LMFDB - Embedded newform 33.3.h.a.14.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,3,Mod(5,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 4]))

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

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

chi := DirichletCharacter("33.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	33.h (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.899184872389$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			14.1
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	33.14
Dual form			33.3.h.a.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(-2.74466 - 1.21113i) q^{3} +(0.927051 - 2.85317i) q^{4} +(3.88998 - 5.35410i) q^{5} +(0.633446 + 2.93236i) q^{6} +(-2.73607 + 8.42075i) q^{7} +(-6.65740 + 2.16312i) q^{8} +(6.06633 + 6.64828i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(-2.74466 - 1.21113i) q^{3} +(0.927051 - 2.85317i) q^{4} +(3.88998 - 5.35410i) q^{5} +(0.633446 + 2.93236i) q^{6} +(-2.73607 + 8.42075i) q^{7} +(-6.65740 + 2.16312i) q^{8} +(6.06633 + 6.64828i) q^{9} -6.61803 q^{10} +(10.8576 - 1.76393i) q^{11} +(-6.00000 + 6.70820i) q^{12} +(10.7082 - 7.77997i) q^{13} +(8.42075 - 2.73607i) q^{14} +(-17.1612 + 9.98392i) q^{15} +(-4.04508 - 2.93893i) q^{16} +(-3.52671 + 4.85410i) q^{17} +(1.81288 - 8.81553i) q^{18} +(2.81966 + 8.67802i) q^{19} +(-11.6699 - 16.0623i) q^{20} +(17.7082 - 19.7984i) q^{21} +(-7.80902 - 7.74721i) q^{22} +17.5279i q^{23} +(20.8921 + 2.12594i) q^{24} +(-5.80902 - 17.8783i) q^{25} +(-12.5882 - 4.09017i) q^{26} +(-8.59808 - 25.5944i) q^{27} +(21.4894 + 15.6129i) q^{28} +(-25.1033 - 8.15654i) q^{29} +(18.1643 + 8.01530i) q^{30} +(5.01722 - 3.64522i) q^{31} +33.0000i q^{32} +(-31.9369 - 8.30863i) q^{33} +6.00000 q^{34} +(34.4423 + 47.4058i) q^{35} +(24.5925 - 11.1450i) q^{36} +(-6.05573 + 18.6376i) q^{37} +(5.36331 - 7.38197i) q^{38} +(-38.8129 + 8.38434i) q^{39} +(-14.3156 + 44.0589i) q^{40} +(5.32282 - 1.72949i) q^{41} +(-26.4258 - 2.68905i) q^{42} -26.2918 q^{43} +(5.03280 - 32.6140i) q^{44} +(59.1935 - 6.61803i) q^{45} +(14.1803 - 10.3026i) q^{46} +(-16.8415 + 5.47214i) q^{47} +(7.54297 + 12.9655i) q^{48} +(-23.7812 - 17.2780i) q^{49} +(-11.0494 + 15.2082i) q^{50} +(15.5586 - 9.05156i) q^{51} +(-12.2705 - 37.7647i) q^{52} +(13.0903 + 18.0172i) q^{53} +(-15.6525 + 22.0000i) q^{54} +(32.7918 - 64.9946i) q^{55} -61.9787i q^{56} +(2.77120 - 27.2332i) q^{57} +(8.15654 + 25.1033i) q^{58} +(-20.8375 - 6.77051i) q^{59} +(12.5765 + 58.2194i) q^{60} +(75.5410 + 54.8838i) q^{61} +(-5.89810 - 1.91641i) q^{62} +(-72.5814 + 32.8929i) q^{63} +(10.5172 - 7.64121i) q^{64} -87.5967i q^{65} +(12.0502 + 30.7212i) q^{66} -76.7902 q^{67} +(10.5801 + 14.5623i) q^{68} +(21.2285 - 48.1080i) q^{69} +(18.1074 - 55.7288i) q^{70} +(38.6878 - 53.2492i) q^{71} +(-54.7670 - 31.1381i) q^{72} +(4.64183 - 14.2861i) q^{73} +(18.6376 - 6.05573i) q^{74} +(-5.70918 + 56.1054i) q^{75} +27.3738 q^{76} +(-14.8536 + 96.2558i) q^{77} +(29.5967 + 26.4721i) q^{78} +(-95.5132 + 69.3944i) q^{79} +(-31.4706 + 10.2254i) q^{80} +(-7.39933 + 80.6613i) q^{81} +(-4.52786 - 3.28969i) q^{82} +(65.3531 - 89.9508i) q^{83} +(-40.0717 - 68.8786i) q^{84} +(12.2705 + 37.7647i) q^{85} +(15.4539 + 21.2705i) q^{86} +(59.0213 + 52.7902i) q^{87} +(-68.4681 + 35.2296i) q^{88} +97.6656i q^{89} +(-40.1472 - 43.9986i) q^{90} +(36.2148 + 111.458i) q^{91} +(50.0100 + 16.2492i) q^{92} +(-18.1854 + 3.92840i) q^{93} +(14.3262 + 10.4086i) q^{94} +(57.4314 + 18.6606i) q^{95} +(39.9673 - 90.5738i) q^{96} +(98.0410 - 71.2310i) q^{97} +29.3951i q^{98} +(77.5932 + 61.4841i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 6 q^{4} + 10 q^{6} - 4 q^{7} + 2 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 6 * q^4 + 10 * q^6 - 4 * q^7 + 2 * q^9	$ 8 q + 4 q^{3} - 6 q^{4} + 10 q^{6} - 4 q^{7} + 2 q^{9} - 44 q^{10} - 48 q^{12} + 32 q^{13} - 50 q^{15} - 10 q^{16} + 40 q^{18} + 112 q^{19} + 88 q^{21} - 58 q^{22} + 70 q^{24} - 42 q^{25} - 44 q^{27} + 78 q^{28} - 12 q^{30} - 18 q^{31} - 90 q^{33} + 48 q^{34} + 6 q^{36} - 120 q^{37} - 64 q^{39} + 42 q^{40} - 70 q^{42} - 264 q^{43} + 80 q^{45} + 24 q^{46} + 20 q^{48} - 150 q^{49} + 60 q^{51} + 36 q^{52} + 316 q^{55} + 136 q^{57} + 186 q^{58} + 180 q^{60} + 336 q^{61} + 4 q^{63} + 26 q^{64} - 124 q^{66} - 24 q^{67} - 240 q^{69} + 42 q^{70} - 280 q^{72} - 182 q^{73} - 136 q^{75} - 264 q^{76} + 40 q^{78} - 460 q^{79} + 158 q^{81} - 72 q^{82} + 24 q^{84} - 36 q^{85} + 660 q^{87} - 266 q^{88} - 16 q^{90} + 84 q^{91} + 36 q^{93} + 52 q^{94} - 330 q^{96} + 516 q^{97} + 40 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 6 * q^4 + 10 * q^6 - 4 * q^7 + 2 * q^9 - 44 * q^10 - 48 * q^12 + 32 * q^13 - 50 * q^15 - 10 * q^16 + 40 * q^18 + 112 * q^19 + 88 * q^21 - 58 * q^22 + 70 * q^24 - 42 * q^25 - 44 * q^27 + 78 * q^28 - 12 * q^30 - 18 * q^31 - 90 * q^33 + 48 * q^34 + 6 * q^36 - 120 * q^37 - 64 * q^39 + 42 * q^40 - 70 * q^42 - 264 * q^43 + 80 * q^45 + 24 * q^46 + 20 * q^48 - 150 * q^49 + 60 * q^51 + 36 * q^52 + 316 * q^55 + 136 * q^57 + 186 * q^58 + 180 * q^60 + 336 * q^61 + 4 * q^63 + 26 * q^64 - 124 * q^66 - 24 * q^67 - 240 * q^69 + 42 * q^70 - 280 * q^72 - 182 * q^73 - 136 * q^75 - 264 * q^76 + 40 * q^78 - 460 * q^79 + 158 * q^81 - 72 * q^82 + 24 * q^84 - 36 * q^85 + 660 * q^87 - 266 * q^88 - 16 * q^90 + 84 * q^91 + 36 * q^93 + 52 * q^94 - 330 * q^96 + 516 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

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 $

$2$	−0.587785	−	0.809017i	−0.293893	−	0.404508i	0.636381	−	0.771375i	$-0.280431\pi$
$2$	−0.587785	−	0.809017i	−0.293893	−	0.404508i	−0.930274	+	0.366866i	$0.880431\pi$
$3$	−2.74466	−	1.21113i	−0.914887	−	0.403710i
$3$	−2.74466	−	1.21113i	−0.914887	−	0.403710i
$4$	0.927051	−	2.85317i	0.231763	−	0.713292i
$5$	3.88998	−	5.35410i	0.777997	−	1.07082i	−0.217504	−	0.976060i	$-0.569791\pi$
$5$	3.88998	−	5.35410i	0.777997	−	1.07082i	0.995500	−	0.0947609i	$-0.0302086\pi$
$6$	0.633446	+	2.93236i	0.105574	+	0.488727i
$7$	−2.73607	+	8.42075i	−0.390867	+	1.20296i	0.541267	+	0.840851i	$0.317945\pi$
$7$	−2.73607	+	8.42075i	−0.390867	+	1.20296i	−0.932134	+	0.362114i	$0.882055\pi$
$8$	−6.65740	+	2.16312i	−0.832174	+	0.270390i
$9$	6.06633	+	6.64828i	0.674036	+	0.738698i
$10$	−6.61803			−0.661803
$11$	10.8576	−	1.76393i	0.987059	−	0.160357i
$11$	10.8576	−	1.76393i	0.987059	−	0.160357i
$12$	−6.00000	+	6.70820i	−0.500000	+	0.559017i
$13$	10.7082	−	7.77997i	0.823708	−	0.598459i	−0.0940642	−	0.995566i	$-0.529986\pi$
$13$	10.7082	−	7.77997i	0.823708	−	0.598459i	0.917772	+	0.397107i	$0.129986\pi$
$14$	8.42075	−	2.73607i	0.601482	−	0.195433i
$15$	−17.1612	+	9.98392i	−1.14408	+	0.665595i
$16$	−4.04508	−	2.93893i	−0.252818	−	0.183683i
$17$	−3.52671	+	4.85410i	−0.207454	+	0.285535i	−0.900047	−	0.435793i	$-0.856468\pi$
$17$	−3.52671	+	4.85410i	−0.207454	+	0.285535i	0.692593	+	0.721328i	$0.256468\pi$
$18$	1.81288	−	8.81553i	0.100715	−	0.489751i
$19$	2.81966	+	8.67802i	0.148403	+	0.456738i	0.997433	−	0.0716071i	$-0.0228128\pi$
$19$	2.81966	+	8.67802i	0.148403	+	0.456738i	−0.849030	+	0.528345i	$0.822813\pi$
$20$	−11.6699	−	16.0623i	−0.583497	−	0.803115i
$21$	17.7082	−	19.7984i	0.843248	−	0.942780i
$22$	−7.80902	−	7.74721i	−0.354955	−	0.352146i
$23$			17.5279i			0.762081i	0.924558	+	0.381041i	$0.124434\pi$
$23$			17.5279i			0.762081i	−0.924558	+	0.381041i	$0.875566\pi$
$24$	20.8921	+	2.12594i	0.870505	+	0.0885810i
$25$	−5.80902	−	17.8783i	−0.232361	−	0.715133i
$26$	−12.5882	−	4.09017i	−0.484163	−	0.157314i
$27$	−8.59808	−	25.5944i	−0.318447	−	0.947941i
$28$	21.4894	+	15.6129i	0.767477	+	0.557605i
$29$	−25.1033	−	8.15654i	−0.865629	−	0.281260i	−0.157652	−	0.987495i	$-0.550392\pi$
$29$	−25.1033	−	8.15654i	−0.865629	−	0.281260i	−0.707978	+	0.706235i	$0.750392\pi$
$30$	18.1643	+	8.01530i	0.605475	+	0.267177i
$31$	5.01722	−	3.64522i	0.161846	−	0.117588i	−0.503914	−	0.863754i	$-0.668107\pi$
$31$	5.01722	−	3.64522i	0.161846	−	0.117588i	0.665760	+	0.746166i	$0.268107\pi$
$32$			33.0000i			1.03125i
$33$	−31.9369	−	8.30863i	−0.967785	−	0.251777i
$34$	6.00000			0.176471
$35$	34.4423	+	47.4058i	0.984066	+	1.35445i
$36$	24.5925	−	11.1450i	0.683124	−	0.309582i
$37$	−6.05573	+	18.6376i	−0.163668	+	0.503719i	−0.998936	−	0.0461247i	$-0.985313\pi$
$37$	−6.05573	+	18.6376i	−0.163668	+	0.503719i	0.835267	+	0.549844i	$0.185313\pi$
$38$	5.36331	−	7.38197i	0.141140	−	0.194262i
$39$	−38.8129	+	8.38434i	−0.995204	+	0.214983i
$40$	−14.3156	+	44.0589i	−0.357890	+	1.10147i
$41$	5.32282	−	1.72949i	0.129825	−	0.0421827i	−0.243384	−	0.969930i	$-0.578257\pi$
$41$	5.32282	−	1.72949i	0.129825	−	0.0421827i	0.373209	+	0.927747i	$0.378257\pi$
$42$	−26.4258	−	2.68905i	−0.629187	−	0.0640249i
$43$	−26.2918			−0.611437			−0.305719	−	0.952122i	$-0.598897\pi$
$43$	−26.2918			−0.611437			−0.305719	+	0.952122i	$0.598897\pi$
$44$	5.03280	−	32.6140i	0.114382	−	0.741227i
$45$	59.1935	−	6.61803i	1.31541	−	0.147067i
$46$	14.1803	−	10.3026i	0.308268	−	0.223970i
$47$	−16.8415	+	5.47214i	−0.358330	+	0.116428i	−0.482649	−	0.875814i	$-0.660325\pi$
$47$	−16.8415	+	5.47214i	−0.358330	+	0.116428i	0.124319	+	0.992242i	$0.460325\pi$
$48$	7.54297	+	12.9655i	0.157145	+	0.270114i
$49$	−23.7812	−	17.2780i	−0.485330	−	0.352613i
$50$	−11.0494	+	15.2082i	−0.220988	+	0.304164i
$51$	15.5586	−	9.05156i	0.305070	−	0.177482i
$52$	−12.2705	−	37.7647i	−0.235971	−	0.726245i
$53$	13.0903	+	18.0172i	0.246986	+	0.339948i	0.914453	−	0.404692i	$-0.132621\pi$
$53$	13.0903	+	18.0172i	0.246986	+	0.339948i	−0.667467	+	0.744640i	$0.732621\pi$
$54$	−15.6525	+	22.0000i	−0.289861	+	0.407407i
$55$	32.7918	−	64.9946i	0.596214	−	1.18172i
$56$		−	61.9787i		−	1.10676i
$57$	2.77120	−	27.2332i	0.0486176	−	0.477775i
$58$	8.15654	+	25.1033i	0.140630	+	0.432815i
$59$	−20.8375	−	6.77051i	−0.353178	−	0.114754i	0.127055	−	0.991896i	$-0.459448\pi$
$59$	−20.8375	−	6.77051i	−0.353178	−	0.114754i	−0.480232	+	0.877141i	$0.659448\pi$
$60$	12.5765	+	58.2194i	0.209609	+	0.970323i
$61$	75.5410	+	54.8838i	1.23838	+	0.899734i	0.997489	−	0.0708190i	$-0.0225613\pi$
$61$	75.5410	+	54.8838i	1.23838	+	0.899734i	0.240888	+	0.970553i	$0.422561\pi$
$62$	−5.89810	−	1.91641i	−0.0951306	−	0.0309098i
$63$	−72.5814	+	32.8929i	−1.15209	+	0.522109i
$64$	10.5172	−	7.64121i	0.164332	−	0.119394i
$65$		−	87.5967i		−	1.34764i
$66$	12.0502	+	30.7212i	0.182579	+	0.465473i
$67$	−76.7902			−1.14612			−0.573062	−	0.819512i	$-0.694244\pi$
$67$	−76.7902			−1.14612			−0.573062	+	0.819512i	$0.694244\pi$
$68$	10.5801	+	14.5623i	0.155590	+	0.214152i
$69$	21.2285	−	48.1080i	0.307660	−	0.697218i
$70$	18.1074	−	55.7288i	0.258677	−	0.796126i
$71$	38.6878	−	53.2492i	0.544899	−	0.749989i	−0.444410	−	0.895823i	$-0.646587\pi$
$71$	38.6878	−	53.2492i	0.544899	−	0.749989i	0.989309	+	0.145834i	$0.0465867\pi$
$72$	−54.7670	−	31.1381i	−0.760652	−	0.432473i
$73$	4.64183	−	14.2861i	0.0635867	−	0.195700i	−0.914216	−	0.405227i	$-0.867192\pi$
$73$	4.64183	−	14.2861i	0.0635867	−	0.195700i	0.977803	+	0.209527i	$0.0671925\pi$
$74$	18.6376	−	6.05573i	0.251860	−	0.0818342i
$75$	−5.70918	+	56.1054i	−0.0761224	+	0.748072i
$76$	27.3738			0.360182
$77$	−14.8536	+	96.2558i	−0.192904	+	1.25008i
$78$	29.5967	+	26.4721i	0.379445	+	0.339386i
$79$	−95.5132	+	69.3944i	−1.20903	+	0.878410i	−0.995142	−	0.0984491i	$-0.968612\pi$
$79$	−95.5132	+	69.3944i	−1.20903	+	0.878410i	−0.213885	+	0.976859i	$0.568612\pi$
$80$	−31.4706	+	10.2254i	−0.393383	+	0.127818i
$81$	−7.39933	+	80.6613i	−0.0913497	+	0.995819i
$82$	−4.52786	−	3.28969i	−0.0552179	−	0.0401181i
$83$	65.3531	−	89.9508i	0.787387	−	1.08375i	−0.207042	−	0.978332i	$-0.566384\pi$
$83$	65.3531	−	89.9508i	0.787387	−	1.08375i	0.994429	−	0.105413i	$-0.0336165\pi$
$84$	−40.0717	−	68.8786i	−0.477044	−	0.819983i
$85$	12.2705	+	37.7647i	0.144359	+	0.444291i
$86$	15.4539	+	21.2705i	0.179697	+	0.247332i
$87$	59.0213	+	52.7902i	0.678406	+	0.606784i
$88$	−68.4681	+	35.2296i	−0.778046	+	0.400336i
$89$			97.6656i			1.09737i	0.836030	+	0.548683i	$0.184871\pi$
$89$			97.6656i			1.09737i	−0.836030	+	0.548683i	$0.815129\pi$
$90$	−40.1472	−	43.9986i	−0.446080	−	0.488873i
$91$	36.2148	+	111.458i	0.397965	+	1.22481i
$92$	50.0100	+	16.2492i	0.543587	+	0.176622i
$93$	−18.1854	+	3.92840i	−0.195542	+	0.0422408i
$94$	14.3262	+	10.4086i	0.152407	+	0.110730i
$95$	57.4314	+	18.6606i	0.604541	+	0.196427i
$96$	39.9673	−	90.5738i	0.416326	−	0.943477i
$97$	98.0410	−	71.2310i	1.01073	−	0.734340i	0.0463696	−	0.998924i	$-0.485235\pi$
$97$	98.0410	−	71.2310i	1.01073	−	0.734340i	0.964363	+	0.264584i	$0.0852348\pi$
$98$			29.3951i			0.299950i
$99$	77.5932	+	61.4841i	0.783770	+	0.621052i
$100$	−56.3951			−0.563951
$101$	−109.086	−	150.144i	−1.08006	−	1.48658i	−0.859453	−	0.511215i	$-0.829195\pi$
$101$	−109.086	−	150.144i	−1.08006	−	1.48658i	−0.220609	−	0.975362i	$-0.570805\pi$
$102$	−16.4680	−	7.26678i	−0.161451	−	0.0712429i
$103$	53.3328	−	164.142i	0.517794	−	1.59361i	−0.260345	−	0.965516i	$-0.583836\pi$
$103$	53.3328	−	164.142i	0.517794	−	1.59361i	0.778140	−	0.628091i	$-0.216164\pi$
$104$	−54.4598	+	74.9574i	−0.523652	+	0.720744i
$105$	−37.1179	−	171.827i	−0.353504	−	1.63645i
$106$	6.88197	−	21.1805i	0.0649242	−	0.199816i
$107$	−62.5625	+	20.3278i	−0.584696	+	0.189979i	−0.586403	−	0.810019i	$-0.699457\pi$
$107$	−62.5625	+	20.3278i	−0.584696	+	0.189979i	0.00170704	+	0.999999i	$0.499457\pi$
$108$	−80.9960	+	0.804470i	−0.749963	+	0.00744879i
$109$	−107.331			−0.984690			−0.492345	−	0.870400i	$-0.663860\pi$
$109$	−107.331			−0.984690			−0.492345	+	0.870400i	$0.663860\pi$
$110$	−71.8563	+	11.6738i	−0.653239	+	0.106125i
$111$	39.1935	−	43.8197i	0.353095	−	0.394772i
$112$	35.8156	−	26.0216i	0.319782	−	0.232335i
$113$	−30.1158	+	9.78522i	−0.266512	+	0.0865949i	−0.439224	−	0.898377i	$-0.644747\pi$
$113$	−30.1158	+	9.78522i	−0.266512	+	0.0865949i	0.172713	+	0.984972i	$0.444747\pi$
$114$	−23.6610	+	13.7653i	−0.207553	+	0.120748i
$115$	93.8460	+	68.1831i	0.816052	+	0.592896i
$116$	−46.5440	+	64.0623i	−0.401241	+	0.552261i
$117$	116.683	+	23.9953i	0.997290	+	0.205088i
$118$	6.77051	+	20.8375i	0.0573772	+	0.176589i
$119$	−31.2259	−	42.9787i	−0.262402	−	0.361166i
$120$	92.6525	−	103.589i	0.772104	−	0.863238i
$121$	114.777	−	38.3043i	0.948571	−	0.316565i
$122$		−	93.3738i		−	0.765359i
$123$	−16.7040	−	1.69977i	−0.135805	−	0.0138192i
$124$	−5.74922	−	17.6943i	−0.0463647	−	0.142696i
$125$	39.0338	+	12.6829i	0.312270	+	0.101463i
$126$	69.2732	+	39.3856i	0.549787	+	0.312585i
$127$	−82.0476	−	59.6111i	−0.646044	−	0.469378i	0.215877	−	0.976421i	$-0.430739\pi$
$127$	−82.0476	−	59.6111i	−0.646044	−	0.469378i	−0.861921	+	0.507042i	$0.830739\pi$
$128$	113.176	+	36.7730i	0.884185	+	0.287289i
$129$	72.1621	+	31.8428i	0.559396	+	0.246843i
$130$	−70.8673	+	51.4881i	−0.545133	+	0.396062i
$131$			130.992i			0.999938i	0.866043	+	0.499969i	$0.166655\pi$
$131$			130.992i			0.999938i	−0.866043	+	0.499969i	$0.833345\pi$
$132$	−53.3131	+	83.4189i	−0.403887	+	0.631961i
$133$	−80.7902			−0.607445
$134$	45.1362	+	62.1246i	0.336837	+	0.463617i
$135$	−170.481	−	53.5268i	−1.26283	−	0.396495i
$136$	12.9787	−	39.9444i	0.0954317	−	0.293709i
$137$	−122.699	+	168.880i	−0.895612	+	1.23270i	0.0762351	+	0.997090i	$0.475710\pi$
$137$	−122.699	+	168.880i	−0.895612	+	1.23270i	−0.971847	+	0.235614i	$0.924290\pi$
$138$	−51.3980	+	11.1030i	−0.372450	+	0.0804563i
$139$	−25.2098	+	77.5877i	−0.181365	+	0.558185i	−0.999867	−	0.0163196i	$-0.994805\pi$
$139$	−25.2098	+	77.5877i	−0.181365	+	0.558185i	0.818502	+	0.574504i	$0.194805\pi$
$140$	167.186	−	54.3222i	1.19419	−	0.388016i
$141$	52.8517	+	5.37809i	0.374835	+	0.0381425i
$142$	−65.8197			−0.463519
$143$	102.543	−	103.361i	0.717081	−	0.722802i
$144$	−5.00000	−	44.7214i	−0.0347222	−	0.310565i
$145$	−141.322	+	102.677i	−0.974636	+	0.708114i
$146$	−14.2861	+	4.64183i	−0.0978499	+	0.0317934i
$147$	44.3453	+	76.2244i	0.301669	+	0.518533i
$148$	47.5623	+	34.5560i	0.321367	+	0.233487i
$149$	−4.10972	+	5.65654i	−0.0275820	+	0.0379634i	−0.822585	−	0.568642i	$-0.807469\pi$
$149$	−4.10972	+	5.65654i	−0.0275820	+	0.0379634i	0.795003	+	0.606605i	$0.207469\pi$
$150$	48.7460	−	28.3591i	0.324973	−	0.189061i
$151$	−17.1353	−	52.7369i	−0.113479	−	0.349251i	0.878148	−	0.478389i	$-0.158779\pi$
$151$	−17.1353	−	52.7369i	−0.113479	−	0.349251i	−0.991627	+	0.129138i	$0.958779\pi$
$152$	−37.5432	−	51.6738i	−0.246995	−	0.339959i
$153$	−53.6656	+	6.00000i	−0.350756	+	0.0392157i
$154$	86.6033	−	44.5609i	0.562359	−	0.289356i
$155$		−	41.0426i		−	0.264791i
$156$	−12.0596	+	118.513i	−0.0773053	+	0.759696i
$157$	12.9787	+	39.9444i	0.0826670	+	0.254423i	0.983844	−	0.179029i	$-0.0572955\pi$
$157$	12.9787	+	39.9444i	0.0826670	+	0.254423i	−0.901177	+	0.433452i	$0.857296\pi$
$158$	112.282	+	36.4828i	0.710648	+	0.230904i
$159$	−14.1072	−	65.3052i	−0.0887244	−	0.410724i
$160$	176.685	+	128.369i	1.10428	+	0.802309i
$161$	−147.598	−	47.9574i	−0.916756	−	0.297872i
$162$	69.6056	−	41.4254i	0.429664	−	0.255712i
$163$	128.464	−	93.3346i	0.788123	−	0.572605i	−0.119283	−	0.992860i	$-0.538060\pi$
$163$	128.464	−	93.3346i	0.788123	−	0.572605i	0.907406	+	0.420256i	$0.138060\pi$
$164$		−	16.7902i		−	0.102380i
$165$	−168.719	+	138.673i	−1.02254	+	0.840443i
$166$	−111.185			−0.669791
$167$	−167.623	−	230.713i	−1.00373	−	1.38152i	−0.923008	−	0.384780i	$-0.874277\pi$
$167$	−167.623	−	230.713i	−1.00373	−	1.38152i	−0.0807219	−	0.996737i	$-0.525723\pi$
$168$	−75.0643	+	170.111i	−0.446811	+	1.01256i
$169$	1.91390	−	5.89036i	0.0113248	−	0.0348542i
$170$	23.3399	−	32.1246i	0.137294	−	0.188968i
$171$	−40.5890	+	71.3896i	−0.237362	+	0.417483i
$172$	−24.3738	+	75.0150i	−0.141708	+	0.436133i
$173$	−56.8716	+	18.4787i	−0.328738	+	0.106813i	−0.468736	−	0.883338i	$-0.655290\pi$
$173$	−56.8716	+	18.4787i	−0.328738	+	0.106813i	0.139998	+	0.990152i	$0.455290\pi$
$174$	8.01636	−	78.7786i	0.0460710	−	0.452750i
$175$	166.443			0.951101
$176$	−49.1042	−	24.7746i	−0.279001	−	0.140765i
$177$	48.9919	+	43.8197i	0.276790	+	0.247569i
$178$	79.0132	−	57.4064i	0.443894	−	0.322508i
$179$	250.925	−	81.5304i	1.40181	−	0.455477i	0.492037	−	0.870574i	$-0.336252\pi$
$179$	250.925	−	81.5304i	1.40181	−	0.455477i	0.909777	+	0.415097i	$0.136252\pi$
$180$	35.9930	−	175.024i	0.199961	−	0.972357i
$181$	−182.812	−	132.820i	−1.01001	−	0.733814i	−0.0457976	−	0.998951i	$-0.514583\pi$
$181$	−182.812	−	132.820i	−1.01001	−	0.733814i	−0.964211	+	0.265137i	$0.914583\pi$
$182$	68.8846	−	94.8115i	0.378487	−	0.520942i
$183$	−140.863	−	242.127i	−0.769744	−	1.32310i
$184$	−37.9149	−	116.690i	−0.206059	−	0.634184i
$185$	76.2310	+	104.923i	0.412060	+	0.567151i
$186$	13.8673	+	12.4033i	0.0745551	+	0.0666842i
$187$	−29.7295	+	58.9250i	−0.158981	+	0.315107i
$188$			53.1246i			0.282578i
$189$	239.049	−	2.37429i	1.26481	−	0.0125624i
$190$	−18.6606	−	57.4314i	−0.0982137	−	0.302271i
$191$	−57.1444	−	18.5673i	−0.299185	−	0.0972112i	0.155578	−	0.987824i	$-0.450276\pi$
$191$	−57.1444	−	18.5673i	−0.299185	−	0.0972112i	−0.454763	+	0.890612i	$0.650276\pi$
$192$	−38.1207	+	8.23480i	−0.198545	+	0.0428896i
$193$	−28.8713	−	20.9762i	−0.149592	−	0.108685i	0.510472	−	0.859895i	$-0.329471\pi$
$193$	−28.8713	−	20.9762i	−0.149592	−	0.108685i	−0.660064	+	0.751209i	$0.729471\pi$
$194$	−115.254	−	37.4483i	−0.594093	−	0.193033i
$195$	−106.091	+	240.423i	−0.544057	+	1.23294i
$196$	−71.3435	+	51.8341i	−0.363997	+	0.264459i
$197$		−	145.605i		−	0.739111i	−0.929209	−	0.369556i	$-0.879510\pi$
$197$		−	145.605i		−	0.739111i	0.929209	−	0.369556i	$-0.120490\pi$
$198$	4.13358	−	98.9137i	0.0208767	−	0.499564i
$199$	241.185			1.21199			0.605993	−	0.795470i	$-0.292776\pi$
$199$	241.185			1.21199			0.605993	+	0.795470i	$0.292776\pi$
$200$	77.3458	+	106.457i	0.386729	+	0.532287i
$201$	210.763	+	93.0030i	1.04857	+	0.462701i
$202$	−57.3500	+	176.505i	−0.283911	+	0.873788i
$203$	137.368	−	189.071i	0.676692	−	0.931386i
$204$	−11.4020	−	52.7825i	−0.0558923	−	0.258738i
$205$	11.4458	−	35.2266i	0.0558333	−	0.171837i
$206$	−164.142	+	53.3328i	−0.796804	+	0.258897i
$207$	−116.530	+	106.330i	−0.562948	+	0.513670i
$208$	−66.1803			−0.318175
$209$	45.9223	+	89.2492i	0.219724	+	0.427030i
$210$	−117.193	+	131.026i	−0.558064	+	0.623935i
$211$	−34.5755	+	25.1205i	−0.163865	+	0.119055i	−0.666696	−	0.745330i	$-0.732292\pi$
$211$	−34.5755	+	25.1205i	−0.163865	+	0.119055i	0.502831	+	0.864385i	$0.332292\pi$
$212$	63.5415	−	20.6459i	0.299724	−	0.0973863i
$213$	−170.677	+	99.2951i	−0.801299	+	0.466174i
$214$	53.2188	+	38.6658i	0.248686	+	0.180681i
$215$	−102.275	+	140.769i	−0.475696	+	0.654739i
$216$	112.605	+	151.793i	0.521317	+	0.702747i
$217$	16.9681	+	52.2224i	0.0781939	+	0.240656i
$218$	63.0877	+	86.8328i	0.289393	+	0.398316i
$219$	−30.0426	+	33.5886i	−0.137181	+	0.153373i
$220$	−155.041	−	153.814i	−0.704732	−	0.699154i
$221$			79.4164i			0.359350i
$222$	−58.4882	−	5.95165i	−0.263460	−	0.0268093i
$223$	−51.2943	−	157.868i	−0.230019	−	0.707927i	−0.997743	−	0.0671458i	$-0.978611\pi$
$223$	−51.2943	−	157.868i	−0.230019	−	0.707927i	0.767724	−	0.640781i	$-0.221389\pi$
$224$	−277.885	−	90.2902i	−1.24056	−	0.403081i
$225$	83.6207	−	147.076i	0.371648	−	0.653670i
$226$	25.6180	+	18.6126i	0.113354	+	0.0823566i
$227$	324.855	+	105.552i	1.43108	+	0.464985i	0.919104	−	0.394016i	$-0.128914\pi$
$227$	324.855	+	105.552i	1.43108	+	0.464985i	0.511974	+	0.859001i	$0.328914\pi$
$228$	−75.1319	−	33.1533i	−0.329526	−	0.145409i
$229$	−199.644	+	145.050i	−0.871809	+	0.633407i	−0.931072	−	0.364836i	$-0.881125\pi$
$229$	−199.644	+	145.050i	−0.871809	+	0.633407i	0.0592625	+	0.998242i	$0.481125\pi$
$230$		−	116.000i		−	0.504348i
$231$	157.346	−	246.200i	0.681154	−	1.06580i
$232$	184.766			0.796405
$233$	234.156	+	322.289i	1.00496	+	1.38321i	0.922230	+	0.386642i	$0.126365\pi$
$233$	234.156	+	322.289i	1.00496	+	1.38321i	0.0827332	+	0.996572i	$0.473635\pi$
$234$	−49.1718	−	108.503i	−0.210136	−	0.463686i
$235$	−36.2148	+	111.458i	−0.154105	+	0.474288i
$236$	−38.6348	+	53.1763i	−0.163707	+	0.225323i
$237$	346.197	−	74.7852i	1.46075	−	0.315549i
$238$	−16.4164	+	50.5245i	−0.0689765	+	0.212288i
$239$	−153.320	+	49.8166i	−0.641505	+	0.208437i	−0.611665	−	0.791117i	$-0.709500\pi$
$239$	−153.320	+	49.8166i	−0.641505	+	0.208437i	−0.0298400	+	0.999555i	$0.509500\pi$
$240$	98.7605	+	10.0497i	0.411502	+	0.0418737i
$241$	−159.644			−0.662425			−0.331212	−	0.943556i	$-0.607458\pi$
$241$	−159.644			−0.662425			−0.331212	+	0.943556i	$0.607458\pi$
$242$	−98.4531	−	70.3419i	−0.406831	−	0.290669i
$243$	118.000	−	212.426i	0.485597	−	0.874183i
$244$	226.623	−	164.651i	0.928783	−	0.674800i
$245$	−185.017	+	60.1155i	−0.755170	+	0.245369i
$246$	8.44321	+	14.5129i	0.0343220	+	0.0589955i
$247$	97.7082	+	70.9892i	0.395580	+	0.287406i
$248$	−25.5166	+	35.1205i	−0.102889	+	0.141615i
$249$	−288.314	+	167.733i	−1.15789	+	0.673628i
$250$	−12.6829	−	39.0338i	−0.0507314	−	0.156135i
$251$	28.7139	+	39.5213i	0.114398	+	0.157455i	0.862376	−	0.506268i	$-0.168975\pi$
$251$	28.7139	+	39.5213i	0.114398	+	0.157455i	−0.747978	+	0.663723i	$0.768975\pi$
$252$	26.5623	+	237.580i	0.105406	+	0.942780i
$253$	30.9180	+	190.311i	0.122205	+	0.752219i
$254$			101.416i			0.399277i
$255$	12.0596	−	118.513i	0.0472927	−	0.464755i
$256$	−52.8419	−	162.631i	−0.206414	−	0.635276i
$257$	−152.774	−	49.6393i	−0.594452	−	0.193149i	−0.00368740	−	0.999993i	$-0.501174\pi$
$257$	−152.774	−	49.6393i	−0.594452	−	0.193149i	−0.590764	+	0.806844i	$0.701174\pi$
$258$	−16.6544	−	77.0971i	−0.0645521	−	0.298826i
$259$	−140.374	−	101.988i	−0.541984	−	0.393774i
$260$	−249.928	−	81.2067i	−0.961263	−	0.312333i
$261$	−98.0576	−	216.374i	−0.375700	−	0.829018i
$262$	105.975	−	76.9951i	0.404483	−	0.293874i
$263$			140.420i			0.533914i	0.963708	+	0.266957i	$0.0860183\pi$
$263$			140.420i			0.533914i	−0.963708	+	0.266957i	$0.913982\pi$
$264$	230.589	−	13.7695i	0.873444	−	0.0521573i
$265$	147.387			0.556177
$266$	47.4873	+	65.3607i	0.178524	+	0.245717i
$267$	118.286	−	268.059i	0.443018	−	1.00397i
$268$	−71.1885	+	219.096i	−0.265629	+	0.817521i
$269$	243.193	−	334.726i	0.904063	−	1.24434i	−0.0650908	−	0.997879i	$-0.520734\pi$
$269$	243.193	−	334.726i	0.904063	−	1.24434i	0.969154	−	0.246457i	$-0.0792663\pi$
$270$	56.9024	+	169.385i	0.210750	+	0.627350i
$271$	17.8541	−	54.9493i	0.0658823	−	0.202765i	−0.912696	−	0.408639i	$-0.866004\pi$
$271$	17.8541	−	54.9493i	0.0658823	−	0.202765i	0.978579	+	0.205874i	$0.0660036\pi$
$272$	28.5317	−	9.27051i	0.104896	−	0.0340828i
$273$	35.5924	−	349.774i	0.130375	−	1.28122i
$274$	208.748			0.761853
$275$	−94.6084	−	183.870i	−0.344031	−	0.668617i
$276$	−117.580	−	105.167i	−0.426016	−	0.381041i
$277$	266.276	−	193.461i	0.961284	−	0.698413i	0.00783504	−	0.999969i	$-0.497506\pi$
$277$	266.276	−	193.461i	0.961284	−	0.698413i	0.953448	+	0.301556i	$0.0975060\pi$
$278$	77.5877	−	25.2098i	0.279092	−	0.0906826i
$279$	54.6706	+	11.2428i	0.195952	+	0.0402967i
$280$	−331.840	−	241.096i	−1.18514	−	0.861058i
$281$	−232.270	+	319.692i	−0.826583	+	1.13769i	0.161967	+	0.986796i	$0.448216\pi$
$281$	−232.270	+	319.692i	−0.826583	+	1.13769i	−0.988549	+	0.150897i	$0.951784\pi$
$282$	−26.7145	−	45.9191i	−0.0947322	−	0.162834i
$283$	88.7132	+	273.031i	0.313474	+	0.964775i	0.976378	+	0.216070i	$0.0693239\pi$
$283$	88.7132	+	273.031i	0.313474	+	0.964775i	−0.662904	+	0.748705i	$0.730676\pi$
$284$	−116.063	−	159.748i	−0.408674	−	0.562492i
$285$	−135.029	−	120.774i	−0.473787	−	0.423768i
$286$	−143.894	−	22.2048i	−0.503124	−	0.0776392i
$287$			49.5542i			0.172663i
$288$	−219.393	+	200.189i	−0.761782	+	0.695100i
$289$	78.1813	+	240.617i	0.270524	+	0.832586i
$290$	166.134	+	53.9803i	0.572876	+	0.186139i
$291$	−355.359	+	76.7644i	−1.22117	+	0.263795i
$292$	−36.4574	−	26.4879i	−0.124854	−	0.0907119i
$293$	−68.2534	−	22.1769i	−0.232947	−	0.0756890i	0.190218	−	0.981742i	$-0.439081\pi$
$293$	−68.2534	−	22.1769i	−0.232947	−	0.0756890i	−0.423164	+	0.906053i	$0.639081\pi$
$294$	35.6013	−	80.6796i	0.121093	−	0.274421i
$295$	−117.307	+	85.2289i	−0.397652	+	0.288911i
$296$		−	137.177i		−	0.463437i
$297$	−138.502	−	262.729i	−0.466336	−	0.884608i
$298$	6.99187			0.0234626
$299$	136.366	+	187.692i	0.456074	+	0.627732i
$300$	154.785	+	68.3018i	0.515952	+	0.227673i
$301$	71.9361	−	221.397i	0.238991	−	0.735537i
$302$	−32.5932	+	44.8607i	−0.107924	+	0.148545i
$303$	117.560	+	544.213i	0.387988	+	1.79608i
$304$	14.0983	−	43.3901i	0.0463760	−	0.142731i
$305$	587.707	−	190.957i	1.92691	−	0.626090i
$306$	36.3980	+	39.8897i	0.118948	+	0.130358i
$307$	116.961			0.380979			0.190489	−	0.981689i	$-0.438992\pi$
$307$	116.961			0.380979			0.190489	+	0.981689i	$0.438992\pi$
$308$	260.864	+	131.614i	0.846961	+	0.427318i
$309$	−345.177	+	385.920i	−1.11708	+	1.24893i
$310$	−33.2041	+	24.1242i	−0.107110	+	0.0778201i
$311$	−174.177	+	56.5936i	−0.560056	+	0.181973i	−0.575346	−	0.817910i	$-0.695133\pi$
$311$	−174.177	+	56.5936i	−0.560056	+	0.181973i	0.0152905	+	0.999883i	$0.495133\pi$
$312$	240.257	−	139.775i	0.770054	−	0.447996i
$313$	60.5000	+	43.9558i	0.193291	+	0.140434i	0.680221	−	0.733007i	$-0.261884\pi$
$313$	60.5000	+	43.9558i	0.193291	+	0.140434i	−0.486931	+	0.873441i	$0.661884\pi$
$314$	24.6870	−	33.9787i	0.0786210	−	0.108212i
$315$	−106.229	+	516.561i	−0.337234	+	1.63988i
$316$	109.448	+	336.847i	0.346355	+	1.06597i
$317$	10.3872	+	14.2968i	0.0327673	+	0.0451004i	0.825086	−	0.565007i	$-0.191126\pi$
$317$	10.3872	+	14.2968i	0.0327673	+	0.0451004i	−0.792319	+	0.610107i	$0.791126\pi$
$318$	−44.5410	+	49.7984i	−0.140066	+	0.156599i
$319$	−286.950	−	44.2804i	−0.899529	−	0.138810i
$320$		−	86.0344i		−	0.268858i
$321$	196.332	+	19.9784i	0.611628	+	0.0622381i
$322$	47.9574	+	147.598i	0.148936	+	0.458378i
$323$	−52.0681	−	16.9180i	−0.161202	−	0.0523776i
$324$	223.281	+	95.8887i	0.689139	+	0.295953i
$325$	−201.297	−	146.251i	−0.619375	−	0.450002i
$326$	−151.018	−	49.0689i	−0.463247	−	0.150518i
$327$	294.588	+	129.992i	0.900881	+	0.397529i
$328$	−31.6950	+	23.0278i	−0.0966312	+	0.0702067i
$329$		−	156.790i		−	0.476566i
$330$	211.360	+	54.9868i	0.640484	+	0.166627i
$331$	−395.580			−1.19511			−0.597554	−	0.801829i	$-0.703860\pi$
$331$	−395.580			−1.19511			−0.597554	+	0.801829i	$0.703860\pi$
$332$	−196.059	−	269.853i	−0.590540	−	0.812809i
$333$	−160.644	+	72.8017i	−0.482415	+	0.218624i
$334$	−88.1246	+	271.220i	−0.263846	+	0.812035i
$335$	−298.713	+	411.143i	−0.891680	+	1.22729i
$336$	−129.817	+	28.0430i	−0.386361	+	0.0834613i
$337$	154.602	−	475.815i	0.458759	−	1.41191i	−0.407906	−	0.913024i	$-0.633741\pi$
$337$	154.602	−	475.815i	0.458759	−	1.41191i	0.866665	−	0.498891i	$-0.166259\pi$
$338$	−5.89036	+	1.91390i	−0.0174271	+	0.00566241i
$339$	94.5088	+	9.61705i	0.278787	+	0.0283689i
$340$	119.125			0.350367
$341$	48.0453	−	48.4286i	0.140895	−	0.142019i
$342$	81.6130	−	9.12461i	0.238635	−	0.0266802i
$343$	−140.432	+	102.030i	−0.409423	+	0.297463i
$344$	175.035	−	56.8723i	0.508822	−	0.165326i
$345$	−174.997	−	300.799i	−0.507237	−	0.871882i
$346$	48.3779	+	35.1486i	0.139821	+	0.101586i
$347$	362.649	−	499.144i	1.04510	−	1.43845i	0.152116	−	0.988363i	$-0.451391\pi$
$347$	362.649	−	499.144i	1.04510	−	1.43845i	0.892982	−	0.450092i	$-0.148609\pi$
$348$	205.335	−	119.458i	0.590044	−	0.343272i
$349$	−95.8572	−	295.018i	−0.274662	−	0.845324i	−0.989308	−	0.145838i	$-0.953412\pi$
$349$	−95.8572	−	295.018i	−0.274662	−	0.845324i	0.714646	−	0.699486i	$-0.246588\pi$
$350$	−97.8326	−	134.655i	−0.279522	−	0.384729i
$351$	−291.193	−	207.177i	−0.829611	−	0.590249i
$352$	58.2098	+	358.302i	0.165369	+	1.01790i
$353$		−	308.577i		−	0.874157i	−0.899423	−	0.437078i	$-0.856013\pi$
$353$		−	308.577i		−	0.874157i	0.899423	−	0.437078i	$-0.143987\pi$
$354$	6.65415	−	65.3918i	0.0187970	−	0.184723i
$355$	−134.607	−	414.277i	−0.379174	−	1.16698i
$356$	278.657	+	90.5410i	0.782743	+	0.254329i
$357$	33.6516	+	155.781i	0.0942622	+	0.436360i
$358$	−213.449	−	155.080i	−0.596227	−	0.433184i
$359$	130.095	+	42.2705i	0.362382	+	0.117745i	0.484548	−	0.874765i	$-0.338984\pi$
$359$	130.095	+	42.2705i	0.362382	+	0.117745i	−0.122166	+	0.992510i	$0.538984\pi$
$360$	−379.759	+	172.101i	−1.05489	+	0.478060i
$361$	224.698	−	163.252i	0.622431	−	0.452223i
$362$			225.967i			0.624220i
$363$	−361.416	−	33.8776i	−0.995636	−	0.0933268i
$364$	351.580			0.965880
$365$	−58.4325	−	80.4255i	−0.160089	−	0.220344i
$366$	−113.088	+	256.280i	−0.308983	+	0.700217i
$367$	−38.9437	+	119.856i	−0.106114	+	0.326584i	−0.989990	−	0.141136i	$-0.954924\pi$
$367$	−38.9437	+	119.856i	−0.106114	+	0.326584i	0.883877	+	0.467720i	$0.154924\pi$
$368$	51.5131	−	70.9017i	0.139981	−	0.192668i
$369$	43.7881	+	24.8960i	0.118667	+	0.0674688i
$370$	40.0770	−	123.344i	0.108316	−	0.333363i
$371$	−187.534	+	60.9336i	−0.505484	+	0.164242i
$372$	−5.65042	+	55.5279i	−0.0151893	+	0.149269i
$373$	347.528			0.931710			0.465855	−	0.884861i	$-0.345747\pi$
$373$	347.528			0.931710			0.465855	+	0.884861i	$0.345747\pi$
$374$	65.1459	−	10.5836i	0.174187	−	0.0282984i
$375$	−91.7740	−	82.0851i	−0.244731	−	0.218894i
$376$	100.284	−	72.8603i	0.266712	−	0.193778i
$377$	−332.268	+	107.961i	−0.881348	+	0.286367i
$378$	−142.430	−	191.999i	−0.376800	−	0.507934i
$379$	383.761	+	278.819i	1.01256	+	0.735669i	0.964745	−	0.263187i	$-0.0847737\pi$
$379$	383.761	+	278.819i	1.01256	+	0.735669i	0.0478167	+	0.998856i	$0.484774\pi$
$380$	106.484	−	146.562i	0.280220	−	0.385690i
$381$	152.996	+	262.982i	0.401565	+	0.690243i
$382$	18.5673	+	57.1444i	0.0486056	+	0.149593i
$383$	−171.901	−	236.602i	−0.448828	−	0.617759i	0.523317	−	0.852138i	$-0.324694\pi$
$383$	−171.901	−	236.602i	−0.448828	−	0.617759i	−0.972145	+	0.234379i	$0.924694\pi$
$384$	−266.092	−	238.000i	−0.692948	−	0.619792i
$385$	457.583	+	453.961i	1.18853	+	1.17912i
$386$			35.6869i			0.0924532i
$387$	−159.495	−	174.795i	−0.412131	−	0.451667i
$388$	−112.345	−	345.762i	−0.289549	−	0.891140i
$389$	−74.7065	−	24.2736i	−0.192048	−	0.0624000i	0.211414	−	0.977397i	$-0.432193\pi$
$389$	−74.7065	−	24.2736i	−0.192048	−	0.0624000i	−0.403462	+	0.914997i	$0.632193\pi$
$390$	256.865	−	55.4879i	0.658629	−	0.142277i
$391$	−85.0820	−	61.8157i	−0.217601	−	0.158096i
$392$	195.695	+	63.5851i	0.499222	+	0.162207i
$393$	158.648	−	359.528i	0.403685	−	0.914830i
$394$	−117.797	+	85.5844i	−0.298977	+	0.217219i
$395$			781.330i			1.97805i
$396$	247.357	−	164.388i	0.624640	−	0.415120i
$397$	166.741			0.420004			0.210002	−	0.977701i	$-0.432653\pi$
$397$	166.741			0.420004			0.210002	+	0.977701i	$0.432653\pi$
$398$	−141.765	−	195.123i	−0.356194	−	0.490259i
$399$	221.742	+	97.8475i	0.555744	+	0.245232i
$400$	−29.0451	+	89.3916i	−0.0726127	+	0.223479i
$401$	115.745	−	159.310i	0.288642	−	0.397282i	−0.639930	−	0.768433i	$-0.721037\pi$
$401$	115.745	−	159.310i	0.288642	−	0.397282i	0.928572	+	0.371151i	$0.121037\pi$
$402$	−48.6425	−	225.177i	−0.121001	−	0.560141i
$403$	25.3657	−	78.0676i	0.0629422	−	0.193716i
$404$	−529.516	+	172.050i	−1.31068	+	0.425867i
$405$	403.086	+	353.388i	0.995273	+	0.872563i
$406$	−233.705			−0.575628
$407$	−32.8755	+	213.043i	−0.0807751	+	0.523446i
$408$	−84.0000	+	93.9149i	−0.205882	+	0.230183i
$409$	−583.159	+	423.690i	−1.42582	+	1.03592i	−0.435041	+	0.900411i	$0.643266\pi$
$409$	−583.159	+	423.690i	−1.42582	+	1.03592i	−0.990776	+	0.135507i	$0.956734\pi$
$410$	−35.2266	+	11.4458i	−0.0859186	+	0.0279166i
$411$	541.303	−	314.915i	1.31704	−	0.766217i
$412$	−418.881	−	304.335i	−1.01670	−	0.738678i
$413$	114.026	−	156.943i	0.276091	−	0.380007i
$414$	154.517	+	31.7758i	0.373230	+	0.0767532i
$415$	−227.384	−	699.815i	−0.547912	−	1.68630i
$416$	256.739	+	353.371i	0.617161	+	0.849449i
$417$	163.161	−	182.420i	0.391273	−	0.437457i
$418$	45.2117	−	89.6113i	0.108162	−	0.214381i
$419$			267.408i			0.638206i	0.947720	+	0.319103i	$0.103382\pi$
$419$			267.408i			0.638206i	−0.947720	+	0.319103i	$0.896618\pi$
$420$	−524.661	−	53.3886i	−1.24919	−	0.127116i
$421$	211.976	+	652.394i	0.503505	+	1.54963i	0.803269	+	0.595616i	$0.203092\pi$
$421$	211.976	+	652.394i	0.503505	+	1.54963i	−0.299764	+	0.954013i	$0.596908\pi$
$422$	40.6459	+	13.2067i	0.0963173	+	0.0312954i
$423$	−138.546	−	78.7713i	−0.327533	−	0.186221i
$424$	−126.121	−	91.6319i	−0.297454	−	0.216113i
$425$	107.270	+	34.8541i	0.252400	+	0.0820097i
$426$	180.653	+	79.7162i	0.424067	+	0.187127i
$427$	−668.848	+	485.946i	−1.56639	+	1.13805i
$428$			197.346i			0.461090i
$429$	−406.628	+	159.498i	−0.947851	+	0.371789i
$430$	174.000			0.404651
$431$	−324.685	−	446.890i	−0.753329	−	1.03687i	−0.997740	−	0.0671970i	$-0.978594\pi$
$431$	−324.685	−	446.890i	−0.753329	−	1.03687i	0.244410	−	0.969672i	$-0.421406\pi$
$432$	−40.4401	+	128.801i	−0.0936113	+	0.298150i
$433$	−87.9528	+	270.691i	−0.203124	+	0.625152i	0.796661	+	0.604426i	$0.206598\pi$
$433$	−87.9528	+	270.691i	−0.203124	+	0.625152i	−0.999785	+	0.0207256i	$0.993402\pi$
$434$	32.2752	−	44.4230i	0.0743668	−	0.102357i
$435$	512.236	−	110.653i	1.17755	−	0.254374i
$436$	−99.5016	+	306.234i	−0.228215	+	0.702372i
$437$	−152.107	+	49.4226i	−0.348071	+	0.113095i
$438$	44.8323	+	4.56206i	0.102357	+	0.0104157i
$439$	532.058			1.21198			0.605988	−	0.795474i	$-0.292778\pi$
$439$	532.058			1.21198			0.605988	+	0.795474i	$0.292778\pi$
$440$	−77.7169	+	503.627i	−0.176629	+	1.14461i
$441$	−29.3951	−	262.918i	−0.0666556	−	0.596186i
$442$	64.2492	−	46.6798i	0.145360	−	0.105610i
$443$	114.409	−	37.1738i	0.258260	−	0.0839137i	−0.177026	−	0.984206i	$-0.556648\pi$
$443$	114.409	−	37.1738i	0.258260	−	0.0839137i	0.435285	+	0.900293i	$0.356648\pi$
$444$	−88.6906	−	152.449i	−0.199753	−	0.343353i
$445$	522.912	+	379.918i	1.17508	+	0.853747i
$446$	−97.5676	+	134.290i	−0.218761	+	0.301099i
$447$	18.1306	−	10.5479i	0.0405606	−	0.0235971i
$448$	35.5689	+	109.470i	0.0793948	+	0.244352i
$449$	40.3625	+	55.5542i	0.0898941	+	0.123729i	0.851595	−	0.524200i	$-0.175636\pi$
$449$	40.3625	+	55.5542i	0.0898941	+	0.123729i	−0.761701	+	0.647929i	$0.775636\pi$
$450$	−168.138	+	18.7984i	−0.373639	+	0.0417742i
$451$	54.7426	−	28.1673i	0.121381	−	0.0624552i
$452$			94.9969i			0.210170i
$453$	−16.8408	+	165.498i	−0.0371761	+	0.365338i
$454$	−105.552	−	324.855i	−0.232493	−	0.715539i
$455$	737.630	+	239.671i	1.62117	+	0.526749i
$456$	40.4597	+	187.297i	0.0887274	+	0.410738i
$457$	−562.677	−	408.809i	−1.23124	−	0.894549i	−0.234259	−	0.972174i	$-0.575266\pi$
$457$	−562.677	−	408.809i	−1.23124	−	0.894549i	−0.996983	+	0.0776252i	$0.975266\pi$
$458$	234.696	+	76.2574i	0.512437	+	0.166501i
$459$	154.561	+	48.5281i	0.336734	+	0.105726i
$460$	281.538	−	204.549i	0.612039	−	0.444672i
$461$		−	824.322i		−	1.78812i	−0.447950	−	0.894059i	$-0.647846\pi$
$461$		−	824.322i		−	1.78812i	0.447950	−	0.894059i	$-0.352154\pi$
$462$	−291.666	+	17.4167i	−0.631311	+	0.0376984i
$463$	−158.137			−0.341548			−0.170774	−	0.985310i	$-0.554627\pi$
$463$	−158.137			−0.341548			−0.170774	+	0.985310i	$0.554627\pi$
$464$	77.5733	+	106.771i	0.167184	+	0.230109i
$465$	−49.7079	+	112.648i	−0.106899	+	0.242254i
$466$	123.103	−	378.873i	0.264170	−	0.813032i
$467$	−448.662	+	617.531i	−0.960733	+	1.32234i	−0.0141417	+	0.999900i	$0.504502\pi$
$467$	−448.662	+	617.531i	−0.960733	+	1.32234i	−0.946591	+	0.322436i	$0.895498\pi$
$468$	176.634	−	310.671i	0.377423	−	0.663827i
$469$	210.103	−	646.632i	0.447982	−	1.37875i
$470$	111.458	−	36.2148i	0.237144	−	0.0770527i
$471$	12.7557	−	125.353i	0.0270821	−	0.266142i
$472$	153.369			0.324934
$473$	−285.467	+	46.3769i	−0.603525	+	0.0980485i
$474$	−263.992	−	236.122i	−0.556945	−	0.498147i
$475$	138.769	−	100.822i	0.292145	−	0.212256i
$476$	−151.574	+	49.2492i	−0.318432	+	0.103465i
$477$	−40.3737	+	196.326i	−0.0846408	+	0.411585i
$478$	130.421	+	94.7567i	0.272848	+	0.198236i
$479$	−43.9797	+	60.5329i	−0.0918157	+	0.126373i	−0.852454	−	0.522803i	$-0.824886\pi$
$479$	−43.9797	+	60.5329i	−0.0918157	+	0.126373i	0.760638	+	0.649176i	$0.224886\pi$
$480$	−329.469	−	566.320i	−0.686394	−	1.17983i
$481$	80.1540	+	246.689i	0.166640	+	0.512866i
$482$	93.8366	+	129.155i	0.194682	+	0.267956i
$483$	347.023	+	310.387i	0.718475	+	0.642623i
$484$	−2.88448	−	362.989i	−0.00595967	−	0.749976i
$485$		−	802.009i		−	1.65363i
$486$	−241.215	+	29.3971i	−0.496328	+	0.0604879i
$487$	93.6246	+	288.147i	0.192248	+	0.591677i	0.999998	+	0.00215232i	$0.000685104\pi$
$487$	93.6246	+	288.147i	0.192248	+	0.591677i	−0.807750	+	0.589525i	$0.799315\pi$
$488$	−621.627	−	201.979i	−1.27382	−	0.413891i
$489$	−465.630	+	100.585i	−0.952209	+	0.205696i
$490$	157.384	+	114.347i	0.321193	+	0.233360i
$491$	−759.679	−	246.835i	−1.54721	−	0.502718i	−0.593854	−	0.804573i	$-0.702394\pi$
$491$	−759.679	−	246.835i	−1.54721	−	0.502718i	−0.953354	+	0.301854i	$0.902394\pi$
$492$	−20.3352	+	46.0835i	−0.0413316	+	0.0936657i
$493$	128.125	−	93.0880i	0.259888	−	0.188819i
$494$		−	120.774i		−	0.244482i
$495$	631.028	−	176.270i	1.27480	−	0.356100i
$496$	−31.0081			−0.0625164
$497$	342.546	+	471.474i	0.689227	+	0.948640i
$498$	305.166	+	134.660i	0.612783	+	0.270401i
$499$	180.695	−	556.122i	0.362114	−	1.11447i	−0.589654	−	0.807656i	$-0.700736\pi$
$499$	180.695	−	556.122i	0.362114	−	1.11447i	0.951768	−	0.306817i	$-0.0992641\pi$
$500$	72.3727	−	99.6124i	0.144745	−	0.199225i
$501$	180.645	+	836.243i	0.360568	+	1.66915i
$502$	15.0958	−	46.4601i	0.0300713	−	0.0925499i
$503$	526.823	−	171.175i	1.04736	−	0.340309i	0.265730	−	0.964048i	$-0.414387\pi$
$503$	526.823	−	171.175i	1.04736	−	0.340309i	0.781633	+	0.623739i	$0.214387\pi$
$504$	412.052	−	375.983i	0.817564	−	0.745998i
$505$	−1228.23			−2.43214
$506$	135.792	−	136.875i	0.268364	−	0.270505i
$507$	−12.3870	+	13.8491i	−0.0244319	+	0.0273157i
$508$	−246.143	+	178.833i	−0.484533	+	0.352034i
$509$	−81.6860	+	26.5414i	−0.160483	+	0.0521442i	−0.388157	−	0.921593i	$-0.626888\pi$
$509$	−81.6860	+	26.5414i	−0.160483	+	0.0521442i	0.227674	+	0.973738i	$0.426888\pi$
$510$	−102.967	+	59.9035i	−0.201896	+	0.117458i
$511$	107.599	+	78.1754i	0.210566	+	0.152985i
$512$	179.275	−	246.750i	0.350146	−	0.481934i
$513$	197.865	−	146.782i	0.385702	−	0.286124i
$514$	49.6393	+	152.774i	0.0965746	+	0.297226i
$515$	−671.367	−	924.057i	−1.30362	−	1.79429i
$516$	157.751	−	176.371i	0.305719	−	0.341804i
$517$	−173.207	+	89.1218i	−0.335023	+	0.172383i
$518$			173.512i			0.334964i
$519$	178.473	+	18.1611i	0.343880	+	0.0349926i
$520$	189.482	+	583.166i	0.364389	+	1.12147i
$521$	697.705	+	226.698i	1.33917	+	0.435121i	0.889034	−	0.457841i	$-0.151377\pi$
$521$	697.705	+	226.698i	1.33917	+	0.435121i	0.450131	+	0.892962i	$0.351377\pi$
$522$	−117.413	+	206.512i	−0.224930	+	0.395616i
$523$	243.517	+	176.925i	0.465615	+	0.338289i	0.795730	−	0.605652i	$-0.207088\pi$
$523$	243.517	+	176.925i	0.465615	+	0.338289i	−0.330115	+	0.943941i	$0.607088\pi$
$524$	373.742	+	121.436i	0.713248	+	0.231748i
$525$	−456.829	−	201.584i	−0.870150	−	0.383969i
$526$	113.602	−	82.5365i	0.215973	−	0.156914i
$527$			37.2098i			0.0706067i
$528$	104.769	+	127.469i	0.198426	+	0.241419i
$529$	221.774			0.419232
$530$	−86.6319	−	119.239i	−0.163456	−	0.224978i
$531$	−81.3948	−	179.606i	−0.153286	−	0.338240i
$532$	−74.8967	+	230.508i	−0.140783	+	0.433286i
$533$	43.5425	−	59.9311i	0.0816933	−	0.112441i
$534$	−286.391	+	61.8660i	−0.536313	+	0.115854i
$535$	−134.530	+	414.041i	−0.251458	+	0.773908i
$536$	511.223	−	166.106i	0.953774	−	0.309900i
$537$	−787.447	−	80.1292i	−1.46638	−	0.149216i
$538$	−413.745			−0.769042
$539$	−288.685	−	145.650i	−0.535593	−	0.270223i
$540$	−310.766	+	436.790i	−0.575492	+	0.808871i
$541$	308.904	−	224.432i	0.570986	−	0.414846i	−0.264477	−	0.964392i	$-0.585199\pi$
$541$	308.904	−	224.432i	0.570986	−	0.414846i	0.835463	+	0.549546i	$0.185199\pi$
$542$	−54.9493	+	17.8541i	−0.101382	+	0.0329411i
$543$	340.893	+	585.955i	0.627796	+	1.07911i
$544$	−160.185	−	116.381i	−0.294458	−	0.213937i
$545$	−417.517	+	574.663i	−0.766086	+	1.05443i
$546$	−303.894	+	176.797i	−0.556582	+	0.323805i
$547$	−57.4853	−	176.922i	−0.105092	−	0.323440i	0.884660	−	0.466237i	$-0.154390\pi$
$547$	−57.4853	−	176.922i	−0.105092	−	0.323440i	−0.989752	+	0.142797i	$0.954390\pi$
$548$	368.096	+	506.641i	0.671709	+	0.924528i
$549$	93.3738	+	835.161i	0.170080	+	1.52124i
$550$	−93.1443	+	184.616i	−0.169353	+	0.335665i
$551$		−	240.845i		−	0.437106i
$552$	−37.2632	+	366.194i	−0.0675059	+	0.663395i
$553$	−323.022	−	994.160i	−0.584127	−	1.79776i
$554$	−313.026	−	101.708i	−0.565028	−	0.183589i
$555$	−82.1529	−	380.304i	−0.148023	−	0.685232i
$556$	198.000	+	143.855i	0.356115	+	0.258733i
$557$	415.236	+	134.918i	0.745486	+	0.242223i	0.657038	−	0.753858i	$-0.271809\pi$
$557$	415.236	+	134.918i	0.745486	+	0.242223i	0.0884485	+	0.996081i	$0.471809\pi$
$558$	−23.0390	−	50.8378i	−0.0412885	−	0.0911071i
$559$	−281.538	+	204.549i	−0.503646	+	0.365920i
$560$		−	292.984i		−	0.523185i
$561$	152.963	−	125.723i	0.272662	−	0.224105i
$562$	395.161			0.703133
$563$	145.562	+	200.349i	0.258548	+	0.355860i	0.918482	−	0.395463i	$-0.129416\pi$
$563$	145.562	+	200.349i	0.258548	+	0.355860i	−0.659934	+	0.751323i	$0.729416\pi$
$564$	64.3408	−	145.809i	0.114079	−	0.258527i
$565$	−64.7589	+	199.307i	−0.114618	+	0.352756i
$566$	168.743	−	232.254i	0.298132	−	0.410343i
$567$	−658.984	−	283.003i	−1.16223	−	0.499123i
$568$	−142.376	+	438.188i	−0.250662	+	0.771457i
$569$	264.026	−	85.7871i	0.464017	−	0.150768i	−0.0676726	−	0.997708i	$-0.521557\pi$
$569$	264.026	−	85.7871i	0.464017	−	0.150768i	0.531690	+	0.846939i	$0.321557\pi$
$570$	−18.3399	+	180.230i	−0.0321753	+	0.316193i
$571$	1010.88			1.77037			0.885187	−	0.465236i	$-0.154031\pi$
$571$	1010.88			1.77037			0.885187	+	0.465236i	$0.154031\pi$
$572$	−199.843	−	388.392i	−0.349376	−	0.679007i
$573$	134.354	+	120.170i	0.234476	+	0.209721i
$574$	40.0902	−	29.1272i	0.0698435	−	0.0507443i
$575$	313.369	−	101.820i	0.544989	−	0.177078i
$576$	114.602	+	23.5674i	0.198962	+	0.0409156i
$577$	−210.494	−	152.933i	−0.364808	−	0.265049i	0.390247	−	0.920710i	$-0.372390\pi$
$577$	−210.494	−	152.933i	−0.364808	−	0.265049i	−0.755055	+	0.655662i	$0.772390\pi$
$578$	148.710	−	204.681i	0.257283	−	0.354120i
$579$	53.8370	+	92.5396i	0.0929828	+	0.159827i
$580$	161.941	+	498.403i	0.279208	+	0.859315i
$581$	578.643	+	796.434i	0.995943	+	1.37080i
$582$	270.979	+	242.371i	0.465599	+	0.416445i
$583$	173.911	+	172.534i	0.298303	+	0.295942i
$584$			105.149i			0.180050i
$585$	582.368	−	531.391i	0.995501	−	0.908360i
$586$	22.1769	+	68.2534i	0.0378445	+	0.116473i
$587$	−957.959	−	311.260i	−1.63196	−	0.530255i	−0.657238	−	0.753683i	$-0.728275\pi$
$587$	−957.959	−	311.260i	−1.63196	−	0.530255i	−0.974720	+	0.223428i	$0.928275\pi$
$588$	258.591	−	55.8607i	0.439781	−	0.0950012i
$589$	45.7802	+	33.2613i	0.0777253	+	0.0564707i
$590$	137.903	+	44.8075i	0.233734	+	0.0759449i
$591$	−176.346	+	399.636i	−0.298387	+	0.676203i
$592$	79.2705	−	57.5934i	0.133903	−	0.0972861i
$593$		−	13.9837i		−	0.0235813i	−0.999930	−	0.0117907i	$-0.996247\pi$
$593$		−	13.9837i		−	0.0235813i	0.999930	−	0.0117907i	$-0.00375317\pi$
$594$	−131.143	+	266.478i	−0.220779	+	0.448616i
$595$	−351.580			−0.590892
$596$	12.3292	+	16.9696i	0.0206865	+	0.0284725i
$597$	−661.972	−	292.107i	−1.10883	−	0.489291i
$598$	71.6919	−	220.645i	0.119886	−	0.368972i
$599$	101.903	−	140.257i	0.170122	−	0.234153i	−0.715440	−	0.698674i	$-0.753774\pi$
$599$	101.903	−	140.257i	0.170122	−	0.234153i	0.885562	+	0.464522i	$0.153774\pi$
$600$	−83.3543	−	385.865i	−0.138924	−	0.643109i
$601$	−242.618	+	746.703i	−0.403691	+	1.24243i	0.518292	+	0.855204i	$0.326568\pi$
$601$	−242.618	+	746.703i	−0.403691	+	1.24243i	−0.921983	+	0.387230i	$0.873432\pi$
$602$	−221.397	+	71.9361i	−0.367769	+	0.119495i
$603$	−465.835	−	510.523i	−0.772529	−	0.846639i
$604$	−166.353			−0.275418
$605$	241.396	−	763.531i	0.399001	−	1.26204i
$606$	371.177	−	414.989i	0.612504	−	0.684800i
$607$	−10.7953	+	7.84322i	−0.0177846	+	0.0129213i	−0.596642	−	0.802507i	$-0.703499\pi$
$607$	−10.7953	+	7.84322i	−0.0177846	+	0.0129213i	0.578857	+	0.815429i	$0.303499\pi$
$608$	−286.375	+	93.0488i	−0.471011	+	0.153041i
$609$	−606.020	+	352.566i	−0.995106	+	0.578926i
$610$	−499.933	−	363.223i	−0.819562	−	0.595447i
$611$	−137.769	+	189.623i	−0.225482	+	0.310349i
$612$	−32.6318	+	158.679i	−0.0533199	+	0.259280i
$613$	−192.851	−	593.534i	−0.314602	−	0.968245i	−0.975918	−	0.218138i	$-0.930002\pi$
$613$	−192.851	−	593.534i	−0.314602	−	0.968245i	0.661316	−	0.750107i	$-0.269998\pi$
$614$	−68.7477	−	94.6231i	−0.111967	−	0.154109i
$615$	−74.0789	+	82.8228i	−0.120454	+	0.134671i
$616$	−109.326	−	672.943i	−0.177478	−	1.09244i
$617$			1103.25i			1.78808i	0.447986	+	0.894041i	$0.352141\pi$
$617$			1103.25i			1.78808i	−0.447986	+	0.894041i	$0.647859\pi$
$618$	515.106	+	52.4162i	0.833505	+	0.0848159i
$619$	−56.6149	−	174.243i	−0.0914619	−	0.281491i	0.894854	−	0.446360i	$-0.147280\pi$
$619$	−56.6149	−	174.243i	−0.0914619	−	0.281491i	−0.986315	+	0.164869i	$0.947280\pi$
$620$	−117.101	−	38.0486i	−0.188873	−	0.0613686i
$621$	448.615	−	150.706i	0.722408	−	0.242683i
$622$	148.164	+	107.648i	0.238206	+	0.173067i
$623$	−822.418	−	267.220i	−1.32009	−	0.428924i
$624$	181.643	+	80.1530i	0.291094	+	0.128450i
$625$	599.951	−	435.890i	0.959922	−	0.697424i
$626$		−	74.7821i		−	0.119460i
$627$	−17.9488	−	300.577i	−0.0286265	−	0.479389i
$628$	126.000			0.200637
$629$	−69.1121	−	95.1246i	−0.109876	−	0.151231i
$630$	480.346	−	217.686i	0.762454	−	0.345534i
$631$	86.1635	−	265.184i	0.136551	−	0.420260i	−0.859277	−	0.511510i	$-0.829086\pi$
$631$	86.1635	−	265.184i	0.136551	−	0.420260i	0.995828	+	0.0912502i	$0.0290863\pi$
$632$	485.761	−	668.592i	0.768609	−	1.05790i
$633$	125.322	−	27.0720i	0.197981	−	0.0427678i
$634$	5.46090	−	16.8069i	0.00861341	−	0.0265093i
$635$	−638.327	+	207.405i	−1.00524	+	0.326622i
$636$	−199.405	−	20.2911i	−0.313530	−	0.0319042i
$637$	−389.076			−0.610794
$638$	132.841	+	258.175i	0.208215	+	0.404663i
$639$	588.709	−	65.8197i	0.921297	−	0.103004i
$640$	637.138	−	462.908i	0.995528	−	0.723294i
$641$	652.737	−	212.087i	1.01831	−	0.330869i	0.248151	−	0.968721i	$-0.420177\pi$
$641$	652.737	−	212.087i	1.01831	−	0.330869i	0.770159	+	0.637852i	$0.220177\pi$
$642$	−99.2384	−	170.579i	−0.154577	−	0.265700i
$643$	109.348	+	79.4456i	0.170058	+	0.123555i	0.669559	−	0.742759i	$-0.266483\pi$
$643$	109.348	+	79.4456i	0.170058	+	0.123555i	−0.499501	+	0.866314i	$0.666483\pi$
$644$	−273.661	+	376.663i	−0.424940	+	0.584880i
$645$	451.199	−	262.495i	0.699533	−	0.406969i
$646$	16.9180	+	52.0681i	0.0261888	+	0.0806008i
$647$	−53.9930	−	74.3150i	−0.0834513	−	0.114861i	0.765250	−	0.643733i	$-0.222615\pi$
$647$	−53.9930	−	74.3150i	−0.0834513	−	0.114861i	−0.848702	+	0.528872i	$0.822615\pi$
$648$	−125.220	−	553.000i	−0.193240	−	0.853395i
$649$	−238.189	−	36.7559i	−0.367009	−	0.0566347i
$650$			248.817i			0.382795i
$651$	16.6765	−	163.883i	0.0256167	−	0.251741i
$652$	−147.207	−	453.055i	−0.225777	−	0.694870i
$653$	−750.681	−	243.911i	−1.14959	−	0.373524i	−0.328600	−	0.944469i	$-0.606577\pi$
$653$	−750.681	−	243.911i	−1.14959	−	0.373524i	−0.820988	+	0.570945i	$0.806577\pi$
$654$	−67.9886	−	314.734i	−0.103958	−	0.481245i
$655$	701.344	+	509.556i	1.07075	+	0.777948i
$656$	−26.6141	−	8.64745i	−0.0405703	−	0.0131821i
$657$	123.137	−	55.8039i	0.187423	−	0.0849375i
$658$	−126.846	+	92.1590i	−0.192775	+	0.140059i
$659$			4.76585i			0.00723194i	0.999993	+	0.00361597i	$0.00115100\pi$
$659$			4.76585i			0.00723194i	−0.999993	+	0.00361597i	$0.998849\pi$
$660$	239.246	+	609.942i	0.362495	+	0.924154i
$661$	−1267.85			−1.91808			−0.959042	−	0.283264i	$-0.908583\pi$
$661$	−1267.85			−1.91808			−0.959042	+	0.283264i	$0.908583\pi$
$662$	232.516	+	320.031i	0.351233	+	0.483431i
$663$	96.1836	−	217.971i	0.145073	−	0.328765i
$664$	−240.507	+	740.205i	−0.362210	+	1.11477i
$665$	−314.273	+	432.559i	−0.472590	+	0.650465i
$666$	153.322	+	87.1721i	0.230213	+	0.130889i
$667$	142.967	−	440.006i	0.214343	−	0.659680i
$668$	−813.659	+	264.374i	−1.21805	+	0.395769i
$669$	−50.4128	+	495.417i	−0.0753554	+	0.740534i
$670$	508.200			0.758508
$671$	917.009	+	462.659i	1.36663	+	0.689507i
$672$	653.346	+	584.371i	0.972242	+	0.869599i
$673$	148.412	−	107.827i	0.220523	−	0.160219i	−0.472039	−	0.881578i	$-0.656482\pi$
$673$	148.412	−	107.827i	0.220523	−	0.160219i	0.692562	+	0.721358i	$0.256482\pi$
$674$	−475.815	+	154.602i	−0.705957	+	0.229379i
$675$	−407.638	+	302.397i	−0.603909	+	0.447996i
$676$	−15.0319	−	10.9213i	−0.0222366	−	0.0161558i
$677$	89.4236	−	123.081i	0.132088	−	0.181804i	−0.737850	−	0.674965i	$-0.764159\pi$
$677$	89.4236	−	123.081i	0.132088	−	0.181804i	0.869938	+	0.493161i	$0.164159\pi$
$678$	−47.7706	−	82.1120i	−0.0704580	−	0.121109i
$679$	331.571	+	1020.47i	0.488323	+	1.50290i
$680$	−163.379	−	224.872i	−0.240264	−	0.330695i
$681$	−763.779	−	683.145i	−1.12156	−	1.00315i
$682$	−67.4199	−	10.4038i	−0.0988561	−	0.0152549i
$683$			778.746i			1.14019i	0.821580	+	0.570093i	$0.193093\pi$
$683$			778.746i			1.14019i	−0.821580	+	0.570093i	$0.806907\pi$
$684$	166.059	+	181.989i	0.242776	+	0.266066i
$685$	426.907	+	1313.88i	0.623221	+	1.91808i
$686$	165.088	+	53.6403i	0.240653	+	0.0781928i
$687$	723.631	−	156.318i	1.05332	−	0.227537i
$688$	106.353	+	77.2696i	0.154582	+	0.112311i
$689$	280.347	+	91.0902i	0.406889	+	0.132206i
$690$	−140.491	+	318.381i	−0.203610	+	0.461421i
$691$	366.328	−	266.153i	0.530142	−	0.385171i	−0.290269	−	0.956945i	$-0.593745\pi$
$691$	366.328	−	266.153i	0.530142	−	0.385171i	0.820411	+	0.571774i	$0.193745\pi$
$692$			179.395i			0.259242i
$693$	−730.043	+	485.168i	−1.05345	+	0.700098i
$694$	−616.976			−0.889014
$695$	317.347	+	436.790i	0.456614	+	0.628475i
$696$	−507.120	−	223.775i	−0.728620	−	0.321516i
$697$	−10.3769	+	31.9369i	−0.0148880	+	0.0458206i
$698$	−182.331	+	250.957i	−0.261220	+	0.359538i
$699$	−252.347	−	1168.17i	−0.361011	−	1.67120i
$700$	154.301	−	474.889i	0.220430	−	0.678413i
$701$	50.5591	−	16.4276i	0.0721242	−	0.0234346i	−0.272733	−	0.962090i	$-0.587927\pi$
$701$	50.5591	−	16.4276i	0.0721242	−	0.0234346i	0.344857	+	0.938655i	$0.387927\pi$
$702$	3.54934	+	357.356i	0.00505604	+	0.509054i
$703$	−178.813			−0.254357
$704$	100.714	−	101.517i	0.143059	−	0.144201i
$705$	234.387	−	262.053i	0.332464	−	0.371706i
$706$	−249.644	+	181.377i	−0.353604	+	0.256908i
$707$	1562.80	−	507.783i	2.21046	−	0.718222i
$708$	170.443	−	99.1591i	0.240739	−	0.140055i
$709$	−874.272	−	635.196i	−1.23311	−	0.895904i	−0.235987	−	0.971756i	$-0.575832\pi$
$709$	−874.272	−	635.196i	−1.23311	−	0.895904i	−0.997119	+	0.0758519i	$0.975832\pi$
$710$	−256.037	+	352.405i	−0.360616	+	0.496345i
$711$	−1040.77	−	214.029i	−1.46381	−	0.301026i
$712$	−211.262	−	650.199i	−0.296717	−	0.913200i
$713$	63.8930	+	87.9412i	0.0896115	+	0.123340i
$714$	106.249	−	118.790i	0.148808	−	0.166373i
$715$	−154.515	−	951.095i	−0.216104	−	1.33020i
$716$		−	791.514i		−	1.10547i
$717$	481.145	+	48.9604i	0.671052	+	0.0682851i
$718$	−42.2705	−	130.095i	−0.0588726	−	0.181191i
$719$	863.891	+	280.695i	1.20152	+	0.390396i	0.840319	−	0.542093i	$-0.182368\pi$
$719$	863.891	+	280.695i	1.20152	+	0.390396i	0.361198	+	0.932489i	$0.382368\pi$
$720$	−258.893	−	147.195i	−0.359573	−	0.204437i
$721$	1236.27	+	898.205i	1.71466	+	1.24578i
$722$	−264.148	−	85.8268i	−0.365856	−	0.118874i
$723$	438.170	+	193.350i	0.606044	+	0.267427i
$724$	−548.435	+	398.461i	−0.757506	+	0.550361i
$725$			496.185i			0.684394i
$726$	185.027	+	312.304i	0.254858	+	0.430171i
$727$	−64.4195			−0.0886101			−0.0443050	−	0.999018i	$-0.514107\pi$
$727$	−64.4195			−0.0886101			−0.0443050	+	0.999018i	$0.514107\pi$
$728$	−482.192	−	663.681i	−0.662352	−	0.911649i
$729$	−581.146	+	440.125i	−0.797183	+	0.603738i
$730$	−30.7198	+	94.5458i	−0.0420819	+	0.129515i
$731$	92.7236	−	127.623i	0.126845	−	0.174587i
$732$	−821.418	+	177.442i	−1.12216	+	0.242407i
$733$	−327.582	+	1008.19i	−0.446905	+	1.37543i	0.433475	+	0.901166i	$0.357287\pi$
$733$	−327.582	+	1008.19i	−0.446905	+	1.37543i	−0.880381	+	0.474268i	$0.842713\pi$
$734$	119.856	−	38.9437i	0.163292	−	0.0530568i
$735$	580.615	+	59.0824i	0.789953	+	0.0803842i
$736$	−578.420			−0.785896
$737$	−833.762	+	135.453i	−1.13129	+	0.183789i
$738$	−5.59675	−	50.0588i	−0.00758367	−	0.0678304i
$739$	−129.374	+	93.9956i	−0.175066	+	0.127193i	−0.671868	−	0.740671i	$-0.734508\pi$
$739$	−129.374	+	93.9956i	−0.175066	+	0.127193i	0.496802	+	0.867864i	$0.334508\pi$
$740$	370.033	−	120.231i	0.500045	−	0.162474i
$741$	−182.199	−	313.179i	−0.245882	−	0.422643i
$742$	159.526	+	115.903i	0.214995	+	0.156203i
$743$	−37.1155	+	51.0851i	−0.0499536	+	0.0687552i	−0.833263	−	0.552877i	$-0.813530\pi$
$743$	−37.1155	+	51.0851i	−0.0499536	+	0.0687552i	0.783309	+	0.621632i	$0.213530\pi$
$744$	112.570	−	65.4901i	0.151304	−	0.0880243i
$745$	14.2990	+	44.0077i	0.0191932	+	0.0590707i
$746$	−204.272	−	281.156i	−0.273823	−	0.376885i
$747$	994.472	−	111.185i	1.33129	−	0.148843i
$748$	140.562	+	139.450i	0.187918	+	0.186430i
$749$		−	582.442i		−	0.777626i
$750$	−12.4649	+	122.495i	−0.0166198	+	0.163327i
$751$	50.7783	+	156.279i	0.0676142	+	0.208095i	0.979155	−	0.203115i	$-0.0651064\pi$
$751$	50.7783	+	156.279i	0.0676142	+	0.208095i	−0.911541	+	0.411210i	$0.865106\pi$
$752$	84.2075	+	27.3607i	0.111978	+	0.0363839i
$753$	−30.9445	−	143.249i	−0.0410949	−	0.190237i
$754$	282.644	+	205.353i	0.374860	+	0.272352i
$755$	−349.015	−	113.402i	−0.462271	−	0.150201i
$756$	214.836	−	684.248i	0.284175	−	0.905090i
$757$	733.190	−	532.694i	0.968547	−	0.703691i	0.0134274	−	0.999910i	$-0.495726\pi$
$757$	733.190	−	532.694i	0.968547	−	0.703691i	0.955120	+	0.296219i	$0.0957258\pi$
$758$		−	474.354i		−	0.625797i
$759$	145.633	−	559.786i	0.191874	−	0.737531i
$760$	−422.709			−0.556196
$761$	−134.755	−	185.474i	−0.177076	−	0.243724i	0.711248	−	0.702941i	$-0.248130\pi$
$761$	−134.755	−	185.474i	−0.177076	−	0.243724i	−0.888324	+	0.459217i	$0.848130\pi$
$762$	122.828	−	278.354i	0.161192	−	0.365294i
$763$	293.666	−	903.810i	0.384883	−	1.18455i
$764$	−105.951	+	145.830i	−0.138680	+	0.190877i
$765$	−176.634	+	310.671i	−0.230894	+	0.406106i
$766$	−90.3738	+	278.142i	−0.117982	+	0.363110i
$767$	−275.806	+	89.6149i	−0.359591	+	0.116838i
$768$	−51.9338	+	510.364i	−0.0676221	+	0.664537i
$769$	541.254			0.703842			0.351921	−	0.936030i	$-0.385529\pi$
$769$	541.254			0.703842			0.351921	+	0.936030i	$0.385529\pi$
$770$	98.3018	−	637.024i	0.127665	−	0.827304i
$771$	359.193	+	321.272i	0.465880	+	0.416696i
$772$	−86.6140	+	62.9287i	−0.112194	+	0.0815139i
$773$	−712.265	+	231.429i	−0.921430	+	0.299391i	−0.731053	−	0.682321i	$-0.760971\pi$
$773$	−712.265	+	231.429i	−0.921430	+	0.299391i	−0.190377	+	0.981711i	$0.560971\pi$
$774$	−47.6638	+	231.776i	−0.0615811	+	0.299452i
$775$	−94.3156	−	68.5243i	−0.121698	−	0.0884184i
$776$	−498.617	+	686.287i	−0.642547	+	0.884391i
$777$	261.758	+	449.932i	0.336883	+	0.579063i
$778$	24.2736	+	74.7065i	0.0312000	+	0.0960238i
$779$	30.0171	+	41.3150i	0.0385329	+	0.0530359i
$780$	587.617	+	525.580i	0.753355	+	0.673821i
$781$	326.131	−	646.404i	0.417581	−	0.827662i
$782$			105.167i			0.134485i
$783$	7.07803	+	712.633i	0.00903962	+	0.910132i
$784$	45.4180	+	139.782i	0.0579311	+	0.178294i
$785$	264.353	+	85.8936i	0.336756	+	0.109419i
$786$	−384.116	+	82.9763i	−0.488697	+	0.105568i
$787$	−199.225	−	144.745i	−0.253145	−	0.183920i	0.453975	−	0.891015i	$-0.350006\pi$
$787$	−199.225	−	144.745i	−0.253145	−	0.183920i	−0.707119	+	0.707094i	$0.750006\pi$
$788$	−415.435	−	134.983i	−0.527202	−	0.171298i
$789$	170.066	−	385.404i	0.215547	−	0.488471i
$790$	632.109	−	459.254i	0.800138	−	0.581335i
$791$		−	280.371i		−	0.354451i
$792$	−649.566	−	241.481i	−0.820159	−	0.304900i
$793$	1235.90			1.55852
$794$	−98.0082	−	134.897i	−0.123436	−	0.169895i
$795$	−404.527	−	178.505i	−0.508839	−	0.224534i
$796$	223.591	−	688.143i	0.280893	−	0.864501i
$797$	590.334	−	812.526i	0.740696	−	1.01948i	−0.257883	−	0.966176i	$-0.583025\pi$
$797$	590.334	−	812.526i	0.740696	−	1.01948i	0.998578	−	0.0533039i	$-0.0169752\pi$
$798$	−51.1763	−	236.906i	−0.0641307	−	0.296875i
$799$	32.8328	−	101.049i	0.0410924	−	0.126469i
$800$	589.984	−	191.698i	0.737481	−	0.239622i
$801$	−649.309	+	592.472i	−0.810623	+	0.739665i
$802$	−196.918			−0.245534
$803$	25.1997	−	163.301i	0.0313819	−	0.203364i
$804$	460.741	−	515.125i	0.573062	−	0.640702i
$805$	−830.922	+	603.700i	−1.03220	+	0.749938i
$806$	−78.0676	+	25.3657i	−0.0968581	+	0.0314711i
$807$	−1072.88	+	624.172i	−1.32947	+	0.773448i
$808$	1051.01	+	763.604i	1.30076	+	0.945054i
$809$	779.602	−	1073.03i	0.963661	−	1.32637i	0.0184769	−	0.999829i	$-0.494118\pi$
$809$	779.602	−	1073.03i	0.963661	−	1.32637i	0.945184	−	0.326537i	$-0.105882\pi$
$810$	48.9690	−	533.819i	0.0604555	−	0.659036i
$811$	−359.177	−	1105.43i	−0.442882	−	1.36305i	−0.884790	−	0.465990i	$-0.845698\pi$
$811$	−359.177	−	1105.43i	−0.442882	−	1.36305i	0.441908	−	0.897060i	$-0.354302\pi$
$812$	−412.105	−	567.214i	−0.507519	−	0.698540i
$813$	−115.554	+	129.193i	−0.142133	+	0.158910i
$814$	191.679	−	98.6265i	0.235478	−	0.121163i
$815$		−	1050.88i		−	1.28942i
$816$	−89.5376	−	9.11119i	−0.109727	−	0.0111657i
$817$	−74.1339	−	228.161i	−0.0907392	−	0.279267i
$818$	685.545	+	222.747i	0.838075	+	0.272307i
$819$	−521.311	+	916.905i	−0.636522	+	1.11954i
$820$	−89.8967	−	65.3138i	−0.109630	−	0.0796509i
$821$	901.762	+	293.000i	1.09837	+	0.356882i	0.801475	−	0.598028i	$-0.204049\pi$
$821$	901.762	+	293.000i	1.09837	+	0.356882i	0.296895	+	0.954910i	$0.404049\pi$
$822$	−572.942	−	252.821i	−0.697009	−	0.307568i
$823$	−1195.59	+	868.646i	−1.45272	+	1.05546i	−0.467534	+	0.883975i	$0.654858\pi$
$823$	−1195.59	+	868.646i	−1.45272	+	1.05546i	−0.985186	+	0.171488i	$0.945142\pi$
$824$			1208.12i			1.46617i
$825$	36.9778	+	619.243i	0.0448216	+	0.750598i
$826$	−193.992			−0.234857
$827$	94.4203	+	129.958i	0.114172	+	0.157144i	0.862278	−	0.506434i	$-0.169037\pi$
$827$	94.4203	+	129.958i	0.114172	+	0.157144i	−0.748106	+	0.663579i	$0.769037\pi$
$828$	195.347	+	431.054i	0.235927	+	0.520596i
$829$	67.2361	−	206.931i	0.0811050	−	0.249616i	−0.902279	−	0.431152i	$-0.858107\pi$
$829$	67.2361	−	206.931i	0.0811050	−	0.249616i	0.983384	+	0.181537i	$0.0581071\pi$
$830$	−432.509	+	595.298i	−0.521095	+	0.717226i
$831$	−965.142	+	208.489i	−1.16142	+	0.250890i
$832$	53.1722	−	163.647i	0.0639089	−	0.196691i
$833$	167.739	−	54.5016i	0.201367	−	0.0654280i
$834$	−243.484	−	24.7765i	−0.291947	−	0.0297080i
$835$	−1887.31			−2.26025
$836$	297.215	−	48.2856i	0.355521	−	0.0577579i
$837$	−136.436	−	97.0708i	−0.163006	−	0.115975i
$838$	216.338	−	157.179i	0.258160	−	0.187564i
$839$	−521.092	+	169.313i	−0.621087	+	0.201803i	−0.602623	−	0.798026i	$-0.705878\pi$
$839$	−521.092	+	169.313i	−0.621087	+	0.201803i	−0.0184642	+	0.999830i	$0.505878\pi$
$840$	618.791	+	1063.63i	0.736655	+	1.26622i
$841$	−116.739	−	84.8160i	−0.138810	−	0.100851i
$842$	403.202	−	554.959i	0.478862	−	0.659097i
$843$	1024.69	−	596.137i	1.21553	−	0.707161i
$844$	39.6200	+	121.938i	0.0469431	+	0.144476i
$845$	−24.0926	−	33.1606i	−0.0285119	−	0.0392433i
$846$	17.7082	+	158.387i	0.0209317	+	0.187219i
$847$	8.51316	+	1071.31i	0.0100510	+	1.26483i
$848$		−	111.353i		−	0.131312i
$849$	87.1886	−	856.821i	0.102696	−	1.00921i
$850$	−34.8541	−	107.270i	−0.0410048	−	0.126200i
$851$	−326.678	−	106.144i	−0.383875	−	0.124729i
$852$	125.080	+	579.021i	0.146807	+	0.679602i
$853$	−591.753	−	429.933i	−0.693731	−	0.504025i	0.184153	−	0.982898i	$-0.441046\pi$
$853$	−591.753	−	429.933i	−0.693731	−	0.504025i	−0.877885	+	0.478872i	$0.841046\pi$
$854$	786.278	+	255.477i	0.920700	+	0.299154i
$855$	224.337	+	495.022i	0.262382	+	0.578973i
$856$	372.532	−	270.660i	0.435201	−	0.316192i
$857$			333.112i			0.388696i	0.980933	+	0.194348i	$0.0622590\pi$
$857$			333.112i			0.388696i	−0.980933	+	0.194348i	$0.937741\pi$
$858$	368.046	+	235.219i	0.428958	+	0.274147i
$859$	146.468			0.170510			0.0852551	−	0.996359i	$-0.472829\pi$
$859$	146.468			0.170510			0.0852551	+	0.996359i	$0.472829\pi$
$860$	306.824	+	422.307i	0.356772	+	0.491055i
$861$	60.0165	−	136.009i	0.0697056	−	0.157967i
$862$	−170.697	+	525.351i	−0.198024	+	0.609456i
$863$	−374.117	+	514.928i	−0.433508	+	0.596672i	−0.968754	−	0.248024i	$-0.920219\pi$
$863$	−374.117	+	514.928i	−0.433508	+	0.596672i	0.535246	+	0.844696i	$0.320219\pi$
$864$	844.615	−	283.737i	0.977564	−	0.328399i
$865$	−122.293	+	376.378i	−0.141379	+	0.435120i
$866$	270.691	−	87.9528i	0.312576	−	0.101562i
$867$	76.8377	−	755.101i	0.0886248	−	0.870935i
$868$	164.729			0.189781
$869$	−914.641	+	921.938i	−1.05252	+	1.06092i
$870$	−390.605	−	349.368i	−0.448971	−	0.401572i
$871$	−822.286	+	597.425i	−0.944071	+	0.685908i
$872$	714.547	−	232.170i	0.819434	−	0.266250i
$873$	1068.31	+	219.694i	1.22373	+	0.251654i
$874$	129.390	+	94.0074i	0.148044	+	0.107560i
$875$	−213.598	+	293.993i	−0.244112	+	0.335992i
$876$	67.9830	+	116.855i	0.0776062	+	0.133396i
$877$	392.099	+	1206.76i	0.447091	+	1.37601i	0.880174	+	0.474651i	$0.157426\pi$
$877$	392.099	+	1206.76i	0.447091	+	1.37601i	−0.433083	+	0.901354i	$0.642574\pi$
$878$	−312.736	−	430.444i	−0.356191	−	0.490255i
$879$	160.473	+	143.532i	0.182564	+	0.163290i
$880$	−323.660	+	166.536i	−0.367795	+	0.189246i
$881$		−	425.862i		−	0.483385i	−0.970353	−	0.241693i	$-0.922297\pi$
$881$		−	425.862i		−	0.483385i	0.970353	−	0.241693i	$-0.0777025\pi$
$882$	−195.427	+	178.320i	−0.221573	+	0.202177i
$883$	214.827	+	661.168i	0.243292	+	0.748775i	0.995913	+	0.0903210i	$0.0287893\pi$
$883$	214.827	+	661.168i	0.243292	+	0.748775i	−0.752621	+	0.658454i	$0.771211\pi$
$884$	226.588	+	73.6231i	0.256322	+	0.0832840i
$885$	425.192	−	91.8497i	0.480443	−	0.103785i
$886$	−97.3222	−	70.7087i	−0.109844	−	0.0798067i
$887$	405.855	+	131.870i	0.457559	+	0.148670i	0.528723	−	0.848795i	$-0.322671\pi$
$887$	405.855	+	131.870i	0.457559	+	0.148670i	−0.0711633	+	0.997465i	$0.522671\pi$
$888$	−166.139	+	376.505i	−0.187094	+	0.423992i
$889$	726.458	−	527.802i	0.817163	−	0.593704i
$890$		−	646.354i		−	0.726241i
$891$	61.9418	+	888.844i	0.0695194	+	0.997581i
$892$	−497.976			−0.558269
$893$	−94.9746	−	130.721i	−0.106355	−	0.146385i
$894$	−19.1903	−	8.46806i	−0.0214657	−	0.00947211i
$895$	539.571	−	1660.63i	0.602872	−	1.85545i
$896$	−619.313	+	852.411i	−0.691197	+	0.951352i
$897$	−146.960	−	680.308i	−0.163835	−	0.758426i
$898$	21.2198	−	65.3078i	0.0236301	−	0.0727259i
$899$	−155.681	+	50.5838i	−0.173171	+	0.0562668i
$900$	−342.111	−	374.931i	−0.380124	−	0.416590i
$901$	−133.623			−0.148305
$902$	−54.9647	−	27.7314i	−0.0609365	−	0.0307444i
$903$	−465.580	+	520.535i	−0.515593	+	0.576451i
$904$	179.326	−	130.288i	0.198370	−	0.144124i
$905$	−1422.27	+	462.123i	−1.57157	+	0.510633i
$906$	143.789	−	83.6528i	0.158708	−	0.0923320i
$907$	556.564	+	404.368i	0.613632	+	0.445830i	0.850691	−	0.525665i	$-0.176184\pi$
$907$	556.564	+	404.368i	0.613632	+	0.445830i	−0.237059	+	0.971495i	$0.576184\pi$
$908$	602.314	−	829.014i	0.663341	−	0.913010i
$909$	336.449	−	1636.06i	0.370131	−	1.79985i
$910$	−239.671	−	737.630i	−0.263374	−	0.810583i
$911$	1005.46	+	1383.90i	1.10369	+	1.51910i	0.830402	+	0.557164i	$0.188111\pi$
$911$	1005.46	+	1383.90i	1.10369	+	1.51910i	0.273286	+	0.961933i	$0.411889\pi$
$912$	−91.2461	+	102.016i	−0.100051	+	0.111860i
$913$	550.914	−	1091.93i	0.603411	−	1.19598i
$914$			695.507i			0.760949i
$915$	−1844.33	−	187.676i	−2.01566	−	0.205110i
$916$	228.772	+	704.088i	0.249751	+	0.768655i
$917$	−1103.05	−	358.403i	−1.20289	−	0.390843i
$918$	−51.5885	−	153.566i	−0.0561966	−	0.167284i
$919$	−312.333	−	226.923i	−0.339862	−	0.246924i	0.404742	−	0.914431i	$-0.367361\pi$
$919$	−312.333	−	226.923i	−0.339862	−	0.246924i	−0.744603	+	0.667507i	$0.767361\pi$
$920$	−772.258	−	250.922i	−0.839411	−	0.272741i
$921$	−321.017	−	141.654i	−0.348553	−	0.153805i
$922$	−666.890	+	484.524i	−0.723309	+	0.525514i
$923$		−	871.193i		−	0.943872i
$924$	−556.582	−	677.176i	−0.602361	−	0.732874i
$925$	368.387			0.398256
$926$	92.9504	+	127.935i	0.100378	+	0.138159i
$927$	1414.79	−	641.165i	1.52621	−	0.691656i
$928$	269.166	−	828.407i	0.290049	−	0.892680i
$929$	−43.8819	+	60.3982i	−0.0472356	+	0.0650142i	−0.831981	−	0.554803i	$-0.812793\pi$
$929$	−43.8819	+	60.3982i	−0.0472356	+	0.0650142i	0.784746	+	0.619818i	$0.212793\pi$
$930$	120.352	−	25.9983i	0.129410	−	0.0279551i
$931$	82.8843	−	255.091i	0.0890271	−	0.273997i
$932$	1136.62	−	369.310i	1.21955	−	0.396255i
$933$	546.600	+	55.6210i	0.585852	+	0.0596152i
$934$	763.310			0.817248
$935$	199.843	+	388.392i	0.213736	+	0.415393i
$936$	−828.709	+	92.6525i	−0.885373	+	0.0989877i
$937$	459.767	−	334.040i	0.490680	−	0.356500i	−0.314766	−	0.949169i	$-0.601926\pi$
$937$	459.767	−	334.040i	0.490680	−	0.356500i	0.805446	+	0.592670i	$0.201926\pi$
$938$	−646.632	+	210.103i	−0.689373	+	0.223991i
$939$	−112.816	−	193.917i	−0.120145	−	0.206515i
$940$	284.435	+	206.654i	0.302590	+	0.219844i
$941$	117.253	−	161.385i	0.124605	−	0.171504i	−0.742157	−	0.670226i	$-0.766197\pi$
$941$	117.253	−	161.385i	0.124605	−	0.171504i	0.866762	+	0.498722i	$0.166197\pi$
$942$	−108.910	+	63.3609i	−0.115616	+	0.0672621i
$943$	30.3143	+	93.2977i	0.0321466	+	0.0989371i
$944$	64.3914	+	88.6271i	0.0682112	+	0.0938847i
$945$	917.184	−	1289.13i	0.970565	−	1.36416i
$946$	205.313	+	203.688i	0.217033	+	0.215315i
$947$			984.860i			1.03998i	0.854173	+	0.519990i	$0.174064\pi$
$947$			984.860i			1.03998i	−0.854173	+	0.519990i	$0.825936\pi$
$948$	107.567	−	1057.09i	0.113468	−	1.11507i
$949$	−61.4396	−	189.092i	−0.0647414	−	0.199254i
$950$	−163.133	−	53.0050i	−0.171719	−	0.0557948i
$951$	−11.1942	−	51.8202i	−0.0117709	−	0.0544903i
$952$	300.851	+	218.581i	0.316020	+	0.229602i
$953$	−725.058	−	235.586i	−0.760816	−	0.247204i	−0.0971872	−	0.995266i	$-0.530985\pi$
$953$	−725.058	−	235.586i	−0.760816	−	0.247204i	−0.663629	+	0.748062i	$0.730985\pi$
$954$	182.562	−	82.7347i	0.191365	−	0.0867240i
$955$	−321.702	+	233.730i	−0.336861	+	0.244744i
$956$			483.629i			0.505888i
$957$	733.951	+	469.068i	0.766929	+	0.490145i
$958$	74.8228			0.0781031
$959$	−1086.39	−	1495.28i	−1.13283	−	1.55921i
$960$	−104.199	+	236.135i	−0.108541	+	0.245974i
$961$	−285.080	+	877.388i	−0.296650	+	0.912994i
$962$	152.462	−	209.846i	0.158484	−	0.218135i
$963$	−514.670	−	292.618i	−0.534444	−	0.303861i
$964$	−147.998	+	455.492i	−0.153525	+	0.472502i
$965$	−224.618	+	72.9828i	−0.232765	+	0.0756298i
$966$	47.1332	−	463.189i	0.0487922	−	0.479491i
$967$	1466.73			1.51679			0.758394	−	0.651797i	$-0.225985\pi$
$967$	1466.73			1.51679			0.758394	+	0.651797i	$0.225985\pi$
$968$	−681.260	+	503.283i	−0.703781	+	0.519921i
$969$	122.420	+	109.495i	0.126336	+	0.112998i
$970$	−648.839	+	471.409i	−0.668906	+	0.485989i
$971$	−1086.64	+	353.070i	−1.11909	+	0.363615i	−0.809421	−	0.587229i	$-0.800219\pi$
$971$	−1086.64	+	353.070i	−1.11909	+	0.363615i	−0.309671	+	0.950844i	$0.600219\pi$
$972$	−496.697	−	533.604i	−0.511005	−	0.548975i
$973$	−584.371	−	424.570i	−0.600587	−	0.436352i
$974$	178.085	−	245.112i	0.182838	−	0.251655i
$975$	375.363	+	645.205i	0.384988	+	0.661749i
$976$	−144.271	−	444.019i	−0.147818	−	0.454937i
$977$	22.7466	+	31.3081i	0.0232821	+	0.0320451i	0.820499	−	0.571647i	$-0.193695\pi$
$977$	22.7466	+	31.3081i	0.0232821	+	0.0320451i	−0.797217	+	0.603693i	$0.793695\pi$
$978$	355.066	+	317.580i	0.363053	+	0.324724i
$979$	172.276	+	1060.42i	0.175971	+	1.08317i
$980$			583.614i			0.595524i
$981$	−651.107	−	713.569i	−0.663717	−	0.727389i
$982$	246.835	+	759.679i	0.251359	+	0.773604i
$983$	1153.25	+	374.713i	1.17319	+	0.381194i	0.829834	−	0.558011i	$-0.188435\pi$
$983$	1153.25	+	374.713i	1.17319	+	0.381194i	0.343359	+	0.939204i	$0.388435\pi$
$984$	114.882	−	24.8167i	0.116750	−	0.0252202i
$985$	−779.583	−	566.400i	−0.791455	−	0.575026i
$986$	−150.620	−	48.9392i	−0.152758	−	0.0496341i
$987$	−189.893	+	430.336i	−0.192395	+	0.436004i
$988$	293.125	−	212.967i	0.296685	−	0.215554i
$989$		−	460.839i		−	0.465965i
$990$	−513.514	−	406.904i	−0.518701	−	0.411014i
$991$	−1413.89			−1.42673			−0.713367	−	0.700790i	$-0.752831\pi$
$991$	−1413.89			−1.42673			−0.713367	+	0.700790i	$0.752831\pi$
$992$	120.292	+	165.568i	0.121263	+	0.166904i
$993$	1085.73	+	479.099i	1.09339	+	0.482477i
$994$	180.087	−	554.251i	0.181174	−	0.557597i
$995$	938.207	−	1291.33i	0.942922	−	1.29782i
$996$	211.290	+	978.107i	0.212138	+	0.982035i
$997$	291.405	−	896.853i	0.292282	−	0.899552i	−0.691839	−	0.722052i	$-0.743199\pi$
$997$	291.405	−	896.853i	0.292282	−	0.899552i	0.984121	−	0.177500i	$-0.0568009\pi$
$998$	−556.122	+	180.695i	−0.557237	+	0.181057i
$999$	529.086	−	5.25500i	0.529616	−	0.00526026i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.3.h.a.14.1	✓	8
3.2	odd	2	inner	33.3.h.a.14.2	yes	8
11.2	odd	10		363.3.b.g.122.2		4
11.3	even	5		363.3.h.h.269.1		8
11.4	even	5	inner	33.3.h.a.26.2	yes	8
11.5	even	5		363.3.h.h.251.2		8
11.6	odd	10		363.3.h.i.251.1		8
11.7	odd	10		363.3.h.g.323.1		8
11.8	odd	10		363.3.h.i.269.2		8
11.9	even	5		363.3.b.f.122.4		4
11.10	odd	2		363.3.h.g.245.2		8
33.2	even	10		363.3.b.g.122.3		4
33.5	odd	10		363.3.h.h.251.1		8
33.8	even	10		363.3.h.i.269.1		8
33.14	odd	10		363.3.h.h.269.2		8
33.17	even	10		363.3.h.i.251.2		8
33.20	odd	10		363.3.b.f.122.1		4
33.26	odd	10	inner	33.3.h.a.26.1	yes	8
33.29	even	10		363.3.h.g.323.2		8
33.32	even	2		363.3.h.g.245.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.3.h.a.14.1	✓	8	1.1	even	1	trivial
33.3.h.a.14.2	yes	8	3.2	odd	2	inner
33.3.h.a.26.1	yes	8	33.26	odd	10	inner
33.3.h.a.26.2	yes	8	11.4	even	5	inner
363.3.b.f.122.1		4	33.20	odd	10
363.3.b.f.122.4		4	11.9	even	5
363.3.b.g.122.2		4	11.2	odd	10
363.3.b.g.122.3		4	33.2	even	10
363.3.h.g.245.1		8	33.32	even	2
363.3.h.g.245.2		8	11.10	odd	2
363.3.h.g.323.1		8	11.7	odd	10
363.3.h.g.323.2		8	33.29	even	10
363.3.h.h.251.1		8	33.5	odd	10
363.3.h.h.251.2		8	11.5	even	5
363.3.h.h.269.1		8	11.3	even	5
363.3.h.h.269.2		8	33.14	odd	10
363.3.h.i.251.1		8	11.6	odd	10
363.3.h.i.251.2		8	33.17	even	10
363.3.h.i.269.1		8	33.8	even	10
363.3.h.i.269.2		8	11.8	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	33.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-2.74466 - 1.21113i) q^{3} +(0.927051 - 2.85317i) q^{4} +(3.88998 - 5.35410i) q^{5} +(0.633446 + 2.93236i) q^{6} +(-2.73607 + 8.42075i) q^{7} +(-6.65740 + 2.16312i) q^{8} +(6.06633 + 6.64828i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-2.74466 - 1.21113i) q^{3} +(0.927051 - 2.85317i) q^{4} +(3.88998 - 5.35410i) q^{5} +(0.633446 + 2.93236i) q^{6} +(-2.73607 + 8.42075i) q^{7} +(-6.65740 + 2.16312i) q^{8} +(6.06633 + 6.64828i) q^{9} -6.61803 q^{10} +(10.8576 - 1.76393i) q^{11} +(-6.00000 + 6.70820i) q^{12} +(10.7082 - 7.77997i) q^{13} +(8.42075 - 2.73607i) q^{14} +(-17.1612 + 9.98392i) q^{15} +(-4.04508 - 2.93893i) q^{16} +(-3.52671 + 4.85410i) q^{17} +(1.81288 - 8.81553i) q^{18} +(2.81966 + 8.67802i) q^{19} +(-11.6699 - 16.0623i) q^{20} +(17.7082 - 19.7984i) q^{21} +(-7.80902 - 7.74721i) q^{22} +17.5279i q^{23} +(20.8921 + 2.12594i) q^{24} +(-5.80902 - 17.8783i) q^{25} +(-12.5882 - 4.09017i) q^{26} +(-8.59808 - 25.5944i) q^{27} +(21.4894 + 15.6129i) q^{28} +(-25.1033 - 8.15654i) q^{29} +(18.1643 + 8.01530i) q^{30} +(5.01722 - 3.64522i) q^{31} +33.0000i q^{32} +(-31.9369 - 8.30863i) q^{33} +6.00000 q^{34} +(34.4423 + 47.4058i) q^{35} +(24.5925 - 11.1450i) q^{36} +(-6.05573 + 18.6376i) q^{37} +(5.36331 - 7.38197i) q^{38} +(-38.8129 + 8.38434i) q^{39} +(-14.3156 + 44.0589i) q^{40} +(5.32282 - 1.72949i) q^{41} +(-26.4258 - 2.68905i) q^{42} -26.2918 q^{43} +(5.03280 - 32.6140i) q^{44} +(59.1935 - 6.61803i) q^{45} +(14.1803 - 10.3026i) q^{46} +(-16.8415 + 5.47214i) q^{47} +(7.54297 + 12.9655i) q^{48} +(-23.7812 - 17.2780i) q^{49} +(-11.0494 + 15.2082i) q^{50} +(15.5586 - 9.05156i) q^{51} +(-12.2705 - 37.7647i) q^{52} +(13.0903 + 18.0172i) q^{53} +(-15.6525 + 22.0000i) q^{54} +(32.7918 - 64.9946i) q^{55} -61.9787i q^{56} +(2.77120 - 27.2332i) q^{57} +(8.15654 + 25.1033i) q^{58} +(-20.8375 - 6.77051i) q^{59} +(12.5765 + 58.2194i) q^{60} +(75.5410 + 54.8838i) q^{61} +(-5.89810 - 1.91641i) q^{62} +(-72.5814 + 32.8929i) q^{63} +(10.5172 - 7.64121i) q^{64} -87.5967i q^{65} +(12.0502 + 30.7212i) q^{66} -76.7902 q^{67} +(10.5801 + 14.5623i) q^{68} +(21.2285 - 48.1080i) q^{69} +(18.1074 - 55.7288i) q^{70} +(38.6878 - 53.2492i) q^{71} +(-54.7670 - 31.1381i) q^{72} +(4.64183 - 14.2861i) q^{73} +(18.6376 - 6.05573i) q^{74} +(-5.70918 + 56.1054i) q^{75} +27.3738 q^{76} +(-14.8536 + 96.2558i) q^{77} +(29.5967 + 26.4721i) q^{78} +(-95.5132 + 69.3944i) q^{79} +(-31.4706 + 10.2254i) q^{80} +(-7.39933 + 80.6613i) q^{81} +(-4.52786 - 3.28969i) q^{82} +(65.3531 - 89.9508i) q^{83} +(-40.0717 - 68.8786i) q^{84} +(12.2705 + 37.7647i) q^{85} +(15.4539 + 21.2705i) q^{86} +(59.0213 + 52.7902i) q^{87} +(-68.4681 + 35.2296i) q^{88} +97.6656i q^{89} +(-40.1472 - 43.9986i) q^{90} +(36.2148 + 111.458i) q^{91} +(50.0100 + 16.2492i) q^{92} +(-18.1854 + 3.92840i) q^{93} +(14.3262 + 10.4086i) q^{94} +(57.4314 + 18.6606i) q^{95} +(39.9673 - 90.5738i) q^{96} +(98.0410 - 71.2310i) q^{97} +29.3951i q^{98} +(77.5932 + 61.4841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 6 q^{4} + 10 q^{6} - 4 q^{7} + 2 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 6 * q^4 + 10 * q^6 - 4 * q^7 + 2 * q^9	\( 8 q + 4 q^{3} - 6 q^{4} + 10 q^{6} - 4 q^{7} + 2 q^{9} - 44 q^{10} - 48 q^{12} + 32 q^{13} - 50 q^{15} - 10 q^{16} + 40 q^{18} + 112 q^{19} + 88 q^{21} - 58 q^{22} + 70 q^{24} - 42 q^{25} - 44 q^{27} + 78 q^{28} - 12 q^{30} - 18 q^{31} - 90 q^{33} + 48 q^{34} + 6 q^{36} - 120 q^{37} - 64 q^{39} + 42 q^{40} - 70 q^{42} - 264 q^{43} + 80 q^{45} + 24 q^{46} + 20 q^{48} - 150 q^{49} + 60 q^{51} + 36 q^{52} + 316 q^{55} + 136 q^{57} + 186 q^{58} + 180 q^{60} + 336 q^{61} + 4 q^{63} + 26 q^{64} - 124 q^{66} - 24 q^{67} - 240 q^{69} + 42 q^{70} - 280 q^{72} - 182 q^{73} - 136 q^{75} - 264 q^{76} + 40 q^{78} - 460 q^{79} + 158 q^{81} - 72 q^{82} + 24 q^{84} - 36 q^{85} + 660 q^{87} - 266 q^{88} - 16 q^{90} + 84 q^{91} + 36 q^{93} + 52 q^{94} - 330 q^{96} + 516 q^{97} + 40 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 6 * q^4 + 10 * q^6 - 4 * q^7 + 2 * q^9 - 44 * q^10 - 48 * q^12 + 32 * q^13 - 50 * q^15 - 10 * q^16 + 40 * q^18 + 112 * q^19 + 88 * q^21 - 58 * q^22 + 70 * q^24 - 42 * q^25 - 44 * q^27 + 78 * q^28 - 12 * q^30 - 18 * q^31 - 90 * q^33 + 48 * q^34 + 6 * q^36 - 120 * q^37 - 64 * q^39 + 42 * q^40 - 70 * q^42 - 264 * q^43 + 80 * q^45 + 24 * q^46 + 20 * q^48 - 150 * q^49 + 60 * q^51 + 36 * q^52 + 316 * q^55 + 136 * q^57 + 186 * q^58 + 180 * q^60 + 336 * q^61 + 4 * q^63 + 26 * q^64 - 124 * q^66 - 24 * q^67 - 240 * q^69 + 42 * q^70 - 280 * q^72 - 182 * q^73 - 136 * q^75 - 264 * q^76 + 40 * q^78 - 460 * q^79 + 158 * q^81 - 72 * q^82 + 24 * q^84 - 36 * q^85 + 660 * q^87 - 266 * q^88 - 16 * q^90 + 84 * q^91 + 36 * q^93 + 52 * q^94 - 330 * q^96 + 516 * q^97 + 40 * q^99

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