LMFDB - Embedded newform 55.3.i.c.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,3,Mod(6,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("55.6");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	55.i (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.49864145398$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 6 x^{10} + 5 x^{9} - 30 x^{8} + 88 x^{7} - 131 x^{6} - 12 x^{5} + 240 x^{4} + \cdots + 1331 $ x^12 - 2x^11 + 6x^10 + 5x^9 - 30x^8 + 88x^7 - 131x^6 - 12x^5 + 240x^4 - 925x^3 + 1386x^2 - 1452*x + 1331
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			46.1
Root			$0.344310 + 1.50447i$ of defining polynomial
Character	$\chi$	$=$	55.46
Dual form			55.3.i.c.6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.35007 - 1.08850i) q^{2} +(4.10532 - 2.98269i) q^{3} +(6.80207 + 4.94199i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-16.9998 + 5.52357i) q^{6} +(4.13101 - 5.68585i) q^{7} +(-9.12620 - 12.5611i) q^{8} +(5.17608 - 15.9303i) q^{9} -7.87649i q^{10} +(-10.8790 + 1.62675i) q^{11} +42.6651 q^{12} +(-1.31604 - 0.427606i) q^{13} +(-20.0282 + 14.5514i) q^{14} +(9.17978 + 6.66950i) q^{15} +(6.50794 + 20.0294i) q^{16} +(-8.29537 + 2.69533i) q^{17} +(-34.6804 + 47.7335i) q^{18} +(15.7882 + 21.7306i) q^{19} +(-5.80966 + 17.8803i) q^{20} -35.6638i q^{21} +(38.2163 + 6.39217i) q^{22} +19.2951 q^{23} +(-74.9320 - 24.3469i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(3.94336 + 2.86502i) q^{26} +(-12.1529 - 37.4029i) q^{27} +(56.1988 - 18.2601i) q^{28} +(7.84308 - 10.7951i) q^{29} +(-23.4931 - 32.3355i) q^{30} +(-13.6245 + 41.9320i) q^{31} -12.0781i q^{32} +(-39.8099 + 39.1272i) q^{33} +30.7240 q^{34} +(14.9461 + 4.85629i) q^{35} +(113.936 - 82.7790i) q^{36} +(-35.4749 - 25.7741i) q^{37} +(-29.2377 - 89.9845i) q^{38} +(-6.67817 + 2.16987i) q^{39} +(20.4068 - 28.0876i) q^{40} +(27.4136 + 37.7315i) q^{41} +(-38.8202 + 119.476i) q^{42} -0.643266i q^{43} +(-82.0394 - 42.6989i) q^{44} +37.4544 q^{45} +(-64.6401 - 21.0028i) q^{46} +(-30.8740 + 22.4313i) q^{47} +(86.4587 + 62.8159i) q^{48} +(-0.121778 - 0.374794i) q^{49} +(16.7504 - 5.44252i) q^{50} +(-26.0158 + 35.8077i) q^{51} +(-6.83854 - 9.41244i) q^{52} +(7.09822 - 21.8461i) q^{53} +138.531i q^{54} +(-10.9767 - 22.0116i) q^{55} -109.121 q^{56} +(129.631 + 42.1197i) q^{57} +(-38.0254 + 27.6270i) q^{58} +(39.1061 + 28.4122i) q^{59} +(29.4809 + 90.7328i) q^{60} +(22.6511 - 7.35977i) q^{61} +(91.2863 - 125.645i) q^{62} +(-69.1949 - 95.2387i) q^{63} +(12.8847 - 39.6551i) q^{64} -3.09418i q^{65} +(175.956 - 87.7456i) q^{66} -87.4921 q^{67} +(-69.7460 - 22.6618i) q^{68} +(79.2128 - 57.5515i) q^{69} +(-44.7845 - 32.5379i) q^{70} +(-24.6333 - 75.8135i) q^{71} +(-247.341 + 80.3659i) q^{72} +(-17.5224 + 24.1175i) q^{73} +(90.7884 + 124.960i) q^{74} +(-7.84047 + 24.1305i) q^{75} +225.838i q^{76} +(-35.6920 + 68.5767i) q^{77} +24.7342 q^{78} +(-45.9661 - 14.9353i) q^{79} +(-38.0981 + 27.6799i) q^{80} +(-39.4928 - 28.6932i) q^{81} +(-50.7665 - 156.243i) q^{82} +(-0.345084 + 0.112125i) q^{83} +(176.250 - 242.587i) q^{84} +(-11.4639 - 15.7787i) q^{85} +(-0.700197 + 2.15499i) q^{86} -67.7108i q^{87} +(119.718 + 121.807i) q^{88} +9.77933 q^{89} +(-125.475 - 40.7693i) q^{90} +(-7.86786 + 5.71633i) q^{91} +(131.247 + 95.3564i) q^{92} +(69.1371 + 212.782i) q^{93} +(127.847 - 41.5399i) q^{94} +(-35.3035 + 48.5910i) q^{95} +(-36.0252 - 49.5844i) q^{96} +(13.2503 - 40.7803i) q^{97} +1.38814i q^{98} +(-30.3962 + 181.727i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 5 q^{2} + 7 q^{3} + 13 q^{4} + 15 q^{5} - 15 q^{6} - 40 q^{7} - 15 q^{8} - 16 q^{9} - 8 q^{11} + 68 q^{12} - 15 q^{13} - 5 q^{14} + 35 q^{15} + 77 q^{16} - 5 q^{17} - 115 q^{18} + 15 q^{19} - 20 q^{20}+ \cdots + 509 q^{99}+O(q^{100}) $ 12 * q - 5 * q^2 + 7 * q^3 + 13 * q^4 + 15 * q^5 - 15 * q^6 - 40 * q^7 - 15 * q^8 - 16 * q^9 - 8 * q^11 + 68 * q^12 - 15 * q^13 - 5 * q^14 + 35 * q^15 + 77 * q^16 - 5 * q^17 - 115 * q^18 + 15 * q^19 - 20 * q^20 - 90 * q^22 + 112 * q^23 - 235 * q^24 - 15 * q^25 + 80 * q^26 + 106 * q^27 + 110 * q^28 + 45 * q^29 - 10 * q^30 - 146 * q^31 - 133 * q^33 + 60 * q^34 - 70 * q^35 + 216 * q^36 + 8 * q^37 + 45 * q^38 + 195 * q^39 + 65 * q^40 - 145 * q^41 + 105 * q^42 - 167 * q^44 - 20 * q^45 - 475 * q^46 + 158 * q^47 + 227 * q^48 + 153 * q^49 + 25 * q^50 - 55 * q^51 + 60 * q^52 + 107 * q^53 - 60 * q^55 - 140 * q^56 + 125 * q^57 + 40 * q^58 - 59 * q^59 + 40 * q^60 + 210 * q^61 + 110 * q^62 - 640 * q^63 + 173 * q^64 + 195 * q^66 - 62 * q^67 - 225 * q^68 + 7 * q^69 - 15 * q^70 + 114 * q^71 - 795 * q^72 - 165 * q^73 - 30 * q^74 + 35 * q^75 - 430 * q^77 + 360 * q^78 - 355 * q^79 + 100 * q^80 + 145 * q^81 - 210 * q^82 + 105 * q^83 + 460 * q^84 + 70 * q^85 + 75 * q^86 + 270 * q^88 - 274 * q^89 - 265 * q^90 + 285 * q^91 + 428 * q^92 + 109 * q^93 + 410 * q^94 + 55 * q^95 - 75 * q^96 + 198 * q^97 + 509 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−3.35007	−	1.08850i	−1.67504	−	0.544252i	−0.691097	−	0.722762i	$-0.742872\pi$
$2$	−3.35007	−	1.08850i	−1.67504	−	0.544252i	−0.983938	+	0.178510i	$0.942872\pi$
$3$	4.10532	−	2.98269i	1.36844	−	0.994231i	0.370584	−	0.928799i	$-0.379158\pi$
$3$	4.10532	−	2.98269i	1.36844	−	0.994231i	0.997857	−	0.0654317i	$-0.0208425\pi$
$4$	6.80207	+	4.94199i	1.70052	+	1.23550i
$5$	0.690983	+	2.12663i	0.138197	+	0.425325i
$5$	0.690983	+	2.12663i	0.138197	+	0.425325i
$6$	−16.9998	+	5.52357i	−2.83330	+	0.920595i
$7$	4.13101	−	5.68585i	0.590144	−	0.812264i	−0.404617	−	0.914486i	$-0.632595\pi$
$7$	4.13101	−	5.68585i	0.590144	−	0.812264i	0.994762	+	0.102222i	$0.0325953\pi$
$8$	−9.12620	−	12.5611i	−1.14078	−	1.57014i
$9$	5.17608	−	15.9303i	0.575119	−	1.77004i
$10$		−	7.87649i		−	0.787649i
$11$	−10.8790	+	1.62675i	−0.989004	+	0.147886i
$11$	−10.8790	+	1.62675i	−0.989004	+	0.147886i
$12$	42.6651			3.55543
$13$	−1.31604	−	0.427606i	−0.101233	−	0.0328928i	0.257962	−	0.966155i	$-0.416949\pi$
$13$	−1.31604	−	0.427606i	−0.101233	−	0.0328928i	−0.359196	+	0.933262i	$0.616949\pi$
$14$	−20.0282	+	14.5514i	−1.43059	+	1.03938i
$15$	9.17978	+	6.66950i	0.611985	+	0.444633i
$16$	6.50794	+	20.0294i	0.406746	+	1.25184i
$17$	−8.29537	+	2.69533i	−0.487963	+	0.158549i	−0.542657	−	0.839954i	$-0.682582\pi$
$17$	−8.29537	+	2.69533i	−0.487963	+	0.158549i	0.0546941	+	0.998503i	$0.482582\pi$
$18$	−34.6804	+	47.7335i	−1.92669	+	2.65186i
$19$	15.7882	+	21.7306i	0.830957	+	1.14371i	0.987744	+	0.156082i	$0.0498864\pi$
$19$	15.7882	+	21.7306i	0.830957	+	1.14371i	−0.156787	+	0.987632i	$0.550114\pi$
$20$	−5.80966	+	17.8803i	−0.290483	+	0.894015i
$21$		−	35.6638i		−	1.69827i
$22$	38.2163	+	6.39217i	1.73710	+	0.290553i
$23$	19.2951			0.838919			0.419460	−	0.907774i	$-0.362220\pi$
$23$	19.2951			0.838919			0.419460	+	0.907774i	$0.362220\pi$
$24$	−74.9320	−	24.3469i	−3.12217	−	1.01445i
$25$	−4.04508	+	2.93893i	−0.161803	+	0.117557i
$26$	3.94336	+	2.86502i	0.151668	+	0.110193i
$27$	−12.1529	−	37.4029i	−0.450109	−	1.38529i
$28$	56.1988	−	18.2601i	2.00710	−	0.652146i
$29$	7.84308	−	10.7951i	0.270451	−	0.372244i	−0.652091	−	0.758141i	$-0.726108\pi$
$29$	7.84308	−	10.7951i	0.270451	−	0.372244i	0.922542	+	0.385897i	$0.126108\pi$
$30$	−23.4931	−	32.3355i	−0.783105	−	1.07785i
$31$	−13.6245	+	41.9320i	−0.439501	+	1.35265i	0.448902	+	0.893581i	$0.351815\pi$
$31$	−13.6245	+	41.9320i	−0.439501	+	1.35265i	−0.888403	+	0.459064i	$0.848185\pi$
$32$		−	12.0781i		−	0.377440i
$33$	−39.8099	+	39.1272i	−1.20636	+	1.18567i
$34$	30.7240			0.903646
$35$	14.9461	+	4.85629i	0.427032	+	0.138751i
$36$	113.936	−	82.7790i	3.16488	−	2.29942i
$37$	−35.4749	−	25.7741i	−0.958782	−	0.696596i	−0.00591474	−	0.999983i	$-0.501883\pi$
$37$	−35.4749	−	25.7741i	−0.958782	−	0.696596i	−0.952868	+	0.303386i	$0.901883\pi$
$38$	−29.2377	−	89.9845i	−0.769414	−	2.36801i
$39$	−6.67817	+	2.16987i	−0.171235	+	0.0556376i
$40$	20.4068	−	28.0876i	0.510170	−	0.702189i
$41$	27.4136	+	37.7315i	0.668623	+	0.920281i	0.999728	−	0.0233128i	$-0.00742137\pi$
$41$	27.4136	+	37.7315i	0.668623	+	0.920281i	−0.331105	+	0.943594i	$0.607421\pi$
$42$	−38.8202	+	119.476i	−0.924289	+	2.84467i
$43$		−	0.643266i		−	0.0149597i	−0.999972	−	0.00747983i	$-0.997619\pi$
$43$		−	0.643266i		−	0.0149597i	0.999972	−	0.00747983i	$-0.00238093\pi$
$44$	−82.0394	−	42.6989i	−1.86453	−	0.970430i
$45$	37.4544			0.832321
$46$	−64.6401	−	21.0028i	−1.40522	−	0.456584i
$47$	−30.8740	+	22.4313i	−0.656894	+	0.477262i	−0.865613	−	0.500714i	$-0.833071\pi$
$47$	−30.8740	+	22.4313i	−0.656894	+	0.477262i	0.208719	+	0.977976i	$0.433071\pi$
$48$	86.4587	+	62.8159i	1.80122	+	1.30866i
$49$	−0.121778	−	0.374794i	−0.00248526	−	0.00764885i
$50$	16.7504	−	5.44252i	0.335007	−	0.108850i
$51$	−26.0158	+	35.8077i	−0.510114	+	0.702112i
$52$	−6.83854	−	9.41244i	−0.131510	−	0.181008i
$53$	7.09822	−	21.8461i	0.133929	−	0.412190i	−0.861493	−	0.507769i	$-0.830470\pi$
$53$	7.09822	−	21.8461i	0.133929	−	0.412190i	0.995422	+	0.0955790i	$0.0304702\pi$
$54$			138.531i			2.56539i
$55$	−10.9767	−	22.0116i	−0.199577	−	0.400211i
$56$	−109.121			−1.94859
$57$	129.631	+	42.1197i	2.27423	+	0.738943i
$58$	−38.0254	+	27.6270i	−0.655610	+	0.476328i
$59$	39.1061	+	28.4122i	0.662815	+	0.481563i	0.867612	−	0.497241i	$-0.165654\pi$
$59$	39.1061	+	28.4122i	0.662815	+	0.481563i	−0.204797	+	0.978804i	$0.565654\pi$
$60$	29.4809	+	90.7328i	0.491348	+	1.51221i
$61$	22.6511	−	7.35977i	0.371329	−	0.120652i	−0.117407	−	0.993084i	$-0.537458\pi$
$61$	22.6511	−	7.35977i	0.371329	−	0.120652i	0.488736	+	0.872432i	$0.337458\pi$
$62$	91.2863	−	125.645i	1.47236	−	2.02653i
$63$	−69.1949	−	95.2387i	−1.09833	−	1.51172i
$64$	12.8847	−	39.6551i	0.201324	−	0.619611i
$65$		−	3.09418i		−	0.0476028i
$66$	175.956	−	87.7456i	2.66600	−	1.32948i
$67$	−87.4921			−1.30585			−0.652926	−	0.757422i	$-0.726459\pi$
$67$	−87.4921			−1.30585			−0.652926	+	0.757422i	$0.726459\pi$
$68$	−69.7460	−	22.6618i	−1.02568	−	0.333262i
$69$	79.2128	−	57.5515i	1.14801	−	0.834079i
$70$	−44.7845	−	32.5379i	−0.639779	−	0.464826i
$71$	−24.6333	−	75.8135i	−0.346948	−	1.06780i	−0.960533	−	0.278167i	$-0.910273\pi$
$71$	−24.6333	−	75.8135i	−0.346948	−	1.06780i	0.613585	−	0.789629i	$-0.289727\pi$
$72$	−247.341	+	80.3659i	−3.43529	+	1.11619i
$73$	−17.5224	+	24.1175i	−0.240033	+	0.330376i	−0.911989	−	0.410214i	$-0.865454\pi$
$73$	−17.5224	+	24.1175i	−0.240033	+	0.330376i	0.671957	+	0.740590i	$0.265454\pi$
$74$	90.7884	+	124.960i	1.22687	+	1.68864i
$75$	−7.84047	+	24.1305i	−0.104540	+	0.321740i
$76$			225.838i			2.97155i
$77$	−35.6920	+	68.5767i	−0.463533	+	0.890607i
$78$	24.7342			0.317106
$79$	−45.9661	−	14.9353i	−0.581849	−	0.189054i	0.00327973	−	0.999995i	$-0.498956\pi$
$79$	−45.9661	−	14.9353i	−0.581849	−	0.189054i	−0.585129	+	0.810940i	$0.698956\pi$
$80$	−38.0981	+	27.6799i	−0.476227	+	0.345999i
$81$	−39.4928	−	28.6932i	−0.487565	−	0.354237i
$82$	−50.7665	−	156.243i	−0.619103	−	1.90540i
$83$	−0.345084	+	0.112125i	−0.00415764	+	0.00135090i	−0.311095	−	0.950379i	$-0.600696\pi$
$83$	−0.345084	+	0.112125i	−0.00415764	+	0.00135090i	0.306937	+	0.951730i	$0.400696\pi$
$84$	176.250	−	242.587i	2.09821	−	2.88794i
$85$	−11.4639	−	15.7787i	−0.134870	−	0.185632i
$86$	−0.700197	+	2.15499i	−0.00814183	+	0.0250580i
$87$		−	67.7108i		−	0.778285i
$88$	119.718	+	121.807i	1.36043	+	1.38417i
$89$	9.77933			0.109880			0.0549401	−	0.998490i	$-0.482503\pi$
$89$	9.77933			0.109880			0.0549401	+	0.998490i	$0.482503\pi$
$90$	−125.475	−	40.7693i	−1.39417	−	0.452992i
$91$	−7.86786	+	5.71633i	−0.0864599	+	0.0628168i
$92$	131.247	+	95.3564i	1.42660	+	1.03648i
$93$	69.1371	+	212.782i	0.743410	+	2.28798i
$94$	127.847	−	41.5399i	1.36007	−	0.441914i
$95$	−35.3035	+	48.5910i	−0.371615	+	0.511485i
$96$	−36.0252	−	49.5844i	−0.375262	−	0.516505i
$97$	13.2503	−	40.7803i	0.136601	−	0.420415i	−0.859234	−	0.511582i	$-0.829060\pi$
$97$	13.2503	−	40.7803i	0.136601	−	0.420415i	0.995836	+	0.0911669i	$0.0290597\pi$
$98$			1.38814i			0.0141647i
$99$	−30.3962	+	181.727i	−0.307032	+	1.83563i
$100$	−42.0391			−0.420391
$101$	−121.223	−	39.3878i	−1.20023	−	0.389978i	−0.360384	−	0.932804i	$-0.617354\pi$
$101$	−121.223	−	39.3878i	−1.20023	−	0.389978i	−0.839845	+	0.542826i	$0.817354\pi$
$102$	126.132	−	91.6401i	1.23659	−	0.898432i
$103$	−45.1623	−	32.8123i	−0.438469	−	0.318566i	0.346557	−	0.938029i	$-0.387351\pi$
$103$	−45.1623	−	32.8123i	−0.438469	−	0.318566i	−0.785026	+	0.619462i	$0.787351\pi$
$104$	6.63919	+	20.4333i	0.0638384	+	0.196474i
$105$	75.8435	−	24.6431i	0.722319	−	0.234696i
$106$	−47.5591	+	65.4595i	−0.448671	+	0.617542i
$107$	23.5956	+	32.4765i	0.220519	+	0.303519i	0.904915	−	0.425592i	$-0.139934\pi$
$107$	23.5956	+	32.4765i	0.220519	+	0.303519i	−0.684396	+	0.729111i	$0.739934\pi$
$108$	102.180	−	314.477i	0.946108	−	2.91182i
$109$		−	157.965i		−	1.44922i	−0.689159	−	0.724610i	$-0.742020\pi$
$109$		−	157.965i		−	1.44922i	0.689159	−	0.724610i	$-0.257980\pi$
$110$	12.8131	+	85.6887i	0.116482	+	0.778988i
$111$	−222.512			−2.00461
$112$	140.768	+	45.7384i	1.25686	+	0.408379i
$113$	133.752	−	97.1766i	1.18365	−	0.859970i	0.191069	−	0.981577i	$-0.438805\pi$
$113$	133.752	−	97.1766i	1.18365	−	0.859970i	0.992578	+	0.121606i	$0.0388046\pi$
$114$	−388.426	−	282.208i	−3.40725	−	2.47551i
$115$	13.3326	+	41.0336i	0.115936	+	0.356814i
$116$	106.698	−	34.6684i	0.919813	−	0.298865i
$117$	−13.6238	+	18.7515i	−0.116443	+	0.160270i
$118$	−100.081	−	137.750i	−0.848147	−	1.16737i
$119$	−18.9430	+	58.3006i	−0.159185	+	0.489921i
$120$		−	176.176i		−	1.46813i
$121$	115.707	−	35.3949i	0.956259	−	0.292520i
$122$	−83.8938			−0.687654
$123$	225.083	+	73.1339i	1.82994	+	0.594585i
$124$	−299.903	+	217.892i	−2.41857	+	1.75719i
$125$	−9.04508	−	6.57164i	−0.0723607	−	0.0525731i
$126$	128.140	+	394.375i	1.01699	+	3.12996i
$127$	76.9214	−	24.9933i	0.605680	−	0.196797i	0.00990806	−	0.999951i	$-0.496846\pi$
$127$	76.9214	−	24.9933i	0.605680	−	0.196797i	0.595772	+	0.803153i	$0.296846\pi$
$128$	−114.727	+	157.908i	−0.896303	+	1.23365i
$129$	−1.91866	−	2.64081i	−0.0148734	−	0.0204714i
$130$	−3.36803	+	10.3657i	−0.0259079	+	0.0797365i
$131$		−	217.878i		−	1.66319i	−0.555383	−	0.831595i	$-0.687428\pi$
$131$		−	217.878i		−	1.66319i	0.555383	−	0.831595i	$-0.312572\pi$
$132$	−464.156	+	69.4054i	−3.51633	+	0.525799i
$133$	188.778			1.41938
$134$	293.105	+	95.2355i	2.18735	+	0.710713i
$135$	71.1445	−	51.6895i	0.526996	−	0.382885i
$136$	109.562	+	79.6012i	0.805600	+	0.585303i
$137$	14.1875	+	43.6645i	0.103558	+	0.318719i	0.989389	−	0.145288i	$-0.0464110\pi$
$137$	14.1875	+	43.6645i	0.103558	+	0.318719i	−0.885831	+	0.464008i	$0.846411\pi$
$138$	−328.014	+	106.578i	−2.37691	+	0.772305i
$139$	−111.105	+	152.922i	−0.799314	+	1.10016i	0.193571	+	0.981086i	$0.437993\pi$
$139$	−111.105	+	152.922i	−0.799314	+	1.10016i	−0.992885	+	0.119075i	$0.962007\pi$
$140$	77.6648	+	106.896i	0.554749	+	0.763546i
$141$	−59.8422	+	184.175i	−0.424413	+	1.30621i
$142$			280.794i			1.97742i
$143$	15.0128	+	2.51109i	0.104985	+	0.0175600i
$144$	352.760			2.44972
$145$	28.3765	+	9.22009i	0.195700	+	0.0635869i
$146$	84.9532	−	61.7221i	0.581871	−	0.422754i
$147$	−1.61783	−	1.17542i	−0.0110057	−	0.00799608i
$148$	−113.928	−	350.634i	−0.769783	−	2.36915i
$149$	67.5694	−	21.9546i	0.453486	−	0.147347i	−0.0733632	−	0.997305i	$-0.523373\pi$
$149$	67.5694	−	21.9546i	0.453486	−	0.147347i	0.526849	+	0.849959i	$0.323373\pi$
$150$	52.5323	−	72.3045i	0.350215	−	0.482030i
$151$	−135.014	−	185.830i	−0.894130	−	1.23066i	−0.972303	−	0.233724i	$-0.924909\pi$
$151$	−135.014	−	185.830i	−0.894130	−	1.23066i	0.0781732	−	0.996940i	$-0.475091\pi$
$152$	128.875	−	396.635i	0.847859	−	2.60944i
$153$			146.099i			0.954896i
$154$	194.217	−	190.886i	1.26115	−	1.23952i
$155$	−98.5881			−0.636052
$156$	−56.1488	−	18.2439i	−0.359928	−	0.116948i
$157$	−157.402	+	114.359i	−1.00256	+	0.728402i	−0.962636	−	0.270800i	$-0.912712\pi$
$157$	−157.402	+	114.359i	−1.00256	+	0.728402i	−0.0399244	+	0.999203i	$0.512712\pi$
$158$	137.732	+	100.069i	0.871725	+	0.633345i
$159$	−36.0196	−	110.857i	−0.226539	−	0.697214i
$160$	25.6856	−	8.34575i	0.160535	−	0.0521609i
$161$	79.7084	−	109.709i	0.495083	−	0.681424i
$162$	101.071	+	139.112i	0.623894	+	0.858717i
$163$	−61.7552	+	190.063i	−0.378866	+	1.16603i	0.561966	+	0.827160i	$0.310045\pi$
$163$	−61.7552	+	190.063i	−0.378866	+	1.16603i	−0.940833	+	0.338871i	$0.889955\pi$
$164$			392.130i			2.39104i
$165$	−110.717	−	57.6246i	−0.671011	−	0.349240i
$166$	1.27810			0.00769942
$167$	−187.455	−	60.9077i	−1.12248	−	0.364717i	−0.311768	−	0.950158i	$-0.600921\pi$
$167$	−187.455	−	60.9077i	−1.12248	−	0.364717i	−0.810715	+	0.585441i	$0.800921\pi$
$168$	−447.978	+	325.475i	−2.66653	+	1.93735i
$169$	−135.175	−	98.2102i	−0.799851	−	0.581126i
$170$	21.2297	+	65.3384i	0.124881	+	0.384344i
$171$	427.896	−	139.032i	2.50232	−	0.813052i
$172$	3.17901	−	4.37554i	0.0184826	−	0.0254392i
$173$	−55.8009	−	76.8033i	−0.322548	−	0.443950i	0.616695	−	0.787202i	$-0.288471\pi$
$173$	−55.8009	−	76.8033i	−0.322548	−	0.443950i	−0.939243	+	0.343253i	$0.888471\pi$
$174$	−73.7034	+	226.836i	−0.423583	+	1.30365i
$175$			35.1405i			0.200803i
$176$	−103.383	−	207.314i	−0.587403	−	1.17792i
$177$	245.288			1.38581
$178$	−32.7615	−	10.6448i	−0.184053	−	0.0598025i
$179$	−92.8713	+	67.4749i	−0.518834	+	0.376955i	−0.816164	−	0.577820i	$-0.803904\pi$
$179$	−92.8713	+	67.4749i	−0.518834	+	0.376955i	0.297331	+	0.954775i	$0.403904\pi$
$180$	254.768	+	185.099i	1.41538	+	1.02833i
$181$	9.40537	+	28.9468i	0.0519634	+	0.159927i	0.973671	−	0.227959i	$-0.0732053\pi$
$181$	9.40537	+	28.9468i	0.0519634	+	0.159927i	−0.921707	+	0.387886i	$0.873205\pi$
$182$	32.5801	−	10.5859i	0.179012	−	0.0581644i
$183$	71.0380	−	97.7754i	0.388186	−	0.534292i
$184$	−176.091	−	242.369i	−0.957018	−	1.31722i
$185$	30.2992	−	93.2514i	0.163780	−	0.504062i
$186$		−	788.092i		−	4.23705i
$187$	85.8611	−	42.8171i	0.459150	−	0.228968i
$188$	−320.862			−1.70672
$189$	−262.871	−	85.4119i	−1.39085	−	0.451915i
$190$	171.161	−	124.355i	0.900846	−	0.654503i
$191$	270.543	+	196.561i	1.41646	+	1.02912i	0.992344	+	0.123506i	$0.0394137\pi$
$191$	270.543	+	196.561i	1.41646	+	1.02912i	0.424112	+	0.905610i	$0.360586\pi$
$192$	−65.3830	−	201.228i	−0.340536	−	1.04806i
$193$	77.4563	−	25.1671i	0.401328	−	0.130399i	−0.101397	−	0.994846i	$-0.532331\pi$
$193$	77.4563	−	25.1671i	0.401328	−	0.130399i	0.502724	+	0.864447i	$0.332331\pi$
$194$	−88.7790	+	122.194i	−0.457624	+	0.629865i
$195$	−9.22900	−	12.7026i	−0.0473282	−	0.0651417i
$196$	1.02389	−	3.15120i	0.00522391	−	0.0160775i
$197$		−	181.283i		−	0.920220i	−0.887862	−	0.460110i	$-0.847810\pi$
$197$		−	181.283i		−	0.920220i	0.887862	−	0.460110i	$-0.152190\pi$
$198$	299.640	−	575.712i	1.51333	−	2.90764i
$199$	324.592			1.63111			0.815557	−	0.578676i	$-0.196431\pi$
$199$	324.592			1.63111			0.815557	+	0.578676i	$0.196431\pi$
$200$	73.8325	+	23.9896i	0.369163	+	0.119948i
$201$	−359.183	+	260.962i	−1.78698	+	1.29832i
$202$	363.232	+	263.904i	1.79818	+	1.30645i
$203$	−28.9793	−	89.1891i	−0.142755	−	0.439355i
$204$	−353.923	+	114.997i	−1.73492	+	0.563709i
$205$	−61.2986	+	84.3703i	−0.299017	+	0.411562i
$206$	115.581	+	159.083i	0.561071	+	0.772248i
$207$	99.8731	−	307.378i	0.482479	−	1.48492i
$208$		−	29.1422i		−	0.140107i
$209$	−207.111	−	210.725i	−0.990960	−	1.00825i
$210$	−280.905			−1.33764
$211$	193.344	+	62.8214i	0.916324	+	0.297732i	0.728958	−	0.684558i	$-0.240005\pi$
$211$	193.344	+	62.8214i	0.916324	+	0.297732i	0.187366	+	0.982290i	$0.440005\pi$
$212$	156.246	−	113.519i	0.737008	−	0.535468i
$213$	−327.256	−	237.766i	−1.53641	−	1.11627i
$214$	−43.6960	−	134.482i	−0.204187	−	0.628423i
$215$	1.36799	−	0.444486i	0.00636273	−	0.00206737i
$216$	−358.913	+	494.001i	−1.66163	+	2.28704i
$217$	182.136	+	250.688i	0.839336	+	1.15525i
$218$	−171.946	+	529.194i	−0.788741	+	2.42750i
$219$			151.274i			0.690748i
$220$	34.1168	−	203.971i	0.155077	−	0.927143i
$221$	12.0695			0.0546133
$222$	745.432	+	242.205i	3.35780	+	1.09102i
$223$	272.507	−	197.988i	1.22201	−	0.887840i	0.225741	−	0.974187i	$-0.427520\pi$
$223$	272.507	−	197.988i	1.22201	−	0.887840i	0.996265	+	0.0863476i	$0.0275196\pi$
$224$	−68.6741	−	49.8947i	−0.306581	−	0.222744i
$225$	25.8804	+	79.6516i	0.115024	+	0.354007i
$226$	−553.856	+	179.959i	−2.45069	+	0.796278i
$227$	−201.019	+	276.679i	−0.885548	+	1.21885i	0.0893055	+	0.996004i	$0.471535\pi$
$227$	−201.019	+	276.679i	−0.885548	+	1.21885i	−0.974853	+	0.222848i	$0.928465\pi$
$228$	673.605	+	927.138i	2.95441	+	4.06639i
$229$	82.7537	−	254.690i	0.361370	−	1.11218i	−0.590853	−	0.806779i	$-0.701209\pi$
$229$	82.7537	−	254.690i	0.361370	−	1.11218i	0.952223	−	0.305403i	$-0.0987913\pi$
$230$		−	151.978i		−	0.660774i
$231$	58.0160	+	387.988i	0.251151	+	1.67960i
$232$	−207.176			−0.893000
$233$	−63.8765	−	20.7547i	−0.274148	−	0.0890761i	0.168717	−	0.985665i	$-0.446038\pi$
$233$	−63.8765	−	20.7547i	−0.274148	−	0.0890761i	−0.442865	+	0.896589i	$0.646038\pi$
$234$	66.0518	−	47.9895i	0.282273	−	0.205083i
$235$	−69.0364	−	50.1579i	−0.293772	−	0.213438i
$236$	125.589	+	386.524i	0.532158	+	1.63781i
$237$	−233.253	+	75.7885i	−0.984190	+	0.319783i
$238$	126.921	−	174.692i	0.533281	−	0.733999i
$239$	41.9930	+	57.7984i	0.175703	+	0.241834i	0.887781	−	0.460266i	$-0.152246\pi$
$239$	41.9930	+	57.7984i	0.175703	+	0.241834i	−0.712078	+	0.702100i	$0.752246\pi$
$240$	−73.8445	+	227.270i	−0.307686	+	0.946959i
$241$			376.422i			1.56192i	0.624584	+	0.780958i	$0.285268\pi$
$241$			376.422i			1.56192i	−0.624584	+	0.780958i	$0.714732\pi$
$242$	−426.156	−	7.37240i	−1.76097	−	0.0304645i
$243$	106.236			0.437186
$244$	190.446	+	61.8796i	0.780516	+	0.253605i
$245$	0.712900	−	0.517952i	0.00290980	−	0.00211409i
$246$	−674.438	−	490.008i	−2.74162	−	1.99190i
$247$	−11.4857	−	35.3493i	−0.0465008	−	0.143115i
$248$	651.054	−	211.540i	2.62522	−	0.852985i
$249$	−1.08225	+	1.48959i	−0.00434638	+	0.00598228i
$250$	23.1484	+	31.8611i	0.0925937	+	0.127444i
$251$	83.9714	−	258.437i	0.334548	−	1.02963i	−0.632397	−	0.774644i	$-0.717929\pi$
$251$	83.9714	−	258.437i	0.334548	−	1.02963i	0.966944	−	0.254987i	$-0.0820712\pi$
$252$		−	989.781i		−	3.92770i
$253$	−209.913	+	31.3883i	−0.829695	+	0.124065i
$254$	−284.897			−1.12164
$255$	−94.1262	−	30.5835i	−0.369122	−	0.119935i
$256$	421.295	−	306.089i	1.64569	−	1.19566i
$257$	−76.6625	−	55.6986i	−0.298298	−	0.216726i	0.428561	−	0.903513i	$-0.359021\pi$
$257$	−76.6625	−	55.6986i	−0.298298	−	0.216726i	−0.726859	+	0.686787i	$0.759021\pi$
$258$	3.55312	+	10.9354i	0.0137718	+	0.0423852i
$259$	−293.095	+	95.2322i	−1.13164	+	0.367692i
$260$	15.2914	−	21.0469i	0.0588132	−	0.0809494i
$261$	−131.373	−	180.819i	−0.503343	−	0.692793i
$262$	−237.161	+	729.906i	−0.905194	+	2.78590i
$263$			240.380i			0.913991i	0.889469	+	0.456996i	$0.151074\pi$
$263$			240.380i			0.913991i	−0.889469	+	0.456996i	$0.848926\pi$
$264$	854.795	+	142.975i	3.23786	+	0.541574i
$265$	51.3632			0.193824
$266$	−632.419	−	205.485i	−2.37752	−	0.772502i
$267$	40.1473	−	29.1687i	0.150365	−	0.109246i
$268$	−595.127	−	432.385i	−2.22062	−	1.61338i
$269$	−33.7200	−	103.779i	−0.125353	−	0.385797i	0.868612	−	0.495493i	$-0.165012\pi$
$269$	−33.7200	−	103.779i	−0.125353	−	0.385797i	−0.993965	+	0.109696i	$0.965012\pi$
$270$	−294.603	+	95.7225i	−1.09112	+	0.354528i
$271$	−171.743	+	236.384i	−0.633737	+	0.872264i	−0.998262	−	0.0589293i	$-0.981231\pi$
$271$	−171.743	+	236.384i	−0.633737	+	0.872264i	0.364525	+	0.931194i	$0.381231\pi$
$272$	−107.972	−	148.610i	−0.396954	−	0.546361i
$273$	−15.2500	+	46.9348i	−0.0558609	+	0.171922i
$274$		−	161.722i		−	0.590228i
$275$	39.2258	−	38.5531i	0.142639	−	0.140193i
$276$	823.230			2.98272
$277$	−98.0954	−	31.8731i	−0.354135	−	0.115065i	0.126546	−	0.991961i	$-0.459611\pi$
$277$	−98.0954	−	31.8731i	−0.354135	−	0.115065i	−0.480682	+	0.876895i	$0.659611\pi$
$278$	538.665	−	391.363i	1.93764	−	1.40778i
$279$	597.469	+	434.086i	2.14146	+	1.55587i
$280$	−75.4009	−	232.060i	−0.269289	−	0.828786i
$281$	324.936	−	105.578i	1.15636	−	0.375723i	0.332822	−	0.942990i	$-0.391999\pi$
$281$	324.936	−	105.578i	1.15636	−	0.375723i	0.823534	+	0.567267i	$0.191999\pi$
$282$	400.951	−	551.862i	1.42181	−	1.95696i
$283$	−11.9948	−	16.5094i	−0.0423844	−	0.0583371i	0.787299	−	0.616572i	$-0.211479\pi$
$283$	−11.9948	−	16.5094i	−0.0423844	−	0.0583371i	−0.829683	+	0.558235i	$0.811479\pi$
$284$	207.112	−	637.426i	0.729269	−	2.24446i
$285$			304.781i			1.06941i
$286$	−47.5607	−	24.7538i	−0.166296	−	0.0865519i
$287$	327.781			1.14210
$288$	−192.408	−	62.5171i	−0.668082	−	0.217073i
$289$	−172.258	+	125.152i	−0.596047	+	0.433053i
$290$	−85.0273	−	61.7759i	−0.293198	−	0.213020i
$291$	−67.2382	−	206.938i	−0.231059	−	0.711126i
$292$	−238.377	+	77.4533i	−0.816359	+	0.265251i
$293$	58.4929	−	80.5085i	0.199634	−	0.274773i	−0.697449	−	0.716634i	$-0.745682\pi$
$293$	58.4929	−	80.5085i	0.199634	−	0.274773i	0.897083	+	0.441861i	$0.145682\pi$
$294$	4.14040	+	5.69877i	0.0140830	+	0.0193836i
$295$	−33.4006	+	102.796i	−0.113222	+	0.348462i
$296$			680.825i			2.30008i
$297$	193.057	+	387.138i	0.650025	+	1.30350i
$298$	−250.260			−0.839799
$299$	−25.3931	−	8.25072i	−0.0849267	−	0.0275944i
$300$	−172.584	+	125.390i	−0.575280	+	0.417966i
$301$	−3.65751	−	2.65734i	−0.0121512	−	0.00882836i
$302$	250.028	+	769.507i	0.827908	+	2.54804i
$303$	−615.142	+	199.872i	−2.03017	+	0.659643i
$304$	−332.501	+	457.649i	−1.09375	+	1.50542i
$305$	31.3030	+	43.0849i	0.102633	+	0.141262i
$306$	159.030	−	489.443i	0.519704	−	1.59949i
$307$		−	461.259i		−	1.50247i	−0.660034	−	0.751236i	$-0.729458\pi$
$307$		−	461.259i		−	1.50247i	0.660034	−	0.751236i	$-0.270542\pi$
$308$	−581.685	+	290.074i	−1.88859	+	0.941798i
$309$	−283.275			−0.916748
$310$	330.277	+	107.314i	1.06541	+	0.346173i
$311$	−353.614	+	256.915i	−1.13702	+	0.826094i	−0.986701	−	0.162543i	$-0.948030\pi$
$311$	−353.614	+	256.915i	−1.13702	+	0.826094i	−0.150320	+	0.988637i	$0.548030\pi$
$312$	88.2023	+	64.0827i	0.282700	+	0.205393i
$313$	25.8727	+	79.6280i	0.0826604	+	0.254403i	0.983842	−	0.179039i	$-0.0572989\pi$
$313$	25.8727	+	79.6280i	0.0826604	+	0.254403i	−0.901182	+	0.433442i	$0.857299\pi$
$314$	651.788	−	211.779i	2.07576	−	0.674455i
$315$	154.725	−	212.960i	0.491189	−	0.676064i
$316$	−238.854	−	328.755i	−0.755868	−	1.04036i
$317$	−10.2957	+	31.6870i	−0.0324787	+	0.0999591i	−0.965982	−	0.258610i	$-0.916735\pi$
$317$	−10.2957	+	31.6870i	−0.0324787	+	0.0999591i	0.933503	+	0.358570i	$0.116735\pi$
$318$			410.587i			1.29115i
$319$	−67.7644	+	130.199i	−0.212428	+	0.408147i
$320$	93.2347			0.291358
$321$	193.735	+	62.9483i	0.603535	+	0.196101i
$322$	−386.448	+	280.771i	−1.20015	+	0.871959i
$323$	−189.540	−	137.709i	−0.586811	−	0.426343i
$324$	−126.831	−	390.346i	−0.391454	−	1.20477i
$325$	6.58018	−	2.13803i	0.0202467	−	0.00657855i
$326$	413.769	−	569.504i	1.26923	−	1.74694i
$327$	−471.161	−	648.498i	−1.44086	−	1.98317i
$328$	223.769	−	688.691i	0.682224	−	2.09967i
$329$			268.209i			0.815224i
$330$	308.185	+	313.562i	0.933893	+	0.950189i
$331$	158.074			0.477566			0.238783	−	0.971073i	$-0.423252\pi$
$331$	158.074			0.477566			0.238783	+	0.971073i	$0.423252\pi$
$332$	−2.90140	−	0.942723i	−0.00873917	−	0.00283953i
$333$	−594.210	+	431.719i	−1.78441	+	1.29645i
$334$	561.688	+	408.090i	1.68170	+	1.22183i
$335$	−60.4556	−	186.063i	−0.180464	−	0.555412i
$336$	714.323	−	232.098i	2.12596	−	0.690767i
$337$	221.891	−	305.407i	0.658432	−	0.906253i	−0.340997	−	0.940065i	$-0.610764\pi$
$337$	221.891	−	305.407i	0.658432	−	0.906253i	0.999428	+	0.0338111i	$0.0107645\pi$
$338$	345.943	+	476.150i	1.02350	+	1.40873i
$339$	259.248	−	797.883i	0.764743	−	2.35364i
$340$		−	163.983i		−	0.482302i
$341$	80.0092	−	478.344i	0.234631	−	1.40277i
$342$	−1584.82			−4.63397
$343$	324.887	+	105.562i	0.947194	+	0.307762i
$344$	−8.08015	+	5.87057i	−0.0234888	+	0.0170656i
$345$	177.125	+	128.689i	0.513406	+	0.373012i
$346$	103.336	+	318.036i	0.298660	+	0.919179i
$347$	−638.027	+	207.307i	−1.83869	+	0.597428i	−0.840217	+	0.542250i	$0.817573\pi$
$347$	−638.027	+	207.307i	−1.83869	+	0.597428i	−0.998477	+	0.0551779i	$0.982427\pi$
$348$	334.626	−	460.573i	0.961569	−	1.32349i
$349$	218.524	+	300.773i	0.626144	+	0.861813i	0.997782	−	0.0665649i	$-0.0212039\pi$
$349$	218.524	+	300.773i	0.626144	+	0.861813i	−0.371639	+	0.928377i	$0.621204\pi$
$350$	38.2505	−	117.723i	0.109287	−	0.336352i
$351$			54.4202i			0.155043i
$352$	19.6480	+	131.398i	0.0558182	+	0.373290i
$353$	189.013			0.535449			0.267724	−	0.963496i	$-0.413728\pi$
$353$	189.013			0.535449			0.267724	+	0.963496i	$0.413728\pi$
$354$	−821.732	−	266.997i	−2.32128	−	0.754229i
$355$	144.206	−	104.772i	0.406214	−	0.295132i
$356$	66.5197	+	48.3294i	0.186853	+	0.135757i
$357$	96.1256	+	295.844i	0.269259	+	0.828695i
$358$	384.572	−	124.955i	1.07422	−	0.349036i
$359$	−36.7416	+	50.5704i	−0.102344	+	0.140865i	−0.857117	−	0.515121i	$-0.827747\pi$
$359$	−36.7416	+	50.5704i	−0.102344	+	0.140865i	0.754773	+	0.655986i	$0.227747\pi$
$360$	−341.817	−	470.470i	−0.949491	−	1.30686i
$361$	−111.396	+	342.841i	−0.308576	+	0.949699i
$362$		−	107.211i		−	0.296164i
$363$	369.444	−	490.427i	1.01775	−	1.35104i
$364$	−81.7677			−0.224637
$365$	−63.3966	−	20.5988i	−0.173689	−	0.0564350i
$366$	−344.411	+	250.229i	−0.941014	+	0.683687i
$367$	243.134	+	176.647i	0.662491	+	0.481328i	0.867503	−	0.497432i	$-0.165724\pi$
$367$	243.134	+	176.647i	0.662491	+	0.481328i	−0.205013	+	0.978759i	$0.565724\pi$
$368$	125.572	+	386.470i	0.341227	+	1.05019i
$369$	742.970	−	241.406i	2.01347	−	0.654216i
$370$	−203.009	+	279.418i	−0.548673	+	0.755184i
$371$	−94.8907	−	130.606i	−0.255770	−	0.352037i
$372$	−581.293	+	1789.03i	−1.56261	+	4.80923i
$373$		−	306.810i		−	0.822546i	−0.911512	−	0.411273i	$-0.865084\pi$
$373$		−	306.810i		−	0.822546i	0.911512	−	0.411273i	$-0.134916\pi$
$374$	−334.247	+	49.9801i	−0.893710	+	0.133637i
$375$	−56.7342			−0.151291
$376$	563.525	+	183.100i	1.49874	+	0.486969i
$377$	−14.9378	+	10.8530i	−0.0396228	+	0.0287877i
$378$	787.665	+	572.272i	2.08377	+	1.51395i
$379$	137.394	+	422.855i	0.362517	+	1.11571i	0.951522	+	0.307582i	$0.0995198\pi$
$379$	137.394	+	422.855i	0.362517	+	1.11571i	−0.589005	+	0.808129i	$0.700480\pi$
$380$	−480.273	+	156.050i	−1.26388	+	0.410658i
$381$	241.240	−	332.038i	0.633176	−	0.871492i
$382$	−692.381	−	952.981i	−1.81252	−	2.49471i
$383$	−23.7402	+	73.0650i	−0.0619850	+	0.190770i	−0.977254	−	0.212074i	$-0.931978\pi$
$383$	−23.7402	+	73.0650i	−0.0619850	+	0.190770i	0.915269	+	0.402844i	$0.131978\pi$
$384$			990.457i			2.57932i
$385$	−170.500	−	28.5183i	−0.442856	−	0.0740734i
$386$	−286.878			−0.743208
$387$	−10.2474	−	3.32959i	−0.0264791	−	0.00860359i
$388$	291.665	−	211.907i	0.751714	−	0.546153i
$389$	−124.773	−	90.6528i	−0.320753	−	0.233041i	0.415744	−	0.909482i	$-0.363521\pi$
$389$	−124.773	−	90.6528i	−0.320753	−	0.233041i	−0.736497	+	0.676441i	$0.763521\pi$
$390$	17.0909	+	52.6005i	0.0438229	+	0.134873i
$391$	−160.060	+	52.0068i	−0.409362	+	0.133010i
$392$	−3.59647	+	4.95011i	−0.00917466	+	0.0126278i
$393$	−649.862	−	894.459i	−1.65359	−	2.27598i
$394$	−197.328	+	607.312i	−0.500832	+	1.54140i
$395$		−	108.073i		−	0.273602i
$396$	−1104.85	+	1085.90i	−2.79002	+	2.74217i
$397$	249.821			0.629271			0.314636	−	0.949213i	$-0.398118\pi$
$397$	249.821			0.629271			0.314636	+	0.949213i	$0.398118\pi$
$398$	−1087.41	−	353.320i	−2.73217	−	0.887737i
$399$	774.994	−	563.066i	1.94234	−	1.41119i
$400$	−85.1900	−	61.8942i	−0.212975	−	0.154735i
$401$	−210.623	−	648.231i	−0.525244	−	1.61654i	−0.763832	−	0.645415i	$-0.776684\pi$
$401$	−210.623	−	648.231i	−0.525244	−	1.61654i	0.238588	−	0.971121i	$-0.423316\pi$
$402$	1487.35	−	483.269i	3.69987	−	1.20216i
$403$	35.8607	−	49.3581i	0.0889845	−	0.122477i
$404$	−629.914	−	867.002i	−1.55919	−	2.14605i
$405$	33.7308	−	103.813i	0.0832860	−	0.256328i
$406$			330.334i			0.813630i
$407$	427.862	+	222.688i	1.05126	+	0.547146i
$408$	687.212			1.68434
$409$	32.8400	+	10.6704i	0.0802934	+	0.0260889i	0.348888	−	0.937164i	$-0.386559\pi$
$409$	32.8400	+	10.6704i	0.0802934	+	0.0260889i	−0.268595	+	0.963253i	$0.586559\pi$
$410$	297.192	−	215.923i	0.724859	−	0.526641i
$411$	188.482	+	136.940i	0.458594	+	0.333188i
$412$	−145.039	−	446.384i	−0.352036	−	1.08346i
$413$	323.095	−	104.980i	0.782313	−	0.254189i
$414$	−669.164	+	921.025i	−1.61634	+	2.22470i
$415$	−0.476894	−	0.656389i	−0.00114914	−	0.00158166i
$416$	−5.16466	+	15.8952i	−0.0124150	+	0.0382096i
$417$			959.187i			2.30021i
$418$	464.461	+	931.383i	1.11115	+	2.22819i
$419$	−479.485			−1.14436			−0.572178	−	0.820130i	$-0.693901\pi$
$419$	−479.485			−1.14436			−0.572178	+	0.820130i	$0.693901\pi$
$420$	637.679	+	207.194i	1.51828	+	0.493320i
$421$	294.374	−	213.875i	0.699226	−	0.508017i	−0.180454	−	0.983583i	$-0.557757\pi$
$421$	294.374	−	213.875i	0.699226	−	0.508017i	0.879680	+	0.475566i	$0.157757\pi$
$422$	−579.336	−	420.912i	−1.37283	−	0.997423i
$423$	197.531	+	607.939i	0.466977	+	1.43721i
$424$	−339.192	+	110.210i	−0.799980	+	0.259929i
$425$	25.6341	−	35.2823i	0.0603155	−	0.0830172i
$426$	837.523	+	1152.75i	1.96602	+	2.70599i
$427$	51.7252	−	159.194i	0.121136	−	0.372819i
$428$			337.517i			0.788590i
$429$	69.1223	−	34.4698i	0.161124	−	0.0803492i
$430$	−5.06667			−0.0117830
$431$	424.328	+	137.873i	0.984520	+	0.319890i	0.756663	−	0.653805i	$-0.226828\pi$
$431$	424.328	+	137.873i	0.984520	+	0.319890i	0.227856	+	0.973695i	$0.426828\pi$
$432$	670.066	−	486.832i	1.55108	−	1.12692i
$433$	162.759	+	118.251i	0.375886	+	0.273097i	0.759648	−	0.650335i	$-0.225371\pi$
$433$	162.759	+	118.251i	0.375886	+	0.273097i	−0.383761	+	0.923432i	$0.625371\pi$
$434$	−337.293	−	1038.08i	−0.777172	−	2.39189i
$435$	143.996	−	46.7870i	0.331024	−	0.107556i
$436$	780.662	−	1074.49i	1.79051	−	2.46442i
$437$	304.635	+	419.295i	0.697106	+	0.959484i
$438$	164.662	−	506.778i	0.375941	−	1.15703i
$439$		−	294.210i		−	0.670182i	−0.942186	−	0.335091i	$-0.891233\pi$
$439$		−	294.210i		−	0.670182i	0.942186	−	0.335091i	$-0.108767\pi$
$440$	−176.315	+	338.763i	−0.400717	+	0.769915i
$441$	−6.60092			−0.0149681
$442$	−40.4338	−	13.1377i	−0.0914792	−	0.0297234i
$443$	−674.795	+	490.267i	−1.52324	+	1.10670i	−0.563387	+	0.826193i	$0.690502\pi$
$443$	−674.795	+	490.267i	−1.52324	+	1.10670i	−0.959853	+	0.280505i	$0.909498\pi$
$444$	−1513.54	−	1099.65i	−3.40888	−	2.47670i
$445$	6.75735	+	20.7970i	0.0151851	+	0.0467348i
$446$	−1128.43	+	366.649i	−2.53011	+	0.822084i
$447$	211.910	−	291.670i	0.474072	−	0.652505i
$448$	−172.246	−	237.076i	−0.384477	−	0.529188i
$449$	123.808	−	381.041i	0.275741	−	0.848645i	−0.713281	−	0.700878i	$-0.752792\pi$
$449$	123.808	−	381.041i	0.275741	−	0.848645i	0.989022	−	0.147766i	$-0.0472084\pi$
$450$		−	295.009i		−	0.655577i
$451$	−359.613	−	365.888i	−0.797368	−	0.811282i
$452$	1390.04			3.07530
$453$	−1108.55	−	360.189i	−2.44713	−	0.795120i
$454$	974.596	−	708.085i	2.14669	−	1.55966i
$455$	−17.5931	−	12.7821i	−0.0386661	−	0.0280925i
$456$	−653.969	−	2012.71i	−1.43414	−	4.41384i
$457$	389.643	−	126.603i	0.852610	−	0.277030i	0.150071	−	0.988675i	$-0.452050\pi$
$457$	389.643	−	126.603i	0.852610	−	0.277030i	0.702539	+	0.711645i	$0.252050\pi$
$458$	−554.462	+	763.151i	−1.21062	+	1.66627i
$459$	201.626	+	277.515i	0.439273	+	0.604607i
$460$	−112.098	+	345.003i	−0.243692	+	0.750006i
$461$		−	144.172i		−	0.312738i	−0.987699	−	0.156369i	$-0.950021\pi$
$461$		−	144.172i		−	0.312738i	0.987699	−	0.156369i	$-0.0499789\pi$
$462$	227.969	−	1362.94i	0.493439	−	2.95008i
$463$	−650.569			−1.40512			−0.702558	−	0.711627i	$-0.747959\pi$
$463$	−650.569			−1.40512			−0.702558	+	0.711627i	$0.747959\pi$
$464$	267.261	+	86.8383i	0.575993	+	0.187152i
$465$	−404.736	+	294.058i	−0.870400	+	0.632382i
$466$	191.399	+	139.060i	0.410728	+	0.298411i
$467$	191.750	+	590.147i	0.410600	+	1.26370i	0.916128	+	0.400887i	$0.131298\pi$
$467$	191.750	+	590.147i	0.410600	+	1.26370i	−0.505528	+	0.862810i	$0.668702\pi$
$468$	−185.340	+	60.2206i	−0.396026	+	0.128677i
$469$	−361.431	+	497.467i	−0.770641	+	1.06070i
$470$	176.680	+	243.179i	0.375915	+	0.517402i
$471$	−305.088	+	938.963i	−0.647744	+	1.99355i
$472$		−	750.513i		−	1.59007i
$473$	1.04643	+	6.99812i	0.00221233	+	0.0147952i
$474$	863.910			1.82259
$475$	−127.729	−	41.5017i	−0.268903	−	0.0873720i
$476$	−416.973	+	302.949i	−0.875994	+	0.636447i
$477$	−311.274	−	226.154i	−0.652567	−	0.474117i
$478$	−77.7657	−	239.338i	−0.162690	−	0.500708i
$479$	175.919	−	57.1597i	0.367264	−	0.119331i	−0.119570	−	0.992826i	$-0.538152\pi$
$479$	175.919	−	57.1597i	0.367264	−	0.119331i	0.486834	+	0.873494i	$0.338152\pi$
$480$	80.5548	−	110.874i	0.167822	−	0.230988i
$481$	35.6652	+	49.0889i	0.0741479	+	0.102056i
$482$	409.736	−	1261.04i	0.850075	−	2.61626i
$483$		−	688.137i		−	1.42472i
$484$	961.971	+	331.066i	1.98754	+	0.684021i
$485$	95.8801			0.197691
$486$	−355.899	−	115.638i	−0.732302	−	0.237939i
$487$	362.280	−	263.212i	0.743901	−	0.540475i	−0.150030	−	0.988681i	$-0.547937\pi$
$487$	362.280	−	263.212i	0.743901	−	0.540475i	0.893930	+	0.448206i	$0.147937\pi$
$488$	−299.165	−	217.356i	−0.613044	−	0.445402i
$489$	313.374	+	964.467i	0.640847	+	1.97233i
$490$	−2.95206	+	0.959182i	−0.00602461	+	0.00195751i
$491$	−262.558	+	361.380i	−0.534742	+	0.736009i	−0.987844	−	0.155450i	$-0.950317\pi$
$491$	−262.558	+	361.380i	−0.534742	+	0.736009i	0.453102	+	0.891459i	$0.350317\pi$
$492$	1169.60	+	1609.82i	2.37724	+	3.27199i
$493$	−35.9650	+	110.689i	−0.0729513	+	0.224521i
$494$			130.925i			0.265030i
$495$	−407.469	+	60.9289i	−0.823169	+	0.123089i
$496$	−928.540			−1.87206
$497$	−532.825	−	173.125i	−1.07208	−	0.348340i
$498$	5.24703	−	3.81219i	0.0105362	−	0.00765500i
$499$	243.249	+	176.731i	0.487473	+	0.354170i	0.804212	−	0.594343i	$-0.202588\pi$
$499$	243.249	+	176.731i	0.487473	+	0.354170i	−0.316739	+	0.948513i	$0.602588\pi$
$500$	−29.0483	−	89.4015i	−0.0580966	−	0.178803i
$501$	−951.231	+	309.074i	−1.89866	+	0.616914i
$502$	−562.621	+	774.381i	−1.12076	+	1.54259i
$503$	461.634	+	635.385i	0.917762	+	1.26319i	0.964446	+	0.264281i	$0.0851347\pi$
$503$	461.634	+	635.385i	0.917762	+	1.26319i	−0.0466837	+	0.998910i	$0.514865\pi$
$504$	−564.819	+	1738.33i	−1.12067	+	3.44908i
$505$		−	285.013i		−	0.564382i
$506$	737.389	+	123.338i	1.45729	+	0.243751i
$507$	−847.867			−1.67232
$508$	646.741	+	210.139i	1.27311	+	0.413659i
$509$	−582.553	+	423.249i	−1.14450	+	0.831531i	−0.987740	−	0.156105i	$-0.950106\pi$
$509$	−582.553	+	423.249i	−1.14450	+	0.831531i	−0.156764	+	0.987636i	$0.550106\pi$
$510$	282.039	+	204.913i	0.553018	+	0.401791i
$511$	64.7432	+	199.259i	0.126699	+	0.389939i
$512$	−1002.02	+	325.577i	−1.95707	+	0.635892i
$513$	620.913	−	854.614i	1.21036	−	1.66591i
$514$	196.197	+	270.042i	0.381706	+	0.525373i
$515$	38.5732	−	118.716i	0.0748995	−	0.230517i
$516$		−	27.4450i		−	0.0531880i
$517$	299.390	−	294.255i	0.579091	−	0.569159i
$518$	1085.55			2.09565
$519$	−458.161	−	148.866i	−0.882777	−	0.286832i
$520$	−38.8665	+	28.2382i	−0.0747432	+	0.0543041i
$521$	584.860	+	424.925i	1.12257	+	0.815596i	0.984597	−	0.174840i	$-0.0559408\pi$
$521$	584.860	+	424.925i	1.12257	+	0.815596i	0.137974	+	0.990436i	$0.455941\pi$
$522$	243.286	+	748.756i	0.466064	+	1.43440i
$523$	−603.092	+	195.956i	−1.15314	+	0.374678i	−0.822325	−	0.569018i	$-0.807323\pi$
$523$	−603.092	+	195.956i	−1.15314	+	0.374678i	−0.330814	+	0.943696i	$0.607323\pi$
$524$	1076.75	−	1482.02i	2.05487	−	2.82828i
$525$	104.813	+	144.263i	0.199644	+	0.274787i
$526$	261.654	−	805.289i	0.497442	−	1.53097i
$527$		−	384.564i		−	0.729723i
$528$	−1042.77	−	542.731i	−1.97495	−	1.02790i
$529$	−156.697			−0.296214
$530$	−172.070	−	55.9091i	−0.324661	−	0.105489i
$531$	655.032	−	475.909i	1.23358	−	0.896250i
$532$	1284.08	+	932.939i	2.41368	+	1.75364i
$533$	−19.9430	−	61.3782i	−0.0374165	−	0.115156i
$534$	−166.247	+	54.0168i	−0.311323	+	0.101155i
$535$	−52.7613	+	72.6197i	−0.0986192	+	0.135738i
$536$	798.471	+	1099.00i	1.48968	+	2.05037i
$537$	−180.010	+	554.013i	−0.335213	+	1.03168i
$538$			384.373i			0.714447i
$539$	1.93452	+	3.87930i	0.00358910	+	0.00719721i
$540$	739.379			1.36922
$541$	−28.3507	−	9.21172i	−0.0524043	−	0.0170272i	0.282698	−	0.959209i	$-0.408771\pi$
$541$	−28.3507	−	9.21172i	−0.0524043	−	0.0170272i	−0.335102	+	0.942182i	$0.608771\pi$
$542$	832.655	−	604.959i	1.53626	−	1.11616i
$543$	124.951	+	90.7825i	0.230113	+	0.167187i
$544$	32.5544	+	100.192i	0.0598427	+	0.184177i
$545$	335.933	−	109.151i	0.616390	−	0.200277i
$546$	102.177	−	140.635i	0.187138	−	0.257573i
$547$	−333.214	−	458.629i	−0.609165	−	0.838444i	0.387343	−	0.921936i	$-0.373393\pi$
$547$	−333.214	−	458.629i	−0.609165	−	0.838444i	−0.996509	+	0.0834913i	$0.973393\pi$
$548$	−119.286	+	367.123i	−0.217675	+	0.669933i
$549$		−	398.933i		−	0.726655i
$550$	−173.374	+	86.4581i	−0.315226	+	0.157196i
$551$	358.411			0.650474
$552$	−1445.82	−	469.777i	−2.61925	−	0.851045i
$553$	−274.806	+	199.658i	−0.496937	+	0.361046i
$554$	293.933	+	213.555i	0.530564	+	0.385478i
$555$	−153.752	−	473.200i	−0.277031	−	0.852613i
$556$	−1511.48	+	491.111i	−2.71849	+	0.883292i
$557$	−259.771	+	357.544i	−0.466375	+	0.641910i	−0.975816	−	0.218596i	$-0.929852\pi$
$557$	−259.771	+	357.544i	−0.466375	+	0.641910i	0.509440	+	0.860506i	$0.329852\pi$
$558$	−1529.06	−	2104.57i	−2.74025	−	3.77163i
$559$	−0.275064	+	0.846560i	−0.000492065	+	0.00151442i
$560$			330.966i			0.591011i
$561$	224.777	−	431.875i	0.400673	−	0.769831i
$562$	−1203.48			−2.14142
$563$	867.024	+	281.713i	1.54001	+	0.500379i	0.951378	−	0.308025i	$-0.0996680\pi$
$563$	867.024	+	281.713i	1.54001	+	0.500379i	0.588629	+	0.808403i	$0.299668\pi$
$564$	−1317.24	+	957.034i	−2.33554	+	1.69687i
$565$	299.079	+	217.294i	0.529343	+	0.384590i
$566$	22.2128	+	68.3641i	0.0392453	+	0.120785i
$567$	−326.290	+	106.018i	−0.575467	+	0.186981i
$568$	−727.496	+	1001.31i	−1.28080	+	1.76287i
$569$	83.3233	+	114.685i	0.146438	+	0.201555i	0.875935	−	0.482430i	$-0.160246\pi$
$569$	83.3233	+	114.685i	0.146438	+	0.201555i	−0.729497	+	0.683984i	$0.760246\pi$
$570$	331.756	−	1021.04i	0.582028	−	1.79130i
$571$			313.919i			0.549771i	0.961477	+	0.274885i	$0.0886399\pi$
$571$			313.919i			0.549771i	−0.961477	+	0.274885i	$0.911360\pi$
$572$	89.7085	+	91.2738i	0.156833	+	0.159570i
$573$	1696.95			2.96151
$574$	−1098.09	−	356.791i	−1.91305	−	0.621588i
$575$	−78.0505	+	56.7070i	−0.135740	+	0.0986209i
$576$	−565.026	−	410.515i	−0.980948	−	0.712700i
$577$	−44.1138	−	135.768i	−0.0764537	−	0.235300i	0.905525	−	0.424294i	$-0.139478\pi$
$577$	−44.1138	−	135.768i	−0.0764537	−	0.235300i	−0.981978	+	0.188993i	$0.939478\pi$
$578$	713.304	−	231.767i	1.23409	−	0.400980i
$579$	242.917	−	334.347i	0.419546	−	0.577456i
$580$	147.453	+	202.952i	0.254230	+	0.349918i
$581$	−0.788022	+	2.42528i	−0.00135632	+	0.00417432i
$582$			766.445i			1.31692i
$583$	−41.6838	+	249.212i	−0.0714989	+	0.427464i
$584$	462.856			0.792561
$585$	−49.2914	−	16.0157i	−0.0842587	−	0.0273773i
$586$	−283.589	+	206.040i	−0.483940	+	0.351603i
$587$	663.273	+	481.896i	1.12994	+	0.820947i	0.985686	−	0.168594i	$-0.0539228\pi$
$587$	663.273	+	481.896i	1.12994	+	0.820947i	0.144251	+	0.989541i	$0.453923\pi$
$588$	−5.19567	−	15.9906i	−0.00883617	−	0.0271949i
$589$	−1126.31	+	365.961i	−1.91225	+	0.621327i
$590$	223.789	−	308.019i	0.379303	−	0.522065i
$591$	−540.712	−	744.227i	−0.914911	−	1.25927i
$592$	285.370	−	878.277i	0.482043	−	1.48358i
$593$		−	855.267i		−	1.44227i	−0.692793	−	0.721136i	$-0.743620\pi$
$593$		−	855.267i		−	1.44227i	0.692793	−	0.721136i	$-0.256380\pi$
$594$	−225.355	−	1507.08i	−0.379385	−	2.53718i
$595$	−137.073			−0.230375
$596$	568.111	+	184.591i	0.953207	+	0.309716i
$597$	1332.55	−	968.157i	2.23208	−	1.62170i
$598$	76.0877	+	55.2810i	0.127237	+	0.0924431i
$599$	−77.9607	−	239.938i	−0.130151	−	0.400565i	0.864653	−	0.502370i	$-0.167538\pi$
$599$	−77.9607	−	239.938i	−0.130151	−	0.400565i	−0.994804	+	0.101805i	$0.967538\pi$
$600$	374.660	−	121.734i	0.624434	−	0.202891i
$601$	−73.8436	+	101.637i	−0.122868	+	0.169113i	−0.866020	−	0.500009i	$-0.833330\pi$
$601$	−73.8436	+	101.637i	−0.122868	+	0.169113i	0.743152	+	0.669123i	$0.233330\pi$
$602$	9.36040	+	12.8835i	0.0155488	+	0.0214011i
$603$	−452.866	+	1393.78i	−0.751021	+	2.31141i
$604$		−	1931.27i		−	3.19746i
$605$	155.224	+	221.609i	0.256568	+	0.366296i
$606$	2278.33			3.75962
$607$	275.319	+	89.4566i	0.453573	+	0.147375i	0.526889	−	0.849934i	$-0.323358\pi$
$607$	275.319	+	89.4566i	0.453573	+	0.147375i	−0.0733160	+	0.997309i	$0.523358\pi$
$608$	262.464	−	190.691i	0.431684	−	0.313637i
$609$	−384.993	−	279.714i	−0.632172	−	0.459300i
$610$	−57.9692	−	178.411i	−0.0950315	−	0.292477i
$611$	50.2231	−	16.3185i	0.0821981	−	0.0267078i
$612$	−722.021	+	993.776i	−1.17977	+	1.62382i
$613$	194.770	+	268.077i	0.317732	+	0.437320i	0.937773	−	0.347249i	$-0.112884\pi$
$613$	194.770	+	268.077i	0.317732	+	0.437320i	−0.620041	+	0.784569i	$0.712884\pi$
$614$	−502.082	+	1545.25i	−0.817723	+	2.51669i
$615$			529.202i			0.860491i
$616$	1187.13	−	177.513i	1.92717	−	0.288170i
$617$	−753.160			−1.22068			−0.610340	−	0.792139i	$-0.708967\pi$
$617$	−753.160			−1.22068			−0.610340	+	0.792139i	$0.708967\pi$
$618$	948.991	+	308.346i	1.53558	+	0.498942i
$619$	280.470	−	203.774i	0.453102	−	0.329198i	−0.337717	−	0.941248i	$-0.609655\pi$
$619$	280.470	−	203.774i	0.453102	−	0.329198i	0.790819	+	0.612050i	$0.209655\pi$
$620$	−670.603	−	487.221i	−1.08162	−	0.785841i
$621$	−234.493	−	721.694i	−0.377605	−	1.16215i
$622$	1464.28	−	475.775i	2.35415	−	0.764911i
$623$	40.3985	−	55.6038i	0.0648451	−	0.0892517i
$624$	−86.9222	−	119.638i	−0.139298	−	0.191728i
$625$	7.72542	−	23.7764i	0.0123607	−	0.0380423i
$626$		−	294.922i		−	0.471121i
$627$	−1478.78	−	247.345i	−2.35850	−	0.394490i
$628$	−1635.82			−2.60481
$629$	363.747	+	118.189i	0.578295	+	0.187899i
$630$	−750.146	+	545.013i	−1.19071	+	0.865100i
$631$	−789.719	−	573.764i	−1.25154	−	0.909293i	−0.253225	−	0.967407i	$-0.581491\pi$
$631$	−789.719	−	573.764i	−1.25154	−	0.909293i	−0.998310	+	0.0581139i	$0.981491\pi$
$632$	231.892	+	713.689i	0.366917	+	1.12925i
$633$	981.119	−	318.785i	1.54995	−	0.503609i
$634$	68.9829	−	94.9469i	0.108806	−	0.149758i
$635$	106.303	+	146.313i	0.167406	+	0.230414i
$636$	302.847	−	932.066i	0.476174	−	1.46551i
$637$			0.545315i			0.000856067i
$638$	368.737	−	362.414i	0.577958	−	0.568046i
$639$	−1335.24			−2.08957
$640$	−415.085	−	134.869i	−0.648571	−	0.210733i
$641$	328.612	−	238.751i	0.512655	−	0.372466i	−0.301175	−	0.953569i	$-0.597379\pi$
$641$	328.612	−	238.751i	0.512655	−	0.372466i	0.813830	+	0.581103i	$0.197379\pi$
$642$	−580.506	−	421.762i	−0.904215	−	0.656951i
$643$	55.6814	+	171.370i	0.0865963	+	0.266516i	0.984973	−	0.172711i	$-0.0552525\pi$
$643$	55.6814	+	171.370i	0.0865963	+	0.266516i	−0.898376	+	0.439227i	$0.855253\pi$
$644$	1084.36	−	352.331i	1.68380	−	0.547098i
$645$	4.29026	−	5.90504i	0.00665157	−	0.00915510i
$646$	485.076	+	667.649i	0.750891	+	1.03351i
$647$	−4.54333	+	13.9829i	−0.00702215	+	0.0216120i	−0.954506	−	0.298191i	$-0.903617\pi$
$647$	−4.54333	+	13.9829i	−0.00702215	+	0.0216120i	0.947484	+	0.319803i	$0.103617\pi$
$648$			757.934i			1.16965i
$649$	−471.656	−	245.482i	−0.726743	−	0.378247i
$650$	−24.3713			−0.0374943
$651$	1495.45	+	485.902i	2.29716	+	0.746394i
$652$	−1359.35	+	987.628i	−2.08490	+	1.51477i
$653$	−259.719	−	188.697i	−0.397732	−	0.288969i	0.370885	−	0.928679i	$-0.379055\pi$
$653$	−259.719	−	188.697i	−0.397732	−	0.288969i	−0.768617	+	0.639710i	$0.779055\pi$
$654$	872.531	+	2685.37i	1.33415	+	4.10608i
$655$	463.345	−	150.550i	0.707397	−	0.229847i
$656$	−577.333	+	794.631i	−0.880081	+	1.21133i
$657$	293.502	+	403.971i	0.446731	+	0.614872i
$658$	291.946	−	898.519i	0.443688	−	1.36553i
$659$			589.500i			0.894536i	0.894400	+	0.447268i	$0.147603\pi$
$659$			589.500i			0.894536i	−0.894400	+	0.447268i	$0.852397\pi$
$660$	−468.323	−	939.129i	−0.709581	−	1.42292i
$661$	−303.814			−0.459628			−0.229814	−	0.973235i	$-0.573812\pi$
$661$	−303.814			−0.459628			−0.229814	+	0.973235i	$0.573812\pi$
$662$	−529.560	−	172.065i	−0.799940	−	0.259916i
$663$	49.5494	−	35.9997i	0.0747351	−	0.0542982i
$664$	4.55772	+	3.31138i	0.00686403	+	0.00498701i
$665$	130.442	+	401.460i	0.196154	+	0.603699i
$666$	2460.57	−	799.489i	3.69456	−	1.20043i
$667$	151.333	−	208.293i	0.226887	−	0.312283i
$668$	−974.074	−	1340.70i	−1.45819	−	2.00703i
$669$	528.193	−	1625.61i	0.789526	−	2.42991i
$670$			689.131i			1.02855i
$671$	−234.449	+	116.915i	−0.349403	+	0.174240i
$672$	−430.750			−0.640997
$673$	689.638	+	224.077i	1.02472	+	0.332952i	0.772702	−	0.634770i	$-0.218905\pi$
$673$	689.638	+	224.077i	1.02472	+	0.332952i	0.252020	+	0.967722i	$0.418905\pi$
$674$	−1075.79	+	781.607i	−1.59613	+	1.15965i
$675$	159.084	+	115.581i	0.235680	+	0.171232i
$676$	−434.114	−	1336.07i	−0.642180	−	1.97643i
$677$	−331.808	+	107.811i	−0.490115	+	0.159248i	−0.543640	−	0.839318i	$-0.682954\pi$
$677$	−331.808	+	107.811i	−0.490115	+	0.159248i	0.0535250	+	0.998567i	$0.482954\pi$
$678$	−1737.00	+	2390.77i	−2.56194	+	3.52621i
$679$	−177.133	−	243.803i	−0.260874	−	0.359062i
$680$	−93.5768	+	288.000i	−0.137613	+	0.423529i
$681$			1735.44i			2.54837i
$682$	−788.716	+	1515.40i	−1.15647	+	2.22199i
$683$	−320.721			−0.469578			−0.234789	−	0.972046i	$-0.575440\pi$
$683$	−320.721			−0.469578			−0.234789	+	0.972046i	$0.575440\pi$
$684$	3597.67	+	1168.95i	5.25975	+	1.70900i
$685$	−83.0549	+	60.3429i	−0.121248	+	0.0880918i
$686$	−973.491	−	707.283i	−1.41908	−	1.03102i
$687$	−419.930	−	1292.41i	−0.611252	−	1.88124i
$688$	12.8842	−	4.18633i	0.0187271	−	0.00608479i
$689$	−18.6830	+	25.7150i	−0.0271162	+	0.0373222i
$690$	−453.304	−	623.919i	−0.656962	−	0.904230i
$691$	195.510	−	601.717i	0.282937	−	0.870791i	−0.704072	−	0.710128i	$-0.748637\pi$
$691$	195.510	−	601.717i	0.282937	−	0.870791i	0.987009	−	0.160663i	$-0.0513631\pi$
$692$		−	798.189i		−	1.15345i
$693$	907.704	+	923.543i	1.30982	+	1.33267i
$694$	2363.09			3.40503
$695$	−401.980	−	130.611i	−0.578389	−	0.187930i
$696$	−850.524	+	617.942i	−1.22202	+	0.887848i
$697$	−329.105	−	239.108i	−0.472173	−	0.343054i
$698$	−404.679	−	1245.47i	−0.579769	−	1.78435i
$699$	−324.139	+	105.319i	−0.463718	+	0.150671i
$700$	−173.664	+	239.028i	−0.248091	+	0.341468i
$701$	152.233	+	209.530i	0.217165	+	0.298902i	0.903676	−	0.428218i	$-0.140858\pi$
$701$	152.233	+	209.530i	0.217165	+	0.298902i	−0.686510	+	0.727120i	$0.740858\pi$
$702$	59.2366	−	182.312i	0.0843826	−	0.259703i
$703$		−	1177.82i		−	1.67541i
$704$	−75.6647	+	452.370i	−0.107478	+	0.642571i
$705$	−433.022			−0.614216
$706$	−633.209	−	205.742i	−0.896896	−	0.291419i
$707$	−724.727	+	526.545i	−1.02507	+	0.744759i
$708$	1668.47	+	1212.21i	2.35659	+	1.71216i
$709$	−412.437	−	1269.35i	−0.581716	−	1.79034i	−0.612076	−	0.790799i	$-0.709665\pi$
$709$	−412.437	−	1269.35i	−0.581716	−	1.79034i	0.0303602	−	0.999539i	$-0.490335\pi$
$710$	−597.145	+	194.024i	−0.841049	+	0.273273i
$711$	−475.848	+	654.948i	−0.669265	+	0.921165i
$712$	−89.2482	−	122.840i	−0.125349	−	0.172528i
$713$	−262.887	+	809.084i	−0.368706	+	1.13476i
$714$		−	1095.73i		−	1.53464i
$715$	5.03346	+	33.6618i	0.00703980	+	0.0470794i
$716$	−965.177			−1.34801
$717$	344.790	+	112.029i	0.480878	+	0.156247i
$718$	178.133	−	129.421i	0.248096	−	0.180252i
$719$	504.172	+	366.303i	0.701213	+	0.509461i	0.880327	−	0.474367i	$-0.157323\pi$
$719$	504.172	+	366.303i	0.701213	+	0.509461i	−0.179114	+	0.983828i	$0.557323\pi$
$720$	243.751	+	750.189i	0.338543	+	1.04193i
$721$	−373.132	+	121.238i	−0.517520	+	0.168152i
$722$	746.369	−	1027.29i	1.03375	−	1.42284i
$723$	1122.75	+	1545.33i	1.55290	+	2.13739i
$724$	−79.0787	+	243.379i	−0.109225	+	0.336159i
$725$			66.7172i			0.0920238i
$726$	−1771.50	+	1240.82i	−2.44008	+	1.70912i
$727$	512.020			0.704292			0.352146	−	0.935945i	$-0.385452\pi$
$727$	512.020			0.704292			0.352146	+	0.935945i	$0.385452\pi$
$728$	143.607	+	46.6608i	0.197263	+	0.0640946i
$729$	791.568	−	575.108i	1.08583	−	0.788900i
$730$	189.961	+	138.015i	0.260221	+	0.189061i
$731$	1.73381	+	5.33613i	0.00237184	+	0.00729976i
$732$	966.410	−	314.006i	1.32023	−	0.428970i
$733$	182.666	−	251.419i	0.249204	−	0.342999i	−0.666029	−	0.745926i	$-0.732007\pi$
$733$	182.666	−	251.419i	0.249204	−	0.342999i	0.915232	+	0.402927i	$0.132007\pi$
$734$	−622.235	−	856.433i	−0.847732	−	1.16680i
$735$	1.38179	−	4.25272i	0.00187999	−	0.00578602i
$736$		−	233.048i		−	0.316642i
$737$	951.831	−	142.328i	1.29149	−	0.193117i
$738$	−2751.77			−3.72869
$739$	−1161.65	−	377.444i	−1.57192	−	0.510749i	−0.611964	−	0.790886i	$-0.709620\pi$
$739$	−1161.65	−	377.444i	−1.57192	−	0.510749i	−0.959960	+	0.280137i	$0.909620\pi$
$740$	666.945	−	484.564i	0.901277	−	0.654816i
$741$	−152.589	−	110.862i	−0.205923	−	0.149612i
$742$	175.726	+	540.828i	0.236827	+	0.728878i
$743$	971.621	−	315.699i	1.30770	−	0.424898i	0.429447	−	0.903092i	$-0.358709\pi$
$743$	971.621	−	315.699i	1.30770	−	0.424898i	0.878254	+	0.478195i	$0.158709\pi$
$744$	2041.83	−	2810.34i	2.74439	−	3.77733i
$745$	93.3786	+	128.525i	0.125340	+	0.172516i
$746$	−333.964	+	1027.83i	−0.447672	+	1.37779i
$747$			6.07766i			0.00813610i
$748$	795.635	+	133.080i	1.06368	+	0.177915i
$749$	282.130			0.376675
$750$	190.064	+	61.7554i	0.253418	+	0.0823405i
$751$	−300.333	+	218.205i	−0.399911	+	0.290552i	−0.769505	−	0.638641i	$-0.779497\pi$
$751$	−300.333	+	218.205i	−0.399911	+	0.290552i	0.369594	+	0.929193i	$0.379497\pi$
$752$	−650.211	−	472.406i	−0.864643	−	0.628200i
$753$	−426.110	−	1311.43i	−0.565883	−	1.74161i
$754$	61.8562	−	20.0983i	0.0820374	−	0.0266556i
$755$	301.900	−	415.529i	0.399867	−	0.550370i
$756$	−1365.96	−	1880.08i	−1.80683	−	2.48688i
$757$	252.489	−	777.082i	0.333539	−	1.02653i	−0.633898	−	0.773417i	$-0.718546\pi$
$757$	252.489	−	777.082i	0.333539	−	1.02653i	0.967437	−	0.253112i	$-0.0814540\pi$
$758$		−	1566.15i		−	2.06616i
$759$	−768.138	+	754.965i	−1.01204	+	0.994683i
$760$	932.545			1.22703
$761$	284.940	+	92.5825i	0.374428	+	0.121659i	0.490185	−	0.871619i	$-0.336929\pi$
$761$	284.940	+	92.5825i	0.374428	+	0.121659i	−0.115757	+	0.993278i	$0.536929\pi$
$762$	−1169.60	+	849.761i	−1.53490	+	1.11517i
$763$	−898.165	−	652.555i	−1.17715	−	0.855249i
$764$	868.849	+	2674.04i	1.13724	+	3.50006i
$765$	−310.698	+	100.952i	−0.406142	+	0.131963i
$766$	159.063	−	218.931i	0.207654	−	0.285811i
$767$	−39.3157	−	54.1135i	−0.0512591	−	0.0705521i
$768$	816.585	−	2513.19i	1.06326	−	3.27238i
$769$			1280.08i			1.66460i	0.554327	+	0.832299i	$0.312976\pi$
$769$			1280.08i			1.66460i	−0.554327	+	0.832299i	$0.687024\pi$
$770$	540.144	+	281.128i	0.701485	+	0.365101i
$771$	−480.856			−0.623679
$772$	651.238	+	211.600i	0.843573	+	0.274093i
$773$	−530.985	+	385.783i	−0.686914	+	0.499072i	−0.875644	−	0.482957i	$-0.839563\pi$
$773$	−530.985	+	385.783i	−0.686914	+	0.499072i	0.188730	+	0.982029i	$0.439563\pi$
$774$	30.7053	+	22.3087i	0.0396710	+	0.0288227i
$775$	−68.1227	−	209.660i	−0.0879002	−	0.270529i
$776$	−633.172	+	205.730i	−0.815943	+	0.265116i
$777$	−919.200	+	1265.17i	−1.18301	+	1.62828i
$778$	319.322	+	439.509i	0.410440	+	0.564922i
$779$	−387.117	+	1191.42i	−0.496941	+	1.52943i
$780$		−	132.014i		−	0.169248i
$781$	391.316	+	784.707i	0.501045	+	1.00475i
$782$	592.823			0.758086
$783$	−499.083	−	162.162i	−0.637399	−	0.207103i
$784$	6.71436	−	4.87827i	0.00856424	−	0.00622229i
$785$	−351.961	−	255.715i	−0.448358	−	0.325751i
$786$	1203.46	+	3703.88i	1.53112	+	4.71231i
$787$	176.218	−	57.2567i	0.223911	−	0.0727531i	−0.194913	−	0.980821i	$-0.562442\pi$
$787$	176.218	−	57.2567i	0.223911	−	0.0727531i	0.418824	+	0.908067i	$0.362442\pi$
$788$	895.901	−	1233.10i	1.13693	−	1.56485i
$789$	716.978	+	986.836i	0.908718	+	1.25074i
$790$	−117.638	+	362.051i	−0.148908	+	0.458293i
$791$		−	1161.93i		−	1.46894i
$792$	2560.10	−	1276.67i	3.23245	−	1.61195i
$793$	−32.9567			−0.0415595
$794$	−836.917	−	271.931i	−1.05405	−	0.342482i
$795$	210.863	−	153.201i	0.265236	−	0.192705i
$796$	2207.90	+	1604.13i	2.77374	+	2.01524i
$797$	218.892	+	673.681i	0.274645	+	0.845272i	0.989313	+	0.145807i	$0.0465780\pi$
$797$	218.892	+	673.681i	0.274645	+	0.845272i	−0.714668	+	0.699464i	$0.753422\pi$
$798$	−3209.19	+	1042.73i	−4.02154	+	1.30668i
$799$	195.652	−	269.292i	0.244871	−	0.337036i
$800$	35.4966	+	48.8569i	0.0443707	+	0.0610711i
$801$	50.6186	−	155.788i	0.0631942	−	0.194492i
$802$			2400.88i			2.99362i
$803$	151.394	−	290.880i	0.188535	−	0.362241i
$804$	−3732.86			−4.64286
$805$	288.388	+	93.7029i	0.358246	+	0.116401i
$806$	−173.862	+	126.318i	−0.215710	+	0.156723i
$807$	−447.973	−	325.472i	−0.555110	−	0.403311i
$808$	611.552	+	1882.16i	0.756871	+	2.32941i
$809$	848.378	−	275.655i	1.04867	−	0.340735i	0.266527	−	0.963828i	$-0.414124\pi$
$809$	848.378	−	275.655i	1.04867	−	0.340735i	0.782148	+	0.623093i	$0.214124\pi$
$810$	−226.001	+	311.064i	−0.279014	+	0.384030i
$811$	−163.153	−	224.561i	−0.201175	−	0.276893i	0.696495	−	0.717561i	$-0.254742\pi$
$811$	−163.153	−	224.561i	−0.201175	−	0.276893i	−0.897670	+	0.440668i	$0.854742\pi$
$812$	243.653	−	749.886i	0.300065	−	0.923505i
$813$			1482.69i			1.82372i
$814$	−1190.97	−	1211.75i	−1.46311	−	1.48864i
$815$	−446.865			−0.548301
$816$	−886.516	−	288.047i	−1.08642	−	0.352998i
$817$	13.9785	−	10.1560i	0.0171096	−	0.0124308i
$818$	−98.4017	−	71.4930i	−0.120295	−	0.0873997i
$819$	50.3384	+	154.926i	0.0614632	+	0.189164i
$820$	−833.914	+	270.955i	−1.01697	+	0.330433i
$821$	461.140	−	634.705i	0.561681	−	0.773088i	−0.429858	−	0.902897i	$-0.641436\pi$
$821$	461.140	−	634.705i	0.561681	−	0.773088i	0.991539	+	0.129809i	$0.0414363\pi$
$822$	−482.368	−	663.923i	−0.586822	−	0.807692i
$823$	327.948	−	1009.32i	0.398479	−	1.22639i	−0.527740	−	0.849406i	$-0.676960\pi$
$823$	327.948	−	1009.32i	0.398479	−	1.22639i	0.926219	−	0.376986i	$-0.123040\pi$
$824$			866.742i			1.05187i
$825$	46.0426	−	275.271i	0.0558093	−	0.333662i
$826$	−1196.66			−1.44874
$827$	809.495	+	263.021i	0.978833	+	0.318042i	0.754376	−	0.656442i	$-0.227939\pi$
$827$	809.495	+	263.021i	0.978833	+	0.318042i	0.224456	+	0.974484i	$0.427939\pi$
$828$	2198.40	−	1597.23i	2.65508	−	1.92903i
$829$	−429.985	−	312.403i	−0.518680	−	0.376843i	0.297427	−	0.954745i	$-0.403872\pi$
$829$	−429.985	−	312.403i	−0.518680	−	0.376843i	−0.816106	+	0.577902i	$0.803872\pi$
$830$	0.883148	+	2.71805i	0.00106403	+	0.00327476i
$831$	−497.781	+	161.739i	−0.599015	+	0.194632i
$832$	−33.9135	+	46.6779i	−0.0407614	+	0.0561033i
$833$	2.02039	+	2.78082i	0.00242543	+	0.00333832i
$834$	1044.08	−	3213.34i	1.25189	−	3.85293i
$835$		−	440.732i		−	0.527823i
$836$	−367.381	−	2456.90i	−0.439451	−	2.93888i
$837$	1733.96			2.07163
$838$	1606.31	+	521.921i	1.91684	+	0.622818i
$839$	548.789	−	398.718i	0.654098	−	0.475230i	−0.210566	−	0.977580i	$-0.567531\pi$
$839$	548.789	−	398.718i	0.654098	−	0.475230i	0.864665	+	0.502349i	$0.167531\pi$
$840$	−1001.71	−	727.784i	−1.19251	−	0.866409i
$841$	204.864	+	630.505i	0.243595	+	0.749709i
$842$	−1218.98	+	396.070i	−1.44772	+	0.470392i
$843$	1019.06	−	1402.62i	1.20885	−	1.66384i
$844$	1004.68	+	1382.82i	1.19038	+	1.63842i
$845$	115.453	−	355.328i	0.136631	−	0.420506i
$846$		−	2251.65i		−	2.66153i
$847$	276.738	−	804.111i	0.326727	−	0.949364i
$848$	483.758			0.570470
$849$	−98.4850	−	31.9997i	−0.116001	−	0.0376910i
$850$	−124.281	+	90.2954i	−0.146213	+	0.106230i
$851$	−684.494	−	497.314i	−0.804341	−	0.584388i
$852$	−1050.98	−	3234.59i	−1.23355	−	3.79647i
$853$	−987.480	+	320.852i	−1.15766	+	0.376145i	−0.824022	−	0.566558i	$-0.808275\pi$
$853$	−987.480	+	320.852i	−1.15766	+	0.376145i	−0.333633	+	0.942703i	$0.608275\pi$
$854$	−346.566	+	477.007i	−0.405815	+	0.558556i
$855$	591.338	+	813.906i	0.691623	+	0.951937i
$856$	192.604	−	592.774i	0.225005	−	0.692494i
$857$		−	912.313i		−	1.06454i	−0.846574	−	0.532271i	$-0.821339\pi$
$857$		−	912.313i		−	1.06454i	0.846574	−	0.532271i	$-0.178661\pi$
$858$	−269.085	+	40.2364i	−0.313619	+	0.0468956i
$859$	1634.47			1.90276			0.951381	−	0.308017i	$-0.0996654\pi$
$859$	1634.47			1.90276			0.951381	+	0.308017i	$0.0996654\pi$
$860$	11.5018	+	3.73715i	0.0133742	+	0.00434553i
$861$	1345.65	−	977.671i	1.56289	−	1.13551i
$862$	−1271.45	−	923.765i	−1.47500	−	1.07165i
$863$	−92.7185	−	285.358i	−0.107437	−	0.330659i	0.882857	−	0.469641i	$-0.155617\pi$
$863$	−92.7185	−	285.358i	−0.107437	−	0.330659i	−0.990295	+	0.138983i	$0.955617\pi$
$864$	−451.755	+	146.784i	−0.522865	+	0.169889i
$865$	124.775	−	171.737i	0.144248	−	0.198540i
$866$	−416.536	−	573.313i	−0.480989	−	0.662024i
$867$	−333.882	+	1027.58i	−0.385100	+	1.18522i
$868$			2605.31i			3.00151i
$869$	524.363	+	87.7064i	0.603410	+	0.100928i
$870$	−533.323			−0.613015
$871$	115.143	+	37.4121i	0.132196	+	0.0429531i
$872$	−1984.22	+	1441.62i	−2.27548	+	1.65324i
$873$	−581.058	−	422.163i	−0.665588	−	0.483578i
$874$	−564.146	−	1736.26i	−0.645476	−	1.98657i
$875$	−74.7307	+	24.2815i	−0.0854065	+	0.0277502i
$876$	−747.594	+	1028.98i	−0.853418	+	1.17463i
$877$	−545.422	−	750.709i	−0.621918	−	0.855997i	0.375573	−	0.926793i	$-0.377446\pi$
$877$	−545.422	−	750.709i	−0.621918	−	0.855997i	−0.997491	+	0.0707963i	$0.977446\pi$
$878$	−320.249	+	985.624i	−0.364748	+	1.12258i
$879$		−	504.980i		−	0.574493i
$880$	369.443	−	363.107i	0.419822	−	0.412622i
$881$	−672.698			−0.763562			−0.381781	−	0.924253i	$-0.624689\pi$
$881$	−672.698			−0.763562			−0.381781	+	0.924253i	$0.624689\pi$
$882$	22.1135	+	7.18513i	0.0250720	+	0.00814640i
$883$	−297.083	+	215.844i	−0.336448	+	0.244443i	−0.743161	−	0.669112i	$-0.766675\pi$
$883$	−297.083	+	215.844i	−0.336448	+	0.244443i	0.406714	+	0.913556i	$0.366675\pi$
$884$	82.0978	+	59.6476i	0.0928708	+	0.0674746i
$885$	169.490	+	521.636i	0.191514	+	0.589419i
$886$	2794.27	−	907.913i	3.15380	−	1.02473i
$887$	−59.0634	+	81.2937i	−0.0665878	+	0.0916502i	−0.841012	−	0.541016i	$-0.818040\pi$
$887$	−59.0634	+	81.2937i	−0.0665878	+	0.0916502i	0.774424	+	0.632667i	$0.218040\pi$
$888$	2030.69	+	2795.01i	2.28681	+	3.14753i
$889$	175.655	−	540.611i	0.197587	−	0.608111i
$890$		−	77.0268i		−	0.0865470i
$891$	476.320	+	247.910i	0.534590	+	0.278237i
$892$	2832.07			3.17497
$893$	−974.890	−	316.761i	−1.09170	−	0.354715i
$894$	−1027.40	+	746.449i	−1.14922	+	0.834954i
$895$	−207.666	−	150.878i	−0.232030	−	0.168579i
$896$	423.902	+	1304.64i	0.473105	+	1.45607i
$897$	−128.856	+	41.8679i	−0.143652	+	0.0466755i
$898$	−829.530	+	1141.75i	−0.923753	+	1.27144i
$899$	345.801	+	475.954i	0.384650	+	0.529426i
$900$	−217.598	+	669.696i	−0.241775	+	0.744107i
$901$			200.353i			0.222368i
$902$	806.459	+	1617.19i	0.894079	+	1.79290i
$903$	−22.9413			−0.0254056
$904$	−2441.30	−	793.226i	−2.70055	−	0.877462i
$905$	−55.0600	+	40.0034i	−0.0608398	+	0.0442027i
$906$	3321.65	+	2413.32i	3.66628	+	2.66371i
$907$	273.782	+	842.615i	0.301855	+	0.929014i	0.980832	+	0.194854i	$0.0624234\pi$
$907$	273.782	+	842.615i	0.301855	+	0.929014i	−0.678977	+	0.734159i	$0.737577\pi$
$908$	−2734.69	+	888.556i	−3.01178	+	0.978586i
$909$	−1254.92	+	1727.25i	−1.38055	+	1.90016i
$910$	45.0246	+	61.9711i	0.0494776	+	0.0681001i
$911$	−140.808	+	433.363i	−0.154564	+	0.475700i	−0.998116	−	0.0613472i	$-0.980460\pi$
$911$	−140.808	+	433.363i	−0.154564	+	0.475700i	0.843552	+	0.537047i	$0.180460\pi$
$912$			2870.55i			3.14753i
$913$	3.57179	−	1.78117i	0.00391214	−	0.00195090i
$914$	−1443.14			−1.57893
$915$	257.018	+	83.5101i	0.280894	+	0.0912679i
$916$	1821.57	−	1323.45i	1.98862	−	1.44481i
$917$	−1238.82	−	900.055i	−1.35095	−	0.981522i
$918$	−373.386	−	1149.16i	−0.406739	−	1.25181i
$919$	432.307	−	140.465i	0.470410	−	0.152845i	−0.0642130	−	0.997936i	$-0.520454\pi$
$919$	432.307	−	140.465i	0.470410	−	0.152845i	0.534623	+	0.845091i	$0.320454\pi$
$920$	393.752	−	541.954i	0.427992	−	0.589080i
$921$	−1375.79	−	1893.62i	−1.49380	−	2.05604i
$922$	−156.932	+	482.987i	−0.170208	+	0.523848i
$923$			110.307i			0.119509i
$924$	−1522.80	+	2925.83i	−1.64806	+	3.16649i
$925$	219.247			0.237024
$926$	2179.45	+	708.147i	2.35362	+	0.764737i
$927$	−756.475	+	549.611i	−0.816046	+	0.592892i
$928$	−130.384	−	94.7294i	−0.140500	−	0.102079i
$929$	−513.395	−	1580.07i	−0.552632	−	1.70083i	−0.702115	−	0.712063i	$-0.747761\pi$
$929$	−513.395	−	1580.07i	−0.552632	−	1.70083i	0.149483	−	0.988764i	$-0.452239\pi$
$930$	1675.98	−	544.558i	1.80213	−	0.585546i
$931$	6.22183	−	8.56362i	0.00668296	−	0.00919830i
$932$	−331.923	−	456.852i	−0.356140	−	0.490185i
$933$	−685.399	+	2109.44i	−0.734618	+	2.26092i
$934$		−	2185.75i		−	2.34021i
$935$	150.385	+	153.009i	0.160839	+	0.163646i
$936$	359.874			0.384481
$937$	−222.178	−	72.1899i	−0.237116	−	0.0770437i	0.188049	−	0.982160i	$-0.439784\pi$
$937$	−222.178	−	72.1899i	−0.237116	−	0.0770437i	−0.425165	+	0.905116i	$0.639784\pi$
$938$	1752.31	−	1273.13i	1.86814	−	1.35728i
$939$	343.722	+	249.728i	0.366051	+	0.265951i
$940$	−221.711	−	682.355i	−0.235862	−	0.725909i
$941$	123.774	−	40.2166i	0.131535	−	0.0427382i	−0.242510	−	0.970149i	$-0.577971\pi$
$941$	123.774	−	40.2166i	0.131535	−	0.0427382i	0.374045	+	0.927411i	$0.377971\pi$
$942$	2044.13	−	2813.50i	2.16999	−	2.98673i
$943$	528.949	+	728.035i	0.560921	+	0.772042i
$944$	−314.579	+	968.176i	−0.333241	+	1.02561i
$945$		−	618.047i		−	0.654018i
$946$	4.11186	−	24.5832i	0.00434658	−	0.0259865i
$947$	−494.426			−0.522097			−0.261049	−	0.965326i	$-0.584068\pi$
$947$	−494.426			−0.522097			−0.261049	+	0.965326i	$0.584068\pi$
$948$	−1961.15	−	637.216i	−2.06872	−	0.672168i
$949$	33.3728	−	24.2468i	0.0351663	−	0.0255498i
$950$	382.727	+	278.067i	0.402870	+	0.292702i
$951$	52.2453	+	160.795i	0.0549372	+	0.169079i
$952$	905.200	−	294.117i	0.950841	−	0.308947i
$953$	118.233	−	162.733i	0.124064	−	0.170759i	−0.742467	−	0.669882i	$-0.766345\pi$
$953$	118.233	−	162.733i	0.124064	−	0.170759i	0.866531	+	0.499123i	$0.166345\pi$
$954$	796.621	+	1096.46i	0.835033	+	1.14932i
$955$	−231.071	+	711.165i	−0.241960	+	0.744675i
$956$			600.678i			0.628324i
$957$	110.148	+	736.629i	0.115098	+	0.769727i
$958$	−651.561			−0.680127
$959$	306.878	+	99.7108i	0.319998	+	0.103974i
$960$	382.759	−	278.090i	0.398707	−	0.289678i
$961$	−795.200	−	577.746i	−0.827471	−	0.601193i
$962$	−66.0474	−	203.273i	−0.0686563	−	0.211302i
$963$	639.494	−	207.784i	0.664064	−	0.215768i
$964$	−1860.27	+	2560.44i	−1.92974	+	2.65606i
$965$	107.042	+	147.331i	0.110924	+	0.152674i
$966$	−749.040	+	2305.31i	−0.775404	+	2.38645i
$967$			1141.38i			1.18034i	0.807281	+	0.590168i	$0.200938\pi$
$967$			1141.38i			1.18034i	−0.807281	+	0.590168i	$0.799062\pi$
$968$	−1500.57	−	1130.40i	−1.55018	−	1.16776i
$969$	−1188.87			−1.22690
$970$	−321.205	−	104.366i	−0.331139	−	0.107594i
$971$	−104.856	+	76.1826i	−0.107988	+	0.0784578i	−0.640469	−	0.767984i	$-0.721260\pi$
$971$	−104.856	+	76.1826i	−0.107988	+	0.0784578i	0.532481	+	0.846442i	$0.321260\pi$
$972$	722.625	+	525.018i	0.743442	+	0.540142i
$973$	410.519	+	1263.45i	0.421911	+	1.29851i
$974$	−1500.17	+	487.434i	−1.54021	+	0.500446i
$975$	20.6367	−	28.4039i	0.0211658	−	0.0291322i
$976$	294.823	+	405.790i	0.302073	+	0.415768i
$977$	−293.806	+	904.243i	−0.300723	+	0.925530i	0.680516	+	0.732734i	$0.261756\pi$
$977$	−293.806	+	904.243i	−0.300723	+	0.925530i	−0.981239	+	0.192797i	$0.938244\pi$
$978$		−	3572.14i		−	3.65250i
$979$	−106.390	+	15.9085i	−0.108672	+	0.0162498i
$980$	7.40891			0.00756011
$981$	−2516.43	−	817.639i	−2.56517	−	0.833475i
$982$	1272.95	−	924.855i	1.29629	−	0.941807i
$983$	578.345	+	420.192i	0.588347	+	0.427459i	0.841724	−	0.539908i	$-0.181541\pi$
$983$	578.345	+	420.192i	0.588347	+	0.427459i	−0.253377	+	0.967368i	$0.581541\pi$
$984$	−1135.51	−	3494.73i	−1.15397	−	3.55156i
$985$	385.522	−	125.264i	0.391393	−	0.127171i
$986$	240.970	−	331.667i	0.244392	−	0.336377i
$987$	799.984	+	1101.08i	0.810521	+	1.11559i
$988$	96.5696	−	297.211i	0.0977425	−	0.300821i
$989$		−	12.4119i		−	0.0125500i
$990$	1431.37	+	239.415i	1.44583	+	0.241833i
$991$	−143.520			−0.144823			−0.0724117	−	0.997375i	$-0.523070\pi$
$991$	−143.520			−0.144823			−0.0724117	+	0.997375i	$0.523070\pi$
$992$	506.458	+	164.558i	0.510543	+	0.165885i
$993$	648.946	−	471.487i	0.653521	−	0.474811i
$994$	1596.55	+	1159.96i	1.60619	+	1.16697i
$995$	224.287	+	690.286i	0.225414	+	0.693754i
$996$	−14.7231	+	4.78381i	−0.0147822	+	0.00480302i
$997$	−748.896	+	1030.77i	−0.751149	+	1.03387i	0.246750	+	0.969079i	$0.420637\pi$
$997$	−748.896	+	1030.77i	−0.751149	+	1.03387i	−0.997899	+	0.0647888i	$0.979363\pi$
$998$	−622.530	−	856.839i	−0.623777	−	0.858556i
$999$	−532.899	+	1640.10i	−0.533433	+	1.64174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.3.i.c.46.1	yes	12
5.2	odd	4		275.3.q.e.24.6		24
5.3	odd	4		275.3.q.e.24.1		24
5.4	even	2		275.3.x.g.101.3		12
11.4	even	5		605.3.c.c.241.1		12
11.6	odd	10	inner	55.3.i.c.6.1	✓	12
11.7	odd	10		605.3.c.c.241.12		12
55.17	even	20		275.3.q.e.149.1		24
55.28	even	20		275.3.q.e.149.6		24
55.39	odd	10		275.3.x.g.226.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.c.6.1	✓	12	11.6	odd	10	inner
55.3.i.c.46.1	yes	12	1.1	even	1	trivial
275.3.q.e.24.1		24	5.3	odd	4
275.3.q.e.24.6		24	5.2	odd	4
275.3.q.e.149.1		24	55.17	even	20
275.3.q.e.149.6		24	55.28	even	20
275.3.x.g.101.3		12	5.4	even	2
275.3.x.g.226.3		12	55.39	odd	10
605.3.c.c.241.1		12	11.4	even	5
605.3.c.c.241.12		12	11.7	odd	10

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	55.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.35007 - 1.08850i) q^{2} +(4.10532 - 2.98269i) q^{3} +(6.80207 + 4.94199i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-16.9998 + 5.52357i) q^{6} +(4.13101 - 5.68585i) q^{7} +(-9.12620 - 12.5611i) q^{8} +(5.17608 - 15.9303i) q^{9} -7.87649i q^{10} +(-10.8790 + 1.62675i) q^{11} +42.6651 q^{12} +(-1.31604 - 0.427606i) q^{13} +(-20.0282 + 14.5514i) q^{14} +(9.17978 + 6.66950i) q^{15} +(6.50794 + 20.0294i) q^{16} +(-8.29537 + 2.69533i) q^{17} +(-34.6804 + 47.7335i) q^{18} +(15.7882 + 21.7306i) q^{19} +(-5.80966 + 17.8803i) q^{20} -35.6638i q^{21} +(38.2163 + 6.39217i) q^{22} +19.2951 q^{23} +(-74.9320 - 24.3469i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(3.94336 + 2.86502i) q^{26} +(-12.1529 - 37.4029i) q^{27} +(56.1988 - 18.2601i) q^{28} +(7.84308 - 10.7951i) q^{29} +(-23.4931 - 32.3355i) q^{30} +(-13.6245 + 41.9320i) q^{31} -12.0781i q^{32} +(-39.8099 + 39.1272i) q^{33} +30.7240 q^{34} +(14.9461 + 4.85629i) q^{35} +(113.936 - 82.7790i) q^{36} +(-35.4749 - 25.7741i) q^{37} +(-29.2377 - 89.9845i) q^{38} +(-6.67817 + 2.16987i) q^{39} +(20.4068 - 28.0876i) q^{40} +(27.4136 + 37.7315i) q^{41} +(-38.8202 + 119.476i) q^{42} -0.643266i q^{43} +(-82.0394 - 42.6989i) q^{44} +37.4544 q^{45} +(-64.6401 - 21.0028i) q^{46} +(-30.8740 + 22.4313i) q^{47} +(86.4587 + 62.8159i) q^{48} +(-0.121778 - 0.374794i) q^{49} +(16.7504 - 5.44252i) q^{50} +(-26.0158 + 35.8077i) q^{51} +(-6.83854 - 9.41244i) q^{52} +(7.09822 - 21.8461i) q^{53} +138.531i q^{54} +(-10.9767 - 22.0116i) q^{55} -109.121 q^{56} +(129.631 + 42.1197i) q^{57} +(-38.0254 + 27.6270i) q^{58} +(39.1061 + 28.4122i) q^{59} +(29.4809 + 90.7328i) q^{60} +(22.6511 - 7.35977i) q^{61} +(91.2863 - 125.645i) q^{62} +(-69.1949 - 95.2387i) q^{63} +(12.8847 - 39.6551i) q^{64} -3.09418i q^{65} +(175.956 - 87.7456i) q^{66} -87.4921 q^{67} +(-69.7460 - 22.6618i) q^{68} +(79.2128 - 57.5515i) q^{69} +(-44.7845 - 32.5379i) q^{70} +(-24.6333 - 75.8135i) q^{71} +(-247.341 + 80.3659i) q^{72} +(-17.5224 + 24.1175i) q^{73} +(90.7884 + 124.960i) q^{74} +(-7.84047 + 24.1305i) q^{75} +225.838i q^{76} +(-35.6920 + 68.5767i) q^{77} +24.7342 q^{78} +(-45.9661 - 14.9353i) q^{79} +(-38.0981 + 27.6799i) q^{80} +(-39.4928 - 28.6932i) q^{81} +(-50.7665 - 156.243i) q^{82} +(-0.345084 + 0.112125i) q^{83} +(176.250 - 242.587i) q^{84} +(-11.4639 - 15.7787i) q^{85} +(-0.700197 + 2.15499i) q^{86} -67.7108i q^{87} +(119.718 + 121.807i) q^{88} +9.77933 q^{89} +(-125.475 - 40.7693i) q^{90} +(-7.86786 + 5.71633i) q^{91} +(131.247 + 95.3564i) q^{92} +(69.1371 + 212.782i) q^{93} +(127.847 - 41.5399i) q^{94} +(-35.3035 + 48.5910i) q^{95} +(-36.0252 - 49.5844i) q^{96} +(13.2503 - 40.7803i) q^{97} +1.38814i q^{98} +(-30.3962 + 181.727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 5 q^{2} + 7 q^{3} + 13 q^{4} + 15 q^{5} - 15 q^{6} - 40 q^{7} - 15 q^{8} - 16 q^{9} - 8 q^{11} + 68 q^{12} - 15 q^{13} - 5 q^{14} + 35 q^{15} + 77 q^{16} - 5 q^{17} - 115 q^{18} + 15 q^{19} - 20 q^{20}+ \cdots + 509 q^{99}+O(q^{100}) \) 12 * q - 5 * q^2 + 7 * q^3 + 13 * q^4 + 15 * q^5 - 15 * q^6 - 40 * q^7 - 15 * q^8 - 16 * q^9 - 8 * q^11 + 68 * q^12 - 15 * q^13 - 5 * q^14 + 35 * q^15 + 77 * q^16 - 5 * q^17 - 115 * q^18 + 15 * q^19 - 20 * q^20 - 90 * q^22 + 112 * q^23 - 235 * q^24 - 15 * q^25 + 80 * q^26 + 106 * q^27 + 110 * q^28 + 45 * q^29 - 10 * q^30 - 146 * q^31 - 133 * q^33 + 60 * q^34 - 70 * q^35 + 216 * q^36 + 8 * q^37 + 45 * q^38 + 195 * q^39 + 65 * q^40 - 145 * q^41 + 105 * q^42 - 167 * q^44 - 20 * q^45 - 475 * q^46 + 158 * q^47 + 227 * q^48 + 153 * q^49 + 25 * q^50 - 55 * q^51 + 60 * q^52 + 107 * q^53 - 60 * q^55 - 140 * q^56 + 125 * q^57 + 40 * q^58 - 59 * q^59 + 40 * q^60 + 210 * q^61 + 110 * q^62 - 640 * q^63 + 173 * q^64 + 195 * q^66 - 62 * q^67 - 225 * q^68 + 7 * q^69 - 15 * q^70 + 114 * q^71 - 795 * q^72 - 165 * q^73 - 30 * q^74 + 35 * q^75 - 430 * q^77 + 360 * q^78 - 355 * q^79 + 100 * q^80 + 145 * q^81 - 210 * q^82 + 105 * q^83 + 460 * q^84 + 70 * q^85 + 75 * q^86 + 270 * q^88 - 274 * q^89 - 265 * q^90 + 285 * q^91 + 428 * q^92 + 109 * q^93 + 410 * q^94 + 55 * q^95 - 75 * q^96 + 198 * q^97 + 509 * q^99

Introduction

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