LMFDB - Embedded newform 196.3.o.a.11.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,3,Mod(11,196)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("196.11"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([21, 40])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	196.o (of order $42$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.34061318146$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	196.11
Dual form			196.3.o.a.107.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.99274 - 0.170222i) q^{2} +(-0.201068 - 1.33400i) q^{3} +(3.94205 + 0.678419i) q^{4} +(3.01252 - 7.67577i) q^{5} +(0.173600 + 2.69254i) q^{6} +(-6.53373 - 2.51206i) q^{7} +(-7.74001 - 2.02294i) q^{8} +(6.86104 - 2.11635i) q^{9} +(-7.30976 + 14.7830i) q^{10} +(0.180239 - 0.584320i) q^{11} +(0.112390 - 5.39509i) q^{12} +(0.695840 + 3.04867i) q^{13} +(12.5924 + 6.11807i) q^{14} +(-10.8452 - 2.47534i) q^{15} +(15.0795 + 5.34872i) q^{16} +(-2.98737 + 2.03675i) q^{17} +(-14.0325 + 3.04944i) q^{18} +(-17.4578 + 10.0793i) q^{19} +(17.0829 - 28.2145i) q^{20} +(-2.03735 + 9.22106i) q^{21} +(-0.458634 + 1.13372i) q^{22} +(10.8059 - 15.8493i) q^{23} +(-1.14233 + 10.7319i) q^{24} +(-31.5159 - 29.2425i) q^{25} +(-0.867677 - 6.19367i) q^{26} +(-9.47077 - 19.6663i) q^{27} +(-24.0520 - 14.3353i) q^{28} +(-27.3869 - 13.1888i) q^{29} +(21.1903 + 6.77880i) q^{30} +(-18.8189 - 10.8651i) q^{31} +(-29.1391 - 13.2255i) q^{32} +(-0.815721 - 0.122950i) q^{33} +(6.29975 - 3.55021i) q^{34} +(-38.9649 + 42.5838i) q^{35} +(28.4823 - 3.68810i) q^{36} +(-2.23580 - 29.8347i) q^{37} +(36.5046 - 17.1137i) q^{38} +(3.92701 - 1.54124i) q^{39} +(-38.8445 + 53.3164i) q^{40} +(43.3837 + 54.4014i) q^{41} +(5.62956 - 18.0284i) q^{42} +(-29.8735 - 23.8233i) q^{43} +(1.10692 - 2.18114i) q^{44} +(4.42438 - 59.0393i) q^{45} +(-24.2313 + 29.7442i) q^{46} +(39.3963 + 42.4591i) q^{47} +(4.10318 - 21.1914i) q^{48} +(36.3791 + 32.8262i) q^{49} +(57.8253 + 63.6374i) q^{50} +(3.31768 + 3.57561i) q^{51} +(0.674756 + 12.4901i) q^{52} +(6.96518 - 92.9439i) q^{53} +(15.5252 + 40.8019i) q^{54} +(-3.94214 - 3.14375i) q^{55} +(45.4893 + 32.6607i) q^{56} +(16.9559 + 21.2620i) q^{57} +(52.3300 + 30.9438i) q^{58} +(43.3299 - 17.0057i) q^{59} +(-41.0729 - 17.1155i) q^{60} +(5.55713 + 74.1548i) q^{61} +(35.6518 + 24.8548i) q^{62} +(-50.1445 - 3.40767i) q^{63} +(55.8154 + 31.3151i) q^{64} +(25.4971 + 3.84308i) q^{65} +(1.60459 + 0.383862i) q^{66} +(-12.5479 - 7.24451i) q^{67} +(-13.1581 + 6.00229i) q^{68} +(-23.3157 - 11.2282i) q^{69} +(84.8958 - 78.2258i) q^{70} +(10.8237 + 22.4756i) q^{71} +(-57.3857 + 2.50110i) q^{72} +(-53.7717 - 49.8929i) q^{73} +(-0.623157 + 59.8335i) q^{74} +(-32.6725 + 47.9218i) q^{75} +(-75.6575 + 27.8893i) q^{76} +(-2.64548 + 3.36502i) q^{77} +(-8.08787 + 2.40282i) q^{78} +(100.498 - 58.0223i) q^{79} +(86.4828 - 99.6336i) q^{80} +(29.0613 - 19.8137i) q^{81} +(-77.1922 - 115.793i) q^{82} +(129.911 + 29.6514i) q^{83} +(-14.2871 + 34.9677i) q^{84} +(6.63414 + 29.0661i) q^{85} +(55.4750 + 52.5589i) q^{86} +(-12.0872 + 39.1858i) q^{87} +(-2.57710 + 4.15803i) q^{88} +(-30.1566 + 9.30207i) q^{89} +(-18.8665 + 116.897i) q^{90} +(3.11202 - 21.6672i) q^{91} +(53.3498 - 55.1479i) q^{92} +(-10.7102 + 27.2890i) q^{93} +(-71.2792 - 91.3162i) q^{94} +(24.7742 + 164.366i) q^{95} +(-11.7838 + 41.5306i) q^{96} -87.2158 q^{97} +(-66.9065 - 71.6067i) q^{98} -4.39049i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 13 q^{4} - 26 q^{5} - 2 q^{6} - 16 q^{8} - 176 q^{9} - 12 q^{10} + 45 q^{12} - 4 q^{13} + 89 q^{14} - 25 q^{16} - 26 q^{17} - 48 q^{18} - 166 q^{20} + 50 q^{21} + 10 q^{22} - 96 q^{24}+ \cdots + 771 q^{98}+O(q^{100}) $ 648 * q - 13 * q^2 - 13 * q^4 - 26 * q^5 - 2 * q^6 - 16 * q^8 - 176 * q^9 - 12 * q^10 + 45 * q^12 - 4 * q^13 + 89 * q^14 - 25 * q^16 - 26 * q^17 - 48 * q^18 - 166 * q^20 + 50 * q^21 + 10 * q^22 - 96 * q^24 + 212 * q^25 - 70 * q^26 + 188 * q^28 + 100 * q^29 + 57 * q^30 + 57 * q^32 - 14 * q^33 - 230 * q^34 - 44 * q^36 - 346 * q^37 - 40 * q^38 - 258 * q^40 - 36 * q^41 - 82 * q^42 - 366 * q^44 - 184 * q^45 - 100 * q^46 - 540 * q^48 - 136 * q^49 - 112 * q^50 + 50 * q^52 - 34 * q^53 - 259 * q^54 + 600 * q^56 + 34 * q^57 + 100 * q^58 + 562 * q^60 + 278 * q^61 + 490 * q^62 - 100 * q^64 + 64 * q^65 + 1340 * q^66 + 61 * q^68 + 160 * q^69 + 666 * q^70 - 412 * q^72 + 206 * q^73 - 202 * q^74 - 177 * q^76 + 234 * q^77 - 632 * q^78 - 364 * q^80 + 618 * q^81 - 2246 * q^82 - 1988 * q^84 - 264 * q^85 - 1025 * q^86 - 1283 * q^88 - 34 * q^89 - 1124 * q^90 - 910 * q^92 - 268 * q^93 + 94 * q^94 - 814 * q^96 - 800 * q^97 + 771 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{20}{21}\right)$

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 $

$2$	−1.99274	−	0.170222i	−0.996371	−	0.0851112i
$2$	−1.99274	−	0.170222i	−0.996371	−	0.0851112i
$3$	−0.201068	−	1.33400i	−0.0670225	−	0.444665i	−0.997023	−	0.0771067i	$-0.975432\pi$
$3$	−0.201068	−	1.33400i	−0.0670225	−	0.444665i	0.930000	−	0.367559i	$-0.119806\pi$
$4$	3.94205	+	0.678419i	0.985512	+	0.169605i
$5$	3.01252	−	7.67577i	0.602504	−	1.53515i	−0.225390	−	0.974269i	$-0.572366\pi$
$5$	3.01252	−	7.67577i	0.602504	−	1.53515i	0.827893	−	0.560885i	$-0.189539\pi$
$6$	0.173600	+	2.69254i	0.0289333	+	0.448756i
$7$	−6.53373	−	2.51206i	−0.933389	−	0.358865i
$7$	−6.53373	−	2.51206i	−0.933389	−	0.358865i
$8$	−7.74001	−	2.02294i	−0.967501	−	0.252867i
$9$	6.86104	−	2.11635i	0.762337	−	0.235150i
$10$	−7.30976	+	14.7830i	−0.730976	+	1.47830i
$11$	0.180239	−	0.584320i	0.0163854	−	0.0531200i	−0.947011	−	0.321201i	$-0.895913\pi$
$11$	0.180239	−	0.584320i	0.0163854	−	0.0531200i	0.963396	+	0.268081i	$0.0863896\pi$
$12$	0.112390	−	5.39509i	0.00936585	−	0.449591i
$13$	0.695840	+	3.04867i	0.0535261	+	0.234513i	0.994614	−	0.103649i	$-0.0330519\pi$
$13$	0.695840	+	3.04867i	0.0535261	+	0.234513i	−0.941088	+	0.338162i	$0.890195\pi$
$14$	12.5924	+	6.11807i	0.899459	+	0.437005i
$15$	−10.8452	−	2.47534i	−0.723011	−	0.165023i
$16$	15.0795	+	5.34872i	0.942468	+	0.334295i
$17$	−2.98737	+	2.03675i	−0.175727	+	0.119809i	−0.647990	−	0.761649i	$-0.724390\pi$
$17$	−2.98737	+	2.03675i	−0.175727	+	0.119809i	0.472262	+	0.881458i	$0.343438\pi$
$18$	−14.0325	+	3.04944i	−0.779585	+	0.169413i
$19$	−17.4578	+	10.0793i	−0.918832	+	0.530488i	−0.883262	−	0.468879i	$-0.844658\pi$
$19$	−17.4578	+	10.0793i	−0.918832	+	0.530488i	−0.0355698	+	0.999367i	$0.511325\pi$
$20$	17.0829	−	28.2145i	0.854144	−	1.41073i
$21$	−2.03735	+	9.22106i	−0.0970169	+	0.439098i
$22$	−0.458634	+	1.13372i	−0.0208470	+	0.0515327i
$23$	10.8059	−	15.8493i	0.469821	−	0.689101i	−0.516059	−	0.856553i	$-0.672601\pi$
$23$	10.8059	−	15.8493i	0.469821	−	0.689101i	0.985880	+	0.167452i	$0.0535539\pi$
$24$	−1.14233	+	10.7319i	−0.0475971	+	0.447162i
$25$	−31.5159	−	29.2425i	−1.26064	−	1.16970i
$26$	−0.867677	−	6.19367i	−0.0333722	−	0.238218i
$27$	−9.47077	−	19.6663i	−0.350769	−	0.728380i
$28$	−24.0520	−	14.3353i	−0.859001	−	0.511973i
$29$	−27.3869	−	13.1888i	−0.944375	−	0.454787i	−0.102664	−	0.994716i	$-0.532737\pi$
$29$	−27.3869	−	13.1888i	−0.944375	−	0.454787i	−0.841711	+	0.539929i	$0.818451\pi$
$30$	21.1903	+	6.77880i	0.706342	+	0.225960i
$31$	−18.8189	−	10.8651i	−0.607063	−	0.350488i	0.164752	−	0.986335i	$-0.447318\pi$
$31$	−18.8189	−	10.8651i	−0.607063	−	0.350488i	−0.771815	+	0.635847i	$0.780651\pi$
$32$	−29.1391	−	13.2255i	−0.910596	−	0.413297i
$33$	−0.815721	−	0.122950i	−0.0247188	−	0.00372576i
$34$	6.29975	−	3.55021i	0.185287	−	0.104418i
$35$	−38.9649	+	42.5838i	−1.11328	+	1.21668i
$36$	28.4823	−	3.68810i	0.791175	−	0.102447i
$37$	−2.23580	−	29.8347i	−0.0604271	−	0.806344i	−0.942281	−	0.334822i	$-0.891324\pi$
$37$	−2.23580	−	29.8347i	−0.0604271	−	0.806344i	0.881854	−	0.471522i	$-0.156295\pi$
$38$	36.5046	−	17.1137i	0.960649	−	0.450360i
$39$	3.92701	−	1.54124i	0.100692	−	0.0395189i
$40$	−38.8445	+	53.3164i	−0.971113	+	1.33291i
$41$	43.3837	+	54.4014i	1.05814	+	1.32686i	0.942734	+	0.333545i	$0.108245\pi$
$41$	43.3837	+	54.4014i	1.05814	+	1.32686i	0.115404	+	0.993319i	$0.463184\pi$
$42$	5.62956	−	18.0284i	0.134037	−	0.429248i
$43$	−29.8735	−	23.8233i	−0.694733	−	0.554031i	0.211205	−	0.977442i	$-0.432261\pi$
$43$	−29.8735	−	23.8233i	−0.694733	−	0.554031i	−0.905938	+	0.423411i	$0.860833\pi$
$44$	1.10692	−	2.18114i	0.0251574	−	0.0495714i
$45$	4.42438	−	59.0393i	0.0983196	−	1.31198i
$46$	−24.2313	+	29.7442i	−0.526767	+	0.646614i
$47$	39.3963	+	42.4591i	0.838219	+	0.903386i	0.996465	−	0.0840143i	$-0.0267741\pi$
$47$	39.3963	+	42.4591i	0.838219	+	0.903386i	−0.158245	+	0.987400i	$0.550584\pi$
$48$	4.10318	−	21.1914i	0.0854829	−	0.441488i
$49$	36.3791	+	32.8262i	0.742431	+	0.669922i
$50$	57.8253	+	63.6374i	1.15651	+	1.27275i
$51$	3.31768	+	3.57561i	0.0650526	+	0.0701100i
$52$	0.674756	+	12.4901i	0.0129761	+	0.240194i
$53$	6.96518	−	92.9439i	0.131419	−	1.75366i	−0.409250	−	0.912422i	$-0.634210\pi$
$53$	6.96518	−	92.9439i	0.131419	−	1.75366i	0.540668	−	0.841236i	$-0.318171\pi$
$54$	15.5252	+	40.8019i	0.287503	+	0.755591i
$55$	−3.94214	−	3.14375i	−0.0716752	−	0.0571591i
$56$	45.4893	+	32.6607i	0.812310	+	0.583226i
$57$	16.9559	+	21.2620i	0.297472	+	0.373018i
$58$	52.3300	+	30.9438i	0.902241	+	0.533514i
$59$	43.3299	−	17.0057i	0.734405	−	0.288233i	0.0314877	−	0.999504i	$-0.489975\pi$
$59$	43.3299	−	17.0057i	0.734405	−	0.288233i	0.702918	+	0.711271i	$0.251880\pi$
$60$	−41.0729	−	17.1155i	−0.684548	−	0.285258i
$61$	5.55713	+	74.1548i	0.0911005	+	1.21565i	0.836096	+	0.548583i	$0.184832\pi$
$61$	5.55713	+	74.1548i	0.0911005	+	1.21565i	−0.744996	+	0.667069i	$0.767549\pi$
$62$	35.6518	+	24.8548i	0.575030	+	0.400884i
$63$	−50.1445	−	3.40767i	−0.795945	−	0.0540900i
$64$	55.8154	+	31.3151i	0.872116	+	0.489299i
$65$	25.4971	+	3.84308i	0.392264	+	0.0591242i
$66$	1.60459	+	0.383862i	0.0243120	+	0.00581609i
$67$	−12.5479	−	7.24451i	−0.187281	−	0.108127i	0.403428	−	0.915011i	$-0.367819\pi$
$67$	−12.5479	−	7.24451i	−0.187281	−	0.108127i	−0.590709	+	0.806884i	$0.701152\pi$
$68$	−13.1581	+	6.00229i	−0.193502	+	0.0882689i
$69$	−23.3157	−	11.2282i	−0.337908	−	0.162728i
$70$	84.8958	−	78.2258i	1.21280	−	1.11751i
$71$	10.8237	+	22.4756i	0.152446	+	0.316557i	0.963180	−	0.268857i	$-0.0866460\pi$
$71$	10.8237	+	22.4756i	0.152446	+	0.316557i	−0.810734	+	0.585415i	$0.800932\pi$
$72$	−57.3857	+	2.50110i	−0.797024	+	0.0347375i
$73$	−53.7717	−	49.8929i	−0.736599	−	0.683464i	0.219794	−	0.975546i	$-0.429461\pi$
$73$	−53.7717	−	49.8929i	−0.736599	−	0.683464i	−0.956393	+	0.292082i	$0.905652\pi$
$74$	−0.623157	+	59.8335i	−0.00842104	+	0.808561i
$75$	−32.6725	+	47.9218i	−0.435634	+	0.638957i
$76$	−75.6575	+	27.8893i	−0.995494	+	0.366964i
$77$	−2.64548	+	3.36502i	−0.0343569	+	0.0437015i
$78$	−8.08787	+	2.40282i	−0.103691	+	0.0308054i
$79$	100.498	−	58.0223i	1.27212	−	0.734459i	0.296734	−	0.954960i	$-0.404103\pi$
$79$	100.498	−	58.0223i	1.27212	−	0.734459i	0.975387	+	0.220501i	$0.0707693\pi$
$80$	86.4828	−	99.6336i	1.08104	−	1.24542i
$81$	29.0613	−	19.8137i	0.358781	−	0.244613i
$82$	−77.1922	−	115.793i	−0.941368	−	1.41211i
$83$	129.911	+	29.6514i	1.56520	+	0.357246i	0.915299	−	0.402776i	$-0.131955\pi$
$83$	129.911	+	29.6514i	1.56520	+	0.357246i	0.649898	+	0.760022i	$0.274812\pi$
$84$	−14.2871	+	34.9677i	−0.170084	+	0.416282i
$85$	6.63414	+	29.0661i	0.0780488	+	0.341954i
$86$	55.4750	+	52.5589i	0.645058	+	0.611151i
$87$	−12.0872	+	39.1858i	−0.138934	+	0.450412i
$88$	−2.57710	+	4.15803i	−0.0292852	+	0.0472504i
$89$	−30.1566	+	9.30207i	−0.338838	+	0.104518i	−0.459504	−	0.888175i	$-0.651973\pi$
$89$	−30.1566	+	9.30207i	−0.338838	+	0.104518i	0.120667	+	0.992693i	$0.461497\pi$
$90$	−18.8665	+	116.897i	−0.209627	+	1.29886i
$91$	3.11202	−	21.6672i	0.0341980	−	0.238101i
$92$	53.3498	−	55.1479i	0.579889	−	0.599434i
$93$	−10.7102	+	27.2890i	−0.115163	+	0.293430i
$94$	−71.2792	−	91.3162i	−0.758290	−	0.971449i
$95$	24.7742	+	164.366i	0.260781	+	1.73017i
$96$	−11.7838	+	41.5306i	−0.122748	+	0.432611i
$97$	−87.2158			−0.899132			−0.449566	−	0.893247i	$-0.648421\pi$
$97$	−87.2158			−0.899132			−0.449566	+	0.893247i	$0.648421\pi$
$98$	−66.9065	−	71.6067i	−0.682719	−	0.730681i
$99$		−	4.39049i		−	0.0443484i
$100$	−104.399	−	136.656i	−1.04399	−	1.36656i
$101$	13.4418	−	2.02603i	0.133087	−	0.0200597i	−0.0821607	−	0.996619i	$-0.526182\pi$
$101$	13.4418	−	2.02603i	0.133087	−	0.0200597i	0.215248	+	0.976559i	$0.430944\pi$
$102$	−6.00264	−	7.69002i	−0.0588494	−	0.0753923i
$103$	12.0111	+	4.71402i	0.116613	+	0.0457672i	0.422930	−	0.906162i	$-0.361002\pi$
$103$	12.0111	+	4.71402i	0.116613	+	0.0457672i	−0.306317	+	0.951929i	$0.599097\pi$
$104$	0.781477	−	25.0044i	0.00751420	−	0.240427i
$105$	64.6412	+	43.4169i	0.615630	+	0.413494i
$106$	−29.7009	+	184.028i	−0.280198	+	1.73611i
$107$	19.2515	+	62.4117i	0.179920	+	0.583287i	0.999940	+	0.0109521i	$0.00348622\pi$
$107$	19.2515	+	62.4117i	0.179920	+	0.583287i	−0.820020	+	0.572335i	$0.806038\pi$
$108$	−23.9923	−	83.9505i	−0.222151	−	0.777319i
$109$	−48.7495	−	15.0372i	−0.447243	−	0.137956i	0.0629491	−	0.998017i	$-0.479949\pi$
$109$	−48.7495	−	15.0372i	−0.447243	−	0.137956i	−0.510192	+	0.860061i	$0.670426\pi$
$110$	7.32053	+	6.93572i	0.0665502	+	0.0630520i
$111$	−39.3499	+	8.98135i	−0.354503	+	0.0809131i
$112$	−85.0890	−	72.8276i	−0.759723	−	0.650247i
$113$	−18.0847	+	79.2341i	−0.160041	+	0.701187i	0.829687	+	0.558228i	$0.188519\pi$
$113$	−18.0847	+	79.2341i	−0.160041	+	0.701187i	−0.989729	+	0.142958i	$0.954339\pi$
$114$	−30.1695	−	45.2561i	−0.264645	−	0.396983i
$115$	−89.1029	−	130.690i	−0.774808	−	1.13643i
$116$	−99.0128	−	70.5708i	−0.853559	−	0.608369i
$117$	11.2262	+	19.4444i	0.0959508	+	0.166192i
$118$	−89.2401	+	26.5123i	−0.756272	+	0.224681i
$119$	24.6351	−	5.80314i	0.207017	−	0.0487659i
$120$	78.9342	+	41.0983i	0.657785	+	0.342486i
$121$	99.6659	+	67.9511i	0.823686	+	0.561579i
$122$	1.54887	−	148.717i	0.0126956	−	1.21899i
$123$	63.8482	−	68.8120i	0.519091	−	0.559447i
$124$	−66.8141	−	55.5980i	−0.538823	−	0.448371i
$125$	−133.671	+	64.3726i	−1.06937	+	0.514981i
$126$	99.3451	+	15.3263i	0.788453	+	0.121638i
$127$	105.137	−	218.319i	0.827850	−	1.71905i	0.143809	−	0.989606i	$-0.454065\pi$
$127$	105.137	−	218.319i	0.827850	−	1.71905i	0.684042	−	0.729443i	$-0.260221\pi$
$128$	−105.895	−	71.9041i	−0.827307	−	0.561750i
$129$	−25.7737	+	44.6413i	−0.199796	+	0.346056i
$130$	−50.1551	−	11.9984i	−0.385808	−	0.0922957i
$131$	36.2028	−	240.190i	0.276357	−	1.83351i	−0.232423	−	0.972615i	$-0.574665\pi$
$131$	36.2028	−	240.190i	0.276357	−	1.83351i	0.508781	−	0.860896i	$-0.330096\pi$
$132$	−3.13220	−	1.03808i	−0.0237288	−	0.00786422i
$133$	139.384	−	22.0002i	1.04800	−	0.165415i
$134$	23.7715	+	16.5724i	0.177399	+	0.123674i
$135$	−179.484	+	13.4505i	−1.32951	+	0.0996334i
$136$	27.2425	−	9.72121i	0.200312	−	0.0714795i
$137$	−23.6843	−	60.3465i	−0.172878	−	0.440486i	0.818005	−	0.575211i	$-0.195080\pi$
$137$	−23.6843	−	60.3465i	−0.172878	−	0.440486i	−0.990883	+	0.134725i	$0.956985\pi$
$138$	44.5508	+	26.3438i	0.322832	+	0.190897i
$139$	98.3567	−	78.4368i	0.707602	−	0.564294i	−0.202196	−	0.979345i	$-0.564808\pi$
$139$	98.3567	−	78.4368i	0.707602	−	0.564294i	0.909798	+	0.415051i	$0.136236\pi$
$140$	−182.491	+	141.433i	−1.30351	+	1.01023i
$141$	48.7190	−	61.0917i	0.345525	−	0.433274i
$142$	−17.7429	−	46.6305i	−0.124950	−	0.328384i
$143$	1.90682	+	0.142896i	0.0133344	+	0.000999275i
$144$	114.781	+	4.78429i	0.797089	+	0.0332243i
$145$	−183.738	+	170.484i	−1.26716	+	1.17575i
$146$	98.6603	+	108.577i	0.675756	+	0.743677i
$147$	36.4753	−	55.1299i	0.248132	−	0.375033i
$148$	11.4268	−	119.127i	0.0772081	−	0.804910i
$149$	203.709	−	189.014i	1.36718	−	1.26855i	0.437970	−	0.898989i	$-0.355698\pi$
$149$	203.709	−	189.014i	1.36718	−	1.26855i	0.929205	−	0.369564i	$-0.120493\pi$
$150$	73.2653	−	89.9342i	0.488435	−	0.599561i
$151$	−76.7217	−	5.74949i	−0.508091	−	0.0380761i	−0.181781	−	0.983339i	$-0.558186\pi$
$151$	−76.7217	−	5.74949i	−0.508091	−	0.0380761i	−0.326310	+	0.945263i	$0.605805\pi$
$152$	155.513	−	42.6975i	1.02311	−	0.280905i
$153$	−16.1860	+	20.2965i	−0.105791	+	0.132657i
$154$	5.84456	−	6.25530i	0.0379517	−	0.0406188i
$155$	−140.091	+	111.719i	−0.903810	+	0.720765i
$156$	16.5261	−	3.41147i	0.105936	−	0.0218684i
$157$	102.441	+	261.016i	0.652493	+	1.66253i	0.745207	+	0.666833i	$0.232350\pi$
$157$	102.441	+	261.016i	0.652493	+	1.66253i	−0.0927143	+	0.995693i	$0.529554\pi$
$158$	−210.142	+	98.5165i	−1.33002	+	0.623522i
$159$	−125.387	+	9.39648i	−0.788599	+	0.0590973i
$160$	−189.298	+	183.823i	−1.18311	+	1.14889i
$161$	−110.417	+	76.4101i	−0.685821	+	0.474597i
$162$	−61.2844	+	34.5366i	−0.378299	+	0.213189i
$163$	−30.5375	+	202.603i	−0.187347	+	1.24296i	0.675448	+	0.737408i	$0.263950\pi$
$163$	−30.5375	+	202.603i	−0.187347	+	1.24296i	−0.862794	+	0.505555i	$0.831288\pi$
$164$	134.114	+	243.885i	0.817766	+	1.48711i
$165$	−3.40111	+	5.89090i	−0.0206128	+	0.0357024i
$166$	−253.832	−	81.2014i	−1.52911	−	0.489165i
$167$	51.9136	−	107.800i	0.310860	−	0.645508i	−0.685745	−	0.727842i	$-0.740523\pi$
$167$	51.9136	−	107.800i	0.310860	−	0.645508i	0.996605	+	0.0823345i	$0.0262376\pi$
$168$	34.4228	−	67.2496i	0.204898	−	0.400295i
$169$	143.454	−	69.0836i	0.848837	−	0.408779i
$170$	−8.27245	−	59.0505i	−0.0486614	−	0.347356i
$171$	−98.4474	+	106.101i	−0.575716	+	0.620474i
$172$	−101.601	−	114.180i	−0.590702	−	0.663835i
$173$	−4.48591	−	3.05844i	−0.0259301	−	0.0176788i	0.550286	−	0.834976i	$-0.314519\pi$
$173$	−4.48591	−	3.05844i	−0.0259301	−	0.0176788i	−0.576216	+	0.817298i	$0.695471\pi$
$174$	30.7570	−	76.0298i	0.176765	−	0.436953i
$175$	132.457	+	270.232i	0.756899	+	1.54418i
$176$	5.84328	−	7.84721i	0.0332004	−	0.0445864i
$177$	−31.3978	−	54.3826i	−0.177389	−	0.307247i
$178$	61.6777	−	13.4033i	0.346504	−	0.0752995i
$179$	−19.1836	−	28.1371i	−0.107171	−	0.157191i	0.768907	−	0.639361i	$-0.220801\pi$
$179$	−19.1836	−	28.1371i	−0.107171	−	0.157191i	−0.876077	+	0.482170i	$0.839849\pi$
$180$	57.4945	−	229.734i	0.319414	−	1.27630i
$181$	22.3804	−	98.0551i	0.123649	−	0.541741i	−0.874719	−	0.484630i	$-0.838954\pi$
$181$	22.3804	−	98.0551i	0.123649	−	0.541741i	0.998368	−	0.0571104i	$-0.0181887\pi$
$182$	−9.88969	+	42.6474i	−0.0543389	+	0.234326i
$183$	97.8048	−	22.3233i	0.534453	−	0.121985i
$184$	−115.700	+	100.814i	−0.628804	+	0.547904i
$185$	−235.740	−	72.7161i	−1.27427	−	0.393060i
$186$	25.9878	−	52.5569i	0.139719	−	0.282564i
$187$	0.651676	+	2.11268i	0.00348490	+	0.0112978i
$188$	126.497	+	194.103i	0.672857	+	1.03246i
$189$	12.4766	+	152.285i	0.0660140	+	0.805741i
$190$	−21.3898	−	331.757i	−0.112578	−	1.74609i
$191$	336.895	+	132.222i	1.76385	+	0.692260i	0.998835	+	0.0482476i	$0.0153637\pi$
$191$	336.895	+	132.222i	1.76385	+	0.692260i	0.765015	+	0.644013i	$0.222732\pi$
$192$	30.5516	−	80.7540i	0.159123	−	0.420594i
$193$	−309.922	+	46.7132i	−1.60581	+	0.242037i	−0.889902	−	0.456153i	$-0.849227\pi$
$193$	−309.922	+	46.7132i	−1.60581	+	0.242037i	−0.715912	+	0.698190i	$0.753989\pi$
$194$	173.799	+	14.8461i	0.895870	+	0.0765263i
$195$		−	34.7858i		−	0.178389i
$196$	121.138	+	154.083i	0.618053	+	0.786136i
$197$	28.8911			0.146656			0.0733278	−	0.997308i	$-0.476638\pi$
$197$	28.8911			0.146656			0.0733278	+	0.997308i	$0.476638\pi$
$198$	−0.747360	+	8.74912i	−0.00377455	+	0.0441875i
$199$	6.46474	+	42.8907i	0.0324861	+	0.215531i	0.999184	−	0.0403889i	$-0.0128597\pi$
$199$	6.46474	+	42.8907i	0.0324861	+	0.215531i	−0.966698	+	0.255920i	$0.917622\pi$
$200$	184.777	+	290.092i	0.923887	+	1.45046i
$201$	−7.14118	+	18.1954i	−0.0355283	+	0.0905245i
$202$	−27.1310	+	1.74926i	−0.134312	+	0.00865969i
$203$	145.807	+	154.970i	0.718262	+	0.763397i
$204$	10.6527	+	16.3460i	0.0522191	+	0.0801275i
$205$	548.267	−	169.118i	2.67447	−	0.824965i
$206$	−23.1326	−	11.4384i	−0.112294	−	0.0555262i
$207$	40.5969	−	131.612i	0.196120	−	0.635806i
$208$	−5.81359	+	49.6943i	−0.0279500	+	0.238915i
$209$	2.74295	+	12.0176i	0.0131241	+	0.0575006i
$210$	−121.423	−	97.5220i	−0.578203	−	0.464391i
$211$	147.360	+	33.6338i	0.698386	+	0.159402i	0.556951	−	0.830545i	$-0.311971\pi$
$211$	147.360	+	33.6338i	0.698386	+	0.159402i	0.141435	+	0.989947i	$0.454828\pi$
$212$	90.5120	−	361.664i	0.426943	−	1.70596i
$213$	27.8060	−	18.9578i	0.130545	−	0.0890040i
$214$	−27.7394	−	127.648i	−0.129623	−	0.596484i
$215$	−272.857	+	157.534i	−1.26910	+	0.732717i
$216$	33.5202	+	171.376i	0.155186	+	0.793406i
$217$	95.6640	+	118.264i	0.440848	+	0.544995i
$218$	94.5855	+	38.2636i	0.433878	+	0.175521i
$219$	−55.7452	+	81.7631i	−0.254544	+	0.373348i
$220$	−13.4073	−	15.0672i	−0.0609423	−	0.0684874i
$221$	−8.28812	−	7.69025i	−0.0375028	−	0.0347975i
$222$	79.9430	−	11.1993i	0.360104	−	0.0504473i
$223$	37.5767	+	78.0288i	0.168505	+	0.349905i	0.968072	−	0.250673i	$-0.0806517\pi$
$223$	37.5767	+	78.0288i	0.168505	+	0.349905i	−0.799567	+	0.600577i	$0.794937\pi$
$224$	157.164	+	159.611i	0.701623	+	0.712548i
$225$	−278.119	−	133.935i	−1.23608	−	0.595267i
$226$	49.5255	−	154.815i	0.219139	−	0.685021i
$227$	−267.290	−	154.320i	−1.17749	−	0.679823i	−0.222056	−	0.975034i	$-0.571277\pi$
$227$	−267.290	−	154.320i	−1.17749	−	0.679823i	−0.955432	+	0.295211i	$0.904610\pi$
$228$	52.4165	+	95.3192i	0.229897	+	0.418067i
$229$	−14.7025	−	2.21604i	−0.0642029	−	0.00967703i	0.116862	−	0.993148i	$-0.462716\pi$
$229$	−14.7025	−	2.21604i	−0.0642029	−	0.00967703i	−0.181065	+	0.983471i	$0.557954\pi$
$230$	155.313	+	275.599i	0.675273	+	1.19826i
$231$	5.02084	+	2.85246i	0.0217352	+	0.0123483i
$232$	185.294	+	157.484i	0.798683	+	0.678809i
$233$	−16.0690	−	214.426i	−0.0689658	−	0.920285i	−0.919177	−	0.393844i	$-0.871145\pi$
$233$	−16.0690	−	214.426i	−0.0689658	−	0.920285i	0.850212	−	0.526441i	$-0.176474\pi$
$234$	−19.0611	−	40.6587i	−0.0814578	−	0.173755i
$235$	444.589	−	174.488i	1.89187	−	0.742503i
$236$	182.346	−	37.6416i	0.772651	−	0.159498i
$237$	−97.6083	−	122.397i	−0.411849	−	0.516443i
$238$	−50.0792	+	7.37073i	−0.210417	+	0.0309694i
$239$	−274.680	−	219.050i	−1.14929	−	0.916528i	−0.151876	−	0.988400i	$-0.548531\pi$
$239$	−274.680	−	219.050i	−1.14929	−	0.916528i	−0.997414	+	0.0718714i	$0.977103\pi$
$240$	−150.300	−	95.3346i	−0.626249	−	0.397228i
$241$	−17.6790	+	235.910i	−0.0733567	+	0.978878i	0.832151	+	0.554549i	$0.187109\pi$
$241$	−17.6790	+	235.910i	−0.0733567	+	0.978878i	−0.905508	+	0.424329i	$0.860510\pi$
$242$	−187.042	−	152.374i	−0.772900	−	0.629646i
$243$	−165.895	−	178.793i	−0.682697	−	0.735772i
$244$	−28.4015	+	296.092i	−0.116400	+	1.21349i
$245$	361.559	−	180.348i	1.47575	−	0.736116i
$246$	−138.946	+	126.256i	−0.564823	+	0.513237i
$247$	−42.8762	−	46.2096i	−0.173588	−	0.187083i
$248$	123.679	+	122.166i	0.498707	+	0.492604i
$249$	13.4339	−	179.263i	0.0539515	−	0.719932i
$250$	277.330	−	105.524i	1.10932	−	0.422097i
$251$	−148.390	−	118.337i	−0.591197	−	0.471464i	0.281610	−	0.959529i	$-0.409131\pi$
$251$	−148.390	−	118.337i	−0.591197	−	0.471464i	−0.872807	+	0.488065i	$0.837703\pi$
$252$	−195.360	−	47.4522i	−0.775239	−	0.188302i
$253$	−7.31344	−	9.17077i	−0.0289069	−	0.0362481i
$254$	−246.674	+	417.157i	−0.971157	+	1.64235i
$255$	37.4401	−	14.6942i	0.146824	−	0.0576242i
$256$	198.782	+	161.312i	0.776494	+	0.630125i
$257$	−1.53182	−	20.4407i	−0.00596040	−	0.0795359i	0.993430	−	0.114439i	$-0.0365069\pi$
$257$	−1.53182	−	20.4407i	−0.00596040	−	0.0795359i	−0.999391	+	0.0349027i	$0.988888\pi$
$258$	58.9592	−	84.5713i	0.228524	−	0.327796i
$259$	−60.3384	+	200.548i	−0.232967	+	0.774318i
$260$	97.9038	+	32.4473i	0.376553	+	0.124797i
$261$	−215.815	−	32.5288i	−0.826876	−	0.124631i
$262$	−113.029	+	472.474i	−0.431407	+	1.80334i
$263$	175.841	+	101.522i	0.668596	+	0.386014i	0.795544	−	0.605895i	$-0.207185\pi$
$263$	175.841	+	101.522i	0.668596	+	0.386014i	−0.126949	+	0.991909i	$0.540518\pi$
$264$	6.06497	+	2.60179i	0.0229734	+	0.00985527i
$265$	−692.433	−	333.458i	−2.61296	−	1.25833i
$266$	−281.502	+	20.1144i	−1.05828	+	0.0756179i
$267$	18.4724	+	38.3584i	0.0691851	+	0.143664i
$268$	−44.5494	−	37.0709i	−0.166229	−	0.138324i
$269$	−120.650	−	111.947i	−0.448514	−	0.416160i	0.423306	−	0.905987i	$-0.360870\pi$
$269$	−120.650	−	111.947i	−0.448514	−	0.416160i	−0.871820	+	0.489827i	$0.837060\pi$
$270$	359.956	+	3.74889i	1.33317	+	0.0138848i
$271$	−215.056	+	315.429i	−0.793563	+	1.16394i	0.189716	+	0.981839i	$0.439243\pi$
$271$	−215.056	+	315.429i	−0.793563	+	1.16394i	−0.983279	+	0.182104i	$0.941709\pi$
$272$	−55.9420	+	14.7346i	−0.205669	+	0.0541713i
$273$	−29.5297	+	0.205150i	−0.108167	+	0.000751465i
$274$	36.9243	+	124.287i	0.134760	+	0.453601i
$275$	−22.7674	+	13.1447i	−0.0827904	+	0.0477991i
$276$	−84.2940	−	60.0800i	−0.305413	−	0.217681i
$277$	254.580	−	173.570i	0.919062	−	0.626606i	−0.00862610	−	0.999963i	$-0.502746\pi$
$277$	254.580	−	173.570i	0.919062	−	0.626606i	0.927688	+	0.373357i	$0.121793\pi$
$278$	−209.351	+	139.562i	−0.753062	+	0.502021i
$279$	−152.112	−	34.7185i	−0.545204	−	0.124439i
$280$	387.733	−	250.775i	1.38476	−	0.895625i
$281$	22.3962	+	98.1240i	0.0797017	+	0.349196i	0.999017	−	0.0443255i	$-0.0141139\pi$
$281$	22.3962	+	98.1240i	0.0797017	+	0.349196i	−0.919315	+	0.393521i	$0.871257\pi$
$282$	−107.484	+	113.447i	−0.381147	+	0.402294i
$283$	−103.578	+	335.791i	−0.365999	+	1.18654i	0.566099	+	0.824337i	$0.308452\pi$
$283$	−103.578	+	335.791i	−0.365999	+	1.18654i	−0.932099	+	0.362204i	$0.882024\pi$
$284$	27.4196	+	95.9428i	0.0965478	+	0.337827i
$285$	214.283	−	66.0974i	0.751868	−	0.231921i
$286$	−3.77548	−	0.609339i	−0.0132010	−	0.00213056i
$287$	−146.798	−	464.426i	−0.511490	−	1.61821i
$288$	−227.914	−	29.0721i	−0.791368	−	0.100945i
$289$	−100.808	+	256.853i	−0.348815	+	0.888766i
$290$	395.162	−	308.454i	1.36263	−	1.06363i
$291$	17.5363	+	116.346i	0.0602621	+	0.399813i
$292$	−178.122	−	233.160i	−0.610009	−	0.798493i
$293$	375.278			1.28081			0.640405	−	0.768037i	$-0.278766\pi$
$293$	375.278			1.28081			0.640405	+	0.768037i	$0.278766\pi$
$294$	−82.0703	+	103.651i	−0.279151	+	0.352554i
$295$		−	383.821i		−	1.30109i
$296$	−43.0487	+	235.444i	−0.145435	+	0.795418i
$297$	−13.1984	+	1.98934i	−0.0444390	+	0.00669811i
$298$	−438.114	+	341.981i	−1.47018	+	1.14759i
$299$	55.8386	+	21.9150i	0.186751	+	0.0732944i
$300$	−161.308	+	166.744i	−0.537692	+	0.555815i
$301$	135.340	+	230.699i	0.449634	+	0.766443i
$302$	151.908	+	24.5170i	0.503006	+	0.0811822i
$303$	−5.40543	−	17.5240i	−0.0178397	−	0.0578349i
$304$	−317.166	+	58.6134i	−1.04331	+	0.192807i
$305$	585.936	+	180.737i	1.92110	+	0.592581i
$306$	35.7094	−	37.6906i	0.116697	−	0.123172i
$307$	275.392	−	62.8565i	0.897044	−	0.204744i	0.250948	−	0.968001i	$-0.419258\pi$
$307$	275.392	−	62.8565i	0.897044	−	0.204744i	0.646096	+	0.763256i	$0.276401\pi$
$308$	−12.7115	+	11.4703i	−0.0412711	+	0.0372413i
$309$	3.87344	−	16.9706i	0.0125354	−	0.0549211i
$310$	298.182	−	198.780i	0.961876	−	0.641225i
$311$	−119.807	−	175.724i	−0.385231	−	0.565030i	0.583822	−	0.811881i	$-0.301556\pi$
$311$	−119.807	−	175.724i	−0.385231	−	0.565030i	−0.969053	+	0.246851i	$0.920604\pi$
$312$	−33.5129	+	3.98509i	−0.107413	+	0.0127727i
$313$	141.858	+	245.705i	0.453219	+	0.784999i	0.998584	−	0.0532003i	$-0.0169422\pi$
$313$	141.858	+	245.705i	0.453219	+	0.784999i	−0.545365	+	0.838199i	$0.683609\pi$
$314$	−159.709	−	537.577i	−0.508626	−	1.71203i
$315$	−177.218	+	374.632i	−0.562596	+	1.18931i
$316$	435.529	−	160.547i	1.37826	−	0.508061i
$317$	−476.712	−	325.017i	−1.50382	−	1.02529i	−0.985417	−	0.170154i	$-0.945573\pi$
$317$	−476.712	−	325.017i	−1.50382	−	1.02529i	−0.518406	−	0.855135i	$-0.673474\pi$
$318$	251.464	+	2.61896i	0.790768	+	0.00823573i
$319$	−12.6427	+	13.6256i	−0.0396322	+	0.0427134i
$320$	408.513	−	334.089i	1.27660	−	1.04403i
$321$	79.3862	−	38.2304i	0.247309	−	0.119098i
$322$	233.040	−	133.470i	0.723726	−	0.414504i
$323$	31.6239	−	65.6677i	0.0979068	−	0.203306i
$324$	128.003	−	58.3907i	0.395071	−	0.180218i
$325$	67.2207	−	116.430i	0.206833	−	0.358245i
$326$	95.3409	−	398.538i	0.292457	−	1.22251i
$327$	−10.2577	+	68.0551i	−0.0313690	+	0.208120i
$328$	−225.739	−	508.830i	−0.688229	−	1.55131i
$329$	−150.745	−	376.382i	−0.458191	−	1.14402i
$330$	7.78031	−	11.1601i	0.0235767	−	0.0338185i
$331$	−407.439	+	30.5334i	−1.23093	+	0.0922458i	−0.674266	−	0.738489i	$-0.735540\pi$
$331$	−407.439	+	30.5334i	−1.23093	+	0.0922458i	−0.556669	+	0.830734i	$0.687921\pi$
$332$	492.001	+	205.022i	1.48193	+	0.617535i
$333$	−78.4806	−	199.965i	−0.235678	−	0.600497i
$334$	−121.800	+	205.980i	−0.364672	+	0.616708i
$335$	−93.4078	+	74.4903i	−0.278829	+	0.222359i
$336$	−80.0432	+	128.152i	−0.238224	+	0.381404i
$337$	−317.835	+	398.552i	−0.943129	+	1.18265i	0.0399009	+	0.999204i	$0.487296\pi$
$337$	−317.835	+	398.552i	−0.943129	+	1.18265i	−0.983030	+	0.183443i	$0.941276\pi$
$338$	−297.626	+	113.247i	−0.880549	+	0.335050i
$339$	109.334	+	8.19347i	0.322520	+	0.0241695i
$340$	6.43313	+	119.081i	0.0189210	+	0.350237i
$341$	−9.74062	+	9.03797i	−0.0285649	+	0.0265043i
$342$	214.241	−	194.674i	0.626436	−	0.569223i
$343$	−155.230	−	305.864i	−0.452566	−	0.891731i
$344$	183.028	+	244.825i	0.532059	+	0.711701i
$345$	−156.424	+	145.140i	−0.453403	+	0.420697i
$346$	8.41864	+	6.85829i	0.0243313	+	0.0198216i
$347$	−216.429	−	16.2191i	−0.623715	−	0.0467410i	−0.240876	−	0.970556i	$-0.577435\pi$
$347$	−216.429	−	16.2191i	−0.623715	−	0.0467410i	−0.382839	+	0.923815i	$0.625054\pi$
$348$	−74.2329	+	146.272i	−0.213313	+	0.420323i
$349$	204.310	−	256.197i	0.585417	−	0.734089i	−0.397609	−	0.917555i	$-0.630160\pi$
$349$	204.310	−	256.197i	0.585417	−	0.734089i	0.983026	+	0.183465i	$0.0587315\pi$
$350$	−217.954	−	561.050i	−0.622726	−	1.60300i
$351$	53.3658	−	42.5578i	0.152039	−	0.121247i
$352$	−12.9799	+	14.6428i	−0.0368748	+	0.0415989i
$353$	115.600	+	294.544i	0.327478	+	0.834401i	0.995887	+	0.0906067i	$0.0288806\pi$
$353$	115.600	+	294.544i	0.327478	+	0.834401i	−0.668408	+	0.743794i	$0.733024\pi$
$354$	53.3107	+	113.715i	0.150595	+	0.321229i
$355$	205.124	−	15.3719i	0.577814	−	0.0433012i
$356$	−125.189	+	16.2104i	−0.351655	+	0.0455349i
$357$	−12.6947	−	31.6963i	−0.0355593	−	0.0887851i
$358$	33.4383	+	59.3355i	0.0934032	+	0.165742i
$359$	−47.1544	+	312.849i	−0.131349	+	0.871446i	0.821980	+	0.569516i	$0.192869\pi$
$359$	−47.1544	+	312.849i	−0.131349	+	0.871446i	−0.953330	+	0.301931i	$0.902369\pi$
$360$	−153.678	+	448.014i	−0.426882	+	1.24448i
$361$	22.6834	−	39.2889i	0.0628350	−	0.108833i
$362$	−61.2896	+	191.589i	−0.169308	+	0.529251i
$363$	70.6069	−	146.617i	0.194509	−	0.403903i
$364$	26.9671	−	83.3018i	0.0740856	−	0.228851i
$365$	−544.954	+	262.436i	−1.49303	+	0.719003i
$366$	−198.700	+	27.8361i	−0.542896	+	0.0760548i
$367$	245.887	−	265.003i	0.669992	−	0.722079i	−0.302982	−	0.952996i	$-0.597982\pi$
$367$	245.887	−	265.003i	0.669992	−	0.722079i	0.972973	+	0.230917i	$0.0741726\pi$
$368$	247.721	−	181.202i	0.673155	−	0.492397i
$369$	412.789	+	281.435i	1.11867	+	0.762697i
$370$	457.391	+	185.033i	1.23619	+	0.500088i
$371$	−278.989	+	589.773i	−0.751992	+	1.58968i
$372$	−60.7333	+	100.309i	−0.163262	+	0.269647i
$373$	195.305	+	338.278i	0.523605	+	0.906911i	0.999622	+	0.0274749i	$0.00874665\pi$
$373$	195.305	+	338.278i	0.523605	+	0.906911i	−0.476017	+	0.879436i	$0.657920\pi$
$374$	−0.938996	−	4.32096i	−0.00251069	−	0.0115534i
$375$	112.750	+	165.374i	0.300666	+	0.440996i
$376$	−219.035	−	408.330i	−0.582541	−	1.08598i
$377$	21.1515	−	92.6709i	0.0561049	−	0.245811i
$378$	1.05958	−	305.589i	0.00280313	−	0.808436i
$379$	−156.391	+	35.6953i	−0.412642	+	0.0941828i	−0.423802	−	0.905755i	$-0.639305\pi$
$379$	−156.391	+	35.6953i	−0.412642	+	0.0941828i	0.0111600	+	0.999938i	$0.496448\pi$
$380$	−13.8480	+	664.747i	−0.0364420	+	1.74933i
$381$	−312.377	−	96.3554i	−0.819886	−	0.252901i
$382$	−648.839	−	320.831i	−1.69853	−	0.839872i
$383$	145.913	+	473.038i	0.380974	+	1.23509i	0.919705	+	0.392609i	$0.128428\pi$
$383$	145.913	+	473.038i	0.380974	+	1.23509i	−0.538731	+	0.842478i	$0.681096\pi$
$384$	−74.6276	+	155.721i	−0.194343	+	0.405525i
$385$	17.8596	+	30.4433i	0.0463885	+	0.0790734i
$386$	625.547	−	40.3318i	1.62059	−	0.104486i
$387$	−255.382	−	100.230i	−0.659902	−	0.258992i
$388$	−343.809	−	59.1689i	−0.886106	−	0.152497i
$389$	200.400	−	30.2054i	0.515167	−	0.0776489i	0.113687	−	0.993517i	$-0.463734\pi$
$389$	200.400	−	30.2054i	0.515167	−	0.0776489i	0.401480	+	0.915868i	$0.368496\pi$
$390$	−5.92132	+	69.3192i	−0.0151829	+	0.177741i
$391$			69.3567i			0.177383i
$392$	−215.169	−	327.668i	−0.548901	−	0.835887i
$393$	−327.692			−0.833821
$394$	−57.5726	−	4.91792i	−0.146123	−	0.0124820i
$395$	−142.615	−	946.189i	−0.361051	−	2.39541i
$396$	2.97859	−	17.3075i	0.00752170	−	0.0437059i
$397$	75.7186	−	192.928i	0.190727	−	0.485965i	−0.803238	−	0.595658i	$-0.796892\pi$
$397$	75.7186	−	192.928i	0.190727	−	0.485965i	0.993966	+	0.109693i	$0.0349868\pi$
$398$	−5.58160	−	86.5706i	−0.0140241	−	0.217514i
$399$	−57.3738	−	181.515i	−0.143794	−	0.454924i
$400$	−318.834	−	609.531i	−0.797085	−	1.52383i
$401$	5.97407	−	1.84276i	0.0148979	−	0.00459540i	−0.287297	−	0.957841i	$-0.592757\pi$
$401$	5.97407	−	1.84276i	0.0148979	−	0.00459540i	0.302195	+	0.953246i	$0.402281\pi$
$402$	17.3278	−	35.0432i	0.0431040	−	0.0871722i
$403$	20.0292	−	64.9332i	0.0497003	−	0.161125i
$404$	54.3629	+	1.13249i	0.134562	+	0.00280318i
$405$	−64.5374	−	282.757i	−0.159352	−	0.698165i
$406$	−264.177	−	333.634i	−0.650682	−	0.821759i
$407$	−17.8360	−	4.07095i	−0.0438231	−	0.0100023i
$408$	−18.4456	−	34.3867i	−0.0452099	−	0.0842812i
$409$	82.2985	−	56.1102i	0.201219	−	0.137189i	−0.458519	−	0.888685i	$-0.651620\pi$
$409$	82.2985	−	56.1102i	0.201219	−	0.137189i	0.659738	+	0.751496i	$0.270667\pi$
$410$	−1121.34	+	243.681i	−2.73498	+	0.594344i
$411$	−75.7399	+	43.7284i	−0.184282	+	0.106395i
$412$	44.1503	+	26.7315i	0.107161	+	0.0648822i
$413$	−325.825	+	2.26359i	−0.788923	+	0.00548085i
$414$	−103.302	+	255.358i	−0.249523	+	0.616807i
$415$	618.957	−	907.844i	1.49146	−	2.18758i
$416$	20.0441	−	98.0384i	0.0481829	−	0.235669i
$417$	−124.411	−	115.436i	−0.298347	−	0.276826i
$418$	−3.42032	−	24.4150i	−0.00818257	−	0.0584090i
$419$	112.589	+	233.793i	0.268708	+	0.557978i	0.991040	−	0.133569i	$-0.0426437\pi$
$419$	112.589	+	233.793i	0.268708	+	0.557978i	−0.722331	+	0.691547i	$0.756929\pi$
$420$	225.364	+	215.005i	0.536580	+	0.511917i
$421$	−113.346	−	54.5844i	−0.269230	−	0.129654i	0.294399	−	0.955683i	$-0.404881\pi$
$421$	−113.346	−	54.5844i	−0.269230	−	0.129654i	−0.563628	+	0.826029i	$0.690595\pi$
$422$	−287.924	−	92.1075i	−0.682285	−	0.218264i
$423$	360.158	+	207.937i	0.851437	+	0.491577i
$424$	−241.930	+	705.296i	−0.570591	+	1.66343i
$425$	153.709	+	23.1679i	0.361669	+	0.0545128i
$426$	−58.6374	+	33.0449i	−0.137646	+	0.0775702i
$427$	149.972	−	498.467i	0.351223	−	1.16737i
$428$	33.5489	+	259.091i	0.0783854	+	0.605352i
$429$	−0.192776	−	2.57242i	−0.000449362	−	0.00599632i
$430$	570.550	−	267.479i	1.32686	−	0.622043i
$431$	218.139	−	85.6132i	0.506123	−	0.198638i	−0.0985205	−	0.995135i	$-0.531411\pi$
$431$	218.139	−	85.6132i	0.506123	−	0.198638i	0.604643	+	0.796497i	$0.293316\pi$
$432$	−37.6251	−	347.214i	−0.0870951	−	0.803735i
$433$	363.419	+	455.713i	0.839306	+	1.05246i	0.997878	+	0.0651088i	$0.0207394\pi$
$433$	363.419	+	455.713i	0.839306	+	1.05246i	−0.158572	+	0.987347i	$0.550689\pi$
$434$	−170.503	−	251.954i	−0.392863	−	0.580539i
$435$	264.368	+	210.827i	0.607744	+	0.484659i
$436$	−181.971	−	92.3500i	−0.417365	−	0.211812i
$437$	−28.8975	+	385.610i	−0.0661270	+	0.882403i
$438$	125.004	−	153.444i	0.285397	−	0.350328i
$439$	−173.076	−	186.531i	−0.394250	−	0.424901i	0.504466	−	0.863432i	$-0.331689\pi$
$439$	−173.076	−	186.531i	−0.394250	−	0.424901i	−0.898716	+	0.438531i	$0.855499\pi$
$440$	24.1525	+	32.3073i	0.0548921	+	0.0734258i
$441$	319.070	+	148.231i	0.723515	+	0.336124i
$442$	15.2070	+	16.7355i	0.0344051	+	0.0378632i
$443$	532.305	+	573.688i	1.20159	+	1.29501i	0.944458	+	0.328631i	$0.106587\pi$
$443$	532.305	+	573.688i	1.20159	+	1.29501i	0.257132	+	0.966376i	$0.417222\pi$
$444$	−161.212	+	8.70922i	−0.363091	+	0.0196154i
$445$	−19.4466	+	259.497i	−0.0437003	+	0.583140i
$446$	−61.5984	−	161.888i	−0.138113	−	0.362977i
$447$	−293.104	−	233.743i	−0.655713	−	0.522914i
$448$	−286.017	−	344.816i	−0.638431	−	0.769679i
$449$	−142.988	−	179.302i	−0.318460	−	0.399336i	0.596676	−	0.802483i	$-0.296488\pi$
$449$	−142.988	−	179.302i	−0.318460	−	0.399336i	−0.915135	+	0.403147i	$0.867916\pi$
$450$	531.421	+	314.240i	1.18094	+	0.698312i
$451$	39.6073	−	15.5447i	0.0878210	−	0.0344672i
$452$	−125.045	+	300.076i	−0.276647	+	0.663884i
$453$	7.75644	+	103.502i	0.0171224	+	0.228482i
$454$	506.371	+	353.018i	1.11535	+	0.777574i
$455$	−156.937	−	89.1599i	−0.344917	−	0.195956i
$456$	−88.2270	−	198.869i	−0.193480	−	0.436117i
$457$	−97.0803	−	14.6325i	−0.212430	−	0.0320186i	0.0419652	−	0.999119i	$-0.486638\pi$
$457$	−97.0803	−	14.6325i	−0.212430	−	0.0320186i	−0.254395	+	0.967100i	$0.581876\pi$
$458$	28.9210	+	6.91869i	0.0631463	+	0.0151063i
$459$	68.3479	+	39.4607i	0.148906	+	0.0859710i
$460$	−262.585	−	575.635i	−0.570838	−	1.25138i
$461$	259.610	+	125.021i	0.563145	+	0.271196i	0.693723	−	0.720242i	$-0.255969\pi$
$461$	259.610	+	125.021i	0.563145	+	0.271196i	−0.130578	+	0.991438i	$0.541683\pi$
$462$	−9.51969	−	6.53888i	−0.0206054	−	0.0141534i
$463$	69.0705	+	143.426i	0.149180	+	0.309776i	0.962146	−	0.272536i	$-0.0878624\pi$
$463$	69.0705	+	143.426i	0.149180	+	0.309776i	−0.812965	+	0.582312i	$0.802148\pi$
$464$	−342.437	−	345.366i	−0.738011	−	0.744322i
$465$	177.200	+	164.417i	0.381075	+	0.353586i
$466$	−4.47872	+	430.032i	−0.00961099	+	0.922816i
$467$	432.589	−	634.491i	0.926314	−	1.35865i	−0.00714660	−	0.999974i	$-0.502275\pi$
$467$	432.589	−	634.491i	0.926314	−	1.35865i	0.933461	−	0.358679i	$-0.116773\pi$
$468$	31.0629	+	84.2669i	0.0663738	+	0.180058i
$469$	63.7856	+	78.8546i	0.136003	+	0.168133i
$470$	−915.652	+	272.031i	−1.94820	+	0.578790i
$471$	327.597	−	189.138i	0.695536	−	0.401568i
$472$	−369.775	+	43.9707i	−0.783423	+	0.0931583i
$473$	−19.3048	+	13.1618i	−0.0408136	+	0.0278262i
$474$	173.673	+	260.521i	0.366400	+	0.549622i
$475$	844.941	+	192.852i	1.77882	+	0.406005i
$476$	101.050	−	6.16337i	0.212289	−	0.0129482i
$477$	−148.913	−	652.432i	−0.312187	−	1.36778i
$478$	510.080	+	483.268i	1.06711	+	1.01102i
$479$	−268.693	+	871.081i	−0.560946	+	1.81854i	0.0133744	+	0.999911i	$0.495743\pi$
$479$	−268.693	+	871.081i	−0.560946	+	1.81854i	−0.574320	+	0.818631i	$0.694734\pi$
$480$	283.281	+	215.562i	0.590168	+	0.449087i
$481$	89.4005	−	27.5764i	0.185864	−	0.0573314i
$482$	75.3867	−	467.098i	0.156404	−	0.969082i
$483$	124.132	+	131.932i	0.257002	+	0.273152i
$484$	346.789	+	335.482i	0.716506	+	0.693144i
$485$	−262.739	+	669.449i	−0.541731	+	1.38031i
$486$	300.152	+	384.527i	0.617597	+	0.791207i
$487$	117.165	+	777.337i	0.240585	+	1.59617i	0.704110	+	0.710091i	$0.251346\pi$
$487$	117.165	+	777.337i	0.240585	+	1.59617i	−0.463525	+	0.886084i	$0.653416\pi$
$488$	106.998	−	585.200i	0.219259	−	1.19918i
$489$	276.412			0.565259
$490$	−751.194	+	297.843i	−1.53305	+	0.607842i
$491$			304.721i			0.620613i	0.950637	+	0.310307i	$0.100432\pi$
$491$			304.721i			0.620613i	−0.950637	+	0.310307i	$0.899568\pi$
$492$	298.376	−	227.944i	0.606456	−	0.463302i
$493$	108.677	−	16.3804i	0.220440	−	0.0332260i
$494$	77.5754	+	99.3823i	0.157035	+	0.201179i
$495$	−33.7004	−	13.2264i	−0.0680816	−	0.0267201i
$496$	−225.666	−	264.498i	−0.454971	−	0.533262i
$497$	−14.2589	−	174.039i	−0.0286900	−	0.350179i
$498$	−57.2849	+	354.939i	−0.115030	+	0.712728i
$499$	28.8915	+	93.6640i	0.0578988	+	0.187703i	0.979902	−	0.199478i	$-0.0639248\pi$
$499$	28.8915	+	93.6640i	0.0578988	+	0.187703i	−0.922003	+	0.387182i	$0.873449\pi$
$500$	−570.610	+	163.075i	−1.14122	+	0.326150i
$501$	−154.243	−	47.5776i	−0.307870	−	0.0949652i
$502$	275.560	+	261.075i	0.548925	+	0.520071i
$503$	−698.815	+	159.500i	−1.38929	+	0.317097i	−0.850781	−	0.525520i	$-0.823871\pi$
$503$	−698.815	+	159.500i	−1.38929	+	0.317097i	−0.538513	+	0.842617i	$0.681014\pi$
$504$	381.225	+	127.815i	0.756400	+	0.253601i
$505$	24.9424	−	109.280i	0.0493909	−	0.216396i
$506$	13.0127	+	19.5199i	0.0257169	+	0.0385769i
$507$	−121.001	−	177.476i	−0.238661	−	0.350051i
$508$	562.567	−	789.298i	1.10742	−	1.55374i
$509$	−327.760	−	567.698i	−0.643930	−	1.11532i	−0.984548	−	0.175118i	$-0.943969\pi$
$509$	−327.760	−	567.698i	−0.643930	−	1.11532i	0.340617	−	0.940202i	$-0.389364\pi$
$510$	−77.1098	+	22.9086i	−0.151196	+	0.0449187i
$511$	225.996	+	461.064i	0.442262	+	0.902278i
$512$	−368.663	−	355.291i	−0.720045	−	0.693927i
$513$	363.560	+	247.871i	0.708695	+	0.483180i
$514$	−0.426945	+	40.9939i	−0.000830633	+	0.0797546i
$515$	72.3674	−	77.9935i	0.140519	−	0.151444i
$516$	−131.886	+	158.493i	−0.255594	+	0.307157i
$517$	31.9105	−	15.3673i	0.0617224	−	0.0297239i
$518$	154.377	−	389.370i	0.298025	−	0.751680i
$519$	−3.17798	+	6.59914i	−0.00612327	+	0.0127151i
$520$	−189.574	−	81.3246i	−0.364565	−	0.156393i
$521$	−298.464	+	516.954i	−0.572867	+	0.992234i	0.423403	+	0.905941i	$0.360835\pi$
$521$	−298.464	+	516.954i	−0.572867	+	0.992234i	−0.996270	+	0.0862930i	$0.972498\pi$
$522$	424.526	+	101.558i	0.813268	+	0.194556i
$523$	−88.1301	+	584.705i	−0.168509	+	1.11798i	0.731414	+	0.681933i	$0.238861\pi$
$523$	−88.1301	+	584.705i	−0.168509	+	1.11798i	−0.899923	+	0.436049i	$0.856377\pi$
$524$	305.663	−	922.280i	0.583326	−	1.76008i
$525$	333.856	−	231.033i	0.635915	−	0.440062i
$526$	−333.124	−	232.239i	−0.633316	−	0.441518i
$527$	78.3486	−	5.87142i	0.148669	−	0.0111412i
$528$	−11.6430	−	6.21709i	−0.0220512	−	0.0117748i
$529$	58.8314	+	149.900i	0.111213	+	0.283365i
$530$	1323.08	+	782.364i	2.49638	+	1.47616i
$531$	261.298	−	208.378i	0.492087	−	0.392426i
$532$	564.385	+	7.83519i	1.06087	+	0.0147278i
$533$	−135.664	+	170.117i	−0.254529	+	0.319169i
$534$	−30.2813	−	79.5828i	−0.0567066	−	0.149032i
$535$	537.054	+	40.2466i	1.00384	+	0.0752273i
$536$	82.4653	+	81.4561i	0.153853	+	0.151970i
$537$	−33.6776	+	31.2483i	−0.0627144	+	0.0581904i
$538$	221.369	+	243.619i	0.411467	+	0.452824i
$539$	25.7379	−	15.3405i	0.0477513	−	0.0284611i
$540$	−716.662	−	68.7432i	−1.32715	−	0.127302i
$541$	197.103	−	182.885i	0.364330	−	0.338049i	−0.476671	−	0.879082i	$-0.658157\pi$
$541$	197.103	−	182.885i	0.364330	−	0.338049i	0.841002	+	0.541032i	$0.181966\pi$
$542$	482.243	−	591.961i	0.889748	−	1.09218i
$543$	−135.305	−	10.1397i	−0.249181	−	0.0186735i
$544$	113.986	−	19.8397i	0.209533	−	0.0364700i
$545$	−262.281	+	328.890i	−0.481249	+	0.603468i
$546$	58.8799	+	4.61780i	0.107839	+	0.00845751i
$547$	100.055	−	79.7908i	0.182915	−	0.145870i	−0.527752	−	0.849399i	$-0.676965\pi$
$547$	100.055	−	79.7908i	0.182915	−	0.145870i	0.710667	+	0.703529i	$0.248393\pi$
$548$	−52.4243	−	253.957i	−0.0956648	−	0.463425i
$549$	195.065	+	497.018i	0.355310	+	0.905315i
$550$	47.6070	−	22.3186i	0.0865582	−	0.0405792i
$551$	611.049	−	45.7918i	1.10898	−	0.0831066i
$552$	157.749	+	134.073i	0.285778	+	0.242885i
$553$	−802.378	+	126.646i	−1.45096	+	0.229016i
$554$	−536.858	+	302.545i	−0.969058	+	0.546109i
$555$	−49.6034	+	329.097i	−0.0893755	+	0.592967i
$556$	440.940	−	242.475i	0.793057	−	0.436106i
$557$	−222.152	+	384.778i	−0.398836	+	0.690804i	−0.993583	−	0.113109i	$-0.963919\pi$
$557$	−222.152	+	384.778i	−0.398836	+	0.690804i	0.594746	+	0.803913i	$0.297252\pi$
$558$	297.210	+	95.0780i	0.532634	+	0.170391i
$559$	51.8424	−	107.652i	0.0927413	−	0.192579i
$560$	−815.340	+	433.729i	−1.45596	+	0.774516i
$561$	2.68728	−	1.29412i	0.00479016	−	0.00230682i
$562$	−27.9269	−	199.348i	−0.0496920	−	0.354712i
$563$	253.217	−	272.903i	0.449764	−	0.484731i	−0.466945	−	0.884287i	$-0.654645\pi$
$563$	253.217	−	272.903i	0.449764	−	0.484731i	0.916709	+	0.399556i	$0.130836\pi$
$564$	233.498	−	207.774i	0.414004	−	0.368394i
$565$	553.702	+	377.508i	0.980004	+	0.668155i
$566$	263.563	−	651.514i	0.465659	−	1.15108i
$567$	−239.652	+	56.4533i	−0.422666	+	0.0995650i
$568$	−38.3085	−	195.857i	−0.0674446	−	0.344818i
$569$	−172.588	−	298.931i	−0.303318	−	0.525362i	0.673568	−	0.739126i	$-0.264761\pi$
$569$	−172.588	−	298.931i	−0.303318	−	0.525362i	−0.976885	+	0.213764i	$0.931428\pi$
$570$	−438.261	+	95.2394i	−0.768879	+	0.167087i
$571$	−495.072	−	726.138i	−0.867027	−	1.27169i	−0.961120	−	0.276131i	$-0.910948\pi$
$571$	−495.072	−	726.138i	−0.867027	−	1.27169i	0.0940934	−	0.995563i	$-0.470005\pi$
$572$	7.41983	+	1.85693i	0.0129717	+	0.00324637i
$573$	108.645	−	476.003i	0.189606	−	0.830720i
$574$	213.474	+	950.470i	0.371906	+	1.65587i
$575$	−804.031	+	183.515i	−1.39831	+	0.319156i
$576$	449.226	+	96.7294i	0.779905	+	0.167933i
$577$	−347.404	−	107.160i	−0.602086	−	0.185719i	−0.0212973	−	0.999773i	$-0.506780\pi$
$577$	−347.404	−	107.160i	−0.602086	−	0.185719i	−0.580789	+	0.814054i	$0.697256\pi$
$578$	244.606	−	494.683i	0.423193	−	0.855853i
$579$	124.631	+	404.042i	0.215251	+	0.697828i
$580$	−839.963	+	547.404i	−1.44821	+	0.943800i
$581$	−774.319	−	520.079i	−1.33273	−	0.895144i
$582$	−15.1407	−	234.832i	−0.0260149	−	0.403491i
$583$	−53.0536	−	20.8220i	−0.0910010	−	0.0357153i
$584$	315.263	+	494.948i	0.539834	+	0.847514i
$585$	183.070	−	27.5934i	0.312940	−	0.0471682i
$586$	−747.832	−	63.8807i	−1.27616	−	0.109011i
$587$		−	261.203i		−	0.444980i	−0.974935	−	0.222490i	$-0.928581\pi$
$587$		−	261.203i		−	0.444980i	0.974935	−	0.222490i	$-0.0714185\pi$
$588$	181.189	−	192.579i	0.308144	−	0.327516i
$589$	438.050			0.743718
$590$	−65.3349	+	764.856i	−0.110737	+	1.29637i
$591$	−5.80907	−	38.5407i	−0.00982923	−	0.0652127i
$592$	125.863	−	461.851i	0.212606	−	0.780154i
$593$	−29.5308	+	75.2432i	−0.0497989	+	0.126886i	−0.953609	−	0.301049i	$-0.902663\pi$
$593$	−29.5308	+	75.2432i	−0.0497989	+	0.126886i	0.903810	+	0.427934i	$0.140759\pi$
$594$	26.6396	−	1.71758i	0.0448479	−	0.00289154i
$595$	29.6700	−	206.575i	0.0498655	−	0.347185i
$596$	931.262	−	606.904i	1.56252	−	1.01830i
$597$	55.9162	−	17.2479i	0.0936620	−	0.0288909i
$598$	−107.542	−	53.1760i	−0.179835	−	0.0889231i
$599$	−107.591	+	348.802i	−0.179618	+	0.582307i	0.820328	+	0.571894i	$0.193791\pi$
$599$	−107.591	+	348.802i	−0.179618	+	0.582307i	−0.999946	+	0.0104135i	$0.996685\pi$
$600$	349.828	−	304.820i	0.583047	−	0.508034i
$601$	−10.3880	−	45.5126i	−0.0172845	−	0.0757282i	0.965550	−	0.260217i	$-0.0837941\pi$
$601$	−10.3880	−	45.5126i	−0.0172845	−	0.0757282i	−0.982835	+	0.184489i	$0.940937\pi$
$602$	−230.427	−	482.762i	−0.382770	−	0.801930i
$603$	−101.423	−	23.1492i	−0.168198	−	0.0383900i
$604$	−298.540	−	74.7142i	−0.494272	−	0.123699i
$605$	821.822	−	560.309i	1.35838	−	0.926131i
$606$	7.78867	+	35.8409i	0.0128526	+	0.0591434i
$607$	179.605	−	103.695i	0.295889	−	0.170832i	−0.344705	−	0.938711i	$-0.612021\pi$
$607$	179.605	−	103.695i	0.295889	−	0.170832i	0.640595	+	0.767879i	$0.278688\pi$
$608$	642.008	−	62.8126i	1.05593	−	0.103310i
$609$	177.412	−	225.666i	0.291316	−	0.370551i
$610$	−1136.85	−	459.902i	−1.86370	−	0.753938i
$611$	−102.030	+	149.651i	−0.166989	+	0.244928i
$612$	−77.5754	+	69.0291i	−0.126757	+	0.112793i
$613$	−72.1702	−	66.9641i	−0.117733	−	0.109240i	0.619110	−	0.785304i	$-0.287494\pi$
$613$	−72.1702	−	66.9641i	−0.117733	−	0.109240i	−0.736842	+	0.676064i	$0.763684\pi$
$614$	−559.486	+	78.3789i	−0.911215	+	0.127653i
$615$	−335.841	−	697.382i	−0.546083	−	1.13395i
$616$	27.2832	−	20.6936i	0.0442910	−	0.0335935i
$617$	712.135	+	342.946i	1.15419	+	0.555828i	0.910290	−	0.413972i	$-0.135859\pi$
$617$	712.135	+	342.946i	1.15419	+	0.555828i	0.243900	+	0.969800i	$0.421573\pi$
$618$	−10.6075	+	33.1588i	−0.0171643	+	0.0536549i
$619$	−857.818	−	495.261i	−1.38581	−	0.800099i	−0.392973	−	0.919550i	$-0.628553\pi$
$619$	−857.818	−	495.261i	−1.38581	−	0.800099i	−0.992840	+	0.119451i	$0.961887\pi$
$620$	−628.036	+	345.360i	−1.01296	+	0.557032i
$621$	−414.037	−	62.4060i	−0.666726	−	0.100493i
$622$	208.832	+	370.567i	0.335743	+	0.595767i
$623$	220.402	+	14.9779i	0.353775	+	0.0240415i
$624$	67.4609	−	2.23660i	0.108110	−	0.00358430i
$625$	11.1016	+	148.140i	0.0177625	+	0.237024i
$626$	−240.861	−	513.773i	−0.384762	−	0.820724i
$627$	15.4800	−	6.07544i	0.0246889	−	0.00968969i
$628$	226.751	+	1098.44i	0.361068	+	1.74911i
$629$	67.4451	+	84.5735i	0.107226	+	0.134457i
$630$	416.920	−	716.379i	0.661778	−	1.13711i
$631$	708.811	+	565.258i	1.12331	+	0.895813i	0.995384	−	0.0959706i	$-0.0305955\pi$
$631$	708.811	+	565.258i	1.12331	+	0.895813i	0.127929	+	0.991783i	$0.459167\pi$
$632$	−895.227	+	245.792i	−1.41650	+	0.388912i
$633$	15.2382	−	203.340i	0.0240730	−	0.321232i
$634$	894.639	+	728.822i	1.41110	+	1.14956i
$635$	−1359.04	−	1464.70i	−2.14022	−	2.30661i
$636$	−500.657	−	48.0237i	−0.787197	−	0.0755090i
$637$	−74.7623	+	133.750i	−0.117366	+	0.209968i
$638$	27.5130	−	25.0002i	0.0431238	−	0.0391852i
$639$	121.828	+	131.299i	0.190654	+	0.205476i
$640$	−870.930	+	596.215i	−1.36083	+	0.931587i
$641$	6.44752	−	86.0362i	0.0100585	−	0.134222i	−0.989914	−	0.141672i	$-0.954752\pi$
$641$	6.44752	−	86.0362i	0.0100585	−	0.134222i	0.999972	+	0.00744975i	$0.00237135\pi$
$642$	−164.704	+	62.6700i	−0.256548	+	0.0976168i
$643$	353.654	+	282.030i	0.550006	+	0.438615i	0.858650	−	0.512562i	$-0.171304\pi$
$643$	353.654	+	282.030i	0.550006	+	0.438615i	−0.308644	+	0.951178i	$0.599875\pi$
$644$	−487.108	+	226.303i	−0.756379	+	0.351403i
$645$	265.013	+	332.315i	0.410872	+	0.515218i
$646$	−74.1964	+	125.476i	−0.114855	+	0.194235i
$647$	−594.770	+	233.430i	−0.919273	+	0.360788i	−0.777334	−	0.629088i	$-0.783429\pi$
$647$	−594.770	+	233.430i	−0.919273	+	0.360788i	−0.141938	+	0.989876i	$0.545333\pi$
$648$	−265.017	+	94.5686i	−0.408976	+	0.145939i
$649$	−2.12706	−	28.3836i	−0.00327744	−	0.0437344i
$650$	−153.773	+	220.572i	−0.236573	+	0.339342i
$651$	138.529	−	151.394i	0.212794	−	0.232557i
$652$	−257.830	+	777.954i	−0.395445	+	1.19318i
$653$	−36.3971	−	5.48598i	−0.0557382	−	0.00840119i	0.121114	−	0.992639i	$-0.461353\pi$
$653$	−36.3971	−	5.48598i	−0.0557382	−	0.00840119i	−0.176852	+	0.984237i	$0.556591\pi$
$654$	32.0254	−	133.870i	0.0489685	−	0.204695i
$655$	−1734.58	−	1001.46i	−2.64822	−	1.52895i
$656$	363.226	+	1052.39i	0.553698	+	1.60426i
$657$	−474.521	−	228.517i	−0.722254	−	0.347819i
$658$	236.327	+	775.693i	0.359160	+	1.17886i
$659$	−327.705	−	680.487i	−0.497276	−	1.03261i	−0.986999	−	0.160727i	$-0.948616\pi$
$659$	−327.705	−	680.487i	−0.497276	−	1.03261i	0.489722	−	0.871878i	$-0.337098\pi$
$660$	−17.4038	+	20.9148i	−0.0263695	+	0.0316891i
$661$	169.451	+	157.228i	0.256356	+	0.237863i	0.797872	−	0.602827i	$-0.205959\pi$
$661$	169.451	+	157.228i	0.256356	+	0.237863i	−0.541516	+	0.840690i	$0.682150\pi$
$662$	817.119	+	8.51018i	1.23432	+	0.0128553i
$663$	−8.59229	+	12.6026i	−0.0129597	+	0.0190084i
$664$	−945.531	−	492.305i	−1.42399	−	0.741423i
$665$	251.029	−	1136.16i	0.377488	−	1.70851i
$666$	122.353	+	411.839i	0.183713	+	0.618377i
$667$	−504.974	+	291.547i	−0.757082	+	0.437101i
$668$	277.780	−	389.733i	0.415838	−	0.583432i
$669$	96.5346	−	65.8162i	0.144297	−	0.0983800i
$670$	198.818	−	132.540i	0.296743	−	0.197821i
$671$	44.3318	+	10.1184i	0.0660682	+	0.0150796i
$672$	181.320	−	241.748i	0.269821	−	0.359744i
$673$	−145.536	−	637.635i	−0.216250	−	0.947451i	−0.960221	−	0.279240i	$-0.909917\pi$
$673$	−145.536	−	637.635i	−0.216250	−	0.947451i	0.743972	−	0.668211i	$-0.232940\pi$
$674$	701.205	−	740.109i	1.04036	−	1.09808i
$675$	−276.610	+	896.748i	−0.409793	+	1.32852i
$676$	612.368	−	175.009i	0.905870	−	0.258889i
$677$	175.158	−	54.0291i	0.258727	−	0.0798067i	−0.162678	−	0.986679i	$-0.552013\pi$
$677$	175.158	−	54.0291i	0.258727	−	0.0798067i	0.421405	+	0.906873i	$0.361537\pi$
$678$	−216.480	−	34.9386i	−0.319292	−	0.0515319i
$679$	569.844	+	219.091i	0.839241	+	0.322667i
$680$	7.45061	−	238.392i	0.0109568	−	0.350577i
$681$	−152.119	+	387.592i	−0.223376	+	0.569152i
$682$	20.9490	−	16.3523i	0.0307170	−	0.0239770i
$683$	70.0328	+	464.637i	0.102537	+	0.680289i	0.979756	+	0.200198i	$0.0641584\pi$
$683$	70.0328	+	464.637i	0.102537	+	0.680289i	−0.877219	+	0.480091i	$0.840604\pi$
$684$	−460.066	+	351.467i	−0.672610	+	0.513841i
$685$	−534.555			−0.780373
$686$	257.269	+	635.931i	0.375027	+	0.927014i
$687$			20.0586i			0.0291974i
$688$	−323.053	−	519.029i	−0.469554	−	0.754403i
$689$	288.202	−	43.4395i	0.418290	−	0.0630471i
$690$	336.419	−	262.601i	0.487564	−	0.380581i
$691$	−182.677	−	71.6956i	−0.264367	−	0.103756i	0.229456	−	0.973319i	$-0.426305\pi$
$691$	−182.677	−	71.6956i	−0.264367	−	0.103756i	−0.493822	+	0.869563i	$0.664401\pi$
$692$	−15.6088	−	15.0998i	−0.0225560	−	0.0218206i
$693$	−11.0292	+	28.6863i	−0.0159151	+	0.0413943i
$694$	428.527	+	69.1617i	0.617474	+	0.0996566i
$695$	−305.762	−	991.255i	−0.439945	−	1.42627i
$696$	172.826	−	278.847i	0.248313	−	0.400642i
$697$	−240.405	−	74.1552i	−0.344914	−	0.106392i
$698$	−450.749	+	475.757i	−0.645772	+	0.681600i
$699$	−282.813	+	64.5502i	−0.404597	+	0.0923466i
$700$	338.823	+	1155.13i	0.484033	+	1.65018i
$701$	135.221	−	592.441i	0.192897	−	0.845137i	−0.782141	−	0.623101i	$-0.785873\pi$
$701$	135.221	−	592.441i	0.192897	−	0.845137i	0.975038	−	0.222036i	$-0.0712703\pi$
$702$	−113.589	+	75.7228i	−0.161807	+	0.107867i
$703$	339.745	+	498.314i	0.483278	+	0.708839i
$704$	28.3582	−	26.9699i	0.0402815	−	0.0383095i
$705$	−322.159	−	557.996i	−0.456963	−	0.791483i
$706$	−180.223	−	606.627i	−0.255273	−	0.859246i
$707$	−92.9148	−	20.5291i	−0.131421	−	0.0290370i
$708$	−86.8776	−	235.680i	−0.122708	−	0.332881i
$709$	−363.140	−	247.585i	−0.512186	−	0.349202i	0.279485	−	0.960150i	$-0.409836\pi$
$709$	−363.140	−	247.585i	−0.512186	−	0.349202i	−0.791671	+	0.610948i	$0.790789\pi$
$710$	−411.376	−	4.28442i	−0.579402	−	0.00603439i
$711$	566.722	−	610.781i	0.797077	−	0.859045i
$712$	252.229	−	10.9932i	0.354255	−	0.0154398i
$713$	−375.560	+	180.860i	−0.526733	+	0.253661i
$714$	19.9018	+	65.3234i	0.0278737	+	0.0914894i
$715$	6.84116	−	14.2058i	0.00956806	−	0.0198683i
$716$	−56.5338	−	123.932i	−0.0789578	−	0.173090i
$717$	−236.983	+	410.466i	−0.330520	+	0.572478i
$718$	147.221	−	615.401i	0.205043	−	0.857105i
$719$	98.8192	−	655.622i	0.137440	−	0.911853i	−0.808730	−	0.588181i	$-0.799844\pi$
$719$	98.8192	−	655.622i	0.137440	−	0.911853i	0.946169	−	0.323672i	$-0.104918\pi$
$720$	382.502	−	866.618i	0.531253	−	1.20364i
$721$	−66.6355	−	60.9727i	−0.0924209	−	0.0845669i
$722$	−51.8901	+	74.4314i	−0.0718699	+	0.103091i
$723$	318.257	−	23.8501i	0.440190	−	0.0329877i
$724$	154.747	−	371.354i	0.213739	−	0.512921i
$725$	477.448	+	1216.52i	0.658549	+	1.67795i
$726$	−165.659	+	280.151i	−0.228180	+	0.385882i
$727$	−367.282	+	292.898i	−0.505203	+	0.402886i	−0.842652	−	0.538458i	$-0.819007\pi$
$727$	−367.282	+	292.898i	−0.505203	+	0.402886i	0.337450	+	0.941344i	$0.390436\pi$
$728$	−67.9184	+	161.409i	−0.0932945	+	0.221715i
$729$	−7.78240	+	9.75882i	−0.0106754	+	0.0133866i
$730$	1130.63	−	430.204i	1.54880	−	0.589321i
$731$	137.765	+	10.3241i	0.188462	+	0.0141232i
$732$	400.696	−	21.6469i	0.547399	−	0.0295723i
$733$	−552.968	+	513.080i	−0.754391	+	0.699972i	−0.960415	−	0.278575i	$-0.910138\pi$
$733$	−552.968	+	513.080i	−0.754391	+	0.699972i	0.206024	+	0.978547i	$0.433948\pi$
$734$	−535.099	+	486.228i	−0.729018	+	0.662436i
$735$	−313.282	−	446.056i	−0.426234	−	0.606879i
$736$	−524.489	+	318.922i	−0.712621	+	0.433318i
$737$	−6.49473	+	6.02622i	−0.00881238	+	0.00817670i
$738$	−774.677	−	631.094i	−1.04970	−	0.855141i
$739$	−141.039	−	10.5694i	−0.190851	−	0.0143023i	−0.0210386	−	0.999779i	$-0.506697\pi$
$739$	−141.039	−	10.5694i	−0.190851	−	0.0143023i	−0.169813	+	0.985476i	$0.554316\pi$
$740$	−879.966	−	446.581i	−1.18914	−	0.603488i
$741$	−53.0224	+	66.4880i	−0.0715552	+	0.0897274i
$742$	656.346	−	1127.78i	0.884563	−	1.51991i
$743$	−258.304	+	205.991i	−0.347650	+	0.277242i	−0.781710	−	0.623642i	$-0.785652\pi$
$743$	−258.304	+	205.991i	−0.347650	+	0.277242i	0.434060	+	0.900884i	$0.357081\pi$
$744$	138.101	−	189.551i	0.185619	−	0.254773i
$745$	−837.154	−	2133.03i	−1.12370	−	2.86313i
$746$	−331.610	−	707.346i	−0.444517	−	0.948185i
$747$	954.079	−	71.4983i	1.27721	−	0.0957140i
$748$	1.13565	+	8.77040i	0.00151825	+	0.0117251i
$749$	30.9980	−	456.142i	0.0413859	−	0.609001i
$750$	−196.531	−	348.739i	−0.262041	−	0.464986i
$751$	−32.4217	+	215.104i	−0.0431714	+	0.286424i	−0.999991	−	0.00425901i	$-0.998644\pi$
$751$	−32.4217	+	215.104i	−0.0431714	+	0.286424i	0.956820	+	0.290683i	$0.0938824\pi$
$752$	366.974	+	850.982i	0.487998	+	1.13162i
$753$	−128.025	+	221.746i	−0.170020	+	0.294484i
$754$	−57.9242	+	181.069i	−0.0768226	+	0.240144i
$755$	−275.257	+	571.577i	−0.364579	+	0.757056i
$756$	−54.1295	+	608.779i	−0.0715999	+	0.805264i
$757$	90.5999	−	43.6306i	0.119683	−	0.0576362i	−0.373084	−	0.927797i	$-0.621700\pi$
$757$	90.5999	−	43.6306i	0.119683	−	0.0576362i	0.492767	+	0.870161i	$0.335985\pi$
$758$	317.724	−	44.5102i	0.419161	−	0.0587206i
$759$	−10.7633	+	11.6000i	−0.0141809	+	0.0152833i
$760$	140.750	−	1322.31i	0.185198	−	1.73988i
$761$	−964.381	−	657.504i	−1.26726	−	0.864000i	−0.272095	−	0.962270i	$-0.587717\pi$
$761$	−964.381	−	657.504i	−1.26726	−	0.864000i	−0.995160	+	0.0982704i	$0.968669\pi$
$762$	606.084	+	245.185i	0.795386	+	0.321765i
$763$	280.741	+	220.711i	0.367944	+	0.289267i
$764$	1238.36	+	749.781i	1.62089	+	0.981388i
$765$	107.031	+	185.383i	0.139910	+	0.242331i
$766$	−210.245	−	967.481i	−0.274472	−	1.26303i
$767$	81.9956	+	120.265i	0.106904	+	0.156800i
$768$	175.221	−	297.610i	0.228152	−	0.387512i
$769$	89.8198	−	393.526i	0.116801	−	0.511738i	−0.882352	−	0.470590i	$-0.844041\pi$
$769$	89.8198	−	393.526i	0.116801	−	0.511738i	0.999153	−	0.0411482i	$-0.0131016\pi$
$770$	−30.4074	−	63.7057i	−0.0394901	−	0.0827346i
$771$	−26.9599	+	6.15341i	−0.0349674	+	0.00798108i
$772$	−1253.42	−	26.1112i	−1.62360	−	0.0338228i
$773$	104.021	+	32.0864i	0.134568	+	0.0415089i	0.361308	−	0.932447i	$-0.382330\pi$
$773$	104.021	+	32.0864i	0.134568	+	0.0415089i	−0.226739	+	0.973955i	$0.572807\pi$
$774$	491.849	+	243.204i	0.635464	+	0.314218i
$775$	275.373	+	892.736i	0.355320	+	1.15192i
$776$	675.051	+	176.432i	0.869911	+	0.227361i
$777$	279.663	+	40.1674i	0.359926	+	0.0516956i
$778$	−404.487	+	26.0791i	−0.519906	+	0.0335207i
$779$	−1305.71	−	512.454i	−1.67614	−	0.657835i
$780$	23.5994	−	137.127i	0.0302556	−	0.175804i
$781$	15.0838	−	2.27351i	0.0193134	−	0.00291103i
$782$	11.8061	−	138.210i	0.0150973	−	0.176739i
$783$			663.505i			0.847389i
$784$	373.001	+	689.584i	0.475766	+	0.879572i
$785$	2312.11			2.94536
$786$	653.005	+	55.7805i	0.830796	+	0.0709675i
$787$	71.4398	+	473.972i	0.0907749	+	0.602252i	0.987252	+	0.159163i	$0.0508795\pi$
$787$	71.4398	+	473.972i	0.0907749	+	0.602252i	−0.896477	+	0.443089i	$0.853882\pi$
$788$	113.890	+	19.6003i	0.144531	+	0.0248735i
$789$	100.074	−	254.984i	0.126836	−	0.323173i
$790$	123.133	+	1909.79i	0.155864	+	2.41745i
$791$	317.201	−	472.264i	0.401012	−	0.597047i
$792$	−8.88170	+	33.9824i	−0.0112143	+	0.0429071i
$793$	−222.207	+	68.5417i	−0.280210	+	0.0864334i
$794$	−183.728	+	371.567i	−0.231396	+	0.467968i
$795$	−305.606	+	990.751i	−0.384410	+	1.24623i
$796$	−3.61358	+	173.463i	−0.00453967	+	0.217918i
$797$	228.223	+	999.910i	0.286352	+	1.25459i	0.889490	+	0.456955i	$0.151060\pi$
$797$	228.223	+	999.910i	0.286352	+	1.25459i	−0.603138	+	0.797637i	$0.706083\pi$
$798$	83.4334	+	371.478i	0.104553	+	0.465511i
$799$	−204.170	−	46.6004i	−0.255532	−	0.0583235i
$800$	531.598	+	1268.91i	0.664497	+	1.58614i
$801$	−187.219	+	127.644i	−0.233731	+	0.159355i
$802$	−12.2185	+	2.65522i	−0.0152350	+	0.00331075i
$803$	−38.8452	+	22.4273i	−0.0483751	+	0.0279294i
$804$	−40.4950	+	66.8826i	−0.0503669	+	0.0831873i
$805$	253.873	+	1077.72i	0.315370	+	1.33879i
$806$	−50.9662	+	125.986i	−0.0632335	+	0.156310i
$807$	−125.078	+	183.456i	−0.154991	+	0.227331i
$808$	−108.138	−	11.5105i	−0.133835	−	0.0142457i
$809$	−122.922	−	114.055i	−0.151944	−	0.140983i	0.600538	−	0.799596i	$-0.294953\pi$
$809$	−122.922	−	114.055i	−0.151944	−	0.140983i	−0.752482	+	0.658613i	$0.771143\pi$
$810$	80.4749	+	574.447i	0.0993517	+	0.709194i
$811$	330.247	+	685.764i	0.407209	+	0.845579i	0.999214	+	0.0396441i	$0.0126224\pi$
$811$	330.247	+	685.764i	0.407209	+	0.845579i	−0.592005	+	0.805935i	$0.701663\pi$
$812$	469.645	+	709.816i	0.578380	+	0.874158i
$813$	464.021	+	223.461i	0.570752	+	0.274860i
$814$	34.8496	+	11.1485i	0.0428128	+	0.0136959i
$815$	1463.14	+	844.744i	1.79526	+	1.03650i
$816$	30.9040	+	71.6638i	0.0378726	+	0.0878232i
$817$	761.648	+	114.800i	0.932250	+	0.140514i
$818$	−173.551	+	97.8041i	−0.212165	+	0.119565i
$819$	−24.5037	−	155.245i	−0.0299190	−	0.189555i
$820$	2276.03	−	294.716i	2.77564	−	0.359410i
$821$	10.8031	+	144.158i	0.0131585	+	0.175588i	0.999911	+	0.0133542i	$0.00425090\pi$
$821$	10.8031	+	144.158i	0.0131585	+	0.175588i	−0.986752	+	0.162234i	$0.948130\pi$
$822$	158.374	−	74.2469i	0.192669	−	0.0903247i
$823$	585.939	−	229.964i	0.711955	−	0.279422i	0.0184053	−	0.999831i	$-0.494141\pi$
$823$	585.939	−	229.964i	0.711955	−	0.279422i	0.693550	+	0.720409i	$0.256046\pi$
$824$	−83.4300	−	60.7843i	−0.101250	−	0.0737674i
$825$	22.1128	+	27.7286i	0.0268034	+	0.0336104i
$826$	649.671	+	50.9520i	0.786527	+	0.0616852i
$827$	990.193	+	789.653i	1.19733	+	0.954840i	0.999677	−	0.0254315i	$-0.00809596\pi$
$827$	990.193	+	789.653i	1.19733	+	0.954840i	0.197655	+	0.980272i	$0.436667\pi$
$828$	249.323	−	491.279i	0.301115	−	0.593332i
$829$	70.0728	−	935.056i	0.0845268	−	1.12793i	−0.780146	−	0.625597i	$-0.784855\pi$
$829$	70.0728	−	935.056i	0.0845268	−	1.12793i	0.864673	−	0.502335i	$-0.167526\pi$
$830$	−1387.96	+	1703.74i	−1.67224	+	2.05270i
$831$	−282.729	−	304.710i	−0.340228	−	0.366678i
$832$	−56.6310	+	191.953i	−0.0680661	+	0.230713i
$833$	−175.537	−	23.9686i	−0.210728	−	0.0287738i
$834$	228.269	+	251.212i	0.273704	+	0.301214i
$835$	−671.056	−	723.226i	−0.803659	−	0.866139i
$836$	2.65984	+	49.2350i	0.00318162	+	0.0588935i
$837$	−35.4464	+	472.999i	−0.0423493	+	0.565112i
$838$	−184.564	−	485.054i	−0.220243	−	0.578824i
$839$	−558.514	−	445.400i	−0.665690	−	0.530870i	0.231321	−	0.972877i	$-0.425695\pi$
$839$	−558.514	−	445.400i	−0.665690	−	0.530870i	−0.897011	+	0.442007i	$0.854267\pi$
$840$	−412.493	−	466.812i	−0.491063	−	0.555729i
$841$	51.7409	+	64.8811i	0.0615231	+	0.0771475i
$842$	216.577	+	128.067i	0.257218	+	0.152098i
$843$	126.394	−	49.6060i	0.149934	−	0.0588446i
$844$	558.081	+	232.558i	0.661233	+	0.275542i
$845$	−98.1134	−	1309.23i	−0.116110	−	1.54939i
$846$	−682.306	−	475.672i	−0.806509	−	0.562261i
$847$	−480.493	−	694.340i	−0.567288	−	0.819764i
$848$	602.162	−	1364.29i	0.710097	−	1.60883i
$849$	468.770	+	70.6557i	0.552144	+	0.0832223i
$850$	−302.359	−	72.3325i	−0.355717	−	0.0850970i
$851$	−497.020	−	286.955i	−0.584042	−	0.337197i
$852$	122.474	−	55.8686i	0.143749	−	0.0655735i
$853$	421.275	+	202.875i	0.493875	+	0.237837i	0.664206	−	0.747549i	$-0.268770\pi$
$853$	421.275	+	202.875i	0.493875	+	0.237837i	−0.170332	+	0.985387i	$0.554484\pi$
$854$	−383.706	+	967.787i	−0.449305	+	1.13324i
$855$	517.833	+	1075.29i	0.605653	+	1.25765i
$856$	−22.7514	−	522.012i	−0.0265787	−	0.609827i
$857$	953.565	+	884.779i	1.11268	+	1.03241i	0.999244	+	0.0388689i	$0.0123755\pi$
$857$	953.565	+	884.779i	1.11268	+	1.03241i	0.113434	+	0.993546i	$0.463815\pi$
$858$	−0.0537301	+	5.15899i	−6.26225e−5	+	0.00601281i
$859$	−317.516	+	465.710i	−0.369634	+	0.542154i	−0.965322	−	0.261062i	$-0.915927\pi$
$859$	−317.516	+	465.710i	−0.369634	+	0.542154i	0.595688	+	0.803216i	$0.296880\pi$
$860$	−1182.49	+	435.896i	−1.37499	+	0.506855i
$861$	−590.027	+	289.208i	−0.685281	+	0.335898i
$862$	−449.268	+	133.473i	−0.521192	+	0.154841i
$863$	−15.9853	+	9.22910i	−0.0185229	+	0.0106942i	−0.509233	−	0.860629i	$-0.670071\pi$
$863$	−15.9853	+	9.22910i	−0.0185229	+	0.0106942i	0.490710	+	0.871323i	$0.336737\pi$
$864$	15.8736	+	698.312i	0.0183722	+	0.808232i
$865$	−36.9898	+	25.2192i	−0.0427627	+	0.0291551i
$866$	−646.629	−	969.982i	−0.746684	−	1.12007i
$867$	362.911	+	82.8320i	0.418582	+	0.0955386i
$868$	296.880	+	531.103i	0.342027	+	0.611869i
$869$	−15.7900	−	69.1806i	−0.0181703	−	0.0796094i
$870$	−490.931	−	465.125i	−0.564288	−	0.534627i
$871$	13.3548	−	43.2953i	0.0153328	−	0.0497076i
$872$	346.902	+	215.005i	0.397823	+	0.246566i
$873$	−598.391	+	184.579i	−0.685442	+	0.211431i
$874$	123.225	−	763.503i	0.140989	−	0.873573i
$875$	1035.08	−	84.8035i	1.18295	−	0.0969183i
$876$	−275.220	+	284.496i	−0.314178	+	0.324767i
$877$	496.802	−	1265.83i	0.566478	−	1.44336i	−0.304724	−	0.952441i	$-0.598564\pi$
$877$	496.802	−	1265.83i	0.566478	−	1.44336i	0.871203	−	0.490923i	$-0.163340\pi$
$878$	313.144	+	401.170i	0.356656	+	0.456914i
$879$	−75.4562	−	500.619i	−0.0858432	−	0.569532i
$880$	−42.6304	−	68.4915i	−0.0484436	−	0.0778313i
$881$	1261.85			1.43229			0.716147	−	0.697950i	$-0.245904\pi$
$881$	1261.85			1.43229			0.716147	+	0.697950i	$0.245904\pi$
$882$	−610.593	−	349.699i	−0.692282	−	0.396484i
$883$		−	1019.22i		−	1.15428i	−0.816647	−	0.577138i	$-0.804170\pi$
$883$		−	1019.22i		−	1.15428i	0.816647	−	0.577138i	$-0.195830\pi$
$884$	−27.4550	−	35.9382i	−0.0310576	−	0.0406540i
$885$	−512.015	+	77.1739i	−0.578548	+	0.0872021i
$886$	−963.092	−	1233.82i	−1.08701	−	1.39258i
$887$	480.815	+	188.706i	0.542068	+	0.212746i	0.620546	−	0.784170i	$-0.286911\pi$
$887$	480.815	+	188.706i	0.542068	+	0.212746i	−0.0784782	+	0.996916i	$0.525006\pi$
$888$	322.737	+	10.0867i	0.363443	+	0.0113589i
$889$	−1235.37	+	1162.33i	−1.38961	+	1.30745i
$890$	82.9244	−	513.801i	0.0931735	−	0.577305i
$891$	−6.33954	−	20.5523i	−0.00711509	−	0.0230666i
$892$	95.1929	+	333.086i	0.106718	+	0.373415i
$893$	−1115.73	−	344.157i	−1.24942	−	0.385394i
$894$	544.293	+	515.682i	0.608828	+	0.576825i
$895$	−273.765	+	62.4850i	−0.305883	+	0.0698157i
$896$	511.263	+	735.816i	0.570607	+	0.821224i
$897$	18.0072	−	78.8949i	0.0200750	−	0.0879541i
$898$	254.418	+	381.642i	0.283316	+	0.424991i
$899$	372.094	+	545.761i	0.413898	+	0.607076i
$900$	−1005.49	−	716.660i	−1.11722	−	0.796288i
$901$	168.496	+	291.844i	0.187010	+	0.323911i
$902$	−81.5732	+	24.2346i	−0.0904359	+	0.0268676i
$903$	280.539	−	226.929i	0.310675	−	0.251306i
$904$	300.261	−	576.688i	0.332147	−	0.637929i
$905$	−685.227	−	467.180i	−0.757156	−	0.516221i
$906$	2.16185	−	207.574i	0.00238615	−	0.229111i
$907$	−381.127	+	410.757i	−0.420206	+	0.452874i	−0.907305	−	0.420472i	$-0.861864\pi$
$907$	−381.127	+	410.757i	−0.420206	+	0.452874i	0.487100	+	0.873346i	$0.338055\pi$
$908$	−948.976	−	789.671i	−1.04513	−	0.869681i
$909$	87.9371	−	42.3483i	0.0967405	−	0.0465878i
$910$	297.559	+	204.387i	0.326988	+	0.224601i
$911$	399.522	−	829.615i	0.438553	−	0.910664i	−0.558166	−	0.829729i	$-0.688495\pi$
$911$	399.522	−	829.615i	0.438553	−	0.910664i	0.996719	−	0.0809355i	$-0.0257908\pi$
$912$	141.962	+	411.313i	0.155660	+	0.451001i
$913$	40.7410	−	70.5655i	0.0446232	−	0.0772897i
$914$	190.965	+	45.6841i	0.208934	+	0.0499825i
$915$	123.290	−	817.977i	0.134743	−	0.893964i
$916$	−56.4544	−	18.7102i	−0.0616315	−	0.0204259i
$917$	−839.910	+	1478.39i	−0.915933	+	1.61220i
$918$	−129.483	−	90.2694i	−0.141049	−	0.0983326i
$919$	141.144	−	10.5772i	0.153584	−	0.0115095i	0.00228372	−	0.999997i	$-0.499273\pi$
$919$	141.144	−	10.5772i	0.153584	−	0.0115095i	0.151300	+	0.988488i	$0.451654\pi$
$920$	425.279	+	1191.79i	0.462260	+	1.29542i
$921$	−139.223	−	354.734i	−0.151165	−	0.385162i
$922$	−496.054	−	293.327i	−0.538019	−	0.318142i
$923$	−60.9891	+	48.6372i	−0.0660771	+	0.0526947i
$924$	17.8572	+	14.6508i	0.0193260	+	0.0158558i
$925$	−801.978	+	1005.65i	−0.867003	+	1.08719i
$926$	−113.225	−	297.569i	−0.122274	−	0.321349i
$927$	92.3853	+	6.92332i	0.0996605	+	0.00746852i
$928$	623.600	+	746.515i	0.671982	+	0.804435i
$929$	848.735	−	787.511i	0.913601	−	0.847698i	−0.0751649	−	0.997171i	$-0.523948\pi$
$929$	848.735	−	787.511i	0.913601	−	0.847698i	0.988766	+	0.149473i	$0.0477579\pi$
$930$	−325.126	−	357.805i	−0.349598	−	0.384736i
$931$	−965.964	−	206.398i	−1.03756	−	0.221695i
$932$	82.1260	−	856.181i	0.0881181	−	0.918649i
$933$	−210.326	+	195.154i	−0.225430	+	0.209169i
$934$	−970.043	+	1190.74i	−1.03859	+	1.27488i
$935$	18.1796	+	1.36238i	0.0194435	+	0.00145709i
$936$	−47.5563	−	173.210i	−0.0508080	−	0.185053i
$937$	−216.799	+	271.857i	−0.231375	+	0.290135i	−0.883943	−	0.467595i	$-0.845120\pi$
$937$	−216.799	+	271.857i	−0.231375	+	0.290135i	0.652567	+	0.757731i	$0.273692\pi$
$938$	−113.686	−	167.995i	−0.121200	−	0.179099i
$939$	299.246	−	238.641i	0.318686	−	0.254143i
$940$	1870.97	−	386.223i	1.99039	−	0.410876i
$941$	−126.923	−	323.396i	−0.134881	−	0.343672i	0.847435	−	0.530899i	$-0.178145\pi$
$941$	−126.923	−	323.396i	−0.134881	−	0.343672i	−0.982317	+	0.187226i	$0.940050\pi$
$942$	−685.013	+	321.140i	−0.727190	+	0.340913i
$943$	1331.02	−	99.7465i	1.41148	−	0.105776i
$944$	744.352	−	24.6783i	0.788509	−	0.0261423i
$945$	1206.49	+	362.993i	1.27671	+	0.384120i
$946$	40.7100	−	22.9420i	0.0430338	−	0.0242516i
$947$	154.338	−	1023.96i	0.162975	−	1.08127i	−0.746461	−	0.665429i	$-0.768249\pi$
$947$	154.338	−	1023.96i	0.162975	−	1.08127i	0.909437	−	0.415843i	$-0.136513\pi$
$948$	−301.740	−	548.714i	−0.318291	−	0.578812i
$949$	114.691	−	198.650i	0.120854	−	0.209325i
$950$	−1650.92	−	528.133i	−1.73781	−	0.555929i
$951$	−337.720	+	701.282i	−0.355121	+	0.737416i
$952$	−202.415	−	4.91890i	−0.212621	−	0.00516691i
$953$	309.310	−	148.956i	0.324565	−	0.156302i	−0.264505	−	0.964384i	$-0.585209\pi$
$953$	309.310	−	148.956i	0.324565	−	0.156302i	0.589070	+	0.808082i	$0.299494\pi$
$954$	185.688	+	1325.48i	0.194641	+	1.38939i
$955$	2029.81	−	2187.61i	2.12545	−	2.29069i
$956$	−934.195	−	1049.85i	−0.977192	−	1.09817i
$957$	20.7185	+	14.1256i	0.0216494	+	0.0147603i
$958$	683.714	−	1690.10i	0.713689	−	1.76420i
$959$	3.15255	+	453.784i	0.00328733	+	0.473184i
$960$	−527.812	−	477.780i	−0.549804	−	0.497688i
$961$	−244.398	−	423.310i	−0.254317	−	0.440489i
$962$	−182.846	+	39.7347i	−0.190069	+	0.0413043i
$963$	264.170	+	387.466i	0.274320	+	0.402354i
$964$	−229.737	+	917.973i	−0.238316	+	0.952254i
$965$	−575.086	+	2519.62i	−0.595944	+	2.61100i
$966$	−224.906	−	284.038i	−0.232822	−	0.294035i
$967$	−1728.78	+	394.584i	−1.78778	+	0.408049i	−0.982713	−	0.185133i	$-0.940728\pi$
$967$	−1728.78	+	394.584i	−1.78778	+	0.408049i	−0.805068	+	0.593182i	$0.797871\pi$
$968$	−633.954	−	727.560i	−0.654911	−	0.751612i
$969$	−93.9590	−	28.9825i	−0.0969649	−	0.0299097i
$970$	637.527	−	1289.32i	0.657244	−	1.32919i
$971$	355.551	+	1152.67i	0.366170	+	1.18710i	0.931965	+	0.362549i	$0.118093\pi$
$971$	355.551	+	1152.67i	0.366170	+	1.18710i	−0.565794	+	0.824546i	$0.691430\pi$
$972$	−532.671	−	817.356i	−0.548015	−	0.840901i
$973$	−839.673	+	265.407i	−0.862973	+	0.272772i
$974$	−101.159	−	1568.98i	−0.103859	−	1.61086i
$975$	−168.833	−	66.2619i	−0.173162	−	0.0679610i
$976$	−312.834	+	1147.94i	−0.320527	+	1.17617i
$977$	0.810533	−	0.122168i	0.000829614	−	0.000125044i	−0.148627	−	0.988893i	$-0.547486\pi$
$977$	0.810533	−	0.122168i	0.000829614	−	0.000125044i	0.149457	+	0.988768i	$0.452247\pi$
$978$	−550.818	−	47.0515i	−0.563208	−	0.0481099i
$979$			19.2977i			0.0197116i
$980$	1547.64	−	465.654i	1.57922	−	0.475157i
$981$	−366.296			−0.373390
$982$	51.8704	−	607.231i	0.0528211	−	0.618361i
$983$	−55.7791	−	370.070i	−0.0567437	−	0.376470i	−0.999121	−	0.0419181i	$-0.986653\pi$
$983$	−55.7791	−	370.070i	−0.0567437	−	0.376470i	0.942377	−	0.334552i	$-0.108585\pi$
$984$	−633.388	+	403.444i	−0.643687	+	0.410005i
$985$	87.0351	−	221.762i	0.0883605	−	0.225139i
$986$	−219.354	+	14.1427i	−0.222468	+	0.0143435i
$987$	−471.782	+	276.771i	−0.477996	+	0.280417i
$988$	−137.671	−	211.249i	−0.139343	−	0.213814i
$989$	−700.394	+	216.043i	−0.708184	+	0.218446i
$990$	64.9048	+	32.0935i	0.0655604	+	0.0324176i
$991$	−55.1278	+	178.720i	−0.0556284	+	0.180343i	−0.979123	−	0.203268i	$-0.934844\pi$
$991$	−55.1278	+	178.720i	−0.0556284	+	0.180343i	0.923495	+	0.383611i	$0.125320\pi$
$992$	404.670	+	565.490i	0.407934	+	0.570050i
$993$	122.654	+	537.383i	0.123519	+	0.541172i
$994$	−1.21094	+	349.242i	−0.00121825	+	0.351350i
$995$	348.694	+	79.5872i	0.350447	+	0.0799872i
$996$	174.573	−	697.550i	0.175274	−	0.700351i
$997$	595.896	−	406.275i	0.597689	−	0.407498i	−0.226337	−	0.974049i	$-0.572675\pi$
$997$	595.896	−	406.275i	0.597689	−	0.407498i	0.824026	+	0.566551i	$0.191723\pi$
$998$	−41.6296	−	191.566i	−0.0417131	−	0.191950i
$999$	−565.562	+	326.528i	−0.566129	+	0.326854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.3.o.a.11.2	✓	648
4.3	odd	2	inner	196.3.o.a.11.28	yes	648
49.9	even	21	inner	196.3.o.a.107.28	yes	648
196.107	odd	42	inner	196.3.o.a.107.2	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.3.o.a.11.2	✓	648	1.1	even	1	trivial
196.3.o.a.11.28	yes	648	4.3	odd	2	inner
196.3.o.a.107.2	yes	648	196.107	odd	42	inner
196.3.o.a.107.28	yes	648	49.9	even	21	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	196.o (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99274 - 0.170222i) q^{2} +(-0.201068 - 1.33400i) q^{3} +(3.94205 + 0.678419i) q^{4} +(3.01252 - 7.67577i) q^{5} +(0.173600 + 2.69254i) q^{6} +(-6.53373 - 2.51206i) q^{7} +(-7.74001 - 2.02294i) q^{8} +(6.86104 - 2.11635i) q^{9} +(-7.30976 + 14.7830i) q^{10} +(0.180239 - 0.584320i) q^{11} +(0.112390 - 5.39509i) q^{12} +(0.695840 + 3.04867i) q^{13} +(12.5924 + 6.11807i) q^{14} +(-10.8452 - 2.47534i) q^{15} +(15.0795 + 5.34872i) q^{16} +(-2.98737 + 2.03675i) q^{17} +(-14.0325 + 3.04944i) q^{18} +(-17.4578 + 10.0793i) q^{19} +(17.0829 - 28.2145i) q^{20} +(-2.03735 + 9.22106i) q^{21} +(-0.458634 + 1.13372i) q^{22} +(10.8059 - 15.8493i) q^{23} +(-1.14233 + 10.7319i) q^{24} +(-31.5159 - 29.2425i) q^{25} +(-0.867677 - 6.19367i) q^{26} +(-9.47077 - 19.6663i) q^{27} +(-24.0520 - 14.3353i) q^{28} +(-27.3869 - 13.1888i) q^{29} +(21.1903 + 6.77880i) q^{30} +(-18.8189 - 10.8651i) q^{31} +(-29.1391 - 13.2255i) q^{32} +(-0.815721 - 0.122950i) q^{33} +(6.29975 - 3.55021i) q^{34} +(-38.9649 + 42.5838i) q^{35} +(28.4823 - 3.68810i) q^{36} +(-2.23580 - 29.8347i) q^{37} +(36.5046 - 17.1137i) q^{38} +(3.92701 - 1.54124i) q^{39} +(-38.8445 + 53.3164i) q^{40} +(43.3837 + 54.4014i) q^{41} +(5.62956 - 18.0284i) q^{42} +(-29.8735 - 23.8233i) q^{43} +(1.10692 - 2.18114i) q^{44} +(4.42438 - 59.0393i) q^{45} +(-24.2313 + 29.7442i) q^{46} +(39.3963 + 42.4591i) q^{47} +(4.10318 - 21.1914i) q^{48} +(36.3791 + 32.8262i) q^{49} +(57.8253 + 63.6374i) q^{50} +(3.31768 + 3.57561i) q^{51} +(0.674756 + 12.4901i) q^{52} +(6.96518 - 92.9439i) q^{53} +(15.5252 + 40.8019i) q^{54} +(-3.94214 - 3.14375i) q^{55} +(45.4893 + 32.6607i) q^{56} +(16.9559 + 21.2620i) q^{57} +(52.3300 + 30.9438i) q^{58} +(43.3299 - 17.0057i) q^{59} +(-41.0729 - 17.1155i) q^{60} +(5.55713 + 74.1548i) q^{61} +(35.6518 + 24.8548i) q^{62} +(-50.1445 - 3.40767i) q^{63} +(55.8154 + 31.3151i) q^{64} +(25.4971 + 3.84308i) q^{65} +(1.60459 + 0.383862i) q^{66} +(-12.5479 - 7.24451i) q^{67} +(-13.1581 + 6.00229i) q^{68} +(-23.3157 - 11.2282i) q^{69} +(84.8958 - 78.2258i) q^{70} +(10.8237 + 22.4756i) q^{71} +(-57.3857 + 2.50110i) q^{72} +(-53.7717 - 49.8929i) q^{73} +(-0.623157 + 59.8335i) q^{74} +(-32.6725 + 47.9218i) q^{75} +(-75.6575 + 27.8893i) q^{76} +(-2.64548 + 3.36502i) q^{77} +(-8.08787 + 2.40282i) q^{78} +(100.498 - 58.0223i) q^{79} +(86.4828 - 99.6336i) q^{80} +(29.0613 - 19.8137i) q^{81} +(-77.1922 - 115.793i) q^{82} +(129.911 + 29.6514i) q^{83} +(-14.2871 + 34.9677i) q^{84} +(6.63414 + 29.0661i) q^{85} +(55.4750 + 52.5589i) q^{86} +(-12.0872 + 39.1858i) q^{87} +(-2.57710 + 4.15803i) q^{88} +(-30.1566 + 9.30207i) q^{89} +(-18.8665 + 116.897i) q^{90} +(3.11202 - 21.6672i) q^{91} +(53.3498 - 55.1479i) q^{92} +(-10.7102 + 27.2890i) q^{93} +(-71.2792 - 91.3162i) q^{94} +(24.7742 + 164.366i) q^{95} +(-11.7838 + 41.5306i) q^{96} -87.2158 q^{97} +(-66.9065 - 71.6067i) q^{98} -4.39049i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 13 q^{4} - 26 q^{5} - 2 q^{6} - 16 q^{8} - 176 q^{9} - 12 q^{10} + 45 q^{12} - 4 q^{13} + 89 q^{14} - 25 q^{16} - 26 q^{17} - 48 q^{18} - 166 q^{20} + 50 q^{21} + 10 q^{22} - 96 q^{24}+ \cdots + 771 q^{98}+O(q^{100}) \) 648 * q - 13 * q^2 - 13 * q^4 - 26 * q^5 - 2 * q^6 - 16 * q^8 - 176 * q^9 - 12 * q^10 + 45 * q^12 - 4 * q^13 + 89 * q^14 - 25 * q^16 - 26 * q^17 - 48 * q^18 - 166 * q^20 + 50 * q^21 + 10 * q^22 - 96 * q^24 + 212 * q^25 - 70 * q^26 + 188 * q^28 + 100 * q^29 + 57 * q^30 + 57 * q^32 - 14 * q^33 - 230 * q^34 - 44 * q^36 - 346 * q^37 - 40 * q^38 - 258 * q^40 - 36 * q^41 - 82 * q^42 - 366 * q^44 - 184 * q^45 - 100 * q^46 - 540 * q^48 - 136 * q^49 - 112 * q^50 + 50 * q^52 - 34 * q^53 - 259 * q^54 + 600 * q^56 + 34 * q^57 + 100 * q^58 + 562 * q^60 + 278 * q^61 + 490 * q^62 - 100 * q^64 + 64 * q^65 + 1340 * q^66 + 61 * q^68 + 160 * q^69 + 666 * q^70 - 412 * q^72 + 206 * q^73 - 202 * q^74 - 177 * q^76 + 234 * q^77 - 632 * q^78 - 364 * q^80 + 618 * q^81 - 2246 * q^82 - 1988 * q^84 - 264 * q^85 - 1025 * q^86 - 1283 * q^88 - 34 * q^89 - 1124 * q^90 - 910 * q^92 - 268 * q^93 + 94 * q^94 - 814 * q^96 - 800 * q^97 + 771 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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