LMFDB - Embedded newform 105.3.r.a.94.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(19,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("105.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.r (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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			94.1
Character	$\chi$	$=$	105.94
Dual form			105.3.r.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.26825 + 1.88692i) q^{2} +(0.866025 - 1.50000i) q^{3} +(5.12097 - 8.86977i) q^{4} +(-3.80462 - 3.24421i) q^{5} +6.53650i q^{6} +(-1.16497 + 6.90238i) q^{7} +23.5561i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-3.26825 + 1.88692i) q^{2} +(0.866025 - 1.50000i) q^{3} +(5.12097 - 8.86977i) q^{4} +(-3.80462 - 3.24421i) q^{5} +6.53650i q^{6} +(-1.16497 + 6.90238i) q^{7} +23.5561i q^{8} +(-1.50000 - 2.59808i) q^{9} +(18.5560 + 3.42385i) q^{10} +(-8.95926 + 15.5179i) q^{11} +(-8.86977 - 15.3629i) q^{12} -1.69555 q^{13} +(-9.21686 - 24.7569i) q^{14} +(-8.16121 + 2.89736i) q^{15} +(-23.9647 - 41.5081i) q^{16} +(1.48936 - 2.57964i) q^{17} +(9.80475 + 5.66077i) q^{18} +(-21.6426 + 12.4954i) q^{19} +(-48.2587 + 17.1326i) q^{20} +(9.34468 + 7.72509i) q^{21} -67.6218i q^{22} +(-7.89777 + 4.55978i) q^{23} +(35.3342 + 20.4002i) q^{24} +(3.95023 + 24.6859i) q^{25} +(5.54149 - 3.19938i) q^{26} -5.19615 q^{27} +(55.2568 + 45.6799i) q^{28} +17.4522 q^{29} +(21.2058 - 24.8689i) q^{30} +(-4.27835 - 2.47011i) q^{31} +(75.0446 + 43.3270i) q^{32} +(15.5179 + 26.8778i) q^{33} +11.2412i q^{34} +(26.8250 - 22.4815i) q^{35} -30.7258 q^{36} +(-47.3050 + 27.3115i) q^{37} +(47.1557 - 81.6761i) q^{38} +(-1.46839 + 2.54333i) q^{39} +(76.4209 - 89.6220i) q^{40} -29.2216i q^{41} +(-45.1174 - 7.61481i) q^{42} +18.1962i q^{43} +(91.7602 + 158.933i) q^{44} +(-2.72177 + 14.7510i) q^{45} +(17.2079 - 29.8050i) q^{46} +(2.28224 + 3.95295i) q^{47} -83.0162 q^{48} +(-46.2857 - 16.0821i) q^{49} +(-59.4908 - 73.2260i) q^{50} +(-2.57964 - 4.46807i) q^{51} +(-8.68286 + 15.0392i) q^{52} +(-21.8280 - 12.6024i) q^{53} +(16.9823 - 9.80475i) q^{54} +(84.4299 - 29.9740i) q^{55} +(-162.593 - 27.4421i) q^{56} +43.2853i q^{57} +(-57.0383 + 32.9311i) q^{58} +(-19.6602 - 11.3508i) q^{59} +(-16.0943 + 87.2253i) q^{60} +(52.1535 - 30.1108i) q^{61} +18.6436 q^{62} +(19.6804 - 7.32689i) q^{63} -135.301 q^{64} +(6.45093 + 5.50072i) q^{65} +(-101.433 - 58.5622i) q^{66} +(39.4034 + 22.7496i) q^{67} +(-15.2539 - 26.4205i) q^{68} +15.7955i q^{69} +(-45.2499 + 124.092i) q^{70} +21.4512 q^{71} +(61.2005 - 35.3342i) q^{72} +(46.4748 - 80.4966i) q^{73} +(103.070 - 178.522i) q^{74} +(40.4499 + 15.4533i) q^{75} +255.954i q^{76} +(-96.6732 - 79.9181i) q^{77} -11.0830i q^{78} +(-35.5708 - 61.6105i) q^{79} +(-43.4843 + 235.669i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(55.1390 + 95.5035i) q^{82} -10.3791 q^{83} +(116.374 - 43.3253i) q^{84} +(-14.0353 + 4.98276i) q^{85} +(-34.3348 - 59.4696i) q^{86} +(15.1141 - 26.1784i) q^{87} +(-365.541 - 211.045i) q^{88} +(10.8707 - 6.27621i) q^{89} +(-18.9386 - 53.3457i) q^{90} +(1.97526 - 11.7033i) q^{91} +93.4019i q^{92} +(-7.41032 + 4.27835i) q^{93} +(-14.9178 - 8.61282i) q^{94} +(122.880 + 22.6731i) q^{95} +(129.981 - 75.0446i) q^{96} -127.247 q^{97} +(181.619 - 34.7773i) q^{98} +53.7556 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 - 6 * q^5 - 48 * q^9	$ 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9} + 78 q^{10} - 28 q^{11} + 60 q^{14} - 24 q^{15} - 40 q^{16} - 60 q^{19} + 12 q^{21} - 34 q^{25} - 96 q^{26} - 88 q^{29} + 84 q^{31} - 170 q^{35} - 192 q^{36} + 36 q^{39} + 330 q^{40} + 320 q^{44} + 18 q^{45} - 60 q^{46} + 356 q^{49} + 12 q^{51} - 468 q^{56} - 804 q^{59} - 198 q^{60} + 336 q^{61} - 400 q^{64} - 46 q^{65} - 108 q^{66} - 438 q^{70} + 344 q^{71} + 900 q^{74} + 144 q^{75} - 20 q^{79} + 1140 q^{80} - 144 q^{81} + 780 q^{84} + 304 q^{85} + 144 q^{86} + 24 q^{89} - 224 q^{91} - 924 q^{94} - 342 q^{95} + 900 q^{96} + 168 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 - 6 * q^5 - 48 * q^9 + 78 * q^10 - 28 * q^11 + 60 * q^14 - 24 * q^15 - 40 * q^16 - 60 * q^19 + 12 * q^21 - 34 * q^25 - 96 * q^26 - 88 * q^29 + 84 * q^31 - 170 * q^35 - 192 * q^36 + 36 * q^39 + 330 * q^40 + 320 * q^44 + 18 * q^45 - 60 * q^46 + 356 * q^49 + 12 * q^51 - 468 * q^56 - 804 * q^59 - 198 * q^60 + 336 * q^61 - 400 * q^64 - 46 * q^65 - 108 * q^66 - 438 * q^70 + 344 * q^71 + 900 * q^74 + 144 * q^75 - 20 * q^79 + 1140 * q^80 - 144 * q^81 + 780 * q^84 + 304 * q^85 + 144 * q^86 + 24 * q^89 - 224 * q^91 - 924 * q^94 - 342 * q^95 + 900 * q^96 + 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−3.26825	+	1.88692i	−1.63412	+	0.943462i	−0.651322	+	0.758802i	$0.725785\pi$
$2$	−3.26825	+	1.88692i	−1.63412	+	0.943462i	−0.982802	+	0.184661i	$0.940881\pi$
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$4$	5.12097	−	8.86977i	1.28024	−	2.21744i
$5$	−3.80462	−	3.24421i	−0.760923	−	0.648842i
$5$	−3.80462	−	3.24421i	−0.760923	−	0.648842i
$6$			6.53650i			1.08942i
$7$	−1.16497	+	6.90238i	−0.166424	+	0.986054i
$7$	−1.16497	+	6.90238i	−0.166424	+	0.986054i
$8$			23.5561i			2.94451i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$	18.5560	+	3.42385i	1.85560	+	0.342385i
$11$	−8.95926	+	15.5179i	−0.814479	+	1.41072i	0.0952232	+	0.995456i	$0.469644\pi$
$11$	−8.95926	+	15.5179i	−0.814479	+	1.41072i	−0.909702	+	0.415262i	$0.863690\pi$
$12$	−8.86977	−	15.3629i	−0.739148	−	1.28024i
$13$	−1.69555			−0.130427			−0.0652135	−	0.997871i	$-0.520773\pi$
$13$	−1.69555			−0.130427			−0.0652135	+	0.997871i	$0.520773\pi$
$14$	−9.21686	−	24.7569i	−0.658347	−	1.76835i
$15$	−8.16121	+	2.89736i	−0.544080	+	0.193157i
$16$	−23.9647	−	41.5081i	−1.49779	−	2.59426i
$17$	1.48936	−	2.57964i	0.0876091	−	0.151743i	−0.818891	−	0.573949i	$-0.805411\pi$
$17$	1.48936	−	2.57964i	0.0876091	−	0.151743i	0.906500	+	0.422206i	$0.138744\pi$
$18$	9.80475	+	5.66077i	0.544708	+	0.314487i
$19$	−21.6426	+	12.4954i	−1.13909	+	0.657652i	−0.946204	−	0.323570i	$-0.895117\pi$
$19$	−21.6426	+	12.4954i	−1.13909	+	0.657652i	−0.192882	+	0.981222i	$0.561784\pi$
$20$	−48.2587	+	17.1326i	−2.41294	+	0.856631i
$21$	9.34468	+	7.72509i	0.444985	+	0.367861i
$22$		−	67.6218i		−	3.07372i
$23$	−7.89777	+	4.55978i	−0.343381	+	0.198251i	−0.661766	−	0.749710i	$-0.730193\pi$
$23$	−7.89777	+	4.55978i	−0.343381	+	0.198251i	0.318385	+	0.947961i	$0.396860\pi$
$24$	35.3342	+	20.4002i	1.47226	+	0.850008i
$25$	3.95023	+	24.6859i	0.158009	+	0.987438i
$26$	5.54149	−	3.19938i	0.213134	−	0.123053i
$27$	−5.19615			−0.192450
$28$	55.2568	+	45.6799i	1.97346	+	1.63142i
$29$	17.4522			0.601801			0.300901	−	0.953655i	$-0.402713\pi$
$29$	17.4522			0.601801			0.300901	+	0.953655i	$0.402713\pi$
$30$	21.2058	−	24.8689i	0.706859	−	0.828962i
$31$	−4.27835	−	2.47011i	−0.138011	−	0.0796808i	0.429405	−	0.903112i	$-0.358723\pi$
$31$	−4.27835	−	2.47011i	−0.138011	−	0.0796808i	−0.567416	+	0.823431i	$0.692057\pi$
$32$	75.0446	+	43.3270i	2.34514	+	1.35397i
$33$	15.5179	+	26.8778i	0.470239	+	0.814479i
$34$			11.2412i			0.330624i
$35$	26.8250	−	22.4815i	0.766429	−	0.642329i
$36$	−30.7258			−0.853494
$37$	−47.3050	+	27.3115i	−1.27851	+	0.738150i	−0.976575	−	0.215178i	$-0.930967\pi$
$37$	−47.3050	+	27.3115i	−1.27851	+	0.738150i	−0.301938	+	0.953328i	$0.597634\pi$
$38$	47.1557	−	81.6761i	1.24094	−	2.14937i
$39$	−1.46839	+	2.54333i	−0.0376511	+	0.0652135i
$40$	76.4209	−	89.6220i	1.91052	−	2.24055i
$41$		−	29.2216i		−	0.712723i	−0.934348	−	0.356361i	$-0.884017\pi$
$41$		−	29.2216i		−	0.712723i	0.934348	−	0.356361i	$-0.115983\pi$
$42$	−45.1174	−	7.61481i	−1.07422	−	0.181305i
$43$			18.1962i			0.423167i	0.977360	+	0.211583i	$0.0678620\pi$
$43$			18.1962i			0.423167i	−0.977360	+	0.211583i	$0.932138\pi$
$44$	91.7602	+	158.933i	2.08546	+	3.61212i
$45$	−2.72177	+	14.7510i	−0.0604839	+	0.327800i
$46$	17.2079	−	29.8050i	0.374085	−	0.647934i
$47$	2.28224	+	3.95295i	0.0485583	+	0.0841054i	0.889283	−	0.457357i	$-0.151204\pi$
$47$	2.28224	+	3.95295i	0.0485583	+	0.0841054i	−0.840725	+	0.541463i	$0.817871\pi$
$48$	−83.0162			−1.72950
$49$	−46.2857	−	16.0821i	−0.944606	−	0.328206i
$50$	−59.4908	−	73.2260i	−1.18982	−	1.46452i
$51$	−2.57964	−	4.46807i	−0.0505812	−	0.0876091i
$52$	−8.68286	+	15.0392i	−0.166978	+	0.289215i
$53$	−21.8280	−	12.6024i	−0.411850	−	0.237782i	0.279734	−	0.960077i	$-0.409754\pi$
$53$	−21.8280	−	12.6024i	−0.411850	−	0.237782i	−0.691584	+	0.722296i	$0.743087\pi$
$54$	16.9823	−	9.80475i	0.314487	−	0.181569i
$55$	84.4299	−	29.9740i	1.53509	−	0.544981i
$56$	−162.593	−	27.4421i	−2.90345	−	0.490038i
$57$			43.2853i			0.759391i
$58$	−57.0383	+	32.9311i	−0.983418	+	0.567777i
$59$	−19.6602	−	11.3508i	−0.333224	−	0.192387i	0.324048	−	0.946041i	$-0.394956\pi$
$59$	−19.6602	−	11.3508i	−0.333224	−	0.192387i	−0.657271	+	0.753654i	$0.728290\pi$
$60$	−16.0943	+	87.2253i	−0.268239	+	1.45376i
$61$	52.1535	−	30.1108i	0.854975	−	0.493620i	−0.00735138	−	0.999973i	$-0.502340\pi$
$61$	52.1535	−	30.1108i	0.854975	−	0.493620i	0.862326	+	0.506353i	$0.169007\pi$
$62$	18.6436			0.300703
$63$	19.6804	−	7.32689i	0.312387	−	0.116300i
$64$	−135.301			−2.11408
$65$	6.45093	+	5.50072i	0.0992450	+	0.0846265i
$66$	−101.433	−	58.5622i	−1.53686	−	0.887306i
$67$	39.4034	+	22.7496i	0.588111	+	0.339546i	0.764350	−	0.644802i	$-0.223060\pi$
$67$	39.4034	+	22.7496i	0.588111	+	0.339546i	−0.176239	+	0.984347i	$0.556393\pi$
$68$	−15.2539	−	26.4205i	−0.224322	−	0.388537i
$69$			15.7955i			0.228921i
$70$	−45.2499	+	124.092i	−0.646427	+	1.77274i
$71$	21.4512			0.302130			0.151065	−	0.988524i	$-0.451730\pi$
$71$	21.4512			0.302130			0.151065	+	0.988524i	$0.451730\pi$
$72$	61.2005	−	35.3342i	0.850008	−	0.490752i
$73$	46.4748	−	80.4966i	0.636640	−	1.10269i	−0.349525	−	0.936927i	$-0.613657\pi$
$73$	46.4748	−	80.4966i	0.636640	−	1.10269i	0.986165	−	0.165766i	$-0.0530098\pi$
$74$	103.070	−	178.522i	1.39283	−	2.41246i
$75$	40.4499	+	15.4533i	0.539332	+	0.206044i
$76$			255.954i			3.36781i
$77$	−96.6732	−	79.9181i	−1.25550	−	1.03790i
$78$		−	11.0830i		−	0.142089i
$79$	−35.5708	−	61.6105i	−0.450263	−	0.779879i	0.548139	−	0.836387i	$-0.315337\pi$
$79$	−35.5708	−	61.6105i	−0.450263	−	0.779879i	−0.998402	+	0.0565083i	$0.982003\pi$
$80$	−43.4843	+	235.669i	−0.543554	+	2.94586i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	55.1390	+	95.5035i	0.672427	+	1.16468i
$83$	−10.3791			−0.125050			−0.0625249	−	0.998043i	$-0.519915\pi$
$83$	−10.3791			−0.125050			−0.0625249	+	0.998043i	$0.519915\pi$
$84$	116.374	−	43.3253i	1.38540	−	0.515777i
$85$	−14.0353	+	4.98276i	−0.165121	+	0.0586207i
$86$	−34.3348	−	59.4696i	−0.399242	−	0.691507i
$87$	15.1141	−	26.1784i	0.173725	−	0.300901i
$88$	−365.541	−	211.045i	−4.15388	−	2.39824i
$89$	10.8707	−	6.27621i	0.122143	−	0.0705192i	−0.437684	−	0.899129i	$-0.644201\pi$
$89$	10.8707	−	6.27621i	0.122143	−	0.0705192i	0.559827	+	0.828610i	$0.310868\pi$
$90$	−18.9386	−	53.3457i	−0.210429	−	0.592730i
$91$	1.97526	−	11.7033i	0.0217062	−	0.128608i
$92$			93.4019i			1.01524i
$93$	−7.41032	+	4.27835i	−0.0796808	+	0.0460037i
$94$	−14.9178	−	8.61282i	−0.158700	−	0.0916257i
$95$	122.880	+	22.6731i	1.29347	+	0.238664i
$96$	129.981	−	75.0446i	1.35397	−	0.781714i
$97$	−127.247			−1.31182			−0.655911	−	0.754839i	$-0.727715\pi$
$97$	−127.247			−1.31182			−0.655911	+	0.754839i	$0.727715\pi$
$98$	181.619	−	34.7773i	1.85325	−	0.354870i
$99$	53.7556			0.542986
$100$	239.188	+	91.3782i	2.39188	+	0.913782i
$101$	110.873	+	64.0126i	1.09775	+	0.633788i	0.935630	−	0.352982i	$-0.114832\pi$
$101$	110.873	+	64.0126i	1.09775	+	0.633788i	0.162123	+	0.986771i	$0.448166\pi$
$102$	16.8618	+	9.73517i	0.165312	+	0.0954428i
$103$	69.6349	+	120.611i	0.676067	+	1.17098i	0.976156	+	0.217071i	$0.0696504\pi$
$103$	69.6349	+	120.611i	0.676067	+	1.17098i	−0.300089	+	0.953911i	$0.597016\pi$
$104$		−	39.9406i		−	0.384044i
$105$	−10.4911	−	59.7071i	−0.0999156	−	0.568639i
$106$	95.1193			0.897351
$107$	−79.1720	+	45.7100i	−0.739925	+	0.427196i	−0.822042	−	0.569427i	$-0.807165\pi$
$107$	−79.1720	+	45.7100i	−0.739925	+	0.427196i	0.0821170	+	0.996623i	$0.473832\pi$
$108$	−26.6093	+	46.0887i	−0.246383	+	0.426747i
$109$	−83.4336	+	144.511i	−0.765446	+	1.32579i	0.174564	+	0.984646i	$0.444148\pi$
$109$	−83.4336	+	144.511i	−0.765446	+	1.32579i	−0.940010	+	0.341146i	$0.889185\pi$
$110$	−219.379	+	257.275i	−1.99436	+	2.33886i
$111$			94.6099i			0.852342i
$112$	314.423	−	117.058i	2.80735	−	1.04516i
$113$		−	52.2679i		−	0.462548i	−0.972889	−	0.231274i	$-0.925711\pi$
$113$		−	52.2679i		−	0.462548i	0.972889	−	0.231274i	$-0.0742894\pi$
$114$	−81.6761	−	141.467i	−0.716457	−	1.24094i
$115$	44.8409	+	8.27379i	0.389920	+	0.0719460i
$116$	89.3723	−	154.797i	0.770451	−	1.33446i
$117$	2.54333	+	4.40517i	0.0217378	+	0.0376511i
$118$	85.6726			0.726039
$119$	16.0706	+	13.2853i	0.135047	+	0.111641i
$120$	−68.2505	−	192.246i	−0.568754	−	1.60205i
$121$	−100.037	−	173.269i	−0.826751	−	1.43197i
$122$	−113.634	+	196.819i	−0.931424	+	1.61327i
$123$	−43.8324	−	25.3067i	−0.356361	−	0.205745i
$124$	−43.8185	+	25.2986i	−0.353375	+	0.204021i
$125$	65.0572	−	106.736i	0.520458	−	0.853887i
$126$	−50.4950	+	61.0815i	−0.400754	+	0.484774i
$127$		−	124.502i		−	0.980329i	−0.871630	−	0.490165i	$-0.836937\pi$
$127$		−	124.502i		−	0.980329i	0.871630	−	0.490165i	$-0.163063\pi$
$128$	142.020	−	81.9953i	1.10953	−	0.640588i
$129$	27.2943	+	15.7583i	0.211583	+	0.122158i
$130$	−31.4627	−	5.80532i	−0.242021	−	0.0446563i
$131$	−177.285	+	102.355i	−1.35332	+	0.781339i	−0.988713	−	0.149823i	$-0.952130\pi$
$131$	−177.285	+	102.355i	−1.35332	+	0.781339i	−0.364606	+	0.931162i	$0.618796\pi$
$132$	317.867			2.40808
$133$	−61.0349	−	163.943i	−0.458909	−	1.23265i
$134$	−171.707			−1.28139
$135$	19.7694	+	16.8574i	0.146440	+	0.124870i
$136$	60.7662	+	35.0834i	0.446811	+	0.257966i
$137$	−204.122	−	117.850i	−1.48994	−	0.860218i	−0.490007	−	0.871718i	$-0.663006\pi$
$137$	−204.122	−	117.850i	−1.48994	−	0.860218i	−0.999934	+	0.0115002i	$0.996339\pi$
$138$	−29.8050	−	51.6237i	−0.215978	−	0.374085i
$139$			112.692i			0.810730i	0.914155	+	0.405365i	$0.132856\pi$
$139$			112.692i			0.810730i	−0.914155	+	0.405365i	$0.867144\pi$
$140$	−62.0360	−	353.059i	−0.443114	−	2.52185i
$141$	7.90590			0.0560702
$142$	−70.1080	+	40.4769i	−0.493718	+	0.285048i
$143$	15.1909	−	26.3114i	0.106230	−	0.183996i
$144$	−71.8941	+	124.524i	−0.499265	+	0.864752i
$145$	−66.3991	−	56.6187i	−0.457925	−	0.390474i
$146$			350.777i			2.40258i
$147$	−64.2077	+	55.5010i	−0.436787	+	0.377558i
$148$			559.446i			3.78004i
$149$	87.0263	+	150.734i	0.584069	+	1.01164i	0.994991	+	0.0999668i	$0.0318737\pi$
$149$	87.0263	+	150.734i	0.584069	+	1.01164i	−0.410922	+	0.911671i	$0.634793\pi$
$150$	−161.360	+	25.8207i	−1.07573	+	0.172138i
$151$	52.5404	−	91.0026i	0.347949	−	0.602666i	−0.637936	−	0.770090i	$-0.720211\pi$
$151$	52.5404	−	91.0026i	0.347949	−	0.602666i	0.985885	+	0.167424i	$0.0535447\pi$
$152$	−294.343	−	509.816i	−1.93646	−	3.35406i
$153$	−8.93613			−0.0584061
$154$	466.751	+	78.7772i	3.03085	+	0.511540i
$155$	8.26394	+	23.2777i	0.0533157	+	0.150178i
$156$	15.0392	+	26.0486i	0.0964049	+	0.166978i
$157$	0.895294	−	1.55069i	0.00570251	−	0.00987703i	−0.863160	−	0.504930i	$-0.831518\pi$
$157$	0.895294	−	1.55069i	0.00570251	−	0.00987703i	0.868863	+	0.495053i	$0.164851\pi$
$158$	232.509	+	134.239i	1.47157	+	0.849613i
$159$	−37.8073	+	21.8280i	−0.237782	+	0.137283i
$160$	−144.954	−	408.303i	−0.905963	−	2.55189i
$161$	−22.2727	−	59.8254i	−0.138340	−	0.371586i
$162$		−	33.9646i		−	0.209658i
$163$	63.2598	−	36.5231i	0.388097	−	0.224068i	−0.293238	−	0.956039i	$-0.594733\pi$
$163$	63.2598	−	36.5231i	0.388097	−	0.224068i	0.681335	+	0.731971i	$0.261400\pi$
$164$	−259.189	−	149.643i	−1.58042	−	0.912457i
$165$	28.1575	−	152.603i	0.170651	−	0.924867i
$166$	33.9216	−	19.5846i	0.204347	−	0.117980i
$167$	319.441			1.91282			0.956409	−	0.292031i	$-0.0943312\pi$
$167$	319.441			1.91282			0.956409	+	0.292031i	$0.0943312\pi$
$168$	−181.973	+	220.124i	−1.08317	+	1.31026i
$169$	−166.125			−0.982989
$170$	36.4688	−	42.7685i	0.214522	−	0.251579i
$171$	64.9279	+	37.4862i	0.379696	+	0.219217i
$172$	161.396	+	93.1820i	0.938348	+	0.541756i
$173$	124.774	+	216.115i	0.721237	+	1.24922i	0.960504	+	0.278265i	$0.0897594\pi$
$173$	124.774	+	216.115i	0.721237	+	1.24922i	−0.239268	+	0.970954i	$0.576907\pi$
$174$			114.077i			0.655612i
$175$	−174.994	−	1.49235i	−0.999964	−	0.00852771i
$176$	858.825			4.87969
$177$	−34.0525	+	19.6602i	−0.192387	+	0.111075i
$178$	−23.6855	+	41.0244i	−0.133064	+	0.230474i
$179$	−163.317	+	282.873i	−0.912386	+	1.58030i	−0.101701	+	0.994815i	$0.532429\pi$
$179$	−163.317	+	282.873i	−0.912386	+	1.58030i	−0.810684	+	0.585483i	$0.800905\pi$
$180$	116.900	+	99.6809i	0.649444	+	0.553783i
$181$		−	166.724i		−	0.921129i	−0.887626	−	0.460565i	$-0.847647\pi$
$181$		−	166.724i		−	0.921129i	0.887626	−	0.460565i	$-0.152353\pi$
$182$	15.6277	+	41.9766i	0.0858663	+	0.230641i
$183$		−	104.307i		−	0.569983i
$184$	−107.411	−	186.041i	−0.583753	−	1.01109i
$185$	268.582	+	49.5572i	1.45179	+	0.267877i
$186$	16.1458	−	27.9654i	0.0868056	−	0.150352i
$187$	26.6871	+	46.2233i	0.142712	+	0.247184i
$188$	46.7490			0.248665
$189$	6.05335	−	35.8658i	0.0320283	−	0.189766i
$190$	−444.384	+	157.763i	−2.33886	+	0.830333i
$191$	25.4649	+	44.1065i	0.133324	+	0.230924i	0.924956	−	0.380074i	$-0.124102\pi$
$191$	25.4649	+	44.1065i	0.133324	+	0.230924i	−0.791632	+	0.610998i	$0.790768\pi$
$192$	−117.174	+	202.952i	−0.610283	+	1.05704i
$193$	40.7224	+	23.5111i	0.210997	+	0.121819i	0.601775	−	0.798666i	$-0.294461\pi$
$193$	40.7224	+	23.5111i	0.210997	+	0.121819i	−0.390778	+	0.920485i	$0.627794\pi$
$194$	415.874	−	240.105i	2.14368	−	1.23765i
$195$	13.8378	−	4.91262i	0.0709628	−	0.0251929i
$196$	−379.672	+	328.188i	−1.93710	+	1.67443i
$197$			66.0845i			0.335454i	0.985833	+	0.167727i	$0.0536427\pi$
$197$			66.0845i			0.335454i	−0.985833	+	0.167727i	$0.946357\pi$
$198$	−175.687	+	101.433i	−0.887306	+	0.512286i
$199$	65.4215	+	37.7711i	0.328751	+	0.189805i	0.655287	−	0.755380i	$-0.272548\pi$
$199$	65.4215	+	37.7711i	0.328751	+	0.189805i	−0.326535	+	0.945185i	$0.605881\pi$
$200$	−581.505	+	93.0520i	−2.90752	+	0.465260i
$201$	68.2487	−	39.4034i	0.339546	−	0.196037i
$202$	−483.148			−2.39182
$203$	−20.3313	+	120.462i	−0.100154	+	0.593409i
$204$	−52.8410			−0.259024
$205$	−94.8010	+	111.177i	−0.462444	+	0.542327i
$206$	−455.168	−	262.792i	−2.20956	−	1.27569i
$207$	23.6933	+	13.6793i	0.114460	+	0.0660837i
$208$	40.6334	+	70.3792i	0.195353	+	0.338361i
$209$		−	447.798i		−	2.14257i
$210$	146.950	+	175.342i	0.699764	+	0.834960i
$211$	307.384			1.45680			0.728398	−	0.685155i	$-0.240265\pi$
$211$	307.384			1.45680			0.728398	+	0.685155i	$0.240265\pi$
$212$	−223.561	+	129.073i	−1.05453	+	0.608836i
$213$	18.5773	−	32.1769i	0.0872174	−	0.151065i
$214$	172.502	−	298.783i	0.806086	−	1.39618i
$215$	59.0322	−	69.2295i	0.274568	−	0.321997i
$216$		−	122.401i		−	0.566672i
$217$	22.0337	−	26.6532i	0.101538	−	0.122826i
$218$		−	629.732i		−	2.88868i
$219$	−80.4966	−	139.424i	−0.367565	−	0.636640i
$220$	166.500	−	902.369i	0.756819	−	4.10168i
$221$	−2.52528	+	4.37391i	−0.0114266	+	0.0197915i
$222$	−178.522	−	309.209i	−0.804152	−	1.39283i
$223$	−6.02940			−0.0270377			−0.0135188	−	0.999909i	$-0.504303\pi$
$223$	−6.02940			−0.0270377			−0.0135188	+	0.999909i	$0.504303\pi$
$224$	−386.484	+	467.511i	−1.72537	+	2.08710i
$225$	58.2106	−	47.2919i	0.258714	−	0.210186i
$226$	98.6256	+	170.825i	0.436397	+	0.755861i
$227$	16.0305	−	27.7656i	0.0706188	−	0.122315i	−0.828554	−	0.559909i	$-0.810836\pi$
$227$	16.0305	−	27.7656i	0.0706188	−	0.122315i	0.899173	+	0.437594i	$0.144169\pi$
$228$	383.931	+	221.663i	1.68391	+	0.972204i
$229$	−17.0450	+	9.84092i	−0.0744322	+	0.0429734i	−0.536754	−	0.843739i	$-0.680350\pi$
$229$	−17.0450	+	9.84092i	−0.0744322	+	0.0429734i	0.462322	+	0.886712i	$0.347016\pi$
$230$	−162.163	+	57.5705i	−0.705057	+	0.250306i
$231$	−203.599	+	75.7987i	−0.881379	+	0.328133i
$232$			411.107i			1.77201i
$233$	−128.526	+	74.2045i	−0.551614	+	0.318474i	−0.749773	−	0.661696i	$-0.769837\pi$
$233$	−128.526	+	74.2045i	−0.551614	+	0.318474i	0.198159	+	0.980170i	$0.436504\pi$
$234$	−16.6245	−	9.59814i	−0.0710447	−	0.0410177i
$235$	4.14116	−	22.4435i	0.0176219	−	0.0955044i
$236$	−201.358	+	116.254i	−0.853214	+	0.492603i
$237$	−123.221			−0.519919
$238$	−77.5910	−	13.0956i	−0.326013	−	0.0550237i
$239$	−208.455			−0.872197			−0.436098	−	0.899899i	$-0.643640\pi$
$239$	−208.455			−0.872197			−0.436098	+	0.899899i	$0.643640\pi$
$240$	315.845	+	269.322i	1.31602	+	1.12217i
$241$	37.5665	+	21.6890i	0.155878	+	0.0899960i	0.575910	−	0.817513i	$-0.304648\pi$
$241$	37.5665	+	21.6890i	0.155878	+	0.0899960i	−0.420032	+	0.907509i	$0.637981\pi$
$242$	653.890	+	377.524i	2.70203	+	1.56002i
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$		−	616.786i		−	2.52781i
$245$	123.926	+	211.347i	0.505819	+	0.862640i
$246$	191.007			0.776451
$247$	36.6962	−	21.1866i	0.148568	−	0.0857757i
$248$	58.1860	−	100.781i	0.234621	−	0.406376i
$249$	−8.98859	+	15.5687i	−0.0360988	+	0.0625249i
$250$	−11.2206	+	471.598i	−0.0448823	+	1.88639i
$251$			37.7937i			0.150573i	0.997162	+	0.0752863i	$0.0239871\pi$
$251$			37.7937i			0.150573i	−0.997162	+	0.0752863i	$0.976013\pi$
$252$	35.7946	−	212.081i	0.142042	−	0.841592i
$253$		−	163.409i		−	0.645885i
$254$	234.925	+	406.903i	0.924903	+	1.60198i
$255$	−4.68080	+	25.3682i	−0.0183561	+	0.0994830i
$256$	−38.8353	+	67.2646i	−0.151700	+	0.262753i
$257$	116.580	+	201.922i	0.453618	+	0.785690i	0.998608	−	0.0527532i	$-0.0167997\pi$
$257$	116.580	+	201.922i	0.453618	+	0.785690i	−0.544989	+	0.838443i	$0.683466\pi$
$258$	−118.939			−0.461005
$259$	−133.406	−	358.334i	−0.515081	−	1.38353i
$260$	81.8252	−	29.0492i	0.314712	−	0.111728i
$261$	−26.1784	−	45.3423i	−0.100300	−	0.173725i
$262$	386.274	−	669.046i	1.47433	−	2.55361i
$263$	214.545	+	123.868i	0.815761	+	0.470980i	0.848952	−	0.528469i	$-0.177234\pi$
$263$	214.545	+	123.868i	0.815761	+	0.470980i	−0.0331918	+	0.999449i	$0.510567\pi$
$264$	−633.136	+	365.541i	−2.39824	+	1.38463i
$265$	42.1624	+	118.762i	0.159104	+	0.448159i
$266$	508.824	+	420.637i	1.91287	+	1.58134i
$267$		−	21.7414i		−	0.0814286i
$268$	403.567	−	233.000i	1.50585	−	0.869401i
$269$	−207.895	−	120.028i	−0.772845	−	0.446202i	0.0610436	−	0.998135i	$-0.480557\pi$
$269$	−207.895	−	120.028i	−0.772845	−	0.446202i	−0.833889	+	0.551933i	$0.813890\pi$
$270$	−96.4199	−	17.7909i	−0.357111	−	0.0658921i
$271$	194.539	−	112.317i	0.717856	−	0.414454i	−0.0961073	−	0.995371i	$-0.530639\pi$
$271$	194.539	−	112.317i	0.717856	−	0.414454i	0.813963	+	0.580917i	$0.197306\pi$
$272$	−142.768			−0.524882
$273$	−15.8444	−	13.0983i	−0.0580381	−	0.0479791i
$274$	889.495			3.24633
$275$	−418.465	−	159.869i	−1.52169	−	0.581340i
$276$	140.103	+	80.8884i	0.507619	+	0.293074i
$277$	72.4643	+	41.8373i	0.261604	+	0.151037i	0.625066	−	0.780572i	$-0.285072\pi$
$277$	72.4643	+	41.8373i	0.261604	+	0.151037i	−0.363462	+	0.931609i	$0.618405\pi$
$278$	−212.640	−	368.304i	−0.764893	−	1.32483i
$279$			14.8206i			0.0531205i
$280$	529.577	+	631.893i	1.89135	+	2.25676i
$281$	−245.753			−0.874567			−0.437283	−	0.899324i	$-0.644059\pi$
$281$	−245.753			−0.874567			−0.437283	+	0.899324i	$0.644059\pi$
$282$	−25.8385	+	14.9178i	−0.0916257	+	0.0529001i
$283$	−267.478	+	463.285i	−0.945151	+	1.63705i	−0.189702	+	0.981842i	$0.560752\pi$
$283$	−267.478	+	463.285i	−0.945151	+	1.63705i	−0.755449	+	0.655207i	$0.772581\pi$
$284$	109.851	−	190.268i	0.386799	−	0.669956i
$285$	140.427	−	164.684i	0.492725	−	0.577839i
$286$			114.656i			0.400896i
$287$	201.699	+	34.0423i	0.702783	+	0.118614i
$288$		−	259.962i		−	0.902646i
$289$	140.064	+	242.597i	0.484649	+	0.839437i
$290$	323.844	+	59.7539i	1.11670	+	0.206048i
$291$	−110.199	+	190.870i	−0.378690	+	0.655911i
$292$	−475.991	−	824.441i	−1.63011	−	2.82343i
$293$	−180.678			−0.616650			−0.308325	−	0.951281i	$-0.599768\pi$
$293$	−180.678			−0.616650			−0.308325	+	0.951281i	$0.599768\pi$
$294$	105.121	−	302.546i	0.357553	−	1.02907i
$295$	37.9751	+	106.967i	0.128729	+	0.362601i
$296$	−643.353	−	1114.32i	−2.17349	−	3.76460i
$297$	46.5537	−	80.6334i	0.156746	−	0.271493i
$298$	−568.847	−	328.424i	−1.90888	−	1.10209i
$299$	13.3911	−	7.73134i	0.0447862	−	0.0258573i
$300$	344.210	−	279.646i	1.14737	−	0.932152i
$301$	−125.597	−	21.1980i	−0.417265	−	0.0704251i
$302$			396.559i			1.31311i
$303$	192.038	−	110.873i	0.633788	−	0.365918i
$304$	1037.32	+	598.897i	3.41224	+	1.97006i
$305$	−296.110	−	54.6366i	−0.970852	−	0.179136i
$306$	29.2055	−	16.8618i	0.0954428	−	0.0551039i
$307$	365.638			1.19100			0.595502	−	0.803354i	$-0.296953\pi$
$307$	365.638			1.19100			0.595502	+	0.803354i	$0.296953\pi$
$308$	−1203.92	+	448.211i	−3.90882	+	1.45523i
$309$	241.222			0.780655
$310$	−70.9318	−	60.4837i	−0.228812	−	0.195109i
$311$	407.510	+	235.276i	1.31032	+	0.756515i	0.982149	−	0.188103i	$-0.0602340\pi$
$311$	407.510	+	235.276i	1.31032	+	0.756515i	0.328172	+	0.944618i	$0.393567\pi$
$312$	−59.9109	−	34.5896i	−0.192022	−	0.110864i
$313$	−96.7895	−	167.644i	−0.309232	−	0.535605i	0.668963	−	0.743296i	$-0.266739\pi$
$313$	−96.7895	−	167.644i	−0.309232	−	0.535605i	−0.978195	+	0.207691i	$0.933405\pi$
$314$			6.75740i			0.0215204i
$315$	−98.6462	−	35.9712i	−0.313163	−	0.114194i
$316$	−728.628			−2.30578
$317$	424.120	−	244.866i	1.33792	−	0.772448i	0.351420	−	0.936218i	$-0.385699\pi$
$317$	424.120	−	244.866i	1.33792	−	0.772448i	0.986498	+	0.163770i	$0.0523656\pi$
$318$	82.3757	−	142.679i	0.259043	−	0.448676i
$319$	−156.359	+	270.822i	−0.490154	+	0.848972i
$320$	514.770	+	438.946i	1.60866	+	1.37170i
$321$			158.344i			0.493283i
$322$	185.679	+	153.497i	0.576642	+	0.476700i
$323$			74.4403i			0.230465i
$324$	46.0887	+	79.8280i	0.142249	+	0.246383i
$325$	−6.69782	−	41.8563i	−0.0206087	−	0.128789i
$326$	−137.833	+	238.733i	−0.422799	+	0.732310i
$327$	144.511	+	250.301i	0.441931	+	0.765446i
$328$	688.348			2.09862
$329$	−29.9435	+	11.1478i	−0.0910137	+	0.0338839i
$330$	195.925	+	551.876i	0.593711	+	1.67235i
$331$	−187.371	−	324.536i	−0.566076	−	0.980472i	−0.996949	−	0.0780594i	$-0.975128\pi$
$331$	−187.371	−	324.536i	−0.566076	−	0.980472i	0.430873	−	0.902413i	$-0.358206\pi$
$332$	−53.1512	+	92.0605i	−0.160094	+	0.277291i
$333$	141.915	+	81.9346i	0.426171	+	0.246050i
$334$	−1044.01	+	602.760i	−3.12578	+	1.80467i
$335$	−76.1106	−	214.386i	−0.227196	−	0.639959i
$336$	96.7112	−	573.009i	0.287831	−	1.70539i
$337$			513.540i			1.52386i	0.647661	+	0.761928i	$0.275747\pi$
$337$			513.540i			1.52386i	−0.647661	+	0.761928i	$0.724253\pi$
$338$	542.938	−	313.465i	1.60633	−	0.927413i
$339$	−78.4019	−	45.2654i	−0.231274	−	0.133526i
$340$	−27.6784	+	150.007i	−0.0814070	+	0.441196i
$341$	76.6617	−	44.2606i	0.224814	−	0.129797i
$342$	−282.934			−0.827293
$343$	164.926	−	300.746i	0.480834	−	0.876812i
$344$	−428.631			−1.24602
$345$	51.2440	−	60.0960i	0.148533	−	0.174191i
$346$	−815.585	−	470.878i	−2.35718	−	1.36092i
$347$	−345.420	−	199.428i	−0.995445	−	0.574721i	−0.0885478	−	0.996072i	$-0.528223\pi$
$347$	−345.420	−	199.428i	−0.995445	−	0.574721i	−0.906898	+	0.421351i	$0.861556\pi$
$348$	−154.797	−	268.117i	−0.444820	−	0.770451i
$349$			653.580i			1.87272i	0.351039	+	0.936361i	$0.385829\pi$
$349$			653.580i			1.87272i	−0.351039	+	0.936361i	$0.614171\pi$
$350$	574.739	−	325.322i	1.64211	−	0.929492i
$351$	8.81035			0.0251007
$352$	−1344.69	+	776.356i	−3.82014	+	2.20556i
$353$	−53.1088	+	91.9872i	−0.150450	+	0.260587i	−0.931393	−	0.364015i	$-0.881406\pi$
$353$	−53.1088	+	91.9872i	−0.150450	+	0.260587i	0.780943	+	0.624602i	$0.214739\pi$
$354$	74.1946	−	128.509i	0.209589	−	0.363019i
$355$	−81.6137	−	69.5923i	−0.229898	−	0.196035i
$356$		−	128.561i		−	0.361127i
$357$	33.8455	−	12.6005i	0.0948053	−	0.0352955i
$358$		−	1232.67i		−	3.44321i
$359$	172.526	+	298.823i	0.480573	+	0.832377i	0.999752	−	0.0222889i	$-0.00709538\pi$
$359$	172.526	+	298.823i	0.480573	+	0.832377i	−0.519179	+	0.854666i	$0.673762\pi$
$360$	−347.476	−	64.1144i	−0.965211	−	0.178095i
$361$	131.770	−	228.231i	0.365012	−	0.632220i
$362$	314.596	+	544.897i	0.869051	+	1.50524i
$363$	−346.538			−0.954649
$364$	−93.6908	−	77.4526i	−0.257392	−	0.212782i
$365$	−437.966	+	155.485i	−1.19991	+	0.425987i
$366$	196.819	+	340.901i	0.537758	+	0.931424i
$367$	−137.224	+	237.679i	−0.373908	+	0.647627i	−0.990163	−	0.139919i	$-0.955316\pi$
$367$	−137.224	+	237.679i	−0.373908	+	0.647627i	0.616255	+	0.787546i	$0.288649\pi$
$368$	378.535	+	218.548i	1.02863	+	0.593879i
$369$	−75.9200	+	43.8324i	−0.205745	+	0.118787i
$370$	−971.302	+	344.828i	−2.62514	+	0.931967i
$371$	112.416	−	135.984i	0.303007	−	0.366534i
$372$			87.6371i			0.235584i
$373$	−394.243	+	227.616i	−1.05695	+	0.610231i	−0.924587	−	0.380970i	$-0.875590\pi$
$373$	−394.243	+	227.616i	−1.05695	+	0.610231i	−0.132364	+	0.991201i	$0.542257\pi$
$374$	−174.440	−	100.713i	−0.466417	−	0.269286i
$375$	−103.763	−	190.022i	−0.276700	−	0.506725i
$376$	−93.1161	+	53.7606i	−0.247649	+	0.142980i
$377$	−29.5912			−0.0784912
$378$	47.8922	+	128.641i	0.126699	+	0.340319i
$379$	609.977			1.60944			0.804720	−	0.593655i	$-0.202316\pi$
$379$	609.977			1.60944			0.804720	+	0.593655i	$0.202316\pi$
$380$	830.367	−	973.806i	2.18518	−	2.56265i
$381$	−186.753	−	107.822i	−0.490165	−	0.282997i
$382$	−166.451	−	96.1007i	−0.435736	−	0.251573i
$383$	−280.151	−	485.235i	−0.731464	−	1.26693i	−0.956257	−	0.292526i	$-0.905504\pi$
$383$	−280.151	−	485.235i	−0.731464	−	1.26693i	0.224793	−	0.974406i	$-0.427829\pi$
$384$		−	284.040i		−	0.739688i
$385$	108.534	+	617.686i	0.281905	+	1.60438i
$386$	−177.454			−0.459727
$387$	47.2750	−	27.2943i	0.122158	−	0.0705278i
$388$	−651.626	+	1128.65i	−1.67945	+	2.90889i
$389$	−158.946	+	275.302i	−0.408601	+	0.707718i	−0.994733	−	0.102498i	$-0.967317\pi$
$389$	−158.946	+	275.302i	−0.408601	+	0.707718i	0.586132	+	0.810216i	$0.300650\pi$
$390$	−35.9555	+	42.1665i	−0.0921935	+	0.108119i
$391$			27.1645i			0.0694745i
$392$	378.832	−	1090.31i	0.966407	−	2.78140i
$393$			354.569i			0.902212i
$394$	−124.696	−	215.980i	−0.316488	−	0.548174i
$395$	−64.5438	+	349.803i	−0.163402	+	0.885578i
$396$	275.280	−	476.800i	0.695153	−	1.20404i
$397$	−170.486	−	295.291i	−0.429437	−	0.743806i	0.567387	−	0.823452i	$-0.307955\pi$
$397$	−170.486	−	295.291i	−0.429437	−	0.743806i	−0.996823	+	0.0796454i	$0.974621\pi$
$398$	−285.085			−0.716294
$399$	−298.772	−	50.4260i	−0.748801	−	0.126381i
$400$	930.000	−	755.558i	2.32500	−	1.88890i
$401$	97.7696	+	169.342i	0.243815	+	0.422299i	0.961798	−	0.273761i	$-0.0882679\pi$
$401$	97.7696	+	169.342i	0.243815	+	0.422299i	−0.717983	+	0.696061i	$0.754935\pi$
$402$	−148.702	+	257.560i	−0.369907	+	0.640697i
$403$	7.25416	+	4.18819i	0.0180004	+	0.0103925i
$404$	1135.55	−	655.613i	2.81078	−	1.62280i
$405$	42.4069	−	15.0551i	0.104708	−	0.0371731i
$406$	−160.855	−	432.063i	−0.396194	−	1.06420i
$407$		−	978.765i		−	2.40483i
$408$	105.250	−	60.7662i	0.257966	−	0.148937i
$409$	−461.432	−	266.408i	−1.12819	−	0.651363i	−0.184714	−	0.982792i	$-0.559136\pi$
$409$	−461.432	−	266.408i	−1.12819	−	0.651363i	−0.943480	+	0.331429i	$0.892469\pi$
$410$	100.051	−	542.237i	0.244026	−	1.32253i
$411$	−353.550	+	204.122i	−0.860218	+	0.496647i
$412$	1426.39			3.46212
$413$	101.251	−	122.479i	0.245160	−	0.296559i
$414$	−103.247			−0.249390
$415$	39.4886	+	33.6721i	0.0951533	+	0.0811375i
$416$	−127.242	−	73.4632i	−0.305870	−	0.176594i
$417$	169.037	+	97.5937i	0.405365	+	0.234038i
$418$	844.961	+	1463.52i	2.02144	+	3.50123i
$419$		−	221.451i		−	0.528523i	−0.964451	−	0.264262i	$-0.914872\pi$
$419$		−	221.451i		−	0.528523i	0.964451	−	0.264262i	$-0.0851282\pi$
$420$	−583.313	−	212.704i	−1.38884	−	0.506438i
$421$	73.0821			0.173592			0.0867958	−	0.996226i	$-0.472337\pi$
$421$	73.0821			0.173592			0.0867958	+	0.996226i	$0.472337\pi$
$422$	−1004.61	+	580.010i	−2.38058	+	1.37443i
$423$	6.84671	−	11.8589i	0.0161861	−	0.0280351i
$424$	296.864	−	514.183i	0.700151	−	1.21270i
$425$	69.5641	+	26.5760i	0.163680	+	0.0625317i
$426$			140.216i			0.329145i
$427$	147.079	+	395.061i	0.344448	+	0.925202i
$428$			936.317i			2.18766i
$429$	−26.3114	−	45.5727i	−0.0613320	−	0.106230i
$430$	−62.3010	+	337.648i	−0.144886	+	0.785229i
$431$	−286.300	+	495.886i	−0.664270	+	1.15055i	0.315213	+	0.949021i	$0.397924\pi$
$431$	−286.300	+	495.886i	−0.664270	+	1.15055i	−0.979483	+	0.201528i	$0.935409\pi$
$432$	124.524	+	215.682i	0.288251	+	0.499265i
$433$	217.665			0.502691			0.251345	−	0.967897i	$-0.419127\pi$
$433$	217.665			0.502691			0.251345	+	0.967897i	$0.419127\pi$
$434$	−21.7192	+	128.685i	−0.0500442	+	0.296510i
$435$	−142.431	+	50.5654i	−0.327428	+	0.116242i
$436$	854.521	+	1480.07i	1.95991	+	3.39467i
$437$	113.952	−	197.371i	0.260761	−	0.451651i
$438$	526.166	+	303.782i	1.20129	+	0.693566i
$439$	634.202	−	366.157i	1.44465	−	0.834070i	0.446496	−	0.894786i	$-0.352672\pi$
$439$	634.202	−	366.157i	1.44465	−	0.834070i	0.998155	+	0.0607162i	$0.0193385\pi$
$440$	706.070	+	1988.84i	1.60470	+	4.52009i
$441$	27.6460	+	144.377i	0.0626894	+	0.327385i
$442$		−	19.0600i		−	0.0431223i
$443$	342.017	−	197.463i	0.772046	−	0.445741i	−0.0615577	−	0.998104i	$-0.519607\pi$
$443$	342.017	−	197.463i	0.772046	−	0.445741i	0.833604	+	0.552362i	$0.186273\pi$
$444$	839.169	+	484.494i	1.89002	+	1.09120i
$445$	−61.7203	−	11.3883i	−0.138697	−	0.0255917i
$446$	19.7056	−	11.3770i	0.0441829	−	0.0255090i
$447$	301.468			0.674425
$448$	157.622	−	933.901i	0.351834	−	2.08460i
$449$	474.587			1.05699			0.528493	−	0.848938i	$-0.322757\pi$
$449$	474.587			1.05699			0.528493	+	0.848938i	$0.322757\pi$
$450$	−101.011	+	264.401i	−0.224468	+	0.587557i
$451$	453.458	+	261.804i	1.00545	+	0.580497i
$452$	−463.605	−	267.662i	−1.02567	−	0.592173i
$453$	−91.0026	−	157.621i	−0.200889	−	0.347949i
$454$			120.993i			0.266505i
$455$	−45.4832	+	38.1186i	−0.0999631	+	0.0837771i
$456$	−1019.63			−2.23604
$457$	356.112	−	205.602i	0.779240	−	0.449894i	−0.0569212	−	0.998379i	$-0.518128\pi$
$457$	356.112	−	205.602i	0.779240	−	0.449894i	0.836161	+	0.548485i	$0.184795\pi$
$458$	37.1381	−	64.3251i	0.0810876	−	0.140448i
$459$	−7.73892	+	13.4042i	−0.0168604	+	0.0292030i
$460$	303.015	−	355.358i	0.658728	−	0.772518i
$461$		−	750.453i		−	1.62788i	−0.580948	−	0.813941i	$-0.697318\pi$
$461$		−	750.453i		−	1.62788i	0.580948	−	0.813941i	$-0.302682\pi$
$462$	522.384	−	631.904i	1.13070	−	1.36776i
$463$			430.641i			0.930110i	0.885282	+	0.465055i	$0.153966\pi$
$463$			430.641i			0.930110i	−0.885282	+	0.465055i	$0.846034\pi$
$464$	−418.238	−	724.409i	−0.901375	−	1.56123i
$465$	42.0733	+	7.76313i	0.0904801	+	0.0166949i
$466$	280.037	−	485.038i	0.600937	−	1.04085i
$467$	−299.997	−	519.611i	−0.642393	−	1.11266i	−0.984897	−	0.173141i	$-0.944608\pi$
$467$	−299.997	−	519.611i	−0.642393	−	1.11266i	0.342504	−	0.939516i	$-0.388725\pi$
$468$	52.0972			0.111319
$469$	−202.930	+	245.475i	−0.432686	+	0.523400i
$470$	28.8149	+	81.1651i	0.0613083	+	0.172692i
$471$	−1.55069	−	2.68588i	−0.00329234	−	0.00570251i
$472$	267.381	−	463.118i	0.566486	−	0.981182i
$473$	−282.366	−	163.024i	−0.596969	−	0.344660i
$474$	402.717	−	232.509i	0.849613	−	0.490524i
$475$	−393.954	−	484.910i	−0.829377	−	1.02086i
$476$	200.134	−	74.5090i	0.420451	−	0.156532i
$477$			75.6145i			0.158521i
$478$	681.283	−	393.339i	1.42528	−	0.822885i
$479$	−578.882	−	334.218i	−1.20852	−	0.697740i	−0.246086	−	0.969248i	$-0.579144\pi$
$479$	−578.882	−	334.218i	−1.20852	−	0.697740i	−0.962436	+	0.271508i	$0.912478\pi$
$480$	−737.988	−	136.170i	−1.53748	−	0.283687i
$481$	80.2081	−	46.3081i	0.166753	−	0.0962747i
$482$	−163.702			−0.339631
$483$	−109.027	−	18.4013i	−0.225728	−	0.0380979i
$484$	−2049.14			−4.23376
$485$	484.125	+	412.815i	0.998196	+	0.851164i
$486$	−50.9470	−	29.4142i	−0.104829	−	0.0605231i
$487$	104.159	+	60.1361i	0.213878	+	0.123483i	0.603112	−	0.797656i	$-0.293927\pi$
$487$	104.159	+	60.1361i	0.213878	+	0.123483i	−0.389234	+	0.921139i	$0.627260\pi$
$488$	709.294	+	1228.53i	1.45347	+	2.51748i
$489$		−	126.520i		−	0.258731i
$490$	−803.815	−	456.895i	−1.64044	−	0.932439i
$491$	−749.043			−1.52555			−0.762773	−	0.646666i	$-0.776163\pi$
$491$	−749.043			−1.52555			−0.762773	+	0.646666i	$0.776163\pi$
$492$	−448.929	+	259.189i	−0.912457	+	0.526807i
$493$	25.9926	−	45.0205i	0.0527233	−	0.0913194i
$494$	−79.9550	+	138.486i	−0.161852	+	0.280336i
$495$	−204.519	−	174.394i	−0.413171	−	0.352312i
$496$			236.781i			0.477382i
$497$	−24.9900	+	148.065i	−0.0502817	+	0.297917i
$498$		−	67.8432i		−	0.136231i
$499$	−213.260	−	369.377i	−0.427375	−	0.740235i	0.569264	−	0.822155i	$-0.307228\pi$
$499$	−213.260	−	369.377i	−0.427375	−	0.740235i	−0.996639	+	0.0819196i	$0.973895\pi$
$500$	−613.568	−	1123.63i	−1.22714	−	2.24727i
$501$	276.644	−	479.161i	0.552183	−	0.956409i
$502$	−71.3139	−	123.519i	−0.142060	−	0.246054i
$503$	−84.6359			−0.168262			−0.0841311	−	0.996455i	$-0.526811\pi$
$503$	−84.6359			−0.168262			−0.0841311	+	0.996455i	$0.526811\pi$
$504$	172.593	+	463.593i	0.342447	+	0.919827i
$505$	−214.159	−	603.239i	−0.424078	−	1.19453i
$506$	308.340	+	534.061i	0.609368	+	1.05546i
$507$	−143.869	+	249.188i	−0.283764	+	0.491494i
$508$	−1104.30	−	637.569i	−2.17382	−	1.25506i
$509$	571.638	−	330.035i	1.12306	−	0.648399i	0.180880	−	0.983505i	$-0.442105\pi$
$509$	571.638	−	330.035i	1.12306	−	0.648399i	0.942181	+	0.335106i	$0.108772\pi$
$510$	−32.5698	−	91.7418i	−0.0638624	−	0.179886i
$511$	501.477	+	414.562i	0.981363	+	0.811277i
$512$			362.846i			0.708683i
$513$	112.459	−	64.9279i	0.219217	−	0.126565i
$514$	−762.024	−	439.955i	−1.48254	−	0.855943i
$515$	126.354	−	684.790i	0.245347	−	1.32969i
$516$	279.546	−	161.396i	0.541756	−	0.312783i
$517$	−81.7887			−0.158199
$518$	1112.15	+	919.398i	2.14701	+	1.77490i
$519$	432.230			0.832813
$520$	−129.576	+	151.959i	−0.249184	+	0.292228i
$521$	124.918	+	72.1212i	0.239765	+	0.138428i	0.615069	−	0.788473i	$-0.289128\pi$
$521$	124.918	+	72.1212i	0.239765	+	0.138428i	−0.375304	+	0.926902i	$0.622462\pi$
$522$	171.115	+	98.7932i	0.327806	+	0.189259i
$523$	−269.701	−	467.135i	−0.515680	−	0.893184i	−0.999834	−	0.0182017i	$-0.994206\pi$
$523$	−269.701	−	467.135i	−0.515680	−	0.893184i	0.484154	−	0.874983i	$-0.339127\pi$
$524$			2096.63i			4.00121i
$525$	−153.787	+	261.198i	−0.292928	+	0.497520i
$526$	−934.915			−1.77741
$527$	−12.7440	+	7.35773i	−0.0241821	+	0.0139615i
$528$	743.764	−	1288.24i	1.40864	−	2.43984i
$529$	−222.917	+	386.103i	−0.421393	+	0.729874i
$530$	−361.892	−	308.587i	−0.682816	−	0.582239i
$531$			68.1049i			0.128258i
$532$	−1766.69	−	298.178i	−3.32085	−	0.560485i
$533$			49.5468i			0.0929583i
$534$	41.0244	+	71.0564i	0.0768248	+	0.133064i
$535$	449.512	+	82.9414i	0.840209	+	0.155031i
$536$	−535.891	+	928.191i	−0.999797	+	1.73170i
$537$	282.873	+	489.951i	0.526766	+	0.912386i
$538$	905.938			1.68390
$539$	664.246	−	574.173i	1.23237	−	1.06526i
$540$	250.760	−	89.0237i	0.464370	−	0.164859i
$541$	−37.9422	−	65.7178i	−0.0701335	−	0.121475i	0.828826	−	0.559506i	$-0.189009\pi$
$541$	−37.9422	−	65.7178i	−0.0701335	−	0.121475i	−0.898960	+	0.438031i	$0.855676\pi$
$542$	−423.868	+	734.160i	−0.782043	+	1.35454i
$543$	−250.087	−	144.388i	−0.460565	−	0.265907i
$544$	223.536	−	129.059i	0.410912	−	0.237240i
$545$	786.258	−	279.134i	1.44267	−	0.512173i
$546$	76.4989	+	12.9113i	0.140108	+	0.0236471i
$547$			555.937i			1.01634i	0.861257	+	0.508169i	$0.169678\pi$
$547$			555.937i			1.01634i	−0.861257	+	0.508169i	$0.830322\pi$
$548$	−2090.60	+	1207.01i	−3.81497	+	2.20257i
$549$	−156.460	−	90.3325i	−0.284992	−	0.164540i
$550$	1669.31	−	267.122i	3.03511	−	0.485676i
$551$	−377.713	+	218.073i	−0.685504	+	0.395776i
$552$	−372.081			−0.674060
$553$	466.698	−	173.749i	0.843938	−	0.314194i
$554$	−315.775			−0.569991
$555$	306.934	−	359.955i	0.553035	−	0.648567i
$556$	999.548	+	577.089i	1.79775	+	1.03793i
$557$	382.083	+	220.596i	0.685965	+	0.396042i	0.802099	−	0.597191i	$-0.203717\pi$
$557$	382.083	+	220.596i	0.685965	+	0.396042i	−0.116134	+	0.993234i	$0.537050\pi$
$558$	−27.9654	−	48.4375i	−0.0501172	−	0.0868056i
$559$		−	30.8526i		−	0.0551924i
$560$	−1576.02	−	574.692i	−2.81432	−	1.02624i
$561$	92.4467			0.164789
$562$	803.183	−	463.718i	1.42915	−	0.825121i
$563$	−179.900	+	311.597i	−0.319539	+	0.553457i	−0.980392	−	0.197058i	$-0.936861\pi$
$563$	−179.900	+	311.597i	−0.319539	+	0.553457i	0.660853	+	0.750515i	$0.270195\pi$
$564$	40.4859	−	70.1236i	0.0717834	−	0.124333i
$565$	−169.568	+	198.860i	−0.300120	+	0.351964i
$566$		−	2018.84i		−	3.56686i
$567$	−48.5564	−	40.1407i	−0.0856373	−	0.0707949i
$568$			505.307i			0.889626i
$569$	155.199	+	268.812i	0.272757	+	0.472429i	0.969567	−	0.244827i	$-0.0787312\pi$
$569$	155.199	+	268.812i	0.272757	+	0.472429i	−0.696810	+	0.717256i	$0.745398\pi$
$570$	−148.203	+	803.202i	−0.260004	+	1.40913i
$571$	−10.9897	+	19.0347i	−0.0192464	+	0.0333357i	−0.875488	−	0.483240i	$-0.839460\pi$
$571$	−10.9897	+	19.0347i	−0.0192464	+	0.0333357i	0.856242	+	0.516575i	$0.172793\pi$
$572$	−155.584	−	269.480i	−0.272000	−	0.471118i
$573$	88.2130			0.153949
$574$	−723.437	+	269.332i	−1.26034	+	0.469219i
$575$	−143.760	−	176.952i	−0.250018	−	0.307742i
$576$	202.952	+	351.523i	0.352347	+	0.610283i
$577$	−135.110	+	234.018i	−0.234160	+	0.405576i	−0.959028	−	0.283311i	$-0.908567\pi$
$577$	−135.110	+	234.018i	−0.234160	+	0.405576i	0.724868	+	0.688887i	$0.241901\pi$
$578$	−915.526	−	528.579i	−1.58395	−	0.914496i
$579$	70.5332	−	40.7224i	0.121819	−	0.0703322i
$580$	−842.222	+	299.003i	−1.45211	+	0.515522i
$581$	12.0914	−	71.6407i	0.0208113	−	0.123306i
$582$		−	831.747i		−	1.42912i
$583$	391.126	−	225.817i	0.670885	−	0.387336i
$584$	1896.19	+	1094.76i	3.24690	+	1.87460i
$585$	4.61491	−	25.0111i	0.00788873	−	0.0427540i
$586$	590.502	−	340.926i	1.00768	−	0.581786i
$587$	−680.487			−1.15926			−0.579632	−	0.814879i	$-0.696804\pi$
$587$	−680.487			−1.15926			−0.579632	+	0.814879i	$0.696804\pi$
$588$	163.476	+	853.727i	0.278020	+	1.45192i
$589$	123.460			0.209609
$590$	−325.951	−	277.940i	−0.552460	−	0.471084i
$591$	99.1267	+	57.2308i	0.167727	+	0.0968373i
$592$	2267.30	+	1309.03i	3.82990	+	2.21119i
$593$	112.498	+	194.852i	0.189709	+	0.328586i	0.945153	−	0.326627i	$-0.105912\pi$
$593$	112.498	+	194.852i	0.189709	+	0.328586i	−0.755444	+	0.655213i	$0.772579\pi$
$594$			351.373i			0.591537i
$595$	−18.0422	−	102.682i	−0.0303231	−	0.172574i
$596$	1782.63			2.99100
$597$	113.313	−	65.4215i	0.189805	−	0.109584i
$598$	−29.1769	+	50.5359i	−0.0487908	+	0.0845082i
$599$	108.428	−	187.804i	0.181016	−	0.313529i	−0.761211	−	0.648504i	$-0.775395\pi$
$599$	108.428	−	187.804i	0.181016	−	0.313529i	0.942227	+	0.334976i	$0.108728\pi$
$600$	−364.020	+	952.842i	−0.606700	+	1.58807i
$601$		−	589.460i		−	0.980798i	−0.871498	−	0.490399i	$-0.836851\pi$
$601$		−	589.460i		−	0.980798i	0.871498	−	0.490399i	$-0.163149\pi$
$602$	450.481	−	167.712i	0.748307	−	0.278591i
$603$		−	136.497i		−	0.226364i
$604$	−538.115	−	932.042i	−0.890919	−	1.54312i
$605$	−181.518	+	983.762i	−0.300030	+	1.62605i
$606$	−418.418	+	724.722i	−0.690459	+	1.19591i
$607$	−402.095	−	696.449i	−0.662430	−	1.14736i	−0.979975	−	0.199119i	$-0.936192\pi$
$607$	−402.095	−	696.449i	−0.662430	−	1.14736i	0.317545	−	0.948243i	$-0.397141\pi$
$608$	−2165.55			−3.56176
$609$	163.086	+	134.820i	0.267792	+	0.221379i
$610$	1070.86	−	380.171i	1.75550	−	0.623231i
$611$	−3.86965	−	6.70244i	−0.00633331	−	0.0109696i
$612$	−45.7616	+	79.2615i	−0.0747739	+	0.129512i
$613$	187.455	+	108.227i	0.305799	+	0.176553i	0.645045	−	0.764144i	$-0.276839\pi$
$613$	187.455	+	108.227i	0.305799	+	0.176553i	−0.339246	+	0.940698i	$0.610172\pi$
$614$	−1195.00	+	689.932i	−1.94625	+	1.12367i
$615$	84.6656	+	238.484i	0.137668	+	0.387778i
$616$	1882.56	−	2277.24i	3.05610	−	3.69682i
$617$		−	519.617i		−	0.842167i	−0.907022	−	0.421084i	$-0.861650\pi$
$617$		−	519.617i		−	0.842167i	0.907022	−	0.421084i	$-0.138350\pi$
$618$	−788.375	+	455.168i	−1.27569	+	0.736518i
$619$	145.355	+	83.9210i	0.234823	+	0.135575i	0.612795	−	0.790242i	$-0.290045\pi$
$619$	145.355	+	83.9210i	0.234823	+	0.135575i	−0.377972	+	0.925817i	$0.623378\pi$
$620$	248.787	+	45.9048i	0.401269	+	0.0740400i
$621$	41.0380	−	23.6933i	0.0660837	−	0.0381535i
$622$	−1775.79			−2.85497
$623$	30.6568	+	82.3454i	0.0492083	+	0.132176i
$624$	140.758			0.225574
$625$	−593.791	+	195.030i	−0.950066	+	0.312048i
$626$	632.664	+	365.269i	1.01065	+	0.583497i
$627$	−671.697	−	387.804i	−1.07129	−	0.618508i
$628$	−9.16953	−	15.8821i	−0.0146012	−	0.0252900i
$629$			162.706i			0.258675i
$630$	390.275	−	68.5753i	0.619484	−	0.108850i
$631$	−17.7243			−0.0280892			−0.0140446	−	0.999901i	$-0.504471\pi$
$631$	−17.7243			−0.0280892			−0.0140446	+	0.999901i	$0.504471\pi$
$632$	1451.30	−	837.910i	2.29636	−	1.32581i
$633$	266.202	−	461.076i	0.420541	−	0.728398i
$634$	−924.087	+	1600.57i	−1.45755	+	2.52455i
$635$	−403.910	+	473.682i	−0.636078	+	0.745956i
$636$			447.122i			0.703023i
$637$	78.4798	+	27.2680i	0.123202	+	0.0428070i
$638$		−	1180.15i		−	1.84977i
$639$	−32.1769	−	55.7319i	−0.0503550	−	0.0872174i
$640$	−806.342	−	148.782i	−1.25991	−	0.232472i
$641$	307.545	−	532.683i	0.479789	−	0.831019i	−0.519942	−	0.854202i	$-0.674046\pi$
$641$	307.545	−	532.683i	0.479789	−	0.831019i	0.999731	+	0.0231821i	$0.00737976\pi$
$642$	−298.783	−	517.507i	−0.465394	−	0.806086i
$643$	−1083.57			−1.68517			−0.842586	−	0.538562i	$-0.818968\pi$
$643$	−1083.57			−1.68517			−0.842586	+	0.538562i	$0.818968\pi$
$644$	−644.695	−	108.810i	−1.00108	−	0.168960i
$645$	−52.7208	−	148.503i	−0.0817377	−	0.230237i
$646$	−140.463	−	243.289i	−0.217435	−	0.376609i
$647$	46.2650	−	80.1333i	0.0715069	−	0.123854i	−0.828055	−	0.560647i	$-0.810553\pi$
$647$	46.2650	−	80.1333i	0.0715069	−	0.123854i	0.899562	+	0.436793i	$0.143886\pi$
$648$	−183.602	−	106.002i	−0.283336	−	0.163584i
$649$	352.282	−	203.390i	0.542807	−	0.313390i
$650$	100.870	+	124.159i	0.155184	+	0.191013i
$651$	−20.8980	−	56.1329i	−0.0321014	−	0.0862257i
$652$		−	748.134i		−	1.14744i
$653$	443.835	−	256.248i	0.679686	−	0.392417i	−0.120051	−	0.992768i	$-0.538306\pi$
$653$	443.835	−	256.248i	0.679686	−	0.392417i	0.799737	+	0.600351i	$0.204972\pi$
$654$	−944.598	−	545.364i	−1.44434	−	0.833889i
$655$	1006.56	+	185.725i	1.53674	+	0.283550i
$656$	−1212.93	+	700.288i	−1.84898	+	1.06751i
$657$	−278.849			−0.424427
$658$	76.8278	−	92.9349i	0.116760	−	0.141239i
$659$	52.4627			0.0796095			0.0398048	−	0.999207i	$-0.487326\pi$
$659$	52.4627			0.0796095			0.0398048	+	0.999207i	$0.487326\pi$
$660$	−1209.36	−	1031.23i	−1.83236	−	1.56246i
$661$	−384.344	−	221.901i	−0.581459	−	0.335705i	0.180254	−	0.983620i	$-0.442308\pi$
$661$	−384.344	−	221.901i	−0.581459	−	0.335705i	−0.761713	+	0.647915i	$0.775641\pi$
$662$	1224.75	+	707.110i	1.85008	+	1.06814i
$663$	4.37391	+	7.57584i	0.00659715	+	0.0114266i
$664$		−	244.492i		−	0.368211i
$665$	−299.649	+	821.749i	−0.450600	+	1.23571i
$666$	−618.418			−0.928555
$667$	−137.834	+	79.5783i	−0.206647	+	0.119308i
$668$	1635.84	−	2833.36i	2.44887	−	4.24156i
$669$	−5.22161	+	9.04410i	−0.00780510	+	0.0135188i
$670$	653.279	+	557.053i	0.975043	+	0.831422i
$671$			1079.08i			1.60817i
$672$	366.562	+	984.603i	0.545480	+	1.46518i
$673$			1281.06i			1.90351i	0.306863	+	0.951754i	$0.400721\pi$
$673$			1281.06i			1.90351i	−0.306863	+	0.951754i	$0.599279\pi$
$674$	−969.011	−	1678.38i	−1.43770	−	2.49017i
$675$	−20.5260	−	128.272i	−0.0304089	−	0.190032i
$676$	−850.721	+	1473.49i	−1.25846	+	2.17972i
$677$	151.137	+	261.777i	0.223245	+	0.386672i	0.955792	−	0.294045i	$-0.0950016\pi$
$677$	151.137	+	261.777i	0.223245	+	0.386672i	−0.732546	+	0.680717i	$0.761668\pi$
$678$	341.649			0.503907
$679$	148.238	−	878.305i	0.218319	−	1.29353i
$680$	−117.374	−	330.617i	−0.172609	−	0.486202i
$681$	−27.7656	−	48.0914i	−0.0407718	−	0.0706188i
$682$	−167.033	+	289.310i	−0.244916	+	0.424208i
$683$	288.405	+	166.511i	0.422262	+	0.243793i	0.696045	−	0.717999i	$-0.254942\pi$
$683$	288.405	+	166.511i	0.422262	+	0.243793i	−0.273783	+	0.961792i	$0.588275\pi$
$684$	664.988	−	383.931i	0.972204	−	0.561302i
$685$	394.276	+	1110.59i	0.575586	+	1.62130i
$686$	28.4660	+	1294.12i	0.0414956	+	1.88647i
$687$			34.0899i			0.0496214i
$688$	755.288	−	436.066i	1.09780	−	0.633817i
$689$	37.0106	+	21.3681i	0.0537164	+	0.0310132i
$690$	−54.0816	+	293.102i	−0.0783791	+	0.424786i
$691$	−895.692	+	517.128i	−1.29623	+	0.748377i	−0.979750	−	0.200224i	$-0.935833\pi$
$691$	−895.692	+	517.128i	−1.29623	+	0.748377i	−0.316476	+	0.948601i	$0.602500\pi$
$692$	2555.85			3.69343
$693$	−62.6235	+	371.041i	−0.0903658	+	0.535413i
$694$	1505.22			2.16891
$695$	365.595	−	428.748i	0.526036	−	0.616904i
$696$	616.660	+	356.029i	0.886006	+	0.511536i
$697$	−75.3812	−	43.5214i	−0.108151	−	0.0624410i
$698$	−1233.26	−	2136.06i	−1.76684	−	3.06026i
$699$			257.052i			0.367742i
$700$	−909.373	+	1544.51i	−1.29910	+	2.20644i
$701$	−1080.76			−1.54174			−0.770871	−	0.636992i	$-0.780178\pi$
$701$	−1080.76			−1.54174			−0.770871	+	0.636992i	$0.780178\pi$
$702$	−28.7944	+	16.6245i	−0.0410177	+	0.0236816i
$703$	682.537	−	1182.19i	0.970891	−	1.68163i
$704$	1212.20	−	2099.59i	1.72188	−	2.98238i
$705$	−30.0789	−	25.6484i	−0.0426652	−	0.0363807i
$706$		−	400.849i		−	0.567775i
$707$	−571.003	+	690.716i	−0.807642	+	0.976967i
$708$			402.717i			0.568809i
$709$	369.689	+	640.320i	0.521423	+	0.903132i	0.999690	+	0.0249167i	$0.00793205\pi$
$709$	369.689	+	640.320i	0.521423	+	0.903132i	−0.478266	+	0.878215i	$0.658735\pi$
$710$	398.049	+	73.4459i	0.560633	+	0.103445i
$711$	−106.712	+	184.831i	−0.150088	+	0.259960i
$712$	147.843	+	256.072i	0.207645	+	0.359651i
$713$	45.0525			0.0631873
$714$	−86.8393	+	105.045i	−0.121624	+	0.147122i
$715$	−143.155	+	50.8224i	−0.200217	+	0.0710803i
$716$	1672.68	+	2897.17i	2.33615	+	4.04633i
$717$	−180.527	+	312.683i	−0.251782	+	0.436098i
$718$	−1127.71	−	651.086i	−1.57063	−	0.906805i
$719$	−835.053	+	482.118i	−1.16141	+	0.670540i	−0.951641	−	0.307212i	$-0.900604\pi$
$719$	−835.053	+	482.118i	−1.16141	+	0.670540i	−0.209767	+	0.977751i	$0.567271\pi$
$720$	677.512	−	240.528i	0.940990	−	0.334066i
$721$	−913.627	+	340.138i	−1.26717	+	0.471759i
$722$			994.556i			1.37750i
$723$	65.0671	−	37.5665i	0.0899960	−	0.0519592i
$724$	−1478.81	−	853.790i	−2.04255	−	1.17927i
$725$	68.9403	+	430.825i	0.0950901	+	0.594241i
$726$	1132.57	−	653.890i	1.56002	−	0.900675i
$727$	−894.210			−1.23000			−0.615000	−	0.788527i	$-0.710844\pi$
$727$	−894.210			−1.23000			−0.615000	+	0.788527i	$0.710844\pi$
$728$	275.685	+	46.5295i	0.378688	+	0.0639142i
$729$	27.0000			0.0370370
$730$	1137.99	−	1334.57i	1.55890	−	1.82818i
$731$	46.9395	+	27.1006i	0.0642128	+	0.0370733i
$732$	−925.179	−	534.152i	−1.26391	−	0.729716i
$733$	125.107	+	216.692i	0.170678	+	0.295624i	0.938657	−	0.344852i	$-0.112071\pi$
$733$	125.107	+	216.692i	0.170678	+	0.295624i	−0.767979	+	0.640475i	$0.778737\pi$
$734$		−	1035.73i		−	1.41107i
$735$	424.343	−	2.85696i	0.577337	−	0.00388702i
$736$	−790.246			−1.07370
$737$	−706.051	+	407.639i	−0.958007	+	0.553105i
$738$	165.417	−	286.511i	0.224142	−	0.388226i
$739$	170.753	−	295.754i	0.231060	−	0.400208i	−0.727060	−	0.686574i	$-0.759114\pi$
$739$	170.753	−	295.754i	0.231060	−	0.400208i	0.958120	+	0.286366i	$0.0924472\pi$
$740$	1814.96	−	2128.48i	2.45265	−	2.87632i
$741$		−	73.3925i		−	0.0990452i
$742$	−110.811	+	656.549i	−0.149341	+	0.884837i
$743$			1076.61i			1.44900i	0.689274	+	0.724501i	$0.257930\pi$
$743$			1076.61i			1.44900i	−0.689274	+	0.724501i	$0.742070\pi$
$744$	−100.781	−	174.558i	−0.135459	−	0.234621i
$745$	157.911	−	855.817i	0.211961	−	1.14875i
$746$	858.989	−	1487.81i	1.15146	−	1.99439i
$747$	15.5687	+	26.9658i	0.0208416	+	0.0360988i
$748$	546.654			0.730821
$749$	−223.275	−	599.726i	−0.298097	−	0.800702i
$750$	697.679	+	425.246i	0.930239	+	0.566995i
$751$	164.065	+	284.168i	0.218462	+	0.378387i	0.954338	−	0.298729i	$-0.0965628\pi$
$751$	164.065	+	284.168i	0.218462	+	0.378387i	−0.735876	+	0.677116i	$0.763229\pi$
$752$	109.386	−	189.463i	0.145461	−	0.251945i
$753$	56.6906	+	32.7303i	0.0752863	+	0.0434666i
$754$	96.7113	−	55.8363i	0.128264	−	0.0740535i
$755$	−495.127	+	175.778i	−0.655798	+	0.232819i
$756$	−287.123	−	237.359i	−0.379792	−	0.313968i
$757$		−	560.744i		−	0.740745i	−0.928883	−	0.370372i	$-0.879230\pi$
$757$		−	560.744i		−	0.740745i	0.928883	−	0.370372i	$-0.120770\pi$
$758$	−1993.56	+	1150.98i	−2.63002	+	1.51844i
$759$	−245.114	−	141.516i	−0.322943	−	0.186451i
$760$	−534.089	+	2894.57i	−0.702749	+	3.80864i
$761$	720.386	−	415.915i	0.946631	−	0.546537i	0.0545979	−	0.998508i	$-0.482612\pi$
$761$	720.386	−	415.915i	0.946631	−	0.546537i	0.892033	+	0.451971i	$0.149279\pi$
$762$	813.806			1.06799
$763$	−900.274	−	744.242i	−1.17991	−	0.975415i
$764$	521.620			0.682748
$765$	33.9986	+	28.9907i	0.0444426	+	0.0378963i
$766$	1831.20	+	1057.25i	2.39061	+	1.38022i
$767$	33.3349	+	19.2459i	0.0434614	+	0.0250925i
$768$	67.2646	+	116.506i	0.0875842	+	0.151700i
$769$		−	715.384i		−	0.930278i	−0.885238	−	0.465139i	$-0.846004\pi$
$769$		−	715.384i		−	0.930278i	0.885238	−	0.465139i	$-0.153996\pi$
$770$	−1520.24	−	1813.96i	−1.97434	−	2.35579i
$771$	403.845			0.523793
$772$	417.076	−	240.799i	0.540254	−	0.311916i
$773$	138.579	−	240.027i	0.179275	−	0.310513i	−0.762358	−	0.647156i	$-0.775958\pi$
$773$	138.579	−	240.027i	0.179275	−	0.310513i	0.941632	+	0.336643i	$0.109292\pi$
$774$	−103.004	+	178.409i	−0.133081	+	0.230502i
$775$	44.0764	−	115.373i	0.0568728	−	0.148868i
$776$		−	2997.44i		−	3.86267i
$777$	−653.034	−	110.218i	−0.840455	−	0.141850i
$778$		−	1199.68i		−	1.54200i
$779$	365.136	+	632.433i	0.468723	+	0.811853i
$780$	27.2888	−	147.895i	0.0349856	−	0.189609i
$781$	−192.187	+	332.878i	−0.246078	+	0.426220i
$782$	−51.2574	−	88.7804i	−0.0655465	−	0.113530i
$783$	−90.6845			−0.115817
$784$	441.686	+	2306.63i	0.563375	+	2.94214i
$785$	−8.43702	+	2.99528i	−0.0107478	+	0.00381564i
$786$	−669.046	−	1158.82i	−0.851203	−	1.47433i
$787$	−451.159	+	781.431i	−0.573265	+	0.992923i	0.422963	+	0.906147i	$0.360990\pi$
$787$	−451.159	+	781.431i	−0.573265	+	0.992923i	−0.996228	+	0.0867766i	$0.972343\pi$
$788$	586.154	+	338.416i	0.743850	+	0.429462i
$789$	371.603	−	214.545i	0.470980	−	0.271920i
$790$	−449.107	−	1265.03i	−0.568490	−	1.60131i
$791$	360.773	+	60.8905i	0.456098	+	0.0769791i
$792$			1266.27i			1.59883i
$793$	−88.4289	+	51.0545i	−0.111512	+	0.0643814i
$794$	1114.38	+	643.390i	1.40351	+	0.810314i
$795$	214.657	+	39.6073i	0.270009	+	0.0498205i
$796$	670.043	−	386.849i	0.841762	−	0.485992i
$797$	159.124			0.199654			0.0998271	−	0.995005i	$-0.468171\pi$
$797$	159.124			0.199654			0.0998271	+	0.995005i	$0.468171\pi$
$798$	1071.61	−	398.955i	1.34287	−	0.499943i
$799$	13.5963			0.0170166
$800$	−773.125	+	2023.70i	−0.966406	+	2.52962i
$801$	−32.6122	−	18.8286i	−0.0407143	−	0.0235064i
$802$	−639.071	−	368.968i	−0.796846	−	0.460060i
$803$	832.759	+	1442.38i	1.03706	+	1.79624i
$804$		−	807.134i		−	1.00390i
$805$	−109.347	+	299.870i	−0.135835	+	0.372509i
$806$	−31.6112			−0.0392199
$807$	−360.085	+	207.895i	−0.446202	+	0.257615i
$808$	−1507.89	+	2611.74i	−1.86620	+	3.23235i
$809$	−196.547	+	340.430i	−0.242951	+	0.420803i	−0.961553	−	0.274618i	$-0.911449\pi$
$809$	−196.547	+	340.430i	−0.242951	+	0.420803i	0.718603	+	0.695421i	$0.244782\pi$
$810$	−110.188	+	129.222i	−0.136035	+	0.159534i
$811$			845.797i			1.04291i	0.853280	+	0.521453i	$0.174610\pi$
$811$			845.797i			1.04291i	−0.853280	+	0.521453i	$0.825390\pi$
$812$	964.355	+	797.216i	1.18763	+	0.981793i
$813$		−	389.078i		−	0.478570i
$814$	1846.86	+	3198.85i	2.26886	+	3.92979i
$815$	−359.168	−	66.2717i	−0.440697	−	0.0813150i
$816$	−123.641	+	214.152i	−0.151520	+	0.262441i
$817$	−227.368	−	393.813i	−0.278296	−	0.482024i
$818$	2010.76			2.45815
$819$	−33.3691	+	12.4231i	−0.0407437	+	0.0151687i
$820$	500.643	+	1410.20i	0.610540	+	1.71975i
$821$	38.0478	+	65.9008i	0.0463433	+	0.0802689i	0.888267	−	0.459328i	$-0.151910\pi$
$821$	38.0478	+	65.9008i	0.0463433	+	0.0802689i	−0.841923	+	0.539597i	$0.818577\pi$
$822$	770.325	−	1334.24i	0.937135	−	1.62317i
$823$	220.424	+	127.262i	0.267829	+	0.154631i	0.627901	−	0.778293i	$-0.283914\pi$
$823$	220.424	+	127.262i	0.267829	+	0.154631i	−0.360071	+	0.932925i	$0.617248\pi$
$824$	−2841.13	+	1640.33i	−3.44797	+	1.99069i
$825$	−602.204	+	489.247i	−0.729945	+	0.593027i
$826$	−99.8058	+	591.345i	−0.120830	+	0.715914i
$827$		−	61.6368i		−	0.0745306i	−0.999305	−	0.0372653i	$-0.988135\pi$
$827$		−	61.6368i		−	0.0745306i	0.999305	−	0.0372653i	$-0.0118647\pi$
$828$	242.665	−	140.103i	0.293074	−	0.169206i
$829$	−1229.02	−	709.573i	−1.48253	−	0.855938i	−0.482725	−	0.875772i	$-0.660353\pi$
$829$	−1229.02	−	709.573i	−1.48253	−	0.855938i	−0.999803	+	0.0198337i	$0.993686\pi$
$830$	−192.595	−	35.5366i	−0.232042	−	0.0428152i
$831$	125.512	−	72.4643i	0.151037	−	0.0872013i
$832$	229.410			0.275734
$833$	−110.422	+	95.4484i	−0.132559	+	0.114584i
$834$	−736.608			−0.883223
$835$	−1215.35	−	1036.33i	−1.45551	−	1.24112i
$836$	−3971.87	−	2293.16i	−4.75104	−	2.74301i
$837$	22.2309	+	12.8350i	0.0265603	+	0.0153346i
$838$	417.862	+	723.757i	0.498642	+	0.863672i
$839$			207.296i			0.247075i	0.992340	+	0.123538i	$0.0394239\pi$
$839$			207.296i			0.247075i	−0.992340	+	0.123538i	$0.960576\pi$
$840$	1406.47	−	247.130i	1.67436	−	0.294203i
$841$	−536.419			−0.637835
$842$	−238.850	+	137.900i	−0.283670	+	0.163777i
$843$	−212.829	+	368.630i	−0.252466	+	0.437283i
$844$	1574.10	−	2726.42i	1.86505	−	3.23036i
$845$	632.042	+	538.944i	0.747979	+	0.637804i
$846$			51.6769i			0.0610838i
$847$	1312.51	−	488.639i	1.54960	−	0.576906i
$848$			1208.05i			1.42459i
$849$	463.285	+	802.433i	0.545683	+	0.945151i
$850$	−277.500	+	44.4053i	−0.326470	+	0.0522415i
$851$	249.069	−	431.400i	0.292678	−	0.506933i
$852$	−190.268	−	329.553i	−0.223319	−	0.386799i
$853$	957.163			1.12211			0.561057	−	0.827777i	$-0.310395\pi$
$853$	957.163			1.12211			0.561057	+	0.827777i	$0.310395\pi$
$854$	−1226.14	−	1013.63i	−1.43576	−	1.18692i
$855$	−125.413	−	353.260i	−0.146682	−	0.413170i
$856$	−1076.75	−	1864.98i	−1.25788	−	2.17872i
$857$	346.658	−	600.429i	0.404502	−	0.700617i	−0.589762	−	0.807577i	$-0.700778\pi$
$857$	346.658	−	600.429i	0.404502	−	0.700617i	0.994263	+	0.106960i	$0.0341117\pi$
$858$	171.984	+	99.2953i	0.200448	+	0.115729i
$859$	186.112	−	107.452i	0.216661	−	0.125089i	−0.387742	−	0.921768i	$-0.626745\pi$
$859$	186.112	−	107.452i	0.216661	−	0.125089i	0.604403	+	0.796679i	$0.293412\pi$
$860$	−311.748	−	878.123i	−0.362498	−	1.02107i
$861$	225.740	−	273.067i	0.262183	−	0.317151i
$862$		−	2160.91i		−	2.50685i
$863$	576.004	−	332.556i	0.667444	−	0.385349i	−0.127663	−	0.991818i	$-0.540748\pi$
$863$	576.004	−	332.556i	0.667444	−	0.385349i	0.795107	+	0.606469i	$0.207414\pi$
$864$	−389.943	−	225.134i	−0.451323	−	0.260571i
$865$	226.404	−	1227.03i	0.261739	−	1.41853i
$866$	−711.384	+	410.718i	−0.821459	+	0.474270i
$867$	485.195			0.559625
$868$	−123.574	−	331.924i	−0.142366	−	0.382401i
$869$	1274.75			1.46692
$870$	370.088	−	434.018i	0.425388	−	0.498871i
$871$	−66.8105	−	38.5731i	−0.0767056	−	0.0442860i
$872$	−3404.12	−	1965.37i	−3.90381	−	2.25387i
$873$	190.870	+	330.597i	0.218637	+	0.378690i
$874$			860.078i			0.984071i
$875$	660.942	+	573.394i	0.755363	+	0.655307i
$876$	−1648.88			−1.88229
$877$	−749.080	+	432.482i	−0.854139	+	0.493138i	−0.862045	−	0.506831i	$-0.830817\pi$
$877$	−749.080	+	432.482i	−0.854139	+	0.493138i	0.00790604	+	0.999969i	$0.497483\pi$
$878$	−1381.82	+	2393.38i	−1.57383	+	2.72595i
$879$	−156.472	+	271.018i	−0.178012	+	0.308325i
$880$	−3267.50	−	2786.21i	−3.71307	−	3.16614i
$881$		−	203.509i		−	0.230998i	−0.993308	−	0.115499i	$-0.963153\pi$
$881$		−	203.509i		−	0.230998i	0.993308	−	0.115499i	$-0.0368466\pi$
$882$	−362.782	−	419.694i	−0.411318	−	0.475843i
$883$			217.585i			0.246416i	0.992381	+	0.123208i	$0.0393182\pi$
$883$			217.585i			0.246416i	−0.992381	+	0.123208i	$0.960682\pi$
$884$	25.8637	+	44.7973i	0.0292576	+	0.0506757i
$885$	193.338	+	35.6738i	0.218462	+	0.0403093i
$886$	−745.197	+	1290.72i	−0.841080	+	1.45679i
$887$	224.944	+	389.615i	0.253601	+	0.439250i	0.964515	−	0.264029i	$-0.0850516\pi$
$887$	224.944	+	389.615i	0.253601	+	0.439250i	−0.710914	+	0.703279i	$0.751718\pi$
$888$	−2228.64			−2.50973
$889$	859.359	+	145.041i	0.966658	+	0.163150i
$890$	223.206	−	79.2417i	0.250793	−	0.0890356i
$891$	−80.6334	−	139.661i	−0.0904976	−	0.156746i
$892$	−30.8764	+	53.4794i	−0.0346147	+	0.0599545i
$893$	−98.7873	−	57.0349i	−0.110624	−	0.0638689i
$894$	−985.272	+	568.847i	−1.10209	+	0.636294i
$895$	1539.06	−	546.391i	1.71962	−	0.610492i
$896$	400.514	+	1075.80i	0.447002	+	1.20067i
$897$		−	26.7822i		−	0.0298575i
$898$	−1551.07	+	895.509i	−1.72725	+	0.997226i
$899$	−74.6668	−	43.1089i	−0.0830553	−	0.0479520i
$900$	−121.374	−	758.495i	−0.134860	−	0.842772i
$901$	−65.0194	+	37.5390i	−0.0721636	+	0.0416637i
$902$	−1976.02			−2.19071
$903$	−140.567	+	170.037i	−0.155667	+	0.188303i
$904$	1231.23			1.36198
$905$	−540.889	+	634.323i	−0.597667	+	0.700909i
$906$	594.838	+	343.430i	0.656554	+	0.379062i
$907$	−215.251	−	124.275i	−0.237322	−	0.137018i	0.376623	−	0.926366i	$-0.377085\pi$
$907$	−215.251	−	124.275i	−0.237322	−	0.137018i	−0.613945	+	0.789349i	$0.710418\pi$
$908$	−164.183	−	284.373i	−0.180818	−	0.313186i
$909$		−	384.076i		−	0.422525i
$910$	76.7236	−	210.404i	0.0843116	−	0.231214i
$911$	1261.28			1.38450			0.692248	−	0.721660i	$-0.256621\pi$
$911$	1261.28			1.38450			0.692248	+	0.721660i	$0.256621\pi$
$912$	1796.69	−	1037.32i	1.97006	−	1.13741i
$913$	92.9894	−	161.062i	0.101850	−	0.176410i
$914$	−775.909	+	1343.91i	−0.848916	+	1.47037i
$915$	−338.393	+	396.848i	−0.369829	+	0.433714i
$916$			201.580i			0.220065i
$917$	−499.965	−	1342.93i	−0.545218	−	1.46448i
$918$		−	58.4110i		−	0.0636285i
$919$	−280.644	−	486.090i	−0.305380	−	0.528934i	0.671966	−	0.740582i	$-0.265450\pi$
$919$	−280.644	−	486.090i	−0.305380	−	0.528934i	−0.977346	+	0.211648i	$0.932117\pi$
$920$	−194.898	+	1056.28i	−0.211846	+	1.14813i
$921$	316.652	−	548.458i	0.343813	−	0.595502i
$922$	1416.05	+	2452.67i	1.53584	+	2.66016i
$923$	−36.3717			−0.0394059
$924$	−370.304	+	2194.04i	−0.400762	+	2.37450i
$925$	−861.077	−	1059.88i	−0.930894	−	1.14582i
$926$	−812.587	−	1407.44i	−0.877524	−	1.51992i
$927$	208.905	−	361.834i	0.225356	−	0.390328i
$928$	1309.70	+	756.153i	1.41131	+	0.814820i
$929$	−617.428	+	356.472i	−0.664616	+	0.383716i	−0.794033	−	0.607874i	$-0.792022\pi$
$929$	−617.428	+	356.472i	−0.664616	+	0.383716i	0.129418	+	0.991590i	$0.458689\pi$
$930$	−152.154	+	54.0172i	−0.163607	+	0.0580830i
$931$	1202.70	−	230.299i	1.29183	−	0.247367i
$932$			1519.99i			1.63090i
$933$	705.828	−	407.510i	0.756515	−	0.436774i
$934$	1960.93	+	1132.14i	2.09950	+	1.21215i
$935$	48.4241	−	262.440i	0.0517905	−	0.280685i
$936$	−103.769	+	59.9109i	−0.110864	+	0.0640074i
$937$	560.643			0.598339			0.299169	−	0.954200i	$-0.403290\pi$
$937$	560.643			0.598339			0.299169	+	0.954200i	$0.403290\pi$
$938$	200.033	−	1185.19i	0.213255	−	1.26352i
$939$	−335.289			−0.357070
$940$	−177.862	−	151.664i	−0.189215	−	0.161344i
$941$	−627.646	−	362.372i	−0.666999	−	0.385092i	0.127939	−	0.991782i	$-0.459164\pi$
$941$	−627.646	−	362.372i	−0.666999	−	0.385092i	−0.794939	+	0.606690i	$0.792497\pi$
$942$	10.1361	+	5.85208i	0.0107602	+	0.00621240i
$943$	133.244	+	230.786i	0.141298	+	0.244736i
$944$			1088.08i			1.15262i
$945$	−139.387	+	116.817i	−0.147499	+	0.123616i
$946$	1230.46			1.30070
$947$	−781.569	+	451.239i	−0.825311	+	0.476493i	−0.852244	−	0.523144i	$-0.824759\pi$
$947$	−781.569	+	451.239i	−0.825311	+	0.476493i	0.0269338	+	0.999637i	$0.491426\pi$
$948$	−631.010	+	1092.94i	−0.665622	+	1.15289i
$949$	−78.8004	+	136.486i	−0.0830352	+	0.143821i
$950$	2202.53	+	841.444i	2.31845	+	0.885730i
$951$		−	848.240i		−	0.891946i
$952$	−312.950	+	378.561i	−0.328729	+	0.397648i
$953$			182.310i			0.191301i	0.995415	+	0.0956506i	$0.0304931\pi$
$953$			182.310i			0.191301i	−0.995415	+	0.0956506i	$0.969507\pi$
$954$	−142.679	−	247.127i	−0.149559	−	0.259043i
$955$	46.2065	−	250.422i	0.0483837	−	0.262222i
$956$	−1067.49	+	1848.95i	−1.11662	+	1.93405i
$957$	270.822	+	469.078i	0.282991	+	0.490154i
$958$	2522.57			2.63317
$959$	1051.24	−	1271.64i	1.09618	−	1.32600i
$960$	1104.22	−	392.017i	1.15023	−	0.408351i
$961$	−468.297	−	811.114i	−0.487302	−	0.844032i
$962$	−174.760	+	302.693i	−0.181663	+	0.314650i
$963$	237.516	+	137.130i	0.246642	+	0.142399i
$964$	384.754	−	222.138i	0.399122	−	0.230433i
$965$	−78.6582	−	221.562i	−0.0815111	−	0.229598i
$966$	391.048	−	145.585i	0.404812	−	0.150709i
$967$			513.340i			0.530859i	0.964130	+	0.265429i	$0.0855137\pi$
$967$			513.340i			0.530859i	−0.964130	+	0.265429i	$0.914486\pi$
$968$	4081.54	−	2356.48i	4.21647	−	2.43438i
$969$	111.660	+	64.4672i	0.115233	+	0.0665296i
$970$	−2361.19	−	435.674i	−2.43422	−	0.449148i
$971$	−475.145	+	274.325i	−0.489335	+	0.282518i	−0.724299	−	0.689486i	$-0.757836\pi$
$971$	−475.145	+	274.325i	−0.489335	+	0.282518i	0.234963	+	0.972004i	$0.424503\pi$
$972$	159.656			0.164255
$973$	−777.840	−	131.282i	−0.799424	−	0.134925i
$974$	−453.889			−0.466005
$975$	−68.5849	−	26.2019i	−0.0703435	−	0.0268737i
$976$	−2499.69	−	1443.19i	−2.56115	−	1.47868i
$977$	−268.436	−	154.981i	−0.274755	−	0.158630i	0.356291	−	0.934375i	$-0.384041\pi$
$977$	−268.436	−	154.981i	−0.274755	−	0.158630i	−0.631047	+	0.775745i	$0.717374\pi$
$978$	238.733	+	413.498i	0.244103	+	0.422799i
$979$			224.921i			0.229746i
$980$	2509.22	−	16.8937i	2.56042	−	0.0172385i
$981$	500.602			0.510297
$982$	2448.06	−	1413.39i	2.49293	−	1.43930i
$983$	548.091	−	949.321i	0.557569	−	0.965738i	−0.440129	−	0.897934i	$-0.645067\pi$
$983$	548.091	−	949.321i	0.557569	−	0.965738i	0.997699	−	0.0678040i	$-0.0215993\pi$
$984$	596.126	−	1032.52i	0.605820	−	1.04931i
$985$	214.392	−	251.426i	0.217657	−	0.255255i
$986$			196.184i			0.198970i
$987$	−9.21012	+	54.5696i	−0.00933143	+	0.0552883i
$988$		−	433.983i		−	0.439254i
$989$	−82.9705	−	143.709i	−0.0838933	−	0.145307i
$990$	997.489	+	184.051i	1.00756	+	0.185910i
$991$	−115.239	+	199.599i	−0.116285	+	0.201412i	−0.918293	−	0.395902i	$-0.870432\pi$
$991$	−115.239	+	199.599i	−0.116285	+	0.201412i	0.802008	+	0.597314i	$0.203765\pi$
$992$	−214.044	−	370.736i	−0.215771	−	0.373726i
$993$	−649.073			−0.653648
$994$	−197.713	−	531.066i	−0.198907	−	0.534272i
$995$	−126.366	−	355.946i	−0.127001	−	0.357734i
$996$	92.0605	+	159.454i	0.0924302	+	0.160094i
$997$	−384.991	+	666.823i	−0.386149	+	0.668830i	−0.991928	−	0.126803i	$-0.959528\pi$
$997$	−384.991	+	666.823i	−0.386149	+	0.668830i	0.605779	+	0.795633i	$0.292862\pi$
$998$	1393.97	+	804.811i	1.39677	+	0.806424i
$999$	245.804	−	141.915i	0.246050	−	0.142057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.r.a.94.1	yes	32
3.2	odd	2		315.3.bi.e.199.16		32
5.2	odd	4		525.3.o.p.451.1		16
5.3	odd	4		525.3.o.q.451.8		16
5.4	even	2	inner	105.3.r.a.94.16	yes	32
7.3	odd	6		735.3.e.a.244.19		32
7.4	even	3		735.3.e.a.244.1		32
7.5	odd	6	inner	105.3.r.a.19.16	yes	32
15.14	odd	2		315.3.bi.e.199.1		32
21.5	even	6		315.3.bi.e.19.1		32
35.4	even	6		735.3.e.a.244.20		32
35.12	even	12		525.3.o.p.376.1		16
35.19	odd	6	inner	105.3.r.a.19.1	✓	32
35.24	odd	6		735.3.e.a.244.2		32
35.33	even	12		525.3.o.q.376.8		16
105.89	even	6		315.3.bi.e.19.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.r.a.19.1	✓	32	35.19	odd	6	inner
105.3.r.a.19.16	yes	32	7.5	odd	6	inner
105.3.r.a.94.1	yes	32	1.1	even	1	trivial
105.3.r.a.94.16	yes	32	5.4	even	2	inner
315.3.bi.e.19.1		32	21.5	even	6
315.3.bi.e.19.16		32	105.89	even	6
315.3.bi.e.199.1		32	15.14	odd	2
315.3.bi.e.199.16		32	3.2	odd	2
525.3.o.p.376.1		16	35.12	even	12
525.3.o.p.451.1		16	5.2	odd	4
525.3.o.q.376.8		16	35.33	even	12
525.3.o.q.451.8		16	5.3	odd	4
735.3.e.a.244.1		32	7.4	even	3
735.3.e.a.244.2		32	35.24	odd	6
735.3.e.a.244.19		32	7.3	odd	6
735.3.e.a.244.20		32	35.4	even	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.26825 + 1.88692i) q^{2} +(0.866025 - 1.50000i) q^{3} +(5.12097 - 8.86977i) q^{4} +(-3.80462 - 3.24421i) q^{5} +6.53650i q^{6} +(-1.16497 + 6.90238i) q^{7} +23.5561i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-3.26825 + 1.88692i) q^{2} +(0.866025 - 1.50000i) q^{3} +(5.12097 - 8.86977i) q^{4} +(-3.80462 - 3.24421i) q^{5} +6.53650i q^{6} +(-1.16497 + 6.90238i) q^{7} +23.5561i q^{8} +(-1.50000 - 2.59808i) q^{9} +(18.5560 + 3.42385i) q^{10} +(-8.95926 + 15.5179i) q^{11} +(-8.86977 - 15.3629i) q^{12} -1.69555 q^{13} +(-9.21686 - 24.7569i) q^{14} +(-8.16121 + 2.89736i) q^{15} +(-23.9647 - 41.5081i) q^{16} +(1.48936 - 2.57964i) q^{17} +(9.80475 + 5.66077i) q^{18} +(-21.6426 + 12.4954i) q^{19} +(-48.2587 + 17.1326i) q^{20} +(9.34468 + 7.72509i) q^{21} -67.6218i q^{22} +(-7.89777 + 4.55978i) q^{23} +(35.3342 + 20.4002i) q^{24} +(3.95023 + 24.6859i) q^{25} +(5.54149 - 3.19938i) q^{26} -5.19615 q^{27} +(55.2568 + 45.6799i) q^{28} +17.4522 q^{29} +(21.2058 - 24.8689i) q^{30} +(-4.27835 - 2.47011i) q^{31} +(75.0446 + 43.3270i) q^{32} +(15.5179 + 26.8778i) q^{33} +11.2412i q^{34} +(26.8250 - 22.4815i) q^{35} -30.7258 q^{36} +(-47.3050 + 27.3115i) q^{37} +(47.1557 - 81.6761i) q^{38} +(-1.46839 + 2.54333i) q^{39} +(76.4209 - 89.6220i) q^{40} -29.2216i q^{41} +(-45.1174 - 7.61481i) q^{42} +18.1962i q^{43} +(91.7602 + 158.933i) q^{44} +(-2.72177 + 14.7510i) q^{45} +(17.2079 - 29.8050i) q^{46} +(2.28224 + 3.95295i) q^{47} -83.0162 q^{48} +(-46.2857 - 16.0821i) q^{49} +(-59.4908 - 73.2260i) q^{50} +(-2.57964 - 4.46807i) q^{51} +(-8.68286 + 15.0392i) q^{52} +(-21.8280 - 12.6024i) q^{53} +(16.9823 - 9.80475i) q^{54} +(84.4299 - 29.9740i) q^{55} +(-162.593 - 27.4421i) q^{56} +43.2853i q^{57} +(-57.0383 + 32.9311i) q^{58} +(-19.6602 - 11.3508i) q^{59} +(-16.0943 + 87.2253i) q^{60} +(52.1535 - 30.1108i) q^{61} +18.6436 q^{62} +(19.6804 - 7.32689i) q^{63} -135.301 q^{64} +(6.45093 + 5.50072i) q^{65} +(-101.433 - 58.5622i) q^{66} +(39.4034 + 22.7496i) q^{67} +(-15.2539 - 26.4205i) q^{68} +15.7955i q^{69} +(-45.2499 + 124.092i) q^{70} +21.4512 q^{71} +(61.2005 - 35.3342i) q^{72} +(46.4748 - 80.4966i) q^{73} +(103.070 - 178.522i) q^{74} +(40.4499 + 15.4533i) q^{75} +255.954i q^{76} +(-96.6732 - 79.9181i) q^{77} -11.0830i q^{78} +(-35.5708 - 61.6105i) q^{79} +(-43.4843 + 235.669i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(55.1390 + 95.5035i) q^{82} -10.3791 q^{83} +(116.374 - 43.3253i) q^{84} +(-14.0353 + 4.98276i) q^{85} +(-34.3348 - 59.4696i) q^{86} +(15.1141 - 26.1784i) q^{87} +(-365.541 - 211.045i) q^{88} +(10.8707 - 6.27621i) q^{89} +(-18.9386 - 53.3457i) q^{90} +(1.97526 - 11.7033i) q^{91} +93.4019i q^{92} +(-7.41032 + 4.27835i) q^{93} +(-14.9178 - 8.61282i) q^{94} +(122.880 + 22.6731i) q^{95} +(129.981 - 75.0446i) q^{96} -127.247 q^{97} +(181.619 - 34.7773i) q^{98} +53.7556 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 - 6 * q^5 - 48 * q^9	\( 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9} + 78 q^{10} - 28 q^{11} + 60 q^{14} - 24 q^{15} - 40 q^{16} - 60 q^{19} + 12 q^{21} - 34 q^{25} - 96 q^{26} - 88 q^{29} + 84 q^{31} - 170 q^{35} - 192 q^{36} + 36 q^{39} + 330 q^{40} + 320 q^{44} + 18 q^{45} - 60 q^{46} + 356 q^{49} + 12 q^{51} - 468 q^{56} - 804 q^{59} - 198 q^{60} + 336 q^{61} - 400 q^{64} - 46 q^{65} - 108 q^{66} - 438 q^{70} + 344 q^{71} + 900 q^{74} + 144 q^{75} - 20 q^{79} + 1140 q^{80} - 144 q^{81} + 780 q^{84} + 304 q^{85} + 144 q^{86} + 24 q^{89} - 224 q^{91} - 924 q^{94} - 342 q^{95} + 900 q^{96} + 168 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 6 * q^5 - 48 * q^9 + 78 * q^10 - 28 * q^11 + 60 * q^14 - 24 * q^15 - 40 * q^16 - 60 * q^19 + 12 * q^21 - 34 * q^25 - 96 * q^26 - 88 * q^29 + 84 * q^31 - 170 * q^35 - 192 * q^36 + 36 * q^39 + 330 * q^40 + 320 * q^44 + 18 * q^45 - 60 * q^46 + 356 * q^49 + 12 * q^51 - 468 * q^56 - 804 * q^59 - 198 * q^60 + 336 * q^61 - 400 * q^64 - 46 * q^65 - 108 * q^66 - 438 * q^70 + 344 * q^71 + 900 * q^74 + 144 * q^75 - 20 * q^79 + 1140 * q^80 - 144 * q^81 + 780 * q^84 + 304 * q^85 + 144 * q^86 + 24 * q^89 - 224 * q^91 - 924 * q^94 - 342 * q^95 + 900 * q^96 + 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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