i	0.847964	−	0.530054i	$-0.177828\pi$
$733$	−0.949151	−	1.64398i	−0.0350577	−	0.0607217i	−0.883022	+	0.469332i	$0.844495\pi$
$734$	27.2609	+	47.2173i	1.00622	+	1.74282i
$735$	1.56948	+	2.71841i	0.0578910	+	0.100270i
$736$	−12.7863	+	22.1465i	−0.471309	+	0.816331i
$737$	−8.03870	+	13.9234i	−0.296109	+	0.512876i
$738$	32.0271	−	55.4726i	1.17893	−	2.04197i
$739$	−8.24591	−	14.2823i	−0.303331	−	0.525384i	0.673558	−	0.739135i	$-0.264765\pi$
$739$	−8.24591	−	14.2823i	−0.303331	−	0.525384i	−0.976888	+	0.213751i	$0.931432\pi$
$740$	−0.121605			−0.00447030
$741$	1.05295	−	1.82376i	0.0386810	−	0.0669975i
$742$	0.386877	+	0.670090i	0.0142027	+	0.0245998i
$743$	7.70708	−	13.3491i	0.282745	−	0.489729i	−0.689315	−	0.724462i	$-0.742088\pi$
$743$	7.70708	−	13.3491i	0.282745	−	0.489729i	0.972060	+	0.234733i	$0.0754216\pi$
$744$	10.5140			0.385464
$745$	7.92330	−	13.7236i	0.290287	−	0.502793i
$746$	−16.9469			−0.620469
$747$	15.7773	−	27.3271i	0.577262	−	0.999847i
$748$	−33.4778			−1.22407
$749$	0.529430			0.0193449
$750$	−10.7065			−0.390948
$751$	0.755027			0.0275513			0.0137757	−	0.999905i	$-0.495615\pi$
$751$	0.755027			0.0275513			0.0137757	+	0.999905i	$0.495615\pi$
$752$	49.0678	+	84.9879i	1.78932	+	3.09919i
$753$	−5.45353			−0.198738
$754$	−54.1631	−	93.8133i	−1.97251	−	3.41648i
$755$	2.28922	−	3.96504i	0.0833131	−	0.144302i
$756$	−1.10630			−0.0402356
$757$	20.8362	+	36.0893i	0.757304	+	1.31169i	0.944221	+	0.329313i	$0.106817\pi$
$757$	20.8362	+	36.0893i	0.757304	+	1.31169i	−0.186917	+	0.982376i	$0.559849\pi$
$758$	13.0286	+	22.5663i	0.473221	+	0.819644i
$759$	−1.12542			−0.0408502
$760$	−3.81436	−	6.60667i	−0.138361	−	0.239649i
$761$	2.12731	−	3.68461i	0.0771150	−	0.133567i	−0.824889	−	0.565295i	$-0.808762\pi$
$761$	2.12731	−	3.68461i	0.0771150	−	0.133567i	0.902004	+	0.431728i	$0.142096\pi$
$762$	−11.6258	−	20.1365i	−0.421160	−	0.729470i
$763$	0.503798			0.0182387
$764$	3.81441			0.138000
$765$	6.63037	+	11.4841i	0.239722	+	0.415210i
$766$	−79.8727			−2.88592
$767$	27.6458			0.998232
$768$	0.0630465	+	0.109200i	0.00227499	+	0.00394040i
$769$	2.87623	+	4.98177i	0.103719	+	0.179647i	0.913214	−	0.407480i	$-0.133592\pi$
$769$	2.87623	+	4.98177i	0.103719	+	0.179647i	−0.809495	+	0.587127i	$0.800259\pi$
$770$	−0.323040			−0.0116416
$771$	7.49193			0.269815
$772$	−21.1761	+	36.6781i	−0.762145	+	1.32007i
$773$	8.31363	+	14.3996i	0.299020	+	0.517919i	0.975912	−	0.218164i	$-0.0700068\pi$
$773$	8.31363	+	14.3996i	0.299020	+	0.517919i	−0.676892	+	0.736083i	$0.736673\pi$
$774$	32.7673	−	56.7546i	1.17780	−	2.04000i
$775$	5.79349	+	10.0346i	0.208108	+	0.360454i
$776$	−61.6358	+	106.756i	−2.21260	+	3.83233i
$777$	0.000447293	0	0.000774735i	1.60466e−5	0	2.77935e-5i
$778$	33.7510	+	58.4585i	1.21003	+	2.09584i
$779$	−3.98598	−	6.90392i	−0.142813	−	0.247359i
$780$	−11.6323			−0.416504
$781$	−1.29320	+	2.23989i	−0.0462743	+	0.0801494i
$782$	−11.1364	−	19.2888i	−0.398236	−	0.689765i
$783$	−10.2481	−	17.7503i	−0.366239	−	0.634344i
$784$	−80.3420			−2.86936
$785$	4.12089	−	7.13759i	0.147081	−	0.254751i
$786$	−1.75720	+	3.04355i	−0.0626771	+	0.108560i
$787$	22.1057			0.787982			0.393991	−	0.919114i	$-0.371094\pi$
$787$	22.1057			0.787982			0.393991	+	0.919114i	$0.371094\pi$
$788$	30.8417	−	53.4195i	1.09869	−	1.90299i
$789$	−4.42006	−	7.65576i	−0.157358	−	0.272552i
$790$	17.5595	+	30.4139i	0.624739	+	1.08208i
$791$	0.803422	−	1.39157i	0.0285664	−	0.0494785i
$792$	−16.1292	+	27.9366i	−0.573126	+	0.992684i
$793$	−19.1013	+	33.0845i	−0.678308	+	1.17486i
$794$	12.0320	+	20.8400i	0.426999	+	0.739584i
$795$	0.769679	+	1.33312i	0.0272977	+	0.0472810i
$796$	42.7397			1.51487
$797$	−21.4979	+	37.2354i	−0.761494	+	1.31895i	0.180586	+	0.983559i	$0.442201\pi$
$797$	−21.4979	+	37.2354i	−0.761494	+	1.31895i	−0.942080	+	0.335387i	$0.891133\pi$
$798$	−0.0463961	+	0.0803604i	−0.00164240	+	0.00284473i
$799$	−39.9333			−1.41274
$800$	28.3570	−	49.1158i	1.00257	−	1.73651i
$801$	16.3756	−	28.3634i	0.578603	−	1.00217i
$802$	94.8765			3.35021
$803$	−0.0954223	−	0.165276i	−0.00336738	−	0.00583247i
$804$	12.7547	−	22.0918i	0.449824	−	0.779119i
$805$	−0.0770204	−	0.133403i	−0.00271461	−	0.00470185i
$806$	19.8254	+	34.3386i	0.698319	+	1.20952i
$807$	−4.04212	+	7.00115i	−0.142289	+	0.246452i
$808$	−65.4852			−2.30376
$809$	−0.936329	−	1.62177i	−0.0329196	−	0.0570184i	0.849096	−	0.528238i	$-0.177147\pi$
$809$	−0.936329	−	1.62177i	−0.0329196	−	0.0570184i	−0.882016	+	0.471220i	$0.843814\pi$
$810$	19.5398			0.686559
$811$	−18.8566	−	32.6606i	−0.662146	−	1.14687i	−0.980051	−	0.198748i	$-0.936313\pi$
$811$	−18.8566	−	32.6606i	−0.662146	−	1.14687i	0.317905	−	0.948123i	$-0.397021\pi$
$812$	1.71057	+	2.96280i	0.0600293	+	0.103974i
$813$	−5.75266	+	9.96389i	−0.201754	+	0.349449i
$814$	0.0892890			0.00312958
$815$	4.40730	−	7.63367i	0.154381	−	0.267396i
$816$	23.8294			0.834197
$817$	−4.07810	−	7.06348i	−0.142675	−	0.247120i
$818$	3.81991	+	6.61627i	0.133560	+	0.231333i
$819$	−0.609422	−	1.05555i	−0.0212949	−	0.0368839i
$820$	−22.0174	+	38.1352i	−0.768879	+	1.33174i
$821$	−18.2828			−0.638073			−0.319036	−	0.947742i	$-0.603359\pi$
$821$	−18.2828			−0.638073			−0.319036	+	0.947742i	$0.603359\pi$
$822$	9.77968	−	16.9389i	0.341105	−	0.590812i
$823$	13.6292	−	23.6065i	0.475084	−	0.822870i	−0.524509	−	0.851405i	$-0.675751\pi$
$823$	13.6292	−	23.6065i	0.475084	−	0.822870i	0.999593	+	0.0285351i	$0.00908424\pi$
$824$	−83.4491			−2.90709
$825$	2.49592			0.0868969
$826$	−1.21816			−0.0423852
$827$	2.44392	−	4.23299i	0.0849834	−	0.147196i	−0.820401	−	0.571789i	$-0.806250\pi$
$827$	2.44392	−	4.23299i	0.0849834	−	0.147196i	0.905384	+	0.424593i	$0.139583\pi$
$828$	−25.4339			−0.883888
$829$	−21.0242			−0.730199			−0.365100	−	0.930968i	$-0.618965\pi$
$829$	−21.0242			−0.730199			−0.365100	+	0.930968i	$0.618965\pi$
$830$	−15.1327	+	26.2107i	−0.525265	+	0.909786i
$831$	2.32287	−	4.02333i	0.0805795	−	0.139568i
$832$	38.2058	−	66.1744i	1.32455	−	2.29419i
$833$	16.3464	−	28.3128i	0.566368	−	0.980979i
$834$	−27.0206			−0.935647
$835$	3.61520	−	6.26170i	0.125109	−	0.216695i
$836$	3.31910	+	5.74885i	0.114793	+	0.198828i
$837$	3.75114	+	6.49716i	0.129658	+	0.224575i
$838$	63.8070			2.20418
$839$	4.64305			0.160296			0.0801479	−	0.996783i	$-0.474461\pi$
$839$	4.64305			0.160296			0.0801479	+	0.996783i	$0.474461\pi$
$840$	0.309993			0.0106958
$841$	−17.1917	+	29.7769i	−0.592818	+	1.02679i
$842$	−22.0545	−	38.1996i	−0.760049	−	1.31644i
$843$	−0.703119	+	1.21784i	−0.0242167	+	0.0419446i
$844$	49.7394	−	86.1511i	1.71210	−	2.96544i
$845$	−6.68865	−	11.5851i	−0.230097	−	0.398539i
$846$	−31.8113	+	55.0987i	−1.09369	+	1.89433i
$847$	−0.764035			−0.0262525
$848$	−39.4001			−1.35301
$849$	8.94593			0.307023
$850$	24.6979	+	42.7780i	0.847131	+	1.46727i
$851$	0.0212886	+	0.0368730i	0.000729764	+	0.00126399i
$852$	2.05187	−	3.55395i	0.0702960	−	0.121756i
$853$	−36.2000			−1.23946			−0.619732	−	0.784814i	$-0.712759\pi$
$853$	−36.2000			−1.23946			−0.619732	+	0.784814i	$0.712759\pi$
$854$	0.841663	−	1.45780i	0.0288011	−	0.0498850i
$855$	1.31471	−	2.27715i	0.0449622	−	0.0778769i
$856$	−25.3542	+	43.9147i	−0.866587	+	1.50097i
$857$	−6.44208	+	11.1580i	−0.220057	+	0.381151i	−0.954825	−	0.297168i	$-0.903958\pi$
$857$	−6.44208	+	11.1580i	−0.220057	+	0.381151i	0.734768	+	0.678319i	$0.237291\pi$
$858$	8.54107			0.291587
$859$	−51.0202			−1.74079			−0.870394	−	0.492356i	$-0.836136\pi$
$859$	−51.0202			−1.74079			−0.870394	+	0.492356i	$0.836136\pi$
$860$	−22.5262	+	39.0165i	−0.768137	+	1.33045i
$861$	0.323940			0.0110399
$862$	−95.2370			−3.24378
$863$	22.2076			0.755954			0.377977	−	0.925815i	$-0.376620\pi$
$863$	22.2076			0.755954			0.377977	+	0.925815i	$0.376620\pi$
$864$	18.3604	−	31.8012i	0.624635	−	1.08190i
$865$	−7.10784	+	12.3111i	−0.241674	+	0.418591i
$866$	52.1331			1.77155
$867$	−1.07748	+	1.86625i	−0.0365932	+	0.0633813i
$868$	−0.626122	−	1.08448i	−0.0212520	−	0.0368095i
$869$	−9.24103	−	16.0059i	−0.313480	−	0.542964i
$870$	4.74806	+	8.22388i	0.160974	+	0.278815i
$871$	58.1825			1.97144
$872$	−24.1267	+	41.7886i	−0.817033	+	1.41514i
$873$	−42.4885			−1.43802
$874$	−2.20819	+	3.82470i	−0.0746932	+	0.129372i
$875$	0.385610	+	0.667896i	0.0130360	+	0.0225790i
$876$	0.151403	+	0.262238i	0.00511544	+	0.00886020i
$877$	0.641664			0.0216675			0.0108337	−	0.999941i	$-0.496551\pi$
$877$	0.641664			0.0216675			0.0108337	+	0.999941i	$0.496551\pi$
$878$	−20.0746	−	34.7703i	−0.677486	−	1.17344i
$879$	−3.06081			−0.103239
$880$	8.22473	−	14.2456i	0.277256	−	0.480221i
$881$	11.2389	+	19.4663i	0.378648	+	0.655837i	0.990866	−	0.134852i	$-0.0430558\pi$
$881$	11.2389	+	19.4663i	0.378648	+	0.655837i	−0.612218	+	0.790689i	$0.709722\pi$
$882$	−26.0434	−	45.1084i	−0.876926	−	1.51888i
$883$	6.39656	−	11.0792i	0.215261	−	0.372844i	−0.738092	−	0.674700i	$-0.764273\pi$
$883$	6.39656	−	11.0792i	0.215261	−	0.372844i	0.953353	+	0.301856i	$0.0976063\pi$
$884$	60.5764	+	104.921i	2.03741	+	3.52889i
$885$	−2.42349			−0.0814647
$886$	−13.0247	+	22.5594i	−0.437572	+	0.757897i
$887$	−22.8369	+	39.5547i	−0.766789	+	1.32812i	0.172506	+	0.985008i	$0.444814\pi$
$887$	−22.8369	+	39.5547i	−0.766789	+	1.32812i	−0.939295	+	0.343109i	$0.888520\pi$
$888$	−0.0856827			−0.00287532
$889$	−0.837439	+	1.45049i	−0.0280868	+	0.0486478i
$890$	−15.7066	+	27.2046i	−0.526486	+	0.911900i
$891$	−10.2832			−0.344501
$892$	13.1969	+	22.8576i	0.441864	+	0.765331i
$893$	3.95912	+	6.85739i	0.132487	+	0.229474i
$894$	9.23075	−	15.9881i	0.308722	−	0.534723i
$895$	−9.08030	+	15.7275i	−0.303521	+	0.525714i
$896$	−0.472314	+	0.818072i	−0.0157789	+	0.0273299i
$897$	2.03639	+	3.52714i	0.0679932	+	0.117768i
$898$	54.0611	+	93.6365i	1.80404	+	3.12469i
$899$	11.6001	−	20.0920i	0.386886	−	0.670107i
$900$	56.4064			1.88021
$901$	8.01635	−	13.8847i	0.267063	−	0.462567i
$902$	16.1663	−	28.0008i	0.538279	−	0.932326i
$903$	0.331427			0.0110292
$904$	76.9511	+	133.283i	2.55935	+	4.43293i
$905$	−1.00145	−	1.73457i	−0.0332894	−	0.0576590i
$906$	2.66696	−	4.61932i	0.0886040	−	0.153467i
$907$	14.6719			0.487172			0.243586	−	0.969879i	$-0.421676\pi$
$907$	14.6719			0.487172			0.243586	+	0.969879i	$0.421676\pi$
$908$	38.6282	+	66.9061i	1.28192	+	2.22036i
$909$	−11.2855	−	19.5471i	−0.374318	−	0.648337i
$910$	0.584525	+	1.01243i	0.0193768	+	0.0335616i
$911$	18.1045	−	31.3579i	0.599829	−	1.03893i	−0.393016	−	0.919531i	$-0.628568\pi$
$911$	18.1045	−	31.3579i	0.599829	−	1.03893i	0.992846	−	0.119403i	$-0.0380982\pi$
$912$	−2.36253	−	4.09202i	−0.0782311	−	0.135500i
$913$	7.96390	−	13.7939i	0.263567	−	0.456511i
$914$	29.8490	+	51.7000i	0.987317	+	1.71008i
$915$	1.67446	−	2.90025i	0.0553560	−	0.0958794i
$916$	44.4704			1.46934
$917$	0.253151			0.00835978
$918$	15.9912	+	27.6976i	0.527790	+	0.914159i
$919$	−5.01199	−	8.68103i	−0.165330	−	0.286361i	0.771442	−	0.636299i	$-0.219536\pi$
$919$	−5.01199	−	8.68103i	−0.165330	−	0.286361i	−0.936773	+	0.349939i	$0.886202\pi$
$920$	14.7539			0.486422
$921$	−13.2087			−0.435241
$922$	3.24362	+	5.61812i	0.106823	+	0.185023i
$923$	9.35991			0.308085
$924$	−0.269743			−0.00887389
$925$	−0.0472132	−	0.0817757i	−0.00155236	−	0.00268877i
$926$	−46.1660	+	79.9619i	−1.51711	+	2.62771i
$927$	−14.3814	−	24.9093i	−0.472347	−	0.818128i
$928$	−113.557			−3.72769
$929$	3.23054	+	5.59545i	0.105990	+	0.183581i	0.914142	−	0.405393i	$-0.132865\pi$
$929$	3.23054	+	5.59545i	0.105990	+	0.183581i	−0.808152	+	0.588974i	$0.799532\pi$
$930$	−1.73793	−	3.01019i	−0.0569891	−	0.0987081i
$931$	−6.48253			−0.212456
$932$	2.83719	−	4.91416i	0.0929354	−	0.160969i
$933$	6.63347	+	11.4895i	0.217170	+	0.376149i
$934$	−42.2292			−1.38178
$935$	3.34681	+	5.79684i	0.109452	+	0.189577i
$936$	116.740			3.81576
$937$	−45.2276			−1.47752			−0.738760	−	0.673968i	$-0.764589\pi$
$937$	−45.2276			−1.47752			−0.738760	+	0.673968i	$0.764589\pi$
$938$	−2.56370			−0.0837078
$939$	6.92129			0.225868
$940$	21.8690	−	37.8782i	0.713287	−	1.23545i
$941$	35.4626			1.15605			0.578024	−	0.816019i	$-0.303824\pi$
$941$	35.4626			1.15605			0.578024	+	0.816019i	$0.303824\pi$
$942$	4.80089	−	8.31538i	0.156421	−	0.270930i
$943$	15.4177			0.502070
$944$	31.0148	−	53.7192i	1.00945	−	1.74841i
$945$	0.110597	+	0.191560i	0.00359773	+	0.00623145i
$946$	16.5399	−	28.6480i	0.537759	−	0.931426i
$947$	−0.746658			−0.0242631			−0.0121316	−	0.999926i	$-0.503862\pi$
$947$	−0.746658			−0.0242631			−0.0121316	+	0.999926i	$0.503862\pi$
$948$	14.6624	+	25.3960i	0.476213	+	0.824825i
$949$	−0.345324	+	0.598118i	−0.0112097	+	0.0194157i
$950$	4.89726	−	8.48230i	0.158888	−	0.275202i
$951$	−4.54438	+	7.87110i	−0.147362	+	0.255238i
$952$	−1.61432	−	2.79608i	−0.0523203	−	0.0906214i
$953$	−18.8116	−	32.5826i	−0.609367	−	1.05545i	−0.991345	−	0.131283i	$-0.958090\pi$
$953$	−18.8116	−	32.5826i	−0.609367	−	1.05545i	0.381978	−	0.924172i	$-0.375243\pi$
$954$	−12.7718	−	22.1214i	−0.413503	−	0.716207i
$955$	−0.381329	−	0.660482i	−0.0123395	−	0.0213727i
$956$	−116.047			−3.75322
$957$	−2.49876	−	4.32797i	−0.0807734	−	0.139904i
$958$	−4.05761			−0.131095
$959$	−1.40891			−0.0454961
$960$	−3.34920	+	5.80099i	−0.108095	+	0.187226i
$961$	11.2540	−	19.4925i	0.363032	−	0.628790i
$962$	−0.161564	−	0.279837i	−0.00520903	−	0.00902231i
$963$	−17.4778			−0.563216
$964$	−4.27884	+	78.4465i	−0.137812	+	2.52659i
$965$	8.46798			0.272594
$966$	−0.0897297	−	0.155416i	−0.00288701	−	0.00500044i
$967$	0.689534	−	1.19431i	0.0221739	−	0.0384064i	−0.854726	−	0.519080i	$-0.826275\pi$
$967$	0.689534	−	1.19431i	0.0221739	−	0.0384064i	0.876899	+	0.480674i	$0.159608\pi$
$968$	36.5893	−	63.3745i	1.17602	−	2.03693i
$969$	1.92272			0.0617666
$970$	40.7527			1.30849
$971$	−2.72914	−	4.72701i	−0.0875822	−	0.151697i	0.818906	−	0.573927i	$-0.194581\pi$
$971$	−2.72914	−	4.72701i	−0.0875822	−	0.151697i	−0.906489	+	0.422230i	$0.861247\pi$
$972$	55.4018			1.77701
$973$	0.973182	+	1.68560i	0.0311988	+	0.0540379i
$974$	24.6648	+	42.7207i	0.790312	+	1.36886i
$975$	−4.51625	−	7.82237i	−0.144636	−	0.250516i
$976$	42.8581	+	74.2325i	1.37186	+	2.37612i
$977$	−11.1619	+	19.3330i	−0.357101	+	0.618517i	−0.987475	−	0.157774i	$-0.949568\pi$
$977$	−11.1619	+	19.3330i	−0.357101	+	0.618517i	0.630374	+	0.776291i	$0.282901\pi$
$978$	5.13456	−	8.89332i	0.164185	−	0.284377i
$979$	8.26589	−	14.3169i	0.264179	−	0.457572i
$980$	17.9038	+	31.0102i	0.571915	+	0.990586i
$981$	−16.6317			−0.531009
$982$	22.0133	−	38.1282i	0.702474	−	1.21672i
$983$	−15.0421	−	26.0537i	−0.479769	−	0.830984i	0.519962	−	0.854190i	$-0.325946\pi$
$983$	−15.0421	−	26.0537i	−0.479769	−	0.830984i	−0.999731	+	0.0232053i	$0.992613\pi$
$984$	−15.5134	+	26.8699i	−0.494548	+	0.856582i
$985$	−12.3331			−0.392965
$986$	49.4519	−	85.6531i	1.57487	−	2.72775i
$987$	−0.321757			−0.0102416
$988$	12.0115	−	20.8045i	0.382136	−	0.661879i
$989$	15.7740			0.501585
$990$	10.6644			0.338937
$991$	9.64148			0.306272			0.153136	−	0.988205i	$-0.451063\pi$
$991$	9.64148			0.306272			0.153136	+	0.988205i	$0.451063\pi$
$992$	41.5653			1.31970
$993$	−7.36671	−	12.7595i	−0.233775	−	0.404911i
$994$	−0.412427			−0.0130814
$995$	−4.27272	−	7.40057i	−0.135454	−	0.234614i
$996$	−12.6360	+	21.8863i	−0.400388	+	0.693493i
$997$	9.48487			0.300389			0.150194	−	0.988656i	$-0.452010\pi$
$997$	9.48487			0.300389			0.150194	+	0.988656i	$0.452010\pi$
$998$	−49.3498	−	85.4763i	−1.56214	−	2.70570i
$999$	−0.0305693	−	0.0529477i	−0.000967171	−	0.00167519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.c.a.15.1	✓	38
241.225	even	3	inner	241.2.c.a.225.1	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.c.a.15.1	✓	38	1.1	even	1	trivial
241.2.c.a.225.1	yes	38	241.225	even	3	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:	\( N \)	\(=\)	\( 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	241.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32860 - 2.30120i) q^{2} +(-0.221815 + 0.384194i) q^{3} +(-2.53035 + 4.38269i) q^{4} +1.01184 q^{5} +1.17881 q^{6} +(-0.0424564 - 0.0735367i) q^{7} +8.13288 q^{8} +(1.40160 + 2.42764i) q^{9} +O(q^{10})\)	\(q+(-1.32860 - 2.30120i) q^{2} +(-0.221815 + 0.384194i) q^{3} +(-2.53035 + 4.38269i) q^{4} +1.01184 q^{5} +1.17881 q^{6} +(-0.0424564 - 0.0735367i) q^{7} +8.13288 q^{8} +(1.40160 + 2.42764i) q^{9} +(-1.34434 - 2.32846i) q^{10} +(0.707483 + 1.22540i) q^{11} +(-1.12254 - 1.94429i) q^{12} +(2.56031 - 4.43458i) q^{13} +(-0.112815 + 0.195401i) q^{14} +(-0.224442 + 0.388745i) q^{15} +(-5.74463 - 9.94999i) q^{16} +4.67521 q^{17} +(3.72432 - 6.45071i) q^{18} +(-0.463515 - 0.802832i) q^{19} +(-2.56032 + 4.43460i) q^{20} +0.0376698 q^{21} +(1.87992 - 3.25612i) q^{22} +1.79287 q^{23} +(-1.80399 + 3.12461i) q^{24} -3.97617 q^{25} -13.6065 q^{26} -2.57447 q^{27} +0.429718 q^{28} +(3.98069 + 6.89475i) q^{29} +1.19277 q^{30} +(-1.45705 - 2.52369i) q^{31} +(-7.13174 + 12.3525i) q^{32} -0.627720 q^{33} +(-6.21148 - 10.7586i) q^{34} +(-0.0429593 - 0.0744077i) q^{35} -14.1861 q^{36} +(0.0118740 + 0.0205664i) q^{37} +(-1.23165 + 2.13328i) q^{38} +(1.13583 + 1.96731i) q^{39} +8.22921 q^{40} +8.59946 q^{41} +(-0.0500481 - 0.0866858i) q^{42} +8.79820 q^{43} -7.16071 q^{44} +(1.41820 + 2.45639i) q^{45} +(-2.38201 - 4.12575i) q^{46} -8.54150 q^{47} +5.09698 q^{48} +(3.49639 - 6.05593i) q^{49} +(5.28273 + 9.14997i) q^{50} +(-1.03703 + 1.79619i) q^{51} +(12.9569 + 22.4421i) q^{52} +(1.71465 - 2.96986i) q^{53} +(3.42043 + 5.92437i) q^{54} +(0.715862 + 1.23991i) q^{55} +(-0.345293 - 0.598065i) q^{56} +0.411258 q^{57} +(10.5775 - 18.3207i) q^{58} +(2.69946 + 4.67560i) q^{59} +(-1.13583 - 1.96732i) q^{60} -7.46055 q^{61} +(-3.87168 + 6.70594i) q^{62} +(0.119014 - 0.206137i) q^{63} +14.9224 q^{64} +(2.59063 - 4.48711i) q^{65} +(0.833988 + 1.44451i) q^{66} +(5.68120 + 9.84013i) q^{67} +(-11.8299 + 20.4900i) q^{68} +(-0.397685 + 0.688811i) q^{69} +(-0.114151 + 0.197716i) q^{70} +(0.913944 + 1.58300i) q^{71} +(11.3990 + 19.7437i) q^{72} -0.134876 q^{73} +(0.0315517 - 0.0546491i) q^{74} +(0.881973 - 1.52762i) q^{75} +4.69142 q^{76} +(0.0600743 - 0.104052i) q^{77} +(3.01812 - 5.22754i) q^{78} -13.0618 q^{79} +(-5.81267 - 10.0678i) q^{80} +(-3.63373 + 6.29381i) q^{81} +(-11.4252 - 19.7891i) q^{82} +(-5.62834 - 9.74857i) q^{83} +(-0.0953178 + 0.165095i) q^{84} +4.73058 q^{85} +(-11.6893 - 20.2464i) q^{86} -3.53190 q^{87} +(5.75387 + 9.96599i) q^{88} +(-5.84176 - 10.1182i) q^{89} +(3.76843 - 6.52711i) q^{90} -0.434806 q^{91} +(-4.53659 + 7.85760i) q^{92} +1.29278 q^{93} +(11.3482 + 19.6557i) q^{94} +(-0.469005 - 0.812341i) q^{95} +(-3.16385 - 5.47995i) q^{96} +(-7.57860 + 13.1265i) q^{97} -18.5812 q^{98} +(-1.98321 + 3.43502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + q^{2} + 2 q^{3} - 21 q^{4} - 4 q^{5} - 5 q^{7} - 12 q^{8} - 13 q^{9}+O(q^{10}) \) 38 * q + q^2 + 2 * q^3 - 21 * q^4 - 4 * q^5 - 5 * q^7 - 12 * q^8 - 13 * q^9	\( 38 q + q^{2} + 2 q^{3} - 21 q^{4} - 4 q^{5} - 5 q^{7} - 12 q^{8} - 13 q^{9} - 8 q^{10} - 4 q^{11} + 21 q^{12} - 9 q^{13} + 6 q^{14} + 4 q^{15} - 25 q^{16} - 18 q^{17} + 5 q^{18} + 3 q^{19} - 5 q^{20} + 10 q^{21} - 7 q^{22} - 10 q^{23} - 9 q^{24} + 54 q^{25} + 20 q^{26} - 4 q^{27} + 8 q^{28} + 25 q^{29} - 22 q^{30} - 8 q^{31} + 23 q^{32} - 28 q^{33} - 4 q^{34} - 7 q^{35} + 18 q^{36} + 12 q^{37} + 30 q^{38} + 20 q^{39} - 4 q^{40} - 20 q^{41} - 30 q^{42} + 12 q^{43} - 2 q^{44} - 9 q^{45} - 19 q^{46} - 42 q^{47} - 84 q^{48} + 6 q^{49} + 31 q^{50} + 11 q^{51} - 16 q^{52} + q^{53} + 42 q^{54} - 11 q^{55} - 5 q^{56} - 22 q^{57} - 2 q^{58} + 22 q^{59} + 48 q^{60} - 26 q^{61} - 44 q^{62} - q^{63} + 72 q^{64} - 19 q^{65} + 55 q^{66} + 18 q^{67} - 25 q^{68} + 3 q^{69} + 68 q^{70} - 14 q^{71} - 8 q^{72} - 38 q^{73} + 27 q^{74} + 26 q^{75} + 70 q^{76} + 17 q^{77} + 2 q^{78} + 12 q^{79} - 56 q^{80} + 5 q^{81} - 27 q^{82} + 14 q^{83} - 17 q^{84} - 50 q^{85} + 35 q^{86} + 44 q^{87} - 20 q^{88} - 32 q^{89} - 44 q^{90} + 56 q^{91} + 28 q^{92} + 10 q^{93} + 14 q^{94} + 17 q^{95} - 70 q^{96} - 35 q^{97} - 10 q^{98} - 10 q^{99}+O(q^{100}) \) 38 * q + q^2 + 2 * q^3 - 21 * q^4 - 4 * q^5 - 5 * q^7 - 12 * q^8 - 13 * q^9 - 8 * q^10 - 4 * q^11 + 21 * q^12 - 9 * q^13 + 6 * q^14 + 4 * q^15 - 25 * q^16 - 18 * q^17 + 5 * q^18 + 3 * q^19 - 5 * q^20 + 10 * q^21 - 7 * q^22 - 10 * q^23 - 9 * q^24 + 54 * q^25 + 20 * q^26 - 4 * q^27 + 8 * q^28 + 25 * q^29 - 22 * q^30 - 8 * q^31 + 23 * q^32 - 28 * q^33 - 4 * q^34 - 7 * q^35 + 18 * q^36 + 12 * q^37 + 30 * q^38 + 20 * q^39 - 4 * q^40 - 20 * q^41 - 30 * q^42 + 12 * q^43 - 2 * q^44 - 9 * q^45 - 19 * q^46 - 42 * q^47 - 84 * q^48 + 6 * q^49 + 31 * q^50 + 11 * q^51 - 16 * q^52 + q^53 + 42 * q^54 - 11 * q^55 - 5 * q^56 - 22 * q^57 - 2 * q^58 + 22 * q^59 + 48 * q^60 - 26 * q^61 - 44 * q^62 - q^63 + 72 * q^64 - 19 * q^65 + 55 * q^66 + 18 * q^67 - 25 * q^68 + 3 * q^69 + 68 * q^70 - 14 * q^71 - 8 * q^72 - 38 * q^73 + 27 * q^74 + 26 * q^75 + 70 * q^76 + 17 * q^77 + 2 * q^78 + 12 * q^79 - 56 * q^80 + 5 * q^81 - 27 * q^82 + 14 * q^83 - 17 * q^84 - 50 * q^85 + 35 * q^86 + 44 * q^87 - 20 * q^88 - 32 * q^89 - 44 * q^90 + 56 * q^91 + 28 * q^92 + 10 * q^93 + 14 * q^94 + 17 * q^95 - 70 * q^96 - 35 * q^97 - 10 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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