LMFDB - Embedded newform 210.3.o.a.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(31,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("210.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.o (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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Root			$1.72286 - 0.178197i$ of defining polynomial
Character	$\chi$	$=$	210.31
Dual form			210.3.o.a.61.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +2.44949i q^{6} +(5.10237 + 4.79227i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +2.44949i q^{6} +(5.10237 + 4.79227i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.73861 + 1.58114i) q^{10} +(0.919414 - 1.59247i) q^{11} +(-3.00000 + 1.73205i) q^{12} +5.40765i q^{13} +(-2.26139 + 9.63774i) q^{14} +3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(8.71093 + 5.02926i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-7.96084 + 4.59619i) q^{19} +4.47214i q^{20} +(3.50333 + 11.6072i) q^{21} +2.60049 q^{22} +(0.460644 + 0.797858i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-6.62299 + 3.82378i) q^{26} +5.19615i q^{27} +(-13.4028 + 4.04529i) q^{28} +12.5573 q^{29} +(2.73861 + 4.74342i) q^{30} +(-36.1874 - 20.8928i) q^{31} +(2.82843 - 4.89898i) q^{32} +(2.75824 - 1.59247i) q^{33} +14.2249i q^{34} +(15.2386 + 3.57557i) q^{35} -6.00000 q^{36} +(-3.64194 - 6.30803i) q^{37} +(-11.2583 - 6.50000i) q^{38} +(-4.68316 + 8.11147i) q^{39} +(-5.47723 + 3.16228i) q^{40} -52.3877i q^{41} +(-11.7386 + 12.4982i) q^{42} -8.12312 q^{43} +(1.83883 + 3.18494i) q^{44} +(5.80948 + 3.35410i) q^{45} +(-0.651449 + 1.12834i) q^{46} +(29.4117 - 16.9809i) q^{47} -6.92820i q^{48} +(3.06832 + 48.9038i) q^{49} +7.07107 q^{50} +(8.71093 + 15.0878i) q^{51} +(-9.36632 - 5.40765i) q^{52} +(52.0396 - 90.1353i) q^{53} +(-6.36396 + 3.67423i) q^{54} -4.11174i q^{55} +(-14.4317 - 13.5546i) q^{56} -15.9217 q^{57} +(8.87938 + 15.3795i) q^{58} +(12.5918 + 7.26989i) q^{59} +(-3.87298 + 6.70820i) q^{60} +(20.5913 - 11.8884i) q^{61} -59.0937i q^{62} +(-4.79713 + 20.4447i) q^{63} +8.00000 q^{64} +(6.04593 + 10.4719i) q^{65} +(3.90074 + 2.25209i) q^{66} +(7.46339 - 12.9270i) q^{67} +(-17.4219 + 10.0585i) q^{68} +1.59572i q^{69} +(6.39617 + 21.1917i) q^{70} -17.9620 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-107.705 - 62.1833i) q^{73} +(5.15048 - 8.92090i) q^{74} +(7.50000 - 4.33013i) q^{75} -18.3848i q^{76} +(12.3227 - 3.71930i) q^{77} -13.2460 q^{78} +(40.4683 + 70.0931i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(64.1616 - 37.0437i) q^{82} -154.716i q^{83} +(-23.6076 - 5.53924i) q^{84} +22.4915 q^{85} +(-5.74391 - 9.94875i) q^{86} +(18.8360 + 10.8750i) q^{87} +(-2.60049 + 4.50419i) q^{88} +(58.9956 - 34.0611i) q^{89} +9.48683i q^{90} +(-25.9149 + 27.5918i) q^{91} -1.84258 q^{92} +(-36.1874 - 62.6784i) q^{93} +(41.5944 + 24.0146i) q^{94} +(-10.2774 + 17.8010i) q^{95} +(8.48528 - 4.89898i) q^{96} -88.1736i q^{97} +(-57.7251 + 38.3381i) q^{98} +5.51648 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) $ 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9	$ 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} - 24 q^{12} - 40 q^{14} - 16 q^{16} + 84 q^{17} + 108 q^{19} - 48 q^{22} + 12 q^{23} + 20 q^{25} - 96 q^{26} + 72 q^{29} - 132 q^{31} - 12 q^{33} + 100 q^{35} - 48 q^{36} - 96 q^{37} - 168 q^{38} + 24 q^{39} - 72 q^{42} - 112 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} + 156 q^{49} + 84 q^{51} + 48 q^{52} + 32 q^{53} + 16 q^{56} + 216 q^{57} + 104 q^{58} + 132 q^{59} + 96 q^{61} + 64 q^{64} + 20 q^{65} - 72 q^{66} - 120 q^{67} - 168 q^{68} + 8 q^{71} + 24 q^{73} - 16 q^{74} + 60 q^{75} - 216 q^{77} - 192 q^{78} + 12 q^{79} - 36 q^{81} + 24 q^{82} + 120 q^{85} - 40 q^{86} + 108 q^{87} + 48 q^{88} + 492 q^{89} - 308 q^{91} - 48 q^{92} - 132 q^{93} + 480 q^{94} - 40 q^{95} - 24 q^{99}+O(q^{100}) $ 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 - 24 * q^12 - 40 * q^14 - 16 * q^16 + 84 * q^17 + 108 * q^19 - 48 * q^22 + 12 * q^23 + 20 * q^25 - 96 * q^26 + 72 * q^29 - 132 * q^31 - 12 * q^33 + 100 * q^35 - 48 * q^36 - 96 * q^37 - 168 * q^38 + 24 * q^39 - 72 * q^42 - 112 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 + 156 * q^49 + 84 * q^51 + 48 * q^52 + 32 * q^53 + 16 * q^56 + 216 * q^57 + 104 * q^58 + 132 * q^59 + 96 * q^61 + 64 * q^64 + 20 * q^65 - 72 * q^66 - 120 * q^67 - 168 * q^68 + 8 * q^71 + 24 * q^73 - 16 * q^74 + 60 * q^75 - 216 * q^77 - 192 * q^78 + 12 * q^79 - 36 * q^81 + 24 * q^82 + 120 * q^85 - 40 * q^86 + 108 * q^87 + 48 * q^88 + 492 * q^89 - 308 * q^91 - 48 * q^92 - 132 * q^93 + 480 * q^94 - 40 * q^95 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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 $

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$3$	1.50000	+	0.866025i	0.500000	+	0.288675i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$6$			2.44949i			0.408248i
$7$	5.10237	+	4.79227i	0.728910	+	0.684610i
$7$	5.10237	+	4.79227i	0.728910	+	0.684610i
$8$	−2.82843			−0.353553
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	2.73861	+	1.58114i	0.273861	+	0.158114i
$11$	0.919414	−	1.59247i	0.0835831	−	0.144770i	−0.821203	−	0.570635i	$-0.806697\pi$
$11$	0.919414	−	1.59247i	0.0835831	−	0.144770i	0.904787	+	0.425865i	$0.140030\pi$
$12$	−3.00000	+	1.73205i	−0.250000	+	0.144338i
$13$			5.40765i			0.415973i	0.978132	+	0.207986i	$0.0666910\pi$
$13$			5.40765i			0.415973i	−0.978132	+	0.207986i	$0.933309\pi$
$14$	−2.26139	+	9.63774i	−0.161528	+	0.688410i
$15$	3.87298			0.258199
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	8.71093	+	5.02926i	0.512408	+	0.295839i	0.733823	−	0.679341i	$-0.237734\pi$
$17$	8.71093	+	5.02926i	0.512408	+	0.295839i	−0.221415	+	0.975180i	$0.571068\pi$
$18$	−2.12132	+	3.67423i	−0.117851	+	0.204124i
$19$	−7.96084	+	4.59619i	−0.418992	+	0.241905i	−0.694646	−	0.719352i	$-0.744439\pi$
$19$	−7.96084	+	4.59619i	−0.418992	+	0.241905i	0.275654	+	0.961257i	$0.411106\pi$
$20$			4.47214i			0.223607i
$21$	3.50333	+	11.6072i	0.166825	+	0.552723i
$22$	2.60049			0.118204
$23$	0.460644	+	0.797858i	0.0200280	+	0.0346895i	0.875866	−	0.482555i	$-0.160291\pi$
$23$	0.460644	+	0.797858i	0.0200280	+	0.0346895i	−0.855838	+	0.517244i	$0.826958\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	−6.62299	+	3.82378i	−0.254730	+	0.147069i
$27$			5.19615i			0.192450i
$28$	−13.4028	+	4.04529i	−0.478672	+	0.144475i
$29$	12.5573			0.433012			0.216506	−	0.976281i	$-0.430534\pi$
$29$	12.5573			0.433012			0.216506	+	0.976281i	$0.430534\pi$
$30$	2.73861	+	4.74342i	0.0912871	+	0.158114i
$31$	−36.1874	−	20.8928i	−1.16733	−	0.673961i	−0.214284	−	0.976771i	$-0.568742\pi$
$31$	−36.1874	−	20.8928i	−1.16733	−	0.673961i	−0.953051	+	0.302811i	$0.902075\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$	2.75824	−	1.59247i	0.0835831	−	0.0482567i
$34$			14.2249i			0.418379i
$35$	15.2386	+	3.57557i	0.435389	+	0.102159i
$36$	−6.00000			−0.166667
$37$	−3.64194	−	6.30803i	−0.0984308	−	0.170487i	0.812604	−	0.582816i	$-0.198049\pi$
$37$	−3.64194	−	6.30803i	−0.0984308	−	0.170487i	−0.911035	+	0.412328i	$0.864716\pi$
$38$	−11.2583	−	6.50000i	−0.296272	−	0.171053i
$39$	−4.68316	+	8.11147i	−0.120081	+	0.207986i
$40$	−5.47723	+	3.16228i	−0.136931	+	0.0790569i
$41$		−	52.3877i		−	1.27775i	−0.769311	−	0.638875i	$-0.779400\pi$
$41$		−	52.3877i		−	1.27775i	0.769311	−	0.638875i	$-0.220600\pi$
$42$	−11.7386	+	12.4982i	−0.279491	+	0.297576i
$43$	−8.12312			−0.188910			−0.0944549	−	0.995529i	$-0.530111\pi$
$43$	−8.12312			−0.188910			−0.0944549	+	0.995529i	$0.530111\pi$
$44$	1.83883	+	3.18494i	0.0417915	+	0.0723850i
$45$	5.80948	+	3.35410i	0.129099	+	0.0745356i
$46$	−0.651449	+	1.12834i	−0.0141619	+	0.0245292i
$47$	29.4117	−	16.9809i	0.625781	−	0.361295i	−0.153335	−	0.988174i	$-0.549001\pi$
$47$	29.4117	−	16.9809i	0.625781	−	0.361295i	0.779116	+	0.626879i	$0.215668\pi$
$48$		−	6.92820i		−	0.144338i
$49$	3.06832	+	48.9038i	0.0626188	+	0.998038i
$50$	7.07107			0.141421
$51$	8.71093	+	15.0878i	0.170803	+	0.295839i
$52$	−9.36632	−	5.40765i	−0.180122	−	0.103993i
$53$	52.0396	−	90.1353i	0.981880	−	1.70067i	0.326825	−	0.945085i	$-0.394021\pi$
$53$	52.0396	−	90.1353i	0.981880	−	1.70067i	0.655055	−	0.755582i	$-0.272646\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		−	4.11174i		−	0.0747590i
$56$	−14.4317	−	13.5546i	−0.257709	−	0.242046i
$57$	−15.9217			−0.279328
$58$	8.87938	+	15.3795i	0.153093	+	0.265164i
$59$	12.5918	+	7.26989i	0.213421	+	0.123218i	0.602900	−	0.797817i	$-0.294012\pi$
$59$	12.5918	+	7.26989i	0.213421	+	0.123218i	−0.389479	+	0.921035i	$0.627345\pi$
$60$	−3.87298	+	6.70820i	−0.0645497	+	0.111803i
$61$	20.5913	−	11.8884i	0.337562	−	0.194892i	−0.321631	−	0.946865i	$-0.604231\pi$
$61$	20.5913	−	11.8884i	0.337562	−	0.194892i	0.659194	+	0.751973i	$0.270898\pi$
$62$		−	59.0937i		−	0.953125i
$63$	−4.79713	+	20.4447i	−0.0761449	+	0.324520i
$64$	8.00000			0.125000
$65$	6.04593	+	10.4719i	0.0930144	+	0.161106i
$66$	3.90074	+	2.25209i	0.0591021	+	0.0341226i
$67$	7.46339	−	12.9270i	0.111394	−	0.192940i	−0.804939	−	0.593358i	$-0.797802\pi$
$67$	7.46339	−	12.9270i	0.111394	−	0.192940i	0.916332	+	0.400418i	$0.131135\pi$
$68$	−17.4219	+	10.0585i	−0.256204	+	0.147919i
$69$			1.59572i			0.0231263i
$70$	6.39617	+	21.1917i	0.0913738	+	0.302739i
$71$	−17.9620			−0.252987			−0.126493	−	0.991967i	$-0.540372\pi$
$71$	−17.9620			−0.252987			−0.126493	+	0.991967i	$0.540372\pi$
$72$	−4.24264	−	7.34847i	−0.0589256	−	0.102062i
$73$	−107.705	−	62.1833i	−1.47541	−	0.851826i	−0.475791	−	0.879558i	$-0.657838\pi$
$73$	−107.705	−	62.1833i	−1.47541	−	0.851826i	−0.999615	+	0.0277318i	$0.991172\pi$
$74$	5.15048	−	8.92090i	0.0696011	−	0.120553i
$75$	7.50000	−	4.33013i	0.100000	−	0.0577350i
$76$		−	18.3848i		−	0.241905i
$77$	12.3227	−	3.71930i	0.160036	−	0.0483026i
$78$	−13.2460			−0.169820
$79$	40.4683	+	70.0931i	0.512257	+	0.887254i	0.999899	+	0.0142110i	$0.00452366\pi$
$79$	40.4683	+	70.0931i	0.512257	+	0.887254i	−0.487642	+	0.873043i	$0.662143\pi$
$80$	−7.74597	−	4.47214i	−0.0968246	−	0.0559017i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	64.1616	−	37.0437i	0.782459	−	0.451753i
$83$		−	154.716i		−	1.86405i	−0.362395	−	0.932025i	$-0.618041\pi$
$83$		−	154.716i		−	1.86405i	0.362395	−	0.932025i	$-0.381959\pi$
$84$	−23.6076	−	5.53924i	−0.281042	−	0.0659434i
$85$	22.4915			0.264606
$86$	−5.74391	−	9.94875i	−0.0667897	−	0.115683i
$87$	18.8360	+	10.8750i	0.216506	+	0.125000i
$88$	−2.60049	+	4.50419i	−0.0295511	+	0.0511840i
$89$	58.9956	−	34.0611i	0.662872	−	0.382709i	−0.130498	−	0.991449i	$-0.541658\pi$
$89$	58.9956	−	34.0611i	0.662872	−	0.382709i	0.793371	+	0.608739i	$0.208324\pi$
$90$			9.48683i			0.105409i
$91$	−25.9149	+	27.5918i	−0.284779	+	0.303207i
$92$	−1.84258			−0.0200280
$93$	−36.1874	−	62.6784i	−0.389111	−	0.673961i
$94$	41.5944	+	24.0146i	0.442494	+	0.255474i
$95$	−10.2774	+	17.8010i	−0.108183	+	0.187379i
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$		−	88.1736i		−	0.909006i	−0.890745	−	0.454503i	$-0.849817\pi$
$97$		−	88.1736i		−	0.909006i	0.890745	−	0.454503i	$-0.150183\pi$
$98$	−57.7251	+	38.3381i	−0.589032	+	0.391206i
$99$	5.51648			0.0557220
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	−96.4537	−	55.6876i	−0.954987	−	0.551362i	−0.0603607	−	0.998177i	$-0.519225\pi$
$101$	−96.4537	−	55.6876i	−0.954987	−	0.551362i	−0.894627	+	0.446814i	$0.852558\pi$
$102$	−12.3191	+	21.3373i	−0.120776	+	0.209190i
$103$	−40.6847	+	23.4893i	−0.394997	+	0.228051i	−0.684323	−	0.729179i	$-0.739902\pi$
$103$	−40.6847	+	23.4893i	−0.394997	+	0.228051i	0.289326	+	0.957231i	$0.406569\pi$
$104$		−	15.2951i		−	0.147069i
$105$	19.7614	+	18.5604i	0.188204	+	0.176765i
$106$	147.190			1.38859
$107$	92.8409	+	160.805i	0.867672	+	1.50285i	0.864370	+	0.502857i	$0.167718\pi$
$107$	92.8409	+	160.805i	0.867672	+	1.50285i	0.00330196	+	0.999995i	$0.498949\pi$
$108$	−9.00000	−	5.19615i	−0.0833333	−	0.0481125i
$109$	−43.1448	+	74.7290i	−0.395824	+	0.685587i	−0.993206	−	0.116369i	$-0.962874\pi$
$109$	−43.1448	+	74.7290i	−0.395824	+	0.685587i	0.597382	+	0.801957i	$0.296208\pi$
$110$	5.03584	−	2.90744i	0.0457803	−	0.0264313i
$111$		−	12.6161i		−	0.113658i
$112$	6.39617	−	27.2597i	0.0571087	−	0.243390i
$113$	−85.8206			−0.759474			−0.379737	−	0.925094i	$-0.623986\pi$
$113$	−85.8206			−0.759474			−0.379737	+	0.925094i	$0.623986\pi$
$114$	−11.2583	−	19.5000i	−0.0987572	−	0.171053i
$115$	1.78407	+	1.03003i	0.0155136	+	0.00895679i
$116$	−12.5573	+	21.7500i	−0.108253	+	0.187500i
$117$	−14.0495	+	8.11147i	−0.120081	+	0.0693288i
$118$			20.5624i			0.174257i
$119$	20.3448	+	67.4062i	0.170965	+	0.566439i
$120$	−10.9545			−0.0912871
$121$	58.8094	+	101.861i	0.486028	+	0.841825i
$122$	29.1205	+	16.8127i	0.238693	+	0.137809i
$123$	45.3691	−	78.5816i	0.368855	−	0.638875i
$124$	72.3747	−	41.7856i	0.583667	−	0.336980i
$125$		−	11.1803i		−	0.0894427i
$126$	−28.4317	+	8.58136i	−0.225648	+	0.0681060i
$127$	−131.740			−1.03733			−0.518663	−	0.854979i	$-0.673570\pi$
$127$	−131.740			−1.03733			−0.518663	+	0.854979i	$0.673570\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$	−12.1847	−	7.03483i	−0.0944549	−	0.0545336i
$130$	−8.55024	+	14.8095i	−0.0657711	+	0.113919i
$131$	−102.856	+	59.3839i	−0.785160	+	0.453312i	−0.838256	−	0.545277i	$-0.816424\pi$
$131$	−102.856	+	59.3839i	−0.785160	+	0.453312i	0.0530960	+	0.998589i	$0.483091\pi$
$132$			6.36988i			0.0482567i
$133$	−62.6453	−	14.6990i	−0.471017	−	0.110519i
$134$	21.1096			0.157535
$135$	5.80948	+	10.0623i	0.0430331	+	0.0745356i
$136$	−24.6382	−	14.2249i	−0.181163	−	0.104595i
$137$	−40.5765	+	70.2805i	−0.296179	+	0.512997i	−0.975258	−	0.221068i	$-0.929046\pi$
$137$	−40.5765	+	70.2805i	−0.296179	+	0.512997i	0.679080	+	0.734065i	$0.262379\pi$
$138$	−1.95435	+	1.12834i	−0.0141619	+	0.00817639i
$139$			248.311i			1.78641i	0.449646	+	0.893207i	$0.351550\pi$
$139$			248.311i			1.78641i	−0.449646	+	0.893207i	$0.648450\pi$
$140$	−21.4317	+	22.8185i	−0.153083	+	0.162989i
$141$	58.8234			0.417187
$142$	−12.7011	−	21.9989i	−0.0894442	−	0.154922i
$143$	8.61152	+	4.97186i	0.0602204	+	0.0347683i
$144$	6.00000	−	10.3923i	0.0416667	−	0.0721688i
$145$	24.3172	−	14.0395i	0.167705	−	0.0968244i
$146$		−	175.881i		−	1.20466i
$147$	−37.7495	+	76.0130i	−0.256799	+	0.517095i
$148$	14.5678			0.0984308
$149$	75.0048	+	129.912i	0.503388	+	0.871894i	0.999992	+	0.00391672i	$0.00124673\pi$
$149$	75.0048	+	129.912i	0.503388	+	0.871894i	−0.496604	+	0.867977i	$0.665420\pi$
$150$	10.6066	+	6.12372i	0.0707107	+	0.0408248i
$151$	−91.5149	+	158.509i	−0.606059	+	1.04973i	0.385824	+	0.922572i	$0.373917\pi$
$151$	−91.5149	+	158.509i	−0.606059	+	1.04973i	−0.991883	+	0.127153i	$0.959416\pi$
$152$	22.5167	−	13.0000i	0.148136	−	0.0855263i
$153$			30.1755i			0.197226i
$154$	13.2687	+	12.4623i	0.0861603	+	0.0809238i
$155$	−93.4354			−0.602809
$156$	−9.36632	−	16.2229i	−0.0600405	−	0.103993i
$157$	−255.724	−	147.643i	−1.62882	−	0.940398i	−0.984446	−	0.175685i	$-0.943786\pi$
$157$	−255.724	−	147.643i	−1.62882	−	0.940398i	−0.644371	−	0.764713i	$-0.722881\pi$
$158$	−57.2308	+	99.1266i	−0.362220	+	0.627384i
$159$	156.119	−	90.1353i	0.981880	−	0.566889i
$160$		−	12.6491i		−	0.0790569i
$161$	−1.47318	+	6.27850i	−0.00915017	+	0.0389969i
$162$	−12.7279			−0.0785674
$163$	59.1631	+	102.473i	0.362964	+	0.628671i	0.988447	−	0.151566i	$-0.0484316\pi$
$163$	59.1631	+	102.473i	0.362964	+	0.628671i	−0.625484	+	0.780237i	$0.715098\pi$
$164$	90.7382	+	52.3877i	0.553282	+	0.319437i
$165$	3.56087	−	6.16761i	0.0215811	−	0.0373795i
$166$	189.488	−	109.401i	1.14149	−	0.659041i
$167$			205.186i			1.22866i	0.789050	+	0.614329i	$0.210573\pi$
$167$			205.186i			1.22866i	−0.789050	+	0.614329i	$0.789427\pi$
$168$	−9.90890	−	32.8301i	−0.0589816	−	0.195417i
$169$	139.757			0.826967
$170$	15.9039	+	27.5464i	0.0935524	+	0.162038i
$171$	−23.8825	−	13.7886i	−0.139664	−	0.0806350i
$172$	8.12312	−	14.0697i	0.0472274	−	0.0818003i
$173$	97.4572	−	56.2670i	0.563337	−	0.325242i	−0.191147	−	0.981561i	$-0.561221\pi$
$173$	97.4572	−	56.2670i	0.563337	−	0.325242i	0.754484	+	0.656319i	$0.227887\pi$
$174$			30.7591i			0.176776i
$175$	33.5071	−	10.1132i	0.191469	−	0.0577899i
$176$	−7.35531			−0.0417915
$177$	12.5918	+	21.8097i	0.0711402	+	0.123218i
$178$	83.4324	+	48.1697i	0.468721	+	0.270616i
$179$	22.2349	−	38.5120i	0.124217	−	0.215151i	−0.797209	−	0.603703i	$-0.793691\pi$
$179$	22.2349	−	38.5120i	0.124217	−	0.215151i	0.921427	+	0.388552i	$0.127025\pi$
$180$	−11.6190	+	6.70820i	−0.0645497	+	0.0372678i
$181$		−	9.24555i		−	0.0510804i	−0.999674	−	0.0255402i	$-0.991869\pi$
$181$		−	9.24555i		−	0.0510804i	0.999674	−	0.0255402i	$-0.00813058\pi$
$182$	−52.1175	−	12.2288i	−0.286360	−	0.0671911i
$183$	41.1826			0.225041
$184$	−1.30290	−	2.25668i	−0.00708096	−	0.0122646i
$185$	−14.1052	−	8.14363i	−0.0762442	−	0.0440196i
$186$	51.1767	−	88.6406i	0.275143	−	0.476562i
$187$	16.0179	−	9.24793i	0.0856572	−	0.0494542i
$188$			67.9234i			0.361295i
$189$	−24.9014	+	26.5127i	−0.131753	+	0.140279i
$190$	−29.0689			−0.152994
$191$	68.4044	+	118.480i	0.358138	+	0.620314i	0.987650	−	0.156677i	$-0.0500783\pi$
$191$	68.4044	+	118.480i	0.358138	+	0.620314i	−0.629511	+	0.776991i	$0.716745\pi$
$192$	12.0000	+	6.92820i	0.0625000	+	0.0360844i
$193$	182.937	−	316.856i	0.947860	−	1.64174i	0.197939	−	0.980214i	$-0.436575\pi$
$193$	182.937	−	316.856i	0.947860	−	1.64174i	0.749921	−	0.661527i	$-0.230091\pi$
$194$	107.990	−	62.3481i	0.556650	−	0.321382i
$195$			20.9437i			0.107404i
$196$	−87.7723	−	43.5893i	−0.447818	−	0.222395i
$197$	−194.925			−0.989468			−0.494734	−	0.869045i	$-0.664734\pi$
$197$	−194.925			−0.989468			−0.494734	+	0.869045i	$0.664734\pi$
$198$	3.90074	+	6.75628i	0.0197007	+	0.0341226i
$199$	−210.301	−	121.418i	−1.05679	−	0.610138i	−0.132248	−	0.991217i	$-0.542219\pi$
$199$	−210.301	−	121.418i	−1.05679	−	0.610138i	−0.924543	+	0.381078i	$0.875553\pi$
$200$	−7.07107	+	12.2474i	−0.0353553	+	0.0612372i
$201$	22.3902	−	12.9270i	0.111394	−	0.0643133i
$202$		−	157.508i		−	0.779744i
$203$	64.0722	+	60.1782i	0.315627	+	0.296444i
$204$	−34.8437			−0.170803
$205$	−58.5713	−	101.448i	−0.285714	−	0.494870i
$206$	−57.5368	−	33.2189i	−0.279305	−	0.161257i
$207$	−1.38193	+	2.39358i	−0.00667600	+	0.0115632i
$208$	18.7326	−	10.8153i	0.0900608	−	0.0519966i
$209$			16.9032i			0.0808766i
$210$	−8.75832	+	37.3268i	−0.0417063	+	0.177747i
$211$	185.930			0.881184			0.440592	−	0.897707i	$-0.354769\pi$
$211$	185.930			0.881184			0.440592	+	0.897707i	$0.354769\pi$
$212$	104.079	+	180.271i	0.490940	+	0.850333i
$213$	−26.9431	−	15.5556i	−0.126493	−	0.0730309i
$214$	−131.297	+	227.413i	−0.613537	+	1.06268i
$215$	−15.7304	+	9.08192i	−0.0731644	+	0.0422415i
$216$		−	14.6969i		−	0.0680414i
$217$	−84.5174	−	280.022i	−0.389481	−	1.29043i
$218$	−122.032			−0.559780
$219$	−107.705	−	186.550i	−0.491802	−	0.851826i
$220$	7.12175	+	4.11174i	0.0323716	+	0.0186897i
$221$	−27.1965	+	47.1056i	−0.123061	+	0.213148i
$222$	15.4514	−	8.92090i	0.0696011	−	0.0401842i
$223$			53.6348i			0.240515i	0.992743	+	0.120257i	$0.0383720\pi$
$223$			53.6348i			0.240515i	−0.992743	+	0.120257i	$0.961628\pi$
$224$	37.9089	−	11.4418i	0.169236	−	0.0510795i
$225$	15.0000			0.0666667
$226$	−60.6843	−	105.108i	−0.268515	−	0.465081i
$227$	146.392	+	84.5195i	0.644899	+	0.372333i	0.786499	−	0.617591i	$-0.211891\pi$
$227$	146.392	+	84.5195i	0.644899	+	0.372333i	−0.141600	+	0.989924i	$0.545225\pi$
$228$	15.9217	−	27.5772i	0.0698319	−	0.120952i
$229$	247.698	−	143.009i	1.08165	−	0.624492i	0.150310	−	0.988639i	$-0.451973\pi$
$229$	247.698	−	143.009i	1.08165	−	0.624492i	0.931342	+	0.364147i	$0.118639\pi$
$230$			2.91337i			0.0126668i
$231$	21.7051	+	5.09286i	0.0939615	+	0.0220470i
$232$	−35.5175			−0.153093
$233$	90.9194	+	157.477i	0.390212	+	0.675867i	0.992477	−	0.122429i	$-0.0390684\pi$
$233$	90.9194	+	157.477i	0.390212	+	0.675867i	−0.602265	+	0.798296i	$0.705735\pi$
$234$	−19.8690	−	11.4714i	−0.0849101	−	0.0490229i
$235$	37.9703	−	65.7666i	0.161576	−	0.279858i
$236$	−25.1836	+	14.5398i	−0.106710	+	0.0616092i
$237$			140.186i			0.591503i
$238$	−68.1695	+	72.5806i	−0.286426	+	0.304961i
$239$	−382.489			−1.60037			−0.800185	−	0.599753i	$-0.795266\pi$
$239$	−382.489			−1.60037			−0.800185	+	0.599753i	$0.795266\pi$
$240$	−7.74597	−	13.4164i	−0.0322749	−	0.0559017i
$241$	−180.324	−	104.110i	−0.748230	−	0.431991i	0.0768238	−	0.997045i	$-0.475522\pi$
$241$	−180.324	−	104.110i	−0.748230	−	0.431991i	−0.825054	+	0.565054i	$0.808855\pi$
$242$	−83.1690	+	144.053i	−0.343674	+	0.595260i
$243$	−13.5000	+	7.79423i	−0.0555556	+	0.0320750i
$244$			47.5536i			0.194892i
$245$	60.6179	+	91.2714i	0.247420	+	0.372536i
$246$	128.323			0.521639
$247$	−24.8546	−	43.0494i	−0.100626	−	0.174289i
$248$	102.353	+	59.0937i	0.412715	+	0.238281i
$249$	133.988	−	232.074i	0.538105	−	0.932025i
$250$	13.6931	−	7.90569i	0.0547723	−	0.0316228i
$251$			43.4959i			0.173291i	0.996239	+	0.0866453i	$0.0276147\pi$
$251$			43.4959i			0.173291i	−0.996239	+	0.0866453i	$0.972385\pi$
$252$	−30.6142	−	28.7536i	−0.121485	−	0.114102i
$253$	1.69409			0.00669600
$254$	−93.1545	−	161.348i	−0.366750	−	0.635229i
$255$	33.7373	+	19.4782i	0.132303	+	0.0763852i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	3.68915	−	2.12993i	0.0143547	−	0.00828766i	−0.492806	−	0.870139i	$-0.664029\pi$
$257$	3.68915	−	2.12993i	0.0143547	−	0.00828766i	0.507160	+	0.861852i	$0.330695\pi$
$258$		−	19.8975i		−	0.0771221i
$259$	11.6472	−	49.6390i	0.0449700	−	0.191656i
$260$	−24.1837			−0.0930144
$261$	18.8360	+	32.6249i	0.0721686	+	0.125000i
$262$	−145.460	−	83.9815i	−0.555192	−	0.320540i
$263$	209.187	−	362.323i	0.795388	−	1.37765i	−0.127204	−	0.991877i	$-0.540600\pi$
$263$	209.187	−	362.323i	0.795388	−	1.37765i	0.922592	−	0.385776i	$-0.126066\pi$
$264$	−7.80148	+	4.50419i	−0.0295511	+	0.0170613i
$265$		−	232.728i		−	0.878220i
$266$	−26.2944	−	87.1183i	−0.0988511	−	0.327512i
$267$	117.991			0.441915
$268$	14.9268	+	25.8539i	0.0556969	+	0.0964699i
$269$	−319.086	−	184.224i	−1.18619	−	0.684848i	−0.228753	−	0.973484i	$-0.573465\pi$
$269$	−319.086	−	184.224i	−1.18619	−	0.684848i	−0.957439	+	0.288636i	$0.906798\pi$
$270$	−8.21584	+	14.2302i	−0.0304290	+	0.0527046i
$271$	−191.411	+	110.511i	−0.706312	+	0.407790i	−0.809694	−	0.586852i	$-0.800367\pi$
$271$	−191.411	+	110.511i	−0.706312	+	0.407790i	0.103382	+	0.994642i	$0.467034\pi$
$272$		−	40.2341i		−	0.147919i
$273$	−62.7676	+	18.9448i	−0.229918	+	0.0693947i
$274$	−114.768			−0.418860
$275$	−4.59707	−	7.96235i	−0.0167166	−	0.0289540i
$276$	−2.76386	−	1.59572i	−0.0100140	−	0.00578158i
$277$	198.427	−	343.686i	0.716343	−	1.24074i	−0.246096	−	0.969245i	$-0.579148\pi$
$277$	198.427	−	343.686i	0.716343	−	1.24074i	0.962439	−	0.271497i	$-0.0875187\pi$
$278$	−304.118	+	175.583i	−1.09395	+	0.631593i
$279$		−	125.357i		−	0.449307i
$280$	−43.1013	−	10.1132i	−0.153933	−	0.0361187i
$281$	−114.244			−0.406562			−0.203281	−	0.979120i	$-0.565161\pi$
$281$	−114.244			−0.406562			−0.203281	+	0.979120i	$0.565161\pi$
$282$	41.5944	+	72.0437i	0.147498	+	0.255474i
$283$	391.819	+	226.217i	1.38452	+	0.799353i	0.992691	−	0.120685i	$-0.0385092\pi$
$283$	391.819	+	226.217i	1.38452	+	0.799353i	0.391829	+	0.920038i	$0.371843\pi$
$284$	17.9620	−	31.1112i	0.0632466	−	0.109546i
$285$	−30.8322	+	17.8010i	−0.108183	+	0.0624596i
$286$			14.0626i			0.0491698i
$287$	251.056	−	267.302i	0.874760	−	0.931364i
$288$	16.9706			0.0589256
$289$	−93.9131	−	162.662i	−0.324959	−	0.562845i
$290$	34.3897	+	19.8549i	0.118585	+	0.0684652i
$291$	76.3606	−	132.260i	0.262407	−	0.454503i
$292$	215.409	−	124.367i	0.737703	−	0.425913i
$293$		−	119.134i		−	0.406600i	−0.979116	−	0.203300i	$-0.934833\pi$
$293$		−	119.134i		−	0.406600i	0.979116	−	0.203300i	$-0.0651667\pi$
$294$	−119.789	+	7.51583i	−0.407447	+	0.0255640i
$295$	32.5119			0.110210
$296$	10.3010	+	17.8418i	0.0348006	+	0.0602763i
$297$	8.27472	+	4.77741i	0.0278610	+	0.0160856i
$298$	−106.073	+	183.724i	−0.355949	+	0.616522i
$299$	−4.31454	+	2.49100i	−0.0144299	+	0.00833110i
$300$			17.3205i			0.0577350i
$301$	−41.4471	−	38.9282i	−0.137698	−	0.129329i
$302$	−258.843			−0.857097
$303$	−96.4537	−	167.063i	−0.318329	−	0.551362i
$304$	31.8434	+	18.3848i	0.104748	+	0.0604762i
$305$	26.5833	−	46.0435i	0.0871582	−	0.150962i
$306$	−36.9573	+	21.3373i	−0.120776	+	0.0697298i
$307$			272.643i			0.888087i	0.896005	+	0.444043i	$0.146456\pi$
$307$			272.643i			0.888087i	−0.896005	+	0.444043i	$0.853544\pi$
$308$	−5.88072	+	25.0629i	−0.0190933	+	0.0813731i
$309$	−81.3693			−0.263331
$310$	−66.0688	−	114.435i	−0.213125	−	0.369144i
$311$	65.4476	+	37.7862i	0.210443	+	0.121499i	0.601517	−	0.798860i	$-0.294563\pi$
$311$	65.4476	+	37.7862i	0.210443	+	0.121499i	−0.391074	+	0.920359i	$0.627897\pi$
$312$	13.2460	−	22.9427i	0.0424551	−	0.0735343i
$313$	−55.1057	+	31.8153i	−0.176057	+	0.101646i	−0.585439	−	0.810717i	$-0.699078\pi$
$313$	−55.1057	+	31.8153i	−0.176057	+	0.101646i	0.409382	+	0.912363i	$0.365744\pi$
$314$		−	417.596i		−	1.32992i
$315$	13.5683	+	44.9544i	0.0430740	+	0.142712i
$316$	−161.873			−0.512257
$317$	−7.72605	−	13.3819i	−0.0243724	−	0.0422142i	0.853582	−	0.520959i	$-0.174425\pi$
$317$	−7.72605	−	13.3819i	−0.0243724	−	0.0422142i	−0.877954	+	0.478744i	$0.841092\pi$
$318$	220.786	+	127.471i	0.694294	+	0.400851i
$319$	11.5454	−	19.9972i	0.0361924	−	0.0626872i
$320$	15.4919	−	8.94427i	0.0484123	−	0.0279508i
$321$			321.610i			1.00190i
$322$	−8.73125	+	2.63530i	−0.0271157	+	0.00818416i
$323$	−92.4617			−0.286259
$324$	−9.00000	−	15.5885i	−0.0277778	−	0.0481125i
$325$	23.4158	+	13.5191i	0.0720486	+	0.0415973i
$326$	−83.6692	+	144.919i	−0.256654	+	0.444538i
$327$	−129.434	+	74.7290i	−0.395824	+	0.228529i
$328$			148.175i			0.451753i
$329$	231.446	+	54.3062i	0.703484	+	0.165064i
$330$	10.0717			0.0305202
$331$	186.540	+	323.096i	0.563564	+	0.976121i	0.997182	+	0.0750241i	$0.0239034\pi$
$331$	186.540	+	323.096i	0.563564	+	0.976121i	−0.433618	+	0.901097i	$0.642763\pi$
$332$	267.976	+	154.716i	0.807157	+	0.466012i
$333$	10.9258	−	18.9241i	0.0328103	−	0.0568291i
$334$	−251.301	+	145.088i	−0.752397	+	0.434397i
$335$		−	33.3773i		−	0.0996337i
$336$	33.2018	−	35.3502i	0.0988149	−	0.105209i
$337$	642.919			1.90777			0.953885	−	0.300171i	$-0.0970437\pi$
$337$	642.919			1.90777			0.953885	+	0.300171i	$0.0970437\pi$
$338$	98.8234	+	171.167i	0.292377	+	0.506412i
$339$	−128.731	−	74.3228i	−0.379737	−	0.219241i
$340$	−22.4915	+	38.9565i	−0.0661515	+	0.114578i
$341$	−66.5423	+	38.4182i	−0.195139	+	0.112663i
$342$		−	39.0000i		−	0.114035i
$343$	−218.705	+	264.230i	−0.637623	+	0.770349i
$344$	22.9757			0.0667897
$345$	1.78407	+	3.09009i	0.00517120	+	0.00895679i
$346$	137.825	+	79.5735i	0.398339	+	0.229981i
$347$	−72.0043	+	124.715i	−0.207505	+	0.359409i	−0.950928	−	0.309412i	$-0.899868\pi$
$347$	−72.0043	+	124.715i	−0.207505	+	0.359409i	0.743423	+	0.668822i	$0.233201\pi$
$348$	−37.6720	+	21.7500i	−0.108253	+	0.0624999i
$349$			566.507i			1.62323i	0.584194	+	0.811614i	$0.301411\pi$
$349$			566.507i			1.62323i	−0.584194	+	0.811614i	$0.698589\pi$
$350$	36.0792	+	33.8865i	0.103083	+	0.0968184i
$351$	−28.0990			−0.0800540
$352$	−5.20099	−	9.00838i	−0.0147755	−	0.0255920i
$353$	441.814	+	255.082i	1.25160	+	0.722611i	0.971427	−	0.237339i	$-0.0762753\pi$
$353$	441.814	+	255.082i	1.25160	+	0.722611i	0.280172	+	0.959950i	$0.409609\pi$
$354$	−17.8075	+	30.8435i	−0.0503037	+	0.0871286i
$355$	−34.7833	+	20.0822i	−0.0979813	+	0.0565695i
$356$			136.245i			0.382709i
$357$	−27.8583	+	118.728i	−0.0780344	+	0.332573i
$358$	62.8898			0.175670
$359$	−333.931	−	578.386i	−0.930171	−	1.61110i	−0.783026	−	0.621989i	$-0.786325\pi$
$359$	−333.931	−	578.386i	−0.930171	−	1.61110i	−0.147145	−	0.989115i	$-0.547008\pi$
$360$	−16.4317	−	9.48683i	−0.0456435	−	0.0263523i
$361$	−138.250	+	239.456i	−0.382964	+	0.663313i
$362$	11.3234	−	6.53759i	0.0312802	−	0.0180596i
$363$			203.722i			0.561217i
$364$	−21.8755	−	72.4777i	−0.0600976	−	0.199115i
$365$	−278.092			−0.761897
$366$	29.1205	+	50.4382i	0.0795642	+	0.137809i
$367$	−30.2216	−	17.4485i	−0.0823478	−	0.0475435i	0.458261	−	0.888818i	$-0.348473\pi$
$367$	−30.2216	−	17.4485i	−0.0823478	−	0.0475435i	−0.540608	+	0.841274i	$0.681806\pi$
$368$	1.84258	−	3.19143i	0.00500700	−	0.00867237i
$369$	136.107	−	78.5816i	0.368855	−	0.212958i
$370$		−	23.0337i		−	0.0622531i
$371$	697.478	−	210.516i	1.87999	−	0.567427i
$372$	144.749			0.389111
$373$	204.012	+	353.360i	0.546950	+	0.947345i	0.998481	+	0.0550895i	$0.0175444\pi$
$373$	204.012	+	353.360i	0.546950	+	0.947345i	−0.451532	+	0.892255i	$0.649122\pi$
$374$	22.6527	+	13.0786i	0.0605688	+	0.0349694i
$375$	9.68246	−	16.7705i	0.0258199	−	0.0447214i
$376$	−83.1888	+	48.0291i	−0.221247	+	0.127737i
$377$			67.9057i			0.180121i
$378$	−50.0792	−	11.7505i	−0.132485	−	0.0310860i
$379$	−10.4706			−0.0276268			−0.0138134	−	0.999905i	$-0.504397\pi$
$379$	−10.4706			−0.0276268			−0.0138134	+	0.999905i	$0.504397\pi$
$380$	−20.5548	−	35.6020i	−0.0540916	−	0.0936893i
$381$	−197.610	−	114.090i	−0.518663	−	0.299450i
$382$	−96.7385	+	167.556i	−0.253242	+	0.438628i
$383$	−199.672	+	115.281i	−0.521337	+	0.300994i	−0.737481	−	0.675367i	$-0.763985\pi$
$383$	−199.672	+	115.281i	−0.521337	+	0.300994i	0.216145	+	0.976361i	$0.430652\pi$
$384$			19.5959i			0.0510310i
$385$	19.7046	−	20.9796i	0.0511807	−	0.0544925i
$386$	517.424			1.34048
$387$	−12.1847	−	21.1045i	−0.0314850	−	0.0545336i
$388$	152.721	+	88.1736i	0.393611	+	0.227251i
$389$	−338.107	+	585.619i	−0.869170	+	1.50545i	−0.00632331	+	0.999980i	$0.502013\pi$
$389$	−338.107	+	585.619i	−0.869170	+	1.50545i	−0.862846	+	0.505466i	$0.831321\pi$
$390$	−25.6507	+	14.8095i	−0.0657711	+	0.0379730i
$391$			9.26678i			0.0237002i
$392$	−8.67853	−	138.321i	−0.0221391	−	0.352860i
$393$	−205.712			−0.523440
$394$	−137.833	−	238.734i	−0.349830	−	0.605923i
$395$	156.733	+	90.4898i	0.396792	+	0.229088i
$396$	−5.51648	+	9.55483i	−0.0139305	+	0.0241283i
$397$	−141.641	+	81.7764i	−0.356778	+	0.205986i	−0.667666	−	0.744461i	$-0.732707\pi$
$397$	−141.641	+	81.7764i	−0.356778	+	0.205986i	0.310889	+	0.950446i	$0.399373\pi$
$398$		−	343.421i		−	0.862866i
$399$	−81.2383	−	76.3010i	−0.203605	−	0.191230i
$400$	−20.0000			−0.0500000
$401$	149.624	+	259.156i	0.373127	+	0.646274i	0.990045	−	0.140753i	$-0.0449524\pi$
$401$	149.624	+	259.156i	0.373127	+	0.646274i	−0.616918	+	0.787027i	$0.711619\pi$
$402$	31.6645	+	18.2815i	0.0787674	+	0.0454764i
$403$	112.981	−	195.689i	0.280349	−	0.485579i
$404$	192.907	−	111.375i	0.477494	−	0.275681i
$405$			20.1246i			0.0496904i
$406$	−28.3970	+	121.024i	−0.0699434	+	0.298090i
$407$	−13.3938			−0.0329086
$408$	−24.6382	−	42.6747i	−0.0603878	−	0.104595i
$409$	403.264	+	232.825i	0.985976	+	0.569253i	0.904069	−	0.427387i	$-0.140566\pi$
$409$	403.264	+	232.825i	0.985976	+	0.569253i	0.0819067	+	0.996640i	$0.473899\pi$
$410$	82.8323	−	143.470i	0.202030	−	0.349926i
$411$	−121.729	+	70.2805i	−0.296179	+	0.170999i
$412$		−	93.9572i		−	0.228051i
$413$	29.4088	+	97.4370i	0.0712078	+	0.235925i
$414$	−3.90869			−0.00944129
$415$	−172.978	−	299.606i	−0.416814	−	0.721943i
$416$	26.4920	+	15.2951i	0.0636826	+	0.0367672i
$417$	−215.044	+	372.467i	−0.515693	+	0.893207i
$418$	−20.7021	+	11.9524i	−0.0495266	+	0.0285942i
$419$		−	575.882i		−	1.37442i	−0.726458	−	0.687211i	$-0.758835\pi$
$419$		−	575.882i		−	1.37442i	0.726458	−	0.687211i	$-0.241165\pi$
$420$	−51.9089	+	15.6674i	−0.123593	+	0.0373032i
$421$	571.149			1.35665			0.678324	−	0.734763i	$-0.262706\pi$
$421$	571.149			1.35665			0.678324	+	0.734763i	$0.262706\pi$
$422$	131.472	+	227.717i	0.311546	+	0.539613i
$423$	88.2351	+	50.9426i	0.208594	+	0.120432i
$424$	−147.190	+	254.941i	−0.347147	+	0.601276i
$425$	43.5546	−	25.1463i	0.102482	−	0.0591677i
$426$		−	43.9978i		−	0.103281i
$427$	162.037	+	38.0201i	0.379477	+	0.0890400i
$428$	−371.363			−0.867672
$429$	8.61152	+	14.9156i	0.0200735	+	0.0347683i
$430$	−22.2461	−	12.8438i	−0.0517351	−	0.0298693i
$431$	13.5697	−	23.5034i	0.0314842	−	0.0545322i	−0.849854	−	0.527018i	$-0.823310\pi$
$431$	13.5697	−	23.5034i	0.0314842	−	0.0545322i	0.881338	+	0.472486i	$0.156643\pi$
$432$	18.0000	−	10.3923i	0.0416667	−	0.0240563i
$433$			363.408i			0.839279i	0.907691	+	0.419640i	$0.137844\pi$
$433$			363.408i			0.839279i	−0.907691	+	0.419640i	$0.862156\pi$
$434$	283.193	−	301.518i	0.652518	−	0.694742i
$435$	48.6344			0.111803
$436$	−86.2897	−	149.458i	−0.197912	−	0.342794i
$437$	−7.33422	−	4.23441i	−0.0167831	−	0.00968974i
$438$	152.317	−	263.822i	0.347757	−	0.602332i
$439$	−403.057	+	232.705i	−0.918124	+	0.530079i	−0.883036	−	0.469305i	$-0.844505\pi$
$439$	−403.057	+	232.705i	−0.918124	+	0.530079i	−0.0350882	+	0.999384i	$0.511171\pi$
$440$			11.6298i			0.0264313i
$441$	−122.453	+	81.3275i	−0.277672	+	0.184416i
$442$	−76.9232			−0.174034
$443$	−243.968	−	422.565i	−0.550718	−	0.953871i	−0.998223	−	0.0595896i	$-0.981021\pi$
$443$	−243.968	−	422.565i	−0.550718	−	0.953871i	0.447505	−	0.894281i	$-0.352313\pi$
$444$	21.8516	+	12.6161i	0.0492154	+	0.0284145i
$445$	76.1630	−	131.918i	0.171153	−	0.296445i
$446$	−65.6889	+	37.9255i	−0.147285	+	0.0850348i
$447$			259.824i			0.581263i
$448$	40.8189	+	38.3381i	0.0911137	+	0.0855762i
$449$	−285.837			−0.636609			−0.318304	−	0.947989i	$-0.603113\pi$
$449$	−285.837			−0.636609			−0.318304	+	0.947989i	$0.603113\pi$
$450$	10.6066	+	18.3712i	0.0235702	+	0.0408248i
$451$	−83.4260	−	48.1660i	−0.184980	−	0.106798i
$452$	85.8206	−	148.646i	0.189869	−	0.328862i
$453$	−274.545	+	158.509i	−0.606059	+	0.349908i
$454$			239.057i			0.526558i
$455$	−19.3354	+	82.4050i	−0.0424954	+	0.181110i
$456$	45.0333			0.0987572
$457$	−211.624	−	366.543i	−0.463071	−	0.802063i	0.536041	−	0.844192i	$-0.319919\pi$
$457$	−211.624	−	366.543i	−0.463071	−	0.802063i	−0.999112	+	0.0421292i	$0.986586\pi$
$458$	350.298	+	202.245i	0.764843	+	0.441583i
$459$	−26.1328	+	45.2633i	−0.0569342	+	0.0986129i
$460$	−3.56813	+	2.06006i	−0.00775681	+	0.00447839i
$461$		−	471.748i		−	1.02331i	−0.859190	−	0.511657i	$-0.829032\pi$
$461$		−	471.748i		−	1.02331i	0.859190	−	0.511657i	$-0.170968\pi$
$462$	9.11038	+	30.1844i	0.0197194	+	0.0653342i
$463$	−194.019			−0.419046			−0.209523	−	0.977804i	$-0.567191\pi$
$463$	−194.019			−0.419046			−0.209523	+	0.977804i	$0.567191\pi$
$464$	−25.1147	−	43.4999i	−0.0541265	−	0.0937498i
$465$	−140.153	−	80.9174i	−0.301404	−	0.174016i
$466$	−128.579	+	222.706i	−0.275921	+	0.477910i
$467$	−9.80955	+	5.66354i	−0.0210055	+	0.0121275i	−0.510466	−	0.859898i	$-0.670527\pi$
$467$	−9.80955	+	5.66354i	−0.0210055	+	0.0121275i	0.489461	+	0.872025i	$0.337194\pi$
$468$		−	32.4459i		−	0.0693288i
$469$	100.030	−	30.1916i	0.213285	−	0.0643744i
$470$	107.396			0.228503
$471$	−255.724	−	442.928i	−0.542939	−	0.940398i
$472$	−35.6150	−	20.5624i	−0.0754556	−	0.0435643i
$473$	−7.46851	+	12.9358i	−0.0157897	+	0.0273485i
$474$	−171.692	+	99.1266i	−0.362220	+	0.209128i
$475$			45.9619i			0.0967619i
$476$	−137.096	−	32.1680i	−0.288016	−	0.0675798i
$477$	312.238			0.654587
$478$	−270.460	−	468.451i	−0.565816	−	0.980023i
$479$	−547.932	−	316.349i	−1.14391	−	0.660435i	−0.196512	−	0.980501i	$-0.562962\pi$
$479$	−547.932	−	316.349i	−1.14391	−	0.660435i	−0.947395	+	0.320066i	$0.896295\pi$
$480$	10.9545	−	18.9737i	0.0228218	−	0.0395285i
$481$	34.1116	−	19.6943i	0.0709181	−	0.0409446i
$482$		−	294.467i		−	0.610927i
$483$	−7.64710	+	8.14193i	−0.0158325	+	0.0168570i
$484$	−235.237			−0.486028
$485$	−98.5811	−	170.747i	−0.203260	−	0.352056i
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	31.5102	−	54.5773i	0.0647027	−	0.112068i	−0.831859	−	0.554986i	$-0.812723\pi$
$487$	31.5102	−	54.5773i	0.0647027	−	0.112068i	0.896562	+	0.442918i	$0.146057\pi$
$488$	−58.2410	+	33.6254i	−0.119346	+	0.0689046i
$489$			204.947i			0.419114i
$490$	−68.9208	+	138.780i	−0.140655	+	0.283225i
$491$	261.092			0.531756			0.265878	−	0.964007i	$-0.414338\pi$
$491$	261.092			0.531756			0.265878	+	0.964007i	$0.414338\pi$
$492$	90.7382	+	157.163i	0.184427	+	0.319437i
$493$	109.386	+	63.1541i	0.221879	+	0.128102i
$494$	35.1497	−	60.8811i	0.0711532	−	0.123241i
$495$	10.6826	−	6.16761i	0.0215811	−	0.0124598i
$496$			167.142i			0.336980i
$497$	−91.6490	−	86.0789i	−0.184404	−	0.173197i
$498$	378.976			0.760995
$499$	−219.481	−	380.153i	−0.439843	−	0.761830i	0.557834	−	0.829952i	$-0.311632\pi$
$499$	−219.481	−	380.153i	−0.439843	−	0.761830i	−0.997677	+	0.0681226i	$0.978299\pi$
$500$	19.3649	+	11.1803i	0.0387298	+	0.0223607i
$501$	−177.696	+	307.779i	−0.354683	+	0.614329i
$502$	−53.2714	+	30.7563i	−0.106118	+	0.0612675i
$503$		−	702.372i		−	1.39637i	−0.715919	−	0.698183i	$-0.753992\pi$
$503$		−	702.372i		−	1.39637i	0.715919	−	0.698183i	$-0.246008\pi$
$504$	13.5683	−	57.8265i	0.0269213	−	0.114735i
$505$	−249.042			−0.493153
$506$	1.19790	+	2.07483i	0.00236739	+	0.00410045i
$507$	209.636	+	121.033i	0.413483	+	0.238725i
$508$	131.740	−	228.181i	0.259331	−	0.449175i
$509$	−103.188	+	59.5758i	−0.202727	+	0.117045i	−0.597927	−	0.801551i	$-0.704009\pi$
$509$	−103.188	+	59.5758i	−0.202727	+	0.117045i	0.395200	+	0.918595i	$0.370675\pi$
$510$			55.0928i			0.108025i
$511$	−251.550	−	833.432i	−0.492270	−	1.63098i
$512$	−22.6274			−0.0441942
$513$	−23.8825	−	41.3657i	−0.0465546	−	0.0806350i
$514$	5.21724	+	3.01217i	0.0101503	+	0.00586026i
$515$	−52.5237	+	90.9736i	−0.101988	+	0.176648i
$516$	24.3694	−	14.0697i	0.0472274	−	0.0272668i
$517$		−	62.4497i		−	0.120792i
$518$	69.0310	−	20.8352i	0.133264	−	0.0402224i
$519$	194.914			0.375558
$520$	−17.1005	−	29.6189i	−0.0328855	−	0.0569594i
$521$	−391.422	−	225.988i	−0.751291	−	0.433758i	0.0748694	−	0.997193i	$-0.476146\pi$
$521$	−391.422	−	225.988i	−0.751291	−	0.433758i	−0.826160	+	0.563435i	$0.809479\pi$
$522$	−26.6381	+	46.1386i	−0.0510309	+	0.0883882i
$523$	−775.007	+	447.451i	−1.48185	+	0.855546i	−0.999788	−	0.0205911i	$-0.993445\pi$
$523$	−775.007	+	447.451i	−1.48185	+	0.855546i	−0.482062	+	0.876137i	$0.660112\pi$
$524$		−	237.536i		−	0.453312i
$525$	59.0189	+	13.8481i	0.112417	+	0.0263774i
$526$	591.670			1.12485
$527$	−210.150	−	363.991i	−0.398767	−	0.690685i
$528$	−11.0330	−	6.36988i	−0.0208958	−	0.0120642i
$529$	264.076	−	457.392i	0.499198	−	0.864636i
$530$	285.033	−	164.564i	0.537798	−	0.310498i
$531$			43.6193i			0.0821457i
$532$	88.1048	−	93.8059i	0.165610	−	0.176327i
$533$	283.294			0.531509
$534$	83.4324	+	144.509i	0.156240	+	0.270616i
$535$	359.571	+	207.598i	0.672096	+	0.388035i
$536$	−21.1096	+	36.5630i	−0.0393837	+	0.0682145i
$537$	66.7047	−	38.5120i	0.124217	−	0.0717169i
$538$		−	521.065i		−	0.968522i
$539$	80.6990	+	40.0766i	0.149720	+	0.0743537i
$540$	−23.2379			−0.0430331
$541$	158.262	+	274.119i	0.292537	+	0.506689i	0.974409	−	0.224783i	$-0.0721672\pi$
$541$	158.262	+	274.119i	0.292537	+	0.506689i	−0.681872	+	0.731472i	$0.738834\pi$
$542$	−270.695	−	156.286i	−0.499438	−	0.288351i
$543$	8.00688	−	13.8683i	0.0147456	−	0.0255402i
$544$	49.2765	−	28.4498i	0.0905817	−	0.0522974i
$545$			192.950i			0.354036i
$546$	−67.5859	−	63.4783i	−0.123784	−	0.116261i
$547$	796.193			1.45556			0.727782	−	0.685809i	$-0.240551\pi$
$547$	796.193			1.45556			0.727782	+	0.685809i	$0.240551\pi$
$548$	−81.1530	−	140.561i	−0.148089	−	0.256498i
$549$	61.7739	+	35.6652i	0.112521	+	0.0649639i
$550$	6.50124	−	11.2605i	0.0118204	−	0.0204736i
$551$	−99.9670	+	57.7160i	−0.181428	+	0.104748i
$552$		−	4.51337i		−	0.00817639i
$553$	−129.421	+	551.576i	−0.234034	+	0.997424i
$554$	561.236			1.01306
$555$	−14.1052	−	24.4309i	−0.0254147	−	0.0440196i
$556$	−430.088	−	248.311i	−0.773540	−	0.446603i
$557$	−155.976	+	270.159i	−0.280029	+	0.485025i	−0.971392	−	0.237484i	$-0.923677\pi$
$557$	−155.976	+	270.159i	−0.280029	+	0.485025i	0.691363	+	0.722508i	$0.257011\pi$
$558$	153.530	−	88.6406i	0.275143	−	0.158854i
$559$		−	43.9270i		−	0.0785813i
$560$	−18.0911	−	59.9392i	−0.0323055	−	0.107034i
$561$	32.0358			0.0571048
$562$	−80.7827	−	139.920i	−0.143741	−	0.248968i
$563$	534.350	+	308.507i	0.949112	+	0.547970i	0.892805	−	0.450443i	$-0.148734\pi$
$563$	534.350	+	308.507i	0.949112	+	0.547970i	0.0563071	+	0.998413i	$0.482067\pi$
$564$	−58.8234	+	101.885i	−0.104297	+	0.180647i
$565$	−166.191	+	95.9504i	−0.294143	+	0.169824i
$566$			639.838i			1.13046i
$567$	−60.3127	+	18.2038i	−0.106372	+	0.0321055i
$568$	50.8043			0.0894442
$569$	391.495	+	678.089i	0.688041	+	1.19172i	0.972471	+	0.233025i	$0.0748623\pi$
$569$	391.495	+	678.089i	0.688041	+	1.19172i	−0.284430	+	0.958697i	$0.591804\pi$
$570$	−43.6033	−	25.1744i	−0.0764970	−	0.0441656i
$571$	−1.06600	+	1.84636i	−0.00186689	+	0.00323355i	−0.866957	−	0.498382i	$-0.833928\pi$
$571$	−1.06600	+	1.84636i	−0.00186689	+	0.00323355i	0.865090	+	0.501616i	$0.167261\pi$
$572$	−17.2230	+	9.94373i	−0.0301102	+	0.0173841i
$573$			236.960i			0.413543i
$574$	504.900	+	118.469i	0.879616	+	0.206392i
$575$	4.60644			0.00801120
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−828.056	−	478.079i	−1.43511	−	0.828559i	−0.437602	−	0.899169i	$-0.644172\pi$
$577$	−828.056	−	478.079i	−1.43511	−	0.828559i	−0.997504	+	0.0706096i	$0.977506\pi$
$578$	132.813	−	230.039i	0.229781	−	0.397992i
$579$	548.811	−	316.856i	0.947860	−	0.547247i
$580$			56.1581i			0.0968244i
$581$	741.441	−	789.419i	1.27615	−	1.35872i
$582$	215.980			0.371100
$583$	−95.6919	−	165.743i	−0.164137	−	0.284294i
$584$	304.635	+	175.881i	0.521635	+	0.301166i
$585$	−18.1378	+	31.4156i	−0.0310048	+	0.0537019i
$586$	145.909	−	84.2403i	0.248991	−	0.143755i
$587$			628.961i			1.07148i	0.844382	+	0.535742i	$0.179968\pi$
$587$			628.961i			1.07148i	−0.844382	+	0.535742i	$0.820032\pi$
$588$	−93.9089	−	141.397i	−0.159709	−	0.240471i
$589$	384.109			0.652138
$590$	22.9894	+	39.8188i	0.0389651	+	0.0674895i
$591$	−292.388	−	168.810i	−0.494734	−	0.285635i
$592$	−14.5678	+	25.2321i	−0.0246077	+	0.0426218i
$593$	−417.691	+	241.154i	−0.704370	+	0.406668i	−0.808973	−	0.587846i	$-0.799976\pi$
$593$	−417.691	+	241.154i	−0.704370	+	0.406668i	0.104603	+	0.994514i	$0.466643\pi$
$594$			13.5126i			0.0227484i
$595$	114.760	+	107.785i	0.192874	+	0.181152i
$596$	−300.019			−0.503388
$597$	−210.301	−	364.253i	−0.352263	−	0.610138i
$598$	−6.10168	−	3.52280i	−0.0102035	−	0.00589098i
$599$	−181.233	+	313.904i	−0.302559	+	0.524047i	−0.976715	−	0.214542i	$-0.931174\pi$
$599$	−181.233	+	313.904i	−0.302559	+	0.524047i	0.674156	+	0.738589i	$0.264508\pi$
$600$	−21.2132	+	12.2474i	−0.0353553	+	0.0204124i
$601$		−	545.450i		−	0.907570i	−0.891111	−	0.453785i	$-0.850073\pi$
$601$		−	545.450i		−	0.907570i	0.891111	−	0.453785i	$-0.149927\pi$
$602$	18.3695	−	78.2886i	0.0305142	−	0.130047i
$603$	44.7803			0.0742626
$604$	−183.030	−	317.017i	−0.303030	−	0.524863i
$605$	227.768	+	131.502i	0.376475	+	0.217358i
$606$	136.406	−	236.262i	0.225093	−	0.389872i
$607$	−554.426	+	320.098i	−0.913388	+	0.527345i	−0.881520	−	0.472147i	$-0.843479\pi$
$607$	−554.426	+	320.098i	−0.913388	+	0.527345i	−0.0318683	+	0.999492i	$0.510146\pi$
$608$			52.0000i			0.0855263i
$609$	43.9925	+	145.755i	0.0722372	+	0.239336i
$610$	75.1888			0.123260
$611$	91.8265	+	159.048i	0.150289	+	0.260308i
$612$	−52.2656	−	30.1755i	−0.0854013	−	0.0493064i
$613$	198.272	−	343.417i	0.323445	−	0.560223i	−0.657751	−	0.753235i	$-0.728492\pi$
$613$	198.272	−	343.417i	0.323445	−	0.560223i	0.981196	+	0.193012i	$0.0618256\pi$
$614$	−333.918	+	192.787i	−0.543840	+	0.313986i
$615$		−	202.897i		−	0.329914i
$616$	−34.8540	+	10.5198i	−0.0565811	+	0.0170775i
$617$	−421.502			−0.683148			−0.341574	−	0.939855i	$-0.610960\pi$
$617$	−421.502			−0.683148			−0.341574	+	0.939855i	$0.610960\pi$
$618$	−57.5368	−	99.6566i	−0.0931016	−	0.161257i
$619$	629.261	+	363.304i	1.01658	+	0.586921i	0.913111	−	0.407712i	$-0.133673\pi$
$619$	629.261	+	363.304i	1.01658	+	0.586921i	0.103467	+	0.994633i	$0.467006\pi$
$620$	93.4354	−	161.835i	0.150702	−	0.261024i
$621$	−4.14579	+	2.39358i	−0.00667600	+	0.00385439i
$622$			106.876i			0.171826i
$623$	464.248	+	108.930i	0.745181	+	0.174848i
$624$	37.4653			0.0600405
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−77.9313	−	44.9936i	−0.124491	−	0.0718748i
$627$	−14.6386	+	25.3548i	−0.0233471	+	0.0404383i
$628$	511.449	−	295.285i	0.814409	−	0.470199i
$629$		−	73.2650i		−	0.116479i
$630$	−45.4635	+	48.4053i	−0.0721642	+	0.0768338i
$631$	−537.550			−0.851901			−0.425950	−	0.904746i	$-0.640060\pi$
$631$	−537.550			−0.851901			−0.425950	+	0.904746i	$0.640060\pi$
$632$	−114.462	−	198.253i	−0.181110	−	0.313692i
$633$	278.895	+	161.020i	0.440592	+	0.254376i
$634$	10.9263	−	18.9249i	0.0172339	−	0.0298500i
$635$	−255.114	+	147.290i	−0.401754	+	0.231953i
$636$			360.541i			0.566889i
$637$	−264.455	+	16.5924i	−0.415157	+	0.0260477i
$638$	32.6553			0.0511838
$639$	−26.9431	−	46.6668i	−0.0421644	−	0.0730309i
$640$	21.9089	+	12.6491i	0.0342327	+	0.0197642i
$641$	−488.924	+	846.841i	−0.762752	+	1.32112i	0.178675	+	0.983908i	$0.442819\pi$
$641$	−488.924	+	846.841i	−0.762752	+	1.32112i	−0.941427	+	0.337217i	$0.890514\pi$
$642$	−393.890	+	227.413i	−0.613537	+	0.354225i
$643$		−	276.520i		−	0.430047i	−0.976609	−	0.215023i	$-0.931017\pi$
$643$		−	276.520i		−	0.430047i	0.976609	−	0.215023i	$-0.0689828\pi$
$644$	−9.40150	−	8.83011i	−0.0145986	−	0.0137114i
$645$	−31.4607			−0.0487763
$646$	−65.3803	−	113.242i	−0.101208	−	0.175297i
$647$	−210.206	−	121.362i	−0.324893	−	0.187577i	0.328679	−	0.944442i	$-0.393397\pi$
$647$	−210.206	−	121.362i	−0.324893	−	0.187577i	−0.653571	+	0.756865i	$0.726730\pi$
$648$	12.7279	−	22.0454i	0.0196419	−	0.0340207i
$649$	23.1542	−	13.3681i	0.0356767	−	0.0205980i
$650$			38.2378i			0.0588275i
$651$	115.730	−	493.228i	0.177773	−	0.757646i
$652$	−236.652			−0.362964
$653$	26.6109	+	46.0914i	0.0407518	+	0.0705841i	0.885682	−	0.464293i	$-0.153691\pi$
$653$	26.6109	+	46.0914i	0.0407518	+	0.0705841i	−0.844930	+	0.534877i	$0.820358\pi$
$654$	−183.048	−	105.683i	−0.279890	−	0.161595i
$655$	−132.786	+	229.993i	−0.202727	+	0.351134i
$656$	−181.476	+	104.775i	−0.276641	+	0.159719i
$657$		−	373.100i		−	0.567884i
$658$	97.1459	+	321.863i	0.147638	+	0.489153i
$659$	640.732			0.972279			0.486139	−	0.873881i	$-0.338405\pi$
$659$	640.732			0.972279			0.486139	+	0.873881i	$0.338405\pi$
$660$	7.12175	+	12.3352i	0.0107905	+	0.0186897i
$661$	10.4335	+	6.02380i	0.0157845	+	0.00911317i	0.507871	−	0.861433i	$-0.330432\pi$
$661$	10.4335	+	6.02380i	0.0157845	+	0.00911317i	−0.492087	+	0.870546i	$0.663766\pi$
$662$	−263.807	+	456.927i	−0.398500	+	0.690222i
$663$	−81.5894	+	47.1056i	−0.123061	+	0.0710492i
$664$			437.603i			0.659041i
$665$	−137.746	+	41.5751i	−0.207137	+	0.0625189i
$666$	30.9029			0.0464007
$667$	5.78446	+	10.0190i	0.00867236	+	0.0150210i
$668$	−355.393	−	205.186i	−0.532025	−	0.307165i
$669$	−46.4491	+	80.4522i	−0.0694306	+	0.120257i
$670$	40.8787	−	23.6013i	0.0610129	−	0.0352258i
$671$		−	43.7214i		−	0.0651586i
$672$	66.7723	+	15.6674i	0.0993635	+	0.0233145i
$673$	−952.008			−1.41457			−0.707286	−	0.706927i	$-0.750081\pi$
$673$	−952.008			−1.41457			−0.707286	+	0.706927i	$0.750081\pi$
$674$	454.612	+	787.412i	0.674499	+	1.16827i
$675$	22.5000	+	12.9904i	0.0333333	+	0.0192450i
$676$	−139.757	+	242.067i	−0.206742	+	0.358087i
$677$	18.2965	−	10.5635i	0.0270259	−	0.0156034i	−0.486426	−	0.873722i	$-0.661700\pi$
$677$	18.2965	−	10.5635i	0.0270259	−	0.0156034i	0.513452	+	0.858118i	$0.328366\pi$
$678$		−	210.217i		−	0.310054i
$679$	422.551	−	449.894i	0.622314	−	0.662583i
$680$	−63.6156			−0.0935524
$681$	146.392	+	253.559i	0.214966	+	0.372333i
$682$	−94.1050	−	54.3316i	−0.137984	−	0.0796651i
$683$	196.448	−	340.259i	0.287626	−	0.498182i	−0.685617	−	0.727963i	$-0.740467\pi$
$683$	196.448	−	340.259i	0.287626	−	0.498182i	0.973243	+	0.229780i	$0.0738007\pi$
$684$	47.7650	−	27.5772i	0.0698319	−	0.0403175i
$685$			181.464i			0.264910i
$686$	−478.261	−	81.0188i	−0.697174	−	0.118103i
$687$	495.397			0.721101
$688$	16.2462	+	28.1393i	0.0236137	+	0.0409002i
$689$	487.420	+	281.412i	0.707431	+	0.408436i
$690$	−2.52305	+	4.37005i	−0.00365659	+	0.00633341i
$691$	230.954	−	133.342i	0.334232	−	0.192969i	−0.323486	−	0.946233i	$-0.604855\pi$
$691$	230.954	−	133.342i	0.334232	−	0.192969i	0.657718	+	0.753264i	$0.271522\pi$
$692$			225.068i			0.325242i
$693$	28.1471	+	26.4365i	0.0406163	+	0.0381479i
$694$	−203.659			−0.293457
$695$	277.621	+	480.853i	0.399454	+	0.691875i
$696$	−53.2763	−	30.7591i	−0.0765464	−	0.0441941i
$697$	263.471	−	456.346i	0.378008	−	0.654729i
$698$	−693.826	+	400.581i	−0.994020	+	0.573898i
$699$			314.954i			0.450578i
$700$	−15.9904	+	68.1491i	−0.0228435	+	0.0973559i
$701$	207.973			0.296680			0.148340	−	0.988936i	$-0.452607\pi$
$701$	207.973			0.296680			0.148340	+	0.988936i	$0.452607\pi$
$702$	−19.8690	−	34.4141i	−0.0283034	−	0.0490229i
$703$	57.9858	+	33.4781i	0.0824834	+	0.0476218i
$704$	7.35531	−	12.7398i	0.0104479	−	0.0180963i
$705$	113.911	−	65.7666i	0.161576	−	0.0932859i
$706$			721.480i			1.02193i
$707$	−225.273	−	746.371i	−0.318632	−	1.05569i
$708$	−50.3673			−0.0711402
$709$	447.714	+	775.463i	0.631472	+	1.09374i	0.987251	+	0.159172i	$0.0508823\pi$
$709$	447.714	+	775.463i	0.631472	+	1.09374i	−0.355779	+	0.934570i	$0.615784\pi$
$710$	−49.1911	−	28.4005i	−0.0692832	−	0.0400007i
$711$	−121.405	+	210.279i	−0.170752	+	0.295751i
$712$	−166.865	+	96.3395i	−0.234361	+	0.135308i
$713$		−	38.4965i		−	0.0539923i
$714$	−165.111	+	49.8344i	−0.231248	+	0.0697961i
$715$	22.2349			0.0310977
$716$	44.4698	+	77.0240i	0.0621087	+	0.107575i
$717$	−573.733	−	331.245i	−0.800185	−	0.461987i
$718$	472.250	−	817.962i	0.657730	−	1.13922i
$719$	−327.729	+	189.215i	−0.455813	+	0.263163i	−0.710282	−	0.703917i	$-0.751433\pi$
$719$	−327.729	+	189.215i	−0.455813	+	0.263163i	0.254469	+	0.967081i	$0.418099\pi$
$720$		−	26.8328i		−	0.0372678i
$721$	−320.155	−	75.1207i	−0.444043	−	0.104190i
$722$	−391.030			−0.541593
$723$	−180.324	−	312.329i	−0.249410	−	0.431991i
$724$	16.0138	+	9.24555i	0.0221185	+	0.0127701i
$725$	31.3934	−	54.3749i	0.0433012	−	0.0749998i
$726$	−249.507	+	144.053i	−0.343674	+	0.198420i
$727$			456.052i			0.627307i	0.949538	+	0.313653i	$0.101553\pi$
$727$			456.052i			0.627307i	−0.949538	+	0.313653i	$0.898447\pi$
$728$	73.2984	−	78.0414i	0.100685	−	0.107200i
$729$	−27.0000			−0.0370370
$730$	−196.641	−	340.592i	−0.269371	−	0.466565i
$731$	−70.7599	−	40.8533i	−0.0967988	−	0.0558868i
$732$	−41.1826	+	71.3303i	−0.0562604	+	0.0974458i
$733$	658.892	−	380.412i	0.898898	−	0.518979i	0.0220553	−	0.999757i	$-0.492979\pi$
$733$	658.892	−	380.412i	0.898898	−	0.518979i	0.876842	+	0.480778i	$0.159646\pi$
$734$		−	49.3517i		−	0.0672367i
$735$	11.8836	+	189.404i	0.0161681	+	0.257692i
$736$	5.21159			0.00708096
$737$	−13.7239	−	23.7705i	−0.0186213	−	0.0322530i
$738$	192.485	+	111.131i	0.260820	+	0.150584i
$739$	14.0833	−	24.3930i	0.0190573	−	0.0330081i	−0.856340	−	0.516413i	$-0.827267\pi$
$739$	14.0833	−	24.3930i	0.0190573	−	0.0330081i	0.875397	+	0.483405i	$0.160600\pi$
$740$	28.2104	−	16.2873i	0.0381221	−	0.0220098i
$741$		−	86.0988i		−	0.116193i
$742$	751.019	+	705.376i	1.01216	+	0.950641i
$743$	−1077.90			−1.45073			−0.725367	−	0.688362i	$-0.758330\pi$
$743$	−1077.90			−1.45073			−0.725367	+	0.688362i	$0.758330\pi$
$744$	102.353	+	177.281i	0.137572	+	0.238281i
$745$	290.492	+	167.716i	0.389923	+	0.225122i
$746$	−288.517	+	499.726i	−0.386752	+	0.669874i
$747$	401.964	−	232.074i	0.538105	−	0.310675i
$748$			36.9917i			0.0494542i
$749$	−296.913	+	1265.41i	−0.396412	+	1.68946i
$750$	27.3861			0.0365148
$751$	−90.0583	−	155.986i	−0.119918	−	0.207704i	0.799817	−	0.600244i	$-0.204930\pi$
$751$	−90.0583	−	155.986i	−0.119918	−	0.207704i	−0.919735	+	0.392540i	$0.871596\pi$
$752$	−117.647	−	67.9234i	−0.156445	−	0.0903237i
$753$	−37.6686	+	65.2439i	−0.0500247	+	0.0866453i
$754$	−83.1671	+	48.0166i	−0.110301	+	0.0636824i
$755$			409.267i			0.542076i
$756$	−21.0200	−	69.6431i	−0.0278042	−	0.0921205i
$757$	219.675			0.290192			0.145096	−	0.989418i	$-0.453651\pi$
$757$	219.675			0.290192			0.145096	+	0.989418i	$0.453651\pi$
$758$	−7.40380	−	12.8238i	−0.00976755	−	0.0169179i
$759$	2.54113	+	1.46712i	0.00334800	+	0.00193297i
$760$	29.0689	−	50.3488i	0.0382485	−	0.0662484i
$761$	1113.97	−	643.150i	1.46382	−	0.845138i	0.464637	−	0.885501i	$-0.346185\pi$
$761$	1113.97	−	643.150i	1.46382	−	0.845138i	0.999185	+	0.0403636i	$0.0128516\pi$
$762$		−	322.697i		−	0.423486i
$763$	−578.262	+	174.533i	−0.757880	+	0.228746i
$764$	−273.618			−0.358138
$765$	33.7373	+	58.4347i	0.0441010	+	0.0763852i
$766$	−282.379	−	163.031i	−0.368641	−	0.212835i
$767$	−39.3130	+	68.0921i	−0.0512555	+	0.0887772i
$768$	−24.0000	+	13.8564i	−0.0312500	+	0.0180422i
$769$		−	365.543i		−	0.475348i	−0.971345	−	0.237674i	$-0.923615\pi$
$769$		−	365.543i		−	0.475348i	0.971345	−	0.237674i	$-0.0763850\pi$
$770$	39.6279	+	9.29824i	0.0514648	+	0.0120756i
$771$	7.37829			0.00956977
$772$	365.874	+	633.712i	0.473930	+	0.820871i
$773$	267.183	+	154.258i	0.345645	+	0.199558i	0.662765	−	0.748827i	$-0.269383\pi$
$773$	267.183	+	154.258i	0.345645	+	0.199558i	−0.317121	+	0.948385i	$0.602716\pi$
$774$	17.2317	−	29.8462i	0.0222632	−	0.0385610i
$775$	−180.937	+	104.464i	−0.233467	+	0.134792i
$776$			249.393i			0.321382i
$777$	60.4595	−	64.3717i	0.0778115	−	0.0828465i
$778$	−956.311			−1.22919
$779$	240.784	+	417.050i	0.309094	+	0.535366i
$780$	−36.2756	−	20.9437i	−0.0465072	−	0.0268509i
$781$	−16.5145	+	28.6040i	−0.0211454	+	0.0366249i
$782$	−11.3494	+	6.55261i	−0.0145134	+	0.00837929i
$783$			65.2499i			0.0833332i
$784$	163.271	−	108.437i	0.208254	−	0.138312i
$785$	−660.277			−0.841118
$786$	−145.460	−	251.945i	−0.185064	−	0.320540i
$787$	1232.85	+	711.787i	1.56652	+	0.904431i	0.996570	+	0.0827517i	$0.0263708\pi$
$787$	1232.85	+	711.787i	1.56652	+	0.904431i	0.569950	+	0.821679i	$0.306963\pi$
$788$	194.925	−	337.620i	0.247367	−	0.428452i
$789$	627.561	−	362.323i	0.795388	−	0.459218i
$790$			255.944i			0.323980i
$791$	−437.888	−	411.275i	−0.553588	−	0.519944i
$792$	−15.6030			−0.0197007
$793$	64.2882	+	111.350i	0.0810696	+	0.140417i
$794$	−200.310	−	115.649i	−0.252280	−	0.145654i
$795$	201.549	−	349.093i	0.253520	−	0.439110i
$796$	420.603	−	242.835i	0.528395	−	0.305069i
$797$		−	475.713i		−	0.596880i	−0.954428	−	0.298440i	$-0.903534\pi$
$797$		−	475.713i		−	0.596880i	0.954428	−	0.298440i	$-0.0964663\pi$
$798$	36.0051	−	153.449i	0.0451191	−	0.192292i
$799$	341.604			0.427540
$800$	−14.1421	−	24.4949i	−0.0176777	−	0.0306186i
$801$	176.987	+	102.183i	0.220957	+	0.127570i
$802$	−211.600	+	366.502i	−0.263840	+	0.456985i
$803$	−198.050	+	114.344i	−0.246638	+	0.142397i
$804$			51.7079i			0.0643133i
$805$	4.16678	+	13.8053i	0.00517612	+	0.0171495i
$806$	319.558			0.396474
$807$	−319.086	−	552.672i	−0.395397	−	0.684848i
$808$	272.812	+	157.508i	0.337639	+	0.194936i
$809$	−363.710	+	629.965i	−0.449580	+	0.778696i	−0.998359	−	0.0572722i	$-0.981760\pi$
$809$	−363.710	+	629.965i	−0.449580	+	0.778696i	0.548779	+	0.835968i	$0.315093\pi$
$810$	−24.6475	+	14.2302i	−0.0304290	+	0.0175682i
$811$		−	673.804i		−	0.830831i	−0.909632	−	0.415415i	$-0.863636\pi$
$811$		−	673.804i		−	0.830831i	0.909632	−	0.415415i	$-0.136364\pi$
$812$	−168.304	+	50.7981i	−0.207271	+	0.0625593i
$813$	−382.821			−0.470875
$814$	−9.47085	−	16.4040i	−0.0116349	−	0.0201523i
$815$	229.138	+	132.293i	0.281150	+	0.162322i
$816$	34.8437	−	60.3511i	0.0427006	−	0.0739597i
$817$	64.6668	−	37.3354i	0.0791516	−	0.0456982i
$818$			658.527i			0.805046i
$819$	−110.558	−	25.9412i	−0.134991	−	0.0316742i
$820$	234.285			0.285714
$821$	445.465	+	771.568i	0.542588	+	0.939790i	0.998754	+	0.0498958i	$0.0158889\pi$
$821$	445.465	+	771.568i	0.542588	+	0.939790i	−0.456166	+	0.889895i	$0.650778\pi$
$822$	−172.151	−	99.3917i	−0.209430	−	0.120914i
$823$	495.873	−	858.877i	0.602519	−	1.04359i	−0.389919	−	0.920849i	$-0.627497\pi$
$823$	495.873	−	858.877i	0.602519	−	1.04359i	0.992438	−	0.122744i	$-0.0391696\pi$
$824$	115.074	−	66.4378i	0.139652	−	0.0806283i
$825$		−	15.9247i		−	0.0193027i
$826$	−98.5403	+	104.917i	−0.119298	+	0.127018i
$827$	1264.47			1.52899			0.764493	−	0.644632i	$-0.222989\pi$
$827$	1264.47			1.52899			0.764493	+	0.644632i	$0.222989\pi$
$828$	−2.76386	−	4.78715i	−0.00333800	−	0.00578158i
$829$	−78.3145	−	45.2149i	−0.0944686	−	0.0545415i	0.452021	−	0.892007i	$-0.350703\pi$
$829$	−78.3145	−	45.2149i	−0.0944686	−	0.0545415i	−0.546490	+	0.837466i	$0.684036\pi$
$830$	244.628	−	423.708i	0.294732	−	0.510491i
$831$	595.281	−	343.686i	0.716343	−	0.413581i
$832$			43.2612i			0.0519966i
$833$	−219.222	+	441.429i	−0.263172	+	0.529927i
$834$	−608.236			−0.729300
$835$	229.405	+	397.341i	0.274736	+	0.475858i
$836$	−29.2772	−	16.9032i	−0.0350206	−	0.0202191i
$837$	108.562	−	188.035i	0.129704	−	0.224654i
$838$	705.309	−	407.210i	0.841658	−	0.485931i
$839$			148.508i			0.177006i	0.996076	+	0.0885032i	$0.0282083\pi$
$839$			148.508i			0.177006i	−0.996076	+	0.0885032i	$0.971792\pi$
$840$	−55.8936	−	52.4967i	−0.0665401	−	0.0624960i
$841$	−683.313			−0.812501
$842$	403.863	+	699.512i	0.479648	+	0.830774i
$843$	−171.366	−	98.9382i	−0.203281	−	0.117364i
$844$	−185.930	+	322.040i	−0.220296	+	0.381564i
$845$	270.639	−	156.253i	0.320283	−	0.184915i
$846$			144.087i			0.170316i
$847$	−188.077	+	801.562i	−0.222051	+	0.946354i
$848$	−416.317			−0.490940
$849$	391.819	+	678.650i	0.461507	+	0.799353i
$850$	61.5956	+	35.5622i	0.0724654	+	0.0418379i
$851$	3.35527	−	5.81151i	0.00394274	−	0.00682903i
$852$	53.8861	−	31.1112i	0.0632466	−	0.0365155i
$853$		−	642.996i		−	0.753805i	−0.926253	−	0.376902i	$-0.876989\pi$
$853$		−	642.996i		−	0.753805i	0.926253	−	0.376902i	$-0.123011\pi$
$854$	68.0124	+	225.338i	0.0796398	+	0.263862i
$855$	−61.6644			−0.0721221
$856$	−262.594	−	454.826i	−0.306768	−	0.531338i
$857$	−109.679	−	63.3232i	−0.127980	−	0.0738894i	0.434643	−	0.900603i	$-0.356875\pi$
$857$	−109.679	−	63.3232i	−0.127980	−	0.0738894i	−0.562623	+	0.826713i	$0.690208\pi$
$858$	−12.1785	+	21.0938i	−0.0141941	+	0.0245849i
$859$	−435.756	+	251.584i	−0.507283	+	0.292880i	−0.731716	−	0.681610i	$-0.761280\pi$
$859$	−435.756	+	251.584i	−0.507283	+	0.292880i	0.224433	+	0.974489i	$0.427947\pi$
$860$		−	36.3277i		−	0.0422415i
$861$	608.074	−	183.531i	0.706242	−	0.213161i
$862$	38.3809			0.0445254
$863$	−633.889	−	1097.93i	−0.734518	−	1.27222i	−0.954935	−	0.296816i	$-0.904075\pi$
$863$	−633.889	−	1097.93i	−0.734518	−	1.27222i	0.220417	−	0.975406i	$-0.429258\pi$
$864$	25.4558	+	14.6969i	0.0294628	+	0.0170103i
$865$	125.817	−	217.921i	0.145453	−	0.251932i
$866$	−445.082	+	256.968i	−0.513951	+	0.296730i
$867$		−	325.325i		−	0.375230i
$868$	569.530	+	133.634i	0.656141	+	0.153956i
$869$	148.828			0.171264
$870$	34.3897	+	59.5647i	0.0395284	+	0.0684652i
$871$	69.9045	+	40.3594i	0.0802577	+	0.0463368i
$872$	122.032	−	211.366i	0.139945	−	0.242392i
$873$	229.082	−	132.260i	0.262407	−	0.151501i
$874$		−	11.9767i		−	0.0137034i
$875$	53.5792	−	57.0462i	0.0612334	−	0.0651957i
$876$	430.819			0.491802
$877$	164.850	+	285.529i	0.187971	+	0.325575i	0.944574	−	0.328300i	$-0.106476\pi$
$877$	164.850	+	285.529i	0.187971	+	0.325575i	−0.756603	+	0.653875i	$0.773142\pi$
$878$	−570.008	−	329.094i	−0.649212	−	0.374823i
$879$	103.173	−	178.701i	0.117375	−	0.203300i
$880$	−14.2435	+	8.22348i	−0.0161858	+	0.00934487i
$881$		−	583.618i		−	0.662449i	−0.943552	−	0.331224i	$-0.892538\pi$
$881$		−	583.618i		−	0.662449i	0.943552	−	0.331224i	$-0.107462\pi$
$882$	−186.193	−	92.4670i	−0.211103	−	0.104838i
$883$	−1172.36			−1.32770			−0.663849	−	0.747867i	$-0.731078\pi$
$883$	−1172.36			−1.32770			−0.663849	+	0.747867i	$0.731078\pi$
$884$	−54.3929	−	94.2113i	−0.0615304	−	0.106574i
$885$	48.7679	+	28.1562i	0.0551050	+	0.0318149i
$886$	345.023	−	597.597i	0.389416	−	0.674489i
$887$	1274.64	−	735.915i	1.43703	−	0.829667i	0.439384	−	0.898299i	$-0.355197\pi$
$887$	1274.64	−	735.915i	1.43703	−	0.829667i	0.997642	+	0.0686323i	$0.0218635\pi$
$888$			35.6836i			0.0401842i
$889$	−672.188	−	631.335i	−0.756117	−	0.710163i
$890$	215.422			0.242047
$891$	8.27472	+	14.3322i	0.00928701	+	0.0160856i
$892$	−92.8982	−	53.6348i	−0.104146	−	0.0601287i
$893$	−156.095	+	270.364i	−0.174798	+	0.302759i
$894$	−318.219	+	183.724i	−0.355949	+	0.205507i
$895$		−	99.4375i		−	0.111103i
$896$	−18.0911	+	77.1020i	−0.0201910	+	0.0860513i
$897$	−8.62907			−0.00961993
$898$	−202.118	−	350.078i	−0.225075	−	0.389842i
$899$	−454.417	−	262.358i	−0.505470	−	0.291833i
$900$	−15.0000	+	25.9808i	−0.0166667	+	0.0288675i
$901$	906.627	−	523.442i	1.00625	−	0.580956i
$902$		−	136.234i		−	0.151035i
$903$	−28.4579	−	94.2865i	−0.0315149	−	0.104415i
$904$	242.737			0.268515
$905$	−10.3368	−	17.9039i	−0.0114219	−	0.0197833i
$906$	−388.265	−	224.165i	−0.428549	−	0.247423i
$907$	−498.599	+	863.598i	−0.549723	+	0.952148i	0.448570	+	0.893748i	$0.351933\pi$
$907$	−498.599	+	863.598i	−0.549723	+	0.952148i	−0.998293	+	0.0584006i	$0.981400\pi$
$908$	−292.784	+	169.039i	−0.322449	+	0.186166i
$909$		−	334.126i		−	0.367575i
$910$	−114.597	+	34.5882i	−0.125931	+	0.0380090i
$911$	−758.955			−0.833101			−0.416550	−	0.909113i	$-0.636761\pi$
$911$	−758.955			−0.833101			−0.416550	+	0.909113i	$0.636761\pi$
$912$	31.8434	+	55.1543i	0.0349160	+	0.0604762i
$913$	−246.381	−	142.248i	−0.269859	−	0.155803i
$914$	299.281	−	518.370i	0.327441	−	0.567144i
$915$	79.7498	−	46.0435i	0.0871582	−	0.0503208i
$916$			572.035i			0.624492i
$917$	−809.393	−	189.915i	−0.882653	−	0.207104i
$918$	−73.9147			−0.0805171
$919$	−703.781	−	1218.99i	−0.765812	−	1.32643i	−0.939816	−	0.341681i	$-0.889004\pi$
$919$	−703.781	−	1218.99i	−0.765812	−	1.32643i	0.174004	−	0.984745i	$-0.444329\pi$
$920$	−5.04610	−	2.91337i	−0.00548489	−	0.00316670i
$921$	−236.115	+	408.964i	−0.256369	+	0.444043i
$922$	577.771	−	333.576i	0.626649	−	0.361796i
$923$		−	97.1324i		−	0.105236i
$924$	−30.5262	+	32.5015i	−0.0330370	+	0.0351748i
$925$	−36.4194			−0.0393723
$926$	−137.192	−	237.623i	−0.148155	−	0.256613i
$927$	−122.054	−	70.4679i	−0.131666	−	0.0760171i
$928$	35.5175	−	61.5182i	0.0382732	−	0.0662911i
$929$	314.575	−	181.620i	0.338617	−	0.195500i	−0.321044	−	0.947064i	$-0.604034\pi$
$929$	314.575	−	181.620i	0.338617	−	0.195500i	0.659660	+	0.751564i	$0.270700\pi$
$930$		−	228.869i		−	0.246096i
$931$	−249.198	−	375.213i	−0.267667	−	0.403021i
$932$	−363.677			−0.390212
$933$	65.4476	+	113.359i	0.0701475	+	0.121499i
$934$	−13.8728	−	8.00946i	−0.0148531	−	0.00857544i
$935$	20.6790	−	35.8171i	0.0221166	−	0.0383071i
$936$	39.7379	−	22.9427i	0.0424551	−	0.0245114i
$937$		−	401.784i		−	0.428798i	−0.976746	−	0.214399i	$-0.931221\pi$
$937$		−	401.784i		−	0.428798i	0.976746	−	0.214399i	$-0.0687793\pi$
$938$	107.709	+	101.163i	0.114829	+	0.107850i
$939$	−110.211			−0.117371
$940$	75.9407	+	131.533i	0.0807880	+	0.139929i
$941$	−731.276	−	422.202i	−0.777126	−	0.448674i	0.0582845	−	0.998300i	$-0.481437\pi$
$941$	−731.276	−	422.202i	−0.777126	−	0.448674i	−0.835411	+	0.549626i	$0.814770\pi$
$942$	361.649	−	626.394i	0.383916	−	0.664962i
$943$	41.7980	−	24.1321i	0.0443245	−	0.0255908i
$944$		−	58.1591i		−	0.0616092i
$945$	−18.5792	+	79.1822i	−0.0196605	+	0.0837906i
$946$	−21.1241			−0.0223299
$947$	−144.083	−	249.560i	−0.152147	−	0.263527i	0.779869	−	0.625942i	$-0.215285\pi$
$947$	−144.083	−	249.560i	−0.152147	−	0.263527i	−0.932017	+	0.362415i	$0.881952\pi$
$948$	−242.810	−	140.186i	−0.256128	−	0.147876i
$949$	336.266	−	582.429i	0.354337	−	0.613729i
$950$	−56.2916	+	32.5000i	−0.0592543	+	0.0342105i
$951$		−	26.7638i		−	0.0281428i
$952$	−57.5438	−	190.654i	−0.0604452	−	0.200266i
$953$	293.080			0.307534			0.153767	−	0.988107i	$-0.450859\pi$
$953$	293.080			0.307534			0.153767	+	0.988107i	$0.450859\pi$
$954$	220.786	+	382.412i	0.231431	+	0.400851i
$955$	264.929	+	152.957i	0.277413	+	0.160164i
$956$	382.489	−	662.490i	0.400093	−	0.692981i
$957$	34.6362	−	19.9972i	0.0361924	−	0.0208957i
$958$		−	894.769i		−	0.933997i
$959$	−543.839	+	164.144i	−0.567090	+	0.171161i
$960$	30.9839			0.0322749
$961$	392.517	+	679.859i	0.408446	+	0.707450i
$962$	48.2411	+	27.8520i	0.0501466	+	0.0289522i
$963$	−278.523	+	482.415i	−0.289224	+	0.500950i
$964$	360.647	−	208.220i	0.374115	−	0.215995i
$965$		−	818.119i		−	0.847792i
$966$	−15.3791	−	3.60853i	−0.0159204	−	0.00373554i
$967$	68.4003			0.0707345			0.0353673	−	0.999374i	$-0.488740\pi$
$967$	68.4003			0.0707345			0.0353673	+	0.999374i	$0.488740\pi$
$968$	−166.338	−	288.106i	−0.171837	−	0.297630i
$969$	−138.693	−	80.0742i	−0.143130	−	0.0826359i
$970$	139.415	−	241.473i	0.143726	−	0.248942i
$971$	253.215	−	146.194i	0.260777	−	0.150560i	−0.363912	−	0.931433i	$-0.618559\pi$
$971$	253.215	−	146.194i	0.260777	−	0.150560i	0.624689	+	0.780874i	$0.285226\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	−1189.98	+	1266.98i	−1.22300	+	1.30213i
$974$	89.1243			0.0915034
$975$	23.4158	+	40.5574i	0.0240162	+	0.0415973i
$976$	−82.3652	−	47.5536i	−0.0843906	−	0.0487229i
$977$	538.697	−	933.051i	0.551379	−	0.955016i	−0.446796	−	0.894636i	$-0.647435\pi$
$977$	538.697	−	933.051i	0.551379	−	0.955016i	0.998175	−	0.0603807i	$-0.0192315\pi$
$978$	−251.008	+	144.919i	−0.256654	+	0.148179i
$979$		−	125.265i		−	0.127952i
$980$	−218.705	+	13.7220i	−0.223168	+	0.0140020i
$981$	−258.869			−0.263883
$982$	184.620	+	319.771i	0.188004	+	0.325632i
$983$	1354.95	+	782.282i	1.37839	+	0.795811i	0.991965	−	0.126511i	$-0.0403781\pi$
$983$	1354.95	+	782.282i	1.37839	+	0.795811i	0.386420	+	0.922323i	$0.373711\pi$
$984$	−128.323	+	222.262i	−0.130410	+	0.225876i
$985$	−377.471	+	217.933i	−0.383219	+	0.221252i
$986$			178.627i			0.181163i
$987$	300.139	+	281.898i	0.304092	+	0.285610i
$988$	99.4184			0.100626
$989$	−3.74186	−	6.48110i	−0.00378348	−	0.00655318i
$990$	15.1075	+	8.72232i	0.0152601	+	0.00881043i
$991$	−726.967	+	1259.14i	−0.733570	+	1.27058i	0.221779	+	0.975097i	$0.428814\pi$
$991$	−726.967	+	1259.14i	−0.733570	+	1.27058i	−0.955348	+	0.295483i	$0.904520\pi$
$992$	−204.707	+	118.187i	−0.206358	+	0.119141i
$993$			646.192i			0.650747i
$994$	40.6191	−	173.114i	0.0408643	−	0.174159i
$995$	−542.996			−0.545724
$996$	267.976	+	464.148i	0.269052	+	0.466012i
$997$	−701.023	−	404.736i	−0.703133	−	0.405954i	0.105380	−	0.994432i	$-0.466394\pi$
$997$	−701.023	−	404.736i	−0.703133	−	0.405954i	−0.808513	+	0.588478i	$0.799727\pi$
$998$	310.394	−	537.618i	0.311016	−	0.538695i
$999$	32.7775	−	18.9241i	0.0328103	−	0.0189430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.o.a.31.4	✓	8
3.2	odd	2		630.3.v.b.451.1		8
5.2	odd	4		1050.3.q.c.199.3		16
5.3	odd	4		1050.3.q.c.199.6		16
5.4	even	2		1050.3.p.b.451.1		8
7.3	odd	6		1470.3.f.a.391.3		8
7.4	even	3		1470.3.f.a.391.2		8
7.5	odd	6	inner	210.3.o.a.61.4	yes	8
21.5	even	6		630.3.v.b.271.1		8
35.12	even	12		1050.3.q.c.649.6		16
35.19	odd	6		1050.3.p.b.901.1		8
35.33	even	12		1050.3.q.c.649.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.a.31.4	✓	8	1.1	even	1	trivial
210.3.o.a.61.4	yes	8	7.5	odd	6	inner
630.3.v.b.271.1		8	21.5	even	6
630.3.v.b.451.1		8	3.2	odd	2
1050.3.p.b.451.1		8	5.4	even	2
1050.3.p.b.901.1		8	35.19	odd	6
1050.3.q.c.199.3		16	5.2	odd	4
1050.3.q.c.199.6		16	5.3	odd	4
1050.3.q.c.649.3		16	35.33	even	12
1050.3.q.c.649.6		16	35.12	even	12
1470.3.f.a.391.2		8	7.4	even	3
1470.3.f.a.391.3		8	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +2.44949i q^{6} +(5.10237 + 4.79227i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +2.44949i q^{6} +(5.10237 + 4.79227i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(2.73861 + 1.58114i) q^{10} +(0.919414 - 1.59247i) q^{11} +(-3.00000 + 1.73205i) q^{12} +5.40765i q^{13} +(-2.26139 + 9.63774i) q^{14} +3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(8.71093 + 5.02926i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-7.96084 + 4.59619i) q^{19} +4.47214i q^{20} +(3.50333 + 11.6072i) q^{21} +2.60049 q^{22} +(0.460644 + 0.797858i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-6.62299 + 3.82378i) q^{26} +5.19615i q^{27} +(-13.4028 + 4.04529i) q^{28} +12.5573 q^{29} +(2.73861 + 4.74342i) q^{30} +(-36.1874 - 20.8928i) q^{31} +(2.82843 - 4.89898i) q^{32} +(2.75824 - 1.59247i) q^{33} +14.2249i q^{34} +(15.2386 + 3.57557i) q^{35} -6.00000 q^{36} +(-3.64194 - 6.30803i) q^{37} +(-11.2583 - 6.50000i) q^{38} +(-4.68316 + 8.11147i) q^{39} +(-5.47723 + 3.16228i) q^{40} -52.3877i q^{41} +(-11.7386 + 12.4982i) q^{42} -8.12312 q^{43} +(1.83883 + 3.18494i) q^{44} +(5.80948 + 3.35410i) q^{45} +(-0.651449 + 1.12834i) q^{46} +(29.4117 - 16.9809i) q^{47} -6.92820i q^{48} +(3.06832 + 48.9038i) q^{49} +7.07107 q^{50} +(8.71093 + 15.0878i) q^{51} +(-9.36632 - 5.40765i) q^{52} +(52.0396 - 90.1353i) q^{53} +(-6.36396 + 3.67423i) q^{54} -4.11174i q^{55} +(-14.4317 - 13.5546i) q^{56} -15.9217 q^{57} +(8.87938 + 15.3795i) q^{58} +(12.5918 + 7.26989i) q^{59} +(-3.87298 + 6.70820i) q^{60} +(20.5913 - 11.8884i) q^{61} -59.0937i q^{62} +(-4.79713 + 20.4447i) q^{63} +8.00000 q^{64} +(6.04593 + 10.4719i) q^{65} +(3.90074 + 2.25209i) q^{66} +(7.46339 - 12.9270i) q^{67} +(-17.4219 + 10.0585i) q^{68} +1.59572i q^{69} +(6.39617 + 21.1917i) q^{70} -17.9620 q^{71} +(-4.24264 - 7.34847i) q^{72} +(-107.705 - 62.1833i) q^{73} +(5.15048 - 8.92090i) q^{74} +(7.50000 - 4.33013i) q^{75} -18.3848i q^{76} +(12.3227 - 3.71930i) q^{77} -13.2460 q^{78} +(40.4683 + 70.0931i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(64.1616 - 37.0437i) q^{82} -154.716i q^{83} +(-23.6076 - 5.53924i) q^{84} +22.4915 q^{85} +(-5.74391 - 9.94875i) q^{86} +(18.8360 + 10.8750i) q^{87} +(-2.60049 + 4.50419i) q^{88} +(58.9956 - 34.0611i) q^{89} +9.48683i q^{90} +(-25.9149 + 27.5918i) q^{91} -1.84258 q^{92} +(-36.1874 - 62.6784i) q^{93} +(41.5944 + 24.0146i) q^{94} +(-10.2774 + 17.8010i) q^{95} +(8.48528 - 4.89898i) q^{96} -88.1736i q^{97} +(-57.7251 + 38.3381i) q^{98} +5.51648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) \) 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9	\( 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} - 24 q^{12} - 40 q^{14} - 16 q^{16} + 84 q^{17} + 108 q^{19} - 48 q^{22} + 12 q^{23} + 20 q^{25} - 96 q^{26} + 72 q^{29} - 132 q^{31} - 12 q^{33} + 100 q^{35} - 48 q^{36} - 96 q^{37} - 168 q^{38} + 24 q^{39} - 72 q^{42} - 112 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} + 156 q^{49} + 84 q^{51} + 48 q^{52} + 32 q^{53} + 16 q^{56} + 216 q^{57} + 104 q^{58} + 132 q^{59} + 96 q^{61} + 64 q^{64} + 20 q^{65} - 72 q^{66} - 120 q^{67} - 168 q^{68} + 8 q^{71} + 24 q^{73} - 16 q^{74} + 60 q^{75} - 216 q^{77} - 192 q^{78} + 12 q^{79} - 36 q^{81} + 24 q^{82} + 120 q^{85} - 40 q^{86} + 108 q^{87} + 48 q^{88} + 492 q^{89} - 308 q^{91} - 48 q^{92} - 132 q^{93} + 480 q^{94} - 40 q^{95} - 24 q^{99}+O(q^{100}) \) 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 - 24 * q^12 - 40 * q^14 - 16 * q^16 + 84 * q^17 + 108 * q^19 - 48 * q^22 + 12 * q^23 + 20 * q^25 - 96 * q^26 + 72 * q^29 - 132 * q^31 - 12 * q^33 + 100 * q^35 - 48 * q^36 - 96 * q^37 - 168 * q^38 + 24 * q^39 - 72 * q^42 - 112 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 + 156 * q^49 + 84 * q^51 + 48 * q^52 + 32 * q^53 + 16 * q^56 + 216 * q^57 + 104 * q^58 + 132 * q^59 + 96 * q^61 + 64 * q^64 + 20 * q^65 - 72 * q^66 - 120 * q^67 - 168 * q^68 + 8 * q^71 + 24 * q^73 - 16 * q^74 + 60 * q^75 - 216 * q^77 - 192 * q^78 + 12 * q^79 - 36 * q^81 + 24 * q^82 + 120 * q^85 - 40 * q^86 + 108 * q^87 + 48 * q^88 + 492 * q^89 - 308 * q^91 - 48 * q^92 - 132 * q^93 + 480 * q^94 - 40 * q^95 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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