LMFDB - Embedded newform 36.3.f.c.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,3,Mod(7,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("36.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	36.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.980928951697$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 $ x^16 - 3x^15 + 7x^14 - 30x^13 + 76x^12 - 144x^11 + 424x^10 - 912x^9 + 1552x^8 - 3648x^7 + 6784x^6 - 9216x^5 + 19456x^4 - 30720x^3 + 28672x^2 - 49152*x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.2
Root			$1.84233 - 0.778342i$ of defining polynomial
Character	$\chi$	$=$	36.31
Dual form			36.3.f.c.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84233 + 0.778342i) q^{2} +(0.262217 - 2.98852i) q^{3} +(2.78837 - 2.86793i) q^{4} +(1.10093 - 1.90686i) q^{5} +(1.84300 + 5.70994i) q^{6} +(7.23844 - 4.17912i) q^{7} +(-2.90487 + 7.45397i) q^{8} +(-8.86248 - 1.56728i) q^{9} +O(q^{10})$	\(q+(-1.84233 + 0.778342i) q^{2} +(0.262217 - 2.98852i) q^{3} +(2.78837 - 2.86793i) q^{4} +(1.10093 - 1.90686i) q^{5} +(1.84300 + 5.70994i) q^{6} +(7.23844 - 4.17912i) q^{7} +(-2.90487 + 7.45397i) q^{8} +(-8.86248 - 1.56728i) q^{9} +(-0.544081 + 4.36996i) q^{10} +(-4.54769 + 2.62561i) q^{11} +(-7.83969 - 9.08511i) q^{12} +(-7.37788 + 12.7789i) q^{13} +(-10.0828 + 13.3333i) q^{14} +(-5.41000 - 3.79015i) q^{15} +(-0.450004 - 15.9937i) q^{16} +28.2789 q^{17} +(17.5475 - 4.01059i) q^{18} +19.1376i q^{19} +(-2.39894 - 8.47440i) q^{20} +(-10.5913 - 22.7281i) q^{21} +(6.33472 - 8.37689i) q^{22} +(3.16702 + 1.82848i) q^{23} +(21.5146 + 10.6358i) q^{24} +(10.0759 + 17.4520i) q^{25} +(3.64618 - 29.2854i) q^{26} +(-7.00775 + 26.0747i) q^{27} +(8.19805 - 32.4122i) q^{28} +(-12.3355 - 21.3657i) q^{29} +(12.9170 + 2.77188i) q^{30} +(-32.9674 - 19.0338i) q^{31} +(13.2776 + 29.1154i) q^{32} +(6.65419 + 14.2793i) q^{33} +(-52.0991 + 22.0106i) q^{34} -18.4036i q^{35} +(-29.2067 + 21.0468i) q^{36} -4.21977 q^{37} +(-14.8956 - 35.2578i) q^{38} +(36.2553 + 25.3998i) q^{39} +(11.0156 + 13.7454i) q^{40} +(-9.92483 + 17.1903i) q^{41} +(37.2029 + 33.6289i) q^{42} +(20.1894 - 11.6564i) q^{43} +(-5.15057 + 20.3636i) q^{44} +(-12.7455 + 15.1740i) q^{45} +(-7.25787 - 0.903640i) q^{46} +(25.8538 - 14.9267i) q^{47} +(-47.9154 - 2.84897i) q^{48} +(10.4300 - 18.0654i) q^{49} +(-32.1468 - 24.3099i) q^{50} +(7.41521 - 84.5120i) q^{51} +(16.0766 + 56.7914i) q^{52} -32.1118 q^{53} +(-7.38445 - 53.4927i) q^{54} +11.5624i q^{55} +(10.1243 + 66.0950i) q^{56} +(57.1930 + 5.01820i) q^{57} +(39.3559 + 29.7615i) q^{58} +(-7.96159 - 4.59663i) q^{59} +(-25.9549 + 4.94716i) q^{60} +(-40.8215 - 70.7049i) q^{61} +(75.5517 + 9.40656i) q^{62} +(-70.7005 + 25.6927i) q^{63} +(-47.1234 - 43.3057i) q^{64} +(16.2450 + 28.1372i) q^{65} +(-23.3734 - 21.1280i) q^{66} +(6.86179 + 3.96166i) q^{67} +(78.8519 - 81.1017i) q^{68} +(6.29489 - 8.98523i) q^{69} +(14.3243 + 33.9055i) q^{70} +62.9286i q^{71} +(37.4269 - 61.5080i) q^{72} +33.3218 q^{73} +(7.77421 - 3.28442i) q^{74} +(54.7978 - 25.5359i) q^{75} +(54.8852 + 53.3626i) q^{76} +(-21.9454 + 38.0106i) q^{77} +(-86.5639 - 18.5758i) q^{78} +(53.7133 - 31.0114i) q^{79} +(-30.9931 - 16.7497i) q^{80} +(76.0873 + 27.7800i) q^{81} +(4.90489 - 39.3951i) q^{82} +(-103.056 + 59.4995i) q^{83} +(-94.7149 - 32.9991i) q^{84} +(31.1329 - 53.9238i) q^{85} +(-28.1230 + 37.1892i) q^{86} +(-67.0864 + 31.2624i) q^{87} +(-6.36077 - 41.5254i) q^{88} -107.361 q^{89} +(11.6709 - 37.8760i) q^{90} +123.332i q^{91} +(14.0747 - 3.98430i) q^{92} +(-65.5274 + 93.5328i) q^{93} +(-36.0132 + 47.6231i) q^{94} +(36.4927 + 21.0690i) q^{95} +(90.4935 - 32.0458i) q^{96} +(1.78621 + 3.09380i) q^{97} +(-5.15457 + 41.4005i) q^{98} +(44.4189 - 16.1419i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - 5 q^{4} + 6 q^{5} + 9 q^{6} - 54 q^{8} + 18 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 - 5 * q^4 + 6 * q^5 + 9 * q^6 - 54 * q^8 + 18 * q^9	$ 16 q - 3 q^{2} - 5 q^{4} + 6 q^{5} + 9 q^{6} - 54 q^{8} + 18 q^{9} + 20 q^{10} - 36 q^{12} - 46 q^{13} - 12 q^{14} - 17 q^{16} + 12 q^{17} + 48 q^{18} + 36 q^{20} - 66 q^{21} + 33 q^{22} + 129 q^{24} - 30 q^{25} + 72 q^{26} + 12 q^{28} + 42 q^{29} + 84 q^{30} + 87 q^{32} - 168 q^{33} + 11 q^{34} - 81 q^{36} + 56 q^{37} - 99 q^{38} + 68 q^{40} + 84 q^{41} - 354 q^{42} - 222 q^{44} + 174 q^{45} - 264 q^{46} - 189 q^{48} + 58 q^{49} - 219 q^{50} + 110 q^{52} - 72 q^{53} - 105 q^{54} + 270 q^{56} + 366 q^{57} - 16 q^{58} + 432 q^{60} - 34 q^{61} + 516 q^{62} - 254 q^{64} - 30 q^{65} + 510 q^{66} + 375 q^{68} - 54 q^{69} + 150 q^{70} - 45 q^{72} + 116 q^{73} - 372 q^{74} - 15 q^{76} - 330 q^{77} - 294 q^{78} - 720 q^{80} - 102 q^{81} + 254 q^{82} - 714 q^{84} - 140 q^{85} - 273 q^{86} + 75 q^{88} - 384 q^{89} + 108 q^{90} + 258 q^{92} - 486 q^{93} + 36 q^{94} + 900 q^{96} - 148 q^{97} + 1170 q^{98}+O(q^{100}) $ 16 * q - 3 * q^2 - 5 * q^4 + 6 * q^5 + 9 * q^6 - 54 * q^8 + 18 * q^9 + 20 * q^10 - 36 * q^12 - 46 * q^13 - 12 * q^14 - 17 * q^16 + 12 * q^17 + 48 * q^18 + 36 * q^20 - 66 * q^21 + 33 * q^22 + 129 * q^24 - 30 * q^25 + 72 * q^26 + 12 * q^28 + 42 * q^29 + 84 * q^30 + 87 * q^32 - 168 * q^33 + 11 * q^34 - 81 * q^36 + 56 * q^37 - 99 * q^38 + 68 * q^40 + 84 * q^41 - 354 * q^42 - 222 * q^44 + 174 * q^45 - 264 * q^46 - 189 * q^48 + 58 * q^49 - 219 * q^50 + 110 * q^52 - 72 * q^53 - 105 * q^54 + 270 * q^56 + 366 * q^57 - 16 * q^58 + 432 * q^60 - 34 * q^61 + 516 * q^62 - 254 * q^64 - 30 * q^65 + 510 * q^66 + 375 * q^68 - 54 * q^69 + 150 * q^70 - 45 * q^72 + 116 * q^73 - 372 * q^74 - 15 * q^76 - 330 * q^77 - 294 * q^78 - 720 * q^80 - 102 * q^81 + 254 * q^82 - 714 * q^84 - 140 * q^85 - 273 * q^86 + 75 * q^88 - 384 * q^89 + 108 * q^90 + 258 * q^92 - 486 * q^93 + 36 * q^94 + 900 * q^96 - 148 * q^97 + 1170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.84233	+	0.778342i	−0.921166	+	0.389171i
$2$	−1.84233	+	0.778342i	−0.921166	+	0.389171i
$3$	0.262217	−	2.98852i	0.0874058	−	0.996173i
$3$	0.262217	−	2.98852i	0.0874058	−	0.996173i
$4$	2.78837	−	2.86793i	0.697092	−	0.716982i
$5$	1.10093	−	1.90686i	0.220185	−	0.381372i	−0.734679	−	0.678415i	$-0.762667\pi$
$5$	1.10093	−	1.90686i	0.220185	−	0.381372i	0.954864	+	0.297043i	$0.0960005\pi$
$6$	1.84300	+	5.70994i	0.307166	+	0.951656i
$7$	7.23844	−	4.17912i	1.03406	−	0.597017i	0.115917	−	0.993259i	$-0.463019\pi$
$7$	7.23844	−	4.17912i	1.03406	−	0.597017i	0.918146	+	0.396242i	$0.129686\pi$
$8$	−2.90487	+	7.45397i	−0.363109	+	0.931747i
$9$	−8.86248	−	1.56728i	−0.984720	−	0.174143i
$10$	−0.544081	+	4.36996i	−0.0544081	+	0.436996i
$11$	−4.54769	+	2.62561i	−0.413426	+	0.238692i	−0.692261	−	0.721648i	$-0.743385\pi$
$11$	−4.54769	+	2.62561i	−0.413426	+	0.238692i	0.278835	+	0.960339i	$0.410052\pi$
$12$	−7.83969	−	9.08511i	−0.653308	−	0.757092i
$13$	−7.37788	+	12.7789i	−0.567529	+	0.982990i	0.429280	+	0.903171i	$0.358767\pi$
$13$	−7.37788	+	12.7789i	−0.567529	+	0.982990i	−0.996809	+	0.0798182i	$0.974566\pi$
$14$	−10.0828	+	13.3333i	−0.720202	+	0.952379i
$15$	−5.41000	−	3.79015i	−0.360667	−	0.252676i
$16$	−0.450004	−	15.9937i	−0.0281253	−	0.999604i
$17$	28.2789			1.66346			0.831732	−	0.555178i	$-0.187350\pi$
$17$	28.2789			1.66346			0.831732	+	0.555178i	$0.187350\pi$
$18$	17.5475	−	4.01059i	0.974862	−	0.222810i
$19$			19.1376i			1.00724i	0.863925	+	0.503620i	$0.167999\pi$
$19$			19.1376i			1.00724i	−0.863925	+	0.503620i	$0.832001\pi$
$20$	−2.39894	−	8.47440i	−0.119947	−	0.423720i
$21$	−10.5913	−	22.7281i	−0.504349	−	1.08229i
$22$	6.33472	−	8.37689i	0.287942	−	0.380768i
$23$	3.16702	+	1.82848i	0.137696	+	0.0794990i	0.567266	−	0.823535i	$-0.308001\pi$
$23$	3.16702	+	1.82848i	0.137696	+	0.0794990i	−0.429569	+	0.903034i	$0.641335\pi$
$24$	21.5146	+	10.6358i	0.896443	+	0.443159i
$25$	10.0759	+	17.4520i	0.403037	+	0.698081i
$26$	3.64618	−	29.2854i	0.140238	−	1.12636i
$27$	−7.00775	+	26.0747i	−0.259546	+	0.965731i
$28$	8.19805	−	32.4122i	0.292787	−	1.15758i
$29$	−12.3355	−	21.3657i	−0.425362	−	0.736748i	0.571092	−	0.820886i	$-0.306520\pi$
$29$	−12.3355	−	21.3657i	−0.425362	−	0.736748i	−0.996454	+	0.0841375i	$0.973187\pi$
$30$	12.9170	+	2.77188i	0.430568	+	0.0923959i
$31$	−32.9674	−	19.0338i	−1.06347	−	0.613992i	−0.137077	−	0.990560i	$-0.543771\pi$
$31$	−32.9674	−	19.0338i	−1.06347	−	0.613992i	−0.926389	+	0.376568i	$0.877104\pi$
$32$	13.2776	+	29.1154i	0.414925	+	0.909856i
$33$	6.65419	+	14.2793i	0.201642	+	0.432707i
$34$	−52.0991	+	22.0106i	−1.53233	+	0.647372i
$35$		−	18.4036i		−	0.525817i
$36$	−29.2067	+	21.0468i	−0.811298	+	0.584633i
$37$	−4.21977			−0.114048			−0.0570239	−	0.998373i	$-0.518161\pi$
$37$	−4.21977			−0.114048			−0.0570239	+	0.998373i	$0.518161\pi$
$38$	−14.8956	−	35.2578i	−0.391989	−	0.927836i
$39$	36.2553	+	25.3998i	0.929622	+	0.651276i
$40$	11.0156	+	13.7454i	0.275391	+	0.343636i
$41$	−9.92483	+	17.1903i	−0.242069	+	0.419276i	−0.961303	−	0.275492i	$-0.911159\pi$
$41$	−9.92483	+	17.1903i	−0.242069	+	0.419276i	0.719235	+	0.694767i	$0.244493\pi$
$42$	37.2029	+	33.6289i	0.885784	+	0.800689i
$43$	20.1894	−	11.6564i	0.469521	−	0.271078i	−0.246518	−	0.969138i	$-0.579286\pi$
$43$	20.1894	−	11.6564i	0.469521	−	0.271078i	0.716039	+	0.698060i	$0.245953\pi$
$44$	−5.15057	+	20.3636i	−0.117058	+	0.462809i
$45$	−12.7455	+	15.1740i	−0.283234	+	0.337201i
$46$	−7.25787	−	0.903640i	−0.157780	−	0.0196444i
$47$	25.8538	−	14.9267i	0.550082	−	0.317590i	−0.199073	−	0.979985i	$-0.563793\pi$
$47$	25.8538	−	14.9267i	0.550082	−	0.317590i	0.749155	+	0.662395i	$0.230460\pi$
$48$	−47.9154	−	2.84897i	−0.998237	−	0.0593536i
$49$	10.4300	−	18.0654i	0.212858	−	0.368681i
$50$	−32.1468	−	24.3099i	−0.642937	−	0.486198i
$51$	7.41521	−	84.5120i	0.145396	−	1.65710i
$52$	16.0766	+	56.7914i	0.309165	+	1.09214i
$53$	−32.1118			−0.605883			−0.302942	−	0.953009i	$-0.597969\pi$
$53$	−32.1118			−0.605883			−0.302942	+	0.953009i	$0.597969\pi$
$54$	−7.38445	−	53.4927i	−0.136749	−	0.990606i
$55$			11.5624i			0.210225i
$56$	10.1243	+	66.0950i	0.180791	+	1.18027i
$57$	57.1930	+	5.01820i	1.00339	+	0.0880387i
$58$	39.3559	+	29.7615i	0.678550	+	0.513129i
$59$	−7.96159	−	4.59663i	−0.134942	−	0.0779089i	0.431009	−	0.902348i	$-0.358158\pi$
$59$	−7.96159	−	4.59663i	−0.134942	−	0.0779089i	−0.565951	+	0.824439i	$0.691491\pi$
$60$	−25.9549	+	4.94716i	−0.432582	+	0.0824526i
$61$	−40.8215	−	70.7049i	−0.669205	−	1.15910i	−0.978127	−	0.208009i	$-0.933302\pi$
$61$	−40.8215	−	70.7049i	−0.669205	−	1.15910i	0.308922	−	0.951087i	$-0.400032\pi$
$62$	75.5517	+	9.40656i	1.21858	+	0.151719i
$63$	−70.7005	+	25.6927i	−1.12223	+	0.407820i
$64$	−47.1234	−	43.3057i	−0.736304	−	0.676651i
$65$	16.2450	+	28.1372i	0.249923	+	0.432879i
$66$	−23.3734	−	21.1280i	−0.354143	−	0.320121i
$67$	6.86179	+	3.96166i	0.102415	+	0.0591292i	0.550333	−	0.834946i	$-0.314501\pi$
$67$	6.86179	+	3.96166i	0.102415	+	0.0591292i	−0.447918	+	0.894075i	$0.647834\pi$
$68$	78.8519	−	81.1017i	1.15959	−	1.19267i
$69$	6.29489	−	8.98523i	0.0912302	−	0.130221i
$70$	14.3243	+	33.9055i	0.204633	+	0.484364i
$71$			62.9286i			0.886318i	0.896443	+	0.443159i	$0.146142\pi$
$71$			62.9286i			0.886318i	−0.896443	+	0.443159i	$0.853858\pi$
$72$	37.4269	−	61.5080i	0.519817	−	0.854277i
$73$	33.3218			0.456463			0.228232	−	0.973607i	$-0.426706\pi$
$73$	33.3218			0.456463			0.228232	+	0.973607i	$0.426706\pi$
$74$	7.77421	−	3.28442i	0.105057	−	0.0443841i
$75$	54.7978	−	25.5359i	0.730637	−	0.340478i
$76$	54.8852	+	53.3626i	0.722173	+	0.702140i
$77$	−21.9454	+	38.0106i	−0.285006	+	0.493644i
$78$	−86.5639	−	18.5758i	−1.10979	−	0.238151i
$79$	53.7133	−	31.0114i	0.679916	−	0.392549i	−0.119908	−	0.992785i	$-0.538260\pi$
$79$	53.7133	−	31.0114i	0.679916	−	0.392549i	0.799823	+	0.600236i	$0.204927\pi$
$80$	−30.9931	−	16.7497i	−0.387414	−	0.209372i
$81$	76.0873	+	27.7800i	0.939349	+	0.342963i
$82$	4.90489	−	39.3951i	0.0598157	−	0.480429i
$83$	−103.056	+	59.4995i	−1.24164	+	0.716861i	−0.969428	−	0.245376i	$-0.921089\pi$
$83$	−103.056	+	59.4995i	−1.24164	+	0.716861i	−0.272212	+	0.962237i	$0.587755\pi$
$84$	−94.7149	−	32.9991i	−1.12756	−	0.392846i
$85$	31.1329	−	53.9238i	0.366270	−	0.634398i
$86$	−28.1230	+	37.1892i	−0.327011	+	0.432432i
$87$	−67.0864	+	31.2624i	−0.771108	+	0.359338i
$88$	−6.36077	−	41.5254i	−0.0722815	−	0.471879i
$89$	−107.361			−1.20630			−0.603152	−	0.797626i	$-0.706089\pi$
$89$	−107.361			−1.20630			−0.603152	+	0.797626i	$0.706089\pi$
$90$	11.6709	−	37.8760i	0.129676	−	0.420844i
$91$			123.332i			1.35530i
$92$	14.0747	−	3.98430i	0.152986	−	0.0433076i
$93$	−65.5274	+	93.5328i	−0.704596	+	1.00573i
$94$	−36.0132	+	47.6231i	−0.383120	+	0.506629i
$95$	36.4927	+	21.0690i	0.384133	+	0.221779i
$96$	90.4935	−	32.0458i	0.942640	−	0.333810i
$97$	1.78621	+	3.09380i	0.0184145	+	0.0318949i	0.875086	−	0.483968i	$-0.160805\pi$
$97$	1.78621	+	3.09380i	0.0184145	+	0.0318949i	−0.856671	+	0.515863i	$0.827471\pi$
$98$	−5.15457	+	41.4005i	−0.0525976	+	0.422454i
$99$	44.4189	−	16.1419i	0.448675	−	0.163049i
$100$	78.1465	+	19.7656i	0.781465	+	0.197656i
$101$	7.54688	+	13.0716i	0.0747216	+	0.129422i	0.900965	−	0.433891i	$-0.142860\pi$
$101$	7.54688	+	13.0716i	0.0747216	+	0.129422i	−0.826244	+	0.563313i	$0.809527\pi$
$102$	52.1179	+	161.471i	0.510960	+	1.58304i
$103$	−112.813	−	65.1324i	−1.09527	−	0.632353i	−0.160294	−	0.987069i	$-0.551244\pi$
$103$	−112.813	−	65.1324i	−1.09527	−	0.632353i	−0.934974	+	0.354716i	$0.884578\pi$
$104$	−73.8215	−	92.1155i	−0.709822	−	0.885726i
$105$	−54.9995	−	4.82574i	−0.523804	−	0.0459594i
$106$	59.1606	−	24.9940i	0.558119	−	0.235792i
$107$		−	51.2733i		−	0.479190i	−0.970873	−	0.239595i	$-0.922985\pi$
$107$		−	51.2733i		−	0.479190i	0.970873	−	0.239595i	$-0.0770146\pi$
$108$	55.2402	+	92.8037i	0.511483	+	0.859293i
$109$	−25.4737			−0.233704			−0.116852	−	0.993149i	$-0.537280\pi$
$109$	−25.4737			−0.233704			−0.116852	+	0.993149i	$0.537280\pi$
$110$	−8.99949	−	21.3018i	−0.0818136	−	0.193652i
$111$	−1.10650	+	12.6108i	−0.00996843	+	0.113611i
$112$	−70.0968	−	113.889i	−0.625864	−	1.01686i
$113$	76.1529	−	131.901i	0.673919	−	1.16726i	−0.302864	−	0.953034i	$-0.597943\pi$
$113$	76.1529	−	131.901i	0.673919	−	1.16726i	0.976783	−	0.214229i	$-0.0687238\pi$
$114$	−109.274	+	35.2705i	−0.958547	+	0.309390i
$115$	6.97330	−	4.02603i	0.0606374	−	0.0350090i
$116$	−95.6712	−	24.1982i	−0.824751	−	0.208605i
$117$	85.4144	−	101.689i	0.730038	−	0.869139i
$118$	18.2456	+	2.27167i	0.154624	+	0.0192514i
$119$	204.695	−	118.181i	1.72013	−	0.993116i
$120$	43.9670	−	29.3161i	0.366392	−	0.244301i
$121$	−46.7124	+	80.9082i	−0.386053	+	0.668663i
$122$	130.239	+	98.4888i	1.06754	+	0.807285i
$123$	48.7711	+	34.1681i	0.396513	+	0.277790i
$124$	−146.513	+	41.4751i	−1.18156	+	0.334476i
$125$	99.4176			0.795341
$126$	110.256	−	102.364i	0.875047	−	0.812409i
$127$		−	147.428i		−	1.16085i	−0.814314	−	0.580425i	$-0.802886\pi$
$127$		−	147.428i		−	1.16085i	0.814314	−	0.580425i	$-0.197114\pi$
$128$	120.524	+	43.1052i	0.941591	+	0.336760i
$129$	−29.5412	−	63.3929i	−0.229002	−	0.491418i
$130$	−51.8290	−	39.1938i	−0.398684	−	0.301491i
$131$	−112.889	−	65.1766i	−0.861750	−	0.497532i	0.00284803	−	0.999996i	$-0.499093\pi$
$131$	−112.889	−	65.1766i	−0.861750	−	0.497532i	−0.864598	+	0.502464i	$0.832427\pi$
$132$	59.5064	+	20.7323i	0.450806	+	0.157063i
$133$	79.9782	+	138.526i	0.601340	+	1.04155i
$134$	−15.7252	−	1.95787i	−0.117352	−	0.0146109i
$135$	42.0058	+	42.0691i	0.311154	+	0.311623i
$136$	−82.1465	+	210.790i	−0.604018	+	1.54993i
$137$	49.9179	+	86.4604i	0.364364	+	0.631098i	0.988674	−	0.150079i	$-0.0479530\pi$
$137$	49.9179	+	86.4604i	0.364364	+	0.631098i	−0.624310	+	0.781177i	$0.714620\pi$
$138$	−4.60369	+	21.4533i	−0.0333600	+	0.155459i
$139$	82.7828	+	47.7947i	0.595560	+	0.343847i	0.767293	−	0.641297i	$-0.221603\pi$
$139$	82.7828	+	47.7947i	0.595560	+	0.343847i	−0.171733	+	0.985144i	$0.554937\pi$
$140$	−52.7801	−	51.3160i	−0.377001	−	0.366543i
$141$	−37.8295	−	81.1787i	−0.268294	−	0.575736i
$142$	−48.9799	−	115.935i	−0.344929	−	0.816445i
$143$		−	77.4857i		−	0.541858i
$144$	−21.0784	+	142.449i	−0.146378	+	0.989229i
$145$	−54.3218			−0.374633
$146$	−61.3898	+	25.9358i	−0.420478	+	0.177642i
$147$	−51.2538	−	35.9074i	−0.348665	−	0.244268i
$148$	−11.7663	+	12.1020i	−0.0795018	+	0.0817701i
$149$	34.3382	−	59.4755i	0.230458	−	0.399164i	−0.727485	−	0.686123i	$-0.759311\pi$
$149$	34.3382	−	59.4755i	0.230458	−	0.399164i	0.957943	+	0.286959i	$0.0926443\pi$
$150$	−81.0800	+	89.6969i	−0.540533	+	0.597979i
$151$	−91.2633	+	52.6909i	−0.604393	+	0.348946i	−0.770768	−	0.637116i	$-0.780127\pi$
$151$	−91.2633	+	52.6909i	−0.604393	+	0.348946i	0.166375	+	0.986063i	$0.446794\pi$
$152$	−142.651	−	55.5922i	−0.938493	−	0.365738i
$153$	−250.621	−	44.3210i	−1.63805	−	0.289680i
$154$	10.8455	−	87.1092i	0.0704255	−	0.565644i
$155$	−72.5894	+	41.9095i	−0.468319	+	0.270384i
$156$	173.938	−	33.1535i	1.11499	−	0.212523i
$157$	−107.502	+	186.200i	−0.684729	+	1.18598i	0.288794	+	0.957391i	$0.406746\pi$
$157$	−107.502	+	186.200i	−0.684729	+	1.18598i	−0.973522	+	0.228593i	$0.926587\pi$
$158$	−74.8203	+	98.9406i	−0.473546	+	0.626206i
$159$	−8.42027	+	95.9667i	−0.0529577	+	0.603564i
$160$	70.1366	+	6.73536i	0.438353	+	0.0420960i
$161$	30.5657			0.189849
$162$	−161.800	+	8.04186i	−0.998767	+	0.0496411i
$163$			33.7439i			0.207018i	0.994629	+	0.103509i	$0.0330071\pi$
$163$			33.7439i			0.207018i	−0.994629	+	0.103509i	$0.966993\pi$
$164$	21.6265	+	76.3966i	0.131869	+	0.465833i
$165$	34.5544	+	3.03186i	0.209421	+	0.0183749i
$166$	143.553	−	189.831i	0.864775	−	1.14356i
$167$	131.565	+	75.9589i	0.787812	+	0.454843i	0.839192	−	0.543836i	$-0.183029\pi$
$167$	131.565	+	75.9589i	0.787812	+	0.454843i	−0.0513797	+	0.998679i	$0.516362\pi$
$168$	200.181	−	12.9254i	1.19155	−	0.0769367i
$169$	−24.3663	−	42.2036i	−0.144179	−	0.249726i
$170$	−15.3860	+	123.578i	−0.0905060	+	0.726927i
$171$	29.9940	−	169.606i	0.175403	−	0.991851i
$172$	22.8659	−	90.4040i	0.132941	−	0.525605i
$173$	−59.4003	−	102.884i	−0.343354	−	0.594707i	0.641699	−	0.766957i	$-0.278230\pi$
$173$	−59.4003	−	102.884i	−0.343354	−	0.594707i	−0.985053	+	0.172249i	$0.944896\pi$
$174$	99.2625	−	109.812i	0.570474	−	0.631102i
$175$	145.868	+	84.2170i	0.833532	+	0.481240i
$176$	44.0396	+	71.5526i	0.250225	+	0.406549i
$177$	−15.8248	+	22.5881i	−0.0894055	+	0.127616i
$178$	197.795	−	83.5636i	1.11121	−	0.469458i
$179$			218.189i			1.21894i	0.792811	+	0.609468i	$0.208617\pi$
$179$			218.189i			1.21894i	−0.792811	+	0.609468i	$0.791383\pi$
$180$	7.97884	+	78.8640i	0.0443269	+	0.438133i
$181$	184.078			1.01701			0.508503	−	0.861060i	$-0.330199\pi$
$181$	184.078			1.01701			0.508503	+	0.861060i	$0.330199\pi$
$182$	−95.9945	−	227.219i	−0.527443	−	1.24845i
$183$	−222.007	+	103.456i	−1.21315	+	0.565332i
$184$	−22.8292	+	18.2954i	−0.124072	+	0.0994313i
$185$	−4.64565	+	8.04650i	−0.0251116	+	0.0434946i
$186$	47.9226	−	223.321i	0.257649	−	1.20065i
$187$	−128.603	+	74.2492i	−0.687719	+	0.397055i
$188$	29.2813	−	115.768i	0.155752	−	0.615788i
$189$	58.2442	+	218.027i	0.308170	+	1.15358i
$190$	−83.6305	−	10.4124i	−0.440160	−	0.0548021i
$191$	−215.775	+	124.578i	−1.12971	+	0.652239i	−0.943862	−	0.330339i	$-0.892837\pi$
$191$	−215.775	+	124.578i	−1.12971	+	0.652239i	−0.185849	+	0.982578i	$0.559503\pi$
$192$	−141.776	+	129.474i	−0.738419	+	0.674343i
$193$	125.086	−	216.656i	0.648115	−	1.12257i	−0.335457	−	0.942055i	$-0.608891\pi$
$193$	125.086	−	216.656i	0.648115	−	1.12257i	0.983573	−	0.180513i	$-0.0577758\pi$
$194$	−5.69882	−	4.30953i	−0.0293754	−	0.0222141i
$195$	88.3481	−	41.1704i	0.453067	−	0.211130i
$196$	−22.7273	−	80.2855i	−0.115956	−	0.409620i
$197$	255.674			1.29784			0.648919	−	0.760858i	$-0.275221\pi$
$197$	255.674			1.29784			0.648919	+	0.760858i	$0.275221\pi$
$198$	−69.2703	+	64.3118i	−0.349850	+	0.324807i
$199$		−	309.110i		−	1.55332i	−0.629921	−	0.776659i	$-0.716913\pi$
$199$		−	309.110i		−	1.55332i	0.629921	−	0.776659i	$-0.283087\pi$
$200$	−159.356	+	24.4098i	−0.796781	+	0.122049i
$201$	13.6388	−	19.4678i	0.0678545	−	0.0968546i
$202$	−24.0780	−	18.2081i	−0.119198	−	0.0901392i
$203$	−178.580	−	103.103i	−0.879702	−	0.507896i
$204$	−221.698	−	256.917i	−1.08675	−	1.25940i
$205$	21.8530	+	37.8505i	0.106600	+	0.184636i
$206$	258.533	+	32.1887i	1.25502	+	0.156256i
$207$	−25.2019	−	21.1685i	−0.121748	−	0.102263i
$208$	207.701	+	112.249i	0.998563	+	0.539658i
$209$	−50.2478	−	87.0317i	−0.240420	−	0.416420i
$210$	105.083	−	33.9178i	0.500397	−	0.161513i
$211$	341.158	+	196.968i	1.61686	+	0.933497i	0.987725	+	0.156205i	$0.0499261\pi$
$211$	341.158	+	196.968i	1.61686	+	0.933497i	0.629140	+	0.777292i	$0.283407\pi$
$212$	−89.5395	+	92.0943i	−0.422356	+	0.434407i
$213$	188.063	+	16.5010i	0.882926	+	0.0774693i
$214$	39.9082	+	94.4624i	0.186487	+	0.441413i
$215$		−	51.3311i		−	0.238750i
$216$	−174.004	−	127.979i	−0.805573	−	0.592497i
$217$	−318.177			−1.46626
$218$	46.9310	−	19.8272i	0.215280	−	0.0909506i
$219$	8.73756	−	99.5829i	0.0398975	−	0.454716i
$220$	33.1601	+	32.2402i	0.150728	+	0.146546i
$221$	−208.638	+	361.372i	−0.944064	+	1.63517i
$222$	−7.77702	−	24.0946i	−0.0350316	−	0.108534i
$223$	−89.4002	+	51.6152i	−0.400898	+	0.231458i	−0.686871	−	0.726779i	$-0.741016\pi$
$223$	−89.4002	+	51.6152i	−0.400898	+	0.231458i	0.285974	+	0.958238i	$0.407683\pi$
$224$	217.786	+	155.261i	0.972258	+	0.693131i
$225$	−61.9455	−	170.460i	−0.275313	−	0.757600i
$226$	−37.6350	+	302.278i	−0.166527	+	1.33751i
$227$	122.210	−	70.5578i	0.538369	−	0.310828i	−0.206049	−	0.978542i	$-0.566061\pi$
$227$	122.210	−	70.5578i	0.538369	−	0.310828i	0.744418	+	0.667714i	$0.232727\pi$
$228$	173.867	−	150.033i	0.762575	−	0.658038i
$229$	105.572	−	182.856i	0.461012	−	0.798496i	−0.538000	−	0.842945i	$-0.680820\pi$
$229$	105.572	−	182.856i	0.461012	−	0.798496i	0.999012	+	0.0444490i	$0.0141532\pi$
$230$	−9.71349	+	12.8449i	−0.0422326	+	0.0558474i
$231$	107.841	+	75.5514i	0.466844	+	0.327062i
$232$	195.092	−	29.8838i	0.840916	−	0.128810i
$233$	−280.109			−1.20219			−0.601093	−	0.799179i	$-0.705268\pi$
$233$	−280.109			−1.20219			−0.601093	+	0.799179i	$0.705268\pi$
$234$	−78.2127	+	253.827i	−0.334242	+	1.08473i
$235$		−	65.7328i		−	0.279714i
$236$	−35.3826	+	10.0162i	−0.149926	+	0.0424414i
$237$	−78.5936	−	168.655i	−0.331619	−	0.711624i
$238$	−285.131	+	377.051i	−1.19803	+	1.58425i
$239$	339.349	+	195.923i	1.41987	+	0.819762i	0.996287	−	0.0860949i	$-0.0274388\pi$
$239$	339.349	+	195.923i	1.41987	+	0.819762i	0.423583	+	0.905857i	$0.360772\pi$
$240$	−58.1838	+	88.2313i	−0.242433	+	0.367631i
$241$	−23.6786	−	41.0125i	−0.0982514	−	0.170176i	0.812710	−	0.582669i	$-0.197992\pi$
$241$	−23.6786	−	41.0125i	−0.0982514	−	0.170176i	−0.910961	+	0.412493i	$0.864658\pi$
$242$	23.0854	−	185.418i	0.0953943	−	0.766190i
$243$	102.973	−	220.104i	0.423755	−	0.905777i
$244$	−316.602	−	80.0783i	−1.29755	−	0.328190i
$245$	−22.9654	−	39.7772i	−0.0937363	−	0.162356i
$246$	−116.447	−	24.9884i	−0.473362	−	0.101579i
$247$	−244.557	−	141.195i	−0.990107	−	0.571639i
$248$	237.643	−	190.448i	0.958239	−	0.767935i
$249$	150.792	+	323.587i	0.605591	+	1.29955i
$250$	−183.160	+	77.3809i	−0.732641	+	0.309524i
$251$		−	389.416i		−	1.55146i	−0.631065	−	0.775730i	$-0.717382\pi$
$251$		−	389.416i		−	1.55146i	0.631065	−	0.775730i	$-0.282618\pi$
$252$	−123.454	+	274.404i	−0.489898	+	1.08891i
$253$	−19.2035			−0.0759030
$254$	114.749	+	271.611i	0.451769	+	1.06933i
$255$	−152.989	−	107.181i	−0.599956	−	0.420318i
$256$	−255.595	+	14.3944i	−0.998418	+	0.0562283i
$257$	−32.5409	+	56.3625i	−0.126618	+	0.219310i	−0.922364	−	0.386321i	$-0.873746\pi$
$257$	−32.5409	+	56.3625i	−0.126618	+	0.219310i	0.795746	+	0.605631i	$0.207079\pi$
$258$	103.766	+	93.7976i	0.402194	+	0.363557i
$259$	−30.5445	+	17.6349i	−0.117933	+	0.0680884i
$260$	125.992	+	31.8673i	0.484586	+	0.122567i
$261$	75.8370	+	208.686i	0.290563	+	0.799565i
$262$	258.709	+	32.2105i	0.987439	+	0.122941i
$263$	124.773	−	72.0378i	0.474423	−	0.273908i	−0.243667	−	0.969859i	$-0.578350\pi$
$263$	124.773	−	72.0378i	0.474423	−	0.273908i	0.718089	+	0.695951i	$0.245017\pi$
$264$	−125.767	+	8.12060i	−0.476391	+	0.0307599i
$265$	−35.3527	+	61.2327i	−0.133406	+	0.231067i
$266$	−255.167	−	192.961i	−0.959275	−	0.725417i
$267$	−28.1519	+	320.850i	−0.105438	+	1.20169i
$268$	30.4949	−	8.63255i	0.113787	−	0.0322110i
$269$	−72.4113			−0.269187			−0.134593	−	0.990901i	$-0.542973\pi$
$269$	−72.4113			−0.269187			−0.134593	+	0.990901i	$0.542973\pi$
$270$	−110.133	−	44.8104i	−0.407899	−	0.165964i
$271$			35.4695i			0.130884i	0.997856	+	0.0654419i	$0.0208457\pi$
$271$			35.4695i			0.130884i	−0.997856	+	0.0654419i	$0.979154\pi$
$272$	−12.7256	−	452.283i	−0.0467854	−	1.66281i
$273$	368.580	+	32.3398i	1.35011	+	0.118461i
$274$	−159.261	−	120.435i	−0.581245	−	0.439545i
$275$	−91.6443	−	52.9109i	−0.333252	−	0.192403i
$276$	−8.21651	−	43.1074i	−0.0297700	−	0.156186i
$277$	−166.922	−	289.118i	−0.602607	−	1.04375i	−0.992425	−	0.122854i	$-0.960795\pi$
$277$	−166.922	−	289.118i	−0.602607	−	1.04375i	0.389818	−	0.920892i	$-0.372538\pi$
$278$	−189.714	−	23.6203i	−0.682424	−	0.0849651i
$279$	262.342	+	220.356i	0.940295	+	0.789806i
$280$	137.180	+	53.4600i	0.489928	+	0.190929i
$281$	−20.5385	−	35.5737i	−0.0730906	−	0.126597i	0.827164	−	0.561961i	$-0.189953\pi$
$281$	−20.5385	−	35.5737i	−0.0730906	−	0.126597i	−0.900254	+	0.435364i	$0.856620\pi$
$282$	132.879	+	120.114i	0.471203	+	0.425936i
$283$	−218.583	−	126.199i	−0.772378	−	0.445933i	0.0613442	−	0.998117i	$-0.480461\pi$
$283$	−218.583	−	126.199i	−0.772378	−	0.445933i	−0.833722	+	0.552184i	$0.813795\pi$
$284$	180.474	+	175.468i	0.635474	+	0.617845i
$285$	72.5342	−	103.534i	0.254506	−	0.363278i
$286$	60.3103	+	142.754i	0.210875	+	0.499141i
$287$			165.908i			0.578077i
$288$	−72.0405	−	278.844i	−0.250141	−	0.968210i
$289$	510.695			1.76711
$290$	100.079	−	42.2809i	0.345099	−	0.145796i
$291$	9.71427	−	4.52687i	0.0333824	−	0.0155562i
$292$	92.9135	−	95.5646i	0.318197	−	0.327276i
$293$	20.3415	−	35.2325i	0.0694248	−	0.120247i	−0.829223	−	0.558917i	$-0.811217\pi$
$293$	20.3415	−	35.2325i	0.0694248	−	0.120247i	0.898648	+	0.438670i	$0.144550\pi$
$294$	122.375	+	26.2605i	0.416240	+	0.0893213i
$295$	−17.5302	+	10.1211i	−0.0594245	+	0.0343088i
$296$	12.2579	−	31.4540i	0.0414117	−	0.106264i
$297$	−36.5930	−	136.979i	−0.123209	−	0.461210i
$298$	−16.9701	+	136.300i	−0.0569465	+	0.457384i
$299$	−46.7317	+	26.9806i	−0.156293	+	0.0902361i
$300$	79.5613	−	228.359i	0.265204	−	0.761198i
$301$	97.4266	−	168.748i	0.323677	−	0.560624i
$302$	127.126	−	168.108i	0.420946	−	0.556650i
$303$	41.0436	−	19.1264i	0.135457	−	0.0631234i
$304$	306.080	−	8.61199i	1.00684	−	0.0283289i
$305$	−179.766			−0.589396
$306$	496.224	−	113.415i	1.62165	−	0.370637i
$307$			136.830i			0.445701i	0.974853	+	0.222850i	$0.0715361\pi$
$307$			136.830i			0.445701i	−0.974853	+	0.222850i	$0.928464\pi$
$308$	47.8197	+	168.926i	0.155259	+	0.548460i
$309$	−224.231	+	320.064i	−0.725666	+	1.03580i
$310$	101.114	−	133.711i	0.326174	−	0.431324i
$311$	−371.260	−	214.347i	−1.19376	−	0.689219i	−0.234605	−	0.972091i	$-0.575380\pi$
$311$	−371.260	−	214.347i	−1.19376	−	0.689219i	−0.959158	+	0.282871i	$0.908713\pi$
$312$	−294.646	+	196.463i	−0.944379	+	0.629688i
$313$	5.98705	+	10.3699i	0.0191280	+	0.0331306i	0.875431	−	0.483343i	$-0.160578\pi$
$313$	5.98705	+	10.3699i	0.0191280	+	0.0331306i	−0.856303	+	0.516474i	$0.827244\pi$
$314$	53.1281	−	426.715i	0.169198	−	1.35896i
$315$	−28.8436	+	163.101i	−0.0915670	+	0.517782i
$316$	60.8341	−	240.517i	0.192513	−	0.761130i
$317$	−23.5266	−	40.7493i	−0.0742164	−	0.128547i	0.826529	−	0.562894i	$-0.190312\pi$
$317$	−23.5266	−	40.7493i	−0.0742164	−	0.128547i	−0.900745	+	0.434348i	$0.856979\pi$
$318$	−59.1820	−	183.356i	−0.186107	−	0.576592i
$319$	112.196	+	64.7763i	0.351711	+	0.203061i
$320$	−134.457	+	42.1814i	−0.420179	+	0.131817i
$321$	−153.231	−	13.4448i	−0.477356	−	0.0418840i
$322$	−56.3121	+	23.7906i	−0.174882	+	0.0738837i
$323$			541.189i			1.67551i
$324$	291.830	−	140.752i	0.900711	−	0.434419i
$325$	−297.356			−0.914941
$326$	−26.2643	−	62.1675i	−0.0805654	−	0.190698i
$327$	−6.67964	+	76.1286i	−0.0204270	+	0.232809i
$328$	−99.3057	−	123.915i	−0.302761	−	0.377790i
$329$	124.761	−	216.092i	0.379213	−	0.656816i
$330$	−66.0205	+	21.3095i	−0.200062	+	0.0645741i
$331$	−73.1501	+	42.2332i	−0.220997	+	0.127593i	−0.606412	−	0.795151i	$-0.707392\pi$
$331$	−73.1501	+	42.2332i	−0.220997	+	0.127593i	0.385415	+	0.922743i	$0.374058\pi$
$332$	−116.718	+	461.464i	−0.351561	+	1.38995i
$333$	37.3976	+	6.61357i	0.112305	+	0.0198606i
$334$	−301.508	−	37.5392i	−0.902717	−	0.112393i
$335$	15.1086	−	8.72297i	0.0451004	−	0.0260387i
$336$	−358.739	+	179.622i	−1.06768	+	0.534589i
$337$	−252.558	+	437.443i	−0.749430	+	1.29805i	0.198667	+	0.980067i	$0.436339\pi$
$337$	−252.558	+	437.443i	−0.749430	+	1.29805i	−0.948096	+	0.317983i	$0.896994\pi$
$338$	77.7396	+	58.7877i	0.229999	+	0.173928i
$339$	−374.219	−	262.171i	−1.10389	−	0.773366i
$340$	−67.8395	−	239.646i	−0.199528	−	0.704842i
$341$	199.901			0.586219
$342$	76.7529	+	335.817i	0.224424	+	0.981921i
$343$			235.200i			0.685714i
$344$	28.2386	+	184.352i	0.0820889	+	0.535906i
$345$	−10.2034	−	21.8955i	−0.0295750	−	0.0634653i
$346$	189.514	+	143.313i	0.547729	+	0.414200i
$347$	424.751	+	245.230i	1.22407	+	0.706715i	0.965782	−	0.259354i	$-0.0835097\pi$
$347$	424.751	+	245.230i	1.22407	+	0.706715i	0.258284	+	0.966069i	$0.416843\pi$
$348$	−97.4033	+	279.570i	−0.279894	+	0.803362i
$349$	186.972	+	323.845i	0.535736	+	0.927923i	0.999127	+	0.0417686i	$0.0132992\pi$
$349$	186.972	+	323.845i	0.535736	+	0.927923i	−0.463391	+	0.886154i	$0.653367\pi$
$350$	−334.287	−	41.6203i	−0.955105	−	0.118915i
$351$	−281.503	−	281.927i	−0.802003	−	0.803212i
$352$	−136.828	−	97.5458i	−0.388716	−	0.277119i
$353$	297.026	+	514.465i	0.841434	+	1.45741i	0.888682	+	0.458523i	$0.151621\pi$
$353$	297.026	+	514.465i	0.841434	+	1.45741i	−0.0472483	+	0.998883i	$0.515045\pi$
$354$	11.5733	−	53.9318i	0.0326928	−	0.152350i
$355$	119.996	+	69.2796i	0.338016	+	0.195154i
$356$	−299.362	+	307.904i	−0.840905	+	0.864898i
$357$	−299.511	−	642.724i	−0.838966	−	1.80035i
$358$	−169.826	−	401.977i	−0.474374	−	1.12284i
$359$		−	410.893i		−	1.14455i	−0.820062	−	0.572274i	$-0.806061\pi$
$359$		−	410.893i		−	1.14455i	0.820062	−	0.572274i	$-0.193939\pi$
$360$	−76.0828	−	139.083i	−0.211341	−	0.386343i
$361$	−5.24690			−0.0145343
$362$	−339.133	+	143.276i	−0.936832	+	0.395789i
$363$	229.547	+	160.816i	0.632360	+	0.443020i
$364$	353.707	+	343.895i	0.971724	+	0.944768i
$365$	36.6848	−	63.5400i	0.100506	−	0.174082i
$366$	328.487	−	363.397i	0.897504	−	0.992888i
$367$	466.176	−	269.147i	1.27023	−	0.733370i	0.295203	−	0.955435i	$-0.404613\pi$
$367$	466.176	−	269.147i	1.27023	−	0.733370i	0.975032	+	0.222064i	$0.0712795\pi$
$368$	27.8189	−	51.4750i	0.0755948	−	0.139878i
$369$	114.901	−	136.794i	0.311384	−	0.370715i
$370$	2.29590	−	18.4402i	0.00620512	−	0.0498384i
$371$	−232.440	+	134.199i	−0.626522	+	0.361722i
$372$	85.5308	+	448.732i	0.229922	+	1.20627i
$373$	−74.9606	+	129.836i	−0.200967	+	0.348085i	−0.948840	−	0.315757i	$-0.897742\pi$
$373$	−74.9606	+	129.836i	−0.200967	+	0.348085i	0.747873	+	0.663841i	$0.231075\pi$
$374$	179.139	−	236.889i	0.478981	−	0.633393i
$375$	26.0690	−	297.111i	0.0695174	−	0.792297i
$376$	36.1613	+	236.074i	0.0961737	+	0.627857i
$377$	364.039			0.965621
$378$	−277.004	−	356.343i	−0.732816	−	0.942708i
$379$		−	184.361i		−	0.486442i	−0.969971	−	0.243221i	$-0.921796\pi$
$379$		−	184.361i		−	0.486442i	0.969971	−	0.243221i	$-0.0782040\pi$
$380$	162.179	−	45.9100i	0.426788	−	0.120816i
$381$	−440.591	−	38.6582i	−1.15641	−	0.101465i
$382$	300.565	−	397.460i	0.786818	−	1.04047i
$383$	−180.514	−	104.220i	−0.471315	−	0.272114i	0.245475	−	0.969403i	$-0.421056\pi$
$383$	−180.514	−	104.220i	−0.471315	−	0.272114i	−0.716790	+	0.697289i	$0.754389\pi$
$384$	160.424	−	348.884i	0.417771	−	0.908552i
$385$	48.3206	+	83.6937i	0.125508	+	0.217386i
$386$	−61.8181	+	496.511i	−0.160150	+	1.28630i
$387$	−197.197	+	71.6618i	−0.509554	+	0.185173i
$388$	13.8534	+	3.50395i	0.0357047	+	0.00903080i
$389$	−150.914	−	261.390i	−0.387953	−	0.671954i	0.604221	−	0.796816i	$-0.293484\pi$
$389$	−150.914	−	261.390i	−0.387953	−	0.671954i	−0.992174	+	0.124863i	$0.960151\pi$
$390$	−130.722	+	144.615i	−0.335184	+	0.370807i
$391$	89.5597	+	51.7073i	0.229053	+	0.132244i
$392$	104.361	+	130.223i	0.266227	+	0.332201i
$393$	−224.383	+	320.281i	−0.570949	+	0.814965i
$394$	−471.036	+	199.002i	−1.19552	+	0.505081i
$395$		−	136.565i		−	0.345734i
$396$	77.5624	−	172.400i	0.195865	−	0.435352i
$397$	−246.672			−0.621341			−0.310670	−	0.950518i	$-0.600553\pi$
$397$	−246.672			−0.621341			−0.310670	+	0.950518i	$0.600553\pi$
$398$	240.593	+	569.483i	0.604506	+	1.43086i
$399$	434.960	−	202.692i	1.09013	−	0.508001i
$400$	274.588	−	169.005i	0.686469	−	0.422511i
$401$	377.516	−	653.877i	0.941437	−	1.63062i	0.178703	−	0.983903i	$-0.442810\pi$
$401$	377.516	−	653.877i	0.941437	−	1.63062i	0.762734	−	0.646713i	$-0.223857\pi$
$402$	−9.97454	+	46.4817i	−0.0248123	+	0.115626i
$403$	486.460	−	280.858i	1.20710	−	0.696917i
$404$	58.5318	+	14.8045i	0.144881	+	0.0366447i
$405$	136.739	−	114.504i	0.337627	−	0.282726i
$406$	409.252	+	50.9539i	1.00801	+	0.125502i
$407$	19.1902	−	11.0794i	0.0471503	−	0.0272222i
$408$	608.410	+	300.769i	1.49120	+	0.737179i
$409$	130.730	−	226.432i	0.319634	−	0.553622i	−0.660778	−	0.750582i	$-0.729773\pi$
$409$	130.730	−	226.432i	0.319634	−	0.553622i	0.980412	+	0.196959i	$0.0631067\pi$
$410$	−69.7210	−	52.7240i	−0.170051	−	0.128595i
$411$	271.478	−	126.509i	0.660530	−	0.307808i
$412$	−501.358	+	141.925i	−1.21689	+	0.344479i
$413$	−76.8394			−0.186052
$414$	62.9065	+	19.3836i	0.151948	+	0.0468204i
$415$			262.018i			0.631369i
$416$	−470.022	−	45.1372i	−1.12986	−	0.108503i
$417$	164.542	−	234.865i	0.394586	−	0.563226i
$418$	160.313	+	121.231i	0.383525	+	0.290027i
$419$	−340.246	−	196.441i	−0.812043	−	0.468833i	0.0356217	−	0.999365i	$-0.488659\pi$
$419$	−340.246	−	196.441i	−0.812043	−	0.468833i	−0.847665	+	0.530532i	$0.821992\pi$
$420$	−167.199	+	144.278i	−0.398092	+	0.343520i
$421$	102.451	+	177.450i	0.243351	+	0.421496i	0.961667	−	0.274221i	$-0.0884200\pi$
$421$	102.451	+	177.450i	0.243351	+	0.421496i	−0.718316	+	0.695717i	$0.755087\pi$
$422$	−781.835	−	97.3423i	−1.85269	−	0.230669i
$423$	−252.524	+	91.7676i	−0.596983	+	0.216945i
$424$	93.2807	−	239.361i	0.220002	−	0.564530i
$425$	284.936	+	493.524i	0.670438	+	1.16123i
$426$	−359.318	+	115.977i	−0.843469	+	0.272247i
$427$	−590.968	−	341.196i	−1.38400	−	0.799053i
$428$	−147.048	−	142.969i	−0.343570	−	0.334039i
$429$	−231.567	−	20.3181i	−0.539784	−	0.0473615i
$430$	39.9532	+	94.5690i	0.0929144	+	0.219928i
$431$			462.725i			1.07361i	0.843707	+	0.536803i	$0.180368\pi$
$431$			462.725i			1.07361i	−0.843707	+	0.536803i	$0.819632\pi$
$432$	420.184	+	100.346i	0.972648	+	0.232282i
$433$	190.574			0.440126			0.220063	−	0.975486i	$-0.429374\pi$
$433$	190.574			0.440126			0.220063	+	0.975486i	$0.429374\pi$
$434$	586.188	−	247.651i	1.35066	−	0.570624i
$435$	−14.2441	+	162.342i	−0.0327451	+	0.373200i
$436$	−71.0300	+	73.0567i	−0.162913	+	0.167561i
$437$	−34.9926	+	60.6090i	−0.0800747	+	0.138693i
$438$	61.4120	+	190.265i	0.140210	+	0.434396i
$439$	−379.279	+	218.977i	−0.863962	+	0.498809i	−0.865337	−	0.501190i	$-0.832896\pi$
$439$	−379.279	+	218.977i	−0.863962	+	0.498809i	0.00137479	+	0.999999i	$0.499562\pi$
$440$	−86.1858	−	33.5873i	−0.195877	−	0.0763347i
$441$	−120.750	+	143.757i	−0.273809	+	0.325980i
$442$	103.110	−	828.159i	0.233280	−	1.87366i
$443$	721.993	−	416.843i	1.62978	−	0.940954i	0.645623	−	0.763657i	$-0.276598\pi$
$443$	721.993	−	416.843i	1.62978	−	0.940954i	0.984157	−	0.177297i	$-0.0567354\pi$
$444$	33.0817	+	38.3370i	0.0745083	+	0.0863447i
$445$	−118.196	+	204.722i	−0.265610	+	0.460050i
$446$	124.530	−	164.676i	0.279216	−	0.369229i
$447$	−168.740	−	118.216i	−0.377493	−	0.264465i
$448$	−522.080	−	116.531i	−1.16536	−	0.260114i
$449$	−480.789			−1.07080			−0.535399	−	0.844599i	$-0.679839\pi$
$449$	−480.789			−1.07080			−0.535399	+	0.844599i	$0.679839\pi$
$450$	246.800	+	265.829i	0.548445	+	0.590731i
$451$		−	104.235i		−	0.231119i
$452$	−165.939	−	586.189i	−0.367122	−	1.29688i
$453$	133.537	+	286.559i	0.294784	+	0.632580i
$454$	−170.233	+	225.112i	−0.374962	+	0.495841i
$455$	235.177	+	135.779i	0.516872	+	0.298416i
$456$	−203.544	+	411.738i	−0.446368	+	0.902934i
$457$	109.313	+	189.336i	0.239197	+	0.414302i	0.960484	−	0.278334i	$-0.0897824\pi$
$457$	109.313	+	189.336i	0.239197	+	0.414302i	−0.721287	+	0.692636i	$0.756449\pi$
$458$	−52.1739	+	419.051i	−0.113917	+	0.914959i
$459$	−198.171	+	737.364i	−0.431746	+	1.60646i
$460$	7.89775	−	31.2250i	0.0171690	−	0.0678804i
$461$	−358.474	−	620.894i	−0.777600	−	1.34684i	−0.933322	−	0.359042i	$-0.883104\pi$
$461$	−358.474	−	620.894i	−0.777600	−	1.34684i	0.155722	−	0.987801i	$-0.450230\pi$
$462$	−257.484	−	55.2536i	−0.557324	−	0.119597i
$463$	26.6250	+	15.3719i	0.0575053	+	0.0332007i	0.528477	−	0.848948i	$-0.322763\pi$
$463$	26.6250	+	15.3719i	0.0575053	+	0.0332007i	−0.470972	+	0.882148i	$0.656097\pi$
$464$	−336.165	+	206.904i	−0.724494	+	0.445915i
$465$	106.213	+	227.924i	0.228415	+	0.490159i
$466$	516.054	−	218.021i	1.10741	−	0.467856i
$467$		−	458.639i		−	0.982096i	−0.871133	−	0.491048i	$-0.836614\pi$
$467$		−	458.639i		−	0.982096i	0.871133	−	0.491048i	$-0.163386\pi$
$468$	−53.4704	−	528.509i	−0.114253	−	1.12929i
$469$	66.2249			0.141204
$470$	51.1626	+	121.102i	0.108857	+	0.257663i
$471$	528.272	+	370.098i	1.12160	+	0.785770i
$472$	57.3905	−	45.9929i	0.121590	−	0.0974426i
$473$	−61.2101	+	106.019i	−0.129408	+	0.224142i
$474$	276.067	+	249.546i	0.582419	+	0.526468i
$475$	−333.989	+	192.829i	−0.703135	+	0.405955i
$476$	231.832	−	916.582i	0.487041	−	1.92559i
$477$	284.590	+	50.3283i	0.596626	+	0.105510i
$478$	−777.688	−	96.8260i	−1.62696	−	0.202565i
$479$	−570.477	+	329.365i	−1.19098	+	0.687610i	−0.958528	−	0.284999i	$-0.908007\pi$
$479$	−570.477	+	329.365i	−1.19098	+	0.687610i	−0.232448	+	0.972609i	$0.574674\pi$
$480$	38.5198	−	207.838i	0.0802495	−	0.432996i
$481$	31.1329	−	53.9238i	0.0647254	−	0.112108i
$482$	75.5456	+	57.1286i	0.156734	+	0.118524i
$483$	8.01485	−	91.3461i	0.0165939	−	0.189122i
$484$	101.787	+	359.570i	0.210305	+	0.742912i
$485$	7.86593			0.0162184
$486$	−18.3936	+	485.652i	−0.0378469	+	0.999284i
$487$			715.589i			1.46938i	0.678402	+	0.734691i	$0.262673\pi$
$487$			715.589i			1.46938i	−0.678402	+	0.734691i	$0.737327\pi$
$488$	645.614	−	98.8937i	1.32298	−	0.202651i
$489$	100.844	+	8.84825i	0.206226	+	0.0180946i
$490$	73.2702	+	55.4079i	0.149531	+	0.113077i
$491$	574.179	+	331.502i	1.16941	+	0.675157i	0.953540	−	0.301266i	$-0.0974091\pi$
$491$	574.179	+	331.502i	1.16941	+	0.675157i	0.215866	+	0.976423i	$0.430742\pi$
$492$	233.983	−	44.5986i	0.475576	−	0.0906475i
$493$	−348.834	−	604.198i	−0.707574	−	1.22555i
$494$	560.452	+	69.7790i	1.13452	+	0.141253i
$495$	18.1215	−	102.472i	0.0366092	−	0.207013i
$496$	−289.584	+	535.836i	−0.583839	+	1.08031i
$497$	262.986	+	455.505i	0.529147	+	0.916509i
$498$	−529.670	−	478.786i	−1.06360	−	0.961419i
$499$	−458.706	−	264.834i	−0.919251	−	0.530730i	−0.0358546	−	0.999357i	$-0.511415\pi$
$499$	−458.706	−	264.834i	−0.919251	−	0.530730i	−0.883396	+	0.468627i	$0.844749\pi$
$500$	277.213	−	285.122i	0.554426	−	0.570245i
$501$	261.503	−	373.266i	0.521962	−	0.745041i
$502$	303.099	+	717.434i	0.603783	+	1.42915i
$503$		−	68.3537i		−	0.135892i	−0.997689	−	0.0679460i	$-0.978355\pi$
$503$		−	68.3537i		−	0.135892i	0.997689	−	0.0679460i	$-0.0216446\pi$
$504$	13.8632	−	601.633i	0.0275063	−	1.19372i
$505$	33.2342			0.0658103
$506$	35.3791	−	14.9469i	0.0699192	−	0.0295392i
$507$	−132.516	+	61.7525i	−0.261372	+	0.121800i
$508$	−422.812	−	411.083i	−0.832308	−	0.809219i
$509$	−400.473	+	693.640i	−0.786784	+	1.36275i	0.141143	+	0.989989i	$0.454922\pi$
$509$	−400.473	+	693.640i	−0.786784	+	1.36275i	−0.927927	+	0.372761i	$0.878411\pi$
$510$	365.279	+	78.3856i	0.716234	+	0.153697i
$511$	241.198	−	139.256i	0.472012	−	0.272516i
$512$	459.687	−	225.460i	0.897826	−	0.440351i
$513$	−499.007	−	134.111i	−0.972723	−	0.261426i
$514$	16.0818	−	129.166i	0.0312876	−	0.251297i
$515$	−248.396	+	143.412i	−0.482323	+	0.278469i
$516$	−264.178	−	92.0408i	−0.511973	−	0.178374i
$517$	−78.3834	+	135.764i	−0.151612	+	0.262600i
$518$	42.5472	−	56.2634i	0.0821374	−	0.108617i
$519$	−323.047	+	150.541i	−0.622442	+	0.290059i
$520$	−256.923	+	39.3549i	−0.494083	+	0.0756826i
$521$	−208.227			−0.399668			−0.199834	−	0.979830i	$-0.564040\pi$
$521$	−208.227			−0.399668			−0.199834	+	0.979830i	$0.564040\pi$
$522$	−302.146	−	325.442i	−0.578824	−	0.623453i
$523$			30.5350i			0.0583843i	0.999574	+	0.0291921i	$0.00929347\pi$
$523$			30.5350i			0.0583843i	−0.999574	+	0.0291921i	$0.990707\pi$
$524$	−501.699	+	142.022i	−0.957440	+	0.271034i
$525$	289.933	−	413.846i	0.552254	−	0.788279i
$526$	−173.803	+	229.834i	−0.330425	+	0.436946i
$527$	−932.283	−	538.254i	−1.76904	−	1.02135i
$528$	225.384	−	112.851i	0.426864	−	0.213732i
$529$	−257.813	−	446.546i	−0.487360	−	0.844132i
$530$	17.4714	−	140.327i	0.0329650	−	0.264769i
$531$	63.3553	+	53.2156i	0.119313	+	0.100218i
$532$	620.292	+	156.891i	1.16596	+	0.294907i
$533$	−146.448	−	253.656i	−0.274762	−	0.475903i
$534$	−197.866	−	613.025i	−0.370536	−	1.14799i
$535$	−97.7710	−	56.4481i	−0.182749	−	0.105510i
$536$	−49.4627	+	39.6395i	−0.0922811	+	0.0739543i
$537$	652.063	+	57.2130i	1.21427	+	0.106542i
$538$	133.406	−	56.3607i	0.247966	−	0.104760i
$539$			109.541i			0.203230i
$540$	237.779	−	3.16539i	0.440331	−	0.00586183i
$541$	526.091			0.972442			0.486221	−	0.873836i	$-0.338375\pi$
$541$	526.091			0.972442			0.486221	+	0.873836i	$0.338375\pi$
$542$	−27.6074	−	65.3466i	−0.0509361	−	0.120566i
$543$	48.2685	−	550.121i	0.0888923	−	1.01311i
$544$	375.476	+	823.350i	0.690213	+	1.51351i
$545$	−28.0446	+	48.5747i	−0.0514580	+	0.0891279i
$546$	−704.219	+	227.301i	−1.28978	+	0.416302i
$547$	823.276	−	475.318i	1.50507	−	0.868955i	0.505092	−	0.863066i	$-0.331459\pi$
$547$	823.276	−	475.318i	1.50507	−	0.868955i	0.999983	−	0.00588962i	$-0.00187474\pi$
$548$	387.151	+	97.9224i	0.706481	+	0.178691i
$549$	250.965	+	690.600i	0.457132	+	1.25792i
$550$	210.022	+	26.1487i	0.381858	+	0.0475432i
$551$	408.888	−	236.071i	0.742083	−	0.428442i
$552$	48.6898	+	73.0228i	0.0882062	+	0.132288i
$553$	259.201	−	448.949i	0.468717	−	0.811842i
$554$	532.558	+	402.728i	0.961297	+	0.726946i
$555$	22.8289	+	15.9935i	0.0411332	+	0.0288172i
$556$	367.901	−	104.146i	0.661692	−	0.187313i
$557$	978.257			1.75630			0.878148	−	0.478390i	$-0.158779\pi$
$557$	978.257			1.75630			0.878148	+	0.478390i	$0.158779\pi$
$558$	−654.833	−	201.776i	−1.17354	−	0.361606i
$559$			343.997i			0.615379i
$560$	−294.341	+	8.28169i	−0.525609	+	0.0147887i
$561$	188.173	+	403.803i	0.335425	+	0.719792i
$562$	65.5271	+	49.5525i	0.116596	+	0.0881718i
$563$	925.131	+	534.125i	1.64322	+	0.948712i	0.979680	+	0.200569i	$0.0642792\pi$
$563$	925.131	+	534.125i	1.64322	+	0.948712i	0.663538	+	0.748143i	$0.269054\pi$
$564$	−338.297	−	117.864i	−0.599818	−	0.208979i
$565$	−167.677	−	290.426i	−0.296774	−	0.514028i
$566$	500.928	+	62.3680i	0.885032	+	0.110191i
$567$	666.849	−	116.893i	1.17610	−	0.206161i
$568$	−469.068	−	182.799i	−0.825824	−	0.321830i
$569$	−481.775	−	834.459i	−0.846705	−	1.46654i	−0.884132	−	0.467237i	$-0.845250\pi$
$569$	−481.775	−	834.459i	−0.846705	−	1.46654i	0.0374271	−	0.999299i	$-0.488084\pi$
$570$	−53.0470	+	247.201i	−0.0930649	+	0.433686i
$571$	−243.132	−	140.372i	−0.425800	−	0.245836i	0.271756	−	0.962366i	$-0.412396\pi$
$571$	−243.132	−	140.372i	−0.425800	−	0.245836i	−0.697556	+	0.716531i	$0.745729\pi$
$572$	−222.223	−	216.059i	−0.388502	−	0.377725i
$573$	315.723	+	677.513i	0.550999	+	1.18240i
$574$	−129.133	−	305.658i	−0.224971	−	0.532505i
$575$			73.6944i			0.128164i
$576$	349.759	+	457.652i	0.607220	+	0.794534i
$577$	−552.228			−0.957068			−0.478534	−	0.878069i	$-0.658832\pi$
$577$	−552.228			−0.957068			−0.478534	+	0.878069i	$0.658832\pi$
$578$	−940.869	+	397.495i	−1.62780	+	0.687708i
$579$	−614.680	−	430.633i	−1.06162	−	0.743754i
$580$	−151.469	+	155.791i	−0.261154	+	0.268605i
$581$	−497.311	+	861.367i	−0.855956	+	1.48256i
$582$	−14.3734	+	15.9010i	−0.0246966	+	0.0273213i
$583$	146.034	−	84.3130i	0.250488	−	0.144619i
$584$	−96.7956	+	248.380i	−0.165746	+	0.425308i
$585$	−99.8721	−	274.826i	−0.170722	−	0.469787i
$586$	−10.0528	+	80.7425i	−0.0171550	+	0.137786i
$587$	141.476	−	81.6811i	0.241015	−	0.139150i	−0.374628	−	0.927175i	$-0.622230\pi$
$587$	141.476	−	81.6811i	0.241015	−	0.139150i	0.615643	+	0.788025i	$0.288896\pi$
$588$	−245.894	+	46.8688i	−0.418188	+	0.0797089i
$589$	364.260	−	630.917i	0.618438	−	1.07117i
$590$	24.4188	−	32.2909i	0.0413879	−	0.0547304i
$591$	67.0421	−	764.086i	0.113438	−	1.29287i
$592$	1.89891	+	67.4895i	0.00320762	+	0.114003i
$593$	−818.460			−1.38020			−0.690101	−	0.723713i	$-0.742434\pi$
$593$	−818.460			−1.38020			−0.690101	+	0.723713i	$0.742434\pi$
$594$	174.033	+	223.879i	0.292985	+	0.376901i
$595$		−	520.433i		−	0.874677i
$596$	−74.8238	−	264.319i	−0.125543	−	0.443488i
$597$	−923.782	−	81.0541i	−1.54737	−	0.135769i
$598$	65.0952	−	86.0804i	0.108855	−	0.143947i
$599$	−398.849	−	230.275i	−0.665857	−	0.384433i	0.128648	−	0.991690i	$-0.458936\pi$
$599$	−398.849	−	230.275i	−0.665857	−	0.384433i	−0.794505	+	0.607257i	$0.792270\pi$
$600$	31.1633	+	482.639i	0.0519388	+	0.804399i
$601$	162.324	+	281.153i	0.270090	+	0.467809i	0.968885	−	0.247513i	$-0.0796132\pi$
$601$	162.324	+	281.153i	0.270090	+	0.467809i	−0.698795	+	0.715322i	$0.746280\pi$
$602$	−48.1486	+	386.721i	−0.0799811	+	0.642393i
$603$	−54.6035	−	45.8645i	−0.0905530	−	0.0760605i
$604$	−103.362	+	408.658i	−0.171129	+	0.676587i
$605$	102.854	+	178.148i	0.170006	+	0.294459i
$606$	−60.7290	+	67.1831i	−0.100213	+	0.110863i
$607$	764.054	+	441.127i	1.25874	+	0.726733i	0.972829	−	0.231524i	$-0.0743712\pi$
$607$	764.054	+	441.127i	1.25874	+	0.726733i	0.285909	+	0.958257i	$0.407705\pi$
$608$	−557.198	+	254.101i	−0.916444	+	0.417929i
$609$	−354.952	+	506.653i	−0.582844	+	0.831942i
$610$	331.188	−	139.919i	0.542931	−	0.229376i
$611$			440.510i			0.720966i
$612$	−825.933	+	595.180i	−1.34956	+	0.972516i
$613$	19.4869			0.0317895			0.0158947	−	0.999874i	$-0.494940\pi$
$613$	19.4869			0.0317895			0.0158947	+	0.999874i	$0.494940\pi$
$614$	−106.501	−	252.086i	−0.173454	−	0.410564i
$615$	118.847	−	55.3830i	0.193247	−	0.0900537i
$616$	−219.582	−	273.997i	−0.356464	−	0.444800i
$617$	−48.3314	+	83.7124i	−0.0783329	+	0.135677i	−0.902531	−	0.430625i	$-0.858293\pi$
$617$	−48.3314	+	83.7124i	−0.0783329	+	0.135677i	0.824198	+	0.566302i	$0.191626\pi$
$618$	163.988	−	764.191i	0.265353	−	1.23656i
$619$	−363.937	+	210.119i	−0.587944	+	0.339449i	−0.764284	−	0.644880i	$-0.776907\pi$
$619$	−363.937	+	210.119i	−0.587944	+	0.339449i	0.176340	+	0.984329i	$0.443574\pi$
$620$	−82.2126	+	325.040i	−0.132601	+	0.524258i
$621$	−69.8707	+	69.7656i	−0.112513	+	0.112344i
$622$	850.820	+	105.931i	1.36788	+	0.170307i
$623$	−777.127	+	448.674i	−1.24739	+	0.720184i
$624$	389.921	−	591.285i	0.624873	−	0.947572i
$625$	−142.447	+	246.725i	−0.227915	+	0.394760i
$626$	−19.1014	−	14.4448i	−0.0305135	−	0.0230747i
$627$	−273.272	+	127.345i	−0.435840	+	0.203102i
$628$	234.250	+	827.502i	0.373010	+	1.31768i
$629$	−119.330			−0.189714
$630$	−73.8092	−	322.937i	−0.117157	−	0.512599i
$631$		−	483.230i		−	0.765816i	−0.923787	−	0.382908i	$-0.874923\pi$
$631$		−	483.230i		−	0.765816i	0.923787	−	0.382908i	$-0.125077\pi$
$632$	75.1279	+	490.462i	0.118873	+	0.776047i
$633$	678.100	−	967.910i	1.07125	−	1.52908i
$634$	75.0607	+	56.7619i	0.118392	+	0.0895299i
$635$	−281.124	−	162.307i	−0.442715	−	0.255602i
$636$	251.747	+	291.739i	0.395828	+	0.458710i
$637$	153.903	+	266.568i	0.241606	+	0.418475i
$638$	−257.120	−	32.0127i	−0.403010	−	0.0501767i
$639$	98.6268	−	557.703i	0.154346	−	0.872775i
$640$	214.883	−	182.366i	0.335755	−	0.284947i
$641$	−45.2967	−	78.4562i	−0.0706657	−	0.122397i	0.828528	−	0.559948i	$-0.189179\pi$
$641$	−45.2967	−	78.4562i	−0.0706657	−	0.122397i	−0.899193	+	0.437552i	$0.855846\pi$
$642$	292.767	−	94.4966i	0.456024	−	0.147191i
$643$	453.773	+	261.986i	0.705713	+	0.407444i	0.809472	−	0.587159i	$-0.199754\pi$
$643$	453.773	+	261.986i	0.705713	+	0.407444i	−0.103759	+	0.994602i	$0.533087\pi$
$644$	85.2284	−	87.6602i	0.132342	−	0.136118i
$645$	−153.404	−	13.4599i	−0.237836	−	0.0208681i
$646$	−421.230	−	997.050i	−0.652059	−	1.54342i
$647$			31.3018i			0.0483799i	0.999707	+	0.0241900i	$0.00770066\pi$
$647$			31.3018i			0.0483799i	−0.999707	+	0.0241900i	$0.992299\pi$
$648$	−428.095	+	486.455i	−0.660641	+	0.750702i
$649$	48.2758			0.0743848
$650$	547.828	−	231.445i	0.842813	−	0.356069i
$651$	−83.4316	+	950.879i	−0.128159	+	1.46064i
$652$	96.7752	+	94.0906i	0.148428	+	0.144311i
$653$	445.115	−	770.961i	0.681646	−	1.18065i	−0.292833	−	0.956164i	$-0.594598\pi$
$653$	445.115	−	770.961i	0.681646	−	1.18065i	0.974478	−	0.224481i	$-0.0720688\pi$
$654$	−46.9479	−	145.453i	−0.0717858	−	0.222405i
$655$	−248.565	+	143.509i	−0.379489	+	0.219098i
$656$	279.402	+	150.999i	0.425918	+	0.230181i
$657$	−295.314	−	52.2247i	−0.449489	−	0.0794897i
$658$	−61.6574	+	495.221i	−0.0937042	+	0.752615i
$659$	41.1783	−	23.7743i	0.0624860	−	0.0360763i	−0.468432	−	0.883500i	$-0.655181\pi$
$659$	41.1783	−	23.7743i	0.0624860	−	0.0360763i	0.530918	+	0.847423i	$0.321847\pi$
$660$	105.046	−	90.6456i	0.159160	−	0.137342i
$661$	−24.8421	+	43.0278i	−0.0375826	+	0.0650950i	−0.884205	−	0.467099i	$-0.845299\pi$
$661$	−24.8421	+	43.0278i	−0.0375826	+	0.0650950i	0.846622	+	0.532194i	$0.178632\pi$
$662$	101.895	−	134.743i	0.153920	−	0.203540i
$663$	1025.26	+	718.277i	1.54639	+	1.08337i
$664$	−144.143	−	941.016i	−0.217083	−	1.41719i
$665$	352.200			0.529624
$666$	−74.0464	+	16.9237i	−0.111181	+	0.0254110i
$667$		−	90.2207i		−	0.135263i
$668$	584.695	−	165.516i	0.875292	−	0.247779i
$669$	130.811	+	280.709i	0.195532	+	0.419594i
$670$	−21.0457	+	27.8303i	−0.0314114	+	0.0415377i
$671$	371.287	+	214.362i	0.553333	+	0.319467i
$672$	521.109	−	610.144i	0.775459	−	0.907953i
$673$	−16.4365	−	28.4688i	−0.0244227	−	0.0423013i	0.853556	−	0.521002i	$-0.174441\pi$
$673$	−16.4365	−	28.4688i	−0.0244227	−	0.0423013i	−0.877978	+	0.478700i	$0.841108\pi$
$674$	124.815	−	1002.49i	0.185185	−	1.48738i
$675$	−525.666	+	140.428i	−0.778765	+	0.208041i
$676$	−188.979	−	47.7986i	−0.279555	−	0.0707079i
$677$	457.417	+	792.269i	0.675653	+	1.17026i	0.976278	+	0.216522i	$0.0694714\pi$
$677$	457.417	+	792.269i	0.675653	+	1.17026i	−0.300625	+	0.953742i	$0.597195\pi$
$678$	893.494	+	191.735i	1.31784	+	0.282796i
$679$	25.8587	+	14.9296i	0.0380836	+	0.0219876i
$680$	311.510	+	388.706i	0.458102	+	0.571626i
$681$	−178.818	−	383.728i	−0.262581	−	0.563477i
$682$	−368.283	+	155.591i	−0.540005	+	0.228139i
$683$		−	870.646i		−	1.27474i	−0.770559	−	0.637369i	$-0.780023\pi$
$683$		−	870.646i		−	1.27474i	0.770559	−	0.637369i	$-0.219977\pi$
$684$	−402.785	−	558.946i	−0.588866	−	0.817172i
$685$	219.824			0.320910
$686$	−183.066	−	433.316i	−0.266860	−	0.631656i
$687$	−518.784	−	363.451i	−0.755145	−	0.529041i
$688$	−195.513	−	317.657i	−0.284176	−	0.461711i
$689$	236.917	−	410.352i	0.343856	−	0.595577i
$690$	35.8402	+	32.3971i	0.0519423	+	0.0469523i
$691$	−800.188	+	461.988i	−1.15801	+	0.668580i	−0.950827	−	0.309722i	$-0.899764\pi$
$691$	−800.188	+	461.988i	−1.15801	+	0.668580i	−0.207187	+	0.978301i	$0.566431\pi$
$692$	−460.695	−	116.524i	−0.665744	−	0.168387i
$693$	254.065	−	302.474i	0.366616	−	0.436470i
$694$	−973.405	−	121.194i	−1.40260	−	0.174631i
$695$	182.275	−	105.237i	0.262267	−	0.151420i
$696$	−38.1518	−	590.873i	−0.0548158	−	0.848956i
$697$	−280.663	+	486.123i	−0.402673	+	0.697450i
$698$	−596.526	−	451.102i	−0.854622	−	0.646277i
$699$	−73.4495	+	837.112i	−0.105078	+	1.19758i
$700$	648.262	−	183.511i	0.926089	−	0.262159i
$701$	1191.44			1.69963			0.849815	−	0.527082i	$-0.176714\pi$
$701$	1191.44			1.69963			0.849815	+	0.527082i	$0.176714\pi$
$702$	738.058	+	300.298i	1.05136	+	0.427775i
$703$		−	80.7561i		−	0.114874i
$704$	328.006	+	73.2129i	0.465918	+	0.103996i
$705$	−196.444	−	17.2363i	−0.278644	−	0.0244486i
$706$	−947.650	−	716.626i	−1.34228	−	1.01505i
$707$	109.255	+	63.0786i	0.154534	+	0.0892201i
$708$	20.6556	+	108.368i	0.0291745	+	0.153062i
$709$	655.954	+	1136.15i	0.925182	+	1.60246i	0.791268	+	0.611469i	$0.209421\pi$
$709$	655.954	+	1136.15i	0.925182	+	1.60246i	0.133914	+	0.990993i	$0.457246\pi$
$710$	−274.995	−	34.2383i	−0.387317	−	0.0482229i
$711$	−524.637	+	190.654i	−0.737886	+	0.268149i
$712$	311.870	−	800.266i	0.438020	−	1.12397i
$713$	−69.6056	−	120.560i	−0.0976236	−	0.169089i
$714$	1052.06	+	950.989i	1.47347	+	1.33192i
$715$	−147.754	−	85.3059i	−0.206649	−	0.119309i
$716$	625.751	+	608.392i	0.873954	+	0.849710i
$717$	674.503	−	962.776i	0.940730	−	1.34278i
$718$	319.815	+	757.001i	0.445425	+	1.05432i
$719$			245.763i			0.341813i	0.985287	+	0.170906i	$0.0546695\pi$
$719$			245.763i			0.341813i	−0.985287	+	0.170906i	$0.945330\pi$
$720$	248.424	+	197.019i	0.345034	+	0.273638i
$721$	−1088.78			−1.51010
$722$	9.66652	−	4.08388i	0.0133885	−	0.00565634i
$723$	−128.776	+	60.0097i	−0.178113	+	0.0830010i
$724$	513.278	−	527.923i	0.708947	−	0.729175i
$725$	248.583	−	430.559i	0.342873	−	0.593874i
$726$	−548.071	−	117.611i	−0.754919	−	0.161999i
$727$	−1041.96	+	601.573i	−1.43323	+	0.827473i	−0.997365	−	0.0725411i	$-0.976889\pi$
$727$	−1041.96	+	601.573i	−1.43323	+	0.827473i	−0.435860	+	0.900014i	$0.643556\pi$
$728$	−919.314	−	358.264i	−1.26279	−	0.492121i
$729$	−630.783	−	365.450i	−0.865271	−	0.501304i
$730$	−18.1298	+	145.615i	−0.0248353	+	0.199473i
$731$	570.934	−	329.629i	0.781032	−	0.450929i
$732$	−322.334	+	925.172i	−0.440347	+	1.26390i
$733$	−510.693	+	884.546i	−0.696716	+	1.20675i	0.272883	+	0.962047i	$0.412023\pi$
$733$	−510.693	+	884.546i	−0.696716	+	1.20675i	−0.969599	+	0.244700i	$0.921310\pi$
$734$	−649.363	+	858.702i	−0.884690	+	1.16989i
$735$	−124.897	+	58.2023i	−0.169928	+	0.0791867i
$736$	−11.1865	+	116.487i	−0.0151990	+	0.158270i
$737$	−41.6070			−0.0564546
$738$	−105.213	+	341.451i	−0.142565	+	0.462671i
$739$		−	259.300i		−	0.350879i	−0.984490	−	0.175439i	$-0.943865\pi$
$739$		−	259.300i		−	0.350879i	0.984490	−	0.175439i	$-0.0561346\pi$
$740$	10.1230	+	35.7600i	0.0136797	+	0.0483243i
$741$	−486.090	+	693.838i	−0.655992	+	0.936354i
$742$	323.778	−	428.156i	0.436358	−	0.577030i
$743$	−100.270	−	57.8907i	−0.134953	−	0.0779149i	0.431004	−	0.902350i	$-0.358160\pi$
$743$	−100.270	−	57.8907i	−0.134953	−	0.0779149i	−0.565956	+	0.824435i	$0.691493\pi$
$744$	−506.843	−	760.140i	−0.681240	−	1.02169i
$745$	−75.6076	−	130.956i	−0.101487	−	0.175780i
$746$	37.0458	−	297.545i	0.0496593	−	0.398854i
$747$	1006.59	−	365.795i	1.34750	−	0.489686i
$748$	−145.652	+	575.859i	−0.194723	+	0.769866i
$749$	−214.277	−	371.139i	−0.286084	−	0.495513i
$750$	183.226	+	567.668i	0.244302	+	0.756891i
$751$	543.581	+	313.837i	0.723809	+	0.417891i	0.816153	−	0.577836i	$-0.196103\pi$
$751$	543.581	+	313.837i	0.723809	+	0.417891i	−0.0923438	+	0.995727i	$0.529436\pi$
$752$	−250.367	−	406.781i	−0.332935	−	0.540932i
$753$	−1163.78	−	102.112i	−1.54552	−	0.135607i
$754$	−670.681	+	283.347i	−0.889497	+	0.375792i
$755$			232.035i			0.307331i
$756$	787.691	+	440.899i	1.04192	+	0.583199i
$757$	49.5546			0.0654618			0.0327309	−	0.999464i	$-0.489580\pi$
$757$	49.5546			0.0654618			0.0327309	+	0.999464i	$0.489580\pi$
$758$	143.496	+	339.655i	0.189309	+	0.448093i
$759$	−5.03548	+	57.3899i	−0.00663436	+	0.0756125i
$760$	−263.055	+	210.812i	−0.346124	+	0.277385i
$761$	−13.0738	+	22.6446i	−0.0171798	+	0.0297563i	−0.874488	−	0.485048i	$-0.838802\pi$
$761$	−13.0738	+	22.6446i	−0.0171798	+	0.0297563i	0.857308	+	0.514804i	$0.172135\pi$
$762$	841.804	−	271.709i	1.10473	−	0.356574i
$763$	−184.390	+	106.458i	−0.241664	+	0.139525i
$764$	−244.380	+	966.195i	−0.319869	+	1.26465i
$765$	−360.429	+	429.105i	−0.471149	+	0.560921i
$766$	413.684	+	51.5057i	0.540058	+	0.0672398i
$767$	117.479	−	67.8267i	0.153167	−	0.0884312i
$768$	−24.0034	+	767.625i	−0.0312544	+	0.999511i
$769$	93.5875	−	162.098i	0.121700	−	0.210791i	−0.798738	−	0.601679i	$-0.794499\pi$
$769$	93.5875	−	162.098i	0.121700	−	0.210791i	0.920438	+	0.390888i	$0.127832\pi$
$770$	−154.165	−	116.582i	−0.200214	−	0.151405i
$771$	159.908	+	112.028i	0.207403	+	0.145303i
$772$	−272.566	−	962.854i	−0.353065	−	1.24722i
$773$	−877.069			−1.13463			−0.567315	−	0.823501i	$-0.692018\pi$
$773$	−877.069			−1.13463			−0.567315	+	0.823501i	$0.692018\pi$
$774$	307.525	−	285.512i	0.397319	−	0.368878i
$775$		−	767.131i		−	0.989847i
$776$	−28.2498	+	4.32725i	−0.0364044	+	0.00557635i
$777$	44.6929	+	95.9071i	0.0575198	+	0.123433i
$778$	481.483	+	364.105i	0.618873	+	0.468001i
$779$	−328.981	−	189.937i	−0.422312	−	0.243822i
$780$	128.273	−	368.174i	0.164453	−	0.472018i
$781$	−165.226	−	286.179i	−0.211557	−	0.366427i
$782$	−205.245	−	25.5539i	−0.262461	−	0.0326777i
$783$	643.549	−	171.919i	0.821902	−	0.219565i
$784$	−293.625	−	158.685i	−0.374522	−	0.202405i
$785$	236.704	+	409.984i	0.301534	+	0.522272i
$786$	164.100	−	764.711i	0.208778	−	0.972914i
$787$	577.106	+	333.192i	0.733298	+	0.423370i	0.819628	−	0.572897i	$-0.194180\pi$
$787$	577.106	+	333.192i	0.733298	+	0.423370i	−0.0863293	+	0.996267i	$0.527514\pi$
$788$	712.913	−	733.254i	0.904712	−	0.930526i
$789$	−182.569	−	391.776i	−0.231392	−	0.496548i
$790$	106.294	+	251.598i	0.134550	+	0.318478i
$791$		−	1273.01i		−	1.60936i
$792$	−8.70978	+	377.987i	−0.0109972	+	0.477256i
$793$	1204.70			1.51917
$794$	454.452	−	191.995i	0.572358	−	0.241808i
$795$	173.725	+	121.708i	0.218522	+	0.153092i
$796$	−886.505	−	861.913i	−1.11370	−	1.08281i
$797$	90.8816	−	157.412i	0.114030	−	0.197505i	−0.803362	−	0.595491i	$-0.796957\pi$
$797$	90.8816	−	157.412i	0.114030	−	0.197505i	0.917391	+	0.397986i	$0.130291\pi$
$798$	−643.577	+	711.974i	−0.806487	+	0.892198i
$799$	731.118	−	422.111i	0.915041	−	0.528299i
$800$	−374.338	+	525.085i	−0.467923	+	0.656357i
$801$	951.486	+	168.265i	1.18787	+	0.210069i
$802$	−186.570	+	1498.49i	−0.232631	+	1.86845i
$803$	−151.537	+	87.4900i	−0.188714	+	0.108954i
$804$	−17.8022	−	93.3983i	−0.0221421	−	0.116167i
$805$	33.6505	−	58.2844i	0.0418019	−	0.0724030i
$806$	−677.617	+	896.065i	−0.840716	+	1.11174i
$807$	−18.9875	+	216.402i	−0.0235285	+	0.268157i
$808$	−119.358	+	18.2830i	−0.147720	+	0.0226275i
$809$	114.921			0.142053			0.0710266	−	0.997474i	$-0.477372\pi$
$809$	114.921			0.142053			0.0710266	+	0.997474i	$0.477372\pi$
$810$	−162.795	+	317.384i	−0.200982	+	0.391832i
$811$		−	1378.48i		−	1.69973i	−0.526997	−	0.849867i	$-0.676682\pi$
$811$		−	1378.48i		−	1.69973i	0.526997	−	0.849867i	$-0.323318\pi$
$812$	−793.637	+	224.664i	−0.977386	+	0.276680i
$813$	106.001	+	9.30072i	0.130383	+	0.0114400i
$814$	−26.7310	+	35.3485i	−0.0328391	+	0.0434257i
$815$	64.3449	+	37.1496i	0.0789508	+	0.0455823i
$816$	−1354.99	−	80.5657i	−1.66053	−	0.0987325i
$817$	223.075	+	386.377i	0.273041	+	0.472921i
$818$	−64.6074	+	518.915i	−0.0789822	+	0.634370i
$819$	193.296	−	1093.03i	0.236015	−	1.33459i
$820$	169.487	+	42.8683i	0.206691	+	0.0522784i
$821$	−160.807	−	278.526i	−0.195867	−	0.339252i	0.751317	−	0.659941i	$-0.229419\pi$
$821$	−160.807	−	278.526i	−0.195867	−	0.339252i	−0.947184	+	0.320689i	$0.896085\pi$
$822$	−401.684	+	444.374i	−0.488667	+	0.540601i
$823$	−56.6805	−	32.7245i	−0.0688706	−	0.0397625i	0.465169	−	0.885222i	$-0.345993\pi$
$823$	−56.6805	−	32.7245i	−0.0688706	−	0.0397625i	−0.534040	+	0.845459i	$0.679327\pi$
$824$	813.201	−	651.701i	0.986895	−	0.790899i
$825$	−182.156	+	260.007i	−0.220795	+	0.315159i
$826$	141.564	−	59.8073i	0.171385	−	0.0724059i
$827$			778.406i			0.941240i	0.882336	+	0.470620i	$0.155970\pi$
$827$			778.406i			0.941240i	−0.882336	+	0.470620i	$0.844030\pi$
$828$	−130.982	+	13.2517i	−0.158191	+	0.0160045i
$829$	−81.3426			−0.0981214			−0.0490607	−	0.998796i	$-0.515623\pi$
$829$	−81.3426			−0.0981214			−0.0490607	+	0.998796i	$0.515623\pi$
$830$	−203.940	−	482.724i	−0.245710	−	0.581595i
$831$	−907.803	+	423.038i	−1.09242	+	0.509071i
$832$	901.068	−	282.680i	1.08301	−	0.339760i
$833$	294.950	−	510.869i	0.354082	−	0.613288i
$834$	−120.336	+	560.770i	−0.144288	+	0.672386i
$835$	289.686	−	167.250i	0.346929	−	0.200299i
$836$	−389.710	−	98.5695i	−0.466160	−	0.117906i
$837$	727.328	−	726.233i	0.868970	−	0.867662i
$838$	779.744	+	97.0820i	0.930483	+	0.115850i
$839$	−553.733	+	319.698i	−0.659992	+	0.381046i	−0.792274	−	0.610166i	$-0.791103\pi$
$839$	−553.733	+	319.698i	−0.659992	+	0.381046i	0.132282	+	0.991212i	$0.457769\pi$
$840$	195.737	−	395.946i	0.233021	−	0.471365i
$841$	116.171	−	201.214i	0.138135	−	0.239256i
$842$	−326.865	−	247.180i	−0.388200	−	0.293563i
$843$	−111.698	+	52.0515i	−0.132501	+	0.0617456i
$844$	1516.16	−	429.198i	1.79640	−	0.508529i
$845$	−107.302			−0.126984
$846$	393.806	−	365.616i	0.465491	−	0.432170i
$847$			780.866i			0.921920i
$848$	14.4505	+	513.586i	0.0170406	+	0.605643i
$849$	−434.464	+	620.148i	−0.511736	+	0.730445i
$850$	−909.076	−	687.456i	−1.06950	−	0.808772i
$851$	−13.3641	−	7.71575i	−0.0157040	−	0.00906668i
$852$	571.713	−	493.341i	0.671024	−	0.579038i
$853$	−38.8069	−	67.2155i	−0.0454946	−	0.0787989i	0.842381	−	0.538882i	$-0.181153\pi$
$853$	−38.8069	−	67.2155i	−0.0454946	−	0.0787989i	−0.887876	+	0.460083i	$0.847820\pi$
$854$	1354.33	+	168.620i	1.58586	+	0.197448i
$855$	−290.394	−	243.918i	−0.339643	−	0.285285i
$856$	382.190	+	148.942i	0.446484	+	0.173998i
$857$	436.010	+	755.192i	0.508763	+	0.881204i	0.999948	+	0.0101489i	$0.00323056\pi$
$857$	436.010	+	755.192i	0.508763	+	0.881204i	−0.491185	+	0.871055i	$0.663436\pi$
$858$	442.438	−	142.806i	0.515662	−	0.166440i
$859$	−136.909	−	79.0444i	−0.159382	−	0.0920191i	0.418188	−	0.908361i	$-0.362665\pi$
$859$	−136.909	−	79.0444i	−0.159382	−	0.0920191i	−0.577570	+	0.816342i	$0.695999\pi$
$860$	−147.214	−	143.130i	−0.171179	−	0.166430i
$861$	495.819	+	43.5040i	0.575865	+	0.0505273i
$862$	−360.158	−	852.492i	−0.417816	−	0.988970i
$863$			685.963i			0.794859i	0.917633	+	0.397429i	$0.130098\pi$
$863$			685.963i			0.794859i	−0.917633	+	0.397429i	$0.869902\pi$
$864$	−852.222	+	142.176i	−0.986368	+	0.164556i
$865$	−261.581			−0.302406
$866$	−351.101	+	148.332i	−0.405429	+	0.171284i
$867$	133.913	−	1526.22i	0.154456	−	1.76035i
$868$	−887.196	+	912.509i	−1.02211	+	1.05128i
$869$	−162.848	+	282.060i	−0.187396	+	0.324580i
$870$	−100.115	−	310.174i	−0.115075	−	0.356522i
$871$	−101.251	+	58.4573i	−0.116247	+	0.0671151i
$872$	73.9978	−	189.880i	0.0848598	−	0.217752i
$873$	−10.9814	−	30.2183i	−0.0125789	−	0.0346143i
$874$	17.2935	−	138.898i	0.0197866	−	0.158922i
$875$	719.629	−	415.478i	0.822433	−	0.474832i
$876$	−261.233	−	302.732i	−0.298211	−	0.345585i
$877$	458.905	−	794.847i	0.523267	−	0.906325i	−0.476366	−	0.879247i	$-0.658046\pi$
$877$	458.905	−	794.847i	0.523267	−	0.906325i	0.999633	−	0.0270780i	$-0.00862025\pi$
$878$	528.319	−	698.637i	0.601731	−	0.795715i
$879$	−99.9590	−	70.0294i	−0.113719	−	0.0796694i
$880$	184.925	−	5.20313i	0.210142	−	0.00591264i
$881$	−657.430			−0.746231			−0.373116	−	0.927785i	$-0.621711\pi$
$881$	−657.430			−0.746231			−0.373116	+	0.927785i	$0.621711\pi$
$882$	110.569	−	358.833i	0.125361	−	0.406840i
$883$			618.879i			0.700882i	0.936585	+	0.350441i	$0.113968\pi$
$883$			618.879i			0.700882i	−0.936585	+	0.350441i	$0.886032\pi$
$884$	454.628	+	1606.00i	0.514285	+	1.81674i
$885$	25.6503	+	55.0434i	0.0289834	+	0.0621959i
$886$	−1005.70	+	1329.92i	−1.13511	+	1.50104i
$887$	110.844	+	63.9959i	0.124965	+	0.0721487i	0.561180	−	0.827694i	$-0.310348\pi$
$887$	110.844	+	63.9959i	0.124965	+	0.0721487i	−0.436214	+	0.899843i	$0.643681\pi$
$888$	−90.7867	−	44.8807i	−0.102237	−	0.0505413i
$889$	−616.119	−	1067.15i	−0.693047	−	1.20039i
$890$	58.4131	−	469.164i	0.0656327	−	0.527150i
$891$	−418.960	+	73.4404i	−0.470214	+	0.0824247i
$892$	−101.252	+	400.315i	−0.113511	+	0.448784i
$893$	285.661	+	494.780i	0.319890	+	0.554065i
$894$	402.886	+	86.4557i	0.450656	+	0.0967066i
$895$	416.056	+	240.210i	0.464867	+	0.268391i
$896$	1052.55	−	191.668i	1.17472	−	0.213915i
$897$	68.3781	+	146.733i	0.0762298	+	0.163582i
$898$	885.772	−	374.218i	0.986383	−	0.416724i
$899$			939.164i			1.04468i
$900$	−661.594	−	297.650i	−0.735104	−	0.330723i
$901$	−908.086			−1.00786
$902$	81.1303	+	192.035i	0.0899449	+	0.212899i
$903$	−478.759	−	335.410i	−0.530187	−	0.371440i
$904$	761.970	+	950.796i	0.842887	+	1.05177i
$905$	202.656	−	351.011i	0.223930	−	0.387858i
$906$	−469.060	−	423.999i	−0.517726	−	0.467990i
$907$	13.7946	−	7.96431i	0.0152090	−	0.00878094i	−0.492376	−	0.870382i	$-0.663872\pi$
$907$	13.7946	−	7.96431i	0.0152090	−	0.00878094i	0.507585	+	0.861602i	$0.330538\pi$
$908$	138.411	−	547.230i	0.152435	−	0.602676i
$909$	−46.3972	−	127.675i	−0.0510421	−	0.140456i
$910$	−538.957	−	67.1027i	−0.592260	−	0.0737393i
$911$	−43.9255	+	25.3604i	−0.0482168	+	0.0278380i	−0.523915	−	0.851771i	$-0.675529\pi$
$911$	−43.9255	+	25.3604i	−0.0482168	+	0.0278380i	0.475698	+	0.879609i	$0.342196\pi$
$912$	54.5224	−	916.984i	0.0597833	−	1.00547i
$913$	312.445	−	541.170i	0.342218	−	0.592738i
$914$	−348.759	−	263.737i	−0.381575	−	0.288552i
$915$	−47.1377	+	537.233i	−0.0515166	+	0.587140i
$916$	−230.043	−	812.641i	−0.251139	−	0.887162i
$917$	−1089.52			−1.18814
$918$	−208.824	−	1512.71i	−0.227477	−	1.64784i
$919$			1065.04i			1.15892i	0.815002	+	0.579458i	$0.196736\pi$
$919$			1065.04i			1.15892i	−0.815002	+	0.579458i	$0.803264\pi$
$920$	9.75343	+	63.6739i	0.0106016	+	0.0692107i
$921$	408.919	+	35.8792i	0.443995	+	0.0389568i
$922$	1143.70	+	864.878i	1.24045	+	0.938046i
$923$	−804.156	−	464.279i	−0.871241	−	0.503011i
$924$	517.376	−	98.6148i	0.559931	−	0.106726i
$925$	−42.5181	−	73.6434i	−0.0459655	−	0.0796145i
$926$	−61.0166	−	7.59686i	−0.0658927	−	0.00820396i
$927$	897.719	+	754.044i	0.968413	+	0.813424i
$928$	458.285	−	642.838i	0.493841	−	0.692713i
$929$	171.699	+	297.392i	0.184822	+	0.320121i	0.943516	−	0.331326i	$-0.107496\pi$
$929$	171.699	+	297.392i	0.184822	+	0.320121i	−0.758695	+	0.651446i	$0.774163\pi$
$930$	−373.083	−	337.242i	−0.401164	−	0.362625i
$931$	345.727	+	199.606i	0.371351	+	0.214399i
$932$	−781.048	+	803.333i	−0.838034	+	0.861945i
$933$	−737.932	+	1053.31i	−0.790923	+	1.12895i
$934$	356.978	+	844.964i	0.382203	+	0.904673i
$935$			326.971i			0.349702i
$936$	509.871	+	932.071i	0.544734	+	0.995803i
$937$	−267.742			−0.285744			−0.142872	−	0.989741i	$-0.545634\pi$
$937$	−267.742			−0.285744			−0.142872	+	0.989741i	$0.545634\pi$
$938$	−122.008	+	51.5456i	−0.130073	+	0.0549527i
$939$	32.5605	−	15.1733i	0.0346757	−	0.0161590i
$940$	−188.517	−	183.287i	−0.200550	−	0.194987i
$941$	−610.126	+	1056.77i	−0.648380	+	1.12303i	0.335130	+	0.942172i	$0.391220\pi$
$941$	−610.126	+	1056.77i	−0.648380	+	1.12303i	−0.983510	+	0.180855i	$0.942113\pi$
$942$	−1261.31	−	270.666i	−1.33897	−	0.287331i
$943$	−62.8642	+	36.2946i	−0.0666640	+	0.0384885i
$944$	−69.9342	+	129.404i	−0.0740828	+	0.137080i
$945$	479.868	+	128.968i	0.507797	+	0.136474i
$946$	30.2503	−	242.964i	0.0319770	−	0.256833i
$947$	−1395.84	+	805.888i	−1.47396	+	0.850991i	−0.999570	−	0.0293240i	$-0.990665\pi$
$947$	−1395.84	+	805.888i	−1.47396	+	0.850991i	−0.474390	+	0.880315i	$0.657331\pi$
$948$	−702.838	−	244.872i	−0.741390	−	0.258303i
$949$	−245.845	+	425.815i	−0.259056	+	0.448699i
$950$	465.232	−	615.212i	0.489718	−	0.647592i
$951$	−127.949	+	59.6245i	−0.134542	+	0.0626967i
$952$	286.303	+	1869.09i	0.300739	+	1.96333i
$953$	242.459			0.254416			0.127208	−	0.991876i	$-0.459398\pi$
$953$	242.459			0.254416			0.127208	+	0.991876i	$0.459398\pi$
$954$	−563.482	+	128.787i	−0.590652	+	0.134997i
$955$			548.603i			0.574453i
$956$	1508.12	−	426.922i	1.57753	−	0.446571i
$957$	223.005	−	318.314i	0.233025	−	0.332617i
$958$	794.650	−	1050.83i	0.829488	−	1.09690i
$959$	722.656	+	417.226i	0.753552	+	0.435063i
$960$	90.8030	+	412.888i	0.0945865	+	0.430092i
$961$	244.068	+	422.739i	0.253973	+	0.439895i
$962$	−15.3860	+	123.578i	−0.0159938	+	0.128459i
$963$	−80.3598	+	454.409i	−0.0834473	+	0.471868i
$964$	−183.646	−	46.4496i	−0.190504	−	0.0481842i
$965$	−275.421	−	477.043i	−0.285411	−	0.494346i
$966$	56.3325	+	174.528i	0.0583152	+	0.180671i
$967$	−1543.81	−	891.320i	−1.59650	−	0.921737i	−0.992155	−	0.125011i	$-0.960103\pi$
$967$	−1543.81	−	891.320i	−1.59650	−	0.921737i	−0.604340	−	0.796726i	$-0.706563\pi$
$968$	−467.394	−	583.221i	−0.482845	−	0.602501i
$969$	1617.35	+	141.909i	1.66910	+	0.146449i
$970$	−14.4916	+	6.12238i	−0.0149398	+	0.00631173i
$971$		−	645.136i		−	0.664404i	−0.943208	−	0.332202i	$-0.892208\pi$
$971$		−	645.136i		−	0.664404i	0.943208	−	0.332202i	$-0.107792\pi$
$972$	−344.116	−	909.048i	−0.354029	−	0.935235i
$973$	798.958			0.821129
$974$	−556.973	−	1318.35i	−0.571841	−	1.35354i
$975$	−77.9719	+	888.654i	−0.0799712	+	0.911440i
$976$	−1112.46	+	684.703i	−1.13982	+	0.701540i
$977$	−689.779	+	1194.73i	−0.706017	+	1.22286i	0.260306	+	0.965526i	$0.416176\pi$
$977$	−689.779	+	1194.73i	−0.706017	+	1.22286i	−0.966323	+	0.257331i	$0.917157\pi$
$978$	−192.676	+	62.1900i	−0.197010	+	0.0635890i
$979$	488.244	−	281.888i	0.498717	−	0.287935i
$980$	−178.114	−	45.0505i	−0.181749	−	0.0459699i
$981$	225.760	+	39.9245i	0.230133	+	0.0406977i
$982$	−1315.85	−	163.830i	−1.33997	−	0.166833i
$983$	639.804	−	369.391i	0.650869	−	0.375779i	−0.137920	−	0.990443i	$-0.544042\pi$
$983$	639.804	−	369.391i	0.650869	−	0.375779i	0.788789	+	0.614664i	$0.210708\pi$
$984$	−396.362	+	264.284i	−0.402807	+	0.268582i
$985$	281.478	−	487.534i	0.285764	−	0.494959i
$986$	1112.94	+	841.621i	1.12874	+	0.853571i
$987$	−613.082	−	429.514i	−0.621157	−	0.435171i
$988$	−1086.85	+	307.667i	−1.10005	+	0.311404i
$989$	85.2536			0.0862018
$990$	46.3720	+	202.891i	0.0468404	+	0.204941i
$991$		−	1533.69i		−	1.54762i	−0.633416	−	0.773811i	$-0.718348\pi$
$991$		−	1533.69i		−	1.54762i	0.633416	−	0.773811i	$-0.281652\pi$
$992$	116.447	−	1212.58i	0.117386	−	1.22236i
$993$	107.034	+	229.685i	0.107788	+	0.231304i
$994$	−839.045	−	634.498i	−0.844110	−	0.638328i
$995$	−589.430	−	340.307i	−0.592391	−	0.342017i
$996$	1348.49	+	469.819i	1.35390	+	0.471705i
$997$	−871.274	−	1509.09i	−0.873896	−	1.51363i	−0.857934	−	0.513760i	$-0.828252\pi$
$997$	−871.274	−	1509.09i	−0.873896	−	1.51363i	−0.0159621	−	0.999873i	$-0.505081\pi$
$998$	1051.22	+	130.882i	1.05333	+	0.131144i
$999$	29.5711	−	110.029i	0.0296007	−	0.110139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.3.f.c.31.2	yes	16
3.2	odd	2		108.3.f.c.91.7		16
4.3	odd	2	inner	36.3.f.c.31.8	yes	16
8.3	odd	2		576.3.o.g.319.5		16
8.5	even	2		576.3.o.g.319.4		16
9.2	odd	6		108.3.f.c.19.1		16
9.4	even	3		324.3.d.i.163.3		8
9.5	odd	6		324.3.d.g.163.6		8
9.7	even	3	inner	36.3.f.c.7.8	yes	16
12.11	even	2		108.3.f.c.91.1		16
24.5	odd	2		1728.3.o.g.1279.4		16
24.11	even	2		1728.3.o.g.1279.3		16
36.7	odd	6	inner	36.3.f.c.7.2	✓	16
36.11	even	6		108.3.f.c.19.7		16
36.23	even	6		324.3.d.g.163.5		8
36.31	odd	6		324.3.d.i.163.4		8
72.11	even	6		1728.3.o.g.127.4		16
72.29	odd	6		1728.3.o.g.127.3		16
72.43	odd	6		576.3.o.g.511.4		16
72.61	even	6		576.3.o.g.511.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.c.7.2	✓	16	36.7	odd	6	inner
36.3.f.c.7.8	yes	16	9.7	even	3	inner
36.3.f.c.31.2	yes	16	1.1	even	1	trivial
36.3.f.c.31.8	yes	16	4.3	odd	2	inner
108.3.f.c.19.1		16	9.2	odd	6
108.3.f.c.19.7		16	36.11	even	6
108.3.f.c.91.1		16	12.11	even	2
108.3.f.c.91.7		16	3.2	odd	2
324.3.d.g.163.5		8	36.23	even	6
324.3.d.g.163.6		8	9.5	odd	6
324.3.d.i.163.3		8	9.4	even	3
324.3.d.i.163.4		8	36.31	odd	6
576.3.o.g.319.4		16	8.5	even	2
576.3.o.g.319.5		16	8.3	odd	2
576.3.o.g.511.4		16	72.43	odd	6
576.3.o.g.511.5		16	72.61	even	6
1728.3.o.g.127.3		16	72.29	odd	6
1728.3.o.g.127.4		16	72.11	even	6
1728.3.o.g.1279.3		16	24.11	even	2
1728.3.o.g.1279.4		16	24.5	odd	2

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	36.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.84233 + 0.778342i) q^{2} +(0.262217 - 2.98852i) q^{3} +(2.78837 - 2.86793i) q^{4} +(1.10093 - 1.90686i) q^{5} +(1.84300 + 5.70994i) q^{6} +(7.23844 - 4.17912i) q^{7} +(-2.90487 + 7.45397i) q^{8} +(-8.86248 - 1.56728i) q^{9} +O(q^{10})\)	\(q+(-1.84233 + 0.778342i) q^{2} +(0.262217 - 2.98852i) q^{3} +(2.78837 - 2.86793i) q^{4} +(1.10093 - 1.90686i) q^{5} +(1.84300 + 5.70994i) q^{6} +(7.23844 - 4.17912i) q^{7} +(-2.90487 + 7.45397i) q^{8} +(-8.86248 - 1.56728i) q^{9} +(-0.544081 + 4.36996i) q^{10} +(-4.54769 + 2.62561i) q^{11} +(-7.83969 - 9.08511i) q^{12} +(-7.37788 + 12.7789i) q^{13} +(-10.0828 + 13.3333i) q^{14} +(-5.41000 - 3.79015i) q^{15} +(-0.450004 - 15.9937i) q^{16} +28.2789 q^{17} +(17.5475 - 4.01059i) q^{18} +19.1376i q^{19} +(-2.39894 - 8.47440i) q^{20} +(-10.5913 - 22.7281i) q^{21} +(6.33472 - 8.37689i) q^{22} +(3.16702 + 1.82848i) q^{23} +(21.5146 + 10.6358i) q^{24} +(10.0759 + 17.4520i) q^{25} +(3.64618 - 29.2854i) q^{26} +(-7.00775 + 26.0747i) q^{27} +(8.19805 - 32.4122i) q^{28} +(-12.3355 - 21.3657i) q^{29} +(12.9170 + 2.77188i) q^{30} +(-32.9674 - 19.0338i) q^{31} +(13.2776 + 29.1154i) q^{32} +(6.65419 + 14.2793i) q^{33} +(-52.0991 + 22.0106i) q^{34} -18.4036i q^{35} +(-29.2067 + 21.0468i) q^{36} -4.21977 q^{37} +(-14.8956 - 35.2578i) q^{38} +(36.2553 + 25.3998i) q^{39} +(11.0156 + 13.7454i) q^{40} +(-9.92483 + 17.1903i) q^{41} +(37.2029 + 33.6289i) q^{42} +(20.1894 - 11.6564i) q^{43} +(-5.15057 + 20.3636i) q^{44} +(-12.7455 + 15.1740i) q^{45} +(-7.25787 - 0.903640i) q^{46} +(25.8538 - 14.9267i) q^{47} +(-47.9154 - 2.84897i) q^{48} +(10.4300 - 18.0654i) q^{49} +(-32.1468 - 24.3099i) q^{50} +(7.41521 - 84.5120i) q^{51} +(16.0766 + 56.7914i) q^{52} -32.1118 q^{53} +(-7.38445 - 53.4927i) q^{54} +11.5624i q^{55} +(10.1243 + 66.0950i) q^{56} +(57.1930 + 5.01820i) q^{57} +(39.3559 + 29.7615i) q^{58} +(-7.96159 - 4.59663i) q^{59} +(-25.9549 + 4.94716i) q^{60} +(-40.8215 - 70.7049i) q^{61} +(75.5517 + 9.40656i) q^{62} +(-70.7005 + 25.6927i) q^{63} +(-47.1234 - 43.3057i) q^{64} +(16.2450 + 28.1372i) q^{65} +(-23.3734 - 21.1280i) q^{66} +(6.86179 + 3.96166i) q^{67} +(78.8519 - 81.1017i) q^{68} +(6.29489 - 8.98523i) q^{69} +(14.3243 + 33.9055i) q^{70} +62.9286i q^{71} +(37.4269 - 61.5080i) q^{72} +33.3218 q^{73} +(7.77421 - 3.28442i) q^{74} +(54.7978 - 25.5359i) q^{75} +(54.8852 + 53.3626i) q^{76} +(-21.9454 + 38.0106i) q^{77} +(-86.5639 - 18.5758i) q^{78} +(53.7133 - 31.0114i) q^{79} +(-30.9931 - 16.7497i) q^{80} +(76.0873 + 27.7800i) q^{81} +(4.90489 - 39.3951i) q^{82} +(-103.056 + 59.4995i) q^{83} +(-94.7149 - 32.9991i) q^{84} +(31.1329 - 53.9238i) q^{85} +(-28.1230 + 37.1892i) q^{86} +(-67.0864 + 31.2624i) q^{87} +(-6.36077 - 41.5254i) q^{88} -107.361 q^{89} +(11.6709 - 37.8760i) q^{90} +123.332i q^{91} +(14.0747 - 3.98430i) q^{92} +(-65.5274 + 93.5328i) q^{93} +(-36.0132 + 47.6231i) q^{94} +(36.4927 + 21.0690i) q^{95} +(90.4935 - 32.0458i) q^{96} +(1.78621 + 3.09380i) q^{97} +(-5.15457 + 41.4005i) q^{98} +(44.4189 - 16.1419i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - 5 q^{4} + 6 q^{5} + 9 q^{6} - 54 q^{8} + 18 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 - 5 * q^4 + 6 * q^5 + 9 * q^6 - 54 * q^8 + 18 * q^9	\( 16 q - 3 q^{2} - 5 q^{4} + 6 q^{5} + 9 q^{6} - 54 q^{8} + 18 q^{9} + 20 q^{10} - 36 q^{12} - 46 q^{13} - 12 q^{14} - 17 q^{16} + 12 q^{17} + 48 q^{18} + 36 q^{20} - 66 q^{21} + 33 q^{22} + 129 q^{24} - 30 q^{25} + 72 q^{26} + 12 q^{28} + 42 q^{29} + 84 q^{30} + 87 q^{32} - 168 q^{33} + 11 q^{34} - 81 q^{36} + 56 q^{37} - 99 q^{38} + 68 q^{40} + 84 q^{41} - 354 q^{42} - 222 q^{44} + 174 q^{45} - 264 q^{46} - 189 q^{48} + 58 q^{49} - 219 q^{50} + 110 q^{52} - 72 q^{53} - 105 q^{54} + 270 q^{56} + 366 q^{57} - 16 q^{58} + 432 q^{60} - 34 q^{61} + 516 q^{62} - 254 q^{64} - 30 q^{65} + 510 q^{66} + 375 q^{68} - 54 q^{69} + 150 q^{70} - 45 q^{72} + 116 q^{73} - 372 q^{74} - 15 q^{76} - 330 q^{77} - 294 q^{78} - 720 q^{80} - 102 q^{81} + 254 q^{82} - 714 q^{84} - 140 q^{85} - 273 q^{86} + 75 q^{88} - 384 q^{89} + 108 q^{90} + 258 q^{92} - 486 q^{93} + 36 q^{94} + 900 q^{96} - 148 q^{97} + 1170 q^{98}+O(q^{100}) \) 16 * q - 3 * q^2 - 5 * q^4 + 6 * q^5 + 9 * q^6 - 54 * q^8 + 18 * q^9 + 20 * q^10 - 36 * q^12 - 46 * q^13 - 12 * q^14 - 17 * q^16 + 12 * q^17 + 48 * q^18 + 36 * q^20 - 66 * q^21 + 33 * q^22 + 129 * q^24 - 30 * q^25 + 72 * q^26 + 12 * q^28 + 42 * q^29 + 84 * q^30 + 87 * q^32 - 168 * q^33 + 11 * q^34 - 81 * q^36 + 56 * q^37 - 99 * q^38 + 68 * q^40 + 84 * q^41 - 354 * q^42 - 222 * q^44 + 174 * q^45 - 264 * q^46 - 189 * q^48 + 58 * q^49 - 219 * q^50 + 110 * q^52 - 72 * q^53 - 105 * q^54 + 270 * q^56 + 366 * q^57 - 16 * q^58 + 432 * q^60 - 34 * q^61 + 516 * q^62 - 254 * q^64 - 30 * q^65 + 510 * q^66 + 375 * q^68 - 54 * q^69 + 150 * q^70 - 45 * q^72 + 116 * q^73 - 372 * q^74 - 15 * q^76 - 330 * q^77 - 294 * q^78 - 720 * q^80 - 102 * q^81 + 254 * q^82 - 714 * q^84 - 140 * q^85 - 273 * q^86 + 75 * q^88 - 384 * q^89 + 108 * q^90 + 258 * q^92 - 486 * q^93 + 36 * q^94 + 900 * q^96 - 148 * q^97 + 1170 * q^98

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