LMFDB - Embedded newform 241.2.c.a.225.3

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			225.3
Character	$\chi$	$=$	241.225
Dual form			241.2.c.a.15.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13508 + 1.96602i) q^{2} +(0.670299 + 1.16099i) q^{3} +(-1.57681 - 2.73112i) q^{4} -3.40659 q^{5} -3.04337 q^{6} +(-0.353709 + 0.612643i) q^{7} +2.61891 q^{8} +(0.601399 - 1.04165i) q^{9} +O(q^{10})$	\(q+(-1.13508 + 1.96602i) q^{2} +(0.670299 + 1.16099i) q^{3} +(-1.57681 - 2.73112i) q^{4} -3.40659 q^{5} -3.04337 q^{6} +(-0.353709 + 0.612643i) q^{7} +2.61891 q^{8} +(0.601399 - 1.04165i) q^{9} +(3.86675 - 6.69740i) q^{10} +(-1.78741 + 3.09589i) q^{11} +(2.11387 - 3.66133i) q^{12} +(-2.82967 - 4.90113i) q^{13} +(-0.802977 - 1.39080i) q^{14} +(-2.28343 - 3.95502i) q^{15} +(0.180949 - 0.313412i) q^{16} +3.20621 q^{17} +(1.36527 + 2.36472i) q^{18} +(-3.21719 + 5.57234i) q^{19} +(5.37155 + 9.30379i) q^{20} -0.948364 q^{21} +(-4.05771 - 7.02816i) q^{22} -8.37067 q^{23} +(1.75545 + 3.04054i) q^{24} +6.60482 q^{25} +12.8476 q^{26} +5.63426 q^{27} +2.23093 q^{28} +(-1.21440 + 2.10340i) q^{29} +10.3675 q^{30} +(-0.800079 + 1.38578i) q^{31} +(3.02970 + 5.24759i) q^{32} -4.79240 q^{33} +(-3.63930 + 6.30346i) q^{34} +(1.20494 - 2.08702i) q^{35} -3.79318 q^{36} +(1.94567 - 3.37000i) q^{37} +(-7.30354 - 12.6501i) q^{38} +(3.79345 - 6.57044i) q^{39} -8.92156 q^{40} -0.245416 q^{41} +(1.07647 - 1.86450i) q^{42} -9.80839 q^{43} +11.2737 q^{44} +(-2.04872 + 3.54848i) q^{45} +(9.50138 - 16.4569i) q^{46} -8.69381 q^{47} +0.485159 q^{48} +(3.24978 + 5.62878i) q^{49} +(-7.49700 + 12.9852i) q^{50} +(2.14912 + 3.72238i) q^{51} +(-8.92372 + 15.4563i) q^{52} +(1.54334 + 2.67314i) q^{53} +(-6.39534 + 11.0770i) q^{54} +(6.08897 - 10.5464i) q^{55} +(-0.926335 + 1.60446i) q^{56} -8.62591 q^{57} +(-2.75688 - 4.77505i) q^{58} +(-5.27133 + 9.13020i) q^{59} +(-7.20108 + 12.4726i) q^{60} +1.68866 q^{61} +(-1.81631 - 3.14594i) q^{62} +(0.425441 + 0.736886i) q^{63} -13.0320 q^{64} +(9.63951 + 16.6961i) q^{65} +(5.43975 - 9.42193i) q^{66} +(-2.15186 + 3.72713i) q^{67} +(-5.05559 - 8.75654i) q^{68} +(-5.61085 - 9.71828i) q^{69} +(2.73541 + 4.73787i) q^{70} +(0.0306693 - 0.0531208i) q^{71} +(1.57501 - 2.72800i) q^{72} -3.62513 q^{73} +(4.41699 + 7.65045i) q^{74} +(4.42721 + 7.66815i) q^{75} +20.2916 q^{76} +(-1.26445 - 2.19009i) q^{77} +(8.61173 + 14.9160i) q^{78} +2.50758 q^{79} +(-0.616417 + 1.06767i) q^{80} +(1.97244 + 3.41637i) q^{81} +(0.278566 - 0.482491i) q^{82} +(-1.26054 + 2.18333i) q^{83} +(1.49539 + 2.59010i) q^{84} -10.9222 q^{85} +(11.1333 - 19.2835i) q^{86} -3.25603 q^{87} +(-4.68108 + 8.10786i) q^{88} +(8.42547 - 14.5933i) q^{89} +(-4.65092 - 8.05562i) q^{90} +4.00352 q^{91} +(13.1990 + 22.8613i) q^{92} -2.14517 q^{93} +(9.86817 - 17.0922i) q^{94} +(10.9596 - 18.9826i) q^{95} +(-4.06160 + 7.03490i) q^{96} +(-8.69349 - 15.0576i) q^{97} -14.7550 q^{98} +(2.14990 + 3.72373i) 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 $\left(\mathbb{Z}/241\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.13508	+	1.96602i	−0.802623	+	1.39018i	0.115262	+	0.993335i	$0.463229\pi$
$2$	−1.13508	+	1.96602i	−0.802623	+	1.39018i	−0.917884	+	0.396848i	$0.870104\pi$
$3$	0.670299	+	1.16099i	0.386997	+	0.670299i	0.992044	−	0.125891i	$-0.0401790\pi$
$3$	0.670299	+	1.16099i	0.386997	+	0.670299i	−0.605047	+	0.796190i	$0.706846\pi$
$4$	−1.57681	−	2.73112i	−0.788406	−	1.36556i
$5$	−3.40659			−1.52347			−0.761736	−	0.647888i	$-0.775653\pi$
$5$	−3.40659			−1.52347			−0.761736	+	0.647888i	$0.775653\pi$
$6$	−3.04337			−1.24245
$7$	−0.353709	+	0.612643i	−0.133690	+	0.231557i	−0.925096	−	0.379733i	$-0.876016\pi$
$7$	−0.353709	+	0.612643i	−0.133690	+	0.231557i	0.791407	+	0.611290i	$0.209349\pi$
$8$	2.61891			0.925926
$9$	0.601399	−	1.04165i	0.200466	−	0.347218i
$10$	3.86675	−	6.69740i	1.22277	−	2.11790i
$11$	−1.78741	+	3.09589i	−0.538925	+	0.933445i	0.460038	+	0.887899i	$0.347836\pi$
$11$	−1.78741	+	3.09589i	−0.538925	+	0.933445i	−0.998962	+	0.0455456i	$0.985497\pi$
$12$	2.11387	−	3.66133i	0.610222	−	1.05694i
$13$	−2.82967	−	4.90113i	−0.784809	−	1.35933i	−0.929113	−	0.369796i	$-0.879428\pi$
$13$	−2.82967	−	4.90113i	−0.784809	−	1.35933i	0.144304	−	0.989533i	$-0.453906\pi$
$14$	−0.802977	−	1.39080i	−0.214605	−	0.371706i
$15$	−2.28343	−	3.95502i	−0.589579	−	1.02118i
$16$	0.180949	−	0.313412i	0.0452372	−	0.0783531i
$17$	3.20621			0.777620			0.388810	−	0.921318i	$-0.372886\pi$
$17$	3.20621			0.777620			0.388810	+	0.921318i	$0.372886\pi$
$18$	1.36527	+	2.36472i	0.321798	+	0.557370i
$19$	−3.21719	+	5.57234i	−0.738074	+	1.27838i	0.215287	+	0.976551i	$0.430931\pi$
$19$	−3.21719	+	5.57234i	−0.738074	+	1.27838i	−0.953361	+	0.301831i	$0.902402\pi$
$20$	5.37155	+	9.30379i	1.20111	+	2.08039i
$21$	−0.948364			−0.206950
$22$	−4.05771	−	7.02816i	−0.865106	−	1.49841i
$23$	−8.37067			−1.74541			−0.872703	−	0.488252i	$-0.837635\pi$
$23$	−8.37067			−1.74541			−0.872703	+	0.488252i	$0.837635\pi$
$24$	1.75545	+	3.04054i	0.358331	+	0.620647i
$25$	6.60482			1.32096
$26$	12.8476			2.51962
$27$	5.63426			1.08431
$28$	2.23093			0.421607
$29$	−1.21440	+	2.10340i	−0.225508	+	0.390591i	−0.956472	−	0.291825i	$-0.905737\pi$
$29$	−1.21440	+	2.10340i	−0.225508	+	0.390591i	0.730964	+	0.682416i	$0.239071\pi$
$30$	10.3675			1.89284
$31$	−0.800079	+	1.38578i	−0.143698	+	0.248893i	−0.928887	−	0.370364i	$-0.879233\pi$
$31$	−0.800079	+	1.38578i	−0.143698	+	0.248893i	0.785188	+	0.619257i	$0.212566\pi$
$32$	3.02970	+	5.24759i	0.535580	+	0.927651i
$33$	−4.79240			−0.834249
$34$	−3.63930	+	6.30346i	−0.624136	+	1.08103i
$35$	1.20494	−	2.08702i	0.203672	−	0.352771i
$36$	−3.79318			−0.632196
$37$	1.94567	−	3.37000i	0.319867	−	0.554025i	−0.660593	−	0.750744i	$-0.729695\pi$
$37$	1.94567	−	3.37000i	0.319867	−	0.554025i	0.980460	+	0.196719i	$0.0630286\pi$
$38$	−7.30354	−	12.6501i	−1.18479	−	2.05212i
$39$	3.79345	−	6.57044i	0.607438	−	1.05211i
$40$	−8.92156			−1.41062
$41$	−0.245416			−0.0383275			−0.0191637	−	0.999816i	$-0.506100\pi$
$41$	−0.245416			−0.0383275			−0.0191637	+	0.999816i	$0.506100\pi$
$42$	1.07647	−	1.86450i	0.166103	−	0.287698i
$43$	−9.80839			−1.49577			−0.747883	−	0.663831i	$-0.768930\pi$
$43$	−9.80839			−1.49577			−0.747883	+	0.663831i	$0.768930\pi$
$44$	11.2737			1.69957
$45$	−2.04872	+	3.54848i	−0.305405	+	0.528977i
$46$	9.50138	−	16.4569i	1.40090	−	2.42643i
$47$	−8.69381			−1.26812			−0.634061	−	0.773283i	$-0.718613\pi$
$47$	−8.69381			−1.26812			−0.634061	+	0.773283i	$0.718613\pi$
$48$	0.485159			0.0700266
$49$	3.24978	+	5.62878i	0.464254	+	0.804112i
$50$	−7.49700	+	12.9852i	−1.06024	+	1.83638i
$51$	2.14912	+	3.72238i	0.300937	+	0.521238i
$52$	−8.92372	+	15.4563i	−1.23750	+	2.14341i
$53$	1.54334	+	2.67314i	0.211994	+	0.367185i	0.952339	−	0.305043i	$-0.0986709\pi$
$53$	1.54334	+	2.67314i	0.211994	+	0.367185i	−0.740344	+	0.672228i	$0.765338\pi$
$54$	−6.39534	+	11.0770i	−0.870295	+	1.50740i
$55$	6.08897	−	10.5464i	0.821036	−	1.42208i
$56$	−0.926335	+	1.60446i	−0.123787	+	0.214405i
$57$	−8.62591			−1.14253
$58$	−2.75688	−	4.77505i	−0.361995	−	0.626994i
$59$	−5.27133	+	9.13020i	−0.686268	+	1.18865i	0.286768	+	0.958000i	$0.407419\pi$
$59$	−5.27133	+	9.13020i	−0.686268	+	1.18865i	−0.973036	+	0.230651i	$0.925914\pi$
$60$	−7.20108	+	12.4726i	−0.929656	+	1.61021i
$61$	1.68866			0.216211			0.108105	−	0.994139i	$-0.465522\pi$
$61$	1.68866			0.216211			0.108105	+	0.994139i	$0.465522\pi$
$62$	−1.81631	−	3.14594i	−0.230671	−	0.399534i
$63$	0.425441	+	0.736886i	0.0536005	+	0.0928389i
$64$	−13.0320			−1.62900
$65$	9.63951	+	16.6961i	1.19563	+	2.07090i
$66$	5.43975	−	9.42193i	0.669587	−	1.15976i
$67$	−2.15186	+	3.72713i	−0.262892	+	0.455342i	−0.967009	−	0.254742i	$-0.918009\pi$
$67$	−2.15186	+	3.72713i	−0.262892	+	0.455342i	0.704117	+	0.710083i	$0.251343\pi$
$68$	−5.05559	−	8.75654i	−0.613081	−	1.06189i
$69$	−5.61085	−	9.71828i	−0.675467	−	1.16994i
$70$	2.73541	+	4.73787i	0.326944	+	0.566284i
$71$	0.0306693	−	0.0531208i	0.00363977	−	0.00630427i	−0.864200	−	0.503149i	$-0.832175\pi$
$71$	0.0306693	−	0.0531208i	0.00363977	−	0.00630427i	0.867840	+	0.496845i	$0.165508\pi$
$72$	1.57501	−	2.72800i	0.185617	−	0.321498i
$73$	−3.62513			−0.424289			−0.212145	−	0.977238i	$-0.568045\pi$
$73$	−3.62513			−0.424289			−0.212145	+	0.977238i	$0.568045\pi$
$74$	4.41699	+	7.65045i	0.513464	+	0.889346i
$75$	4.42721	+	7.66815i	0.511210	+	0.885441i
$76$	20.2916			2.32761
$77$	−1.26445	−	2.19009i	−0.144097	−	0.249584i
$78$	8.61173	+	14.9160i	0.975087	+	1.68890i
$79$	2.50758			0.282125			0.141063	−	0.990001i	$-0.454948\pi$
$79$	2.50758			0.282125			0.141063	+	0.990001i	$0.454948\pi$
$80$	−0.616417	+	1.06767i	−0.0689175	+	0.119369i
$81$	1.97244	+	3.41637i	0.219160	+	0.379596i
$82$	0.278566	−	0.482491i	0.0307625	−	0.0532822i
$83$	−1.26054	+	2.18333i	−0.138363	+	0.239651i	−0.926877	−	0.375365i	$-0.877517\pi$
$83$	−1.26054	+	2.18333i	−0.138363	+	0.239651i	0.788514	+	0.615016i	$0.210851\pi$
$84$	1.49539	+	2.59010i	0.163161	+	0.282603i
$85$	−10.9222			−1.18468
$86$	11.1333	−	19.2835i	1.20054	−	2.07939i
$87$	−3.25603			−0.349084
$88$	−4.68108	+	8.10786i	−0.499004	+	0.864301i
$89$	8.42547	−	14.5933i	0.893098	−	1.54689i	0.0569571	−	0.998377i	$-0.481860\pi$
$89$	8.42547	−	14.5933i	0.893098	−	1.54689i	0.836141	−	0.548515i	$-0.184806\pi$
$90$	−4.65092	−	8.05562i	−0.490250	−	0.849137i
$91$	4.00352			0.419683
$92$	13.1990	+	22.8613i	1.37609	+	2.38346i
$93$	−2.14517			−0.222444
$94$	9.86817	−	17.0922i	1.01782	−	1.76292i
$95$	10.9596	−	18.9826i	1.12443	−	1.94758i
$96$	−4.06160	+	7.03490i	−0.414536	+	0.717997i
$97$	−8.69349	−	15.0576i	−0.882690	−	1.52886i	−0.848338	−	0.529454i	$-0.822397\pi$
$97$	−8.69349	−	15.0576i	−0.882690	−	1.52886i	−0.0343518	−	0.999410i	$-0.510937\pi$
$98$	−14.7550			−1.49048
$99$	2.14990	+	3.72373i	0.216073	+	0.374249i
$100$	−10.4146	−	18.0386i	−1.04146	−	1.80386i
$101$	−2.27777			−0.226647			−0.113323	−	0.993558i	$-0.536150\pi$
$101$	−2.27777			−0.226647			−0.113323	+	0.993558i	$0.536150\pi$
$102$	−9.75768			−0.966155
$103$	7.66487			0.755242			0.377621	−	0.925960i	$-0.376742\pi$
$103$	7.66487			0.755242			0.377621	+	0.925960i	$0.376742\pi$
$104$	−7.41066	−	12.8356i	−0.726675	−	1.25864i
$105$	3.23068			0.315282
$106$	−7.00726			−0.680605
$107$	4.99255	+	8.64736i	0.482648	+	0.835971i	0.999802	−	0.0199214i	$-0.00634161\pi$
$107$	4.99255	+	8.64736i	0.482648	+	0.835971i	−0.517153	+	0.855893i	$0.673008\pi$
$108$	−8.88417	−	15.3878i	−0.854880	−	1.48070i
$109$	9.11577	+	15.7890i	0.873132	+	1.51231i	0.858739	+	0.512413i	$0.171248\pi$
$109$	9.11577	+	15.7890i	0.873132	+	1.51231i	0.0143930	+	0.999896i	$0.495418\pi$
$110$	13.8229	+	23.9420i	1.31796	+	2.28278i
$111$	5.21673			0.495150
$112$	0.128006	+	0.221714i	0.0120955	+	0.0209500i
$113$	3.04789	−	5.27911i	0.286722	−	0.496616i	−0.686304	−	0.727315i	$-0.740768\pi$
$113$	3.04789	−	5.27911i	0.286722	−	0.496616i	0.973025	+	0.230699i	$0.0741012\pi$
$114$	9.79110	−	16.9587i	0.917021	−	1.58833i
$115$	28.5154			2.65907
$116$	7.65951			0.711167
$117$	−6.80704			−0.629311
$118$	−11.9668	−	20.7270i	−1.10163	−	1.90808i
$119$	−1.13407	+	1.96426i	−0.103960	+	0.180064i
$120$	−5.98011	−	10.3578i	−0.545907	−	0.945538i
$121$	−0.889677	−	1.54097i	−0.0808798	−	0.140088i
$122$	−1.91676	+	3.31993i	−0.173535	+	0.300572i
$123$	−0.164502	−	0.284926i	−0.0148326	−	0.0256909i
$124$	5.04630			0.453171
$125$	−5.46697			−0.488981
$126$	−1.93164			−0.172084
$127$	−3.65875	+	6.33714i	−0.324661	+	0.562330i	−0.981444	−	0.191750i	$-0.938584\pi$
$127$	−3.65875	+	6.33714i	−0.324661	+	0.562330i	0.656782	+	0.754080i	$0.271917\pi$
$128$	8.73296	−	15.1259i	0.771892	−	1.33696i
$129$	−6.57455	−	11.3875i	−0.578857	−	1.00261i
$130$	−43.7665			−3.83857
$131$	1.17362	+	2.03277i	0.102540	+	0.177604i	0.912730	−	0.408562i	$-0.133970\pi$
$131$	1.17362	+	2.03277i	0.102540	+	0.177604i	−0.810191	+	0.586167i	$0.800636\pi$
$132$	7.55671	+	13.0886i	0.657728	+	1.13922i
$133$	−2.27590	−	3.94198i	−0.197346	−	0.341813i
$134$	−4.88507	−	8.46118i	−0.422006	−	0.730935i
$135$	−19.1936			−1.65192
$136$	8.39679			0.720019
$137$	5.45517	+	9.44864i	0.466067	+	0.807252i	0.999249	−	0.0387490i	$-0.0123373\pi$
$137$	5.45517	+	9.44864i	0.466067	+	0.807252i	−0.533182	+	0.846001i	$0.679004\pi$
$138$	25.4750			2.16858
$139$	14.7623			1.25212			0.626061	−	0.779774i	$-0.284666\pi$
$139$	14.7623			1.25212			0.626061	+	0.779774i	$0.284666\pi$
$140$	−7.59987			−0.642306
$141$	−5.82745	−	10.0934i	−0.490760	−	0.850021i
$142$	0.0696242	+	0.120593i	0.00584273	+	0.0101199i
$143$	20.2311			1.69181
$144$	−0.217645	−	0.376972i	−0.0181371	−	0.0314143i
$145$	4.13695	−	7.16540i	0.343555	−	0.595054i
$146$	4.11481	−	7.12706i	0.340544	−	0.589840i
$147$	−4.35665	+	7.54593i	−0.359330	+	0.622378i
$148$	−12.2718			−1.00874
$149$	0.423858	+	0.734143i	0.0347238	+	0.0601434i	0.882865	−	0.469627i	$-0.155612\pi$
$149$	0.423858	+	0.734143i	0.0347238	+	0.0601434i	−0.848141	+	0.529770i	$0.822278\pi$
$150$	−20.1009			−1.64123
$151$	8.60348	+	14.9017i	0.700141	+	1.21268i	0.968416	+	0.249338i	$0.0802130\pi$
$151$	8.60348	+	14.9017i	0.700141	+	1.21268i	−0.268275	+	0.963342i	$0.586454\pi$
$152$	−8.42554	+	14.5935i	−0.683402	+	1.18369i
$153$	1.92821	−	3.33976i	0.155887	−	0.270004i
$154$	5.74100			0.462623
$155$	2.72554	−	4.72077i	0.218920	−	0.379181i
$156$	−23.9262			−1.91563
$157$	10.5864	+	18.3362i	0.844888	+	1.46339i	0.885718	+	0.464224i	$0.153667\pi$
$157$	10.5864	+	18.3362i	0.844888	+	1.46339i	−0.0408295	+	0.999166i	$0.513000\pi$
$158$	−2.84631	+	4.92995i	−0.226440	+	0.392206i
$159$	−2.06900	+	3.58361i	−0.164082	+	0.284199i
$160$	−10.3209	−	17.8764i	−0.815940	−	1.41325i
$161$	2.96078	−	5.12823i	0.233343	−	0.404161i
$162$	−8.95551			−0.703611
$163$	−0.0167235	−	0.0289659i	−0.00130988	−	0.00226878i	0.865370	−	0.501134i	$-0.167084\pi$
$163$	−0.0167235	−	0.0289659i	−0.00130988	−	0.00226878i	−0.866680	+	0.498865i	$0.833750\pi$
$164$	0.386975	+	0.670260i	0.0302176	+	0.0523385i
$165$	16.3257			1.27096
$166$	−2.86164	−	4.95650i	−0.222106	−	0.384699i
$167$	−6.27996	−	10.8772i	−0.485958	−	0.841704i	0.513912	−	0.857843i	$-0.328196\pi$
$167$	−6.27996	−	10.8772i	−0.485958	−	0.841704i	−0.999870	+	0.0161394i	$0.994862\pi$
$168$	−2.48368			−0.191620
$169$	−9.51406	+	16.4788i	−0.731851	+	1.26760i
$170$	12.3976	−	21.4733i	0.950853	−	1.64693i
$171$	3.86963	+	6.70240i	0.295918	+	0.512545i
$172$	15.4660	+	26.7879i	1.17927	+	2.04256i
$173$	−11.8055	−	20.4477i	−0.897556	−	1.55461i	−0.830609	−	0.556855i	$-0.812008\pi$
$173$	−11.8055	−	20.4477i	−0.897556	−	1.55461i	−0.0669461	−	0.997757i	$-0.521326\pi$
$174$	3.69586	−	6.40142i	0.280182	−	0.485290i
$175$	−2.33619	+	4.04640i	−0.176599	+	0.305879i
$176$	0.646859	+	1.12039i	0.0487588	+	0.0844528i
$177$	−14.1335			−1.06234
$178$	19.1272	+	33.1292i	1.43364	+	2.48314i
$179$	−7.67668	−	13.2964i	−0.573782	−	0.993819i	−0.996173	−	0.0874055i	$-0.972142\pi$
$179$	−7.67668	−	13.2964i	−0.573782	−	0.993819i	0.422391	−	0.906414i	$-0.361191\pi$
$180$	12.9218			0.963132
$181$	1.63915	−	2.83909i	0.121837	−	0.211028i	−0.798655	−	0.601789i	$-0.794455\pi$
$181$	1.63915	−	2.83909i	0.121837	−	0.211028i	0.920492	+	0.390761i	$0.127788\pi$
$182$	−4.54432	+	7.87099i	−0.336847	+	0.583437i
$183$	1.13191	+	1.96052i	0.0836729	+	0.144926i
$184$	−21.9221			−1.61612
$185$	−6.62810	+	11.4802i	−0.487308	+	0.844041i
$186$	2.43494	−	4.21743i	0.178538	−	0.309237i
$187$	−5.73082	+	9.92606i	−0.419079	+	0.725866i
$188$	13.7085	+	23.7438i	0.999796	+	1.73170i
$189$	−1.99289	+	3.45179i	−0.144962	+	0.251081i
$190$	24.8801	+	43.0936i	1.80499	+	3.12634i
$191$	6.20126	−	10.7409i	0.448707	−	0.777184i	−0.549595	−	0.835431i	$-0.685218\pi$
$191$	6.20126	−	10.7409i	0.448707	−	0.777184i	0.998302	+	0.0582475i	$0.0185512\pi$
$192$	−8.73533	−	15.1300i	−0.630418	−	1.09192i
$193$	−3.03652			−0.218573			−0.109287	−	0.994010i	$-0.534857\pi$
$193$	−3.03652			−0.218573			−0.109287	+	0.994010i	$0.534857\pi$
$194$	39.4712			2.83387
$195$	−12.9227	+	22.3828i	−0.925414	+	1.60286i
$196$	10.2486	−	17.7511i	0.732042	−	1.26793i
$197$	−1.90517			−0.135737			−0.0678687	−	0.997694i	$-0.521620\pi$
$197$	−1.90517			−0.135737			−0.0678687	+	0.997694i	$0.521620\pi$
$198$	−9.76121			−0.693699
$199$	4.89986	−	8.48680i	0.347342	−	0.601613i	−0.638435	−	0.769676i	$-0.720418\pi$
$199$	4.89986	−	8.48680i	0.347342	−	0.601613i	0.985776	+	0.168063i	$0.0537511\pi$
$200$	17.2975			1.22312
$201$	−5.76956			−0.406953
$202$	2.58545	−	4.47814i	0.181912	−	0.315081i
$203$	−0.859087	−	1.48798i	−0.0602961	−	0.104436i
$204$	6.77751	−	11.7390i	0.474521	−	0.821894i
$205$	0.836030			0.0583908
$206$	−8.70024	+	15.0693i	−0.606175	+	1.04993i
$207$	−5.03411	+	8.71934i	−0.349895	+	0.606036i
$208$	−2.04810			−0.142010
$209$	−11.5009	−	19.9201i	−0.795533	−	1.37790i
$210$	−3.66708	+	6.35157i	−0.253053	+	0.438300i
$211$	−23.6028			−1.62488			−0.812442	−	0.583042i	$-0.801862\pi$
$211$	−23.6028			−1.62488			−0.812442	+	0.583042i	$0.801862\pi$
$212$	4.86712	−	8.43009i	0.334275	−	0.578981i
$213$	0.0822303			0.00563433
$214$	−22.6678			−1.54954
$215$	33.4131			2.27876
$216$	14.7556			1.00399
$217$	−0.565991	−	0.980325i	−0.0384220	−	0.0665488i
$218$	−41.3885			−2.80318
$219$	−2.42992	−	4.20874i	−0.164199	−	0.284401i
$220$	−38.4047			−2.58924
$221$	−9.07251	−	15.7141i	−0.610283	−	1.05704i
$222$	−5.92140	+	10.2562i	−0.397418	+	0.688349i
$223$	−0.981046	−	1.69922i	−0.0656957	−	0.113788i	0.831307	−	0.555814i	$-0.187593\pi$
$223$	−0.981046	−	1.69922i	−0.0656957	−	0.113788i	−0.897002	+	0.442026i	$0.854260\pi$
$224$	−4.28653			−0.286406
$225$	3.97214	−	6.87994i	0.264809	−	0.458663i
$226$	6.91920	+	11.9844i	0.460259	+	0.797191i
$227$	−9.87868	−	17.1104i	−0.655671	−	1.13566i	−0.981725	−	0.190304i	$-0.939053\pi$
$227$	−9.87868	−	17.1104i	−0.655671	−	1.13566i	0.326054	−	0.945351i	$-0.394281\pi$
$228$	13.6015	+	23.5584i	0.900778	+	1.56019i
$229$	−8.94108	+	15.4864i	−0.590843	+	1.02337i	0.403276	+	0.915078i	$0.367872\pi$
$229$	−8.94108	+	15.4864i	−0.590843	+	1.02337i	−0.994119	+	0.108292i	$0.965462\pi$
$230$	−32.3673	+	56.0617i	−2.13423	+	3.69660i
$231$	1.69512	−	2.93603i	0.111530	−	0.193176i
$232$	−3.18040	+	5.50862i	−0.208804	+	0.361658i
$233$	4.40910			0.288850			0.144425	−	0.989516i	$-0.453867\pi$
$233$	4.40910			0.288850			0.144425	+	0.989516i	$0.453867\pi$
$234$	7.72654	−	13.3828i	0.505100	−	0.874858i
$235$	29.6162			1.93195
$236$	33.2476			2.16423
$237$	1.68083	+	2.91128i	0.109182	+	0.189108i
$238$	−2.57451	−	4.45919i	−0.166881	−	0.289046i
$239$	−3.12609	+	5.41454i	−0.202210	+	0.350237i	−0.949240	−	0.314552i	$-0.898146\pi$
$239$	−3.12609	+	5.41454i	−0.202210	+	0.350237i	0.747030	+	0.664790i	$0.231479\pi$
$240$	−1.65273			−0.106684
$241$	−15.1349	−	3.45455i	−0.974927	−	0.222527i
$241$	−15.1349	−	3.45455i	−0.974927	−	0.222527i
$242$	4.03942			0.259664
$243$	5.80714	−	10.0583i	0.372528	−	0.645238i
$244$	−2.66270	−	4.61193i	−0.170462	−	0.295248i
$245$	−11.0707	−	19.1749i	−0.707278	−	1.22504i
$246$	0.746891			0.0476200
$247$	36.4143			2.31699
$248$	−2.09534	+	3.62923i	−0.133054	+	0.230457i
$249$	−3.37976			−0.214184
$250$	6.20545	−	10.7482i	0.392467	−	0.679773i
$251$	−10.9454	+	18.9579i	−0.690865	+	1.19661i	0.280690	+	0.959798i	$0.409437\pi$
$251$	−10.9454	+	18.9579i	−0.690865	+	1.19661i	−0.971555	+	0.236814i	$0.923897\pi$
$252$	1.34168	−	2.32386i	0.0845180	−	0.146390i
$253$	14.9618	−	25.9146i	0.940642	−	1.62924i
$254$	−8.30594	−	14.3863i	−0.521161	−	0.902678i
$255$	−7.32116	−	12.6806i	−0.458469	−	0.794091i
$256$	6.79323	+	11.7662i	0.424577	+	0.735388i
$257$	−11.1626	+	19.3342i	−0.696303	+	1.20603i	0.273436	+	0.961890i	$0.411840\pi$
$257$	−11.1626	+	19.3342i	−0.696303	+	1.20603i	−0.969739	+	0.244143i	$0.921493\pi$
$258$	29.8506			1.85842
$259$	1.37641	+	2.38400i	0.0855257	+	0.148135i
$260$	30.3994	−	52.6533i	1.88529	−	3.26542i
$261$	1.46067	+	2.52996i	0.0904135	+	0.156601i
$262$	−5.32862			−0.329203
$263$	4.90257	+	8.49150i	0.302306	+	0.523609i	0.976658	−	0.214801i	$-0.0689104\pi$
$263$	4.90257	+	8.49150i	0.302306	+	0.523609i	−0.674352	+	0.738410i	$0.735577\pi$
$264$	−12.5509			−0.772453
$265$	−5.25752	−	9.10629i	−0.322967	−	0.559395i
$266$	10.3333			0.633576
$267$	22.5903			1.38251
$268$	13.5723			0.829062
$269$	−20.2946			−1.23738			−0.618690	−	0.785635i	$-0.712336\pi$
$269$	−20.2946			−1.23738			−0.618690	+	0.785635i	$0.712336\pi$
$270$	21.7863	−	37.7349i	1.32587	−	2.29647i
$271$	−4.90654			−0.298051			−0.149026	−	0.988833i	$-0.547614\pi$
$271$	−4.90654			−0.298051			−0.149026	+	0.988833i	$0.547614\pi$
$272$	0.580159	−	1.00487i	0.0351773	−	0.0609289i
$273$	2.68356	+	4.64806i	0.162416	+	0.281313i
$274$	−24.7682			−1.49630
$275$	−11.8055	+	20.4478i	−0.711901	+	1.23305i
$276$	−17.6945	+	30.6478i	−1.06508	+	1.84478i
$277$	−11.2451			−0.675650			−0.337825	−	0.941209i	$-0.609691\pi$
$277$	−11.2451			−0.675650			−0.337825	+	0.941209i	$0.609691\pi$
$278$	−16.7564	+	29.0229i	−1.00498	+	1.74068i
$279$	0.962334	+	1.66681i	0.0576134	+	0.0997894i
$280$	3.15564	−	5.46573i	0.188585	−	0.326640i
$281$	16.2880			0.971663			0.485832	−	0.874052i	$-0.338517\pi$
$281$	16.2880			0.971663			0.485832	+	0.874052i	$0.338517\pi$
$282$	26.4585			1.57558
$283$	2.01908	−	3.49716i	0.120022	−	0.207884i	−0.799754	−	0.600328i	$-0.795037\pi$
$283$	2.01908	−	3.49716i	0.120022	−	0.207884i	0.919776	+	0.392443i	$0.128370\pi$
$284$	−0.193439			−0.0114785
$285$	29.3849			1.74061
$286$	−22.9639	+	39.7747i	−1.35789	+	2.35193i
$287$	0.0868059	−	0.150352i	0.00512399	−	0.00887501i
$288$	7.28823			0.429463
$289$	−6.72022			−0.395307
$290$	9.39153	+	16.2666i	0.551490	+	0.955208i
$291$	11.6545	−	20.1861i	0.683197	−	1.18333i
$292$	5.71615	+	9.90066i	0.334512	+	0.579392i
$293$	1.70883	−	2.95978i	0.0998310	−	0.172912i	−0.811784	−	0.583958i	$-0.801503\pi$
$293$	1.70883	−	2.95978i	0.0998310	−	0.172912i	0.911615	+	0.411046i	$0.134836\pi$
$294$	−9.89028	−	17.1305i	−0.576813	−	0.999069i
$295$	17.9572	−	31.1028i	1.04551	−	1.81088i
$296$	5.09555	−	8.82575i	0.296173	−	0.512986i
$297$	−10.0707	+	17.4430i	−0.584364	+	1.01215i
$298$	−1.92445			−0.111480
$299$	23.6862	+	41.0257i	1.36981	+	2.37258i
$300$	13.9617	−	24.1825i	0.806082	−	1.39617i
$301$	3.46932	−	6.00904i	0.199968	−	0.346355i
$302$	−39.0626			−2.24780
$303$	−1.52679	−	2.64448i	−0.0877117	−	0.151921i
$304$	1.16429	+	2.01661i	0.0667767	+	0.115661i
$305$	−5.75256			−0.329391
$306$	4.37735	+	7.58179i	0.250236	+	0.433422i
$307$	9.83368	−	17.0324i	0.561237	−	0.972092i	−0.436151	−	0.899873i	$-0.643659\pi$
$307$	9.83368	−	17.0324i	0.561237	−	0.972092i	0.997389	−	0.0722185i	$-0.0230079\pi$
$308$	−3.98760	+	6.90672i	−0.227214	+	0.393547i
$309$	5.13775	+	8.89885i	0.292277	+	0.506238i
$310$	6.18741	+	10.7169i	0.351421	+	0.608679i
$311$	−13.3308	−	23.0896i	−0.755918	−	1.30929i	−0.944917	−	0.327311i	$-0.893857\pi$
$311$	−13.3308	−	23.0896i	−0.755918	−	1.30929i	0.188998	−	0.981977i	$-0.439476\pi$
$312$	9.93471	−	17.2074i	0.562442	−	0.974179i
$313$	10.7875	−	18.6845i	0.609747	−	1.05611i	−0.381535	−	0.924354i	$-0.624604\pi$
$313$	10.7875	−	18.6845i	0.609747	−	1.05611i	0.991282	−	0.131758i	$-0.0420622\pi$
$314$	−48.0657			−2.71251
$315$	−1.44930	−	2.51026i	−0.0816589	−	0.141437i
$316$	−3.95399	−	6.84851i	−0.222429	−	0.385259i
$317$	15.1171			0.849059			0.424530	−	0.905414i	$-0.360440\pi$
$317$	15.1171			0.849059			0.424530	+	0.905414i	$0.360440\pi$
$318$	−4.69696	−	8.13537i	−0.263392	−	0.456209i
$319$	−4.34125	−	7.51927i	−0.243064	−	0.420998i
$320$	44.3946			2.48173
$321$	−6.69300	+	11.5926i	−0.373567	+	0.647037i
$322$	6.72145	+	11.6419i	0.374572	+	0.648778i
$323$	−10.3150	+	17.8661i	−0.573941	+	0.994095i
$324$	6.22034	−	10.7739i	0.345574	−	0.598552i
$325$	−18.6895	−	32.3711i	−1.03671	−	1.79563i
$326$	0.0759299			0.00420537
$327$	−12.2206	+	21.1667i	−0.675799	+	1.17052i
$328$	−0.642723			−0.0354884
$329$	3.07508	−	5.32620i	0.169535	−	0.293643i
$330$	−18.5310	+	32.0966i	−1.02010	+	1.76686i
$331$	−12.8165	−	22.1988i	−0.704457	−	1.22016i	−0.966887	−	0.255205i	$-0.917857\pi$
$331$	−12.8165	−	22.1988i	−0.704457	−	1.22016i	0.262430	−	0.964951i	$-0.415476\pi$
$332$	7.95056			0.436344
$333$	−2.34025	−	4.05343i	−0.128245	−	0.222127i
$334$	28.5130			1.56016
$335$	7.33050	−	12.6968i	0.400508	−	0.693700i
$336$	−0.171605	+	0.297229i	−0.00936183	+	0.0162152i
$337$	−14.8669	+	25.7502i	−0.809852	+	1.40270i	0.103115	+	0.994669i	$0.467119\pi$
$337$	−14.8669	+	25.7502i	−0.809852	+	1.40270i	−0.912966	+	0.408035i	$0.866214\pi$
$338$	−21.5984	−	37.4096i	−1.17480	−	2.03481i
$339$	8.17199			0.443842
$340$	17.2223	+	29.8299i	0.934011	+	1.61775i
$341$	−2.86014	−	4.95391i	−0.154885	−	0.268269i
$342$	−17.5694			−0.950042
$343$	−9.54984			−0.515643
$344$	−25.6873			−1.38497
$345$	19.1138	+	33.1061i	1.02905	+	1.78237i
$346$	53.6007			2.88159
$347$	−18.6188			−0.999510			−0.499755	−	0.866167i	$-0.666577\pi$
$347$	−18.6188			−0.999510			−0.499755	+	0.866167i	$0.666577\pi$
$348$	5.13416	+	8.89262i	0.275220	+	0.476695i
$349$	9.63404	+	16.6866i	0.515698	+	0.893215i	0.999834	+	0.0182225i	$0.00580071\pi$
$349$	9.63404	+	16.6866i	0.515698	+	0.893215i	−0.484136	+	0.874993i	$0.660866\pi$
$350$	−5.30352	−	9.18597i	−0.283485	−	0.491011i
$351$	−15.9431	−	27.6143i	−0.850979	−	1.47394i
$352$	−21.6613			−1.15455
$353$	2.15939	+	3.74018i	0.114933	+	0.199070i	0.917753	−	0.397152i	$-0.130001\pi$
$353$	2.15939	+	3.74018i	0.114933	+	0.199070i	−0.802820	+	0.596221i	$0.796668\pi$
$354$	16.0426	−	27.7866i	0.852654	−	1.47684i
$355$	−0.104478	+	0.180960i	−0.00554509	+	0.00960438i
$356$	−53.1416			−2.81650
$357$	−3.04065			−0.160928
$358$	34.8546			1.84212
$359$	2.04468	+	3.54150i	0.107914	+	0.186913i	0.914925	−	0.403624i	$-0.132249\pi$
$359$	2.04468	+	3.54150i	0.107914	+	0.186913i	−0.807011	+	0.590537i	$0.798916\pi$
$360$	−5.36542	+	9.29317i	−0.282782	+	0.489793i
$361$	−11.2006	−	19.4000i	−0.589506	−	1.02106i
$362$	3.72113	+	6.44518i	0.195578	+	0.338751i
$363$	1.19270	−	2.06582i	0.0626005	−	0.108427i
$364$	−6.31281	−	10.9341i	−0.330881	−	0.573103i
$365$	12.3493			0.646392
$366$	−5.13921			−0.268631
$367$	−10.5863			−0.552600			−0.276300	−	0.961071i	$-0.589108\pi$
$367$	−10.5863			−0.552600			−0.276300	+	0.961071i	$0.589108\pi$
$368$	−1.51466	+	2.62347i	−0.0789572	+	0.136758i
$369$	−0.147593	+	0.255638i	−0.00768337	+	0.0133080i
$370$	−15.0468	−	26.0619i	−0.782248	−	1.35489i
$371$	−2.18358			−0.113366
$372$	3.38253	+	5.85871i	0.175376	+	0.303760i
$373$	16.2888	+	28.2131i	0.843404	+	1.46082i	0.887000	+	0.461770i	$0.152785\pi$
$373$	16.2888	+	28.2131i	0.843404	+	1.46082i	−0.0435956	+	0.999049i	$0.513881\pi$
$374$	−13.0099	−	22.5337i	−0.672724	−	1.16519i
$375$	−3.66451	−	6.34711i	−0.189234	−	0.327763i
$376$	−22.7683			−1.17419
$377$	13.7454			0.707922
$378$	−4.52418	−	7.83611i	−0.232699	−	0.403046i
$379$	−1.39993			−0.0719097			−0.0359548	−	0.999353i	$-0.511447\pi$
$379$	−1.39993			−0.0719097			−0.0359548	+	0.999353i	$0.511447\pi$
$380$	−69.1252			−3.54605
$381$	−9.80982			−0.502572
$382$	14.0778	+	24.3835i	0.720285	+	1.24757i
$383$	−13.5158	−	23.4101i	−0.690627	−	1.19620i	−0.971633	−	0.236494i	$-0.924001\pi$
$383$	−13.5158	−	23.4101i	−0.690627	−	1.19620i	0.281006	−	0.959706i	$-0.409332\pi$
$384$	23.4148			1.19488
$385$	4.30745	+	7.46073i	0.219528	+	0.380234i
$386$	3.44669	−	5.96984i	0.175432	−	0.303857i
$387$	−5.89876	+	10.2170i	−0.299851	+	0.519357i
$388$	−27.4160	+	47.4859i	−1.39184	+	2.41073i
$389$	−29.9651			−1.51929			−0.759645	−	0.650338i	$-0.774627\pi$
$389$	−29.9651			−1.51929			−0.759645	+	0.650338i	$0.774627\pi$
$390$	−29.3366	−	50.8125i	−1.48552	−	2.57299i
$391$	−26.8381			−1.35726
$392$	8.51089	+	14.7413i	0.429865	+	0.744548i
$393$	−1.57336	+	2.72513i	−0.0793653	+	0.137465i
$394$	2.16251	−	3.74559i	0.108946	−	0.188700i
$395$	−8.54230			−0.429810
$396$	6.77996	−	11.7432i	0.340706	−	0.590120i
$397$	−21.7146			−1.08983			−0.544913	−	0.838493i	$-0.683437\pi$
$397$	−21.7146			−1.08983			−0.544913	+	0.838493i	$0.683437\pi$
$398$	11.1235	+	19.2664i	0.557568	+	0.965737i
$399$	3.05107	−	5.28460i	0.152744	−	0.264561i
$400$	1.19513	−	2.07003i	0.0597567	−	0.103502i
$401$	1.89353	+	3.27968i	0.0945582	+	0.163780i	0.909424	−	0.415870i	$-0.136523\pi$
$401$	1.89353	+	3.27968i	0.0945582	+	0.163780i	−0.814866	+	0.579649i	$0.803190\pi$
$402$	6.54891	−	11.3430i	0.326630	−	0.565740i
$403$	9.05584			0.451103
$404$	3.59162	+	6.22087i	0.178690	+	0.309500i
$405$	−6.71929	−	11.6381i	−0.333884	−	0.578304i
$406$	3.90053			0.193580
$407$	6.95543	+	12.0472i	0.344768	+	0.597156i
$408$	5.62836	+	9.74860i	0.278645	+	0.482628i
$409$	30.6016			1.51315			0.756576	−	0.653905i	$-0.226871\pi$
$409$	30.6016			1.51315			0.756576	+	0.653905i	$0.226871\pi$
$410$	−0.948960	+	1.64365i	−0.0468658	+	0.0811740i
$411$	−7.31319	+	12.6668i	−0.360733	+	0.624808i
$412$	−12.0861	−	20.9337i	−0.595438	−	1.03133i
$413$	−3.72904	−	6.45888i	−0.183494	−	0.317821i
$414$	−11.4282	−	19.7943i	−0.561668	−	0.972837i
$415$	4.29415	−	7.43768i	0.210791	−	0.365102i
$416$	17.1461	−	29.6979i	0.840656	−	1.45606i
$417$	9.89516	+	17.1389i	0.484568	+	0.839296i
$418$	52.2177			2.55405
$419$	−2.60083	−	4.50477i	−0.127059	−	0.220072i	0.795477	−	0.605984i	$-0.207220\pi$
$419$	−2.60083	−	4.50477i	−0.127059	−	0.220072i	−0.922536	+	0.385911i	$0.873887\pi$
$420$	−5.09418	−	8.82338i	−0.248571	−	0.430537i
$421$	−29.9580			−1.46006			−0.730032	−	0.683413i	$-0.760495\pi$
$421$	−29.9580			−1.46006			−0.730032	+	0.683413i	$0.760495\pi$
$422$	26.7911	−	46.4035i	1.30417	−	2.25889i
$423$	−5.22845	+	9.05594i	−0.254216	+	0.440315i
$424$	4.04188	+	7.00073i	0.196291	+	0.339986i
$425$	21.1765			1.02721
$426$	−0.0933380	+	0.161666i	−0.00452224	+	0.00783275i
$427$	−0.597294	+	1.03454i	−0.0289051	+	0.0500651i
$428$	15.7446	−	27.2705i	0.761046	−	1.31817i
$429$	13.5609	+	23.4882i	0.654726	+	1.13402i
$430$	−37.9266	+	65.6907i	−1.82898	+	3.16789i
$431$	20.5630	+	35.6162i	0.990486	+	1.71557i	0.614418	+	0.788981i	$0.289391\pi$
$431$	20.5630	+	35.6162i	0.990486	+	1.71557i	0.376068	+	0.926592i	$0.377276\pi$
$432$	1.01951	−	1.76585i	0.0490513	−	0.0849593i
$433$	12.7685	+	22.1157i	0.613615	+	1.06281i	0.990626	+	0.136604i	$0.0436187\pi$
$433$	12.7685	+	22.1157i	0.613615	+	1.06281i	−0.377011	+	0.926209i	$0.623048\pi$
$434$	2.56978			0.123353
$435$	11.0920			0.531819
$436$	28.7477	−	49.7925i	1.37677	−	2.38463i
$437$	26.9300	−	46.6442i	1.28824	−	2.23129i
$438$	11.0326			0.527158
$439$	37.4592			1.78783			0.893916	−	0.448234i	$-0.147947\pi$
$439$	37.4592			1.78783			0.893916	+	0.448234i	$0.147947\pi$
$440$	15.9465	−	27.6201i	0.760219	−	1.31674i
$441$	7.81766			0.372269
$442$	41.1921			1.95931
$443$	3.30050	−	5.71663i	0.156811	−	0.271605i	−0.776906	−	0.629617i	$-0.783212\pi$
$443$	3.30050	−	5.71663i	0.156811	−	0.271605i	0.933717	+	0.358012i	$0.116545\pi$
$444$	−8.22580	−	14.2475i	−0.390379	−	0.676157i
$445$	−28.7021	+	49.7135i	−1.36061	+	2.35664i
$446$	4.45426			0.210915
$447$	−0.568223	+	0.984191i	−0.0268760	+	0.0465506i
$448$	4.60954	−	7.98396i	0.217780	−	0.377207i
$449$	−8.59403			−0.405577			−0.202789	−	0.979223i	$-0.565000\pi$
$449$	−8.59403			−0.405577			−0.202789	+	0.979223i	$0.565000\pi$
$450$	9.01738	+	15.6186i	0.425084	+	0.736266i
$451$	0.438659	−	0.759779i	0.0206556	−	0.0357766i
$452$	−19.2238			−0.904213
$453$	−11.5338	+	19.9771i	−0.541905	+	0.938608i
$454$	44.8523			2.10502
$455$	−13.6383			−0.639375
$456$	−22.5905			−1.05790
$457$	7.87369			0.368316			0.184158	−	0.982897i	$-0.441044\pi$
$457$	7.87369			0.368316			0.184158	+	0.982897i	$0.441044\pi$
$458$	−20.2977	−	35.1566i	−0.948449	−	1.64276i
$459$	18.0646			0.843184
$460$	−44.9634	−	77.8790i	−2.09643	−	3.63113i
$461$	30.1245			1.40304			0.701519	−	0.712651i	$-0.252506\pi$
$461$	30.1245			1.40304			0.701519	+	0.712651i	$0.252506\pi$
$462$	3.84819	+	6.66525i	0.179034	+	0.310096i
$463$	0.858343	−	1.48669i	0.0398906	−	0.0690925i	−0.845391	−	0.534148i	$-0.820632\pi$
$463$	0.858343	−	1.48669i	0.0398906	−	0.0690925i	0.885281	+	0.465056i	$0.153966\pi$
$464$	0.439487	+	0.761214i	0.0204027	+	0.0353385i
$465$	7.30770			0.338886
$466$	−5.00468	+	8.66835i	−0.231837	+	0.401554i
$467$	−5.18652	−	8.98331i	−0.240003	−	0.415698i	0.720712	−	0.693235i	$-0.243815\pi$
$467$	−5.18652	−	8.98331i	−0.240003	−	0.415698i	−0.960715	+	0.277537i	$0.910482\pi$
$468$	10.7334	+	18.5909i	0.496153	+	0.859362i
$469$	−1.52227	−	2.63664i	−0.0702918	−	0.121749i
$470$	−33.6168	+	58.2259i	−1.55063	+	2.68576i
$471$	−14.1921	+	24.5815i	−0.653939	+	1.13266i
$472$	−13.8052	+	23.9112i	−0.635434	+	1.10060i
$473$	17.5316	−	30.3657i	0.806105	−	1.39622i
$474$	−7.63150			−0.350527
$475$	−21.2490	+	36.8043i	−0.974970	+	1.68870i
$476$	7.15284			0.327850
$477$	3.71265			0.169991
$478$	−7.09671	−	12.2919i	−0.324596	−	0.562217i
$479$	2.31699	+	4.01315i	0.105866	+	0.183366i	0.914092	−	0.405507i	$-0.132905\pi$
$479$	2.31699	+	4.01315i	0.105866	+	0.183366i	−0.808226	+	0.588873i	$0.799572\pi$
$480$	13.8362	−	23.9650i	0.631533	−	1.09385i
$481$	−22.0224			−1.00414
$482$	23.9711	−	25.8343i	1.09185	−	1.17672i
$483$	7.93844			0.361212
$484$	−2.80571	+	4.85963i	−0.127532	+	0.220892i
$485$	29.6151	+	51.2949i	1.34475	+	2.32918i
$486$	13.1831	+	22.8339i	0.597999	+	1.03577i
$487$	12.0628			0.546619			0.273309	−	0.961926i	$-0.411882\pi$
$487$	12.0628			0.546619			0.273309	+	0.961926i	$0.411882\pi$
$488$	4.42245			0.200195
$489$	0.0224194	−	0.0388316i	0.00101384	−	0.00175603i
$490$	50.2643			2.27071
$491$	−12.0104	+	20.8026i	−0.542020	+	0.938806i	0.456768	+	0.889586i	$0.349007\pi$
$491$	−12.0104	+	20.8026i	−0.542020	+	0.938806i	−0.998788	+	0.0492202i	$0.984326\pi$
$492$	−0.518777	+	0.898548i	−0.0233883	+	0.0405097i
$493$	−3.89361	+	6.74393i	−0.175359	+	0.303731i
$494$	−41.3332	+	71.5912i	−1.85967	+	3.22104i
$495$	−7.32380	−	12.6852i	−0.329180	−	0.570157i
$496$	0.289546	+	0.501509i	0.0130010	+	0.0225184i
$497$	0.0216960	+	0.0375786i	0.000973200	+	0.00168563i
$498$	3.83630	−	6.64467i	0.171909	−	0.297755i
$499$	15.8948			0.711550			0.355775	−	0.934572i	$-0.384217\pi$
$499$	15.8948			0.711550			0.355775	+	0.934572i	$0.384217\pi$
$500$	8.62039	+	14.9310i	0.385516	+	0.667733i
$501$	8.41890	−	14.5820i	0.376129	−	0.651474i
$502$	−24.8477	−	43.0375i	−1.10901	−	1.92086i
$503$	−29.7935			−1.32843			−0.664214	−	0.747543i	$-0.731233\pi$
$503$	−29.7935			−1.32843			−0.664214	+	0.747543i	$0.731233\pi$
$504$	1.11419	+	1.92984i	0.0496301	+	0.0859619i
$505$	7.75943			0.345290
$506$	33.9657	+	58.8304i	1.50996	+	2.61533i
$507$	−25.5090			−1.13290
$508$	23.0766			1.02386
$509$	−43.1155			−1.91106			−0.955531	−	0.294891i	$-0.904717\pi$
$509$	−43.1155			−1.91106			−0.955531	+	0.294891i	$0.904717\pi$
$510$	33.2404			1.47191
$511$	1.28224	−	2.22091i	0.0567231	−	0.0982472i
$512$	4.08843			0.180685
$513$	−18.1265	+	31.3960i	−0.800304	+	1.38617i
$514$	−25.3409	−	43.8917i	−1.11774	−	1.93598i
$515$	−26.1110			−1.15059
$516$	−20.7337	+	35.9118i	−0.912749	+	1.58093i
$517$	15.5394	−	26.9151i	0.683423	−	1.18372i
$518$	−6.24932			−0.274579
$519$	15.8264	−	27.4122i	0.694703	−	1.20326i
$520$	25.2451	+	43.7257i	1.10707	+	1.91750i
$521$	20.4334	−	35.3917i	0.895204	−	1.55054i	0.0616518	−	0.998098i	$-0.480363\pi$
$521$	20.4334	−	35.3917i	0.895204	−	1.55054i	0.833552	−	0.552441i	$-0.186304\pi$
$522$	−6.63193			−0.290272
$523$	6.18079			0.270267			0.135134	−	0.990827i	$-0.456854\pi$
$523$	6.18079			0.270267			0.135134	+	0.990827i	$0.456854\pi$
$524$	3.70117	−	6.41061i	0.161686	−	0.280049i
$525$	−6.26378			−0.273374
$526$	−22.2592			−0.970549
$527$	−2.56522	+	4.44309i	−0.111743	+	0.193544i
$528$	−0.867178	+	1.50200i	−0.0377391	+	0.0653660i
$529$	47.0681			2.04644
$530$	23.8708			1.03688
$531$	6.34034	+	10.9818i	0.275147	+	0.476569i
$532$	−7.17734	+	12.4315i	−0.311177	+	0.538975i
$533$	0.694445	+	1.20281i	0.0300798	+	0.0520997i
$534$	−25.6418	+	44.4129i	−1.10963	+	1.92194i
$535$	−17.0076	−	29.4580i	−0.735301	−	1.27358i
$536$	−5.63554	+	9.76104i	−0.243418	+	0.421613i
$537$	10.2913	−	17.8251i	0.444104	−	0.769210i
$538$	23.0359	−	39.8994i	0.993150	−	1.72019i
$539$	−23.2348			−1.00079
$540$	30.2647	+	52.4200i	1.30239	+	2.25580i
$541$	−3.24350	+	5.61791i	−0.139449	+	0.241533i	−0.927288	−	0.374348i	$-0.877866\pi$
$541$	−3.24350	+	5.61791i	−0.139449	+	0.241533i	0.787839	+	0.615881i	$0.211200\pi$
$542$	5.56932	−	9.64634i	0.239223	−	0.414346i
$543$	4.39488			0.188602
$544$	9.71384	+	16.8249i	0.416478	+	0.721360i
$545$	−31.0536	−	53.7865i	−1.33019	−	2.30396i
$546$	−12.1842			−0.521436
$547$	3.85381	+	6.67500i	0.164777	+	0.285402i	0.936576	−	0.350464i	$-0.113976\pi$
$547$	3.85381	+	6.67500i	0.164777	+	0.285402i	−0.771799	+	0.635867i	$0.780643\pi$
$548$	17.2036	−	29.7975i	0.734900	−	1.27288i
$549$	1.01556	−	1.75900i	0.0433430	−	0.0750722i
$550$	−26.8005	−	46.4198i	−1.14278	−	1.97934i
$551$	−7.81389	−	13.5341i	−0.332883	−	0.576570i
$552$	−14.6943	−	25.4513i	−0.625432	−	1.08328i
$553$	−0.886956	+	1.53625i	−0.0377172	+	0.0653281i
$554$	12.7640	−	22.1080i	0.542292	−	0.939277i
$555$	−17.7712			−0.754346
$556$	−23.2774	−	40.3176i	−0.987181	−	1.70985i
$557$	8.88662	+	15.3921i	0.376538	+	0.652183i	0.990556	−	0.137109i	$-0.0437811\pi$
$557$	8.88662	+	15.3921i	0.376538	+	0.652183i	−0.614018	+	0.789292i	$0.710448\pi$
$558$	−4.36930			−0.184967
$559$	27.7545	+	48.0722i	1.17389	+	2.03324i
$560$	−0.436065	−	0.755287i	−0.0184271	−	0.0319167i
$561$	−15.3654			−0.648729
$562$	−18.4882	+	32.0225i	−0.779879	+	1.35079i
$563$	7.29522	+	12.6357i	0.307457	+	0.532531i	0.977805	−	0.209515i	$-0.0671886\pi$
$563$	7.29522	+	12.6357i	0.307457	+	0.532531i	−0.670348	+	0.742047i	$0.733855\pi$
$564$	−18.3776	+	31.8309i	−0.773836	+	1.34032i
$565$	−10.3829	+	17.9837i	−0.436812	+	0.756581i
$566$	4.58364	+	7.93910i	0.192665	+	0.333705i
$567$	−2.79068			−0.117198
$568$	0.0803202	−	0.139119i	0.00337016	−	0.00583729i
$569$	13.6578			0.572565			0.286283	−	0.958145i	$-0.407580\pi$
$569$	13.6578			0.572565			0.286283	+	0.958145i	$0.407580\pi$
$570$	−33.3542	+	57.7712i	−1.39705	+	2.41977i
$571$	8.37841	−	14.5118i	0.350625	−	0.607301i	−0.635734	−	0.771908i	$-0.719302\pi$
$571$	8.37841	−	14.5118i	0.350625	−	0.607301i	0.986359	+	0.164607i	$0.0526357\pi$
$572$	−31.9007	−	55.2536i	−1.33384	−	2.31027i
$573$	16.6268			0.694594
$574$	0.197063	+	0.341323i	0.00822526	+	0.0142466i
$575$	−55.2868			−2.30562
$576$	−7.83743	+	13.5748i	−0.326560	+	0.565618i
$577$	−9.92094	+	17.1836i	−0.413014	+	0.715362i	−0.995218	−	0.0976814i	$-0.968857\pi$
$577$	−9.92094	+	17.1836i	−0.413014	+	0.715362i	0.582203	+	0.813043i	$0.302191\pi$
$578$	7.62798	−	13.2121i	0.317282	−	0.549549i
$579$	−2.03537	−	3.52537i	−0.0845872	−	0.146509i
$580$	−26.0928			−1.08344
$581$	−0.891732	−	1.54453i	−0.0369953	−	0.0640777i
$582$	26.4575	+	45.8258i	1.09670	+	1.89954i
$583$	−11.0343			−0.456995
$584$	−9.49390			−0.392860
$585$	23.1888			0.958738
$586$	3.87932	+	6.71918i	0.160253	+	0.277567i
$587$	−7.47714			−0.308614			−0.154307	−	0.988023i	$-0.549315\pi$
$587$	−7.47714			−0.308614			−0.154307	+	0.988023i	$0.549315\pi$
$588$	27.4785			1.13319
$589$	−5.14801	−	8.91662i	−0.212120	−	0.367403i
$590$	40.7658	+	70.6084i	1.67830	+	2.90690i
$591$	−1.27703	−	2.21188i	−0.0525300	−	0.0909846i
$592$	−0.704133	−	1.21959i	−0.0289397	−	0.0501250i
$593$	18.7130			0.768452			0.384226	−	0.923239i	$-0.374468\pi$
$593$	18.7130			0.768452			0.384226	+	0.923239i	$0.374468\pi$
$594$	−22.8622	−	39.5985i	−0.938047	−	1.62475i
$595$	3.86330	−	6.69142i	0.158380	−	0.274322i
$596$	1.33669	−	2.31521i	0.0547529	−	0.0948348i
$597$	13.1375			0.537681
$598$	−107.543			−4.39776
$599$	−6.37068			−0.260299			−0.130150	−	0.991494i	$-0.541546\pi$
$599$	−6.37068			−0.260299			−0.130150	+	0.991494i	$0.541546\pi$
$600$	11.5945	+	20.0822i	0.473342	+	0.819853i
$601$	−10.5777	+	18.3211i	−0.431473	+	0.747334i	−0.997000	−	0.0773959i	$-0.975339\pi$
$601$	−10.5777	+	18.3211i	−0.431473	+	0.747334i	0.565527	+	0.824730i	$0.308673\pi$
$602$	7.87591	+	13.6415i	0.320998	+	0.555985i
$603$	2.58825	+	4.48299i	0.105402	+	0.182561i
$604$	27.1322	−	46.9943i	1.10399	−	1.91217i
$605$	3.03076	+	5.24943i	0.123218	+	0.213420i
$606$	6.93211			0.281598
$607$	−41.8091			−1.69698			−0.848490	−	0.529211i	$-0.822488\pi$
$607$	−41.8091			−1.69698			−0.848490	+	0.529211i	$0.822488\pi$
$608$	−38.9884			−1.58119
$609$	1.15169	−	1.99479i	0.0466688	−	0.0808328i
$610$	6.52961	−	11.3096i	0.264376	−	0.457913i
$611$	24.6006	+	42.6095i	0.995234	+	1.72380i
$612$	−12.1617			−0.491608
$613$	−21.0202	−	36.4080i	−0.848998	−	1.47051i	−0.882104	−	0.471055i	$-0.843873\pi$
$613$	−21.0202	−	36.4080i	−0.848998	−	1.47051i	0.0331063	−	0.999452i	$-0.489460\pi$
$614$	22.3240	+	38.6663i	0.900924	+	1.56045i
$615$	0.560390	+	0.970623i	0.0225971	+	0.0391393i
$616$	−3.31148	−	5.73565i	−0.133423	−	0.231096i
$617$	−23.6328			−0.951420			−0.475710	−	0.879602i	$-0.657809\pi$
$617$	−23.6328			−0.951420			−0.475710	+	0.879602i	$0.657809\pi$
$618$	−23.3270			−0.938351
$619$	3.75193	+	6.49854i	0.150803	+	0.261198i	0.931523	−	0.363683i	$-0.118481\pi$
$619$	3.75193	+	6.49854i	0.150803	+	0.261198i	−0.780720	+	0.624881i	$0.785147\pi$
$620$	−17.1907			−0.690393
$621$	−47.1625			−1.89257
$622$	60.5259			2.42687
$623$	5.96034	+	10.3236i	0.238796	+	0.413607i
$624$	−1.37284	−	2.37783i	−0.0549575	−	0.0951892i
$625$	−14.4004			−0.576016
$626$	24.4894	+	42.4169i	0.978793	+	1.69532i
$627$	15.4181	−	26.7049i	0.615738	−	1.06649i
$628$	33.3856	−	57.8256i	1.33223	−	2.30749i
$629$	6.23823	−	10.8049i	0.248735	−	0.430821i
$630$	6.58029			0.262165
$631$	7.80204	+	13.5135i	0.310594	+	0.537965i	0.978491	−	0.206289i	$-0.0661387\pi$
$631$	7.80204	+	13.5135i	0.310594	+	0.537965i	−0.667897	+	0.744254i	$0.732805\pi$
$632$	6.56714			0.261227
$633$	−15.8209	−	27.4026i	−0.628825	−	1.08916i
$634$	−17.1591	+	29.7204i	−0.681474	+	1.18035i
$635$	12.4638	−	21.5880i	0.494612	−	0.856694i
$636$	13.0497			0.517454
$637$	18.3916	−	31.8552i	0.728702	−	1.26215i
$638$	19.7107			0.780353
$639$	−0.0368890	−	0.0638936i	−0.00145930	−	0.00252759i
$640$	−29.7496	+	51.5278i	−1.17596	+	2.03681i
$641$	2.39697	−	4.15167i	0.0946746	−	0.163981i	−0.814798	−	0.579745i	$-0.803152\pi$
$641$	2.39697	−	4.15167i	0.0946746	−	0.163981i	0.909473	+	0.415763i	$0.136486\pi$
$642$	−15.1942	−	26.3171i	−0.599667	−	1.03865i
$643$	3.86059	−	6.68674i	0.152247	−	0.263699i	−0.779806	−	0.626021i	$-0.784682\pi$
$643$	3.86059	−	6.68674i	0.152247	−	0.263699i	0.932053	+	0.362322i	$0.118016\pi$
$644$	−18.6744			−0.735875
$645$	22.3968	+	38.7924i	0.881872	+	1.52745i
$646$	−23.4167	−	40.5589i	−0.921316	−	1.59577i
$647$	−9.01634			−0.354469			−0.177235	−	0.984169i	$-0.556715\pi$
$647$	−9.01634			−0.354469			−0.177235	+	0.984169i	$0.556715\pi$
$648$	5.16565	+	8.94717i	0.202926	+	0.351478i
$649$	−18.8441	−	32.6389i	−0.739694	−	1.28119i
$650$	84.8562			3.32833
$651$	0.758766	−	1.31422i	0.0297384	−	0.0515084i
$652$	−0.0527395	+	0.0913476i	−0.00206544	+	0.00357745i
$653$	21.5006	+	37.2401i	0.841383	+	1.45732i	0.888725	+	0.458440i	$0.151592\pi$
$653$	21.5006	+	37.2401i	0.841383	+	1.45732i	−0.0473420	+	0.998879i	$0.515075\pi$
$654$	−27.7427	−	48.0517i	−1.08482	−	1.87897i
$655$	−3.99805	−	6.92482i	−0.156217	−	0.270575i
$656$	−0.0444076	+	0.0769163i	−0.00173383	+	0.00300308i
$657$	−2.18015	+	3.77613i	−0.0850557	+	0.147321i
$658$	6.98093	+	12.0913i	0.272145	+	0.471369i
$659$	49.4515			1.92636			0.963178	−	0.268864i	$-0.0866482\pi$
$659$	49.4515			1.92636			0.963178	+	0.268864i	$0.0866482\pi$
$660$	−25.7426	−	44.5875i	−1.00203	−	1.73557i
$661$	5.52785	+	9.57452i	0.215009	+	0.372406i	0.953275	−	0.302103i	$-0.0976887\pi$
$661$	5.52785	+	9.57452i	0.215009	+	0.372406i	−0.738267	+	0.674509i	$0.764355\pi$
$662$	58.1909			2.26165
$663$	12.1626	−	21.0662i	0.472356	−	0.818144i
$664$	−3.30126	+	5.71794i	−0.128114	+	0.221899i
$665$	7.75305	+	13.4287i	0.300650	+	0.520742i
$666$	10.6255			0.411729
$667$	10.1653	−	17.6068i	0.393603	−	0.681740i
$668$	−19.8046	+	34.3026i	−0.766264	+	1.32721i
$669$	1.31519	−	2.27797i	0.0508481	−	0.0880715i
$670$	16.6414	+	28.8237i	0.642913	+	1.11356i
$671$	−3.01833	+	5.22790i	−0.116521	+	0.201821i
$672$	−2.87326	−	4.97662i	−0.110838	−	0.191977i
$673$	−20.0156	+	34.6680i	−0.771545	+	1.33635i	0.165172	+	0.986265i	$0.447182\pi$
$673$	−20.0156	+	34.6680i	−0.771545	+	1.33635i	−0.936716	+	0.350090i	$0.886151\pi$
$674$	−33.7502	−	58.4571i	−1.30001	−	2.25168i
$675$	37.2133			1.43234
$676$	60.0075			2.30798
$677$	10.8884	−	18.8592i	0.418475	−	0.724819i	−0.577312	−	0.816524i	$-0.695898\pi$
$677$	10.8884	−	18.8592i	0.418475	−	0.724819i	0.995786	+	0.0917045i	$0.0292315\pi$
$678$	−9.27587	+	16.0663i	−0.356238	+	0.617021i
$679$	12.2999			0.472026
$680$	−28.6044			−1.09693
$681$	13.2433	−	22.9381i	0.507485	−	0.878991i
$682$	12.9860			0.497258
$683$	−15.7676			−0.603332			−0.301666	−	0.953414i	$-0.597543\pi$
$683$	−15.7676			−0.603332			−0.301666	+	0.953414i	$0.597543\pi$
$684$	12.2034	−	21.1369i	0.466607	−	0.808188i
$685$	−18.5835	−	32.1876i	−0.710040	−	1.22982i
$686$	10.8398	−	18.7751i	0.413867	−	0.716838i
$687$	−23.9728			−0.914619
$688$	−1.77481	+	3.07407i	−0.0676642	+	0.117198i
$689$	8.73429	−	15.1282i	0.332750	−	0.576340i
$690$	−86.7829			−3.30377
$691$	−6.12207	−	10.6037i	−0.232895	−	0.403385i	0.725764	−	0.687944i	$-0.241486\pi$
$691$	−6.12207	−	10.6037i	−0.232895	−	0.403385i	−0.958659	+	0.284558i	$0.908153\pi$
$692$	−37.2301	+	64.4845i	−1.41528	+	2.45133i
$693$	−3.04175			−0.115547
$694$	21.1338	−	36.6049i	0.802229	−	1.38950i
$695$	−50.2891			−1.90757
$696$	−8.52728			−0.323226
$697$	−0.786854			−0.0298042
$698$	−43.7416			−1.65564
$699$	2.95541	+	5.11892i	0.111784	+	0.193615i
$700$	14.7349			0.556928
$701$	16.5959	+	28.7449i	0.626819	+	1.08568i	0.988186	+	0.153258i	$0.0489766\pi$
$701$	16.5959	+	28.7449i	0.626819	+	1.08568i	−0.361368	+	0.932423i	$0.617690\pi$
$702$	72.3867			2.73206
$703$	12.5192	+	21.6839i	0.472170	+	0.817823i
$704$	23.2935	−	40.3456i	0.877908	−	1.52058i
$705$	19.8517	+	34.3842i	0.747659	+	1.29498i
$706$	−9.80434			−0.368991
$707$	0.805670	−	1.39546i	0.0303003	−	0.0524817i
$708$	22.2858	+	38.6002i	0.837552	+	1.45068i
$709$	−7.19108	−	12.4553i	−0.270067	−	0.467769i	0.698812	−	0.715305i	$-0.253712\pi$
$709$	−7.19108	−	12.4553i	−0.270067	−	0.467769i	−0.968879	+	0.247536i	$0.920379\pi$
$710$	−0.237181	−	0.410809i	−0.00890123	−	0.0154174i
$711$	1.50806	−	2.61203i	0.0565566	−	0.0979589i
$712$	22.0656	−	38.2187i	0.826943	−	1.43231i
$713$	6.69720	−	11.5999i	0.250812	−	0.434419i
$714$	3.45139	−	5.97797i	0.129165	−	0.223720i
$715$	−68.9191			−2.57743
$716$	−24.2094	+	41.9319i	−0.904746	+	1.56707i
$717$	−8.38164			−0.313018
$718$	−9.28352			−0.346458
$719$	5.74009	+	9.94213i	0.214069	+	0.370779i	0.952984	−	0.303020i	$-0.0979949\pi$
$719$	5.74009	+	9.94213i	0.214069	+	0.370779i	−0.738915	+	0.673799i	$0.764662\pi$
$720$	0.741425	+	1.28419i	0.0276313	+	0.0478588i
$721$	−2.71114	+	4.69583i	−0.100968	+	0.174882i
$722$	50.8544			1.89261
$723$	−6.13422	−	19.8871i	−0.228134	−	0.739609i
$724$	−10.3385			−0.384228
$725$	−8.02088	+	13.8926i	−0.297888	+	0.515957i
$726$	2.70762	+	4.68973i	0.100489	+	0.174052i
$727$	2.21003	+	3.82788i	0.0819653	+	0.141968i	0.904094	−	0.427334i	$-0.140547\pi$
$727$	2.21003	+	3.82788i	0.0819653	+	0.141968i	−0.822129	+	0.569302i	$0.807214\pi$
$728$	10.4849			0.388596
$729$	27.4047			1.01499
$730$	−14.0175	+	24.2789i	−0.518809	+	0.898604i
$731$	−31.4478			−1.16314
$732$	3.56961	−	6.18274i	0.131936	−	0.228521i
$733$	21.4133	−	37.0890i	0.790919	−	1.36991i	−0.134479	−	0.990916i	$-0.542936\pi$
$733$	21.4133	−	37.0890i	0.790919	−	1.36991i	0.925398	−	0.378996i	$-0.123731\pi$
$734$	12.0163	−	20.8128i	0.443529	−	0.768215i
$735$	14.8413	−	25.7059i	0.547429	−	0.948175i
$736$	−25.3606	−	43.9258i	−0.934804	−	1.61913i
$737$	−7.69252	−	13.3238i	−0.283358	−	0.490790i
$738$	−0.335059	−	0.580340i	−0.0123337	−	0.0213626i
$739$	4.92732	−	8.53436i	0.181254	−	0.313942i	−0.761054	−	0.648689i	$-0.775318\pi$
$739$	4.92732	−	8.53436i	0.181254	−	0.313942i	0.942308	+	0.334747i	$0.108651\pi$
$740$	41.8051			1.53679
$741$	24.4085	+	42.2767i	0.896668	+	1.55307i
$742$	2.47853	−	4.29295i	0.0909898	−	0.157599i
$743$	−16.2917	−	28.2181i	−0.597685	−	1.03522i	−0.993162	−	0.116745i	$-0.962754\pi$
$743$	−16.2917	−	28.2181i	−0.597685	−	1.03522i	0.395477	−	0.918476i	$-0.370579\pi$
$744$	−5.61801			−0.205966
$745$	−1.44391	−	2.50092i	−0.0529007	−	0.0916267i
$746$	−73.9565			−2.70774
$747$	1.51618	+	2.62610i	0.0554741	+	0.0960840i
$748$	36.1457			1.32162
$749$	−7.06365			−0.258100
$750$	16.6380			0.607535
$751$	11.9161			0.434824			0.217412	−	0.976080i	$-0.430238\pi$
$751$	11.9161			0.434824			0.217412	+	0.976080i	$0.430238\pi$
$752$	−1.57313	+	2.72475i	−0.0573663	+	0.0993613i
$753$	−29.3466			−1.06945
$754$	−15.6021	+	27.0236i	−0.568195	+	0.984142i
$755$	−29.3085	−	50.7638i	−1.06665	−	1.84748i
$756$	12.5697			0.457154
$757$	−6.72834	+	11.6538i	−0.244546	+	0.423566i	−0.962004	−	0.273036i	$-0.911972\pi$
$757$	−6.72834	+	11.6538i	−0.244546	+	0.423566i	0.717458	+	0.696602i	$0.245306\pi$
$758$	1.58904	−	2.75229i	0.0577164	−	0.0999677i
$759$	40.1156			1.45610
$760$	28.7023	−	49.7139i	1.04114	−	1.80331i
$761$	1.01036	+	1.74999i	0.0366255	+	0.0634372i	0.883757	−	0.467946i	$-0.155006\pi$
$761$	1.01036	+	1.74999i	0.0366255	+	0.0634372i	−0.847132	+	0.531383i	$0.821672\pi$
$762$	11.1349	−	19.2863i	0.403376	−	0.698668i
$763$	−12.8973			−0.466915
$764$	−39.1129			−1.41505
$765$	−6.56862	+	11.3772i	−0.237489	+	0.411343i
$766$	61.3662			2.21725
$767$	59.6644			2.15436
$768$	−9.10698	+	15.7738i	−0.328620	+	0.569186i
$769$	−17.1860	+	29.7670i	−0.619743	+	1.07343i	0.369790	+	0.929116i	$0.379430\pi$
$769$	−17.1860	+	29.7670i	−0.619743	+	1.07343i	−0.989532	+	0.144311i	$0.953904\pi$
$770$	−19.5572			−0.704793
$771$	−29.9291			−1.07787
$772$	4.78802	+	8.29309i	0.172324	+	0.298475i
$773$	0.0440275	−	0.0762578i	0.00158356	−	0.00274280i	−0.865233	−	0.501371i	$-0.832829\pi$
$773$	0.0440275	−	0.0762578i	0.00158356	−	0.00274280i	0.866816	+	0.498628i	$0.166163\pi$
$774$	−13.3911	−	23.1941i	−0.481334	−	0.833695i
$775$	−5.28438	+	9.15282i	−0.189821	+	0.328779i
$776$	−22.7675	−	39.4345i	−0.817306	−	1.41562i
$777$	−1.84521	+	3.19599i	−0.0661964	+	0.114655i
$778$	34.0128	−	58.9119i	1.21942	−	2.11209i
$779$	0.789549	−	1.36754i	0.0282885	−	0.0489972i
$780$	81.5067			2.91841
$781$	0.109637	+	0.189897i	0.00392313	+	0.00679506i
$782$	30.4634	−	52.7642i	1.08937	−	1.88684i
$783$	−6.84223	+	11.8511i	−0.244521	+	0.423523i
$784$	2.35217			0.0840062
$785$	−36.0636	−	62.4639i	−1.28716	−	2.22943i
$786$	−3.57177	−	6.18649i	−0.127401	−	0.220665i
$787$	32.6115			1.16248			0.581238	−	0.813734i	$-0.302569\pi$
$787$	32.6115			1.16248			0.581238	+	0.813734i	$0.302569\pi$
$788$	3.00409	+	5.20323i	0.107016	+	0.185358i
$789$	−6.57238	+	11.3837i	−0.233983	+	0.405270i
$790$	9.69619	−	16.7943i	0.344975	−	0.597514i
$791$	2.15614	+	3.73454i	0.0766634	+	0.132785i
$792$	5.63039	+	9.75212i	0.200067	+	0.346527i
$793$	−4.77834	−	8.27634i	−0.169684	−	0.293901i
$794$	24.6478	−	42.6913i	0.874719	−	1.51506i
$795$	7.04822	−	12.2079i	0.249975	−	0.432969i
$796$	−30.9046			−1.09539
$797$	0.406824	+	0.704640i	0.0144105	+	0.0249596i	0.873141	−	0.487468i	$-0.162080\pi$
$797$	0.406824	+	0.704640i	0.0144105	+	0.0249596i	−0.858730	+	0.512428i	$0.828746\pi$
$798$	6.92641	+	11.9969i	0.245192	+	0.424685i
$799$	−27.8742			−0.986118
$800$	20.0106	+	34.6594i	0.707482	+	1.22539i
$801$	−10.1341	−	17.5528i	−0.358072	−	0.620199i
$802$	−8.59721			−0.303578
$803$	6.47960	−	11.2230i	0.228660	−	0.396051i
$804$	9.09751	+	15.7574i	0.320845	+	0.555719i
$805$	−10.0862	+	17.4698i	−0.355491	+	0.615728i
$806$	−10.2791	+	17.8039i	−0.362066	+	0.627116i
$807$	−13.6034	−	23.5618i	−0.478863	−	0.829415i
$808$	−5.96529			−0.209858
$809$	−2.95730	+	5.12220i	−0.103973	+	0.180087i	−0.913318	−	0.407247i	$-0.866489\pi$
$809$	−2.95730	+	5.12220i	−0.103973	+	0.180087i	0.809345	+	0.587334i	$0.199822\pi$
$810$	30.5077			1.07193
$811$	−7.95287	+	13.7748i	−0.279263	+	0.483698i	−0.971202	−	0.238258i	$-0.923424\pi$
$811$	−7.95287	+	13.7748i	−0.279263	+	0.483698i	0.691939	+	0.721956i	$0.256757\pi$
$812$	−2.70924	+	4.69254i	−0.0950757	+	0.164676i
$813$	−3.28885	−	5.69645i	−0.115345	−	0.199783i
$814$	−31.5799			−1.10687
$815$	0.0569699	+	0.0986748i	0.00199557	+	0.00345643i
$816$	1.55552			0.0544541
$817$	31.5555	−	54.6557i	1.10399	−	1.91216i
$818$	−34.7353	+	60.1633i	−1.21449	+	2.10356i
$819$	2.40772	−	4.17029i	0.0841324	−	0.145722i
$820$	−1.31826	−	2.28330i	−0.0460357	−	0.0797362i
$821$	−23.0117			−0.803115			−0.401558	−	0.915834i	$-0.631531\pi$
$821$	−23.0117			−0.803115			−0.401558	+	0.915834i	$0.631531\pi$
$822$	−16.6021	−	28.7557i	−0.579065	−	1.00297i
$823$	−7.17683	−	12.4306i	−0.250169	−	0.433305i	0.713403	−	0.700754i	$-0.247153\pi$
$823$	−7.17683	−	12.4306i	−0.250169	−	0.433305i	−0.963572	+	0.267449i	$0.913819\pi$
$824$	20.0736			0.699299
$825$	−31.6529			−1.10201
$826$	16.9310			0.589105
$827$	19.8005	+	34.2954i	0.688530	+	1.19257i	0.972314	+	0.233680i	$0.0750768\pi$
$827$	19.8005	+	34.2954i	0.688530	+	1.19257i	−0.283784	+	0.958888i	$0.591590\pi$
$828$	31.7514			1.10344
$829$	−37.7768			−1.31204			−0.656021	−	0.754743i	$-0.727762\pi$
$829$	−37.7768			−1.31204			−0.656021	+	0.754743i	$0.727762\pi$
$830$	9.74840	+	16.8847i	0.338372	+	0.586078i
$831$	−7.53755	−	13.0554i	−0.261475	−	0.452887i
$832$	36.8762	+	63.8715i	1.27845	+	2.21435i
$833$	10.4195	+	18.0471i	0.361013	+	0.625294i
$834$	−44.9272			−1.55570
$835$	21.3932	+	37.0541i	0.740343	+	1.28231i
$836$	−36.2695	+	62.8206i	−1.25441	+	2.17270i
$837$	−4.50785	+	7.80783i	−0.155814	+	0.269878i
$838$	11.8086			0.407921
$839$	0.156983			0.00541967			0.00270983	−	0.999996i	$-0.499137\pi$
$839$	0.156983			0.00541967			0.00270983	+	0.999996i	$0.499137\pi$
$840$	8.46088			0.291928
$841$	11.5505	+	20.0060i	0.398292	+	0.689863i
$842$	34.0047	−	58.8979i	1.17188	−	2.02976i
$843$	10.9179	+	18.9103i	0.376031	+	0.651304i
$844$	37.2172	+	64.4621i	1.28107	+	2.21888i
$845$	32.4105	−	56.1365i	1.11495	−	1.93116i
$846$	−11.8694	−	20.5584i	−0.408079	−	0.706814i
$847$	1.25875			0.0432511
$848$	1.11706			0.0383600
$849$	5.41356			0.185793
$850$	−24.0370	+	41.6332i	−0.824461	+	1.42801i
$851$	−16.2866	+	28.2092i	−0.558297	+	0.966998i
$852$	−0.129662	−	0.224581i	−0.00444214	−	0.00769401i
$853$	6.02061			0.206142			0.103071	−	0.994674i	$-0.467133\pi$
$853$	6.02061			0.206142			0.103071	+	0.994674i	$0.467133\pi$
$854$	−1.35595	−	2.34858i	−0.0463998	−	0.0803668i
$855$	−13.1822	−	22.8323i	−0.450823	−	0.780848i
$856$	13.0751	+	22.6467i	0.446897	+	0.774048i
$857$	14.9523	+	25.8981i	0.510761	+	0.884663i	0.999922	+	0.0124701i	$0.00396947\pi$
$857$	14.9523	+	25.8981i	0.510761	+	0.884663i	−0.489162	+	0.872193i	$0.662697\pi$
$858$	−61.5708			−2.10199
$859$	−8.01918			−0.273611			−0.136805	−	0.990598i	$-0.543684\pi$
$859$	−8.01918			−0.273611			−0.136805	+	0.990598i	$0.543684\pi$
$860$	−52.6862	−	91.2552i	−1.79659	−	3.11178i
$861$	0.232743			0.00793187
$862$	−93.3627			−3.17995
$863$	−40.5343			−1.37980			−0.689902	−	0.723902i	$-0.742347\pi$
$863$	−40.5343			−1.37980			−0.689902	+	0.723902i	$0.742347\pi$
$864$	17.0701	+	29.5663i	0.580737	+	1.00587i
$865$	40.2164	+	69.6569i	1.36740	+	2.36841i
$866$	−57.9731			−1.97001
$867$	−4.50455	−	7.80212i	−0.152983	−	0.264974i
$868$	−1.78492	+	3.09158i	−0.0605843	+	0.104935i
$869$	−4.48208	+	7.76319i	−0.152044	+	0.263348i
$870$	−12.5903	+	21.8070i	−0.426850	+	0.739326i
$871$	24.3562			0.825279
$872$	23.8734	+	41.3500i	0.808456	+	1.40029i
$873$	−20.9130			−0.707799
$874$	61.1355	+	105.890i	2.06794	+	3.58177i
$875$	1.93372	−	3.34930i	0.0653717	−	0.113227i
$876$	−7.66305	+	13.2728i	−0.258911	+	0.448446i
$877$	27.2599			0.920503			0.460251	−	0.887789i	$-0.347759\pi$
$877$	27.2599			0.920503			0.460251	+	0.887789i	$0.347759\pi$
$878$	−42.5192	+	73.6455i	−1.43495	+	2.48541i
$879$	4.58171			0.154537
$880$	−2.20358	−	3.81671i	−0.0742827	−	0.128661i
$881$	5.80655	−	10.0572i	0.195628	−	0.338837i	−0.751479	−	0.659758i	$-0.770659\pi$
$881$	5.80655	−	10.0572i	0.195628	−	0.338837i	0.947106	+	0.320921i	$0.103992\pi$
$882$	−8.87367	+	15.3696i	−0.298792	+	0.517523i
$883$	−13.7682	−	23.8472i	−0.463337	−	0.802523i	0.535788	−	0.844353i	$-0.320015\pi$
$883$	−13.7682	−	23.8472i	−0.463337	−	0.802523i	−0.999125	+	0.0418296i	$0.986681\pi$
$884$	−28.6113	+	49.5562i	−0.962303	+	1.66676i
$885$	48.1468			1.61844
$886$	7.49265	+	12.9777i	0.251721	+	0.435993i
$887$	3.24928	+	5.62792i	0.109100	+	0.188967i	0.915406	−	0.402532i	$-0.131870\pi$
$887$	3.24928	+	5.62792i	0.109100	+	0.188967i	−0.806306	+	0.591499i	$0.798536\pi$
$888$	13.6622			0.458472
$889$	−2.58827	−	4.48301i	−0.0868077	−	0.150355i
$890$	−65.1583	−	112.858i	−2.18411	−	3.78299i
$891$	−14.1022			−0.472443
$892$	−3.09385	+	5.35871i	−0.103590	+	0.179423i
$893$	27.9696	−	48.4448i	0.935968	−	1.62114i
$894$	−1.28996	−	2.23427i	−0.0431426	−	0.0747252i
$895$	26.1513	+	45.2953i	0.874140	+	1.51406i
$896$	6.17786	+	10.7004i	0.206388	+	0.357474i
$897$	−31.7537	+	54.9990i	−1.06023	+	1.83636i
$898$	9.75491	−	16.8960i	0.325526	−	0.563827i
$899$	−1.94323	−	3.36577i	−0.0648103	−	0.112255i
$900$	−25.0533			−0.835109
$901$	4.94827	+	8.57066i	0.164851	+	0.285530i
$902$	0.995825	+	1.72482i	0.0331574	+	0.0574302i
$903$	9.30193			0.309549
$904$	7.98217	−	13.8255i	0.265483	−	0.459830i
$905$	−5.58390	+	9.67160i	−0.185615	+	0.321495i
$906$	−26.1836	−	45.3513i	−0.869891	−	1.50670i
$907$	−50.1824			−1.66628			−0.833140	−	0.553062i	$-0.813459\pi$
$907$	−50.1824			−1.66628			−0.833140	+	0.553062i	$0.813459\pi$
$908$	−31.1536	+	53.9597i	−1.03387	+	1.79072i
$909$	−1.36985	+	2.37265i	−0.0454351	+	0.0786959i
$910$	15.4806	−	26.8132i	0.513177	−	0.888849i
$911$	4.85876	+	8.41562i	0.160978	+	0.278822i	0.935220	−	0.354068i	$-0.115202\pi$
$911$	4.85876	+	8.41562i	0.160978	+	0.278822i	−0.774242	+	0.632890i	$0.781869\pi$
$912$	−1.56085	+	2.70347i	−0.0516848	+	0.0895207i
$913$	−4.50622	−	7.80500i	−0.149134	−	0.258308i
$914$	−8.93727	+	15.4798i	−0.295618	+	0.512026i
$915$	−3.85593	−	6.67867i	−0.127473	−	0.220790i
$916$	56.3936			1.86330
$917$	−1.66049			−0.0548341
$918$	−20.5048	+	35.5153i	−0.676759	+	1.17218i
$919$	1.49724	−	2.59330i	0.0493895	−	0.0855451i	−0.840274	−	0.542162i	$-0.817606\pi$
$919$	1.49724	−	2.59330i	0.0493895	−	0.0855451i	0.889663	+	0.456617i	$0.150939\pi$
$920$	74.6794			2.46211
$921$	26.3660			0.868789
$922$	−34.1937	+	59.2252i	−1.12611	+	1.95048i
$923$	−0.347136			−0.0114261
$924$	−10.6915			−0.351725
$925$	12.8508	−	22.2583i	0.422533	−	0.731848i
$926$	1.94858	+	3.37503i	0.0640342	+	0.110910i
$927$	4.60965	−	7.98415i	0.151401	−	0.262234i
$928$	−14.7170			−0.483110
$929$	11.5845	−	20.0650i	0.380076	−	0.658311i	−0.610997	−	0.791633i	$-0.709231\pi$
$929$	11.5845	−	20.0650i	0.380076	−	0.658311i	0.991073	+	0.133322i	$0.0425646\pi$
$930$	−8.29482	+	14.3671i	−0.271998	+	0.471114i
$931$	−41.8206			−1.37062
$932$	−6.95232	−	12.0418i	−0.227731	−	0.394441i
$933$	17.8712	−	30.9538i	0.585076	−	1.01338i
$934$	23.5484			0.770529
$935$	19.5225	−	33.8140i	0.638454	−	1.10584i
$936$	−17.8271			−0.582696
$937$	22.3448			0.729974			0.364987	−	0.931013i	$-0.381073\pi$
$937$	22.3448			0.729974			0.364987	+	0.931013i	$0.381073\pi$
$938$	6.91158			0.225671
$939$	28.9234			0.943881
$940$	−46.6992	−	80.8854i	−1.52316	−	2.63819i
$941$	37.5778			1.22500			0.612501	−	0.790469i	$-0.290163\pi$
$941$	37.5778			1.22500			0.612501	+	0.790469i	$0.290163\pi$
$942$	−32.2184	−	55.8039i	−1.04973	−	1.81819i
$943$	2.05429			0.0668970
$944$	1.90768	+	3.30420i	0.0620896	+	0.107542i
$945$	6.78895	−	11.7588i	0.220845	−	0.382514i
$946$	39.7996	+	68.9349i	1.29400	+	2.24127i
$947$	−3.93563			−0.127891			−0.0639454	−	0.997953i	$-0.520368\pi$
$947$	−3.93563			−0.127891			−0.0639454	+	0.997953i	$0.520368\pi$
$948$	5.30071	−	9.18109i	0.172159	−	0.298188i
$949$	10.2579	+	17.7672i	0.332986	+	0.576749i
$950$	−48.2386	−	83.5517i	−1.56507	−	2.71077i
$951$	10.1330	+	17.5508i	0.328583	+	0.569123i
$952$	−2.97002	+	5.14423i	−0.0962590	+	0.166725i
$953$	−7.85417	+	13.6038i	−0.254421	+	0.440671i	−0.964738	−	0.263211i	$-0.915218\pi$
$953$	−7.85417	+	13.6038i	−0.254421	+	0.440671i	0.710317	+	0.703882i	$0.248552\pi$
$954$	−4.21416	+	7.29914i	−0.136438	+	0.236318i
$955$	−21.1251	+	36.5898i	−0.683593	+	1.18402i
$956$	19.7170			0.637694
$957$	5.81987	−	10.0803i	0.188130	−	0.325850i
$958$	−10.5199			−0.339882
$959$	−7.71818			−0.249233
$960$	29.7576	+	51.5418i	0.960424	+	1.66350i
$961$	14.2197	+	24.6293i	0.458702	+	0.794494i
$962$	24.9972	−	43.2965i	0.805943	−	1.39593i
$963$	12.0101			0.387019
$964$	14.4302	+	46.7825i	0.464764	+	1.50676i
$965$	10.3441			0.332990
$966$	−9.01076	+	15.6071i	−0.289917	+	0.502150i
$967$	−11.6219	−	20.1297i	−0.373734	−	0.647327i	0.616402	−	0.787431i	$-0.288590\pi$
$967$	−11.6219	−	20.1297i	−0.373734	−	0.647327i	−0.990137	+	0.140104i	$0.955256\pi$
$968$	−2.32999	−	4.03566i	−0.0748887	−	0.129711i
$969$	−27.6565			−0.888454
$970$	−134.462			−4.31732
$971$	12.8965	−	22.3374i	0.413869	−	0.716842i	−0.581440	−	0.813589i	$-0.697510\pi$
$971$	12.8965	−	22.3374i	0.413869	−	0.716842i	0.995309	+	0.0967469i	$0.0308437\pi$
$972$	−36.6271			−1.17482
$973$	−5.22157	+	9.04402i	−0.167396	+	0.289938i
$974$	−13.6923	+	23.7157i	−0.438729	+	0.759900i
$975$	25.0551	−	43.3966i	0.802404	−	1.38980i
$976$	0.305560	−	0.529246i	0.00978075	−	0.0169408i
$977$	26.5660	+	46.0136i	0.849921	+	1.47211i	0.881278	+	0.472598i	$0.156684\pi$
$977$	26.5660	+	46.0136i	0.849921	+	1.47211i	−0.0313567	+	0.999508i	$0.509983\pi$
$978$	0.0508957	+	0.0881539i	0.00162746	+	0.00281885i
$979$	30.1196	+	52.1686i	0.962625	+	1.66732i
$980$	−34.9127	+	60.4705i	−1.11524	+	1.93166i
$981$	21.9289			0.700135
$982$	−27.2654	−	47.2251i	−0.870075	−	1.50701i
$983$	−3.20209	+	5.54618i	−0.102131	+	0.176896i	−0.912562	−	0.408938i	$-0.865899\pi$
$983$	−3.20209	+	5.54618i	−0.102131	+	0.176896i	0.810432	+	0.585833i	$0.199233\pi$
$984$	−0.430816	−	0.746196i	−0.0137339	−	0.0237878i
$985$	6.49011			0.206792
$986$	−8.83912	−	15.3098i	−0.281495	−	0.487564i
$987$	8.24490			0.262438
$988$	−57.4186	−	99.4519i	−1.82673	−	3.16399i
$989$	82.1028			2.61072
$990$	33.2524			1.05683
$991$	−30.6132			−0.972460			−0.486230	−	0.873831i	$-0.661628\pi$
$991$	−30.6132			−0.972460			−0.486230	+	0.873831i	$0.661628\pi$
$992$	−9.69599			−0.307848
$993$	17.1817	−	29.7596i	0.545246	−	0.944394i
$994$	−0.0985069			−0.00312445
$995$	−16.6918	+	28.9110i	−0.529165	+	0.916540i
$996$	5.32925	+	9.23054i	0.168864	+	0.292481i
$997$	32.2577			1.02161			0.510806	−	0.859696i	$-0.329347\pi$
$997$	32.2577			1.02161			0.510806	+	0.859696i	$0.329347\pi$
$998$	−18.0419	+	31.2495i	−0.571106	+	0.989185i
$999$	10.9624	−	18.9875i	0.346836	−	0.600737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.c.a.225.3	yes	38
241.15	even	3	inner	241.2.c.a.15.3	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.c.a.15.3	✓	38	241.15	even	3	inner
241.2.c.a.225.3	yes	38	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.13508 + 1.96602i) q^{2} +(0.670299 + 1.16099i) q^{3} +(-1.57681 - 2.73112i) q^{4} -3.40659 q^{5} -3.04337 q^{6} +(-0.353709 + 0.612643i) q^{7} +2.61891 q^{8} +(0.601399 - 1.04165i) q^{9} +O(q^{10})\)	\(q+(-1.13508 + 1.96602i) q^{2} +(0.670299 + 1.16099i) q^{3} +(-1.57681 - 2.73112i) q^{4} -3.40659 q^{5} -3.04337 q^{6} +(-0.353709 + 0.612643i) q^{7} +2.61891 q^{8} +(0.601399 - 1.04165i) q^{9} +(3.86675 - 6.69740i) q^{10} +(-1.78741 + 3.09589i) q^{11} +(2.11387 - 3.66133i) q^{12} +(-2.82967 - 4.90113i) q^{13} +(-0.802977 - 1.39080i) q^{14} +(-2.28343 - 3.95502i) q^{15} +(0.180949 - 0.313412i) q^{16} +3.20621 q^{17} +(1.36527 + 2.36472i) q^{18} +(-3.21719 + 5.57234i) q^{19} +(5.37155 + 9.30379i) q^{20} -0.948364 q^{21} +(-4.05771 - 7.02816i) q^{22} -8.37067 q^{23} +(1.75545 + 3.04054i) q^{24} +6.60482 q^{25} +12.8476 q^{26} +5.63426 q^{27} +2.23093 q^{28} +(-1.21440 + 2.10340i) q^{29} +10.3675 q^{30} +(-0.800079 + 1.38578i) q^{31} +(3.02970 + 5.24759i) q^{32} -4.79240 q^{33} +(-3.63930 + 6.30346i) q^{34} +(1.20494 - 2.08702i) q^{35} -3.79318 q^{36} +(1.94567 - 3.37000i) q^{37} +(-7.30354 - 12.6501i) q^{38} +(3.79345 - 6.57044i) q^{39} -8.92156 q^{40} -0.245416 q^{41} +(1.07647 - 1.86450i) q^{42} -9.80839 q^{43} +11.2737 q^{44} +(-2.04872 + 3.54848i) q^{45} +(9.50138 - 16.4569i) q^{46} -8.69381 q^{47} +0.485159 q^{48} +(3.24978 + 5.62878i) q^{49} +(-7.49700 + 12.9852i) q^{50} +(2.14912 + 3.72238i) q^{51} +(-8.92372 + 15.4563i) q^{52} +(1.54334 + 2.67314i) q^{53} +(-6.39534 + 11.0770i) q^{54} +(6.08897 - 10.5464i) q^{55} +(-0.926335 + 1.60446i) q^{56} -8.62591 q^{57} +(-2.75688 - 4.77505i) q^{58} +(-5.27133 + 9.13020i) q^{59} +(-7.20108 + 12.4726i) q^{60} +1.68866 q^{61} +(-1.81631 - 3.14594i) q^{62} +(0.425441 + 0.736886i) q^{63} -13.0320 q^{64} +(9.63951 + 16.6961i) q^{65} +(5.43975 - 9.42193i) q^{66} +(-2.15186 + 3.72713i) q^{67} +(-5.05559 - 8.75654i) q^{68} +(-5.61085 - 9.71828i) q^{69} +(2.73541 + 4.73787i) q^{70} +(0.0306693 - 0.0531208i) q^{71} +(1.57501 - 2.72800i) q^{72} -3.62513 q^{73} +(4.41699 + 7.65045i) q^{74} +(4.42721 + 7.66815i) q^{75} +20.2916 q^{76} +(-1.26445 - 2.19009i) q^{77} +(8.61173 + 14.9160i) q^{78} +2.50758 q^{79} +(-0.616417 + 1.06767i) q^{80} +(1.97244 + 3.41637i) q^{81} +(0.278566 - 0.482491i) q^{82} +(-1.26054 + 2.18333i) q^{83} +(1.49539 + 2.59010i) q^{84} -10.9222 q^{85} +(11.1333 - 19.2835i) q^{86} -3.25603 q^{87} +(-4.68108 + 8.10786i) q^{88} +(8.42547 - 14.5933i) q^{89} +(-4.65092 - 8.05562i) q^{90} +4.00352 q^{91} +(13.1990 + 22.8613i) q^{92} -2.14517 q^{93} +(9.86817 - 17.0922i) q^{94} +(10.9596 - 18.9826i) q^{95} +(-4.06160 + 7.03490i) q^{96} +(-8.69349 - 15.0576i) q^{97} -14.7550 q^{98} +(2.14990 + 3.72373i) 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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