LMFDB - Embedded newform 210.3.v.b.67.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(37,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("210.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.v (of order $12$, 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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.8
Character	$\chi$	$=$	210.67
Dual form			210.3.v.b.163.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 1.36603i) q^{2} +(0.448288 + 1.67303i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.92336 - 4.61527i) q^{5} -2.44949 q^{6} +(-6.34406 + 2.95853i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(-0.366025 + 1.36603i) q^{2} +(0.448288 + 1.67303i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.92336 - 4.61527i) q^{5} -2.44949 q^{6} +(-6.34406 + 2.95853i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(5.60058 + 4.31666i) q^{10} +(-9.98405 + 17.2929i) q^{11} +(0.896575 - 3.34607i) q^{12} +(-13.3742 + 13.3742i) q^{13} +(-1.71935 - 9.74904i) q^{14} +(8.58371 + 1.14887i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-21.8551 + 5.85604i) q^{17} +(-1.09808 - 4.09808i) q^{18} +(14.8761 - 8.58869i) q^{19} +(-7.94662 + 6.07052i) q^{20} +(-7.79369 - 9.28754i) q^{21} +(-19.9681 - 19.9681i) q^{22} +(20.2664 + 5.43036i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-17.6014 - 17.7536i) q^{25} +(-13.3742 - 23.1648i) q^{26} +(-3.67423 - 3.67423i) q^{27} +(13.9468 + 1.21973i) q^{28} +23.1996i q^{29} +(-4.71124 + 11.3051i) q^{30} +(27.7400 - 48.0470i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(-33.4073 - 8.95145i) q^{33} -31.9980i q^{34} +(1.45255 + 34.9698i) q^{35} +6.00000 q^{36} +(-5.97166 + 22.2866i) q^{37} +(6.28736 + 23.4647i) q^{38} +(-28.3710 - 16.3800i) q^{39} +(-5.38383 - 13.0772i) q^{40} -21.6302 q^{41} +(15.5397 - 7.24690i) q^{42} +(14.6809 - 14.6809i) q^{43} +(34.5858 - 19.9681i) q^{44} +(1.92588 + 14.8759i) q^{45} +(-14.8360 + 25.6967i) q^{46} +(-19.6034 + 73.1609i) q^{47} +(-4.89898 + 4.89898i) q^{48} +(31.4942 - 37.5382i) q^{49} +(30.6944 - 17.5457i) q^{50} +(-19.5947 - 33.9390i) q^{51} +(36.5391 - 9.79062i) q^{52} +(-1.07647 - 4.01743i) q^{53} +(6.36396 - 3.67423i) q^{54} +(60.6084 + 79.3394i) q^{55} +(-6.77105 + 18.6052i) q^{56} +(21.0379 + 21.0379i) q^{57} +(-31.6913 - 8.49165i) q^{58} +(26.7900 + 15.4672i) q^{59} +(-13.7186 - 10.5736i) q^{60} +(-1.75837 - 3.04558i) q^{61} +(55.4799 + 55.4799i) q^{62} +(12.0445 - 17.2026i) q^{63} -8.00000i q^{64} +(36.0023 + 87.4491i) q^{65} +(24.4558 - 42.3587i) q^{66} +(-2.85244 + 0.764309i) q^{67} +(43.7101 + 11.7121i) q^{68} +36.3407i q^{69} +(-48.3014 - 10.8156i) q^{70} -11.8938 q^{71} +(-2.19615 + 8.19615i) q^{72} +(-5.65075 - 21.0889i) q^{73} +(-28.2582 - 16.3149i) q^{74} +(21.8119 - 37.4065i) q^{75} -34.3548 q^{76} +(12.1778 - 139.245i) q^{77} +(32.7600 - 32.7600i) q^{78} +(-65.5559 + 37.8487i) q^{79} +(19.8345 - 2.56784i) q^{80} +(4.50000 - 7.79423i) q^{81} +(7.91720 - 29.5474i) q^{82} +(28.2864 - 28.2864i) q^{83} +(4.21152 + 23.8802i) q^{84} +(-15.0078 + 112.130i) q^{85} +(14.6809 + 25.4281i) q^{86} +(-38.8137 + 10.4001i) q^{87} +(14.6177 + 54.5539i) q^{88} +(124.644 - 71.9632i) q^{89} +(-21.0257 - 2.81414i) q^{90} +(45.2788 - 124.415i) q^{91} +(-29.6720 - 29.6720i) q^{92} +(92.8197 + 24.8710i) q^{93} +(-92.7643 - 53.5575i) q^{94} +(-11.0272 - 85.1761i) q^{95} +(-4.89898 - 8.48528i) q^{96} +(56.0616 + 56.0616i) q^{97} +(39.7505 + 56.7618i) q^{98} -59.9043i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8}+O(q^{10}) $ 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8	$ 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8} + 12 q^{10} + 16 q^{11} + 32 q^{13} + 48 q^{15} + 64 q^{16} - 56 q^{17} + 48 q^{18} + 16 q^{20} + 32 q^{22} - 28 q^{25} + 32 q^{26} + 72 q^{28} + 36 q^{30} + 112 q^{31} - 64 q^{32} + 12 q^{33} - 112 q^{35} + 192 q^{36} - 52 q^{37} - 8 q^{40} - 336 q^{41} - 312 q^{43} + 12 q^{45} - 212 q^{47} + 96 q^{50} - 144 q^{51} - 32 q^{52} - 96 q^{53} - 312 q^{55} + 96 q^{56} + 48 q^{57} - 96 q^{58} - 24 q^{60} + 216 q^{61} + 224 q^{62} + 36 q^{63} + 248 q^{65} - 24 q^{66} + 128 q^{67} + 112 q^{68} - 264 q^{70} - 848 q^{71} + 96 q^{72} + 84 q^{73} - 144 q^{75} - 324 q^{77} + 48 q^{78} + 32 q^{80} + 144 q^{81} - 168 q^{82} - 416 q^{83} + 536 q^{85} - 312 q^{86} - 72 q^{87} + 32 q^{88} - 24 q^{90} + 504 q^{91} + 168 q^{93} + 168 q^{95} + 488 q^{97} - 328 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8 + 12 * q^10 + 16 * q^11 + 32 * q^13 + 48 * q^15 + 64 * q^16 - 56 * q^17 + 48 * q^18 + 16 * q^20 + 32 * q^22 - 28 * q^25 + 32 * q^26 + 72 * q^28 + 36 * q^30 + 112 * q^31 - 64 * q^32 + 12 * q^33 - 112 * q^35 + 192 * q^36 - 52 * q^37 - 8 * q^40 - 336 * q^41 - 312 * q^43 + 12 * q^45 - 212 * q^47 + 96 * q^50 - 144 * q^51 - 32 * q^52 - 96 * q^53 - 312 * q^55 + 96 * q^56 + 48 * q^57 - 96 * q^58 - 24 * q^60 + 216 * q^61 + 224 * q^62 + 36 * q^63 + 248 * q^65 - 24 * q^66 + 128 * q^67 + 112 * q^68 - 264 * q^70 - 848 * q^71 + 96 * q^72 + 84 * q^73 - 144 * q^75 - 324 * q^77 + 48 * q^78 + 32 * q^80 + 144 * q^81 - 168 * q^82 - 416 * q^83 + 536 * q^85 - 312 * q^86 - 72 * q^87 + 32 * q^88 - 24 * q^90 + 504 * q^91 + 168 * q^93 + 168 * q^95 + 488 * q^97 - 328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.366025	+	1.36603i	−0.183013	+	0.683013i
$2$	−0.366025	+	1.36603i	−0.183013	+	0.683013i
$3$	0.448288	+	1.67303i	0.149429	+	0.557678i
$3$	0.448288	+	1.67303i	0.149429	+	0.557678i
$4$	−1.73205	−	1.00000i	−0.433013	−	0.250000i
$5$	1.92336	−	4.61527i	0.384671	−	0.923054i
$5$	1.92336	−	4.61527i	0.384671	−	0.923054i
$6$	−2.44949			−0.408248
$7$	−6.34406	+	2.95853i	−0.906294	+	0.422648i
$7$	−6.34406	+	2.95853i	−0.906294	+	0.422648i
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	−2.59808	+	1.50000i	−0.288675	+	0.166667i
$10$	5.60058	+	4.31666i	0.560058	+	0.431666i
$11$	−9.98405	+	17.2929i	−0.907641	+	1.57208i	−0.0903080	+	0.995914i	$0.528785\pi$
$11$	−9.98405	+	17.2929i	−0.907641	+	1.57208i	−0.817333	+	0.576166i	$0.804548\pi$
$12$	0.896575	−	3.34607i	0.0747146	−	0.278839i
$13$	−13.3742	+	13.3742i	−1.02879	+	1.02879i	−0.0292138	+	0.999573i	$0.509300\pi$
$13$	−13.3742	+	13.3742i	−1.02879	+	1.02879i	−0.999573	+	0.0292138i	$0.990700\pi$
$14$	−1.71935	−	9.74904i	−0.122810	−	0.696360i
$15$	8.58371	+	1.14887i	0.572247	+	0.0765912i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	−21.8551	+	5.85604i	−1.28559	+	0.344473i	−0.835984	−	0.548753i	$-0.815103\pi$
$17$	−21.8551	+	5.85604i	−1.28559	+	0.344473i	−0.449607	+	0.893227i	$0.648436\pi$
$18$	−1.09808	−	4.09808i	−0.0610042	−	0.227671i
$19$	14.8761	−	8.58869i	0.782950	−	0.452037i	−0.0545246	−	0.998512i	$-0.517364\pi$
$19$	14.8761	−	8.58869i	0.782950	−	0.452037i	0.837475	+	0.546476i	$0.184031\pi$
$20$	−7.94662	+	6.07052i	−0.397331	+	0.303526i
$21$	−7.79369	−	9.28754i	−0.371128	−	0.442264i
$22$	−19.9681	−	19.9681i	−0.907641	−	0.907641i
$23$	20.2664	+	5.43036i	0.881147	+	0.236103i	0.670902	−	0.741546i	$-0.265907\pi$
$23$	20.2664	+	5.43036i	0.881147	+	0.236103i	0.210245	+	0.977649i	$0.432574\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$	−17.6014	−	17.7536i	−0.704056	−	0.710144i
$26$	−13.3742	−	23.1648i	−0.514394	−	0.890956i
$27$	−3.67423	−	3.67423i	−0.136083	−	0.136083i
$28$	13.9468	+	1.21973i	0.498099	+	0.0435617i
$29$			23.1996i			0.799987i	0.916518	+	0.399994i	$0.130988\pi$
$29$			23.1996i			0.799987i	−0.916518	+	0.399994i	$0.869012\pi$
$30$	−4.71124	+	11.3051i	−0.157041	+	0.376835i
$31$	27.7400	−	48.0470i	0.894837	−	1.54990i	0.0608318	−	0.998148i	$-0.480625\pi$
$31$	27.7400	−	48.0470i	0.894837	−	1.54990i	0.834006	−	0.551756i	$-0.186042\pi$
$32$	−5.46410	+	1.46410i	−0.170753	+	0.0457532i
$33$	−33.4073	−	8.95145i	−1.01234	−	0.271256i
$34$		−	31.9980i		−	0.941118i
$35$	1.45255	+	34.9698i	0.0415014	+	0.999138i
$36$	6.00000			0.166667
$37$	−5.97166	+	22.2866i	−0.161396	+	0.602339i	0.837076	+	0.547087i	$0.184263\pi$
$37$	−5.97166	+	22.2866i	−0.161396	+	0.602339i	−0.998472	+	0.0552528i	$0.982404\pi$
$38$	6.28736	+	23.4647i	0.165457	+	0.617493i
$39$	−28.3710	−	16.3800i	−0.727462	−	0.420001i
$40$	−5.38383	−	13.0772i	−0.134596	−	0.326931i
$41$	−21.6302			−0.527565			−0.263783	−	0.964582i	$-0.584970\pi$
$41$	−21.6302			−0.527565			−0.263783	+	0.964582i	$0.584970\pi$
$42$	15.5397	−	7.24690i	0.369993	−	0.172545i
$43$	14.6809	−	14.6809i	0.341417	−	0.341417i	−0.515483	−	0.856900i	$-0.672387\pi$
$43$	14.6809	−	14.6809i	0.341417	−	0.341417i	0.856900	+	0.515483i	$0.172387\pi$
$44$	34.5858	−	19.9681i	0.786040	−	0.453820i
$45$	1.92588	+	14.8759i	0.0427973	+	0.330575i
$46$	−14.8360	+	25.6967i	−0.322522	+	0.558625i
$47$	−19.6034	+	73.1609i	−0.417094	+	1.55662i	0.363511	+	0.931590i	$0.381578\pi$
$47$	−19.6034	+	73.1609i	−0.417094	+	1.55662i	−0.780604	+	0.625025i	$0.785089\pi$
$48$	−4.89898	+	4.89898i	−0.102062	+	0.102062i
$49$	31.4942	−	37.5382i	0.642738	−	0.766086i
$50$	30.6944	−	17.5457i	0.613889	−	0.350914i
$51$	−19.5947	−	33.9390i	−0.384210	−	0.665471i
$52$	36.5391	−	9.79062i	0.702675	−	0.188281i
$53$	−1.07647	−	4.01743i	−0.0203107	−	0.0758005i	0.955027	−	0.296520i	$-0.0958261\pi$
$53$	−1.07647	−	4.01743i	−0.0203107	−	0.0758005i	−0.975337	+	0.220719i	$0.929159\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$	60.6084	+	79.3394i	1.10197	+	1.44253i
$56$	−6.77105	+	18.6052i	−0.120912	+	0.332235i
$57$	21.0379	+	21.0379i	0.369086	+	0.369086i
$58$	−31.6913	−	8.49165i	−0.546401	−	0.146408i
$59$	26.7900	+	15.4672i	0.454069	+	0.262157i	0.709547	−	0.704658i	$-0.248900\pi$
$59$	26.7900	+	15.4672i	0.454069	+	0.262157i	−0.255478	+	0.966815i	$0.582233\pi$
$60$	−13.7186	−	10.5736i	−0.228643	−	0.176227i
$61$	−1.75837	−	3.04558i	−0.0288257	−	0.0499275i	0.851253	−	0.524756i	$-0.175843\pi$
$61$	−1.75837	−	3.04558i	−0.0288257	−	0.0499275i	−0.880078	+	0.474828i	$0.842510\pi$
$62$	55.4799	+	55.4799i	0.894837	+	0.894837i
$63$	12.0445	−	17.2026i	0.191183	−	0.273057i
$64$		−	8.00000i		−	0.125000i
$65$	36.0023	+	87.4491i	0.553881	+	1.34537i
$66$	24.4558	−	42.3587i	0.370543	−	0.641799i
$67$	−2.85244	+	0.764309i	−0.0425737	+	0.0114076i	−0.280043	−	0.959987i	$-0.590349\pi$
$67$	−2.85244	+	0.764309i	−0.0425737	+	0.0114076i	0.237469	+	0.971395i	$0.423682\pi$
$68$	43.7101	+	11.7121i	0.642796	+	0.172237i
$69$			36.3407i			0.526676i
$70$	−48.3014	−	10.8156i	−0.690020	−	0.154509i
$71$	−11.8938			−0.167518			−0.0837592	−	0.996486i	$-0.526693\pi$
$71$	−11.8938			−0.167518			−0.0837592	+	0.996486i	$0.526693\pi$
$72$	−2.19615	+	8.19615i	−0.0305021	+	0.113835i
$73$	−5.65075	−	21.0889i	−0.0774075	−	0.288889i	0.916361	−	0.400353i	$-0.131113\pi$
$73$	−5.65075	−	21.0889i	−0.0774075	−	0.288889i	−0.993768	+	0.111464i	$0.964446\pi$
$74$	−28.2582	−	16.3149i	−0.381868	−	0.220472i
$75$	21.8119	−	37.4065i	0.290825	−	0.498753i
$76$	−34.3548			−0.452037
$77$	12.1778	−	139.245i	0.158153	−	1.80838i
$78$	32.7600	−	32.7600i	0.420001	−	0.420001i
$79$	−65.5559	+	37.8487i	−0.829821	+	0.479097i	−0.853791	−	0.520615i	$-0.825703\pi$
$79$	−65.5559	+	37.8487i	−0.829821	+	0.479097i	0.0239704	+	0.999713i	$0.492369\pi$
$80$	19.8345	−	2.56784i	0.247931	−	0.0320980i
$81$	4.50000	−	7.79423i	0.0555556	−	0.0962250i
$82$	7.91720	−	29.5474i	0.0965512	−	0.360334i
$83$	28.2864	−	28.2864i	0.340800	−	0.340800i	−0.515868	−	0.856668i	$-0.672531\pi$
$83$	28.2864	−	28.2864i	0.340800	−	0.340800i	0.856668	+	0.515868i	$0.172531\pi$
$84$	4.21152	+	23.8802i	0.0501372	+	0.284288i
$85$	−15.0078	+	112.130i	−0.176563	+	1.31918i
$86$	14.6809	+	25.4281i	0.170709	+	0.295676i
$87$	−38.8137	+	10.4001i	−0.446135	+	0.119541i
$88$	14.6177	+	54.5539i	0.166110	+	0.619930i
$89$	124.644	−	71.9632i	1.40049	−	0.808575i	0.406050	−	0.913851i	$-0.366906\pi$
$89$	124.644	−	71.9632i	1.40049	−	0.808575i	0.994443	+	0.105276i	$0.0335727\pi$
$90$	−21.0257	−	2.81414i	−0.233619	−	0.0312682i
$91$	45.2788	−	124.415i	0.497569	−	1.36720i
$92$	−29.6720	−	29.6720i	−0.322522	−	0.322522i
$93$	92.8197	+	24.8710i	0.998061	+	0.267430i
$94$	−92.7643	−	53.5575i	−0.986855	−	0.569761i
$95$	−11.0272	−	85.1761i	−0.116076	−	0.896590i
$96$	−4.89898	−	8.48528i	−0.0510310	−	0.0883883i
$97$	56.0616	+	56.0616i	0.577954	+	0.577954i	0.934339	−	0.356385i	$-0.115991\pi$
$97$	56.0616	+	56.0616i	0.577954	+	0.577954i	−0.356385	+	0.934339i	$0.615991\pi$
$98$	39.7505	+	56.7618i	0.405617	+	0.579202i
$99$		−	59.9043i		−	0.605094i
$100$	12.7329	+	48.3516i	0.127329	+	0.483516i
$101$	−56.4634	+	97.7974i	−0.559043	+	0.968291i	0.438533	+	0.898715i	$0.355498\pi$
$101$	−56.4634	+	97.7974i	−0.559043	+	0.968291i	−0.997577	+	0.0695765i	$0.977835\pi$
$102$	53.5337	−	14.3443i	0.524840	−	0.140631i
$103$	190.082	+	50.9322i	1.84545	+	0.494488i	0.999263	−	0.0383934i	$-0.0122240\pi$
$103$	190.082	+	50.9322i	1.84545	+	0.494488i	0.846190	+	0.532881i	$0.178891\pi$
$104$			53.4969i			0.514394i
$105$	−57.8545	+	18.1067i	−0.550996	+	0.172445i
$106$	5.88192			0.0554898
$107$	−42.1506	+	157.308i	−0.393931	+	1.47017i	0.429662	+	0.902990i	$0.358633\pi$
$107$	−42.1506	+	157.308i	−0.393931	+	1.47017i	−0.823593	+	0.567181i	$0.808034\pi$
$108$	2.68973	+	10.0382i	0.0249049	+	0.0929463i
$109$	−50.7768	−	29.3160i	−0.465843	−	0.268954i	0.248655	−	0.968592i	$-0.420011\pi$
$109$	−50.7768	−	29.3160i	−0.465843	−	0.268954i	−0.714498	+	0.699638i	$0.753345\pi$
$110$	−130.564	+	53.7524i	−1.18694	+	0.488658i
$111$	−39.9632			−0.360028
$112$	−22.9368	−	16.0594i	−0.204793	−	0.143387i
$113$	−69.9728	+	69.9728i	−0.619229	+	0.619229i	−0.945334	−	0.326105i	$-0.894264\pi$
$113$	−69.9728	+	69.9728i	−0.619229	+	0.619229i	0.326105	+	0.945334i	$0.394264\pi$
$114$	−36.4387	+	21.0379i	−0.319638	+	0.184543i
$115$	64.0420	−	83.0903i	0.556887	−	0.722524i
$116$	23.1996	−	40.1829i	0.199997	−	0.346405i
$117$	14.6859	−	54.8086i	0.125521	−	0.468450i
$118$	−30.9345	+	30.9345i	−0.262157	+	0.262157i
$119$	121.324	−	101.810i	1.01953	−	0.855546i
$120$	19.4652	−	14.8697i	0.162210	−	0.123914i
$121$	−138.862	−	240.517i	−1.14762	−	1.98774i
$122$	4.80395	−	1.28721i	0.0393766	−	0.0105509i
$123$	−9.69654	−	36.1880i	−0.0788337	−	0.294211i
$124$	−96.0940	+	55.4799i	−0.774952	+	0.447419i
$125$	−115.791	+	47.0887i	−0.926331	+	0.376710i
$126$	19.0906	+	22.7497i	0.151512	+	0.180553i
$127$	−43.1314	−	43.1314i	−0.339617	−	0.339617i	0.516606	−	0.856223i	$-0.327195\pi$
$127$	−43.1314	−	43.1314i	−0.339617	−	0.339617i	−0.856223	+	0.516606i	$0.827195\pi$
$128$	10.9282	+	2.92820i	0.0853766	+	0.0228766i
$129$	31.1430	+	17.9804i	0.241418	+	0.139383i
$130$	−132.635	+	17.1714i	−1.02027	+	0.132088i
$131$	−29.3082	−	50.7632i	−0.223727	−	0.387506i	0.732210	−	0.681079i	$-0.238489\pi$
$131$	−29.3082	−	50.7632i	−0.223727	−	0.387506i	−0.955937	+	0.293573i	$0.905156\pi$
$132$	48.9116	+	48.9116i	0.370543	+	0.370543i
$133$	−68.9646	+	98.4985i	−0.518531	+	0.740590i
$134$		−	4.17626i		−	0.0311661i
$135$	−24.0244	+	9.89072i	−0.177959	+	0.0732646i
$136$	−31.9980	+	55.4222i	−0.235280	+	0.407516i
$137$	−77.6400	+	20.8036i	−0.566716	+	0.151851i	−0.530790	−	0.847503i	$-0.678105\pi$
$137$	−77.6400	+	20.8036i	−0.566716	+	0.151851i	−0.0359258	+	0.999354i	$0.511438\pi$
$138$	−49.6423	−	13.3016i	−0.359727	−	0.0963885i
$139$		−	15.1273i		−	0.108830i	−0.998518	−	0.0544149i	$-0.982671\pi$
$139$		−	15.1273i		−	0.108830i	0.998518	−	0.0544149i	$-0.0173294\pi$
$140$	32.4540	−	62.0221i	0.231814	−	0.443015i
$141$	−131.189			−0.930416
$142$	4.35343	−	16.2472i	0.0306580	−	0.114417i
$143$	−97.7500	−	364.808i	−0.683566	−	2.55110i
$144$	−10.3923	−	6.00000i	−0.0721688	−	0.0416667i
$145$	107.073	+	44.6211i	0.738431	+	0.307732i
$146$	30.8763			0.211481
$147$	76.9211	+	35.8628i	0.523273	+	0.243965i
$148$	32.6298	−	32.6298i	0.220472	−	0.220472i
$149$	−28.5019	+	16.4556i	−0.191288	+	0.110440i	−0.592585	−	0.805508i	$-0.701893\pi$
$149$	−28.5019	+	16.4556i	−0.191288	+	0.110440i	0.401297	+	0.915948i	$0.368559\pi$
$150$	43.1145	+	43.4873i	0.287430	+	0.289915i
$151$	−142.183	+	246.269i	−0.941611	+	1.63092i	−0.179211	+	0.983811i	$0.557355\pi$
$151$	−142.183	+	246.269i	−0.941611	+	1.63092i	−0.762399	+	0.647107i	$0.775979\pi$
$152$	12.5747	−	46.9295i	0.0827284	−	0.308747i
$153$	47.9970	−	47.9970i	0.313706	−	0.313706i
$154$	185.755	+	67.6025i	1.20620	+	0.438977i
$155$	−168.396	−	220.439i	−1.08643	−	1.42219i
$156$	32.7600	+	56.7421i	0.210000	+	0.363731i
$157$	−170.733	+	45.7477i	−1.08747	+	0.291387i	−0.757652	−	0.652658i	$-0.773654\pi$
$157$	−170.733	+	45.7477i	−1.08747	+	0.291387i	−0.329817	+	0.944045i	$0.606987\pi$
$158$	−27.7072	−	103.405i	−0.175362	−	0.654459i
$159$	6.23872	−	3.60193i	0.0392372	−	0.0226536i
$160$	−3.75219	+	28.0343i	−0.0234512	+	0.175214i
$161$	−144.637	+	25.5083i	−0.898366	+	0.158436i
$162$	9.00000	+	9.00000i	0.0555556	+	0.0555556i
$163$	−72.5798	−	19.4477i	−0.445275	−	0.119311i	0.0292129	−	0.999573i	$-0.490700\pi$
$163$	−72.5798	−	19.4477i	−0.445275	−	0.119311i	−0.474487	+	0.880262i	$0.657367\pi$
$164$	37.4646	+	21.6302i	0.228443	+	0.131891i
$165$	−105.567	+	136.967i	−0.639803	+	0.830101i
$166$	28.2864	+	48.9935i	0.170400	+	0.295141i
$167$	115.501	+	115.501i	0.691625	+	0.691625i	0.962589	−	0.270964i	$-0.0873426\pi$
$167$	115.501	+	115.501i	0.691625	+	0.691625i	−0.270964	+	0.962589i	$0.587343\pi$
$168$	−34.1625	−	2.98771i	−0.203348	−	0.0177840i
$169$		−	188.740i		−	1.11681i
$170$	−147.679	−	61.5436i	−0.868703	−	0.362021i
$171$	−25.7661	+	44.6282i	−0.150679	+	0.260983i
$172$	−40.1091	+	10.7472i	−0.233192	+	0.0624837i
$173$	193.397	+	51.8207i	1.11790	+	0.299541i	0.770035	−	0.638002i	$-0.220239\pi$
$173$	193.397	+	51.8207i	1.11790	+	0.299541i	0.347869	+	0.937543i	$0.386905\pi$
$174$		−	56.8272i		−	0.326593i
$175$	164.189	+	60.5555i	0.938223	+	0.346032i
$176$	−79.8724			−0.453820
$177$	−13.8675	+	51.7544i	−0.0783477	+	0.292398i
$178$	52.6807	+	196.607i	0.295959	+	1.10453i
$179$	103.999	+	60.0438i	0.580999	+	0.335440i	0.761530	−	0.648129i	$-0.224448\pi$
$179$	103.999	+	60.0438i	0.580999	+	0.335440i	−0.180531	+	0.983569i	$0.557782\pi$
$180$	11.5401	−	27.6916i	0.0641118	−	0.153842i
$181$	217.830			1.20348			0.601741	−	0.798691i	$-0.294474\pi$
$181$	217.830			1.20348			0.601741	+	0.798691i	$0.294474\pi$
$182$	153.381	+	107.391i	0.842752	+	0.590061i
$183$	4.30710	−	4.30710i	0.0235361	−	0.0235361i
$184$	51.3935	−	29.6720i	0.279312	−	0.161261i
$185$	91.3728	+	70.4258i	0.493907	+	0.380680i
$186$	−67.9487	+	117.691i	−0.365316	+	0.632746i
$187$	116.934	−	436.404i	0.625316	−	2.33371i
$188$	107.115	−	107.115i	0.569761	−	0.569761i
$189$	34.1799	+	12.4392i	0.180846	+	0.0658159i
$190$	120.389	+	16.1132i	0.633626	+	0.0848063i
$191$	−56.1666	−	97.2834i	−0.294066	−	0.509337i	0.680701	−	0.732561i	$-0.261675\pi$
$191$	−56.1666	−	97.2834i	−0.294066	−	0.509337i	−0.974767	+	0.223224i	$0.928342\pi$
$192$	13.3843	−	3.58630i	0.0697097	−	0.0186787i
$193$	1.49926	+	5.59533i	0.00776820	+	0.0289913i	0.969701	−	0.244294i	$-0.0785563\pi$
$193$	1.49926	+	5.59533i	0.00776820	+	0.0289913i	−0.961933	+	0.273286i	$0.911890\pi$
$194$	−97.1015	+	56.0616i	−0.500523	+	0.288977i
$195$	−130.166	+	99.4353i	−0.667517	+	0.509925i
$196$	−92.0877	+	33.5240i	−0.469835	+	0.171041i
$197$	−40.3068	−	40.3068i	−0.204603	−	0.204603i	0.597366	−	0.801969i	$-0.296214\pi$
$197$	−40.3068	−	40.3068i	−0.204603	−	0.204603i	−0.801969	+	0.597366i	$0.796214\pi$
$198$	81.8308	+	21.9265i	0.413287	+	0.110740i
$199$	85.5804	+	49.4099i	0.430052	+	0.248291i	0.699369	−	0.714761i	$-0.253464\pi$
$199$	85.5804	+	49.4099i	0.430052	+	0.248291i	−0.269317	+	0.963052i	$0.586798\pi$
$200$	−70.7100	−	0.304394i	−0.353550	−	0.00152197i
$201$	−2.55743	−	4.42960i	−0.0127235	−	0.0220378i
$202$	−112.927	−	112.927i	−0.559043	−	0.559043i
$203$	−68.6369	−	147.180i	−0.338113	−	0.725024i
$204$			78.3788i			0.384210i
$205$	−41.6025	+	99.8291i	−0.202939	+	0.486971i
$206$	−139.149	+	241.014i	−0.675483	+	1.16997i
$207$	−60.7991	+	16.2911i	−0.293716	+	0.0787009i
$208$	−73.0782	−	19.5812i	−0.351337	−	0.0941405i
$209$			343.000i			1.64115i
$210$	−3.55801	−	85.6583i	−0.0169429	−	0.407897i
$211$	344.348			1.63198			0.815991	−	0.578064i	$-0.196192\pi$
$211$	344.348			1.63198			0.815991	+	0.578064i	$0.196192\pi$
$212$	−2.15293	+	8.03485i	−0.0101553	+	0.0379003i
$213$	−5.33185	−	19.8987i	−0.0250321	−	0.0934212i
$214$	−199.459	−	115.158i	−0.932051	−	0.538120i
$215$	−39.5198	−	95.9932i	−0.183813	−	0.446480i
$216$	−14.6969			−0.0680414
$217$	−33.8352	+	386.883i	−0.155922	+	1.78287i
$218$	58.6321	−	58.6321i	0.268954	−	0.268954i
$219$	32.7492	−	18.9078i	0.149540	−	0.0863369i
$220$	−25.6374	−	198.028i	−0.116534	−	0.900129i
$221$	213.974	−	370.615i	0.968210	−	1.67699i
$222$	14.6275	−	54.5907i	0.0658898	−	0.245904i
$223$	34.8821	−	34.8821i	0.156422	−	0.156422i	−0.624557	−	0.780979i	$-0.714721\pi$
$223$	34.8821	−	34.8821i	0.156422	−	0.156422i	0.780979	+	0.624557i	$0.214721\pi$
$224$	30.3330	−	25.4541i	0.135415	−	0.113634i
$225$	72.3602	+	19.7231i	0.321601	+	0.0876582i
$226$	−69.9728	−	121.197i	−0.309614	−	0.536268i
$227$	−166.766	+	44.6847i	−0.734651	+	0.196849i	−0.606699	−	0.794931i	$-0.707507\pi$
$227$	−166.766	+	44.6847i	−0.734651	+	0.196849i	−0.127951	+	0.991780i	$0.540840\pi$
$228$	−15.4008	−	57.4767i	−0.0675475	−	0.252091i
$229$	18.1914	−	10.5028i	0.0794382	−	0.0458637i	−0.459755	−	0.888046i	$-0.652063\pi$
$229$	18.1914	−	10.5028i	0.0794382	−	0.0458637i	0.539193	+	0.842182i	$0.318729\pi$
$230$	90.0624	+	117.896i	0.391576	+	0.512592i
$231$	238.421	−	42.0480i	1.03213	−	0.182026i
$232$	46.3993	+	46.3993i	0.199997	+	0.199997i
$233$	−193.661	−	51.8914i	−0.831164	−	0.222710i	−0.181943	−	0.983309i	$-0.558239\pi$
$233$	−193.661	−	51.8914i	−0.831164	−	0.222710i	−0.649221	+	0.760599i	$0.724905\pi$
$234$	69.4945	+	40.1227i	0.296985	+	0.171465i
$235$	299.953	+	231.189i	1.27640	+	0.983785i
$236$	−30.9345	−	53.5801i	−0.131078	−	0.227034i
$237$	−92.7100	−	92.7100i	−0.391181	−	0.391181i
$238$	94.6672	+	202.997i	0.397761	+	0.852930i
$239$			282.776i			1.18316i	0.806245	+	0.591581i	$0.201496\pi$
$239$			282.776i			1.18316i	−0.806245	+	0.591581i	$0.798504\pi$
$240$	13.1876	+	32.0326i	0.0549484	+	0.133469i
$241$	45.5745	−	78.9374i	0.189106	−	0.327541i	−0.755846	−	0.654749i	$-0.772774\pi$
$241$	45.5745	−	78.9374i	0.189106	−	0.327541i	0.944952	+	0.327208i	$0.106108\pi$
$242$	379.379	−	101.654i	1.56768	−	0.420059i
$243$	15.0573	+	4.03459i	0.0619642	+	0.0166032i
$244$			7.03346i			0.0288257i
$245$	−112.675	−	217.553i	−0.459896	−	0.887973i
$246$	52.9829			0.215378
$247$	−84.0886	+	313.823i	−0.340440	+	1.27054i
$248$	−40.6141	−	151.574i	−0.163767	−	0.611185i
$249$	60.0045	+	34.6436i	0.240982	+	0.139131i
$250$	−21.9418	−	175.410i	−0.0877672	−	0.701639i
$251$	278.796			1.11074			0.555371	−	0.831603i	$-0.312576\pi$
$251$	278.796			1.11074			0.555371	+	0.831603i	$0.312576\pi$
$252$	−38.0643	+	17.7512i	−0.151049	+	0.0704413i
$253$	−296.247	+	296.247i	−1.17094	+	1.17094i
$254$	74.7058	−	43.1314i	0.294117	−	0.169809i
$255$	−194.325	+	25.1580i	−0.762060	+	0.0986589i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−25.0895	+	93.6352i	−0.0976244	+	0.364339i	−0.997404	−	0.0720049i	$-0.977060\pi$
$257$	−25.0895	+	93.6352i	−0.0976244	+	0.364339i	0.899780	+	0.436344i	$0.143727\pi$
$258$	−35.9608	+	35.9608i	−0.139383	+	0.139383i
$259$	−28.0509	−	159.055i	−0.108305	−	0.614110i
$260$	25.0913	−	187.468i	0.0965050	−	0.721033i
$261$	−34.7994	−	60.2744i	−0.133331	−	0.230936i
$262$	80.0714	−	21.4551i	0.305616	−	0.0818896i
$263$	−54.0055	−	201.551i	−0.205344	−	0.766354i	−0.989344	−	0.145594i	$-0.953491\pi$
$263$	−54.0055	−	201.551i	−0.205344	−	0.766354i	0.784000	−	0.620760i	$-0.213176\pi$
$264$	−84.7175	+	48.9116i	−0.320899	+	0.185271i
$265$	−20.6119	−	2.75876i	−0.0777809	−	0.0104104i
$266$	−109.309	−	130.260i	−0.410935	−	0.489701i
$267$	176.273	+	176.273i	0.660199	+	0.660199i
$268$	5.70488	+	1.52862i	0.0212869	+	0.00570380i
$269$	−177.916	−	102.720i	−0.661397	−	0.381858i	0.131412	−	0.991328i	$-0.458049\pi$
$269$	−177.916	−	102.720i	−0.661397	−	0.381858i	−0.792809	+	0.609470i	$0.791382\pi$
$270$	−4.71742	−	36.4382i	−0.0174719	−	0.134956i
$271$	−55.2715	−	95.7331i	−0.203954	−	0.353259i	0.745845	−	0.666120i	$-0.232046\pi$
$271$	−55.2715	−	95.7331i	−0.203954	−	0.353259i	−0.949799	+	0.312861i	$0.898713\pi$
$272$	−63.9960	−	63.9960i	−0.235280	−	0.235280i
$273$	228.448	+	19.9792i	0.836807	+	0.0731837i
$274$		−	113.673i		−	0.414865i
$275$	482.744	−	127.126i	1.75543	−	0.462277i
$276$	36.3407	−	62.9439i	0.131669	−	0.228058i
$277$	−68.0599	+	18.2366i	−0.245704	+	0.0658361i	−0.379569	−	0.925163i	$-0.623928\pi$
$277$	−68.0599	+	18.2366i	−0.245704	+	0.0658361i	0.133865	+	0.991000i	$0.457261\pi$
$278$	20.6643	+	5.53699i	0.0743321	+	0.0199172i
$279$			166.440i			0.596558i
$280$	72.8448	+	67.0346i	0.260160	+	0.239409i
$281$	172.628			0.614336			0.307168	−	0.951655i	$-0.400619\pi$
$281$	172.628			0.614336			0.307168	+	0.951655i	$0.400619\pi$
$282$	48.0184	−	179.207i	0.170278	−	0.635486i
$283$	7.29175	+	27.2132i	0.0257659	+	0.0961597i	0.977611	−	0.210418i	$-0.0674826\pi$
$283$	7.29175	+	27.2132i	0.0257659	+	0.0961597i	−0.951846	+	0.306578i	$0.900816\pi$
$284$	20.6007	+	11.8938i	0.0725376	+	0.0418796i
$285$	137.559	−	56.6322i	0.482663	−	0.198710i
$286$	534.116			1.86754
$287$	137.223	−	63.9936i	0.478129	−	0.222974i
$288$	12.0000	−	12.0000i	0.0416667	−	0.0416667i
$289$	193.069	−	111.468i	0.668058	−	0.385703i
$290$	−100.145	+	129.931i	−0.345327	+	0.448039i
$291$	−68.6611	+	118.925i	−0.235949	+	0.408675i
$292$	−11.3015	+	42.1778i	−0.0387038	+	0.144444i
$293$	−78.8568	+	78.8568i	−0.269136	+	0.269136i	−0.828752	−	0.559616i	$-0.810949\pi$
$293$	−78.8568	+	78.8568i	−0.269136	+	0.269136i	0.559616	+	0.828752i	$0.310949\pi$
$294$	−77.1446	+	91.9495i	−0.262397	+	0.312753i
$295$	122.912	−	93.8943i	0.416652	−	0.318286i
$296$	32.6298	+	56.5164i	0.110236	+	0.190934i
$297$	100.222	−	26.8544i	0.337447	−	0.0904187i
$298$	−12.0463	−	44.9575i	−0.0404239	−	0.150864i
$299$	−343.674	+	198.420i	−1.14941	+	0.663613i
$300$	−75.1857	+	42.9780i	−0.250619	+	0.143260i
$301$	−49.7027	+	136.571i	−0.165125	+	0.453724i
$302$	−284.366	−	284.366i	−0.941611	−	0.941611i
$303$	−188.930	−	50.6237i	−0.623532	−	0.167075i
$304$	59.5042	+	34.3548i	0.195738	+	0.113009i
$305$	−17.4381	+	2.25760i	−0.0571742	+	0.00740197i
$306$	47.9970	+	83.1333i	0.156853	+	0.271677i
$307$	21.8398	+	21.8398i	0.0711395	+	0.0711395i	0.741781	−	0.670642i	$-0.233981\pi$
$307$	21.8398	+	21.8398i	0.0711395	+	0.0711395i	−0.670642	+	0.741781i	$0.733981\pi$
$308$	−160.338	+	229.002i	−0.520577	+	0.743513i
$309$			340.845i			1.10306i
$310$	362.762	−	149.347i	1.17020	−	0.481765i
$311$	−85.0972	+	147.393i	−0.273624	+	0.473931i	−0.969787	−	0.243953i	$-0.921556\pi$
$311$	−85.0972	+	147.393i	−0.273624	+	0.473931i	0.696163	+	0.717884i	$0.254889\pi$
$312$	−89.5021	+	23.9820i	−0.286866	+	0.0768654i
$313$	−378.982	−	101.548i	−1.21080	−	0.324434i	−0.403727	−	0.914880i	$-0.632285\pi$
$313$	−378.982	−	101.548i	−1.21080	−	0.324434i	−0.807077	+	0.590446i	$0.798952\pi$
$314$		−	249.970i		−	0.796083i
$315$	−56.2286	−	88.6755i	−0.178504	−	0.281510i
$316$	151.395			0.479097
$317$	36.9318	−	137.832i	0.116504	−	0.434800i	−0.882891	−	0.469578i	$-0.844406\pi$
$317$	36.9318	−	137.832i	0.116504	−	0.434800i	0.999395	+	0.0347786i	$0.0110726\pi$
$318$	2.63679	+	9.84065i	0.00829180	+	0.0309454i
$319$	−401.188	−	231.626i	−1.25764	−	0.726101i
$320$	−36.9221	−	15.3868i	−0.115382	−	0.0480839i
$321$	−282.078			−0.878746
$322$	18.0959	−	206.914i	0.0561984	−	0.642592i
$323$	−274.821	+	274.821i	−0.850840	+	0.850840i
$324$	−15.5885	+	9.00000i	−0.0481125	+	0.0277778i
$325$	472.846	+	2.03552i	1.45491	+	0.00626313i
$326$	53.1321	−	92.0274i	0.162982	−	0.282293i
$327$	26.2840	−	98.0933i	0.0803793	−	0.299980i
$328$	−43.2604	+	43.2604i	−0.131891	+	0.131891i
$329$	−92.0839	−	522.135i	−0.279890	−	1.58704i
$330$	−148.460	−	194.341i	−0.449878	−	0.588912i
$331$	−11.5185	−	19.9506i	−0.0347990	−	0.0602736i	0.848101	−	0.529834i	$-0.177746\pi$
$331$	−11.5185	−	19.9506i	−0.0347990	−	0.0602736i	−0.882900	+	0.469560i	$0.844412\pi$
$332$	−77.2798	+	20.7071i	−0.232771	+	0.0623707i
$333$	−17.9150	−	66.8597i	−0.0537988	−	0.200780i
$334$	−200.054	+	115.501i	−0.598965	+	0.345812i
$335$	−1.95877	+	14.6348i	−0.00584706	+	0.0436860i
$336$	16.5856	−	45.5732i	0.0493619	−	0.135635i
$337$	−438.660	−	438.660i	−1.30166	−	1.30166i	−0.927271	−	0.374391i	$-0.877852\pi$
$337$	−438.660	−	438.660i	−1.30166	−	1.30166i	−0.374391	−	0.927271i	$-0.622148\pi$
$338$	257.824	+	69.0837i	0.762792	+	0.204390i
$339$	−148.435	−	85.6989i	−0.437861	−	0.252799i
$340$	138.124	−	179.207i	0.406249	−	0.527080i
$341$	553.914	+	959.408i	1.62438	+	2.81351i
$342$	−51.5322	−	51.5322i	−0.150679	−	0.150679i
$343$	−88.7426	+	331.321i	−0.258725	+	0.965951i
$344$		−	58.7238i		−	0.170709i
$345$	167.722	+	69.8960i	0.486151	+	0.202597i
$346$	−141.577	+	245.218i	−0.409181	+	0.708723i
$347$	441.664	−	118.344i	1.27281	−	0.341048i	0.441702	−	0.897162i	$-0.354375\pi$
$347$	441.664	−	118.344i	1.27281	−	0.341048i	0.831106	+	0.556114i	$0.187708\pi$
$348$	77.6275	+	20.8002i	0.223067	+	0.0597707i
$349$		−	70.3408i		−	0.201549i	−0.994909	−	0.100775i	$-0.967868\pi$
$349$		−	70.3408i		−	0.201549i	0.994909	−	0.100775i	$-0.0321321\pi$
$350$	−142.818	+	202.121i	−0.408051	+	0.577490i
$351$	98.2801			0.280000
$352$	29.2353	−	109.108i	0.0830549	−	0.309965i
$353$	43.1761	+	161.135i	0.122312	+	0.456474i	0.999730	−	0.0232531i	$-0.00740234\pi$
$353$	43.1761	+	161.135i	0.122312	+	0.456474i	−0.877418	+	0.479727i	$0.840736\pi$
$354$	−65.6219	−	37.8868i	−0.185373	−	0.107025i
$355$	−22.8760	+	54.8931i	−0.0644395	+	0.154628i
$356$	−287.853			−0.808575
$357$	224.720	+	157.340i	0.629467	+	0.440727i
$358$	−120.088	+	120.088i	−0.335440	+	0.335440i
$359$	−446.981	+	258.064i	−1.24507	+	0.718842i	−0.970122	−	0.242616i	$-0.921994\pi$
$359$	−446.981	+	258.064i	−1.24507	+	0.718842i	−0.274949	+	0.961459i	$0.588661\pi$
$360$	33.6035	+	25.8999i	0.0933430	+	0.0719443i
$361$	−32.9687	+	57.1034i	−0.0913260	+	0.158181i
$362$	−79.7314	+	297.562i	−0.220253	+	0.821994i
$363$	340.142	−	340.142i	0.937031	−	0.937031i
$364$	−202.840	+	170.214i	−0.557253	+	0.467622i
$365$	−108.199	−	14.4817i	−0.296436	−	0.0396759i
$366$	4.30710	+	7.46012i	0.0117680	+	0.0203828i
$367$	−486.174	+	130.270i	−1.32472	+	0.354959i	−0.850746	−	0.525577i	$-0.823849\pi$
$367$	−486.174	+	130.270i	−1.32472	+	0.354959i	−0.473979	+	0.880536i	$0.657183\pi$
$368$	21.7214	+	81.0655i	0.0590256	+	0.220287i
$369$	56.1969	−	32.4453i	0.152295	−	0.0879276i
$370$	−129.648	+	99.0399i	−0.350401	+	0.267676i
$371$	18.7149	+	22.3020i	0.0504444	+	0.0601133i
$372$	−135.897	−	135.897i	−0.365316	−	0.365316i
$373$	−371.645	−	99.5820i	−0.996368	−	0.266976i	−0.276445	−	0.961030i	$-0.589156\pi$
$373$	−371.645	−	99.5820i	−0.996368	−	0.266976i	−0.719923	+	0.694054i	$0.755823\pi$
$374$	553.338	+	319.470i	1.47951	+	0.854197i
$375$	−130.689	−	172.614i	−0.348504	−	0.460303i
$376$	107.115	+	185.529i	0.284880	+	0.493427i
$377$	−310.277	−	310.277i	−0.823016	−	0.823016i
$378$	−29.5030	+	42.1376i	−0.0780502	+	0.111475i
$379$			352.609i			0.930366i	0.885214	+	0.465183i	$0.154012\pi$
$379$			352.609i			0.930366i	−0.885214	+	0.465183i	$0.845988\pi$
$380$	−66.0764	+	158.557i	−0.173885	+	0.417254i
$381$	52.8250	−	91.4955i	0.138648	−	0.240146i
$382$	153.450	−	41.1168i	0.401701	−	0.107636i
$383$	−58.4854	−	15.6711i	−0.152703	−	0.0409167i	0.181658	−	0.983362i	$-0.441854\pi$
$383$	−58.4854	−	15.6711i	−0.152703	−	0.0409167i	−0.334361	+	0.942445i	$0.608520\pi$
$384$			19.5959i			0.0510310i
$385$	−619.232	−	324.022i	−1.60839	−	0.841615i
$386$	−8.19212			−0.0212231
$387$	−16.1208	+	60.1636i	−0.0416558	+	0.155462i
$388$	−41.0399	−	153.163i	−0.105773	−	0.394750i
$389$	623.238	+	359.827i	1.60215	+	0.925004i	0.991056	+	0.133450i	$0.0426055\pi$
$389$	623.238	+	359.827i	1.60215	+	0.925004i	0.611099	+	0.791554i	$0.290728\pi$
$390$	−88.1872	−	214.206i	−0.226121	−	0.549245i
$391$	−474.723			−1.21413
$392$	−12.0882	−	138.065i	−0.0308371	−	0.352206i
$393$	71.7901	−	71.7901i	0.182672	−	0.182672i
$394$	69.8135	−	40.3068i	0.177192	−	0.102302i
$395$	48.5947	+	375.354i	0.123024	+	0.950264i
$396$	−59.9043	+	103.757i	−0.151273	+	0.262013i
$397$	−25.1399	+	93.8233i	−0.0633246	+	0.236331i	−0.990333	−	0.138710i	$-0.955705\pi$
$397$	−25.1399	+	93.8233i	−0.0633246	+	0.236331i	0.927008	+	0.375040i	$0.122371\pi$
$398$	−98.8197	+	98.8197i	−0.248291	+	0.248291i
$399$	−195.707	−	71.2244i	−0.490494	−	0.178507i
$400$	26.2975	−	96.4803i	0.0657437	−	0.241201i
$401$	−74.7359	−	129.446i	−0.186374	−	0.322809i	0.757665	−	0.652644i	$-0.226340\pi$
$401$	−74.7359	−	129.446i	−0.186374	−	0.322809i	−0.944039	+	0.329835i	$0.893007\pi$
$402$	6.98702	−	1.87217i	0.0173807	−	0.00465713i
$403$	271.591	+	1013.59i	0.673924	+	2.51512i
$404$	195.595	−	112.927i	0.484146	−	0.279522i
$405$	−27.3174	−	35.7598i	−0.0674503	−	0.0882958i
$406$	226.174	−	39.8882i	0.557079	−	0.0982468i
$407$	−325.777	−	325.777i	−0.800436	−	0.800436i
$408$	−107.067	−	28.6886i	−0.262420	−	0.0703153i
$409$	−316.278	−	182.603i	−0.773295	−	0.446462i	0.0607535	−	0.998153i	$-0.480650\pi$
$409$	−316.278	−	182.603i	−0.773295	−	0.446462i	−0.834049	+	0.551690i	$0.813983\pi$
$410$	−121.141	−	93.3701i	−0.295467	−	0.227732i
$411$	−69.6102	−	120.568i	−0.169368	−	0.293354i
$412$	−278.299	−	278.299i	−0.675483	−	0.675483i
$413$	−215.718	−	18.8658i	−0.522320	−	0.0456799i
$414$		−	89.0161i		−	0.215015i
$415$	−76.1445	−	184.954i	−0.183481	−	0.445672i
$416$	53.4969	−	92.6594i	0.128598	−	0.222739i
$417$	25.3085	−	6.78140i	0.0606919	−	0.0162624i
$418$	−468.546	−	125.547i	−1.12092	−	0.300351i
$419$		−	373.960i		−	0.892507i	−0.894907	−	0.446254i	$-0.852758\pi$
$419$		−	373.960i		−	0.892507i	0.894907	−	0.446254i	$-0.147242\pi$
$420$	118.314	+	26.4928i	0.281699	+	0.0630780i
$421$	414.109			0.983631			0.491816	−	0.870699i	$-0.336333\pi$
$421$	414.109			0.983631			0.491816	+	0.870699i	$0.336333\pi$
$422$	−126.040	+	470.389i	−0.298674	+	1.11467i
$423$	−58.8102	−	219.483i	−0.139031	−	0.518872i
$424$	−10.1878	−	5.88192i	−0.0240278	−	0.0138725i
$425$	488.646	+	284.931i	1.14975	+	0.670427i
$426$	29.1338			0.0683891
$427$	20.1656	+	14.1191i	0.0472263	+	0.0330659i
$428$	230.315	−	230.315i	0.538120	−	0.538120i
$429$	566.515	−	327.078i	1.32055	−	0.762419i
$430$	145.594	−	18.8491i	0.338592	−	0.0438352i
$431$	−258.753	+	448.173i	−0.600355	+	1.03985i	0.392412	+	0.919789i	$0.371641\pi$
$431$	−258.753	+	448.173i	−0.600355	+	1.03985i	−0.992767	+	0.120056i	$0.961693\pi$
$432$	5.37945	−	20.0764i	0.0124524	−	0.0464731i
$433$	−28.4380	+	28.4380i	−0.0656767	+	0.0656767i	−0.739182	−	0.673506i	$-0.764788\pi$
$433$	−28.4380	+	28.4380i	−0.0656767	+	0.0656767i	0.673506	+	0.739182i	$0.264788\pi$
$434$	−516.107	−	187.829i	−1.18919	−	0.432785i
$435$	−26.6533	+	199.139i	−0.0612720	+	0.457791i
$436$	58.6321	+	101.554i	0.134477	+	0.232921i
$437$	348.123	−	93.2794i	0.796621	−	0.213454i
$438$	13.8415	+	51.6570i	0.0316015	+	0.117938i
$439$	241.933	−	139.680i	0.551100	−	0.318178i	−0.198466	−	0.980108i	$-0.563596\pi$
$439$	241.933	−	139.680i	0.551100	−	0.318178i	0.749565	+	0.661930i	$0.230262\pi$
$440$	279.896	+	37.4620i	0.636126	+	0.0851410i
$441$	−25.5169	+	144.768i	−0.0578614	+	0.328273i
$442$	427.949	+	427.949i	0.968210	+	0.968210i
$443$	567.996	+	152.194i	1.28216	+	0.343553i	0.834677	−	0.550740i	$-0.185654\pi$
$443$	567.996	+	152.194i	1.28216	+	0.343553i	0.447482	+	0.894293i	$0.352321\pi$
$444$	69.2182	+	39.9632i	0.155897	+	0.0900071i
$445$	−92.3949	−	713.676i	−0.207629	−	1.60377i
$446$	34.8821	+	60.4175i	0.0782109	+	0.135465i
$447$	−40.3078	−	40.3078i	−0.0901739	−	0.0901739i
$448$	23.6683	+	50.7525i	0.0528310	+	0.113287i
$449$			515.916i			1.14903i	0.818493	+	0.574517i	$0.194810\pi$
$449$			515.916i			1.14903i	−0.818493	+	0.574517i	$0.805190\pi$
$450$	−53.4279	+	91.6267i	−0.118729	+	0.203615i
$451$	215.957	−	374.048i	0.478840	−	0.829375i
$452$	191.169	−	51.2237i	0.422941	−	0.113327i
$453$	−475.754	−	127.478i	−1.05023	−	0.281408i
$454$		−	244.162i		−	0.537802i
$455$	−487.122	−	448.268i	−1.07060	−	0.985205i
$456$	84.1517			0.184543
$457$	75.2958	−	281.008i	0.164761	−	0.614896i	−0.833310	−	0.552807i	$-0.813557\pi$
$457$	75.2958	−	281.008i	0.164761	−	0.614896i	0.998071	−	0.0620898i	$-0.0197765\pi$
$458$	7.68857	+	28.6941i	0.0167873	+	0.0626510i
$459$	101.817	+	58.7841i	0.221824	+	0.128070i
$460$	−194.014	+	79.8745i	−0.421770	+	0.173640i
$461$	431.271			0.935511			0.467756	−	0.883858i	$-0.345063\pi$
$461$	431.271			0.935511			0.467756	+	0.883858i	$0.345063\pi$
$462$	−29.8294	+	341.080i	−0.0645659	+	0.738268i
$463$	81.4930	−	81.4930i	0.176011	−	0.176011i	−0.613603	−	0.789614i	$-0.710281\pi$
$463$	81.4930	−	81.4930i	0.176011	−	0.176011i	0.789614	+	0.613603i	$0.210281\pi$
$464$	−80.3659	+	46.3993i	−0.173202	+	0.0999984i
$465$	293.312	−	380.552i	0.630777	−	0.818392i
$466$	141.770	−	245.553i	0.304227	−	0.526937i
$467$	57.0779	−	213.017i	0.122222	−	0.456140i	−0.877503	−	0.479571i	$-0.840792\pi$
$467$	57.0779	−	213.017i	0.122222	−	0.456140i	0.999725	+	0.0234309i	$0.00745896\pi$
$468$	−80.2454	+	80.2454i	−0.171465	+	0.171465i
$469$	15.8348	−	13.2879i	0.0337629	−	0.0283323i
$470$	−425.601	+	325.122i	−0.905534	+	0.691749i
$471$	−153.075	−	265.133i	−0.324999	−	0.562916i
$472$	84.5146	−	22.6456i	0.179056	−	0.0479780i
$473$	107.301	+	400.451i	0.226851	+	0.846619i
$474$	160.578	−	92.7100i	0.338773	−	0.195591i
$475$	−414.320	−	112.930i	−0.872252	−	0.237748i
$476$	−311.950	+	55.0157i	−0.655357	+	0.115579i
$477$	8.82288	+	8.82288i	0.0184966	+	0.0184966i
$478$	−386.279	−	103.503i	−0.808115	−	0.216534i
$479$	−322.538	−	186.218i	−0.673357	−	0.388763i	0.123990	−	0.992283i	$-0.460431\pi$
$479$	−322.538	−	186.218i	−0.673357	−	0.388763i	−0.797348	+	0.603520i	$0.793764\pi$
$480$	−48.5843	+	6.28989i	−0.101217	+	0.0131039i
$481$	−218.199	−	377.932i	−0.453636	−	0.785721i
$482$	91.1491	+	91.1491i	0.189106	+	0.189106i
$483$	−107.515	−	230.547i	−0.222599	−	0.477324i
$484$			555.450i			1.14762i
$485$	366.566	−	150.913i	0.755805	−	0.311161i
$486$	−11.0227	+	19.0919i	−0.0226805	+	0.0392837i
$487$	354.693	−	95.0398i	0.728323	−	0.195154i	0.124441	−	0.992227i	$-0.460286\pi$
$487$	354.693	−	95.0398i	0.728323	−	0.195154i	0.603882	+	0.797073i	$0.293620\pi$
$488$	−9.60789	−	2.57443i	−0.0196883	−	0.00527546i
$489$		−	130.146i		−	0.266148i
$490$	338.425	−	74.2863i	0.690663	−	0.151605i
$491$	8.71393			0.0177473			0.00887366	−	0.999961i	$-0.497175\pi$
$491$	8.71393			0.0177473			0.00887366	+	0.999961i	$0.497175\pi$
$492$	−19.3931	+	72.3760i	−0.0394168	+	0.147106i
$493$	−135.858	−	507.029i	−0.275574	−	1.02846i
$494$	−397.912	−	229.734i	−0.805489	−	0.465049i
$495$	−276.474	−	115.217i	−0.558534	−	0.232762i
$496$	221.920			0.447419
$497$	75.4550	−	35.1882i	0.151821	−	0.0708013i
$498$	−69.2872	+	69.2872i	−0.139131	+	0.139131i
$499$	233.352	−	134.726i	0.467640	−	0.269992i	−0.247611	−	0.968860i	$-0.579646\pi$
$499$	233.352	−	134.726i	0.467640	−	0.269992i	0.715251	+	0.698867i	$0.246312\pi$
$500$	247.645	+	34.2313i	0.495291	+	0.0684627i
$501$	−141.460	+	245.015i	−0.282355	+	0.489053i
$502$	−102.047	+	380.843i	−0.203280	+	0.758651i
$503$	308.184	−	308.184i	0.612693	−	0.612693i	−0.330954	−	0.943647i	$-0.607371\pi$
$503$	308.184	−	308.184i	0.612693	−	0.612693i	0.943647	+	0.330954i	$0.107371\pi$
$504$	−10.3161	−	58.4943i	−0.0204684	−	0.116060i
$505$	342.762	+	448.693i	0.678737	+	0.888501i
$506$	−296.247	−	513.115i	−0.585468	−	1.01406i
$507$	315.768	−	84.6099i	0.622817	−	0.166883i
$508$	31.5744	+	117.837i	0.0621543	+	0.231963i
$509$	−568.117	+	328.003i	−1.11614	+	0.644406i	−0.940414	−	0.340032i	$-0.889562\pi$
$509$	−568.117	+	328.003i	−1.11614	+	0.644406i	−0.175730	+	0.984438i	$0.556229\pi$
$510$	36.7615	−	274.662i	0.0720814	−	0.538552i
$511$	98.2409	+	117.071i	0.192252	+	0.229102i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−86.2150	−	23.1012i	−0.168060	−	0.0450317i
$514$	−118.725	−	68.5457i	−0.230982	−	0.133357i
$515$	600.660	−	779.317i	1.16633	−	1.51324i
$516$	−35.9608	−	62.2860i	−0.0696915	−	0.120709i
$517$	−1069.44	−	1069.44i	−2.06855	−	2.06855i
$518$	227.540	+	19.8997i	0.439266	+	0.0384164i
$519$			346.791i			0.668190i
$520$	246.903	+	102.894i	0.474813	+	0.197872i
$521$	91.8665	−	159.117i	0.176327	−	0.305408i	−0.764293	−	0.644870i	$-0.776912\pi$
$521$	91.8665	−	159.117i	0.176327	−	0.305408i	0.940620	+	0.339462i	$0.110245\pi$
$522$	95.0738	−	25.4750i	0.182134	−	0.0488026i
$523$	795.892	+	213.259i	1.52178	+	0.407760i	0.920328	−	0.391147i	$-0.127922\pi$
$523$	795.892	+	213.259i	1.52178	+	0.407760i	0.601454	+	0.798908i	$0.294588\pi$
$524$			117.233i			0.223727i
$525$	−27.7075	+	301.840i	−0.0527761	+	0.574933i
$526$	295.091			0.561010
$527$	−324.893	+	1212.52i	−0.616495	+	2.30079i
$528$	−35.8058	−	133.629i	−0.0678140	−	0.253085i
$529$	−76.8901	−	44.3925i	−0.145350	−	0.0839179i
$530$	11.3130	−	27.1466i	0.0213453	−	0.0512201i
$531$	−92.8034			−0.174771
$532$	217.949	−	101.640i	0.409678	−	0.191052i
$533$	289.287	−	289.287i	0.542752	−	0.542752i
$534$	−305.314	+	176.273i	−0.571749	+	0.330099i
$535$	644.949	+	497.096i	1.20551	+	0.929152i
$536$	−4.17626	+	7.23350i	−0.00779154	+	0.0134953i
$537$	−53.8338	+	200.910i	−0.100249	+	0.374135i
$538$	205.439	−	205.439i	0.381858	−	0.381858i
$539$	334.705	+	919.408i	0.620974	+	1.70577i
$540$	51.5023	+	6.89321i	0.0953746	+	0.0127652i
$541$	190.462	+	329.891i	0.352056	+	0.609779i	0.986610	−	0.163100i	$-0.0521493\pi$
$541$	190.462	+	329.891i	0.352056	+	0.609779i	−0.634553	+	0.772879i	$0.718816\pi$
$542$	151.005	−	40.4616i	0.278606	−	0.0746524i
$543$	97.6506	+	364.437i	0.179835	+	0.671155i
$544$	110.844	−	63.9960i	0.203758	−	0.117640i
$545$	−232.963	+	177.964i	−0.427456	+	0.326539i
$546$	−110.910	+	304.753i	−0.203132	+	0.558156i
$547$	231.815	+	231.815i	0.423794	+	0.423794i	0.886508	−	0.462714i	$-0.153124\pi$
$547$	231.815	+	231.815i	0.423794	+	0.423794i	−0.462714	+	0.886508i	$0.653124\pi$
$548$	155.280	+	41.6072i	0.283358	+	0.0759255i
$549$	9.13674	+	5.27510i	0.0166425	+	0.00960856i
$550$	−3.03908	+	705.972i	−0.00552560	+	1.28359i
$551$	199.254	+	345.119i	0.361623	+	0.626350i
$552$	72.6814	+	72.6814i	0.131669	+	0.131669i
$553$	303.914	−	434.064i	0.549572	−	0.784925i
$554$		−	99.6466i		−	0.179867i
$555$	−76.8634	+	184.441i	−0.138493	+	0.332326i
$556$	−15.1273	+	26.2013i	−0.0272075	+	0.0471247i
$557$	952.690	−	255.272i	1.71039	−	0.458299i	0.734873	−	0.678204i	$-0.237242\pi$
$557$	952.690	−	255.272i	1.71039	−	0.458299i	0.975521	+	0.219906i	$0.0705750\pi$
$558$	−227.361	−	60.9212i	−0.407457	−	0.109178i
$559$			392.693i			0.702491i
$560$	−118.234	+	74.9715i	−0.211132	+	0.133878i
$561$	782.538			1.39490
$562$	−63.1864	+	235.815i	−0.112431	+	0.419599i
$563$	6.56455	+	24.4993i	0.0116600	+	0.0435155i	0.971511	−	0.236996i	$-0.0761627\pi$
$563$	6.56455	+	24.4993i	0.0116600	+	0.0435155i	−0.959851	+	0.280511i	$0.909496\pi$
$564$	227.225	+	131.189i	0.402882	+	0.232604i
$565$	188.361	+	457.526i	0.333382	+	0.809781i
$566$	−39.8429			−0.0703938
$567$	−5.48877	+	62.7604i	−0.00968037	+	0.110689i
$568$	−23.7876	+	23.7876i	−0.0418796	+	0.0418796i
$569$	731.187	−	422.151i	1.28504	−	0.741917i	0.307273	−	0.951621i	$-0.400583\pi$
$569$	731.187	−	422.151i	1.28504	−	0.741917i	0.977765	+	0.209704i	$0.0672501\pi$
$570$	27.0110	+	208.638i	0.0473877	+	0.366032i
$571$	−442.183	+	765.884i	−0.774402	+	1.34130i	0.160728	+	0.986999i	$0.448616\pi$
$571$	−442.183	+	765.884i	−0.774402	+	1.34130i	−0.935130	+	0.354304i	$0.884718\pi$
$572$	−195.500	+	729.616i	−0.341783	+	1.27555i
$573$	137.579	−	137.579i	0.240104	−	0.240104i
$574$	37.1898	+	210.874i	0.0647905	+	0.367376i
$575$	−260.308	−	455.383i	−0.452710	−	0.791971i
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	755.053	−	202.316i	1.30858	−	0.350634i	0.463894	−	0.885891i	$-0.346452\pi$
$577$	755.053	−	202.316i	1.30858	−	0.350634i	0.844689	+	0.535257i	$0.179785\pi$
$578$	81.6004	+	304.537i	0.141177	+	0.526881i
$579$	−8.68906	+	5.01663i	−0.0150070	+	0.00866430i
$580$	−140.834	−	184.359i	−0.242817	−	0.317860i
$581$	−95.7642	+	263.137i	−0.164827	+	0.452903i
$582$	−137.322	−	137.322i	−0.235949	−	0.235949i
$583$	80.2204	+	21.4950i	0.137599	+	0.0368696i
$584$	−53.4793	−	30.8763i	−0.0915741	−	0.0528703i
$585$	−224.710	−	173.196i	−0.384120	−	0.296061i
$586$	−78.8568	−	136.584i	−0.134568	−	0.233078i
$587$	−198.669	−	198.669i	−0.338449	−	0.338449i	0.517334	−	0.855783i	$-0.326924\pi$
$587$	−198.669	−	198.669i	−0.338449	−	0.338449i	−0.855783	+	0.517334i	$0.826924\pi$
$588$	−97.3685	−	139.037i	−0.165593	−	0.236458i
$589$		−	953.000i		−	1.61800i
$590$	83.2729	+	202.269i	0.141141	+	0.342829i
$591$	49.3656	−	85.5037i	0.0835289	−	0.144676i
$592$	−89.1462	+	23.8867i	−0.150585	+	0.0403491i
$593$	−605.873	−	162.343i	−1.02171	−	0.273766i	−0.291194	−	0.956664i	$-0.594053\pi$
$593$	−605.873	−	162.343i	−1.02171	−	0.273766i	−0.730514	+	0.682898i	$0.760719\pi$
$594$			146.735i			0.247029i
$595$	−236.530	−	755.762i	−0.397530	−	1.27019i
$596$	65.8223			0.110440
$597$	−44.2997	+	165.329i	−0.0742038	+	0.276932i
$598$	−145.254	−	542.094i	−0.242899	−	0.906512i
$599$	−335.297	−	193.584i	−0.559762	−	0.323179i	0.193288	−	0.981142i	$-0.438085\pi$
$599$	−335.297	−	193.584i	−0.559762	−	0.323179i	−0.753050	+	0.657963i	$0.771418\pi$
$600$	−31.1892	−	118.437i	−0.0519820	−	0.197394i
$601$	267.104			0.444433			0.222217	−	0.974997i	$-0.428671\pi$
$601$	267.104			0.444433			0.222217	+	0.974997i	$0.428671\pi$
$602$	−168.367	−	117.884i	−0.279679	−	0.195820i
$603$	6.26439	−	6.26439i	0.0103887	−	0.0103887i
$604$	492.537	−	284.366i	0.815459	−	0.470805i
$605$	−1377.13	+	178.288i	−2.27625	+	0.294691i
$606$	138.306	−	239.554i	0.228228	−	0.395303i
$607$	89.8215	−	335.219i	0.147976	−	0.552255i	−0.851629	−	0.524146i	$-0.824385\pi$
$607$	89.8215	−	335.219i	0.147976	−	0.552255i	0.999605	−	0.0281090i	$-0.00894856\pi$
$608$	−68.7096	+	68.7096i	−0.113009	+	0.113009i
$609$	215.468	−	180.811i	0.353805	−	0.296898i
$610$	3.29886	−	24.6473i	0.00540797	−	0.0404054i
$611$	−716.291	−	1240.65i	−1.17233	−	2.03053i
$612$	−131.130	+	35.1363i	−0.214265	+	0.0574122i
$613$	−107.138	−	399.843i	−0.174776	−	0.652272i	−0.996590	−	0.0825161i	$-0.973704\pi$
$613$	−107.138	−	399.843i	−0.174776	−	0.652272i	0.821814	−	0.569756i	$-0.192962\pi$
$614$	−37.8277	+	21.8398i	−0.0616086	+	0.0355698i
$615$	−185.667	−	24.8502i	−0.301898	−	0.0404069i
$616$	−254.135	−	302.846i	−0.412556	−	0.491633i
$617$	637.339	+	637.339i	1.03297	+	1.03297i	0.999438	+	0.0335273i	$0.0106741\pi$
$617$	637.339	+	637.339i	1.03297	+	1.03297i	0.0335273	+	0.999438i	$0.489326\pi$
$618$	−465.603	−	124.758i	−0.753403	−	0.201874i
$619$	956.137	+	552.026i	1.54465	+	0.891803i	0.998536	+	0.0540914i	$0.0172262\pi$
$619$	956.137	+	552.026i	1.54465	+	0.891803i	0.546113	+	0.837712i	$0.316107\pi$
$620$	71.2317	+	550.207i	0.114890	+	0.887431i
$621$	−54.5110	−	94.4158i	−0.0877794	−	0.152038i
$622$	−170.194	−	170.194i	−0.273624	−	0.273624i
$623$	−577.842	+	825.302i	−0.927516	+	1.32472i
$624$		−	131.040i		−	0.210000i
$625$	−5.38092	+	624.977i	−0.00860948	+	0.999963i
$626$	277.434	−	480.529i	0.443185	−	0.767619i
$627$	−573.850	+	153.763i	−0.915231	+	0.245235i
$628$	341.465	+	91.4954i	0.543735	+	0.145693i
$629$		−	522.044i		−	0.829959i
$630$	141.714	−	44.3522i	0.224943	−	0.0704003i
$631$	−1130.27			−1.79124			−0.895618	−	0.444824i	$-0.853266\pi$
$631$	−1130.27			−1.79124			−0.895618	+	0.444824i	$0.853266\pi$
$632$	−55.4143	+	206.809i	−0.0876809	+	0.327230i
$633$	154.367	+	576.106i	0.243866	+	0.910120i
$634$	174.763	+	100.900i	0.275652	+	0.159148i
$635$	−282.020	+	116.106i	−0.444126	+	0.182844i
$636$	−14.4077			−0.0226536
$637$	80.8349	+	923.255i	0.126899	+	1.44938i
$638$	463.252	−	463.252i	0.726101	−	0.726101i
$639$	30.9010	−	17.8407i	0.0483584	−	0.0279197i
$640$	34.5333	−	44.8046i	0.0539582	−	0.0700072i
$641$	251.753	−	436.050i	0.392751	−	0.680265i	−0.600060	−	0.799955i	$-0.704857\pi$
$641$	251.753	−	436.050i	0.392751	−	0.680265i	0.992811	+	0.119690i	$0.0381901\pi$
$642$	103.248	−	385.325i	0.160822	−	0.600195i
$643$	363.947	−	363.947i	0.566015	−	0.566015i	−0.364995	−	0.931010i	$-0.618929\pi$
$643$	363.947	−	363.947i	0.566015	−	0.566015i	0.931010	+	0.364995i	$0.118929\pi$
$644$	276.027	+	100.455i	0.428613	+	0.155987i
$645$	142.883	−	109.151i	0.221525	−	0.169226i
$646$	−274.821	−	476.004i	−0.425420	−	0.736849i
$647$	13.5224	−	3.62332i	0.0209002	−	0.00560018i	−0.248354	−	0.968669i	$-0.579890\pi$
$647$	13.5224	−	3.62332i	0.0209002	−	0.00560018i	0.269254	+	0.963069i	$0.413223\pi$
$648$	−6.58846	−	24.5885i	−0.0101674	−	0.0379452i
$649$	−534.946	+	308.851i	−0.824262	+	0.475888i
$650$	−175.854	+	645.175i	−0.270545	+	0.992576i
$651$	−662.435	+	116.827i	−1.01757	+	0.179458i
$652$	106.264	+	106.264i	0.162982	+	0.162982i
$653$	−826.082	−	221.348i	−1.26506	−	0.338971i	−0.436921	−	0.899500i	$-0.643931\pi$
$653$	−826.082	−	221.348i	−1.26506	−	0.338971i	−0.828135	+	0.560529i	$0.810598\pi$
$654$	124.377	+	71.8093i	0.190179	+	0.109800i
$655$	−290.656	+	37.6293i	−0.443750	+	0.0574494i
$656$	−43.2604	−	74.9291i	−0.0659457	−	0.114221i
$657$	46.3144	+	46.3144i	0.0704938	+	0.0704938i
$658$	746.954	+	65.3255i	1.13519	+	0.0992789i
$659$		−	254.644i		−	0.386410i	−0.981158	−	0.193205i	$-0.938112\pi$
$659$		−	254.644i		−	0.386410i	0.981158	−	0.193205i	$-0.0618882\pi$
$660$	319.815	−	131.666i	0.484568	−	0.199494i
$661$	2.28118	−	3.95112i	0.00345111	−	0.00597749i	−0.864295	−	0.502986i	$-0.832235\pi$
$661$	2.28118	−	3.95112i	0.00345111	−	0.00597749i	0.867746	+	0.497008i	$0.165568\pi$
$662$	31.4690	−	8.43210i	0.0475363	−	0.0127373i
$663$	715.972	+	191.844i	1.07990	+	0.289358i
$664$		−	113.146i		−	0.170400i
$665$	321.954	+	507.738i	0.484141	+	0.763515i
$666$	97.8893			0.146981
$667$	−125.982	+	470.172i	−0.188879	+	0.704906i
$668$	−84.5529	−	315.556i	−0.126576	−	0.472389i
$669$	73.9961	+	42.7216i	0.110607	+	0.0638590i
$670$	−19.2746	−	8.03244i	−0.0287680	−	0.0119887i
$671$	70.2224			0.104653
$672$	56.1834	+	39.3373i	0.0836063	+	0.0585377i
$673$	183.435	−	183.435i	0.272563	−	0.272563i	−0.557568	−	0.830131i	$-0.688265\pi$
$673$	183.435	−	183.435i	0.272563	−	0.272563i	0.830131	+	0.557568i	$0.188265\pi$
$674$	759.782	−	438.660i	1.12727	−	0.650831i
$675$	−0.559207	+	129.903i	−0.000828455	+	0.192448i
$676$	−188.740	+	326.907i	−0.279201	+	0.483591i
$677$	276.933	−	1033.53i	0.409059	−	1.52663i	−0.387386	−	0.921917i	$-0.626622\pi$
$677$	276.933	−	1033.53i	0.409059	−	1.52663i	0.796445	−	0.604711i	$-0.206711\pi$
$678$	171.398	−	171.398i	0.252799	−	0.252799i
$679$	−521.518	−	189.798i	−0.768068	−	0.279526i
$680$	194.245	+	254.276i	0.285654	+	0.373935i
$681$	−149.518	−	258.973i	−0.219557	−	0.380283i
$682$	−1513.32	+	405.493i	−2.21895	+	0.594565i
$683$	−84.2049	−	314.257i	−0.123287	−	0.460113i	0.876486	−	0.481427i	$-0.159882\pi$
$683$	−84.2049	−	314.257i	−0.123287	−	0.460113i	−0.999773	+	0.0213146i	$0.993215\pi$
$684$	89.2563	−	51.5322i	0.130492	−	0.0753394i
$685$	−53.3153	+	398.342i	−0.0778325	+	0.581522i
$686$	−420.111	−	242.497i	−0.612407	−	0.353494i
$687$	25.7265	+	25.7265i	0.0374475	+	0.0374475i
$688$	80.2182	+	21.4944i	0.116596	+	0.0312418i
$689$	68.1269	+	39.3331i	0.0988780	+	0.0570872i
$690$	−156.870	+	203.529i	−0.227348	+	0.294969i
$691$	−391.517	−	678.127i	−0.566595	−	0.981371i	−0.996899	−	0.0786873i	$-0.974927\pi$
$691$	−391.517	−	678.127i	−0.566595	−	0.981371i	0.430304	−	0.902684i	$-0.358406\pi$
$692$	−283.153	−	283.153i	−0.409181	−	0.409181i
$693$	177.229	+	380.036i	0.255742	+	0.548393i
$694$			646.642i			0.931760i
$695$	−69.8167	−	29.0953i	−0.100456	−	0.0418637i
$696$	−56.8272	+	98.4277i	−0.0816483	+	0.141419i
$697$	472.729	−	126.667i	0.678233	−	0.181732i
$698$	96.0873	+	25.7465i	0.137661	+	0.0368861i
$699$		−	347.264i		−	0.496801i
$700$	−223.828	−	269.074i	−0.319755	−	0.384392i
$701$	−451.488			−0.644063			−0.322031	−	0.946729i	$-0.604366\pi$
$701$	−451.488			−0.644063			−0.322031	+	0.946729i	$0.604366\pi$
$702$	−35.9730	+	134.253i	−0.0512436	+	0.191244i
$703$	102.578	+	382.825i	0.145914	+	0.544559i
$704$	138.343	+	79.8724i	0.196510	+	0.113455i
$705$	−252.322	+	605.471i	−0.357904	+	0.858824i
$706$	−235.918			−0.334162
$707$	68.8699	−	787.481i	0.0974114	−	1.11384i
$708$	75.7737	−	75.7737i	0.107025	−	0.107025i
$709$	−389.602	+	224.937i	−0.549509	+	0.317259i	−0.748924	−	0.662656i	$-0.769429\pi$
$709$	−389.602	+	224.937i	−0.549509	+	0.317259i	0.199415	+	0.979915i	$0.436096\pi$
$710$	−66.6122	−	51.3415i	−0.0938200	−	0.0723120i
$711$	113.546	−	196.668i	0.159699	−	0.276607i
$712$	105.361	−	393.214i	0.147979	−	0.552267i
$713$	823.101	−	823.101i	1.15442	−	1.15442i
$714$	−297.183	+	249.383i	−0.416223	+	0.349275i
$715$	−1871.69	−	250.513i	−2.61775	−	0.350368i
$716$	−120.088	−	207.998i	−0.167720	−	0.290500i
$717$	−473.093	+	126.765i	−0.659823	+	0.176799i
$718$	−188.916	−	705.045i	−0.263115	−	0.981957i
$719$	−825.620	+	476.672i	−1.14829	+	0.662965i	−0.948470	−	0.316868i	$-0.897369\pi$
$719$	−825.620	+	476.672i	−1.14829	+	0.662965i	−0.199820	+	0.979833i	$0.564036\pi$
$720$	−47.6797	+	36.4231i	−0.0662218	+	0.0505877i
$721$	−1356.57	+	239.246i	−1.88152	+	0.331825i
$722$	−65.9374	−	65.9374i	−0.0913260	−	0.0913260i
$723$	152.495	+	40.8610i	0.210920	+	0.0565159i
$724$	−377.293	−	217.830i	−0.521123	−	0.300871i
$725$	411.877	−	408.346i	0.568106	−	0.563236i
$726$	340.142	+	589.143i	0.468515	+	0.811492i
$727$	438.595	+	438.595i	0.603295	+	0.603295i	0.941185	−	0.337890i	$-0.109713\pi$
$727$	438.595	+	438.595i	0.603295	+	0.603295i	−0.337890	+	0.941185i	$0.609713\pi$
$728$	−158.272	−	339.388i	−0.217407	−	0.466192i
$729$			27.0000i			0.0370370i
$730$	59.3860	−	142.502i	0.0813508	−	0.195209i
$731$	−234.881	+	406.825i	−0.321314	+	0.556532i
$732$	−11.7672	+	3.15302i	−0.0160754	+	0.00430740i
$733$	734.941	+	196.927i	1.00265	+	0.268659i	0.722554	−	0.691314i	$-0.242968\pi$
$733$	734.941	+	196.927i	1.00265	+	0.268659i	0.280093	+	0.959973i	$0.409635\pi$
$734$		−	711.808i		−	0.969766i
$735$	313.463	−	286.035i	0.426481	−	0.389163i
$736$	−118.688			−0.161261
$737$	15.2618	−	56.9578i	0.0207080	−	0.0772833i
$738$	23.7516	+	88.6421i	0.0321837	+	0.120111i
$739$	557.758	+	322.022i	0.754747	+	0.435754i	0.827407	−	0.561603i	$-0.189815\pi$
$739$	557.758	+	322.022i	0.754747	+	0.435754i	−0.0726593	+	0.997357i	$0.523149\pi$
$740$	−87.8365	−	213.354i	−0.118698	−	0.288316i
$741$	−562.732			−0.759422
$742$	−37.3153	+	17.4019i	−0.0502901	+	0.0234527i
$743$	−166.104	+	166.104i	−0.223558	+	0.223558i	−0.809995	−	0.586437i	$-0.800530\pi$
$743$	−166.104	+	166.104i	−0.223558	+	0.223558i	0.586437	+	0.809995i	$0.300530\pi$
$744$	235.381	−	135.897i	0.316373	−	0.182658i
$745$	21.1276	+	163.194i	0.0283592	+	0.219052i
$746$	272.063	−	471.227i	0.364696	−	0.631672i
$747$	−31.0606	+	115.920i	−0.0415805	+	0.155180i
$748$	−638.939	+	638.939i	−0.854197	+	0.854197i
$749$	−197.996	−	1122.68i	−0.264347	−	1.49890i
$750$	283.630	−	115.343i	0.378173	−	0.153791i
$751$	560.910	+	971.525i	0.746884	+	1.29364i	0.949309	+	0.314344i	$0.101785\pi$
$751$	560.910	+	971.525i	0.746884	+	1.29364i	−0.202425	+	0.979298i	$0.564882\pi$
$752$	−292.644	+	78.4136i	−0.389154	+	0.104273i
$753$	124.981	+	466.435i	0.165977	+	0.619436i
$754$	537.416	−	310.277i	0.712753	−	0.411508i
$755$	863.127	+	1129.88i	1.14321	+	1.49652i
$756$	−46.7621	−	55.7253i	−0.0618547	−	0.0737106i
$757$	646.859	+	646.859i	0.854504	+	0.854504i	0.990684	−	0.136180i	$-0.0434827\pi$
$757$	646.859	+	646.859i	0.854504	+	0.854504i	−0.136180	+	0.990684i	$0.543483\pi$
$758$	−481.673	−	129.064i	−0.635452	−	0.170269i
$759$	−628.435	−	362.827i	−0.827977	−	0.478033i
$760$	−192.407	−	148.298i	−0.253167	−	0.195129i
$761$	273.840	+	474.305i	0.359842	+	0.623265i	0.987934	−	0.154874i	$-0.0494971\pi$
$761$	273.840	+	474.305i	0.359842	+	0.623265i	−0.628092	+	0.778139i	$0.716164\pi$
$762$	105.650	+	105.650i	0.138648	+	0.138648i
$763$	408.864	+	35.7575i	0.535863	+	0.0468644i
$764$			224.666i			0.294066i
$765$	−129.204	−	313.834i	−0.168894	−	0.410241i
$766$	42.8143	−	74.1565i	0.0558933	−	0.0968101i
$767$	−565.159	+	151.434i	−0.736843	+	0.197437i
$768$	−26.7685	−	7.17260i	−0.0348548	−	0.00933933i
$769$			991.204i			1.28895i	0.764624	+	0.644476i	$0.222925\pi$
$769$			991.204i			1.28895i	−0.764624	+	0.644476i	$0.777075\pi$
$770$	669.277	−	727.286i	0.869190	−	0.944527i
$771$	−167.902			−0.217772
$772$	2.99853	−	11.1907i	0.00388410	−	0.0144957i
$773$	−97.0389	−	362.154i	−0.125535	−	0.468505i	0.874323	−	0.485345i	$-0.161306\pi$
$773$	−97.0389	−	362.154i	−0.125535	−	0.468505i	−0.999858	+	0.0168403i	$0.994639\pi$
$774$	−76.2844	−	44.0428i	−0.0985587	−	0.0569029i
$775$	−1341.27	+	353.211i	−1.73067	+	0.455756i
$776$	224.246			0.288977
$777$	253.529	−	118.232i	0.326292	−	0.152165i
$778$	−719.653	+	719.653i	−0.925004	+	0.925004i
$779$	−321.772	+	185.775i	−0.413057	+	0.238479i
$780$	324.889	−	42.0612i	0.416524	−	0.0539247i
$781$	118.748	−	205.678i	0.152047	−	0.263352i
$782$	173.761	−	648.484i	0.222200	−	0.829263i
$783$	85.2409	−	85.2409i	0.108864	−	0.108864i
$784$	193.025	+	34.0225i	0.246205	+	0.0433960i
$785$	−117.242	+	875.966i	−0.149353	+	1.11588i
$786$	71.7901	+	124.344i	0.0913360	+	0.158199i
$787$	−164.417	+	44.0553i	−0.208916	+	0.0559788i	−0.361759	−	0.932272i	$-0.617824\pi$
$787$	−164.417	+	44.0553i	−0.208916	+	0.0559788i	0.152843	+	0.988250i	$0.451157\pi$
$788$	29.5067	+	110.120i	0.0374450	+	0.139747i
$789$	312.992	−	180.706i	0.396694	−	0.229031i
$790$	−530.530	−	71.0077i	−0.671558	−	0.0898832i
$791$	236.895	−	650.929i	0.299488	−	0.822919i
$792$	−119.809	−	119.809i	−0.151273	−	0.151273i
$793$	64.2491	+	17.2155i	0.0810203	+	0.0217093i
$794$	−118.963	−	68.6834i	−0.149828	−	0.0865030i
$795$	−4.62458	−	35.7212i	−0.00581709	−	0.0449323i
$796$	−98.8197	−	171.161i	−0.124145	−	0.215026i
$797$	−410.228	−	410.228i	−0.514715	−	0.514715i	0.401253	−	0.915967i	$-0.368575\pi$
$797$	−410.228	−	410.228i	−0.514715	−	0.514715i	−0.915967	+	0.401253i	$0.868575\pi$
$798$	168.928	−	241.271i	0.211689	−	0.302345i
$799$		−	1713.73i		−	2.14485i
$800$	122.169	+	71.2372i	0.152711	+	0.0890466i
$801$	−215.889	+	373.932i	−0.269525	+	0.466831i
$802$	204.182	−	54.7105i	0.254591	−	0.0682175i
$803$	421.105	+	112.835i	0.524415	+	0.140516i
$804$			10.2297i			0.0127235i
$805$	−160.461	+	716.600i	−0.199330	+	0.890186i
$806$	−1484.00			−1.84119
$807$	92.0960	−	343.707i	0.114121	−	0.425907i
$808$	82.6681	+	308.522i	0.102312	+	0.381834i
$809$	−870.428	−	502.542i	−1.07593	−	0.621189i	−0.146135	−	0.989265i	$-0.546683\pi$
$809$	−870.428	−	502.542i	−1.07593	−	0.621189i	−0.929796	+	0.368075i	$0.880017\pi$
$810$	58.8476	−	24.2272i	0.0726514	−	0.0299101i
$811$	971.608			1.19804			0.599018	−	0.800735i	$-0.295558\pi$
$811$	971.608			1.19804			0.599018	+	0.800735i	$0.295558\pi$
$812$	−28.2972	+	323.560i	−0.0348488	+	0.398473i
$813$	135.387	−	135.387i	0.166528	−	0.166528i
$814$	564.263	−	325.777i	0.693198	−	0.400218i
$815$	−229.353	+	297.570i	−0.281415	+	0.365117i
$816$	78.3788	−	135.756i	0.0960525	−	0.166368i
$817$	92.3044	−	344.485i	0.112980	−	0.421646i
$818$	365.206	−	365.206i	0.446462	−	0.446462i
$819$	68.9848	+	391.158i	0.0842305	+	0.477604i
$820$	171.887	−	131.307i	0.209618	−	0.160130i
$821$	51.5972	+	89.3690i	0.0628468	+	0.108854i	0.895737	−	0.444585i	$-0.146649\pi$
$821$	51.5972	+	89.3690i	0.0628468	+	0.108854i	−0.832890	+	0.553439i	$0.813315\pi$
$822$	190.178	−	50.9582i	0.231361	−	0.0619929i
$823$	−297.701	−	1111.03i	−0.361726	−	1.34998i	−0.871805	−	0.489853i	$-0.837050\pi$
$823$	−297.701	−	1111.03i	−0.361726	−	1.34998i	0.510079	−	0.860128i	$-0.329616\pi$
$824$	482.028	−	278.299i	0.584985	−	0.337741i
$825$	429.095	+	750.658i	0.520115	+	0.909888i
$826$	104.729	−	287.771i	0.126791	−	0.348391i
$827$	−87.7582	−	87.7582i	−0.106116	−	0.106116i	0.652055	−	0.758172i	$-0.273907\pi$
$827$	−87.7582	−	87.7582i	−0.106116	−	0.106116i	−0.758172	+	0.652055i	$0.773907\pi$
$828$	121.598	+	32.5822i	0.146858	+	0.0393504i
$829$	201.887	+	116.559i	0.243530	+	0.140602i	0.616798	−	0.787121i	$-0.288429\pi$
$829$	201.887	+	116.559i	0.243530	+	0.140602i	−0.373268	+	0.927724i	$0.621763\pi$
$830$	280.523	−	36.3174i	0.337979	−	0.0437559i
$831$	−61.0208	−	105.691i	−0.0734306	−	0.127186i
$832$	106.994	+	106.994i	0.128598	+	0.128598i
$833$	−468.481	+	1004.83i	−0.562402	+	1.20628i
$834$			37.0543i			0.0444296i
$835$	755.220	−	310.920i	0.904455	−	0.372359i
$836$	343.000	−	594.093i	0.410287	−	0.710638i
$837$	−278.459	+	74.6129i	−0.332687	+	0.0891433i
$838$	510.839	+	136.879i	0.609594	+	0.163340i
$839$			1438.36i			1.71438i	0.515002	+	0.857189i	$0.327791\pi$
$839$			1438.36i			1.71438i	−0.515002	+	0.857189i	$0.672209\pi$
$840$	−79.4956	+	151.922i	−0.0946377	+	0.180860i
$841$	302.777			0.360021
$842$	−151.574	+	565.683i	−0.180017	+	0.671833i
$843$	77.3872	+	288.813i	0.0917997	+	0.342601i
$844$	−596.429	−	344.348i	−0.706669	−	0.407996i
$845$	−871.086	−	363.014i	−1.03087	−	0.429603i
$846$	321.345			0.379841
$847$	1592.53	+	1115.02i	1.88020	+	1.31644i
$848$	11.7638	−	11.7638i	0.0138725	−	0.0138725i
$849$	−42.2598	+	24.3987i	−0.0497759	+	0.0287381i
$850$	−568.080	+	563.210i	−0.668330	+	0.662600i
$851$	−242.048	+	419.239i	−0.284428	+	0.492643i
$852$	−10.6637	+	39.7974i	−0.0125161	+	0.0467106i
$853$	−878.537	+	878.537i	−1.02994	+	1.02994i	−0.0304000	+	0.999538i	$0.509678\pi$
$853$	−878.537	+	878.537i	−1.02994	+	1.02994i	−0.999538	+	0.0304000i	$0.990322\pi$
$854$	−26.6682	+	22.3788i	−0.0312275	+	0.0262047i
$855$	156.414	+	204.753i	0.182940	+	0.239477i
$856$	230.315	+	398.918i	0.269060	+	0.466026i
$857$	81.5467	−	21.8504i	0.0951537	−	0.0254964i	−0.210928	−	0.977502i	$-0.567649\pi$
$857$	81.5467	−	21.8504i	0.0951537	−	0.0254964i	0.306082	+	0.952005i	$0.400982\pi$
$858$	239.438	+	893.593i	0.279065	+	1.04148i
$859$	774.281	−	447.031i	0.901375	−	0.520409i	0.0237288	−	0.999718i	$-0.492446\pi$
$859$	774.281	−	447.031i	0.901375	−	0.520409i	0.877646	+	0.479309i	$0.159113\pi$
$860$	−27.5428	+	205.785i	−0.0320265	+	0.239285i
$861$	168.579	+	200.891i	0.195794	+	0.233323i
$862$	−517.506	−	517.506i	−0.600355	−	0.600355i
$863$	1038.02	+	278.137i	1.20281	+	0.322291i	0.803935	−	0.594717i	$-0.202736\pi$
$863$	1038.02	+	278.137i	1.20281	+	0.322291i	0.398870	+	0.917008i	$0.369403\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$	611.138	−	792.911i	0.706518	−	0.916660i
$866$	−28.4380	−	49.2561i	−0.0328383	−	0.0568777i
$867$	273.040	+	273.040i	0.314925	+	0.314925i
$868$	445.487	−	636.265i	0.513234	−	0.733025i
$869$		−	1511.53i		−	1.73939i
$870$	−262.273	−	109.299i	−0.301463	−	0.125631i
$871$	27.9272	−	48.3712i	0.0320633	−	0.0555353i
$872$	−160.186	+	42.9216i	−0.183699	+	0.0492221i
$873$	−229.745	−	61.5599i	−0.263167	−	0.0705153i
$874$			509.688i			0.583167i
$875$	595.274	−	641.306i	0.680313	−	0.732922i
$876$	−75.6311			−0.0863369
$877$	−287.701	+	1073.72i	−0.328051	+	1.22430i	0.583157	+	0.812359i	$0.301817\pi$
$877$	−287.701	+	1073.72i	−0.328051	+	1.22430i	−0.911209	+	0.411945i	$0.864849\pi$
$878$	102.253	+	381.613i	0.116461	+	0.434639i
$879$	−167.281	−	96.5795i	−0.190308	−	0.109874i
$880$	−153.623	+	368.633i	−0.174572	+	0.418901i
$881$	−258.843			−0.293805			−0.146903	−	0.989151i	$-0.546930\pi$
$881$	−258.843			−0.293805			−0.146903	+	0.989151i	$0.546930\pi$
$882$	−188.417	−	87.8456i	−0.213625	−	0.0995982i
$883$	814.683	−	814.683i	0.922631	−	0.922631i	−0.0745837	−	0.997215i	$-0.523763\pi$
$883$	814.683	−	814.683i	0.922631	−	0.922631i	0.997215	+	0.0745837i	$0.0237628\pi$
$884$	−741.229	+	427.949i	−0.838495	+	0.484105i
$885$	212.188	+	163.545i	0.239761	+	0.184796i
$886$	−415.802	+	720.190i	−0.469303	+	0.812856i
$887$	−135.921	+	507.265i	−0.153237	+	0.571888i	0.846013	+	0.533163i	$0.178997\pi$
$887$	−135.921	+	507.265i	−0.153237	+	0.571888i	−0.999250	+	0.0387258i	$0.987670\pi$
$888$	−79.9263	+	79.9263i	−0.0900071	+	0.0900071i
$889$	401.234	+	146.022i	0.451332	+	0.164255i
$890$	1008.72	+	135.010i	1.13339	+	0.151696i
$891$	89.8564	+	155.636i	0.100849	+	0.174676i
$892$	−95.2996	+	25.5355i	−0.106838	+	0.0286272i
$893$	336.735	+	1256.71i	0.377083	+	1.40729i
$894$	69.8151	−	40.3078i	0.0780929	−	0.0450870i
$895$	477.145	−	364.497i	0.533123	−	0.407259i
$896$	−77.9923	+	13.7548i	−0.0870450	+	0.0153513i
$897$	−486.029	−	486.029i	−0.541838	−	0.541838i
$898$	−704.754	−	188.838i	−0.784805	−	0.210288i
$899$	1114.67	+	643.557i	1.23990	+	0.715858i
$900$	−105.608	−	106.522i	−0.117343	−	0.118357i
$901$	47.0525	+	81.4972i	0.0522225	+	0.0904520i
$902$	431.914	+	431.914i	0.478840	+	0.478840i
$903$	−250.769	−	21.9312i	−0.277706	−	0.0242870i
$904$			279.891i			0.309614i
$905$	418.965	−	1005.35i	0.462945	−	1.11088i
$906$	348.276	−	603.232i	0.384411	−	0.665819i
$907$	−369.601	+	99.0344i	−0.407499	+	0.109189i	−0.456745	−	0.889598i	$-0.650985\pi$
$907$	−369.601	+	99.0344i	−0.407499	+	0.109189i	0.0492462	+	0.998787i	$0.484318\pi$
$908$	333.531	+	89.3695i	0.367325	+	0.0984246i
$909$		−	338.780i		−	0.372696i
$910$	790.644	−	501.343i	0.868840	−	0.550926i
$911$	505.532			0.554920			0.277460	−	0.960737i	$-0.410507\pi$
$911$	505.532			0.554920			0.277460	+	0.960737i	$0.410507\pi$
$912$	−30.8016	+	114.953i	−0.0337737	+	0.126045i
$913$	206.740	+	771.566i	0.226441	+	0.845088i
$914$	356.303	+	205.712i	0.389829	+	0.225068i
$915$	−11.5943	−	28.1625i	−0.0126714	−	0.0307787i
$916$	−42.0111			−0.0458637
$917$	336.118	+	235.336i	0.366540	+	0.256637i
$918$	−117.568	+	117.568i	−0.128070	+	0.128070i
$919$	90.0279	−	51.9776i	0.0979629	−	0.0565589i	−0.450218	−	0.892919i	$-0.648654\pi$
$919$	90.0279	−	51.9776i	0.0979629	−	0.0565589i	0.548181	+	0.836360i	$0.315320\pi$
$920$	−38.0965	−	294.265i	−0.0414092	−	0.319853i
$921$	−26.7482	+	46.3293i	−0.0290426	+	0.0503032i
$922$	−157.856	+	589.127i	−0.171210	+	0.638966i
$923$	159.070	−	159.070i	0.172341	−	0.172341i
$924$	−455.005	−	165.592i	−0.492430	−	0.179212i
$925$	500.776	−	286.256i	0.541380	−	0.309466i
$926$	81.4930	+	141.150i	0.0880054	+	0.152430i
$927$	−570.245	+	152.797i	−0.615151	+	0.164829i
$928$	−33.9666	−	126.765i	−0.0366020	−	0.136600i
$929$	−3.46379	+	1.99982i	−0.00372852	+	0.00215266i	−0.501863	−	0.864947i	$-0.667352\pi$
$929$	−3.46379	+	1.99982i	−0.00372852	+	0.00215266i	0.498135	+	0.867100i	$0.334019\pi$
$930$	412.485	+	539.963i	0.443532	+	0.580605i
$931$	146.104	−	828.914i	0.156933	−	0.890348i
$932$	283.540	+	283.540i	0.304227	+	0.304227i
$933$	−284.741	−	76.2960i	−0.305188	−	0.0817750i
$934$	270.095	+	155.940i	0.289181	+	0.166959i
$935$	−1789.21	−	1379.04i	−1.91360	−	1.47491i
$936$	−80.2454	−	138.989i	−0.0857323	−	0.148493i
$937$	−441.544	−	441.544i	−0.471232	−	0.471232i	0.431081	−	0.902313i	$-0.358132\pi$
$937$	−441.544	−	441.544i	−0.471232	−	0.471232i	−0.902313	+	0.431081i	$0.858132\pi$
$938$	12.3556	+	26.4945i	0.0131723	+	0.0282457i
$939$		−	679.571i		−	0.723718i
$940$	−288.344	−	700.385i	−0.306749	−	0.745090i
$941$	586.555	−	1015.94i	0.623332	−	1.07964i	−0.365529	−	0.930800i	$-0.619112\pi$
$941$	586.555	−	1015.94i	0.623332	−	1.07964i	0.988861	−	0.148842i	$-0.0475546\pi$
$942$	418.208	−	112.058i	0.443958	−	0.118958i
$943$	−438.365	−	117.460i	−0.464863	−	0.124560i
$944$			123.738i			0.131078i
$945$	123.150	−	133.824i	0.130318	−	0.141613i
$946$	−586.301			−0.619768
$947$	306.937	−	1145.51i	0.324115	−	1.20962i	−0.591083	−	0.806611i	$-0.701299\pi$
$947$	306.937	−	1145.51i	0.324115	−	1.20962i	0.915198	−	0.403004i	$-0.132034\pi$
$948$	67.8684	+	253.288i	0.0715912	+	0.267182i
$949$	357.622	+	206.473i	0.376841	+	0.217569i
$950$	305.917	−	524.636i	0.322018	−	0.552248i
$951$	247.153			0.259887
$952$	39.0288	−	446.269i	0.0409967	−	0.468770i
$953$	−788.797	+	788.797i	−0.827699	+	0.827699i	−0.987198	−	0.159499i	$-0.949012\pi$
$953$	−788.797	+	788.797i	−0.827699	+	0.827699i	0.159499	+	0.987198i	$0.449012\pi$
$954$	−15.2817	+	8.82288i	−0.0160185	+	0.00924831i
$955$	−557.017	+	72.1133i	−0.583264	+	0.0755113i
$956$	282.776	−	489.782i	0.295791	−	0.512324i
$957$	207.670	−	775.036i	0.217001	−	0.809860i
$958$	372.435	−	372.435i	0.388763	−	0.388763i
$959$	431.005	−	361.680i	0.449432	−	0.377143i
$960$	9.19095	−	68.6697i	0.00957390	−	0.0715309i
$961$	−1058.51	−	1833.39i	−1.10147	−	1.90780i
$962$	596.131	−	159.733i	0.619679	−	0.166042i
$963$	−126.452	−	471.925i	−0.131310	−	0.490057i
$964$	−157.875	+	91.1491i	−0.163771	+	0.0945530i
$965$	28.7075	+	3.84230i	0.0297487	+	0.00398166i
$966$	354.287	−	62.4822i	0.366757	−	0.0646814i
$967$	437.038	+	437.038i	0.451953	+	0.451953i	0.896002	−	0.444050i	$-0.146459\pi$
$967$	437.038	+	437.038i	0.451953	+	0.451953i	−0.444050	+	0.896002i	$0.646459\pi$
$968$	−758.758	−	203.309i	−0.783841	−	0.210030i
$969$	−582.984	−	336.586i	−0.601634	−	0.347354i
$970$	71.9785	+	555.976i	0.0742047	+	0.573171i
$971$	5.97107	+	10.3422i	0.00614940	+	0.0106511i	0.869084	−	0.494665i	$-0.164709\pi$
$971$	5.97107	+	10.3422i	0.00614940	+	0.0106511i	−0.862934	+	0.505316i	$0.831376\pi$
$972$	−22.0454	−	22.0454i	−0.0226805	−	0.0226805i
$973$	44.7548	+	95.9687i	0.0459967	+	0.0986318i
$974$			519.307i			0.533170i
$975$	208.566	+	791.999i	0.213913	+	0.812307i
$976$	7.03346	−	12.1823i	0.00720642	−	0.0124819i
$977$	−1368.21	+	366.611i	−1.40042	+	0.375242i	−0.878496	−	0.477749i	$-0.841453\pi$
$977$	−1368.21	+	366.611i	−1.40042	+	0.375242i	−0.521926	+	0.852991i	$0.674786\pi$
$978$	177.783	+	47.6369i	0.181783	+	0.0487085i
$979$			2873.93i			2.93558i
$980$	−22.3953	+	489.488i	−0.0228523	+	0.499477i
$981$	175.896			0.179303
$982$	−3.18952	+	11.9035i	−0.00324799	+	0.0121216i
$983$	−270.445	−	1009.31i	−0.275122	−	1.02677i	−0.955760	−	0.294149i	$-0.904964\pi$
$983$	−270.445	−	1009.31i	−0.275122	−	1.02677i	0.680638	−	0.732620i	$-0.261703\pi$
$984$	−91.7691	−	52.9829i	−0.0932613	−	0.0538444i
$985$	−263.551	+	108.503i	−0.267565	+	0.110155i
$986$	742.342			0.752882
$987$	832.268	−	388.126i	0.843230	−	0.393238i
$988$	459.469	−	459.469i	0.465049	−	0.465049i
$989$	377.252	−	217.807i	0.381448	−	0.220229i
$990$	258.586	−	335.499i	0.261198	−	0.338887i
$991$	−305.146	+	528.528i	−0.307917	+	0.533328i	−0.977907	−	0.209042i	$-0.932965\pi$
$991$	−305.146	+	528.528i	−0.307917	+	0.533328i	0.669989	+	0.742371i	$0.266299\pi$
$992$	−81.2282	+	303.148i	−0.0818833	+	0.305593i
$993$	28.2143	−	28.2143i	0.0284132	−	0.0284132i
$994$	20.4496	+	115.953i	0.0205730	+	0.116653i
$995$	392.641	−	299.944i	0.394614	−	0.301451i
$996$	−69.2872	−	120.009i	−0.0695655	−	0.120491i
$997$	1323.34	−	354.588i	1.32732	−	0.355655i	0.475605	−	0.879659i	$-0.342229\pi$
$997$	1323.34	−	354.588i	1.32732	−	0.355655i	0.851716	+	0.524004i	$0.175562\pi$
$998$	98.6264	+	368.079i	0.0988240	+	0.368816i
$999$	103.827	−	59.9447i	0.103931	−	0.0600047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.v.b.67.8	yes	32
5.3	odd	4	inner	210.3.v.b.193.1	yes	32
7.2	even	3	inner	210.3.v.b.37.1	✓	32
35.23	odd	12	inner	210.3.v.b.163.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.v.b.37.1	✓	32	7.2	even	3	inner
210.3.v.b.67.8	yes	32	1.1	even	1	trivial
210.3.v.b.163.8	yes	32	35.23	odd	12	inner
210.3.v.b.193.1	yes	32	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 1.36603i) q^{2} +(0.448288 + 1.67303i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.92336 - 4.61527i) q^{5} -2.44949 q^{6} +(-6.34406 + 2.95853i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(-0.366025 + 1.36603i) q^{2} +(0.448288 + 1.67303i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.92336 - 4.61527i) q^{5} -2.44949 q^{6} +(-6.34406 + 2.95853i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(5.60058 + 4.31666i) q^{10} +(-9.98405 + 17.2929i) q^{11} +(0.896575 - 3.34607i) q^{12} +(-13.3742 + 13.3742i) q^{13} +(-1.71935 - 9.74904i) q^{14} +(8.58371 + 1.14887i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-21.8551 + 5.85604i) q^{17} +(-1.09808 - 4.09808i) q^{18} +(14.8761 - 8.58869i) q^{19} +(-7.94662 + 6.07052i) q^{20} +(-7.79369 - 9.28754i) q^{21} +(-19.9681 - 19.9681i) q^{22} +(20.2664 + 5.43036i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-17.6014 - 17.7536i) q^{25} +(-13.3742 - 23.1648i) q^{26} +(-3.67423 - 3.67423i) q^{27} +(13.9468 + 1.21973i) q^{28} +23.1996i q^{29} +(-4.71124 + 11.3051i) q^{30} +(27.7400 - 48.0470i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(-33.4073 - 8.95145i) q^{33} -31.9980i q^{34} +(1.45255 + 34.9698i) q^{35} +6.00000 q^{36} +(-5.97166 + 22.2866i) q^{37} +(6.28736 + 23.4647i) q^{38} +(-28.3710 - 16.3800i) q^{39} +(-5.38383 - 13.0772i) q^{40} -21.6302 q^{41} +(15.5397 - 7.24690i) q^{42} +(14.6809 - 14.6809i) q^{43} +(34.5858 - 19.9681i) q^{44} +(1.92588 + 14.8759i) q^{45} +(-14.8360 + 25.6967i) q^{46} +(-19.6034 + 73.1609i) q^{47} +(-4.89898 + 4.89898i) q^{48} +(31.4942 - 37.5382i) q^{49} +(30.6944 - 17.5457i) q^{50} +(-19.5947 - 33.9390i) q^{51} +(36.5391 - 9.79062i) q^{52} +(-1.07647 - 4.01743i) q^{53} +(6.36396 - 3.67423i) q^{54} +(60.6084 + 79.3394i) q^{55} +(-6.77105 + 18.6052i) q^{56} +(21.0379 + 21.0379i) q^{57} +(-31.6913 - 8.49165i) q^{58} +(26.7900 + 15.4672i) q^{59} +(-13.7186 - 10.5736i) q^{60} +(-1.75837 - 3.04558i) q^{61} +(55.4799 + 55.4799i) q^{62} +(12.0445 - 17.2026i) q^{63} -8.00000i q^{64} +(36.0023 + 87.4491i) q^{65} +(24.4558 - 42.3587i) q^{66} +(-2.85244 + 0.764309i) q^{67} +(43.7101 + 11.7121i) q^{68} +36.3407i q^{69} +(-48.3014 - 10.8156i) q^{70} -11.8938 q^{71} +(-2.19615 + 8.19615i) q^{72} +(-5.65075 - 21.0889i) q^{73} +(-28.2582 - 16.3149i) q^{74} +(21.8119 - 37.4065i) q^{75} -34.3548 q^{76} +(12.1778 - 139.245i) q^{77} +(32.7600 - 32.7600i) q^{78} +(-65.5559 + 37.8487i) q^{79} +(19.8345 - 2.56784i) q^{80} +(4.50000 - 7.79423i) q^{81} +(7.91720 - 29.5474i) q^{82} +(28.2864 - 28.2864i) q^{83} +(4.21152 + 23.8802i) q^{84} +(-15.0078 + 112.130i) q^{85} +(14.6809 + 25.4281i) q^{86} +(-38.8137 + 10.4001i) q^{87} +(14.6177 + 54.5539i) q^{88} +(124.644 - 71.9632i) q^{89} +(-21.0257 - 2.81414i) q^{90} +(45.2788 - 124.415i) q^{91} +(-29.6720 - 29.6720i) q^{92} +(92.8197 + 24.8710i) q^{93} +(-92.7643 - 53.5575i) q^{94} +(-11.0272 - 85.1761i) q^{95} +(-4.89898 - 8.48528i) q^{96} +(56.0616 + 56.0616i) q^{97} +(39.7505 + 56.7618i) q^{98} -59.9043i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8}+O(q^{10}) \) 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8	\( 32 q + 16 q^{2} - 8 q^{5} + 24 q^{7} + 64 q^{8} + 12 q^{10} + 16 q^{11} + 32 q^{13} + 48 q^{15} + 64 q^{16} - 56 q^{17} + 48 q^{18} + 16 q^{20} + 32 q^{22} - 28 q^{25} + 32 q^{26} + 72 q^{28} + 36 q^{30} + 112 q^{31} - 64 q^{32} + 12 q^{33} - 112 q^{35} + 192 q^{36} - 52 q^{37} - 8 q^{40} - 336 q^{41} - 312 q^{43} + 12 q^{45} - 212 q^{47} + 96 q^{50} - 144 q^{51} - 32 q^{52} - 96 q^{53} - 312 q^{55} + 96 q^{56} + 48 q^{57} - 96 q^{58} - 24 q^{60} + 216 q^{61} + 224 q^{62} + 36 q^{63} + 248 q^{65} - 24 q^{66} + 128 q^{67} + 112 q^{68} - 264 q^{70} - 848 q^{71} + 96 q^{72} + 84 q^{73} - 144 q^{75} - 324 q^{77} + 48 q^{78} + 32 q^{80} + 144 q^{81} - 168 q^{82} - 416 q^{83} + 536 q^{85} - 312 q^{86} - 72 q^{87} + 32 q^{88} - 24 q^{90} + 504 q^{91} + 168 q^{93} + 168 q^{95} + 488 q^{97} - 328 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 8 * q^5 + 24 * q^7 + 64 * q^8 + 12 * q^10 + 16 * q^11 + 32 * q^13 + 48 * q^15 + 64 * q^16 - 56 * q^17 + 48 * q^18 + 16 * q^20 + 32 * q^22 - 28 * q^25 + 32 * q^26 + 72 * q^28 + 36 * q^30 + 112 * q^31 - 64 * q^32 + 12 * q^33 - 112 * q^35 + 192 * q^36 - 52 * q^37 - 8 * q^40 - 336 * q^41 - 312 * q^43 + 12 * q^45 - 212 * q^47 + 96 * q^50 - 144 * q^51 - 32 * q^52 - 96 * q^53 - 312 * q^55 + 96 * q^56 + 48 * q^57 - 96 * q^58 - 24 * q^60 + 216 * q^61 + 224 * q^62 + 36 * q^63 + 248 * q^65 - 24 * q^66 + 128 * q^67 + 112 * q^68 - 264 * q^70 - 848 * q^71 + 96 * q^72 + 84 * q^73 - 144 * q^75 - 324 * q^77 + 48 * q^78 + 32 * q^80 + 144 * q^81 - 168 * q^82 - 416 * q^83 + 536 * q^85 - 312 * q^86 - 72 * q^87 + 32 * q^88 - 24 * q^90 + 504 * q^91 + 168 * q^93 + 168 * q^95 + 488 * q^97 - 328 * q^98

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